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intl/icu/source/i18n/decNumber.c@fc2d59ddac77 (annotated)

intl/icu/source/i18n/decNumber.c

Wed, 31 Dec 2014 07:22:50 +0100

author

Michael Schloh von Bennewitz <michael@schloh.com>

date

Wed, 31 Dec 2014 07:22:50 +0100

branch

TOR_BUG_3246

changeset 4

fc2d59ddac77

permissions

-rw-r--r--

Correct previous dual key logic pending first delivery installment.

michael@0	1	/* ------------------------------------------------------------------ */
michael@0	2	/* Decimal Number arithmetic module */
michael@0	3	/* ------------------------------------------------------------------ */
michael@0	4	/* Copyright (c) IBM Corporation, 2000-2012. All rights reserved. */
michael@0	5	/* */
michael@0	6	/* This software is made available under the terms of the */
michael@0	7	/* ICU License -- ICU 1.8.1 and later. */
michael@0	8	/* */
michael@0	9	/* The description and User's Guide ("The decNumber C Library") for */
michael@0	10	/* this software is called decNumber.pdf. This document is */
michael@0	11	/* available, together with arithmetic and format specifications, */
michael@0	12	/* testcases, and Web links, on the General Decimal Arithmetic page. */
michael@0	13	/* */
michael@0	14	/* Please send comments, suggestions, and corrections to the author: */
michael@0	15	/* mfc@uk.ibm.com */
michael@0	16	/* Mike Cowlishaw, IBM Fellow */
michael@0	17	/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */
michael@0	18	/* ------------------------------------------------------------------ */
michael@0	19
michael@0	20	/* Modified version, for use from within ICU.
michael@0	21	* Renamed public functions, to avoid an unwanted export of the
michael@0	22	* standard names from the ICU library.
michael@0	23	*
michael@0	24	* Use ICU's uprv_malloc() and uprv_free()
michael@0	25	*
michael@0	26	* Revert comment syntax to plain C
michael@0	27	*
michael@0	28	* Remove a few compiler warnings.
michael@0	29	*/
michael@0	30
michael@0	31	/* This module comprises the routines for arbitrary-precision General */
michael@0	32	/* Decimal Arithmetic as defined in the specification which may be */
michael@0	33	/* found on the General Decimal Arithmetic pages. It implements both */
michael@0	34	/* the full ('extended') arithmetic and the simpler ('subset') */
michael@0	35	/* arithmetic. */
michael@0	36	/* */
michael@0	37	/* Usage notes: */
michael@0	38	/* */
michael@0	39	/* 1. This code is ANSI C89 except: */
michael@0	40	/* */
michael@0	41	/* a) C99 line comments (double forward slash) are used. (Most C */
michael@0	42	/* compilers accept these. If yours does not, a simple script */
michael@0	43	/* can be used to convert them to ANSI C comments.) */
michael@0	44	/* */
michael@0	45	/* b) Types from C99 stdint.h are used. If you do not have this */
michael@0	46	/* header file, see the User's Guide section of the decNumber */
michael@0	47	/* documentation; this lists the necessary definitions. */
michael@0	48	/* */
michael@0	49	/* c) If DECDPUN>4 or DECUSE64=1, the C99 64-bit int64_t and */
michael@0	50	/* uint64_t types may be used. To avoid these, set DECUSE64=0 */
michael@0	51	/* and DECDPUN<=4 (see documentation). */
michael@0	52	/* */
michael@0	53	/* The code also conforms to C99 restrictions; in particular, */
michael@0	54	/* strict aliasing rules are observed. */
michael@0	55	/* */
michael@0	56	/* 2. The decNumber format which this library uses is optimized for */
michael@0	57	/* efficient processing of relatively short numbers; in particular */
michael@0	58	/* it allows the use of fixed sized structures and minimizes copy */
michael@0	59	/* and move operations. It does, however, support arbitrary */
michael@0	60	/* precision (up to 999,999,999 digits) and arbitrary exponent */
michael@0	61	/* range (Emax in the range 0 through 999,999,999 and Emin in the */
michael@0	62	/* range -999,999,999 through 0). Mathematical functions (for */
michael@0	63	/* example decNumberExp) as identified below are restricted more */
michael@0	64	/* tightly: digits, emax, and -emin in the context must be <= */
michael@0	65	/* DEC_MAX_MATH (999999), and their operand(s) must be within */
michael@0	66	/* these bounds. */
michael@0	67	/* */
michael@0	68	/* 3. Logical functions are further restricted; their operands must */
michael@0	69	/* be finite, positive, have an exponent of zero, and all digits */
michael@0	70	/* must be either 0 or 1. The result will only contain digits */
michael@0	71	/* which are 0 or 1 (and will have exponent=0 and a sign of 0). */
michael@0	72	/* */
michael@0	73	/* 4. Operands to operator functions are never modified unless they */
michael@0	74	/* are also specified to be the result number (which is always */
michael@0	75	/* permitted). Other than that case, operands must not overlap. */
michael@0	76	/* */
michael@0	77	/* 5. Error handling: the type of the error is ORed into the status */
michael@0	78	/* flags in the current context (decContext structure). The */
michael@0	79	/* SIGFPE signal is then raised if the corresponding trap-enabler */
michael@0	80	/* flag in the decContext is set (is 1). */
michael@0	81	/* */
michael@0	82	/* It is the responsibility of the caller to clear the status */
michael@0	83	/* flags as required. */
michael@0	84	/* */
michael@0	85	/* The result of any routine which returns a number will always */
michael@0	86	/* be a valid number (which may be a special value, such as an */
michael@0	87	/* Infinity or NaN). */
michael@0	88	/* */
michael@0	89	/* 6. The decNumber format is not an exchangeable concrete */
michael@0	90	/* representation as it comprises fields which may be machine- */
michael@0	91	/* dependent (packed or unpacked, or special length, for example). */
michael@0	92	/* Canonical conversions to and from strings are provided; other */
michael@0	93	/* conversions are available in separate modules. */
michael@0	94	/* */
michael@0	95	/* 7. Normally, input operands are assumed to be valid. Set DECCHECK */
michael@0	96	/* to 1 for extended operand checking (including NULL operands). */
michael@0	97	/* Results are undefined if a badly-formed structure (or a NULL */
michael@0	98	/* pointer to a structure) is provided, though with DECCHECK */
michael@0	99	/* enabled the operator routines are protected against exceptions. */
michael@0	100	/* (Except if the result pointer is NULL, which is unrecoverable.) */
michael@0	101	/* */
michael@0	102	/* However, the routines will never cause exceptions if they are */
michael@0	103	/* given well-formed operands, even if the value of the operands */
michael@0	104	/* is inappropriate for the operation and DECCHECK is not set. */
michael@0	105	/* (Except for SIGFPE, as and where documented.) */
michael@0	106	/* */
michael@0	107	/* 8. Subset arithmetic is available only if DECSUBSET is set to 1. */
michael@0	108	/* ------------------------------------------------------------------ */
michael@0	109	/* Implementation notes for maintenance of this module: */
michael@0	110	/* */
michael@0	111	/* 1. Storage leak protection: Routines which use malloc are not */
michael@0	112	/* permitted to use return for fastpath or error exits (i.e., */
michael@0	113	/* they follow strict structured programming conventions). */
michael@0	114	/* Instead they have a do{}while(0); construct surrounding the */
michael@0	115	/* code which is protected -- break may be used to exit this. */
michael@0	116	/* Other routines can safely use the return statement inline. */
michael@0	117	/* */
michael@0	118	/* Storage leak accounting can be enabled using DECALLOC. */
michael@0	119	/* */
michael@0	120	/* 2. All loops use the for(;;) construct. Any do construct does */
michael@0	121	/* not loop; it is for allocation protection as just described. */
michael@0	122	/* */
michael@0	123	/* 3. Setting status in the context must always be the very last */
michael@0	124	/* action in a routine, as non-0 status may raise a trap and hence */
michael@0	125	/* the call to set status may not return (if the handler uses long */
michael@0	126	/* jump). Therefore all cleanup must be done first. In general, */
michael@0	127	/* to achieve this status is accumulated and is only applied just */
michael@0	128	/* before return by calling decContextSetStatus (via decStatus). */
michael@0	129	/* */
michael@0	130	/* Routines which allocate storage cannot, in general, use the */
michael@0	131	/* 'top level' routines which could cause a non-returning */
michael@0	132	/* transfer of control. The decXxxxOp routines are safe (do not */
michael@0	133	/* call decStatus even if traps are set in the context) and should */
michael@0	134	/* be used instead (they are also a little faster). */
michael@0	135	/* */
michael@0	136	/* 4. Exponent checking is minimized by allowing the exponent to */
michael@0	137	/* grow outside its limits during calculations, provided that */
michael@0	138	/* the decFinalize function is called later. Multiplication and */
michael@0	139	/* division, and intermediate calculations in exponentiation, */
michael@0	140	/* require more careful checks because of the risk of 31-bit */
michael@0	141	/* overflow (the most negative valid exponent is -1999999997, for */
michael@0	142	/* a 999999999-digit number with adjusted exponent of -999999999). */
michael@0	143	/* */
michael@0	144	/* 5. Rounding is deferred until finalization of results, with any */
michael@0	145	/* 'off to the right' data being represented as a single digit */
michael@0	146	/* residue (in the range -1 through 9). This avoids any double- */
michael@0	147	/* rounding when more than one shortening takes place (for */
michael@0	148	/* example, when a result is subnormal). */
michael@0	149	/* */
michael@0	150	/* 6. The digits count is allowed to rise to a multiple of DECDPUN */
michael@0	151	/* during many operations, so whole Units are handled and exact */
michael@0	152	/* accounting of digits is not needed. The correct digits value */
michael@0	153	/* is found by decGetDigits, which accounts for leading zeros. */
michael@0	154	/* This must be called before any rounding if the number of digits */
michael@0	155	/* is not known exactly. */
michael@0	156	/* */
michael@0	157	/* 7. The multiply-by-reciprocal 'trick' is used for partitioning */
michael@0	158	/* numbers up to four digits, using appropriate constants. This */
michael@0	159	/* is not useful for longer numbers because overflow of 32 bits */
michael@0	160	/* would lead to 4 multiplies, which is almost as expensive as */
michael@0	161	/* a divide (unless a floating-point or 64-bit multiply is */
michael@0	162	/* assumed to be available). */
michael@0	163	/* */
michael@0	164	/* 8. Unusual abbreviations that may be used in the commentary: */
michael@0	165	/* lhs -- left hand side (operand, of an operation) */
michael@0	166	/* lsd -- least significant digit (of coefficient) */
michael@0	167	/* lsu -- least significant Unit (of coefficient) */
michael@0	168	/* msd -- most significant digit (of coefficient) */
michael@0	169	/* msi -- most significant item (in an array) */
michael@0	170	/* msu -- most significant Unit (of coefficient) */
michael@0	171	/* rhs -- right hand side (operand, of an operation) */
michael@0	172	/* +ve -- positive */
michael@0	173	/* -ve -- negative */
michael@0	174	/* ** -- raise to the power */
michael@0	175	/* ------------------------------------------------------------------ */
michael@0	176
michael@0	177	#include <stdlib.h> /* for malloc, free, etc. */
michael@0	178	/* #include <stdio.h> */ /* for printf [if needed] */
michael@0	179	#include <string.h> /* for strcpy */
michael@0	180	#include <ctype.h> /* for lower */
michael@0	181	#include "cmemory.h" /* for uprv_malloc, etc., in ICU */
michael@0	182	#include "decNumber.h" /* base number library */
michael@0	183	#include "decNumberLocal.h" /* decNumber local types, etc. */
michael@0	184	#include "uassert.h"
michael@0	185
michael@0	186	/* Constants */
michael@0	187	/* Public lookup table used by the D2U macro */
michael@0	188	static const uByte d2utable[DECMAXD2U+1]=D2UTABLE;
michael@0	189
michael@0	190	#define DECVERB 1 /* set to 1 for verbose DECCHECK */
michael@0	191	#define powers DECPOWERS /* old internal name */
michael@0	192
michael@0	193	/* Local constants */
michael@0	194	#define DIVIDE 0x80 /* Divide operators */
michael@0	195	#define REMAINDER 0x40 /* .. */
michael@0	196	#define DIVIDEINT 0x20 /* .. */
michael@0	197	#define REMNEAR 0x10 /* .. */
michael@0	198	#define COMPARE 0x01 /* Compare operators */
michael@0	199	#define COMPMAX 0x02 /* .. */
michael@0	200	#define COMPMIN 0x03 /* .. */
michael@0	201	#define COMPTOTAL 0x04 /* .. */
michael@0	202	#define COMPNAN 0x05 /* .. [NaN processing] */
michael@0	203	#define COMPSIG 0x06 /* .. [signaling COMPARE] */
michael@0	204	#define COMPMAXMAG 0x07 /* .. */
michael@0	205	#define COMPMINMAG 0x08 /* .. */
michael@0	206
michael@0	207	#define DEC_sNaN 0x40000000 /* local status: sNaN signal */
michael@0	208	#define BADINT (Int)0x80000000 /* most-negative Int; error indicator */
michael@0	209	/* Next two indicate an integer >= 10**6, and its parity (bottom bit) */
michael@0	210	#define BIGEVEN (Int)0x80000002
michael@0	211	#define BIGODD (Int)0x80000003
michael@0	212
michael@0	213	static const Unit uarrone[1]={1}; /* Unit array of 1, used for incrementing */
michael@0	214
michael@0	215	/* ------------------------------------------------------------------ */
michael@0	216	/* round-for-reround digits */
michael@0	217	/* ------------------------------------------------------------------ */
michael@0	218	static const uByte DECSTICKYTAB[10]={1,1,2,3,4,6,6,7,8,9}; /* used if sticky */
michael@0	219
michael@0	220	/* ------------------------------------------------------------------ */
michael@0	221	/* Powers of ten (powers[n]==10**n, 0<=n<=9) */
michael@0	222	/* ------------------------------------------------------------------ */
michael@0	223	static const uInt DECPOWERS[10]={1, 10, 100, 1000, 10000, 100000, 1000000,
michael@0	224	10000000, 100000000, 1000000000};
michael@0	225
michael@0	226
michael@0	227	/* Granularity-dependent code */
michael@0	228	#if DECDPUN<=4
michael@0	229	#define eInt Int /* extended integer */
michael@0	230	#define ueInt uInt /* unsigned extended integer */
michael@0	231	/* Constant multipliers for divide-by-power-of five using reciprocal */
michael@0	232	/* multiply, after removing powers of 2 by shifting, and final shift */
michael@0	233	/* of 17 [we only need up to **4] */
michael@0	234	static const uInt multies[]={131073, 26215, 5243, 1049, 210};
michael@0	235	/* QUOT10 -- macro to return the quotient of unit u divided by 10**n */
michael@0	236	#define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17)
michael@0	237	#else
michael@0	238	/* For DECDPUN>4 non-ANSI-89 64-bit types are needed. */
michael@0	239	#if !DECUSE64
michael@0	240	#error decNumber.c: DECUSE64 must be 1 when DECDPUN>4
michael@0	241	#endif
michael@0	242	#define eInt Long /* extended integer */
michael@0	243	#define ueInt uLong /* unsigned extended integer */
michael@0	244	#endif
michael@0	245
michael@0	246	/* Local routines */
michael@0	247	static decNumber * decAddOp(decNumber *, const decNumber *, const decNumber *,
michael@0	248	decContext *, uByte, uInt *);
michael@0	249	static Flag decBiStr(const char *, const char *, const char *);
michael@0	250	static uInt decCheckMath(const decNumber *, decContext *, uInt *);
michael@0	251	static void decApplyRound(decNumber *, decContext *, Int, uInt *);
michael@0	252	static Int decCompare(const decNumber *lhs, const decNumber *rhs, Flag);
michael@0	253	static decNumber * decCompareOp(decNumber *, const decNumber *,
michael@0	254	const decNumber *, decContext *,
michael@0	255	Flag, uInt *);
michael@0	256	static void decCopyFit(decNumber *, const decNumber *, decContext *,
michael@0	257	Int *, uInt *);
michael@0	258	static decNumber * decDecap(decNumber *, Int);
michael@0	259	static decNumber * decDivideOp(decNumber *, const decNumber *,
michael@0	260	const decNumber *, decContext *, Flag, uInt *);
michael@0	261	static decNumber * decExpOp(decNumber *, const decNumber *,
michael@0	262	decContext *, uInt *);
michael@0	263	static void decFinalize(decNumber *, decContext *, Int *, uInt *);
michael@0	264	static Int decGetDigits(Unit *, Int);
michael@0	265	static Int decGetInt(const decNumber *);
michael@0	266	static decNumber * decLnOp(decNumber *, const decNumber *,
michael@0	267	decContext *, uInt *);
michael@0	268	static decNumber * decMultiplyOp(decNumber *, const decNumber *,
michael@0	269	const decNumber *, decContext *,
michael@0	270	uInt *);
michael@0	271	static decNumber * decNaNs(decNumber *, const decNumber *,
michael@0	272	const decNumber *, decContext *, uInt *);
michael@0	273	static decNumber * decQuantizeOp(decNumber *, const decNumber *,
michael@0	274	const decNumber *, decContext *, Flag,
michael@0	275	uInt *);
michael@0	276	static void decReverse(Unit *, Unit *);
michael@0	277	static void decSetCoeff(decNumber *, decContext *, const Unit *,
michael@0	278	Int, Int *, uInt *);
michael@0	279	static void decSetMaxValue(decNumber *, decContext *);
michael@0	280	static void decSetOverflow(decNumber *, decContext *, uInt *);
michael@0	281	static void decSetSubnormal(decNumber *, decContext *, Int *, uInt *);
michael@0	282	static Int decShiftToLeast(Unit *, Int, Int);
michael@0	283	static Int decShiftToMost(Unit *, Int, Int);
michael@0	284	static void decStatus(decNumber *, uInt, decContext *);
michael@0	285	static void decToString(const decNumber *, char[], Flag);
michael@0	286	static decNumber * decTrim(decNumber *, decContext *, Flag, Flag, Int *);
michael@0	287	static Int decUnitAddSub(const Unit *, Int, const Unit *, Int, Int,
michael@0	288	Unit *, Int);
michael@0	289	static Int decUnitCompare(const Unit *, Int, const Unit *, Int, Int);
michael@0	290
michael@0	291	#if !DECSUBSET
michael@0	292	/* decFinish == decFinalize when no subset arithmetic needed */
michael@0	293	#define decFinish(a,b,c,d) decFinalize(a,b,c,d)
michael@0	294	#else
michael@0	295	static void decFinish(decNumber *, decContext *, Int *, uInt *);
michael@0	296	static decNumber * decRoundOperand(const decNumber *, decContext *, uInt *);
michael@0	297	#endif
michael@0	298
michael@0	299	/* Local macros */
michael@0	300	/* masked special-values bits */
michael@0	301	#define SPECIALARG (rhs->bits & DECSPECIAL)
michael@0	302	#define SPECIALARGS ((lhs->bits | rhs->bits) & DECSPECIAL)
michael@0	303
michael@0	304	/* For use in ICU */
michael@0	305	#define malloc(a) uprv_malloc(a)
michael@0	306	#define free(a) uprv_free(a)
michael@0	307
michael@0	308	/* Diagnostic macros, etc. */
michael@0	309	#if DECALLOC
michael@0	310	/* Handle malloc/free accounting. If enabled, our accountable routines */
michael@0	311	/* are used; otherwise the code just goes straight to the system malloc */
michael@0	312	/* and free routines. */
michael@0	313	#define malloc(a) decMalloc(a)
michael@0	314	#define free(a) decFree(a)
michael@0	315	#define DECFENCE 0x5a /* corruption detector */
michael@0	316	/* 'Our' malloc and free: */
michael@0	317	static void *decMalloc(size_t);
michael@0	318	static void decFree(void *);
michael@0	319	uInt decAllocBytes=0; /* count of bytes allocated */
michael@0	320	/* Note that DECALLOC code only checks for storage buffer overflow. */
michael@0	321	/* To check for memory leaks, the decAllocBytes variable must be */
michael@0	322	/* checked to be 0 at appropriate times (e.g., after the test */
michael@0	323	/* harness completes a set of tests). This checking may be unreliable */
michael@0	324	/* if the testing is done in a multi-thread environment. */
michael@0	325	#endif
michael@0	326
michael@0	327	#if DECCHECK
michael@0	328	/* Optional checking routines. Enabling these means that decNumber */
michael@0	329	/* and decContext operands to operator routines are checked for */
michael@0	330	/* correctness. This roughly doubles the execution time of the */
michael@0	331	/* fastest routines (and adds 600+ bytes), so should not normally be */
michael@0	332	/* used in 'production'. */
michael@0	333	/* decCheckInexact is used to check that inexact results have a full */
michael@0	334	/* complement of digits (where appropriate -- this is not the case */
michael@0	335	/* for Quantize, for example) */
michael@0	336	#define DECUNRESU ((decNumber *)(void *)0xffffffff)
michael@0	337	#define DECUNUSED ((const decNumber *)(void *)0xffffffff)
michael@0	338	#define DECUNCONT ((decContext *)(void *)(0xffffffff))
michael@0	339	static Flag decCheckOperands(decNumber *, const decNumber *,
michael@0	340	const decNumber *, decContext *);
michael@0	341	static Flag decCheckNumber(const decNumber *);
michael@0	342	static void decCheckInexact(const decNumber *, decContext *);
michael@0	343	#endif
michael@0	344
michael@0	345	#if DECTRACE || DECCHECK
michael@0	346	/* Optional trace/debugging routines (may or may not be used) */
michael@0	347	void decNumberShow(const decNumber *); /* displays the components of a number */
michael@0	348	static void decDumpAr(char, const Unit *, Int);
michael@0	349	#endif
michael@0	350
michael@0	351	/* ================================================================== */
michael@0	352	/* Conversions */
michael@0	353	/* ================================================================== */
michael@0	354
michael@0	355	/* ------------------------------------------------------------------ */
michael@0	356	/* from-int32 -- conversion from Int or uInt */
michael@0	357	/* */
michael@0	358	/* dn is the decNumber to receive the integer */
michael@0	359	/* in or uin is the integer to be converted */
michael@0	360	/* returns dn */
michael@0	361	/* */
michael@0	362	/* No error is possible. */
michael@0	363	/* ------------------------------------------------------------------ */
michael@0	364	U_CAPI decNumber * U_EXPORT2 uprv_decNumberFromInt32(decNumber *dn, Int in) {
michael@0	365	uInt unsig;
michael@0	366	if (in>=0) unsig=in;
michael@0	367	else { /* negative (possibly BADINT) */
michael@0	368	if (in==BADINT) unsig=(uInt)1073741824*2; /* special case */
michael@0	369	else unsig=-in; /* invert */
michael@0	370	}
michael@0	371	/* in is now positive */
michael@0	372	uprv_decNumberFromUInt32(dn, unsig);
michael@0	373	if (in<0) dn->bits=DECNEG; /* sign needed */
michael@0	374	return dn;
michael@0	375	} /* decNumberFromInt32 */
michael@0	376
michael@0	377	U_CAPI decNumber * U_EXPORT2 uprv_decNumberFromUInt32(decNumber *dn, uInt uin) {
michael@0	378	Unit *up; /* work pointer */
michael@0	379	uprv_decNumberZero(dn); /* clean */
michael@0	380	if (uin==0) return dn; /* [or decGetDigits bad call] */
michael@0	381	for (up=dn->lsu; uin>0; up++) {
michael@0	382	*up=(Unit)(uin%(DECDPUNMAX+1));
michael@0	383	uin=uin/(DECDPUNMAX+1);
michael@0	384	}
michael@0	385	dn->digits=decGetDigits(dn->lsu, up-dn->lsu);
michael@0	386	return dn;
michael@0	387	} /* decNumberFromUInt32 */
michael@0	388
michael@0	389	/* ------------------------------------------------------------------ */
michael@0	390	/* to-int32 -- conversion to Int or uInt */
michael@0	391	/* */
michael@0	392	/* dn is the decNumber to convert */
michael@0	393	/* set is the context for reporting errors */
michael@0	394	/* returns the converted decNumber, or 0 if Invalid is set */
michael@0	395	/* */
michael@0	396	/* Invalid is set if the decNumber does not have exponent==0 or if */
michael@0	397	/* it is a NaN, Infinite, or out-of-range. */
michael@0	398	/* ------------------------------------------------------------------ */
michael@0	399	U_CAPI Int U_EXPORT2 uprv_decNumberToInt32(const decNumber *dn, decContext *set) {
michael@0	400	#if DECCHECK
michael@0	401	if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
michael@0	402	#endif
michael@0	403
michael@0	404	/* special or too many digits, or bad exponent */
michael@0	405	if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0) ; /* bad */
michael@0	406	else { /* is a finite integer with 10 or fewer digits */
michael@0	407	Int d; /* work */
michael@0	408	const Unit *up; /* .. */
michael@0	409	uInt hi=0, lo; /* .. */
michael@0	410	up=dn->lsu; /* -> lsu */
michael@0	411	lo=*up; /* get 1 to 9 digits */
michael@0	412	#if DECDPUN>1 /* split to higher */
michael@0	413	hi=lo/10;
michael@0	414	lo=lo%10;
michael@0	415	#endif
michael@0	416	up++;
michael@0	417	/* collect remaining Units, if any, into hi */
michael@0	418	for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1];
michael@0	419	/* now low has the lsd, hi the remainder */
michael@0	420	if (hi>214748364 || (hi==214748364 && lo>7)) { /* out of range? */
michael@0	421	/* most-negative is a reprieve */
michael@0	422	if (dn->bits&DECNEG && hi==214748364 && lo==8) return 0x80000000;
michael@0	423	/* bad -- drop through */
michael@0	424	}
michael@0	425	else { /* in-range always */
michael@0	426	Int i=X10(hi)+lo;
michael@0	427	if (dn->bits&DECNEG) return -i;
michael@0	428	return i;
michael@0	429	}
michael@0	430	} /* integer */
michael@0	431	uprv_decContextSetStatus(set, DEC_Invalid_operation); /* [may not return] */
michael@0	432	return 0;
michael@0	433	} /* decNumberToInt32 */
michael@0	434
michael@0	435	U_CAPI uInt U_EXPORT2 uprv_decNumberToUInt32(const decNumber *dn, decContext *set) {
michael@0	436	#if DECCHECK
michael@0	437	if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
michael@0	438	#endif
michael@0	439	/* special or too many digits, or bad exponent, or negative (<0) */
michael@0	440	if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0
michael@0	441	|| (dn->bits&DECNEG && !ISZERO(dn))); /* bad */
michael@0	442	else { /* is a finite integer with 10 or fewer digits */
michael@0	443	Int d; /* work */
michael@0	444	const Unit *up; /* .. */
michael@0	445	uInt hi=0, lo; /* .. */
michael@0	446	up=dn->lsu; /* -> lsu */
michael@0	447	lo=*up; /* get 1 to 9 digits */
michael@0	448	#if DECDPUN>1 /* split to higher */
michael@0	449	hi=lo/10;
michael@0	450	lo=lo%10;
michael@0	451	#endif
michael@0	452	up++;
michael@0	453	/* collect remaining Units, if any, into hi */
michael@0	454	for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1];
michael@0	455
michael@0	456	/* now low has the lsd, hi the remainder */
michael@0	457	if (hi>429496729 || (hi==429496729 && lo>5)) ; /* no reprieve possible */
michael@0	458	else return X10(hi)+lo;
michael@0	459	} /* integer */
michael@0	460	uprv_decContextSetStatus(set, DEC_Invalid_operation); /* [may not return] */
michael@0	461	return 0;
michael@0	462	} /* decNumberToUInt32 */
michael@0	463
michael@0	464	/* ------------------------------------------------------------------ */
michael@0	465	/* to-scientific-string -- conversion to numeric string */
michael@0	466	/* to-engineering-string -- conversion to numeric string */
michael@0	467	/* */
michael@0	468	/* decNumberToString(dn, string); */
michael@0	469	/* decNumberToEngString(dn, string); */
michael@0	470	/* */
michael@0	471	/* dn is the decNumber to convert */
michael@0	472	/* string is the string where the result will be laid out */
michael@0	473	/* */
michael@0	474	/* string must be at least dn->digits+14 characters long */
michael@0	475	/* */
michael@0	476	/* No error is possible, and no status can be set. */
michael@0	477	/* ------------------------------------------------------------------ */
michael@0	478	U_CAPI char * U_EXPORT2 uprv_decNumberToString(const decNumber *dn, char *string){
michael@0	479	decToString(dn, string, 0);
michael@0	480	return string;
michael@0	481	} /* DecNumberToString */
michael@0	482
michael@0	483	U_CAPI char * U_EXPORT2 uprv_decNumberToEngString(const decNumber *dn, char *string){
michael@0	484	decToString(dn, string, 1);
michael@0	485	return string;
michael@0	486	} /* DecNumberToEngString */
michael@0	487
michael@0	488	/* ------------------------------------------------------------------ */
michael@0	489	/* to-number -- conversion from numeric string */
michael@0	490	/* */
michael@0	491	/* decNumberFromString -- convert string to decNumber */
michael@0	492	/* dn -- the number structure to fill */
michael@0	493	/* chars[] -- the string to convert ('\0' terminated) */
michael@0	494	/* set -- the context used for processing any error, */
michael@0	495	/* determining the maximum precision available */
michael@0	496	/* (set.digits), determining the maximum and minimum */
michael@0	497	/* exponent (set.emax and set.emin), determining if */
michael@0	498	/* extended values are allowed, and checking the */
michael@0	499	/* rounding mode if overflow occurs or rounding is */
michael@0	500	/* needed. */
michael@0	501	/* */
michael@0	502	/* The length of the coefficient and the size of the exponent are */
michael@0	503	/* checked by this routine, so the correct error (Underflow or */
michael@0	504	/* Overflow) can be reported or rounding applied, as necessary. */
michael@0	505	/* */
michael@0	506	/* If bad syntax is detected, the result will be a quiet NaN. */
michael@0	507	/* ------------------------------------------------------------------ */
michael@0	508	U_CAPI decNumber * U_EXPORT2 uprv_decNumberFromString(decNumber *dn, const char chars[],
michael@0	509	decContext *set) {
michael@0	510	Int exponent=0; /* working exponent [assume 0] */
michael@0	511	uByte bits=0; /* working flags [assume +ve] */
michael@0	512	Unit *res; /* where result will be built */
michael@0	513	Unit resbuff[SD2U(DECBUFFER+9)];/* local buffer in case need temporary */
michael@0	514	/* [+9 allows for ln() constants] */
michael@0	515	Unit *allocres=NULL; /* -> allocated result, iff allocated */
michael@0	516	Int d=0; /* count of digits found in decimal part */
michael@0	517	const char *dotchar=NULL; /* where dot was found */
michael@0	518	const char *cfirst=chars; /* -> first character of decimal part */
michael@0	519	const char *last=NULL; /* -> last digit of decimal part */
michael@0	520	const char *c; /* work */
michael@0	521	Unit *up; /* .. */
michael@0	522	#if DECDPUN>1
michael@0	523	Int cut, out; /* .. */
michael@0	524	#endif
michael@0	525	Int residue; /* rounding residue */
michael@0	526	uInt status=0; /* error code */
michael@0	527
michael@0	528	#if DECCHECK
michael@0	529	if (decCheckOperands(DECUNRESU, DECUNUSED, DECUNUSED, set))
michael@0	530	return uprv_decNumberZero(dn);
michael@0	531	#endif
michael@0	532
michael@0	533	do { /* status & malloc protection */
michael@0	534	for (c=chars;; c++) { /* -> input character */
michael@0	535	if (*c>='0' && *c<='9') { /* test for Arabic digit */
michael@0	536	last=c;
michael@0	537	d++; /* count of real digits */
michael@0	538	continue; /* still in decimal part */
michael@0	539	}
michael@0	540	if (*c=='.' && dotchar==NULL) { /* first '.' */
michael@0	541	dotchar=c; /* record offset into decimal part */
michael@0	542	if (c==cfirst) cfirst++; /* first digit must follow */
michael@0	543	continue;}
michael@0	544	if (c==chars) { /* first in string... */
michael@0	545	if (*c=='-') { /* valid - sign */
michael@0	546	cfirst++;
michael@0	547	bits=DECNEG;
michael@0	548	continue;}
michael@0	549	if (*c=='+') { /* valid + sign */
michael@0	550	cfirst++;
michael@0	551	continue;}
michael@0	552	}
michael@0	553	/* *c is not a digit, or a valid +, -, or '.' */
michael@0	554	break;
michael@0	555	} /* c */
michael@0	556
michael@0	557	if (last==NULL) { /* no digits yet */
michael@0	558	status=DEC_Conversion_syntax;/* assume the worst */
michael@0	559	if (*c=='\0') break; /* and no more to come... */
michael@0	560	#if DECSUBSET
michael@0	561	/* if subset then infinities and NaNs are not allowed */
michael@0	562	if (!set->extended) break; /* hopeless */
michael@0	563	#endif
michael@0	564	/* Infinities and NaNs are possible, here */
michael@0	565	if (dotchar!=NULL) break; /* .. unless had a dot */
michael@0	566	uprv_decNumberZero(dn); /* be optimistic */
michael@0	567	if (decBiStr(c, "infinity", "INFINITY")
michael@0	568	|| decBiStr(c, "inf", "INF")) {
michael@0	569	dn->bits=bits | DECINF;
michael@0	570	status=0; /* is OK */
michael@0	571	break; /* all done */
michael@0	572	}
michael@0	573	/* a NaN expected */
michael@0	574	/* 2003.09.10 NaNs are now permitted to have a sign */
michael@0	575	dn->bits=bits | DECNAN; /* assume simple NaN */
michael@0	576	if (*c=='s' || *c=='S') { /* looks like an sNaN */
michael@0	577	c++;
michael@0	578	dn->bits=bits | DECSNAN;
michael@0	579	}
michael@0	580	if (*c!='n' && *c!='N') break; /* check caseless "NaN" */
michael@0	581	c++;
michael@0	582	if (*c!='a' && *c!='A') break; /* .. */
michael@0	583	c++;
michael@0	584	if (*c!='n' && *c!='N') break; /* .. */
michael@0	585	c++;
michael@0	586	/* now either nothing, or nnnn payload, expected */
michael@0	587	/* -> start of integer and skip leading 0s [including plain 0] */
michael@0	588	for (cfirst=c; *cfirst=='0';) cfirst++;
michael@0	589	if (*cfirst=='\0') { /* "NaN" or "sNaN", maybe with all 0s */
michael@0	590	status=0; /* it's good */
michael@0	591	break; /* .. */
michael@0	592	}
michael@0	593	/* something other than 0s; setup last and d as usual [no dots] */
michael@0	594	for (c=cfirst;; c++, d++) {
michael@0	595	if (*c<'0' || *c>'9') break; /* test for Arabic digit */
michael@0	596	last=c;
michael@0	597	}
michael@0	598	if (*c!='\0') break; /* not all digits */
michael@0	599	if (d>set->digits-1) {
michael@0	600	/* [NB: payload in a decNumber can be full length unless */
michael@0	601	/* clamped, in which case can only be digits-1] */
michael@0	602	if (set->clamp) break;
michael@0	603	if (d>set->digits) break;
michael@0	604	} /* too many digits? */
michael@0	605	/* good; drop through to convert the integer to coefficient */
michael@0	606	status=0; /* syntax is OK */
michael@0	607	bits=dn->bits; /* for copy-back */
michael@0	608	} /* last==NULL */
michael@0	609
michael@0	610	else if (*c!='\0') { /* more to process... */
michael@0	611	/* had some digits; exponent is only valid sequence now */
michael@0	612	Flag nege; /* 1=negative exponent */
michael@0	613	const char *firstexp; /* -> first significant exponent digit */
michael@0	614	status=DEC_Conversion_syntax;/* assume the worst */
michael@0	615	if (*c!='e' && *c!='E') break;
michael@0	616	/* Found 'e' or 'E' -- now process explicit exponent */
michael@0	617	/* 1998.07.11: sign no longer required */
michael@0	618	nege=0;
michael@0	619	c++; /* to (possible) sign */
michael@0	620	if (*c=='-') {nege=1; c++;}
michael@0	621	else if (*c=='+') c++;
michael@0	622	if (*c=='\0') break;
michael@0	623
michael@0	624	for (; *c=='0' && *(c+1)!='\0';) c++; /* strip insignificant zeros */
michael@0	625	firstexp=c; /* save exponent digit place */
michael@0	626	for (; ;c++) {
michael@0	627	if (*c<'0' || *c>'9') break; /* not a digit */
michael@0	628	exponent=X10(exponent)+(Int)*c-(Int)'0';
michael@0	629	} /* c */
michael@0	630	/* if not now on a '\0', *c must not be a digit */
michael@0	631	if (*c!='\0') break;
michael@0	632
michael@0	633	/* (this next test must be after the syntax checks) */
michael@0	634	/* if it was too long the exponent may have wrapped, so check */
michael@0	635	/* carefully and set it to a certain overflow if wrap possible */
michael@0	636	if (c>=firstexp+9+1) {
michael@0	637	if (c>firstexp+9+1 || *firstexp>'1') exponent=DECNUMMAXE*2;
michael@0	638	/* [up to 1999999999 is OK, for example 1E-1000000998] */
michael@0	639	}
michael@0	640	if (nege) exponent=-exponent; /* was negative */
michael@0	641	status=0; /* is OK */
michael@0	642	} /* stuff after digits */
michael@0	643
michael@0	644	/* Here when whole string has been inspected; syntax is good */
michael@0	645	/* cfirst->first digit (never dot), last->last digit (ditto) */
michael@0	646
michael@0	647	/* strip leading zeros/dot [leave final 0 if all 0's] */
michael@0	648	if (*cfirst=='0') { /* [cfirst has stepped over .] */
michael@0	649	for (c=cfirst; c<last; c++, cfirst++) {
michael@0	650	if (*c=='.') continue; /* ignore dots */
michael@0	651	if (*c!='0') break; /* non-zero found */
michael@0	652	d--; /* 0 stripped */
michael@0	653	} /* c */
michael@0	654	#if DECSUBSET
michael@0	655	/* make a rapid exit for easy zeros if !extended */
michael@0	656	if (*cfirst=='0' && !set->extended) {
michael@0	657	uprv_decNumberZero(dn); /* clean result */
michael@0	658	break; /* [could be return] */
michael@0	659	}
michael@0	660	#endif
michael@0	661	} /* at least one leading 0 */
michael@0	662
michael@0	663	/* Handle decimal point... */
michael@0	664	if (dotchar!=NULL && dotchar<last) /* non-trailing '.' found? */
michael@0	665	exponent-=(last-dotchar); /* adjust exponent */
michael@0	666	/* [we can now ignore the .] */
michael@0	667
michael@0	668	/* OK, the digits string is good. Assemble in the decNumber, or in */
michael@0	669	/* a temporary units array if rounding is needed */
michael@0	670	if (d<=set->digits) res=dn->lsu; /* fits into supplied decNumber */
michael@0	671	else { /* rounding needed */
michael@0	672	Int needbytes=D2U(d)*sizeof(Unit);/* bytes needed */
michael@0	673	res=resbuff; /* assume use local buffer */
michael@0	674	if (needbytes>(Int)sizeof(resbuff)) { /* too big for local */
michael@0	675	allocres=(Unit *)malloc(needbytes);
michael@0	676	if (allocres==NULL) {status|=DEC_Insufficient_storage; break;}
michael@0	677	res=allocres;
michael@0	678	}
michael@0	679	}
michael@0	680	/* res now -> number lsu, buffer, or allocated storage for Unit array */
michael@0	681
michael@0	682	/* Place the coefficient into the selected Unit array */
michael@0	683	/* [this is often 70% of the cost of this function when DECDPUN>1] */
michael@0	684	#if DECDPUN>1
michael@0	685	out=0; /* accumulator */
michael@0	686	up=res+D2U(d)-1; /* -> msu */
michael@0	687	cut=d-(up-res)*DECDPUN; /* digits in top unit */
michael@0	688	for (c=cfirst;; c++) { /* along the digits */
michael@0	689	if (*c=='.') continue; /* ignore '.' [don't decrement cut] */
michael@0	690	out=X10(out)+(Int)*c-(Int)'0';
michael@0	691	if (c==last) break; /* done [never get to trailing '.'] */
michael@0	692	cut--;
michael@0	693	if (cut>0) continue; /* more for this unit */
michael@0	694	*up=(Unit)out; /* write unit */
michael@0	695	up--; /* prepare for unit below.. */
michael@0	696	cut=DECDPUN; /* .. */
michael@0	697	out=0; /* .. */
michael@0	698	} /* c */
michael@0	699	*up=(Unit)out; /* write lsu */
michael@0	700
michael@0	701	#else
michael@0	702	/* DECDPUN==1 */
michael@0	703	up=res; /* -> lsu */
michael@0	704	for (c=last; c>=cfirst; c--) { /* over each character, from least */
michael@0	705	if (*c=='.') continue; /* ignore . [don't step up] */
michael@0	706	*up=(Unit)((Int)*c-(Int)'0');
michael@0	707	up++;
michael@0	708	} /* c */
michael@0	709	#endif
michael@0	710
michael@0	711	dn->bits=bits;
michael@0	712	dn->exponent=exponent;
michael@0	713	dn->digits=d;
michael@0	714
michael@0	715	/* if not in number (too long) shorten into the number */
michael@0	716	if (d>set->digits) {
michael@0	717	residue=0;
michael@0	718	decSetCoeff(dn, set, res, d, &residue, &status);
michael@0	719	/* always check for overflow or subnormal and round as needed */
michael@0	720	decFinalize(dn, set, &residue, &status);
michael@0	721	}
michael@0	722	else { /* no rounding, but may still have overflow or subnormal */
michael@0	723	/* [these tests are just for performance; finalize repeats them] */
michael@0	724	if ((dn->exponent-1<set->emin-dn->digits)
michael@0	725	|| (dn->exponent-1>set->emax-set->digits)) {
michael@0	726	residue=0;
michael@0	727	decFinalize(dn, set, &residue, &status);
michael@0	728	}
michael@0	729	}
michael@0	730	/* decNumberShow(dn); */
michael@0	731	} while(0); /* [for break] */
michael@0	732
michael@0	733	if (allocres!=NULL) free(allocres); /* drop any storage used */
michael@0	734	if (status!=0) decStatus(dn, status, set);
michael@0	735	return dn;
michael@0	736	} /* decNumberFromString */
michael@0	737
michael@0	738	/* ================================================================== */
michael@0	739	/* Operators */
michael@0	740	/* ================================================================== */
michael@0	741
michael@0	742	/* ------------------------------------------------------------------ */
michael@0	743	/* decNumberAbs -- absolute value operator */
michael@0	744	/* */
michael@0	745	/* This computes C = abs(A) */
michael@0	746	/* */
michael@0	747	/* res is C, the result. C may be A */
michael@0	748	/* rhs is A */
michael@0	749	/* set is the context */
michael@0	750	/* */
michael@0	751	/* See also decNumberCopyAbs for a quiet bitwise version of this. */
michael@0	752	/* C must have space for set->digits digits. */
michael@0	753	/* ------------------------------------------------------------------ */
michael@0	754	/* This has the same effect as decNumberPlus unless A is negative, */
michael@0	755	/* in which case it has the same effect as decNumberMinus. */
michael@0	756	/* ------------------------------------------------------------------ */
michael@0	757	U_CAPI decNumber * U_EXPORT2 uprv_decNumberAbs(decNumber *res, const decNumber *rhs,
michael@0	758	decContext *set) {
michael@0	759	decNumber dzero; /* for 0 */
michael@0	760	uInt status=0; /* accumulator */
michael@0	761
michael@0	762	#if DECCHECK
michael@0	763	if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
michael@0	764	#endif
michael@0	765
michael@0	766	uprv_decNumberZero(&dzero); /* set 0 */
michael@0	767	dzero.exponent=rhs->exponent; /* [no coefficient expansion] */
michael@0	768	decAddOp(res, &dzero, rhs, set, (uByte)(rhs->bits & DECNEG), &status);
michael@0	769	if (status!=0) decStatus(res, status, set);
michael@0	770	#if DECCHECK
michael@0	771	decCheckInexact(res, set);
michael@0	772	#endif
michael@0	773	return res;
michael@0	774	} /* decNumberAbs */
michael@0	775
michael@0	776	/* ------------------------------------------------------------------ */
michael@0	777	/* decNumberAdd -- add two Numbers */
michael@0	778	/* */
michael@0	779	/* This computes C = A + B */
michael@0	780	/* */
michael@0	781	/* res is C, the result. C may be A and/or B (e.g., X=X+X) */
michael@0	782	/* lhs is A */
michael@0	783	/* rhs is B */
michael@0	784	/* set is the context */
michael@0	785	/* */
michael@0	786	/* C must have space for set->digits digits. */
michael@0	787	/* ------------------------------------------------------------------ */
michael@0	788	/* This just calls the routine shared with Subtract */
michael@0	789	U_CAPI decNumber * U_EXPORT2 uprv_decNumberAdd(decNumber *res, const decNumber *lhs,
michael@0	790	const decNumber *rhs, decContext *set) {
michael@0	791	uInt status=0; /* accumulator */
michael@0	792	decAddOp(res, lhs, rhs, set, 0, &status);
michael@0	793	if (status!=0) decStatus(res, status, set);
michael@0	794	#if DECCHECK
michael@0	795	decCheckInexact(res, set);
michael@0	796	#endif
michael@0	797	return res;
michael@0	798	} /* decNumberAdd */
michael@0	799
michael@0	800	/* ------------------------------------------------------------------ */
michael@0	801	/* decNumberAnd -- AND two Numbers, digitwise */
michael@0	802	/* */
michael@0	803	/* This computes C = A & B */
michael@0	804	/* */
michael@0	805	/* res is C, the result. C may be A and/or B (e.g., X=X&X) */
michael@0	806	/* lhs is A */
michael@0	807	/* rhs is B */
michael@0	808	/* set is the context (used for result length and error report) */
michael@0	809	/* */
michael@0	810	/* C must have space for set->digits digits. */
michael@0	811	/* */
michael@0	812	/* Logical function restrictions apply (see above); a NaN is */
michael@0	813	/* returned with Invalid_operation if a restriction is violated. */
michael@0	814	/* ------------------------------------------------------------------ */
michael@0	815	U_CAPI decNumber * U_EXPORT2 uprv_decNumberAnd(decNumber *res, const decNumber *lhs,
michael@0	816	const decNumber *rhs, decContext *set) {
michael@0	817	const Unit *ua, *ub; /* -> operands */
michael@0	818	const Unit *msua, *msub; /* -> operand msus */
michael@0	819	Unit *uc, *msuc; /* -> result and its msu */
michael@0	820	Int msudigs; /* digits in res msu */
michael@0	821	#if DECCHECK
michael@0	822	if (decCheckOperands(res, lhs, rhs, set)) return res;
michael@0	823	#endif
michael@0	824
michael@0	825	if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
michael@0	826	|| rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
michael@0	827	decStatus(res, DEC_Invalid_operation, set);
michael@0	828	return res;
michael@0	829	}
michael@0	830
michael@0	831	/* operands are valid */
michael@0	832	ua=lhs->lsu; /* bottom-up */
michael@0	833	ub=rhs->lsu; /* .. */
michael@0	834	uc=res->lsu; /* .. */
michael@0	835	msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */
michael@0	836	msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */
michael@0	837	msuc=uc+D2U(set->digits)-1; /* -> msu of result */
michael@0	838	msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */
michael@0	839	for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */
michael@0	840	Unit a, b; /* extract units */
michael@0	841	if (ua>msua) a=0;
michael@0	842	else a=*ua;
michael@0	843	if (ub>msub) b=0;
michael@0	844	else b=*ub;
michael@0	845	*uc=0; /* can now write back */
michael@0	846	if (a|b) { /* maybe 1 bits to examine */
michael@0	847	Int i, j;
michael@0	848	*uc=0; /* can now write back */
michael@0	849	/* This loop could be unrolled and/or use BIN2BCD tables */
michael@0	850	for (i=0; i<DECDPUN; i++) {
michael@0	851	if (a&b&1) *uc=*uc+(Unit)powers[i]; /* effect AND */
michael@0	852	j=a%10;
michael@0	853	a=a/10;
michael@0	854	j|=b%10;
michael@0	855	b=b/10;
michael@0	856	if (j>1) {
michael@0	857	decStatus(res, DEC_Invalid_operation, set);
michael@0	858	return res;
michael@0	859	}
michael@0	860	if (uc==msuc && i==msudigs-1) break; /* just did final digit */
michael@0	861	} /* each digit */
michael@0	862	} /* both OK */
michael@0	863	} /* each unit */
michael@0	864	/* [here uc-1 is the msu of the result] */
michael@0	865	res->digits=decGetDigits(res->lsu, uc-res->lsu);
michael@0	866	res->exponent=0; /* integer */
michael@0	867	res->bits=0; /* sign=0 */
michael@0	868	return res; /* [no status to set] */
michael@0	869	} /* decNumberAnd */
michael@0	870
michael@0	871	/* ------------------------------------------------------------------ */
michael@0	872	/* decNumberCompare -- compare two Numbers */
michael@0	873	/* */
michael@0	874	/* This computes C = A ? B */
michael@0	875	/* */
michael@0	876	/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
michael@0	877	/* lhs is A */
michael@0	878	/* rhs is B */
michael@0	879	/* set is the context */
michael@0	880	/* */
michael@0	881	/* C must have space for one digit (or NaN). */
michael@0	882	/* ------------------------------------------------------------------ */
michael@0	883	U_CAPI decNumber * U_EXPORT2 uprv_decNumberCompare(decNumber *res, const decNumber *lhs,
michael@0	884	const decNumber *rhs, decContext *set) {
michael@0	885	uInt status=0; /* accumulator */
michael@0	886	decCompareOp(res, lhs, rhs, set, COMPARE, &status);
michael@0	887	if (status!=0) decStatus(res, status, set);
michael@0	888	return res;
michael@0	889	} /* decNumberCompare */
michael@0	890
michael@0	891	/* ------------------------------------------------------------------ */
michael@0	892	/* decNumberCompareSignal -- compare, signalling on all NaNs */
michael@0	893	/* */
michael@0	894	/* This computes C = A ? B */
michael@0	895	/* */
michael@0	896	/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
michael@0	897	/* lhs is A */
michael@0	898	/* rhs is B */
michael@0	899	/* set is the context */
michael@0	900	/* */
michael@0	901	/* C must have space for one digit (or NaN). */
michael@0	902	/* ------------------------------------------------------------------ */
michael@0	903	U_CAPI decNumber * U_EXPORT2 uprv_decNumberCompareSignal(decNumber *res, const decNumber *lhs,
michael@0	904	const decNumber *rhs, decContext *set) {
michael@0	905	uInt status=0; /* accumulator */
michael@0	906	decCompareOp(res, lhs, rhs, set, COMPSIG, &status);
michael@0	907	if (status!=0) decStatus(res, status, set);
michael@0	908	return res;
michael@0	909	} /* decNumberCompareSignal */
michael@0	910
michael@0	911	/* ------------------------------------------------------------------ */
michael@0	912	/* decNumberCompareTotal -- compare two Numbers, using total ordering */
michael@0	913	/* */
michael@0	914	/* This computes C = A ? B, under total ordering */
michael@0	915	/* */
michael@0	916	/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
michael@0	917	/* lhs is A */
michael@0	918	/* rhs is B */
michael@0	919	/* set is the context */
michael@0	920	/* */
michael@0	921	/* C must have space for one digit; the result will always be one of */
michael@0	922	/* -1, 0, or 1. */
michael@0	923	/* ------------------------------------------------------------------ */
michael@0	924	U_CAPI decNumber * U_EXPORT2 uprv_decNumberCompareTotal(decNumber *res, const decNumber *lhs,
michael@0	925	const decNumber *rhs, decContext *set) {
michael@0	926	uInt status=0; /* accumulator */
michael@0	927	decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status);
michael@0	928	if (status!=0) decStatus(res, status, set);
michael@0	929	return res;
michael@0	930	} /* decNumberCompareTotal */
michael@0	931
michael@0	932	/* ------------------------------------------------------------------ */
michael@0	933	/* decNumberCompareTotalMag -- compare, total ordering of magnitudes */
michael@0	934	/* */
michael@0	935	/* This computes C = |A| ? |B|, under total ordering */
michael@0	936	/* */
michael@0	937	/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
michael@0	938	/* lhs is A */
michael@0	939	/* rhs is B */
michael@0	940	/* set is the context */
michael@0	941	/* */
michael@0	942	/* C must have space for one digit; the result will always be one of */
michael@0	943	/* -1, 0, or 1. */
michael@0	944	/* ------------------------------------------------------------------ */
michael@0	945	U_CAPI decNumber * U_EXPORT2 uprv_decNumberCompareTotalMag(decNumber *res, const decNumber *lhs,
michael@0	946	const decNumber *rhs, decContext *set) {
michael@0	947	uInt status=0; /* accumulator */
michael@0	948	uInt needbytes; /* for space calculations */
michael@0	949	decNumber bufa[D2N(DECBUFFER+1)];/* +1 in case DECBUFFER=0 */
michael@0	950	decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */
michael@0	951	decNumber bufb[D2N(DECBUFFER+1)];
michael@0	952	decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */
michael@0	953	decNumber *a, *b; /* temporary pointers */
michael@0	954
michael@0	955	#if DECCHECK
michael@0	956	if (decCheckOperands(res, lhs, rhs, set)) return res;
michael@0	957	#endif
michael@0	958
michael@0	959	do { /* protect allocated storage */
michael@0	960	/* if either is negative, take a copy and absolute */
michael@0	961	if (decNumberIsNegative(lhs)) { /* lhs<0 */
michael@0	962	a=bufa;
michael@0	963	needbytes=sizeof(decNumber)+(D2U(lhs->digits)-1)*sizeof(Unit);
michael@0	964	if (needbytes>sizeof(bufa)) { /* need malloc space */
michael@0	965	allocbufa=(decNumber *)malloc(needbytes);
michael@0	966	if (allocbufa==NULL) { /* hopeless -- abandon */
michael@0	967	status|=DEC_Insufficient_storage;
michael@0	968	break;}
michael@0	969	a=allocbufa; /* use the allocated space */
michael@0	970	}
michael@0	971	uprv_decNumberCopy(a, lhs); /* copy content */
michael@0	972	a->bits&=~DECNEG; /* .. and clear the sign */
michael@0	973	lhs=a; /* use copy from here on */
michael@0	974	}
michael@0	975	if (decNumberIsNegative(rhs)) { /* rhs<0 */
michael@0	976	b=bufb;
michael@0	977	needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
michael@0	978	if (needbytes>sizeof(bufb)) { /* need malloc space */
michael@0	979	allocbufb=(decNumber *)malloc(needbytes);
michael@0	980	if (allocbufb==NULL) { /* hopeless -- abandon */
michael@0	981	status|=DEC_Insufficient_storage;
michael@0	982	break;}
michael@0	983	b=allocbufb; /* use the allocated space */
michael@0	984	}
michael@0	985	uprv_decNumberCopy(b, rhs); /* copy content */
michael@0	986	b->bits&=~DECNEG; /* .. and clear the sign */
michael@0	987	rhs=b; /* use copy from here on */
michael@0	988	}
michael@0	989	decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status);
michael@0	990	} while(0); /* end protected */
michael@0	991
michael@0	992	if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */
michael@0	993	if (allocbufb!=NULL) free(allocbufb); /* .. */
michael@0	994	if (status!=0) decStatus(res, status, set);
michael@0	995	return res;
michael@0	996	} /* decNumberCompareTotalMag */
michael@0	997
michael@0	998	/* ------------------------------------------------------------------ */
michael@0	999	/* decNumberDivide -- divide one number by another */
michael@0	1000	/* */
michael@0	1001	/* This computes C = A / B */
michael@0	1002	/* */
michael@0	1003	/* res is C, the result. C may be A and/or B (e.g., X=X/X) */
michael@0	1004	/* lhs is A */
michael@0	1005	/* rhs is B */
michael@0	1006	/* set is the context */
michael@0	1007	/* */
michael@0	1008	/* C must have space for set->digits digits. */
michael@0	1009	/* ------------------------------------------------------------------ */
michael@0	1010	U_CAPI decNumber * U_EXPORT2 uprv_decNumberDivide(decNumber *res, const decNumber *lhs,
michael@0	1011	const decNumber *rhs, decContext *set) {
michael@0	1012	uInt status=0; /* accumulator */
michael@0	1013	decDivideOp(res, lhs, rhs, set, DIVIDE, &status);
michael@0	1014	if (status!=0) decStatus(res, status, set);
michael@0	1015	#if DECCHECK
michael@0	1016	decCheckInexact(res, set);
michael@0	1017	#endif
michael@0	1018	return res;
michael@0	1019	} /* decNumberDivide */
michael@0	1020
michael@0	1021	/* ------------------------------------------------------------------ */
michael@0	1022	/* decNumberDivideInteger -- divide and return integer quotient */
michael@0	1023	/* */
michael@0	1024	/* This computes C = A # B, where # is the integer divide operator */
michael@0	1025	/* */
michael@0	1026	/* res is C, the result. C may be A and/or B (e.g., X=X#X) */
michael@0	1027	/* lhs is A */
michael@0	1028	/* rhs is B */
michael@0	1029	/* set is the context */
michael@0	1030	/* */
michael@0	1031	/* C must have space for set->digits digits. */
michael@0	1032	/* ------------------------------------------------------------------ */
michael@0	1033	U_CAPI decNumber * U_EXPORT2 uprv_decNumberDivideInteger(decNumber *res, const decNumber *lhs,
michael@0	1034	const decNumber *rhs, decContext *set) {
michael@0	1035	uInt status=0; /* accumulator */
michael@0	1036	decDivideOp(res, lhs, rhs, set, DIVIDEINT, &status);
michael@0	1037	if (status!=0) decStatus(res, status, set);
michael@0	1038	return res;
michael@0	1039	} /* decNumberDivideInteger */
michael@0	1040
michael@0	1041	/* ------------------------------------------------------------------ */
michael@0	1042	/* decNumberExp -- exponentiation */
michael@0	1043	/* */
michael@0	1044	/* This computes C = exp(A) */
michael@0	1045	/* */
michael@0	1046	/* res is C, the result. C may be A */
michael@0	1047	/* rhs is A */
michael@0	1048	/* set is the context; note that rounding mode has no effect */
michael@0	1049	/* */
michael@0	1050	/* C must have space for set->digits digits. */
michael@0	1051	/* */
michael@0	1052	/* Mathematical function restrictions apply (see above); a NaN is */
michael@0	1053	/* returned with Invalid_operation if a restriction is violated. */
michael@0	1054	/* */
michael@0	1055	/* Finite results will always be full precision and Inexact, except */
michael@0	1056	/* when A is a zero or -Infinity (giving 1 or 0 respectively). */
michael@0	1057	/* */
michael@0	1058	/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */
michael@0	1059	/* almost always be correctly rounded, but may be up to 1 ulp in */
michael@0	1060	/* error in rare cases. */
michael@0	1061	/* ------------------------------------------------------------------ */
michael@0	1062	/* This is a wrapper for decExpOp which can handle the slightly wider */
michael@0	1063	/* (double) range needed by Ln (which has to be able to calculate */
michael@0	1064	/* exp(-a) where a can be the tiniest number (Ntiny). */
michael@0	1065	/* ------------------------------------------------------------------ */
michael@0	1066	U_CAPI decNumber * U_EXPORT2 uprv_decNumberExp(decNumber *res, const decNumber *rhs,
michael@0	1067	decContext *set) {
michael@0	1068	uInt status=0; /* accumulator */
michael@0	1069	#if DECSUBSET
michael@0	1070	decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */
michael@0	1071	#endif
michael@0	1072
michael@0	1073	#if DECCHECK
michael@0	1074	if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
michael@0	1075	#endif
michael@0	1076
michael@0	1077	/* Check restrictions; these restrictions ensure that if h=8 (see */
michael@0	1078	/* decExpOp) then the result will either overflow or underflow to 0. */
michael@0	1079	/* Other math functions restrict the input range, too, for inverses. */
michael@0	1080	/* If not violated then carry out the operation. */
michael@0	1081	if (!decCheckMath(rhs, set, &status)) do { /* protect allocation */
michael@0	1082	#if DECSUBSET
michael@0	1083	if (!set->extended) {
michael@0	1084	/* reduce operand and set lostDigits status, as needed */
michael@0	1085	if (rhs->digits>set->digits) {
michael@0	1086	allocrhs=decRoundOperand(rhs, set, &status);
michael@0	1087	if (allocrhs==NULL) break;
michael@0	1088	rhs=allocrhs;
michael@0	1089	}
michael@0	1090	}
michael@0	1091	#endif
michael@0	1092	decExpOp(res, rhs, set, &status);
michael@0	1093	} while(0); /* end protected */
michael@0	1094
michael@0	1095	#if DECSUBSET
michael@0	1096	if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */
michael@0	1097	#endif
michael@0	1098	/* apply significant status */
michael@0	1099	if (status!=0) decStatus(res, status, set);
michael@0	1100	#if DECCHECK
michael@0	1101	decCheckInexact(res, set);
michael@0	1102	#endif
michael@0	1103	return res;
michael@0	1104	} /* decNumberExp */
michael@0	1105
michael@0	1106	/* ------------------------------------------------------------------ */
michael@0	1107	/* decNumberFMA -- fused multiply add */
michael@0	1108	/* */
michael@0	1109	/* This computes D = (A * B) + C with only one rounding */
michael@0	1110	/* */
michael@0	1111	/* res is D, the result. D may be A or B or C (e.g., X=FMA(X,X,X)) */
michael@0	1112	/* lhs is A */
michael@0	1113	/* rhs is B */
michael@0	1114	/* fhs is C [far hand side] */
michael@0	1115	/* set is the context */
michael@0	1116	/* */
michael@0	1117	/* Mathematical function restrictions apply (see above); a NaN is */
michael@0	1118	/* returned with Invalid_operation if a restriction is violated. */
michael@0	1119	/* */
michael@0	1120	/* C must have space for set->digits digits. */
michael@0	1121	/* ------------------------------------------------------------------ */
michael@0	1122	U_CAPI decNumber * U_EXPORT2 uprv_decNumberFMA(decNumber *res, const decNumber *lhs,
michael@0	1123	const decNumber *rhs, const decNumber *fhs,
michael@0	1124	decContext *set) {
michael@0	1125	uInt status=0; /* accumulator */
michael@0	1126	decContext dcmul; /* context for the multiplication */
michael@0	1127	uInt needbytes; /* for space calculations */
michael@0	1128	decNumber bufa[D2N(DECBUFFER*2+1)];
michael@0	1129	decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */
michael@0	1130	decNumber *acc; /* accumulator pointer */
michael@0	1131	decNumber dzero; /* work */
michael@0	1132
michael@0	1133	#if DECCHECK
michael@0	1134	if (decCheckOperands(res, lhs, rhs, set)) return res;
michael@0	1135	if (decCheckOperands(res, fhs, DECUNUSED, set)) return res;
michael@0	1136	#endif
michael@0	1137
michael@0	1138	do { /* protect allocated storage */
michael@0	1139	#if DECSUBSET
michael@0	1140	if (!set->extended) { /* [undefined if subset] */
michael@0	1141	status|=DEC_Invalid_operation;
michael@0	1142	break;}
michael@0	1143	#endif
michael@0	1144	/* Check math restrictions [these ensure no overflow or underflow] */
michael@0	1145	if ((!decNumberIsSpecial(lhs) && decCheckMath(lhs, set, &status))
michael@0	1146	|| (!decNumberIsSpecial(rhs) && decCheckMath(rhs, set, &status))
michael@0	1147	|| (!decNumberIsSpecial(fhs) && decCheckMath(fhs, set, &status))) break;
michael@0	1148	/* set up context for multiply */
michael@0	1149	dcmul=*set;
michael@0	1150	dcmul.digits=lhs->digits+rhs->digits; /* just enough */
michael@0	1151	/* [The above may be an over-estimate for subset arithmetic, but that's OK] */
michael@0	1152	dcmul.emax=DEC_MAX_EMAX; /* effectively unbounded .. */
michael@0	1153	dcmul.emin=DEC_MIN_EMIN; /* [thanks to Math restrictions] */
michael@0	1154	/* set up decNumber space to receive the result of the multiply */
michael@0	1155	acc=bufa; /* may fit */
michael@0	1156	needbytes=sizeof(decNumber)+(D2U(dcmul.digits)-1)*sizeof(Unit);
michael@0	1157	if (needbytes>sizeof(bufa)) { /* need malloc space */
michael@0	1158	allocbufa=(decNumber *)malloc(needbytes);
michael@0	1159	if (allocbufa==NULL) { /* hopeless -- abandon */
michael@0	1160	status|=DEC_Insufficient_storage;
michael@0	1161	break;}
michael@0	1162	acc=allocbufa; /* use the allocated space */
michael@0	1163	}
michael@0	1164	/* multiply with extended range and necessary precision */
michael@0	1165	/*printf("emin=%ld\n", dcmul.emin); */
michael@0	1166	decMultiplyOp(acc, lhs, rhs, &dcmul, &status);
michael@0	1167	/* Only Invalid operation (from sNaN or Inf * 0) is possible in */
michael@0	1168	/* status; if either is seen than ignore fhs (in case it is */
michael@0	1169	/* another sNaN) and set acc to NaN unless we had an sNaN */
michael@0	1170	/* [decMultiplyOp leaves that to caller] */
michael@0	1171	/* Note sNaN has to go through addOp to shorten payload if */
michael@0	1172	/* necessary */
michael@0	1173	if ((status&DEC_Invalid_operation)!=0) {
michael@0	1174	if (!(status&DEC_sNaN)) { /* but be true invalid */
michael@0	1175	uprv_decNumberZero(res); /* acc not yet set */
michael@0	1176	res->bits=DECNAN;
michael@0	1177	break;
michael@0	1178	}
michael@0	1179	uprv_decNumberZero(&dzero); /* make 0 (any non-NaN would do) */
michael@0	1180	fhs=&dzero; /* use that */
michael@0	1181	}
michael@0	1182	#if DECCHECK
michael@0	1183	else { /* multiply was OK */
michael@0	1184	if (status!=0) printf("Status=%08lx after FMA multiply\n", (LI)status);
michael@0	1185	}
michael@0	1186	#endif
michael@0	1187	/* add the third operand and result -> res, and all is done */
michael@0	1188	decAddOp(res, acc, fhs, set, 0, &status);
michael@0	1189	} while(0); /* end protected */
michael@0	1190
michael@0	1191	if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */
michael@0	1192	if (status!=0) decStatus(res, status, set);
michael@0	1193	#if DECCHECK
michael@0	1194	decCheckInexact(res, set);
michael@0	1195	#endif
michael@0	1196	return res;
michael@0	1197	} /* decNumberFMA */
michael@0	1198
michael@0	1199	/* ------------------------------------------------------------------ */
michael@0	1200	/* decNumberInvert -- invert a Number, digitwise */
michael@0	1201	/* */
michael@0	1202	/* This computes C = ~A */
michael@0	1203	/* */
michael@0	1204	/* res is C, the result. C may be A (e.g., X=~X) */
michael@0	1205	/* rhs is A */
michael@0	1206	/* set is the context (used for result length and error report) */
michael@0	1207	/* */
michael@0	1208	/* C must have space for set->digits digits. */
michael@0	1209	/* */
michael@0	1210	/* Logical function restrictions apply (see above); a NaN is */
michael@0	1211	/* returned with Invalid_operation if a restriction is violated. */
michael@0	1212	/* ------------------------------------------------------------------ */
michael@0	1213	U_CAPI decNumber * U_EXPORT2 uprv_decNumberInvert(decNumber *res, const decNumber *rhs,
michael@0	1214	decContext *set) {
michael@0	1215	const Unit *ua, *msua; /* -> operand and its msu */
michael@0	1216	Unit *uc, *msuc; /* -> result and its msu */
michael@0	1217	Int msudigs; /* digits in res msu */
michael@0	1218	#if DECCHECK
michael@0	1219	if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
michael@0	1220	#endif
michael@0	1221
michael@0	1222	if (rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
michael@0	1223	decStatus(res, DEC_Invalid_operation, set);
michael@0	1224	return res;
michael@0	1225	}
michael@0	1226	/* operand is valid */
michael@0	1227	ua=rhs->lsu; /* bottom-up */
michael@0	1228	uc=res->lsu; /* .. */
michael@0	1229	msua=ua+D2U(rhs->digits)-1; /* -> msu of rhs */
michael@0	1230	msuc=uc+D2U(set->digits)-1; /* -> msu of result */
michael@0	1231	msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */
michael@0	1232	for (; uc<=msuc; ua++, uc++) { /* Unit loop */
michael@0	1233	Unit a; /* extract unit */
michael@0	1234	Int i, j; /* work */
michael@0	1235	if (ua>msua) a=0;
michael@0	1236	else a=*ua;
michael@0	1237	*uc=0; /* can now write back */
michael@0	1238	/* always need to examine all bits in rhs */
michael@0	1239	/* This loop could be unrolled and/or use BIN2BCD tables */
michael@0	1240	for (i=0; i<DECDPUN; i++) {
michael@0	1241	if ((~a)&1) *uc=*uc+(Unit)powers[i]; /* effect INVERT */
michael@0	1242	j=a%10;
michael@0	1243	a=a/10;
michael@0	1244	if (j>1) {
michael@0	1245	decStatus(res, DEC_Invalid_operation, set);
michael@0	1246	return res;
michael@0	1247	}
michael@0	1248	if (uc==msuc && i==msudigs-1) break; /* just did final digit */
michael@0	1249	} /* each digit */
michael@0	1250	} /* each unit */
michael@0	1251	/* [here uc-1 is the msu of the result] */
michael@0	1252	res->digits=decGetDigits(res->lsu, uc-res->lsu);
michael@0	1253	res->exponent=0; /* integer */
michael@0	1254	res->bits=0; /* sign=0 */
michael@0	1255	return res; /* [no status to set] */
michael@0	1256	} /* decNumberInvert */
michael@0	1257
michael@0	1258	/* ------------------------------------------------------------------ */
michael@0	1259	/* decNumberLn -- natural logarithm */
michael@0	1260	/* */
michael@0	1261	/* This computes C = ln(A) */
michael@0	1262	/* */
michael@0	1263	/* res is C, the result. C may be A */
michael@0	1264	/* rhs is A */
michael@0	1265	/* set is the context; note that rounding mode has no effect */
michael@0	1266	/* */
michael@0	1267	/* C must have space for set->digits digits. */
michael@0	1268	/* */
michael@0	1269	/* Notable cases: */
michael@0	1270	/* A<0 -> Invalid */
michael@0	1271	/* A=0 -> -Infinity (Exact) */
michael@0	1272	/* A=+Infinity -> +Infinity (Exact) */
michael@0	1273	/* A=1 exactly -> 0 (Exact) */
michael@0	1274	/* */
michael@0	1275	/* Mathematical function restrictions apply (see above); a NaN is */
michael@0	1276	/* returned with Invalid_operation if a restriction is violated. */
michael@0	1277	/* */
michael@0	1278	/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */
michael@0	1279	/* almost always be correctly rounded, but may be up to 1 ulp in */
michael@0	1280	/* error in rare cases. */
michael@0	1281	/* ------------------------------------------------------------------ */
michael@0	1282	/* This is a wrapper for decLnOp which can handle the slightly wider */
michael@0	1283	/* (+11) range needed by Ln, Log10, etc. (which may have to be able */
michael@0	1284	/* to calculate at p+e+2). */
michael@0	1285	/* ------------------------------------------------------------------ */
michael@0	1286	U_CAPI decNumber * U_EXPORT2 uprv_decNumberLn(decNumber *res, const decNumber *rhs,
michael@0	1287	decContext *set) {
michael@0	1288	uInt status=0; /* accumulator */
michael@0	1289	#if DECSUBSET
michael@0	1290	decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */
michael@0	1291	#endif
michael@0	1292
michael@0	1293	#if DECCHECK
michael@0	1294	if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
michael@0	1295	#endif
michael@0	1296
michael@0	1297	/* Check restrictions; this is a math function; if not violated */
michael@0	1298	/* then carry out the operation. */
michael@0	1299	if (!decCheckMath(rhs, set, &status)) do { /* protect allocation */
michael@0	1300	#if DECSUBSET
michael@0	1301	if (!set->extended) {
michael@0	1302	/* reduce operand and set lostDigits status, as needed */
michael@0	1303	if (rhs->digits>set->digits) {
michael@0	1304	allocrhs=decRoundOperand(rhs, set, &status);
michael@0	1305	if (allocrhs==NULL) break;
michael@0	1306	rhs=allocrhs;
michael@0	1307	}
michael@0	1308	/* special check in subset for rhs=0 */
michael@0	1309	if (ISZERO(rhs)) { /* +/- zeros -> error */
michael@0	1310	status|=DEC_Invalid_operation;
michael@0	1311	break;}
michael@0	1312	} /* extended=0 */
michael@0	1313	#endif
michael@0	1314	decLnOp(res, rhs, set, &status);
michael@0	1315	} while(0); /* end protected */
michael@0	1316
michael@0	1317	#if DECSUBSET
michael@0	1318	if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */
michael@0	1319	#endif
michael@0	1320	/* apply significant status */
michael@0	1321	if (status!=0) decStatus(res, status, set);
michael@0	1322	#if DECCHECK
michael@0	1323	decCheckInexact(res, set);
michael@0	1324	#endif
michael@0	1325	return res;
michael@0	1326	} /* decNumberLn */
michael@0	1327
michael@0	1328	/* ------------------------------------------------------------------ */
michael@0	1329	/* decNumberLogB - get adjusted exponent, by 754 rules */
michael@0	1330	/* */
michael@0	1331	/* This computes C = adjustedexponent(A) */
michael@0	1332	/* */
michael@0	1333	/* res is C, the result. C may be A */
michael@0	1334	/* rhs is A */
michael@0	1335	/* set is the context, used only for digits and status */
michael@0	1336	/* */
michael@0	1337	/* C must have space for 10 digits (A might have 10**9 digits and */
michael@0	1338	/* an exponent of +999999999, or one digit and an exponent of */
michael@0	1339	/* -1999999999). */
michael@0	1340	/* */
michael@0	1341	/* This returns the adjusted exponent of A after (in theory) padding */
michael@0	1342	/* with zeros on the right to set->digits digits while keeping the */
michael@0	1343	/* same value. The exponent is not limited by emin/emax. */
michael@0	1344	/* */
michael@0	1345	/* Notable cases: */
michael@0	1346	/* A<0 -> Use |A| */
michael@0	1347	/* A=0 -> -Infinity (Division by zero) */
michael@0	1348	/* A=Infinite -> +Infinity (Exact) */
michael@0	1349	/* A=1 exactly -> 0 (Exact) */
michael@0	1350	/* NaNs are propagated as usual */
michael@0	1351	/* ------------------------------------------------------------------ */
michael@0	1352	U_CAPI decNumber * U_EXPORT2 uprv_decNumberLogB(decNumber *res, const decNumber *rhs,
michael@0	1353	decContext *set) {
michael@0	1354	uInt status=0; /* accumulator */
michael@0	1355
michael@0	1356	#if DECCHECK
michael@0	1357	if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
michael@0	1358	#endif
michael@0	1359
michael@0	1360	/* NaNs as usual; Infinities return +Infinity; 0->oops */
michael@0	1361	if (decNumberIsNaN(rhs)) decNaNs(res, rhs, NULL, set, &status);
michael@0	1362	else if (decNumberIsInfinite(rhs)) uprv_decNumberCopyAbs(res, rhs);
michael@0	1363	else if (decNumberIsZero(rhs)) {
michael@0	1364	uprv_decNumberZero(res); /* prepare for Infinity */
michael@0	1365	res->bits=DECNEG|DECINF; /* -Infinity */
michael@0	1366	status|=DEC_Division_by_zero; /* as per 754 */
michael@0	1367	}
michael@0	1368	else { /* finite non-zero */
michael@0	1369	Int ae=rhs->exponent+rhs->digits-1; /* adjusted exponent */
michael@0	1370	uprv_decNumberFromInt32(res, ae); /* lay it out */
michael@0	1371	}
michael@0	1372
michael@0	1373	if (status!=0) decStatus(res, status, set);
michael@0	1374	return res;
michael@0	1375	} /* decNumberLogB */
michael@0	1376
michael@0	1377	/* ------------------------------------------------------------------ */
michael@0	1378	/* decNumberLog10 -- logarithm in base 10 */
michael@0	1379	/* */
michael@0	1380	/* This computes C = log10(A) */
michael@0	1381	/* */
michael@0	1382	/* res is C, the result. C may be A */
michael@0	1383	/* rhs is A */
michael@0	1384	/* set is the context; note that rounding mode has no effect */
michael@0	1385	/* */
michael@0	1386	/* C must have space for set->digits digits. */
michael@0	1387	/* */
michael@0	1388	/* Notable cases: */
michael@0	1389	/* A<0 -> Invalid */
michael@0	1390	/* A=0 -> -Infinity (Exact) */
michael@0	1391	/* A=+Infinity -> +Infinity (Exact) */
michael@0	1392	/* A=10**n (if n is an integer) -> n (Exact) */
michael@0	1393	/* */
michael@0	1394	/* Mathematical function restrictions apply (see above); a NaN is */
michael@0	1395	/* returned with Invalid_operation if a restriction is violated. */
michael@0	1396	/* */
michael@0	1397	/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */
michael@0	1398	/* almost always be correctly rounded, but may be up to 1 ulp in */
michael@0	1399	/* error in rare cases. */
michael@0	1400	/* ------------------------------------------------------------------ */
michael@0	1401	/* This calculates ln(A)/ln(10) using appropriate precision. For */
michael@0	1402	/* ln(A) this is the max(p, rhs->digits + t) + 3, where p is the */
michael@0	1403	/* requested digits and t is the number of digits in the exponent */
michael@0	1404	/* (maximum 6). For ln(10) it is p + 3; this is often handled by the */
michael@0	1405	/* fastpath in decLnOp. The final division is done to the requested */
michael@0	1406	/* precision. */
michael@0	1407	/* ------------------------------------------------------------------ */
michael@0	1408	#if defined(__clang__) || U_GCC_MAJOR_MINOR >= 406
michael@0	1409	#pragma GCC diagnostic push
michael@0	1410	#pragma GCC diagnostic ignored "-Warray-bounds"
michael@0	1411	#endif
michael@0	1412	U_CAPI decNumber * U_EXPORT2 uprv_decNumberLog10(decNumber *res, const decNumber *rhs,
michael@0	1413	decContext *set) {
michael@0	1414	uInt status=0, ignore=0; /* status accumulators */
michael@0	1415	uInt needbytes; /* for space calculations */
michael@0	1416	Int p; /* working precision */
michael@0	1417	Int t; /* digits in exponent of A */
michael@0	1418
michael@0	1419	/* buffers for a and b working decimals */
michael@0	1420	/* (adjustment calculator, same size) */
michael@0	1421	decNumber bufa[D2N(DECBUFFER+2)];
michael@0	1422	decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */
michael@0	1423	decNumber *a=bufa; /* temporary a */
michael@0	1424	decNumber bufb[D2N(DECBUFFER+2)];
michael@0	1425	decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */
michael@0	1426	decNumber *b=bufb; /* temporary b */
michael@0	1427	decNumber bufw[D2N(10)]; /* working 2-10 digit number */
michael@0	1428	decNumber *w=bufw; /* .. */
michael@0	1429	#if DECSUBSET
michael@0	1430	decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */
michael@0	1431	#endif
michael@0	1432
michael@0	1433	decContext aset; /* working context */
michael@0	1434
michael@0	1435	#if DECCHECK
michael@0	1436	if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
michael@0	1437	#endif
michael@0	1438
michael@0	1439	/* Check restrictions; this is a math function; if not violated */
michael@0	1440	/* then carry out the operation. */
michael@0	1441	if (!decCheckMath(rhs, set, &status)) do { /* protect malloc */
michael@0	1442	#if DECSUBSET
michael@0	1443	if (!set->extended) {
michael@0	1444	/* reduce operand and set lostDigits status, as needed */
michael@0	1445	if (rhs->digits>set->digits) {
michael@0	1446	allocrhs=decRoundOperand(rhs, set, &status);
michael@0	1447	if (allocrhs==NULL) break;
michael@0	1448	rhs=allocrhs;
michael@0	1449	}
michael@0	1450	/* special check in subset for rhs=0 */
michael@0	1451	if (ISZERO(rhs)) { /* +/- zeros -> error */
michael@0	1452	status|=DEC_Invalid_operation;
michael@0	1453	break;}
michael@0	1454	} /* extended=0 */
michael@0	1455	#endif
michael@0	1456
michael@0	1457	uprv_decContextDefault(&aset, DEC_INIT_DECIMAL64); /* clean context */
michael@0	1458
michael@0	1459	/* handle exact powers of 10; only check if +ve finite */
michael@0	1460	if (!(rhs->bits&(DECNEG|DECSPECIAL)) && !ISZERO(rhs)) {
michael@0	1461	Int residue=0; /* (no residue) */
michael@0	1462	uInt copystat=0; /* clean status */
michael@0	1463
michael@0	1464	/* round to a single digit... */
michael@0	1465	aset.digits=1;
michael@0	1466	decCopyFit(w, rhs, &aset, &residue, &copystat); /* copy & shorten */
michael@0	1467	/* if exact and the digit is 1, rhs is a power of 10 */
michael@0	1468	if (!(copystat&DEC_Inexact) && w->lsu[0]==1) {
michael@0	1469	/* the exponent, conveniently, is the power of 10; making */
michael@0	1470	/* this the result needs a little care as it might not fit, */
michael@0	1471	/* so first convert it into the working number, and then move */
michael@0	1472	/* to res */
michael@0	1473	uprv_decNumberFromInt32(w, w->exponent);
michael@0	1474	residue=0;
michael@0	1475	decCopyFit(res, w, set, &residue, &status); /* copy & round */
michael@0	1476	decFinish(res, set, &residue, &status); /* cleanup/set flags */
michael@0	1477	break;
michael@0	1478	} /* not a power of 10 */
michael@0	1479	} /* not a candidate for exact */
michael@0	1480
michael@0	1481	/* simplify the information-content calculation to use 'total */
michael@0	1482	/* number of digits in a, including exponent' as compared to the */
michael@0	1483	/* requested digits, as increasing this will only rarely cost an */
michael@0	1484	/* iteration in ln(a) anyway */
michael@0	1485	t=6; /* it can never be >6 */
michael@0	1486
michael@0	1487	/* allocate space when needed... */
michael@0	1488	p=(rhs->digits+t>set->digits?rhs->digits+t:set->digits)+3;
michael@0	1489	needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit);
michael@0	1490	if (needbytes>sizeof(bufa)) { /* need malloc space */
michael@0	1491	allocbufa=(decNumber *)malloc(needbytes);
michael@0	1492	if (allocbufa==NULL) { /* hopeless -- abandon */
michael@0	1493	status|=DEC_Insufficient_storage;
michael@0	1494	break;}
michael@0	1495	a=allocbufa; /* use the allocated space */
michael@0	1496	}
michael@0	1497	aset.digits=p; /* as calculated */
michael@0	1498	aset.emax=DEC_MAX_MATH; /* usual bounds */
michael@0	1499	aset.emin=-DEC_MAX_MATH; /* .. */
michael@0	1500	aset.clamp=0; /* and no concrete format */
michael@0	1501	decLnOp(a, rhs, &aset, &status); /* a=ln(rhs) */
michael@0	1502
michael@0	1503	/* skip the division if the result so far is infinite, NaN, or */
michael@0	1504	/* zero, or there was an error; note NaN from sNaN needs copy */
michael@0	1505	if (status&DEC_NaNs && !(status&DEC_sNaN)) break;
michael@0	1506	if (a->bits&DECSPECIAL || ISZERO(a)) {
michael@0	1507	uprv_decNumberCopy(res, a); /* [will fit] */
michael@0	1508	break;}
michael@0	1509
michael@0	1510	/* for ln(10) an extra 3 digits of precision are needed */
michael@0	1511	p=set->digits+3;
michael@0	1512	needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit);
michael@0	1513	if (needbytes>sizeof(bufb)) { /* need malloc space */
michael@0	1514	allocbufb=(decNumber *)malloc(needbytes);
michael@0	1515	if (allocbufb==NULL) { /* hopeless -- abandon */
michael@0	1516	status|=DEC_Insufficient_storage;
michael@0	1517	break;}
michael@0	1518	b=allocbufb; /* use the allocated space */
michael@0	1519	}
michael@0	1520	uprv_decNumberZero(w); /* set up 10... */
michael@0	1521	#if DECDPUN==1
michael@0	1522	w->lsu[1]=1; w->lsu[0]=0; /* .. */
michael@0	1523	#else
michael@0	1524	w->lsu[0]=10; /* .. */
michael@0	1525	#endif
michael@0	1526	w->digits=2; /* .. */
michael@0	1527
michael@0	1528	aset.digits=p;
michael@0	1529	decLnOp(b, w, &aset, &ignore); /* b=ln(10) */
michael@0	1530
michael@0	1531	aset.digits=set->digits; /* for final divide */
michael@0	1532	decDivideOp(res, a, b, &aset, DIVIDE, &status); /* into result */
michael@0	1533	} while(0); /* [for break] */
michael@0	1534
michael@0	1535	if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */
michael@0	1536	if (allocbufb!=NULL) free(allocbufb); /* .. */
michael@0	1537	#if DECSUBSET
michael@0	1538	if (allocrhs !=NULL) free(allocrhs); /* .. */
michael@0	1539	#endif
michael@0	1540	/* apply significant status */
michael@0	1541	if (status!=0) decStatus(res, status, set);
michael@0	1542	#if DECCHECK
michael@0	1543	decCheckInexact(res, set);
michael@0	1544	#endif
michael@0	1545	return res;
michael@0	1546	} /* decNumberLog10 */
michael@0	1547	#if defined(__clang__) || U_GCC_MAJOR_MINOR >= 406
michael@0	1548	#pragma GCC diagnostic pop
michael@0	1549	#endif
michael@0	1550
michael@0	1551	/* ------------------------------------------------------------------ */
michael@0	1552	/* decNumberMax -- compare two Numbers and return the maximum */
michael@0	1553	/* */
michael@0	1554	/* This computes C = A ? B, returning the maximum by 754 rules */
michael@0	1555	/* */
michael@0	1556	/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
michael@0	1557	/* lhs is A */
michael@0	1558	/* rhs is B */
michael@0	1559	/* set is the context */
michael@0	1560	/* */
michael@0	1561	/* C must have space for set->digits digits. */
michael@0	1562	/* ------------------------------------------------------------------ */
michael@0	1563	U_CAPI decNumber * U_EXPORT2 uprv_decNumberMax(decNumber *res, const decNumber *lhs,
michael@0	1564	const decNumber *rhs, decContext *set) {
michael@0	1565	uInt status=0; /* accumulator */
michael@0	1566	decCompareOp(res, lhs, rhs, set, COMPMAX, &status);
michael@0	1567	if (status!=0) decStatus(res, status, set);
michael@0	1568	#if DECCHECK
michael@0	1569	decCheckInexact(res, set);
michael@0	1570	#endif
michael@0	1571	return res;
michael@0	1572	} /* decNumberMax */
michael@0	1573
michael@0	1574	/* ------------------------------------------------------------------ */
michael@0	1575	/* decNumberMaxMag -- compare and return the maximum by magnitude */
michael@0	1576	/* */
michael@0	1577	/* This computes C = A ? B, returning the maximum by 754 rules */
michael@0	1578	/* */
michael@0	1579	/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
michael@0	1580	/* lhs is A */
michael@0	1581	/* rhs is B */
michael@0	1582	/* set is the context */
michael@0	1583	/* */
michael@0	1584	/* C must have space for set->digits digits. */
michael@0	1585	/* ------------------------------------------------------------------ */
michael@0	1586	U_CAPI decNumber * U_EXPORT2 uprv_decNumberMaxMag(decNumber *res, const decNumber *lhs,
michael@0	1587	const decNumber *rhs, decContext *set) {
michael@0	1588	uInt status=0; /* accumulator */
michael@0	1589	decCompareOp(res, lhs, rhs, set, COMPMAXMAG, &status);
michael@0	1590	if (status!=0) decStatus(res, status, set);
michael@0	1591	#if DECCHECK
michael@0	1592	decCheckInexact(res, set);
michael@0	1593	#endif
michael@0	1594	return res;
michael@0	1595	} /* decNumberMaxMag */
michael@0	1596
michael@0	1597	/* ------------------------------------------------------------------ */
michael@0	1598	/* decNumberMin -- compare two Numbers and return the minimum */
michael@0	1599	/* */
michael@0	1600	/* This computes C = A ? B, returning the minimum by 754 rules */
michael@0	1601	/* */
michael@0	1602	/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
michael@0	1603	/* lhs is A */
michael@0	1604	/* rhs is B */
michael@0	1605	/* set is the context */
michael@0	1606	/* */
michael@0	1607	/* C must have space for set->digits digits. */
michael@0	1608	/* ------------------------------------------------------------------ */
michael@0	1609	U_CAPI decNumber * U_EXPORT2 uprv_decNumberMin(decNumber *res, const decNumber *lhs,
michael@0	1610	const decNumber *rhs, decContext *set) {
michael@0	1611	uInt status=0; /* accumulator */
michael@0	1612	decCompareOp(res, lhs, rhs, set, COMPMIN, &status);
michael@0	1613	if (status!=0) decStatus(res, status, set);
michael@0	1614	#if DECCHECK
michael@0	1615	decCheckInexact(res, set);
michael@0	1616	#endif
michael@0	1617	return res;
michael@0	1618	} /* decNumberMin */
michael@0	1619
michael@0	1620	/* ------------------------------------------------------------------ */
michael@0	1621	/* decNumberMinMag -- compare and return the minimum by magnitude */
michael@0	1622	/* */
michael@0	1623	/* This computes C = A ? B, returning the minimum by 754 rules */
michael@0	1624	/* */
michael@0	1625	/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
michael@0	1626	/* lhs is A */
michael@0	1627	/* rhs is B */
michael@0	1628	/* set is the context */
michael@0	1629	/* */
michael@0	1630	/* C must have space for set->digits digits. */
michael@0	1631	/* ------------------------------------------------------------------ */
michael@0	1632	U_CAPI decNumber * U_EXPORT2 uprv_decNumberMinMag(decNumber *res, const decNumber *lhs,
michael@0	1633	const decNumber *rhs, decContext *set) {
michael@0	1634	uInt status=0; /* accumulator */
michael@0	1635	decCompareOp(res, lhs, rhs, set, COMPMINMAG, &status);
michael@0	1636	if (status!=0) decStatus(res, status, set);
michael@0	1637	#if DECCHECK
michael@0	1638	decCheckInexact(res, set);
michael@0	1639	#endif
michael@0	1640	return res;
michael@0	1641	} /* decNumberMinMag */
michael@0	1642
michael@0	1643	/* ------------------------------------------------------------------ */
michael@0	1644	/* decNumberMinus -- prefix minus operator */
michael@0	1645	/* */
michael@0	1646	/* This computes C = 0 - A */
michael@0	1647	/* */
michael@0	1648	/* res is C, the result. C may be A */
michael@0	1649	/* rhs is A */
michael@0	1650	/* set is the context */
michael@0	1651	/* */
michael@0	1652	/* See also decNumberCopyNegate for a quiet bitwise version of this. */
michael@0	1653	/* C must have space for set->digits digits. */
michael@0	1654	/* ------------------------------------------------------------------ */
michael@0	1655	/* Simply use AddOp for the subtract, which will do the necessary. */
michael@0	1656	/* ------------------------------------------------------------------ */
michael@0	1657	U_CAPI decNumber * U_EXPORT2 uprv_decNumberMinus(decNumber *res, const decNumber *rhs,
michael@0	1658	decContext *set) {
michael@0	1659	decNumber dzero;
michael@0	1660	uInt status=0; /* accumulator */
michael@0	1661
michael@0	1662	#if DECCHECK
michael@0	1663	if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
michael@0	1664	#endif
michael@0	1665
michael@0	1666	uprv_decNumberZero(&dzero); /* make 0 */
michael@0	1667	dzero.exponent=rhs->exponent; /* [no coefficient expansion] */
michael@0	1668	decAddOp(res, &dzero, rhs, set, DECNEG, &status);
michael@0	1669	if (status!=0) decStatus(res, status, set);
michael@0	1670	#if DECCHECK
michael@0	1671	decCheckInexact(res, set);
michael@0	1672	#endif
michael@0	1673	return res;
michael@0	1674	} /* decNumberMinus */
michael@0	1675
michael@0	1676	/* ------------------------------------------------------------------ */
michael@0	1677	/* decNumberNextMinus -- next towards -Infinity */
michael@0	1678	/* */
michael@0	1679	/* This computes C = A - infinitesimal, rounded towards -Infinity */
michael@0	1680	/* */
michael@0	1681	/* res is C, the result. C may be A */
michael@0	1682	/* rhs is A */
michael@0	1683	/* set is the context */
michael@0	1684	/* */
michael@0	1685	/* This is a generalization of 754 NextDown. */
michael@0	1686	/* ------------------------------------------------------------------ */
michael@0	1687	U_CAPI decNumber * U_EXPORT2 uprv_decNumberNextMinus(decNumber *res, const decNumber *rhs,
michael@0	1688	decContext *set) {
michael@0	1689	decNumber dtiny; /* constant */
michael@0	1690	decContext workset=*set; /* work */
michael@0	1691	uInt status=0; /* accumulator */
michael@0	1692	#if DECCHECK
michael@0	1693	if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
michael@0	1694	#endif
michael@0	1695
michael@0	1696	/* +Infinity is the special case */
michael@0	1697	if ((rhs->bits&(DECINF|DECNEG))==DECINF) {
michael@0	1698	decSetMaxValue(res, set); /* is +ve */
michael@0	1699	/* there is no status to set */
michael@0	1700	return res;
michael@0	1701	}
michael@0	1702	uprv_decNumberZero(&dtiny); /* start with 0 */
michael@0	1703	dtiny.lsu[0]=1; /* make number that is .. */
michael@0	1704	dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */
michael@0	1705	workset.round=DEC_ROUND_FLOOR;
michael@0	1706	decAddOp(res, rhs, &dtiny, &workset, DECNEG, &status);
michael@0	1707	status&=DEC_Invalid_operation|DEC_sNaN; /* only sNaN Invalid please */
michael@0	1708	if (status!=0) decStatus(res, status, set);
michael@0	1709	return res;
michael@0	1710	} /* decNumberNextMinus */
michael@0	1711
michael@0	1712	/* ------------------------------------------------------------------ */
michael@0	1713	/* decNumberNextPlus -- next towards +Infinity */
michael@0	1714	/* */
michael@0	1715	/* This computes C = A + infinitesimal, rounded towards +Infinity */
michael@0	1716	/* */
michael@0	1717	/* res is C, the result. C may be A */
michael@0	1718	/* rhs is A */
michael@0	1719	/* set is the context */
michael@0	1720	/* */
michael@0	1721	/* This is a generalization of 754 NextUp. */
michael@0	1722	/* ------------------------------------------------------------------ */
michael@0	1723	U_CAPI decNumber * U_EXPORT2 uprv_decNumberNextPlus(decNumber *res, const decNumber *rhs,
michael@0	1724	decContext *set) {
michael@0	1725	decNumber dtiny; /* constant */
michael@0	1726	decContext workset=*set; /* work */
michael@0	1727	uInt status=0; /* accumulator */
michael@0	1728	#if DECCHECK
michael@0	1729	if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
michael@0	1730	#endif
michael@0	1731
michael@0	1732	/* -Infinity is the special case */
michael@0	1733	if ((rhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) {
michael@0	1734	decSetMaxValue(res, set);
michael@0	1735	res->bits=DECNEG; /* negative */
michael@0	1736	/* there is no status to set */
michael@0	1737	return res;
michael@0	1738	}
michael@0	1739	uprv_decNumberZero(&dtiny); /* start with 0 */
michael@0	1740	dtiny.lsu[0]=1; /* make number that is .. */
michael@0	1741	dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */
michael@0	1742	workset.round=DEC_ROUND_CEILING;
michael@0	1743	decAddOp(res, rhs, &dtiny, &workset, 0, &status);
michael@0	1744	status&=DEC_Invalid_operation|DEC_sNaN; /* only sNaN Invalid please */
michael@0	1745	if (status!=0) decStatus(res, status, set);
michael@0	1746	return res;
michael@0	1747	} /* decNumberNextPlus */
michael@0	1748
michael@0	1749	/* ------------------------------------------------------------------ */
michael@0	1750	/* decNumberNextToward -- next towards rhs */
michael@0	1751	/* */
michael@0	1752	/* This computes C = A +/- infinitesimal, rounded towards */
michael@0	1753	/* +/-Infinity in the direction of B, as per 754-1985 nextafter */
michael@0	1754	/* modified during revision but dropped from 754-2008. */
michael@0	1755	/* */
michael@0	1756	/* res is C, the result. C may be A or B. */
michael@0	1757	/* lhs is A */
michael@0	1758	/* rhs is B */
michael@0	1759	/* set is the context */
michael@0	1760	/* */
michael@0	1761	/* This is a generalization of 754-1985 NextAfter. */
michael@0	1762	/* ------------------------------------------------------------------ */
michael@0	1763	U_CAPI decNumber * U_EXPORT2 uprv_decNumberNextToward(decNumber *res, const decNumber *lhs,
michael@0	1764	const decNumber *rhs, decContext *set) {
michael@0	1765	decNumber dtiny; /* constant */
michael@0	1766	decContext workset=*set; /* work */
michael@0	1767	Int result; /* .. */
michael@0	1768	uInt status=0; /* accumulator */
michael@0	1769	#if DECCHECK
michael@0	1770	if (decCheckOperands(res, lhs, rhs, set)) return res;
michael@0	1771	#endif
michael@0	1772
michael@0	1773	if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) {
michael@0	1774	decNaNs(res, lhs, rhs, set, &status);
michael@0	1775	}
michael@0	1776	else { /* Is numeric, so no chance of sNaN Invalid, etc. */
michael@0	1777	result=decCompare(lhs, rhs, 0); /* sign matters */
michael@0	1778	if (result==BADINT) status|=DEC_Insufficient_storage; /* rare */
michael@0	1779	else { /* valid compare */
michael@0	1780	if (result==0) uprv_decNumberCopySign(res, lhs, rhs); /* easy */
michael@0	1781	else { /* differ: need NextPlus or NextMinus */
michael@0	1782	uByte sub; /* add or subtract */
michael@0	1783	if (result<0) { /* lhs<rhs, do nextplus */
michael@0	1784	/* -Infinity is the special case */
michael@0	1785	if ((lhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) {
michael@0	1786	decSetMaxValue(res, set);
michael@0	1787	res->bits=DECNEG; /* negative */
michael@0	1788	return res; /* there is no status to set */
michael@0	1789	}
michael@0	1790	workset.round=DEC_ROUND_CEILING;
michael@0	1791	sub=0; /* add, please */
michael@0	1792	} /* plus */
michael@0	1793	else { /* lhs>rhs, do nextminus */
michael@0	1794	/* +Infinity is the special case */
michael@0	1795	if ((lhs->bits&(DECINF|DECNEG))==DECINF) {
michael@0	1796	decSetMaxValue(res, set);
michael@0	1797	return res; /* there is no status to set */
michael@0	1798	}
michael@0	1799	workset.round=DEC_ROUND_FLOOR;
michael@0	1800	sub=DECNEG; /* subtract, please */
michael@0	1801	} /* minus */
michael@0	1802	uprv_decNumberZero(&dtiny); /* start with 0 */
michael@0	1803	dtiny.lsu[0]=1; /* make number that is .. */
michael@0	1804	dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */
michael@0	1805	decAddOp(res, lhs, &dtiny, &workset, sub, &status); /* + or - */
michael@0	1806	/* turn off exceptions if the result is a normal number */
michael@0	1807	/* (including Nmin), otherwise let all status through */
michael@0	1808	if (uprv_decNumberIsNormal(res, set)) status=0;
michael@0	1809	} /* unequal */
michael@0	1810	} /* compare OK */
michael@0	1811	} /* numeric */
michael@0	1812	if (status!=0) decStatus(res, status, set);
michael@0	1813	return res;
michael@0	1814	} /* decNumberNextToward */
michael@0	1815
michael@0	1816	/* ------------------------------------------------------------------ */
michael@0	1817	/* decNumberOr -- OR two Numbers, digitwise */
michael@0	1818	/* */
michael@0	1819	/* This computes C = A | B */
michael@0	1820	/* */
michael@0	1821	/* res is C, the result. C may be A and/or B (e.g., X=X|X) */
michael@0	1822	/* lhs is A */
michael@0	1823	/* rhs is B */
michael@0	1824	/* set is the context (used for result length and error report) */
michael@0	1825	/* */
michael@0	1826	/* C must have space for set->digits digits. */
michael@0	1827	/* */
michael@0	1828	/* Logical function restrictions apply (see above); a NaN is */
michael@0	1829	/* returned with Invalid_operation if a restriction is violated. */
michael@0	1830	/* ------------------------------------------------------------------ */
michael@0	1831	U_CAPI decNumber * U_EXPORT2 uprv_decNumberOr(decNumber *res, const decNumber *lhs,
michael@0	1832	const decNumber *rhs, decContext *set) {
michael@0	1833	const Unit *ua, *ub; /* -> operands */
michael@0	1834	const Unit *msua, *msub; /* -> operand msus */
michael@0	1835	Unit *uc, *msuc; /* -> result and its msu */
michael@0	1836	Int msudigs; /* digits in res msu */
michael@0	1837	#if DECCHECK
michael@0	1838	if (decCheckOperands(res, lhs, rhs, set)) return res;
michael@0	1839	#endif
michael@0	1840
michael@0	1841	if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
michael@0	1842	|| rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
michael@0	1843	decStatus(res, DEC_Invalid_operation, set);
michael@0	1844	return res;
michael@0	1845	}
michael@0	1846	/* operands are valid */
michael@0	1847	ua=lhs->lsu; /* bottom-up */
michael@0	1848	ub=rhs->lsu; /* .. */
michael@0	1849	uc=res->lsu; /* .. */
michael@0	1850	msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */
michael@0	1851	msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */
michael@0	1852	msuc=uc+D2U(set->digits)-1; /* -> msu of result */
michael@0	1853	msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */
michael@0	1854	for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */
michael@0	1855	Unit a, b; /* extract units */
michael@0	1856	if (ua>msua) a=0;
michael@0	1857	else a=*ua;
michael@0	1858	if (ub>msub) b=0;
michael@0	1859	else b=*ub;
michael@0	1860	*uc=0; /* can now write back */
michael@0	1861	if (a|b) { /* maybe 1 bits to examine */
michael@0	1862	Int i, j;
michael@0	1863	/* This loop could be unrolled and/or use BIN2BCD tables */
michael@0	1864	for (i=0; i<DECDPUN; i++) {
michael@0	1865	if ((a|b)&1) *uc=*uc+(Unit)powers[i]; /* effect OR */
michael@0	1866	j=a%10;
michael@0	1867	a=a/10;
michael@0	1868	j|=b%10;
michael@0	1869	b=b/10;
michael@0	1870	if (j>1) {
michael@0	1871	decStatus(res, DEC_Invalid_operation, set);
michael@0	1872	return res;
michael@0	1873	}
michael@0	1874	if (uc==msuc && i==msudigs-1) break; /* just did final digit */
michael@0	1875	} /* each digit */
michael@0	1876	} /* non-zero */
michael@0	1877	} /* each unit */
michael@0	1878	/* [here uc-1 is the msu of the result] */
michael@0	1879	res->digits=decGetDigits(res->lsu, uc-res->lsu);
michael@0	1880	res->exponent=0; /* integer */
michael@0	1881	res->bits=0; /* sign=0 */
michael@0	1882	return res; /* [no status to set] */
michael@0	1883	} /* decNumberOr */
michael@0	1884
michael@0	1885	/* ------------------------------------------------------------------ */
michael@0	1886	/* decNumberPlus -- prefix plus operator */
michael@0	1887	/* */
michael@0	1888	/* This computes C = 0 + A */
michael@0	1889	/* */
michael@0	1890	/* res is C, the result. C may be A */
michael@0	1891	/* rhs is A */
michael@0	1892	/* set is the context */
michael@0	1893	/* */
michael@0	1894	/* See also decNumberCopy for a quiet bitwise version of this. */
michael@0	1895	/* C must have space for set->digits digits. */
michael@0	1896	/* ------------------------------------------------------------------ */
michael@0	1897	/* This simply uses AddOp; Add will take fast path after preparing A. */
michael@0	1898	/* Performance is a concern here, as this routine is often used to */
michael@0	1899	/* check operands and apply rounding and overflow/underflow testing. */
michael@0	1900	/* ------------------------------------------------------------------ */
michael@0	1901	U_CAPI decNumber * U_EXPORT2 uprv_decNumberPlus(decNumber *res, const decNumber *rhs,
michael@0	1902	decContext *set) {
michael@0	1903	decNumber dzero;
michael@0	1904	uInt status=0; /* accumulator */
michael@0	1905	#if DECCHECK
michael@0	1906	if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
michael@0	1907	#endif
michael@0	1908
michael@0	1909	uprv_decNumberZero(&dzero); /* make 0 */
michael@0	1910	dzero.exponent=rhs->exponent; /* [no coefficient expansion] */
michael@0	1911	decAddOp(res, &dzero, rhs, set, 0, &status);
michael@0	1912	if (status!=0) decStatus(res, status, set);
michael@0	1913	#if DECCHECK
michael@0	1914	decCheckInexact(res, set);
michael@0	1915	#endif
michael@0	1916	return res;
michael@0	1917	} /* decNumberPlus */
michael@0	1918
michael@0	1919	/* ------------------------------------------------------------------ */
michael@0	1920	/* decNumberMultiply -- multiply two Numbers */
michael@0	1921	/* */
michael@0	1922	/* This computes C = A x B */
michael@0	1923	/* */
michael@0	1924	/* res is C, the result. C may be A and/or B (e.g., X=X+X) */
michael@0	1925	/* lhs is A */
michael@0	1926	/* rhs is B */
michael@0	1927	/* set is the context */
michael@0	1928	/* */
michael@0	1929	/* C must have space for set->digits digits. */
michael@0	1930	/* ------------------------------------------------------------------ */
michael@0	1931	U_CAPI decNumber * U_EXPORT2 uprv_decNumberMultiply(decNumber *res, const decNumber *lhs,
michael@0	1932	const decNumber *rhs, decContext *set) {
michael@0	1933	uInt status=0; /* accumulator */
michael@0	1934	decMultiplyOp(res, lhs, rhs, set, &status);
michael@0	1935	if (status!=0) decStatus(res, status, set);
michael@0	1936	#if DECCHECK
michael@0	1937	decCheckInexact(res, set);
michael@0	1938	#endif
michael@0	1939	return res;
michael@0	1940	} /* decNumberMultiply */
michael@0	1941
michael@0	1942	/* ------------------------------------------------------------------ */
michael@0	1943	/* decNumberPower -- raise a number to a power */
michael@0	1944	/* */
michael@0	1945	/* This computes C = A ** B */
michael@0	1946	/* */
michael@0	1947	/* res is C, the result. C may be A and/or B (e.g., X=X**X) */
michael@0	1948	/* lhs is A */
michael@0	1949	/* rhs is B */
michael@0	1950	/* set is the context */
michael@0	1951	/* */
michael@0	1952	/* C must have space for set->digits digits. */
michael@0	1953	/* */
michael@0	1954	/* Mathematical function restrictions apply (see above); a NaN is */
michael@0	1955	/* returned with Invalid_operation if a restriction is violated. */
michael@0	1956	/* */
michael@0	1957	/* However, if 1999999997<=B<=999999999 and B is an integer then the */
michael@0	1958	/* restrictions on A and the context are relaxed to the usual bounds, */
michael@0	1959	/* for compatibility with the earlier (integer power only) version */
michael@0	1960	/* of this function. */
michael@0	1961	/* */
michael@0	1962	/* When B is an integer, the result may be exact, even if rounded. */
michael@0	1963	/* */
michael@0	1964	/* The final result is rounded according to the context; it will */
michael@0	1965	/* almost always be correctly rounded, but may be up to 1 ulp in */
michael@0	1966	/* error in rare cases. */
michael@0	1967	/* ------------------------------------------------------------------ */
michael@0	1968	U_CAPI decNumber * U_EXPORT2 uprv_decNumberPower(decNumber *res, const decNumber *lhs,
michael@0	1969	const decNumber *rhs, decContext *set) {
michael@0	1970	#if DECSUBSET
michael@0	1971	decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */
michael@0	1972	decNumber *allocrhs=NULL; /* .., rhs */
michael@0	1973	#endif
michael@0	1974	decNumber *allocdac=NULL; /* -> allocated acc buffer, iff used */
michael@0	1975	decNumber *allocinv=NULL; /* -> allocated 1/x buffer, iff used */
michael@0	1976	Int reqdigits=set->digits; /* requested DIGITS */
michael@0	1977	Int n; /* rhs in binary */
michael@0	1978	Flag rhsint=0; /* 1 if rhs is an integer */
michael@0	1979	Flag useint=0; /* 1 if can use integer calculation */
michael@0	1980	Flag isoddint=0; /* 1 if rhs is an integer and odd */
michael@0	1981	Int i; /* work */
michael@0	1982	#if DECSUBSET
michael@0	1983	Int dropped; /* .. */
michael@0	1984	#endif
michael@0	1985	uInt needbytes; /* buffer size needed */
michael@0	1986	Flag seenbit; /* seen a bit while powering */
michael@0	1987	Int residue=0; /* rounding residue */
michael@0	1988	uInt status=0; /* accumulators */
michael@0	1989	uByte bits=0; /* result sign if errors */
michael@0	1990	decContext aset; /* working context */
michael@0	1991	decNumber dnOne; /* work value 1... */
michael@0	1992	/* local accumulator buffer [a decNumber, with digits+elength+1 digits] */
michael@0	1993	decNumber dacbuff[D2N(DECBUFFER+9)];
michael@0	1994	decNumber *dac=dacbuff; /* -> result accumulator */
michael@0	1995	/* same again for possible 1/lhs calculation */
michael@0	1996	decNumber invbuff[D2N(DECBUFFER+9)];
michael@0	1997
michael@0	1998	#if DECCHECK
michael@0	1999	if (decCheckOperands(res, lhs, rhs, set)) return res;
michael@0	2000	#endif
michael@0	2001
michael@0	2002	do { /* protect allocated storage */
michael@0	2003	#if DECSUBSET
michael@0	2004	if (!set->extended) { /* reduce operands and set status, as needed */
michael@0	2005	if (lhs->digits>reqdigits) {
michael@0	2006	alloclhs=decRoundOperand(lhs, set, &status);
michael@0	2007	if (alloclhs==NULL) break;
michael@0	2008	lhs=alloclhs;
michael@0	2009	}
michael@0	2010	if (rhs->digits>reqdigits) {
michael@0	2011	allocrhs=decRoundOperand(rhs, set, &status);
michael@0	2012	if (allocrhs==NULL) break;
michael@0	2013	rhs=allocrhs;
michael@0	2014	}
michael@0	2015	}
michael@0	2016	#endif
michael@0	2017	/* [following code does not require input rounding] */
michael@0	2018
michael@0	2019	/* handle NaNs and rhs Infinity (lhs infinity is harder) */
michael@0	2020	if (SPECIALARGS) {
michael@0	2021	if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { /* NaNs */
michael@0	2022	decNaNs(res, lhs, rhs, set, &status);
michael@0	2023	break;}
michael@0	2024	if (decNumberIsInfinite(rhs)) { /* rhs Infinity */
michael@0	2025	Flag rhsneg=rhs->bits&DECNEG; /* save rhs sign */
michael@0	2026	if (decNumberIsNegative(lhs) /* lhs<0 */
michael@0	2027	&& !decNumberIsZero(lhs)) /* .. */
michael@0	2028	status|=DEC_Invalid_operation;
michael@0	2029	else { /* lhs >=0 */
michael@0	2030	uprv_decNumberZero(&dnOne); /* set up 1 */
michael@0	2031	dnOne.lsu[0]=1;
michael@0	2032	uprv_decNumberCompare(dac, lhs, &dnOne, set); /* lhs ? 1 */
michael@0	2033	uprv_decNumberZero(res); /* prepare for 0/1/Infinity */
michael@0	2034	if (decNumberIsNegative(dac)) { /* lhs<1 */
michael@0	2035	if (rhsneg) res->bits|=DECINF; /* +Infinity [else is +0] */
michael@0	2036	}
michael@0	2037	else if (dac->lsu[0]==0) { /* lhs=1 */
michael@0	2038	/* 1**Infinity is inexact, so return fully-padded 1.0000 */
michael@0	2039	Int shift=set->digits-1;
michael@0	2040	*res->lsu=1; /* was 0, make int 1 */
michael@0	2041	res->digits=decShiftToMost(res->lsu, 1, shift);
michael@0	2042	res->exponent=-shift; /* make 1.0000... */
michael@0	2043	status|=DEC_Inexact|DEC_Rounded; /* deemed inexact */
michael@0	2044	}
michael@0	2045	else { /* lhs>1 */
michael@0	2046	if (!rhsneg) res->bits|=DECINF; /* +Infinity [else is +0] */
michael@0	2047	}
michael@0	2048	} /* lhs>=0 */
michael@0	2049	break;}
michael@0	2050	/* [lhs infinity drops through] */
michael@0	2051	} /* specials */
michael@0	2052
michael@0	2053	/* Original rhs may be an integer that fits and is in range */
michael@0	2054	n=decGetInt(rhs);
michael@0	2055	if (n!=BADINT) { /* it is an integer */
michael@0	2056	rhsint=1; /* record the fact for 1**n */
michael@0	2057	isoddint=(Flag)n&1; /* [works even if big] */
michael@0	2058	if (n!=BIGEVEN && n!=BIGODD) /* can use integer path? */
michael@0	2059	useint=1; /* looks good */
michael@0	2060	}
michael@0	2061
michael@0	2062	if (decNumberIsNegative(lhs) /* -x .. */
michael@0	2063	&& isoddint) bits=DECNEG; /* .. to an odd power */
michael@0	2064
michael@0	2065	/* handle LHS infinity */
michael@0	2066	if (decNumberIsInfinite(lhs)) { /* [NaNs already handled] */
michael@0	2067	uByte rbits=rhs->bits; /* save */
michael@0	2068	uprv_decNumberZero(res); /* prepare */
michael@0	2069	if (n==0) *res->lsu=1; /* [-]Inf**0 => 1 */
michael@0	2070	else {
michael@0	2071	/* -Inf**nonint -> error */
michael@0	2072	if (!rhsint && decNumberIsNegative(lhs)) {
michael@0	2073	status|=DEC_Invalid_operation; /* -Inf**nonint is error */
michael@0	2074	break;}
michael@0	2075	if (!(rbits & DECNEG)) bits|=DECINF; /* was not a **-n */
michael@0	2076	/* [otherwise will be 0 or -0] */
michael@0	2077	res->bits=bits;
michael@0	2078	}
michael@0	2079	break;}
michael@0	2080
michael@0	2081	/* similarly handle LHS zero */
michael@0	2082	if (decNumberIsZero(lhs)) {
michael@0	2083	if (n==0) { /* 0**0 => Error */
michael@0	2084	#if DECSUBSET
michael@0	2085	if (!set->extended) { /* [unless subset] */
michael@0	2086	uprv_decNumberZero(res);
michael@0	2087	*res->lsu=1; /* return 1 */
michael@0	2088	break;}
michael@0	2089	#endif
michael@0	2090	status|=DEC_Invalid_operation;
michael@0	2091	}
michael@0	2092	else { /* 0**x */
michael@0	2093	uByte rbits=rhs->bits; /* save */
michael@0	2094	if (rbits & DECNEG) { /* was a 0**(-n) */
michael@0	2095	#if DECSUBSET
michael@0	2096	if (!set->extended) { /* [bad if subset] */
michael@0	2097	status|=DEC_Invalid_operation;
michael@0	2098	break;}
michael@0	2099	#endif
michael@0	2100	bits|=DECINF;
michael@0	2101	}
michael@0	2102	uprv_decNumberZero(res); /* prepare */
michael@0	2103	/* [otherwise will be 0 or -0] */
michael@0	2104	res->bits=bits;
michael@0	2105	}
michael@0	2106	break;}
michael@0	2107
michael@0	2108	/* here both lhs and rhs are finite; rhs==0 is handled in the */
michael@0	2109	/* integer path. Next handle the non-integer cases */
michael@0	2110	if (!useint) { /* non-integral rhs */
michael@0	2111	/* any -ve lhs is bad, as is either operand or context out of */
michael@0	2112	/* bounds */
michael@0	2113	if (decNumberIsNegative(lhs)) {
michael@0	2114	status|=DEC_Invalid_operation;
michael@0	2115	break;}
michael@0	2116	if (decCheckMath(lhs, set, &status)
michael@0	2117	|| decCheckMath(rhs, set, &status)) break; /* variable status */
michael@0	2118
michael@0	2119	uprv_decContextDefault(&aset, DEC_INIT_DECIMAL64); /* clean context */
michael@0	2120	aset.emax=DEC_MAX_MATH; /* usual bounds */
michael@0	2121	aset.emin=-DEC_MAX_MATH; /* .. */
michael@0	2122	aset.clamp=0; /* and no concrete format */
michael@0	2123
michael@0	2124	/* calculate the result using exp(ln(lhs)*rhs), which can */
michael@0	2125	/* all be done into the accumulator, dac. The precision needed */
michael@0	2126	/* is enough to contain the full information in the lhs (which */
michael@0	2127	/* is the total digits, including exponent), or the requested */
michael@0	2128	/* precision, if larger, + 4; 6 is used for the exponent */
michael@0	2129	/* maximum length, and this is also used when it is shorter */
michael@0	2130	/* than the requested digits as it greatly reduces the >0.5 ulp */
michael@0	2131	/* cases at little cost (because Ln doubles digits each */
michael@0	2132	/* iteration so a few extra digits rarely causes an extra */
michael@0	2133	/* iteration) */
michael@0	2134	aset.digits=MAXI(lhs->digits, set->digits)+6+4;
michael@0	2135	} /* non-integer rhs */
michael@0	2136
michael@0	2137	else { /* rhs is in-range integer */
michael@0	2138	if (n==0) { /* x**0 = 1 */
michael@0	2139	/* (0**0 was handled above) */
michael@0	2140	uprv_decNumberZero(res); /* result=1 */
michael@0	2141	*res->lsu=1; /* .. */
michael@0	2142	break;}
michael@0	2143	/* rhs is a non-zero integer */
michael@0	2144	if (n<0) n=-n; /* use abs(n) */
michael@0	2145
michael@0	2146	aset=*set; /* clone the context */
michael@0	2147	aset.round=DEC_ROUND_HALF_EVEN; /* internally use balanced */
michael@0	2148	/* calculate the working DIGITS */
michael@0	2149	aset.digits=reqdigits+(rhs->digits+rhs->exponent)+2;
michael@0	2150	#if DECSUBSET
michael@0	2151	if (!set->extended) aset.digits--; /* use classic precision */
michael@0	2152	#endif
michael@0	2153	/* it's an error if this is more than can be handled */
michael@0	2154	if (aset.digits>DECNUMMAXP) {status|=DEC_Invalid_operation; break;}
michael@0	2155	} /* integer path */
michael@0	2156
michael@0	2157	/* aset.digits is the count of digits for the accumulator needed */
michael@0	2158	/* if accumulator is too long for local storage, then allocate */
michael@0	2159	needbytes=sizeof(decNumber)+(D2U(aset.digits)-1)*sizeof(Unit);
michael@0	2160	/* [needbytes also used below if 1/lhs needed] */
michael@0	2161	if (needbytes>sizeof(dacbuff)) {
michael@0	2162	allocdac=(decNumber *)malloc(needbytes);
michael@0	2163	if (allocdac==NULL) { /* hopeless -- abandon */
michael@0	2164	status|=DEC_Insufficient_storage;
michael@0	2165	break;}
michael@0	2166	dac=allocdac; /* use the allocated space */
michael@0	2167	}
michael@0	2168	/* here, aset is set up and accumulator is ready for use */
michael@0	2169
michael@0	2170	if (!useint) { /* non-integral rhs */
michael@0	2171	/* x ** y; special-case x=1 here as it will otherwise always */
michael@0	2172	/* reduce to integer 1; decLnOp has a fastpath which detects */
michael@0	2173	/* the case of x=1 */
michael@0	2174	decLnOp(dac, lhs, &aset, &status); /* dac=ln(lhs) */
michael@0	2175	/* [no error possible, as lhs 0 already handled] */
michael@0	2176	if (ISZERO(dac)) { /* x==1, 1.0, etc. */
michael@0	2177	/* need to return fully-padded 1.0000 etc., but rhsint->1 */
michael@0	2178	*dac->lsu=1; /* was 0, make int 1 */
michael@0	2179	if (!rhsint) { /* add padding */
michael@0	2180	Int shift=set->digits-1;
michael@0	2181	dac->digits=decShiftToMost(dac->lsu, 1, shift);
michael@0	2182	dac->exponent=-shift; /* make 1.0000... */
michael@0	2183	status|=DEC_Inexact|DEC_Rounded; /* deemed inexact */
michael@0	2184	}
michael@0	2185	}
michael@0	2186	else {
michael@0	2187	decMultiplyOp(dac, dac, rhs, &aset, &status); /* dac=dac*rhs */
michael@0	2188	decExpOp(dac, dac, &aset, &status); /* dac=exp(dac) */
michael@0	2189	}
michael@0	2190	/* and drop through for final rounding */
michael@0	2191	} /* non-integer rhs */
michael@0	2192
michael@0	2193	else { /* carry on with integer */
michael@0	2194	uprv_decNumberZero(dac); /* acc=1 */
michael@0	2195	*dac->lsu=1; /* .. */
michael@0	2196
michael@0	2197	/* if a negative power the constant 1 is needed, and if not subset */
michael@0	2198	/* invert the lhs now rather than inverting the result later */
michael@0	2199	if (decNumberIsNegative(rhs)) { /* was a **-n [hence digits>0] */
michael@0	2200	decNumber *inv=invbuff; /* asssume use fixed buffer */
michael@0	2201	uprv_decNumberCopy(&dnOne, dac); /* dnOne=1; [needed now or later] */
michael@0	2202	#if DECSUBSET
michael@0	2203	if (set->extended) { /* need to calculate 1/lhs */
michael@0	2204	#endif
michael@0	2205	/* divide lhs into 1, putting result in dac [dac=1/dac] */
michael@0	2206	decDivideOp(dac, &dnOne, lhs, &aset, DIVIDE, &status);
michael@0	2207	/* now locate or allocate space for the inverted lhs */
michael@0	2208	if (needbytes>sizeof(invbuff)) {
michael@0	2209	allocinv=(decNumber *)malloc(needbytes);
michael@0	2210	if (allocinv==NULL) { /* hopeless -- abandon */
michael@0	2211	status|=DEC_Insufficient_storage;
michael@0	2212	break;}
michael@0	2213	inv=allocinv; /* use the allocated space */
michael@0	2214	}
michael@0	2215	/* [inv now points to big-enough buffer or allocated storage] */
michael@0	2216	uprv_decNumberCopy(inv, dac); /* copy the 1/lhs */
michael@0	2217	uprv_decNumberCopy(dac, &dnOne); /* restore acc=1 */
michael@0	2218	lhs=inv; /* .. and go forward with new lhs */
michael@0	2219	#if DECSUBSET
michael@0	2220	}
michael@0	2221	#endif
michael@0	2222	}
michael@0	2223
michael@0	2224	/* Raise-to-the-power loop... */
michael@0	2225	seenbit=0; /* set once a 1-bit is encountered */
michael@0	2226	for (i=1;;i++){ /* for each bit [top bit ignored] */
michael@0	2227	/* abandon if had overflow or terminal underflow */
michael@0	2228	if (status & (DEC_Overflow|DEC_Underflow)) { /* interesting? */
michael@0	2229	if (status&DEC_Overflow || ISZERO(dac)) break;
michael@0	2230	}
michael@0	2231	/* [the following two lines revealed an optimizer bug in a C++ */
michael@0	2232	/* compiler, with symptom: 5**3 -> 25, when n=n+n was used] */
michael@0	2233	n=n<<1; /* move next bit to testable position */
michael@0	2234	if (n<0) { /* top bit is set */
michael@0	2235	seenbit=1; /* OK, significant bit seen */
michael@0	2236	decMultiplyOp(dac, dac, lhs, &aset, &status); /* dac=dac*x */
michael@0	2237	}
michael@0	2238	if (i==31) break; /* that was the last bit */
michael@0	2239	if (!seenbit) continue; /* no need to square 1 */
michael@0	2240	decMultiplyOp(dac, dac, dac, &aset, &status); /* dac=dac*dac [square] */
michael@0	2241	} /*i*/ /* 32 bits */
michael@0	2242
michael@0	2243	/* complete internal overflow or underflow processing */
michael@0	2244	if (status & (DEC_Overflow|DEC_Underflow)) {
michael@0	2245	#if DECSUBSET
michael@0	2246	/* If subset, and power was negative, reverse the kind of -erflow */
michael@0	2247	/* [1/x not yet done] */
michael@0	2248	if (!set->extended && decNumberIsNegative(rhs)) {
michael@0	2249	if (status & DEC_Overflow)
michael@0	2250	status^=DEC_Overflow | DEC_Underflow | DEC_Subnormal;
michael@0	2251	else { /* trickier -- Underflow may or may not be set */
michael@0	2252	status&=~(DEC_Underflow | DEC_Subnormal); /* [one or both] */
michael@0	2253	status|=DEC_Overflow;
michael@0	2254	}
michael@0	2255	}
michael@0	2256	#endif
michael@0	2257	dac->bits=(dac->bits & ~DECNEG) | bits; /* force correct sign */
michael@0	2258	/* round subnormals [to set.digits rather than aset.digits] */
michael@0	2259	/* or set overflow result similarly as required */
michael@0	2260	decFinalize(dac, set, &residue, &status);
michael@0	2261	uprv_decNumberCopy(res, dac); /* copy to result (is now OK length) */
michael@0	2262	break;
michael@0	2263	}
michael@0	2264
michael@0	2265	#if DECSUBSET
michael@0	2266	if (!set->extended && /* subset math */
michael@0	2267	decNumberIsNegative(rhs)) { /* was a **-n [hence digits>0] */
michael@0	2268	/* so divide result into 1 [dac=1/dac] */
michael@0	2269	decDivideOp(dac, &dnOne, dac, &aset, DIVIDE, &status);
michael@0	2270	}
michael@0	2271	#endif
michael@0	2272	} /* rhs integer path */
michael@0	2273
michael@0	2274	/* reduce result to the requested length and copy to result */
michael@0	2275	decCopyFit(res, dac, set, &residue, &status);
michael@0	2276	decFinish(res, set, &residue, &status); /* final cleanup */
michael@0	2277	#if DECSUBSET
michael@0	2278	if (!set->extended) decTrim(res, set, 0, 1, &dropped); /* trailing zeros */
michael@0	2279	#endif
michael@0	2280	} while(0); /* end protected */
michael@0	2281
michael@0	2282	if (allocdac!=NULL) free(allocdac); /* drop any storage used */
michael@0	2283	if (allocinv!=NULL) free(allocinv); /* .. */
michael@0	2284	#if DECSUBSET
michael@0	2285	if (alloclhs!=NULL) free(alloclhs); /* .. */
michael@0	2286	if (allocrhs!=NULL) free(allocrhs); /* .. */
michael@0	2287	#endif
michael@0	2288	if (status!=0) decStatus(res, status, set);
michael@0	2289	#if DECCHECK
michael@0	2290	decCheckInexact(res, set);
michael@0	2291	#endif
michael@0	2292	return res;
michael@0	2293	} /* decNumberPower */
michael@0	2294
michael@0	2295	/* ------------------------------------------------------------------ */
michael@0	2296	/* decNumberQuantize -- force exponent to requested value */
michael@0	2297	/* */
michael@0	2298	/* This computes C = op(A, B), where op adjusts the coefficient */
michael@0	2299	/* of C (by rounding or shifting) such that the exponent (-scale) */
michael@0	2300	/* of C has exponent of B. The numerical value of C will equal A, */
michael@0	2301	/* except for the effects of any rounding that occurred. */
michael@0	2302	/* */
michael@0	2303	/* res is C, the result. C may be A or B */
michael@0	2304	/* lhs is A, the number to adjust */
michael@0	2305	/* rhs is B, the number with exponent to match */
michael@0	2306	/* set is the context */
michael@0	2307	/* */
michael@0	2308	/* C must have space for set->digits digits. */
michael@0	2309	/* */
michael@0	2310	/* Unless there is an error or the result is infinite, the exponent */
michael@0	2311	/* after the operation is guaranteed to be equal to that of B. */
michael@0	2312	/* ------------------------------------------------------------------ */
michael@0	2313	U_CAPI decNumber * U_EXPORT2 uprv_decNumberQuantize(decNumber *res, const decNumber *lhs,
michael@0	2314	const decNumber *rhs, decContext *set) {
michael@0	2315	uInt status=0; /* accumulator */
michael@0	2316	decQuantizeOp(res, lhs, rhs, set, 1, &status);
michael@0	2317	if (status!=0) decStatus(res, status, set);
michael@0	2318	return res;
michael@0	2319	} /* decNumberQuantize */
michael@0	2320
michael@0	2321	/* ------------------------------------------------------------------ */
michael@0	2322	/* decNumberReduce -- remove trailing zeros */
michael@0	2323	/* */
michael@0	2324	/* This computes C = 0 + A, and normalizes the result */
michael@0	2325	/* */
michael@0	2326	/* res is C, the result. C may be A */
michael@0	2327	/* rhs is A */
michael@0	2328	/* set is the context */
michael@0	2329	/* */
michael@0	2330	/* C must have space for set->digits digits. */
michael@0	2331	/* ------------------------------------------------------------------ */
michael@0	2332	/* Previously known as Normalize */
michael@0	2333	U_CAPI decNumber * U_EXPORT2 uprv_decNumberNormalize(decNumber *res, const decNumber *rhs,
michael@0	2334	decContext *set) {
michael@0	2335	return uprv_decNumberReduce(res, rhs, set);
michael@0	2336	} /* decNumberNormalize */
michael@0	2337
michael@0	2338	U_CAPI decNumber * U_EXPORT2 uprv_decNumberReduce(decNumber *res, const decNumber *rhs,
michael@0	2339	decContext *set) {
michael@0	2340	#if DECSUBSET
michael@0	2341	decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */
michael@0	2342	#endif
michael@0	2343	uInt status=0; /* as usual */
michael@0	2344	Int residue=0; /* as usual */
michael@0	2345	Int dropped; /* work */
michael@0	2346
michael@0	2347	#if DECCHECK
michael@0	2348	if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
michael@0	2349	#endif
michael@0	2350
michael@0	2351	do { /* protect allocated storage */
michael@0	2352	#if DECSUBSET
michael@0	2353	if (!set->extended) {
michael@0	2354	/* reduce operand and set lostDigits status, as needed */
michael@0	2355	if (rhs->digits>set->digits) {
michael@0	2356	allocrhs=decRoundOperand(rhs, set, &status);
michael@0	2357	if (allocrhs==NULL) break;
michael@0	2358	rhs=allocrhs;
michael@0	2359	}
michael@0	2360	}
michael@0	2361	#endif
michael@0	2362	/* [following code does not require input rounding] */
michael@0	2363
michael@0	2364	/* Infinities copy through; NaNs need usual treatment */
michael@0	2365	if (decNumberIsNaN(rhs)) {
michael@0	2366	decNaNs(res, rhs, NULL, set, &status);
michael@0	2367	break;
michael@0	2368	}
michael@0	2369
michael@0	2370	/* reduce result to the requested length and copy to result */
michael@0	2371	decCopyFit(res, rhs, set, &residue, &status); /* copy & round */
michael@0	2372	decFinish(res, set, &residue, &status); /* cleanup/set flags */
michael@0	2373	decTrim(res, set, 1, 0, &dropped); /* normalize in place */
michael@0	2374	/* [may clamp] */
michael@0	2375	} while(0); /* end protected */
michael@0	2376
michael@0	2377	#if DECSUBSET
michael@0	2378	if (allocrhs !=NULL) free(allocrhs); /* .. */
michael@0	2379	#endif
michael@0	2380	if (status!=0) decStatus(res, status, set);/* then report status */
michael@0	2381	return res;
michael@0	2382	} /* decNumberReduce */
michael@0	2383
michael@0	2384	/* ------------------------------------------------------------------ */
michael@0	2385	/* decNumberRescale -- force exponent to requested value */
michael@0	2386	/* */
michael@0	2387	/* This computes C = op(A, B), where op adjusts the coefficient */
michael@0	2388	/* of C (by rounding or shifting) such that the exponent (-scale) */
michael@0	2389	/* of C has the value B. The numerical value of C will equal A, */
michael@0	2390	/* except for the effects of any rounding that occurred. */
michael@0	2391	/* */
michael@0	2392	/* res is C, the result. C may be A or B */
michael@0	2393	/* lhs is A, the number to adjust */
michael@0	2394	/* rhs is B, the requested exponent */
michael@0	2395	/* set is the context */
michael@0	2396	/* */
michael@0	2397	/* C must have space for set->digits digits. */
michael@0	2398	/* */
michael@0	2399	/* Unless there is an error or the result is infinite, the exponent */
michael@0	2400	/* after the operation is guaranteed to be equal to B. */
michael@0	2401	/* ------------------------------------------------------------------ */
michael@0	2402	U_CAPI decNumber * U_EXPORT2 uprv_decNumberRescale(decNumber *res, const decNumber *lhs,
michael@0	2403	const decNumber *rhs, decContext *set) {
michael@0	2404	uInt status=0; /* accumulator */
michael@0	2405	decQuantizeOp(res, lhs, rhs, set, 0, &status);
michael@0	2406	if (status!=0) decStatus(res, status, set);
michael@0	2407	return res;
michael@0	2408	} /* decNumberRescale */
michael@0	2409
michael@0	2410	/* ------------------------------------------------------------------ */
michael@0	2411	/* decNumberRemainder -- divide and return remainder */
michael@0	2412	/* */
michael@0	2413	/* This computes C = A % B */
michael@0	2414	/* */
michael@0	2415	/* res is C, the result. C may be A and/or B (e.g., X=X%X) */
michael@0	2416	/* lhs is A */
michael@0	2417	/* rhs is B */
michael@0	2418	/* set is the context */
michael@0	2419	/* */
michael@0	2420	/* C must have space for set->digits digits. */
michael@0	2421	/* ------------------------------------------------------------------ */
michael@0	2422	U_CAPI decNumber * U_EXPORT2 uprv_decNumberRemainder(decNumber *res, const decNumber *lhs,
michael@0	2423	const decNumber *rhs, decContext *set) {
michael@0	2424	uInt status=0; /* accumulator */
michael@0	2425	decDivideOp(res, lhs, rhs, set, REMAINDER, &status);
michael@0	2426	if (status!=0) decStatus(res, status, set);
michael@0	2427	#if DECCHECK
michael@0	2428	decCheckInexact(res, set);
michael@0	2429	#endif
michael@0	2430	return res;
michael@0	2431	} /* decNumberRemainder */
michael@0	2432
michael@0	2433	/* ------------------------------------------------------------------ */
michael@0	2434	/* decNumberRemainderNear -- divide and return remainder from nearest */
michael@0	2435	/* */
michael@0	2436	/* This computes C = A % B, where % is the IEEE remainder operator */
michael@0	2437	/* */
michael@0	2438	/* res is C, the result. C may be A and/or B (e.g., X=X%X) */
michael@0	2439	/* lhs is A */
michael@0	2440	/* rhs is B */
michael@0	2441	/* set is the context */
michael@0	2442	/* */
michael@0	2443	/* C must have space for set->digits digits. */
michael@0	2444	/* ------------------------------------------------------------------ */
michael@0	2445	U_CAPI decNumber * U_EXPORT2 uprv_decNumberRemainderNear(decNumber *res, const decNumber *lhs,
michael@0	2446	const decNumber *rhs, decContext *set) {
michael@0	2447	uInt status=0; /* accumulator */
michael@0	2448	decDivideOp(res, lhs, rhs, set, REMNEAR, &status);
michael@0	2449	if (status!=0) decStatus(res, status, set);
michael@0	2450	#if DECCHECK
michael@0	2451	decCheckInexact(res, set);
michael@0	2452	#endif
michael@0	2453	return res;
michael@0	2454	} /* decNumberRemainderNear */
michael@0	2455
michael@0	2456	/* ------------------------------------------------------------------ */
michael@0	2457	/* decNumberRotate -- rotate the coefficient of a Number left/right */
michael@0	2458	/* */
michael@0	2459	/* This computes C = A rot B (in base ten and rotating set->digits */
michael@0	2460	/* digits). */
michael@0	2461	/* */
michael@0	2462	/* res is C, the result. C may be A and/or B (e.g., X=XrotX) */
michael@0	2463	/* lhs is A */
michael@0	2464	/* rhs is B, the number of digits to rotate (-ve to right) */
michael@0	2465	/* set is the context */
michael@0	2466	/* */
michael@0	2467	/* The digits of the coefficient of A are rotated to the left (if B */
michael@0	2468	/* is positive) or to the right (if B is negative) without adjusting */
michael@0	2469	/* the exponent or the sign of A. If lhs->digits is less than */
michael@0	2470	/* set->digits the coefficient is padded with zeros on the left */
michael@0	2471	/* before the rotate. Any leading zeros in the result are removed */
michael@0	2472	/* as usual. */
michael@0	2473	/* */
michael@0	2474	/* B must be an integer (q=0) and in the range -set->digits through */
michael@0	2475	/* +set->digits. */
michael@0	2476	/* C must have space for set->digits digits. */
michael@0	2477	/* NaNs are propagated as usual. Infinities are unaffected (but */
michael@0	2478	/* B must be valid). No status is set unless B is invalid or an */
michael@0	2479	/* operand is an sNaN. */
michael@0	2480	/* ------------------------------------------------------------------ */
michael@0	2481	U_CAPI decNumber * U_EXPORT2 uprv_decNumberRotate(decNumber *res, const decNumber *lhs,
michael@0	2482	const decNumber *rhs, decContext *set) {
michael@0	2483	uInt status=0; /* accumulator */
michael@0	2484	Int rotate; /* rhs as an Int */
michael@0	2485
michael@0	2486	#if DECCHECK
michael@0	2487	if (decCheckOperands(res, lhs, rhs, set)) return res;
michael@0	2488	#endif
michael@0	2489
michael@0	2490	/* NaNs propagate as normal */
michael@0	2491	if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
michael@0	2492	decNaNs(res, lhs, rhs, set, &status);
michael@0	2493	/* rhs must be an integer */
michael@0	2494	else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
michael@0	2495	status=DEC_Invalid_operation;
michael@0	2496	else { /* both numeric, rhs is an integer */
michael@0	2497	rotate=decGetInt(rhs); /* [cannot fail] */
michael@0	2498	if (rotate==BADINT /* something bad .. */
michael@0	2499	|| rotate==BIGODD || rotate==BIGEVEN /* .. very big .. */
michael@0	2500	|| abs(rotate)>set->digits) /* .. or out of range */
michael@0	2501	status=DEC_Invalid_operation;
michael@0	2502	else { /* rhs is OK */
michael@0	2503	uprv_decNumberCopy(res, lhs);
michael@0	2504	/* convert -ve rotate to equivalent positive rotation */
michael@0	2505	if (rotate<0) rotate=set->digits+rotate;
michael@0	2506	if (rotate!=0 && rotate!=set->digits /* zero or full rotation */
michael@0	2507	&& !decNumberIsInfinite(res)) { /* lhs was infinite */
michael@0	2508	/* left-rotate to do; 0 < rotate < set->digits */
michael@0	2509	uInt units, shift; /* work */
michael@0	2510	uInt msudigits; /* digits in result msu */
michael@0	2511	Unit *msu=res->lsu+D2U(res->digits)-1; /* current msu */
michael@0	2512	Unit *msumax=res->lsu+D2U(set->digits)-1; /* rotation msu */
michael@0	2513	for (msu++; msu<=msumax; msu++) *msu=0; /* ensure high units=0 */
michael@0	2514	res->digits=set->digits; /* now full-length */
michael@0	2515	msudigits=MSUDIGITS(res->digits); /* actual digits in msu */
michael@0	2516
michael@0	2517	/* rotation here is done in-place, in three steps */
michael@0	2518	/* 1. shift all to least up to one unit to unit-align final */
michael@0	2519	/* lsd [any digits shifted out are rotated to the left, */
michael@0	2520	/* abutted to the original msd (which may require split)] */
michael@0	2521	/* */
michael@0	2522	/* [if there are no whole units left to rotate, the */
michael@0	2523	/* rotation is now complete] */
michael@0	2524	/* */
michael@0	2525	/* 2. shift to least, from below the split point only, so that */
michael@0	2526	/* the final msd is in the right place in its Unit [any */
michael@0	2527	/* digits shifted out will fit exactly in the current msu, */
michael@0	2528	/* left aligned, no split required] */
michael@0	2529	/* */
michael@0	2530	/* 3. rotate all the units by reversing left part, right */
michael@0	2531	/* part, and then whole */
michael@0	2532	/* */
michael@0	2533	/* example: rotate right 8 digits (2 units + 2), DECDPUN=3. */
michael@0	2534	/* */
michael@0	2535	/* start: 00a bcd efg hij klm npq */
michael@0	2536	/* */
michael@0	2537	/* 1a 000 0ab cde fgh|ijk lmn [pq saved] */
michael@0	2538	/* 1b 00p qab cde fgh|ijk lmn */
michael@0	2539	/* */
michael@0	2540	/* 2a 00p qab cde fgh|00i jkl [mn saved] */
michael@0	2541	/* 2b mnp qab cde fgh|00i jkl */
michael@0	2542	/* */
michael@0	2543	/* 3a fgh cde qab mnp|00i jkl */
michael@0	2544	/* 3b fgh cde qab mnp|jkl 00i */
michael@0	2545	/* 3c 00i jkl mnp qab cde fgh */
michael@0	2546
michael@0	2547	/* Step 1: amount to shift is the partial right-rotate count */
michael@0	2548	rotate=set->digits-rotate; /* make it right-rotate */
michael@0	2549	units=rotate/DECDPUN; /* whole units to rotate */
michael@0	2550	shift=rotate%DECDPUN; /* left-over digits count */
michael@0	2551	if (shift>0) { /* not an exact number of units */
michael@0	2552	uInt save=res->lsu[0]%powers[shift]; /* save low digit(s) */
michael@0	2553	decShiftToLeast(res->lsu, D2U(res->digits), shift);
michael@0	2554	if (shift>msudigits) { /* msumax-1 needs >0 digits */
michael@0	2555	uInt rem=save%powers[shift-msudigits];/* split save */
michael@0	2556	*msumax=(Unit)(save/powers[shift-msudigits]); /* and insert */
michael@0	2557	*(msumax-1)=*(msumax-1)
michael@0	2558	+(Unit)(rem*powers[DECDPUN-(shift-msudigits)]); /* .. */
michael@0	2559	}
michael@0	2560	else { /* all fits in msumax */
michael@0	2561	*msumax=*msumax+(Unit)(save*powers[msudigits-shift]); /* [maybe *1] */
michael@0	2562	}
michael@0	2563	} /* digits shift needed */
michael@0	2564
michael@0	2565	/* If whole units to rotate... */
michael@0	2566	if (units>0) { /* some to do */
michael@0	2567	/* Step 2: the units to touch are the whole ones in rotate, */
michael@0	2568	/* if any, and the shift is DECDPUN-msudigits (which may be */
michael@0	2569	/* 0, again) */
michael@0	2570	shift=DECDPUN-msudigits;
michael@0	2571	if (shift>0) { /* not an exact number of units */
michael@0	2572	uInt save=res->lsu[0]%powers[shift]; /* save low digit(s) */
michael@0	2573	decShiftToLeast(res->lsu, units, shift);
michael@0	2574	*msumax=*msumax+(Unit)(save*powers[msudigits]);
michael@0	2575	} /* partial shift needed */
michael@0	2576
michael@0	2577	/* Step 3: rotate the units array using triple reverse */
michael@0	2578	/* (reversing is easy and fast) */
michael@0	2579	decReverse(res->lsu+units, msumax); /* left part */
michael@0	2580	decReverse(res->lsu, res->lsu+units-1); /* right part */
michael@0	2581	decReverse(res->lsu, msumax); /* whole */
michael@0	2582	} /* whole units to rotate */
michael@0	2583	/* the rotation may have left an undetermined number of zeros */
michael@0	2584	/* on the left, so true length needs to be calculated */
michael@0	2585	res->digits=decGetDigits(res->lsu, msumax-res->lsu+1);
michael@0	2586	} /* rotate needed */
michael@0	2587	} /* rhs OK */
michael@0	2588	} /* numerics */
michael@0	2589	if (status!=0) decStatus(res, status, set);
michael@0	2590	return res;
michael@0	2591	} /* decNumberRotate */
michael@0	2592
michael@0	2593	/* ------------------------------------------------------------------ */
michael@0	2594	/* decNumberSameQuantum -- test for equal exponents */
michael@0	2595	/* */
michael@0	2596	/* res is the result number, which will contain either 0 or 1 */
michael@0	2597	/* lhs is a number to test */
michael@0	2598	/* rhs is the second (usually a pattern) */
michael@0	2599	/* */
michael@0	2600	/* No errors are possible and no context is needed. */
michael@0	2601	/* ------------------------------------------------------------------ */
michael@0	2602	U_CAPI decNumber * U_EXPORT2 uprv_decNumberSameQuantum(decNumber *res, const decNumber *lhs,
michael@0	2603	const decNumber *rhs) {
michael@0	2604	Unit ret=0; /* return value */
michael@0	2605
michael@0	2606	#if DECCHECK
michael@0	2607	if (decCheckOperands(res, lhs, rhs, DECUNCONT)) return res;
michael@0	2608	#endif
michael@0	2609
michael@0	2610	if (SPECIALARGS) {
michael@0	2611	if (decNumberIsNaN(lhs) && decNumberIsNaN(rhs)) ret=1;
michael@0	2612	else if (decNumberIsInfinite(lhs) && decNumberIsInfinite(rhs)) ret=1;
michael@0	2613	/* [anything else with a special gives 0] */
michael@0	2614	}
michael@0	2615	else if (lhs->exponent==rhs->exponent) ret=1;
michael@0	2616
michael@0	2617	uprv_decNumberZero(res); /* OK to overwrite an operand now */
michael@0	2618	*res->lsu=ret;
michael@0	2619	return res;
michael@0	2620	} /* decNumberSameQuantum */
michael@0	2621
michael@0	2622	/* ------------------------------------------------------------------ */
michael@0	2623	/* decNumberScaleB -- multiply by a power of 10 */
michael@0	2624	/* */
michael@0	2625	/* This computes C = A x 10**B where B is an integer (q=0) with */
michael@0	2626	/* maximum magnitude 2*(emax+digits) */
michael@0	2627	/* */
michael@0	2628	/* res is C, the result. C may be A or B */
michael@0	2629	/* lhs is A, the number to adjust */
michael@0	2630	/* rhs is B, the requested power of ten to use */
michael@0	2631	/* set is the context */
michael@0	2632	/* */
michael@0	2633	/* C must have space for set->digits digits. */
michael@0	2634	/* */
michael@0	2635	/* The result may underflow or overflow. */
michael@0	2636	/* ------------------------------------------------------------------ */
michael@0	2637	U_CAPI decNumber * U_EXPORT2 uprv_decNumberScaleB(decNumber *res, const decNumber *lhs,
michael@0	2638	const decNumber *rhs, decContext *set) {
michael@0	2639	Int reqexp; /* requested exponent change [B] */
michael@0	2640	uInt status=0; /* accumulator */
michael@0	2641	Int residue; /* work */
michael@0	2642
michael@0	2643	#if DECCHECK
michael@0	2644	if (decCheckOperands(res, lhs, rhs, set)) return res;
michael@0	2645	#endif
michael@0	2646
michael@0	2647	/* Handle special values except lhs infinite */
michael@0	2648	if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
michael@0	2649	decNaNs(res, lhs, rhs, set, &status);
michael@0	2650	/* rhs must be an integer */
michael@0	2651	else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
michael@0	2652	status=DEC_Invalid_operation;
michael@0	2653	else {
michael@0	2654	/* lhs is a number; rhs is a finite with q==0 */
michael@0	2655	reqexp=decGetInt(rhs); /* [cannot fail] */
michael@0	2656	if (reqexp==BADINT /* something bad .. */
michael@0	2657	|| reqexp==BIGODD || reqexp==BIGEVEN /* .. very big .. */
michael@0	2658	|| abs(reqexp)>(2*(set->digits+set->emax))) /* .. or out of range */
michael@0	2659	status=DEC_Invalid_operation;
michael@0	2660	else { /* rhs is OK */
michael@0	2661	uprv_decNumberCopy(res, lhs); /* all done if infinite lhs */
michael@0	2662	if (!decNumberIsInfinite(res)) { /* prepare to scale */
michael@0	2663	res->exponent+=reqexp; /* adjust the exponent */
michael@0	2664	residue=0;
michael@0	2665	decFinalize(res, set, &residue, &status); /* .. and check */
michael@0	2666	} /* finite LHS */
michael@0	2667	} /* rhs OK */
michael@0	2668	} /* rhs finite */
michael@0	2669	if (status!=0) decStatus(res, status, set);
michael@0	2670	return res;
michael@0	2671	} /* decNumberScaleB */
michael@0	2672
michael@0	2673	/* ------------------------------------------------------------------ */
michael@0	2674	/* decNumberShift -- shift the coefficient of a Number left or right */
michael@0	2675	/* */
michael@0	2676	/* This computes C = A << B or C = A >> -B (in base ten). */
michael@0	2677	/* */
michael@0	2678	/* res is C, the result. C may be A and/or B (e.g., X=X<<X) */
michael@0	2679	/* lhs is A */
michael@0	2680	/* rhs is B, the number of digits to shift (-ve to right) */
michael@0	2681	/* set is the context */
michael@0	2682	/* */
michael@0	2683	/* The digits of the coefficient of A are shifted to the left (if B */
michael@0	2684	/* is positive) or to the right (if B is negative) without adjusting */
michael@0	2685	/* the exponent or the sign of A. */
michael@0	2686	/* */
michael@0	2687	/* B must be an integer (q=0) and in the range -set->digits through */
michael@0	2688	/* +set->digits. */
michael@0	2689	/* C must have space for set->digits digits. */
michael@0	2690	/* NaNs are propagated as usual. Infinities are unaffected (but */
michael@0	2691	/* B must be valid). No status is set unless B is invalid or an */
michael@0	2692	/* operand is an sNaN. */
michael@0	2693	/* ------------------------------------------------------------------ */
michael@0	2694	U_CAPI decNumber * U_EXPORT2 uprv_decNumberShift(decNumber *res, const decNumber *lhs,
michael@0	2695	const decNumber *rhs, decContext *set) {
michael@0	2696	uInt status=0; /* accumulator */
michael@0	2697	Int shift; /* rhs as an Int */
michael@0	2698
michael@0	2699	#if DECCHECK
michael@0	2700	if (decCheckOperands(res, lhs, rhs, set)) return res;
michael@0	2701	#endif
michael@0	2702
michael@0	2703	/* NaNs propagate as normal */
michael@0	2704	if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
michael@0	2705	decNaNs(res, lhs, rhs, set, &status);
michael@0	2706	/* rhs must be an integer */
michael@0	2707	else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
michael@0	2708	status=DEC_Invalid_operation;
michael@0	2709	else { /* both numeric, rhs is an integer */
michael@0	2710	shift=decGetInt(rhs); /* [cannot fail] */
michael@0	2711	if (shift==BADINT /* something bad .. */
michael@0	2712	|| shift==BIGODD || shift==BIGEVEN /* .. very big .. */
michael@0	2713	|| abs(shift)>set->digits) /* .. or out of range */
michael@0	2714	status=DEC_Invalid_operation;
michael@0	2715	else { /* rhs is OK */
michael@0	2716	uprv_decNumberCopy(res, lhs);
michael@0	2717	if (shift!=0 && !decNumberIsInfinite(res)) { /* something to do */
michael@0	2718	if (shift>0) { /* to left */
michael@0	2719	if (shift==set->digits) { /* removing all */
michael@0	2720	*res->lsu=0; /* so place 0 */
michael@0	2721	res->digits=1; /* .. */
michael@0	2722	}
michael@0	2723	else { /* */
michael@0	2724	/* first remove leading digits if necessary */
michael@0	2725	if (res->digits+shift>set->digits) {
michael@0	2726	decDecap(res, res->digits+shift-set->digits);
michael@0	2727	/* that updated res->digits; may have gone to 1 (for a */
michael@0	2728	/* single digit or for zero */
michael@0	2729	}
michael@0	2730	if (res->digits>1 || *res->lsu) /* if non-zero.. */
michael@0	2731	res->digits=decShiftToMost(res->lsu, res->digits, shift);
michael@0	2732	} /* partial left */
michael@0	2733	} /* left */
michael@0	2734	else { /* to right */
michael@0	2735	if (-shift>=res->digits) { /* discarding all */
michael@0	2736	*res->lsu=0; /* so place 0 */
michael@0	2737	res->digits=1; /* .. */
michael@0	2738	}
michael@0	2739	else {
michael@0	2740	decShiftToLeast(res->lsu, D2U(res->digits), -shift);
michael@0	2741	res->digits-=(-shift);
michael@0	2742	}
michael@0	2743	} /* to right */
michael@0	2744	} /* non-0 non-Inf shift */
michael@0	2745	} /* rhs OK */
michael@0	2746	} /* numerics */
michael@0	2747	if (status!=0) decStatus(res, status, set);
michael@0	2748	return res;
michael@0	2749	} /* decNumberShift */
michael@0	2750
michael@0	2751	/* ------------------------------------------------------------------ */
michael@0	2752	/* decNumberSquareRoot -- square root operator */
michael@0	2753	/* */
michael@0	2754	/* This computes C = squareroot(A) */
michael@0	2755	/* */
michael@0	2756	/* res is C, the result. C may be A */
michael@0	2757	/* rhs is A */
michael@0	2758	/* set is the context; note that rounding mode has no effect */
michael@0	2759	/* */
michael@0	2760	/* C must have space for set->digits digits. */
michael@0	2761	/* ------------------------------------------------------------------ */
michael@0	2762	/* This uses the following varying-precision algorithm in: */
michael@0	2763	/* */
michael@0	2764	/* Properly Rounded Variable Precision Square Root, T. E. Hull and */
michael@0	2765	/* A. Abrham, ACM Transactions on Mathematical Software, Vol 11 #3, */
michael@0	2766	/* pp229-237, ACM, September 1985. */
michael@0	2767	/* */
michael@0	2768	/* The square-root is calculated using Newton's method, after which */
michael@0	2769	/* a check is made to ensure the result is correctly rounded. */
michael@0	2770	/* */
michael@0	2771	/* % [Reformatted original Numerical Turing source code follows.] */
michael@0	2772	/* function sqrt(x : real) : real */
michael@0	2773	/* % sqrt(x) returns the properly rounded approximation to the square */
michael@0	2774	/* % root of x, in the precision of the calling environment, or it */
michael@0	2775	/* % fails if x < 0. */
michael@0	2776	/* % t e hull and a abrham, august, 1984 */
michael@0	2777	/* if x <= 0 then */
michael@0	2778	/* if x < 0 then */
michael@0	2779	/* assert false */
michael@0	2780	/* else */
michael@0	2781	/* result 0 */
michael@0	2782	/* end if */
michael@0	2783	/* end if */
michael@0	2784	/* var f := setexp(x, 0) % fraction part of x [0.1 <= x < 1] */
michael@0	2785	/* var e := getexp(x) % exponent part of x */
michael@0	2786	/* var approx : real */
michael@0	2787	/* if e mod 2 = 0 then */
michael@0	2788	/* approx := .259 + .819 * f % approx to root of f */
michael@0	2789	/* else */
michael@0	2790	/* f := f/l0 % adjustments */
michael@0	2791	/* e := e + 1 % for odd */
michael@0	2792	/* approx := .0819 + 2.59 * f % exponent */
michael@0	2793	/* end if */
michael@0	2794	/* */
michael@0	2795	/* var p:= 3 */
michael@0	2796	/* const maxp := currentprecision + 2 */
michael@0	2797	/* loop */
michael@0	2798	/* p := min(2*p - 2, maxp) % p = 4,6,10, . . . , maxp */
michael@0	2799	/* precision p */
michael@0	2800	/* approx := .5 * (approx + f/approx) */
michael@0	2801	/* exit when p = maxp */
michael@0	2802	/* end loop */
michael@0	2803	/* */
michael@0	2804	/* % approx is now within 1 ulp of the properly rounded square root */
michael@0	2805	/* % of f; to ensure proper rounding, compare squares of (approx - */
michael@0	2806	/* % l/2 ulp) and (approx + l/2 ulp) with f. */
michael@0	2807	/* p := currentprecision */
michael@0	2808	/* begin */
michael@0	2809	/* precision p + 2 */
michael@0	2810	/* const approxsubhalf := approx - setexp(.5, -p) */
michael@0	2811	/* if mulru(approxsubhalf, approxsubhalf) > f then */
michael@0	2812	/* approx := approx - setexp(.l, -p + 1) */
michael@0	2813	/* else */
michael@0	2814	/* const approxaddhalf := approx + setexp(.5, -p) */
michael@0	2815	/* if mulrd(approxaddhalf, approxaddhalf) < f then */
michael@0	2816	/* approx := approx + setexp(.l, -p + 1) */
michael@0	2817	/* end if */
michael@0	2818	/* end if */
michael@0	2819	/* end */
michael@0	2820	/* result setexp(approx, e div 2) % fix exponent */
michael@0	2821	/* end sqrt */
michael@0	2822	/* ------------------------------------------------------------------ */
michael@0	2823	#if defined(__clang__) || U_GCC_MAJOR_MINOR >= 406
michael@0	2824	#pragma GCC diagnostic push
michael@0	2825	#pragma GCC diagnostic ignored "-Warray-bounds"
michael@0	2826	#endif
michael@0	2827	U_CAPI decNumber * U_EXPORT2 uprv_decNumberSquareRoot(decNumber *res, const decNumber *rhs,
michael@0	2828	decContext *set) {
michael@0	2829	decContext workset, approxset; /* work contexts */
michael@0	2830	decNumber dzero; /* used for constant zero */
michael@0	2831	Int maxp; /* largest working precision */
michael@0	2832	Int workp; /* working precision */
michael@0	2833	Int residue=0; /* rounding residue */
michael@0	2834	uInt status=0, ignore=0; /* status accumulators */
michael@0	2835	uInt rstatus; /* .. */
michael@0	2836	Int exp; /* working exponent */
michael@0	2837	Int ideal; /* ideal (preferred) exponent */
michael@0	2838	Int needbytes; /* work */
michael@0	2839	Int dropped; /* .. */
michael@0	2840
michael@0	2841	#if DECSUBSET
michael@0	2842	decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */
michael@0	2843	#endif
michael@0	2844	/* buffer for f [needs +1 in case DECBUFFER 0] */
michael@0	2845	decNumber buff[D2N(DECBUFFER+1)];
michael@0	2846	/* buffer for a [needs +2 to match likely maxp] */
michael@0	2847	decNumber bufa[D2N(DECBUFFER+2)];
michael@0	2848	/* buffer for temporary, b [must be same size as a] */
michael@0	2849	decNumber bufb[D2N(DECBUFFER+2)];
michael@0	2850	decNumber *allocbuff=NULL; /* -> allocated buff, iff allocated */
michael@0	2851	decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */
michael@0	2852	decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */
michael@0	2853	decNumber *f=buff; /* reduced fraction */
michael@0	2854	decNumber *a=bufa; /* approximation to result */
michael@0	2855	decNumber *b=bufb; /* intermediate result */
michael@0	2856	/* buffer for temporary variable, up to 3 digits */
michael@0	2857	decNumber buft[D2N(3)];
michael@0	2858	decNumber *t=buft; /* up-to-3-digit constant or work */
michael@0	2859
michael@0	2860	#if DECCHECK
michael@0	2861	if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
michael@0	2862	#endif
michael@0	2863
michael@0	2864	do { /* protect allocated storage */
michael@0	2865	#if DECSUBSET
michael@0	2866	if (!set->extended) {
michael@0	2867	/* reduce operand and set lostDigits status, as needed */
michael@0	2868	if (rhs->digits>set->digits) {
michael@0	2869	allocrhs=decRoundOperand(rhs, set, &status);
michael@0	2870	if (allocrhs==NULL) break;
michael@0	2871	/* [Note: 'f' allocation below could reuse this buffer if */
michael@0	2872	/* used, but as this is rare they are kept separate for clarity.] */
michael@0	2873	rhs=allocrhs;
michael@0	2874	}
michael@0	2875	}
michael@0	2876	#endif
michael@0	2877	/* [following code does not require input rounding] */
michael@0	2878
michael@0	2879	/* handle infinities and NaNs */
michael@0	2880	if (SPECIALARG) {
michael@0	2881	if (decNumberIsInfinite(rhs)) { /* an infinity */
michael@0	2882	if (decNumberIsNegative(rhs)) status|=DEC_Invalid_operation;
michael@0	2883	else uprv_decNumberCopy(res, rhs); /* +Infinity */
michael@0	2884	}
michael@0	2885	else decNaNs(res, rhs, NULL, set, &status); /* a NaN */
michael@0	2886	break;
michael@0	2887	}
michael@0	2888
michael@0	2889	/* calculate the ideal (preferred) exponent [floor(exp/2)] */
michael@0	2890	/* [It would be nicer to write: ideal=rhs->exponent>>1, but this */
michael@0	2891	/* generates a compiler warning. Generated code is the same.] */
michael@0	2892	ideal=(rhs->exponent&~1)/2; /* target */
michael@0	2893
michael@0	2894	/* handle zeros */
michael@0	2895	if (ISZERO(rhs)) {
michael@0	2896	uprv_decNumberCopy(res, rhs); /* could be 0 or -0 */
michael@0	2897	res->exponent=ideal; /* use the ideal [safe] */
michael@0	2898	/* use decFinish to clamp any out-of-range exponent, etc. */
michael@0	2899	decFinish(res, set, &residue, &status);
michael@0	2900	break;
michael@0	2901	}
michael@0	2902
michael@0	2903	/* any other -x is an oops */
michael@0	2904	if (decNumberIsNegative(rhs)) {
michael@0	2905	status|=DEC_Invalid_operation;
michael@0	2906	break;
michael@0	2907	}
michael@0	2908
michael@0	2909	/* space is needed for three working variables */
michael@0	2910	/* f -- the same precision as the RHS, reduced to 0.01->0.99... */
michael@0	2911	/* a -- Hull's approximation -- precision, when assigned, is */
michael@0	2912	/* currentprecision+1 or the input argument precision, */
michael@0	2913	/* whichever is larger (+2 for use as temporary) */
michael@0	2914	/* b -- intermediate temporary result (same size as a) */
michael@0	2915	/* if any is too long for local storage, then allocate */
michael@0	2916	workp=MAXI(set->digits+1, rhs->digits); /* actual rounding precision */
michael@0	2917	workp=MAXI(workp, 7); /* at least 7 for low cases */
michael@0	2918	maxp=workp+2; /* largest working precision */
michael@0	2919
michael@0	2920	needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
michael@0	2921	if (needbytes>(Int)sizeof(buff)) {
michael@0	2922	allocbuff=(decNumber *)malloc(needbytes);
michael@0	2923	if (allocbuff==NULL) { /* hopeless -- abandon */
michael@0	2924	status|=DEC_Insufficient_storage;
michael@0	2925	break;}
michael@0	2926	f=allocbuff; /* use the allocated space */
michael@0	2927	}
michael@0	2928	/* a and b both need to be able to hold a maxp-length number */
michael@0	2929	needbytes=sizeof(decNumber)+(D2U(maxp)-1)*sizeof(Unit);
michael@0	2930	if (needbytes>(Int)sizeof(bufa)) { /* [same applies to b] */
michael@0	2931	allocbufa=(decNumber *)malloc(needbytes);
michael@0	2932	allocbufb=(decNumber *)malloc(needbytes);
michael@0	2933	if (allocbufa==NULL || allocbufb==NULL) { /* hopeless */
michael@0	2934	status|=DEC_Insufficient_storage;
michael@0	2935	break;}
michael@0	2936	a=allocbufa; /* use the allocated spaces */
michael@0	2937	b=allocbufb; /* .. */
michael@0	2938	}
michael@0	2939
michael@0	2940	/* copy rhs -> f, save exponent, and reduce so 0.1 <= f < 1 */
michael@0	2941	uprv_decNumberCopy(f, rhs);
michael@0	2942	exp=f->exponent+f->digits; /* adjusted to Hull rules */
michael@0	2943	f->exponent=-(f->digits); /* to range */
michael@0	2944
michael@0	2945	/* set up working context */
michael@0	2946	uprv_decContextDefault(&workset, DEC_INIT_DECIMAL64);
michael@0	2947	workset.emax=DEC_MAX_EMAX;
michael@0	2948	workset.emin=DEC_MIN_EMIN;
michael@0	2949
michael@0	2950	/* [Until further notice, no error is possible and status bits */
michael@0	2951	/* (Rounded, etc.) should be ignored, not accumulated.] */
michael@0	2952
michael@0	2953	/* Calculate initial approximation, and allow for odd exponent */
michael@0	2954	workset.digits=workp; /* p for initial calculation */
michael@0	2955	t->bits=0; t->digits=3;
michael@0	2956	a->bits=0; a->digits=3;
michael@0	2957	if ((exp & 1)==0) { /* even exponent */
michael@0	2958	/* Set t=0.259, a=0.819 */
michael@0	2959	t->exponent=-3;
michael@0	2960	a->exponent=-3;
michael@0	2961	#if DECDPUN>=3
michael@0	2962	t->lsu[0]=259;
michael@0	2963	a->lsu[0]=819;
michael@0	2964	#elif DECDPUN==2
michael@0	2965	t->lsu[0]=59; t->lsu[1]=2;
michael@0	2966	a->lsu[0]=19; a->lsu[1]=8;
michael@0	2967	#else
michael@0	2968	t->lsu[0]=9; t->lsu[1]=5; t->lsu[2]=2;
michael@0	2969	a->lsu[0]=9; a->lsu[1]=1; a->lsu[2]=8;
michael@0	2970	#endif
michael@0	2971	}
michael@0	2972	else { /* odd exponent */
michael@0	2973	/* Set t=0.0819, a=2.59 */
michael@0	2974	f->exponent--; /* f=f/10 */
michael@0	2975	exp++; /* e=e+1 */
michael@0	2976	t->exponent=-4;
michael@0	2977	a->exponent=-2;
michael@0	2978	#if DECDPUN>=3
michael@0	2979	t->lsu[0]=819;
michael@0	2980	a->lsu[0]=259;
michael@0	2981	#elif DECDPUN==2
michael@0	2982	t->lsu[0]=19; t->lsu[1]=8;
michael@0	2983	a->lsu[0]=59; a->lsu[1]=2;
michael@0	2984	#else
michael@0	2985	t->lsu[0]=9; t->lsu[1]=1; t->lsu[2]=8;
michael@0	2986	a->lsu[0]=9; a->lsu[1]=5; a->lsu[2]=2;
michael@0	2987	#endif
michael@0	2988	}
michael@0	2989
michael@0	2990	decMultiplyOp(a, a, f, &workset, &ignore); /* a=a*f */
michael@0	2991	decAddOp(a, a, t, &workset, 0, &ignore); /* ..+t */
michael@0	2992	/* [a is now the initial approximation for sqrt(f), calculated with */
michael@0	2993	/* currentprecision, which is also a's precision.] */
michael@0	2994
michael@0	2995	/* the main calculation loop */
michael@0	2996	uprv_decNumberZero(&dzero); /* make 0 */
michael@0	2997	uprv_decNumberZero(t); /* set t = 0.5 */
michael@0	2998	t->lsu[0]=5; /* .. */
michael@0	2999	t->exponent=-1; /* .. */
michael@0	3000	workset.digits=3; /* initial p */
michael@0	3001	for (; workset.digits<maxp;) {
michael@0	3002	/* set p to min(2*p - 2, maxp) [hence 3; or: 4, 6, 10, ... , maxp] */
michael@0	3003	workset.digits=MINI(workset.digits*2-2, maxp);
michael@0	3004	/* a = 0.5 * (a + f/a) */
michael@0	3005	/* [calculated at p then rounded to currentprecision] */
michael@0	3006	decDivideOp(b, f, a, &workset, DIVIDE, &ignore); /* b=f/a */
michael@0	3007	decAddOp(b, b, a, &workset, 0, &ignore); /* b=b+a */
michael@0	3008	decMultiplyOp(a, b, t, &workset, &ignore); /* a=b*0.5 */
michael@0	3009	} /* loop */
michael@0	3010
michael@0	3011	/* Here, 0.1 <= a < 1 [Hull], and a has maxp digits */
michael@0	3012	/* now reduce to length, etc.; this needs to be done with a */
michael@0	3013	/* having the correct exponent so as to handle subnormals */
michael@0	3014	/* correctly */
michael@0	3015	approxset=*set; /* get emin, emax, etc. */
michael@0	3016	approxset.round=DEC_ROUND_HALF_EVEN;
michael@0	3017	a->exponent+=exp/2; /* set correct exponent */
michael@0	3018	rstatus=0; /* clear status */
michael@0	3019	residue=0; /* .. and accumulator */
michael@0	3020	decCopyFit(a, a, &approxset, &residue, &rstatus); /* reduce (if needed) */
michael@0	3021	decFinish(a, &approxset, &residue, &rstatus); /* clean and finalize */
michael@0	3022
michael@0	3023	/* Overflow was possible if the input exponent was out-of-range, */
michael@0	3024	/* in which case quit */
michael@0	3025	if (rstatus&DEC_Overflow) {
michael@0	3026	status=rstatus; /* use the status as-is */
michael@0	3027	uprv_decNumberCopy(res, a); /* copy to result */
michael@0	3028	break;
michael@0	3029	}
michael@0	3030
michael@0	3031	/* Preserve status except Inexact/Rounded */
michael@0	3032	status|=(rstatus & ~(DEC_Rounded|DEC_Inexact));
michael@0	3033
michael@0	3034	/* Carry out the Hull correction */
michael@0	3035	a->exponent-=exp/2; /* back to 0.1->1 */
michael@0	3036
michael@0	3037	/* a is now at final precision and within 1 ulp of the properly */
michael@0	3038	/* rounded square root of f; to ensure proper rounding, compare */
michael@0	3039	/* squares of (a - l/2 ulp) and (a + l/2 ulp) with f. */
michael@0	3040	/* Here workset.digits=maxp and t=0.5, and a->digits determines */
michael@0	3041	/* the ulp */
michael@0	3042	workset.digits--; /* maxp-1 is OK now */
michael@0	3043	t->exponent=-a->digits-1; /* make 0.5 ulp */
michael@0	3044	decAddOp(b, a, t, &workset, DECNEG, &ignore); /* b = a - 0.5 ulp */
michael@0	3045	workset.round=DEC_ROUND_UP;
michael@0	3046	decMultiplyOp(b, b, b, &workset, &ignore); /* b = mulru(b, b) */
michael@0	3047	decCompareOp(b, f, b, &workset, COMPARE, &ignore); /* b ? f, reversed */
michael@0	3048	if (decNumberIsNegative(b)) { /* f < b [i.e., b > f] */
michael@0	3049	/* this is the more common adjustment, though both are rare */
michael@0	3050	t->exponent++; /* make 1.0 ulp */
michael@0	3051	t->lsu[0]=1; /* .. */
michael@0	3052	decAddOp(a, a, t, &workset, DECNEG, &ignore); /* a = a - 1 ulp */
michael@0	3053	/* assign to approx [round to length] */
michael@0	3054	approxset.emin-=exp/2; /* adjust to match a */
michael@0	3055	approxset.emax-=exp/2;
michael@0	3056	decAddOp(a, &dzero, a, &approxset, 0, &ignore);
michael@0	3057	}
michael@0	3058	else {
michael@0	3059	decAddOp(b, a, t, &workset, 0, &ignore); /* b = a + 0.5 ulp */
michael@0	3060	workset.round=DEC_ROUND_DOWN;
michael@0	3061	decMultiplyOp(b, b, b, &workset, &ignore); /* b = mulrd(b, b) */
michael@0	3062	decCompareOp(b, b, f, &workset, COMPARE, &ignore); /* b ? f */
michael@0	3063	if (decNumberIsNegative(b)) { /* b < f */
michael@0	3064	t->exponent++; /* make 1.0 ulp */
michael@0	3065	t->lsu[0]=1; /* .. */
michael@0	3066	decAddOp(a, a, t, &workset, 0, &ignore); /* a = a + 1 ulp */
michael@0	3067	/* assign to approx [round to length] */
michael@0	3068	approxset.emin-=exp/2; /* adjust to match a */
michael@0	3069	approxset.emax-=exp/2;
michael@0	3070	decAddOp(a, &dzero, a, &approxset, 0, &ignore);
michael@0	3071	}
michael@0	3072	}
michael@0	3073	/* [no errors are possible in the above, and rounding/inexact during */
michael@0	3074	/* estimation are irrelevant, so status was not accumulated] */
michael@0	3075
michael@0	3076	/* Here, 0.1 <= a < 1 (still), so adjust back */
michael@0	3077	a->exponent+=exp/2; /* set correct exponent */
michael@0	3078
michael@0	3079	/* count droppable zeros [after any subnormal rounding] by */
michael@0	3080	/* trimming a copy */
michael@0	3081	uprv_decNumberCopy(b, a);
michael@0	3082	decTrim(b, set, 1, 1, &dropped); /* [drops trailing zeros] */
michael@0	3083
michael@0	3084	/* Set Inexact and Rounded. The answer can only be exact if */
michael@0	3085	/* it is short enough so that squaring it could fit in workp */
michael@0	3086	/* digits, so this is the only (relatively rare) condition that */
michael@0	3087	/* a careful check is needed */
michael@0	3088	if (b->digits*2-1 > workp) { /* cannot fit */
michael@0	3089	status|=DEC_Inexact|DEC_Rounded;
michael@0	3090	}
michael@0	3091	else { /* could be exact/unrounded */
michael@0	3092	uInt mstatus=0; /* local status */
michael@0	3093	decMultiplyOp(b, b, b, &workset, &mstatus); /* try the multiply */
michael@0	3094	if (mstatus&DEC_Overflow) { /* result just won't fit */
michael@0	3095	status|=DEC_Inexact|DEC_Rounded;
michael@0	3096	}
michael@0	3097	else { /* plausible */
michael@0	3098	decCompareOp(t, b, rhs, &workset, COMPARE, &mstatus); /* b ? rhs */
michael@0	3099	if (!ISZERO(t)) status|=DEC_Inexact|DEC_Rounded; /* not equal */
michael@0	3100	else { /* is Exact */
michael@0	3101	/* here, dropped is the count of trailing zeros in 'a' */
michael@0	3102	/* use closest exponent to ideal... */
michael@0	3103	Int todrop=ideal-a->exponent; /* most that can be dropped */
michael@0	3104	if (todrop<0) status|=DEC_Rounded; /* ideally would add 0s */
michael@0	3105	else { /* unrounded */
michael@0	3106	/* there are some to drop, but emax may not allow all */
michael@0	3107	Int maxexp=set->emax-set->digits+1;
michael@0	3108	Int maxdrop=maxexp-a->exponent;
michael@0	3109	if (todrop>maxdrop && set->clamp) { /* apply clamping */
michael@0	3110	todrop=maxdrop;
michael@0	3111	status|=DEC_Clamped;
michael@0	3112	}
michael@0	3113	if (dropped<todrop) { /* clamp to those available */
michael@0	3114	todrop=dropped;
michael@0	3115	status|=DEC_Clamped;
michael@0	3116	}
michael@0	3117	if (todrop>0) { /* have some to drop */
michael@0	3118	decShiftToLeast(a->lsu, D2U(a->digits), todrop);
michael@0	3119	a->exponent+=todrop; /* maintain numerical value */
michael@0	3120	a->digits-=todrop; /* new length */
michael@0	3121	}
michael@0	3122	}
michael@0	3123	}
michael@0	3124	}
michael@0	3125	}
michael@0	3126
michael@0	3127	/* double-check Underflow, as perhaps the result could not have */
michael@0	3128	/* been subnormal (initial argument too big), or it is now Exact */
michael@0	3129	if (status&DEC_Underflow) {
michael@0	3130	Int ae=rhs->exponent+rhs->digits-1; /* adjusted exponent */
michael@0	3131	/* check if truly subnormal */
michael@0	3132	#if DECEXTFLAG /* DEC_Subnormal too */
michael@0	3133	if (ae>=set->emin*2) status&=~(DEC_Subnormal|DEC_Underflow);
michael@0	3134	#else
michael@0	3135	if (ae>=set->emin*2) status&=~DEC_Underflow;
michael@0	3136	#endif
michael@0	3137	/* check if truly inexact */
michael@0	3138	if (!(status&DEC_Inexact)) status&=~DEC_Underflow;
michael@0	3139	}
michael@0	3140
michael@0	3141	uprv_decNumberCopy(res, a); /* a is now the result */
michael@0	3142	} while(0); /* end protected */
michael@0	3143
michael@0	3144	if (allocbuff!=NULL) free(allocbuff); /* drop any storage used */
michael@0	3145	if (allocbufa!=NULL) free(allocbufa); /* .. */
michael@0	3146	if (allocbufb!=NULL) free(allocbufb); /* .. */
michael@0	3147	#if DECSUBSET
michael@0	3148	if (allocrhs !=NULL) free(allocrhs); /* .. */
michael@0	3149	#endif
michael@0	3150	if (status!=0) decStatus(res, status, set);/* then report status */
michael@0	3151	#if DECCHECK
michael@0	3152	decCheckInexact(res, set);
michael@0	3153	#endif
michael@0	3154	return res;
michael@0	3155	} /* decNumberSquareRoot */
michael@0	3156	#if defined(__clang__) || U_GCC_MAJOR_MINOR >= 406
michael@0	3157	#pragma GCC diagnostic pop
michael@0	3158	#endif
michael@0	3159
michael@0	3160	/* ------------------------------------------------------------------ */
michael@0	3161	/* decNumberSubtract -- subtract two Numbers */
michael@0	3162	/* */
michael@0	3163	/* This computes C = A - B */
michael@0	3164	/* */
michael@0	3165	/* res is C, the result. C may be A and/or B (e.g., X=X-X) */
michael@0	3166	/* lhs is A */
michael@0	3167	/* rhs is B */
michael@0	3168	/* set is the context */
michael@0	3169	/* */
michael@0	3170	/* C must have space for set->digits digits. */
michael@0	3171	/* ------------------------------------------------------------------ */
michael@0	3172	U_CAPI decNumber * U_EXPORT2 uprv_decNumberSubtract(decNumber *res, const decNumber *lhs,
michael@0	3173	const decNumber *rhs, decContext *set) {
michael@0	3174	uInt status=0; /* accumulator */
michael@0	3175
michael@0	3176	decAddOp(res, lhs, rhs, set, DECNEG, &status);
michael@0	3177	if (status!=0) decStatus(res, status, set);
michael@0	3178	#if DECCHECK
michael@0	3179	decCheckInexact(res, set);
michael@0	3180	#endif
michael@0	3181	return res;
michael@0	3182	} /* decNumberSubtract */
michael@0	3183
michael@0	3184	/* ------------------------------------------------------------------ */
michael@0	3185	/* decNumberToIntegralExact -- round-to-integral-value with InExact */
michael@0	3186	/* decNumberToIntegralValue -- round-to-integral-value */
michael@0	3187	/* */
michael@0	3188	/* res is the result */
michael@0	3189	/* rhs is input number */
michael@0	3190	/* set is the context */
michael@0	3191	/* */
michael@0	3192	/* res must have space for any value of rhs. */
michael@0	3193	/* */
michael@0	3194	/* This implements the IEEE special operators and therefore treats */
michael@0	3195	/* special values as valid. For finite numbers it returns */
michael@0	3196	/* rescale(rhs, 0) if rhs->exponent is <0. */
michael@0	3197	/* Otherwise the result is rhs (so no error is possible, except for */
michael@0	3198	/* sNaN). */
michael@0	3199	/* */
michael@0	3200	/* The context is used for rounding mode and status after sNaN, but */
michael@0	3201	/* the digits setting is ignored. The Exact version will signal */
michael@0	3202	/* Inexact if the result differs numerically from rhs; the other */
michael@0	3203	/* never signals Inexact. */
michael@0	3204	/* ------------------------------------------------------------------ */
michael@0	3205	U_CAPI decNumber * U_EXPORT2 uprv_decNumberToIntegralExact(decNumber *res, const decNumber *rhs,
michael@0	3206	decContext *set) {
michael@0	3207	decNumber dn;
michael@0	3208	decContext workset; /* working context */
michael@0	3209	uInt status=0; /* accumulator */
michael@0	3210
michael@0	3211	#if DECCHECK
michael@0	3212	if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
michael@0	3213	#endif
michael@0	3214
michael@0	3215	/* handle infinities and NaNs */
michael@0	3216	if (SPECIALARG) {
michael@0	3217	if (decNumberIsInfinite(rhs)) uprv_decNumberCopy(res, rhs); /* an Infinity */
michael@0	3218	else decNaNs(res, rhs, NULL, set, &status); /* a NaN */
michael@0	3219	}
michael@0	3220	else { /* finite */
michael@0	3221	/* have a finite number; no error possible (res must be big enough) */
michael@0	3222	if (rhs->exponent>=0) return uprv_decNumberCopy(res, rhs);
michael@0	3223	/* that was easy, but if negative exponent there is work to do... */
michael@0	3224	workset=*set; /* clone rounding, etc. */
michael@0	3225	workset.digits=rhs->digits; /* no length rounding */
michael@0	3226	workset.traps=0; /* no traps */
michael@0	3227	uprv_decNumberZero(&dn); /* make a number with exponent 0 */
michael@0	3228	uprv_decNumberQuantize(res, rhs, &dn, &workset);
michael@0	3229	status|=workset.status;
michael@0	3230	}
michael@0	3231	if (status!=0) decStatus(res, status, set);
michael@0	3232	return res;
michael@0	3233	} /* decNumberToIntegralExact */
michael@0	3234
michael@0	3235	U_CAPI decNumber * U_EXPORT2 uprv_decNumberToIntegralValue(decNumber *res, const decNumber *rhs,
michael@0	3236	decContext *set) {
michael@0	3237	decContext workset=*set; /* working context */
michael@0	3238	workset.traps=0; /* no traps */
michael@0	3239	uprv_decNumberToIntegralExact(res, rhs, &workset);
michael@0	3240	/* this never affects set, except for sNaNs; NaN will have been set */
michael@0	3241	/* or propagated already, so no need to call decStatus */
michael@0	3242	set->status|=workset.status&DEC_Invalid_operation;
michael@0	3243	return res;
michael@0	3244	} /* decNumberToIntegralValue */
michael@0	3245
michael@0	3246	/* ------------------------------------------------------------------ */
michael@0	3247	/* decNumberXor -- XOR two Numbers, digitwise */
michael@0	3248	/* */
michael@0	3249	/* This computes C = A ^ B */
michael@0	3250	/* */
michael@0	3251	/* res is C, the result. C may be A and/or B (e.g., X=X^X) */
michael@0	3252	/* lhs is A */
michael@0	3253	/* rhs is B */
michael@0	3254	/* set is the context (used for result length and error report) */
michael@0	3255	/* */
michael@0	3256	/* C must have space for set->digits digits. */
michael@0	3257	/* */
michael@0	3258	/* Logical function restrictions apply (see above); a NaN is */
michael@0	3259	/* returned with Invalid_operation if a restriction is violated. */
michael@0	3260	/* ------------------------------------------------------------------ */
michael@0	3261	U_CAPI decNumber * U_EXPORT2 uprv_decNumberXor(decNumber *res, const decNumber *lhs,
michael@0	3262	const decNumber *rhs, decContext *set) {
michael@0	3263	const Unit *ua, *ub; /* -> operands */
michael@0	3264	const Unit *msua, *msub; /* -> operand msus */
michael@0	3265	Unit *uc, *msuc; /* -> result and its msu */
michael@0	3266	Int msudigs; /* digits in res msu */
michael@0	3267	#if DECCHECK
michael@0	3268	if (decCheckOperands(res, lhs, rhs, set)) return res;
michael@0	3269	#endif
michael@0	3270
michael@0	3271	if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
michael@0	3272	|| rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
michael@0	3273	decStatus(res, DEC_Invalid_operation, set);
michael@0	3274	return res;
michael@0	3275	}
michael@0	3276	/* operands are valid */
michael@0	3277	ua=lhs->lsu; /* bottom-up */
michael@0	3278	ub=rhs->lsu; /* .. */
michael@0	3279	uc=res->lsu; /* .. */
michael@0	3280	msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */
michael@0	3281	msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */
michael@0	3282	msuc=uc+D2U(set->digits)-1; /* -> msu of result */
michael@0	3283	msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */
michael@0	3284	for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */
michael@0	3285	Unit a, b; /* extract units */
michael@0	3286	if (ua>msua) a=0;
michael@0	3287	else a=*ua;
michael@0	3288	if (ub>msub) b=0;
michael@0	3289	else b=*ub;
michael@0	3290	*uc=0; /* can now write back */
michael@0	3291	if (a|b) { /* maybe 1 bits to examine */
michael@0	3292	Int i, j;
michael@0	3293	/* This loop could be unrolled and/or use BIN2BCD tables */
michael@0	3294	for (i=0; i<DECDPUN; i++) {
michael@0	3295	if ((a^b)&1) *uc=*uc+(Unit)powers[i]; /* effect XOR */
michael@0	3296	j=a%10;
michael@0	3297	a=a/10;
michael@0	3298	j|=b%10;
michael@0	3299	b=b/10;
michael@0	3300	if (j>1) {
michael@0	3301	decStatus(res, DEC_Invalid_operation, set);
michael@0	3302	return res;
michael@0	3303	}
michael@0	3304	if (uc==msuc && i==msudigs-1) break; /* just did final digit */
michael@0	3305	} /* each digit */
michael@0	3306	} /* non-zero */
michael@0	3307	} /* each unit */
michael@0	3308	/* [here uc-1 is the msu of the result] */
michael@0	3309	res->digits=decGetDigits(res->lsu, uc-res->lsu);
michael@0	3310	res->exponent=0; /* integer */
michael@0	3311	res->bits=0; /* sign=0 */
michael@0	3312	return res; /* [no status to set] */
michael@0	3313	} /* decNumberXor */
michael@0	3314
michael@0	3315
michael@0	3316	/* ================================================================== */
michael@0	3317	/* Utility routines */
michael@0	3318	/* ================================================================== */
michael@0	3319
michael@0	3320	/* ------------------------------------------------------------------ */
michael@0	3321	/* decNumberClass -- return the decClass of a decNumber */
michael@0	3322	/* dn -- the decNumber to test */
michael@0	3323	/* set -- the context to use for Emin */
michael@0	3324	/* returns the decClass enum */
michael@0	3325	/* ------------------------------------------------------------------ */
michael@0	3326	enum decClass uprv_decNumberClass(const decNumber *dn, decContext *set) {
michael@0	3327	if (decNumberIsSpecial(dn)) {
michael@0	3328	if (decNumberIsQNaN(dn)) return DEC_CLASS_QNAN;
michael@0	3329	if (decNumberIsSNaN(dn)) return DEC_CLASS_SNAN;
michael@0	3330	/* must be an infinity */
michael@0	3331	if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_INF;
michael@0	3332	return DEC_CLASS_POS_INF;
michael@0	3333	}
michael@0	3334	/* is finite */
michael@0	3335	if (uprv_decNumberIsNormal(dn, set)) { /* most common */
michael@0	3336	if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_NORMAL;
michael@0	3337	return DEC_CLASS_POS_NORMAL;
michael@0	3338	}
michael@0	3339	/* is subnormal or zero */
michael@0	3340	if (decNumberIsZero(dn)) { /* most common */
michael@0	3341	if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_ZERO;
michael@0	3342	return DEC_CLASS_POS_ZERO;
michael@0	3343	}
michael@0	3344	if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_SUBNORMAL;
michael@0	3345	return DEC_CLASS_POS_SUBNORMAL;
michael@0	3346	} /* decNumberClass */
michael@0	3347
michael@0	3348	/* ------------------------------------------------------------------ */
michael@0	3349	/* decNumberClassToString -- convert decClass to a string */
michael@0	3350	/* */
michael@0	3351	/* eclass is a valid decClass */
michael@0	3352	/* returns a constant string describing the class (max 13+1 chars) */
michael@0	3353	/* ------------------------------------------------------------------ */
michael@0	3354	const char *uprv_decNumberClassToString(enum decClass eclass) {
michael@0	3355	if (eclass==DEC_CLASS_POS_NORMAL) return DEC_ClassString_PN;
michael@0	3356	if (eclass==DEC_CLASS_NEG_NORMAL) return DEC_ClassString_NN;
michael@0	3357	if (eclass==DEC_CLASS_POS_ZERO) return DEC_ClassString_PZ;
michael@0	3358	if (eclass==DEC_CLASS_NEG_ZERO) return DEC_ClassString_NZ;
michael@0	3359	if (eclass==DEC_CLASS_POS_SUBNORMAL) return DEC_ClassString_PS;
michael@0	3360	if (eclass==DEC_CLASS_NEG_SUBNORMAL) return DEC_ClassString_NS;
michael@0	3361	if (eclass==DEC_CLASS_POS_INF) return DEC_ClassString_PI;
michael@0	3362	if (eclass==DEC_CLASS_NEG_INF) return DEC_ClassString_NI;
michael@0	3363	if (eclass==DEC_CLASS_QNAN) return DEC_ClassString_QN;
michael@0	3364	if (eclass==DEC_CLASS_SNAN) return DEC_ClassString_SN;
michael@0	3365	return DEC_ClassString_UN; /* Unknown */
michael@0	3366	} /* decNumberClassToString */
michael@0	3367
michael@0	3368	/* ------------------------------------------------------------------ */
michael@0	3369	/* decNumberCopy -- copy a number */
michael@0	3370	/* */
michael@0	3371	/* dest is the target decNumber */
michael@0	3372	/* src is the source decNumber */
michael@0	3373	/* returns dest */
michael@0	3374	/* */
michael@0	3375	/* (dest==src is allowed and is a no-op) */
michael@0	3376	/* All fields are updated as required. This is a utility operation, */
michael@0	3377	/* so special values are unchanged and no error is possible. */
michael@0	3378	/* ------------------------------------------------------------------ */
michael@0	3379	U_CAPI decNumber * U_EXPORT2 uprv_decNumberCopy(decNumber *dest, const decNumber *src) {
michael@0	3380
michael@0	3381	#if DECCHECK
michael@0	3382	if (src==NULL) return uprv_decNumberZero(dest);
michael@0	3383	#endif
michael@0	3384
michael@0	3385	if (dest==src) return dest; /* no copy required */
michael@0	3386
michael@0	3387	/* Use explicit assignments here as structure assignment could copy */
michael@0	3388	/* more than just the lsu (for small DECDPUN). This would not affect */
michael@0	3389	/* the value of the results, but could disturb test harness spill */
michael@0	3390	/* checking. */
michael@0	3391	dest->bits=src->bits;
michael@0	3392	dest->exponent=src->exponent;
michael@0	3393	dest->digits=src->digits;
michael@0	3394	dest->lsu[0]=src->lsu[0];
michael@0	3395	if (src->digits>DECDPUN) { /* more Units to come */
michael@0	3396	const Unit *smsup, *s; /* work */
michael@0	3397	Unit *d; /* .. */
michael@0	3398	/* memcpy for the remaining Units would be safe as they cannot */
michael@0	3399	/* overlap. However, this explicit loop is faster in short cases. */
michael@0	3400	d=dest->lsu+1; /* -> first destination */
michael@0	3401	smsup=src->lsu+D2U(src->digits); /* -> source msu+1 */
michael@0	3402	for (s=src->lsu+1; s<smsup; s++, d++) *d=*s;
michael@0	3403	}
michael@0	3404	return dest;
michael@0	3405	} /* decNumberCopy */
michael@0	3406
michael@0	3407	/* ------------------------------------------------------------------ */
michael@0	3408	/* decNumberCopyAbs -- quiet absolute value operator */
michael@0	3409	/* */
michael@0	3410	/* This sets C = abs(A) */
michael@0	3411	/* */
michael@0	3412	/* res is C, the result. C may be A */
michael@0	3413	/* rhs is A */
michael@0	3414	/* */
michael@0	3415	/* C must have space for set->digits digits. */
michael@0	3416	/* No exception or error can occur; this is a quiet bitwise operation.*/
michael@0	3417	/* See also decNumberAbs for a checking version of this. */
michael@0	3418	/* ------------------------------------------------------------------ */
michael@0	3419	U_CAPI decNumber * U_EXPORT2 uprv_decNumberCopyAbs(decNumber *res, const decNumber *rhs) {
michael@0	3420	#if DECCHECK
michael@0	3421	if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
michael@0	3422	#endif
michael@0	3423	uprv_decNumberCopy(res, rhs);
michael@0	3424	res->bits&=~DECNEG; /* turn off sign */
michael@0	3425	return res;
michael@0	3426	} /* decNumberCopyAbs */
michael@0	3427
michael@0	3428	/* ------------------------------------------------------------------ */
michael@0	3429	/* decNumberCopyNegate -- quiet negate value operator */
michael@0	3430	/* */
michael@0	3431	/* This sets C = negate(A) */
michael@0	3432	/* */
michael@0	3433	/* res is C, the result. C may be A */
michael@0	3434	/* rhs is A */
michael@0	3435	/* */
michael@0	3436	/* C must have space for set->digits digits. */
michael@0	3437	/* No exception or error can occur; this is a quiet bitwise operation.*/
michael@0	3438	/* See also decNumberMinus for a checking version of this. */
michael@0	3439	/* ------------------------------------------------------------------ */
michael@0	3440	U_CAPI decNumber * U_EXPORT2 uprv_decNumberCopyNegate(decNumber *res, const decNumber *rhs) {
michael@0	3441	#if DECCHECK
michael@0	3442	if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
michael@0	3443	#endif
michael@0	3444	uprv_decNumberCopy(res, rhs);
michael@0	3445	res->bits^=DECNEG; /* invert the sign */
michael@0	3446	return res;
michael@0	3447	} /* decNumberCopyNegate */
michael@0	3448
michael@0	3449	/* ------------------------------------------------------------------ */
michael@0	3450	/* decNumberCopySign -- quiet copy and set sign operator */
michael@0	3451	/* */
michael@0	3452	/* This sets C = A with the sign of B */
michael@0	3453	/* */
michael@0	3454	/* res is C, the result. C may be A */
michael@0	3455	/* lhs is A */
michael@0	3456	/* rhs is B */
michael@0	3457	/* */
michael@0	3458	/* C must have space for set->digits digits. */
michael@0	3459	/* No exception or error can occur; this is a quiet bitwise operation.*/
michael@0	3460	/* ------------------------------------------------------------------ */
michael@0	3461	U_CAPI decNumber * U_EXPORT2 uprv_decNumberCopySign(decNumber *res, const decNumber *lhs,
michael@0	3462	const decNumber *rhs) {
michael@0	3463	uByte sign; /* rhs sign */
michael@0	3464	#if DECCHECK
michael@0	3465	if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
michael@0	3466	#endif
michael@0	3467	sign=rhs->bits & DECNEG; /* save sign bit */
michael@0	3468	uprv_decNumberCopy(res, lhs);
michael@0	3469	res->bits&=~DECNEG; /* clear the sign */
michael@0	3470	res->bits|=sign; /* set from rhs */
michael@0	3471	return res;
michael@0	3472	} /* decNumberCopySign */
michael@0	3473
michael@0	3474	/* ------------------------------------------------------------------ */
michael@0	3475	/* decNumberGetBCD -- get the coefficient in BCD8 */
michael@0	3476	/* dn is the source decNumber */
michael@0	3477	/* bcd is the uInt array that will receive dn->digits BCD bytes, */
michael@0	3478	/* most-significant at offset 0 */
michael@0	3479	/* returns bcd */
michael@0	3480	/* */
michael@0	3481	/* bcd must have at least dn->digits bytes. No error is possible; if */
michael@0	3482	/* dn is a NaN or Infinite, digits must be 1 and the coefficient 0. */
michael@0	3483	/* ------------------------------------------------------------------ */
michael@0	3484	U_CAPI uByte * U_EXPORT2 uprv_decNumberGetBCD(const decNumber *dn, uByte *bcd) {
michael@0	3485	uByte *ub=bcd+dn->digits-1; /* -> lsd */
michael@0	3486	const Unit *up=dn->lsu; /* Unit pointer, -> lsu */
michael@0	3487
michael@0	3488	#if DECDPUN==1 /* trivial simple copy */
michael@0	3489	for (; ub>=bcd; ub--, up++) *ub=*up;
michael@0	3490	#else /* chopping needed */
michael@0	3491	uInt u=*up; /* work */
michael@0	3492	uInt cut=DECDPUN; /* downcounter through unit */
michael@0	3493	for (; ub>=bcd; ub--) {
michael@0	3494	*ub=(uByte)(u%10); /* [*6554 trick inhibits, here] */
michael@0	3495	u=u/10;
michael@0	3496	cut--;
michael@0	3497	if (cut>0) continue; /* more in this unit */
michael@0	3498	up++;
michael@0	3499	u=*up;
michael@0	3500	cut=DECDPUN;
michael@0	3501	}
michael@0	3502	#endif
michael@0	3503	return bcd;
michael@0	3504	} /* decNumberGetBCD */
michael@0	3505
michael@0	3506	/* ------------------------------------------------------------------ */
michael@0	3507	/* decNumberSetBCD -- set (replace) the coefficient from BCD8 */
michael@0	3508	/* dn is the target decNumber */
michael@0	3509	/* bcd is the uInt array that will source n BCD bytes, most- */
michael@0	3510	/* significant at offset 0 */
michael@0	3511	/* n is the number of digits in the source BCD array (bcd) */
michael@0	3512	/* returns dn */
michael@0	3513	/* */
michael@0	3514	/* dn must have space for at least n digits. No error is possible; */
michael@0	3515	/* if dn is a NaN, or Infinite, or is to become a zero, n must be 1 */
michael@0	3516	/* and bcd[0] zero. */
michael@0	3517	/* ------------------------------------------------------------------ */
michael@0	3518	U_CAPI decNumber * U_EXPORT2 uprv_decNumberSetBCD(decNumber *dn, const uByte *bcd, uInt n) {
michael@0	3519	Unit *up=dn->lsu+D2U(dn->digits)-1; /* -> msu [target pointer] */
michael@0	3520	const uByte *ub=bcd; /* -> source msd */
michael@0	3521
michael@0	3522	#if DECDPUN==1 /* trivial simple copy */
michael@0	3523	for (; ub<bcd+n; ub++, up--) *up=*ub;
michael@0	3524	#else /* some assembly needed */
michael@0	3525	/* calculate how many digits in msu, and hence first cut */
michael@0	3526	Int cut=MSUDIGITS(n); /* [faster than remainder] */
michael@0	3527	for (;up>=dn->lsu; up--) { /* each Unit from msu */
michael@0	3528	*up=0; /* will take <=DECDPUN digits */
michael@0	3529	for (; cut>0; ub++, cut--) *up=X10(*up)+*ub;
michael@0	3530	cut=DECDPUN; /* next Unit has all digits */
michael@0	3531	}
michael@0	3532	#endif
michael@0	3533	dn->digits=n; /* set digit count */
michael@0	3534	return dn;
michael@0	3535	} /* decNumberSetBCD */
michael@0	3536
michael@0	3537	/* ------------------------------------------------------------------ */
michael@0	3538	/* decNumberIsNormal -- test normality of a decNumber */
michael@0	3539	/* dn is the decNumber to test */
michael@0	3540	/* set is the context to use for Emin */
michael@0	3541	/* returns 1 if |dn| is finite and >=Nmin, 0 otherwise */
michael@0	3542	/* ------------------------------------------------------------------ */
michael@0	3543	Int uprv_decNumberIsNormal(const decNumber *dn, decContext *set) {
michael@0	3544	Int ae; /* adjusted exponent */
michael@0	3545	#if DECCHECK
michael@0	3546	if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
michael@0	3547	#endif
michael@0	3548
michael@0	3549	if (decNumberIsSpecial(dn)) return 0; /* not finite */
michael@0	3550	if (decNumberIsZero(dn)) return 0; /* not non-zero */
michael@0	3551
michael@0	3552	ae=dn->exponent+dn->digits-1; /* adjusted exponent */
michael@0	3553	if (ae<set->emin) return 0; /* is subnormal */
michael@0	3554	return 1;
michael@0	3555	} /* decNumberIsNormal */
michael@0	3556
michael@0	3557	/* ------------------------------------------------------------------ */
michael@0	3558	/* decNumberIsSubnormal -- test subnormality of a decNumber */
michael@0	3559	/* dn is the decNumber to test */
michael@0	3560	/* set is the context to use for Emin */
michael@0	3561	/* returns 1 if |dn| is finite, non-zero, and <Nmin, 0 otherwise */
michael@0	3562	/* ------------------------------------------------------------------ */
michael@0	3563	Int uprv_decNumberIsSubnormal(const decNumber *dn, decContext *set) {
michael@0	3564	Int ae; /* adjusted exponent */
michael@0	3565	#if DECCHECK
michael@0	3566	if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
michael@0	3567	#endif
michael@0	3568
michael@0	3569	if (decNumberIsSpecial(dn)) return 0; /* not finite */
michael@0	3570	if (decNumberIsZero(dn)) return 0; /* not non-zero */
michael@0	3571
michael@0	3572	ae=dn->exponent+dn->digits-1; /* adjusted exponent */
michael@0	3573	if (ae<set->emin) return 1; /* is subnormal */
michael@0	3574	return 0;
michael@0	3575	} /* decNumberIsSubnormal */
michael@0	3576
michael@0	3577	/* ------------------------------------------------------------------ */
michael@0	3578	/* decNumberTrim -- remove insignificant zeros */
michael@0	3579	/* */
michael@0	3580	/* dn is the number to trim */
michael@0	3581	/* returns dn */
michael@0	3582	/* */
michael@0	3583	/* All fields are updated as required. This is a utility operation, */
michael@0	3584	/* so special values are unchanged and no error is possible. The */
michael@0	3585	/* zeros are removed unconditionally. */
michael@0	3586	/* ------------------------------------------------------------------ */
michael@0	3587	U_CAPI decNumber * U_EXPORT2 uprv_decNumberTrim(decNumber *dn) {
michael@0	3588	Int dropped; /* work */
michael@0	3589	decContext set; /* .. */
michael@0	3590	#if DECCHECK
michael@0	3591	if (decCheckOperands(DECUNRESU, DECUNUSED, dn, DECUNCONT)) return dn;
michael@0	3592	#endif
michael@0	3593	uprv_decContextDefault(&set, DEC_INIT_BASE); /* clamp=0 */
michael@0	3594	return decTrim(dn, &set, 0, 1, &dropped);
michael@0	3595	} /* decNumberTrim */
michael@0	3596
michael@0	3597	/* ------------------------------------------------------------------ */
michael@0	3598	/* decNumberVersion -- return the name and version of this module */
michael@0	3599	/* */
michael@0	3600	/* No error is possible. */
michael@0	3601	/* ------------------------------------------------------------------ */
michael@0	3602	const char * uprv_decNumberVersion(void) {
michael@0	3603	return DECVERSION;
michael@0	3604	} /* decNumberVersion */
michael@0	3605
michael@0	3606	/* ------------------------------------------------------------------ */
michael@0	3607	/* decNumberZero -- set a number to 0 */
michael@0	3608	/* */
michael@0	3609	/* dn is the number to set, with space for one digit */
michael@0	3610	/* returns dn */
michael@0	3611	/* */
michael@0	3612	/* No error is possible. */
michael@0	3613	/* ------------------------------------------------------------------ */
michael@0	3614	/* Memset is not used as it is much slower in some environments. */
michael@0	3615	U_CAPI decNumber * U_EXPORT2 uprv_decNumberZero(decNumber *dn) {
michael@0	3616
michael@0	3617	#if DECCHECK
michael@0	3618	if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn;
michael@0	3619	#endif
michael@0	3620
michael@0	3621	dn->bits=0;
michael@0	3622	dn->exponent=0;
michael@0	3623	dn->digits=1;
michael@0	3624	dn->lsu[0]=0;
michael@0	3625	return dn;
michael@0	3626	} /* decNumberZero */
michael@0	3627
michael@0	3628	/* ================================================================== */
michael@0	3629	/* Local routines */
michael@0	3630	/* ================================================================== */
michael@0	3631
michael@0	3632	/* ------------------------------------------------------------------ */
michael@0	3633	/* decToString -- lay out a number into a string */
michael@0	3634	/* */
michael@0	3635	/* dn is the number to lay out */
michael@0	3636	/* string is where to lay out the number */
michael@0	3637	/* eng is 1 if Engineering, 0 if Scientific */
michael@0	3638	/* */
michael@0	3639	/* string must be at least dn->digits+14 characters long */
michael@0	3640	/* No error is possible. */
michael@0	3641	/* */
michael@0	3642	/* Note that this routine can generate a -0 or 0.000. These are */
michael@0	3643	/* never generated in subset to-number or arithmetic, but can occur */
michael@0	3644	/* in non-subset arithmetic (e.g., -1*0 or 1.234-1.234). */
michael@0	3645	/* ------------------------------------------------------------------ */
michael@0	3646	/* If DECCHECK is enabled the string "?" is returned if a number is */
michael@0	3647	/* invalid. */
michael@0	3648	static void decToString(const decNumber *dn, char *string, Flag eng) {
michael@0	3649	Int exp=dn->exponent; /* local copy */
michael@0	3650	Int e; /* E-part value */
michael@0	3651	Int pre; /* digits before the '.' */
michael@0	3652	Int cut; /* for counting digits in a Unit */
michael@0	3653	char *c=string; /* work [output pointer] */
michael@0	3654	const Unit *up=dn->lsu+D2U(dn->digits)-1; /* -> msu [input pointer] */
michael@0	3655	uInt u, pow; /* work */
michael@0	3656
michael@0	3657	#if DECCHECK
michael@0	3658	if (decCheckOperands(DECUNRESU, dn, DECUNUSED, DECUNCONT)) {
michael@0	3659	strcpy(string, "?");
michael@0	3660	return;}
michael@0	3661	#endif
michael@0	3662
michael@0	3663	if (decNumberIsNegative(dn)) { /* Negatives get a minus */
michael@0	3664	*c='-';
michael@0	3665	c++;
michael@0	3666	}
michael@0	3667	if (dn->bits&DECSPECIAL) { /* Is a special value */
michael@0	3668	if (decNumberIsInfinite(dn)) {
michael@0	3669	strcpy(c, "Inf");
michael@0	3670	strcpy(c+3, "inity");
michael@0	3671	return;}
michael@0	3672	/* a NaN */
michael@0	3673	if (dn->bits&DECSNAN) { /* signalling NaN */
michael@0	3674	*c='s';
michael@0	3675	c++;
michael@0	3676	}
michael@0	3677	strcpy(c, "NaN");
michael@0	3678	c+=3; /* step past */
michael@0	3679	/* if not a clean non-zero coefficient, that's all there is in a */
michael@0	3680	/* NaN string */
michael@0	3681	if (exp!=0 || (*dn->lsu==0 && dn->digits==1)) return;
michael@0	3682	/* [drop through to add integer] */
michael@0	3683	}
michael@0	3684
michael@0	3685	/* calculate how many digits in msu, and hence first cut */
michael@0	3686	cut=MSUDIGITS(dn->digits); /* [faster than remainder] */
michael@0	3687	cut--; /* power of ten for digit */
michael@0	3688
michael@0	3689	if (exp==0) { /* simple integer [common fastpath] */
michael@0	3690	for (;up>=dn->lsu; up--) { /* each Unit from msu */
michael@0	3691	u=*up; /* contains DECDPUN digits to lay out */
michael@0	3692	for (; cut>=0; c++, cut--) TODIGIT(u, cut, c, pow);
michael@0	3693	cut=DECDPUN-1; /* next Unit has all digits */
michael@0	3694	}
michael@0	3695	*c='\0'; /* terminate the string */
michael@0	3696	return;}
michael@0	3697
michael@0	3698	/* non-0 exponent -- assume plain form */
michael@0	3699	pre=dn->digits+exp; /* digits before '.' */
michael@0	3700	e=0; /* no E */
michael@0	3701	if ((exp>0) || (pre<-5)) { /* need exponential form */
michael@0	3702	e=exp+dn->digits-1; /* calculate E value */
michael@0	3703	pre=1; /* assume one digit before '.' */
michael@0	3704	if (eng && (e!=0)) { /* engineering: may need to adjust */
michael@0	3705	Int adj; /* adjustment */
michael@0	3706	/* The C remainder operator is undefined for negative numbers, so */
michael@0	3707	/* a positive remainder calculation must be used here */
michael@0	3708	if (e<0) {
michael@0	3709	adj=(-e)%3;
michael@0	3710	if (adj!=0) adj=3-adj;
michael@0	3711	}
michael@0	3712	else { /* e>0 */
michael@0	3713	adj=e%3;
michael@0	3714	}
michael@0	3715	e=e-adj;
michael@0	3716	/* if dealing with zero still produce an exponent which is a */
michael@0	3717	/* multiple of three, as expected, but there will only be the */
michael@0	3718	/* one zero before the E, still. Otherwise note the padding. */
michael@0	3719	if (!ISZERO(dn)) pre+=adj;
michael@0	3720	else { /* is zero */
michael@0	3721	if (adj!=0) { /* 0.00Esnn needed */
michael@0	3722	e=e+3;
michael@0	3723	pre=-(2-adj);
michael@0	3724	}
michael@0	3725	} /* zero */
michael@0	3726	} /* eng */
michael@0	3727	} /* need exponent */
michael@0	3728
michael@0	3729	/* lay out the digits of the coefficient, adding 0s and . as needed */
michael@0	3730	u=*up;
michael@0	3731	if (pre>0) { /* xxx.xxx or xx00 (engineering) form */
michael@0	3732	Int n=pre;
michael@0	3733	for (; pre>0; pre--, c++, cut--) {
michael@0	3734	if (cut<0) { /* need new Unit */
michael@0	3735	if (up==dn->lsu) break; /* out of input digits (pre>digits) */
michael@0	3736	up--;
michael@0	3737	cut=DECDPUN-1;
michael@0	3738	u=*up;
michael@0	3739	}
michael@0	3740	TODIGIT(u, cut, c, pow);
michael@0	3741	}
michael@0	3742	if (n<dn->digits) { /* more to come, after '.' */
michael@0	3743	*c='.'; c++;
michael@0	3744	for (;; c++, cut--) {
michael@0	3745	if (cut<0) { /* need new Unit */
michael@0	3746	if (up==dn->lsu) break; /* out of input digits */
michael@0	3747	up--;
michael@0	3748	cut=DECDPUN-1;
michael@0	3749	u=*up;
michael@0	3750	}
michael@0	3751	TODIGIT(u, cut, c, pow);
michael@0	3752	}
michael@0	3753	}
michael@0	3754	else for (; pre>0; pre--, c++) *c='0'; /* 0 padding (for engineering) needed */
michael@0	3755	}
michael@0	3756	else { /* 0.xxx or 0.000xxx form */
michael@0	3757	*c='0'; c++;
michael@0	3758	*c='.'; c++;
michael@0	3759	for (; pre<0; pre++, c++) *c='0'; /* add any 0's after '.' */
michael@0	3760	for (; ; c++, cut--) {
michael@0	3761	if (cut<0) { /* need new Unit */
michael@0	3762	if (up==dn->lsu) break; /* out of input digits */
michael@0	3763	up--;
michael@0	3764	cut=DECDPUN-1;
michael@0	3765	u=*up;
michael@0	3766	}
michael@0	3767	TODIGIT(u, cut, c, pow);
michael@0	3768	}
michael@0	3769	}
michael@0	3770
michael@0	3771	/* Finally add the E-part, if needed. It will never be 0, has a
michael@0	3772	base maximum and minimum of +999999999 through -999999999, but
michael@0	3773	could range down to -1999999998 for anormal numbers */
michael@0	3774	if (e!=0) {
michael@0	3775	Flag had=0; /* 1=had non-zero */
michael@0	3776	*c='E'; c++;
michael@0	3777	*c='+'; c++; /* assume positive */
michael@0	3778	u=e; /* .. */
michael@0	3779	if (e<0) {
michael@0	3780	*(c-1)='-'; /* oops, need - */
michael@0	3781	u=-e; /* uInt, please */
michael@0	3782	}
michael@0	3783	/* lay out the exponent [_itoa or equivalent is not ANSI C] */
michael@0	3784	for (cut=9; cut>=0; cut--) {
michael@0	3785	TODIGIT(u, cut, c, pow);
michael@0	3786	if (*c=='0' && !had) continue; /* skip leading zeros */
michael@0	3787	had=1; /* had non-0 */
michael@0	3788	c++; /* step for next */
michael@0	3789	} /* cut */
michael@0	3790	}
michael@0	3791	*c='\0'; /* terminate the string (all paths) */
michael@0	3792	return;
michael@0	3793	} /* decToString */
michael@0	3794
michael@0	3795	/* ------------------------------------------------------------------ */
michael@0	3796	/* decAddOp -- add/subtract operation */
michael@0	3797	/* */
michael@0	3798	/* This computes C = A + B */
michael@0	3799	/* */
michael@0	3800	/* res is C, the result. C may be A and/or B (e.g., X=X+X) */
michael@0	3801	/* lhs is A */
michael@0	3802	/* rhs is B */
michael@0	3803	/* set is the context */
michael@0	3804	/* negate is DECNEG if rhs should be negated, or 0 otherwise */
michael@0	3805	/* status accumulates status for the caller */
michael@0	3806	/* */
michael@0	3807	/* C must have space for set->digits digits. */
michael@0	3808	/* Inexact in status must be 0 for correct Exact zero sign in result */
michael@0	3809	/* ------------------------------------------------------------------ */
michael@0	3810	/* If possible, the coefficient is calculated directly into C. */
michael@0	3811	/* However, if: */
michael@0	3812	/* -- a digits+1 calculation is needed because the numbers are */
michael@0	3813	/* unaligned and span more than set->digits digits */
michael@0	3814	/* -- a carry to digits+1 digits looks possible */
michael@0	3815	/* -- C is the same as A or B, and the result would destructively */
michael@0	3816	/* overlap the A or B coefficient */
michael@0	3817	/* then the result must be calculated into a temporary buffer. In */
michael@0	3818	/* this case a local (stack) buffer is used if possible, and only if */
michael@0	3819	/* too long for that does malloc become the final resort. */
michael@0	3820	/* */
michael@0	3821	/* Misalignment is handled as follows: */
michael@0	3822	/* Apad: (AExp>BExp) Swap operands and proceed as for BExp>AExp. */
michael@0	3823	/* BPad: Apply the padding by a combination of shifting (whole */
michael@0	3824	/* units) and multiplication (part units). */
michael@0	3825	/* */
michael@0	3826	/* Addition, especially x=x+1, is speed-critical. */
michael@0	3827	/* The static buffer is larger than might be expected to allow for */
michael@0	3828	/* calls from higher-level funtions (notable exp). */
michael@0	3829	/* ------------------------------------------------------------------ */
michael@0	3830	static decNumber * decAddOp(decNumber *res, const decNumber *lhs,
michael@0	3831	const decNumber *rhs, decContext *set,
michael@0	3832	uByte negate, uInt *status) {
michael@0	3833	#if DECSUBSET
michael@0	3834	decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */
michael@0	3835	decNumber *allocrhs=NULL; /* .., rhs */
michael@0	3836	#endif
michael@0	3837	Int rhsshift; /* working shift (in Units) */
michael@0	3838	Int maxdigits; /* longest logical length */
michael@0	3839	Int mult; /* multiplier */
michael@0	3840	Int residue; /* rounding accumulator */
michael@0	3841	uByte bits; /* result bits */
michael@0	3842	Flag diffsign; /* non-0 if arguments have different sign */
michael@0	3843	Unit *acc; /* accumulator for result */
michael@0	3844	Unit accbuff[SD2U(DECBUFFER*2+20)]; /* local buffer [*2+20 reduces many */
michael@0	3845	/* allocations when called from */
michael@0	3846	/* other operations, notable exp] */
michael@0	3847	Unit *allocacc=NULL; /* -> allocated acc buffer, iff allocated */
michael@0	3848	Int reqdigits=set->digits; /* local copy; requested DIGITS */
michael@0	3849	Int padding; /* work */
michael@0	3850
michael@0	3851	#if DECCHECK
michael@0	3852	if (decCheckOperands(res, lhs, rhs, set)) return res;
michael@0	3853	#endif
michael@0	3854
michael@0	3855	do { /* protect allocated storage */
michael@0	3856	#if DECSUBSET
michael@0	3857	if (!set->extended) {
michael@0	3858	/* reduce operands and set lostDigits status, as needed */
michael@0	3859	if (lhs->digits>reqdigits) {
michael@0	3860	alloclhs=decRoundOperand(lhs, set, status);
michael@0	3861	if (alloclhs==NULL) break;
michael@0	3862	lhs=alloclhs;
michael@0	3863	}
michael@0	3864	if (rhs->digits>reqdigits) {
michael@0	3865	allocrhs=decRoundOperand(rhs, set, status);
michael@0	3866	if (allocrhs==NULL) break;
michael@0	3867	rhs=allocrhs;
michael@0	3868	}
michael@0	3869	}
michael@0	3870	#endif
michael@0	3871	/* [following code does not require input rounding] */
michael@0	3872
michael@0	3873	/* note whether signs differ [used all paths] */
michael@0	3874	diffsign=(Flag)((lhs->bits^rhs->bits^negate)&DECNEG);
michael@0	3875
michael@0	3876	/* handle infinities and NaNs */
michael@0	3877	if (SPECIALARGS) { /* a special bit set */
michael@0	3878	if (SPECIALARGS & (DECSNAN | DECNAN)) /* a NaN */
michael@0	3879	decNaNs(res, lhs, rhs, set, status);
michael@0	3880	else { /* one or two infinities */
michael@0	3881	if (decNumberIsInfinite(lhs)) { /* LHS is infinity */
michael@0	3882	/* two infinities with different signs is invalid */
michael@0	3883	if (decNumberIsInfinite(rhs) && diffsign) {
michael@0	3884	*status|=DEC_Invalid_operation;
michael@0	3885	break;
michael@0	3886	}
michael@0	3887	bits=lhs->bits & DECNEG; /* get sign from LHS */
michael@0	3888	}
michael@0	3889	else bits=(rhs->bits^negate) & DECNEG;/* RHS must be Infinity */
michael@0	3890	bits|=DECINF;
michael@0	3891	uprv_decNumberZero(res);
michael@0	3892	res->bits=bits; /* set +/- infinity */
michael@0	3893	} /* an infinity */
michael@0	3894	break;
michael@0	3895	}
michael@0	3896
michael@0	3897	/* Quick exit for add 0s; return the non-0, modified as need be */
michael@0	3898	if (ISZERO(lhs)) {
michael@0	3899	Int adjust; /* work */
michael@0	3900	Int lexp=lhs->exponent; /* save in case LHS==RES */
michael@0	3901	bits=lhs->bits; /* .. */
michael@0	3902	residue=0; /* clear accumulator */
michael@0	3903	decCopyFit(res, rhs, set, &residue, status); /* copy (as needed) */
michael@0	3904	res->bits^=negate; /* flip if rhs was negated */
michael@0	3905	#if DECSUBSET
michael@0	3906	if (set->extended) { /* exponents on zeros count */
michael@0	3907	#endif
michael@0	3908	/* exponent will be the lower of the two */
michael@0	3909	adjust=lexp-res->exponent; /* adjustment needed [if -ve] */
michael@0	3910	if (ISZERO(res)) { /* both 0: special IEEE 754 rules */
michael@0	3911	if (adjust<0) res->exponent=lexp; /* set exponent */
michael@0	3912	/* 0-0 gives +0 unless rounding to -infinity, and -0-0 gives -0 */
michael@0	3913	if (diffsign) {
michael@0	3914	if (set->round!=DEC_ROUND_FLOOR) res->bits=0;
michael@0	3915	else res->bits=DECNEG; /* preserve 0 sign */
michael@0	3916	}
michael@0	3917	}
michael@0	3918	else { /* non-0 res */
michael@0	3919	if (adjust<0) { /* 0-padding needed */
michael@0	3920	if ((res->digits-adjust)>set->digits) {
michael@0	3921	adjust=res->digits-set->digits; /* to fit exactly */
michael@0	3922	*status|=DEC_Rounded; /* [but exact] */
michael@0	3923	}
michael@0	3924	res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
michael@0	3925	res->exponent+=adjust; /* set the exponent. */
michael@0	3926	}
michael@0	3927	} /* non-0 res */
michael@0	3928	#if DECSUBSET
michael@0	3929	} /* extended */
michael@0	3930	#endif
michael@0	3931	decFinish(res, set, &residue, status); /* clean and finalize */
michael@0	3932	break;}
michael@0	3933
michael@0	3934	if (ISZERO(rhs)) { /* [lhs is non-zero] */
michael@0	3935	Int adjust; /* work */
michael@0	3936	Int rexp=rhs->exponent; /* save in case RHS==RES */
michael@0	3937	bits=rhs->bits; /* be clean */
michael@0	3938	residue=0; /* clear accumulator */
michael@0	3939	decCopyFit(res, lhs, set, &residue, status); /* copy (as needed) */
michael@0	3940	#if DECSUBSET
michael@0	3941	if (set->extended) { /* exponents on zeros count */
michael@0	3942	#endif
michael@0	3943	/* exponent will be the lower of the two */
michael@0	3944	/* [0-0 case handled above] */
michael@0	3945	adjust=rexp-res->exponent; /* adjustment needed [if -ve] */
michael@0	3946	if (adjust<0) { /* 0-padding needed */
michael@0	3947	if ((res->digits-adjust)>set->digits) {
michael@0	3948	adjust=res->digits-set->digits; /* to fit exactly */
michael@0	3949	*status|=DEC_Rounded; /* [but exact] */
michael@0	3950	}
michael@0	3951	res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
michael@0	3952	res->exponent+=adjust; /* set the exponent. */
michael@0	3953	}
michael@0	3954	#if DECSUBSET
michael@0	3955	} /* extended */
michael@0	3956	#endif
michael@0	3957	decFinish(res, set, &residue, status); /* clean and finalize */
michael@0	3958	break;}
michael@0	3959
michael@0	3960	/* [NB: both fastpath and mainpath code below assume these cases */
michael@0	3961	/* (notably 0-0) have already been handled] */
michael@0	3962
michael@0	3963	/* calculate the padding needed to align the operands */
michael@0	3964	padding=rhs->exponent-lhs->exponent;
michael@0	3965
michael@0	3966	/* Fastpath cases where the numbers are aligned and normal, the RHS */
michael@0	3967	/* is all in one unit, no operand rounding is needed, and no carry, */
michael@0	3968	/* lengthening, or borrow is needed */
michael@0	3969	if (padding==0
michael@0	3970	&& rhs->digits<=DECDPUN
michael@0	3971	&& rhs->exponent>=set->emin /* [some normals drop through] */
michael@0	3972	&& rhs->exponent<=set->emax-set->digits+1 /* [could clamp] */
michael@0	3973	&& rhs->digits<=reqdigits
michael@0	3974	&& lhs->digits<=reqdigits) {
michael@0	3975	Int partial=*lhs->lsu;
michael@0	3976	if (!diffsign) { /* adding */
michael@0	3977	partial+=*rhs->lsu;
michael@0	3978	if ((partial<=DECDPUNMAX) /* result fits in unit */
michael@0	3979	&& (lhs->digits>=DECDPUN || /* .. and no digits-count change */
michael@0	3980	partial<(Int)powers[lhs->digits])) { /* .. */
michael@0	3981	if (res!=lhs) uprv_decNumberCopy(res, lhs); /* not in place */
michael@0	3982	*res->lsu=(Unit)partial; /* [copy could have overwritten RHS] */
michael@0	3983	break;
michael@0	3984	}
michael@0	3985	/* else drop out for careful add */
michael@0	3986	}
michael@0	3987	else { /* signs differ */
michael@0	3988	partial-=*rhs->lsu;
michael@0	3989	if (partial>0) { /* no borrow needed, and non-0 result */
michael@0	3990	if (res!=lhs) uprv_decNumberCopy(res, lhs); /* not in place */
michael@0	3991	*res->lsu=(Unit)partial;
michael@0	3992	/* this could have reduced digits [but result>0] */
michael@0	3993	res->digits=decGetDigits(res->lsu, D2U(res->digits));
michael@0	3994	break;
michael@0	3995	}
michael@0	3996	/* else drop out for careful subtract */
michael@0	3997	}
michael@0	3998	}
michael@0	3999
michael@0	4000	/* Now align (pad) the lhs or rhs so they can be added or */
michael@0	4001	/* subtracted, as necessary. If one number is much larger than */
michael@0	4002	/* the other (that is, if in plain form there is a least one */
michael@0	4003	/* digit between the lowest digit of one and the highest of the */
michael@0	4004	/* other) padding with up to DIGITS-1 trailing zeros may be */
michael@0	4005	/* needed; then apply rounding (as exotic rounding modes may be */
michael@0	4006	/* affected by the residue). */
michael@0	4007	rhsshift=0; /* rhs shift to left (padding) in Units */
michael@0	4008	bits=lhs->bits; /* assume sign is that of LHS */
michael@0	4009	mult=1; /* likely multiplier */
michael@0	4010
michael@0	4011	/* [if padding==0 the operands are aligned; no padding is needed] */
michael@0	4012	if (padding!=0) {
michael@0	4013	/* some padding needed; always pad the RHS, as any required */
michael@0	4014	/* padding can then be effected by a simple combination of */
michael@0	4015	/* shifts and a multiply */
michael@0	4016	Flag swapped=0;
michael@0	4017	if (padding<0) { /* LHS needs the padding */
michael@0	4018	const decNumber *t;
michael@0	4019	padding=-padding; /* will be +ve */
michael@0	4020	bits=(uByte)(rhs->bits^negate); /* assumed sign is now that of RHS */
michael@0	4021	t=lhs; lhs=rhs; rhs=t;
michael@0	4022	swapped=1;
michael@0	4023	}
michael@0	4024
michael@0	4025	/* If, after pad, rhs would be longer than lhs by digits+1 or */
michael@0	4026	/* more then lhs cannot affect the answer, except as a residue, */
michael@0	4027	/* so only need to pad up to a length of DIGITS+1. */
michael@0	4028	if (rhs->digits+padding > lhs->digits+reqdigits+1) {
michael@0	4029	/* The RHS is sufficient */
michael@0	4030	/* for residue use the relative sign indication... */
michael@0	4031	Int shift=reqdigits-rhs->digits; /* left shift needed */
michael@0	4032	residue=1; /* residue for rounding */
michael@0	4033	if (diffsign) residue=-residue; /* signs differ */
michael@0	4034	/* copy, shortening if necessary */
michael@0	4035	decCopyFit(res, rhs, set, &residue, status);
michael@0	4036	/* if it was already shorter, then need to pad with zeros */
michael@0	4037	if (shift>0) {
michael@0	4038	res->digits=decShiftToMost(res->lsu, res->digits, shift);
michael@0	4039	res->exponent-=shift; /* adjust the exponent. */
michael@0	4040	}
michael@0	4041	/* flip the result sign if unswapped and rhs was negated */
michael@0	4042	if (!swapped) res->bits^=negate;
michael@0	4043	decFinish(res, set, &residue, status); /* done */
michael@0	4044	break;}
michael@0	4045
michael@0	4046	/* LHS digits may affect result */
michael@0	4047	rhsshift=D2U(padding+1)-1; /* this much by Unit shift .. */
michael@0	4048	mult=powers[padding-(rhsshift*DECDPUN)]; /* .. this by multiplication */
michael@0	4049	} /* padding needed */
michael@0	4050
michael@0	4051	if (diffsign) mult=-mult; /* signs differ */
michael@0	4052
michael@0	4053	/* determine the longer operand */
michael@0	4054	maxdigits=rhs->digits+padding; /* virtual length of RHS */
michael@0	4055	if (lhs->digits>maxdigits) maxdigits=lhs->digits;
michael@0	4056
michael@0	4057	/* Decide on the result buffer to use; if possible place directly */
michael@0	4058	/* into result. */
michael@0	4059	acc=res->lsu; /* assume add direct to result */
michael@0	4060	/* If destructive overlap, or the number is too long, or a carry or */
michael@0	4061	/* borrow to DIGITS+1 might be possible, a buffer must be used. */
michael@0	4062	/* [Might be worth more sophisticated tests when maxdigits==reqdigits] */
michael@0	4063	if ((maxdigits>=reqdigits) /* is, or could be, too large */
michael@0	4064	|| (res==rhs && rhsshift>0)) { /* destructive overlap */
michael@0	4065	/* buffer needed, choose it; units for maxdigits digits will be */
michael@0	4066	/* needed, +1 Unit for carry or borrow */
michael@0	4067	Int need=D2U(maxdigits)+1;
michael@0	4068	acc=accbuff; /* assume use local buffer */
michael@0	4069	if (need*sizeof(Unit)>sizeof(accbuff)) {
michael@0	4070	/* printf("malloc add %ld %ld\n", need, sizeof(accbuff)); */
michael@0	4071	allocacc=(Unit *)malloc(need*sizeof(Unit));
michael@0	4072	if (allocacc==NULL) { /* hopeless -- abandon */
michael@0	4073	*status|=DEC_Insufficient_storage;
michael@0	4074	break;}
michael@0	4075	acc=allocacc;
michael@0	4076	}
michael@0	4077	}
michael@0	4078
michael@0	4079	res->bits=(uByte)(bits&DECNEG); /* it's now safe to overwrite.. */
michael@0	4080	res->exponent=lhs->exponent; /* .. operands (even if aliased) */
michael@0	4081
michael@0	4082	#if DECTRACE
michael@0	4083	decDumpAr('A', lhs->lsu, D2U(lhs->digits));
michael@0	4084	decDumpAr('B', rhs->lsu, D2U(rhs->digits));
michael@0	4085	printf(" :h: %ld %ld\n", rhsshift, mult);
michael@0	4086	#endif
michael@0	4087
michael@0	4088	/* add [A+B*m] or subtract [A+B*(-m)] */
michael@0	4089	U_ASSERT(rhs->digits > 0);
michael@0	4090	U_ASSERT(lhs->digits > 0);
michael@0	4091	res->digits=decUnitAddSub(lhs->lsu, D2U(lhs->digits),
michael@0	4092	rhs->lsu, D2U(rhs->digits),
michael@0	4093	rhsshift, acc, mult)
michael@0	4094	*DECDPUN; /* [units -> digits] */
michael@0	4095	if (res->digits<0) { /* borrowed... */
michael@0	4096	res->digits=-res->digits;
michael@0	4097	res->bits^=DECNEG; /* flip the sign */
michael@0	4098	}
michael@0	4099	#if DECTRACE
michael@0	4100	decDumpAr('+', acc, D2U(res->digits));
michael@0	4101	#endif
michael@0	4102
michael@0	4103	/* If a buffer was used the result must be copied back, possibly */
michael@0	4104	/* shortening. (If no buffer was used then the result must have */
michael@0	4105	/* fit, so can't need rounding and residue must be 0.) */
michael@0	4106	residue=0; /* clear accumulator */
michael@0	4107	if (acc!=res->lsu) {
michael@0	4108	#if DECSUBSET
michael@0	4109	if (set->extended) { /* round from first significant digit */
michael@0	4110	#endif
michael@0	4111	/* remove leading zeros that were added due to rounding up to */
michael@0	4112	/* integral Units -- before the test for rounding. */
michael@0	4113	if (res->digits>reqdigits)
michael@0	4114	res->digits=decGetDigits(acc, D2U(res->digits));
michael@0	4115	decSetCoeff(res, set, acc, res->digits, &residue, status);
michael@0	4116	#if DECSUBSET
michael@0	4117	}
michael@0	4118	else { /* subset arithmetic rounds from original significant digit */
michael@0	4119	/* May have an underestimate. This only occurs when both */
michael@0	4120	/* numbers fit in DECDPUN digits and are padding with a */
michael@0	4121	/* negative multiple (-10, -100...) and the top digit(s) become */
michael@0	4122	/* 0. (This only matters when using X3.274 rules where the */
michael@0	4123	/* leading zero could be included in the rounding.) */
michael@0	4124	if (res->digits<maxdigits) {
michael@0	4125	*(acc+D2U(res->digits))=0; /* ensure leading 0 is there */
michael@0	4126	res->digits=maxdigits;
michael@0	4127	}
michael@0	4128	else {
michael@0	4129	/* remove leading zeros that added due to rounding up to */
michael@0	4130	/* integral Units (but only those in excess of the original */
michael@0	4131	/* maxdigits length, unless extended) before test for rounding. */
michael@0	4132	if (res->digits>reqdigits) {
michael@0	4133	res->digits=decGetDigits(acc, D2U(res->digits));
michael@0	4134	if (res->digits<maxdigits) res->digits=maxdigits;
michael@0	4135	}
michael@0	4136	}
michael@0	4137	decSetCoeff(res, set, acc, res->digits, &residue, status);
michael@0	4138	/* Now apply rounding if needed before removing leading zeros. */
michael@0	4139	/* This is safe because subnormals are not a possibility */
michael@0	4140	if (residue!=0) {
michael@0	4141	decApplyRound(res, set, residue, status);
michael@0	4142	residue=0; /* did what needed to be done */
michael@0	4143	}
michael@0	4144	} /* subset */
michael@0	4145	#endif
michael@0	4146	} /* used buffer */
michael@0	4147
michael@0	4148	/* strip leading zeros [these were left on in case of subset subtract] */
michael@0	4149	res->digits=decGetDigits(res->lsu, D2U(res->digits));
michael@0	4150
michael@0	4151	/* apply checks and rounding */
michael@0	4152	decFinish(res, set, &residue, status);
michael@0	4153
michael@0	4154	/* "When the sum of two operands with opposite signs is exactly */
michael@0	4155	/* zero, the sign of that sum shall be '+' in all rounding modes */
michael@0	4156	/* except round toward -Infinity, in which mode that sign shall be */
michael@0	4157	/* '-'." [Subset zeros also never have '-', set by decFinish.] */
michael@0	4158	if (ISZERO(res) && diffsign
michael@0	4159	#if DECSUBSET
michael@0	4160	&& set->extended
michael@0	4161	#endif
michael@0	4162	&& (*status&DEC_Inexact)==0) {
michael@0	4163	if (set->round==DEC_ROUND_FLOOR) res->bits|=DECNEG; /* sign - */
michael@0	4164	else res->bits&=~DECNEG; /* sign + */
michael@0	4165	}
michael@0	4166	} while(0); /* end protected */
michael@0	4167
michael@0	4168	if (allocacc!=NULL) free(allocacc); /* drop any storage used */
michael@0	4169	#if DECSUBSET
michael@0	4170	if (allocrhs!=NULL) free(allocrhs); /* .. */
michael@0	4171	if (alloclhs!=NULL) free(alloclhs); /* .. */
michael@0	4172	#endif
michael@0	4173	return res;
michael@0	4174	} /* decAddOp */
michael@0	4175
michael@0	4176	/* ------------------------------------------------------------------ */
michael@0	4177	/* decDivideOp -- division operation */
michael@0	4178	/* */
michael@0	4179	/* This routine performs the calculations for all four division */
michael@0	4180	/* operators (divide, divideInteger, remainder, remainderNear). */
michael@0	4181	/* */
michael@0	4182	/* C=A op B */
michael@0	4183	/* */
michael@0	4184	/* res is C, the result. C may be A and/or B (e.g., X=X/X) */
michael@0	4185	/* lhs is A */
michael@0	4186	/* rhs is B */
michael@0	4187	/* set is the context */
michael@0	4188	/* op is DIVIDE, DIVIDEINT, REMAINDER, or REMNEAR respectively. */
michael@0	4189	/* status is the usual accumulator */
michael@0	4190	/* */
michael@0	4191	/* C must have space for set->digits digits. */
michael@0	4192	/* */
michael@0	4193	/* ------------------------------------------------------------------ */
michael@0	4194	/* The underlying algorithm of this routine is the same as in the */
michael@0	4195	/* 1981 S/370 implementation, that is, non-restoring long division */
michael@0	4196	/* with bi-unit (rather than bi-digit) estimation for each unit */
michael@0	4197	/* multiplier. In this pseudocode overview, complications for the */
michael@0	4198	/* Remainder operators and division residues for exact rounding are */
michael@0	4199	/* omitted for clarity. */
michael@0	4200	/* */
michael@0	4201	/* Prepare operands and handle special values */
michael@0	4202	/* Test for x/0 and then 0/x */
michael@0	4203	/* Exp =Exp1 - Exp2 */
michael@0	4204	/* Exp =Exp +len(var1) -len(var2) */
michael@0	4205	/* Sign=Sign1 * Sign2 */
michael@0	4206	/* Pad accumulator (Var1) to double-length with 0's (pad1) */
michael@0	4207	/* Pad Var2 to same length as Var1 */
michael@0	4208	/* msu2pair/plus=1st 2 or 1 units of var2, +1 to allow for round */
michael@0	4209	/* have=0 */
michael@0	4210	/* Do until (have=digits+1 OR residue=0) */
michael@0	4211	/* if exp<0 then if integer divide/residue then leave */
michael@0	4212	/* this_unit=0 */
michael@0	4213	/* Do forever */
michael@0	4214	/* compare numbers */
michael@0	4215	/* if <0 then leave inner_loop */
michael@0	4216	/* if =0 then (* quick exit without subtract *) do */
michael@0	4217	/* this_unit=this_unit+1; output this_unit */
michael@0	4218	/* leave outer_loop; end */
michael@0	4219	/* Compare lengths of numbers (mantissae): */
michael@0	4220	/* If same then tops2=msu2pair -- {units 1&2 of var2} */
michael@0	4221	/* else tops2=msu2plus -- {0, unit 1 of var2} */
michael@0	4222	/* tops1=first_unit_of_Var1*10**DECDPUN +second_unit_of_var1 */
michael@0	4223	/* mult=tops1/tops2 -- Good and safe guess at divisor */
michael@0	4224	/* if mult=0 then mult=1 */
michael@0	4225	/* this_unit=this_unit+mult */
michael@0	4226	/* subtract */
michael@0	4227	/* end inner_loop */
michael@0	4228	/* if have\=0 | this_unit\=0 then do */
michael@0	4229	/* output this_unit */
michael@0	4230	/* have=have+1; end */
michael@0	4231	/* var2=var2/10 */
michael@0	4232	/* exp=exp-1 */
michael@0	4233	/* end outer_loop */
michael@0	4234	/* exp=exp+1 -- set the proper exponent */
michael@0	4235	/* if have=0 then generate answer=0 */
michael@0	4236	/* Return (Result is defined by Var1) */
michael@0	4237	/* */
michael@0	4238	/* ------------------------------------------------------------------ */
michael@0	4239	/* Two working buffers are needed during the division; one (digits+ */
michael@0	4240	/* 1) to accumulate the result, and the other (up to 2*digits+1) for */
michael@0	4241	/* long subtractions. These are acc and var1 respectively. */
michael@0	4242	/* var1 is a copy of the lhs coefficient, var2 is the rhs coefficient.*/
michael@0	4243	/* The static buffers may be larger than might be expected to allow */
michael@0	4244	/* for calls from higher-level funtions (notable exp). */
michael@0	4245	/* ------------------------------------------------------------------ */
michael@0	4246	static decNumber * decDivideOp(decNumber *res,
michael@0	4247	const decNumber *lhs, const decNumber *rhs,
michael@0	4248	decContext *set, Flag op, uInt *status) {
michael@0	4249	#if DECSUBSET
michael@0	4250	decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */
michael@0	4251	decNumber *allocrhs=NULL; /* .., rhs */
michael@0	4252	#endif
michael@0	4253	Unit accbuff[SD2U(DECBUFFER+DECDPUN+10)]; /* local buffer */
michael@0	4254	Unit *acc=accbuff; /* -> accumulator array for result */
michael@0	4255	Unit *allocacc=NULL; /* -> allocated buffer, iff allocated */
michael@0	4256	Unit *accnext; /* -> where next digit will go */
michael@0	4257	Int acclength; /* length of acc needed [Units] */
michael@0	4258	Int accunits; /* count of units accumulated */
michael@0	4259	Int accdigits; /* count of digits accumulated */
michael@0	4260
michael@0	4261	Unit varbuff[SD2U(DECBUFFER*2+DECDPUN)]; /* buffer for var1 */
michael@0	4262	Unit *var1=varbuff; /* -> var1 array for long subtraction */
michael@0	4263	Unit *varalloc=NULL; /* -> allocated buffer, iff used */
michael@0	4264	Unit *msu1; /* -> msu of var1 */
michael@0	4265
michael@0	4266	const Unit *var2; /* -> var2 array */
michael@0	4267	const Unit *msu2; /* -> msu of var2 */
michael@0	4268	Int msu2plus; /* msu2 plus one [does not vary] */
michael@0	4269	eInt msu2pair; /* msu2 pair plus one [does not vary] */
michael@0	4270
michael@0	4271	Int var1units, var2units; /* actual lengths */
michael@0	4272	Int var2ulen; /* logical length (units) */
michael@0	4273	Int var1initpad=0; /* var1 initial padding (digits) */
michael@0	4274	Int maxdigits; /* longest LHS or required acc length */
michael@0	4275	Int mult; /* multiplier for subtraction */
michael@0	4276	Unit thisunit; /* current unit being accumulated */
michael@0	4277	Int residue; /* for rounding */
michael@0	4278	Int reqdigits=set->digits; /* requested DIGITS */
michael@0	4279	Int exponent; /* working exponent */
michael@0	4280	Int maxexponent=0; /* DIVIDE maximum exponent if unrounded */
michael@0	4281	uByte bits; /* working sign */
michael@0	4282	Unit *target; /* work */
michael@0	4283	const Unit *source; /* .. */
michael@0	4284	uInt const *pow; /* .. */
michael@0	4285	Int shift, cut; /* .. */
michael@0	4286	#if DECSUBSET
michael@0	4287	Int dropped; /* work */
michael@0	4288	#endif
michael@0	4289
michael@0	4290	#if DECCHECK
michael@0	4291	if (decCheckOperands(res, lhs, rhs, set)) return res;
michael@0	4292	#endif
michael@0	4293
michael@0	4294	do { /* protect allocated storage */
michael@0	4295	#if DECSUBSET
michael@0	4296	if (!set->extended) {
michael@0	4297	/* reduce operands and set lostDigits status, as needed */
michael@0	4298	if (lhs->digits>reqdigits) {
michael@0	4299	alloclhs=decRoundOperand(lhs, set, status);
michael@0	4300	if (alloclhs==NULL) break;
michael@0	4301	lhs=alloclhs;
michael@0	4302	}
michael@0	4303	if (rhs->digits>reqdigits) {
michael@0	4304	allocrhs=decRoundOperand(rhs, set, status);
michael@0	4305	if (allocrhs==NULL) break;
michael@0	4306	rhs=allocrhs;
michael@0	4307	}
michael@0	4308	}
michael@0	4309	#endif
michael@0	4310	/* [following code does not require input rounding] */
michael@0	4311
michael@0	4312	bits=(lhs->bits^rhs->bits)&DECNEG; /* assumed sign for divisions */
michael@0	4313
michael@0	4314	/* handle infinities and NaNs */
michael@0	4315	if (SPECIALARGS) { /* a special bit set */
michael@0	4316	if (SPECIALARGS & (DECSNAN | DECNAN)) { /* one or two NaNs */
michael@0	4317	decNaNs(res, lhs, rhs, set, status);
michael@0	4318	break;
michael@0	4319	}
michael@0	4320	/* one or two infinities */
michael@0	4321	if (decNumberIsInfinite(lhs)) { /* LHS (dividend) is infinite */
michael@0	4322	if (decNumberIsInfinite(rhs) || /* two infinities are invalid .. */
michael@0	4323	op & (REMAINDER | REMNEAR)) { /* as is remainder of infinity */
michael@0	4324	*status|=DEC_Invalid_operation;
michael@0	4325	break;
michael@0	4326	}
michael@0	4327	/* [Note that infinity/0 raises no exceptions] */
michael@0	4328	uprv_decNumberZero(res);
michael@0	4329	res->bits=bits|DECINF; /* set +/- infinity */
michael@0	4330	break;
michael@0	4331	}
michael@0	4332	else { /* RHS (divisor) is infinite */
michael@0	4333	residue=0;
michael@0	4334	if (op&(REMAINDER|REMNEAR)) {
michael@0	4335	/* result is [finished clone of] lhs */
michael@0	4336	decCopyFit(res, lhs, set, &residue, status);
michael@0	4337	}
michael@0	4338	else { /* a division */
michael@0	4339	uprv_decNumberZero(res);
michael@0	4340	res->bits=bits; /* set +/- zero */
michael@0	4341	/* for DIVIDEINT the exponent is always 0. For DIVIDE, result */
michael@0	4342	/* is a 0 with infinitely negative exponent, clamped to minimum */
michael@0	4343	if (op&DIVIDE) {
michael@0	4344	res->exponent=set->emin-set->digits+1;
michael@0	4345	*status|=DEC_Clamped;
michael@0	4346	}
michael@0	4347	}
michael@0	4348	decFinish(res, set, &residue, status);
michael@0	4349	break;
michael@0	4350	}
michael@0	4351	}
michael@0	4352
michael@0	4353	/* handle 0 rhs (x/0) */
michael@0	4354	if (ISZERO(rhs)) { /* x/0 is always exceptional */
michael@0	4355	if (ISZERO(lhs)) {
michael@0	4356	uprv_decNumberZero(res); /* [after lhs test] */
michael@0	4357	*status|=DEC_Division_undefined;/* 0/0 will become NaN */
michael@0	4358	}
michael@0	4359	else {
michael@0	4360	uprv_decNumberZero(res);
michael@0	4361	if (op&(REMAINDER|REMNEAR)) *status|=DEC_Invalid_operation;
michael@0	4362	else {
michael@0	4363	*status|=DEC_Division_by_zero; /* x/0 */
michael@0	4364	res->bits=bits|DECINF; /* .. is +/- Infinity */
michael@0	4365	}
michael@0	4366	}
michael@0	4367	break;}
michael@0	4368
michael@0	4369	/* handle 0 lhs (0/x) */
michael@0	4370	if (ISZERO(lhs)) { /* 0/x [x!=0] */
michael@0	4371	#if DECSUBSET
michael@0	4372	if (!set->extended) uprv_decNumberZero(res);
michael@0	4373	else {
michael@0	4374	#endif
michael@0	4375	if (op&DIVIDE) {
michael@0	4376	residue=0;
michael@0	4377	exponent=lhs->exponent-rhs->exponent; /* ideal exponent */
michael@0	4378	uprv_decNumberCopy(res, lhs); /* [zeros always fit] */
michael@0	4379	res->bits=bits; /* sign as computed */
michael@0	4380	res->exponent=exponent; /* exponent, too */
michael@0	4381	decFinalize(res, set, &residue, status); /* check exponent */
michael@0	4382	}
michael@0	4383	else if (op&DIVIDEINT) {
michael@0	4384	uprv_decNumberZero(res); /* integer 0 */
michael@0	4385	res->bits=bits; /* sign as computed */
michael@0	4386	}
michael@0	4387	else { /* a remainder */
michael@0	4388	exponent=rhs->exponent; /* [save in case overwrite] */
michael@0	4389	uprv_decNumberCopy(res, lhs); /* [zeros always fit] */
michael@0	4390	if (exponent<res->exponent) res->exponent=exponent; /* use lower */
michael@0	4391	}
michael@0	4392	#if DECSUBSET
michael@0	4393	}
michael@0	4394	#endif
michael@0	4395	break;}
michael@0	4396
michael@0	4397	/* Precalculate exponent. This starts off adjusted (and hence fits */
michael@0	4398	/* in 31 bits) and becomes the usual unadjusted exponent as the */
michael@0	4399	/* division proceeds. The order of evaluation is important, here, */
michael@0	4400	/* to avoid wrap. */
michael@0	4401	exponent=(lhs->exponent+lhs->digits)-(rhs->exponent+rhs->digits);
michael@0	4402
michael@0	4403	/* If the working exponent is -ve, then some quick exits are */
michael@0	4404	/* possible because the quotient is known to be <1 */
michael@0	4405	/* [for REMNEAR, it needs to be < -1, as -0.5 could need work] */
michael@0	4406	if (exponent<0 && !(op==DIVIDE)) {
michael@0	4407	if (op&DIVIDEINT) {
michael@0	4408	uprv_decNumberZero(res); /* integer part is 0 */
michael@0	4409	#if DECSUBSET
michael@0	4410	if (set->extended)
michael@0	4411	#endif
michael@0	4412	res->bits=bits; /* set +/- zero */
michael@0	4413	break;}
michael@0	4414	/* fastpath remainders so long as the lhs has the smaller */
michael@0	4415	/* (or equal) exponent */
michael@0	4416	if (lhs->exponent<=rhs->exponent) {
michael@0	4417	if (op&REMAINDER || exponent<-1) {
michael@0	4418	/* It is REMAINDER or safe REMNEAR; result is [finished */
michael@0	4419	/* clone of] lhs (r = x - 0*y) */
michael@0	4420	residue=0;
michael@0	4421	decCopyFit(res, lhs, set, &residue, status);
michael@0	4422	decFinish(res, set, &residue, status);
michael@0	4423	break;
michael@0	4424	}
michael@0	4425	/* [unsafe REMNEAR drops through] */
michael@0	4426	}
michael@0	4427	} /* fastpaths */
michael@0	4428
michael@0	4429	/* Long (slow) division is needed; roll up the sleeves... */
michael@0	4430
michael@0	4431	/* The accumulator will hold the quotient of the division. */
michael@0	4432	/* If it needs to be too long for stack storage, then allocate. */
michael@0	4433	acclength=D2U(reqdigits+DECDPUN); /* in Units */
michael@0	4434	if (acclength*sizeof(Unit)>sizeof(accbuff)) {
michael@0	4435	/* printf("malloc dvacc %ld units\n", acclength); */
michael@0	4436	allocacc=(Unit *)malloc(acclength*sizeof(Unit));
michael@0	4437	if (allocacc==NULL) { /* hopeless -- abandon */
michael@0	4438	*status|=DEC_Insufficient_storage;
michael@0	4439	break;}
michael@0	4440	acc=allocacc; /* use the allocated space */
michael@0	4441	}
michael@0	4442
michael@0	4443	/* var1 is the padded LHS ready for subtractions. */
michael@0	4444	/* If it needs to be too long for stack storage, then allocate. */
michael@0	4445	/* The maximum units needed for var1 (long subtraction) is: */
michael@0	4446	/* Enough for */
michael@0	4447	/* (rhs->digits+reqdigits-1) -- to allow full slide to right */
michael@0	4448	/* or (lhs->digits) -- to allow for long lhs */
michael@0	4449	/* whichever is larger */
michael@0	4450	/* +1 -- for rounding of slide to right */
michael@0	4451	/* +1 -- for leading 0s */
michael@0	4452	/* +1 -- for pre-adjust if a remainder or DIVIDEINT */
michael@0	4453	/* [Note: unused units do not participate in decUnitAddSub data] */
michael@0	4454	maxdigits=rhs->digits+reqdigits-1;
michael@0	4455	if (lhs->digits>maxdigits) maxdigits=lhs->digits;
michael@0	4456	var1units=D2U(maxdigits)+2;
michael@0	4457	/* allocate a guard unit above msu1 for REMAINDERNEAR */
michael@0	4458	if (!(op&DIVIDE)) var1units++;
michael@0	4459	if ((var1units+1)*sizeof(Unit)>sizeof(varbuff)) {
michael@0	4460	/* printf("malloc dvvar %ld units\n", var1units+1); */
michael@0	4461	varalloc=(Unit *)malloc((var1units+1)*sizeof(Unit));
michael@0	4462	if (varalloc==NULL) { /* hopeless -- abandon */
michael@0	4463	*status|=DEC_Insufficient_storage;
michael@0	4464	break;}
michael@0	4465	var1=varalloc; /* use the allocated space */
michael@0	4466	}
michael@0	4467
michael@0	4468	/* Extend the lhs and rhs to full long subtraction length. The lhs */
michael@0	4469	/* is truly extended into the var1 buffer, with 0 padding, so a */
michael@0	4470	/* subtract in place is always possible. The rhs (var2) has */
michael@0	4471	/* virtual padding (implemented by decUnitAddSub). */
michael@0	4472	/* One guard unit was allocated above msu1 for rem=rem+rem in */
michael@0	4473	/* REMAINDERNEAR. */
michael@0	4474	msu1=var1+var1units-1; /* msu of var1 */
michael@0	4475	source=lhs->lsu+D2U(lhs->digits)-1; /* msu of input array */
michael@0	4476	for (target=msu1; source>=lhs->lsu; source--, target--) *target=*source;
michael@0	4477	for (; target>=var1; target--) *target=0;
michael@0	4478
michael@0	4479	/* rhs (var2) is left-aligned with var1 at the start */
michael@0	4480	var2ulen=var1units; /* rhs logical length (units) */
michael@0	4481	var2units=D2U(rhs->digits); /* rhs actual length (units) */
michael@0	4482	var2=rhs->lsu; /* -> rhs array */
michael@0	4483	msu2=var2+var2units-1; /* -> msu of var2 [never changes] */
michael@0	4484	/* now set up the variables which will be used for estimating the */
michael@0	4485	/* multiplication factor. If these variables are not exact, add */
michael@0	4486	/* 1 to make sure that the multiplier is never overestimated. */
michael@0	4487	msu2plus=*msu2; /* it's value .. */
michael@0	4488	if (var2units>1) msu2plus++; /* .. +1 if any more */
michael@0	4489	msu2pair=(eInt)*msu2*(DECDPUNMAX+1);/* top two pair .. */
michael@0	4490	if (var2units>1) { /* .. [else treat 2nd as 0] */
michael@0	4491	msu2pair+=*(msu2-1); /* .. */
michael@0	4492	if (var2units>2) msu2pair++; /* .. +1 if any more */
michael@0	4493	}
michael@0	4494
michael@0	4495	/* The calculation is working in units, which may have leading zeros, */
michael@0	4496	/* but the exponent was calculated on the assumption that they are */
michael@0	4497	/* both left-aligned. Adjust the exponent to compensate: add the */
michael@0	4498	/* number of leading zeros in var1 msu and subtract those in var2 msu. */
michael@0	4499	/* [This is actually done by counting the digits and negating, as */
michael@0	4500	/* lead1=DECDPUN-digits1, and similarly for lead2.] */
michael@0	4501	for (pow=&powers[1]; *msu1>=*pow; pow++) exponent--;
michael@0	4502	for (pow=&powers[1]; *msu2>=*pow; pow++) exponent++;
michael@0	4503
michael@0	4504	/* Now, if doing an integer divide or remainder, ensure that */
michael@0	4505	/* the result will be Unit-aligned. To do this, shift the var1 */
michael@0	4506	/* accumulator towards least if need be. (It's much easier to */
michael@0	4507	/* do this now than to reassemble the residue afterwards, if */
michael@0	4508	/* doing a remainder.) Also ensure the exponent is not negative. */
michael@0	4509	if (!(op&DIVIDE)) {
michael@0	4510	Unit *u; /* work */
michael@0	4511	/* save the initial 'false' padding of var1, in digits */
michael@0	4512	var1initpad=(var1units-D2U(lhs->digits))*DECDPUN;
michael@0	4513	/* Determine the shift to do. */
michael@0	4514	if (exponent<0) cut=-exponent;
michael@0	4515	else cut=DECDPUN-exponent%DECDPUN;
michael@0	4516	decShiftToLeast(var1, var1units, cut);
michael@0	4517	exponent+=cut; /* maintain numerical value */
michael@0	4518	var1initpad-=cut; /* .. and reduce padding */
michael@0	4519	/* clean any most-significant units which were just emptied */
michael@0	4520	for (u=msu1; cut>=DECDPUN; cut-=DECDPUN, u--) *u=0;
michael@0	4521	} /* align */
michael@0	4522	else { /* is DIVIDE */
michael@0	4523	maxexponent=lhs->exponent-rhs->exponent; /* save */
michael@0	4524	/* optimization: if the first iteration will just produce 0, */
michael@0	4525	/* preadjust to skip it [valid for DIVIDE only] */
michael@0	4526	if (*msu1<*msu2) {
michael@0	4527	var2ulen--; /* shift down */
michael@0	4528	exponent-=DECDPUN; /* update the exponent */
michael@0	4529	}
michael@0	4530	}
michael@0	4531
michael@0	4532	/* ---- start the long-division loops ------------------------------ */
michael@0	4533	accunits=0; /* no units accumulated yet */
michael@0	4534	accdigits=0; /* .. or digits */
michael@0	4535	accnext=acc+acclength-1; /* -> msu of acc [NB: allows digits+1] */
michael@0	4536	for (;;) { /* outer forever loop */
michael@0	4537	thisunit=0; /* current unit assumed 0 */
michael@0	4538	/* find the next unit */
michael@0	4539	for (;;) { /* inner forever loop */
michael@0	4540	/* strip leading zero units [from either pre-adjust or from */
michael@0	4541	/* subtract last time around]. Leave at least one unit. */
michael@0	4542	for (; *msu1==0 && msu1>var1; msu1--) var1units--;
michael@0	4543
michael@0	4544	if (var1units<var2ulen) break; /* var1 too low for subtract */
michael@0	4545	if (var1units==var2ulen) { /* unit-by-unit compare needed */
michael@0	4546	/* compare the two numbers, from msu */
michael@0	4547	const Unit *pv1, *pv2;
michael@0	4548	Unit v2; /* units to compare */
michael@0	4549	pv2=msu2; /* -> msu */
michael@0	4550	for (pv1=msu1; ; pv1--, pv2--) {
michael@0	4551	/* v1=*pv1 -- always OK */
michael@0	4552	v2=0; /* assume in padding */
michael@0	4553	if (pv2>=var2) v2=*pv2; /* in range */
michael@0	4554	if (*pv1!=v2) break; /* no longer the same */
michael@0	4555	if (pv1==var1) break; /* done; leave pv1 as is */
michael@0	4556	}
michael@0	4557	/* here when all inspected or a difference seen */
michael@0	4558	if (*pv1<v2) break; /* var1 too low to subtract */
michael@0	4559	if (*pv1==v2) { /* var1 == var2 */
michael@0	4560	/* reach here if var1 and var2 are identical; subtraction */
michael@0	4561	/* would increase digit by one, and the residue will be 0 so */
michael@0	4562	/* the calculation is done; leave the loop with residue=0. */
michael@0	4563	thisunit++; /* as though subtracted */
michael@0	4564	*var1=0; /* set var1 to 0 */
michael@0	4565	var1units=1; /* .. */
michael@0	4566	break; /* from inner */
michael@0	4567	} /* var1 == var2 */
michael@0	4568	/* *pv1>v2. Prepare for real subtraction; the lengths are equal */
michael@0	4569	/* Estimate the multiplier (there's always a msu1-1)... */
michael@0	4570	/* Bring in two units of var2 to provide a good estimate. */
michael@0	4571	mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2pair);
michael@0	4572	} /* lengths the same */
michael@0	4573	else { /* var1units > var2ulen, so subtraction is safe */
michael@0	4574	/* The var2 msu is one unit towards the lsu of the var1 msu, */
michael@0	4575	/* so only one unit for var2 can be used. */
michael@0	4576	mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2plus);
michael@0	4577	}
michael@0	4578	if (mult==0) mult=1; /* must always be at least 1 */
michael@0	4579	/* subtraction needed; var1 is > var2 */
michael@0	4580	thisunit=(Unit)(thisunit+mult); /* accumulate */
michael@0	4581	/* subtract var1-var2, into var1; only the overlap needs */
michael@0	4582	/* processing, as this is an in-place calculation */
michael@0	4583	shift=var2ulen-var2units;
michael@0	4584	#if DECTRACE
michael@0	4585	decDumpAr('1', &var1[shift], var1units-shift);
michael@0	4586	decDumpAr('2', var2, var2units);
michael@0	4587	printf("m=%ld\n", -mult);
michael@0	4588	#endif
michael@0	4589	decUnitAddSub(&var1[shift], var1units-shift,
michael@0	4590	var2, var2units, 0,
michael@0	4591	&var1[shift], -mult);
michael@0	4592	#if DECTRACE
michael@0	4593	decDumpAr('#', &var1[shift], var1units-shift);
michael@0	4594	#endif
michael@0	4595	/* var1 now probably has leading zeros; these are removed at the */
michael@0	4596	/* top of the inner loop. */
michael@0	4597	} /* inner loop */
michael@0	4598
michael@0	4599	/* The next unit has been calculated in full; unless it's a */
michael@0	4600	/* leading zero, add to acc */
michael@0	4601	if (accunits!=0 || thisunit!=0) { /* is first or non-zero */
michael@0	4602	*accnext=thisunit; /* store in accumulator */
michael@0	4603	/* account exactly for the new digits */
michael@0	4604	if (accunits==0) {
michael@0	4605	accdigits++; /* at least one */
michael@0	4606	for (pow=&powers[1]; thisunit>=*pow; pow++) accdigits++;
michael@0	4607	}
michael@0	4608	else accdigits+=DECDPUN;
michael@0	4609	accunits++; /* update count */
michael@0	4610	accnext--; /* ready for next */
michael@0	4611	if (accdigits>reqdigits) break; /* have enough digits */
michael@0	4612	}
michael@0	4613
michael@0	4614	/* if the residue is zero, the operation is done (unless divide */
michael@0	4615	/* or divideInteger and still not enough digits yet) */
michael@0	4616	if (*var1==0 && var1units==1) { /* residue is 0 */
michael@0	4617	if (op&(REMAINDER|REMNEAR)) break;
michael@0	4618	if ((op&DIVIDE) && (exponent<=maxexponent)) break;
michael@0	4619	/* [drop through if divideInteger] */
michael@0	4620	}
michael@0	4621	/* also done enough if calculating remainder or integer */
michael@0	4622	/* divide and just did the last ('units') unit */
michael@0	4623	if (exponent==0 && !(op&DIVIDE)) break;
michael@0	4624
michael@0	4625	/* to get here, var1 is less than var2, so divide var2 by the per- */
michael@0	4626	/* Unit power of ten and go for the next digit */
michael@0	4627	var2ulen--; /* shift down */
michael@0	4628	exponent-=DECDPUN; /* update the exponent */
michael@0	4629	} /* outer loop */
michael@0	4630
michael@0	4631	/* ---- division is complete --------------------------------------- */
michael@0	4632	/* here: acc has at least reqdigits+1 of good results (or fewer */
michael@0	4633	/* if early stop), starting at accnext+1 (its lsu) */
michael@0	4634	/* var1 has any residue at the stopping point */
michael@0	4635	/* accunits is the number of digits collected in acc */
michael@0	4636	if (accunits==0) { /* acc is 0 */
michael@0	4637	accunits=1; /* show have a unit .. */
michael@0	4638	accdigits=1; /* .. */
michael@0	4639	*accnext=0; /* .. whose value is 0 */
michael@0	4640	}
michael@0	4641	else accnext++; /* back to last placed */
michael@0	4642	/* accnext now -> lowest unit of result */
michael@0	4643
michael@0	4644	residue=0; /* assume no residue */
michael@0	4645	if (op&DIVIDE) {
michael@0	4646	/* record the presence of any residue, for rounding */
michael@0	4647	if (*var1!=0 || var1units>1) residue=1;
michael@0	4648	else { /* no residue */
michael@0	4649	/* Had an exact division; clean up spurious trailing 0s. */
michael@0	4650	/* There will be at most DECDPUN-1, from the final multiply, */
michael@0	4651	/* and then only if the result is non-0 (and even) and the */
michael@0	4652	/* exponent is 'loose'. */
michael@0	4653	#if DECDPUN>1
michael@0	4654	Unit lsu=*accnext;
michael@0	4655	if (!(lsu&0x01) && (lsu!=0)) {
michael@0	4656	/* count the trailing zeros */
michael@0	4657	Int drop=0;
michael@0	4658	for (;; drop++) { /* [will terminate because lsu!=0] */
michael@0	4659	if (exponent>=maxexponent) break; /* don't chop real 0s */
michael@0	4660	#if DECDPUN<=4
michael@0	4661	if ((lsu-QUOT10(lsu, drop+1)
michael@0	4662	*powers[drop+1])!=0) break; /* found non-0 digit */
michael@0	4663	#else
michael@0	4664	if (lsu%powers[drop+1]!=0) break; /* found non-0 digit */
michael@0	4665	#endif
michael@0	4666	exponent++;
michael@0	4667	}
michael@0	4668	if (drop>0) {
michael@0	4669	accunits=decShiftToLeast(accnext, accunits, drop);
michael@0	4670	accdigits=decGetDigits(accnext, accunits);
michael@0	4671	accunits=D2U(accdigits);
michael@0	4672	/* [exponent was adjusted in the loop] */
michael@0	4673	}
michael@0	4674	} /* neither odd nor 0 */
michael@0	4675	#endif
michael@0	4676	} /* exact divide */
michael@0	4677	} /* divide */
michael@0	4678	else /* op!=DIVIDE */ {
michael@0	4679	/* check for coefficient overflow */
michael@0	4680	if (accdigits+exponent>reqdigits) {
michael@0	4681	*status|=DEC_Division_impossible;
michael@0	4682	break;
michael@0	4683	}
michael@0	4684	if (op & (REMAINDER|REMNEAR)) {
michael@0	4685	/* [Here, the exponent will be 0, because var1 was adjusted */
michael@0	4686	/* appropriately.] */
michael@0	4687	Int postshift; /* work */
michael@0	4688	Flag wasodd=0; /* integer was odd */
michael@0	4689	Unit *quotlsu; /* for save */
michael@0	4690	Int quotdigits; /* .. */
michael@0	4691
michael@0	4692	bits=lhs->bits; /* remainder sign is always as lhs */
michael@0	4693
michael@0	4694	/* Fastpath when residue is truly 0 is worthwhile [and */
michael@0	4695	/* simplifies the code below] */
michael@0	4696	if (*var1==0 && var1units==1) { /* residue is 0 */
michael@0	4697	Int exp=lhs->exponent; /* save min(exponents) */
michael@0	4698	if (rhs->exponent<exp) exp=rhs->exponent;
michael@0	4699	uprv_decNumberZero(res); /* 0 coefficient */
michael@0	4700	#if DECSUBSET
michael@0	4701	if (set->extended)
michael@0	4702	#endif
michael@0	4703	res->exponent=exp; /* .. with proper exponent */
michael@0	4704	res->bits=(uByte)(bits&DECNEG); /* [cleaned] */
michael@0	4705	decFinish(res, set, &residue, status); /* might clamp */
michael@0	4706	break;
michael@0	4707	}
michael@0	4708	/* note if the quotient was odd */
michael@0	4709	if (*accnext & 0x01) wasodd=1; /* acc is odd */
michael@0	4710	quotlsu=accnext; /* save in case need to reinspect */
michael@0	4711	quotdigits=accdigits; /* .. */
michael@0	4712
michael@0	4713	/* treat the residue, in var1, as the value to return, via acc */
michael@0	4714	/* calculate the unused zero digits. This is the smaller of: */
michael@0	4715	/* var1 initial padding (saved above) */
michael@0	4716	/* var2 residual padding, which happens to be given by: */
michael@0	4717	postshift=var1initpad+exponent-lhs->exponent+rhs->exponent;
michael@0	4718	/* [the 'exponent' term accounts for the shifts during divide] */
michael@0	4719	if (var1initpad<postshift) postshift=var1initpad;
michael@0	4720
michael@0	4721	/* shift var1 the requested amount, and adjust its digits */
michael@0	4722	var1units=decShiftToLeast(var1, var1units, postshift);
michael@0	4723	accnext=var1;
michael@0	4724	accdigits=decGetDigits(var1, var1units);
michael@0	4725	accunits=D2U(accdigits);
michael@0	4726
michael@0	4727	exponent=lhs->exponent; /* exponent is smaller of lhs & rhs */
michael@0	4728	if (rhs->exponent<exponent) exponent=rhs->exponent;
michael@0	4729
michael@0	4730	/* Now correct the result if doing remainderNear; if it */
michael@0	4731	/* (looking just at coefficients) is > rhs/2, or == rhs/2 and */
michael@0	4732	/* the integer was odd then the result should be rem-rhs. */
michael@0	4733	if (op&REMNEAR) {
michael@0	4734	Int compare, tarunits; /* work */
michael@0	4735	Unit *up; /* .. */
michael@0	4736	/* calculate remainder*2 into the var1 buffer (which has */
michael@0	4737	/* 'headroom' of an extra unit and hence enough space) */
michael@0	4738	/* [a dedicated 'double' loop would be faster, here] */
michael@0	4739	tarunits=decUnitAddSub(accnext, accunits, accnext, accunits,
michael@0	4740	0, accnext, 1);
michael@0	4741	/* decDumpAr('r', accnext, tarunits); */
michael@0	4742
michael@0	4743	/* Here, accnext (var1) holds tarunits Units with twice the */
michael@0	4744	/* remainder's coefficient, which must now be compared to the */
michael@0	4745	/* RHS. The remainder's exponent may be smaller than the RHS's. */
michael@0	4746	compare=decUnitCompare(accnext, tarunits, rhs->lsu, D2U(rhs->digits),
michael@0	4747	rhs->exponent-exponent);
michael@0	4748	if (compare==BADINT) { /* deep trouble */
michael@0	4749	*status|=DEC_Insufficient_storage;
michael@0	4750	break;}
michael@0	4751
michael@0	4752	/* now restore the remainder by dividing by two; the lsu */
michael@0	4753	/* is known to be even. */
michael@0	4754	for (up=accnext; up<accnext+tarunits; up++) {
michael@0	4755	Int half; /* half to add to lower unit */
michael@0	4756	half=*up & 0x01;
michael@0	4757	*up/=2; /* [shift] */
michael@0	4758	if (!half) continue;
michael@0	4759	*(up-1)+=(DECDPUNMAX+1)/2;
michael@0	4760	}
michael@0	4761	/* [accunits still describes the original remainder length] */
michael@0	4762
michael@0	4763	if (compare>0 || (compare==0 && wasodd)) { /* adjustment needed */
michael@0	4764	Int exp, expunits, exprem; /* work */
michael@0	4765	/* This is effectively causing round-up of the quotient, */
michael@0	4766	/* so if it was the rare case where it was full and all */
michael@0	4767	/* nines, it would overflow and hence division-impossible */
michael@0	4768	/* should be raised */
michael@0	4769	Flag allnines=0; /* 1 if quotient all nines */
michael@0	4770	if (quotdigits==reqdigits) { /* could be borderline */
michael@0	4771	for (up=quotlsu; ; up++) {
michael@0	4772	if (quotdigits>DECDPUN) {
michael@0	4773	if (*up!=DECDPUNMAX) break;/* non-nines */
michael@0	4774	}
michael@0	4775	else { /* this is the last Unit */
michael@0	4776	if (*up==powers[quotdigits]-1) allnines=1;
michael@0	4777	break;
michael@0	4778	}
michael@0	4779	quotdigits-=DECDPUN; /* checked those digits */
michael@0	4780	} /* up */
michael@0	4781	} /* borderline check */
michael@0	4782	if (allnines) {
michael@0	4783	*status|=DEC_Division_impossible;
michael@0	4784	break;}
michael@0	4785
michael@0	4786	/* rem-rhs is needed; the sign will invert. Again, var1 */
michael@0	4787	/* can safely be used for the working Units array. */
michael@0	4788	exp=rhs->exponent-exponent; /* RHS padding needed */
michael@0	4789	/* Calculate units and remainder from exponent. */
michael@0	4790	expunits=exp/DECDPUN;
michael@0	4791	exprem=exp%DECDPUN;
michael@0	4792	/* subtract [A+B*(-m)]; the result will always be negative */
michael@0	4793	accunits=-decUnitAddSub(accnext, accunits,
michael@0	4794	rhs->lsu, D2U(rhs->digits),
michael@0	4795	expunits, accnext, -(Int)powers[exprem]);
michael@0	4796	accdigits=decGetDigits(accnext, accunits); /* count digits exactly */
michael@0	4797	accunits=D2U(accdigits); /* and recalculate the units for copy */
michael@0	4798	/* [exponent is as for original remainder] */
michael@0	4799	bits^=DECNEG; /* flip the sign */
michael@0	4800	}
michael@0	4801	} /* REMNEAR */
michael@0	4802	} /* REMAINDER or REMNEAR */
michael@0	4803	} /* not DIVIDE */
michael@0	4804
michael@0	4805	/* Set exponent and bits */
michael@0	4806	res->exponent=exponent;
michael@0	4807	res->bits=(uByte)(bits&DECNEG); /* [cleaned] */
michael@0	4808
michael@0	4809	/* Now the coefficient. */
michael@0	4810	decSetCoeff(res, set, accnext, accdigits, &residue, status);
michael@0	4811
michael@0	4812	decFinish(res, set, &residue, status); /* final cleanup */
michael@0	4813
michael@0	4814	#if DECSUBSET
michael@0	4815	/* If a divide then strip trailing zeros if subset [after round] */
michael@0	4816	if (!set->extended && (op==DIVIDE)) decTrim(res, set, 0, 1, &dropped);
michael@0	4817	#endif
michael@0	4818	} while(0); /* end protected */
michael@0	4819
michael@0	4820	if (varalloc!=NULL) free(varalloc); /* drop any storage used */
michael@0	4821	if (allocacc!=NULL) free(allocacc); /* .. */
michael@0	4822	#if DECSUBSET
michael@0	4823	if (allocrhs!=NULL) free(allocrhs); /* .. */
michael@0	4824	if (alloclhs!=NULL) free(alloclhs); /* .. */
michael@0	4825	#endif
michael@0	4826	return res;
michael@0	4827	} /* decDivideOp */
michael@0	4828
michael@0	4829	/* ------------------------------------------------------------------ */
michael@0	4830	/* decMultiplyOp -- multiplication operation */
michael@0	4831	/* */
michael@0	4832	/* This routine performs the multiplication C=A x B. */
michael@0	4833	/* */
michael@0	4834	/* res is C, the result. C may be A and/or B (e.g., X=X*X) */
michael@0	4835	/* lhs is A */
michael@0	4836	/* rhs is B */
michael@0	4837	/* set is the context */
michael@0	4838	/* status is the usual accumulator */
michael@0	4839	/* */
michael@0	4840	/* C must have space for set->digits digits. */
michael@0	4841	/* */
michael@0	4842	/* ------------------------------------------------------------------ */
michael@0	4843	/* 'Classic' multiplication is used rather than Karatsuba, as the */
michael@0	4844	/* latter would give only a minor improvement for the short numbers */
michael@0	4845	/* expected to be handled most (and uses much more memory). */
michael@0	4846	/* */
michael@0	4847	/* There are two major paths here: the general-purpose ('old code') */
michael@0	4848	/* path which handles all DECDPUN values, and a fastpath version */
michael@0	4849	/* which is used if 64-bit ints are available, DECDPUN<=4, and more */
michael@0	4850	/* than two calls to decUnitAddSub would be made. */
michael@0	4851	/* */
michael@0	4852	/* The fastpath version lumps units together into 8-digit or 9-digit */
michael@0	4853	/* chunks, and also uses a lazy carry strategy to minimise expensive */
michael@0	4854	/* 64-bit divisions. The chunks are then broken apart again into */
michael@0	4855	/* units for continuing processing. Despite this overhead, the */
michael@0	4856	/* fastpath can speed up some 16-digit operations by 10x (and much */
michael@0	4857	/* more for higher-precision calculations). */
michael@0	4858	/* */
michael@0	4859	/* A buffer always has to be used for the accumulator; in the */
michael@0	4860	/* fastpath, buffers are also always needed for the chunked copies of */
michael@0	4861	/* of the operand coefficients. */
michael@0	4862	/* Static buffers are larger than needed just for multiply, to allow */
michael@0	4863	/* for calls from other operations (notably exp). */
michael@0	4864	/* ------------------------------------------------------------------ */
michael@0	4865	#define FASTMUL (DECUSE64 && DECDPUN<5)
michael@0	4866	static decNumber * decMultiplyOp(decNumber *res, const decNumber *lhs,
michael@0	4867	const decNumber *rhs, decContext *set,
michael@0	4868	uInt *status) {
michael@0	4869	Int accunits; /* Units of accumulator in use */
michael@0	4870	Int exponent; /* work */
michael@0	4871	Int residue=0; /* rounding residue */
michael@0	4872	uByte bits; /* result sign */
michael@0	4873	Unit *acc; /* -> accumulator Unit array */
michael@0	4874	Int needbytes; /* size calculator */
michael@0	4875	void *allocacc=NULL; /* -> allocated accumulator, iff allocated */
michael@0	4876	Unit accbuff[SD2U(DECBUFFER*4+1)]; /* buffer (+1 for DECBUFFER==0, */
michael@0	4877	/* *4 for calls from other operations) */
michael@0	4878	const Unit *mer, *mermsup; /* work */
michael@0	4879	Int madlength; /* Units in multiplicand */
michael@0	4880	Int shift; /* Units to shift multiplicand by */
michael@0	4881
michael@0	4882	#if FASTMUL
michael@0	4883	/* if DECDPUN is 1 or 3 work in base 10**9, otherwise */
michael@0	4884	/* (DECDPUN is 2 or 4) then work in base 10**8 */
michael@0	4885	#if DECDPUN & 1 /* odd */
michael@0	4886	#define FASTBASE 1000000000 /* base */
michael@0	4887	#define FASTDIGS 9 /* digits in base */
michael@0	4888	#define FASTLAZY 18 /* carry resolution point [1->18] */
michael@0	4889	#else
michael@0	4890	#define FASTBASE 100000000
michael@0	4891	#define FASTDIGS 8
michael@0	4892	#define FASTLAZY 1844 /* carry resolution point [1->1844] */
michael@0	4893	#endif
michael@0	4894	/* three buffers are used, two for chunked copies of the operands */
michael@0	4895	/* (base 10**8 or base 10**9) and one base 2**64 accumulator with */
michael@0	4896	/* lazy carry evaluation */
michael@0	4897	uInt zlhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0) */
michael@0	4898	uInt *zlhi=zlhibuff; /* -> lhs array */
michael@0	4899	uInt *alloclhi=NULL; /* -> allocated buffer, iff allocated */
michael@0	4900	uInt zrhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0) */
michael@0	4901	uInt *zrhi=zrhibuff; /* -> rhs array */
michael@0	4902	uInt *allocrhi=NULL; /* -> allocated buffer, iff allocated */
michael@0	4903	uLong zaccbuff[(DECBUFFER*2+1)/4+2]; /* buffer (+1 for DECBUFFER==0) */
michael@0	4904	/* [allocacc is shared for both paths, as only one will run] */
michael@0	4905	uLong *zacc=zaccbuff; /* -> accumulator array for exact result */
michael@0	4906	#if DECDPUN==1
michael@0	4907	Int zoff; /* accumulator offset */
michael@0	4908	#endif
michael@0	4909	uInt *lip, *rip; /* item pointers */
michael@0	4910	uInt *lmsi, *rmsi; /* most significant items */
michael@0	4911	Int ilhs, irhs, iacc; /* item counts in the arrays */
michael@0	4912	Int lazy; /* lazy carry counter */
michael@0	4913	uLong lcarry; /* uLong carry */
michael@0	4914	uInt carry; /* carry (NB not uLong) */
michael@0	4915	Int count; /* work */
michael@0	4916	const Unit *cup; /* .. */
michael@0	4917	Unit *up; /* .. */
michael@0	4918	uLong *lp; /* .. */
michael@0	4919	Int p; /* .. */
michael@0	4920	#endif
michael@0	4921
michael@0	4922	#if DECSUBSET
michael@0	4923	decNumber *alloclhs=NULL; /* -> allocated buffer, iff allocated */
michael@0	4924	decNumber *allocrhs=NULL; /* -> allocated buffer, iff allocated */
michael@0	4925	#endif
michael@0	4926
michael@0	4927	#if DECCHECK
michael@0	4928	if (decCheckOperands(res, lhs, rhs, set)) return res;
michael@0	4929	#endif
michael@0	4930
michael@0	4931	/* precalculate result sign */
michael@0	4932	bits=(uByte)((lhs->bits^rhs->bits)&DECNEG);
michael@0	4933
michael@0	4934	/* handle infinities and NaNs */
michael@0	4935	if (SPECIALARGS) { /* a special bit set */
michael@0	4936	if (SPECIALARGS & (DECSNAN | DECNAN)) { /* one or two NaNs */
michael@0	4937	decNaNs(res, lhs, rhs, set, status);
michael@0	4938	return res;}
michael@0	4939	/* one or two infinities; Infinity * 0 is invalid */
michael@0	4940	if (((lhs->bits & DECINF)==0 && ISZERO(lhs))
michael@0	4941	||((rhs->bits & DECINF)==0 && ISZERO(rhs))) {
michael@0	4942	*status|=DEC_Invalid_operation;
michael@0	4943	return res;}
michael@0	4944	uprv_decNumberZero(res);
michael@0	4945	res->bits=bits|DECINF; /* infinity */
michael@0	4946	return res;}
michael@0	4947
michael@0	4948	/* For best speed, as in DMSRCN [the original Rexx numerics */
michael@0	4949	/* module], use the shorter number as the multiplier (rhs) and */
michael@0	4950	/* the longer as the multiplicand (lhs) to minimise the number of */
michael@0	4951	/* adds (partial products) */
michael@0	4952	if (lhs->digits<rhs->digits) { /* swap... */
michael@0	4953	const decNumber *hold=lhs;
michael@0	4954	lhs=rhs;
michael@0	4955	rhs=hold;
michael@0	4956	}
michael@0	4957
michael@0	4958	do { /* protect allocated storage */
michael@0	4959	#if DECSUBSET
michael@0	4960	if (!set->extended) {
michael@0	4961	/* reduce operands and set lostDigits status, as needed */
michael@0	4962	if (lhs->digits>set->digits) {
michael@0	4963	alloclhs=decRoundOperand(lhs, set, status);
michael@0	4964	if (alloclhs==NULL) break;
michael@0	4965	lhs=alloclhs;
michael@0	4966	}
michael@0	4967	if (rhs->digits>set->digits) {
michael@0	4968	allocrhs=decRoundOperand(rhs, set, status);
michael@0	4969	if (allocrhs==NULL) break;
michael@0	4970	rhs=allocrhs;
michael@0	4971	}
michael@0	4972	}
michael@0	4973	#endif
michael@0	4974	/* [following code does not require input rounding] */
michael@0	4975
michael@0	4976	#if FASTMUL /* fastpath can be used */
michael@0	4977	/* use the fast path if there are enough digits in the shorter */
michael@0	4978	/* operand to make the setup and takedown worthwhile */
michael@0	4979	#define NEEDTWO (DECDPUN*2) /* within two decUnitAddSub calls */
michael@0	4980	if (rhs->digits>NEEDTWO) { /* use fastpath... */
michael@0	4981	/* calculate the number of elements in each array */
michael@0	4982	ilhs=(lhs->digits+FASTDIGS-1)/FASTDIGS; /* [ceiling] */
michael@0	4983	irhs=(rhs->digits+FASTDIGS-1)/FASTDIGS; /* .. */
michael@0	4984	iacc=ilhs+irhs;
michael@0	4985
michael@0	4986	/* allocate buffers if required, as usual */
michael@0	4987	needbytes=ilhs*sizeof(uInt);
michael@0	4988	if (needbytes>(Int)sizeof(zlhibuff)) {
michael@0	4989	alloclhi=(uInt *)malloc(needbytes);
michael@0	4990	zlhi=alloclhi;}
michael@0	4991	needbytes=irhs*sizeof(uInt);
michael@0	4992	if (needbytes>(Int)sizeof(zrhibuff)) {
michael@0	4993	allocrhi=(uInt *)malloc(needbytes);
michael@0	4994	zrhi=allocrhi;}
michael@0	4995
michael@0	4996	/* Allocating the accumulator space needs a special case when */
michael@0	4997	/* DECDPUN=1 because when converting the accumulator to Units */
michael@0	4998	/* after the multiplication each 8-byte item becomes 9 1-byte */
michael@0	4999	/* units. Therefore iacc extra bytes are needed at the front */
michael@0	5000	/* (rounded up to a multiple of 8 bytes), and the uLong */
michael@0	5001	/* accumulator starts offset the appropriate number of units */
michael@0	5002	/* to the right to avoid overwrite during the unchunking. */
michael@0	5003
michael@0	5004	/* Make sure no signed int overflow below. This is always true */
michael@0	5005	/* if the given numbers have less digits than DEC_MAX_DIGITS. */
michael@0	5006	U_ASSERT(iacc <= INT32_MAX/sizeof(uLong));
michael@0	5007	needbytes=iacc*sizeof(uLong);
michael@0	5008	#if DECDPUN==1
michael@0	5009	zoff=(iacc+7)/8; /* items to offset by */
michael@0	5010	needbytes+=zoff*8;
michael@0	5011	#endif
michael@0	5012	if (needbytes>(Int)sizeof(zaccbuff)) {
michael@0	5013	allocacc=(uLong *)malloc(needbytes);
michael@0	5014	zacc=(uLong *)allocacc;}
michael@0	5015	if (zlhi==NULL||zrhi==NULL||zacc==NULL) {
michael@0	5016	*status|=DEC_Insufficient_storage;
michael@0	5017	break;}
michael@0	5018
michael@0	5019	acc=(Unit *)zacc; /* -> target Unit array */
michael@0	5020	#if DECDPUN==1
michael@0	5021	zacc+=zoff; /* start uLong accumulator to right */
michael@0	5022	#endif
michael@0	5023
michael@0	5024	/* assemble the chunked copies of the left and right sides */
michael@0	5025	for (count=lhs->digits, cup=lhs->lsu, lip=zlhi; count>0; lip++)
michael@0	5026	for (p=0, *lip=0; p<FASTDIGS && count>0;
michael@0	5027	p+=DECDPUN, cup++, count-=DECDPUN)
michael@0	5028	*lip+=*cup*powers[p];
michael@0	5029	lmsi=lip-1; /* save -> msi */
michael@0	5030	for (count=rhs->digits, cup=rhs->lsu, rip=zrhi; count>0; rip++)
michael@0	5031	for (p=0, *rip=0; p<FASTDIGS && count>0;
michael@0	5032	p+=DECDPUN, cup++, count-=DECDPUN)
michael@0	5033	*rip+=*cup*powers[p];
michael@0	5034	rmsi=rip-1; /* save -> msi */
michael@0	5035
michael@0	5036	/* zero the accumulator */
michael@0	5037	for (lp=zacc; lp<zacc+iacc; lp++) *lp=0;
michael@0	5038
michael@0	5039	/* Start the multiplication */
michael@0	5040	/* Resolving carries can dominate the cost of accumulating the */
michael@0	5041	/* partial products, so this is only done when necessary. */
michael@0	5042	/* Each uLong item in the accumulator can hold values up to */
michael@0	5043	/* 2**64-1, and each partial product can be as large as */
michael@0	5044	/* (10**FASTDIGS-1)**2. When FASTDIGS=9, this can be added to */
michael@0	5045	/* itself 18.4 times in a uLong without overflowing, so during */
michael@0	5046	/* the main calculation resolution is carried out every 18th */
michael@0	5047	/* add -- every 162 digits. Similarly, when FASTDIGS=8, the */
michael@0	5048	/* partial products can be added to themselves 1844.6 times in */
michael@0	5049	/* a uLong without overflowing, so intermediate carry */
michael@0	5050	/* resolution occurs only every 14752 digits. Hence for common */
michael@0	5051	/* short numbers usually only the one final carry resolution */
michael@0	5052	/* occurs. */
michael@0	5053	/* (The count is set via FASTLAZY to simplify experiments to */
michael@0	5054	/* measure the value of this approach: a 35% improvement on a */
michael@0	5055	/* [34x34] multiply.) */
michael@0	5056	lazy=FASTLAZY; /* carry delay count */
michael@0	5057	for (rip=zrhi; rip<=rmsi; rip++) { /* over each item in rhs */
michael@0	5058	lp=zacc+(rip-zrhi); /* where to add the lhs */
michael@0	5059	for (lip=zlhi; lip<=lmsi; lip++, lp++) { /* over each item in lhs */
michael@0	5060	*lp+=(uLong)(*lip)*(*rip); /* [this should in-line] */
michael@0	5061	} /* lip loop */
michael@0	5062	lazy--;
michael@0	5063	if (lazy>0 && rip!=rmsi) continue;
michael@0	5064	lazy=FASTLAZY; /* reset delay count */
michael@0	5065	/* spin up the accumulator resolving overflows */
michael@0	5066	for (lp=zacc; lp<zacc+iacc; lp++) {
michael@0	5067	if (*lp<FASTBASE) continue; /* it fits */
michael@0	5068	lcarry=*lp/FASTBASE; /* top part [slow divide] */
michael@0	5069	/* lcarry can exceed 2**32-1, so check again; this check */
michael@0	5070	/* and occasional extra divide (slow) is well worth it, as */
michael@0	5071	/* it allows FASTLAZY to be increased to 18 rather than 4 */
michael@0	5072	/* in the FASTDIGS=9 case */
michael@0	5073	if (lcarry<FASTBASE) carry=(uInt)lcarry; /* [usual] */
michael@0	5074	else { /* two-place carry [fairly rare] */
michael@0	5075	uInt carry2=(uInt)(lcarry/FASTBASE); /* top top part */
michael@0	5076	*(lp+2)+=carry2; /* add to item+2 */
michael@0	5077	*lp-=((uLong)FASTBASE*FASTBASE*carry2); /* [slow] */
michael@0	5078	carry=(uInt)(lcarry-((uLong)FASTBASE*carry2)); /* [inline] */
michael@0	5079	}
michael@0	5080	*(lp+1)+=carry; /* add to item above [inline] */
michael@0	5081	*lp-=((uLong)FASTBASE*carry); /* [inline] */
michael@0	5082	} /* carry resolution */
michael@0	5083	} /* rip loop */
michael@0	5084
michael@0	5085	/* The multiplication is complete; time to convert back into */
michael@0	5086	/* units. This can be done in-place in the accumulator and in */
michael@0	5087	/* 32-bit operations, because carries were resolved after the */
michael@0	5088	/* final add. This needs N-1 divides and multiplies for */
michael@0	5089	/* each item in the accumulator (which will become up to N */
michael@0	5090	/* units, where 2<=N<=9). */
michael@0	5091	for (lp=zacc, up=acc; lp<zacc+iacc; lp++) {
michael@0	5092	uInt item=(uInt)*lp; /* decapitate to uInt */
michael@0	5093	for (p=0; p<FASTDIGS-DECDPUN; p+=DECDPUN, up++) {
michael@0	5094	uInt part=item/(DECDPUNMAX+1);
michael@0	5095	*up=(Unit)(item-(part*(DECDPUNMAX+1)));
michael@0	5096	item=part;
michael@0	5097	} /* p */
michael@0	5098	*up=(Unit)item; up++; /* [final needs no division] */
michael@0	5099	} /* lp */
michael@0	5100	accunits=up-acc; /* count of units */
michael@0	5101	}
michael@0	5102	else { /* here to use units directly, without chunking ['old code'] */
michael@0	5103	#endif
michael@0	5104
michael@0	5105	/* if accumulator will be too long for local storage, then allocate */
michael@0	5106	acc=accbuff; /* -> assume buffer for accumulator */
michael@0	5107	needbytes=(D2U(lhs->digits)+D2U(rhs->digits))*sizeof(Unit);
michael@0	5108	if (needbytes>(Int)sizeof(accbuff)) {
michael@0	5109	allocacc=(Unit *)malloc(needbytes);
michael@0	5110	if (allocacc==NULL) {*status|=DEC_Insufficient_storage; break;}
michael@0	5111	acc=(Unit *)allocacc; /* use the allocated space */
michael@0	5112	}
michael@0	5113
michael@0	5114	/* Now the main long multiplication loop */
michael@0	5115	/* Unlike the equivalent in the IBM Java implementation, there */
michael@0	5116	/* is no advantage in calculating from msu to lsu. So, do it */
michael@0	5117	/* by the book, as it were. */
michael@0	5118	/* Each iteration calculates ACC=ACC+MULTAND*MULT */
michael@0	5119	accunits=1; /* accumulator starts at '0' */
michael@0	5120	*acc=0; /* .. (lsu=0) */
michael@0	5121	shift=0; /* no multiplicand shift at first */
michael@0	5122	madlength=D2U(lhs->digits); /* this won't change */
michael@0	5123	mermsup=rhs->lsu+D2U(rhs->digits); /* -> msu+1 of multiplier */
michael@0	5124
michael@0	5125	for (mer=rhs->lsu; mer<mermsup; mer++) {
michael@0	5126	/* Here, *mer is the next Unit in the multiplier to use */
michael@0	5127	/* If non-zero [optimization] add it... */
michael@0	5128	if (*mer!=0) accunits=decUnitAddSub(&acc[shift], accunits-shift,
michael@0	5129	lhs->lsu, madlength, 0,
michael@0	5130	&acc[shift], *mer)
michael@0	5131	+ shift;
michael@0	5132	else { /* extend acc with a 0; it will be used shortly */
michael@0	5133	*(acc+accunits)=0; /* [this avoids length of <=0 later] */
michael@0	5134	accunits++;
michael@0	5135	}
michael@0	5136	/* multiply multiplicand by 10**DECDPUN for next Unit to left */
michael@0	5137	shift++; /* add this for 'logical length' */
michael@0	5138	} /* n */
michael@0	5139	#if FASTMUL
michael@0	5140	} /* unchunked units */
michael@0	5141	#endif
michael@0	5142	/* common end-path */
michael@0	5143	#if DECTRACE
michael@0	5144	decDumpAr('*', acc, accunits); /* Show exact result */
michael@0	5145	#endif
michael@0	5146
michael@0	5147	/* acc now contains the exact result of the multiplication, */
michael@0	5148	/* possibly with a leading zero unit; build the decNumber from */
michael@0	5149	/* it, noting if any residue */
michael@0	5150	res->bits=bits; /* set sign */
michael@0	5151	res->digits=decGetDigits(acc, accunits); /* count digits exactly */
michael@0	5152
michael@0	5153	/* There can be a 31-bit wrap in calculating the exponent. */
michael@0	5154	/* This can only happen if both input exponents are negative and */
michael@0	5155	/* both their magnitudes are large. If there was a wrap, set a */
michael@0	5156	/* safe very negative exponent, from which decFinalize() will */
michael@0	5157	/* raise a hard underflow shortly. */
michael@0	5158	exponent=lhs->exponent+rhs->exponent; /* calculate exponent */
michael@0	5159	if (lhs->exponent<0 && rhs->exponent<0 && exponent>0)
michael@0	5160	exponent=-2*DECNUMMAXE; /* force underflow */
michael@0	5161	res->exponent=exponent; /* OK to overwrite now */
michael@0	5162
michael@0	5163
michael@0	5164	/* Set the coefficient. If any rounding, residue records */
michael@0	5165	decSetCoeff(res, set, acc, res->digits, &residue, status);
michael@0	5166	decFinish(res, set, &residue, status); /* final cleanup */
michael@0	5167	} while(0); /* end protected */
michael@0	5168
michael@0	5169	if (allocacc!=NULL) free(allocacc); /* drop any storage used */
michael@0	5170	#if DECSUBSET
michael@0	5171	if (allocrhs!=NULL) free(allocrhs); /* .. */
michael@0	5172	if (alloclhs!=NULL) free(alloclhs); /* .. */
michael@0	5173	#endif
michael@0	5174	#if FASTMUL
michael@0	5175	if (allocrhi!=NULL) free(allocrhi); /* .. */
michael@0	5176	if (alloclhi!=NULL) free(alloclhi); /* .. */
michael@0	5177	#endif
michael@0	5178	return res;
michael@0	5179	} /* decMultiplyOp */
michael@0	5180
michael@0	5181	/* ------------------------------------------------------------------ */
michael@0	5182	/* decExpOp -- effect exponentiation */
michael@0	5183	/* */
michael@0	5184	/* This computes C = exp(A) */
michael@0	5185	/* */
michael@0	5186	/* res is C, the result. C may be A */
michael@0	5187	/* rhs is A */
michael@0	5188	/* set is the context; note that rounding mode has no effect */
michael@0	5189	/* */
michael@0	5190	/* C must have space for set->digits digits. status is updated but */
michael@0	5191	/* not set. */
michael@0	5192	/* */
michael@0	5193	/* Restrictions: */
michael@0	5194	/* */
michael@0	5195	/* digits, emax, and -emin in the context must be less than */
michael@0	5196	/* 2*DEC_MAX_MATH (1999998), and the rhs must be within these */
michael@0	5197	/* bounds or a zero. This is an internal routine, so these */
michael@0	5198	/* restrictions are contractual and not enforced. */
michael@0	5199	/* */
michael@0	5200	/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */
michael@0	5201	/* almost always be correctly rounded, but may be up to 1 ulp in */
michael@0	5202	/* error in rare cases. */
michael@0	5203	/* */
michael@0	5204	/* Finite results will always be full precision and Inexact, except */
michael@0	5205	/* when A is a zero or -Infinity (giving 1 or 0 respectively). */
michael@0	5206	/* ------------------------------------------------------------------ */
michael@0	5207	/* This approach used here is similar to the algorithm described in */
michael@0	5208	/* */
michael@0	5209	/* Variable Precision Exponential Function, T. E. Hull and */
michael@0	5210	/* A. Abrham, ACM Transactions on Mathematical Software, Vol 12 #2, */
michael@0	5211	/* pp79-91, ACM, June 1986. */
michael@0	5212	/* */
michael@0	5213	/* with the main difference being that the iterations in the series */
michael@0	5214	/* evaluation are terminated dynamically (which does not require the */
michael@0	5215	/* extra variable-precision variables which are expensive in this */
michael@0	5216	/* context). */
michael@0	5217	/* */
michael@0	5218	/* The error analysis in Hull & Abrham's paper applies except for the */
michael@0	5219	/* round-off error accumulation during the series evaluation. This */
michael@0	5220	/* code does not precalculate the number of iterations and so cannot */
michael@0	5221	/* use Horner's scheme. Instead, the accumulation is done at double- */
michael@0	5222	/* precision, which ensures that the additions of the terms are exact */
michael@0	5223	/* and do not accumulate round-off (and any round-off errors in the */
michael@0	5224	/* terms themselves move 'to the right' faster than they can */
michael@0	5225	/* accumulate). This code also extends the calculation by allowing, */
michael@0	5226	/* in the spirit of other decNumber operators, the input to be more */
michael@0	5227	/* precise than the result (the precision used is based on the more */
michael@0	5228	/* precise of the input or requested result). */
michael@0	5229	/* */
michael@0	5230	/* Implementation notes: */
michael@0	5231	/* */
michael@0	5232	/* 1. This is separated out as decExpOp so it can be called from */
michael@0	5233	/* other Mathematical functions (notably Ln) with a wider range */
michael@0	5234	/* than normal. In particular, it can handle the slightly wider */
michael@0	5235	/* (double) range needed by Ln (which has to be able to calculate */
michael@0	5236	/* exp(-x) where x can be the tiniest number (Ntiny). */
michael@0	5237	/* */
michael@0	5238	/* 2. Normalizing x to be <=0.1 (instead of <=1) reduces loop */
michael@0	5239	/* iterations by appoximately a third with additional (although */
michael@0	5240	/* diminishing) returns as the range is reduced to even smaller */
michael@0	5241	/* fractions. However, h (the power of 10 used to correct the */
michael@0	5242	/* result at the end, see below) must be kept <=8 as otherwise */
michael@0	5243	/* the final result cannot be computed. Hence the leverage is a */
michael@0	5244	/* sliding value (8-h), where potentially the range is reduced */
michael@0	5245	/* more for smaller values. */
michael@0	5246	/* */
michael@0	5247	/* The leverage that can be applied in this way is severely */
michael@0	5248	/* limited by the cost of the raise-to-the power at the end, */
michael@0	5249	/* which dominates when the number of iterations is small (less */
michael@0	5250	/* than ten) or when rhs is short. As an example, the adjustment */
michael@0	5251	/* x**10,000,000 needs 31 multiplications, all but one full-width. */
michael@0	5252	/* */
michael@0	5253	/* 3. The restrictions (especially precision) could be raised with */
michael@0	5254	/* care, but the full decNumber range seems very hard within the */
michael@0	5255	/* 32-bit limits. */
michael@0	5256	/* */
michael@0	5257	/* 4. The working precisions for the static buffers are twice the */
michael@0	5258	/* obvious size to allow for calls from decNumberPower. */
michael@0	5259	/* ------------------------------------------------------------------ */
michael@0	5260	decNumber * decExpOp(decNumber *res, const decNumber *rhs,
michael@0	5261	decContext *set, uInt *status) {
michael@0	5262	uInt ignore=0; /* working status */
michael@0	5263	Int h; /* adjusted exponent for 0.xxxx */
michael@0	5264	Int p; /* working precision */
michael@0	5265	Int residue; /* rounding residue */
michael@0	5266	uInt needbytes; /* for space calculations */
michael@0	5267	const decNumber *x=rhs; /* (may point to safe copy later) */
michael@0	5268	decContext aset, tset, dset; /* working contexts */
michael@0	5269	Int comp; /* work */
michael@0	5270
michael@0	5271	/* the argument is often copied to normalize it, so (unusually) it */
michael@0	5272	/* is treated like other buffers, using DECBUFFER, +1 in case */
michael@0	5273	/* DECBUFFER is 0 */
michael@0	5274	decNumber bufr[D2N(DECBUFFER*2+1)];
michael@0	5275	decNumber *allocrhs=NULL; /* non-NULL if rhs buffer allocated */
michael@0	5276
michael@0	5277	/* the working precision will be no more than set->digits+8+1 */
michael@0	5278	/* so for on-stack buffers DECBUFFER+9 is used, +1 in case DECBUFFER */
michael@0	5279	/* is 0 (and twice that for the accumulator) */
michael@0	5280
michael@0	5281	/* buffer for t, term (working precision plus) */
michael@0	5282	decNumber buft[D2N(DECBUFFER*2+9+1)];
michael@0	5283	decNumber *allocbuft=NULL; /* -> allocated buft, iff allocated */
michael@0	5284	decNumber *t=buft; /* term */
michael@0	5285	/* buffer for a, accumulator (working precision * 2), at least 9 */
michael@0	5286	decNumber bufa[D2N(DECBUFFER*4+18+1)];
michael@0	5287	decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */
michael@0	5288	decNumber *a=bufa; /* accumulator */
michael@0	5289	/* decNumber for the divisor term; this needs at most 9 digits */
michael@0	5290	/* and so can be fixed size [16 so can use standard context] */
michael@0	5291	decNumber bufd[D2N(16)];
michael@0	5292	decNumber *d=bufd; /* divisor */
michael@0	5293	decNumber numone; /* constant 1 */
michael@0	5294
michael@0	5295	#if DECCHECK
michael@0	5296	Int iterations=0; /* for later sanity check */
michael@0	5297	if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
michael@0	5298	#endif
michael@0	5299
michael@0	5300	do { /* protect allocated storage */
michael@0	5301	if (SPECIALARG) { /* handle infinities and NaNs */
michael@0	5302	if (decNumberIsInfinite(rhs)) { /* an infinity */
michael@0	5303	if (decNumberIsNegative(rhs)) /* -Infinity -> +0 */
michael@0	5304	uprv_decNumberZero(res);
michael@0	5305	else uprv_decNumberCopy(res, rhs); /* +Infinity -> self */
michael@0	5306	}
michael@0	5307	else decNaNs(res, rhs, NULL, set, status); /* a NaN */
michael@0	5308	break;}
michael@0	5309
michael@0	5310	if (ISZERO(rhs)) { /* zeros -> exact 1 */
michael@0	5311	uprv_decNumberZero(res); /* make clean 1 */
michael@0	5312	*res->lsu=1; /* .. */
michael@0	5313	break;} /* [no status to set] */
michael@0	5314
michael@0	5315	/* e**x when 0 < x < 0.66 is < 1+3x/2, hence can fast-path */
michael@0	5316	/* positive and negative tiny cases which will result in inexact */
michael@0	5317	/* 1. This also allows the later add-accumulate to always be */
michael@0	5318	/* exact (because its length will never be more than twice the */
michael@0	5319	/* working precision). */
michael@0	5320	/* The comparator (tiny) needs just one digit, so use the */
michael@0	5321	/* decNumber d for it (reused as the divisor, etc., below); its */
michael@0	5322	/* exponent is such that if x is positive it will have */
michael@0	5323	/* set->digits-1 zeros between the decimal point and the digit, */
michael@0	5324	/* which is 4, and if x is negative one more zero there as the */
michael@0	5325	/* more precise result will be of the form 0.9999999 rather than */
michael@0	5326	/* 1.0000001. Hence, tiny will be 0.0000004 if digits=7 and x>0 */
michael@0	5327	/* or 0.00000004 if digits=7 and x<0. If RHS not larger than */
michael@0	5328	/* this then the result will be 1.000000 */
michael@0	5329	uprv_decNumberZero(d); /* clean */
michael@0	5330	*d->lsu=4; /* set 4 .. */
michael@0	5331	d->exponent=-set->digits; /* * 10**(-d) */
michael@0	5332	if (decNumberIsNegative(rhs)) d->exponent--; /* negative case */
michael@0	5333	comp=decCompare(d, rhs, 1); /* signless compare */
michael@0	5334	if (comp==BADINT) {
michael@0	5335	*status|=DEC_Insufficient_storage;
michael@0	5336	break;}
michael@0	5337	if (comp>=0) { /* rhs < d */
michael@0	5338	Int shift=set->digits-1;
michael@0	5339	uprv_decNumberZero(res); /* set 1 */
michael@0	5340	*res->lsu=1; /* .. */
michael@0	5341	res->digits=decShiftToMost(res->lsu, 1, shift);
michael@0	5342	res->exponent=-shift; /* make 1.0000... */
michael@0	5343	*status|=DEC_Inexact | DEC_Rounded; /* .. inexactly */
michael@0	5344	break;} /* tiny */
michael@0	5345
michael@0	5346	/* set up the context to be used for calculating a, as this is */
michael@0	5347	/* used on both paths below */
michael@0	5348	uprv_decContextDefault(&aset, DEC_INIT_DECIMAL64);
michael@0	5349	/* accumulator bounds are as requested (could underflow) */
michael@0	5350	aset.emax=set->emax; /* usual bounds */
michael@0	5351	aset.emin=set->emin; /* .. */
michael@0	5352	aset.clamp=0; /* and no concrete format */
michael@0	5353
michael@0	5354	/* calculate the adjusted (Hull & Abrham) exponent (where the */
michael@0	5355	/* decimal point is just to the left of the coefficient msd) */
michael@0	5356	h=rhs->exponent+rhs->digits;
michael@0	5357	/* if h>8 then 10**h cannot be calculated safely; however, when */
michael@0	5358	/* h=8 then exp(|rhs|) will be at least exp(1E+7) which is at */
michael@0	5359	/* least 6.59E+4342944, so (due to the restriction on Emax/Emin) */
michael@0	5360	/* overflow (or underflow to 0) is guaranteed -- so this case can */
michael@0	5361	/* be handled by simply forcing the appropriate excess */
michael@0	5362	if (h>8) { /* overflow/underflow */
michael@0	5363	/* set up here so Power call below will over or underflow to */
michael@0	5364	/* zero; set accumulator to either 2 or 0.02 */
michael@0	5365	/* [stack buffer for a is always big enough for this] */
michael@0	5366	uprv_decNumberZero(a);
michael@0	5367	*a->lsu=2; /* not 1 but < exp(1) */
michael@0	5368	if (decNumberIsNegative(rhs)) a->exponent=-2; /* make 0.02 */
michael@0	5369	h=8; /* clamp so 10**h computable */
michael@0	5370	p=9; /* set a working precision */
michael@0	5371	}
michael@0	5372	else { /* h<=8 */
michael@0	5373	Int maxlever=(rhs->digits>8?1:0);
michael@0	5374	/* [could/should increase this for precisions >40 or so, too] */
michael@0	5375
michael@0	5376	/* if h is 8, cannot normalize to a lower upper limit because */
michael@0	5377	/* the final result will not be computable (see notes above), */
michael@0	5378	/* but leverage can be applied whenever h is less than 8. */
michael@0	5379	/* Apply as much as possible, up to a MAXLEVER digits, which */
michael@0	5380	/* sets the tradeoff against the cost of the later a**(10**h). */
michael@0	5381	/* As h is increased, the working precision below also */
michael@0	5382	/* increases to compensate for the "constant digits at the */
michael@0	5383	/* front" effect. */
michael@0	5384	Int lever=MINI(8-h, maxlever); /* leverage attainable */
michael@0	5385	Int use=-rhs->digits-lever; /* exponent to use for RHS */
michael@0	5386	h+=lever; /* apply leverage selected */
michael@0	5387	if (h<0) { /* clamp */
michael@0	5388	use+=h; /* [may end up subnormal] */
michael@0	5389	h=0;
michael@0	5390	}
michael@0	5391	/* Take a copy of RHS if it needs normalization (true whenever x>=1) */
michael@0	5392	if (rhs->exponent!=use) {
michael@0	5393	decNumber *newrhs=bufr; /* assume will fit on stack */
michael@0	5394	needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
michael@0	5395	if (needbytes>sizeof(bufr)) { /* need malloc space */
michael@0	5396	allocrhs=(decNumber *)malloc(needbytes);
michael@0	5397	if (allocrhs==NULL) { /* hopeless -- abandon */
michael@0	5398	*status|=DEC_Insufficient_storage;
michael@0	5399	break;}
michael@0	5400	newrhs=allocrhs; /* use the allocated space */
michael@0	5401	}
michael@0	5402	uprv_decNumberCopy(newrhs, rhs); /* copy to safe space */
michael@0	5403	newrhs->exponent=use; /* normalize; now <1 */
michael@0	5404	x=newrhs; /* ready for use */
michael@0	5405	/* decNumberShow(x); */
michael@0	5406	}
michael@0	5407
michael@0	5408	/* Now use the usual power series to evaluate exp(x). The */
michael@0	5409	/* series starts as 1 + x + x^2/2 ... so prime ready for the */
michael@0	5410	/* third term by setting the term variable t=x, the accumulator */
michael@0	5411	/* a=1, and the divisor d=2. */
michael@0	5412
michael@0	5413	/* First determine the working precision. From Hull & Abrham */
michael@0	5414	/* this is set->digits+h+2. However, if x is 'over-precise' we */
michael@0	5415	/* need to allow for all its digits to potentially participate */
michael@0	5416	/* (consider an x where all the excess digits are 9s) so in */
michael@0	5417	/* this case use x->digits+h+2 */
michael@0	5418	p=MAXI(x->digits, set->digits)+h+2; /* [h<=8] */
michael@0	5419
michael@0	5420	/* a and t are variable precision, and depend on p, so space */
michael@0	5421	/* must be allocated for them if necessary */
michael@0	5422
michael@0	5423	/* the accumulator needs to be able to hold 2p digits so that */
michael@0	5424	/* the additions on the second and subsequent iterations are */
michael@0	5425	/* sufficiently exact. */
michael@0	5426	needbytes=sizeof(decNumber)+(D2U(p*2)-1)*sizeof(Unit);
michael@0	5427	if (needbytes>sizeof(bufa)) { /* need malloc space */
michael@0	5428	allocbufa=(decNumber *)malloc(needbytes);
michael@0	5429	if (allocbufa==NULL) { /* hopeless -- abandon */
michael@0	5430	*status|=DEC_Insufficient_storage;
michael@0	5431	break;}
michael@0	5432	a=allocbufa; /* use the allocated space */
michael@0	5433	}
michael@0	5434	/* the term needs to be able to hold p digits (which is */
michael@0	5435	/* guaranteed to be larger than x->digits, so the initial copy */
michael@0	5436	/* is safe); it may also be used for the raise-to-power */
michael@0	5437	/* calculation below, which needs an extra two digits */
michael@0	5438	needbytes=sizeof(decNumber)+(D2U(p+2)-1)*sizeof(Unit);
michael@0	5439	if (needbytes>sizeof(buft)) { /* need malloc space */
michael@0	5440	allocbuft=(decNumber *)malloc(needbytes);
michael@0	5441	if (allocbuft==NULL) { /* hopeless -- abandon */
michael@0	5442	*status|=DEC_Insufficient_storage;
michael@0	5443	break;}
michael@0	5444	t=allocbuft; /* use the allocated space */
michael@0	5445	}
michael@0	5446
michael@0	5447	uprv_decNumberCopy(t, x); /* term=x */
michael@0	5448	uprv_decNumberZero(a); *a->lsu=1; /* accumulator=1 */
michael@0	5449	uprv_decNumberZero(d); *d->lsu=2; /* divisor=2 */
michael@0	5450	uprv_decNumberZero(&numone); *numone.lsu=1; /* constant 1 for increment */
michael@0	5451
michael@0	5452	/* set up the contexts for calculating a, t, and d */
michael@0	5453	uprv_decContextDefault(&tset, DEC_INIT_DECIMAL64);
michael@0	5454	dset=tset;
michael@0	5455	/* accumulator bounds are set above, set precision now */
michael@0	5456	aset.digits=p*2; /* double */
michael@0	5457	/* term bounds avoid any underflow or overflow */
michael@0	5458	tset.digits=p;
michael@0	5459	tset.emin=DEC_MIN_EMIN; /* [emax is plenty] */
michael@0	5460	/* [dset.digits=16, etc., are sufficient] */
michael@0	5461
michael@0	5462	/* finally ready to roll */
michael@0	5463	for (;;) {
michael@0	5464	#if DECCHECK
michael@0	5465	iterations++;
michael@0	5466	#endif
michael@0	5467	/* only the status from the accumulation is interesting */
michael@0	5468	/* [but it should remain unchanged after first add] */
michael@0	5469	decAddOp(a, a, t, &aset, 0, status); /* a=a+t */
michael@0	5470	decMultiplyOp(t, t, x, &tset, &ignore); /* t=t*x */
michael@0	5471	decDivideOp(t, t, d, &tset, DIVIDE, &ignore); /* t=t/d */
michael@0	5472	/* the iteration ends when the term cannot affect the result, */
michael@0	5473	/* if rounded to p digits, which is when its value is smaller */
michael@0	5474	/* than the accumulator by p+1 digits. There must also be */
michael@0	5475	/* full precision in a. */
michael@0	5476	if (((a->digits+a->exponent)>=(t->digits+t->exponent+p+1))
michael@0	5477	&& (a->digits>=p)) break;
michael@0	5478	decAddOp(d, d, &numone, &dset, 0, &ignore); /* d=d+1 */
michael@0	5479	} /* iterate */
michael@0	5480
michael@0	5481	#if DECCHECK
michael@0	5482	/* just a sanity check; comment out test to show always */
michael@0	5483	if (iterations>p+3)
michael@0	5484	printf("Exp iterations=%ld, status=%08lx, p=%ld, d=%ld\n",
michael@0	5485	(LI)iterations, (LI)*status, (LI)p, (LI)x->digits);
michael@0	5486	#endif
michael@0	5487	} /* h<=8 */
michael@0	5488
michael@0	5489	/* apply postconditioning: a=a**(10**h) -- this is calculated */
michael@0	5490	/* at a slightly higher precision than Hull & Abrham suggest */
michael@0	5491	if (h>0) {
michael@0	5492	Int seenbit=0; /* set once a 1-bit is seen */
michael@0	5493	Int i; /* counter */
michael@0	5494	Int n=powers[h]; /* always positive */
michael@0	5495	aset.digits=p+2; /* sufficient precision */
michael@0	5496	/* avoid the overhead and many extra digits of decNumberPower */
michael@0	5497	/* as all that is needed is the short 'multipliers' loop; here */
michael@0	5498	/* accumulate the answer into t */
michael@0	5499	uprv_decNumberZero(t); *t->lsu=1; /* acc=1 */
michael@0	5500	for (i=1;;i++){ /* for each bit [top bit ignored] */
michael@0	5501	/* abandon if have had overflow or terminal underflow */
michael@0	5502	if (*status & (DEC_Overflow|DEC_Underflow)) { /* interesting? */
michael@0	5503	if (*status&DEC_Overflow || ISZERO(t)) break;}
michael@0	5504	n=n<<1; /* move next bit to testable position */
michael@0	5505	if (n<0) { /* top bit is set */
michael@0	5506	seenbit=1; /* OK, have a significant bit */
michael@0	5507	decMultiplyOp(t, t, a, &aset, status); /* acc=acc*x */
michael@0	5508	}
michael@0	5509	if (i==31) break; /* that was the last bit */
michael@0	5510	if (!seenbit) continue; /* no need to square 1 */
michael@0	5511	decMultiplyOp(t, t, t, &aset, status); /* acc=acc*acc [square] */
michael@0	5512	} /*i*/ /* 32 bits */
michael@0	5513	/* decNumberShow(t); */
michael@0	5514	a=t; /* and carry on using t instead of a */
michael@0	5515	}
michael@0	5516
michael@0	5517	/* Copy and round the result to res */
michael@0	5518	residue=1; /* indicate dirt to right .. */
michael@0	5519	if (ISZERO(a)) residue=0; /* .. unless underflowed to 0 */
michael@0	5520	aset.digits=set->digits; /* [use default rounding] */
michael@0	5521	decCopyFit(res, a, &aset, &residue, status); /* copy & shorten */
michael@0	5522	decFinish(res, set, &residue, status); /* cleanup/set flags */
michael@0	5523	} while(0); /* end protected */
michael@0	5524
michael@0	5525	if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */
michael@0	5526	if (allocbufa!=NULL) free(allocbufa); /* .. */
michael@0	5527	if (allocbuft!=NULL) free(allocbuft); /* .. */
michael@0	5528	/* [status is handled by caller] */
michael@0	5529	return res;
michael@0	5530	} /* decExpOp */
michael@0	5531
michael@0	5532	/* ------------------------------------------------------------------ */
michael@0	5533	/* Initial-estimate natural logarithm table */
michael@0	5534	/* */
michael@0	5535	/* LNnn -- 90-entry 16-bit table for values from .10 through .99. */
michael@0	5536	/* The result is a 4-digit encode of the coefficient (c=the */
michael@0	5537	/* top 14 bits encoding 0-9999) and a 2-digit encode of the */
michael@0	5538	/* exponent (e=the bottom 2 bits encoding 0-3) */
michael@0	5539	/* */
michael@0	5540	/* The resulting value is given by: */
michael@0	5541	/* */
michael@0	5542	/* v = -c * 10**(-e-3) */
michael@0	5543	/* */
michael@0	5544	/* where e and c are extracted from entry k = LNnn[x-10] */
michael@0	5545	/* where x is truncated (NB) into the range 10 through 99, */
michael@0	5546	/* and then c = k>>2 and e = k&3. */
michael@0	5547	/* ------------------------------------------------------------------ */
michael@0	5548	static const uShort LNnn[90]={9016, 8652, 8316, 8008, 7724, 7456, 7208,
michael@0	5549	6972, 6748, 6540, 6340, 6148, 5968, 5792, 5628, 5464, 5312,
michael@0	5550	5164, 5020, 4884, 4748, 4620, 4496, 4376, 4256, 4144, 4032,
michael@0	5551	39233, 38181, 37157, 36157, 35181, 34229, 33297, 32389, 31501, 30629,
michael@0	5552	29777, 28945, 28129, 27329, 26545, 25777, 25021, 24281, 23553, 22837,
michael@0	5553	22137, 21445, 20769, 20101, 19445, 18801, 18165, 17541, 16925, 16321,
michael@0	5554	15721, 15133, 14553, 13985, 13421, 12865, 12317, 11777, 11241, 10717,
michael@0	5555	10197, 9685, 9177, 8677, 8185, 7697, 7213, 6737, 6269, 5801,
michael@0	5556	5341, 4889, 4437, 39930, 35534, 31186, 26886, 22630, 18418, 14254,
michael@0	5557	10130, 6046, 20055};
michael@0	5558
michael@0	5559	/* ------------------------------------------------------------------ */
michael@0	5560	/* decLnOp -- effect natural logarithm */
michael@0	5561	/* */
michael@0	5562	/* This computes C = ln(A) */
michael@0	5563	/* */
michael@0	5564	/* res is C, the result. C may be A */
michael@0	5565	/* rhs is A */
michael@0	5566	/* set is the context; note that rounding mode has no effect */
michael@0	5567	/* */
michael@0	5568	/* C must have space for set->digits digits. */
michael@0	5569	/* */
michael@0	5570	/* Notable cases: */
michael@0	5571	/* A<0 -> Invalid */
michael@0	5572	/* A=0 -> -Infinity (Exact) */
michael@0	5573	/* A=+Infinity -> +Infinity (Exact) */
michael@0	5574	/* A=1 exactly -> 0 (Exact) */
michael@0	5575	/* */
michael@0	5576	/* Restrictions (as for Exp): */
michael@0	5577	/* */
michael@0	5578	/* digits, emax, and -emin in the context must be less than */
michael@0	5579	/* DEC_MAX_MATH+11 (1000010), and the rhs must be within these */
michael@0	5580	/* bounds or a zero. This is an internal routine, so these */
michael@0	5581	/* restrictions are contractual and not enforced. */
michael@0	5582	/* */
michael@0	5583	/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */
michael@0	5584	/* almost always be correctly rounded, but may be up to 1 ulp in */
michael@0	5585	/* error in rare cases. */
michael@0	5586	/* ------------------------------------------------------------------ */
michael@0	5587	/* The result is calculated using Newton's method, with each */
michael@0	5588	/* iteration calculating a' = a + x * exp(-a) - 1. See, for example, */
michael@0	5589	/* Epperson 1989. */
michael@0	5590	/* */
michael@0	5591	/* The iteration ends when the adjustment x*exp(-a)-1 is tiny enough. */
michael@0	5592	/* This has to be calculated at the sum of the precision of x and the */
michael@0	5593	/* working precision. */
michael@0	5594	/* */
michael@0	5595	/* Implementation notes: */
michael@0	5596	/* */
michael@0	5597	/* 1. This is separated out as decLnOp so it can be called from */
michael@0	5598	/* other Mathematical functions (e.g., Log 10) with a wider range */
michael@0	5599	/* than normal. In particular, it can handle the slightly wider */
michael@0	5600	/* (+9+2) range needed by a power function. */
michael@0	5601	/* */
michael@0	5602	/* 2. The speed of this function is about 10x slower than exp, as */
michael@0	5603	/* it typically needs 4-6 iterations for short numbers, and the */
michael@0	5604	/* extra precision needed adds a squaring effect, twice. */
michael@0	5605	/* */
michael@0	5606	/* 3. Fastpaths are included for ln(10) and ln(2), up to length 40, */
michael@0	5607	/* as these are common requests. ln(10) is used by log10(x). */
michael@0	5608	/* */
michael@0	5609	/* 4. An iteration might be saved by widening the LNnn table, and */
michael@0	5610	/* would certainly save at least one if it were made ten times */
michael@0	5611	/* bigger, too (for truncated fractions 0.100 through 0.999). */
michael@0	5612	/* However, for most practical evaluations, at least four or five */
michael@0	5613	/* iterations will be neede -- so this would only speed up by */
michael@0	5614	/* 20-25% and that probably does not justify increasing the table */
michael@0	5615	/* size. */
michael@0	5616	/* */
michael@0	5617	/* 5. The static buffers are larger than might be expected to allow */
michael@0	5618	/* for calls from decNumberPower. */
michael@0	5619	/* ------------------------------------------------------------------ */
michael@0	5620	#if defined(__clang__) || U_GCC_MAJOR_MINOR >= 406
michael@0	5621	#pragma GCC diagnostic push
michael@0	5622	#pragma GCC diagnostic ignored "-Warray-bounds"
michael@0	5623	#endif
michael@0	5624	decNumber * decLnOp(decNumber *res, const decNumber *rhs,
michael@0	5625	decContext *set, uInt *status) {
michael@0	5626	uInt ignore=0; /* working status accumulator */
michael@0	5627	uInt needbytes; /* for space calculations */
michael@0	5628	Int residue; /* rounding residue */
michael@0	5629	Int r; /* rhs=f*10**r [see below] */
michael@0	5630	Int p; /* working precision */
michael@0	5631	Int pp; /* precision for iteration */
michael@0	5632	Int t; /* work */
michael@0	5633
michael@0	5634	/* buffers for a (accumulator, typically precision+2) and b */
michael@0	5635	/* (adjustment calculator, same size) */
michael@0	5636	decNumber bufa[D2N(DECBUFFER+12)];
michael@0	5637	decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */
michael@0	5638	decNumber *a=bufa; /* accumulator/work */
michael@0	5639	decNumber bufb[D2N(DECBUFFER*2+2)];
michael@0	5640	decNumber *allocbufb=NULL; /* -> allocated bufa, iff allocated */
michael@0	5641	decNumber *b=bufb; /* adjustment/work */
michael@0	5642
michael@0	5643	decNumber numone; /* constant 1 */
michael@0	5644	decNumber cmp; /* work */
michael@0	5645	decContext aset, bset; /* working contexts */
michael@0	5646
michael@0	5647	#if DECCHECK
michael@0	5648	Int iterations=0; /* for later sanity check */
michael@0	5649	if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
michael@0	5650	#endif
michael@0	5651
michael@0	5652	do { /* protect allocated storage */
michael@0	5653	if (SPECIALARG) { /* handle infinities and NaNs */
michael@0	5654	if (decNumberIsInfinite(rhs)) { /* an infinity */
michael@0	5655	if (decNumberIsNegative(rhs)) /* -Infinity -> error */
michael@0	5656	*status|=DEC_Invalid_operation;
michael@0	5657	else uprv_decNumberCopy(res, rhs); /* +Infinity -> self */
michael@0	5658	}
michael@0	5659	else decNaNs(res, rhs, NULL, set, status); /* a NaN */
michael@0	5660	break;}
michael@0	5661
michael@0	5662	if (ISZERO(rhs)) { /* +/- zeros -> -Infinity */
michael@0	5663	uprv_decNumberZero(res); /* make clean */
michael@0	5664	res->bits=DECINF|DECNEG; /* set - infinity */
michael@0	5665	break;} /* [no status to set] */
michael@0	5666
michael@0	5667	/* Non-zero negatives are bad... */
michael@0	5668	if (decNumberIsNegative(rhs)) { /* -x -> error */
michael@0	5669	*status|=DEC_Invalid_operation;
michael@0	5670	break;}
michael@0	5671
michael@0	5672	/* Here, rhs is positive, finite, and in range */
michael@0	5673
michael@0	5674	/* lookaside fastpath code for ln(2) and ln(10) at common lengths */
michael@0	5675	if (rhs->exponent==0 && set->digits<=40) {
michael@0	5676	#if DECDPUN==1
michael@0	5677	if (rhs->lsu[0]==0 && rhs->lsu[1]==1 && rhs->digits==2) { /* ln(10) */
michael@0	5678	#else
michael@0	5679	if (rhs->lsu[0]==10 && rhs->digits==2) { /* ln(10) */
michael@0	5680	#endif
michael@0	5681	aset=*set; aset.round=DEC_ROUND_HALF_EVEN;
michael@0	5682	#define LN10 "2.302585092994045684017991454684364207601"
michael@0	5683	uprv_decNumberFromString(res, LN10, &aset);
michael@0	5684	*status|=(DEC_Inexact | DEC_Rounded); /* is inexact */
michael@0	5685	break;}
michael@0	5686	if (rhs->lsu[0]==2 && rhs->digits==1) { /* ln(2) */
michael@0	5687	aset=*set; aset.round=DEC_ROUND_HALF_EVEN;
michael@0	5688	#define LN2 "0.6931471805599453094172321214581765680755"
michael@0	5689	uprv_decNumberFromString(res, LN2, &aset);
michael@0	5690	*status|=(DEC_Inexact | DEC_Rounded);
michael@0	5691	break;}
michael@0	5692	} /* integer and short */
michael@0	5693
michael@0	5694	/* Determine the working precision. This is normally the */
michael@0	5695	/* requested precision + 2, with a minimum of 9. However, if */
michael@0	5696	/* the rhs is 'over-precise' then allow for all its digits to */
michael@0	5697	/* potentially participate (consider an rhs where all the excess */
michael@0	5698	/* digits are 9s) so in this case use rhs->digits+2. */
michael@0	5699	p=MAXI(rhs->digits, MAXI(set->digits, 7))+2;
michael@0	5700
michael@0	5701	/* Allocate space for the accumulator and the high-precision */
michael@0	5702	/* adjustment calculator, if necessary. The accumulator must */
michael@0	5703	/* be able to hold p digits, and the adjustment up to */
michael@0	5704	/* rhs->digits+p digits. They are also made big enough for 16 */
michael@0	5705	/* digits so that they can be used for calculating the initial */
michael@0	5706	/* estimate. */
michael@0	5707	needbytes=sizeof(decNumber)+(D2U(MAXI(p,16))-1)*sizeof(Unit);
michael@0	5708	if (needbytes>sizeof(bufa)) { /* need malloc space */
michael@0	5709	allocbufa=(decNumber *)malloc(needbytes);
michael@0	5710	if (allocbufa==NULL) { /* hopeless -- abandon */
michael@0	5711	*status|=DEC_Insufficient_storage;
michael@0	5712	break;}
michael@0	5713	a=allocbufa; /* use the allocated space */
michael@0	5714	}
michael@0	5715	pp=p+rhs->digits;
michael@0	5716	needbytes=sizeof(decNumber)+(D2U(MAXI(pp,16))-1)*sizeof(Unit);
michael@0	5717	if (needbytes>sizeof(bufb)) { /* need malloc space */
michael@0	5718	allocbufb=(decNumber *)malloc(needbytes);
michael@0	5719	if (allocbufb==NULL) { /* hopeless -- abandon */
michael@0	5720	*status|=DEC_Insufficient_storage;
michael@0	5721	break;}
michael@0	5722	b=allocbufb; /* use the allocated space */
michael@0	5723	}
michael@0	5724
michael@0	5725	/* Prepare an initial estimate in acc. Calculate this by */
michael@0	5726	/* considering the coefficient of x to be a normalized fraction, */
michael@0	5727	/* f, with the decimal point at far left and multiplied by */
michael@0	5728	/* 10**r. Then, rhs=f*10**r and 0.1<=f<1, and */
michael@0	5729	/* ln(x) = ln(f) + ln(10)*r */
michael@0	5730	/* Get the initial estimate for ln(f) from a small lookup */
michael@0	5731	/* table (see above) indexed by the first two digits of f, */
michael@0	5732	/* truncated. */
michael@0	5733
michael@0	5734	uprv_decContextDefault(&aset, DEC_INIT_DECIMAL64); /* 16-digit extended */
michael@0	5735	r=rhs->exponent+rhs->digits; /* 'normalised' exponent */
michael@0	5736	uprv_decNumberFromInt32(a, r); /* a=r */
michael@0	5737	uprv_decNumberFromInt32(b, 2302585); /* b=ln(10) (2.302585) */
michael@0	5738	b->exponent=-6; /* .. */
michael@0	5739	decMultiplyOp(a, a, b, &aset, &ignore); /* a=a*b */
michael@0	5740	/* now get top two digits of rhs into b by simple truncate and */
michael@0	5741	/* force to integer */
michael@0	5742	residue=0; /* (no residue) */
michael@0	5743	aset.digits=2; aset.round=DEC_ROUND_DOWN;
michael@0	5744	decCopyFit(b, rhs, &aset, &residue, &ignore); /* copy & shorten */
michael@0	5745	b->exponent=0; /* make integer */
michael@0	5746	t=decGetInt(b); /* [cannot fail] */
michael@0	5747	if (t<10) t=X10(t); /* adjust single-digit b */
michael@0	5748	t=LNnn[t-10]; /* look up ln(b) */
michael@0	5749	uprv_decNumberFromInt32(b, t>>2); /* b=ln(b) coefficient */
michael@0	5750	b->exponent=-(t&3)-3; /* set exponent */
michael@0	5751	b->bits=DECNEG; /* ln(0.10)->ln(0.99) always -ve */
michael@0	5752	aset.digits=16; aset.round=DEC_ROUND_HALF_EVEN; /* restore */
michael@0	5753	decAddOp(a, a, b, &aset, 0, &ignore); /* acc=a+b */
michael@0	5754	/* the initial estimate is now in a, with up to 4 digits correct. */
michael@0	5755	/* When rhs is at or near Nmax the estimate will be low, so we */
michael@0	5756	/* will approach it from below, avoiding overflow when calling exp. */
michael@0	5757
michael@0	5758	uprv_decNumberZero(&numone); *numone.lsu=1; /* constant 1 for adjustment */
michael@0	5759
michael@0	5760	/* accumulator bounds are as requested (could underflow, but */
michael@0	5761	/* cannot overflow) */
michael@0	5762	aset.emax=set->emax;
michael@0	5763	aset.emin=set->emin;
michael@0	5764	aset.clamp=0; /* no concrete format */
michael@0	5765	/* set up a context to be used for the multiply and subtract */
michael@0	5766	bset=aset;
michael@0	5767	bset.emax=DEC_MAX_MATH*2; /* use double bounds for the */
michael@0	5768	bset.emin=-DEC_MAX_MATH*2; /* adjustment calculation */
michael@0	5769	/* [see decExpOp call below] */
michael@0	5770	/* for each iteration double the number of digits to calculate, */
michael@0	5771	/* up to a maximum of p */
michael@0	5772	pp=9; /* initial precision */
michael@0	5773	/* [initially 9 as then the sequence starts 7+2, 16+2, and */
michael@0	5774	/* 34+2, which is ideal for standard-sized numbers] */
michael@0	5775	aset.digits=pp; /* working context */
michael@0	5776	bset.digits=pp+rhs->digits; /* wider context */
michael@0	5777	for (;;) { /* iterate */
michael@0	5778	#if DECCHECK
michael@0	5779	iterations++;
michael@0	5780	if (iterations>24) break; /* consider 9 * 2**24 */
michael@0	5781	#endif
michael@0	5782	/* calculate the adjustment (exp(-a)*x-1) into b. This is a */
michael@0	5783	/* catastrophic subtraction but it really is the difference */
michael@0	5784	/* from 1 that is of interest. */
michael@0	5785	/* Use the internal entry point to Exp as it allows the double */
michael@0	5786	/* range for calculating exp(-a) when a is the tiniest subnormal. */
michael@0	5787	a->bits^=DECNEG; /* make -a */
michael@0	5788	decExpOp(b, a, &bset, &ignore); /* b=exp(-a) */
michael@0	5789	a->bits^=DECNEG; /* restore sign of a */
michael@0	5790	/* now multiply by rhs and subtract 1, at the wider precision */
michael@0	5791	decMultiplyOp(b, b, rhs, &bset, &ignore); /* b=b*rhs */
michael@0	5792	decAddOp(b, b, &numone, &bset, DECNEG, &ignore); /* b=b-1 */
michael@0	5793
michael@0	5794	/* the iteration ends when the adjustment cannot affect the */
michael@0	5795	/* result by >=0.5 ulp (at the requested digits), which */
michael@0	5796	/* is when its value is smaller than the accumulator by */
michael@0	5797	/* set->digits+1 digits (or it is zero) -- this is a looser */
michael@0	5798	/* requirement than for Exp because all that happens to the */
michael@0	5799	/* accumulator after this is the final rounding (but note that */
michael@0	5800	/* there must also be full precision in a, or a=0). */
michael@0	5801
michael@0	5802	if (decNumberIsZero(b) ||
michael@0	5803	(a->digits+a->exponent)>=(b->digits+b->exponent+set->digits+1)) {
michael@0	5804	if (a->digits==p) break;
michael@0	5805	if (decNumberIsZero(a)) {
michael@0	5806	decCompareOp(&cmp, rhs, &numone, &aset, COMPARE, &ignore); /* rhs=1 ? */
michael@0	5807	if (cmp.lsu[0]==0) a->exponent=0; /* yes, exact 0 */
michael@0	5808	else *status|=(DEC_Inexact | DEC_Rounded); /* no, inexact */
michael@0	5809	break;
michael@0	5810	}
michael@0	5811	/* force padding if adjustment has gone to 0 before full length */
michael@0	5812	if (decNumberIsZero(b)) b->exponent=a->exponent-p;
michael@0	5813	}
michael@0	5814
michael@0	5815	/* not done yet ... */
michael@0	5816	decAddOp(a, a, b, &aset, 0, &ignore); /* a=a+b for next estimate */
michael@0	5817	if (pp==p) continue; /* precision is at maximum */
michael@0	5818	/* lengthen the next calculation */
michael@0	5819	pp=pp*2; /* double precision */
michael@0	5820	if (pp>p) pp=p; /* clamp to maximum */
michael@0	5821	aset.digits=pp; /* working context */
michael@0	5822	bset.digits=pp+rhs->digits; /* wider context */
michael@0	5823	} /* Newton's iteration */
michael@0	5824
michael@0	5825	#if DECCHECK
michael@0	5826	/* just a sanity check; remove the test to show always */
michael@0	5827	if (iterations>24)
michael@0	5828	printf("Ln iterations=%ld, status=%08lx, p=%ld, d=%ld\n",
michael@0	5829	(LI)iterations, (LI)*status, (LI)p, (LI)rhs->digits);
michael@0	5830	#endif
michael@0	5831
michael@0	5832	/* Copy and round the result to res */
michael@0	5833	residue=1; /* indicate dirt to right */
michael@0	5834	if (ISZERO(a)) residue=0; /* .. unless underflowed to 0 */
michael@0	5835	aset.digits=set->digits; /* [use default rounding] */
michael@0	5836	decCopyFit(res, a, &aset, &residue, status); /* copy & shorten */
michael@0	5837	decFinish(res, set, &residue, status); /* cleanup/set flags */
michael@0	5838	} while(0); /* end protected */
michael@0	5839
michael@0	5840	if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */
michael@0	5841	if (allocbufb!=NULL) free(allocbufb); /* .. */
michael@0	5842	/* [status is handled by caller] */
michael@0	5843	return res;
michael@0	5844	} /* decLnOp */
michael@0	5845	#if defined(__clang__) || U_GCC_MAJOR_MINOR >= 406
michael@0	5846	#pragma GCC diagnostic pop
michael@0	5847	#endif
michael@0	5848
michael@0	5849	/* ------------------------------------------------------------------ */
michael@0	5850	/* decQuantizeOp -- force exponent to requested value */
michael@0	5851	/* */
michael@0	5852	/* This computes C = op(A, B), where op adjusts the coefficient */
michael@0	5853	/* of C (by rounding or shifting) such that the exponent (-scale) */
michael@0	5854	/* of C has the value B or matches the exponent of B. */
michael@0	5855	/* The numerical value of C will equal A, except for the effects of */
michael@0	5856	/* any rounding that occurred. */
michael@0	5857	/* */
michael@0	5858	/* res is C, the result. C may be A or B */
michael@0	5859	/* lhs is A, the number to adjust */
michael@0	5860	/* rhs is B, the requested exponent */
michael@0	5861	/* set is the context */
michael@0	5862	/* quant is 1 for quantize or 0 for rescale */
michael@0	5863	/* status is the status accumulator (this can be called without */
michael@0	5864	/* risk of control loss) */
michael@0	5865	/* */
michael@0	5866	/* C must have space for set->digits digits. */
michael@0	5867	/* */
michael@0	5868	/* Unless there is an error or the result is infinite, the exponent */
michael@0	5869	/* after the operation is guaranteed to be that requested. */
michael@0	5870	/* ------------------------------------------------------------------ */
michael@0	5871	static decNumber * decQuantizeOp(decNumber *res, const decNumber *lhs,
michael@0	5872	const decNumber *rhs, decContext *set,
michael@0	5873	Flag quant, uInt *status) {
michael@0	5874	#if DECSUBSET
michael@0	5875	decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */
michael@0	5876	decNumber *allocrhs=NULL; /* .., rhs */
michael@0	5877	#endif
michael@0	5878	const decNumber *inrhs=rhs; /* save original rhs */
michael@0	5879	Int reqdigits=set->digits; /* requested DIGITS */
michael@0	5880	Int reqexp; /* requested exponent [-scale] */
michael@0	5881	Int residue=0; /* rounding residue */
michael@0	5882	Int etiny=set->emin-(reqdigits-1);
michael@0	5883
michael@0	5884	#if DECCHECK
michael@0	5885	if (decCheckOperands(res, lhs, rhs, set)) return res;
michael@0	5886	#endif
michael@0	5887
michael@0	5888	do { /* protect allocated storage */
michael@0	5889	#if DECSUBSET
michael@0	5890	if (!set->extended) {
michael@0	5891	/* reduce operands and set lostDigits status, as needed */
michael@0	5892	if (lhs->digits>reqdigits) {
michael@0	5893	alloclhs=decRoundOperand(lhs, set, status);
michael@0	5894	if (alloclhs==NULL) break;
michael@0	5895	lhs=alloclhs;
michael@0	5896	}
michael@0	5897	if (rhs->digits>reqdigits) { /* [this only checks lostDigits] */
michael@0	5898	allocrhs=decRoundOperand(rhs, set, status);
michael@0	5899	if (allocrhs==NULL) break;
michael@0	5900	rhs=allocrhs;
michael@0	5901	}
michael@0	5902	}
michael@0	5903	#endif
michael@0	5904	/* [following code does not require input rounding] */
michael@0	5905
michael@0	5906	/* Handle special values */
michael@0	5907	if (SPECIALARGS) {
michael@0	5908	/* NaNs get usual processing */
michael@0	5909	if (SPECIALARGS & (DECSNAN | DECNAN))
michael@0	5910	decNaNs(res, lhs, rhs, set, status);
michael@0	5911	/* one infinity but not both is bad */
michael@0	5912	else if ((lhs->bits ^ rhs->bits) & DECINF)
michael@0	5913	*status|=DEC_Invalid_operation;
michael@0	5914	/* both infinity: return lhs */
michael@0	5915	else uprv_decNumberCopy(res, lhs); /* [nop if in place] */
michael@0	5916	break;
michael@0	5917	}
michael@0	5918
michael@0	5919	/* set requested exponent */
michael@0	5920	if (quant) reqexp=inrhs->exponent; /* quantize -- match exponents */
michael@0	5921	else { /* rescale -- use value of rhs */
michael@0	5922	/* Original rhs must be an integer that fits and is in range, */
michael@0	5923	/* which could be from -1999999997 to +999999999, thanks to */
michael@0	5924	/* subnormals */
michael@0	5925	reqexp=decGetInt(inrhs); /* [cannot fail] */
michael@0	5926	}
michael@0	5927
michael@0	5928	#if DECSUBSET
michael@0	5929	if (!set->extended) etiny=set->emin; /* no subnormals */
michael@0	5930	#endif
michael@0	5931
michael@0	5932	if (reqexp==BADINT /* bad (rescale only) or .. */
michael@0	5933	|| reqexp==BIGODD || reqexp==BIGEVEN /* very big (ditto) or .. */
michael@0	5934	|| (reqexp<etiny) /* < lowest */
michael@0	5935	|| (reqexp>set->emax)) { /* > emax */
michael@0	5936	*status|=DEC_Invalid_operation;
michael@0	5937	break;}
michael@0	5938
michael@0	5939	/* the RHS has been processed, so it can be overwritten now if necessary */
michael@0	5940	if (ISZERO(lhs)) { /* zero coefficient unchanged */
michael@0	5941	uprv_decNumberCopy(res, lhs); /* [nop if in place] */
michael@0	5942	res->exponent=reqexp; /* .. just set exponent */
michael@0	5943	#if DECSUBSET
michael@0	5944	if (!set->extended) res->bits=0; /* subset specification; no -0 */
michael@0	5945	#endif
michael@0	5946	}
michael@0	5947	else { /* non-zero lhs */
michael@0	5948	Int adjust=reqexp-lhs->exponent; /* digit adjustment needed */
michael@0	5949	/* if adjusted coefficient will definitely not fit, give up now */
michael@0	5950	if ((lhs->digits-adjust)>reqdigits) {
michael@0	5951	*status|=DEC_Invalid_operation;
michael@0	5952	break;
michael@0	5953	}
michael@0	5954
michael@0	5955	if (adjust>0) { /* increasing exponent */
michael@0	5956	/* this will decrease the length of the coefficient by adjust */
michael@0	5957	/* digits, and must round as it does so */
michael@0	5958	decContext workset; /* work */
michael@0	5959	workset=*set; /* clone rounding, etc. */
michael@0	5960	workset.digits=lhs->digits-adjust; /* set requested length */
michael@0	5961	/* [note that the latter can be <1, here] */
michael@0	5962	decCopyFit(res, lhs, &workset, &residue, status); /* fit to result */
michael@0	5963	decApplyRound(res, &workset, residue, status); /* .. and round */
michael@0	5964	residue=0; /* [used] */
michael@0	5965	/* If just rounded a 999s case, exponent will be off by one; */
michael@0	5966	/* adjust back (after checking space), if so. */
michael@0	5967	if (res->exponent>reqexp) {
michael@0	5968	/* re-check needed, e.g., for quantize(0.9999, 0.001) under */
michael@0	5969	/* set->digits==3 */
michael@0	5970	if (res->digits==reqdigits) { /* cannot shift by 1 */
michael@0	5971	*status&=~(DEC_Inexact | DEC_Rounded); /* [clean these] */
michael@0	5972	*status|=DEC_Invalid_operation;
michael@0	5973	break;
michael@0	5974	}
michael@0	5975	res->digits=decShiftToMost(res->lsu, res->digits, 1); /* shift */
michael@0	5976	res->exponent--; /* (re)adjust the exponent. */
michael@0	5977	}
michael@0	5978	#if DECSUBSET
michael@0	5979	if (ISZERO(res) && !set->extended) res->bits=0; /* subset; no -0 */
michael@0	5980	#endif
michael@0	5981	} /* increase */
michael@0	5982	else /* adjust<=0 */ { /* decreasing or = exponent */
michael@0	5983	/* this will increase the length of the coefficient by -adjust */
michael@0	5984	/* digits, by adding zero or more trailing zeros; this is */
michael@0	5985	/* already checked for fit, above */
michael@0	5986	uprv_decNumberCopy(res, lhs); /* [it will fit] */
michael@0	5987	/* if padding needed (adjust<0), add it now... */
michael@0	5988	if (adjust<0) {
michael@0	5989	res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
michael@0	5990	res->exponent+=adjust; /* adjust the exponent */
michael@0	5991	}
michael@0	5992	} /* decrease */
michael@0	5993	} /* non-zero */
michael@0	5994
michael@0	5995	/* Check for overflow [do not use Finalize in this case, as an */
michael@0	5996	/* overflow here is a "don't fit" situation] */
michael@0	5997	if (res->exponent>set->emax-res->digits+1) { /* too big */
michael@0	5998	*status|=DEC_Invalid_operation;
michael@0	5999	break;
michael@0	6000	}
michael@0	6001	else {
michael@0	6002	decFinalize(res, set, &residue, status); /* set subnormal flags */
michael@0	6003	*status&=~DEC_Underflow; /* suppress Underflow [as per 754] */
michael@0	6004	}
michael@0	6005	} while(0); /* end protected */
michael@0	6006
michael@0	6007	#if DECSUBSET
michael@0	6008	if (allocrhs!=NULL) free(allocrhs); /* drop any storage used */
michael@0	6009	if (alloclhs!=NULL) free(alloclhs); /* .. */
michael@0	6010	#endif
michael@0	6011	return res;
michael@0	6012	} /* decQuantizeOp */
michael@0	6013
michael@0	6014	/* ------------------------------------------------------------------ */
michael@0	6015	/* decCompareOp -- compare, min, or max two Numbers */
michael@0	6016	/* */
michael@0	6017	/* This computes C = A ? B and carries out one of four operations: */
michael@0	6018	/* COMPARE -- returns the signum (as a number) giving the */
michael@0	6019	/* result of a comparison unless one or both */
michael@0	6020	/* operands is a NaN (in which case a NaN results) */
michael@0	6021	/* COMPSIG -- as COMPARE except that a quiet NaN raises */
michael@0	6022	/* Invalid operation. */
michael@0	6023	/* COMPMAX -- returns the larger of the operands, using the */
michael@0	6024	/* 754 maxnum operation */
michael@0	6025	/* COMPMAXMAG -- ditto, comparing absolute values */
michael@0	6026	/* COMPMIN -- the 754 minnum operation */
michael@0	6027	/* COMPMINMAG -- ditto, comparing absolute values */
michael@0	6028	/* COMTOTAL -- returns the signum (as a number) giving the */
michael@0	6029	/* result of a comparison using 754 total ordering */
michael@0	6030	/* */
michael@0	6031	/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
michael@0	6032	/* lhs is A */
michael@0	6033	/* rhs is B */
michael@0	6034	/* set is the context */
michael@0	6035	/* op is the operation flag */
michael@0	6036	/* status is the usual accumulator */
michael@0	6037	/* */
michael@0	6038	/* C must have space for one digit for COMPARE or set->digits for */
michael@0	6039	/* COMPMAX, COMPMIN, COMPMAXMAG, or COMPMINMAG. */
michael@0	6040	/* ------------------------------------------------------------------ */
michael@0	6041	/* The emphasis here is on speed for common cases, and avoiding */
michael@0	6042	/* coefficient comparison if possible. */
michael@0	6043	/* ------------------------------------------------------------------ */
michael@0	6044	static decNumber * decCompareOp(decNumber *res, const decNumber *lhs,
michael@0	6045	const decNumber *rhs, decContext *set,
michael@0	6046	Flag op, uInt *status) {
michael@0	6047	#if DECSUBSET
michael@0	6048	decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */
michael@0	6049	decNumber *allocrhs=NULL; /* .., rhs */
michael@0	6050	#endif
michael@0	6051	Int result=0; /* default result value */
michael@0	6052	uByte merged; /* work */
michael@0	6053
michael@0	6054	#if DECCHECK
michael@0	6055	if (decCheckOperands(res, lhs, rhs, set)) return res;
michael@0	6056	#endif
michael@0	6057
michael@0	6058	do { /* protect allocated storage */
michael@0	6059	#if DECSUBSET
michael@0	6060	if (!set->extended) {
michael@0	6061	/* reduce operands and set lostDigits status, as needed */
michael@0	6062	if (lhs->digits>set->digits) {
michael@0	6063	alloclhs=decRoundOperand(lhs, set, status);
michael@0	6064	if (alloclhs==NULL) {result=BADINT; break;}
michael@0	6065	lhs=alloclhs;
michael@0	6066	}
michael@0	6067	if (rhs->digits>set->digits) {
michael@0	6068	allocrhs=decRoundOperand(rhs, set, status);
michael@0	6069	if (allocrhs==NULL) {result=BADINT; break;}
michael@0	6070	rhs=allocrhs;
michael@0	6071	}
michael@0	6072	}
michael@0	6073	#endif
michael@0	6074	/* [following code does not require input rounding] */
michael@0	6075
michael@0	6076	/* If total ordering then handle differing signs 'up front' */
michael@0	6077	if (op==COMPTOTAL) { /* total ordering */
michael@0	6078	if (decNumberIsNegative(lhs) && !decNumberIsNegative(rhs)) {
michael@0	6079	result=-1;
michael@0	6080	break;
michael@0	6081	}
michael@0	6082	if (!decNumberIsNegative(lhs) && decNumberIsNegative(rhs)) {
michael@0	6083	result=+1;
michael@0	6084	break;
michael@0	6085	}
michael@0	6086	}
michael@0	6087
michael@0	6088	/* handle NaNs specially; let infinities drop through */
michael@0	6089	/* This assumes sNaN (even just one) leads to NaN. */
michael@0	6090	merged=(lhs->bits | rhs->bits) & (DECSNAN | DECNAN);
michael@0	6091	if (merged) { /* a NaN bit set */
michael@0	6092	if (op==COMPARE); /* result will be NaN */
michael@0	6093	else if (op==COMPSIG) /* treat qNaN as sNaN */
michael@0	6094	*status|=DEC_Invalid_operation | DEC_sNaN;
michael@0	6095	else if (op==COMPTOTAL) { /* total ordering, always finite */
michael@0	6096	/* signs are known to be the same; compute the ordering here */
michael@0	6097	/* as if the signs are both positive, then invert for negatives */
michael@0	6098	if (!decNumberIsNaN(lhs)) result=-1;
michael@0	6099	else if (!decNumberIsNaN(rhs)) result=+1;
michael@0	6100	/* here if both NaNs */
michael@0	6101	else if (decNumberIsSNaN(lhs) && decNumberIsQNaN(rhs)) result=-1;
michael@0	6102	else if (decNumberIsQNaN(lhs) && decNumberIsSNaN(rhs)) result=+1;
michael@0	6103	else { /* both NaN or both sNaN */
michael@0	6104	/* now it just depends on the payload */
michael@0	6105	result=decUnitCompare(lhs->lsu, D2U(lhs->digits),
michael@0	6106	rhs->lsu, D2U(rhs->digits), 0);
michael@0	6107	/* [Error not possible, as these are 'aligned'] */
michael@0	6108	} /* both same NaNs */
michael@0	6109	if (decNumberIsNegative(lhs)) result=-result;
michael@0	6110	break;
michael@0	6111	} /* total order */
michael@0	6112
michael@0	6113	else if (merged & DECSNAN); /* sNaN -> qNaN */
michael@0	6114	else { /* here if MIN or MAX and one or two quiet NaNs */
michael@0	6115	/* min or max -- 754 rules ignore single NaN */
michael@0	6116	if (!decNumberIsNaN(lhs) || !decNumberIsNaN(rhs)) {
michael@0	6117	/* just one NaN; force choice to be the non-NaN operand */
michael@0	6118	op=COMPMAX;
michael@0	6119	if (lhs->bits & DECNAN) result=-1; /* pick rhs */
michael@0	6120	else result=+1; /* pick lhs */
michael@0	6121	break;
michael@0	6122	}
michael@0	6123	} /* max or min */
michael@0	6124	op=COMPNAN; /* use special path */
michael@0	6125	decNaNs(res, lhs, rhs, set, status); /* propagate NaN */
michael@0	6126	break;
michael@0	6127	}
michael@0	6128	/* have numbers */
michael@0	6129	if (op==COMPMAXMAG || op==COMPMINMAG) result=decCompare(lhs, rhs, 1);
michael@0	6130	else result=decCompare(lhs, rhs, 0); /* sign matters */
michael@0	6131	} while(0); /* end protected */
michael@0	6132
michael@0	6133	if (result==BADINT) *status|=DEC_Insufficient_storage; /* rare */
michael@0	6134	else {
michael@0	6135	if (op==COMPARE || op==COMPSIG ||op==COMPTOTAL) { /* returning signum */
michael@0	6136	if (op==COMPTOTAL && result==0) {
michael@0	6137	/* operands are numerically equal or same NaN (and same sign, */
michael@0	6138	/* tested first); if identical, leave result 0 */
michael@0	6139	if (lhs->exponent!=rhs->exponent) {
michael@0	6140	if (lhs->exponent<rhs->exponent) result=-1;
michael@0	6141	else result=+1;
michael@0	6142	if (decNumberIsNegative(lhs)) result=-result;
michael@0	6143	} /* lexp!=rexp */
michael@0	6144	} /* total-order by exponent */
michael@0	6145	uprv_decNumberZero(res); /* [always a valid result] */
michael@0	6146	if (result!=0) { /* must be -1 or +1 */
michael@0	6147	*res->lsu=1;
michael@0	6148	if (result<0) res->bits=DECNEG;
michael@0	6149	}
michael@0	6150	}
michael@0	6151	else if (op==COMPNAN); /* special, drop through */
michael@0	6152	else { /* MAX or MIN, non-NaN result */
michael@0	6153	Int residue=0; /* rounding accumulator */
michael@0	6154	/* choose the operand for the result */
michael@0	6155	const decNumber *choice;
michael@0	6156	if (result==0) { /* operands are numerically equal */
michael@0	6157	/* choose according to sign then exponent (see 754) */
michael@0	6158	uByte slhs=(lhs->bits & DECNEG);
michael@0	6159	uByte srhs=(rhs->bits & DECNEG);
michael@0	6160	#if DECSUBSET
michael@0	6161	if (!set->extended) { /* subset: force left-hand */
michael@0	6162	op=COMPMAX;
michael@0	6163	result=+1;
michael@0	6164	}
michael@0	6165	else
michael@0	6166	#endif
michael@0	6167	if (slhs!=srhs) { /* signs differ */
michael@0	6168	if (slhs) result=-1; /* rhs is max */
michael@0	6169	else result=+1; /* lhs is max */
michael@0	6170	}
michael@0	6171	else if (slhs && srhs) { /* both negative */
michael@0	6172	if (lhs->exponent<rhs->exponent) result=+1;
michael@0	6173	else result=-1;
michael@0	6174	/* [if equal, use lhs, technically identical] */
michael@0	6175	}
michael@0	6176	else { /* both positive */
michael@0	6177	if (lhs->exponent>rhs->exponent) result=+1;
michael@0	6178	else result=-1;
michael@0	6179	/* [ditto] */
michael@0	6180	}
michael@0	6181	} /* numerically equal */
michael@0	6182	/* here result will be non-0; reverse if looking for MIN */
michael@0	6183	if (op==COMPMIN || op==COMPMINMAG) result=-result;
michael@0	6184	choice=(result>0 ? lhs : rhs); /* choose */
michael@0	6185	/* copy chosen to result, rounding if need be */
michael@0	6186	decCopyFit(res, choice, set, &residue, status);
michael@0	6187	decFinish(res, set, &residue, status);
michael@0	6188	}
michael@0	6189	}
michael@0	6190	#if DECSUBSET
michael@0	6191	if (allocrhs!=NULL) free(allocrhs); /* free any storage used */
michael@0	6192	if (alloclhs!=NULL) free(alloclhs); /* .. */
michael@0	6193	#endif
michael@0	6194	return res;
michael@0	6195	} /* decCompareOp */
michael@0	6196
michael@0	6197	/* ------------------------------------------------------------------ */
michael@0	6198	/* decCompare -- compare two decNumbers by numerical value */
michael@0	6199	/* */
michael@0	6200	/* This routine compares A ? B without altering them. */
michael@0	6201	/* */
michael@0	6202	/* Arg1 is A, a decNumber which is not a NaN */
michael@0	6203	/* Arg2 is B, a decNumber which is not a NaN */
michael@0	6204	/* Arg3 is 1 for a sign-independent compare, 0 otherwise */
michael@0	6205	/* */
michael@0	6206	/* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */
michael@0	6207	/* (the only possible failure is an allocation error) */
michael@0	6208	/* ------------------------------------------------------------------ */
michael@0	6209	static Int decCompare(const decNumber *lhs, const decNumber *rhs,
michael@0	6210	Flag abs_c) {
michael@0	6211	Int result; /* result value */
michael@0	6212	Int sigr; /* rhs signum */
michael@0	6213	Int compare; /* work */
michael@0	6214
michael@0	6215	result=1; /* assume signum(lhs) */
michael@0	6216	if (ISZERO(lhs)) result=0;
michael@0	6217	if (abs_c) {
michael@0	6218	if (ISZERO(rhs)) return result; /* LHS wins or both 0 */
michael@0	6219	/* RHS is non-zero */
michael@0	6220	if (result==0) return -1; /* LHS is 0; RHS wins */
michael@0	6221	/* [here, both non-zero, result=1] */
michael@0	6222	}
michael@0	6223	else { /* signs matter */
michael@0	6224	if (result && decNumberIsNegative(lhs)) result=-1;
michael@0	6225	sigr=1; /* compute signum(rhs) */
michael@0	6226	if (ISZERO(rhs)) sigr=0;
michael@0	6227	else if (decNumberIsNegative(rhs)) sigr=-1;
michael@0	6228	if (result > sigr) return +1; /* L > R, return 1 */
michael@0	6229	if (result < sigr) return -1; /* L < R, return -1 */
michael@0	6230	if (result==0) return 0; /* both 0 */
michael@0	6231	}
michael@0	6232
michael@0	6233	/* signums are the same; both are non-zero */
michael@0	6234	if ((lhs->bits | rhs->bits) & DECINF) { /* one or more infinities */
michael@0	6235	if (decNumberIsInfinite(rhs)) {
michael@0	6236	if (decNumberIsInfinite(lhs)) result=0;/* both infinite */
michael@0	6237	else result=-result; /* only rhs infinite */
michael@0	6238	}
michael@0	6239	return result;
michael@0	6240	}
michael@0	6241	/* must compare the coefficients, allowing for exponents */
michael@0	6242	if (lhs->exponent>rhs->exponent) { /* LHS exponent larger */
michael@0	6243	/* swap sides, and sign */
michael@0	6244	const decNumber *temp=lhs;
michael@0	6245	lhs=rhs;
michael@0	6246	rhs=temp;
michael@0	6247	result=-result;
michael@0	6248	}
michael@0	6249	compare=decUnitCompare(lhs->lsu, D2U(lhs->digits),
michael@0	6250	rhs->lsu, D2U(rhs->digits),
michael@0	6251	rhs->exponent-lhs->exponent);
michael@0	6252	if (compare!=BADINT) compare*=result; /* comparison succeeded */
michael@0	6253	return compare;
michael@0	6254	} /* decCompare */
michael@0	6255
michael@0	6256	/* ------------------------------------------------------------------ */
michael@0	6257	/* decUnitCompare -- compare two >=0 integers in Unit arrays */
michael@0	6258	/* */
michael@0	6259	/* This routine compares A ? B*10**E where A and B are unit arrays */
michael@0	6260	/* A is a plain integer */
michael@0	6261	/* B has an exponent of E (which must be non-negative) */
michael@0	6262	/* */
michael@0	6263	/* Arg1 is A first Unit (lsu) */
michael@0	6264	/* Arg2 is A length in Units */
michael@0	6265	/* Arg3 is B first Unit (lsu) */
michael@0	6266	/* Arg4 is B length in Units */
michael@0	6267	/* Arg5 is E (0 if the units are aligned) */
michael@0	6268	/* */
michael@0	6269	/* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */
michael@0	6270	/* (the only possible failure is an allocation error, which can */
michael@0	6271	/* only occur if E!=0) */
michael@0	6272	/* ------------------------------------------------------------------ */
michael@0	6273	static Int decUnitCompare(const Unit *a, Int alength,
michael@0	6274	const Unit *b, Int blength, Int exp) {
michael@0	6275	Unit *acc; /* accumulator for result */
michael@0	6276	Unit accbuff[SD2U(DECBUFFER*2+1)]; /* local buffer */
michael@0	6277	Unit *allocacc=NULL; /* -> allocated acc buffer, iff allocated */
michael@0	6278	Int accunits, need; /* units in use or needed for acc */
michael@0	6279	const Unit *l, *r, *u; /* work */
michael@0	6280	Int expunits, exprem, result; /* .. */
michael@0	6281
michael@0	6282	if (exp==0) { /* aligned; fastpath */
michael@0	6283	if (alength>blength) return 1;
michael@0	6284	if (alength<blength) return -1;
michael@0	6285	/* same number of units in both -- need unit-by-unit compare */
michael@0	6286	l=a+alength-1;
michael@0	6287	r=b+alength-1;
michael@0	6288	for (;l>=a; l--, r--) {
michael@0	6289	if (*l>*r) return 1;
michael@0	6290	if (*l<*r) return -1;
michael@0	6291	}
michael@0	6292	return 0; /* all units match */
michael@0	6293	} /* aligned */
michael@0	6294
michael@0	6295	/* Unaligned. If one is >1 unit longer than the other, padded */
michael@0	6296	/* approximately, then can return easily */
michael@0	6297	if (alength>blength+(Int)D2U(exp)) return 1;
michael@0	6298	if (alength+1<blength+(Int)D2U(exp)) return -1;
michael@0	6299
michael@0	6300	/* Need to do a real subtract. For this, a result buffer is needed */
michael@0	6301	/* even though only the sign is of interest. Its length needs */
michael@0	6302	/* to be the larger of alength and padded blength, +2 */
michael@0	6303	need=blength+D2U(exp); /* maximum real length of B */
michael@0	6304	if (need<alength) need=alength;
michael@0	6305	need+=2;
michael@0	6306	acc=accbuff; /* assume use local buffer */
michael@0	6307	if (need*sizeof(Unit)>sizeof(accbuff)) {
michael@0	6308	allocacc=(Unit *)malloc(need*sizeof(Unit));
michael@0	6309	if (allocacc==NULL) return BADINT; /* hopeless -- abandon */
michael@0	6310	acc=allocacc;
michael@0	6311	}
michael@0	6312	/* Calculate units and remainder from exponent. */
michael@0	6313	expunits=exp/DECDPUN;
michael@0	6314	exprem=exp%DECDPUN;
michael@0	6315	/* subtract [A+B*(-m)] */
michael@0	6316	accunits=decUnitAddSub(a, alength, b, blength, expunits, acc,
michael@0	6317	-(Int)powers[exprem]);
michael@0	6318	/* [UnitAddSub result may have leading zeros, even on zero] */
michael@0	6319	if (accunits<0) result=-1; /* negative result */
michael@0	6320	else { /* non-negative result */
michael@0	6321	/* check units of the result before freeing any storage */
michael@0	6322	for (u=acc; u<acc+accunits-1 && *u==0;) u++;
michael@0	6323	result=(*u==0 ? 0 : +1);
michael@0	6324	}
michael@0	6325	/* clean up and return the result */
michael@0	6326	if (allocacc!=NULL) free(allocacc); /* drop any storage used */
michael@0	6327	return result;
michael@0	6328	} /* decUnitCompare */
michael@0	6329
michael@0	6330	/* ------------------------------------------------------------------ */
michael@0	6331	/* decUnitAddSub -- add or subtract two >=0 integers in Unit arrays */
michael@0	6332	/* */
michael@0	6333	/* This routine performs the calculation: */
michael@0	6334	/* */
michael@0	6335	/* C=A+(B*M) */
michael@0	6336	/* */
michael@0	6337	/* Where M is in the range -DECDPUNMAX through +DECDPUNMAX. */
michael@0	6338	/* */
michael@0	6339	/* A may be shorter or longer than B. */
michael@0	6340	/* */
michael@0	6341	/* Leading zeros are not removed after a calculation. The result is */
michael@0	6342	/* either the same length as the longer of A and B (adding any */
michael@0	6343	/* shift), or one Unit longer than that (if a Unit carry occurred). */
michael@0	6344	/* */
michael@0	6345	/* A and B content are not altered unless C is also A or B. */
michael@0	6346	/* C may be the same array as A or B, but only if no zero padding is */
michael@0	6347	/* requested (that is, C may be B only if bshift==0). */
michael@0	6348	/* C is filled from the lsu; only those units necessary to complete */
michael@0	6349	/* the calculation are referenced. */
michael@0	6350	/* */
michael@0	6351	/* Arg1 is A first Unit (lsu) */
michael@0	6352	/* Arg2 is A length in Units */
michael@0	6353	/* Arg3 is B first Unit (lsu) */
michael@0	6354	/* Arg4 is B length in Units */
michael@0	6355	/* Arg5 is B shift in Units (>=0; pads with 0 units if positive) */
michael@0	6356	/* Arg6 is C first Unit (lsu) */
michael@0	6357	/* Arg7 is M, the multiplier */
michael@0	6358	/* */
michael@0	6359	/* returns the count of Units written to C, which will be non-zero */
michael@0	6360	/* and negated if the result is negative. That is, the sign of the */
michael@0	6361	/* returned Int is the sign of the result (positive for zero) and */
michael@0	6362	/* the absolute value of the Int is the count of Units. */
michael@0	6363	/* */
michael@0	6364	/* It is the caller's responsibility to make sure that C size is */
michael@0	6365	/* safe, allowing space if necessary for a one-Unit carry. */
michael@0	6366	/* */
michael@0	6367	/* This routine is severely performance-critical; *any* change here */
michael@0	6368	/* must be measured (timed) to assure no performance degradation. */
michael@0	6369	/* In particular, trickery here tends to be counter-productive, as */
michael@0	6370	/* increased complexity of code hurts register optimizations on */
michael@0	6371	/* register-poor architectures. Avoiding divisions is nearly */
michael@0	6372	/* always a Good Idea, however. */
michael@0	6373	/* */
michael@0	6374	/* Special thanks to Rick McGuire (IBM Cambridge, MA) and Dave Clark */
michael@0	6375	/* (IBM Warwick, UK) for some of the ideas used in this routine. */
michael@0	6376	/* ------------------------------------------------------------------ */
michael@0	6377	static Int decUnitAddSub(const Unit *a, Int alength,
michael@0	6378	const Unit *b, Int blength, Int bshift,
michael@0	6379	Unit *c, Int m) {
michael@0	6380	const Unit *alsu=a; /* A lsu [need to remember it] */
michael@0	6381	Unit *clsu=c; /* C ditto */
michael@0	6382	Unit *minC; /* low water mark for C */
michael@0	6383	Unit *maxC; /* high water mark for C */
michael@0	6384	eInt carry=0; /* carry integer (could be Long) */
michael@0	6385	Int add; /* work */
michael@0	6386	#if DECDPUN<=4 /* myriadal, millenary, etc. */
michael@0	6387	Int est; /* estimated quotient */
michael@0	6388	#endif
michael@0	6389
michael@0	6390	#if DECTRACE
michael@0	6391	if (alength<1 || blength<1)
michael@0	6392	printf("decUnitAddSub: alen blen m %ld %ld [%ld]\n", alength, blength, m);
michael@0	6393	#endif
michael@0	6394
michael@0	6395	maxC=c+alength; /* A is usually the longer */
michael@0	6396	minC=c+blength; /* .. and B the shorter */
michael@0	6397	if (bshift!=0) { /* B is shifted; low As copy across */
michael@0	6398	minC+=bshift;
michael@0	6399	/* if in place [common], skip copy unless there's a gap [rare] */
michael@0	6400	if (a==c && bshift<=alength) {
michael@0	6401	c+=bshift;
michael@0	6402	a+=bshift;
michael@0	6403	}
michael@0	6404	else for (; c<clsu+bshift; a++, c++) { /* copy needed */
michael@0	6405	if (a<alsu+alength) *c=*a;
michael@0	6406	else *c=0;
michael@0	6407	}
michael@0	6408	}
michael@0	6409	if (minC>maxC) { /* swap */
michael@0	6410	Unit *hold=minC;
michael@0	6411	minC=maxC;
michael@0	6412	maxC=hold;
michael@0	6413	}
michael@0	6414
michael@0	6415	/* For speed, do the addition as two loops; the first where both A */
michael@0	6416	/* and B contribute, and the second (if necessary) where only one or */
michael@0	6417	/* other of the numbers contribute. */
michael@0	6418	/* Carry handling is the same (i.e., duplicated) in each case. */
michael@0	6419	for (; c<minC; c++) {
michael@0	6420	carry+=*a;
michael@0	6421	a++;
michael@0	6422	carry+=((eInt)*b)*m; /* [special-casing m=1/-1 */
michael@0	6423	b++; /* here is not a win] */
michael@0	6424	/* here carry is new Unit of digits; it could be +ve or -ve */
michael@0	6425	if ((ueInt)carry<=DECDPUNMAX) { /* fastpath 0-DECDPUNMAX */
michael@0	6426	*c=(Unit)carry;
michael@0	6427	carry=0;
michael@0	6428	continue;
michael@0	6429	}
michael@0	6430	#if DECDPUN==4 /* use divide-by-multiply */
michael@0	6431	if (carry>=0) {
michael@0	6432	est=(((ueInt)carry>>11)*53687)>>18;
michael@0	6433	*c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
michael@0	6434	carry=est; /* likely quotient [89%] */
michael@0	6435	if (*c<DECDPUNMAX+1) continue; /* estimate was correct */
michael@0	6436	carry++;
michael@0	6437	*c-=DECDPUNMAX+1;
michael@0	6438	continue;
michael@0	6439	}
michael@0	6440	/* negative case */
michael@0	6441	carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
michael@0	6442	est=(((ueInt)carry>>11)*53687)>>18;
michael@0	6443	*c=(Unit)(carry-est*(DECDPUNMAX+1));
michael@0	6444	carry=est-(DECDPUNMAX+1); /* correctly negative */
michael@0	6445	if (*c<DECDPUNMAX+1) continue; /* was OK */
michael@0	6446	carry++;
michael@0	6447	*c-=DECDPUNMAX+1;
michael@0	6448	#elif DECDPUN==3
michael@0	6449	if (carry>=0) {
michael@0	6450	est=(((ueInt)carry>>3)*16777)>>21;
michael@0	6451	*c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
michael@0	6452	carry=est; /* likely quotient [99%] */
michael@0	6453	if (*c<DECDPUNMAX+1) continue; /* estimate was correct */
michael@0	6454	carry++;
michael@0	6455	*c-=DECDPUNMAX+1;
michael@0	6456	continue;
michael@0	6457	}
michael@0	6458	/* negative case */
michael@0	6459	carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
michael@0	6460	est=(((ueInt)carry>>3)*16777)>>21;
michael@0	6461	*c=(Unit)(carry-est*(DECDPUNMAX+1));
michael@0	6462	carry=est-(DECDPUNMAX+1); /* correctly negative */
michael@0	6463	if (*c<DECDPUNMAX+1) continue; /* was OK */
michael@0	6464	carry++;
michael@0	6465	*c-=DECDPUNMAX+1;
michael@0	6466	#elif DECDPUN<=2
michael@0	6467	/* Can use QUOT10 as carry <= 4 digits */
michael@0	6468	if (carry>=0) {
michael@0	6469	est=QUOT10(carry, DECDPUN);
michael@0	6470	*c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
michael@0	6471	carry=est; /* quotient */
michael@0	6472	continue;
michael@0	6473	}
michael@0	6474	/* negative case */
michael@0	6475	carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
michael@0	6476	est=QUOT10(carry, DECDPUN);
michael@0	6477	*c=(Unit)(carry-est*(DECDPUNMAX+1));
michael@0	6478	carry=est-(DECDPUNMAX+1); /* correctly negative */
michael@0	6479	#else
michael@0	6480	/* remainder operator is undefined if negative, so must test */
michael@0	6481	if ((ueInt)carry<(DECDPUNMAX+1)*2) { /* fastpath carry +1 */
michael@0	6482	*c=(Unit)(carry-(DECDPUNMAX+1)); /* [helps additions] */
michael@0	6483	carry=1;
michael@0	6484	continue;
michael@0	6485	}
michael@0	6486	if (carry>=0) {
michael@0	6487	*c=(Unit)(carry%(DECDPUNMAX+1));
michael@0	6488	carry=carry/(DECDPUNMAX+1);
michael@0	6489	continue;
michael@0	6490	}
michael@0	6491	/* negative case */
michael@0	6492	carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
michael@0	6493	*c=(Unit)(carry%(DECDPUNMAX+1));
michael@0	6494	carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1);
michael@0	6495	#endif
michael@0	6496	} /* c */
michael@0	6497
michael@0	6498	/* now may have one or other to complete */
michael@0	6499	/* [pretest to avoid loop setup/shutdown] */
michael@0	6500	if (c<maxC) for (; c<maxC; c++) {
michael@0	6501	if (a<alsu+alength) { /* still in A */
michael@0	6502	carry+=*a;
michael@0	6503	a++;
michael@0	6504	}
michael@0	6505	else { /* inside B */
michael@0	6506	carry+=((eInt)*b)*m;
michael@0	6507	b++;
michael@0	6508	}
michael@0	6509	/* here carry is new Unit of digits; it could be +ve or -ve and */
michael@0	6510	/* magnitude up to DECDPUNMAX squared */
michael@0	6511	if ((ueInt)carry<=DECDPUNMAX) { /* fastpath 0-DECDPUNMAX */
michael@0	6512	*c=(Unit)carry;
michael@0	6513	carry=0;
michael@0	6514	continue;
michael@0	6515	}
michael@0	6516	/* result for this unit is negative or >DECDPUNMAX */
michael@0	6517	#if DECDPUN==4 /* use divide-by-multiply */
michael@0	6518	if (carry>=0) {
michael@0	6519	est=(((ueInt)carry>>11)*53687)>>18;
michael@0	6520	*c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
michael@0	6521	carry=est; /* likely quotient [79.7%] */
michael@0	6522	if (*c<DECDPUNMAX+1) continue; /* estimate was correct */
michael@0	6523	carry++;
michael@0	6524	*c-=DECDPUNMAX+1;
michael@0	6525	continue;
michael@0	6526	}
michael@0	6527	/* negative case */
michael@0	6528	carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
michael@0	6529	est=(((ueInt)carry>>11)*53687)>>18;
michael@0	6530	*c=(Unit)(carry-est*(DECDPUNMAX+1));
michael@0	6531	carry=est-(DECDPUNMAX+1); /* correctly negative */
michael@0	6532	if (*c<DECDPUNMAX+1) continue; /* was OK */
michael@0	6533	carry++;
michael@0	6534	*c-=DECDPUNMAX+1;
michael@0	6535	#elif DECDPUN==3
michael@0	6536	if (carry>=0) {
michael@0	6537	est=(((ueInt)carry>>3)*16777)>>21;
michael@0	6538	*c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
michael@0	6539	carry=est; /* likely quotient [99%] */
michael@0	6540	if (*c<DECDPUNMAX+1) continue; /* estimate was correct */
michael@0	6541	carry++;
michael@0	6542	*c-=DECDPUNMAX+1;
michael@0	6543	continue;
michael@0	6544	}
michael@0	6545	/* negative case */
michael@0	6546	carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
michael@0	6547	est=(((ueInt)carry>>3)*16777)>>21;
michael@0	6548	*c=(Unit)(carry-est*(DECDPUNMAX+1));
michael@0	6549	carry=est-(DECDPUNMAX+1); /* correctly negative */
michael@0	6550	if (*c<DECDPUNMAX+1) continue; /* was OK */
michael@0	6551	carry++;
michael@0	6552	*c-=DECDPUNMAX+1;
michael@0	6553	#elif DECDPUN<=2
michael@0	6554	if (carry>=0) {
michael@0	6555	est=QUOT10(carry, DECDPUN);
michael@0	6556	*c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
michael@0	6557	carry=est; /* quotient */
michael@0	6558	continue;
michael@0	6559	}
michael@0	6560	/* negative case */
michael@0	6561	carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
michael@0	6562	est=QUOT10(carry, DECDPUN);
michael@0	6563	*c=(Unit)(carry-est*(DECDPUNMAX+1));
michael@0	6564	carry=est-(DECDPUNMAX+1); /* correctly negative */
michael@0	6565	#else
michael@0	6566	if ((ueInt)carry<(DECDPUNMAX+1)*2){ /* fastpath carry 1 */
michael@0	6567	*c=(Unit)(carry-(DECDPUNMAX+1));
michael@0	6568	carry=1;
michael@0	6569	continue;
michael@0	6570	}
michael@0	6571	/* remainder operator is undefined if negative, so must test */
michael@0	6572	if (carry>=0) {
michael@0	6573	*c=(Unit)(carry%(DECDPUNMAX+1));
michael@0	6574	carry=carry/(DECDPUNMAX+1);
michael@0	6575	continue;
michael@0	6576	}
michael@0	6577	/* negative case */
michael@0	6578	carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
michael@0	6579	*c=(Unit)(carry%(DECDPUNMAX+1));
michael@0	6580	carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1);
michael@0	6581	#endif
michael@0	6582	} /* c */
michael@0	6583
michael@0	6584	/* OK, all A and B processed; might still have carry or borrow */
michael@0	6585	/* return number of Units in the result, negated if a borrow */
michael@0	6586	if (carry==0) return c-clsu; /* no carry, so no more to do */
michael@0	6587	if (carry>0) { /* positive carry */
michael@0	6588	*c=(Unit)carry; /* place as new unit */
michael@0	6589	c++; /* .. */
michael@0	6590	return c-clsu;
michael@0	6591	}
michael@0	6592	/* -ve carry: it's a borrow; complement needed */
michael@0	6593	add=1; /* temporary carry... */
michael@0	6594	for (c=clsu; c<maxC; c++) {
michael@0	6595	add=DECDPUNMAX+add-*c;
michael@0	6596	if (add<=DECDPUNMAX) {
michael@0	6597	*c=(Unit)add;
michael@0	6598	add=0;
michael@0	6599	}
michael@0	6600	else {
michael@0	6601	*c=0;
michael@0	6602	add=1;
michael@0	6603	}
michael@0	6604	}
michael@0	6605	/* add an extra unit iff it would be non-zero */
michael@0	6606	#if DECTRACE
michael@0	6607	printf("UAS borrow: add %ld, carry %ld\n", add, carry);
michael@0	6608	#endif
michael@0	6609	if ((add-carry-1)!=0) {
michael@0	6610	*c=(Unit)(add-carry-1);
michael@0	6611	c++; /* interesting, include it */
michael@0	6612	}
michael@0	6613	return clsu-c; /* -ve result indicates borrowed */
michael@0	6614	} /* decUnitAddSub */
michael@0	6615
michael@0	6616	/* ------------------------------------------------------------------ */
michael@0	6617	/* decTrim -- trim trailing zeros or normalize */
michael@0	6618	/* */
michael@0	6619	/* dn is the number to trim or normalize */
michael@0	6620	/* set is the context to use to check for clamp */
michael@0	6621	/* all is 1 to remove all trailing zeros, 0 for just fraction ones */
michael@0	6622	/* noclamp is 1 to unconditional (unclamped) trim */
michael@0	6623	/* dropped returns the number of discarded trailing zeros */
michael@0	6624	/* returns dn */
michael@0	6625	/* */
michael@0	6626	/* If clamp is set in the context then the number of zeros trimmed */
michael@0	6627	/* may be limited if the exponent is high. */
michael@0	6628	/* All fields are updated as required. This is a utility operation, */
michael@0	6629	/* so special values are unchanged and no error is possible. */
michael@0	6630	/* ------------------------------------------------------------------ */
michael@0	6631	static decNumber * decTrim(decNumber *dn, decContext *set, Flag all,
michael@0	6632	Flag noclamp, Int *dropped) {
michael@0	6633	Int d, exp; /* work */
michael@0	6634	uInt cut; /* .. */
michael@0	6635	Unit *up; /* -> current Unit */
michael@0	6636
michael@0	6637	#if DECCHECK
michael@0	6638	if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn;
michael@0	6639	#endif
michael@0	6640
michael@0	6641	*dropped=0; /* assume no zeros dropped */
michael@0	6642	if ((dn->bits & DECSPECIAL) /* fast exit if special .. */
michael@0	6643	|| (*dn->lsu & 0x01)) return dn; /* .. or odd */
michael@0	6644	if (ISZERO(dn)) { /* .. or 0 */
michael@0	6645	dn->exponent=0; /* (sign is preserved) */
michael@0	6646	return dn;
michael@0	6647	}
michael@0	6648
michael@0	6649	/* have a finite number which is even */
michael@0	6650	exp=dn->exponent;
michael@0	6651	cut=1; /* digit (1-DECDPUN) in Unit */
michael@0	6652	up=dn->lsu; /* -> current Unit */
michael@0	6653	for (d=0; d<dn->digits-1; d++) { /* [don't strip the final digit] */
michael@0	6654	/* slice by powers */
michael@0	6655	#if DECDPUN<=4
michael@0	6656	uInt quot=QUOT10(*up, cut);
michael@0	6657	if ((*up-quot*powers[cut])!=0) break; /* found non-0 digit */
michael@0	6658	#else
michael@0	6659	if (*up%powers[cut]!=0) break; /* found non-0 digit */
michael@0	6660	#endif
michael@0	6661	/* have a trailing 0 */
michael@0	6662	if (!all) { /* trimming */
michael@0	6663	/* [if exp>0 then all trailing 0s are significant for trim] */
michael@0	6664	if (exp<=0) { /* if digit might be significant */
michael@0	6665	if (exp==0) break; /* then quit */
michael@0	6666	exp++; /* next digit might be significant */
michael@0	6667	}
michael@0	6668	}
michael@0	6669	cut++; /* next power */
michael@0	6670	if (cut>DECDPUN) { /* need new Unit */
michael@0	6671	up++;
michael@0	6672	cut=1;
michael@0	6673	}
michael@0	6674	} /* d */
michael@0	6675	if (d==0) return dn; /* none to drop */
michael@0	6676
michael@0	6677	/* may need to limit drop if clamping */
michael@0	6678	if (set->clamp && !noclamp) {
michael@0	6679	Int maxd=set->emax-set->digits+1-dn->exponent;
michael@0	6680	if (maxd<=0) return dn; /* nothing possible */
michael@0	6681	if (d>maxd) d=maxd;
michael@0	6682	}
michael@0	6683
michael@0	6684	/* effect the drop */
michael@0	6685	decShiftToLeast(dn->lsu, D2U(dn->digits), d);
michael@0	6686	dn->exponent+=d; /* maintain numerical value */
michael@0	6687	dn->digits-=d; /* new length */
michael@0	6688	*dropped=d; /* report the count */
michael@0	6689	return dn;
michael@0	6690	} /* decTrim */
michael@0	6691
michael@0	6692	/* ------------------------------------------------------------------ */
michael@0	6693	/* decReverse -- reverse a Unit array in place */
michael@0	6694	/* */
michael@0	6695	/* ulo is the start of the array */
michael@0	6696	/* uhi is the end of the array (highest Unit to include) */
michael@0	6697	/* */
michael@0	6698	/* The units ulo through uhi are reversed in place (if the number */
michael@0	6699	/* of units is odd, the middle one is untouched). Note that the */
michael@0	6700	/* digit(s) in each unit are unaffected. */
michael@0	6701	/* ------------------------------------------------------------------ */
michael@0	6702	static void decReverse(Unit *ulo, Unit *uhi) {
michael@0	6703	Unit temp;
michael@0	6704	for (; ulo<uhi; ulo++, uhi--) {
michael@0	6705	temp=*ulo;
michael@0	6706	*ulo=*uhi;
michael@0	6707	*uhi=temp;
michael@0	6708	}
michael@0	6709	return;
michael@0	6710	} /* decReverse */
michael@0	6711
michael@0	6712	/* ------------------------------------------------------------------ */
michael@0	6713	/* decShiftToMost -- shift digits in array towards most significant */
michael@0	6714	/* */
michael@0	6715	/* uar is the array */
michael@0	6716	/* digits is the count of digits in use in the array */
michael@0	6717	/* shift is the number of zeros to pad with (least significant); */
michael@0	6718	/* it must be zero or positive */
michael@0	6719	/* */
michael@0	6720	/* returns the new length of the integer in the array, in digits */
michael@0	6721	/* */
michael@0	6722	/* No overflow is permitted (that is, the uar array must be known to */
michael@0	6723	/* be large enough to hold the result, after shifting). */
michael@0	6724	/* ------------------------------------------------------------------ */
michael@0	6725	static Int decShiftToMost(Unit *uar, Int digits, Int shift) {
michael@0	6726	Unit *target, *source, *first; /* work */
michael@0	6727	Int cut; /* odd 0's to add */
michael@0	6728	uInt next; /* work */
michael@0	6729
michael@0	6730	if (shift==0) return digits; /* [fastpath] nothing to do */
michael@0	6731	if ((digits+shift)<=DECDPUN) { /* [fastpath] single-unit case */
michael@0	6732	*uar=(Unit)(*uar*powers[shift]);
michael@0	6733	return digits+shift;
michael@0	6734	}
michael@0	6735
michael@0	6736	next=0; /* all paths */
michael@0	6737	source=uar+D2U(digits)-1; /* where msu comes from */
michael@0	6738	target=source+D2U(shift); /* where upper part of first cut goes */
michael@0	6739	cut=DECDPUN-MSUDIGITS(shift); /* where to slice */
michael@0	6740	if (cut==0) { /* unit-boundary case */
michael@0	6741	for (; source>=uar; source--, target--) *target=*source;
michael@0	6742	}
michael@0	6743	else {
michael@0	6744	first=uar+D2U(digits+shift)-1; /* where msu of source will end up */
michael@0	6745	for (; source>=uar; source--, target--) {
michael@0	6746	/* split the source Unit and accumulate remainder for next */
michael@0	6747	#if DECDPUN<=4
michael@0	6748	uInt quot=QUOT10(*source, cut);
michael@0	6749	uInt rem=*source-quot*powers[cut];
michael@0	6750	next+=quot;
michael@0	6751	#else
michael@0	6752	uInt rem=*source%powers[cut];
michael@0	6753	next+=*source/powers[cut];
michael@0	6754	#endif
michael@0	6755	if (target<=first) *target=(Unit)next; /* write to target iff valid */
michael@0	6756	next=rem*powers[DECDPUN-cut]; /* save remainder for next Unit */
michael@0	6757	}
michael@0	6758	} /* shift-move */
michael@0	6759
michael@0	6760	/* propagate any partial unit to one below and clear the rest */
michael@0	6761	for (; target>=uar; target--) {
michael@0	6762	*target=(Unit)next;
michael@0	6763	next=0;
michael@0	6764	}
michael@0	6765	return digits+shift;
michael@0	6766	} /* decShiftToMost */
michael@0	6767
michael@0	6768	/* ------------------------------------------------------------------ */
michael@0	6769	/* decShiftToLeast -- shift digits in array towards least significant */
michael@0	6770	/* */
michael@0	6771	/* uar is the array */
michael@0	6772	/* units is length of the array, in units */
michael@0	6773	/* shift is the number of digits to remove from the lsu end; it */
michael@0	6774	/* must be zero or positive and <= than units*DECDPUN. */
michael@0	6775	/* */
michael@0	6776	/* returns the new length of the integer in the array, in units */
michael@0	6777	/* */
michael@0	6778	/* Removed digits are discarded (lost). Units not required to hold */
michael@0	6779	/* the final result are unchanged. */
michael@0	6780	/* ------------------------------------------------------------------ */
michael@0	6781	static Int decShiftToLeast(Unit *uar, Int units, Int shift) {
michael@0	6782	Unit *target, *up; /* work */
michael@0	6783	Int cut, count; /* work */
michael@0	6784	Int quot, rem; /* for division */
michael@0	6785
michael@0	6786	if (shift==0) return units; /* [fastpath] nothing to do */
michael@0	6787	if (shift==units*DECDPUN) { /* [fastpath] little to do */
michael@0	6788	*uar=0; /* all digits cleared gives zero */
michael@0	6789	return 1; /* leaves just the one */
michael@0	6790	}
michael@0	6791
michael@0	6792	target=uar; /* both paths */
michael@0	6793	cut=MSUDIGITS(shift);
michael@0	6794	if (cut==DECDPUN) { /* unit-boundary case; easy */
michael@0	6795	up=uar+D2U(shift);
michael@0	6796	for (; up<uar+units; target++, up++) *target=*up;
michael@0	6797	return target-uar;
michael@0	6798	}
michael@0	6799
michael@0	6800	/* messier */
michael@0	6801	up=uar+D2U(shift-cut); /* source; correct to whole Units */
michael@0	6802	count=units*DECDPUN-shift; /* the maximum new length */
michael@0	6803	#if DECDPUN<=4
michael@0	6804	quot=QUOT10(*up, cut);
michael@0	6805	#else
michael@0	6806	quot=*up/powers[cut];
michael@0	6807	#endif
michael@0	6808	for (; ; target++) {
michael@0	6809	*target=(Unit)quot;
michael@0	6810	count-=(DECDPUN-cut);
michael@0	6811	if (count<=0) break;
michael@0	6812	up++;
michael@0	6813	quot=*up;
michael@0	6814	#if DECDPUN<=4
michael@0	6815	quot=QUOT10(quot, cut);
michael@0	6816	rem=*up-quot*powers[cut];
michael@0	6817	#else
michael@0	6818	rem=quot%powers[cut];
michael@0	6819	quot=quot/powers[cut];
michael@0	6820	#endif
michael@0	6821	*target=(Unit)(*target+rem*powers[DECDPUN-cut]);
michael@0	6822	count-=cut;
michael@0	6823	if (count<=0) break;
michael@0	6824	}
michael@0	6825	return target-uar+1;
michael@0	6826	} /* decShiftToLeast */
michael@0	6827
michael@0	6828	#if DECSUBSET
michael@0	6829	/* ------------------------------------------------------------------ */
michael@0	6830	/* decRoundOperand -- round an operand [used for subset only] */
michael@0	6831	/* */
michael@0	6832	/* dn is the number to round (dn->digits is > set->digits) */
michael@0	6833	/* set is the relevant context */
michael@0	6834	/* status is the status accumulator */
michael@0	6835	/* */
michael@0	6836	/* returns an allocated decNumber with the rounded result. */
michael@0	6837	/* */
michael@0	6838	/* lostDigits and other status may be set by this. */
michael@0	6839	/* */
michael@0	6840	/* Since the input is an operand, it must not be modified. */
michael@0	6841	/* Instead, return an allocated decNumber, rounded as required. */
michael@0	6842	/* It is the caller's responsibility to free the allocated storage. */
michael@0	6843	/* */
michael@0	6844	/* If no storage is available then the result cannot be used, so NULL */
michael@0	6845	/* is returned. */
michael@0	6846	/* ------------------------------------------------------------------ */
michael@0	6847	static decNumber *decRoundOperand(const decNumber *dn, decContext *set,
michael@0	6848	uInt *status) {
michael@0	6849	decNumber *res; /* result structure */
michael@0	6850	uInt newstatus=0; /* status from round */
michael@0	6851	Int residue=0; /* rounding accumulator */
michael@0	6852
michael@0	6853	/* Allocate storage for the returned decNumber, big enough for the */
michael@0	6854	/* length specified by the context */
michael@0	6855	res=(decNumber *)malloc(sizeof(decNumber)
michael@0	6856	+(D2U(set->digits)-1)*sizeof(Unit));
michael@0	6857	if (res==NULL) {
michael@0	6858	*status|=DEC_Insufficient_storage;
michael@0	6859	return NULL;
michael@0	6860	}
michael@0	6861	decCopyFit(res, dn, set, &residue, &newstatus);
michael@0	6862	decApplyRound(res, set, residue, &newstatus);
michael@0	6863
michael@0	6864	/* If that set Inexact then "lost digits" is raised... */
michael@0	6865	if (newstatus & DEC_Inexact) newstatus|=DEC_Lost_digits;
michael@0	6866	*status|=newstatus;
michael@0	6867	return res;
michael@0	6868	} /* decRoundOperand */
michael@0	6869	#endif
michael@0	6870
michael@0	6871	/* ------------------------------------------------------------------ */
michael@0	6872	/* decCopyFit -- copy a number, truncating the coefficient if needed */
michael@0	6873	/* */
michael@0	6874	/* dest is the target decNumber */
michael@0	6875	/* src is the source decNumber */
michael@0	6876	/* set is the context [used for length (digits) and rounding mode] */
michael@0	6877	/* residue is the residue accumulator */
michael@0	6878	/* status contains the current status to be updated */
michael@0	6879	/* */
michael@0	6880	/* (dest==src is allowed and will be a no-op if fits) */
michael@0	6881	/* All fields are updated as required. */
michael@0	6882	/* ------------------------------------------------------------------ */
michael@0	6883	static void decCopyFit(decNumber *dest, const decNumber *src,
michael@0	6884	decContext *set, Int *residue, uInt *status) {
michael@0	6885	dest->bits=src->bits;
michael@0	6886	dest->exponent=src->exponent;
michael@0	6887	decSetCoeff(dest, set, src->lsu, src->digits, residue, status);
michael@0	6888	} /* decCopyFit */
michael@0	6889
michael@0	6890	/* ------------------------------------------------------------------ */
michael@0	6891	/* decSetCoeff -- set the coefficient of a number */
michael@0	6892	/* */
michael@0	6893	/* dn is the number whose coefficient array is to be set. */
michael@0	6894	/* It must have space for set->digits digits */
michael@0	6895	/* set is the context [for size] */
michael@0	6896	/* lsu -> lsu of the source coefficient [may be dn->lsu] */
michael@0	6897	/* len is digits in the source coefficient [may be dn->digits] */
michael@0	6898	/* residue is the residue accumulator. This has values as in */
michael@0	6899	/* decApplyRound, and will be unchanged unless the */
michael@0	6900	/* target size is less than len. In this case, the */
michael@0	6901	/* coefficient is truncated and the residue is updated to */
michael@0	6902	/* reflect the previous residue and the dropped digits. */
michael@0	6903	/* status is the status accumulator, as usual */
michael@0	6904	/* */
michael@0	6905	/* The coefficient may already be in the number, or it can be an */
michael@0	6906	/* external intermediate array. If it is in the number, lsu must == */
michael@0	6907	/* dn->lsu and len must == dn->digits. */
michael@0	6908	/* */
michael@0	6909	/* Note that the coefficient length (len) may be < set->digits, and */
michael@0	6910	/* in this case this merely copies the coefficient (or is a no-op */
michael@0	6911	/* if dn->lsu==lsu). */
michael@0	6912	/* */
michael@0	6913	/* Note also that (only internally, from decQuantizeOp and */
michael@0	6914	/* decSetSubnormal) the value of set->digits may be less than one, */
michael@0	6915	/* indicating a round to left. This routine handles that case */
michael@0	6916	/* correctly; caller ensures space. */
michael@0	6917	/* */
michael@0	6918	/* dn->digits, dn->lsu (and as required), and dn->exponent are */
michael@0	6919	/* updated as necessary. dn->bits (sign) is unchanged. */
michael@0	6920	/* */
michael@0	6921	/* DEC_Rounded status is set if any digits are discarded. */
michael@0	6922	/* DEC_Inexact status is set if any non-zero digits are discarded, or */
michael@0	6923	/* incoming residue was non-0 (implies rounded) */
michael@0	6924	/* ------------------------------------------------------------------ */
michael@0	6925	/* mapping array: maps 0-9 to canonical residues, so that a residue */
michael@0	6926	/* can be adjusted in the range [-1, +1] and achieve correct rounding */
michael@0	6927	/* 0 1 2 3 4 5 6 7 8 9 */
michael@0	6928	static const uByte resmap[10]={0, 3, 3, 3, 3, 5, 7, 7, 7, 7};
michael@0	6929	static void decSetCoeff(decNumber *dn, decContext *set, const Unit *lsu,
michael@0	6930	Int len, Int *residue, uInt *status) {
michael@0	6931	Int discard; /* number of digits to discard */
michael@0	6932	uInt cut; /* cut point in Unit */
michael@0	6933	const Unit *up; /* work */
michael@0	6934	Unit *target; /* .. */
michael@0	6935	Int count; /* .. */
michael@0	6936	#if DECDPUN<=4
michael@0	6937	uInt temp; /* .. */
michael@0	6938	#endif
michael@0	6939
michael@0	6940	discard=len-set->digits; /* digits to discard */
michael@0	6941	if (discard<=0) { /* no digits are being discarded */
michael@0	6942	if (dn->lsu!=lsu) { /* copy needed */
michael@0	6943	/* copy the coefficient array to the result number; no shift needed */
michael@0	6944	count=len; /* avoids D2U */
michael@0	6945	up=lsu;
michael@0	6946	for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN)
michael@0	6947	*target=*up;
michael@0	6948	dn->digits=len; /* set the new length */
michael@0	6949	}
michael@0	6950	/* dn->exponent and residue are unchanged, record any inexactitude */
michael@0	6951	if (*residue!=0) *status|=(DEC_Inexact | DEC_Rounded);
michael@0	6952	return;
michael@0	6953	}
michael@0	6954
michael@0	6955	/* some digits must be discarded ... */
michael@0	6956	dn->exponent+=discard; /* maintain numerical value */
michael@0	6957	*status|=DEC_Rounded; /* accumulate Rounded status */
michael@0	6958	if (*residue>1) *residue=1; /* previous residue now to right, so reduce */
michael@0	6959
michael@0	6960	if (discard>len) { /* everything, +1, is being discarded */
michael@0	6961	/* guard digit is 0 */
michael@0	6962	/* residue is all the number [NB could be all 0s] */
michael@0	6963	if (*residue<=0) { /* not already positive */
michael@0	6964	count=len; /* avoids D2U */
michael@0	6965	for (up=lsu; count>0; up++, count-=DECDPUN) if (*up!=0) { /* found non-0 */
michael@0	6966	*residue=1;
michael@0	6967	break; /* no need to check any others */
michael@0	6968	}
michael@0	6969	}
michael@0	6970	if (*residue!=0) *status|=DEC_Inexact; /* record inexactitude */
michael@0	6971	*dn->lsu=0; /* coefficient will now be 0 */
michael@0	6972	dn->digits=1; /* .. */
michael@0	6973	return;
michael@0	6974	} /* total discard */
michael@0	6975
michael@0	6976	/* partial discard [most common case] */
michael@0	6977	/* here, at least the first (most significant) discarded digit exists */
michael@0	6978
michael@0	6979	/* spin up the number, noting residue during the spin, until get to */
michael@0	6980	/* the Unit with the first discarded digit. When reach it, extract */
michael@0	6981	/* it and remember its position */
michael@0	6982	count=0;
michael@0	6983	for (up=lsu;; up++) {
michael@0	6984	count+=DECDPUN;
michael@0	6985	if (count>=discard) break; /* full ones all checked */
michael@0	6986	if (*up!=0) *residue=1;
michael@0	6987	} /* up */
michael@0	6988
michael@0	6989	/* here up -> Unit with first discarded digit */
michael@0	6990	cut=discard-(count-DECDPUN)-1;
michael@0	6991	if (cut==DECDPUN-1) { /* unit-boundary case (fast) */
michael@0	6992	Unit half=(Unit)powers[DECDPUN]>>1;
michael@0	6993	/* set residue directly */
michael@0	6994	if (*up>=half) {
michael@0	6995	if (*up>half) *residue=7;
michael@0	6996	else *residue+=5; /* add sticky bit */
michael@0	6997	}
michael@0	6998	else { /* <half */
michael@0	6999	if (*up!=0) *residue=3; /* [else is 0, leave as sticky bit] */
michael@0	7000	}
michael@0	7001	if (set->digits<=0) { /* special for Quantize/Subnormal :-( */
michael@0	7002	*dn->lsu=0; /* .. result is 0 */
michael@0	7003	dn->digits=1; /* .. */
michael@0	7004	}
michael@0	7005	else { /* shift to least */
michael@0	7006	count=set->digits; /* now digits to end up with */
michael@0	7007	dn->digits=count; /* set the new length */
michael@0	7008	up++; /* move to next */
michael@0	7009	/* on unit boundary, so shift-down copy loop is simple */
michael@0	7010	for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN)
michael@0	7011	*target=*up;
michael@0	7012	}
michael@0	7013	} /* unit-boundary case */
michael@0	7014
michael@0	7015	else { /* discard digit is in low digit(s), and not top digit */
michael@0	7016	uInt discard1; /* first discarded digit */
michael@0	7017	uInt quot, rem; /* for divisions */
michael@0	7018	if (cut==0) quot=*up; /* is at bottom of unit */
michael@0	7019	else /* cut>0 */ { /* it's not at bottom of unit */
michael@0	7020	#if DECDPUN<=4
michael@0	7021	U_ASSERT(/* cut >= 0 &&*/ cut <= 4);
michael@0	7022	quot=QUOT10(*up, cut);
michael@0	7023	rem=*up-quot*powers[cut];
michael@0	7024	#else
michael@0	7025	rem=*up%powers[cut];
michael@0	7026	quot=*up/powers[cut];
michael@0	7027	#endif
michael@0	7028	if (rem!=0) *residue=1;
michael@0	7029	}
michael@0	7030	/* discard digit is now at bottom of quot */
michael@0	7031	#if DECDPUN<=4
michael@0	7032	temp=(quot*6554)>>16; /* fast /10 */
michael@0	7033	/* Vowels algorithm here not a win (9 instructions) */
michael@0	7034	discard1=quot-X10(temp);
michael@0	7035	quot=temp;
michael@0	7036	#else
michael@0	7037	discard1=quot%10;
michael@0	7038	quot=quot/10;
michael@0	7039	#endif
michael@0	7040	/* here, discard1 is the guard digit, and residue is everything */
michael@0	7041	/* else [use mapping array to accumulate residue safely] */
michael@0	7042	*residue+=resmap[discard1];
michael@0	7043	cut++; /* update cut */
michael@0	7044	/* here: up -> Unit of the array with bottom digit */
michael@0	7045	/* cut is the division point for each Unit */
michael@0	7046	/* quot holds the uncut high-order digits for the current unit */
michael@0	7047	if (set->digits<=0) { /* special for Quantize/Subnormal :-( */
michael@0	7048	*dn->lsu=0; /* .. result is 0 */
michael@0	7049	dn->digits=1; /* .. */
michael@0	7050	}
michael@0	7051	else { /* shift to least needed */
michael@0	7052	count=set->digits; /* now digits to end up with */
michael@0	7053	dn->digits=count; /* set the new length */
michael@0	7054	/* shift-copy the coefficient array to the result number */
michael@0	7055	for (target=dn->lsu; ; target++) {
michael@0	7056	*target=(Unit)quot;
michael@0	7057	count-=(DECDPUN-cut);
michael@0	7058	if (count<=0) break;
michael@0	7059	up++;
michael@0	7060	quot=*up;
michael@0	7061	#if DECDPUN<=4
michael@0	7062	quot=QUOT10(quot, cut);
michael@0	7063	rem=*up-quot*powers[cut];
michael@0	7064	#else
michael@0	7065	rem=quot%powers[cut];
michael@0	7066	quot=quot/powers[cut];
michael@0	7067	#endif
michael@0	7068	*target=(Unit)(*target+rem*powers[DECDPUN-cut]);
michael@0	7069	count-=cut;
michael@0	7070	if (count<=0) break;
michael@0	7071	} /* shift-copy loop */
michael@0	7072	} /* shift to least */
michael@0	7073	} /* not unit boundary */
michael@0	7074
michael@0	7075	if (*residue!=0) *status|=DEC_Inexact; /* record inexactitude */
michael@0	7076	return;
michael@0	7077	} /* decSetCoeff */
michael@0	7078
michael@0	7079	/* ------------------------------------------------------------------ */
michael@0	7080	/* decApplyRound -- apply pending rounding to a number */
michael@0	7081	/* */
michael@0	7082	/* dn is the number, with space for set->digits digits */
michael@0	7083	/* set is the context [for size and rounding mode] */
michael@0	7084	/* residue indicates pending rounding, being any accumulated */
michael@0	7085	/* guard and sticky information. It may be: */
michael@0	7086	/* 6-9: rounding digit is >5 */
michael@0	7087	/* 5: rounding digit is exactly half-way */
michael@0	7088	/* 1-4: rounding digit is <5 and >0 */
michael@0	7089	/* 0: the coefficient is exact */
michael@0	7090	/* -1: as 1, but the hidden digits are subtractive, that */
michael@0	7091	/* is, of the opposite sign to dn. In this case the */
michael@0	7092	/* coefficient must be non-0. This case occurs when */
michael@0	7093	/* subtracting a small number (which can be reduced to */
michael@0	7094	/* a sticky bit); see decAddOp. */
michael@0	7095	/* status is the status accumulator, as usual */
michael@0	7096	/* */
michael@0	7097	/* This routine applies rounding while keeping the length of the */
michael@0	7098	/* coefficient constant. The exponent and status are unchanged */
michael@0	7099	/* except if: */
michael@0	7100	/* */
michael@0	7101	/* -- the coefficient was increased and is all nines (in which */
michael@0	7102	/* case Overflow could occur, and is handled directly here so */
michael@0	7103	/* the caller does not need to re-test for overflow) */
michael@0	7104	/* */
michael@0	7105	/* -- the coefficient was decreased and becomes all nines (in which */
michael@0	7106	/* case Underflow could occur, and is also handled directly). */
michael@0	7107	/* */
michael@0	7108	/* All fields in dn are updated as required. */
michael@0	7109	/* */
michael@0	7110	/* ------------------------------------------------------------------ */
michael@0	7111	static void decApplyRound(decNumber *dn, decContext *set, Int residue,
michael@0	7112	uInt *status) {
michael@0	7113	Int bump; /* 1 if coefficient needs to be incremented */
michael@0	7114	/* -1 if coefficient needs to be decremented */
michael@0	7115
michael@0	7116	if (residue==0) return; /* nothing to apply */
michael@0	7117
michael@0	7118	bump=0; /* assume a smooth ride */
michael@0	7119
michael@0	7120	/* now decide whether, and how, to round, depending on mode */
michael@0	7121	switch (set->round) {
michael@0	7122	case DEC_ROUND_05UP: { /* round zero or five up (for reround) */
michael@0	7123	/* This is the same as DEC_ROUND_DOWN unless there is a */
michael@0	7124	/* positive residue and the lsd of dn is 0 or 5, in which case */
michael@0	7125	/* it is bumped; when residue is <0, the number is therefore */
michael@0	7126	/* bumped down unless the final digit was 1 or 6 (in which */
michael@0	7127	/* case it is bumped down and then up -- a no-op) */
michael@0	7128	Int lsd5=*dn->lsu%5; /* get lsd and quintate */
michael@0	7129	if (residue<0 && lsd5!=1) bump=-1;
michael@0	7130	else if (residue>0 && lsd5==0) bump=1;
michael@0	7131	/* [bump==1 could be applied directly; use common path for clarity] */
michael@0	7132	break;} /* r-05 */
michael@0	7133
michael@0	7134	case DEC_ROUND_DOWN: {
michael@0	7135	/* no change, except if negative residue */
michael@0	7136	if (residue<0) bump=-1;
michael@0	7137	break;} /* r-d */
michael@0	7138
michael@0	7139	case DEC_ROUND_HALF_DOWN: {
michael@0	7140	if (residue>5) bump=1;
michael@0	7141	break;} /* r-h-d */
michael@0	7142
michael@0	7143	case DEC_ROUND_HALF_EVEN: {
michael@0	7144	if (residue>5) bump=1; /* >0.5 goes up */
michael@0	7145	else if (residue==5) { /* exactly 0.5000... */
michael@0	7146	/* 0.5 goes up iff [new] lsd is odd */
michael@0	7147	if (*dn->lsu & 0x01) bump=1;
michael@0	7148	}
michael@0	7149	break;} /* r-h-e */
michael@0	7150
michael@0	7151	case DEC_ROUND_HALF_UP: {
michael@0	7152	if (residue>=5) bump=1;
michael@0	7153	break;} /* r-h-u */
michael@0	7154
michael@0	7155	case DEC_ROUND_UP: {
michael@0	7156	if (residue>0) bump=1;
michael@0	7157	break;} /* r-u */
michael@0	7158
michael@0	7159	case DEC_ROUND_CEILING: {
michael@0	7160	/* same as _UP for positive numbers, and as _DOWN for negatives */
michael@0	7161	/* [negative residue cannot occur on 0] */
michael@0	7162	if (decNumberIsNegative(dn)) {
michael@0	7163	if (residue<0) bump=-1;
michael@0	7164	}
michael@0	7165	else {
michael@0	7166	if (residue>0) bump=1;
michael@0	7167	}
michael@0	7168	break;} /* r-c */
michael@0	7169
michael@0	7170	case DEC_ROUND_FLOOR: {
michael@0	7171	/* same as _UP for negative numbers, and as _DOWN for positive */
michael@0	7172	/* [negative residue cannot occur on 0] */
michael@0	7173	if (!decNumberIsNegative(dn)) {
michael@0	7174	if (residue<0) bump=-1;
michael@0	7175	}
michael@0	7176	else {
michael@0	7177	if (residue>0) bump=1;
michael@0	7178	}
michael@0	7179	break;} /* r-f */
michael@0	7180
michael@0	7181	default: { /* e.g., DEC_ROUND_MAX */
michael@0	7182	*status|=DEC_Invalid_context;
michael@0	7183	#if DECTRACE || (DECCHECK && DECVERB)
michael@0	7184	printf("Unknown rounding mode: %d\n", set->round);
michael@0	7185	#endif
michael@0	7186	break;}
michael@0	7187	} /* switch */
michael@0	7188
michael@0	7189	/* now bump the number, up or down, if need be */
michael@0	7190	if (bump==0) return; /* no action required */
michael@0	7191
michael@0	7192	/* Simply use decUnitAddSub unless bumping up and the number is */
michael@0	7193	/* all nines. In this special case set to 100... explicitly */
michael@0	7194	/* and adjust the exponent by one (as otherwise could overflow */
michael@0	7195	/* the array) */
michael@0	7196	/* Similarly handle all-nines result if bumping down. */
michael@0	7197	if (bump>0) {
michael@0	7198	Unit *up; /* work */
michael@0	7199	uInt count=dn->digits; /* digits to be checked */
michael@0	7200	for (up=dn->lsu; ; up++) {
michael@0	7201	if (count<=DECDPUN) {
michael@0	7202	/* this is the last Unit (the msu) */
michael@0	7203	if (*up!=powers[count]-1) break; /* not still 9s */
michael@0	7204	/* here if it, too, is all nines */
michael@0	7205	*up=(Unit)powers[count-1]; /* here 999 -> 100 etc. */
michael@0	7206	for (up=up-1; up>=dn->lsu; up--) *up=0; /* others all to 0 */
michael@0	7207	dn->exponent++; /* and bump exponent */
michael@0	7208	/* [which, very rarely, could cause Overflow...] */
michael@0	7209	if ((dn->exponent+dn->digits)>set->emax+1) {
michael@0	7210	decSetOverflow(dn, set, status);
michael@0	7211	}
michael@0	7212	return; /* done */
michael@0	7213	}
michael@0	7214	/* a full unit to check, with more to come */
michael@0	7215	if (*up!=DECDPUNMAX) break; /* not still 9s */
michael@0	7216	count-=DECDPUN;
michael@0	7217	} /* up */
michael@0	7218	} /* bump>0 */
michael@0	7219	else { /* -1 */
michael@0	7220	/* here checking for a pre-bump of 1000... (leading 1, all */
michael@0	7221	/* other digits zero) */
michael@0	7222	Unit *up, *sup; /* work */
michael@0	7223	uInt count=dn->digits; /* digits to be checked */
michael@0	7224	for (up=dn->lsu; ; up++) {
michael@0	7225	if (count<=DECDPUN) {
michael@0	7226	/* this is the last Unit (the msu) */
michael@0	7227	if (*up!=powers[count-1]) break; /* not 100.. */
michael@0	7228	/* here if have the 1000... case */
michael@0	7229	sup=up; /* save msu pointer */
michael@0	7230	*up=(Unit)powers[count]-1; /* here 100 in msu -> 999 */
michael@0	7231	/* others all to all-nines, too */
michael@0	7232	for (up=up-1; up>=dn->lsu; up--) *up=(Unit)powers[DECDPUN]-1;
michael@0	7233	dn->exponent--; /* and bump exponent */
michael@0	7234
michael@0	7235	/* iff the number was at the subnormal boundary (exponent=etiny) */
michael@0	7236	/* then the exponent is now out of range, so it will in fact get */
michael@0	7237	/* clamped to etiny and the final 9 dropped. */
michael@0	7238	/* printf(">> emin=%d exp=%d sdig=%d\n", set->emin, */
michael@0	7239	/* dn->exponent, set->digits); */
michael@0	7240	if (dn->exponent+1==set->emin-set->digits+1) {
michael@0	7241	if (count==1 && dn->digits==1) *sup=0; /* here 9 -> 0[.9] */
michael@0	7242	else {
michael@0	7243	*sup=(Unit)powers[count-1]-1; /* here 999.. in msu -> 99.. */
michael@0	7244	dn->digits--;
michael@0	7245	}
michael@0	7246	dn->exponent++;
michael@0	7247	*status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded;
michael@0	7248	}
michael@0	7249	return; /* done */
michael@0	7250	}
michael@0	7251
michael@0	7252	/* a full unit to check, with more to come */
michael@0	7253	if (*up!=0) break; /* not still 0s */
michael@0	7254	count-=DECDPUN;
michael@0	7255	} /* up */
michael@0	7256
michael@0	7257	} /* bump<0 */
michael@0	7258
michael@0	7259	/* Actual bump needed. Do it. */
michael@0	7260	decUnitAddSub(dn->lsu, D2U(dn->digits), uarrone, 1, 0, dn->lsu, bump);
michael@0	7261	} /* decApplyRound */
michael@0	7262
michael@0	7263	#if DECSUBSET
michael@0	7264	/* ------------------------------------------------------------------ */
michael@0	7265	/* decFinish -- finish processing a number */
michael@0	7266	/* */
michael@0	7267	/* dn is the number */
michael@0	7268	/* set is the context */
michael@0	7269	/* residue is the rounding accumulator (as in decApplyRound) */
michael@0	7270	/* status is the accumulator */
michael@0	7271	/* */
michael@0	7272	/* This finishes off the current number by: */
michael@0	7273	/* 1. If not extended: */
michael@0	7274	/* a. Converting a zero result to clean '0' */
michael@0	7275	/* b. Reducing positive exponents to 0, if would fit in digits */
michael@0	7276	/* 2. Checking for overflow and subnormals (always) */
michael@0	7277	/* Note this is just Finalize when no subset arithmetic. */
michael@0	7278	/* All fields are updated as required. */
michael@0	7279	/* ------------------------------------------------------------------ */
michael@0	7280	static void decFinish(decNumber *dn, decContext *set, Int *residue,
michael@0	7281	uInt *status) {
michael@0	7282	if (!set->extended) {
michael@0	7283	if ISZERO(dn) { /* value is zero */
michael@0	7284	dn->exponent=0; /* clean exponent .. */
michael@0	7285	dn->bits=0; /* .. and sign */
michael@0	7286	return; /* no error possible */
michael@0	7287	}
michael@0	7288	if (dn->exponent>=0) { /* non-negative exponent */
michael@0	7289	/* >0; reduce to integer if possible */
michael@0	7290	if (set->digits >= (dn->exponent+dn->digits)) {
michael@0	7291	dn->digits=decShiftToMost(dn->lsu, dn->digits, dn->exponent);
michael@0	7292	dn->exponent=0;
michael@0	7293	}
michael@0	7294	}
michael@0	7295	} /* !extended */
michael@0	7296
michael@0	7297	decFinalize(dn, set, residue, status);
michael@0	7298	} /* decFinish */
michael@0	7299	#endif
michael@0	7300
michael@0	7301	/* ------------------------------------------------------------------ */
michael@0	7302	/* decFinalize -- final check, clamp, and round of a number */
michael@0	7303	/* */
michael@0	7304	/* dn is the number */
michael@0	7305	/* set is the context */
michael@0	7306	/* residue is the rounding accumulator (as in decApplyRound) */
michael@0	7307	/* status is the status accumulator */
michael@0	7308	/* */
michael@0	7309	/* This finishes off the current number by checking for subnormal */
michael@0	7310	/* results, applying any pending rounding, checking for overflow, */
michael@0	7311	/* and applying any clamping. */
michael@0	7312	/* Underflow and overflow conditions are raised as appropriate. */
michael@0	7313	/* All fields are updated as required. */
michael@0	7314	/* ------------------------------------------------------------------ */
michael@0	7315	static void decFinalize(decNumber *dn, decContext *set, Int *residue,
michael@0	7316	uInt *status) {
michael@0	7317	Int shift; /* shift needed if clamping */
michael@0	7318	Int tinyexp=set->emin-dn->digits+1; /* precalculate subnormal boundary */
michael@0	7319
michael@0	7320	/* Must be careful, here, when checking the exponent as the */
michael@0	7321	/* adjusted exponent could overflow 31 bits [because it may already */
michael@0	7322	/* be up to twice the expected]. */
michael@0	7323
michael@0	7324	/* First test for subnormal. This must be done before any final */
michael@0	7325	/* round as the result could be rounded to Nmin or 0. */
michael@0	7326	if (dn->exponent<=tinyexp) { /* prefilter */
michael@0	7327	Int comp;
michael@0	7328	decNumber nmin;
michael@0	7329	/* A very nasty case here is dn == Nmin and residue<0 */
michael@0	7330	if (dn->exponent<tinyexp) {
michael@0	7331	/* Go handle subnormals; this will apply round if needed. */
michael@0	7332	decSetSubnormal(dn, set, residue, status);
michael@0	7333	return;
michael@0	7334	}
michael@0	7335	/* Equals case: only subnormal if dn=Nmin and negative residue */
michael@0	7336	uprv_decNumberZero(&nmin);
michael@0	7337	nmin.lsu[0]=1;
michael@0	7338	nmin.exponent=set->emin;
michael@0	7339	comp=decCompare(dn, &nmin, 1); /* (signless compare) */
michael@0	7340	if (comp==BADINT) { /* oops */
michael@0	7341	*status|=DEC_Insufficient_storage; /* abandon... */
michael@0	7342	return;
michael@0	7343	}
michael@0	7344	if (*residue<0 && comp==0) { /* neg residue and dn==Nmin */
michael@0	7345	decApplyRound(dn, set, *residue, status); /* might force down */
michael@0	7346	decSetSubnormal(dn, set, residue, status);
michael@0	7347	return;
michael@0	7348	}
michael@0	7349	}
michael@0	7350
michael@0	7351	/* now apply any pending round (this could raise overflow). */
michael@0	7352	if (*residue!=0) decApplyRound(dn, set, *residue, status);
michael@0	7353
michael@0	7354	/* Check for overflow [redundant in the 'rare' case] or clamp */
michael@0	7355	if (dn->exponent<=set->emax-set->digits+1) return; /* neither needed */
michael@0	7356
michael@0	7357
michael@0	7358	/* here when might have an overflow or clamp to do */
michael@0	7359	if (dn->exponent>set->emax-dn->digits+1) { /* too big */
michael@0	7360	decSetOverflow(dn, set, status);
michael@0	7361	return;
michael@0	7362	}
michael@0	7363	/* here when the result is normal but in clamp range */
michael@0	7364	if (!set->clamp) return;
michael@0	7365
michael@0	7366	/* here when need to apply the IEEE exponent clamp (fold-down) */
michael@0	7367	shift=dn->exponent-(set->emax-set->digits+1);
michael@0	7368
michael@0	7369	/* shift coefficient (if non-zero) */
michael@0	7370	if (!ISZERO(dn)) {
michael@0	7371	dn->digits=decShiftToMost(dn->lsu, dn->digits, shift);
michael@0	7372	}
michael@0	7373	dn->exponent-=shift; /* adjust the exponent to match */
michael@0	7374	*status|=DEC_Clamped; /* and record the dirty deed */
michael@0	7375	return;
michael@0	7376	} /* decFinalize */
michael@0	7377
michael@0	7378	/* ------------------------------------------------------------------ */
michael@0	7379	/* decSetOverflow -- set number to proper overflow value */
michael@0	7380	/* */
michael@0	7381	/* dn is the number (used for sign [only] and result) */
michael@0	7382	/* set is the context [used for the rounding mode, etc.] */
michael@0	7383	/* status contains the current status to be updated */
michael@0	7384	/* */
michael@0	7385	/* This sets the sign of a number and sets its value to either */
michael@0	7386	/* Infinity or the maximum finite value, depending on the sign of */
michael@0	7387	/* dn and the rounding mode, following IEEE 754 rules. */
michael@0	7388	/* ------------------------------------------------------------------ */
michael@0	7389	static void decSetOverflow(decNumber *dn, decContext *set, uInt *status) {
michael@0	7390	Flag needmax=0; /* result is maximum finite value */
michael@0	7391	uByte sign=dn->bits&DECNEG; /* clean and save sign bit */
michael@0	7392
michael@0	7393	if (ISZERO(dn)) { /* zero does not overflow magnitude */
michael@0	7394	Int emax=set->emax; /* limit value */
michael@0	7395	if (set->clamp) emax-=set->digits-1; /* lower if clamping */
michael@0	7396	if (dn->exponent>emax) { /* clamp required */
michael@0	7397	dn->exponent=emax;
michael@0	7398	*status|=DEC_Clamped;
michael@0	7399	}
michael@0	7400	return;
michael@0	7401	}
michael@0	7402
michael@0	7403	uprv_decNumberZero(dn);
michael@0	7404	switch (set->round) {
michael@0	7405	case DEC_ROUND_DOWN: {
michael@0	7406	needmax=1; /* never Infinity */
michael@0	7407	break;} /* r-d */
michael@0	7408	case DEC_ROUND_05UP: {
michael@0	7409	needmax=1; /* never Infinity */
michael@0	7410	break;} /* r-05 */
michael@0	7411	case DEC_ROUND_CEILING: {
michael@0	7412	if (sign) needmax=1; /* Infinity if non-negative */
michael@0	7413	break;} /* r-c */
michael@0	7414	case DEC_ROUND_FLOOR: {
michael@0	7415	if (!sign) needmax=1; /* Infinity if negative */
michael@0	7416	break;} /* r-f */
michael@0	7417	default: break; /* Infinity in all other cases */
michael@0	7418	}
michael@0	7419	if (needmax) {
michael@0	7420	decSetMaxValue(dn, set);
michael@0	7421	dn->bits=sign; /* set sign */
michael@0	7422	}
michael@0	7423	else dn->bits=sign|DECINF; /* Value is +/-Infinity */
michael@0	7424	*status|=DEC_Overflow | DEC_Inexact | DEC_Rounded;
michael@0	7425	} /* decSetOverflow */
michael@0	7426
michael@0	7427	/* ------------------------------------------------------------------ */
michael@0	7428	/* decSetMaxValue -- set number to +Nmax (maximum normal value) */
michael@0	7429	/* */
michael@0	7430	/* dn is the number to set */
michael@0	7431	/* set is the context [used for digits and emax] */
michael@0	7432	/* */
michael@0	7433	/* This sets the number to the maximum positive value. */
michael@0	7434	/* ------------------------------------------------------------------ */
michael@0	7435	static void decSetMaxValue(decNumber *dn, decContext *set) {
michael@0	7436	Unit *up; /* work */
michael@0	7437	Int count=set->digits; /* nines to add */
michael@0	7438	dn->digits=count;
michael@0	7439	/* fill in all nines to set maximum value */
michael@0	7440	for (up=dn->lsu; ; up++) {
michael@0	7441	if (count>DECDPUN) *up=DECDPUNMAX; /* unit full o'nines */
michael@0	7442	else { /* this is the msu */
michael@0	7443	*up=(Unit)(powers[count]-1);
michael@0	7444	break;
michael@0	7445	}
michael@0	7446	count-=DECDPUN; /* filled those digits */
michael@0	7447	} /* up */
michael@0	7448	dn->bits=0; /* + sign */
michael@0	7449	dn->exponent=set->emax-set->digits+1;
michael@0	7450	} /* decSetMaxValue */
michael@0	7451
michael@0	7452	/* ------------------------------------------------------------------ */
michael@0	7453	/* decSetSubnormal -- process value whose exponent is <Emin */
michael@0	7454	/* */
michael@0	7455	/* dn is the number (used as input as well as output; it may have */
michael@0	7456	/* an allowed subnormal value, which may need to be rounded) */
michael@0	7457	/* set is the context [used for the rounding mode] */
michael@0	7458	/* residue is any pending residue */
michael@0	7459	/* status contains the current status to be updated */
michael@0	7460	/* */
michael@0	7461	/* If subset mode, set result to zero and set Underflow flags. */
michael@0	7462	/* */
michael@0	7463	/* Value may be zero with a low exponent; this does not set Subnormal */
michael@0	7464	/* but the exponent will be clamped to Etiny. */
michael@0	7465	/* */
michael@0	7466	/* Otherwise ensure exponent is not out of range, and round as */
michael@0	7467	/* necessary. Underflow is set if the result is Inexact. */
michael@0	7468	/* ------------------------------------------------------------------ */
michael@0	7469	static void decSetSubnormal(decNumber *dn, decContext *set, Int *residue,
michael@0	7470	uInt *status) {
michael@0	7471	decContext workset; /* work */
michael@0	7472	Int etiny, adjust; /* .. */
michael@0	7473
michael@0	7474	#if DECSUBSET
michael@0	7475	/* simple set to zero and 'hard underflow' for subset */
michael@0	7476	if (!set->extended) {
michael@0	7477	uprv_decNumberZero(dn);
michael@0	7478	/* always full overflow */
michael@0	7479	*status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded;
michael@0	7480	return;
michael@0	7481	}
michael@0	7482	#endif
michael@0	7483
michael@0	7484	/* Full arithmetic -- allow subnormals, rounded to minimum exponent */
michael@0	7485	/* (Etiny) if needed */
michael@0	7486	etiny=set->emin-(set->digits-1); /* smallest allowed exponent */
michael@0	7487
michael@0	7488	if ISZERO(dn) { /* value is zero */
michael@0	7489	/* residue can never be non-zero here */
michael@0	7490	#if DECCHECK
michael@0	7491	if (*residue!=0) {
michael@0	7492	printf("++ Subnormal 0 residue %ld\n", (LI)*residue);
michael@0	7493	*status|=DEC_Invalid_operation;
michael@0	7494	}
michael@0	7495	#endif
michael@0	7496	if (dn->exponent<etiny) { /* clamp required */
michael@0	7497	dn->exponent=etiny;
michael@0	7498	*status|=DEC_Clamped;
michael@0	7499	}
michael@0	7500	return;
michael@0	7501	}
michael@0	7502
michael@0	7503	*status|=DEC_Subnormal; /* have a non-zero subnormal */
michael@0	7504	adjust=etiny-dn->exponent; /* calculate digits to remove */
michael@0	7505	if (adjust<=0) { /* not out of range; unrounded */
michael@0	7506	/* residue can never be non-zero here, except in the Nmin-residue */
michael@0	7507	/* case (which is a subnormal result), so can take fast-path here */
michael@0	7508	/* it may already be inexact (from setting the coefficient) */
michael@0	7509	if (*status&DEC_Inexact) *status|=DEC_Underflow;
michael@0	7510	return;
michael@0	7511	}
michael@0	7512
michael@0	7513	/* adjust>0, so need to rescale the result so exponent becomes Etiny */
michael@0	7514	/* [this code is similar to that in rescale] */
michael@0	7515	workset=*set; /* clone rounding, etc. */
michael@0	7516	workset.digits=dn->digits-adjust; /* set requested length */
michael@0	7517	workset.emin-=adjust; /* and adjust emin to match */
michael@0	7518	/* [note that the latter can be <1, here, similar to Rescale case] */
michael@0	7519	decSetCoeff(dn, &workset, dn->lsu, dn->digits, residue, status);
michael@0	7520	decApplyRound(dn, &workset, *residue, status);
michael@0	7521
michael@0	7522	/* Use 754 default rule: Underflow is set iff Inexact */
michael@0	7523	/* [independent of whether trapped] */
michael@0	7524	if (*status&DEC_Inexact) *status|=DEC_Underflow;
michael@0	7525
michael@0	7526	/* if rounded up a 999s case, exponent will be off by one; adjust */
michael@0	7527	/* back if so [it will fit, because it was shortened earlier] */
michael@0	7528	if (dn->exponent>etiny) {
michael@0	7529	dn->digits=decShiftToMost(dn->lsu, dn->digits, 1);
michael@0	7530	dn->exponent--; /* (re)adjust the exponent. */
michael@0	7531	}
michael@0	7532
michael@0	7533	/* if rounded to zero, it is by definition clamped... */
michael@0	7534	if (ISZERO(dn)) *status|=DEC_Clamped;
michael@0	7535	} /* decSetSubnormal */
michael@0	7536
michael@0	7537	/* ------------------------------------------------------------------ */
michael@0	7538	/* decCheckMath - check entry conditions for a math function */
michael@0	7539	/* */
michael@0	7540	/* This checks the context and the operand */
michael@0	7541	/* */
michael@0	7542	/* rhs is the operand to check */
michael@0	7543	/* set is the context to check */
michael@0	7544	/* status is unchanged if both are good */
michael@0	7545	/* */
michael@0	7546	/* returns non-zero if status is changed, 0 otherwise */
michael@0	7547	/* */
michael@0	7548	/* Restrictions enforced: */
michael@0	7549	/* */
michael@0	7550	/* digits, emax, and -emin in the context must be less than */
michael@0	7551	/* DEC_MAX_MATH (999999), and A must be within these bounds if */
michael@0	7552	/* non-zero. Invalid_operation is set in the status if a */
michael@0	7553	/* restriction is violated. */
michael@0	7554	/* ------------------------------------------------------------------ */
michael@0	7555	static uInt decCheckMath(const decNumber *rhs, decContext *set,
michael@0	7556	uInt *status) {
michael@0	7557	uInt save=*status; /* record */
michael@0	7558	if (set->digits>DEC_MAX_MATH
michael@0	7559	|| set->emax>DEC_MAX_MATH
michael@0	7560	|| -set->emin>DEC_MAX_MATH) *status|=DEC_Invalid_context;
michael@0	7561	else if ((rhs->digits>DEC_MAX_MATH
michael@0	7562	|| rhs->exponent+rhs->digits>DEC_MAX_MATH+1
michael@0	7563	|| rhs->exponent+rhs->digits<2*(1-DEC_MAX_MATH))
michael@0	7564	&& !ISZERO(rhs)) *status|=DEC_Invalid_operation;
michael@0	7565	return (*status!=save);
michael@0	7566	} /* decCheckMath */
michael@0	7567
michael@0	7568	/* ------------------------------------------------------------------ */
michael@0	7569	/* decGetInt -- get integer from a number */
michael@0	7570	/* */
michael@0	7571	/* dn is the number [which will not be altered] */
michael@0	7572	/* */
michael@0	7573	/* returns one of: */
michael@0	7574	/* BADINT if there is a non-zero fraction */
michael@0	7575	/* the converted integer */
michael@0	7576	/* BIGEVEN if the integer is even and magnitude > 2*10**9 */
michael@0	7577	/* BIGODD if the integer is odd and magnitude > 2*10**9 */
michael@0	7578	/* */
michael@0	7579	/* This checks and gets a whole number from the input decNumber. */
michael@0	7580	/* The sign can be determined from dn by the caller when BIGEVEN or */
michael@0	7581	/* BIGODD is returned. */
michael@0	7582	/* ------------------------------------------------------------------ */
michael@0	7583	static Int decGetInt(const decNumber *dn) {
michael@0	7584	Int theInt; /* result accumulator */
michael@0	7585	const Unit *up; /* work */
michael@0	7586	Int got; /* digits (real or not) processed */
michael@0	7587	Int ilength=dn->digits+dn->exponent; /* integral length */
michael@0	7588	Flag neg=decNumberIsNegative(dn); /* 1 if -ve */
michael@0	7589
michael@0	7590	/* The number must be an integer that fits in 10 digits */
michael@0	7591	/* Assert, here, that 10 is enough for any rescale Etiny */
michael@0	7592	#if DEC_MAX_EMAX > 999999999
michael@0	7593	#error GetInt may need updating [for Emax]
michael@0	7594	#endif
michael@0	7595	#if DEC_MIN_EMIN < -999999999
michael@0	7596	#error GetInt may need updating [for Emin]
michael@0	7597	#endif
michael@0	7598	if (ISZERO(dn)) return 0; /* zeros are OK, with any exponent */
michael@0	7599
michael@0	7600	up=dn->lsu; /* ready for lsu */
michael@0	7601	theInt=0; /* ready to accumulate */
michael@0	7602	if (dn->exponent>=0) { /* relatively easy */
michael@0	7603	/* no fractional part [usual]; allow for positive exponent */
michael@0	7604	got=dn->exponent;
michael@0	7605	}
michael@0	7606	else { /* -ve exponent; some fractional part to check and discard */
michael@0	7607	Int count=-dn->exponent; /* digits to discard */
michael@0	7608	/* spin up whole units until reach the Unit with the unit digit */
michael@0	7609	for (; count>=DECDPUN; up++) {
michael@0	7610	if (*up!=0) return BADINT; /* non-zero Unit to discard */
michael@0	7611	count-=DECDPUN;
michael@0	7612	}
michael@0	7613	if (count==0) got=0; /* [a multiple of DECDPUN] */
michael@0	7614	else { /* [not multiple of DECDPUN] */
michael@0	7615	Int rem; /* work */
michael@0	7616	/* slice off fraction digits and check for non-zero */
michael@0	7617	#if DECDPUN<=4
michael@0	7618	theInt=QUOT10(*up, count);
michael@0	7619	rem=*up-theInt*powers[count];
michael@0	7620	#else
michael@0	7621	rem=*up%powers[count]; /* slice off discards */
michael@0	7622	theInt=*up/powers[count];
michael@0	7623	#endif
michael@0	7624	if (rem!=0) return BADINT; /* non-zero fraction */
michael@0	7625	/* it looks good */
michael@0	7626	got=DECDPUN-count; /* number of digits so far */
michael@0	7627	up++; /* ready for next */
michael@0	7628	}
michael@0	7629	}
michael@0	7630	/* now it's known there's no fractional part */
michael@0	7631
michael@0	7632	/* tricky code now, to accumulate up to 9.3 digits */
michael@0	7633	if (got==0) {theInt=*up; got+=DECDPUN; up++;} /* ensure lsu is there */
michael@0	7634
michael@0	7635	if (ilength<11) {
michael@0	7636	Int save=theInt;
michael@0	7637	/* collect any remaining unit(s) */
michael@0	7638	for (; got<ilength; up++) {
michael@0	7639	theInt+=*up*powers[got];
michael@0	7640	got+=DECDPUN;
michael@0	7641	}
michael@0	7642	if (ilength==10) { /* need to check for wrap */
michael@0	7643	if (theInt/(Int)powers[got-DECDPUN]!=(Int)*(up-1)) ilength=11;
michael@0	7644	/* [that test also disallows the BADINT result case] */
michael@0	7645	else if (neg && theInt>1999999997) ilength=11;
michael@0	7646	else if (!neg && theInt>999999999) ilength=11;
michael@0	7647	if (ilength==11) theInt=save; /* restore correct low bit */
michael@0	7648	}
michael@0	7649	}
michael@0	7650
michael@0	7651	if (ilength>10) { /* too big */
michael@0	7652	if (theInt&1) return BIGODD; /* bottom bit 1 */
michael@0	7653	return BIGEVEN; /* bottom bit 0 */
michael@0	7654	}
michael@0	7655
michael@0	7656	if (neg) theInt=-theInt; /* apply sign */
michael@0	7657	return theInt;
michael@0	7658	} /* decGetInt */
michael@0	7659
michael@0	7660	/* ------------------------------------------------------------------ */
michael@0	7661	/* decDecap -- decapitate the coefficient of a number */
michael@0	7662	/* */
michael@0	7663	/* dn is the number to be decapitated */
michael@0	7664	/* drop is the number of digits to be removed from the left of dn; */
michael@0	7665	/* this must be <= dn->digits (if equal, the coefficient is */
michael@0	7666	/* set to 0) */
michael@0	7667	/* */
michael@0	7668	/* Returns dn; dn->digits will be <= the initial digits less drop */
michael@0	7669	/* (after removing drop digits there may be leading zero digits */
michael@0	7670	/* which will also be removed). Only dn->lsu and dn->digits change. */
michael@0	7671	/* ------------------------------------------------------------------ */
michael@0	7672	static decNumber *decDecap(decNumber *dn, Int drop) {
michael@0	7673	Unit *msu; /* -> target cut point */
michael@0	7674	Int cut; /* work */
michael@0	7675	if (drop>=dn->digits) { /* losing the whole thing */
michael@0	7676	#if DECCHECK
michael@0	7677	if (drop>dn->digits)
michael@0	7678	printf("decDecap called with drop>digits [%ld>%ld]\n",
michael@0	7679	(LI)drop, (LI)dn->digits);
michael@0	7680	#endif
michael@0	7681	dn->lsu[0]=0;
michael@0	7682	dn->digits=1;
michael@0	7683	return dn;
michael@0	7684	}
michael@0	7685	msu=dn->lsu+D2U(dn->digits-drop)-1; /* -> likely msu */
michael@0	7686	cut=MSUDIGITS(dn->digits-drop); /* digits to be in use in msu */
michael@0	7687	if (cut!=DECDPUN) *msu%=powers[cut]; /* clear left digits */
michael@0	7688	/* that may have left leading zero digits, so do a proper count... */
michael@0	7689	dn->digits=decGetDigits(dn->lsu, msu-dn->lsu+1);
michael@0	7690	return dn;
michael@0	7691	} /* decDecap */
michael@0	7692
michael@0	7693	/* ------------------------------------------------------------------ */
michael@0	7694	/* decBiStr -- compare string with pairwise options */
michael@0	7695	/* */
michael@0	7696	/* targ is the string to compare */
michael@0	7697	/* str1 is one of the strings to compare against (length may be 0) */
michael@0	7698	/* str2 is the other; it must be the same length as str1 */
michael@0	7699	/* */
michael@0	7700	/* returns 1 if strings compare equal, (that is, it is the same */
michael@0	7701	/* length as str1 and str2, and each character of targ is in either */
michael@0	7702	/* str1 or str2 in the corresponding position), or 0 otherwise */
michael@0	7703	/* */
michael@0	7704	/* This is used for generic caseless compare, including the awkward */
michael@0	7705	/* case of the Turkish dotted and dotless Is. Use as (for example): */
michael@0	7706	/* if (decBiStr(test, "mike", "MIKE")) ... */
michael@0	7707	/* ------------------------------------------------------------------ */
michael@0	7708	static Flag decBiStr(const char *targ, const char *str1, const char *str2) {
michael@0	7709	for (;;targ++, str1++, str2++) {
michael@0	7710	if (*targ!=*str1 && *targ!=*str2) return 0;
michael@0	7711	/* *targ has a match in one (or both, if terminator) */
michael@0	7712	if (*targ=='\0') break;
michael@0	7713	} /* forever */
michael@0	7714	return 1;
michael@0	7715	} /* decBiStr */
michael@0	7716
michael@0	7717	/* ------------------------------------------------------------------ */
michael@0	7718	/* decNaNs -- handle NaN operand or operands */
michael@0	7719	/* */
michael@0	7720	/* res is the result number */
michael@0	7721	/* lhs is the first operand */
michael@0	7722	/* rhs is the second operand, or NULL if none */
michael@0	7723	/* context is used to limit payload length */
michael@0	7724	/* status contains the current status */
michael@0	7725	/* returns res in case convenient */
michael@0	7726	/* */
michael@0	7727	/* Called when one or both operands is a NaN, and propagates the */
michael@0	7728	/* appropriate result to res. When an sNaN is found, it is changed */
michael@0	7729	/* to a qNaN and Invalid operation is set. */
michael@0	7730	/* ------------------------------------------------------------------ */
michael@0	7731	static decNumber * decNaNs(decNumber *res, const decNumber *lhs,
michael@0	7732	const decNumber *rhs, decContext *set,
michael@0	7733	uInt *status) {
michael@0	7734	/* This decision tree ends up with LHS being the source pointer, */
michael@0	7735	/* and status updated if need be */
michael@0	7736	if (lhs->bits & DECSNAN)
michael@0	7737	*status|=DEC_Invalid_operation | DEC_sNaN;
michael@0	7738	else if (rhs==NULL);
michael@0	7739	else if (rhs->bits & DECSNAN) {
michael@0	7740	lhs=rhs;
michael@0	7741	*status|=DEC_Invalid_operation | DEC_sNaN;
michael@0	7742	}
michael@0	7743	else if (lhs->bits & DECNAN);
michael@0	7744	else lhs=rhs;
michael@0	7745
michael@0	7746	/* propagate the payload */
michael@0	7747	if (lhs->digits<=set->digits) uprv_decNumberCopy(res, lhs); /* easy */
michael@0	7748	else { /* too long */
michael@0	7749	const Unit *ul;
michael@0	7750	Unit *ur, *uresp1;
michael@0	7751	/* copy safe number of units, then decapitate */
michael@0	7752	res->bits=lhs->bits; /* need sign etc. */
michael@0	7753	uresp1=res->lsu+D2U(set->digits);
michael@0	7754	for (ur=res->lsu, ul=lhs->lsu; ur<uresp1; ur++, ul++) *ur=*ul;
michael@0	7755	res->digits=D2U(set->digits)*DECDPUN;
michael@0	7756	/* maybe still too long */
michael@0	7757	if (res->digits>set->digits) decDecap(res, res->digits-set->digits);
michael@0	7758	}
michael@0	7759
michael@0	7760	res->bits&=~DECSNAN; /* convert any sNaN to NaN, while */
michael@0	7761	res->bits|=DECNAN; /* .. preserving sign */
michael@0	7762	res->exponent=0; /* clean exponent */
michael@0	7763	/* [coefficient was copied/decapitated] */
michael@0	7764	return res;
michael@0	7765	} /* decNaNs */
michael@0	7766
michael@0	7767	/* ------------------------------------------------------------------ */
michael@0	7768	/* decStatus -- apply non-zero status */
michael@0	7769	/* */
michael@0	7770	/* dn is the number to set if error */
michael@0	7771	/* status contains the current status (not yet in context) */
michael@0	7772	/* set is the context */
michael@0	7773	/* */
michael@0	7774	/* If the status is an error status, the number is set to a NaN, */
michael@0	7775	/* unless the error was an overflow, divide-by-zero, or underflow, */
michael@0	7776	/* in which case the number will have already been set. */
michael@0	7777	/* */
michael@0	7778	/* The context status is then updated with the new status. Note that */
michael@0	7779	/* this may raise a signal, so control may never return from this */
michael@0	7780	/* routine (hence resources must be recovered before it is called). */
michael@0	7781	/* ------------------------------------------------------------------ */
michael@0	7782	static void decStatus(decNumber *dn, uInt status, decContext *set) {
michael@0	7783	if (status & DEC_NaNs) { /* error status -> NaN */
michael@0	7784	/* if cause was an sNaN, clear and propagate [NaN is already set up] */
michael@0	7785	if (status & DEC_sNaN) status&=~DEC_sNaN;
michael@0	7786	else {
michael@0	7787	uprv_decNumberZero(dn); /* other error: clean throughout */
michael@0	7788	dn->bits=DECNAN; /* and make a quiet NaN */
michael@0	7789	}
michael@0	7790	}
michael@0	7791	uprv_decContextSetStatus(set, status); /* [may not return] */
michael@0	7792	return;
michael@0	7793	} /* decStatus */
michael@0	7794
michael@0	7795	/* ------------------------------------------------------------------ */
michael@0	7796	/* decGetDigits -- count digits in a Units array */
michael@0	7797	/* */
michael@0	7798	/* uar is the Unit array holding the number (this is often an */
michael@0	7799	/* accumulator of some sort) */
michael@0	7800	/* len is the length of the array in units [>=1] */
michael@0	7801	/* */
michael@0	7802	/* returns the number of (significant) digits in the array */
michael@0	7803	/* */
michael@0	7804	/* All leading zeros are excluded, except the last if the array has */
michael@0	7805	/* only zero Units. */
michael@0	7806	/* ------------------------------------------------------------------ */
michael@0	7807	/* This may be called twice during some operations. */
michael@0	7808	static Int decGetDigits(Unit *uar, Int len) {
michael@0	7809	Unit *up=uar+(len-1); /* -> msu */
michael@0	7810	Int digits=(len-1)*DECDPUN+1; /* possible digits excluding msu */
michael@0	7811	#if DECDPUN>4
michael@0	7812	uInt const *pow; /* work */
michael@0	7813	#endif
michael@0	7814	/* (at least 1 in final msu) */
michael@0	7815	#if DECCHECK
michael@0	7816	if (len<1) printf("decGetDigits called with len<1 [%ld]\n", (LI)len);
michael@0	7817	#endif
michael@0	7818
michael@0	7819	for (; up>=uar; up--) {
michael@0	7820	if (*up==0) { /* unit is all 0s */
michael@0	7821	if (digits==1) break; /* a zero has one digit */
michael@0	7822	digits-=DECDPUN; /* adjust for 0 unit */
michael@0	7823	continue;}
michael@0	7824	/* found the first (most significant) non-zero Unit */
michael@0	7825	#if DECDPUN>1 /* not done yet */
michael@0	7826	if (*up<10) break; /* is 1-9 */
michael@0	7827	digits++;
michael@0	7828	#if DECDPUN>2 /* not done yet */
michael@0	7829	if (*up<100) break; /* is 10-99 */
michael@0	7830	digits++;
michael@0	7831	#if DECDPUN>3 /* not done yet */
michael@0	7832	if (*up<1000) break; /* is 100-999 */
michael@0	7833	digits++;
michael@0	7834	#if DECDPUN>4 /* count the rest ... */
michael@0	7835	for (pow=&powers[4]; *up>=*pow; pow++) digits++;
michael@0	7836	#endif
michael@0	7837	#endif
michael@0	7838	#endif
michael@0	7839	#endif
michael@0	7840	break;
michael@0	7841	} /* up */
michael@0	7842	return digits;
michael@0	7843	} /* decGetDigits */
michael@0	7844
michael@0	7845	#if DECTRACE | DECCHECK
michael@0	7846	/* ------------------------------------------------------------------ */
michael@0	7847	/* decNumberShow -- display a number [debug aid] */
michael@0	7848	/* dn is the number to show */
michael@0	7849	/* */
michael@0	7850	/* Shows: sign, exponent, coefficient (msu first), digits */
michael@0	7851	/* or: sign, special-value */
michael@0	7852	/* ------------------------------------------------------------------ */
michael@0	7853	/* this is public so other modules can use it */
michael@0	7854	void uprv_decNumberShow(const decNumber *dn) {
michael@0	7855	const Unit *up; /* work */
michael@0	7856	uInt u, d; /* .. */
michael@0	7857	Int cut; /* .. */
michael@0	7858	char isign='+'; /* main sign */
michael@0	7859	if (dn==NULL) {
michael@0	7860	printf("NULL\n");
michael@0	7861	return;}
michael@0	7862	if (decNumberIsNegative(dn)) isign='-';
michael@0	7863	printf(" >> %c ", isign);
michael@0	7864	if (dn->bits&DECSPECIAL) { /* Is a special value */
michael@0	7865	if (decNumberIsInfinite(dn)) printf("Infinity");
michael@0	7866	else { /* a NaN */
michael@0	7867	if (dn->bits&DECSNAN) printf("sNaN"); /* signalling NaN */
michael@0	7868	else printf("NaN");
michael@0	7869	}
michael@0	7870	/* if coefficient and exponent are 0, no more to do */
michael@0	7871	if (dn->exponent==0 && dn->digits==1 && *dn->lsu==0) {
michael@0	7872	printf("\n");
michael@0	7873	return;}
michael@0	7874	/* drop through to report other information */
michael@0	7875	printf(" ");
michael@0	7876	}
michael@0	7877
michael@0	7878	/* now carefully display the coefficient */
michael@0	7879	up=dn->lsu+D2U(dn->digits)-1; /* msu */
michael@0	7880	printf("%ld", (LI)*up);
michael@0	7881	for (up=up-1; up>=dn->lsu; up--) {
michael@0	7882	u=*up;
michael@0	7883	printf(":");
michael@0	7884	for (cut=DECDPUN-1; cut>=0; cut--) {
michael@0	7885	d=u/powers[cut];
michael@0	7886	u-=d*powers[cut];
michael@0	7887	printf("%ld", (LI)d);
michael@0	7888	} /* cut */
michael@0	7889	} /* up */
michael@0	7890	if (dn->exponent!=0) {
michael@0	7891	char esign='+';
michael@0	7892	if (dn->exponent<0) esign='-';
michael@0	7893	printf(" E%c%ld", esign, (LI)abs(dn->exponent));
michael@0	7894	}
michael@0	7895	printf(" [%ld]\n", (LI)dn->digits);
michael@0	7896	} /* decNumberShow */
michael@0	7897	#endif
michael@0	7898
michael@0	7899	#if DECTRACE || DECCHECK
michael@0	7900	/* ------------------------------------------------------------------ */
michael@0	7901	/* decDumpAr -- display a unit array [debug/check aid] */
michael@0	7902	/* name is a single-character tag name */
michael@0	7903	/* ar is the array to display */
michael@0	7904	/* len is the length of the array in Units */
michael@0	7905	/* ------------------------------------------------------------------ */
michael@0	7906	static void decDumpAr(char name, const Unit *ar, Int len) {
michael@0	7907	Int i;
michael@0	7908	const char *spec;
michael@0	7909	#if DECDPUN==9
michael@0	7910	spec="%09d ";
michael@0	7911	#elif DECDPUN==8
michael@0	7912	spec="%08d ";
michael@0	7913	#elif DECDPUN==7
michael@0	7914	spec="%07d ";
michael@0	7915	#elif DECDPUN==6
michael@0	7916	spec="%06d ";
michael@0	7917	#elif DECDPUN==5
michael@0	7918	spec="%05d ";
michael@0	7919	#elif DECDPUN==4
michael@0	7920	spec="%04d ";
michael@0	7921	#elif DECDPUN==3
michael@0	7922	spec="%03d ";
michael@0	7923	#elif DECDPUN==2
michael@0	7924	spec="%02d ";
michael@0	7925	#else
michael@0	7926	spec="%d ";
michael@0	7927	#endif
michael@0	7928	printf(" :%c: ", name);
michael@0	7929	for (i=len-1; i>=0; i--) {
michael@0	7930	if (i==len-1) printf("%ld ", (LI)ar[i]);
michael@0	7931	else printf(spec, ar[i]);
michael@0	7932	}
michael@0	7933	printf("\n");
michael@0	7934	return;}
michael@0	7935	#endif
michael@0	7936
michael@0	7937	#if DECCHECK
michael@0	7938	/* ------------------------------------------------------------------ */
michael@0	7939	/* decCheckOperands -- check operand(s) to a routine */
michael@0	7940	/* res is the result structure (not checked; it will be set to */
michael@0	7941	/* quiet NaN if error found (and it is not NULL)) */
michael@0	7942	/* lhs is the first operand (may be DECUNRESU) */
michael@0	7943	/* rhs is the second (may be DECUNUSED) */
michael@0	7944	/* set is the context (may be DECUNCONT) */
michael@0	7945	/* returns 0 if both operands, and the context are clean, or 1 */
michael@0	7946	/* otherwise (in which case the context will show an error, */
michael@0	7947	/* unless NULL). Note that res is not cleaned; caller should */
michael@0	7948	/* handle this so res=NULL case is safe. */
michael@0	7949	/* The caller is expected to abandon immediately if 1 is returned. */
michael@0	7950	/* ------------------------------------------------------------------ */
michael@0	7951	static Flag decCheckOperands(decNumber *res, const decNumber *lhs,
michael@0	7952	const decNumber *rhs, decContext *set) {
michael@0	7953	Flag bad=0;
michael@0	7954	if (set==NULL) { /* oops; hopeless */
michael@0	7955	#if DECTRACE || DECVERB
michael@0	7956	printf("Reference to context is NULL.\n");
michael@0	7957	#endif
michael@0	7958	bad=1;
michael@0	7959	return 1;}
michael@0	7960	else if (set!=DECUNCONT
michael@0	7961	&& (set->digits<1 || set->round>=DEC_ROUND_MAX)) {
michael@0	7962	bad=1;
michael@0	7963	#if DECTRACE || DECVERB
michael@0	7964	printf("Bad context [digits=%ld round=%ld].\n",
michael@0	7965	(LI)set->digits, (LI)set->round);
michael@0	7966	#endif
michael@0	7967	}
michael@0	7968	else {
michael@0	7969	if (res==NULL) {
michael@0	7970	bad=1;
michael@0	7971	#if DECTRACE
michael@0	7972	/* this one not DECVERB as standard tests include NULL */
michael@0	7973	printf("Reference to result is NULL.\n");
michael@0	7974	#endif
michael@0	7975	}
michael@0	7976	if (!bad && lhs!=DECUNUSED) bad=(decCheckNumber(lhs));
michael@0	7977	if (!bad && rhs!=DECUNUSED) bad=(decCheckNumber(rhs));
michael@0	7978	}
michael@0	7979	if (bad) {
michael@0	7980	if (set!=DECUNCONT) uprv_decContextSetStatus(set, DEC_Invalid_operation);
michael@0	7981	if (res!=DECUNRESU && res!=NULL) {
michael@0	7982	uprv_decNumberZero(res);
michael@0	7983	res->bits=DECNAN; /* qNaN */
michael@0	7984	}
michael@0	7985	}
michael@0	7986	return bad;
michael@0	7987	} /* decCheckOperands */
michael@0	7988
michael@0	7989	/* ------------------------------------------------------------------ */
michael@0	7990	/* decCheckNumber -- check a number */
michael@0	7991	/* dn is the number to check */
michael@0	7992	/* returns 0 if the number is clean, or 1 otherwise */
michael@0	7993	/* */
michael@0	7994	/* The number is considered valid if it could be a result from some */
michael@0	7995	/* operation in some valid context. */
michael@0	7996	/* ------------------------------------------------------------------ */
michael@0	7997	static Flag decCheckNumber(const decNumber *dn) {
michael@0	7998	const Unit *up; /* work */
michael@0	7999	uInt maxuint; /* .. */
michael@0	8000	Int ae, d, digits; /* .. */
michael@0	8001	Int emin, emax; /* .. */
michael@0	8002
michael@0	8003	if (dn==NULL) { /* hopeless */
michael@0	8004	#if DECTRACE
michael@0	8005	/* this one not DECVERB as standard tests include NULL */
michael@0	8006	printf("Reference to decNumber is NULL.\n");
michael@0	8007	#endif
michael@0	8008	return 1;}
michael@0	8009
michael@0	8010	/* check special values */
michael@0	8011	if (dn->bits & DECSPECIAL) {
michael@0	8012	if (dn->exponent!=0) {
michael@0	8013	#if DECTRACE || DECVERB
michael@0	8014	printf("Exponent %ld (not 0) for a special value [%02x].\n",
michael@0	8015	(LI)dn->exponent, dn->bits);
michael@0	8016	#endif
michael@0	8017	return 1;}
michael@0	8018
michael@0	8019	/* 2003.09.08: NaNs may now have coefficients, so next tests Inf only */
michael@0	8020	if (decNumberIsInfinite(dn)) {
michael@0	8021	if (dn->digits!=1) {
michael@0	8022	#if DECTRACE || DECVERB
michael@0	8023	printf("Digits %ld (not 1) for an infinity.\n", (LI)dn->digits);
michael@0	8024	#endif
michael@0	8025	return 1;}
michael@0	8026	if (*dn->lsu!=0) {
michael@0	8027	#if DECTRACE || DECVERB
michael@0	8028	printf("LSU %ld (not 0) for an infinity.\n", (LI)*dn->lsu);
michael@0	8029	#endif
michael@0	8030	decDumpAr('I', dn->lsu, D2U(dn->digits));
michael@0	8031	return 1;}
michael@0	8032	} /* Inf */
michael@0	8033	/* 2002.12.26: negative NaNs can now appear through proposed IEEE */
michael@0	8034	/* concrete formats (decimal64, etc.). */
michael@0	8035	return 0;
michael@0	8036	}
michael@0	8037
michael@0	8038	/* check the coefficient */
michael@0	8039	if (dn->digits<1 || dn->digits>DECNUMMAXP) {
michael@0	8040	#if DECTRACE || DECVERB
michael@0	8041	printf("Digits %ld in number.\n", (LI)dn->digits);
michael@0	8042	#endif
michael@0	8043	return 1;}
michael@0	8044
michael@0	8045	d=dn->digits;
michael@0	8046
michael@0	8047	for (up=dn->lsu; d>0; up++) {
michael@0	8048	if (d>DECDPUN) maxuint=DECDPUNMAX;
michael@0	8049	else { /* reached the msu */
michael@0	8050	maxuint=powers[d]-1;
michael@0	8051	if (dn->digits>1 && *up<powers[d-1]) {
michael@0	8052	#if DECTRACE || DECVERB
michael@0	8053	printf("Leading 0 in number.\n");
michael@0	8054	uprv_decNumberShow(dn);
michael@0	8055	#endif
michael@0	8056	return 1;}
michael@0	8057	}
michael@0	8058	if (*up>maxuint) {
michael@0	8059	#if DECTRACE || DECVERB
michael@0	8060	printf("Bad Unit [%08lx] in %ld-digit number at offset %ld [maxuint %ld].\n",
michael@0	8061	(LI)*up, (LI)dn->digits, (LI)(up-dn->lsu), (LI)maxuint);
michael@0	8062	#endif
michael@0	8063	return 1;}
michael@0	8064	d-=DECDPUN;
michael@0	8065	}
michael@0	8066
michael@0	8067	/* check the exponent. Note that input operands can have exponents */
michael@0	8068	/* which are out of the set->emin/set->emax and set->digits range */
michael@0	8069	/* (just as they can have more digits than set->digits). */
michael@0	8070	ae=dn->exponent+dn->digits-1; /* adjusted exponent */
michael@0	8071	emax=DECNUMMAXE;
michael@0	8072	emin=DECNUMMINE;
michael@0	8073	digits=DECNUMMAXP;
michael@0	8074	if (ae<emin-(digits-1)) {
michael@0	8075	#if DECTRACE || DECVERB
michael@0	8076	printf("Adjusted exponent underflow [%ld].\n", (LI)ae);
michael@0	8077	uprv_decNumberShow(dn);
michael@0	8078	#endif
michael@0	8079	return 1;}
michael@0	8080	if (ae>+emax) {
michael@0	8081	#if DECTRACE || DECVERB
michael@0	8082	printf("Adjusted exponent overflow [%ld].\n", (LI)ae);
michael@0	8083	uprv_decNumberShow(dn);
michael@0	8084	#endif
michael@0	8085	return 1;}
michael@0	8086
michael@0	8087	return 0; /* it's OK */
michael@0	8088	} /* decCheckNumber */
michael@0	8089
michael@0	8090	/* ------------------------------------------------------------------ */
michael@0	8091	/* decCheckInexact -- check a normal finite inexact result has digits */
michael@0	8092	/* dn is the number to check */
michael@0	8093	/* set is the context (for status and precision) */
michael@0	8094	/* sets Invalid operation, etc., if some digits are missing */
michael@0	8095	/* [this check is not made for DECSUBSET compilation or when */
michael@0	8096	/* subnormal is not set] */
michael@0	8097	/* ------------------------------------------------------------------ */
michael@0	8098	static void decCheckInexact(const decNumber *dn, decContext *set) {
michael@0	8099	#if !DECSUBSET && DECEXTFLAG
michael@0	8100	if ((set->status & (DEC_Inexact|DEC_Subnormal))==DEC_Inexact
michael@0	8101	&& (set->digits!=dn->digits) && !(dn->bits & DECSPECIAL)) {
michael@0	8102	#if DECTRACE || DECVERB
michael@0	8103	printf("Insufficient digits [%ld] on normal Inexact result.\n",
michael@0	8104	(LI)dn->digits);
michael@0	8105	uprv_decNumberShow(dn);
michael@0	8106	#endif
michael@0	8107	uprv_decContextSetStatus(set, DEC_Invalid_operation);
michael@0	8108	}
michael@0	8109	#else
michael@0	8110	/* next is a noop for quiet compiler */
michael@0	8111	if (dn!=NULL && dn->digits==0) set->status|=DEC_Invalid_operation;
michael@0	8112	#endif
michael@0	8113	return;
michael@0	8114	} /* decCheckInexact */
michael@0	8115	#endif
michael@0	8116
michael@0	8117	#if DECALLOC
michael@0	8118	#undef malloc
michael@0	8119	#undef free
michael@0	8120	/* ------------------------------------------------------------------ */
michael@0	8121	/* decMalloc -- accountable allocation routine */
michael@0	8122	/* n is the number of bytes to allocate */
michael@0	8123	/* */
michael@0	8124	/* Semantics is the same as the stdlib malloc routine, but bytes */
michael@0	8125	/* allocated are accounted for globally, and corruption fences are */
michael@0	8126	/* added before and after the 'actual' storage. */
michael@0	8127	/* ------------------------------------------------------------------ */
michael@0	8128	/* This routine allocates storage with an extra twelve bytes; 8 are */
michael@0	8129	/* at the start and hold: */
michael@0	8130	/* 0-3 the original length requested */
michael@0	8131	/* 4-7 buffer corruption detection fence (DECFENCE, x4) */
michael@0	8132	/* The 4 bytes at the end also hold a corruption fence (DECFENCE, x4) */
michael@0	8133	/* ------------------------------------------------------------------ */
michael@0	8134	static void *decMalloc(size_t n) {
michael@0	8135	uInt size=n+12; /* true size */
michael@0	8136	void *alloc; /* -> allocated storage */
michael@0	8137	uByte *b, *b0; /* work */
michael@0	8138	uInt uiwork; /* for macros */
michael@0	8139
michael@0	8140	alloc=malloc(size); /* -> allocated storage */
michael@0	8141	if (alloc==NULL) return NULL; /* out of strorage */
michael@0	8142	b0=(uByte *)alloc; /* as bytes */
michael@0	8143	decAllocBytes+=n; /* account for storage */
michael@0	8144	UBFROMUI(alloc, n); /* save n */
michael@0	8145	/* printf(" alloc ++ dAB: %ld (%ld)\n", (LI)decAllocBytes, (LI)n); */
michael@0	8146	for (b=b0+4; b<b0+8; b++) *b=DECFENCE;
michael@0	8147	for (b=b0+n+8; b<b0+n+12; b++) *b=DECFENCE;
michael@0	8148	return b0+8; /* -> play area */
michael@0	8149	} /* decMalloc */
michael@0	8150
michael@0	8151	/* ------------------------------------------------------------------ */
michael@0	8152	/* decFree -- accountable free routine */
michael@0	8153	/* alloc is the storage to free */
michael@0	8154	/* */
michael@0	8155	/* Semantics is the same as the stdlib malloc routine, except that */
michael@0	8156	/* the global storage accounting is updated and the fences are */
michael@0	8157	/* checked to ensure that no routine has written 'out of bounds'. */
michael@0	8158	/* ------------------------------------------------------------------ */
michael@0	8159	/* This routine first checks that the fences have not been corrupted. */
michael@0	8160	/* It then frees the storage using the 'truw' storage address (that */
michael@0	8161	/* is, offset by 8). */
michael@0	8162	/* ------------------------------------------------------------------ */
michael@0	8163	static void decFree(void *alloc) {
michael@0	8164	uInt n; /* original length */
michael@0	8165	uByte *b, *b0; /* work */
michael@0	8166	uInt uiwork; /* for macros */
michael@0	8167
michael@0	8168	if (alloc==NULL) return; /* allowed; it's a nop */
michael@0	8169	b0=(uByte *)alloc; /* as bytes */
michael@0	8170	b0-=8; /* -> true start of storage */
michael@0	8171	n=UBTOUI(b0); /* lift length */
michael@0	8172	for (b=b0+4; b<b0+8; b++) if (*b!=DECFENCE)
michael@0	8173	printf("=== Corrupt byte [%02x] at offset %d from %ld ===\n", *b,
michael@0	8174	b-b0-8, (LI)b0);
michael@0	8175	for (b=b0+n+8; b<b0+n+12; b++) if (*b!=DECFENCE)
michael@0	8176	printf("=== Corrupt byte [%02x] at offset +%d from %ld, n=%ld ===\n", *b,
michael@0	8177	b-b0-8, (LI)b0, (LI)n);
michael@0	8178	free(b0); /* drop the storage */
michael@0	8179	decAllocBytes-=n; /* account for storage */
michael@0	8180	/* printf(" free -- dAB: %d (%d)\n", decAllocBytes, -n); */
michael@0	8181	} /* decFree */
michael@0	8182	#define malloc(a) decMalloc(a)
michael@0	8183	#define free(a) decFree(a)
michael@0	8184	#endif