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nsprpub/pr/src/misc/prdtoa.c@6474c204b198 (annotated)

nsprpub/pr/src/misc/prdtoa.c

Wed, 31 Dec 2014 06:09:35 +0100

author

Michael Schloh von Bennewitz <michael@schloh.com>

date

Wed, 31 Dec 2014 06:09:35 +0100

changeset 0

6474c204b198

permissions

-rw-r--r--

Cloned upstream origin tor-browser at tor-browser-31.3.0esr-4.5-1-build1
revision ID fc1c9ff7c1b2defdbc039f12214767608f46423f for hacking purpose.

michael@0	1	/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*- */
michael@0	2	/* This Source Code Form is subject to the terms of the Mozilla Public
michael@0	3	* License, v. 2.0. If a copy of the MPL was not distributed with this
michael@0	4	* file, You can obtain one at http://mozilla.org/MPL/2.0/. */
michael@0	5
michael@0	6	/*
michael@0	7	* This file is based on the third-party code dtoa.c. We minimize our
michael@0	8	* modifications to third-party code to make it easy to merge new versions.
michael@0	9	* The author of dtoa.c was not willing to add the parentheses suggested by
michael@0	10	* GCC, so we suppress these warnings.
michael@0	11	*/
michael@0	12	#if (__GNUC__ > 4) || (__GNUC__ == 4 && __GNUC_MINOR__ >= 2)
michael@0	13	#pragma GCC diagnostic ignored "-Wparentheses"
michael@0	14	#endif
michael@0	15
michael@0	16	#include "primpl.h"
michael@0	17	#include "prbit.h"
michael@0	18
michael@0	19	#define MULTIPLE_THREADS
michael@0	20	#define ACQUIRE_DTOA_LOCK(n) PR_Lock(dtoa_lock[n])
michael@0	21	#define FREE_DTOA_LOCK(n) PR_Unlock(dtoa_lock[n])
michael@0	22
michael@0	23	static PRLock *dtoa_lock[2];
michael@0	24
michael@0	25	void _PR_InitDtoa(void)
michael@0	26	{
michael@0	27	dtoa_lock[0] = PR_NewLock();
michael@0	28	dtoa_lock[1] = PR_NewLock();
michael@0	29	}
michael@0	30
michael@0	31	void _PR_CleanupDtoa(void)
michael@0	32	{
michael@0	33	PR_DestroyLock(dtoa_lock[0]);
michael@0	34	dtoa_lock[0] = NULL;
michael@0	35	PR_DestroyLock(dtoa_lock[1]);
michael@0	36	dtoa_lock[1] = NULL;
michael@0	37
michael@0	38	/* FIXME: deal with freelist and p5s. */
michael@0	39	}
michael@0	40
michael@0	41	#if !defined(__ARM_EABI__) \
michael@0	42	&& (defined(__arm) || defined(__arm__) || defined(__arm26__) \
michael@0	43	|| defined(__arm32__))
michael@0	44	#define IEEE_ARM
michael@0	45	#elif defined(IS_LITTLE_ENDIAN)
michael@0	46	#define IEEE_8087
michael@0	47	#else
michael@0	48	#define IEEE_MC68k
michael@0	49	#endif
michael@0	50
michael@0	51	#define Long PRInt32
michael@0	52	#define ULong PRUint32
michael@0	53	#define NO_LONG_LONG
michael@0	54
michael@0	55	#define No_Hex_NaN
michael@0	56
michael@0	57	/****************************************************************
michael@0	58	*
michael@0	59	* The author of this software is David M. Gay.
michael@0	60	*
michael@0	61	* Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
michael@0	62	*
michael@0	63	* Permission to use, copy, modify, and distribute this software for any
michael@0	64	* purpose without fee is hereby granted, provided that this entire notice
michael@0	65	* is included in all copies of any software which is or includes a copy
michael@0	66	* or modification of this software and in all copies of the supporting
michael@0	67	* documentation for such software.
michael@0	68	*
michael@0	69	* THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
michael@0	70	* WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY
michael@0	71	* REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
michael@0	72	* OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
michael@0	73	*
michael@0	74	***************************************************************/
michael@0	75
michael@0	76	/* Please send bug reports to David M. Gay (dmg at acm dot org,
michael@0	77	* with " at " changed at "@" and " dot " changed to "."). */
michael@0	78
michael@0	79	/* On a machine with IEEE extended-precision registers, it is
michael@0	80	* necessary to specify double-precision (53-bit) rounding precision
michael@0	81	* before invoking strtod or dtoa. If the machine uses (the equivalent
michael@0	82	* of) Intel 80x87 arithmetic, the call
michael@0	83	* _control87(PC_53, MCW_PC);
michael@0	84	* does this with many compilers. Whether this or another call is
michael@0	85	* appropriate depends on the compiler; for this to work, it may be
michael@0	86	* necessary to #include "float.h" or another system-dependent header
michael@0	87	* file.
michael@0	88	*/
michael@0	89
michael@0	90	/* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
michael@0	91	*
michael@0	92	* This strtod returns a nearest machine number to the input decimal
michael@0	93	* string (or sets errno to ERANGE). With IEEE arithmetic, ties are
michael@0	94	* broken by the IEEE round-even rule. Otherwise ties are broken by
michael@0	95	* biased rounding (add half and chop).
michael@0	96	*
michael@0	97	* Inspired loosely by William D. Clinger's paper "How to Read Floating
michael@0	98	* Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
michael@0	99	*
michael@0	100	* Modifications:
michael@0	101	*
michael@0	102	* 1. We only require IEEE, IBM, or VAX double-precision
michael@0	103	* arithmetic (not IEEE double-extended).
michael@0	104	* 2. We get by with floating-point arithmetic in a case that
michael@0	105	* Clinger missed -- when we're computing d * 10^n
michael@0	106	* for a small integer d and the integer n is not too
michael@0	107	* much larger than 22 (the maximum integer k for which
michael@0	108	* we can represent 10^k exactly), we may be able to
michael@0	109	* compute (d*10^k) * 10^(e-k) with just one roundoff.
michael@0	110	* 3. Rather than a bit-at-a-time adjustment of the binary
michael@0	111	* result in the hard case, we use floating-point
michael@0	112	* arithmetic to determine the adjustment to within
michael@0	113	* one bit; only in really hard cases do we need to
michael@0	114	* compute a second residual.
michael@0	115	* 4. Because of 3., we don't need a large table of powers of 10
michael@0	116	* for ten-to-e (just some small tables, e.g. of 10^k
michael@0	117	* for 0 <= k <= 22).
michael@0	118	*/
michael@0	119
michael@0	120	/*
michael@0	121	* #define IEEE_8087 for IEEE-arithmetic machines where the least
michael@0	122	* significant byte has the lowest address.
michael@0	123	* #define IEEE_MC68k for IEEE-arithmetic machines where the most
michael@0	124	* significant byte has the lowest address.
michael@0	125	* #define IEEE_ARM for IEEE-arithmetic machines where the two words
michael@0	126	* in a double are stored in big endian order but the two shorts
michael@0	127	* in a word are still stored in little endian order.
michael@0	128	* #define Long int on machines with 32-bit ints and 64-bit longs.
michael@0	129	* #define IBM for IBM mainframe-style floating-point arithmetic.
michael@0	130	* #define VAX for VAX-style floating-point arithmetic (D_floating).
michael@0	131	* #define No_leftright to omit left-right logic in fast floating-point
michael@0	132	* computation of dtoa.
michael@0	133	* #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
michael@0	134	* and strtod and dtoa should round accordingly.
michael@0	135	* #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
michael@0	136	* and Honor_FLT_ROUNDS is not #defined.
michael@0	137	* #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
michael@0	138	* that use extended-precision instructions to compute rounded
michael@0	139	* products and quotients) with IBM.
michael@0	140	* #define ROUND_BIASED for IEEE-format with biased rounding.
michael@0	141	* #define Inaccurate_Divide for IEEE-format with correctly rounded
michael@0	142	* products but inaccurate quotients, e.g., for Intel i860.
michael@0	143	* #define NO_LONG_LONG on machines that do not have a "long long"
michael@0	144	* integer type (of >= 64 bits). On such machines, you can
michael@0	145	* #define Just_16 to store 16 bits per 32-bit Long when doing
michael@0	146	* high-precision integer arithmetic. Whether this speeds things
michael@0	147	* up or slows things down depends on the machine and the number
michael@0	148	* being converted. If long long is available and the name is
michael@0	149	* something other than "long long", #define Llong to be the name,
michael@0	150	* and if "unsigned Llong" does not work as an unsigned version of
michael@0	151	* Llong, #define #ULLong to be the corresponding unsigned type.
michael@0	152	* #define KR_headers for old-style C function headers.
michael@0	153	* #define Bad_float_h if your system lacks a float.h or if it does not
michael@0	154	* define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
michael@0	155	* FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
michael@0	156	* #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
michael@0	157	* if memory is available and otherwise does something you deem
michael@0	158	* appropriate. If MALLOC is undefined, malloc will be invoked
michael@0	159	* directly -- and assumed always to succeed. Similarly, if you
michael@0	160	* want something other than the system's free() to be called to
michael@0	161	* recycle memory acquired from MALLOC, #define FREE to be the
michael@0	162	* name of the alternate routine. (FREE or free is only called in
michael@0	163	* pathological cases, e.g., in a dtoa call after a dtoa return in
michael@0	164	* mode 3 with thousands of digits requested.)
michael@0	165	* #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
michael@0	166	* memory allocations from a private pool of memory when possible.
michael@0	167	* When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes,
michael@0	168	* unless #defined to be a different length. This default length
michael@0	169	* suffices to get rid of MALLOC calls except for unusual cases,
michael@0	170	* such as decimal-to-binary conversion of a very long string of
michael@0	171	* digits. The longest string dtoa can return is about 751 bytes
michael@0	172	* long. For conversions by strtod of strings of 800 digits and
michael@0	173	* all dtoa conversions in single-threaded executions with 8-byte
michael@0	174	* pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte
michael@0	175	* pointers, PRIVATE_MEM >= 7112 appears adequate.
michael@0	176	* #define INFNAN_CHECK on IEEE systems to cause strtod to check for
michael@0	177	* Infinity and NaN (case insensitively). On some systems (e.g.,
michael@0	178	* some HP systems), it may be necessary to #define NAN_WORD0
michael@0	179	* appropriately -- to the most significant word of a quiet NaN.
michael@0	180	* (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
michael@0	181	* When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
michael@0	182	* strtod also accepts (case insensitively) strings of the form
michael@0	183	* NaN(x), where x is a string of hexadecimal digits and spaces;
michael@0	184	* if there is only one string of hexadecimal digits, it is taken
michael@0	185	* for the 52 fraction bits of the resulting NaN; if there are two
michael@0	186	* or more strings of hex digits, the first is for the high 20 bits,
michael@0	187	* the second and subsequent for the low 32 bits, with intervening
michael@0	188	* white space ignored; but if this results in none of the 52
michael@0	189	* fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0
michael@0	190	* and NAN_WORD1 are used instead.
michael@0	191	* #define MULTIPLE_THREADS if the system offers preemptively scheduled
michael@0	192	* multiple threads. In this case, you must provide (or suitably
michael@0	193	* #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
michael@0	194	* by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed
michael@0	195	* in pow5mult, ensures lazy evaluation of only one copy of high
michael@0	196	* powers of 5; omitting this lock would introduce a small
michael@0	197	* probability of wasting memory, but would otherwise be harmless.)
michael@0	198	* You must also invoke freedtoa(s) to free the value s returned by
michael@0	199	* dtoa. You may do so whether or not MULTIPLE_THREADS is #defined.
michael@0	200	* #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
michael@0	201	* avoids underflows on inputs whose result does not underflow.
michael@0	202	* If you #define NO_IEEE_Scale on a machine that uses IEEE-format
michael@0	203	* floating-point numbers and flushes underflows to zero rather
michael@0	204	* than implementing gradual underflow, then you must also #define
michael@0	205	* Sudden_Underflow.
michael@0	206	* #define USE_LOCALE to use the current locale's decimal_point value.
michael@0	207	* #define SET_INEXACT if IEEE arithmetic is being used and extra
michael@0	208	* computation should be done to set the inexact flag when the
michael@0	209	* result is inexact and avoid setting inexact when the result
michael@0	210	* is exact. In this case, dtoa.c must be compiled in
michael@0	211	* an environment, perhaps provided by #include "dtoa.c" in a
michael@0	212	* suitable wrapper, that defines two functions,
michael@0	213	* int get_inexact(void);
michael@0	214	* void clear_inexact(void);
michael@0	215	* such that get_inexact() returns a nonzero value if the
michael@0	216	* inexact bit is already set, and clear_inexact() sets the
michael@0	217	* inexact bit to 0. When SET_INEXACT is #defined, strtod
michael@0	218	* also does extra computations to set the underflow and overflow
michael@0	219	* flags when appropriate (i.e., when the result is tiny and
michael@0	220	* inexact or when it is a numeric value rounded to +-infinity).
michael@0	221	* #define NO_ERRNO if strtod should not assign errno = ERANGE when
michael@0	222	* the result overflows to +-Infinity or underflows to 0.
michael@0	223	*/
michael@0	224
michael@0	225	#ifndef Long
michael@0	226	#define Long long
michael@0	227	#endif
michael@0	228	#ifndef ULong
michael@0	229	typedef unsigned Long ULong;
michael@0	230	#endif
michael@0	231
michael@0	232	#ifdef DEBUG
michael@0	233	#include "stdio.h"
michael@0	234	#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
michael@0	235	#endif
michael@0	236
michael@0	237	#include "stdlib.h"
michael@0	238	#include "string.h"
michael@0	239
michael@0	240	#ifdef USE_LOCALE
michael@0	241	#include "locale.h"
michael@0	242	#endif
michael@0	243
michael@0	244	#ifdef MALLOC
michael@0	245	#ifdef KR_headers
michael@0	246	extern char *MALLOC();
michael@0	247	#else
michael@0	248	extern void *MALLOC(size_t);
michael@0	249	#endif
michael@0	250	#else
michael@0	251	#define MALLOC malloc
michael@0	252	#endif
michael@0	253
michael@0	254	#ifndef Omit_Private_Memory
michael@0	255	#ifndef PRIVATE_MEM
michael@0	256	#define PRIVATE_MEM 2304
michael@0	257	#endif
michael@0	258	#define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
michael@0	259	static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
michael@0	260	#endif
michael@0	261
michael@0	262	#undef IEEE_Arith
michael@0	263	#undef Avoid_Underflow
michael@0	264	#ifdef IEEE_MC68k
michael@0	265	#define IEEE_Arith
michael@0	266	#endif
michael@0	267	#ifdef IEEE_8087
michael@0	268	#define IEEE_Arith
michael@0	269	#endif
michael@0	270	#ifdef IEEE_ARM
michael@0	271	#define IEEE_Arith
michael@0	272	#endif
michael@0	273
michael@0	274	#include "errno.h"
michael@0	275
michael@0	276	#ifdef Bad_float_h
michael@0	277
michael@0	278	#ifdef IEEE_Arith
michael@0	279	#define DBL_DIG 15
michael@0	280	#define DBL_MAX_10_EXP 308
michael@0	281	#define DBL_MAX_EXP 1024
michael@0	282	#define FLT_RADIX 2
michael@0	283	#endif /*IEEE_Arith*/
michael@0	284
michael@0	285	#ifdef IBM
michael@0	286	#define DBL_DIG 16
michael@0	287	#define DBL_MAX_10_EXP 75
michael@0	288	#define DBL_MAX_EXP 63
michael@0	289	#define FLT_RADIX 16
michael@0	290	#define DBL_MAX 7.2370055773322621e+75
michael@0	291	#endif
michael@0	292
michael@0	293	#ifdef VAX
michael@0	294	#define DBL_DIG 16
michael@0	295	#define DBL_MAX_10_EXP 38
michael@0	296	#define DBL_MAX_EXP 127
michael@0	297	#define FLT_RADIX 2
michael@0	298	#define DBL_MAX 1.7014118346046923e+38
michael@0	299	#endif
michael@0	300
michael@0	301	#ifndef LONG_MAX
michael@0	302	#define LONG_MAX 2147483647
michael@0	303	#endif
michael@0	304
michael@0	305	#else /* ifndef Bad_float_h */
michael@0	306	#include "float.h"
michael@0	307	/*
michael@0	308	* MacOS 10.2 defines the macro FLT_ROUNDS to an internal function
michael@0	309	* which does not exist on 10.1. We can safely #define it to 1 here
michael@0	310	* to allow 10.2 builds to run on 10.1, since we can't use fesetround()
michael@0	311	* (which does not exist on 10.1 either).
michael@0	312	*/
michael@0	313	#if defined(XP_MACOSX) && (!defined(MAC_OS_X_VERSION_10_2) || \
michael@0	314	MAC_OS_X_VERSION_MIN_REQUIRED < MAC_OS_X_VERSION_10_2)
michael@0	315	#undef FLT_ROUNDS
michael@0	316	#define FLT_ROUNDS 1
michael@0	317	#endif /* DT < 10.2 */
michael@0	318	#endif /* Bad_float_h */
michael@0	319
michael@0	320	#ifndef __MATH_H__
michael@0	321	#include "math.h"
michael@0	322	#endif
michael@0	323
michael@0	324	#ifdef __cplusplus
michael@0	325	extern "C" {
michael@0	326	#endif
michael@0	327
michael@0	328	#ifndef CONST
michael@0	329	#ifdef KR_headers
michael@0	330	#define CONST /* blank */
michael@0	331	#else
michael@0	332	#define CONST const
michael@0	333	#endif
michael@0	334	#endif
michael@0	335
michael@0	336	#if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(IEEE_ARM) + defined(VAX) + defined(IBM) != 1
michael@0	337	Exactly one of IEEE_8087, IEEE_MC68k, IEEE_ARM, VAX, or IBM should be defined.
michael@0	338	#endif
michael@0	339
michael@0	340	typedef union { double d; ULong L[2]; } U;
michael@0	341
michael@0	342	#define dval(x) (x).d
michael@0	343	#ifdef IEEE_8087
michael@0	344	#define word0(x) (x).L[1]
michael@0	345	#define word1(x) (x).L[0]
michael@0	346	#else
michael@0	347	#define word0(x) (x).L[0]
michael@0	348	#define word1(x) (x).L[1]
michael@0	349	#endif
michael@0	350
michael@0	351	/* The following definition of Storeinc is appropriate for MIPS processors.
michael@0	352	* An alternative that might be better on some machines is
michael@0	353	* #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
michael@0	354	*/
michael@0	355	#if defined(IEEE_8087) + defined(IEEE_ARM) + defined(VAX)
michael@0	356	#define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
michael@0	357	((unsigned short *)a)[0] = (unsigned short)c, a++)
michael@0	358	#else
michael@0	359	#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
michael@0	360	((unsigned short *)a)[1] = (unsigned short)c, a++)
michael@0	361	#endif
michael@0	362
michael@0	363	/* #define P DBL_MANT_DIG */
michael@0	364	/* Ten_pmax = floor(P*log(2)/log(5)) */
michael@0	365	/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
michael@0	366	/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
michael@0	367	/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
michael@0	368
michael@0	369	#ifdef IEEE_Arith
michael@0	370	#define Exp_shift 20
michael@0	371	#define Exp_shift1 20
michael@0	372	#define Exp_msk1 0x100000
michael@0	373	#define Exp_msk11 0x100000
michael@0	374	#define Exp_mask 0x7ff00000
michael@0	375	#define P 53
michael@0	376	#define Bias 1023
michael@0	377	#define Emin (-1022)
michael@0	378	#define Exp_1 0x3ff00000
michael@0	379	#define Exp_11 0x3ff00000
michael@0	380	#define Ebits 11
michael@0	381	#define Frac_mask 0xfffff
michael@0	382	#define Frac_mask1 0xfffff
michael@0	383	#define Ten_pmax 22
michael@0	384	#define Bletch 0x10
michael@0	385	#define Bndry_mask 0xfffff
michael@0	386	#define Bndry_mask1 0xfffff
michael@0	387	#define LSB 1
michael@0	388	#define Sign_bit 0x80000000
michael@0	389	#define Log2P 1
michael@0	390	#define Tiny0 0
michael@0	391	#define Tiny1 1
michael@0	392	#define Quick_max 14
michael@0	393	#define Int_max 14
michael@0	394	#ifndef NO_IEEE_Scale
michael@0	395	#define Avoid_Underflow
michael@0	396	#ifdef Flush_Denorm /* debugging option */
michael@0	397	#undef Sudden_Underflow
michael@0	398	#endif
michael@0	399	#endif
michael@0	400
michael@0	401	#ifndef Flt_Rounds
michael@0	402	#ifdef FLT_ROUNDS
michael@0	403	#define Flt_Rounds FLT_ROUNDS
michael@0	404	#else
michael@0	405	#define Flt_Rounds 1
michael@0	406	#endif
michael@0	407	#endif /*Flt_Rounds*/
michael@0	408
michael@0	409	#ifdef Honor_FLT_ROUNDS
michael@0	410	#define Rounding rounding
michael@0	411	#undef Check_FLT_ROUNDS
michael@0	412	#define Check_FLT_ROUNDS
michael@0	413	#else
michael@0	414	#define Rounding Flt_Rounds
michael@0	415	#endif
michael@0	416
michael@0	417	#else /* ifndef IEEE_Arith */
michael@0	418	#undef Check_FLT_ROUNDS
michael@0	419	#undef Honor_FLT_ROUNDS
michael@0	420	#undef SET_INEXACT
michael@0	421	#undef Sudden_Underflow
michael@0	422	#define Sudden_Underflow
michael@0	423	#ifdef IBM
michael@0	424	#undef Flt_Rounds
michael@0	425	#define Flt_Rounds 0
michael@0	426	#define Exp_shift 24
michael@0	427	#define Exp_shift1 24
michael@0	428	#define Exp_msk1 0x1000000
michael@0	429	#define Exp_msk11 0x1000000
michael@0	430	#define Exp_mask 0x7f000000
michael@0	431	#define P 14
michael@0	432	#define Bias 65
michael@0	433	#define Exp_1 0x41000000
michael@0	434	#define Exp_11 0x41000000
michael@0	435	#define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
michael@0	436	#define Frac_mask 0xffffff
michael@0	437	#define Frac_mask1 0xffffff
michael@0	438	#define Bletch 4
michael@0	439	#define Ten_pmax 22
michael@0	440	#define Bndry_mask 0xefffff
michael@0	441	#define Bndry_mask1 0xffffff
michael@0	442	#define LSB 1
michael@0	443	#define Sign_bit 0x80000000
michael@0	444	#define Log2P 4
michael@0	445	#define Tiny0 0x100000
michael@0	446	#define Tiny1 0
michael@0	447	#define Quick_max 14
michael@0	448	#define Int_max 15
michael@0	449	#else /* VAX */
michael@0	450	#undef Flt_Rounds
michael@0	451	#define Flt_Rounds 1
michael@0	452	#define Exp_shift 23
michael@0	453	#define Exp_shift1 7
michael@0	454	#define Exp_msk1 0x80
michael@0	455	#define Exp_msk11 0x800000
michael@0	456	#define Exp_mask 0x7f80
michael@0	457	#define P 56
michael@0	458	#define Bias 129
michael@0	459	#define Exp_1 0x40800000
michael@0	460	#define Exp_11 0x4080
michael@0	461	#define Ebits 8
michael@0	462	#define Frac_mask 0x7fffff
michael@0	463	#define Frac_mask1 0xffff007f
michael@0	464	#define Ten_pmax 24
michael@0	465	#define Bletch 2
michael@0	466	#define Bndry_mask 0xffff007f
michael@0	467	#define Bndry_mask1 0xffff007f
michael@0	468	#define LSB 0x10000
michael@0	469	#define Sign_bit 0x8000
michael@0	470	#define Log2P 1
michael@0	471	#define Tiny0 0x80
michael@0	472	#define Tiny1 0
michael@0	473	#define Quick_max 15
michael@0	474	#define Int_max 15
michael@0	475	#endif /* IBM, VAX */
michael@0	476	#endif /* IEEE_Arith */
michael@0	477
michael@0	478	#ifndef IEEE_Arith
michael@0	479	#define ROUND_BIASED
michael@0	480	#endif
michael@0	481
michael@0	482	#ifdef RND_PRODQUOT
michael@0	483	#define rounded_product(a,b) a = rnd_prod(a, b)
michael@0	484	#define rounded_quotient(a,b) a = rnd_quot(a, b)
michael@0	485	#ifdef KR_headers
michael@0	486	extern double rnd_prod(), rnd_quot();
michael@0	487	#else
michael@0	488	extern double rnd_prod(double, double), rnd_quot(double, double);
michael@0	489	#endif
michael@0	490	#else
michael@0	491	#define rounded_product(a,b) a *= b
michael@0	492	#define rounded_quotient(a,b) a /= b
michael@0	493	#endif
michael@0	494
michael@0	495	#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
michael@0	496	#define Big1 0xffffffff
michael@0	497
michael@0	498	#ifndef Pack_32
michael@0	499	#define Pack_32
michael@0	500	#endif
michael@0	501
michael@0	502	#ifdef KR_headers
michael@0	503	#define FFFFFFFF ((((unsigned long)0xffff)<<16)|(unsigned long)0xffff)
michael@0	504	#else
michael@0	505	#define FFFFFFFF 0xffffffffUL
michael@0	506	#endif
michael@0	507
michael@0	508	#ifdef NO_LONG_LONG
michael@0	509	#undef ULLong
michael@0	510	#ifdef Just_16
michael@0	511	#undef Pack_32
michael@0	512	/* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
michael@0	513	* This makes some inner loops simpler and sometimes saves work
michael@0	514	* during multiplications, but it often seems to make things slightly
michael@0	515	* slower. Hence the default is now to store 32 bits per Long.
michael@0	516	*/
michael@0	517	#endif
michael@0	518	#else /* long long available */
michael@0	519	#ifndef Llong
michael@0	520	#define Llong long long
michael@0	521	#endif
michael@0	522	#ifndef ULLong
michael@0	523	#define ULLong unsigned Llong
michael@0	524	#endif
michael@0	525	#endif /* NO_LONG_LONG */
michael@0	526
michael@0	527	#ifndef MULTIPLE_THREADS
michael@0	528	#define ACQUIRE_DTOA_LOCK(n) /*nothing*/
michael@0	529	#define FREE_DTOA_LOCK(n) /*nothing*/
michael@0	530	#endif
michael@0	531
michael@0	532	#define Kmax 7
michael@0	533
michael@0	534	struct
michael@0	535	Bigint {
michael@0	536	struct Bigint *next;
michael@0	537	int k, maxwds, sign, wds;
michael@0	538	ULong x[1];
michael@0	539	};
michael@0	540
michael@0	541	typedef struct Bigint Bigint;
michael@0	542
michael@0	543	static Bigint *freelist[Kmax+1];
michael@0	544
michael@0	545	static Bigint *
michael@0	546	Balloc
michael@0	547	#ifdef KR_headers
michael@0	548	(k) int k;
michael@0	549	#else
michael@0	550	(int k)
michael@0	551	#endif
michael@0	552	{
michael@0	553	int x;
michael@0	554	Bigint *rv;
michael@0	555	#ifndef Omit_Private_Memory
michael@0	556	unsigned int len;
michael@0	557	#endif
michael@0	558
michael@0	559	ACQUIRE_DTOA_LOCK(0);
michael@0	560	/* The k > Kmax case does not need ACQUIRE_DTOA_LOCK(0), */
michael@0	561	/* but this case seems very unlikely. */
michael@0	562	if (k <= Kmax && (rv = freelist[k]))
michael@0	563	freelist[k] = rv->next;
michael@0	564	else {
michael@0	565	x = 1 << k;
michael@0	566	#ifdef Omit_Private_Memory
michael@0	567	rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
michael@0	568	#else
michael@0	569	len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
michael@0	570	/sizeof(double);
michael@0	571	if (k <= Kmax && pmem_next - private_mem + len <= PRIVATE_mem) {
michael@0	572	rv = (Bigint*)pmem_next;
michael@0	573	pmem_next += len;
michael@0	574	}
michael@0	575	else
michael@0	576	rv = (Bigint*)MALLOC(len*sizeof(double));
michael@0	577	#endif
michael@0	578	rv->k = k;
michael@0	579	rv->maxwds = x;
michael@0	580	}
michael@0	581	FREE_DTOA_LOCK(0);
michael@0	582	rv->sign = rv->wds = 0;
michael@0	583	return rv;
michael@0	584	}
michael@0	585
michael@0	586	static void
michael@0	587	Bfree
michael@0	588	#ifdef KR_headers
michael@0	589	(v) Bigint *v;
michael@0	590	#else
michael@0	591	(Bigint *v)
michael@0	592	#endif
michael@0	593	{
michael@0	594	if (v) {
michael@0	595	if (v->k > Kmax)
michael@0	596	#ifdef FREE
michael@0	597	FREE((void*)v);
michael@0	598	#else
michael@0	599	free((void*)v);
michael@0	600	#endif
michael@0	601	else {
michael@0	602	ACQUIRE_DTOA_LOCK(0);
michael@0	603	v->next = freelist[v->k];
michael@0	604	freelist[v->k] = v;
michael@0	605	FREE_DTOA_LOCK(0);
michael@0	606	}
michael@0	607	}
michael@0	608	}
michael@0	609
michael@0	610	#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
michael@0	611	y->wds*sizeof(Long) + 2*sizeof(int))
michael@0	612
michael@0	613	static Bigint *
michael@0	614	multadd
michael@0	615	#ifdef KR_headers
michael@0	616	(b, m, a) Bigint *b; int m, a;
michael@0	617	#else
michael@0	618	(Bigint *b, int m, int a) /* multiply by m and add a */
michael@0	619	#endif
michael@0	620	{
michael@0	621	int i, wds;
michael@0	622	#ifdef ULLong
michael@0	623	ULong *x;
michael@0	624	ULLong carry, y;
michael@0	625	#else
michael@0	626	ULong carry, *x, y;
michael@0	627	#ifdef Pack_32
michael@0	628	ULong xi, z;
michael@0	629	#endif
michael@0	630	#endif
michael@0	631	Bigint *b1;
michael@0	632
michael@0	633	wds = b->wds;
michael@0	634	x = b->x;
michael@0	635	i = 0;
michael@0	636	carry = a;
michael@0	637	do {
michael@0	638	#ifdef ULLong
michael@0	639	y = *x * (ULLong)m + carry;
michael@0	640	carry = y >> 32;
michael@0	641	*x++ = y & FFFFFFFF;
michael@0	642	#else
michael@0	643	#ifdef Pack_32
michael@0	644	xi = *x;
michael@0	645	y = (xi & 0xffff) * m + carry;
michael@0	646	z = (xi >> 16) * m + (y >> 16);
michael@0	647	carry = z >> 16;
michael@0	648	*x++ = (z << 16) + (y & 0xffff);
michael@0	649	#else
michael@0	650	y = *x * m + carry;
michael@0	651	carry = y >> 16;
michael@0	652	*x++ = y & 0xffff;
michael@0	653	#endif
michael@0	654	#endif
michael@0	655	}
michael@0	656	while(++i < wds);
michael@0	657	if (carry) {
michael@0	658	if (wds >= b->maxwds) {
michael@0	659	b1 = Balloc(b->k+1);
michael@0	660	Bcopy(b1, b);
michael@0	661	Bfree(b);
michael@0	662	b = b1;
michael@0	663	}
michael@0	664	b->x[wds++] = carry;
michael@0	665	b->wds = wds;
michael@0	666	}
michael@0	667	return b;
michael@0	668	}
michael@0	669
michael@0	670	static Bigint *
michael@0	671	s2b
michael@0	672	#ifdef KR_headers
michael@0	673	(s, nd0, nd, y9) CONST char *s; int nd0, nd; ULong y9;
michael@0	674	#else
michael@0	675	(CONST char *s, int nd0, int nd, ULong y9)
michael@0	676	#endif
michael@0	677	{
michael@0	678	Bigint *b;
michael@0	679	int i, k;
michael@0	680	Long x, y;
michael@0	681
michael@0	682	x = (nd + 8) / 9;
michael@0	683	for(k = 0, y = 1; x > y; y <<= 1, k++) ;
michael@0	684	#ifdef Pack_32
michael@0	685	b = Balloc(k);
michael@0	686	b->x[0] = y9;
michael@0	687	b->wds = 1;
michael@0	688	#else
michael@0	689	b = Balloc(k+1);
michael@0	690	b->x[0] = y9 & 0xffff;
michael@0	691	b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
michael@0	692	#endif
michael@0	693
michael@0	694	i = 9;
michael@0	695	if (9 < nd0) {
michael@0	696	s += 9;
michael@0	697	do b = multadd(b, 10, *s++ - '0');
michael@0	698	while(++i < nd0);
michael@0	699	s++;
michael@0	700	}
michael@0	701	else
michael@0	702	s += 10;
michael@0	703	for(; i < nd; i++)
michael@0	704	b = multadd(b, 10, *s++ - '0');
michael@0	705	return b;
michael@0	706	}
michael@0	707
michael@0	708	static int
michael@0	709	hi0bits
michael@0	710	#ifdef KR_headers
michael@0	711	(x) register ULong x;
michael@0	712	#else
michael@0	713	(register ULong x)
michael@0	714	#endif
michael@0	715	{
michael@0	716	#ifdef PR_HAVE_BUILTIN_BITSCAN32
michael@0	717	return( (!x) ? 32 : pr_bitscan_clz32(x) );
michael@0	718	#else
michael@0	719	register int k = 0;
michael@0	720
michael@0	721	if (!(x & 0xffff0000)) {
michael@0	722	k = 16;
michael@0	723	x <<= 16;
michael@0	724	}
michael@0	725	if (!(x & 0xff000000)) {
michael@0	726	k += 8;
michael@0	727	x <<= 8;
michael@0	728	}
michael@0	729	if (!(x & 0xf0000000)) {
michael@0	730	k += 4;
michael@0	731	x <<= 4;
michael@0	732	}
michael@0	733	if (!(x & 0xc0000000)) {
michael@0	734	k += 2;
michael@0	735	x <<= 2;
michael@0	736	}
michael@0	737	if (!(x & 0x80000000)) {
michael@0	738	k++;
michael@0	739	if (!(x & 0x40000000))
michael@0	740	return 32;
michael@0	741	}
michael@0	742	return k;
michael@0	743	#endif /* PR_HAVE_BUILTIN_BITSCAN32 */
michael@0	744	}
michael@0	745
michael@0	746	static int
michael@0	747	lo0bits
michael@0	748	#ifdef KR_headers
michael@0	749	(y) ULong *y;
michael@0	750	#else
michael@0	751	(ULong *y)
michael@0	752	#endif
michael@0	753	{
michael@0	754	#ifdef PR_HAVE_BUILTIN_BITSCAN32
michael@0	755	int k;
michael@0	756	ULong x = *y;
michael@0	757
michael@0	758	if (x>1)
michael@0	759	*y = ( x >> (k = pr_bitscan_ctz32(x)) );
michael@0	760	else
michael@0	761	k = ((x ^ 1) << 5);
michael@0	762	#else
michael@0	763	register int k;
michael@0	764	register ULong x = *y;
michael@0	765
michael@0	766	if (x & 7) {
michael@0	767	if (x & 1)
michael@0	768	return 0;
michael@0	769	if (x & 2) {
michael@0	770	*y = x >> 1;
michael@0	771	return 1;
michael@0	772	}
michael@0	773	*y = x >> 2;
michael@0	774	return 2;
michael@0	775	}
michael@0	776	k = 0;
michael@0	777	if (!(x & 0xffff)) {
michael@0	778	k = 16;
michael@0	779	x >>= 16;
michael@0	780	}
michael@0	781	if (!(x & 0xff)) {
michael@0	782	k += 8;
michael@0	783	x >>= 8;
michael@0	784	}
michael@0	785	if (!(x & 0xf)) {
michael@0	786	k += 4;
michael@0	787	x >>= 4;
michael@0	788	}
michael@0	789	if (!(x & 0x3)) {
michael@0	790	k += 2;
michael@0	791	x >>= 2;
michael@0	792	}
michael@0	793	if (!(x & 1)) {
michael@0	794	k++;
michael@0	795	x >>= 1;
michael@0	796	if (!x)
michael@0	797	return 32;
michael@0	798	}
michael@0	799	*y = x;
michael@0	800	#endif /* PR_HAVE_BUILTIN_BITSCAN32 */
michael@0	801	return k;
michael@0	802	}
michael@0	803
michael@0	804	static Bigint *
michael@0	805	i2b
michael@0	806	#ifdef KR_headers
michael@0	807	(i) int i;
michael@0	808	#else
michael@0	809	(int i)
michael@0	810	#endif
michael@0	811	{
michael@0	812	Bigint *b;
michael@0	813
michael@0	814	b = Balloc(1);
michael@0	815	b->x[0] = i;
michael@0	816	b->wds = 1;
michael@0	817	return b;
michael@0	818	}
michael@0	819
michael@0	820	static Bigint *
michael@0	821	mult
michael@0	822	#ifdef KR_headers
michael@0	823	(a, b) Bigint *a, *b;
michael@0	824	#else
michael@0	825	(Bigint *a, Bigint *b)
michael@0	826	#endif
michael@0	827	{
michael@0	828	Bigint *c;
michael@0	829	int k, wa, wb, wc;
michael@0	830	ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
michael@0	831	ULong y;
michael@0	832	#ifdef ULLong
michael@0	833	ULLong carry, z;
michael@0	834	#else
michael@0	835	ULong carry, z;
michael@0	836	#ifdef Pack_32
michael@0	837	ULong z2;
michael@0	838	#endif
michael@0	839	#endif
michael@0	840
michael@0	841	if (a->wds < b->wds) {
michael@0	842	c = a;
michael@0	843	a = b;
michael@0	844	b = c;
michael@0	845	}
michael@0	846	k = a->k;
michael@0	847	wa = a->wds;
michael@0	848	wb = b->wds;
michael@0	849	wc = wa + wb;
michael@0	850	if (wc > a->maxwds)
michael@0	851	k++;
michael@0	852	c = Balloc(k);
michael@0	853	for(x = c->x, xa = x + wc; x < xa; x++)
michael@0	854	*x = 0;
michael@0	855	xa = a->x;
michael@0	856	xae = xa + wa;
michael@0	857	xb = b->x;
michael@0	858	xbe = xb + wb;
michael@0	859	xc0 = c->x;
michael@0	860	#ifdef ULLong
michael@0	861	for(; xb < xbe; xc0++) {
michael@0	862	if (y = *xb++) {
michael@0	863	x = xa;
michael@0	864	xc = xc0;
michael@0	865	carry = 0;
michael@0	866	do {
michael@0	867	z = *x++ * (ULLong)y + *xc + carry;
michael@0	868	carry = z >> 32;
michael@0	869	*xc++ = z & FFFFFFFF;
michael@0	870	}
michael@0	871	while(x < xae);
michael@0	872	*xc = carry;
michael@0	873	}
michael@0	874	}
michael@0	875	#else
michael@0	876	#ifdef Pack_32
michael@0	877	for(; xb < xbe; xb++, xc0++) {
michael@0	878	if (y = *xb & 0xffff) {
michael@0	879	x = xa;
michael@0	880	xc = xc0;
michael@0	881	carry = 0;
michael@0	882	do {
michael@0	883	z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
michael@0	884	carry = z >> 16;
michael@0	885	z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
michael@0	886	carry = z2 >> 16;
michael@0	887	Storeinc(xc, z2, z);
michael@0	888	}
michael@0	889	while(x < xae);
michael@0	890	*xc = carry;
michael@0	891	}
michael@0	892	if (y = *xb >> 16) {
michael@0	893	x = xa;
michael@0	894	xc = xc0;
michael@0	895	carry = 0;
michael@0	896	z2 = *xc;
michael@0	897	do {
michael@0	898	z = (*x & 0xffff) * y + (*xc >> 16) + carry;
michael@0	899	carry = z >> 16;
michael@0	900	Storeinc(xc, z, z2);
michael@0	901	z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
michael@0	902	carry = z2 >> 16;
michael@0	903	}
michael@0	904	while(x < xae);
michael@0	905	*xc = z2;
michael@0	906	}
michael@0	907	}
michael@0	908	#else
michael@0	909	for(; xb < xbe; xc0++) {
michael@0	910	if (y = *xb++) {
michael@0	911	x = xa;
michael@0	912	xc = xc0;
michael@0	913	carry = 0;
michael@0	914	do {
michael@0	915	z = *x++ * y + *xc + carry;
michael@0	916	carry = z >> 16;
michael@0	917	*xc++ = z & 0xffff;
michael@0	918	}
michael@0	919	while(x < xae);
michael@0	920	*xc = carry;
michael@0	921	}
michael@0	922	}
michael@0	923	#endif
michael@0	924	#endif
michael@0	925	for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
michael@0	926	c->wds = wc;
michael@0	927	return c;
michael@0	928	}
michael@0	929
michael@0	930	static Bigint *p5s;
michael@0	931
michael@0	932	static Bigint *
michael@0	933	pow5mult
michael@0	934	#ifdef KR_headers
michael@0	935	(b, k) Bigint *b; int k;
michael@0	936	#else
michael@0	937	(Bigint *b, int k)
michael@0	938	#endif
michael@0	939	{
michael@0	940	Bigint *b1, *p5, *p51;
michael@0	941	int i;
michael@0	942	static int p05[3] = { 5, 25, 125 };
michael@0	943
michael@0	944	if (i = k & 3)
michael@0	945	b = multadd(b, p05[i-1], 0);
michael@0	946
michael@0	947	if (!(k >>= 2))
michael@0	948	return b;
michael@0	949	if (!(p5 = p5s)) {
michael@0	950	/* first time */
michael@0	951	#ifdef MULTIPLE_THREADS
michael@0	952	ACQUIRE_DTOA_LOCK(1);
michael@0	953	if (!(p5 = p5s)) {
michael@0	954	p5 = p5s = i2b(625);
michael@0	955	p5->next = 0;
michael@0	956	}
michael@0	957	FREE_DTOA_LOCK(1);
michael@0	958	#else
michael@0	959	p5 = p5s = i2b(625);
michael@0	960	p5->next = 0;
michael@0	961	#endif
michael@0	962	}
michael@0	963	for(;;) {
michael@0	964	if (k & 1) {
michael@0	965	b1 = mult(b, p5);
michael@0	966	Bfree(b);
michael@0	967	b = b1;
michael@0	968	}
michael@0	969	if (!(k >>= 1))
michael@0	970	break;
michael@0	971	if (!(p51 = p5->next)) {
michael@0	972	#ifdef MULTIPLE_THREADS
michael@0	973	ACQUIRE_DTOA_LOCK(1);
michael@0	974	if (!(p51 = p5->next)) {
michael@0	975	p51 = p5->next = mult(p5,p5);
michael@0	976	p51->next = 0;
michael@0	977	}
michael@0	978	FREE_DTOA_LOCK(1);
michael@0	979	#else
michael@0	980	p51 = p5->next = mult(p5,p5);
michael@0	981	p51->next = 0;
michael@0	982	#endif
michael@0	983	}
michael@0	984	p5 = p51;
michael@0	985	}
michael@0	986	return b;
michael@0	987	}
michael@0	988
michael@0	989	static Bigint *
michael@0	990	lshift
michael@0	991	#ifdef KR_headers
michael@0	992	(b, k) Bigint *b; int k;
michael@0	993	#else
michael@0	994	(Bigint *b, int k)
michael@0	995	#endif
michael@0	996	{
michael@0	997	int i, k1, n, n1;
michael@0	998	Bigint *b1;
michael@0	999	ULong *x, *x1, *xe, z;
michael@0	1000
michael@0	1001	#ifdef Pack_32
michael@0	1002	n = k >> 5;
michael@0	1003	#else
michael@0	1004	n = k >> 4;
michael@0	1005	#endif
michael@0	1006	k1 = b->k;
michael@0	1007	n1 = n + b->wds + 1;
michael@0	1008	for(i = b->maxwds; n1 > i; i <<= 1)
michael@0	1009	k1++;
michael@0	1010	b1 = Balloc(k1);
michael@0	1011	x1 = b1->x;
michael@0	1012	for(i = 0; i < n; i++)
michael@0	1013	*x1++ = 0;
michael@0	1014	x = b->x;
michael@0	1015	xe = x + b->wds;
michael@0	1016	#ifdef Pack_32
michael@0	1017	if (k &= 0x1f) {
michael@0	1018	k1 = 32 - k;
michael@0	1019	z = 0;
michael@0	1020	do {
michael@0	1021	*x1++ = *x << k | z;
michael@0	1022	z = *x++ >> k1;
michael@0	1023	}
michael@0	1024	while(x < xe);
michael@0	1025	if (*x1 = z)
michael@0	1026	++n1;
michael@0	1027	}
michael@0	1028	#else
michael@0	1029	if (k &= 0xf) {
michael@0	1030	k1 = 16 - k;
michael@0	1031	z = 0;
michael@0	1032	do {
michael@0	1033	*x1++ = *x << k & 0xffff | z;
michael@0	1034	z = *x++ >> k1;
michael@0	1035	}
michael@0	1036	while(x < xe);
michael@0	1037	if (*x1 = z)
michael@0	1038	++n1;
michael@0	1039	}
michael@0	1040	#endif
michael@0	1041	else do
michael@0	1042	*x1++ = *x++;
michael@0	1043	while(x < xe);
michael@0	1044	b1->wds = n1 - 1;
michael@0	1045	Bfree(b);
michael@0	1046	return b1;
michael@0	1047	}
michael@0	1048
michael@0	1049	static int
michael@0	1050	cmp
michael@0	1051	#ifdef KR_headers
michael@0	1052	(a, b) Bigint *a, *b;
michael@0	1053	#else
michael@0	1054	(Bigint *a, Bigint *b)
michael@0	1055	#endif
michael@0	1056	{
michael@0	1057	ULong *xa, *xa0, *xb, *xb0;
michael@0	1058	int i, j;
michael@0	1059
michael@0	1060	i = a->wds;
michael@0	1061	j = b->wds;
michael@0	1062	#ifdef DEBUG
michael@0	1063	if (i > 1 && !a->x[i-1])
michael@0	1064	Bug("cmp called with a->x[a->wds-1] == 0");
michael@0	1065	if (j > 1 && !b->x[j-1])
michael@0	1066	Bug("cmp called with b->x[b->wds-1] == 0");
michael@0	1067	#endif
michael@0	1068	if (i -= j)
michael@0	1069	return i;
michael@0	1070	xa0 = a->x;
michael@0	1071	xa = xa0 + j;
michael@0	1072	xb0 = b->x;
michael@0	1073	xb = xb0 + j;
michael@0	1074	for(;;) {
michael@0	1075	if (*--xa != *--xb)
michael@0	1076	return *xa < *xb ? -1 : 1;
michael@0	1077	if (xa <= xa0)
michael@0	1078	break;
michael@0	1079	}
michael@0	1080	return 0;
michael@0	1081	}
michael@0	1082
michael@0	1083	static Bigint *
michael@0	1084	diff
michael@0	1085	#ifdef KR_headers
michael@0	1086	(a, b) Bigint *a, *b;
michael@0	1087	#else
michael@0	1088	(Bigint *a, Bigint *b)
michael@0	1089	#endif
michael@0	1090	{
michael@0	1091	Bigint *c;
michael@0	1092	int i, wa, wb;
michael@0	1093	ULong *xa, *xae, *xb, *xbe, *xc;
michael@0	1094	#ifdef ULLong
michael@0	1095	ULLong borrow, y;
michael@0	1096	#else
michael@0	1097	ULong borrow, y;
michael@0	1098	#ifdef Pack_32
michael@0	1099	ULong z;
michael@0	1100	#endif
michael@0	1101	#endif
michael@0	1102
michael@0	1103	i = cmp(a,b);
michael@0	1104	if (!i) {
michael@0	1105	c = Balloc(0);
michael@0	1106	c->wds = 1;
michael@0	1107	c->x[0] = 0;
michael@0	1108	return c;
michael@0	1109	}
michael@0	1110	if (i < 0) {
michael@0	1111	c = a;
michael@0	1112	a = b;
michael@0	1113	b = c;
michael@0	1114	i = 1;
michael@0	1115	}
michael@0	1116	else
michael@0	1117	i = 0;
michael@0	1118	c = Balloc(a->k);
michael@0	1119	c->sign = i;
michael@0	1120	wa = a->wds;
michael@0	1121	xa = a->x;
michael@0	1122	xae = xa + wa;
michael@0	1123	wb = b->wds;
michael@0	1124	xb = b->x;
michael@0	1125	xbe = xb + wb;
michael@0	1126	xc = c->x;
michael@0	1127	borrow = 0;
michael@0	1128	#ifdef ULLong
michael@0	1129	do {
michael@0	1130	y = (ULLong)*xa++ - *xb++ - borrow;
michael@0	1131	borrow = y >> 32 & (ULong)1;
michael@0	1132	*xc++ = y & FFFFFFFF;
michael@0	1133	}
michael@0	1134	while(xb < xbe);
michael@0	1135	while(xa < xae) {
michael@0	1136	y = *xa++ - borrow;
michael@0	1137	borrow = y >> 32 & (ULong)1;
michael@0	1138	*xc++ = y & FFFFFFFF;
michael@0	1139	}
michael@0	1140	#else
michael@0	1141	#ifdef Pack_32
michael@0	1142	do {
michael@0	1143	y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
michael@0	1144	borrow = (y & 0x10000) >> 16;
michael@0	1145	z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
michael@0	1146	borrow = (z & 0x10000) >> 16;
michael@0	1147	Storeinc(xc, z, y);
michael@0	1148	}
michael@0	1149	while(xb < xbe);
michael@0	1150	while(xa < xae) {
michael@0	1151	y = (*xa & 0xffff) - borrow;
michael@0	1152	borrow = (y & 0x10000) >> 16;
michael@0	1153	z = (*xa++ >> 16) - borrow;
michael@0	1154	borrow = (z & 0x10000) >> 16;
michael@0	1155	Storeinc(xc, z, y);
michael@0	1156	}
michael@0	1157	#else
michael@0	1158	do {
michael@0	1159	y = *xa++ - *xb++ - borrow;
michael@0	1160	borrow = (y & 0x10000) >> 16;
michael@0	1161	*xc++ = y & 0xffff;
michael@0	1162	}
michael@0	1163	while(xb < xbe);
michael@0	1164	while(xa < xae) {
michael@0	1165	y = *xa++ - borrow;
michael@0	1166	borrow = (y & 0x10000) >> 16;
michael@0	1167	*xc++ = y & 0xffff;
michael@0	1168	}
michael@0	1169	#endif
michael@0	1170	#endif
michael@0	1171	while(!*--xc)
michael@0	1172	wa--;
michael@0	1173	c->wds = wa;
michael@0	1174	return c;
michael@0	1175	}
michael@0	1176
michael@0	1177	static double
michael@0	1178	ulp
michael@0	1179	#ifdef KR_headers
michael@0	1180	(dx) double dx;
michael@0	1181	#else
michael@0	1182	(double dx)
michael@0	1183	#endif
michael@0	1184	{
michael@0	1185	register Long L;
michael@0	1186	U x, a;
michael@0	1187
michael@0	1188	dval(x) = dx;
michael@0	1189	L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
michael@0	1190	#ifndef Avoid_Underflow
michael@0	1191	#ifndef Sudden_Underflow
michael@0	1192	if (L > 0) {
michael@0	1193	#endif
michael@0	1194	#endif
michael@0	1195	#ifdef IBM
michael@0	1196	L |= Exp_msk1 >> 4;
michael@0	1197	#endif
michael@0	1198	word0(a) = L;
michael@0	1199	word1(a) = 0;
michael@0	1200	#ifndef Avoid_Underflow
michael@0	1201	#ifndef Sudden_Underflow
michael@0	1202	}
michael@0	1203	else {
michael@0	1204	L = -L >> Exp_shift;
michael@0	1205	if (L < Exp_shift) {
michael@0	1206	word0(a) = 0x80000 >> L;
michael@0	1207	word1(a) = 0;
michael@0	1208	}
michael@0	1209	else {
michael@0	1210	word0(a) = 0;
michael@0	1211	L -= Exp_shift;
michael@0	1212	word1(a) = L >= 31 ? 1 : 1 << 31 - L;
michael@0	1213	}
michael@0	1214	}
michael@0	1215	#endif
michael@0	1216	#endif
michael@0	1217	return dval(a);
michael@0	1218	}
michael@0	1219
michael@0	1220	static double
michael@0	1221	b2d
michael@0	1222	#ifdef KR_headers
michael@0	1223	(a, e) Bigint *a; int *e;
michael@0	1224	#else
michael@0	1225	(Bigint *a, int *e)
michael@0	1226	#endif
michael@0	1227	{
michael@0	1228	ULong *xa, *xa0, w, y, z;
michael@0	1229	int k;
michael@0	1230	U d;
michael@0	1231	#ifdef VAX
michael@0	1232	ULong d0, d1;
michael@0	1233	#else
michael@0	1234	#define d0 word0(d)
michael@0	1235	#define d1 word1(d)
michael@0	1236	#endif
michael@0	1237
michael@0	1238	xa0 = a->x;
michael@0	1239	xa = xa0 + a->wds;
michael@0	1240	y = *--xa;
michael@0	1241	#ifdef DEBUG
michael@0	1242	if (!y) Bug("zero y in b2d");
michael@0	1243	#endif
michael@0	1244	k = hi0bits(y);
michael@0	1245	*e = 32 - k;
michael@0	1246	#ifdef Pack_32
michael@0	1247	if (k < Ebits) {
michael@0	1248	d0 = Exp_1 | y >> Ebits - k;
michael@0	1249	w = xa > xa0 ? *--xa : 0;
michael@0	1250	d1 = y << (32-Ebits) + k | w >> Ebits - k;
michael@0	1251	goto ret_d;
michael@0	1252	}
michael@0	1253	z = xa > xa0 ? *--xa : 0;
michael@0	1254	if (k -= Ebits) {
michael@0	1255	d0 = Exp_1 | y << k | z >> 32 - k;
michael@0	1256	y = xa > xa0 ? *--xa : 0;
michael@0	1257	d1 = z << k | y >> 32 - k;
michael@0	1258	}
michael@0	1259	else {
michael@0	1260	d0 = Exp_1 | y;
michael@0	1261	d1 = z;
michael@0	1262	}
michael@0	1263	#else
michael@0	1264	if (k < Ebits + 16) {
michael@0	1265	z = xa > xa0 ? *--xa : 0;
michael@0	1266	d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
michael@0	1267	w = xa > xa0 ? *--xa : 0;
michael@0	1268	y = xa > xa0 ? *--xa : 0;
michael@0	1269	d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
michael@0	1270	goto ret_d;
michael@0	1271	}
michael@0	1272	z = xa > xa0 ? *--xa : 0;
michael@0	1273	w = xa > xa0 ? *--xa : 0;
michael@0	1274	k -= Ebits + 16;
michael@0	1275	d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
michael@0	1276	y = xa > xa0 ? *--xa : 0;
michael@0	1277	d1 = w << k + 16 | y << k;
michael@0	1278	#endif
michael@0	1279	ret_d:
michael@0	1280	#ifdef VAX
michael@0	1281	word0(d) = d0 >> 16 | d0 << 16;
michael@0	1282	word1(d) = d1 >> 16 | d1 << 16;
michael@0	1283	#else
michael@0	1284	#undef d0
michael@0	1285	#undef d1
michael@0	1286	#endif
michael@0	1287	return dval(d);
michael@0	1288	}
michael@0	1289
michael@0	1290	static Bigint *
michael@0	1291	d2b
michael@0	1292	#ifdef KR_headers
michael@0	1293	(dd, e, bits) double dd; int *e, *bits;
michael@0	1294	#else
michael@0	1295	(double dd, int *e, int *bits)
michael@0	1296	#endif
michael@0	1297	{
michael@0	1298	U d;
michael@0	1299	Bigint *b;
michael@0	1300	int de, k;
michael@0	1301	ULong *x, y, z;
michael@0	1302	#ifndef Sudden_Underflow
michael@0	1303	int i;
michael@0	1304	#endif
michael@0	1305	#ifdef VAX
michael@0	1306	ULong d0, d1;
michael@0	1307	#endif
michael@0	1308
michael@0	1309	dval(d) = dd;
michael@0	1310	#ifdef VAX
michael@0	1311	d0 = word0(d) >> 16 | word0(d) << 16;
michael@0	1312	d1 = word1(d) >> 16 | word1(d) << 16;
michael@0	1313	#else
michael@0	1314	#define d0 word0(d)
michael@0	1315	#define d1 word1(d)
michael@0	1316	#endif
michael@0	1317
michael@0	1318	#ifdef Pack_32
michael@0	1319	b = Balloc(1);
michael@0	1320	#else
michael@0	1321	b = Balloc(2);
michael@0	1322	#endif
michael@0	1323	x = b->x;
michael@0	1324
michael@0	1325	z = d0 & Frac_mask;
michael@0	1326	d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
michael@0	1327	#ifdef Sudden_Underflow
michael@0	1328	de = (int)(d0 >> Exp_shift);
michael@0	1329	#ifndef IBM
michael@0	1330	z |= Exp_msk11;
michael@0	1331	#endif
michael@0	1332	#else
michael@0	1333	if (de = (int)(d0 >> Exp_shift))
michael@0	1334	z |= Exp_msk1;
michael@0	1335	#endif
michael@0	1336	#ifdef Pack_32
michael@0	1337	if (y = d1) {
michael@0	1338	if (k = lo0bits(&y)) {
michael@0	1339	x[0] = y | z << 32 - k;
michael@0	1340	z >>= k;
michael@0	1341	}
michael@0	1342	else
michael@0	1343	x[0] = y;
michael@0	1344	#ifndef Sudden_Underflow
michael@0	1345	i =
michael@0	1346	#endif
michael@0	1347	b->wds = (x[1] = z) ? 2 : 1;
michael@0	1348	}
michael@0	1349	else {
michael@0	1350	k = lo0bits(&z);
michael@0	1351	x[0] = z;
michael@0	1352	#ifndef Sudden_Underflow
michael@0	1353	i =
michael@0	1354	#endif
michael@0	1355	b->wds = 1;
michael@0	1356	k += 32;
michael@0	1357	}
michael@0	1358	#else
michael@0	1359	if (y = d1) {
michael@0	1360	if (k = lo0bits(&y))
michael@0	1361	if (k >= 16) {
michael@0	1362	x[0] = y | z << 32 - k & 0xffff;
michael@0	1363	x[1] = z >> k - 16 & 0xffff;
michael@0	1364	x[2] = z >> k;
michael@0	1365	i = 2;
michael@0	1366	}
michael@0	1367	else {
michael@0	1368	x[0] = y & 0xffff;
michael@0	1369	x[1] = y >> 16 | z << 16 - k & 0xffff;
michael@0	1370	x[2] = z >> k & 0xffff;
michael@0	1371	x[3] = z >> k+16;
michael@0	1372	i = 3;
michael@0	1373	}
michael@0	1374	else {
michael@0	1375	x[0] = y & 0xffff;
michael@0	1376	x[1] = y >> 16;
michael@0	1377	x[2] = z & 0xffff;
michael@0	1378	x[3] = z >> 16;
michael@0	1379	i = 3;
michael@0	1380	}
michael@0	1381	}
michael@0	1382	else {
michael@0	1383	#ifdef DEBUG
michael@0	1384	if (!z)
michael@0	1385	Bug("Zero passed to d2b");
michael@0	1386	#endif
michael@0	1387	k = lo0bits(&z);
michael@0	1388	if (k >= 16) {
michael@0	1389	x[0] = z;
michael@0	1390	i = 0;
michael@0	1391	}
michael@0	1392	else {
michael@0	1393	x[0] = z & 0xffff;
michael@0	1394	x[1] = z >> 16;
michael@0	1395	i = 1;
michael@0	1396	}
michael@0	1397	k += 32;
michael@0	1398	}
michael@0	1399	while(!x[i])
michael@0	1400	--i;
michael@0	1401	b->wds = i + 1;
michael@0	1402	#endif
michael@0	1403	#ifndef Sudden_Underflow
michael@0	1404	if (de) {
michael@0	1405	#endif
michael@0	1406	#ifdef IBM
michael@0	1407	*e = (de - Bias - (P-1) << 2) + k;
michael@0	1408	*bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
michael@0	1409	#else
michael@0	1410	*e = de - Bias - (P-1) + k;
michael@0	1411	*bits = P - k;
michael@0	1412	#endif
michael@0	1413	#ifndef Sudden_Underflow
michael@0	1414	}
michael@0	1415	else {
michael@0	1416	*e = de - Bias - (P-1) + 1 + k;
michael@0	1417	#ifdef Pack_32
michael@0	1418	*bits = 32*i - hi0bits(x[i-1]);
michael@0	1419	#else
michael@0	1420	*bits = (i+2)*16 - hi0bits(x[i]);
michael@0	1421	#endif
michael@0	1422	}
michael@0	1423	#endif
michael@0	1424	return b;
michael@0	1425	}
michael@0	1426	#undef d0
michael@0	1427	#undef d1
michael@0	1428
michael@0	1429	static double
michael@0	1430	ratio
michael@0	1431	#ifdef KR_headers
michael@0	1432	(a, b) Bigint *a, *b;
michael@0	1433	#else
michael@0	1434	(Bigint *a, Bigint *b)
michael@0	1435	#endif
michael@0	1436	{
michael@0	1437	U da, db;
michael@0	1438	int k, ka, kb;
michael@0	1439
michael@0	1440	dval(da) = b2d(a, &ka);
michael@0	1441	dval(db) = b2d(b, &kb);
michael@0	1442	#ifdef Pack_32
michael@0	1443	k = ka - kb + 32*(a->wds - b->wds);
michael@0	1444	#else
michael@0	1445	k = ka - kb + 16*(a->wds - b->wds);
michael@0	1446	#endif
michael@0	1447	#ifdef IBM
michael@0	1448	if (k > 0) {
michael@0	1449	word0(da) += (k >> 2)*Exp_msk1;
michael@0	1450	if (k &= 3)
michael@0	1451	dval(da) *= 1 << k;
michael@0	1452	}
michael@0	1453	else {
michael@0	1454	k = -k;
michael@0	1455	word0(db) += (k >> 2)*Exp_msk1;
michael@0	1456	if (k &= 3)
michael@0	1457	dval(db) *= 1 << k;
michael@0	1458	}
michael@0	1459	#else
michael@0	1460	if (k > 0)
michael@0	1461	word0(da) += k*Exp_msk1;
michael@0	1462	else {
michael@0	1463	k = -k;
michael@0	1464	word0(db) += k*Exp_msk1;
michael@0	1465	}
michael@0	1466	#endif
michael@0	1467	return dval(da) / dval(db);
michael@0	1468	}
michael@0	1469
michael@0	1470	static CONST double
michael@0	1471	tens[] = {
michael@0	1472	1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
michael@0	1473	1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
michael@0	1474	1e20, 1e21, 1e22
michael@0	1475	#ifdef VAX
michael@0	1476	, 1e23, 1e24
michael@0	1477	#endif
michael@0	1478	};
michael@0	1479
michael@0	1480	static CONST double
michael@0	1481	#ifdef IEEE_Arith
michael@0	1482	bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
michael@0	1483	static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
michael@0	1484	#ifdef Avoid_Underflow
michael@0	1485	9007199254740992.*9007199254740992.e-256
michael@0	1486	/* = 2^106 * 1e-53 */
michael@0	1487	#else
michael@0	1488	1e-256
michael@0	1489	#endif
michael@0	1490	};
michael@0	1491	/* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
michael@0	1492	/* flag unnecessarily. It leads to a song and dance at the end of strtod. */
michael@0	1493	#define Scale_Bit 0x10
michael@0	1494	#define n_bigtens 5
michael@0	1495	#else
michael@0	1496	#ifdef IBM
michael@0	1497	bigtens[] = { 1e16, 1e32, 1e64 };
michael@0	1498	static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
michael@0	1499	#define n_bigtens 3
michael@0	1500	#else
michael@0	1501	bigtens[] = { 1e16, 1e32 };
michael@0	1502	static CONST double tinytens[] = { 1e-16, 1e-32 };
michael@0	1503	#define n_bigtens 2
michael@0	1504	#endif
michael@0	1505	#endif
michael@0	1506
michael@0	1507	#ifndef IEEE_Arith
michael@0	1508	#undef INFNAN_CHECK
michael@0	1509	#endif
michael@0	1510
michael@0	1511	#ifdef INFNAN_CHECK
michael@0	1512
michael@0	1513	#ifndef NAN_WORD0
michael@0	1514	#define NAN_WORD0 0x7ff80000
michael@0	1515	#endif
michael@0	1516
michael@0	1517	#ifndef NAN_WORD1
michael@0	1518	#define NAN_WORD1 0
michael@0	1519	#endif
michael@0	1520
michael@0	1521	static int
michael@0	1522	match
michael@0	1523	#ifdef KR_headers
michael@0	1524	(sp, t) char **sp, *t;
michael@0	1525	#else
michael@0	1526	(CONST char **sp, char *t)
michael@0	1527	#endif
michael@0	1528	{
michael@0	1529	int c, d;
michael@0	1530	CONST char *s = *sp;
michael@0	1531
michael@0	1532	while(d = *t++) {
michael@0	1533	if ((c = *++s) >= 'A' && c <= 'Z')
michael@0	1534	c += 'a' - 'A';
michael@0	1535	if (c != d)
michael@0	1536	return 0;
michael@0	1537	}
michael@0	1538	*sp = s + 1;
michael@0	1539	return 1;
michael@0	1540	}
michael@0	1541
michael@0	1542	#ifndef No_Hex_NaN
michael@0	1543	static void
michael@0	1544	hexnan
michael@0	1545	#ifdef KR_headers
michael@0	1546	(rvp, sp) double *rvp; CONST char **sp;
michael@0	1547	#else
michael@0	1548	(double *rvp, CONST char **sp)
michael@0	1549	#endif
michael@0	1550	{
michael@0	1551	ULong c, x[2];
michael@0	1552	CONST char *s;
michael@0	1553	int havedig, udx0, xshift;
michael@0	1554
michael@0	1555	x[0] = x[1] = 0;
michael@0	1556	havedig = xshift = 0;
michael@0	1557	udx0 = 1;
michael@0	1558	s = *sp;
michael@0	1559	while(c = *(CONST unsigned char*)++s) {
michael@0	1560	if (c >= '0' && c <= '9')
michael@0	1561	c -= '0';
michael@0	1562	else if (c >= 'a' && c <= 'f')
michael@0	1563	c += 10 - 'a';
michael@0	1564	else if (c >= 'A' && c <= 'F')
michael@0	1565	c += 10 - 'A';
michael@0	1566	else if (c <= ' ') {
michael@0	1567	if (udx0 && havedig) {
michael@0	1568	udx0 = 0;
michael@0	1569	xshift = 1;
michael@0	1570	}
michael@0	1571	continue;
michael@0	1572	}
michael@0	1573	else if (/*(*/ c == ')' && havedig) {
michael@0	1574	*sp = s + 1;
michael@0	1575	break;
michael@0	1576	}
michael@0	1577	else
michael@0	1578	return; /* invalid form: don't change *sp */
michael@0	1579	havedig = 1;
michael@0	1580	if (xshift) {
michael@0	1581	xshift = 0;
michael@0	1582	x[0] = x[1];
michael@0	1583	x[1] = 0;
michael@0	1584	}
michael@0	1585	if (udx0)
michael@0	1586	x[0] = (x[0] << 4) | (x[1] >> 28);
michael@0	1587	x[1] = (x[1] << 4) | c;
michael@0	1588	}
michael@0	1589	if ((x[0] &= 0xfffff) || x[1]) {
michael@0	1590	word0(*rvp) = Exp_mask | x[0];
michael@0	1591	word1(*rvp) = x[1];
michael@0	1592	}
michael@0	1593	}
michael@0	1594	#endif /*No_Hex_NaN*/
michael@0	1595	#endif /* INFNAN_CHECK */
michael@0	1596
michael@0	1597	PR_IMPLEMENT(double)
michael@0	1598	PR_strtod
michael@0	1599	#ifdef KR_headers
michael@0	1600	(s00, se) CONST char *s00; char **se;
michael@0	1601	#else
michael@0	1602	(CONST char *s00, char **se)
michael@0	1603	#endif
michael@0	1604	{
michael@0	1605	#ifdef Avoid_Underflow
michael@0	1606	int scale;
michael@0	1607	#endif
michael@0	1608	int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
michael@0	1609	e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
michael@0	1610	CONST char *s, *s0, *s1;
michael@0	1611	double aadj, aadj1, adj;
michael@0	1612	U aadj2, rv, rv0;
michael@0	1613	Long L;
michael@0	1614	ULong y, z;
michael@0	1615	Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
michael@0	1616	#ifdef SET_INEXACT
michael@0	1617	int inexact, oldinexact;
michael@0	1618	#endif
michael@0	1619	#ifdef Honor_FLT_ROUNDS
michael@0	1620	int rounding;
michael@0	1621	#endif
michael@0	1622	#ifdef USE_LOCALE
michael@0	1623	CONST char *s2;
michael@0	1624	#endif
michael@0	1625
michael@0	1626	if (!_pr_initialized) _PR_ImplicitInitialization();
michael@0	1627
michael@0	1628	sign = nz0 = nz = 0;
michael@0	1629	dval(rv) = 0.;
michael@0	1630	for(s = s00;;s++) switch(*s) {
michael@0	1631	case '-':
michael@0	1632	sign = 1;
michael@0	1633	/* no break */
michael@0	1634	case '+':
michael@0	1635	if (*++s)
michael@0	1636	goto break2;
michael@0	1637	/* no break */
michael@0	1638	case 0:
michael@0	1639	goto ret0;
michael@0	1640	case '\t':
michael@0	1641	case '\n':
michael@0	1642	case '\v':
michael@0	1643	case '\f':
michael@0	1644	case '\r':
michael@0	1645	case ' ':
michael@0	1646	continue;
michael@0	1647	default:
michael@0	1648	goto break2;
michael@0	1649	}
michael@0	1650	break2:
michael@0	1651	if (*s == '0') {
michael@0	1652	nz0 = 1;
michael@0	1653	while(*++s == '0') ;
michael@0	1654	if (!*s)
michael@0	1655	goto ret;
michael@0	1656	}
michael@0	1657	s0 = s;
michael@0	1658	y = z = 0;
michael@0	1659	for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
michael@0	1660	if (nd < 9)
michael@0	1661	y = 10*y + c - '0';
michael@0	1662	else if (nd < 16)
michael@0	1663	z = 10*z + c - '0';
michael@0	1664	nd0 = nd;
michael@0	1665	#ifdef USE_LOCALE
michael@0	1666	s1 = localeconv()->decimal_point;
michael@0	1667	if (c == *s1) {
michael@0	1668	c = '.';
michael@0	1669	if (*++s1) {
michael@0	1670	s2 = s;
michael@0	1671	for(;;) {
michael@0	1672	if (*++s2 != *s1) {
michael@0	1673	c = 0;
michael@0	1674	break;
michael@0	1675	}
michael@0	1676	if (!*++s1) {
michael@0	1677	s = s2;
michael@0	1678	break;
michael@0	1679	}
michael@0	1680	}
michael@0	1681	}
michael@0	1682	}
michael@0	1683	#endif
michael@0	1684	if (c == '.') {
michael@0	1685	c = *++s;
michael@0	1686	if (!nd) {
michael@0	1687	for(; c == '0'; c = *++s)
michael@0	1688	nz++;
michael@0	1689	if (c > '0' && c <= '9') {
michael@0	1690	s0 = s;
michael@0	1691	nf += nz;
michael@0	1692	nz = 0;
michael@0	1693	goto have_dig;
michael@0	1694	}
michael@0	1695	goto dig_done;
michael@0	1696	}
michael@0	1697	for(; c >= '0' && c <= '9'; c = *++s) {
michael@0	1698	have_dig:
michael@0	1699	nz++;
michael@0	1700	if (c -= '0') {
michael@0	1701	nf += nz;
michael@0	1702	for(i = 1; i < nz; i++)
michael@0	1703	if (nd++ < 9)
michael@0	1704	y *= 10;
michael@0	1705	else if (nd <= DBL_DIG + 1)
michael@0	1706	z *= 10;
michael@0	1707	if (nd++ < 9)
michael@0	1708	y = 10*y + c;
michael@0	1709	else if (nd <= DBL_DIG + 1)
michael@0	1710	z = 10*z + c;
michael@0	1711	nz = 0;
michael@0	1712	}
michael@0	1713	}
michael@0	1714	}
michael@0	1715	dig_done:
michael@0	1716	if (nd > 64 * 1024)
michael@0	1717	goto ret0;
michael@0	1718	e = 0;
michael@0	1719	if (c == 'e' || c == 'E') {
michael@0	1720	if (!nd && !nz && !nz0) {
michael@0	1721	goto ret0;
michael@0	1722	}
michael@0	1723	s00 = s;
michael@0	1724	esign = 0;
michael@0	1725	switch(c = *++s) {
michael@0	1726	case '-':
michael@0	1727	esign = 1;
michael@0	1728	case '+':
michael@0	1729	c = *++s;
michael@0	1730	}
michael@0	1731	if (c >= '0' && c <= '9') {
michael@0	1732	while(c == '0')
michael@0	1733	c = *++s;
michael@0	1734	if (c > '0' && c <= '9') {
michael@0	1735	L = c - '0';
michael@0	1736	s1 = s;
michael@0	1737	while((c = *++s) >= '0' && c <= '9')
michael@0	1738	L = 10*L + c - '0';
michael@0	1739	if (s - s1 > 8 || L > 19999)
michael@0	1740	/* Avoid confusion from exponents
michael@0	1741	* so large that e might overflow.
michael@0	1742	*/
michael@0	1743	e = 19999; /* safe for 16 bit ints */
michael@0	1744	else
michael@0	1745	e = (int)L;
michael@0	1746	if (esign)
michael@0	1747	e = -e;
michael@0	1748	}
michael@0	1749	else
michael@0	1750	e = 0;
michael@0	1751	}
michael@0	1752	else
michael@0	1753	s = s00;
michael@0	1754	}
michael@0	1755	if (!nd) {
michael@0	1756	if (!nz && !nz0) {
michael@0	1757	#ifdef INFNAN_CHECK
michael@0	1758	/* Check for Nan and Infinity */
michael@0	1759	switch(c) {
michael@0	1760	case 'i':
michael@0	1761	case 'I':
michael@0	1762	if (match(&s,"nf")) {
michael@0	1763	--s;
michael@0	1764	if (!match(&s,"inity"))
michael@0	1765	++s;
michael@0	1766	word0(rv) = 0x7ff00000;
michael@0	1767	word1(rv) = 0;
michael@0	1768	goto ret;
michael@0	1769	}
michael@0	1770	break;
michael@0	1771	case 'n':
michael@0	1772	case 'N':
michael@0	1773	if (match(&s, "an")) {
michael@0	1774	word0(rv) = NAN_WORD0;
michael@0	1775	word1(rv) = NAN_WORD1;
michael@0	1776	#ifndef No_Hex_NaN
michael@0	1777	if (*s == '(') /*)*/
michael@0	1778	hexnan(&rv, &s);
michael@0	1779	#endif
michael@0	1780	goto ret;
michael@0	1781	}
michael@0	1782	}
michael@0	1783	#endif /* INFNAN_CHECK */
michael@0	1784	ret0:
michael@0	1785	s = s00;
michael@0	1786	sign = 0;
michael@0	1787	}
michael@0	1788	goto ret;
michael@0	1789	}
michael@0	1790	e1 = e -= nf;
michael@0	1791
michael@0	1792	/* Now we have nd0 digits, starting at s0, followed by a
michael@0	1793	* decimal point, followed by nd-nd0 digits. The number we're
michael@0	1794	* after is the integer represented by those digits times
michael@0	1795	* 10**e */
michael@0	1796
michael@0	1797	if (!nd0)
michael@0	1798	nd0 = nd;
michael@0	1799	k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
michael@0	1800	dval(rv) = y;
michael@0	1801	if (k > 9) {
michael@0	1802	#ifdef SET_INEXACT
michael@0	1803	if (k > DBL_DIG)
michael@0	1804	oldinexact = get_inexact();
michael@0	1805	#endif
michael@0	1806	dval(rv) = tens[k - 9] * dval(rv) + z;
michael@0	1807	}
michael@0	1808	bd0 = 0;
michael@0	1809	if (nd <= DBL_DIG
michael@0	1810	#ifndef RND_PRODQUOT
michael@0	1811	#ifndef Honor_FLT_ROUNDS
michael@0	1812	&& Flt_Rounds == 1
michael@0	1813	#endif
michael@0	1814	#endif
michael@0	1815	) {
michael@0	1816	if (!e)
michael@0	1817	goto ret;
michael@0	1818	if (e > 0) {
michael@0	1819	if (e <= Ten_pmax) {
michael@0	1820	#ifdef VAX
michael@0	1821	goto vax_ovfl_check;
michael@0	1822	#else
michael@0	1823	#ifdef Honor_FLT_ROUNDS
michael@0	1824	/* round correctly FLT_ROUNDS = 2 or 3 */
michael@0	1825	if (sign) {
michael@0	1826	rv = -rv;
michael@0	1827	sign = 0;
michael@0	1828	}
michael@0	1829	#endif
michael@0	1830	/* rv = */ rounded_product(dval(rv), tens[e]);
michael@0	1831	goto ret;
michael@0	1832	#endif
michael@0	1833	}
michael@0	1834	i = DBL_DIG - nd;
michael@0	1835	if (e <= Ten_pmax + i) {
michael@0	1836	/* A fancier test would sometimes let us do
michael@0	1837	* this for larger i values.
michael@0	1838	*/
michael@0	1839	#ifdef Honor_FLT_ROUNDS
michael@0	1840	/* round correctly FLT_ROUNDS = 2 or 3 */
michael@0	1841	if (sign) {
michael@0	1842	rv = -rv;
michael@0	1843	sign = 0;
michael@0	1844	}
michael@0	1845	#endif
michael@0	1846	e -= i;
michael@0	1847	dval(rv) *= tens[i];
michael@0	1848	#ifdef VAX
michael@0	1849	/* VAX exponent range is so narrow we must
michael@0	1850	* worry about overflow here...
michael@0	1851	*/
michael@0	1852	vax_ovfl_check:
michael@0	1853	word0(rv) -= P*Exp_msk1;
michael@0	1854	/* rv = */ rounded_product(dval(rv), tens[e]);
michael@0	1855	if ((word0(rv) & Exp_mask)
michael@0	1856	> Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
michael@0	1857	goto ovfl;
michael@0	1858	word0(rv) += P*Exp_msk1;
michael@0	1859	#else
michael@0	1860	/* rv = */ rounded_product(dval(rv), tens[e]);
michael@0	1861	#endif
michael@0	1862	goto ret;
michael@0	1863	}
michael@0	1864	}
michael@0	1865	#ifndef Inaccurate_Divide
michael@0	1866	else if (e >= -Ten_pmax) {
michael@0	1867	#ifdef Honor_FLT_ROUNDS
michael@0	1868	/* round correctly FLT_ROUNDS = 2 or 3 */
michael@0	1869	if (sign) {
michael@0	1870	rv = -rv;
michael@0	1871	sign = 0;
michael@0	1872	}
michael@0	1873	#endif
michael@0	1874	/* rv = */ rounded_quotient(dval(rv), tens[-e]);
michael@0	1875	goto ret;
michael@0	1876	}
michael@0	1877	#endif
michael@0	1878	}
michael@0	1879	e1 += nd - k;
michael@0	1880
michael@0	1881	#ifdef IEEE_Arith
michael@0	1882	#ifdef SET_INEXACT
michael@0	1883	inexact = 1;
michael@0	1884	if (k <= DBL_DIG)
michael@0	1885	oldinexact = get_inexact();
michael@0	1886	#endif
michael@0	1887	#ifdef Avoid_Underflow
michael@0	1888	scale = 0;
michael@0	1889	#endif
michael@0	1890	#ifdef Honor_FLT_ROUNDS
michael@0	1891	if ((rounding = Flt_Rounds) >= 2) {
michael@0	1892	if (sign)
michael@0	1893	rounding = rounding == 2 ? 0 : 2;
michael@0	1894	else
michael@0	1895	if (rounding != 2)
michael@0	1896	rounding = 0;
michael@0	1897	}
michael@0	1898	#endif
michael@0	1899	#endif /*IEEE_Arith*/
michael@0	1900
michael@0	1901	/* Get starting approximation = rv * 10**e1 */
michael@0	1902
michael@0	1903	if (e1 > 0) {
michael@0	1904	if (i = e1 & 15)
michael@0	1905	dval(rv) *= tens[i];
michael@0	1906	if (e1 &= ~15) {
michael@0	1907	if (e1 > DBL_MAX_10_EXP) {
michael@0	1908	ovfl:
michael@0	1909	#ifndef NO_ERRNO
michael@0	1910	PR_SetError(PR_RANGE_ERROR, 0);
michael@0	1911	#endif
michael@0	1912	/* Can't trust HUGE_VAL */
michael@0	1913	#ifdef IEEE_Arith
michael@0	1914	#ifdef Honor_FLT_ROUNDS
michael@0	1915	switch(rounding) {
michael@0	1916	case 0: /* toward 0 */
michael@0	1917	case 3: /* toward -infinity */
michael@0	1918	word0(rv) = Big0;
michael@0	1919	word1(rv) = Big1;
michael@0	1920	break;
michael@0	1921	default:
michael@0	1922	word0(rv) = Exp_mask;
michael@0	1923	word1(rv) = 0;
michael@0	1924	}
michael@0	1925	#else /*Honor_FLT_ROUNDS*/
michael@0	1926	word0(rv) = Exp_mask;
michael@0	1927	word1(rv) = 0;
michael@0	1928	#endif /*Honor_FLT_ROUNDS*/
michael@0	1929	#ifdef SET_INEXACT
michael@0	1930	/* set overflow bit */
michael@0	1931	dval(rv0) = 1e300;
michael@0	1932	dval(rv0) *= dval(rv0);
michael@0	1933	#endif
michael@0	1934	#else /*IEEE_Arith*/
michael@0	1935	word0(rv) = Big0;
michael@0	1936	word1(rv) = Big1;
michael@0	1937	#endif /*IEEE_Arith*/
michael@0	1938	if (bd0)
michael@0	1939	goto retfree;
michael@0	1940	goto ret;
michael@0	1941	}
michael@0	1942	e1 >>= 4;
michael@0	1943	for(j = 0; e1 > 1; j++, e1 >>= 1)
michael@0	1944	if (e1 & 1)
michael@0	1945	dval(rv) *= bigtens[j];
michael@0	1946	/* The last multiplication could overflow. */
michael@0	1947	word0(rv) -= P*Exp_msk1;
michael@0	1948	dval(rv) *= bigtens[j];
michael@0	1949	if ((z = word0(rv) & Exp_mask)
michael@0	1950	> Exp_msk1*(DBL_MAX_EXP+Bias-P))
michael@0	1951	goto ovfl;
michael@0	1952	if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
michael@0	1953	/* set to largest number */
michael@0	1954	/* (Can't trust DBL_MAX) */
michael@0	1955	word0(rv) = Big0;
michael@0	1956	word1(rv) = Big1;
michael@0	1957	}
michael@0	1958	else
michael@0	1959	word0(rv) += P*Exp_msk1;
michael@0	1960	}
michael@0	1961	}
michael@0	1962	else if (e1 < 0) {
michael@0	1963	e1 = -e1;
michael@0	1964	if (i = e1 & 15)
michael@0	1965	dval(rv) /= tens[i];
michael@0	1966	if (e1 >>= 4) {
michael@0	1967	if (e1 >= 1 << n_bigtens)
michael@0	1968	goto undfl;
michael@0	1969	#ifdef Avoid_Underflow
michael@0	1970	if (e1 & Scale_Bit)
michael@0	1971	scale = 2*P;
michael@0	1972	for(j = 0; e1 > 0; j++, e1 >>= 1)
michael@0	1973	if (e1 & 1)
michael@0	1974	dval(rv) *= tinytens[j];
michael@0	1975	if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
michael@0	1976	>> Exp_shift)) > 0) {
michael@0	1977	/* scaled rv is denormal; zap j low bits */
michael@0	1978	if (j >= 32) {
michael@0	1979	word1(rv) = 0;
michael@0	1980	if (j >= 53)
michael@0	1981	word0(rv) = (P+2)*Exp_msk1;
michael@0	1982	else
michael@0	1983	word0(rv) &= 0xffffffff << j-32;
michael@0	1984	}
michael@0	1985	else
michael@0	1986	word1(rv) &= 0xffffffff << j;
michael@0	1987	}
michael@0	1988	#else
michael@0	1989	for(j = 0; e1 > 1; j++, e1 >>= 1)
michael@0	1990	if (e1 & 1)
michael@0	1991	dval(rv) *= tinytens[j];
michael@0	1992	/* The last multiplication could underflow. */
michael@0	1993	dval(rv0) = dval(rv);
michael@0	1994	dval(rv) *= tinytens[j];
michael@0	1995	if (!dval(rv)) {
michael@0	1996	dval(rv) = 2.*dval(rv0);
michael@0	1997	dval(rv) *= tinytens[j];
michael@0	1998	#endif
michael@0	1999	if (!dval(rv)) {
michael@0	2000	undfl:
michael@0	2001	dval(rv) = 0.;
michael@0	2002	#ifndef NO_ERRNO
michael@0	2003	PR_SetError(PR_RANGE_ERROR, 0);
michael@0	2004	#endif
michael@0	2005	if (bd0)
michael@0	2006	goto retfree;
michael@0	2007	goto ret;
michael@0	2008	}
michael@0	2009	#ifndef Avoid_Underflow
michael@0	2010	word0(rv) = Tiny0;
michael@0	2011	word1(rv) = Tiny1;
michael@0	2012	/* The refinement below will clean
michael@0	2013	* this approximation up.
michael@0	2014	*/
michael@0	2015	}
michael@0	2016	#endif
michael@0	2017	}
michael@0	2018	}
michael@0	2019
michael@0	2020	/* Now the hard part -- adjusting rv to the correct value.*/
michael@0	2021
michael@0	2022	/* Put digits into bd: true value = bd * 10^e */
michael@0	2023
michael@0	2024	bd0 = s2b(s0, nd0, nd, y);
michael@0	2025
michael@0	2026	for(;;) {
michael@0	2027	bd = Balloc(bd0->k);
michael@0	2028	Bcopy(bd, bd0);
michael@0	2029	bb = d2b(dval(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */
michael@0	2030	bs = i2b(1);
michael@0	2031
michael@0	2032	if (e >= 0) {
michael@0	2033	bb2 = bb5 = 0;
michael@0	2034	bd2 = bd5 = e;
michael@0	2035	}
michael@0	2036	else {
michael@0	2037	bb2 = bb5 = -e;
michael@0	2038	bd2 = bd5 = 0;
michael@0	2039	}
michael@0	2040	if (bbe >= 0)
michael@0	2041	bb2 += bbe;
michael@0	2042	else
michael@0	2043	bd2 -= bbe;
michael@0	2044	bs2 = bb2;
michael@0	2045	#ifdef Honor_FLT_ROUNDS
michael@0	2046	if (rounding != 1)
michael@0	2047	bs2++;
michael@0	2048	#endif
michael@0	2049	#ifdef Avoid_Underflow
michael@0	2050	j = bbe - scale;
michael@0	2051	i = j + bbbits - 1; /* logb(rv) */
michael@0	2052	if (i < Emin) /* denormal */
michael@0	2053	j += P - Emin;
michael@0	2054	else
michael@0	2055	j = P + 1 - bbbits;
michael@0	2056	#else /*Avoid_Underflow*/
michael@0	2057	#ifdef Sudden_Underflow
michael@0	2058	#ifdef IBM
michael@0	2059	j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
michael@0	2060	#else
michael@0	2061	j = P + 1 - bbbits;
michael@0	2062	#endif
michael@0	2063	#else /*Sudden_Underflow*/
michael@0	2064	j = bbe;
michael@0	2065	i = j + bbbits - 1; /* logb(rv) */
michael@0	2066	if (i < Emin) /* denormal */
michael@0	2067	j += P - Emin;
michael@0	2068	else
michael@0	2069	j = P + 1 - bbbits;
michael@0	2070	#endif /*Sudden_Underflow*/
michael@0	2071	#endif /*Avoid_Underflow*/
michael@0	2072	bb2 += j;
michael@0	2073	bd2 += j;
michael@0	2074	#ifdef Avoid_Underflow
michael@0	2075	bd2 += scale;
michael@0	2076	#endif
michael@0	2077	i = bb2 < bd2 ? bb2 : bd2;
michael@0	2078	if (i > bs2)
michael@0	2079	i = bs2;
michael@0	2080	if (i > 0) {
michael@0	2081	bb2 -= i;
michael@0	2082	bd2 -= i;
michael@0	2083	bs2 -= i;
michael@0	2084	}
michael@0	2085	if (bb5 > 0) {
michael@0	2086	bs = pow5mult(bs, bb5);
michael@0	2087	bb1 = mult(bs, bb);
michael@0	2088	Bfree(bb);
michael@0	2089	bb = bb1;
michael@0	2090	}
michael@0	2091	if (bb2 > 0)
michael@0	2092	bb = lshift(bb, bb2);
michael@0	2093	if (bd5 > 0)
michael@0	2094	bd = pow5mult(bd, bd5);
michael@0	2095	if (bd2 > 0)
michael@0	2096	bd = lshift(bd, bd2);
michael@0	2097	if (bs2 > 0)
michael@0	2098	bs = lshift(bs, bs2);
michael@0	2099	delta = diff(bb, bd);
michael@0	2100	dsign = delta->sign;
michael@0	2101	delta->sign = 0;
michael@0	2102	i = cmp(delta, bs);
michael@0	2103	#ifdef Honor_FLT_ROUNDS
michael@0	2104	if (rounding != 1) {
michael@0	2105	if (i < 0) {
michael@0	2106	/* Error is less than an ulp */
michael@0	2107	if (!delta->x[0] && delta->wds <= 1) {
michael@0	2108	/* exact */
michael@0	2109	#ifdef SET_INEXACT
michael@0	2110	inexact = 0;
michael@0	2111	#endif
michael@0	2112	break;
michael@0	2113	}
michael@0	2114	if (rounding) {
michael@0	2115	if (dsign) {
michael@0	2116	adj = 1.;
michael@0	2117	goto apply_adj;
michael@0	2118	}
michael@0	2119	}
michael@0	2120	else if (!dsign) {
michael@0	2121	adj = -1.;
michael@0	2122	if (!word1(rv)
michael@0	2123	&& !(word0(rv) & Frac_mask)) {
michael@0	2124	y = word0(rv) & Exp_mask;
michael@0	2125	#ifdef Avoid_Underflow
michael@0	2126	if (!scale || y > 2*P*Exp_msk1)
michael@0	2127	#else
michael@0	2128	if (y)
michael@0	2129	#endif
michael@0	2130	{
michael@0	2131	delta = lshift(delta,Log2P);
michael@0	2132	if (cmp(delta, bs) <= 0)
michael@0	2133	adj = -0.5;
michael@0	2134	}
michael@0	2135	}
michael@0	2136	apply_adj:
michael@0	2137	#ifdef Avoid_Underflow
michael@0	2138	if (scale && (y = word0(rv) & Exp_mask)
michael@0	2139	<= 2*P*Exp_msk1)
michael@0	2140	word0(adj) += (2*P+1)*Exp_msk1 - y;
michael@0	2141	#else
michael@0	2142	#ifdef Sudden_Underflow
michael@0	2143	if ((word0(rv) & Exp_mask) <=
michael@0	2144	P*Exp_msk1) {
michael@0	2145	word0(rv) += P*Exp_msk1;
michael@0	2146	dval(rv) += adj*ulp(dval(rv));
michael@0	2147	word0(rv) -= P*Exp_msk1;
michael@0	2148	}
michael@0	2149	else
michael@0	2150	#endif /*Sudden_Underflow*/
michael@0	2151	#endif /*Avoid_Underflow*/
michael@0	2152	dval(rv) += adj*ulp(dval(rv));
michael@0	2153	}
michael@0	2154	break;
michael@0	2155	}
michael@0	2156	adj = ratio(delta, bs);
michael@0	2157	if (adj < 1.)
michael@0	2158	adj = 1.;
michael@0	2159	if (adj <= 0x7ffffffe) {
michael@0	2160	/* adj = rounding ? ceil(adj) : floor(adj); */
michael@0	2161	y = adj;
michael@0	2162	if (y != adj) {
michael@0	2163	if (!((rounding>>1) ^ dsign))
michael@0	2164	y++;
michael@0	2165	adj = y;
michael@0	2166	}
michael@0	2167	}
michael@0	2168	#ifdef Avoid_Underflow
michael@0	2169	if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
michael@0	2170	word0(adj) += (2*P+1)*Exp_msk1 - y;
michael@0	2171	#else
michael@0	2172	#ifdef Sudden_Underflow
michael@0	2173	if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
michael@0	2174	word0(rv) += P*Exp_msk1;
michael@0	2175	adj *= ulp(dval(rv));
michael@0	2176	if (dsign)
michael@0	2177	dval(rv) += adj;
michael@0	2178	else
michael@0	2179	dval(rv) -= adj;
michael@0	2180	word0(rv) -= P*Exp_msk1;
michael@0	2181	goto cont;
michael@0	2182	}
michael@0	2183	#endif /*Sudden_Underflow*/
michael@0	2184	#endif /*Avoid_Underflow*/
michael@0	2185	adj *= ulp(dval(rv));
michael@0	2186	if (dsign)
michael@0	2187	dval(rv) += adj;
michael@0	2188	else
michael@0	2189	dval(rv) -= adj;
michael@0	2190	goto cont;
michael@0	2191	}
michael@0	2192	#endif /*Honor_FLT_ROUNDS*/
michael@0	2193
michael@0	2194	if (i < 0) {
michael@0	2195	/* Error is less than half an ulp -- check for
michael@0	2196	* special case of mantissa a power of two.
michael@0	2197	*/
michael@0	2198	if (dsign || word1(rv) || word0(rv) & Bndry_mask
michael@0	2199	#ifdef IEEE_Arith
michael@0	2200	#ifdef Avoid_Underflow
michael@0	2201	|| (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
michael@0	2202	#else
michael@0	2203	|| (word0(rv) & Exp_mask) <= Exp_msk1
michael@0	2204	#endif
michael@0	2205	#endif
michael@0	2206	) {
michael@0	2207	#ifdef SET_INEXACT
michael@0	2208	if (!delta->x[0] && delta->wds <= 1)
michael@0	2209	inexact = 0;
michael@0	2210	#endif
michael@0	2211	break;
michael@0	2212	}
michael@0	2213	if (!delta->x[0] && delta->wds <= 1) {
michael@0	2214	/* exact result */
michael@0	2215	#ifdef SET_INEXACT
michael@0	2216	inexact = 0;
michael@0	2217	#endif
michael@0	2218	break;
michael@0	2219	}
michael@0	2220	delta = lshift(delta,Log2P);
michael@0	2221	if (cmp(delta, bs) > 0)
michael@0	2222	goto drop_down;
michael@0	2223	break;
michael@0	2224	}
michael@0	2225	if (i == 0) {
michael@0	2226	/* exactly half-way between */
michael@0	2227	if (dsign) {
michael@0	2228	if ((word0(rv) & Bndry_mask1) == Bndry_mask1
michael@0	2229	&& word1(rv) == (
michael@0	2230	#ifdef Avoid_Underflow
michael@0	2231	(scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
michael@0	2232	? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
michael@0	2233	#endif
michael@0	2234	0xffffffff)) {
michael@0	2235	/*boundary case -- increment exponent*/
michael@0	2236	word0(rv) = (word0(rv) & Exp_mask)
michael@0	2237	+ Exp_msk1
michael@0	2238	#ifdef IBM
michael@0	2239	| Exp_msk1 >> 4
michael@0	2240	#endif
michael@0	2241	;
michael@0	2242	word1(rv) = 0;
michael@0	2243	#ifdef Avoid_Underflow
michael@0	2244	dsign = 0;
michael@0	2245	#endif
michael@0	2246	break;
michael@0	2247	}
michael@0	2248	}
michael@0	2249	else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
michael@0	2250	drop_down:
michael@0	2251	/* boundary case -- decrement exponent */
michael@0	2252	#ifdef Sudden_Underflow /*{{*/
michael@0	2253	L = word0(rv) & Exp_mask;
michael@0	2254	#ifdef IBM
michael@0	2255	if (L < Exp_msk1)
michael@0	2256	#else
michael@0	2257	#ifdef Avoid_Underflow
michael@0	2258	if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
michael@0	2259	#else
michael@0	2260	if (L <= Exp_msk1)
michael@0	2261	#endif /*Avoid_Underflow*/
michael@0	2262	#endif /*IBM*/
michael@0	2263	goto undfl;
michael@0	2264	L -= Exp_msk1;
michael@0	2265	#else /*Sudden_Underflow}{*/
michael@0	2266	#ifdef Avoid_Underflow
michael@0	2267	if (scale) {
michael@0	2268	L = word0(rv) & Exp_mask;
michael@0	2269	if (L <= (2*P+1)*Exp_msk1) {
michael@0	2270	if (L > (P+2)*Exp_msk1)
michael@0	2271	/* round even ==> */
michael@0	2272	/* accept rv */
michael@0	2273	break;
michael@0	2274	/* rv = smallest denormal */
michael@0	2275	goto undfl;
michael@0	2276	}
michael@0	2277	}
michael@0	2278	#endif /*Avoid_Underflow*/
michael@0	2279	L = (word0(rv) & Exp_mask) - Exp_msk1;
michael@0	2280	#endif /*Sudden_Underflow}}*/
michael@0	2281	word0(rv) = L | Bndry_mask1;
michael@0	2282	word1(rv) = 0xffffffff;
michael@0	2283	#ifdef IBM
michael@0	2284	goto cont;
michael@0	2285	#else
michael@0	2286	break;
michael@0	2287	#endif
michael@0	2288	}
michael@0	2289	#ifndef ROUND_BIASED
michael@0	2290	if (!(word1(rv) & LSB))
michael@0	2291	break;
michael@0	2292	#endif
michael@0	2293	if (dsign)
michael@0	2294	dval(rv) += ulp(dval(rv));
michael@0	2295	#ifndef ROUND_BIASED
michael@0	2296	else {
michael@0	2297	dval(rv) -= ulp(dval(rv));
michael@0	2298	#ifndef Sudden_Underflow
michael@0	2299	if (!dval(rv))
michael@0	2300	goto undfl;
michael@0	2301	#endif
michael@0	2302	}
michael@0	2303	#ifdef Avoid_Underflow
michael@0	2304	dsign = 1 - dsign;
michael@0	2305	#endif
michael@0	2306	#endif
michael@0	2307	break;
michael@0	2308	}
michael@0	2309	if ((aadj = ratio(delta, bs)) <= 2.) {
michael@0	2310	if (dsign)
michael@0	2311	aadj = aadj1 = 1.;
michael@0	2312	else if (word1(rv) || word0(rv) & Bndry_mask) {
michael@0	2313	#ifndef Sudden_Underflow
michael@0	2314	if (word1(rv) == Tiny1 && !word0(rv))
michael@0	2315	goto undfl;
michael@0	2316	#endif
michael@0	2317	aadj = 1.;
michael@0	2318	aadj1 = -1.;
michael@0	2319	}
michael@0	2320	else {
michael@0	2321	/* special case -- power of FLT_RADIX to be */
michael@0	2322	/* rounded down... */
michael@0	2323
michael@0	2324	if (aadj < 2./FLT_RADIX)
michael@0	2325	aadj = 1./FLT_RADIX;
michael@0	2326	else
michael@0	2327	aadj *= 0.5;
michael@0	2328	aadj1 = -aadj;
michael@0	2329	}
michael@0	2330	}
michael@0	2331	else {
michael@0	2332	aadj *= 0.5;
michael@0	2333	aadj1 = dsign ? aadj : -aadj;
michael@0	2334	#ifdef Check_FLT_ROUNDS
michael@0	2335	switch(Rounding) {
michael@0	2336	case 2: /* towards +infinity */
michael@0	2337	aadj1 -= 0.5;
michael@0	2338	break;
michael@0	2339	case 0: /* towards 0 */
michael@0	2340	case 3: /* towards -infinity */
michael@0	2341	aadj1 += 0.5;
michael@0	2342	}
michael@0	2343	#else
michael@0	2344	if (Flt_Rounds == 0)
michael@0	2345	aadj1 += 0.5;
michael@0	2346	#endif /*Check_FLT_ROUNDS*/
michael@0	2347	}
michael@0	2348	y = word0(rv) & Exp_mask;
michael@0	2349
michael@0	2350	/* Check for overflow */
michael@0	2351
michael@0	2352	if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
michael@0	2353	dval(rv0) = dval(rv);
michael@0	2354	word0(rv) -= P*Exp_msk1;
michael@0	2355	adj = aadj1 * ulp(dval(rv));
michael@0	2356	dval(rv) += adj;
michael@0	2357	if ((word0(rv) & Exp_mask) >=
michael@0	2358	Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
michael@0	2359	if (word0(rv0) == Big0 && word1(rv0) == Big1)
michael@0	2360	goto ovfl;
michael@0	2361	word0(rv) = Big0;
michael@0	2362	word1(rv) = Big1;
michael@0	2363	goto cont;
michael@0	2364	}
michael@0	2365	else
michael@0	2366	word0(rv) += P*Exp_msk1;
michael@0	2367	}
michael@0	2368	else {
michael@0	2369	#ifdef Avoid_Underflow
michael@0	2370	if (scale && y <= 2*P*Exp_msk1) {
michael@0	2371	if (aadj <= 0x7fffffff) {
michael@0	2372	if ((z = aadj) <= 0)
michael@0	2373	z = 1;
michael@0	2374	aadj = z;
michael@0	2375	aadj1 = dsign ? aadj : -aadj;
michael@0	2376	}
michael@0	2377	dval(aadj2) = aadj1;
michael@0	2378	word0(aadj2) += (2*P+1)*Exp_msk1 - y;
michael@0	2379	aadj1 = dval(aadj2);
michael@0	2380	}
michael@0	2381	adj = aadj1 * ulp(dval(rv));
michael@0	2382	dval(rv) += adj;
michael@0	2383	#else
michael@0	2384	#ifdef Sudden_Underflow
michael@0	2385	if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
michael@0	2386	dval(rv0) = dval(rv);
michael@0	2387	word0(rv) += P*Exp_msk1;
michael@0	2388	adj = aadj1 * ulp(dval(rv));
michael@0	2389	dval(rv) += adj;
michael@0	2390	#ifdef IBM
michael@0	2391	if ((word0(rv) & Exp_mask) < P*Exp_msk1)
michael@0	2392	#else
michael@0	2393	if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
michael@0	2394	#endif
michael@0	2395	{
michael@0	2396	if (word0(rv0) == Tiny0
michael@0	2397	&& word1(rv0) == Tiny1)
michael@0	2398	goto undfl;
michael@0	2399	word0(rv) = Tiny0;
michael@0	2400	word1(rv) = Tiny1;
michael@0	2401	goto cont;
michael@0	2402	}
michael@0	2403	else
michael@0	2404	word0(rv) -= P*Exp_msk1;
michael@0	2405	}
michael@0	2406	else {
michael@0	2407	adj = aadj1 * ulp(dval(rv));
michael@0	2408	dval(rv) += adj;
michael@0	2409	}
michael@0	2410	#else /*Sudden_Underflow*/
michael@0	2411	/* Compute adj so that the IEEE rounding rules will
michael@0	2412	* correctly round rv + adj in some half-way cases.
michael@0	2413	* If rv * ulp(rv) is denormalized (i.e.,
michael@0	2414	* y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
michael@0	2415	* trouble from bits lost to denormalization;
michael@0	2416	* example: 1.2e-307 .
michael@0	2417	*/
michael@0	2418	if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
michael@0	2419	aadj1 = (double)(int)(aadj + 0.5);
michael@0	2420	if (!dsign)
michael@0	2421	aadj1 = -aadj1;
michael@0	2422	}
michael@0	2423	adj = aadj1 * ulp(dval(rv));
michael@0	2424	dval(rv) += adj;
michael@0	2425	#endif /*Sudden_Underflow*/
michael@0	2426	#endif /*Avoid_Underflow*/
michael@0	2427	}
michael@0	2428	z = word0(rv) & Exp_mask;
michael@0	2429	#ifndef SET_INEXACT
michael@0	2430	#ifdef Avoid_Underflow
michael@0	2431	if (!scale)
michael@0	2432	#endif
michael@0	2433	if (y == z) {
michael@0	2434	/* Can we stop now? */
michael@0	2435	L = (Long)aadj;
michael@0	2436	aadj -= L;
michael@0	2437	/* The tolerances below are conservative. */
michael@0	2438	if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
michael@0	2439	if (aadj < .4999999 || aadj > .5000001)
michael@0	2440	break;
michael@0	2441	}
michael@0	2442	else if (aadj < .4999999/FLT_RADIX)
michael@0	2443	break;
michael@0	2444	}
michael@0	2445	#endif
michael@0	2446	cont:
michael@0	2447	Bfree(bb);
michael@0	2448	Bfree(bd);
michael@0	2449	Bfree(bs);
michael@0	2450	Bfree(delta);
michael@0	2451	}
michael@0	2452	#ifdef SET_INEXACT
michael@0	2453	if (inexact) {
michael@0	2454	if (!oldinexact) {
michael@0	2455	word0(rv0) = Exp_1 + (70 << Exp_shift);
michael@0	2456	word1(rv0) = 0;
michael@0	2457	dval(rv0) += 1.;
michael@0	2458	}
michael@0	2459	}
michael@0	2460	else if (!oldinexact)
michael@0	2461	clear_inexact();
michael@0	2462	#endif
michael@0	2463	#ifdef Avoid_Underflow
michael@0	2464	if (scale) {
michael@0	2465	word0(rv0) = Exp_1 - 2*P*Exp_msk1;
michael@0	2466	word1(rv0) = 0;
michael@0	2467	dval(rv) *= dval(rv0);
michael@0	2468	#ifndef NO_ERRNO
michael@0	2469	/* try to avoid the bug of testing an 8087 register value */
michael@0	2470	if (word0(rv) == 0 && word1(rv) == 0)
michael@0	2471	PR_SetError(PR_RANGE_ERROR, 0);
michael@0	2472	#endif
michael@0	2473	}
michael@0	2474	#endif /* Avoid_Underflow */
michael@0	2475	#ifdef SET_INEXACT
michael@0	2476	if (inexact && !(word0(rv) & Exp_mask)) {
michael@0	2477	/* set underflow bit */
michael@0	2478	dval(rv0) = 1e-300;
michael@0	2479	dval(rv0) *= dval(rv0);
michael@0	2480	}
michael@0	2481	#endif
michael@0	2482	retfree:
michael@0	2483	Bfree(bb);
michael@0	2484	Bfree(bd);
michael@0	2485	Bfree(bs);
michael@0	2486	Bfree(bd0);
michael@0	2487	Bfree(delta);
michael@0	2488	ret:
michael@0	2489	if (se)
michael@0	2490	*se = (char *)s;
michael@0	2491	return sign ? -dval(rv) : dval(rv);
michael@0	2492	}
michael@0	2493
michael@0	2494	static int
michael@0	2495	quorem
michael@0	2496	#ifdef KR_headers
michael@0	2497	(b, S) Bigint *b, *S;
michael@0	2498	#else
michael@0	2499	(Bigint *b, Bigint *S)
michael@0	2500	#endif
michael@0	2501	{
michael@0	2502	int n;
michael@0	2503	ULong *bx, *bxe, q, *sx, *sxe;
michael@0	2504	#ifdef ULLong
michael@0	2505	ULLong borrow, carry, y, ys;
michael@0	2506	#else
michael@0	2507	ULong borrow, carry, y, ys;
michael@0	2508	#ifdef Pack_32
michael@0	2509	ULong si, z, zs;
michael@0	2510	#endif
michael@0	2511	#endif
michael@0	2512
michael@0	2513	n = S->wds;
michael@0	2514	#ifdef DEBUG
michael@0	2515	/*debug*/ if (b->wds > n)
michael@0	2516	/*debug*/ Bug("oversize b in quorem");
michael@0	2517	#endif
michael@0	2518	if (b->wds < n)
michael@0	2519	return 0;
michael@0	2520	sx = S->x;
michael@0	2521	sxe = sx + --n;
michael@0	2522	bx = b->x;
michael@0	2523	bxe = bx + n;
michael@0	2524	q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
michael@0	2525	#ifdef DEBUG
michael@0	2526	/*debug*/ if (q > 9)
michael@0	2527	/*debug*/ Bug("oversized quotient in quorem");
michael@0	2528	#endif
michael@0	2529	if (q) {
michael@0	2530	borrow = 0;
michael@0	2531	carry = 0;
michael@0	2532	do {
michael@0	2533	#ifdef ULLong
michael@0	2534	ys = *sx++ * (ULLong)q + carry;
michael@0	2535	carry = ys >> 32;
michael@0	2536	y = *bx - (ys & FFFFFFFF) - borrow;
michael@0	2537	borrow = y >> 32 & (ULong)1;
michael@0	2538	*bx++ = y & FFFFFFFF;
michael@0	2539	#else
michael@0	2540	#ifdef Pack_32
michael@0	2541	si = *sx++;
michael@0	2542	ys = (si & 0xffff) * q + carry;
michael@0	2543	zs = (si >> 16) * q + (ys >> 16);
michael@0	2544	carry = zs >> 16;
michael@0	2545	y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
michael@0	2546	borrow = (y & 0x10000) >> 16;
michael@0	2547	z = (*bx >> 16) - (zs & 0xffff) - borrow;
michael@0	2548	borrow = (z & 0x10000) >> 16;
michael@0	2549	Storeinc(bx, z, y);
michael@0	2550	#else
michael@0	2551	ys = *sx++ * q + carry;
michael@0	2552	carry = ys >> 16;
michael@0	2553	y = *bx - (ys & 0xffff) - borrow;
michael@0	2554	borrow = (y & 0x10000) >> 16;
michael@0	2555	*bx++ = y & 0xffff;
michael@0	2556	#endif
michael@0	2557	#endif
michael@0	2558	}
michael@0	2559	while(sx <= sxe);
michael@0	2560	if (!*bxe) {
michael@0	2561	bx = b->x;
michael@0	2562	while(--bxe > bx && !*bxe)
michael@0	2563	--n;
michael@0	2564	b->wds = n;
michael@0	2565	}
michael@0	2566	}
michael@0	2567	if (cmp(b, S) >= 0) {
michael@0	2568	q++;
michael@0	2569	borrow = 0;
michael@0	2570	carry = 0;
michael@0	2571	bx = b->x;
michael@0	2572	sx = S->x;
michael@0	2573	do {
michael@0	2574	#ifdef ULLong
michael@0	2575	ys = *sx++ + carry;
michael@0	2576	carry = ys >> 32;
michael@0	2577	y = *bx - (ys & FFFFFFFF) - borrow;
michael@0	2578	borrow = y >> 32 & (ULong)1;
michael@0	2579	*bx++ = y & FFFFFFFF;
michael@0	2580	#else
michael@0	2581	#ifdef Pack_32
michael@0	2582	si = *sx++;
michael@0	2583	ys = (si & 0xffff) + carry;
michael@0	2584	zs = (si >> 16) + (ys >> 16);
michael@0	2585	carry = zs >> 16;
michael@0	2586	y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
michael@0	2587	borrow = (y & 0x10000) >> 16;
michael@0	2588	z = (*bx >> 16) - (zs & 0xffff) - borrow;
michael@0	2589	borrow = (z & 0x10000) >> 16;
michael@0	2590	Storeinc(bx, z, y);
michael@0	2591	#else
michael@0	2592	ys = *sx++ + carry;
michael@0	2593	carry = ys >> 16;
michael@0	2594	y = *bx - (ys & 0xffff) - borrow;
michael@0	2595	borrow = (y & 0x10000) >> 16;
michael@0	2596	*bx++ = y & 0xffff;
michael@0	2597	#endif
michael@0	2598	#endif
michael@0	2599	}
michael@0	2600	while(sx <= sxe);
michael@0	2601	bx = b->x;
michael@0	2602	bxe = bx + n;
michael@0	2603	if (!*bxe) {
michael@0	2604	while(--bxe > bx && !*bxe)
michael@0	2605	--n;
michael@0	2606	b->wds = n;
michael@0	2607	}
michael@0	2608	}
michael@0	2609	return q;
michael@0	2610	}
michael@0	2611
michael@0	2612	#ifndef MULTIPLE_THREADS
michael@0	2613	static char *dtoa_result;
michael@0	2614	#endif
michael@0	2615
michael@0	2616	static char *
michael@0	2617	#ifdef KR_headers
michael@0	2618	rv_alloc(i) int i;
michael@0	2619	#else
michael@0	2620	rv_alloc(int i)
michael@0	2621	#endif
michael@0	2622	{
michael@0	2623	int j, k, *r;
michael@0	2624
michael@0	2625	j = sizeof(ULong);
michael@0	2626	for(k = 0;
michael@0	2627	sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= i;
michael@0	2628	j <<= 1)
michael@0	2629	k++;
michael@0	2630	r = (int*)Balloc(k);
michael@0	2631	*r = k;
michael@0	2632	return
michael@0	2633	#ifndef MULTIPLE_THREADS
michael@0	2634	dtoa_result =
michael@0	2635	#endif
michael@0	2636	(char *)(r+1);
michael@0	2637	}
michael@0	2638
michael@0	2639	static char *
michael@0	2640	#ifdef KR_headers
michael@0	2641	nrv_alloc(s, rve, n) char *s, **rve; int n;
michael@0	2642	#else
michael@0	2643	nrv_alloc(char *s, char **rve, int n)
michael@0	2644	#endif
michael@0	2645	{
michael@0	2646	char *rv, *t;
michael@0	2647
michael@0	2648	t = rv = rv_alloc(n);
michael@0	2649	while(*t = *s++) t++;
michael@0	2650	if (rve)
michael@0	2651	*rve = t;
michael@0	2652	return rv;
michael@0	2653	}
michael@0	2654
michael@0	2655	/* freedtoa(s) must be used to free values s returned by dtoa
michael@0	2656	* when MULTIPLE_THREADS is #defined. It should be used in all cases,
michael@0	2657	* but for consistency with earlier versions of dtoa, it is optional
michael@0	2658	* when MULTIPLE_THREADS is not defined.
michael@0	2659	*/
michael@0	2660
michael@0	2661	static void
michael@0	2662	#ifdef KR_headers
michael@0	2663	freedtoa(s) char *s;
michael@0	2664	#else
michael@0	2665	freedtoa(char *s)
michael@0	2666	#endif
michael@0	2667	{
michael@0	2668	Bigint *b = (Bigint *)((int *)s - 1);
michael@0	2669	b->maxwds = 1 << (b->k = *(int*)b);
michael@0	2670	Bfree(b);
michael@0	2671	#ifndef MULTIPLE_THREADS
michael@0	2672	if (s == dtoa_result)
michael@0	2673	dtoa_result = 0;
michael@0	2674	#endif
michael@0	2675	}
michael@0	2676
michael@0	2677	/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
michael@0	2678	*
michael@0	2679	* Inspired by "How to Print Floating-Point Numbers Accurately" by
michael@0	2680	* Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
michael@0	2681	*
michael@0	2682	* Modifications:
michael@0	2683	* 1. Rather than iterating, we use a simple numeric overestimate
michael@0	2684	* to determine k = floor(log10(d)). We scale relevant
michael@0	2685	* quantities using O(log2(k)) rather than O(k) multiplications.
michael@0	2686	* 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
michael@0	2687	* try to generate digits strictly left to right. Instead, we
michael@0	2688	* compute with fewer bits and propagate the carry if necessary
michael@0	2689	* when rounding the final digit up. This is often faster.
michael@0	2690	* 3. Under the assumption that input will be rounded nearest,
michael@0	2691	* mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
michael@0	2692	* That is, we allow equality in stopping tests when the
michael@0	2693	* round-nearest rule will give the same floating-point value
michael@0	2694	* as would satisfaction of the stopping test with strict
michael@0	2695	* inequality.
michael@0	2696	* 4. We remove common factors of powers of 2 from relevant
michael@0	2697	* quantities.
michael@0	2698	* 5. When converting floating-point integers less than 1e16,
michael@0	2699	* we use floating-point arithmetic rather than resorting
michael@0	2700	* to multiple-precision integers.
michael@0	2701	* 6. When asked to produce fewer than 15 digits, we first try
michael@0	2702	* to get by with floating-point arithmetic; we resort to
michael@0	2703	* multiple-precision integer arithmetic only if we cannot
michael@0	2704	* guarantee that the floating-point calculation has given
michael@0	2705	* the correctly rounded result. For k requested digits and
michael@0	2706	* "uniformly" distributed input, the probability is
michael@0	2707	* something like 10^(k-15) that we must resort to the Long
michael@0	2708	* calculation.
michael@0	2709	*/
michael@0	2710
michael@0	2711	static char *
michael@0	2712	dtoa
michael@0	2713	#ifdef KR_headers
michael@0	2714	(dd, mode, ndigits, decpt, sign, rve)
michael@0	2715	double dd; int mode, ndigits, *decpt, *sign; char **rve;
michael@0	2716	#else
michael@0	2717	(double dd, int mode, int ndigits, int *decpt, int *sign, char **rve)
michael@0	2718	#endif
michael@0	2719	{
michael@0	2720	/* Arguments ndigits, decpt, sign are similar to those
michael@0	2721	of ecvt and fcvt; trailing zeros are suppressed from
michael@0	2722	the returned string. If not null, *rve is set to point
michael@0	2723	to the end of the return value. If d is +-Infinity or NaN,
michael@0	2724	then *decpt is set to 9999.
michael@0	2725
michael@0	2726	mode:
michael@0	2727	0 ==> shortest string that yields d when read in
michael@0	2728	and rounded to nearest.
michael@0	2729	1 ==> like 0, but with Steele & White stopping rule;
michael@0	2730	e.g. with IEEE P754 arithmetic , mode 0 gives
michael@0	2731	1e23 whereas mode 1 gives 9.999999999999999e22.
michael@0	2732	2 ==> max(1,ndigits) significant digits. This gives a
michael@0	2733	return value similar to that of ecvt, except
michael@0	2734	that trailing zeros are suppressed.
michael@0	2735	3 ==> through ndigits past the decimal point. This
michael@0	2736	gives a return value similar to that from fcvt,
michael@0	2737	except that trailing zeros are suppressed, and
michael@0	2738	ndigits can be negative.
michael@0	2739	4,5 ==> similar to 2 and 3, respectively, but (in
michael@0	2740	round-nearest mode) with the tests of mode 0 to
michael@0	2741	possibly return a shorter string that rounds to d.
michael@0	2742	With IEEE arithmetic and compilation with
michael@0	2743	-DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
michael@0	2744	as modes 2 and 3 when FLT_ROUNDS != 1.
michael@0	2745	6-9 ==> Debugging modes similar to mode - 4: don't try
michael@0	2746	fast floating-point estimate (if applicable).
michael@0	2747
michael@0	2748	Values of mode other than 0-9 are treated as mode 0.
michael@0	2749
michael@0	2750	Sufficient space is allocated to the return value
michael@0	2751	to hold the suppressed trailing zeros.
michael@0	2752	*/
michael@0	2753
michael@0	2754	int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
michael@0	2755	j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
michael@0	2756	spec_case, try_quick;
michael@0	2757	Long L;
michael@0	2758	#ifndef Sudden_Underflow
michael@0	2759	int denorm;
michael@0	2760	ULong x;
michael@0	2761	#endif
michael@0	2762	Bigint *b, *b1, *delta, *mlo, *mhi, *S;
michael@0	2763	U d, d2, eps;
michael@0	2764	double ds;
michael@0	2765	char *s, *s0;
michael@0	2766	#ifdef Honor_FLT_ROUNDS
michael@0	2767	int rounding;
michael@0	2768	#endif
michael@0	2769	#ifdef SET_INEXACT
michael@0	2770	int inexact, oldinexact;
michael@0	2771	#endif
michael@0	2772
michael@0	2773	#ifndef MULTIPLE_THREADS
michael@0	2774	if (dtoa_result) {
michael@0	2775	freedtoa(dtoa_result);
michael@0	2776	dtoa_result = 0;
michael@0	2777	}
michael@0	2778	#endif
michael@0	2779
michael@0	2780	dval(d) = dd;
michael@0	2781	if (word0(d) & Sign_bit) {
michael@0	2782	/* set sign for everything, including 0's and NaNs */
michael@0	2783	*sign = 1;
michael@0	2784	word0(d) &= ~Sign_bit; /* clear sign bit */
michael@0	2785	}
michael@0	2786	else
michael@0	2787	*sign = 0;
michael@0	2788
michael@0	2789	#if defined(IEEE_Arith) + defined(VAX)
michael@0	2790	#ifdef IEEE_Arith
michael@0	2791	if ((word0(d) & Exp_mask) == Exp_mask)
michael@0	2792	#else
michael@0	2793	if (word0(d) == 0x8000)
michael@0	2794	#endif
michael@0	2795	{
michael@0	2796	/* Infinity or NaN */
michael@0	2797	*decpt = 9999;
michael@0	2798	#ifdef IEEE_Arith
michael@0	2799	if (!word1(d) && !(word0(d) & 0xfffff))
michael@0	2800	return nrv_alloc("Infinity", rve, 8);
michael@0	2801	#endif
michael@0	2802	return nrv_alloc("NaN", rve, 3);
michael@0	2803	}
michael@0	2804	#endif
michael@0	2805	#ifdef IBM
michael@0	2806	dval(d) += 0; /* normalize */
michael@0	2807	#endif
michael@0	2808	if (!dval(d)) {
michael@0	2809	*decpt = 1;
michael@0	2810	return nrv_alloc("0", rve, 1);
michael@0	2811	}
michael@0	2812
michael@0	2813	#ifdef SET_INEXACT
michael@0	2814	try_quick = oldinexact = get_inexact();
michael@0	2815	inexact = 1;
michael@0	2816	#endif
michael@0	2817	#ifdef Honor_FLT_ROUNDS
michael@0	2818	if ((rounding = Flt_Rounds) >= 2) {
michael@0	2819	if (*sign)
michael@0	2820	rounding = rounding == 2 ? 0 : 2;
michael@0	2821	else
michael@0	2822	if (rounding != 2)
michael@0	2823	rounding = 0;
michael@0	2824	}
michael@0	2825	#endif
michael@0	2826
michael@0	2827	b = d2b(dval(d), &be, &bbits);
michael@0	2828	#ifdef Sudden_Underflow
michael@0	2829	i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
michael@0	2830	#else
michael@0	2831	if (i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1))) {
michael@0	2832	#endif
michael@0	2833	dval(d2) = dval(d);
michael@0	2834	word0(d2) &= Frac_mask1;
michael@0	2835	word0(d2) |= Exp_11;
michael@0	2836	#ifdef IBM
michael@0	2837	if (j = 11 - hi0bits(word0(d2) & Frac_mask))
michael@0	2838	dval(d2) /= 1 << j;
michael@0	2839	#endif
michael@0	2840
michael@0	2841	/* log(x) ~=~ log(1.5) + (x-1.5)/1.5
michael@0	2842	* log10(x) = log(x) / log(10)
michael@0	2843	* ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
michael@0	2844	* log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
michael@0	2845	*
michael@0	2846	* This suggests computing an approximation k to log10(d) by
michael@0	2847	*
michael@0	2848	* k = (i - Bias)*0.301029995663981
michael@0	2849	* + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
michael@0	2850	*
michael@0	2851	* We want k to be too large rather than too small.
michael@0	2852	* The error in the first-order Taylor series approximation
michael@0	2853	* is in our favor, so we just round up the constant enough
michael@0	2854	* to compensate for any error in the multiplication of
michael@0	2855	* (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
michael@0	2856	* and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
michael@0	2857	* adding 1e-13 to the constant term more than suffices.
michael@0	2858	* Hence we adjust the constant term to 0.1760912590558.
michael@0	2859	* (We could get a more accurate k by invoking log10,
michael@0	2860	* but this is probably not worthwhile.)
michael@0	2861	*/
michael@0	2862
michael@0	2863	i -= Bias;
michael@0	2864	#ifdef IBM
michael@0	2865	i <<= 2;
michael@0	2866	i += j;
michael@0	2867	#endif
michael@0	2868	#ifndef Sudden_Underflow
michael@0	2869	denorm = 0;
michael@0	2870	}
michael@0	2871	else {
michael@0	2872	/* d is denormalized */
michael@0	2873
michael@0	2874	i = bbits + be + (Bias + (P-1) - 1);
michael@0	2875	x = i > 32 ? word0(d) << 64 - i | word1(d) >> i - 32
michael@0	2876	: word1(d) << 32 - i;
michael@0	2877	dval(d2) = x;
michael@0	2878	word0(d2) -= 31*Exp_msk1; /* adjust exponent */
michael@0	2879	i -= (Bias + (P-1) - 1) + 1;
michael@0	2880	denorm = 1;
michael@0	2881	}
michael@0	2882	#endif
michael@0	2883	ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
michael@0	2884	k = (int)ds;
michael@0	2885	if (ds < 0. && ds != k)
michael@0	2886	k--; /* want k = floor(ds) */
michael@0	2887	k_check = 1;
michael@0	2888	if (k >= 0 && k <= Ten_pmax) {
michael@0	2889	if (dval(d) < tens[k])
michael@0	2890	k--;
michael@0	2891	k_check = 0;
michael@0	2892	}
michael@0	2893	j = bbits - i - 1;
michael@0	2894	if (j >= 0) {
michael@0	2895	b2 = 0;
michael@0	2896	s2 = j;
michael@0	2897	}
michael@0	2898	else {
michael@0	2899	b2 = -j;
michael@0	2900	s2 = 0;
michael@0	2901	}
michael@0	2902	if (k >= 0) {
michael@0	2903	b5 = 0;
michael@0	2904	s5 = k;
michael@0	2905	s2 += k;
michael@0	2906	}
michael@0	2907	else {
michael@0	2908	b2 -= k;
michael@0	2909	b5 = -k;
michael@0	2910	s5 = 0;
michael@0	2911	}
michael@0	2912	if (mode < 0 || mode > 9)
michael@0	2913	mode = 0;
michael@0	2914
michael@0	2915	#ifndef SET_INEXACT
michael@0	2916	#ifdef Check_FLT_ROUNDS
michael@0	2917	try_quick = Rounding == 1;
michael@0	2918	#else
michael@0	2919	try_quick = 1;
michael@0	2920	#endif
michael@0	2921	#endif /*SET_INEXACT*/
michael@0	2922
michael@0	2923	if (mode > 5) {
michael@0	2924	mode -= 4;
michael@0	2925	try_quick = 0;
michael@0	2926	}
michael@0	2927	leftright = 1;
michael@0	2928	switch(mode) {
michael@0	2929	case 0:
michael@0	2930	case 1:
michael@0	2931	ilim = ilim1 = -1;
michael@0	2932	i = 18;
michael@0	2933	ndigits = 0;
michael@0	2934	break;
michael@0	2935	case 2:
michael@0	2936	leftright = 0;
michael@0	2937	/* no break */
michael@0	2938	case 4:
michael@0	2939	if (ndigits <= 0)
michael@0	2940	ndigits = 1;
michael@0	2941	ilim = ilim1 = i = ndigits;
michael@0	2942	break;
michael@0	2943	case 3:
michael@0	2944	leftright = 0;
michael@0	2945	/* no break */
michael@0	2946	case 5:
michael@0	2947	i = ndigits + k + 1;
michael@0	2948	ilim = i;
michael@0	2949	ilim1 = i - 1;
michael@0	2950	if (i <= 0)
michael@0	2951	i = 1;
michael@0	2952	}
michael@0	2953	s = s0 = rv_alloc(i);
michael@0	2954
michael@0	2955	#ifdef Honor_FLT_ROUNDS
michael@0	2956	if (mode > 1 && rounding != 1)
michael@0	2957	leftright = 0;
michael@0	2958	#endif
michael@0	2959
michael@0	2960	if (ilim >= 0 && ilim <= Quick_max && try_quick) {
michael@0	2961
michael@0	2962	/* Try to get by with floating-point arithmetic. */
michael@0	2963
michael@0	2964	i = 0;
michael@0	2965	dval(d2) = dval(d);
michael@0	2966	k0 = k;
michael@0	2967	ilim0 = ilim;
michael@0	2968	ieps = 2; /* conservative */
michael@0	2969	if (k > 0) {
michael@0	2970	ds = tens[k&0xf];
michael@0	2971	j = k >> 4;
michael@0	2972	if (j & Bletch) {
michael@0	2973	/* prevent overflows */
michael@0	2974	j &= Bletch - 1;
michael@0	2975	dval(d) /= bigtens[n_bigtens-1];
michael@0	2976	ieps++;
michael@0	2977	}
michael@0	2978	for(; j; j >>= 1, i++)
michael@0	2979	if (j & 1) {
michael@0	2980	ieps++;
michael@0	2981	ds *= bigtens[i];
michael@0	2982	}
michael@0	2983	dval(d) /= ds;
michael@0	2984	}
michael@0	2985	else if (j1 = -k) {
michael@0	2986	dval(d) *= tens[j1 & 0xf];
michael@0	2987	for(j = j1 >> 4; j; j >>= 1, i++)
michael@0	2988	if (j & 1) {
michael@0	2989	ieps++;
michael@0	2990	dval(d) *= bigtens[i];
michael@0	2991	}
michael@0	2992	}
michael@0	2993	if (k_check && dval(d) < 1. && ilim > 0) {
michael@0	2994	if (ilim1 <= 0)
michael@0	2995	goto fast_failed;
michael@0	2996	ilim = ilim1;
michael@0	2997	k--;
michael@0	2998	dval(d) *= 10.;
michael@0	2999	ieps++;
michael@0	3000	}
michael@0	3001	dval(eps) = ieps*dval(d) + 7.;
michael@0	3002	word0(eps) -= (P-1)*Exp_msk1;
michael@0	3003	if (ilim == 0) {
michael@0	3004	S = mhi = 0;
michael@0	3005	dval(d) -= 5.;
michael@0	3006	if (dval(d) > dval(eps))
michael@0	3007	goto one_digit;
michael@0	3008	if (dval(d) < -dval(eps))
michael@0	3009	goto no_digits;
michael@0	3010	goto fast_failed;
michael@0	3011	}
michael@0	3012	#ifndef No_leftright
michael@0	3013	if (leftright) {
michael@0	3014	/* Use Steele & White method of only
michael@0	3015	* generating digits needed.
michael@0	3016	*/
michael@0	3017	dval(eps) = 0.5/tens[ilim-1] - dval(eps);
michael@0	3018	for(i = 0;;) {
michael@0	3019	L = dval(d);
michael@0	3020	dval(d) -= L;
michael@0	3021	*s++ = '0' + (int)L;
michael@0	3022	if (dval(d) < dval(eps))
michael@0	3023	goto ret1;
michael@0	3024	if (1. - dval(d) < dval(eps))
michael@0	3025	goto bump_up;
michael@0	3026	if (++i >= ilim)
michael@0	3027	break;
michael@0	3028	dval(eps) *= 10.;
michael@0	3029	dval(d) *= 10.;
michael@0	3030	}
michael@0	3031	}
michael@0	3032	else {
michael@0	3033	#endif
michael@0	3034	/* Generate ilim digits, then fix them up. */
michael@0	3035	dval(eps) *= tens[ilim-1];
michael@0	3036	for(i = 1;; i++, dval(d) *= 10.) {
michael@0	3037	L = (Long)(dval(d));
michael@0	3038	if (!(dval(d) -= L))
michael@0	3039	ilim = i;
michael@0	3040	*s++ = '0' + (int)L;
michael@0	3041	if (i == ilim) {
michael@0	3042	if (dval(d) > 0.5 + dval(eps))
michael@0	3043	goto bump_up;
michael@0	3044	else if (dval(d) < 0.5 - dval(eps)) {
michael@0	3045	while(*--s == '0');
michael@0	3046	s++;
michael@0	3047	goto ret1;
michael@0	3048	}
michael@0	3049	break;
michael@0	3050	}
michael@0	3051	}
michael@0	3052	#ifndef No_leftright
michael@0	3053	}
michael@0	3054	#endif
michael@0	3055	fast_failed:
michael@0	3056	s = s0;
michael@0	3057	dval(d) = dval(d2);
michael@0	3058	k = k0;
michael@0	3059	ilim = ilim0;
michael@0	3060	}
michael@0	3061
michael@0	3062	/* Do we have a "small" integer? */
michael@0	3063
michael@0	3064	if (be >= 0 && k <= Int_max) {
michael@0	3065	/* Yes. */
michael@0	3066	ds = tens[k];
michael@0	3067	if (ndigits < 0 && ilim <= 0) {
michael@0	3068	S = mhi = 0;
michael@0	3069	if (ilim < 0 || dval(d) <= 5*ds)
michael@0	3070	goto no_digits;
michael@0	3071	goto one_digit;
michael@0	3072	}
michael@0	3073	for(i = 1; i <= k+1; i++, dval(d) *= 10.) {
michael@0	3074	L = (Long)(dval(d) / ds);
michael@0	3075	dval(d) -= L*ds;
michael@0	3076	#ifdef Check_FLT_ROUNDS
michael@0	3077	/* If FLT_ROUNDS == 2, L will usually be high by 1 */
michael@0	3078	if (dval(d) < 0) {
michael@0	3079	L--;
michael@0	3080	dval(d) += ds;
michael@0	3081	}
michael@0	3082	#endif
michael@0	3083	*s++ = '0' + (int)L;
michael@0	3084	if (!dval(d)) {
michael@0	3085	#ifdef SET_INEXACT
michael@0	3086	inexact = 0;
michael@0	3087	#endif
michael@0	3088	break;
michael@0	3089	}
michael@0	3090	if (i == ilim) {
michael@0	3091	#ifdef Honor_FLT_ROUNDS
michael@0	3092	if (mode > 1)
michael@0	3093	switch(rounding) {
michael@0	3094	case 0: goto ret1;
michael@0	3095	case 2: goto bump_up;
michael@0	3096	}
michael@0	3097	#endif
michael@0	3098	dval(d) += dval(d);
michael@0	3099	if (dval(d) > ds || dval(d) == ds && L & 1) {
michael@0	3100	bump_up:
michael@0	3101	while(*--s == '9')
michael@0	3102	if (s == s0) {
michael@0	3103	k++;
michael@0	3104	*s = '0';
michael@0	3105	break;
michael@0	3106	}
michael@0	3107	++*s++;
michael@0	3108	}
michael@0	3109	break;
michael@0	3110	}
michael@0	3111	}
michael@0	3112	goto ret1;
michael@0	3113	}
michael@0	3114
michael@0	3115	m2 = b2;
michael@0	3116	m5 = b5;
michael@0	3117	mhi = mlo = 0;
michael@0	3118	if (leftright) {
michael@0	3119	i =
michael@0	3120	#ifndef Sudden_Underflow
michael@0	3121	denorm ? be + (Bias + (P-1) - 1 + 1) :
michael@0	3122	#endif
michael@0	3123	#ifdef IBM
michael@0	3124	1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
michael@0	3125	#else
michael@0	3126	1 + P - bbits;
michael@0	3127	#endif
michael@0	3128	b2 += i;
michael@0	3129	s2 += i;
michael@0	3130	mhi = i2b(1);
michael@0	3131	}
michael@0	3132	if (m2 > 0 && s2 > 0) {
michael@0	3133	i = m2 < s2 ? m2 : s2;
michael@0	3134	b2 -= i;
michael@0	3135	m2 -= i;
michael@0	3136	s2 -= i;
michael@0	3137	}
michael@0	3138	if (b5 > 0) {
michael@0	3139	if (leftright) {
michael@0	3140	if (m5 > 0) {
michael@0	3141	mhi = pow5mult(mhi, m5);
michael@0	3142	b1 = mult(mhi, b);
michael@0	3143	Bfree(b);
michael@0	3144	b = b1;
michael@0	3145	}
michael@0	3146	if (j = b5 - m5)
michael@0	3147	b = pow5mult(b, j);
michael@0	3148	}
michael@0	3149	else
michael@0	3150	b = pow5mult(b, b5);
michael@0	3151	}
michael@0	3152	S = i2b(1);
michael@0	3153	if (s5 > 0)
michael@0	3154	S = pow5mult(S, s5);
michael@0	3155
michael@0	3156	/* Check for special case that d is a normalized power of 2. */
michael@0	3157
michael@0	3158	spec_case = 0;
michael@0	3159	if ((mode < 2 || leftright)
michael@0	3160	#ifdef Honor_FLT_ROUNDS
michael@0	3161	&& rounding == 1
michael@0	3162	#endif
michael@0	3163	) {
michael@0	3164	if (!word1(d) && !(word0(d) & Bndry_mask)
michael@0	3165	#ifndef Sudden_Underflow
michael@0	3166	&& word0(d) & (Exp_mask & ~Exp_msk1)
michael@0	3167	#endif
michael@0	3168	) {
michael@0	3169	/* The special case */
michael@0	3170	b2 += Log2P;
michael@0	3171	s2 += Log2P;
michael@0	3172	spec_case = 1;
michael@0	3173	}
michael@0	3174	}
michael@0	3175
michael@0	3176	/* Arrange for convenient computation of quotients:
michael@0	3177	* shift left if necessary so divisor has 4 leading 0 bits.
michael@0	3178	*
michael@0	3179	* Perhaps we should just compute leading 28 bits of S once
michael@0	3180	* and for all and pass them and a shift to quorem, so it
michael@0	3181	* can do shifts and ors to compute the numerator for q.
michael@0	3182	*/
michael@0	3183	#ifdef Pack_32
michael@0	3184	if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f)
michael@0	3185	i = 32 - i;
michael@0	3186	#else
michael@0	3187	if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf)
michael@0	3188	i = 16 - i;
michael@0	3189	#endif
michael@0	3190	if (i > 4) {
michael@0	3191	i -= 4;
michael@0	3192	b2 += i;
michael@0	3193	m2 += i;
michael@0	3194	s2 += i;
michael@0	3195	}
michael@0	3196	else if (i < 4) {
michael@0	3197	i += 28;
michael@0	3198	b2 += i;
michael@0	3199	m2 += i;
michael@0	3200	s2 += i;
michael@0	3201	}
michael@0	3202	if (b2 > 0)
michael@0	3203	b = lshift(b, b2);
michael@0	3204	if (s2 > 0)
michael@0	3205	S = lshift(S, s2);
michael@0	3206	if (k_check) {
michael@0	3207	if (cmp(b,S) < 0) {
michael@0	3208	k--;
michael@0	3209	b = multadd(b, 10, 0); /* we botched the k estimate */
michael@0	3210	if (leftright)
michael@0	3211	mhi = multadd(mhi, 10, 0);
michael@0	3212	ilim = ilim1;
michael@0	3213	}
michael@0	3214	}
michael@0	3215	if (ilim <= 0 && (mode == 3 || mode == 5)) {
michael@0	3216	if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
michael@0	3217	/* no digits, fcvt style */
michael@0	3218	no_digits:
michael@0	3219	k = -1 - ndigits;
michael@0	3220	goto ret;
michael@0	3221	}
michael@0	3222	one_digit:
michael@0	3223	*s++ = '1';
michael@0	3224	k++;
michael@0	3225	goto ret;
michael@0	3226	}
michael@0	3227	if (leftright) {
michael@0	3228	if (m2 > 0)
michael@0	3229	mhi = lshift(mhi, m2);
michael@0	3230
michael@0	3231	/* Compute mlo -- check for special case
michael@0	3232	* that d is a normalized power of 2.
michael@0	3233	*/
michael@0	3234
michael@0	3235	mlo = mhi;
michael@0	3236	if (spec_case) {
michael@0	3237	mhi = Balloc(mhi->k);
michael@0	3238	Bcopy(mhi, mlo);
michael@0	3239	mhi = lshift(mhi, Log2P);
michael@0	3240	}
michael@0	3241
michael@0	3242	for(i = 1;;i++) {
michael@0	3243	dig = quorem(b,S) + '0';
michael@0	3244	/* Do we yet have the shortest decimal string
michael@0	3245	* that will round to d?
michael@0	3246	*/
michael@0	3247	j = cmp(b, mlo);
michael@0	3248	delta = diff(S, mhi);
michael@0	3249	j1 = delta->sign ? 1 : cmp(b, delta);
michael@0	3250	Bfree(delta);
michael@0	3251	#ifndef ROUND_BIASED
michael@0	3252	if (j1 == 0 && mode != 1 && !(word1(d) & 1)
michael@0	3253	#ifdef Honor_FLT_ROUNDS
michael@0	3254	&& rounding >= 1
michael@0	3255	#endif
michael@0	3256	) {
michael@0	3257	if (dig == '9')
michael@0	3258	goto round_9_up;
michael@0	3259	if (j > 0)
michael@0	3260	dig++;
michael@0	3261	#ifdef SET_INEXACT
michael@0	3262	else if (!b->x[0] && b->wds <= 1)
michael@0	3263	inexact = 0;
michael@0	3264	#endif
michael@0	3265	*s++ = dig;
michael@0	3266	goto ret;
michael@0	3267	}
michael@0	3268	#endif
michael@0	3269	if (j < 0 || j == 0 && mode != 1
michael@0	3270	#ifndef ROUND_BIASED
michael@0	3271	&& !(word1(d) & 1)
michael@0	3272	#endif
michael@0	3273	) {
michael@0	3274	if (!b->x[0] && b->wds <= 1) {
michael@0	3275	#ifdef SET_INEXACT
michael@0	3276	inexact = 0;
michael@0	3277	#endif
michael@0	3278	goto accept_dig;
michael@0	3279	}
michael@0	3280	#ifdef Honor_FLT_ROUNDS
michael@0	3281	if (mode > 1)
michael@0	3282	switch(rounding) {
michael@0	3283	case 0: goto accept_dig;
michael@0	3284	case 2: goto keep_dig;
michael@0	3285	}
michael@0	3286	#endif /*Honor_FLT_ROUNDS*/
michael@0	3287	if (j1 > 0) {
michael@0	3288	b = lshift(b, 1);
michael@0	3289	j1 = cmp(b, S);
michael@0	3290	if ((j1 > 0 || j1 == 0 && dig & 1)
michael@0	3291	&& dig++ == '9')
michael@0	3292	goto round_9_up;
michael@0	3293	}
michael@0	3294	accept_dig:
michael@0	3295	*s++ = dig;
michael@0	3296	goto ret;
michael@0	3297	}
michael@0	3298	if (j1 > 0) {
michael@0	3299	#ifdef Honor_FLT_ROUNDS
michael@0	3300	if (!rounding)
michael@0	3301	goto accept_dig;
michael@0	3302	#endif
michael@0	3303	if (dig == '9') { /* possible if i == 1 */
michael@0	3304	round_9_up:
michael@0	3305	*s++ = '9';
michael@0	3306	goto roundoff;
michael@0	3307	}
michael@0	3308	*s++ = dig + 1;
michael@0	3309	goto ret;
michael@0	3310	}
michael@0	3311	#ifdef Honor_FLT_ROUNDS
michael@0	3312	keep_dig:
michael@0	3313	#endif
michael@0	3314	*s++ = dig;
michael@0	3315	if (i == ilim)
michael@0	3316	break;
michael@0	3317	b = multadd(b, 10, 0);
michael@0	3318	if (mlo == mhi)
michael@0	3319	mlo = mhi = multadd(mhi, 10, 0);
michael@0	3320	else {
michael@0	3321	mlo = multadd(mlo, 10, 0);
michael@0	3322	mhi = multadd(mhi, 10, 0);
michael@0	3323	}
michael@0	3324	}
michael@0	3325	}
michael@0	3326	else
michael@0	3327	for(i = 1;; i++) {
michael@0	3328	*s++ = dig = quorem(b,S) + '0';
michael@0	3329	if (!b->x[0] && b->wds <= 1) {
michael@0	3330	#ifdef SET_INEXACT
michael@0	3331	inexact = 0;
michael@0	3332	#endif
michael@0	3333	goto ret;
michael@0	3334	}
michael@0	3335	if (i >= ilim)
michael@0	3336	break;
michael@0	3337	b = multadd(b, 10, 0);
michael@0	3338	}
michael@0	3339
michael@0	3340	/* Round off last digit */
michael@0	3341
michael@0	3342	#ifdef Honor_FLT_ROUNDS
michael@0	3343	switch(rounding) {
michael@0	3344	case 0: goto trimzeros;
michael@0	3345	case 2: goto roundoff;
michael@0	3346	}
michael@0	3347	#endif
michael@0	3348	b = lshift(b, 1);
michael@0	3349	j = cmp(b, S);
michael@0	3350	if (j > 0 || j == 0 && dig & 1) {
michael@0	3351	roundoff:
michael@0	3352	while(*--s == '9')
michael@0	3353	if (s == s0) {
michael@0	3354	k++;
michael@0	3355	*s++ = '1';
michael@0	3356	goto ret;
michael@0	3357	}
michael@0	3358	++*s++;
michael@0	3359	}
michael@0	3360	else {
michael@0	3361	#ifdef Honor_FLT_ROUNDS
michael@0	3362	trimzeros:
michael@0	3363	#endif
michael@0	3364	while(*--s == '0');
michael@0	3365	s++;
michael@0	3366	}
michael@0	3367	ret:
michael@0	3368	Bfree(S);
michael@0	3369	if (mhi) {
michael@0	3370	if (mlo && mlo != mhi)
michael@0	3371	Bfree(mlo);
michael@0	3372	Bfree(mhi);
michael@0	3373	}
michael@0	3374	ret1:
michael@0	3375	#ifdef SET_INEXACT
michael@0	3376	if (inexact) {
michael@0	3377	if (!oldinexact) {
michael@0	3378	word0(d) = Exp_1 + (70 << Exp_shift);
michael@0	3379	word1(d) = 0;
michael@0	3380	dval(d) += 1.;
michael@0	3381	}
michael@0	3382	}
michael@0	3383	else if (!oldinexact)
michael@0	3384	clear_inexact();
michael@0	3385	#endif
michael@0	3386	Bfree(b);
michael@0	3387	*s = 0;
michael@0	3388	*decpt = k + 1;
michael@0	3389	if (rve)
michael@0	3390	*rve = s;
michael@0	3391	return s0;
michael@0	3392	}
michael@0	3393	#ifdef __cplusplus
michael@0	3394	}
michael@0	3395	#endif
michael@0	3396
michael@0	3397	PR_IMPLEMENT(PRStatus)
michael@0	3398	PR_dtoa(PRFloat64 d, PRIntn mode, PRIntn ndigits,
michael@0	3399	PRIntn *decpt, PRIntn *sign, char **rve, char *buf, PRSize bufsize)
michael@0	3400	{
michael@0	3401	char *result;
michael@0	3402	PRSize resultlen;
michael@0	3403	PRStatus rv = PR_FAILURE;
michael@0	3404
michael@0	3405	if (!_pr_initialized) _PR_ImplicitInitialization();
michael@0	3406
michael@0	3407	if (mode < 0 || mode > 3) {
michael@0	3408	PR_SetError(PR_INVALID_ARGUMENT_ERROR, 0);
michael@0	3409	return rv;
michael@0	3410	}
michael@0	3411	result = dtoa(d, mode, ndigits, decpt, sign, rve);
michael@0	3412	if (!result) {
michael@0	3413	PR_SetError(PR_OUT_OF_MEMORY_ERROR, 0);
michael@0	3414	return rv;
michael@0	3415	}
michael@0	3416	resultlen = strlen(result)+1;
michael@0	3417	if (bufsize < resultlen) {
michael@0	3418	PR_SetError(PR_BUFFER_OVERFLOW_ERROR, 0);
michael@0	3419	} else {
michael@0	3420	memcpy(buf, result, resultlen);
michael@0	3421	if (rve) {
michael@0	3422	*rve = buf + (*rve - result);
michael@0	3423	}
michael@0	3424	rv = PR_SUCCESS;
michael@0	3425	}
michael@0	3426	freedtoa(result);
michael@0	3427	return rv;
michael@0	3428	}
michael@0	3429
michael@0	3430	/*
michael@0	3431	** conversion routines for floating point
michael@0	3432	** prcsn - number of digits of precision to generate floating
michael@0	3433	** point value.
michael@0	3434	** This should be reparameterized so that you can send in a
michael@0	3435	** prcn for the positive and negative ranges. For now,
michael@0	3436	** conform to the ECMA JavaScript spec which says numbers
michael@0	3437	** less than 1e-6 are in scientific notation.
michael@0	3438	** Also, the ECMA spec says that there should always be a
michael@0	3439	** '+' or '-' after the 'e' in scientific notation
michael@0	3440	*/
michael@0	3441	PR_IMPLEMENT(void)
michael@0	3442	PR_cnvtf(char *buf, int bufsz, int prcsn, double dfval)
michael@0	3443	{
michael@0	3444	PRIntn decpt, sign, numdigits;
michael@0	3445	char *num, *nump;
michael@0	3446	char *bufp = buf;
michael@0	3447	char *endnum;
michael@0	3448	U fval;
michael@0	3449
michael@0	3450	dval(fval) = dfval;
michael@0	3451	/* If anything fails, we store an empty string in 'buf' */
michael@0	3452	num = (char*)PR_MALLOC(bufsz);
michael@0	3453	if (num == NULL) {
michael@0	3454	buf[0] = '\0';
michael@0	3455	return;
michael@0	3456	}
michael@0	3457	/* XXX Why use mode 1? */
michael@0	3458	if (PR_dtoa(dval(fval),1,prcsn,&decpt,&sign,&endnum,num,bufsz)
michael@0	3459	== PR_FAILURE) {
michael@0	3460	buf[0] = '\0';
michael@0	3461	goto done;
michael@0	3462	}
michael@0	3463	numdigits = endnum - num;
michael@0	3464	nump = num;
michael@0	3465
michael@0	3466	if (sign &&
michael@0	3467	!(word0(fval) == Sign_bit && word1(fval) == 0) &&
michael@0	3468	!((word0(fval) & Exp_mask) == Exp_mask &&
michael@0	3469	(word1(fval) || (word0(fval) & 0xfffff)))) {
michael@0	3470	*bufp++ = '-';
michael@0	3471	}
michael@0	3472
michael@0	3473	if (decpt == 9999) {
michael@0	3474	while ((*bufp++ = *nump++) != 0) {} /* nothing to execute */
michael@0	3475	goto done;
michael@0	3476	}
michael@0	3477
michael@0	3478	if (decpt > (prcsn+1) || decpt < -(prcsn-1) || decpt < -5) {
michael@0	3479	*bufp++ = *nump++;
michael@0	3480	if (numdigits != 1) {
michael@0	3481	*bufp++ = '.';
michael@0	3482	}
michael@0	3483
michael@0	3484	while (*nump != '\0') {
michael@0	3485	*bufp++ = *nump++;
michael@0	3486	}
michael@0	3487	*bufp++ = 'e';
michael@0	3488	PR_snprintf(bufp, bufsz - (bufp - buf), "%+d", decpt-1);
michael@0	3489	} else if (decpt >= 0) {
michael@0	3490	if (decpt == 0) {
michael@0	3491	*bufp++ = '0';
michael@0	3492	} else {
michael@0	3493	while (decpt--) {
michael@0	3494	if (*nump != '\0') {
michael@0	3495	*bufp++ = *nump++;
michael@0	3496	} else {
michael@0	3497	*bufp++ = '0';
michael@0	3498	}
michael@0	3499	}
michael@0	3500	}
michael@0	3501	if (*nump != '\0') {
michael@0	3502	*bufp++ = '.';
michael@0	3503	while (*nump != '\0') {
michael@0	3504	*bufp++ = *nump++;
michael@0	3505	}
michael@0	3506	}
michael@0	3507	*bufp++ = '\0';
michael@0	3508	} else if (decpt < 0) {
michael@0	3509	*bufp++ = '0';
michael@0	3510	*bufp++ = '.';
michael@0	3511	while (decpt++) {
michael@0	3512	*bufp++ = '0';
michael@0	3513	}
michael@0	3514
michael@0	3515	while (*nump != '\0') {
michael@0	3516	*bufp++ = *nump++;
michael@0	3517	}
michael@0	3518	*bufp++ = '\0';
michael@0	3519	}
michael@0	3520	done:
michael@0	3521	PR_DELETE(num);
michael@0	3522	}