The Tor Browser: security/sandbox/chromium/base/third_party/dmg

security/sandbox/chromium/base/third_party/dmg_fp/dtoa.cc@44a2da4a2ab2 (annotated)

security/sandbox/chromium/base/third_party/dmg_fp/dtoa.cc

Fri, 16 Jan 2015 04:50:19 +0100

author: Michael Schloh von Bennewitz <michael@schloh.com>
date: Fri, 16 Jan 2015 04:50:19 +0100
branch: TOR_BUG_9701
changeset 13: 44a2da4a2ab2
permissions: -rw-r--r--

Replace accessor implementation with direct member state manipulation, by
request https://trac.torproject.org/projects/tor/ticket/9701#comment:32

 /****************************************************************
  *
  * The author of this software is David M. Gay.
  *
  * Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
  *
  * Permission to use, copy, modify, and distribute this software for any
  * purpose without fee is hereby granted, provided that this entire notice
  * is included in all copies of any software which is or includes a copy
  * or modification of this software and in all copies of the supporting
  * documentation for such software.
  *
  * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
  * WARRANTY.  IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY
  * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
  * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
  *
  ***************************************************************/
 /* Please send bug reports to David M. Gay (dmg at acm dot org,
  * with " at " changed at "@" and " dot " changed to ".").	*/
 /* On a machine with IEEE extended-precision registers, it is
  * necessary to specify double-precision (53-bit) rounding precision
  * before invoking strtod or dtoa.  If the machine uses (the equivalent
  * of) Intel 80x87 arithmetic, the call
  *	_control87(PC_53, MCW_PC);
  * does this with many compilers.  Whether this or another call is
  * appropriate depends on the compiler; for this to work, it may be
  * necessary to #include "float.h" or another system-dependent header
  * file.
  */
 /* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
  *
  * This strtod returns a nearest machine number to the input decimal
  * string (or sets errno to ERANGE).  With IEEE arithmetic, ties are
  * broken by the IEEE round-even rule.  Otherwise ties are broken by
  * biased rounding (add half and chop).
  *
  * Inspired loosely by William D. Clinger's paper "How to Read Floating
  * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
  *
  * Modifications:
  *
  *	1. We only require IEEE, IBM, or VAX double-precision
  *		arithmetic (not IEEE double-extended).
  *	2. We get by with floating-point arithmetic in a case that
  *		Clinger missed -- when we're computing d * 10^n
  *		for a small integer d and the integer n is not too
  *		much larger than 22 (the maximum integer k for which
  *		we can represent 10^k exactly), we may be able to
  *		compute (d*10^k) * 10^(e-k) with just one roundoff.
  *	3. Rather than a bit-at-a-time adjustment of the binary
  *		result in the hard case, we use floating-point
  *		arithmetic to determine the adjustment to within
  *		one bit; only in really hard cases do we need to
  *		compute a second residual.
  *	4. Because of 3., we don't need a large table of powers of 10
  *		for ten-to-e (just some small tables, e.g. of 10^k
  *		for 0 <= k <= 22).
  */
 /*
  * #define IEEE_8087 for IEEE-arithmetic machines where the least
  *	significant byte has the lowest address.
  * #define IEEE_MC68k for IEEE-arithmetic machines where the most
  *	significant byte has the lowest address.
  * #define Long int on machines with 32-bit ints and 64-bit longs.
  * #define IBM for IBM mainframe-style floating-point arithmetic.
  * #define VAX for VAX-style floating-point arithmetic (D_floating).
  * #define No_leftright to omit left-right logic in fast floating-point
  *	computation of dtoa.
  * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
  *	and strtod and dtoa should round accordingly.  Unless Trust_FLT_ROUNDS
  *	is also #defined, fegetround() will be queried for the rounding mode.
  *	Note that both FLT_ROUNDS and fegetround() are specified by the C99
  *	standard (and are specified to be consistent, with fesetround()
  *	affecting the value of FLT_ROUNDS), but that some (Linux) systems
  *	do not work correctly in this regard, so using fegetround() is more
  *	portable than using FLT_FOUNDS directly.
  * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
  *	and Honor_FLT_ROUNDS is not #defined.
  * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
  *	that use extended-precision instructions to compute rounded
  *	products and quotients) with IBM.
  * #define ROUND_BIASED for IEEE-format with biased rounding.
  * #define Inaccurate_Divide for IEEE-format with correctly rounded
  *	products but inaccurate quotients, e.g., for Intel i860.
  * #define NO_LONG_LONG on machines that do not have a "long long"
  *	integer type (of >= 64 bits).  On such machines, you can
  *	#define Just_16 to store 16 bits per 32-bit Long when doing
  *	high-precision integer arithmetic.  Whether this speeds things
  *	up or slows things down depends on the machine and the number
  *	being converted.  If long long is available and the name is
  *	something other than "long long", #define Llong to be the name,
  *	and if "unsigned Llong" does not work as an unsigned version of
  *	Llong, #define #ULLong to be the corresponding unsigned type.
  * #define KR_headers for old-style C function headers.
  * #define Bad_float_h if your system lacks a float.h or if it does not
  *	define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
  *	FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
  * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
  *	if memory is available and otherwise does something you deem
  *	appropriate.  If MALLOC is undefined, malloc will be invoked
  *	directly -- and assumed always to succeed.  Similarly, if you
  *	want something other than the system's free() to be called to
  *	recycle memory acquired from MALLOC, #define FREE to be the
  *	name of the alternate routine.  (FREE or free is only called in
  *	pathological cases, e.g., in a dtoa call after a dtoa return in
  *	mode 3 with thousands of digits requested.)
  * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
  *	memory allocations from a private pool of memory when possible.
  *	When used, the private pool is PRIVATE_MEM bytes long:  2304 bytes,
  *	unless #defined to be a different length.  This default length
  *	suffices to get rid of MALLOC calls except for unusual cases,
  *	such as decimal-to-binary conversion of a very long string of
  *	digits.  The longest string dtoa can return is about 751 bytes
  *	long.  For conversions by strtod of strings of 800 digits and
  *	all dtoa conversions in single-threaded executions with 8-byte
  *	pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte
  *	pointers, PRIVATE_MEM >= 7112 appears adequate.
  * #define NO_INFNAN_CHECK if you do not wish to have INFNAN_CHECK
  *	#defined automatically on IEEE systems.  On such systems,
  *	when INFNAN_CHECK is #defined, strtod checks
  *	for Infinity and NaN (case insensitively).  On some systems
  *	(e.g., some HP systems), it may be necessary to #define NAN_WORD0
  *	appropriately -- to the most significant word of a quiet NaN.
  *	(On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
  *	When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
  *	strtod also accepts (case insensitively) strings of the form
  *	NaN(x), where x is a string of hexadecimal digits and spaces;
  *	if there is only one string of hexadecimal digits, it is taken
  *	for the 52 fraction bits of the resulting NaN; if there are two
  *	or more strings of hex digits, the first is for the high 20 bits,
  *	the second and subsequent for the low 32 bits, with intervening
  *	white space ignored; but if this results in none of the 52
  *	fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0
  *	and NAN_WORD1 are used instead.
  * #define MULTIPLE_THREADS if the system offers preemptively scheduled
  *	multiple threads.  In this case, you must provide (or suitably
  *	#define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
  *	by FREE_DTOA_LOCK(n) for n = 0 or 1.  (The second lock, accessed
  *	in pow5mult, ensures lazy evaluation of only one copy of high
  *	powers of 5; omitting this lock would introduce a small
  *	probability of wasting memory, but would otherwise be harmless.)
  *	You must also invoke freedtoa(s) to free the value s returned by
  *	dtoa.  You may do so whether or not MULTIPLE_THREADS is #defined.
  * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
  *	avoids underflows on inputs whose result does not underflow.
  *	If you #define NO_IEEE_Scale on a machine that uses IEEE-format
  *	floating-point numbers and flushes underflows to zero rather
  *	than implementing gradual underflow, then you must also #define
  *	Sudden_Underflow.
  * #define USE_LOCALE to use the current locale's decimal_point value.
  * #define SET_INEXACT if IEEE arithmetic is being used and extra
  *	computation should be done to set the inexact flag when the
  *	result is inexact and avoid setting inexact when the result
  *	is exact.  In this case, dtoa.c must be compiled in
  *	an environment, perhaps provided by #include "dtoa.c" in a
  *	suitable wrapper, that defines two functions,
  *		int get_inexact(void);
  *		void clear_inexact(void);
  *	such that get_inexact() returns a nonzero value if the
  *	inexact bit is already set, and clear_inexact() sets the
  *	inexact bit to 0.  When SET_INEXACT is #defined, strtod
  *	also does extra computations to set the underflow and overflow
  *	flags when appropriate (i.e., when the result is tiny and
  *	inexact or when it is a numeric value rounded to +-infinity).
  * #define NO_ERRNO if strtod should not assign errno = ERANGE when
  *	the result overflows to +-Infinity or underflows to 0.
  * #define NO_HEX_FP to omit recognition of hexadecimal floating-point
  *	values by strtod.
  * #define NO_STRTOD_BIGCOMP (on IEEE-arithmetic systems only for now)
  *	to disable logic for "fast" testing of very long input strings
  *	to strtod.  This testing proceeds by initially truncating the
  *	input string, then if necessary comparing the whole string with
  *	a decimal expansion to decide close cases. This logic is only
  *	used for input more than STRTOD_DIGLIM digits long (default 40).
  */
 #define IEEE_8087
 #define NO_HEX_FP
 #ifndef Long
 #if __LP64__
 #define Long int
 #else
 #define Long long
 #endif
 #endif
 #ifndef ULong
 typedef unsigned Long ULong;
 #endif
 #ifdef DEBUG
 #include "stdio.h"
 #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
 #endif
 #include "stdlib.h"
 #include "string.h"
 #ifdef USE_LOCALE
 #include "locale.h"
 #endif
 #ifdef Honor_FLT_ROUNDS
 #ifndef Trust_FLT_ROUNDS
 #include <fenv.h>
 #endif
 #endif
 #ifdef MALLOC
 #ifdef KR_headers
 extern char *MALLOC();
 #else
 extern void *MALLOC(size_t);
 #endif
 #else
 #define MALLOC malloc
 #endif
 #ifndef Omit_Private_Memory
 #ifndef PRIVATE_MEM
 #define PRIVATE_MEM 2304
 #endif
 #define PRIVATE_mem ((unsigned)((PRIVATE_MEM+sizeof(double)-1)/sizeof(double)))
 static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
 #endif
 #undef IEEE_Arith
 #undef Avoid_Underflow
 #ifdef IEEE_MC68k
 #define IEEE_Arith
 #endif
 #ifdef IEEE_8087
 #define IEEE_Arith
 #endif
 #ifdef IEEE_Arith
 #ifndef NO_INFNAN_CHECK
 #undef INFNAN_CHECK
 #define INFNAN_CHECK
 #endif
 #else
 #undef INFNAN_CHECK
 #define NO_STRTOD_BIGCOMP
 #endif
 #include "errno.h"
 #ifdef Bad_float_h
 #ifdef IEEE_Arith
 #define DBL_DIG 15
 #define DBL_MAX_10_EXP 308
 #define DBL_MAX_EXP 1024
 #define FLT_RADIX 2
 #endif /*IEEE_Arith*/
 #ifdef IBM
 #define DBL_DIG 16
 #define DBL_MAX_10_EXP 75
 #define DBL_MAX_EXP 63
 #define FLT_RADIX 16
 #define DBL_MAX 7.2370055773322621e+75
 #endif
 #ifdef VAX
 #define DBL_DIG 16
 #define DBL_MAX_10_EXP 38
 #define DBL_MAX_EXP 127
 #define FLT_RADIX 2
 #define DBL_MAX 1.7014118346046923e+38
 #endif
 #ifndef LONG_MAX
 #define LONG_MAX 2147483647
 #endif
 #else /* ifndef Bad_float_h */
 #include "float.h"
 #endif /* Bad_float_h */
 #ifndef __MATH_H__
 #include "math.h"
 #endif
 namespace dmg_fp {
 #ifndef CONST
 #ifdef KR_headers
 #define CONST /* blank */
 #else
 #define CONST const
 #endif
 #endif
 #if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
 Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
 #endif
 typedef union { double d; ULong L[2]; } U;
 #ifdef IEEE_8087
 #define word0(x) (x)->L[1]
 #define word1(x) (x)->L[0]
 #else
 #define word0(x) (x)->L[0]
 #define word1(x) (x)->L[1]
 #endif
 #define dval(x) (x)->d
 #ifndef STRTOD_DIGLIM
 #define STRTOD_DIGLIM 40
 #endif
 #ifdef DIGLIM_DEBUG
 extern int strtod_diglim;
 #else
 #define strtod_diglim STRTOD_DIGLIM
 #endif
 /* The following definition of Storeinc is appropriate for MIPS processors.
  * An alternative that might be better on some machines is
  * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
  */
 #if defined(IEEE_8087) + defined(VAX)
 #define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
 ((unsigned short *)a)[0] = (unsigned short)c, a++)
 #else
 #define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
 ((unsigned short *)a)[1] = (unsigned short)c, a++)
 #endif
 /* #define P DBL_MANT_DIG */
 /* Ten_pmax = floor(P*log(2)/log(5)) */
 /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
 /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
 /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
 #ifdef IEEE_Arith
 #define Exp_shift  20
 #define Exp_shift1 20
 #define Exp_msk1    0x100000
 #define Exp_msk11   0x100000
 #define Exp_mask  0x7ff00000
 #define P 53
 #define Nbits 53
 #define Bias 1023
 #define Emax 1023
 #define Emin (-1022)
 #define Exp_1  0x3ff00000
 #define Exp_11 0x3ff00000
 #define Ebits 11
 #define Frac_mask  0xfffff
 #define Frac_mask1 0xfffff
 #define Ten_pmax 22
 #define Bletch 0x10
 #define Bndry_mask  0xfffff
 #define Bndry_mask1 0xfffff
 #define LSB 1
 #define Sign_bit 0x80000000
 #define Log2P 1
 #define Tiny0 0
 #define Tiny1 1
 #define Quick_max 14
 #define Int_max 14
 #ifndef NO_IEEE_Scale
 #define Avoid_Underflow
 #ifdef Flush_Denorm	/* debugging option */
 #undef Sudden_Underflow
 #endif
 #endif
 #ifndef Flt_Rounds
 #ifdef FLT_ROUNDS
 #define Flt_Rounds FLT_ROUNDS
 #else
 #define Flt_Rounds 1
 #endif
 #endif /*Flt_Rounds*/
 #ifdef Honor_FLT_ROUNDS
 #undef Check_FLT_ROUNDS
 #define Check_FLT_ROUNDS
 #else
 #define Rounding Flt_Rounds
 #endif
 #else /* ifndef IEEE_Arith */
 #undef Check_FLT_ROUNDS
 #undef Honor_FLT_ROUNDS
 #undef SET_INEXACT
 #undef  Sudden_Underflow
 #define Sudden_Underflow
 #ifdef IBM
 #undef Flt_Rounds
 #define Flt_Rounds 0
 #define Exp_shift  24
 #define Exp_shift1 24
 #define Exp_msk1   0x1000000
 #define Exp_msk11  0x1000000
 #define Exp_mask  0x7f000000
 #define P 14
 #define Nbits 56
 #define Bias 65
 #define Emax 248
 #define Emin (-260)
 #define Exp_1  0x41000000
 #define Exp_11 0x41000000
 #define Ebits 8	/* exponent has 7 bits, but 8 is the right value in b2d */
 #define Frac_mask  0xffffff
 #define Frac_mask1 0xffffff
 #define Bletch 4
 #define Ten_pmax 22
 #define Bndry_mask  0xefffff
 #define Bndry_mask1 0xffffff
 #define LSB 1
 #define Sign_bit 0x80000000
 #define Log2P 4
 #define Tiny0 0x100000
 #define Tiny1 0
 #define Quick_max 14
 #define Int_max 15
 #else /* VAX */
 #undef Flt_Rounds
 #define Flt_Rounds 1
 #define Exp_shift  23
 #define Exp_shift1 7
 #define Exp_msk1    0x80
 #define Exp_msk11   0x800000
 #define Exp_mask  0x7f80
 #define P 56
 #define Nbits 56
 #define Bias 129
 #define Emax 126
 #define Emin (-129)
 #define Exp_1  0x40800000
 #define Exp_11 0x4080
 #define Ebits 8
 #define Frac_mask  0x7fffff
 #define Frac_mask1 0xffff007f
 #define Ten_pmax 24
 #define Bletch 2
 #define Bndry_mask  0xffff007f
 #define Bndry_mask1 0xffff007f
 #define LSB 0x10000
 #define Sign_bit 0x8000
 #define Log2P 1
 #define Tiny0 0x80
 #define Tiny1 0
 #define Quick_max 15
 #define Int_max 15
 #endif /* IBM, VAX */
 #endif /* IEEE_Arith */
 #ifndef IEEE_Arith
 #define ROUND_BIASED
 #endif
 #ifdef RND_PRODQUOT
 #define rounded_product(a,b) a = rnd_prod(a, b)
 #define rounded_quotient(a,b) a = rnd_quot(a, b)
 #ifdef KR_headers
 extern double rnd_prod(), rnd_quot();
 #else
 extern double rnd_prod(double, double), rnd_quot(double, double);
 #endif
 #else
 #define rounded_product(a,b) a *= b
 #define rounded_quotient(a,b) a /= b
 #endif
 #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
 #define Big1 0xffffffff
 #ifndef Pack_32
 #define Pack_32
 #endif
 typedef struct BCinfo BCinfo;
  struct
 BCinfo { int dp0, dp1, dplen, dsign, e0, inexact, nd, nd0, rounding, scale, uflchk; };
 #ifdef KR_headers
 #define FFFFFFFF ((((unsigned long)0xffff)<<16)|(unsigned long)0xffff)
 #else
 #define FFFFFFFF 0xffffffffUL
 #endif
 #ifdef NO_LONG_LONG
 #undef ULLong
 #ifdef Just_16
 #undef Pack_32
 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
  * This makes some inner loops simpler and sometimes saves work
  * during multiplications, but it often seems to make things slightly
  * slower.  Hence the default is now to store 32 bits per Long.
  */
 #endif
 #else	/* long long available */
 #ifndef Llong
 #define Llong long long
 #endif
 #ifndef ULLong
 #define ULLong unsigned Llong
 #endif
 #endif /* NO_LONG_LONG */
 #ifndef MULTIPLE_THREADS
 #define ACQUIRE_DTOA_LOCK(n)	/*nothing*/
 #define FREE_DTOA_LOCK(n)	/*nothing*/
 #endif
 #define Kmax 7
 double strtod(const char *s00, char **se);
 char *dtoa(double d, int mode, int ndigits,
 			int *decpt, int *sign, char **rve);
  struct
 Bigint {
 	struct Bigint *next;
 	int k, maxwds, sign, wds;
 	ULong x[1];
 	};
  typedef struct Bigint Bigint;
  static Bigint *freelist[Kmax+1];
  static Bigint *
 Balloc
 #ifdef KR_headers
 	(k) int k;
 #else
 	(int k)
 #endif
 {
 	int x;
 	Bigint *rv;
 #ifndef Omit_Private_Memory
 	unsigned int len;
 #endif
 	ACQUIRE_DTOA_LOCK(0);
 	/* The k > Kmax case does not need ACQUIRE_DTOA_LOCK(0), */
 	/* but this case seems very unlikely. */
 	if (k <= Kmax && (rv = freelist[k]))
 		freelist[k] = rv->next;
 	else {
 		x = 1 << k;
 #ifdef Omit_Private_Memory
 		rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
 #else
 		len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
 			/sizeof(double);
 		if (k <= Kmax && pmem_next - private_mem + len <= PRIVATE_mem) {
 			rv = (Bigint*)pmem_next;
 			pmem_next += len;
 			}
 		else
 			rv = (Bigint*)MALLOC(len*sizeof(double));
 #endif
 		rv->k = k;
 		rv->maxwds = x;
 		}
 	FREE_DTOA_LOCK(0);
 	rv->sign = rv->wds = 0;
 	return rv;
 	}
  static void
 Bfree
 #ifdef KR_headers
 	(v) Bigint *v;
 #else
 	(Bigint *v)
 #endif
 {
 	if (v) {
 		if (v->k > Kmax)
 #ifdef FREE
 			FREE((void*)v);
 #else
 			free((void*)v);
 #endif
 		else {
 			ACQUIRE_DTOA_LOCK(0);
 			v->next = freelist[v->k];
 			freelist[v->k] = v;
 			FREE_DTOA_LOCK(0);
 			}
 		}
 	}
 #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
 y->wds*sizeof(Long) + 2*sizeof(int))
  static Bigint *
 multadd
 #ifdef KR_headers
 	(b, m, a) Bigint *b; int m, a;
 #else
 	(Bigint *b, int m, int a)	/* multiply by m and add a */
 #endif
 {
 	int i, wds;
 #ifdef ULLong
 	ULong *x;
 	ULLong carry, y;
 #else
 	ULong carry, *x, y;
 #ifdef Pack_32
 	ULong xi, z;
 #endif
 #endif
 	Bigint *b1;
 	wds = b->wds;
 	x = b->x;
 	i = 0;
 	carry = a;
 	do {
 #ifdef ULLong
 		y = *x * (ULLong)m + carry;
 		carry = y >> 32;
 		*x++ = y & FFFFFFFF;
 #else
 #ifdef Pack_32
 		xi = *x;
 		y = (xi & 0xffff) * m + carry;
 		z = (xi >> 16) * m + (y >> 16);
 		carry = z >> 16;
 		*x++ = (z << 16) + (y & 0xffff);
 #else
 		y = *x * m + carry;
 		carry = y >> 16;
 		*x++ = y & 0xffff;
 #endif
 #endif
 		}
 		while(++i < wds);
 	if (carry) {
 		if (wds >= b->maxwds) {
 			b1 = Balloc(b->k+1);
 			Bcopy(b1, b);
 			Bfree(b);
 			b = b1;
 			}
 		b->x[wds++] = carry;
 		b->wds = wds;
 		}
 	return b;
 	}
  static Bigint *
 s2b
 #ifdef KR_headers
 	(s, nd0, nd, y9, dplen) CONST char *s; int nd0, nd, dplen; ULong y9;
 #else
 	(CONST char *s, int nd0, int nd, ULong y9, int dplen)
 #endif
 {
 	Bigint *b;
 	int i, k;
 	Long x, y;
 	x = (nd + 8) / 9;
 	for(k = 0, y = 1; x > y; y <<= 1, k++) ;
 #ifdef Pack_32
 	b = Balloc(k);
 	b->x[0] = y9;
 	b->wds = 1;
 #else
 	b = Balloc(k+1);
 	b->x[0] = y9 & 0xffff;
 	b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
 #endif
 	i = 9;
 	if (9 < nd0) {
 		s += 9;
 		do b = multadd(b, 10, *s++ - '0');
 			while(++i < nd0);
 		s += dplen;
 		}
 	else
 		s += dplen + 9;
 	for(; i < nd; i++)
 		b = multadd(b, 10, *s++ - '0');
 	return b;
 	}
  static int
 hi0bits
 #ifdef KR_headers
 	(x) ULong x;
 #else
 	(ULong x)
 #endif
 {
 	int k = 0;
 	if (!(x & 0xffff0000)) {
 		k = 16;
 		x <<= 16;
 		}
 	if (!(x & 0xff000000)) {
 		k += 8;
 		x <<= 8;
 		}
 	if (!(x & 0xf0000000)) {
 		k += 4;
 		x <<= 4;
 		}
 	if (!(x & 0xc0000000)) {
 		k += 2;
 		x <<= 2;
 		}
 	if (!(x & 0x80000000)) {
 		k++;
 		if (!(x & 0x40000000))
 			return 32;
 		}
 	return k;
 	}
  static int
 lo0bits
 #ifdef KR_headers
 	(y) ULong *y;
 #else
 	(ULong *y)
 #endif
 {
 	int k;
 	ULong x = *y;
 	if (x & 7) {
 		if (x & 1)
 			return 0;
 		if (x & 2) {
 			*y = x >> 1;
 			return 1;
 			}
 		*y = x >> 2;
 		return 2;
 		}
 	k = 0;
 	if (!(x & 0xffff)) {
 		k = 16;
 		x >>= 16;
 		}
 	if (!(x & 0xff)) {
 		k += 8;
 		x >>= 8;
 		}
 	if (!(x & 0xf)) {
 		k += 4;
 		x >>= 4;
 		}
 	if (!(x & 0x3)) {
 		k += 2;
 		x >>= 2;
 		}
 	if (!(x & 1)) {
 		k++;
 		x >>= 1;
 		if (!x)
 			return 32;
 		}
 	*y = x;
 	return k;
 	}
  static Bigint *
 i2b
 #ifdef KR_headers
 	(i) int i;
 #else
 	(int i)
 #endif
 {
 	Bigint *b;
 	b = Balloc(1);
 	b->x[0] = i;
 	b->wds = 1;
 	return b;
 	}
  static Bigint *
 mult
 #ifdef KR_headers
 	(a, b) Bigint *a, *b;
 #else
 	(Bigint *a, Bigint *b)
 #endif
 {
 	Bigint *c;
 	int k, wa, wb, wc;
 	ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
 	ULong y;
 #ifdef ULLong
 	ULLong carry, z;
 #else
 	ULong carry, z;
 #ifdef Pack_32
 	ULong z2;
 #endif
 #endif
 	if (a->wds < b->wds) {
 		c = a;
 		a = b;
 		b = c;
 		}
 	k = a->k;
 	wa = a->wds;
 	wb = b->wds;
 	wc = wa + wb;
 	if (wc > a->maxwds)
 		k++;
 	c = Balloc(k);
 	for(x = c->x, xa = x + wc; x < xa; x++)
 		*x = 0;
 	xa = a->x;
 	xae = xa + wa;
 	xb = b->x;
 	xbe = xb + wb;
 	xc0 = c->x;
 #ifdef ULLong
 	for(; xb < xbe; xc0++) {
 		if ((y = *xb++)) {
 			x = xa;
 			xc = xc0;
 			carry = 0;
 			do {
 				z = *x++ * (ULLong)y + *xc + carry;
 				carry = z >> 32;
 				*xc++ = z & FFFFFFFF;
 				}
 				while(x < xae);
 			*xc = carry;
 			}
 		}
 #else
 #ifdef Pack_32
 	for(; xb < xbe; xb++, xc0++) {
 		if (y = *xb & 0xffff) {
 			x = xa;
 			xc = xc0;
 			carry = 0;
 			do {
 				z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
 				carry = z >> 16;
 				z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
 				carry = z2 >> 16;
 				Storeinc(xc, z2, z);
 				}
 				while(x < xae);
 			*xc = carry;
 			}
 		if (y = *xb >> 16) {
 			x = xa;
 			xc = xc0;
 			carry = 0;
 			z2 = *xc;
 			do {
 				z = (*x & 0xffff) * y + (*xc >> 16) + carry;
 				carry = z >> 16;
 				Storeinc(xc, z, z2);
 				z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
 				carry = z2 >> 16;
 				}
 				while(x < xae);
 			*xc = z2;
 			}
 		}
 #else
 	for(; xb < xbe; xc0++) {
 		if (y = *xb++) {
 			x = xa;
 			xc = xc0;
 			carry = 0;
 			do {
 				z = *x++ * y + *xc + carry;
 				carry = z >> 16;
 				*xc++ = z & 0xffff;
 				}
 				while(x < xae);
 			*xc = carry;
 			}
 		}
 #endif
 #endif
 	for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
 	c->wds = wc;
 	return c;
 	}
  static Bigint *p5s;
  static Bigint *
 pow5mult
 #ifdef KR_headers
 	(b, k) Bigint *b; int k;
 #else
 	(Bigint *b, int k)
 #endif
 {
 	Bigint *b1, *p5, *p51;
 	int i;
 	static int p05[3] = { 5, 25, 125 };
 	if ((i = k & 3))
 		b = multadd(b, p05[i-1], 0);
 	if (!(k >>= 2))
 		return b;
 	if (!(p5 = p5s)) {
 		/* first time */
 #ifdef MULTIPLE_THREADS
 		ACQUIRE_DTOA_LOCK(1);
 		if (!(p5 = p5s)) {
 			p5 = p5s = i2b(625);
 			p5->next = 0;
 			}
 		FREE_DTOA_LOCK(1);
 #else
 		p5 = p5s = i2b(625);
 		p5->next = 0;
 #endif
 		}
 	for(;;) {
 		if (k & 1) {
 			b1 = mult(b, p5);
 			Bfree(b);
 			b = b1;
 			}
 		if (!(k >>= 1))
 			break;
 		if (!(p51 = p5->next)) {
 #ifdef MULTIPLE_THREADS
 			ACQUIRE_DTOA_LOCK(1);
 			if (!(p51 = p5->next)) {
 				p51 = p5->next = mult(p5,p5);
 				p51->next = 0;
 				}
 			FREE_DTOA_LOCK(1);
 #else
 			p51 = p5->next = mult(p5,p5);
 			p51->next = 0;
 #endif
 			}
 		p5 = p51;
 		}
 	return b;
 	}
  static Bigint *
 lshift
 #ifdef KR_headers
 	(b, k) Bigint *b; int k;
 #else
 	(Bigint *b, int k)
 #endif
 {
 	int i, k1, n, n1;
 	Bigint *b1;
 	ULong *x, *x1, *xe, z;
 #ifdef Pack_32
 	n = k >> 5;
 #else
 	n = k >> 4;
 #endif
 	k1 = b->k;
 	n1 = n + b->wds + 1;
 	for(i = b->maxwds; n1 > i; i <<= 1)
 		k1++;
 	b1 = Balloc(k1);
 	x1 = b1->x;
 	for(i = 0; i < n; i++)
 		*x1++ = 0;
 	x = b->x;
 	xe = x + b->wds;
 #ifdef Pack_32
 	if (k &= 0x1f) {
 		k1 = 32 - k;
 		z = 0;
 		do {
 			*x1++ = *x << k | z;
 			z = *x++ >> k1;
 			}
 			while(x < xe);
 		if ((*x1 = z))
 			++n1;
 		}
 #else
 	if (k &= 0xf) {
 		k1 = 16 - k;
 		z = 0;
 		do {
 			*x1++ = *x << k  & 0xffff | z;
 			z = *x++ >> k1;
 			}
 			while(x < xe);
 		if (*x1 = z)
 			++n1;
 		}
 #endif
 	else do
 		*x1++ = *x++;
 		while(x < xe);
 	b1->wds = n1 - 1;
 	Bfree(b);
 	return b1;
 	}
  static int
 cmp
 #ifdef KR_headers
 	(a, b) Bigint *a, *b;
 #else
 	(Bigint *a, Bigint *b)
 #endif
 {
 	ULong *xa, *xa0, *xb, *xb0;
 	int i, j;
 	i = a->wds;
 	j = b->wds;
 #ifdef DEBUG
 	if (i > 1 && !a->x[i-1])
 		Bug("cmp called with a->x[a->wds-1] == 0");
 	if (j > 1 && !b->x[j-1])
 		Bug("cmp called with b->x[b->wds-1] == 0");
 #endif
 	if (i -= j)
 		return i;
 	xa0 = a->x;
 	xa = xa0 + j;
 	xb0 = b->x;
 	xb = xb0 + j;
 	for(;;) {
 		if (*--xa != *--xb)
 			return *xa < *xb ? -1 : 1;
 		if (xa <= xa0)
 			break;
 		}
 	return 0;
 	}
  static Bigint *
 diff
 #ifdef KR_headers
 	(a, b) Bigint *a, *b;
 #else
 	(Bigint *a, Bigint *b)
 #endif
 {
 	Bigint *c;
 	int i, wa, wb;
 	ULong *xa, *xae, *xb, *xbe, *xc;
 #ifdef ULLong
 	ULLong borrow, y;
 #else
 	ULong borrow, y;
 #ifdef Pack_32
 	ULong z;
 #endif
 #endif
 	i = cmp(a,b);
 	if (!i) {
 		c = Balloc(0);
 		c->wds = 1;
 		c->x[0] = 0;
 		return c;
 		}
 	if (i < 0) {
 		c = a;
 		a = b;
 		b = c;
 		i = 1;
 		}
 	else
 		i = 0;
 	c = Balloc(a->k);
 	c->sign = i;
 	wa = a->wds;
 	xa = a->x;
 	xae = xa + wa;
 	wb = b->wds;
 	xb = b->x;
 	xbe = xb + wb;
 	xc = c->x;
 	borrow = 0;
 #ifdef ULLong
 	do {
 		y = (ULLong)*xa++ - *xb++ - borrow;
 		borrow = y >> 32 & (ULong)1;
 		*xc++ = y & FFFFFFFF;
 		}
 		while(xb < xbe);
 	while(xa < xae) {
 		y = *xa++ - borrow;
 		borrow = y >> 32 & (ULong)1;
 		*xc++ = y & FFFFFFFF;
 		}
 #else
 #ifdef Pack_32
 	do {
 		y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
 		borrow = (y & 0x10000) >> 16;
 		z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
 		borrow = (z & 0x10000) >> 16;
 		Storeinc(xc, z, y);
 		}
 		while(xb < xbe);
 	while(xa < xae) {
 		y = (*xa & 0xffff) - borrow;
 		borrow = (y & 0x10000) >> 16;
 		z = (*xa++ >> 16) - borrow;
 		borrow = (z & 0x10000) >> 16;
 		Storeinc(xc, z, y);
 		}
 #else
 	do {
 		y = *xa++ - *xb++ - borrow;
 		borrow = (y & 0x10000) >> 16;
 		*xc++ = y & 0xffff;
 		}
 		while(xb < xbe);
 	while(xa < xae) {
 		y = *xa++ - borrow;
 		borrow = (y & 0x10000) >> 16;
 		*xc++ = y & 0xffff;
 		}
 #endif
 #endif
 	while(!*--xc)
 		wa--;
 	c->wds = wa;
 	return c;
 	}
  static double
 ulp
 #ifdef KR_headers
 	(x) U *x;
 #else
 	(U *x)
 #endif
 {
 	Long L;
 	U u;
 	L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
 #ifndef Avoid_Underflow
 #ifndef Sudden_Underflow
 	if (L > 0) {
 #endif
 #endif
 #ifdef IBM
 		L |= Exp_msk1 >> 4;
 #endif
 		word0(&u) = L;
 		word1(&u) = 0;
 #ifndef Avoid_Underflow
 #ifndef Sudden_Underflow
 		}
 	else {
 		L = -L >> Exp_shift;
 		if (L < Exp_shift) {
 			word0(&u) = 0x80000 >> L;
 			word1(&u) = 0;
 			}
 		else {
 			word0(&u) = 0;
 			L -= Exp_shift;
 			word1(&u) = L >= 31 ? 1 : 1 << 31 - L;
 			}
 		}
 #endif
 #endif
 	return dval(&u);
 	}
  static double
 b2d
 #ifdef KR_headers
 	(a, e) Bigint *a; int *e;
 #else
 	(Bigint *a, int *e)
 #endif
 {
 	ULong *xa, *xa0, w, y, z;
 	int k;
 	U d;
 #ifdef VAX
 	ULong d0, d1;
 #else
 #define d0 word0(&d)
 #define d1 word1(&d)
 #endif
 	xa0 = a->x;
 	xa = xa0 + a->wds;
 	y = *--xa;
 #ifdef DEBUG
 	if (!y) Bug("zero y in b2d");
 #endif
 	k = hi0bits(y);
 	*e = 32 - k;
 #ifdef Pack_32
 	if (k < Ebits) {
 		d0 = Exp_1 | y >> (Ebits - k);
 		w = xa > xa0 ? *--xa : 0;
 		d1 = y << ((32-Ebits) + k) | w >> (Ebits - k);
 		goto ret_d;
 		}
 	z = xa > xa0 ? *--xa : 0;
 	if (k -= Ebits) {
 		d0 = Exp_1 | y << k | z >> (32 - k);
 		y = xa > xa0 ? *--xa : 0;
 		d1 = z << k | y >> (32 - k);
 		}
 	else {
 		d0 = Exp_1 | y;
 		d1 = z;
 		}
 #else
 	if (k < Ebits + 16) {
 		z = xa > xa0 ? *--xa : 0;
 		d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
 		w = xa > xa0 ? *--xa : 0;
 		y = xa > xa0 ? *--xa : 0;
 		d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
 		goto ret_d;
 		}
 	z = xa > xa0 ? *--xa : 0;
 	w = xa > xa0 ? *--xa : 0;
 	k -= Ebits + 16;
 	d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
 	y = xa > xa0 ? *--xa : 0;
 	d1 = w << k + 16 | y << k;
 #endif
  ret_d:
 #ifdef VAX
 	word0(&d) = d0 >> 16 | d0 << 16;
 	word1(&d) = d1 >> 16 | d1 << 16;
 #else
 #undef d0
 #undef d1
 #endif
 	return dval(&d);
 	}
  static Bigint *
 d2b
 #ifdef KR_headers
 	(d, e, bits) U *d; int *e, *bits;
 #else
 	(U *d, int *e, int *bits)
 #endif
 {
 	Bigint *b;
 	int de, k;
 	ULong *x, y, z;
 #ifndef Sudden_Underflow
 	int i;
 #endif
 #ifdef VAX
 	ULong d0, d1;
 	d0 = word0(d) >> 16 | word0(d) << 16;
 	d1 = word1(d) >> 16 | word1(d) << 16;
 #else
 #define d0 word0(d)
 #define d1 word1(d)
 #endif
 #ifdef Pack_32
 	b = Balloc(1);
 #else
 	b = Balloc(2);
 #endif
 	x = b->x;
 	z = d0 & Frac_mask;
 	d0 &= 0x7fffffff;	/* clear sign bit, which we ignore */
 #ifdef Sudden_Underflow
 	de = (int)(d0 >> Exp_shift);
 #ifndef IBM
 	z |= Exp_msk11;
 #endif
 #else
 	if ((de = (int)(d0 >> Exp_shift)))
 		z |= Exp_msk1;
 #endif
 #ifdef Pack_32
 	if ((y = d1)) {
 		if ((k = lo0bits(&y))) {
 			x[0] = y | z << (32 - k);
 			z >>= k;
 			}
 		else
 			x[0] = y;
 #ifndef Sudden_Underflow
 		i =
 #endif
 		    b->wds = (x[1] = z) ? 2 : 1;
 		}
 	else {
 		k = lo0bits(&z);
 		x[0] = z;
 #ifndef Sudden_Underflow
 		i =
 #endif
 		    b->wds = 1;
 		k += 32;
 		}
 #else
 	if (y = d1) {
 		if (k = lo0bits(&y))
 			if (k >= 16) {
 				x[0] = y | z << 32 - k & 0xffff;
 				x[1] = z >> k - 16 & 0xffff;
 				x[2] = z >> k;
 				i = 2;
 				}
 			else {
 				x[0] = y & 0xffff;
 				x[1] = y >> 16 | z << 16 - k & 0xffff;
 				x[2] = z >> k & 0xffff;
 				x[3] = z >> k+16;
 				i = 3;
 				}
 		else {
 			x[0] = y & 0xffff;
 			x[1] = y >> 16;
 			x[2] = z & 0xffff;
 			x[3] = z >> 16;
 			i = 3;
 			}
 		}
 	else {
 #ifdef DEBUG
 		if (!z)
 			Bug("Zero passed to d2b");
 #endif
 		k = lo0bits(&z);
 		if (k >= 16) {
 			x[0] = z;
 			i = 0;
 			}
 		else {
 			x[0] = z & 0xffff;
 			x[1] = z >> 16;
 			i = 1;
 			}
 		k += 32;
 		}
 	while(!x[i])
 		--i;
 	b->wds = i + 1;
 #endif
 #ifndef Sudden_Underflow
 	if (de) {
 #endif
 #ifdef IBM
 		*e = (de - Bias - (P-1) << 2) + k;
 		*bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
 #else
 		*e = de - Bias - (P-1) + k;
 		*bits = P - k;
 #endif
 #ifndef Sudden_Underflow
 		}
 	else {
 		*e = de - Bias - (P-1) + 1 + k;
 #ifdef Pack_32
 		*bits = 32*i - hi0bits(x[i-1]);
 #else
 		*bits = (i+2)*16 - hi0bits(x[i]);
 #endif
 		}
 #endif
 	return b;
 	}
 #undef d0
 #undef d1
  static double
 ratio
 #ifdef KR_headers
 	(a, b) Bigint *a, *b;
 #else
 	(Bigint *a, Bigint *b)
 #endif
 {
 	U da, db;
 	int k, ka, kb;
 	dval(&da) = b2d(a, &ka);
 	dval(&db) = b2d(b, &kb);
 #ifdef Pack_32
 	k = ka - kb + 32*(a->wds - b->wds);
 #else
 	k = ka - kb + 16*(a->wds - b->wds);
 #endif
 #ifdef IBM
 	if (k > 0) {
 		word0(&da) += (k >> 2)*Exp_msk1;
 		if (k &= 3)
 			dval(&da) *= 1 << k;
 		}
 	else {
 		k = -k;
 		word0(&db) += (k >> 2)*Exp_msk1;
 		if (k &= 3)
 			dval(&db) *= 1 << k;
 		}
 #else
 	if (k > 0)
 		word0(&da) += k*Exp_msk1;
 	else {
 		k = -k;
 		word0(&db) += k*Exp_msk1;
 		}
 #endif
 	return dval(&da) / dval(&db);
 	}
  static CONST double
 tens[] = {
 e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
 e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
 e20, 1e21, 1e22
 #ifdef VAX
 		, 1e23, 1e24
 #endif
 		};
  static CONST double
 #ifdef IEEE_Arith
 bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
 #ifdef Avoid_Underflow
 		9007199254740992.*9007199254740992.e-256
 		/* = 2^106 * 1e-256 */
 #else
 e-256
 #endif
 		};
 /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
 /* flag unnecessarily.  It leads to a song and dance at the end of strtod. */
 #define Scale_Bit 0x10
 #define n_bigtens 5
 #else
 #ifdef IBM
 bigtens[] = { 1e16, 1e32, 1e64 };
 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
 #define n_bigtens 3
 #else
 bigtens[] = { 1e16, 1e32 };
 static CONST double tinytens[] = { 1e-16, 1e-32 };
 #define n_bigtens 2
 #endif
 #endif
 #undef Need_Hexdig
 #ifdef INFNAN_CHECK
 #ifndef No_Hex_NaN
 #define Need_Hexdig
 #endif
 #endif
 #ifndef Need_Hexdig
 #ifndef NO_HEX_FP
 #define Need_Hexdig
 #endif
 #endif
 #ifdef Need_Hexdig /*{*/
 static unsigned char hexdig[256];
  static void
 #ifdef KR_headers
 htinit(h, s, inc) unsigned char *h; unsigned char *s; int inc;
 #else
 htinit(unsigned char *h, unsigned char *s, int inc)
 #endif
 {
 	int i, j;
 	for(i = 0; (j = s[i]) !=0; i++)
 		h[j] = i + inc;
 	}
  static void
 #ifdef KR_headers
 hexdig_init()
 #else
 hexdig_init(void)
 #endif
 {
 #define USC (unsigned char *)
 	htinit(hexdig, USC "0123456789", 0x10);
 	htinit(hexdig, USC "abcdef", 0x10 + 10);
 	htinit(hexdig, USC "ABCDEF", 0x10 + 10);
 	}
 #endif /* } Need_Hexdig */
 #ifdef INFNAN_CHECK
 #ifndef NAN_WORD0
 #define NAN_WORD0 0x7ff80000
 #endif
 #ifndef NAN_WORD1
 #define NAN_WORD1 0
 #endif
  static int
 match
 #ifdef KR_headers
 	(sp, t) char **sp, *t;
 #else
 	(CONST char **sp, CONST char *t)
 #endif
 {
 	int c, d;
 	CONST char *s = *sp;
 	while((d = *t++)) {
 		if ((c = *++s) >= 'A' && c <= 'Z')
 			c += 'a' - 'A';
 		if (c != d)
 			return 0;
 		}
 	*sp = s + 1;
 	return 1;
 	}
 #ifndef No_Hex_NaN
  static void
 hexnan
 #ifdef KR_headers
 	(rvp, sp) U *rvp; CONST char **sp;
 #else
 	(U *rvp, CONST char **sp)
 #endif
 {
 	ULong c, x[2];
 	CONST char *s;
 	int c1, havedig, udx0, xshift;
 	if (!hexdig['0'])
 		hexdig_init();
 	x[0] = x[1] = 0;
 	havedig = xshift = 0;
 	udx0 = 1;
 	s = *sp;
 	/* allow optional initial 0x or 0X */
 	while((c = *(CONST unsigned char*)(s+1)) && c <= ' ')
 		++s;
 	if (s[1] == '0' && (s[2] == 'x' || s[2] == 'X'))
 		s += 2;
 	while((c = *(CONST unsigned char*)++s)) {
 		if ((c1 = hexdig[c]))
 			c  = c1 & 0xf;
 		else if (c <= ' ') {
 			if (udx0 && havedig) {
 				udx0 = 0;
 				xshift = 1;
 				}
 			continue;
 			}
 #ifdef GDTOA_NON_PEDANTIC_NANCHECK
 		else if (/*(*/ c == ')' && havedig) {
 			*sp = s + 1;
 			break;
 			}
 		else
 			return;	/* invalid form: don't change *sp */
 #else
 		else {
 			do {
 				if (/*(*/ c == ')') {
 					*sp = s + 1;
 					break;
 					}
 				} while((c = *++s));
 			break;
 			}
 #endif
 		havedig = 1;
 		if (xshift) {
 			xshift = 0;
 			x[0] = x[1];
 			x[1] = 0;
 			}
 		if (udx0)
 			x[0] = (x[0] << 4) | (x[1] >> 28);
 		x[1] = (x[1] << 4) | c;
 		}
 	if ((x[0] &= 0xfffff) || x[1]) {
 		word0(rvp) = Exp_mask | x[0];
 		word1(rvp) = x[1];
 		}
 	}
 #endif /*No_Hex_NaN*/
 #endif /* INFNAN_CHECK */
 #ifdef Pack_32
 #define ULbits 32
 #define kshift 5
 #define kmask 31
 #else
 #define ULbits 16
 #define kshift 4
 #define kmask 15
 #endif
 #ifndef NO_HEX_FP /*{*/
  static void
 #ifdef KR_headers
 rshift(b, k) Bigint *b; int k;
 #else
 rshift(Bigint *b, int k)
 #endif
 {
 	ULong *x, *x1, *xe, y;
 	int n;
 	x = x1 = b->x;
 	n = k >> kshift;
 	if (n < b->wds) {
 		xe = x + b->wds;
 		x += n;
 		if (k &= kmask) {
 			n = 32 - k;
 			y = *x++ >> k;
 			while(x < xe) {
 				*x1++ = (y | (*x << n)) & 0xffffffff;
 				y = *x++ >> k;
 				}
 			if ((*x1 = y) !=0)
 				x1++;
 			}
 		else
 			while(x < xe)
 				*x1++ = *x++;
 		}
 	if ((b->wds = x1 - b->x) == 0)
 		b->x[0] = 0;
 	}
  static ULong
 #ifdef KR_headers
 any_on(b, k) Bigint *b; int k;
 #else
 any_on(Bigint *b, int k)
 #endif
 {
 	int n, nwds;
 	ULong *x, *x0, x1, x2;
 	x = b->x;
 	nwds = b->wds;
 	n = k >> kshift;
 	if (n > nwds)
 		n = nwds;
 	else if (n < nwds && (k &= kmask)) {
 		x1 = x2 = x[n];
 		x1 >>= k;
 		x1 <<= k;
 		if (x1 != x2)
 			return 1;
 		}
 	x0 = x;
 	x += n;
 	while(x > x0)
 		if (*--x)
 			return 1;
 	return 0;
 	}
 enum {	/* rounding values: same as FLT_ROUNDS */
 	Round_zero = 0,
 	Round_near = 1,
 	Round_up = 2,
 	Round_down = 3
 	};
  static Bigint *
 #ifdef KR_headers
 increment(b) Bigint *b;
 #else
 increment(Bigint *b)
 #endif
 {
 	ULong *x, *xe;
 	Bigint *b1;
 	x = b->x;
 	xe = x + b->wds;
 	do {
 		if (*x < (ULong)0xffffffffL) {
 			++*x;
 			return b;
 			}
 		*x++ = 0;
 		} while(x < xe);
 	{
 		if (b->wds >= b->maxwds) {
 			b1 = Balloc(b->k+1);
 			Bcopy(b1,b);
 			Bfree(b);
 			b = b1;
 			}
 		b->x[b->wds++] = 1;
 		}
 	return b;
 	}
  void
 #ifdef KR_headers
 gethex(sp, rvp, rounding, sign)
 	CONST char **sp; U *rvp; int rounding, sign;
 #else
 gethex( CONST char **sp, U *rvp, int rounding, int sign)
 #endif
 {
 	Bigint *b;
 	CONST unsigned char *decpt, *s0, *s, *s1;
 	Long e, e1;
 	ULong L, lostbits, *x;
 	int big, denorm, esign, havedig, k, n, nbits, up, zret;
 #ifdef IBM
 	int j;
 #endif
 	enum {
 #ifdef IEEE_Arith /*{{*/
 		emax = 0x7fe - Bias - P + 1,
 		emin = Emin - P + 1
 #else /*}{*/
 		emin = Emin - P,
 #ifdef VAX
 		emax = 0x7ff - Bias - P + 1
 #endif
 #ifdef IBM
 		emax = 0x7f - Bias - P
 #endif
 #endif /*}}*/
 		};
 #ifdef USE_LOCALE
 	int i;
 #ifdef NO_LOCALE_CACHE
 	const unsigned char *decimalpoint = (unsigned char*)
 		localeconv()->decimal_point;
 #else
 	const unsigned char *decimalpoint;
 	static unsigned char *decimalpoint_cache;
 	if (!(s0 = decimalpoint_cache)) {
 		s0 = (unsigned char*)localeconv()->decimal_point;
 		if ((decimalpoint_cache = (unsigned char*)
 				MALLOC(strlen((CONST char*)s0) + 1))) {
 			strcpy((char*)decimalpoint_cache, (CONST char*)s0);
 			s0 = decimalpoint_cache;
 			}
 		}
 	decimalpoint = s0;
 #endif
 #endif
 	if (!hexdig['0'])
 		hexdig_init();
 	havedig = 0;
 	s0 = *(CONST unsigned char **)sp + 2;
 	while(s0[havedig] == '0')
 		havedig++;
 	s0 += havedig;
 	s = s0;
 	decpt = 0;
 	zret = 0;
 	e = 0;
 	if (hexdig[*s])
 		havedig++;
 	else {
 		zret = 1;
 #ifdef USE_LOCALE
 		for(i = 0; decimalpoint[i]; ++i) {
 			if (s[i] != decimalpoint[i])
 				goto pcheck;
 			}
 		decpt = s += i;
 #else
 		if (*s != '.')
 			goto pcheck;
 		decpt = ++s;
 #endif
 		if (!hexdig[*s])
 			goto pcheck;
 		while(*s == '0')
 			s++;
 		if (hexdig[*s])
 			zret = 0;
 		havedig = 1;
 		s0 = s;
 		}
 	while(hexdig[*s])
 		s++;
 #ifdef USE_LOCALE
 	if (*s == *decimalpoint && !decpt) {
 		for(i = 1; decimalpoint[i]; ++i) {
 			if (s[i] != decimalpoint[i])
 				goto pcheck;
 			}
 		decpt = s += i;
 #else
 	if (*s == '.' && !decpt) {
 		decpt = ++s;
 #endif
 		while(hexdig[*s])
 			s++;
 		}/*}*/
 	if (decpt)
 		e = -(((Long)(s-decpt)) << 2);
  pcheck:
 	s1 = s;
 	big = esign = 0;
 	switch(*s) {
 	  case 'p':
 	  case 'P':
 		switch(*++s) {
 		  case '-':
 			esign = 1;
 			/* no break */
 		  case '+':
 			s++;
 		  }
 		if ((n = hexdig[*s]) == 0 || n > 0x19) {
 			s = s1;
 			break;
 			}
 		e1 = n - 0x10;
 		while((n = hexdig[*++s]) !=0 && n <= 0x19) {
 			if (e1 & 0xf8000000)
 				big = 1;
 			e1 = 10*e1 + n - 0x10;
 			}
 		if (esign)
 			e1 = -e1;
 		e += e1;
 	  }
 	*sp = (char*)s;
 	if (!havedig)
 		*sp = (char*)s0 - 1;
 	if (zret)
 		goto retz1;
 	if (big) {
 		if (esign) {
 #ifdef IEEE_Arith
 			switch(rounding) {
 			  case Round_up:
 				if (sign)
 					break;
 				goto ret_tiny;
 			  case Round_down:
 				if (!sign)
 					break;
 				goto ret_tiny;
 			  }
 #endif
 			goto retz;
 #ifdef IEEE_Arith
  ret_tiny:
 #ifndef NO_ERRNO
 			errno = ERANGE;
 #endif
 			word0(rvp) = 0;
 			word1(rvp) = 1;
 			return;
 #endif /* IEEE_Arith */
 			}
 		switch(rounding) {
 		  case Round_near:
 			goto ovfl1;
 		  case Round_up:
 			if (!sign)
 				goto ovfl1;
 			goto ret_big;
 		  case Round_down:
 			if (sign)
 				goto ovfl1;
 			goto ret_big;
 		  }
  ret_big:
 		word0(rvp) = Big0;
 		word1(rvp) = Big1;
 		return;
 		}
 	n = s1 - s0 - 1;
 	for(k = 0; n > (1 << (kshift-2)) - 1; n >>= 1)
 		k++;
 	b = Balloc(k);
 	x = b->x;
 	n = 0;
 	L = 0;
 #ifdef USE_LOCALE
 	for(i = 0; decimalpoint[i+1]; ++i);
 #endif
 	while(s1 > s0) {
 #ifdef USE_LOCALE
 		if (*--s1 == decimalpoint[i]) {
 			s1 -= i;
 			continue;
 			}
 #else
 		if (*--s1 == '.')
 			continue;
 #endif
 		if (n == ULbits) {
 			*x++ = L;
 			L = 0;
 			n = 0;
 			}
 		L |= (hexdig[*s1] & 0x0f) << n;
 		n += 4;
 		}
 	*x++ = L;
 	b->wds = n = x - b->x;
 	n = ULbits*n - hi0bits(L);
 	nbits = Nbits;
 	lostbits = 0;
 	x = b->x;
 	if (n > nbits) {
 		n -= nbits;
 		if (any_on(b,n)) {
 			lostbits = 1;
 			k = n - 1;
 			if (x[k>>kshift] & 1 << (k & kmask)) {
 				lostbits = 2;
 				if (k > 0 && any_on(b,k))
 					lostbits = 3;
 				}
 			}
 		rshift(b, n);
 		e += n;
 		}
 	else if (n < nbits) {
 		n = nbits - n;
 		b = lshift(b, n);
 		e -= n;
 		x = b->x;
 		}
 	if (e > Emax) {
  ovfl:
 		Bfree(b);
  ovfl1:
 #ifndef NO_ERRNO
 		errno = ERANGE;
 #endif
 		word0(rvp) = Exp_mask;
 		word1(rvp) = 0;
 		return;
 		}
 	denorm = 0;
 	if (e < emin) {
 		denorm = 1;
 		n = emin - e;
 		if (n >= nbits) {
 #ifdef IEEE_Arith /*{*/
 			switch (rounding) {
 			  case Round_near:
 				if (n == nbits && (n < 2 || any_on(b,n-1)))
 					goto ret_tiny;
 				break;
 			  case Round_up:
 				if (!sign)
 					goto ret_tiny;
 				break;
 			  case Round_down:
 				if (sign)
 					goto ret_tiny;
 			  }
 #endif /* } IEEE_Arith */
 			Bfree(b);
  retz:
 #ifndef NO_ERRNO
 			errno = ERANGE;
 #endif
  retz1:
 			rvp->d = 0.;
 			return;
 			}
 		k = n - 1;
 		if (lostbits)
 			lostbits = 1;
 		else if (k > 0)
 			lostbits = any_on(b,k);
 		if (x[k>>kshift] & 1 << (k & kmask))
 			lostbits |= 2;
 		nbits -= n;
 		rshift(b,n);
 		e = emin;
 		}
 	if (lostbits) {
 		up = 0;
 		switch(rounding) {
 		  case Round_zero:
 			break;
 		  case Round_near:
 			if (lostbits & 2
 			 && (lostbits & 1) | (x[0] & 1))
 				up = 1;
 			break;
 		  case Round_up:
 			up = 1 - sign;
 			break;
 		  case Round_down:
 			up = sign;
 		  }
 		if (up) {
 			k = b->wds;
 			b = increment(b);
 			x = b->x;
 			if (denorm) {
 #if 0
 				if (nbits == Nbits - 1
 				 && x[nbits >> kshift] & 1 << (nbits & kmask))
 					denorm = 0; /* not currently used */
 #endif
 				}
 			else if (b->wds > k
 			 || ((n = nbits & kmask) !=0
 			     && hi0bits(x[k-1]) < 32-n)) {
 				rshift(b,1);
 				if (++e > Emax)
 					goto ovfl;
 				}
 			}
 		}
 #ifdef IEEE_Arith
 	if (denorm)
 		word0(rvp) = b->wds > 1 ? b->x[1] & ~0x100000 : 0;
 	else
 		word0(rvp) = (b->x[1] & ~0x100000) | ((e + 0x3ff + 52) << 20);
 	word1(rvp) = b->x[0];
 #endif
 #ifdef IBM
 	if ((j = e & 3)) {
 		k = b->x[0] & ((1 << j) - 1);
 		rshift(b,j);
 		if (k) {
 			switch(rounding) {
 			  case Round_up:
 				if (!sign)
 					increment(b);
 				break;
 			  case Round_down:
 				if (sign)
 					increment(b);
 				break;
 			  case Round_near:
 				j = 1 << (j-1);
 				if (k & j && ((k & (j-1)) | lostbits))
 					increment(b);
 			  }
 			}
 		}
 	e >>= 2;
 	word0(rvp) = b->x[1] | ((e + 65 + 13) << 24);
 	word1(rvp) = b->x[0];
 #endif
 #ifdef VAX
 	/* The next two lines ignore swap of low- and high-order 2 bytes. */
 	/* word0(rvp) = (b->x[1] & ~0x800000) | ((e + 129 + 55) << 23); */
 	/* word1(rvp) = b->x[0]; */
 	word0(rvp) = ((b->x[1] & ~0x800000) >> 16) | ((e + 129 + 55) << 7) | (b->x[1] << 16);
 	word1(rvp) = (b->x[0] >> 16) | (b->x[0] << 16);
 #endif
 	Bfree(b);
 	}
 #endif /*}!NO_HEX_FP*/
  static int
 #ifdef KR_headers
 dshift(b, p2) Bigint *b; int p2;
 #else
 dshift(Bigint *b, int p2)
 #endif
 {
 	int rv = hi0bits(b->x[b->wds-1]) - 4;
 	if (p2 > 0)
 		rv -= p2;
 	return rv & kmask;
 	}
  static int
 quorem
 #ifdef KR_headers
 	(b, S) Bigint *b, *S;
 #else
 	(Bigint *b, Bigint *S)
 #endif
 {
 	int n;
 	ULong *bx, *bxe, q, *sx, *sxe;
 #ifdef ULLong
 	ULLong borrow, carry, y, ys;
 #else
 	ULong borrow, carry, y, ys;
 #ifdef Pack_32
 	ULong si, z, zs;
 #endif
 #endif
 	n = S->wds;
 #ifdef DEBUG
 	/*debug*/ if (b->wds > n)
 	/*debug*/	Bug("oversize b in quorem");
 #endif
 	if (b->wds < n)
 		return 0;
 	sx = S->x;
 	sxe = sx + --n;
 	bx = b->x;
 	bxe = bx + n;
 	q = *bxe / (*sxe + 1);	/* ensure q <= true quotient */
 #ifdef DEBUG
 	/*debug*/ if (q > 9)
 	/*debug*/	Bug("oversized quotient in quorem");
 #endif
 	if (q) {
 		borrow = 0;
 		carry = 0;
 		do {
 #ifdef ULLong
 			ys = *sx++ * (ULLong)q + carry;
 			carry = ys >> 32;
 			y = *bx - (ys & FFFFFFFF) - borrow;
 			borrow = y >> 32 & (ULong)1;
 			*bx++ = y & FFFFFFFF;
 #else
 #ifdef Pack_32
 			si = *sx++;
 			ys = (si & 0xffff) * q + carry;
 			zs = (si >> 16) * q + (ys >> 16);
 			carry = zs >> 16;
 			y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
 			borrow = (y & 0x10000) >> 16;
 			z = (*bx >> 16) - (zs & 0xffff) - borrow;
 			borrow = (z & 0x10000) >> 16;
 			Storeinc(bx, z, y);
 #else
 			ys = *sx++ * q + carry;
 			carry = ys >> 16;
 			y = *bx - (ys & 0xffff) - borrow;
 			borrow = (y & 0x10000) >> 16;
 			*bx++ = y & 0xffff;
 #endif
 #endif
 			}
 			while(sx <= sxe);
 		if (!*bxe) {
 			bx = b->x;
 			while(--bxe > bx && !*bxe)
 				--n;
 			b->wds = n;
 			}
 		}
 	if (cmp(b, S) >= 0) {
 		q++;
 		borrow = 0;
 		carry = 0;
 		bx = b->x;
 		sx = S->x;
 		do {
 #ifdef ULLong
 			ys = *sx++ + carry;
 			carry = ys >> 32;
 			y = *bx - (ys & FFFFFFFF) - borrow;
 			borrow = y >> 32 & (ULong)1;
 			*bx++ = y & FFFFFFFF;
 #else
 #ifdef Pack_32
 			si = *sx++;
 			ys = (si & 0xffff) + carry;
 			zs = (si >> 16) + (ys >> 16);
 			carry = zs >> 16;
 			y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
 			borrow = (y & 0x10000) >> 16;
 			z = (*bx >> 16) - (zs & 0xffff) - borrow;
 			borrow = (z & 0x10000) >> 16;
 			Storeinc(bx, z, y);
 #else
 			ys = *sx++ + carry;
 			carry = ys >> 16;
 			y = *bx - (ys & 0xffff) - borrow;
 			borrow = (y & 0x10000) >> 16;
 			*bx++ = y & 0xffff;
 #endif
 #endif
 			}
 			while(sx <= sxe);
 		bx = b->x;
 		bxe = bx + n;
 		if (!*bxe) {
 			while(--bxe > bx && !*bxe)
 				--n;
 			b->wds = n;
 			}
 		}
 	return q;
 	}
 #ifndef NO_STRTOD_BIGCOMP
  static void
 bigcomp
 #ifdef KR_headers
 	(rv, s0, bc)
 	U *rv; CONST char *s0; BCinfo *bc;
 #else
 	(U *rv, CONST char *s0, BCinfo *bc)
 #endif
 {
 	Bigint *b, *d;
 	int b2, bbits, d2, dd, dig, dsign, i, j, nd, nd0, p2, p5, speccase;
 	dsign = bc->dsign;
 	nd = bc->nd;
 	nd0 = bc->nd0;
 	p5 = nd + bc->e0 - 1;
 	dd = speccase = 0;
 #ifndef Sudden_Underflow
 	if (rv->d == 0.) {	/* special case: value near underflow-to-zero */
 				/* threshold was rounded to zero */
 		b = i2b(1);
 		p2 = Emin - P + 1;
 		bbits = 1;
 #ifdef Avoid_Underflow
 		word0(rv) = (P+2) << Exp_shift;
 #else
 		word1(rv) = 1;
 #endif
 		i = 0;
 #ifdef Honor_FLT_ROUNDS
 		if (bc->rounding == 1)
 #endif
 			{
 			speccase = 1;
 			--p2;
 			dsign = 0;
 			goto have_i;
 			}
 		}
 	else
 #endif
 		b = d2b(rv, &p2, &bbits);
 #ifdef Avoid_Underflow
 	p2 -= bc->scale;
 #endif
 	/* floor(log2(rv)) == bbits - 1 + p2 */
 	/* Check for denormal case. */
 	i = P - bbits;
 	if (i > (j = P - Emin - 1 + p2)) {
 #ifdef Sudden_Underflow
 		Bfree(b);
 		b = i2b(1);
 		p2 = Emin;
 		i = P - 1;
 #ifdef Avoid_Underflow
 		word0(rv) = (1 + bc->scale) << Exp_shift;
 #else
 		word0(rv) = Exp_msk1;
 #endif
 		word1(rv) = 0;
 #else
 		i = j;
 #endif
 		}
 #ifdef Honor_FLT_ROUNDS
 	if (bc->rounding != 1) {
 		if (i > 0)
 			b = lshift(b, i);
 		if (dsign)
 			b = increment(b);
 		}
 	else
 #endif
 		{
 		b = lshift(b, ++i);
 		b->x[0] |= 1;
 		}
 #ifndef Sudden_Underflow
  have_i:
 #endif
 	p2 -= p5 + i;
 	d = i2b(1);
 	/* Arrange for convenient computation of quotients:
 	 * shift left if necessary so divisor has 4 leading 0 bits.
 	 */
 	if (p5 > 0)
 		d = pow5mult(d, p5);
 	else if (p5 < 0)
 		b = pow5mult(b, -p5);
 	if (p2 > 0) {
 		b2 = p2;
 		d2 = 0;
 		}
 	else {
 		b2 = 0;
 		d2 = -p2;
 		}
 	i = dshift(d, d2);
 	if ((b2 += i) > 0)
 		b = lshift(b, b2);
 	if ((d2 += i) > 0)
 		d = lshift(d, d2);
 	/* Now b/d = exactly half-way between the two floating-point values */
 	/* on either side of the input string.  Compute first digit of b/d. */
 	if (!(dig = quorem(b,d))) {
 		b = multadd(b, 10, 0);	/* very unlikely */
 		dig = quorem(b,d);
 		}
 	/* Compare b/d with s0 */
 	for(i = 0; i < nd0; ) {
 		if ((dd = s0[i++] - '0' - dig))
 			goto ret;
 		if (!b->x[0] && b->wds == 1) {
 			if (i < nd)
 				dd = 1;
 			goto ret;
 			}
 		b = multadd(b, 10, 0);
 		dig = quorem(b,d);
 		}
 	for(j = bc->dp1; i++ < nd;) {
 		if ((dd = s0[j++] - '0' - dig))
 			goto ret;
 		if (!b->x[0] && b->wds == 1) {
 			if (i < nd)
 				dd = 1;
 			goto ret;
 			}
 		b = multadd(b, 10, 0);
 		dig = quorem(b,d);
 		}
 	if (b->x[0] || b->wds > 1)
 		dd = -1;
  ret:
 	Bfree(b);
 	Bfree(d);
 #ifdef Honor_FLT_ROUNDS
 	if (bc->rounding != 1) {
 		if (dd < 0) {
 			if (bc->rounding == 0) {
 				if (!dsign)
 					goto retlow1;
 				}
 			else if (dsign)
 				goto rethi1;
 			}
 		else if (dd > 0) {
 			if (bc->rounding == 0) {
 				if (dsign)
 					goto rethi1;
 				goto ret1;
 				}
 			if (!dsign)
 				goto rethi1;
 			dval(rv) += 2.*ulp(rv);
 			}
 		else {
 			bc->inexact = 0;
 			if (dsign)
 				goto rethi1;
 			}
 		}
 	else
 #endif
 	if (speccase) {
 		if (dd <= 0)
 			rv->d = 0.;
 		}
 	else if (dd < 0) {
 		if (!dsign)	/* does not happen for round-near */
 retlow1:
 			dval(rv) -= ulp(rv);
 		}
 	else if (dd > 0) {
 		if (dsign) {
  rethi1:
 			dval(rv) += ulp(rv);
 			}
 		}
 	else {
 		/* Exact half-way case:  apply round-even rule. */
 		if (word1(rv) & 1) {
 			if (dsign)
 				goto rethi1;
 			goto retlow1;
 			}
 		}
 #ifdef Honor_FLT_ROUNDS
  ret1:
 #endif
 	return;
 	}
 #endif /* NO_STRTOD_BIGCOMP */
  double
 strtod
 #ifdef KR_headers
 	(s00, se) CONST char *s00; char **se;
 #else
 	(CONST char *s00, char **se)
 #endif
 {
 	int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, e, e1;
 	int esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
 	CONST char *s, *s0, *s1;
 	double aadj, aadj1;
 	Long L;
 	U aadj2, adj, rv, rv0;
 	ULong y, z;
 	BCinfo bc;
 	Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
 #ifdef SET_INEXACT
 	int oldinexact;
 #endif
 #ifdef Honor_FLT_ROUNDS /*{*/
 #ifdef Trust_FLT_ROUNDS /*{{ only define this if FLT_ROUNDS really works! */
 	bc.rounding = Flt_Rounds;
 #else /*}{*/
 	bc.rounding = 1;
 	switch(fegetround()) {
 	  case FE_TOWARDZERO:	bc.rounding = 0; break;
 	  case FE_UPWARD:	bc.rounding = 2; break;
 	  case FE_DOWNWARD:	bc.rounding = 3;
 	  }
 #endif /*}}*/
 #endif /*}*/
 #ifdef USE_LOCALE
 	CONST char *s2;
 #endif
 	sign = nz0 = nz = bc.dplen = bc.uflchk = 0;
 	dval(&rv) = 0.;
 	for(s = s00;;s++) switch(*s) {
 		case '-':
 			sign = 1;
 			/* no break */
 		case '+':
 			if (*++s)
 				goto break2;
 			/* no break */
 		case 0:
 			goto ret0;
 		case '\t':
 		case '\n':
 		case '\v':
 		case '\f':
 		case '\r':
 		case ' ':
 			continue;
 		default:
 			goto break2;
 		}
  break2:
 	if (*s == '0') {
 #ifndef NO_HEX_FP /*{*/
 		switch(s[1]) {
 		  case 'x':
 		  case 'X':
 #ifdef Honor_FLT_ROUNDS
 			gethex(&s, &rv, bc.rounding, sign);
 #else
 			gethex(&s, &rv, 1, sign);
 #endif
 			goto ret;
 		  }
 #endif /*}*/
 		nz0 = 1;
 		while(*++s == '0') ;
 		if (!*s)
 			goto ret;
 		}
 	s0 = s;
 	y = z = 0;
 	for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
 		if (nd < 9)
 			y = 10*y + c - '0';
 		else if (nd < 16)
 			z = 10*z + c - '0';
 	nd0 = nd;
 	bc.dp0 = bc.dp1 = s - s0;
 #ifdef USE_LOCALE
 	s1 = localeconv()->decimal_point;
 	if (c == *s1) {
 		c = '.';
 		if (*++s1) {
 			s2 = s;
 			for(;;) {
 				if (*++s2 != *s1) {
 					c = 0;
 					break;
 					}
 				if (!*++s1) {
 					s = s2;
 					break;
 					}
 				}
 			}
 		}
 #endif
 	if (c == '.') {
 		c = *++s;
 		bc.dp1 = s - s0;
 		bc.dplen = bc.dp1 - bc.dp0;
 		if (!nd) {
 			for(; c == '0'; c = *++s)
 				nz++;
 			if (c > '0' && c <= '9') {
 				s0 = s;
 				nf += nz;
 				nz = 0;
 				goto have_dig;
 				}
 			goto dig_done;
 			}
 		for(; c >= '0' && c <= '9'; c = *++s) {
  have_dig:
 			nz++;
 			if (c -= '0') {
 				nf += nz;
 				for(i = 1; i < nz; i++)
 					if (nd++ < 9)
 						y *= 10;
 					else if (nd <= DBL_DIG + 1)
 						z *= 10;
 				if (nd++ < 9)
 					y = 10*y + c;
 				else if (nd <= DBL_DIG + 1)
 					z = 10*z + c;
 				nz = 0;
 				}
 			}
 		}
  dig_done:
 	e = 0;
 	if (c == 'e' || c == 'E') {
 		if (!nd && !nz && !nz0) {
 			goto ret0;
 			}
 		s00 = s;
 		esign = 0;
 		switch(c = *++s) {
 			case '-':
 				esign = 1;
 			case '+':
 				c = *++s;
 			}
 		if (c >= '0' && c <= '9') {
 			while(c == '0')
 				c = *++s;
 			if (c > '0' && c <= '9') {
 				L = c - '0';
 				s1 = s;
 				while((c = *++s) >= '0' && c <= '9')
 					L = 10*L + c - '0';
 				if (s - s1 > 8 || L > 19999)
 					/* Avoid confusion from exponents
 					 * so large that e might overflow.
 					 */
 					e = 19999; /* safe for 16 bit ints */
 				else
 					e = (int)L;
 				if (esign)
 					e = -e;
 				}
 			else
 				e = 0;
 			}
 		else
 			s = s00;
 		}
 	if (!nd) {
 		if (!nz && !nz0) {
 #ifdef INFNAN_CHECK
 			/* Check for Nan and Infinity */
 			if (!bc.dplen)
 			 switch(c) {
 			  case 'i':
 			  case 'I':
 				if (match(&s,"nf")) {
 					--s;
 					if (!match(&s,"inity"))
 						++s;
 					word0(&rv) = 0x7ff00000;
 					word1(&rv) = 0;
 					goto ret;
 					}
 				break;
 			  case 'n':
 			  case 'N':
 				if (match(&s, "an")) {
 					word0(&rv) = NAN_WORD0;
 					word1(&rv) = NAN_WORD1;
 #ifndef No_Hex_NaN
 					if (*s == '(') /*)*/
 						hexnan(&rv, &s);
 #endif
 					goto ret;
 					}
 			  }
 #endif /* INFNAN_CHECK */
  ret0:
 			s = s00;
 			sign = 0;
 			}
 		goto ret;
 		}
 	bc.e0 = e1 = e -= nf;
 	/* Now we have nd0 digits, starting at s0, followed by a
 	 * decimal point, followed by nd-nd0 digits.  The number we're
 	 * after is the integer represented by those digits times
 	 * 10**e */
 	if (!nd0)
 		nd0 = nd;
 	k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
 	dval(&rv) = y;
 	if (k > 9) {
 #ifdef SET_INEXACT
 		if (k > DBL_DIG)
 			oldinexact = get_inexact();
 #endif
 		dval(&rv) = tens[k - 9] * dval(&rv) + z;
 		}
 	bd0 = 0;
 	if (nd <= DBL_DIG
 #ifndef RND_PRODQUOT
 #ifndef Honor_FLT_ROUNDS
 		&& Flt_Rounds == 1
 #endif
 #endif
 			) {
 		if (!e)
 			goto ret;
 		if (e > 0) {
 			if (e <= Ten_pmax) {
 #ifdef VAX
 				goto vax_ovfl_check;
 #else
 #ifdef Honor_FLT_ROUNDS
 				/* round correctly FLT_ROUNDS = 2 or 3 */
 				if (sign) {
 					rv.d = -rv.d;
 					sign = 0;
 					}
 #endif
 				/* rv = */ rounded_product(dval(&rv), tens[e]);
 				goto ret;
 #endif
 				}
 			i = DBL_DIG - nd;
 			if (e <= Ten_pmax + i) {
 				/* A fancier test would sometimes let us do
 				 * this for larger i values.
 				 */
 #ifdef Honor_FLT_ROUNDS
 				/* round correctly FLT_ROUNDS = 2 or 3 */
 				if (sign) {
 					rv.d = -rv.d;
 					sign = 0;
 					}
 #endif
 				e -= i;
 				dval(&rv) *= tens[i];
 #ifdef VAX
 				/* VAX exponent range is so narrow we must
 				 * worry about overflow here...
 				 */
  vax_ovfl_check:
 				word0(&rv) -= P*Exp_msk1;
 				/* rv = */ rounded_product(dval(&rv), tens[e]);
 				if ((word0(&rv) & Exp_mask)
 				 > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
 					goto ovfl;
 				word0(&rv) += P*Exp_msk1;
 #else
 				/* rv = */ rounded_product(dval(&rv), tens[e]);
 #endif
 				goto ret;
 				}
 			}
 #ifndef Inaccurate_Divide
 		else if (e >= -Ten_pmax) {
 #ifdef Honor_FLT_ROUNDS
 			/* round correctly FLT_ROUNDS = 2 or 3 */
 			if (sign) {
 				rv.d = -rv.d;
 				sign = 0;
 				}
 #endif
 			/* rv = */ rounded_quotient(dval(&rv), tens[-e]);
 			goto ret;
 			}
 #endif
 		}
 	e1 += nd - k;
 #ifdef IEEE_Arith
 #ifdef SET_INEXACT
 	bc.inexact = 1;
 	if (k <= DBL_DIG)
 		oldinexact = get_inexact();
 #endif
 #ifdef Avoid_Underflow
 	bc.scale = 0;
 #endif
 #ifdef Honor_FLT_ROUNDS
 	if (bc.rounding >= 2) {
 		if (sign)
 			bc.rounding = bc.rounding == 2 ? 0 : 2;
 		else
 			if (bc.rounding != 2)
 				bc.rounding = 0;
 		}
 #endif
 #endif /*IEEE_Arith*/
 	/* Get starting approximation = rv * 10**e1 */
 	if (e1 > 0) {
 		if ((i = e1 & 15))
 			dval(&rv) *= tens[i];
 		if (e1 &= ~15) {
 			if (e1 > DBL_MAX_10_EXP) {
  ovfl:
 #ifndef NO_ERRNO
 				errno = ERANGE;
 #endif
 				/* Can't trust HUGE_VAL */
 #ifdef IEEE_Arith
 #ifdef Honor_FLT_ROUNDS
 				switch(bc.rounding) {
 				  case 0: /* toward 0 */
 				  case 3: /* toward -infinity */
 					word0(&rv) = Big0;
 					word1(&rv) = Big1;
 					break;
 				  default:
 					word0(&rv) = Exp_mask;
 					word1(&rv) = 0;
 				  }
 #else /*Honor_FLT_ROUNDS*/
 				word0(&rv) = Exp_mask;
 				word1(&rv) = 0;
 #endif /*Honor_FLT_ROUNDS*/
 #ifdef SET_INEXACT
 				/* set overflow bit */
 				dval(&rv0) = 1e300;
 				dval(&rv0) *= dval(&rv0);
 #endif
 #else /*IEEE_Arith*/
 				word0(&rv) = Big0;
 				word1(&rv) = Big1;
 #endif /*IEEE_Arith*/
 				goto ret;
 				}
 			e1 >>= 4;
 			for(j = 0; e1 > 1; j++, e1 >>= 1)
 				if (e1 & 1)
 					dval(&rv) *= bigtens[j];
 		/* The last multiplication could overflow. */
 			word0(&rv) -= P*Exp_msk1;
 			dval(&rv) *= bigtens[j];
 			if ((z = word0(&rv) & Exp_mask)
 			 > Exp_msk1*(DBL_MAX_EXP+Bias-P))
 				goto ovfl;
 			if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
 				/* set to largest number */
 				/* (Can't trust DBL_MAX) */
 				word0(&rv) = Big0;
 				word1(&rv) = Big1;
 				}
 			else
 				word0(&rv) += P*Exp_msk1;
 			}
 		}
 	else if (e1 < 0) {
 		e1 = -e1;
 		if ((i = e1 & 15))
 			dval(&rv) /= tens[i];
 		if (e1 >>= 4) {
 			if (e1 >= 1 << n_bigtens)
 				goto undfl;
 #ifdef Avoid_Underflow
 			if (e1 & Scale_Bit)
 				bc.scale = 2*P;
 			for(j = 0; e1 > 0; j++, e1 >>= 1)
 				if (e1 & 1)
 					dval(&rv) *= tinytens[j];
 			if (bc.scale && (j = 2*P + 1 - ((word0(&rv) & Exp_mask)
 						>> Exp_shift)) > 0) {
 				/* scaled rv is denormal; clear j low bits */
 				if (j >= 32) {
 					word1(&rv) = 0;
 					if (j >= 53)
 					 word0(&rv) = (P+2)*Exp_msk1;
 					else
 					 word0(&rv) &= 0xffffffff << (j-32);
 					}
 				else
 					word1(&rv) &= 0xffffffff << j;
 				}
 #else
 			for(j = 0; e1 > 1; j++, e1 >>= 1)
 				if (e1 & 1)
 					dval(&rv) *= tinytens[j];
 			/* The last multiplication could underflow. */
 			dval(&rv0) = dval(&rv);
 			dval(&rv) *= tinytens[j];
 			if (!dval(&rv)) {
 				dval(&rv) = 2.*dval(&rv0);
 				dval(&rv) *= tinytens[j];
 #endif
 				if (!dval(&rv)) {
  undfl:
 					dval(&rv) = 0.;
 #ifndef NO_ERRNO
 					errno = ERANGE;
 #endif
 					goto ret;
 					}
 #ifndef Avoid_Underflow
 				word0(&rv) = Tiny0;
 				word1(&rv) = Tiny1;
 				/* The refinement below will clean
 				 * this approximation up.
 				 */
 				}
 #endif
 			}
 		}
 	/* Now the hard part -- adjusting rv to the correct value.*/
 	/* Put digits into bd: true value = bd * 10^e */
 	bc.nd = nd;
 #ifndef NO_STRTOD_BIGCOMP
 	bc.nd0 = nd0;	/* Only needed if nd > strtod_diglim, but done here */
 			/* to silence an erroneous warning about bc.nd0 */
 			/* possibly not being initialized. */
 	if (nd > strtod_diglim) {
 		/* ASSERT(strtod_diglim >= 18); 18 == one more than the */
 		/* minimum number of decimal digits to distinguish double values */
 		/* in IEEE arithmetic. */
 		i = j = 18;
 		if (i > nd0)
 			j += bc.dplen;
 		for(;;) {
 			if (--j <= bc.dp1 && j >= bc.dp0)
 				j = bc.dp0 - 1;
 			if (s0[j] != '0')
 				break;
 			--i;
 			}
 		e += nd - i;
 		nd = i;
 		if (nd0 > nd)
 			nd0 = nd;
 		if (nd < 9) { /* must recompute y */
 			y = 0;
 			for(i = 0; i < nd0; ++i)
 				y = 10*y + s0[i] - '0';
 			for(j = bc.dp1; i < nd; ++i)
 				y = 10*y + s0[j++] - '0';
 			}
 		}
 #endif
 	bd0 = s2b(s0, nd0, nd, y, bc.dplen);
 	for(;;) {
 		bd = Balloc(bd0->k);
 		Bcopy(bd, bd0);
 		bb = d2b(&rv, &bbe, &bbbits);	/* rv = bb * 2^bbe */
 		bs = i2b(1);
 		if (e >= 0) {
 			bb2 = bb5 = 0;
 			bd2 = bd5 = e;
 			}
 		else {
 			bb2 = bb5 = -e;
 			bd2 = bd5 = 0;
 			}
 		if (bbe >= 0)
 			bb2 += bbe;
 		else
 			bd2 -= bbe;
 		bs2 = bb2;
 #ifdef Honor_FLT_ROUNDS
 		if (bc.rounding != 1)
 			bs2++;
 #endif
 #ifdef Avoid_Underflow
 		j = bbe - bc.scale;
 		i = j + bbbits - 1;	/* logb(rv) */
 		if (i < Emin)	/* denormal */
 			j += P - Emin;
 		else
 			j = P + 1 - bbbits;
 #else /*Avoid_Underflow*/
 #ifdef Sudden_Underflow
 #ifdef IBM
 		j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
 #else
 		j = P + 1 - bbbits;
 #endif
 #else /*Sudden_Underflow*/
 		j = bbe;
 		i = j + bbbits - 1;	/* logb(rv) */
 		if (i < Emin)	/* denormal */
 			j += P - Emin;
 		else
 			j = P + 1 - bbbits;
 #endif /*Sudden_Underflow*/
 #endif /*Avoid_Underflow*/
 		bb2 += j;
 		bd2 += j;
 #ifdef Avoid_Underflow
 		bd2 += bc.scale;
 #endif
 		i = bb2 < bd2 ? bb2 : bd2;
 		if (i > bs2)
 			i = bs2;
 		if (i > 0) {
 			bb2 -= i;
 			bd2 -= i;
 			bs2 -= i;
 			}
 		if (bb5 > 0) {
 			bs = pow5mult(bs, bb5);
 			bb1 = mult(bs, bb);
 			Bfree(bb);
 			bb = bb1;
 			}
 		if (bb2 > 0)
 			bb = lshift(bb, bb2);
 		if (bd5 > 0)
 			bd = pow5mult(bd, bd5);
 		if (bd2 > 0)
 			bd = lshift(bd, bd2);
 		if (bs2 > 0)
 			bs = lshift(bs, bs2);
 		delta = diff(bb, bd);
 		bc.dsign = delta->sign;
 		delta->sign = 0;
 		i = cmp(delta, bs);
 #ifndef NO_STRTOD_BIGCOMP
 		if (bc.nd > nd && i <= 0) {
 			if (bc.dsign)
 				break;	/* Must use bigcomp(). */
 #ifdef Honor_FLT_ROUNDS
 			if (bc.rounding != 1) {
 				if (i < 0)
 					break;
 				}
 			else
 #endif
 				{
 				bc.nd = nd;
 				i = -1;	/* Discarded digits make delta smaller. */
 				}
 			}
 #endif
 #ifdef Honor_FLT_ROUNDS
 		if (bc.rounding != 1) {
 			if (i < 0) {
 				/* Error is less than an ulp */
 				if (!delta->x[0] && delta->wds <= 1) {
 					/* exact */
 #ifdef SET_INEXACT
 					bc.inexact = 0;
 #endif
 					break;
 					}
 				if (bc.rounding) {
 					if (bc.dsign) {
 						adj.d = 1.;
 						goto apply_adj;
 						}
 					}
 				else if (!bc.dsign) {
 					adj.d = -1.;
 					if (!word1(&rv)
 					 && !(word0(&rv) & Frac_mask)) {
 						y = word0(&rv) & Exp_mask;
 #ifdef Avoid_Underflow
 						if (!bc.scale || y > 2*P*Exp_msk1)
 #else
 						if (y)
 #endif
 						  {
 						  delta = lshift(delta,Log2P);
 						  if (cmp(delta, bs) <= 0)
 							adj.d = -0.5;
 						  }
 						}
  apply_adj:
 #ifdef Avoid_Underflow
 					if (bc.scale && (y = word0(&rv) & Exp_mask)
 						<= 2*P*Exp_msk1)
 					  word0(&adj) += (2*P+1)*Exp_msk1 - y;
 #else
 #ifdef Sudden_Underflow
 					if ((word0(&rv) & Exp_mask) <=
 							P*Exp_msk1) {
 						word0(&rv) += P*Exp_msk1;
 						dval(&rv) += adj.d*ulp(dval(&rv));
 						word0(&rv) -= P*Exp_msk1;
 						}
 					else
 #endif /*Sudden_Underflow*/
 #endif /*Avoid_Underflow*/
 					dval(&rv) += adj.d*ulp(&rv);
 					}
 				break;
 				}
 			adj.d = ratio(delta, bs);
 			if (adj.d < 1.)
 				adj.d = 1.;
 			if (adj.d <= 0x7ffffffe) {
 				/* adj = rounding ? ceil(adj) : floor(adj); */
 				y = adj.d;
 				if (y != adj.d) {
 					if (!((bc.rounding>>1) ^ bc.dsign))
 						y++;
 					adj.d = y;
 					}
 				}
 #ifdef Avoid_Underflow
 			if (bc.scale && (y = word0(&rv) & Exp_mask) <= 2*P*Exp_msk1)
 				word0(&adj) += (2*P+1)*Exp_msk1 - y;
 #else
 #ifdef Sudden_Underflow
 			if ((word0(&rv) & Exp_mask) <= P*Exp_msk1) {
 				word0(&rv) += P*Exp_msk1;
 				adj.d *= ulp(dval(&rv));
 				if (bc.dsign)
 					dval(&rv) += adj.d;
 				else
 					dval(&rv) -= adj.d;
 				word0(&rv) -= P*Exp_msk1;
 				goto cont;
 				}
 #endif /*Sudden_Underflow*/
 #endif /*Avoid_Underflow*/
 			adj.d *= ulp(&rv);
 			if (bc.dsign) {
 				if (word0(&rv) == Big0 && word1(&rv) == Big1)
 					goto ovfl;
 				dval(&rv) += adj.d;
 				}
 			else
 				dval(&rv) -= adj.d;
 			goto cont;
 			}
 #endif /*Honor_FLT_ROUNDS*/
 		if (i < 0) {
 			/* Error is less than half an ulp -- check for
 			 * special case of mantissa a power of two.
 			 */
 			if (bc.dsign || word1(&rv) || word0(&rv) & Bndry_mask
 #ifdef IEEE_Arith
 #ifdef Avoid_Underflow
 			 || (word0(&rv) & Exp_mask) <= (2*P+1)*Exp_msk1
 #else
 			 || (word0(&rv) & Exp_mask) <= Exp_msk1
 #endif
 #endif
 				) {
 #ifdef SET_INEXACT
 				if (!delta->x[0] && delta->wds <= 1)
 					bc.inexact = 0;
 #endif
 				break;
 				}
 			if (!delta->x[0] && delta->wds <= 1) {
 				/* exact result */
 #ifdef SET_INEXACT
 				bc.inexact = 0;
 #endif
 				break;
 				}
 			delta = lshift(delta,Log2P);
 			if (cmp(delta, bs) > 0)
 				goto drop_down;
 			break;
 			}
 		if (i == 0) {
 			/* exactly half-way between */
 			if (bc.dsign) {
 				if ((word0(&rv) & Bndry_mask1) == Bndry_mask1
 				 &&  word1(&rv) == (
 #ifdef Avoid_Underflow
 			(bc.scale && (y = word0(&rv) & Exp_mask) <= 2*P*Exp_msk1)
 		? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
 #endif
 xffffffff)) {
 					/*boundary case -- increment exponent*/
 					word0(&rv) = (word0(&rv) & Exp_mask)
 						+ Exp_msk1
 #ifdef IBM
 						| Exp_msk1 >> 4
 #endif
 						;
 					word1(&rv) = 0;
 #ifdef Avoid_Underflow
 					bc.dsign = 0;
 #endif
 					break;
 					}
 				}
 			else if (!(word0(&rv) & Bndry_mask) && !word1(&rv)) {
  drop_down:
 				/* boundary case -- decrement exponent */
 #ifdef Sudden_Underflow /*{{*/
 				L = word0(&rv) & Exp_mask;
 #ifdef IBM
 				if (L <  Exp_msk1)
 #else
 #ifdef Avoid_Underflow
 				if (L <= (bc.scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
 #else
 				if (L <= Exp_msk1)
 #endif /*Avoid_Underflow*/
 #endif /*IBM*/
 					{
 					if (bc.nd >nd) {
 						bc.uflchk = 1;
 						break;
 						}
 					goto undfl;
 					}
 				L -= Exp_msk1;
 #else /*Sudden_Underflow}{*/
 #ifdef Avoid_Underflow
 				if (bc.scale) {
 					L = word0(&rv) & Exp_mask;
 					if (L <= (2*P+1)*Exp_msk1) {
 						if (L > (P+2)*Exp_msk1)
 							/* round even ==> */
 							/* accept rv */
 							break;
 						/* rv = smallest denormal */
 						if (bc.nd >nd) {
 							bc.uflchk = 1;
 							break;
 							}
 						goto undfl;
 						}
 					}
 #endif /*Avoid_Underflow*/
 				L = (word0(&rv) & Exp_mask) - Exp_msk1;
 #endif /*Sudden_Underflow}}*/
 				word0(&rv) = L | Bndry_mask1;
 				word1(&rv) = 0xffffffff;
 #ifdef IBM
 				goto cont;
 #else
 				break;
 #endif
 				}
 #ifndef ROUND_BIASED
 			if (!(word1(&rv) & LSB))
 				break;
 #endif
 			if (bc.dsign)
 				dval(&rv) += ulp(&rv);
 #ifndef ROUND_BIASED
 			else {
 				dval(&rv) -= ulp(&rv);
 #ifndef Sudden_Underflow
 				if (!dval(&rv)) {
 					if (bc.nd >nd) {
 						bc.uflchk = 1;
 						break;
 						}
 					goto undfl;
 					}
 #endif
 				}
 #ifdef Avoid_Underflow
 			bc.dsign = 1 - bc.dsign;
 #endif
 #endif
 			break;
 			}
 		if ((aadj = ratio(delta, bs)) <= 2.) {
 			if (bc.dsign)
 				aadj = aadj1 = 1.;
 			else if (word1(&rv) || word0(&rv) & Bndry_mask) {
 #ifndef Sudden_Underflow
 				if (word1(&rv) == Tiny1 && !word0(&rv)) {
 					if (bc.nd >nd) {
 						bc.uflchk = 1;
 						break;
 						}
 					goto undfl;
 					}
 #endif
 				aadj = 1.;
 				aadj1 = -1.;
 				}
 			else {
 				/* special case -- power of FLT_RADIX to be */
 				/* rounded down... */
 				if (aadj < 2./FLT_RADIX)
 					aadj = 1./FLT_RADIX;
 				else
 					aadj *= 0.5;
 				aadj1 = -aadj;
 				}
 			}
 		else {
 			aadj *= 0.5;
 			aadj1 = bc.dsign ? aadj : -aadj;
 #ifdef Check_FLT_ROUNDS
 			switch(bc.rounding) {
 				case 2: /* towards +infinity */
 					aadj1 -= 0.5;
 					break;
 				case 0: /* towards 0 */
 				case 3: /* towards -infinity */
 					aadj1 += 0.5;
 				}
 #else
 			if (Flt_Rounds == 0)
 				aadj1 += 0.5;
 #endif /*Check_FLT_ROUNDS*/
 			}
 		y = word0(&rv) & Exp_mask;
 		/* Check for overflow */
 		if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
 			dval(&rv0) = dval(&rv);
 			word0(&rv) -= P*Exp_msk1;
 			adj.d = aadj1 * ulp(&rv);
 			dval(&rv) += adj.d;
 			if ((word0(&rv) & Exp_mask) >=
 					Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
 				if (word0(&rv0) == Big0 && word1(&rv0) == Big1)
 					goto ovfl;
 				word0(&rv) = Big0;
 				word1(&rv) = Big1;
 				goto cont;
 				}
 			else
 				word0(&rv) += P*Exp_msk1;
 			}
 		else {
 #ifdef Avoid_Underflow
 			if (bc.scale && y <= 2*P*Exp_msk1) {
 				if (aadj <= 0x7fffffff) {
 					if ((z = aadj) <= 0)
 						z = 1;
 					aadj = z;
 					aadj1 = bc.dsign ? aadj : -aadj;
 					}
 				dval(&aadj2) = aadj1;
 				word0(&aadj2) += (2*P+1)*Exp_msk1 - y;
 				aadj1 = dval(&aadj2);
 				}
 			adj.d = aadj1 * ulp(&rv);
 			dval(&rv) += adj.d;
 #else
 #ifdef Sudden_Underflow
 			if ((word0(&rv) & Exp_mask) <= P*Exp_msk1) {
 				dval(&rv0) = dval(&rv);
 				word0(&rv) += P*Exp_msk1;
 				adj.d = aadj1 * ulp(&rv);
 				dval(&rv) += adj.d;
 #ifdef IBM
 				if ((word0(&rv) & Exp_mask) <  P*Exp_msk1)
 #else
 				if ((word0(&rv) & Exp_mask) <= P*Exp_msk1)
 #endif
 					{
 					if (word0(&rv0) == Tiny0
 					 && word1(&rv0) == Tiny1) {
 						if (bc.nd >nd) {
 							bc.uflchk = 1;
 							break;
 							}
 						goto undfl;
 						}
 					word0(&rv) = Tiny0;
 					word1(&rv) = Tiny1;
 					goto cont;
 					}
 				else
 					word0(&rv) -= P*Exp_msk1;
 				}
 			else {
 				adj.d = aadj1 * ulp(&rv);
 				dval(&rv) += adj.d;
 				}
 #else /*Sudden_Underflow*/
 			/* Compute adj so that the IEEE rounding rules will
 			 * correctly round rv + adj in some half-way cases.
 			 * If rv * ulp(rv) is denormalized (i.e.,
 			 * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
 			 * trouble from bits lost to denormalization;
 			 * example: 1.2e-307 .
 			 */
 			if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
 				aadj1 = (double)(int)(aadj + 0.5);
 				if (!bc.dsign)
 					aadj1 = -aadj1;
 				}
 			adj.d = aadj1 * ulp(&rv);
 			dval(&rv) += adj.d;
 #endif /*Sudden_Underflow*/
 #endif /*Avoid_Underflow*/
 			}
 		z = word0(&rv) & Exp_mask;
 #ifndef SET_INEXACT
 		if (bc.nd == nd) {
 #ifdef Avoid_Underflow
 		if (!bc.scale)
 #endif
 		if (y == z) {
 			/* Can we stop now? */
 			L = (Long)aadj;
 			aadj -= L;
 			/* The tolerances below are conservative. */
 			if (bc.dsign || word1(&rv) || word0(&rv) & Bndry_mask) {
 				if (aadj < .4999999 || aadj > .5000001)
 					break;
 				}
 			else if (aadj < .4999999/FLT_RADIX)
 				break;
 			}
 		}
 #endif
  cont:
 		Bfree(bb);
 		Bfree(bd);
 		Bfree(bs);
 		Bfree(delta);
 		}
 	Bfree(bb);
 	Bfree(bd);
 	Bfree(bs);
 	Bfree(bd0);
 	Bfree(delta);
 #ifndef NO_STRTOD_BIGCOMP
 	if (bc.nd > nd)
 		bigcomp(&rv, s0, &bc);
 #endif
 #ifdef SET_INEXACT
 	if (bc.inexact) {
 		if (!oldinexact) {
 			word0(&rv0) = Exp_1 + (70 << Exp_shift);
 			word1(&rv0) = 0;
 			dval(&rv0) += 1.;
 			}
 		}
 	else if (!oldinexact)
 		clear_inexact();
 #endif
 #ifdef Avoid_Underflow
 	if (bc.scale) {
 		word0(&rv0) = Exp_1 - 2*P*Exp_msk1;
 		word1(&rv0) = 0;
 		dval(&rv) *= dval(&rv0);
 #ifndef NO_ERRNO
 		/* try to avoid the bug of testing an 8087 register value */
 #ifdef IEEE_Arith
 		if (!(word0(&rv) & Exp_mask))
 #else
 		if (word0(&rv) == 0 && word1(&rv) == 0)
 #endif
 			errno = ERANGE;
 #endif
 		}
 #endif /* Avoid_Underflow */
 #ifdef SET_INEXACT
 	if (bc.inexact && !(word0(&rv) & Exp_mask)) {
 		/* set underflow bit */
 		dval(&rv0) = 1e-300;
 		dval(&rv0) *= dval(&rv0);
 		}
 #endif
  ret:
 	if (se)
 		*se = (char *)s;
 	return sign ? -dval(&rv) : dval(&rv);
 	}
 #ifndef MULTIPLE_THREADS
  static char *dtoa_result;
 #endif
  static char *
 #ifdef KR_headers
 rv_alloc(i) int i;
 #else
 rv_alloc(int i)
 #endif
 {
 	int j, k, *r;
 	j = sizeof(ULong);
 	for(k = 0;
 		sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= (size_t)i;
 		j <<= 1)
 			k++;
 	r = (int*)Balloc(k);
 	*r = k;
 	return
 #ifndef MULTIPLE_THREADS
 	dtoa_result =
 #endif
 		(char *)(r+1);
 	}
  static char *
 #ifdef KR_headers
 nrv_alloc(s, rve, n) char *s, **rve; int n;
 #else
 nrv_alloc(CONST char *s, char **rve, int n)
 #endif
 {
 	char *rv, *t;
 	t = rv = rv_alloc(n);
 	while((*t = *s++)) t++;
 	if (rve)
 		*rve = t;
 	return rv;
 	}
 /* freedtoa(s) must be used to free values s returned by dtoa
  * when MULTIPLE_THREADS is #defined.  It should be used in all cases,
  * but for consistency with earlier versions of dtoa, it is optional
  * when MULTIPLE_THREADS is not defined.
  */
  void
 #ifdef KR_headers
 freedtoa(s) char *s;
 #else
 freedtoa(char *s)
 #endif
 {
 	Bigint *b = (Bigint *)((int *)s - 1);
 	b->maxwds = 1 << (b->k = *(int*)b);
 	Bfree(b);
 #ifndef MULTIPLE_THREADS
 	if (s == dtoa_result)
 		dtoa_result = 0;
 #endif
 	}
 /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
  *
  * Inspired by "How to Print Floating-Point Numbers Accurately" by
  * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
  *
  * Modifications:
  *	1. Rather than iterating, we use a simple numeric overestimate
  *	   to determine k = floor(log10(d)).  We scale relevant
  *	   quantities using O(log2(k)) rather than O(k) multiplications.
  *	2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
  *	   try to generate digits strictly left to right.  Instead, we
  *	   compute with fewer bits and propagate the carry if necessary
  *	   when rounding the final digit up.  This is often faster.
  *	3. Under the assumption that input will be rounded nearest,
  *	   mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
  *	   That is, we allow equality in stopping tests when the
  *	   round-nearest rule will give the same floating-point value
  *	   as would satisfaction of the stopping test with strict
  *	   inequality.
  *	4. We remove common factors of powers of 2 from relevant
  *	   quantities.
  *	5. When converting floating-point integers less than 1e16,
  *	   we use floating-point arithmetic rather than resorting
  *	   to multiple-precision integers.
  *	6. When asked to produce fewer than 15 digits, we first try
  *	   to get by with floating-point arithmetic; we resort to
  *	   multiple-precision integer arithmetic only if we cannot
  *	   guarantee that the floating-point calculation has given
  *	   the correctly rounded result.  For k requested digits and
  *	   "uniformly" distributed input, the probability is
  *	   something like 10^(k-15) that we must resort to the Long
  *	   calculation.
  */
  char *
 dtoa
 #ifdef KR_headers
 	(dd, mode, ndigits, decpt, sign, rve)
 	double dd; int mode, ndigits, *decpt, *sign; char **rve;
 #else
 	(double dd, int mode, int ndigits, int *decpt, int *sign, char **rve)
 #endif
 {
  /*	Arguments ndigits, decpt, sign are similar to those
 	of ecvt and fcvt; trailing zeros are suppressed from
 	the returned string.  If not null, *rve is set to point
 	to the end of the return value.  If d is +-Infinity or NaN,
 	then *decpt is set to 9999.
 	mode:
 ==> shortest string that yields d when read in
 			and rounded to nearest.
 ==> like 0, but with Steele & White stopping rule;
 			e.g. with IEEE P754 arithmetic , mode 0 gives
 e23 whereas mode 1 gives 9.999999999999999e22.
 ==> max(1,ndigits) significant digits.  This gives a
 			return value similar to that of ecvt, except
 			that trailing zeros are suppressed.
 ==> through ndigits past the decimal point.  This
 			gives a return value similar to that from fcvt,
 			except that trailing zeros are suppressed, and
 			ndigits can be negative.
 ,5 ==> similar to 2 and 3, respectively, but (in
 			round-nearest mode) with the tests of mode 0 to
 			possibly return a shorter string that rounds to d.
 			With IEEE arithmetic and compilation with
 			-DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
 			as modes 2 and 3 when FLT_ROUNDS != 1.
 -9 ==> Debugging modes similar to mode - 4:  don't try
 			fast floating-point estimate (if applicable).
 		Values of mode other than 0-9 are treated as mode 0.
 		Sufficient space is allocated to the return value
 		to hold the suppressed trailing zeros.
 	*/
 	int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
 		j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
 		spec_case, try_quick;
 	Long L;
 #ifndef Sudden_Underflow
 	int denorm;
 	ULong x;
 #endif
 	Bigint *b, *b1, *delta, *mlo = NULL, *mhi, *S;
 	U d2, eps, u;
 	double ds;
 	char *s, *s0;
 #ifdef SET_INEXACT
 	int inexact, oldinexact;
 #endif
 #ifdef Honor_FLT_ROUNDS /*{*/
 	int Rounding;
 #ifdef Trust_FLT_ROUNDS /*{{ only define this if FLT_ROUNDS really works! */
 	Rounding = Flt_Rounds;
 #else /*}{*/
 	Rounding = 1;
 	switch(fegetround()) {
 	  case FE_TOWARDZERO:	Rounding = 0; break;
 	  case FE_UPWARD:	Rounding = 2; break;
 	  case FE_DOWNWARD:	Rounding = 3;
 	  }
 #endif /*}}*/
 #endif /*}*/
 #ifndef MULTIPLE_THREADS
 	if (dtoa_result) {
 		freedtoa(dtoa_result);
 		dtoa_result = 0;
 		}
 #endif
 	u.d = dd;
 	if (word0(&u) & Sign_bit) {
 		/* set sign for everything, including 0's and NaNs */
 		*sign = 1;
 		word0(&u) &= ~Sign_bit;	/* clear sign bit */
 		}
 	else
 		*sign = 0;
 #if defined(IEEE_Arith) + defined(VAX)
 #ifdef IEEE_Arith
 	if ((word0(&u) & Exp_mask) == Exp_mask)
 #else
 	if (word0(&u)  == 0x8000)
 #endif
 		{
 		/* Infinity or NaN */
 		*decpt = 9999;
 #ifdef IEEE_Arith
 		if (!word1(&u) && !(word0(&u) & 0xfffff))
 			return nrv_alloc("Infinity", rve, 8);
 #endif
 		return nrv_alloc("NaN", rve, 3);
 		}
 #endif
 #ifdef IBM
 	dval(&u) += 0; /* normalize */
 #endif
 	if (!dval(&u)) {
 		*decpt = 1;
 		return nrv_alloc("0", rve, 1);
 		}
 #ifdef SET_INEXACT
 	try_quick = oldinexact = get_inexact();
 	inexact = 1;
 #endif
 #ifdef Honor_FLT_ROUNDS
 	if (Rounding >= 2) {
 		if (*sign)
 			Rounding = Rounding == 2 ? 0 : 2;
 		else
 			if (Rounding != 2)
 				Rounding = 0;
 		}
 #endif
 	b = d2b(&u, &be, &bbits);
 #ifdef Sudden_Underflow
 	i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
 #else
 	if ((i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) {
 #endif
 		dval(&d2) = dval(&u);
 		word0(&d2) &= Frac_mask1;
 		word0(&d2) |= Exp_11;
 #ifdef IBM
 		if (j = 11 - hi0bits(word0(&d2) & Frac_mask))
 			dval(&d2) /= 1 << j;
 #endif
 		/* log(x)	~=~ log(1.5) + (x-1.5)/1.5
 		 * log10(x)	 =  log(x) / log(10)
 		 *		~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
 		 * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
 		 *
 		 * This suggests computing an approximation k to log10(d) by
 		 *
 		 * k = (i - Bias)*0.301029995663981
 		 *	+ ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
 		 *
 		 * We want k to be too large rather than too small.
 		 * The error in the first-order Taylor series approximation
 		 * is in our favor, so we just round up the constant enough
 		 * to compensate for any error in the multiplication of
 		 * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
 		 * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
 		 * adding 1e-13 to the constant term more than suffices.
 		 * Hence we adjust the constant term to 0.1760912590558.
 		 * (We could get a more accurate k by invoking log10,
 		 *  but this is probably not worthwhile.)
 		 */
 		i -= Bias;
 #ifdef IBM
 		i <<= 2;
 		i += j;
 #endif
 #ifndef Sudden_Underflow
 		denorm = 0;
 		}
 	else {
 		/* d is denormalized */
 		i = bbits + be + (Bias + (P-1) - 1);
 		x = i > 32  ? word0(&u) << (64 - i) | word1(&u) >> (i - 32)
 			    : word1(&u) << (32 - i);
 		dval(&d2) = x;
 		word0(&d2) -= 31*Exp_msk1; /* adjust exponent */
 		i -= (Bias + (P-1) - 1) + 1;
 		denorm = 1;
 		}
 #endif
 	ds = (dval(&d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
 	k = (int)ds;
 	if (ds < 0. && ds != k)
 		k--;	/* want k = floor(ds) */
 	k_check = 1;
 	if (k >= 0 && k <= Ten_pmax) {
 		if (dval(&u) < tens[k])
 			k--;
 		k_check = 0;
 		}
 	j = bbits - i - 1;
 	if (j >= 0) {
 		b2 = 0;
 		s2 = j;
 		}
 	else {
 		b2 = -j;
 		s2 = 0;
 		}
 	if (k >= 0) {
 		b5 = 0;
 		s5 = k;
 		s2 += k;
 		}
 	else {
 		b2 -= k;
 		b5 = -k;
 		s5 = 0;
 		}
 	if (mode < 0 || mode > 9)
 		mode = 0;
 #ifndef SET_INEXACT
 #ifdef Check_FLT_ROUNDS
 	try_quick = Rounding == 1;
 #else
 	try_quick = 1;
 #endif
 #endif /*SET_INEXACT*/
 	if (mode > 5) {
 		mode -= 4;
 		try_quick = 0;
 		}
 	leftright = 1;
 	ilim = ilim1 = -1;	/* Values for cases 0 and 1; done here to */
 				/* silence erroneous "gcc -Wall" warning. */
 	switch(mode) {
 		case 0:
 		case 1:
 			i = 18;
 			ndigits = 0;
 			break;
 		case 2:
 			leftright = 0;
 			/* no break */
 		case 4:
 			if (ndigits <= 0)
 				ndigits = 1;
 			ilim = ilim1 = i = ndigits;
 			break;
 		case 3:
 			leftright = 0;
 			/* no break */
 		case 5:
 			i = ndigits + k + 1;
 			ilim = i;
 			ilim1 = i - 1;
 			if (i <= 0)
 				i = 1;
 		}
 	s = s0 = rv_alloc(i);
 #ifdef Honor_FLT_ROUNDS
 	if (mode > 1 && Rounding != 1)
 		leftright = 0;
 #endif
 	if (ilim >= 0 && ilim <= Quick_max && try_quick) {
 		/* Try to get by with floating-point arithmetic. */
 		i = 0;
 		dval(&d2) = dval(&u);
 		k0 = k;
 		ilim0 = ilim;
 		ieps = 2; /* conservative */
 		if (k > 0) {
 			ds = tens[k&0xf];
 			j = k >> 4;
 			if (j & Bletch) {
 				/* prevent overflows */
 				j &= Bletch - 1;
 				dval(&u) /= bigtens[n_bigtens-1];
 				ieps++;
 				}
 			for(; j; j >>= 1, i++)
 				if (j & 1) {
 					ieps++;
 					ds *= bigtens[i];
 					}
 			dval(&u) /= ds;
 			}
 		else if ((j1 = -k)) {
 			dval(&u) *= tens[j1 & 0xf];
 			for(j = j1 >> 4; j; j >>= 1, i++)
 				if (j & 1) {
 					ieps++;
 					dval(&u) *= bigtens[i];
 					}
 			}
 		if (k_check && dval(&u) < 1. && ilim > 0) {
 			if (ilim1 <= 0)
 				goto fast_failed;
 			ilim = ilim1;
 			k--;
 			dval(&u) *= 10.;
 			ieps++;
 			}
 		dval(&eps) = ieps*dval(&u) + 7.;
 		word0(&eps) -= (P-1)*Exp_msk1;
 		if (ilim == 0) {
 			S = mhi = 0;
 			dval(&u) -= 5.;
 			if (dval(&u) > dval(&eps))
 				goto one_digit;
 			if (dval(&u) < -dval(&eps))
 				goto no_digits;
 			goto fast_failed;
 			}
 #ifndef No_leftright
 		if (leftright) {
 			/* Use Steele & White method of only
 			 * generating digits needed.
 			 */
 			dval(&eps) = 0.5/tens[ilim-1] - dval(&eps);
 			for(i = 0;;) {
 				L = dval(&u);
 				dval(&u) -= L;
 				*s++ = '0' + (int)L;
 				if (dval(&u) < dval(&eps))
 					goto ret1;
 				if (1. - dval(&u) < dval(&eps))
 					goto bump_up;
 				if (++i >= ilim)
 					break;
 				dval(&eps) *= 10.;
 				dval(&u) *= 10.;
 				}
 			}
 		else {
 #endif
 			/* Generate ilim digits, then fix them up. */
 			dval(&eps) *= tens[ilim-1];
 			for(i = 1;; i++, dval(&u) *= 10.) {
 				L = (Long)(dval(&u));
 				if (!(dval(&u) -= L))
 					ilim = i;
 				*s++ = '0' + (int)L;
 				if (i == ilim) {
 					if (dval(&u) > 0.5 + dval(&eps))
 						goto bump_up;
 					else if (dval(&u) < 0.5 - dval(&eps)) {
 						while(*--s == '0') {}
 						s++;
 						goto ret1;
 						}
 					break;
 					}
 				}
 #ifndef No_leftright
 			}
 #endif
  fast_failed:
 		s = s0;
 		dval(&u) = dval(&d2);
 		k = k0;
 		ilim = ilim0;
 		}
 	/* Do we have a "small" integer? */
 	if (be >= 0 && k <= Int_max) {
 		/* Yes. */
 		ds = tens[k];
 		if (ndigits < 0 && ilim <= 0) {
 			S = mhi = 0;
 			if (ilim < 0 || dval(&u) <= 5*ds)
 				goto no_digits;
 			goto one_digit;
 			}
 		for(i = 1; i <= k + 1; i++, dval(&u) *= 10.) {
 			L = (Long)(dval(&u) / ds);
 			dval(&u) -= L*ds;
 #ifdef Check_FLT_ROUNDS
 			/* If FLT_ROUNDS == 2, L will usually be high by 1 */
 			if (dval(&u) < 0) {
 				L--;
 				dval(&u) += ds;
 				}
 #endif
 			*s++ = '0' + (int)L;
 			if (!dval(&u)) {
 #ifdef SET_INEXACT
 				inexact = 0;
 #endif
 				break;
 				}
 			if (i == ilim) {
 #ifdef Honor_FLT_ROUNDS
 				if (mode > 1)
 				switch(Rounding) {
 				  case 0: goto ret1;
 				  case 2: goto bump_up;
 				  }
 #endif
 				dval(&u) += dval(&u);
 				if (dval(&u) > ds || (dval(&u) == ds && L & 1)) {
  bump_up:
 					while(*--s == '9')
 						if (s == s0) {
 							k++;
 							*s = '0';
 							break;
 							}
 					++*s++;
 					}
 				break;
 				}
 			}
 		goto ret1;
 		}
 	m2 = b2;
 	m5 = b5;
 	mhi = mlo = 0;
 	if (leftright) {
 		i =
 #ifndef Sudden_Underflow
 			denorm ? be + (Bias + (P-1) - 1 + 1) :
 #endif
 #ifdef IBM
 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
 #else
 + P - bbits;
 #endif
 		b2 += i;
 		s2 += i;
 		mhi = i2b(1);
 		}
 	if (m2 > 0 && s2 > 0) {
 		i = m2 < s2 ? m2 : s2;
 		b2 -= i;
 		m2 -= i;
 		s2 -= i;
 		}
 	if (b5 > 0) {
 		if (leftright) {
 			if (m5 > 0) {
 				mhi = pow5mult(mhi, m5);
 				b1 = mult(mhi, b);
 				Bfree(b);
 				b = b1;
 				}
 			if ((j = b5 - m5))
 				b = pow5mult(b, j);
 			}
 		else
 			b = pow5mult(b, b5);
 		}
 	S = i2b(1);
 	if (s5 > 0)
 		S = pow5mult(S, s5);
 	/* Check for special case that d is a normalized power of 2. */
 	spec_case = 0;
 	if ((mode < 2 || leftright)
 #ifdef Honor_FLT_ROUNDS
 			&& Rounding == 1
 #endif
 				) {
 		if (!word1(&u) && !(word0(&u) & Bndry_mask)
 #ifndef Sudden_Underflow
 		 && word0(&u) & (Exp_mask & ~Exp_msk1)
 #endif
 				) {
 			/* The special case */
 			b2 += Log2P;
 			s2 += Log2P;
 			spec_case = 1;
 			}
 		}
 	/* Arrange for convenient computation of quotients:
 	 * shift left if necessary so divisor has 4 leading 0 bits.
 	 *
 	 * Perhaps we should just compute leading 28 bits of S once
 	 * and for all and pass them and a shift to quorem, so it
 	 * can do shifts and ors to compute the numerator for q.
 	 */
 #ifdef Pack_32
 	if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f))
 		i = 32 - i;
 #define iInc 28
 #else
 	if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf)
 		i = 16 - i;
 #define iInc 12
 #endif
 	i = dshift(S, s2);
 	b2 += i;
 	m2 += i;
 	s2 += i;
 	if (b2 > 0)
 		b = lshift(b, b2);
 	if (s2 > 0)
 		S = lshift(S, s2);
 	if (k_check) {
 		if (cmp(b,S) < 0) {
 			k--;
 			b = multadd(b, 10, 0);	/* we botched the k estimate */
 			if (leftright)
 				mhi = multadd(mhi, 10, 0);
 			ilim = ilim1;
 			}
 		}
 	if (ilim <= 0 && (mode == 3 || mode == 5)) {
 		if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
 			/* no digits, fcvt style */
  no_digits:
 			k = -1 - ndigits;
 			goto ret;
 			}
  one_digit:
 		*s++ = '1';
 		k++;
 		goto ret;
 		}
 	if (leftright) {
 		if (m2 > 0)
 			mhi = lshift(mhi, m2);
 		/* Compute mlo -- check for special case
 		 * that d is a normalized power of 2.
 		 */
 		mlo = mhi;
 		if (spec_case) {
 			mhi = Balloc(mhi->k);
 			Bcopy(mhi, mlo);
 			mhi = lshift(mhi, Log2P);
 			}
 		for(i = 1;;i++) {
 			dig = quorem(b,S) + '0';
 			/* Do we yet have the shortest decimal string
 			 * that will round to d?
 			 */
 			j = cmp(b, mlo);
 			delta = diff(S, mhi);
 			j1 = delta->sign ? 1 : cmp(b, delta);
 			Bfree(delta);
 #ifndef ROUND_BIASED
 			if (j1 == 0 && mode != 1 && !(word1(&u) & 1)
 #ifdef Honor_FLT_ROUNDS
 				&& Rounding >= 1
 #endif
 								   ) {
 				if (dig == '9')
 					goto round_9_up;
 				if (j > 0)
 					dig++;
 #ifdef SET_INEXACT
 				else if (!b->x[0] && b->wds <= 1)
 					inexact = 0;
 #endif
 				*s++ = dig;
 				goto ret;
 				}
 #endif
 			if (j < 0 || (j == 0 && mode != 1
 #ifndef ROUND_BIASED
 							&& !(word1(&u) & 1)
 #endif
 					)) {
 				if (!b->x[0] && b->wds <= 1) {
 #ifdef SET_INEXACT
 					inexact = 0;
 #endif
 					goto accept_dig;
 					}
 #ifdef Honor_FLT_ROUNDS
 				if (mode > 1)
 				 switch(Rounding) {
 				  case 0: goto accept_dig;
 				  case 2: goto keep_dig;
 				  }
 #endif /*Honor_FLT_ROUNDS*/
 				if (j1 > 0) {
 					b = lshift(b, 1);
 					j1 = cmp(b, S);
 					if ((j1 > 0 || (j1 == 0 && dig & 1))
 					&& dig++ == '9')
 						goto round_9_up;
 					}
  accept_dig:
 				*s++ = dig;
 				goto ret;
 				}
 			if (j1 > 0) {
 #ifdef Honor_FLT_ROUNDS
 				if (!Rounding)
 					goto accept_dig;
 #endif
 				if (dig == '9') { /* possible if i == 1 */
  round_9_up:
 					*s++ = '9';
 					goto roundoff;
 					}
 				*s++ = dig + 1;
 				goto ret;
 				}
 #ifdef Honor_FLT_ROUNDS
  keep_dig:
 #endif
 			*s++ = dig;
 			if (i == ilim)
 				break;
 			b = multadd(b, 10, 0);
 			if (mlo == mhi)
 				mlo = mhi = multadd(mhi, 10, 0);
 			else {
 				mlo = multadd(mlo, 10, 0);
 				mhi = multadd(mhi, 10, 0);
 				}
 			}
 		}
 	else
 		for(i = 1;; i++) {
 			*s++ = dig = quorem(b,S) + '0';
 			if (!b->x[0] && b->wds <= 1) {
 #ifdef SET_INEXACT
 				inexact = 0;
 #endif
 				goto ret;
 				}
 			if (i >= ilim)
 				break;
 			b = multadd(b, 10, 0);
 			}
 	/* Round off last digit */
 #ifdef Honor_FLT_ROUNDS
 	switch(Rounding) {
 	  case 0: goto trimzeros;
 	  case 2: goto roundoff;
 	  }
 #endif
 	b = lshift(b, 1);
 	j = cmp(b, S);
 	if (j > 0 || (j == 0 && dig & 1)) {
  roundoff:
 		while(*--s == '9')
 			if (s == s0) {
 				k++;
 				*s++ = '1';
 				goto ret;
 				}
 		++*s++;
 		}
 	else {
 #ifdef Honor_FLT_ROUNDS
  trimzeros:
 #endif
 		while(*--s == '0') {}
 		s++;
 		}
  ret:
 	Bfree(S);
 	if (mhi) {
 		if (mlo && mlo != mhi)
 			Bfree(mlo);
 		Bfree(mhi);
 		}
  ret1:
 #ifdef SET_INEXACT
 	if (inexact) {
 		if (!oldinexact) {
 			word0(&u) = Exp_1 + (70 << Exp_shift);
 			word1(&u) = 0;
 			dval(&u) += 1.;
 			}
 		}
 	else if (!oldinexact)
 		clear_inexact();
 #endif
 	Bfree(b);
 	*s = 0;
 	*decpt = k + 1;
 	if (rve)
 		*rve = s;
 	return s0;
 	}
 }  // namespace dmg_fp

The Tor Browser / annotate

security/sandbox/chromium/base/third_party/dmg_fp/dtoa.cc@44a2da4a2ab2 (annotated)

security/sandbox/chromium/base/third_party/dmg_fp/dtoa.cc