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-/****************************************************************
-
-The author of this software is David M. Gay.
-
-Copyright (C) 1998-2000 by Lucent Technologies
-All Rights Reserved
-
-Permission to use, copy, modify, and distribute this software and
-its documentation for any purpose and without fee is hereby
-granted, provided that the above copyright notice appear in all
-copies and that both that the copyright notice and this
-permission notice and warranty disclaimer appear in supporting
-documentation, and that the name of Lucent or any of its entities
-not be used in advertising or publicity pertaining to
-distribution of the software without specific, written prior
-permission.
-
-LUCENT DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE,
-INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS.
-IN NO EVENT SHALL LUCENT OR ANY OF ITS ENTITIES BE LIABLE FOR ANY
-SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
-WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER
-IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION,
-ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF
-THIS SOFTWARE.
-
-****************************************************************/
-
-/* This is a variation on dtoa.c that converts arbitary binary
- floating-point formats to and from decimal notation. It uses
- double-precision arithmetic internally, so there are still
- various #ifdefs that adapt the calculations to the native
- double-precision arithmetic (any of IEEE, VAX D_floating,
- or IBM mainframe arithmetic).
-
- 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. 112-126].
- *
- * 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 Sudden_Underflow for IEEE-format machines without gradual
- * underflow (i.e., that flush to zero on underflow).
- * #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 Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3.
- * #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.
- * #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. When converting IEEE double precision values, the
- * longest string gdtoa can return is about 751 bytes long. For
- * conversions by strtod of strings of 800 digits and all gdtoa
- * conversions of IEEE doubles in single-threaded executions with
- * 8-byte pointers, PRIVATE_MEM >= 7400 appears to suffice; with
- * 4-byte pointers, PRIVATE_MEM >= 7112 appears adequate.
- * #define INFNAN_CHECK on IEEE systems to cause strtod to check for
- * Infinity and NaN (case insensitively).
- * When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
- * strtodg 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 fraction bits of the resulting NaN; if there are two or
- * more strings of hexadecimal digits, each string is assigned
- * to the next available sequence of 32-bit words of fractions
- * bits (starting with the most significant), right-aligned in
- * each sequence.
- * #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 IMPRECISE_INEXACT if you do not care about the setting of
- * the STRTOG_Inexact bits in the special case of doing IEEE double
- * precision conversions (which could also be done by the strtog in
- * dtoa.c).
- * #define NO_HEX_FP to disable recognition of C9x's hexadecimal
- * floating-point constants.
- * #define -DNO_ERRNO to suppress setting errno (in strtod.c and
- * strtodg.c).
- * #define NO_STRING_H to use private versions of memcpy.
- * On some K&R systems, it may also be necessary to
- * #define DECLARE_SIZE_T in this case.
- * #define YES_ALIAS to permit aliasing certain double values with
- * arrays of ULongs. This leads to slightly better code with
- * some compilers and was always used prior to 19990916, but it
- * is not strictly legal and can cause trouble with aggressively
- * optimizing compilers (e.g., gcc 2.95.1 under -O2).
- * #define USE_LOCALE to use the current locale's decimal_point value.
- */
-
-#ifndef GDTOAIMP_H_INCLUDED
-#define GDTOAIMP_H_INCLUDED
-#include "gdtoa.h"
-#include "gd_qnan.h"
-
-#define INFNAN_CHECK 1
-#define MULTIPLE_THREADS 1
-
-#ifdef DEBUG
-#include <stdio.h>
-#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
-#endif
-
-#include <stdlib.h>
-#include <string.h>
-
-#ifdef KR_headers
-#define Char char
-#else
-#define Char void
-#endif
-
-#ifdef MALLOC
-extern Char *MALLOC ANSI((size_t));
-#else
-#define MALLOC malloc
-#endif
-
-#undef IEEE_Arith
-#undef Avoid_Underflow
-#ifdef IEEE_MC68k
-#define IEEE_Arith
-#endif
-#ifdef IEEE_8087
-#define IEEE_Arith
-#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
-#define DBL_MAX 1.7976931348623157e+308
-#endif
-
-#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
-#define n_bigtens 2
-#endif
-
-#ifndef LONG_MAX
-#define LONG_MAX 2147483647
-#endif
-
-#else /* ifndef Bad_float_h */
-#include <float.h>
-#endif /* Bad_float_h */
-
-#ifdef IEEE_Arith
-#define Scale_Bit 0x10
-#define n_bigtens 5
-#endif
-
-#ifdef IBM
-#define n_bigtens 3
-#endif
-
-#ifdef VAX
-#define n_bigtens 2
-#endif
-
-#ifndef __MATH_H__
-#include <math.h>
-#endif
-
-#ifdef __cplusplus
-extern "C" {
-#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 YES_ALIAS
-#define dval(x) x
-#ifdef IEEE_8087
-#define word0(x) ((ULong *)&x)[1]
-#define word1(x) ((ULong *)&x)[0]
-#else
-#define word0(x) ((ULong *)&x)[0]
-#define word1(x) ((ULong *)&x)[1]
-#endif
-#else /* !YES_ALIAS */
-#ifdef IEEE_8087
-#define word0(x) ((U*)&x)->L[1]
-#define word1(x) ((U*)&x)->L[0]
-#else
-#define word0(x) ((U*)&x)->L[0]
-#define word1(x) ((U*)&x)->L[1]
-#endif
-#define dval(x) ((U*)&x)->d
-#endif /* YES_ALIAS */
-
-/* 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 Bias 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 Flt_Rounds
-#ifdef FLT_ROUNDS
-#define Flt_Rounds FLT_ROUNDS
-#else
-#define Flt_Rounds 1
-#endif
-#endif /*Flt_Rounds*/
-
-#else /* ifndef IEEE_Arith */
-#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 Bias 65
-#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 Bias 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
-
-#undef Pack_16
-#ifndef Pack_32
-#define Pack_32
-#endif
-
-#ifdef NO_LONG_LONG
-#undef ULLong
-#ifdef Just_16
-#undef Pack_32
-#define Pack_16
-/* 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 */
-
-#ifdef Pack_32
-#define ULbits 32
-#define kshift 5
-#define kmask 31
-#define ALL_ON 0xffffffff
-#else
-#define ULbits 16
-#define kshift 4
-#define kmask 15
-#define ALL_ON 0xffff
-#endif
-
-#ifndef MULTIPLE_THREADS
-#define ACQUIRE_DTOA_LOCK(n) /*nothing*/
-#define FREE_DTOA_LOCK(n) /*nothing*/
-#endif
-
-#define Kmax 15
-
-#define Bigint __Bigint
- struct
-Bigint {
- struct Bigint *next;
- int k, maxwds, sign, wds;
- ULong x[1];
- };
-
- typedef struct Bigint Bigint;
-
-#ifdef NO_STRING_H
-#ifdef DECLARE_SIZE_T
-typedef unsigned int size_t;
-#endif
-extern void memcpy_D2A ANSI((void*, const void*, size_t));
-#define Bcopy(x,y) memcpy_D2A(&x->sign,&y->sign,y->wds*sizeof(ULong) + 2*sizeof(int))
-#else /* !NO_STRING_H */
-#define Bcopy(x,y) memcpy(&x->sign,&y->sign,y->wds*sizeof(ULong) + 2*sizeof(int))
-#endif /* NO_STRING_H */
-
-#ifdef __GNUC__
-static inline int
-__lo0bits_D2A (ULong *y)
-{
- int ret = __builtin_ctz(*y);
- *y = *y >> ret;
- return ret;
-}
-
-static inline int
-__hi0bits_D2A (ULong y)
-{
- return __builtin_clz(y);
-}
-#endif
-
-#define Balloc __Balloc_D2A
-#define Bfree __Bfree_D2A
-#define ULtoQ __ULtoQ_D2A
-#define ULtof __ULtof_D2A
-#define ULtod __ULtod_D2A
-#define ULtodd __ULtodd_D2A
-#define ULtox __ULtox_D2A
-#define ULtoxL __ULtoxL_D2A
-#define any_on __any_on_D2A
-#define b2d __b2d_D2A
-#define bigtens __bigtens_D2A
-#define cmp __cmp_D2A
-#define copybits __copybits_D2A
-#define d2b __d2b_D2A
-#define decrement __decrement_D2A
-#define diff __diff_D2A
-#define dtoa_result __dtoa_result_D2A
-#define gethex __gethex_D2A
-#define hexdig __hexdig_D2A
-#define hexnan __hexnan_D2A
-#define hi0bits_D2A __hi0bits_D2A
-#define hi0bits(x) __hi0bits_D2A((ULong)(x))
-#define i2b __i2b_D2A
-#define increment __increment_D2A
-#define lo0bits __lo0bits_D2A
-#define lshift __lshift_D2A
-#define match __match_D2A
-#define mult __mult_D2A
-#define multadd __multadd_D2A
-#define nrv_alloc __nrv_alloc_D2A
-#define pow5mult __pow5mult_D2A
-#define quorem __quorem_D2A
-#define ratio __ratio_D2A
-#define rshift __rshift_D2A
-#define rv_alloc __rv_alloc_D2A
-#define s2b __s2b_D2A
-#define set_ones __set_ones_D2A
-#define strcp_D2A __strcp_D2A
-#define strcp __strcp_D2A
-#define strtoIg __strtoIg_D2A
-#define sum __sum_D2A
-#define tens __tens_D2A
-#define tinytens __tinytens_D2A
-#define tinytens __tinytens_D2A
-#define trailz __trailz_D2A
-#define ulp __ulp_D2A
-
- extern char *dtoa_result;
- extern CONST double bigtens[], tens[], tinytens[];
- extern unsigned char hexdig[];
-
- extern Bigint *Balloc ANSI((int));
- extern void Bfree ANSI((Bigint*));
- extern void ULtof ANSI((ULong*, ULong*, Long, int));
- extern void ULtod ANSI((ULong*, ULong*, Long, int));
- extern void ULtodd ANSI((ULong*, ULong*, Long, int));
- extern void ULtoQ ANSI((ULong*, ULong*, Long, int));
- extern void ULtox ANSI((UShort*, ULong*, Long, int));
- extern void ULtoxL ANSI((ULong*, ULong*, Long, int));
- extern ULong any_on ANSI((Bigint*, int));
- extern double b2d ANSI((Bigint*, int*));
- extern int cmp ANSI((Bigint*, Bigint*));
- extern void copybits ANSI((ULong*, int, Bigint*));
- extern Bigint *d2b ANSI((double, int*, int*));
- extern int decrement ANSI((Bigint*));
- extern Bigint *diff ANSI((Bigint*, Bigint*));
- extern int gethex ANSI((CONST char**, FPI*, Long*, Bigint**, int));
- extern void hexdig_init_D2A(Void);
- extern int hexnan ANSI((CONST char**, FPI*, ULong*));
- extern int hi0bits_D2A ANSI((ULong));
- extern Bigint *i2b ANSI((int));
- extern Bigint *increment ANSI((Bigint*));
- extern int lo0bits ANSI((ULong*));
- extern Bigint *lshift ANSI((Bigint*, int));
- extern int match ANSI((CONST char**, char*));
- extern Bigint *mult ANSI((Bigint*, Bigint*));
- extern Bigint *multadd ANSI((Bigint*, int, int));
- extern char *nrv_alloc ANSI((char*, char **, int));
- extern Bigint *pow5mult ANSI((Bigint*, int));
- extern int quorem ANSI((Bigint*, Bigint*));
- extern double ratio ANSI((Bigint*, Bigint*));
- extern void rshift ANSI((Bigint*, int));
- extern char *rv_alloc ANSI((int));
- extern Bigint *s2b ANSI((CONST char*, int, int, ULong));
- extern Bigint *set_ones ANSI((Bigint*, int));
- extern char *strcp ANSI((char*, const char*));
- extern Bigint *sum ANSI((Bigint*, Bigint*));
- extern int trailz ANSI((Bigint*));
- extern double ulp ANSI((double));
-
-#ifdef __cplusplus
-}
-#endif
-/*
- * NAN_WORD0 and NAN_WORD1 are only referenced in strtod.c. Prior to
- * 20050115, they used to be hard-wired here (to 0x7ff80000 and 0,
- * respectively), but now are determined by compiling and running
- * qnan.c to generate gd_qnan.h, which specifies d_QNAN0 and d_QNAN1.
- * Formerly gdtoaimp.h recommended supplying suitable -DNAN_WORD0=...
- * and -DNAN_WORD1=... values if necessary. This should still work.
- * (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
- */
-#ifdef IEEE_Arith
-#ifdef IEEE_MC68k
-#define _0 0
-#define _1 1
-#ifndef NAN_WORD0
-#define NAN_WORD0 d_QNAN0
-#endif
-#ifndef NAN_WORD1
-#define NAN_WORD1 d_QNAN1
-#endif
-#else
-#define _0 1
-#define _1 0
-#ifndef NAN_WORD0
-#define NAN_WORD0 d_QNAN1
-#endif
-#ifndef NAN_WORD1
-#define NAN_WORD1 d_QNAN0
-#endif
-#endif
-#else
-#undef INFNAN_CHECK
-#endif
-
-#undef SI
-#ifdef Sudden_Underflow
-#define SI 1
-#else
-#define SI 0
-#endif
-
-#endif /* GDTOAIMP_H_INCLUDED */