1/**************************************************************** 2 3The author of this software is David M. Gay. 4 5Copyright (C) 1998-2000 by Lucent Technologies 6All Rights Reserved 7 8Permission to use, copy, modify, and distribute this software and 9its documentation for any purpose and without fee is hereby 10granted, provided that the above copyright notice appear in all 11copies and that both that the copyright notice and this 12permission notice and warranty disclaimer appear in supporting 13documentation, and that the name of Lucent or any of its entities 14not be used in advertising or publicity pertaining to 15distribution of the software without specific, written prior 16permission. 17 18LUCENT DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE, 19INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS. 20IN NO EVENT SHALL LUCENT OR ANY OF ITS ENTITIES BE LIABLE FOR ANY 21SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES 22WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER 23IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, 24ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF 25THIS SOFTWARE. 26 27****************************************************************/ 28 29/* This is a variation on dtoa.c that converts arbitary binary 30 floating-point formats to and from decimal notation. It uses 31 double-precision arithmetic internally, so there are still 32 various #ifdefs that adapt the calculations to the native 33 double-precision arithmetic (any of IEEE, VAX D_floating, 34 or IBM mainframe arithmetic). 35 36 Please send bug reports to David M. Gay (dmg at acm dot org, 37 with " at " changed at "@" and " dot " changed to "."). 38 */ 39 40/* On a machine with IEEE extended-precision registers, it is 41 * necessary to specify double-precision (53-bit) rounding precision 42 * before invoking strtod or dtoa. If the machine uses (the equivalent 43 * of) Intel 80x87 arithmetic, the call 44 * _control87(PC_53, MCW_PC); 45 * does this with many compilers. Whether this or another call is 46 * appropriate depends on the compiler; for this to work, it may be 47 * necessary to #include "float.h" or another system-dependent header 48 * file. 49 */ 50 51/* strtod for IEEE-, VAX-, and IBM-arithmetic machines. 52 * 53 * This strtod returns a nearest machine number to the input decimal 54 * string (or sets errno to ERANGE). With IEEE arithmetic, ties are 55 * broken by the IEEE round-even rule. Otherwise ties are broken by 56 * biased rounding (add half and chop). 57 * 58 * Inspired loosely by William D. Clinger's paper "How to Read Floating 59 * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 112-126]. 60 * 61 * Modifications: 62 * 63 * 1. We only require IEEE, IBM, or VAX double-precision 64 * arithmetic (not IEEE double-extended). 65 * 2. We get by with floating-point arithmetic in a case that 66 * Clinger missed -- when we're computing d * 10^n 67 * for a small integer d and the integer n is not too 68 * much larger than 22 (the maximum integer k for which 69 * we can represent 10^k exactly), we may be able to 70 * compute (d*10^k) * 10^(e-k) with just one roundoff. 71 * 3. Rather than a bit-at-a-time adjustment of the binary 72 * result in the hard case, we use floating-point 73 * arithmetic to determine the adjustment to within 74 * one bit; only in really hard cases do we need to 75 * compute a second residual. 76 * 4. Because of 3., we don't need a large table of powers of 10 77 * for ten-to-e (just some small tables, e.g. of 10^k 78 * for 0 <= k <= 22). 79 */ 80 81/* 82 * #define IEEE_8087 for IEEE-arithmetic machines where the least 83 * significant byte has the lowest address. 84 * #define IEEE_MC68k for IEEE-arithmetic machines where the most 85 * significant byte has the lowest address. 86 * #define Long int on machines with 32-bit ints and 64-bit longs. 87 * #define Sudden_Underflow for IEEE-format machines without gradual 88 * underflow (i.e., that flush to zero on underflow). 89 * #define IBM for IBM mainframe-style floating-point arithmetic. 90 * #define VAX for VAX-style floating-point arithmetic (D_floating). 91 * #define No_leftright to omit left-right logic in fast floating-point 92 * computation of dtoa. 93 * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3. 94 * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines 95 * that use extended-precision instructions to compute rounded 96 * products and quotients) with IBM. 97 * #define ROUND_BIASED for IEEE-format with biased rounding. 98 * #define Inaccurate_Divide for IEEE-format with correctly rounded 99 * products but inaccurate quotients, e.g., for Intel i860. 100 * #define NO_LONG_LONG on machines that do not have a "long long" 101 * integer type (of >= 64 bits). On such machines, you can 102 * #define Just_16 to store 16 bits per 32-bit Long when doing 103 * high-precision integer arithmetic. Whether this speeds things 104 * up or slows things down depends on the machine and the number 105 * being converted. If long long is available and the name is 106 * something other than "long long", #define Llong to be the name, 107 * and if "unsigned Llong" does not work as an unsigned version of 108 * Llong, #define #ULLong to be the corresponding unsigned type. 109 * #define KR_headers for old-style C function headers. 110 * #define Bad_float_h if your system lacks a float.h or if it does not 111 * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP, 112 * FLT_RADIX, FLT_ROUNDS, and DBL_MAX. 113 * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n) 114 * if memory is available and otherwise does something you deem 115 * appropriate. If MALLOC is undefined, malloc will be invoked 116 * directly -- and assumed always to succeed. Similarly, if you 117 * want something other than the system's free() to be called to 118 * recycle memory acquired from MALLOC, #define FREE to be the 119 * name of the alternate routine. (FREE or free is only called in 120 * pathological cases, e.g., in a gdtoa call after a gdtoa return in 121 * mode 3 with thousands of digits requested.) 122 * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making 123 * memory allocations from a private pool of memory when possible. 124 * When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes, 125 * unless #defined to be a different length. This default length 126 * suffices to get rid of MALLOC calls except for unusual cases, 127 * such as decimal-to-binary conversion of a very long string of 128 * digits. When converting IEEE double precision values, the 129 * longest string gdtoa can return is about 751 bytes long. For 130 * conversions by strtod of strings of 800 digits and all gdtoa 131 * conversions of IEEE doubles in single-threaded executions with 132 * 8-byte pointers, PRIVATE_MEM >= 7400 appears to suffice; with 133 * 4-byte pointers, PRIVATE_MEM >= 7112 appears adequate. 134 * #define NO_INFNAN_CHECK if you do not wish to have INFNAN_CHECK 135 * #defined automatically on IEEE systems. On such systems, 136 * when INFNAN_CHECK is #defined, strtod checks 137 * for Infinity and NaN (case insensitively). 138 * When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined, 139 * strtodg also accepts (case insensitively) strings of the form 140 * NaN(x), where x is a string of hexadecimal digits (optionally 141 * preceded by 0x or 0X) and spaces; if there is only one string 142 * of hexadecimal digits, it is taken for the fraction bits of the 143 * resulting NaN; if there are two or more strings of hexadecimal 144 * digits, each string is assigned to the next available sequence 145 * of 32-bit words of fractions bits (starting with the most 146 * significant), right-aligned in each sequence. 147 * Unless GDTOA_NON_PEDANTIC_NANCHECK is #defined, input "NaN(...)" 148 * is consumed even when ... has the wrong form (in which case the 149 * "(...)" is consumed but ignored). 150 * #define MULTIPLE_THREADS if the system offers preemptively scheduled 151 * multiple threads. In this case, you must provide (or suitably 152 * #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed 153 * by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed 154 * in pow5mult, ensures lazy evaluation of only one copy of high 155 * powers of 5; omitting this lock would introduce a small 156 * probability of wasting memory, but would otherwise be harmless.) 157 * You must also invoke freedtoa(s) to free the value s returned by 158 * dtoa. You may do so whether or not MULTIPLE_THREADS is #defined. 159 * #define IMPRECISE_INEXACT if you do not care about the setting of 160 * the STRTOG_Inexact bits in the special case of doing IEEE double 161 * precision conversions (which could also be done by the strtod in 162 * dtoa.c). 163 * #define NO_HEX_FP to disable recognition of C9x's hexadecimal 164 * floating-point constants. 165 * #define -DNO_ERRNO to suppress setting errno (in strtod.c and 166 * strtodg.c). 167 * #define NO_STRING_H to use private versions of memcpy. 168 * On some K&R systems, it may also be necessary to 169 * #define DECLARE_SIZE_T in this case. 170 * #define USE_LOCALE to use the current locale's decimal_point value. 171 */ 172 173#ifndef GDTOAIMP_H_INCLUDED 174#define GDTOAIMP_H_INCLUDED 175/* 176 * Paranoia: Protect exported symbols, including ones in files we don't 177 * compile right now. The standard strtof and strtod survive. 178 */ 179#define dtoa __dtoa 180#define gdtoa __gdtoa 181#define freedtoa __freedtoa 182#define strtodg __strtodg 183#define g_ddfmt __g_ddfmt 184#define g_dfmt __g_dfmt 185#define g_ffmt __g_ffmt 186#define g_Qfmt __g_Qfmt 187#define g_xfmt __g_xfmt 188#define g_xLfmt __g_xLfmt 189#define strtoId __strtoId 190#define strtoIdd __strtoIdd 191#define strtoIf __strtoIf 192#define strtoIQ __strtoIQ 193#define strtoIx __strtoIx 194#define strtoIxL __strtoIxL 195#define strtord __strtord 196#define strtordd __strtordd 197#define strtorf __strtorf 198#define strtorQ __strtorQ 199#define strtorx __strtorx 200#define strtorxL __strtorxL 201#define strtodI __strtodI 202#define strtopd __strtopd 203#define strtopdd __strtopdd 204#define strtopf __strtopf 205#define strtopQ __strtopQ 206#define strtopx __strtopx 207#define strtopxL __strtopxL 208 209/* Protect gdtoa-internal symbols */ 210#define Balloc __Balloc_D2A 211#define Bfree __Bfree_D2A 212#define ULtoQ __ULtoQ_D2A 213#define ULtof __ULtof_D2A 214#define ULtod __ULtod_D2A 215#define ULtodd __ULtodd_D2A 216#define ULtox __ULtox_D2A 217#define ULtoxL __ULtoxL_D2A 218#define any_on __any_on_D2A 219#define b2d __b2d_D2A 220#define bigtens __bigtens_D2A 221#define cmp __cmp_D2A 222#define copybits __copybits_D2A 223#define d2b __d2b_D2A 224#define decrement __decrement_D2A 225#define diff __diff_D2A 226#define dtoa_result __dtoa_result_D2A 227#define g__fmt __g__fmt_D2A 228#define gethex __gethex_D2A 229#define hexdig __hexdig_D2A 230#define hexdig_init_D2A __hexdig_init_D2A 231#define hexnan __hexnan_D2A 232#define hi0bits __hi0bits_D2A 233#define hi0bits_D2A __hi0bits_D2A 234#define i2b __i2b_D2A 235#define increment __increment_D2A 236#define lo0bits __lo0bits_D2A 237#define lshift __lshift_D2A 238#define match __match_D2A 239#define mult __mult_D2A 240#define multadd __multadd_D2A 241#define nrv_alloc __nrv_alloc_D2A 242#define pow5mult __pow5mult_D2A 243#define quorem __quorem_D2A 244#define ratio __ratio_D2A 245#define rshift __rshift_D2A 246#define rv_alloc __rv_alloc_D2A 247#define s2b __s2b_D2A 248#define set_ones __set_ones_D2A 249#define strcp __strcp_D2A 250#define strcp_D2A __strcp_D2A 251#define strtoIg __strtoIg_D2A 252#define sum __sum_D2A 253#define tens __tens_D2A 254#define tinytens __tinytens_D2A 255#define tinytens __tinytens_D2A 256#define trailz __trailz_D2A 257#define ulp __ulp_D2A 258 259#include <xlocale.h> 260#include "gdtoa.h" 261#include "gd_qnan.h" 262#ifdef Honor_FLT_ROUNDS 263#include <fenv.h> 264#endif 265 266#ifdef DEBUG 267#include "stdio.h" 268#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);} 269#endif 270 271#include "limits.h" 272#include "stdlib.h" 273#include "string.h" 274#include "libc_private.h" 275#include "spinlock.h" 276 277#ifdef KR_headers 278#define Char char 279#else 280#define Char void 281#endif 282 283#ifdef MALLOC 284extern Char *MALLOC ANSI((size_t)); 285#else 286#define MALLOC malloc 287#endif 288 289#define INFNAN_CHECK 290#define USE_LOCALE 291#define NO_LOCALE_CACHE 292 293#undef IEEE_Arith 294#undef Avoid_Underflow 295#ifdef IEEE_MC68k 296#define IEEE_Arith 297#endif 298#ifdef IEEE_8087 299#define IEEE_Arith 300#endif 301 302#include "errno.h" 303#ifdef Bad_float_h 304 305#ifdef IEEE_Arith 306#define DBL_DIG 15 307#define DBL_MAX_10_EXP 308 308#define DBL_MAX_EXP 1024 309#define FLT_RADIX 2 310#define DBL_MAX 1.7976931348623157e+308 311#endif 312 313#ifdef IBM 314#define DBL_DIG 16 315#define DBL_MAX_10_EXP 75 316#define DBL_MAX_EXP 63 317#define FLT_RADIX 16 318#define DBL_MAX 7.2370055773322621e+75 319#endif 320 321#ifdef VAX 322#define DBL_DIG 16 323#define DBL_MAX_10_EXP 38 324#define DBL_MAX_EXP 127 325#define FLT_RADIX 2 326#define DBL_MAX 1.7014118346046923e+38 327#define n_bigtens 2 328#endif 329 330#ifndef LONG_MAX 331#define LONG_MAX 2147483647 332#endif 333 334#else /* ifndef Bad_float_h */ 335#include "float.h" 336#endif /* Bad_float_h */ 337 338#ifdef IEEE_Arith 339#define Scale_Bit 0x10 340#define n_bigtens 5 341#endif 342 343#ifdef IBM 344#define n_bigtens 3 345#endif 346 347#ifdef VAX 348#define n_bigtens 2 349#endif 350 351#ifndef __MATH_H__ 352#include "math.h" 353#endif 354 355#ifdef __cplusplus 356extern "C" { 357#endif 358 359#if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1 360Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined. 361#endif 362 363typedef union { double d; ULong L[2]; } U; 364 365#ifdef IEEE_8087 366#define word0(x) (x)->L[1] 367#define word1(x) (x)->L[0] 368#else 369#define word0(x) (x)->L[0] 370#define word1(x) (x)->L[1] 371#endif 372#define dval(x) (x)->d 373 374/* The following definition of Storeinc is appropriate for MIPS processors. 375 * An alternative that might be better on some machines is 376 * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff) 377 */ 378#if defined(IEEE_8087) + defined(VAX) 379#define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \ 380((unsigned short *)a)[0] = (unsigned short)c, a++) 381#else 382#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \ 383((unsigned short *)a)[1] = (unsigned short)c, a++) 384#endif 385 386/* #define P DBL_MANT_DIG */ 387/* Ten_pmax = floor(P*log(2)/log(5)) */ 388/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */ 389/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */ 390/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */ 391 392#ifdef IEEE_Arith 393#define Exp_shift 20 394#define Exp_shift1 20 395#define Exp_msk1 0x100000 396#define Exp_msk11 0x100000 397#define Exp_mask 0x7ff00000 398#define P 53 399#define Bias 1023 400#define Emin (-1022) 401#define Exp_1 0x3ff00000 402#define Exp_11 0x3ff00000 403#define Ebits 11 404#define Frac_mask 0xfffff 405#define Frac_mask1 0xfffff 406#define Ten_pmax 22 407#define Bletch 0x10 408#define Bndry_mask 0xfffff 409#define Bndry_mask1 0xfffff 410#define LSB 1 411#define Sign_bit 0x80000000 412#define Log2P 1 413#define Tiny0 0 414#define Tiny1 1 415#define Quick_max 14 416#define Int_max 14 417 418#ifndef Flt_Rounds 419#ifdef FLT_ROUNDS 420#define Flt_Rounds FLT_ROUNDS 421#else 422#define Flt_Rounds 1 423#endif 424#endif /*Flt_Rounds*/ 425 426#else /* ifndef IEEE_Arith */ 427#undef Sudden_Underflow 428#define Sudden_Underflow 429#ifdef IBM 430#undef Flt_Rounds 431#define Flt_Rounds 0 432#define Exp_shift 24 433#define Exp_shift1 24 434#define Exp_msk1 0x1000000 435#define Exp_msk11 0x1000000 436#define Exp_mask 0x7f000000 437#define P 14 438#define Bias 65 439#define Exp_1 0x41000000 440#define Exp_11 0x41000000 441#define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */ 442#define Frac_mask 0xffffff 443#define Frac_mask1 0xffffff 444#define Bletch 4 445#define Ten_pmax 22 446#define Bndry_mask 0xefffff 447#define Bndry_mask1 0xffffff 448#define LSB 1 449#define Sign_bit 0x80000000 450#define Log2P 4 451#define Tiny0 0x100000 452#define Tiny1 0 453#define Quick_max 14 454#define Int_max 15 455#else /* VAX */ 456#undef Flt_Rounds 457#define Flt_Rounds 1 458#define Exp_shift 23 459#define Exp_shift1 7 460#define Exp_msk1 0x80 461#define Exp_msk11 0x800000 462#define Exp_mask 0x7f80 463#define P 56 464#define Bias 129 465#define Exp_1 0x40800000 466#define Exp_11 0x4080 467#define Ebits 8 468#define Frac_mask 0x7fffff 469#define Frac_mask1 0xffff007f 470#define Ten_pmax 24 471#define Bletch 2 472#define Bndry_mask 0xffff007f 473#define Bndry_mask1 0xffff007f 474#define LSB 0x10000 475#define Sign_bit 0x8000 476#define Log2P 1 477#define Tiny0 0x80 478#define Tiny1 0 479#define Quick_max 15 480#define Int_max 15 481#endif /* IBM, VAX */ 482#endif /* IEEE_Arith */ 483 484#ifndef IEEE_Arith 485#define ROUND_BIASED 486#endif 487 488#ifdef RND_PRODQUOT 489#define rounded_product(a,b) a = rnd_prod(a, b) 490#define rounded_quotient(a,b) a = rnd_quot(a, b) 491#ifdef KR_headers 492extern double rnd_prod(), rnd_quot(); 493#else 494extern double rnd_prod(double, double), rnd_quot(double, double); 495#endif 496#else 497#define rounded_product(a,b) a *= b 498#define rounded_quotient(a,b) a /= b 499#endif 500 501#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1)) 502#define Big1 0xffffffff 503 504#undef Pack_16 505#ifndef Pack_32 506#define Pack_32 507#endif 508 509#ifdef NO_LONG_LONG 510#undef ULLong 511#ifdef Just_16 512#undef Pack_32 513#define Pack_16 514/* When Pack_32 is not defined, we store 16 bits per 32-bit Long. 515 * This makes some inner loops simpler and sometimes saves work 516 * during multiplications, but it often seems to make things slightly 517 * slower. Hence the default is now to store 32 bits per Long. 518 */ 519#endif 520#else /* long long available */ 521#ifndef Llong 522#define Llong long long 523#endif 524#ifndef ULLong 525#define ULLong unsigned Llong 526#endif 527#endif /* NO_LONG_LONG */ 528 529#ifdef Pack_32 530#define ULbits 32 531#define kshift 5 532#define kmask 31 533#define ALL_ON 0xffffffff 534#else 535#define ULbits 16 536#define kshift 4 537#define kmask 15 538#define ALL_ON 0xffff 539#endif 540 541#define MULTIPLE_THREADS 542extern spinlock_t __gdtoa_locks[2]; 543#define ACQUIRE_DTOA_LOCK(n) do { \ 544 if (__isthreaded) _SPINLOCK(&__gdtoa_locks[n]); \ 545} while(0) 546#define FREE_DTOA_LOCK(n) do { \ 547 if (__isthreaded) _SPINUNLOCK(&__gdtoa_locks[n]); \ 548} while(0) 549 550#define Kmax 9 551 552 struct 553Bigint { 554 struct Bigint *next; 555 int k, maxwds, sign, wds; 556 ULong x[1]; 557 }; 558 559 typedef struct Bigint Bigint; 560 561#ifdef NO_STRING_H 562#ifdef DECLARE_SIZE_T 563typedef unsigned int size_t; 564#endif 565extern void memcpy_D2A ANSI((void*, const void*, size_t)); 566#define Bcopy(x,y) memcpy_D2A(&x->sign,&y->sign,y->wds*sizeof(ULong) + 2*sizeof(int)) 567#else /* !NO_STRING_H */ 568#define Bcopy(x,y) memcpy(&x->sign,&y->sign,y->wds*sizeof(ULong) + 2*sizeof(int)) 569#endif /* NO_STRING_H */ 570 571 extern char *dtoa_result; 572 extern CONST double bigtens[], tens[], tinytens[]; 573 extern CONST unsigned char hexdig[]; 574 575 extern Bigint *Balloc ANSI((int)); 576 extern void Bfree ANSI((Bigint*)); 577 extern void ULtof ANSI((ULong*, ULong*, Long, int)); 578 extern void ULtod ANSI((ULong*, ULong*, Long, int)); 579 extern void ULtodd ANSI((ULong*, ULong*, Long, int)); 580 extern void ULtoQ ANSI((ULong*, ULong*, Long, int)); 581 extern void ULtox ANSI((UShort*, ULong*, Long, int)); 582 extern void ULtoxL ANSI((ULong*, ULong*, Long, int)); 583 extern ULong any_on ANSI((Bigint*, int)); 584 extern double b2d ANSI((Bigint*, int*)); 585 extern int cmp ANSI((Bigint*, Bigint*)); 586 extern void copybits ANSI((ULong*, int, Bigint*)); 587 extern Bigint *d2b ANSI((double, int*, int*)); 588 extern void decrement ANSI((Bigint*)); 589 extern Bigint *diff ANSI((Bigint*, Bigint*)); 590 extern char *dtoa ANSI((double d, int mode, int ndigits, 591 int *decpt, int *sign, char **rve)); 592 extern char *g__fmt ANSI((char*, char*, char*, int, ULong, size_t)); 593 extern int gethex ANSI((CONST char**, CONST FPI*, Long*, Bigint**, int, locale_t)); 594 extern void hexdig_init_D2A(Void); 595 extern int hexnan ANSI((CONST char**, CONST FPI*, ULong*)); 596 extern int hi0bits_D2A ANSI((ULong)); 597 extern Bigint *i2b ANSI((int)); 598 extern Bigint *increment ANSI((Bigint*)); 599 extern int lo0bits ANSI((ULong*)); 600 extern Bigint *lshift ANSI((Bigint*, int)); 601 extern int match ANSI((CONST char**, char*)); 602 extern Bigint *mult ANSI((Bigint*, Bigint*)); 603 extern Bigint *multadd ANSI((Bigint*, int, int)); 604 extern char *nrv_alloc ANSI((char*, char **, int)); 605 extern Bigint *pow5mult ANSI((Bigint*, int)); 606 extern int quorem ANSI((Bigint*, Bigint*)); 607 extern double ratio ANSI((Bigint*, Bigint*)); 608 extern void rshift ANSI((Bigint*, int)); 609 extern char *rv_alloc ANSI((int)); 610 extern Bigint *s2b ANSI((CONST char*, int, int, ULong, int)); 611 extern Bigint *set_ones ANSI((Bigint*, int)); 612 extern char *strcp ANSI((char*, const char*)); 613 extern int strtoIg ANSI((CONST char*, char**, FPI*, Long*, Bigint**, int*)); 614 extern double strtod ANSI((const char *s00, char **se)); 615 extern double strtod_l ANSI((const char *s00, char **se, locale_t)); 616 extern Bigint *sum ANSI((Bigint*, Bigint*)); 617 extern int trailz ANSI((Bigint*)); 618 extern double ulp ANSI((U*)); 619 620#ifdef __cplusplus 621} 622#endif 623/* 624 * NAN_WORD0 and NAN_WORD1 are only referenced in strtod.c. Prior to 625 * 20050115, they used to be hard-wired here (to 0x7ff80000 and 0, 626 * respectively), but now are determined by compiling and running 627 * qnan.c to generate gd_qnan.h, which specifies d_QNAN0 and d_QNAN1. 628 * Formerly gdtoaimp.h recommended supplying suitable -DNAN_WORD0=... 629 * and -DNAN_WORD1=... values if necessary. This should still work. 630 * (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.) 631 */ 632#ifdef IEEE_Arith 633#ifndef NO_INFNAN_CHECK 634#undef INFNAN_CHECK 635#define INFNAN_CHECK 636#endif 637#ifdef IEEE_MC68k 638#define _0 0 639#define _1 1 640#ifndef NAN_WORD0 641#define NAN_WORD0 d_QNAN0 642#endif 643#ifndef NAN_WORD1 644#define NAN_WORD1 d_QNAN1 645#endif 646#else 647#define _0 1 648#define _1 0 649#ifndef NAN_WORD0 650#define NAN_WORD0 d_QNAN1 651#endif 652#ifndef NAN_WORD1 653#define NAN_WORD1 d_QNAN0 654#endif 655#endif 656#else 657#undef INFNAN_CHECK 658#endif 659 660#undef SI 661#ifdef Sudden_Underflow 662#define SI 1 663#else 664#define SI 0 665#endif 666 667/* 668 * For very large strings, strtod and family might exhaust memory in tight 669 * memory conditions (especially in 32-bits). Such large strings could also 670 * tie up a CPU for minutes at a time. Either can be considered a denial-of- 671 * service vunerability. 672 * 673 * To fix, we limit the string size to the maximum we need to calculate the 674 * rounding point correctly. The longest string corresponding to the exact 675 * value of a floating point number occuring at 1.f...f p^-n, where n is 676 * the (absolute value of the) smallest exponent for a normalize number. 677 * 678 * To calculate this number of decimal digits, we use the formula: 679 * 680 * (n + m) - int(n * log10(2)) + 3 681 * 682 * where m is the number of bits in the f...f fraction. This is the number 683 * of decimal digits for the least significant bit minus the number of leading 684 * zeros for the most significant bit (the '1'), plus a few to compensate for 685 * an extra digits due to the full 1.f...f value, an extra digit for the 686 * mid-way point for rounding and an extra guard digit. 687 * 688 * Using the approximation log10(2) ~ 1233 / (2^12), converting to the fpi.emin 689 * and fpi.nbits values, we get: 690 * 691 * -fpi.emin -((1233 * (-fpi.nbits - fpi.emin)) >> 12) + 3 692 * 693 * Finally, we add an extra digit, either '1' or '0', to represent whether 694 * to-be-truncated digits contain a non-zero digit, or are all zeros, 695 * respectively. 696 * 697 * The truncated string is allocated on the heap, so code using 698 * TRUNCATE_DIGITS() will need to free that space when no longer needed. 699 * Pass a char * as the second argument, initialized to NULL; if its value 700 * becomes non-NULL, memory was allocated. 701 */ 702#define LOG2NUM 1233 703#define LOG2DENOMSHIFT 12 704#define TRUNCATEDIGITS(_nbits, _emin) (-(_emin) - ((LOG2NUM * (-(_nbits) - (_emin))) >> LOG2DENOMSHIFT) + 3) 705 706#define TRUNCATE_DIGITS(_s0, _temp, _nd, _nd0, _nf, _nbits, _emin, _dplen) \ 707{ \ 708 int _maxdigits = TRUNCATEDIGITS((_nbits), (_emin)); \ 709 if ((_nd) > _maxdigits && \ 710 ((_temp) = MALLOC(_maxdigits + (_dplen) + 2)) != NULL) { \ 711 char *_tp = (_temp) + _maxdigits; \ 712 if ((_nd0) >= _maxdigits) { \ 713 memcpy((_temp), (_s0), _maxdigits); \ 714 if ((_nd) > (_nd0)) *_tp++ = '1'; \ 715 else { \ 716 const char *_q = (_s0) + _maxdigits; \ 717 int _n = (_nd0) - _maxdigits; \ 718 for(; _n > 0 && *_q == '0'; _n--, _q++) {} \ 719 *_tp++ = _n > 0 ? '1' : '0'; \ 720 } \ 721 (_nf) = -((_nd0) - (_maxdigits + 1)); \ 722 (_nd0) = _maxdigits + 1; \ 723 } \ 724 else if ((_nd0) == 0) { \ 725 memcpy((_temp), (_s0), _maxdigits); \ 726 *_tp++ = '1'; \ 727 (_nf) -= ((_nd) - (_maxdigits + 1)); \ 728 } \ 729 else { \ 730 memcpy((_temp), (_s0), _maxdigits + (_dplen)); \ 731 _tp += (_dplen); \ 732 *_tp++ = '1'; \ 733 (_nf) = (_maxdigits + 1) - (_nd0); \ 734 } \ 735 *_tp = 0; \ 736 (_nd) = _maxdigits + 1; \ 737 (_s0) = (_temp); \ 738 } \ 739 } 740 741#endif /* GDTOAIMP_H_INCLUDED */ 742