projects / apple / libc.git / blame
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| 9385eb3d A |
1 | /**************************************************************** |
| 2 | ||
| 3 | The author of this software is David M. Gay. | |
| 4 | ||
| 5 | Copyright (C) 1998-2000 by Lucent Technologies | |
| 6 | All Rights Reserved | |
| 7 | ||
| 8 | Permission to use, copy, modify, and distribute this software and | |
| 9 | its documentation for any purpose and without fee is hereby | |
| 10 | granted, provided that the above copyright notice appear in all | |
| 11 | copies and that both that the copyright notice and this | |
| 12 | permission notice and warranty disclaimer appear in supporting | |
| 13 | documentation, and that the name of Lucent or any of its entities | |
| 14 | not be used in advertising or publicity pertaining to | |
| 15 | distribution of the software without specific, written prior | |
| 16 | permission. | |
| 17 | ||
| 18 | LUCENT DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE, | |
| 19 | INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS. | |
| 20 | IN NO EVENT SHALL LUCENT OR ANY OF ITS ENTITIES BE LIABLE FOR ANY | |
| 21 | SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES | |
| 22 | WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER | |
| 23 | IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, | |
| 24 | ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF | |
| 25 | THIS SOFTWARE. | |
| 26 | ||
| 27 | ****************************************************************/ | |
| 28 | ||
| 9385eb3d A |
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 | ||
| 3d9156a7 A |
36 | Please send bug reports to David M. Gay (dmg at acm dot org, |
| 37 | with " at " changed at "@" and " dot " changed to "."). | |
| 9385eb3d A |
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 | |
| 3d9156a7 | 59 | * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 112-126]. |
| 9385eb3d A |
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 | |
| 1f2f436a A |
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.) | |
| 9385eb3d A |
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. | |
| 1f2f436a A |
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). | |
| 9385eb3d A |
138 | * When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined, |
| 139 | * strtodg also accepts (case insensitively) strings of the form | |
| 34e8f829 A |
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). | |
| 9385eb3d A |
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 | |
| 34e8f829 | 161 | * precision conversions (which could also be done by the strtod in |
| 9385eb3d A |
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. | |
| 9385eb3d A |
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 | |
| ad3c9f2a A |
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> | |
| 9385eb3d | 260 | #include "gdtoa.h" |
| 3d9156a7 | 261 | #include "gd_qnan.h" |
| 34e8f829 A |
262 | #ifdef Honor_FLT_ROUNDS |
| 263 | #include <fenv.h> | |
| 264 | #endif | |
| 9385eb3d A |
265 | |
| 266 | #ifdef DEBUG | |
| 267 | #include "stdio.h" | |
| 268 | #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);} | |
| 269 | #endif | |
| 270 | ||
| ad3c9f2a | 271 | #include "limits.h" |
| 9385eb3d A |
272 | #include "stdlib.h" |
| 273 | #include "string.h" | |
| ad3c9f2a A |
274 | #include "libc_private.h" |
| 275 | #include "spinlock.h" | |
| 9385eb3d A |
276 | |
| 277 | #ifdef KR_headers | |
| 278 | #define Char char | |
| 279 | #else | |
| 280 | #define Char void | |
| 281 | #endif | |
| 282 | ||
| 283 | #ifdef MALLOC | |
| 284 | extern Char *MALLOC ANSI((size_t)); | |
| 285 | #else | |
| 286 | #define MALLOC malloc | |
| 287 | #endif | |
| 288 | ||
| ad3c9f2a A |
289 | #define INFNAN_CHECK |
| 290 | #define USE_LOCALE | |
| 291 | #define NO_LOCALE_CACHE | |
| 292 | ||
| 9385eb3d A |
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 | |
| 356 | extern "C" { | |
| 357 | #endif | |
| 358 | ||
| 359 | #if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1 | |
| 360 | Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined. | |
| 361 | #endif | |
| 362 | ||
| 363 | typedef union { double d; ULong L[2]; } U; | |
| 364 | ||
| 9385eb3d | 365 | #ifdef IEEE_8087 |
| 1f2f436a A |
366 | #define word0(x) (x)->L[1] |
| 367 | #define word1(x) (x)->L[0] | |
| 9385eb3d | 368 | #else |
| 1f2f436a A |
369 | #define word0(x) (x)->L[0] |
| 370 | #define word1(x) (x)->L[1] | |
| 9385eb3d | 371 | #endif |
| 1f2f436a | 372 | #define dval(x) (x)->d |
| 9385eb3d A |
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 | |
| 492 | extern double rnd_prod(), rnd_quot(); | |
| 493 | #else | |
| 494 | extern 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 | ||
| ad3c9f2a A |
541 | #define MULTIPLE_THREADS |
| 542 | extern 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) | |
| 9385eb3d | 549 | |
| 1f2f436a | 550 | #define Kmax 9 |
| 9385eb3d A |
551 | |
| 552 | struct | |
| 553 | Bigint { | |
| 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 | |
| 563 | typedef unsigned int size_t; | |
| 564 | #endif | |
| 565 | extern 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 | ||
| 9385eb3d A |
571 | extern char *dtoa_result; |
| 572 | extern CONST double bigtens[], tens[], tinytens[]; | |
| 6465356a | 573 | extern CONST unsigned char hexdig[]; |
| 9385eb3d A |
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*)); | |
| 34e8f829 | 588 | extern void decrement ANSI((Bigint*)); |
| 9385eb3d A |
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)); | |
| 34e8f829 | 592 | extern char *g__fmt ANSI((char*, char*, char*, int, ULong, size_t)); |
| 6465356a | 593 | extern int gethex ANSI((CONST char**, CONST FPI*, Long*, Bigint**, int, locale_t)); |
| 9385eb3d | 594 | extern void hexdig_init_D2A(Void); |
| 6465356a | 595 | extern int hexnan ANSI((CONST char**, CONST FPI*, ULong*)); |
| 3d9156a7 | 596 | extern int hi0bits_D2A ANSI((ULong)); |
| 9385eb3d A |
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)); | |
| 1f2f436a | 610 | extern Bigint *s2b ANSI((CONST char*, int, int, ULong, int)); |
| 9385eb3d A |
611 | extern Bigint *set_ones ANSI((Bigint*, int)); |
| 612 | extern char *strcp ANSI((char*, const char*)); | |
| 9385eb3d | 613 | extern int strtoIg ANSI((CONST char*, char**, FPI*, Long*, Bigint**, int*)); |
| 9385eb3d | 614 | extern double strtod ANSI((const char *s00, char **se)); |
| ad3c9f2a | 615 | extern double strtod_l ANSI((const char *s00, char **se, locale_t)); |
| 9385eb3d A |
616 | extern Bigint *sum ANSI((Bigint*, Bigint*)); |
| 617 | extern int trailz ANSI((Bigint*)); | |
| 1f2f436a | 618 | extern double ulp ANSI((U*)); |
| 9385eb3d A |
619 | |
| 620 | #ifdef __cplusplus | |
| 621 | } | |
| 622 | #endif | |
| 3d9156a7 A |
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 | */ | |
| 9385eb3d | 632 | #ifdef IEEE_Arith |
| 1f2f436a A |
633 | #ifndef NO_INFNAN_CHECK |
| 634 | #undef INFNAN_CHECK | |
| 635 | #define INFNAN_CHECK | |
| 636 | #endif | |
| 9385eb3d A |
637 | #ifdef IEEE_MC68k |
| 638 | #define _0 0 | |
| 639 | #define _1 1 | |
| 3d9156a7 A |
640 | #ifndef NAN_WORD0 |
| 641 | #define NAN_WORD0 d_QNAN0 | |
| 642 | #endif | |
| 643 | #ifndef NAN_WORD1 | |
| 644 | #define NAN_WORD1 d_QNAN1 | |
| 645 | #endif | |
| 9385eb3d A |
646 | #else |
| 647 | #define _0 1 | |
| 648 | #define _1 0 | |
| 9385eb3d | 649 | #ifndef NAN_WORD0 |
| 3d9156a7 | 650 | #define NAN_WORD0 d_QNAN1 |
| 9385eb3d | 651 | #endif |
| 9385eb3d | 652 | #ifndef NAN_WORD1 |
| 3d9156a7 A |
653 | #define NAN_WORD1 d_QNAN0 |
| 654 | #endif | |
| 655 | #endif | |
| 656 | #else | |
| 657 | #undef INFNAN_CHECK | |
| 9385eb3d | 658 | #endif |
| 9385eb3d A |
659 | |
| 660 | #undef SI | |
| 661 | #ifdef Sudden_Underflow | |
| 662 | #define SI 1 | |
| 663 | #else | |
| 664 | #define SI 0 | |
| 665 | #endif | |
| 666 | ||
| ad3c9f2a A |
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 | ||
| 9385eb3d | 741 | #endif /* GDTOAIMP_H_INCLUDED */ |