SphinxBase
0.6
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00001 /**************************************************************** 00002 * 00003 * The author of this software is David M. Gay. 00004 * 00005 * Copyright (c) 1991, 2000, 2001 by Lucent Technologies. 00006 * 00007 * Permission to use, copy, modify, and distribute this software for any 00008 * purpose without fee is hereby granted, provided that this entire notice 00009 * is included in all copies of any software which is or includes a copy 00010 * or modification of this software and in all copies of the supporting 00011 * documentation for such software. 00012 * 00013 * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED 00014 * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY 00015 * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY 00016 * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE. 00017 * 00018 ***************************************************************/ 00019 00020 /* Please send bug reports to David M. Gay (dmg at acm dot org, 00021 * with " at " changed at "@" and " dot " changed to "."). */ 00022 00023 /* On a machine with IEEE extended-precision registers, it is 00024 * necessary to specify double-precision (53-bit) rounding precision 00025 * before invoking strtod or dtoa. If the machine uses (the equivalent 00026 * of) Intel 80x87 arithmetic, the call 00027 * _control87(PC_53, MCW_PC); 00028 * does this with many compilers. Whether this or another call is 00029 * appropriate depends on the compiler; for this to work, it may be 00030 * necessary to #include "float.h" or another system-dependent header 00031 * file. 00032 */ 00033 00034 /* strtod for IEEE-, VAX-, and IBM-arithmetic machines. 00035 * 00036 * This strtod returns a nearest machine number to the input decimal 00037 * string (or sets errno to ERANGE). With IEEE arithmetic, ties are 00038 * broken by the IEEE round-even rule. Otherwise ties are broken by 00039 * biased rounding (add half and chop). 00040 * 00041 * Inspired loosely by William D. Clinger's paper "How to Read Floating 00042 * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101]. 00043 * 00044 * Modifications: 00045 * 00046 * 1. We only require IEEE, IBM, or VAX double-precision 00047 * arithmetic (not IEEE double-extended). 00048 * 2. We get by with floating-point arithmetic in a case that 00049 * Clinger missed -- when we're computing d * 10^n 00050 * for a small integer d and the integer n is not too 00051 * much larger than 22 (the maximum integer k for which 00052 * we can represent 10^k exactly), we may be able to 00053 * compute (d*10^k) * 10^(e-k) with just one roundoff. 00054 * 3. Rather than a bit-at-a-time adjustment of the binary 00055 * result in the hard case, we use floating-point 00056 * arithmetic to determine the adjustment to within 00057 * one bit; only in really hard cases do we need to 00058 * compute a second residual. 00059 * 4. Because of 3., we don't need a large table of powers of 10 00060 * for ten-to-e (just some small tables, e.g. of 10^k 00061 * for 0 <= k <= 22). 00062 */ 00063 00064 /* 00065 * This file has been modified to remove dtoa() and all 00066 * non-reentrancy. This makes it slower, but it also makes life a lot 00067 * easier on Windows and other platforms without static lock 00068 * initializers (grumble). 00069 */ 00070 00071 /* Added by dhuggins@cs.cmu.edu to use autoconf results. */ 00072 /* We do not care about the VAX. */ 00073 #include "config.h" 00074 #ifdef WORDS_BIGENDIAN 00075 #define IEEE_MC68k 00076 #else 00077 #define IEEE_8087 00078 #endif 00079 #ifndef HAVE_LONG_LONG 00080 #define NO_LONG_LONG 00081 #endif 00082 #define Omit_Private_Memory 00083 #include "sphinxbase/ckd_alloc.h" 00084 #undef USE_LOCALE 00085 00086 /* Correct totally bogus typedefs in this code. */ 00087 #include "sphinxbase/prim_type.h" 00088 #define Long int32 /* ZOMG */ 00089 #define ULong uint32 /* WTF */ 00090 00091 /* 00092 * #define IEEE_8087 for IEEE-arithmetic machines where the least 00093 * significant byte has the lowest address. 00094 * #define IEEE_MC68k for IEEE-arithmetic machines where the most 00095 * significant byte has the lowest address. 00096 * #define Long int on machines with 32-bit ints and 64-bit longs. 00097 * #define IBM for IBM mainframe-style floating-point arithmetic. 00098 * #define VAX for VAX-style floating-point arithmetic (D_floating). 00099 * #define No_leftright to omit left-right logic in fast floating-point 00100 * computation of dtoa. 00101 * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3 00102 * and strtod and dtoa should round accordingly. 00103 * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3 00104 * and Honor_FLT_ROUNDS is not #defined. 00105 * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines 00106 * that use extended-precision instructions to compute rounded 00107 * products and quotients) with IBM. 00108 * #define ROUND_BIASED for IEEE-format with biased rounding. 00109 * #define Inaccurate_Divide for IEEE-format with correctly rounded 00110 * products but inaccurate quotients, e.g., for Intel i860. 00111 * #define NO_LONG_LONG on machines that do not have a "long long" 00112 * integer type (of >= 64 bits). On such machines, you can 00113 * #define Just_16 to store 16 bits per 32-bit Long when doing 00114 * high-precision integer arithmetic. Whether this speeds things 00115 * up or slows things down depends on the machine and the number 00116 * being converted. If long long is available and the name is 00117 * something other than "long long", #define Llong to be the name, 00118 * and if "unsigned Llong" does not work as an unsigned version of 00119 * Llong, #define #ULLong to be the corresponding unsigned type. 00120 * #define KR_headers for old-style C function headers. 00121 * #define Bad_float_h if your system lacks a float.h or if it does not 00122 * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP, 00123 * FLT_RADIX, FLT_ROUNDS, and DBL_MAX. 00124 * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n) 00125 * if memory is available and otherwise does something you deem 00126 * appropriate. If MALLOC is undefined, malloc will be invoked 00127 * directly -- and assumed always to succeed. 00128 * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making 00129 * memory allocations from a private pool of memory when possible. 00130 * When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes, 00131 * unless #defined to be a different length. This default length 00132 * suffices to get rid of MALLOC calls except for unusual cases, 00133 * such as decimal-to-binary conversion of a very long string of 00134 * digits. The longest string dtoa can return is about 751 bytes 00135 * long. For conversions by strtod of strings of 800 digits and 00136 * all dtoa conversions in single-threaded executions with 8-byte 00137 * pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte 00138 * pointers, PRIVATE_MEM >= 7112 appears adequate. 00139 * #define NO_INFNAN_CHECK if you do not wish to have INFNAN_CHECK 00140 * #defined automatically on IEEE systems. On such systems, 00141 * when INFNAN_CHECK is #defined, strtod checks 00142 * for Infinity and NaN (case insensitively). On some systems 00143 * (e.g., some HP systems), it may be necessary to #define NAN_WORD0 00144 * appropriately -- to the most significant word of a quiet NaN. 00145 * (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.) 00146 * When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined, 00147 * strtod also accepts (case insensitively) strings of the form 00148 * NaN(x), where x is a string of hexadecimal digits and spaces; 00149 * if there is only one string of hexadecimal digits, it is taken 00150 * for the 52 fraction bits of the resulting NaN; if there are two 00151 * or more strings of hex digits, the first is for the high 20 bits, 00152 * the second and subsequent for the low 32 bits, with intervening 00153 * white space ignored; but if this results in none of the 52 00154 * fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0 00155 * and NAN_WORD1 are used instead. 00156 * #define MULTIPLE_THREADS if the system offers preemptively scheduled 00157 * multiple threads. In this case, you must provide (or suitably 00158 * #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed 00159 * by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed 00160 * in pow5mult, ensures lazy evaluation of only one copy of high 00161 * powers of 5; omitting this lock would introduce a small 00162 * probability of wasting memory, but would otherwise be harmless.) 00163 * You must also invoke freedtoa(s) to free the value s returned by 00164 * dtoa. You may do so whether or not MULTIPLE_THREADS is #defined. 00165 * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that 00166 * avoids underflows on inputs whose result does not underflow. 00167 * If you #define NO_IEEE_Scale on a machine that uses IEEE-format 00168 * floating-point numbers and flushes underflows to zero rather 00169 * than implementing gradual underflow, then you must also #define 00170 * Sudden_Underflow. 00171 * #define YES_ALIAS to permit aliasing certain double values with 00172 * arrays of ULongs. This leads to slightly better code with 00173 * some compilers and was always used prior to 19990916, but it 00174 * is not strictly legal and can cause trouble with aggressively 00175 * optimizing compilers (e.g., gcc 2.95.1 under -O2). 00176 * #define USE_LOCALE to use the current locale's decimal_point value. 00177 * #define SET_INEXACT if IEEE arithmetic is being used and extra 00178 * computation should be done to set the inexact flag when the 00179 * result is inexact and avoid setting inexact when the result 00180 * is exact. In this case, dtoa.c must be compiled in 00181 * an environment, perhaps provided by #include "dtoa.c" in a 00182 * suitable wrapper, that defines two functions, 00183 * int get_inexact(void); 00184 * void clear_inexact(void); 00185 * such that get_inexact() returns a nonzero value if the 00186 * inexact bit is already set, and clear_inexact() sets the 00187 * inexact bit to 0. When SET_INEXACT is #defined, strtod 00188 * also does extra computations to set the underflow and overflow 00189 * flags when appropriate (i.e., when the result is tiny and 00190 * inexact or when it is a numeric value rounded to +-infinity). 00191 * #define NO_ERRNO if strtod should not assign errno = ERANGE when 00192 * the result overflows to +-Infinity or underflows to 0. 00193 */ 00194 00195 #ifndef Long 00196 #define Long long 00197 #endif 00198 #ifndef ULong 00199 typedef unsigned Long ULong; 00200 #endif 00201 00202 #ifdef DEBUG 00203 #include "stdio.h" 00204 #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);} 00205 #endif 00206 00207 #include "stdlib.h" 00208 #include "string.h" 00209 00210 #ifdef USE_LOCALE 00211 #include "locale.h" 00212 #endif 00213 00214 /* Private memory and other non-reentrant stuff removed. */ 00215 00216 #undef IEEE_Arith 00217 #undef Avoid_Underflow 00218 #ifdef IEEE_MC68k 00219 #define IEEE_Arith 00220 #endif 00221 #ifdef IEEE_8087 00222 #define IEEE_Arith 00223 #endif 00224 00225 #ifdef IEEE_Arith 00226 #ifndef NO_INFNAN_CHECK 00227 #undef INFNAN_CHECK 00228 #define INFNAN_CHECK 00229 #endif 00230 #else 00231 #undef INFNAN_CHECK 00232 #endif 00233 00234 #include "errno.h" 00235 00236 #ifdef Bad_float_h 00237 00238 #ifdef IEEE_Arith 00239 #define DBL_DIG 15 00240 #define DBL_MAX_10_EXP 308 00241 #define DBL_MAX_EXP 1024 00242 #define FLT_RADIX 2 00243 #endif /*IEEE_Arith*/ 00244 00245 #ifdef IBM 00246 #define DBL_DIG 16 00247 #define DBL_MAX_10_EXP 75 00248 #define DBL_MAX_EXP 63 00249 #define FLT_RADIX 16 00250 #define DBL_MAX 7.2370055773322621e+75 00251 #endif 00252 00253 #ifdef VAX 00254 #define DBL_DIG 16 00255 #define DBL_MAX_10_EXP 38 00256 #define DBL_MAX_EXP 127 00257 #define FLT_RADIX 2 00258 #define DBL_MAX 1.7014118346046923e+38 00259 #endif 00260 00261 #ifndef LONG_MAX 00262 #define LONG_MAX 2147483647 00263 #endif 00264 00265 #else /* ifndef Bad_float_h */ 00266 #include "float.h" 00267 #endif /* Bad_float_h */ 00268 00269 #ifndef __MATH_H__ 00270 #include "math.h" 00271 #endif 00272 00273 #ifdef __cplusplus 00274 extern "C" { 00275 #endif 00276 00277 #ifndef CONST 00278 #ifdef KR_headers 00279 #define CONST /* blank */ 00280 #else 00281 #define CONST const 00282 #endif 00283 #endif 00284 00285 00286 #if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1 00287 Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined. 00288 #endif 00289 00291 typedef union { double d; ULong L[2]; } U; 00292 00293 #ifdef YES_ALIAS 00294 #define dval(x) x 00295 #ifdef IEEE_8087 00296 #define word0(x) ((ULong *)&x)[1] 00297 #define word1(x) ((ULong *)&x)[0] 00298 #else 00299 #define word0(x) ((ULong *)&x)[0] 00300 #define word1(x) ((ULong *)&x)[1] 00301 #endif 00302 #else 00303 #ifdef IEEE_8087 00304 #define word0(x) ((U*)&x)->L[1] 00305 #define word1(x) ((U*)&x)->L[0] 00306 #else 00307 #define word0(x) ((U*)&x)->L[0] 00308 #define word1(x) ((U*)&x)->L[1] 00309 #endif 00310 #define dval(x) ((U*)&x)->d 00311 #endif 00312 00313 /* The following definition of Storeinc is appropriate for MIPS processors. 00314 * An alternative that might be better on some machines is 00315 * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff) 00316 */ 00317 #if defined(IEEE_8087) + defined(VAX) 00318 #define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \ 00319 ((unsigned short *)a)[0] = (unsigned short)c, a++) 00320 #else 00321 #define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \ 00322 ((unsigned short *)a)[1] = (unsigned short)c, a++) 00323 #endif 00324 00325 /* #define P DBL_MANT_DIG */ 00326 /* Ten_pmax = floor(P*log(2)/log(5)) */ 00327 /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */ 00328 /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */ 00329 /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */ 00330 00331 #ifdef IEEE_Arith 00332 #define Exp_shift 20 00333 #define Exp_shift1 20 00334 #define Exp_msk1 0x100000 00335 #define Exp_msk11 0x100000 00336 #define Exp_mask 0x7ff00000 00337 #define P 53 00338 #define Bias 1023 00339 #define Emin (-1022) 00340 #define Exp_1 0x3ff00000 00341 #define Exp_11 0x3ff00000 00342 #define Ebits 11 00343 #define Frac_mask 0xfffff 00344 #define Frac_mask1 0xfffff 00345 #define Ten_pmax 22 00346 #define Bletch 0x10 00347 #define Bndry_mask 0xfffff 00348 #define Bndry_mask1 0xfffff 00349 #define LSB 1 00350 #define Sign_bit 0x80000000 00351 #define Log2P 1 00352 #define Tiny0 0 00353 #define Tiny1 1 00354 #define Quick_max 14 00355 #define Int_max 14 00356 #ifndef NO_IEEE_Scale 00357 #define Avoid_Underflow 00358 #ifdef Flush_Denorm /* debugging option */ 00359 #undef Sudden_Underflow 00360 #endif 00361 #endif 00362 00363 #ifndef Flt_Rounds 00364 #ifdef FLT_ROUNDS 00365 #define Flt_Rounds FLT_ROUNDS 00366 #else 00367 #define Flt_Rounds 1 00368 #endif 00369 #endif /*Flt_Rounds*/ 00370 00371 #ifdef Honor_FLT_ROUNDS 00372 #define Rounding rounding 00373 #undef Check_FLT_ROUNDS 00374 #define Check_FLT_ROUNDS 00375 #else 00376 #define Rounding Flt_Rounds 00377 #endif 00378 00379 #else /* ifndef IEEE_Arith */ 00380 #undef Check_FLT_ROUNDS 00381 #undef Honor_FLT_ROUNDS 00382 #undef SET_INEXACT 00383 #undef Sudden_Underflow 00384 #define Sudden_Underflow 00385 #ifdef IBM 00386 #undef Flt_Rounds 00387 #define Flt_Rounds 0 00388 #define Exp_shift 24 00389 #define Exp_shift1 24 00390 #define Exp_msk1 0x1000000 00391 #define Exp_msk11 0x1000000 00392 #define Exp_mask 0x7f000000 00393 #define P 14 00394 #define Bias 65 00395 #define Exp_1 0x41000000 00396 #define Exp_11 0x41000000 00397 #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */ 00398 #define Frac_mask 0xffffff 00399 #define Frac_mask1 0xffffff 00400 #define Bletch 4 00401 #define Ten_pmax 22 00402 #define Bndry_mask 0xefffff 00403 #define Bndry_mask1 0xffffff 00404 #define LSB 1 00405 #define Sign_bit 0x80000000 00406 #define Log2P 4 00407 #define Tiny0 0x100000 00408 #define Tiny1 0 00409 #define Quick_max 14 00410 #define Int_max 15 00411 #else /* VAX */ 00412 #undef Flt_Rounds 00413 #define Flt_Rounds 1 00414 #define Exp_shift 23 00415 #define Exp_shift1 7 00416 #define Exp_msk1 0x80 00417 #define Exp_msk11 0x800000 00418 #define Exp_mask 0x7f80 00419 #define P 56 00420 #define Bias 129 00421 #define Exp_1 0x40800000 00422 #define Exp_11 0x4080 00423 #define Ebits 8 00424 #define Frac_mask 0x7fffff 00425 #define Frac_mask1 0xffff007f 00426 #define Ten_pmax 24 00427 #define Bletch 2 00428 #define Bndry_mask 0xffff007f 00429 #define Bndry_mask1 0xffff007f 00430 #define LSB 0x10000 00431 #define Sign_bit 0x8000 00432 #define Log2P 1 00433 #define Tiny0 0x80 00434 #define Tiny1 0 00435 #define Quick_max 15 00436 #define Int_max 15 00437 #endif /* IBM, VAX */ 00438 #endif /* IEEE_Arith */ 00439 00440 #ifndef IEEE_Arith 00441 #define ROUND_BIASED 00442 #endif 00443 00444 #ifdef RND_PRODQUOT 00445 #define rounded_product(a,b) a = rnd_prod(a, b) 00446 #define rounded_quotient(a,b) a = rnd_quot(a, b) 00447 #ifdef KR_headers 00448 extern double rnd_prod(), rnd_quot(); 00449 #else 00450 extern double rnd_prod(double, double), rnd_quot(double, double); 00451 #endif 00452 #else 00453 #define rounded_product(a,b) a *= b 00454 #define rounded_quotient(a,b) a /= b 00455 #endif 00456 00457 #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1)) 00458 #define Big1 0xffffffff 00459 00460 #ifndef Pack_32 00461 #define Pack_32 00462 #endif 00463 00464 #ifdef KR_headers 00465 #define FFFFFFFF ((((unsigned long)0xffff)<<16)|(unsigned long)0xffff) 00466 #else 00467 #define FFFFFFFF 0xffffffffUL 00468 #endif 00469 00470 #ifdef NO_LONG_LONG 00471 #undef ULLong 00472 #ifdef Just_16 00473 #undef Pack_32 00474 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long. 00475 * This makes some inner loops simpler and sometimes saves work 00476 * during multiplications, but it often seems to make things slightly 00477 * slower. Hence the default is now to store 32 bits per Long. 00478 */ 00479 #endif 00480 #else /* long long available */ 00481 #ifndef Llong 00482 #define Llong long long 00483 #endif 00484 #ifndef ULLong 00485 #define ULLong unsigned Llong 00486 #endif 00487 #endif /* NO_LONG_LONG */ 00488 00489 #ifndef MULTIPLE_THREADS 00490 #define ACQUIRE_DTOA_LOCK(n) /*nothing*/ 00491 #define FREE_DTOA_LOCK(n) /*nothing*/ 00492 #endif 00493 00494 #define Kmax 15 00495 00496 #ifdef __cplusplus 00497 extern "C" double sb_strtod(const char *s00, char **se); 00498 #endif 00499 00500 struct 00501 Bigint { 00502 struct Bigint *next; 00503 int k, maxwds, sign, wds; 00504 ULong x[1]; 00505 }; 00506 00507 typedef struct Bigint Bigint; 00508 00509 static Bigint * 00510 Balloc 00511 #ifdef KR_headers 00512 (k) int k; 00513 #else 00514 (int k) 00515 #endif 00516 { 00517 int x; 00518 size_t len; 00519 Bigint *rv; 00520 00521 x = 1 << k; 00522 len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1) 00523 /sizeof(double); 00524 rv = ckd_malloc(len*sizeof(double)); 00525 rv->k = k; 00526 rv->maxwds = x; 00527 rv->sign = rv->wds = 0; 00528 return rv; 00529 } 00530 00531 static void 00532 Bfree 00533 #ifdef KR_headers 00534 (v) Bigint *v; 00535 #else 00536 (Bigint *v) 00537 #endif 00538 { 00539 ckd_free(v); 00540 } 00541 00542 #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \ 00543 y->wds*sizeof(Long) + 2*sizeof(int)) 00544 00545 static Bigint * 00546 multadd 00547 #ifdef KR_headers 00548 (b, m, a) Bigint *b; int m, a; 00549 #else 00550 (Bigint *b, int m, int a) /* multiply by m and add a */ 00551 #endif 00552 { 00553 int i, wds; 00554 #ifdef ULLong 00555 ULong *x; 00556 ULLong carry, y; 00557 #else 00558 ULong carry, *x, y; 00559 #ifdef Pack_32 00560 ULong xi, z; 00561 #endif 00562 #endif 00563 Bigint *b1; 00564 00565 wds = b->wds; 00566 x = b->x; 00567 i = 0; 00568 carry = a; 00569 do { 00570 #ifdef ULLong 00571 y = *x * (ULLong)m + carry; 00572 carry = y >> 32; 00573 *x++ = y & FFFFFFFF; 00574 #else 00575 #ifdef Pack_32 00576 xi = *x; 00577 y = (xi & 0xffff) * m + carry; 00578 z = (xi >> 16) * m + (y >> 16); 00579 carry = z >> 16; 00580 *x++ = (z << 16) + (y & 0xffff); 00581 #else 00582 y = *x * m + carry; 00583 carry = y >> 16; 00584 *x++ = y & 0xffff; 00585 #endif 00586 #endif 00587 } 00588 while(++i < wds); 00589 if (carry) { 00590 if (wds >= b->maxwds) { 00591 b1 = Balloc(b->k+1); 00592 Bcopy(b1, b); 00593 Bfree(b); 00594 b = b1; 00595 } 00596 b->x[wds++] = carry; 00597 b->wds = wds; 00598 } 00599 return b; 00600 } 00601 00602 static Bigint * 00603 s2b 00604 #ifdef KR_headers 00605 (s, nd0, nd, y9) CONST char *s; int nd0, nd; ULong y9; 00606 #else 00607 (CONST char *s, int nd0, int nd, ULong y9) 00608 #endif 00609 { 00610 Bigint *b; 00611 int i, k; 00612 Long x, y; 00613 00614 x = (nd + 8) / 9; 00615 for(k = 0, y = 1; x > y; y <<= 1, k++) ; 00616 #ifdef Pack_32 00617 b = Balloc(k); 00618 b->x[0] = y9; 00619 b->wds = 1; 00620 #else 00621 b = Balloc(k+1); 00622 b->x[0] = y9 & 0xffff; 00623 b->wds = (b->x[1] = y9 >> 16) ? 2 : 1; 00624 #endif 00625 00626 i = 9; 00627 if (9 < nd0) { 00628 s += 9; 00629 do b = multadd(b, 10, *s++ - '0'); 00630 while(++i < nd0); 00631 s++; 00632 } 00633 else 00634 s += 10; 00635 for(; i < nd; i++) 00636 b = multadd(b, 10, *s++ - '0'); 00637 return b; 00638 } 00639 00640 static int 00641 hi0bits 00642 #ifdef KR_headers 00643 (x) register ULong x; 00644 #else 00645 (register ULong x) 00646 #endif 00647 { 00648 register int k = 0; 00649 00650 if (!(x & 0xffff0000)) { 00651 k = 16; 00652 x <<= 16; 00653 } 00654 if (!(x & 0xff000000)) { 00655 k += 8; 00656 x <<= 8; 00657 } 00658 if (!(x & 0xf0000000)) { 00659 k += 4; 00660 x <<= 4; 00661 } 00662 if (!(x & 0xc0000000)) { 00663 k += 2; 00664 x <<= 2; 00665 } 00666 if (!(x & 0x80000000)) { 00667 k++; 00668 if (!(x & 0x40000000)) 00669 return 32; 00670 } 00671 return k; 00672 } 00673 00674 static int 00675 lo0bits 00676 #ifdef KR_headers 00677 (y) ULong *y; 00678 #else 00679 (ULong *y) 00680 #endif 00681 { 00682 register int k; 00683 register ULong x = *y; 00684 00685 if (x & 7) { 00686 if (x & 1) 00687 return 0; 00688 if (x & 2) { 00689 *y = x >> 1; 00690 return 1; 00691 } 00692 *y = x >> 2; 00693 return 2; 00694 } 00695 k = 0; 00696 if (!(x & 0xffff)) { 00697 k = 16; 00698 x >>= 16; 00699 } 00700 if (!(x & 0xff)) { 00701 k += 8; 00702 x >>= 8; 00703 } 00704 if (!(x & 0xf)) { 00705 k += 4; 00706 x >>= 4; 00707 } 00708 if (!(x & 0x3)) { 00709 k += 2; 00710 x >>= 2; 00711 } 00712 if (!(x & 1)) { 00713 k++; 00714 x >>= 1; 00715 if (!x) 00716 return 32; 00717 } 00718 *y = x; 00719 return k; 00720 } 00721 00722 static Bigint * 00723 i2b 00724 #ifdef KR_headers 00725 (i) int i; 00726 #else 00727 (int i) 00728 #endif 00729 { 00730 Bigint *b; 00731 00732 b = Balloc(1); 00733 b->x[0] = i; 00734 b->wds = 1; 00735 return b; 00736 } 00737 00738 static Bigint * 00739 mult 00740 #ifdef KR_headers 00741 (a, b) Bigint *a, *b; 00742 #else 00743 (Bigint *a, Bigint *b) 00744 #endif 00745 { 00746 Bigint *c; 00747 int k, wa, wb, wc; 00748 ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0; 00749 ULong y; 00750 #ifdef ULLong 00751 ULLong carry, z; 00752 #else 00753 ULong carry, z; 00754 #ifdef Pack_32 00755 ULong z2; 00756 #endif 00757 #endif 00758 00759 if (a->wds < b->wds) { 00760 c = a; 00761 a = b; 00762 b = c; 00763 } 00764 k = a->k; 00765 wa = a->wds; 00766 wb = b->wds; 00767 wc = wa + wb; 00768 if (wc > a->maxwds) 00769 k++; 00770 c = Balloc(k); 00771 for(x = c->x, xa = x + wc; x < xa; x++) 00772 *x = 0; 00773 xa = a->x; 00774 xae = xa + wa; 00775 xb = b->x; 00776 xbe = xb + wb; 00777 xc0 = c->x; 00778 #ifdef ULLong 00779 for(; xb < xbe; xc0++) { 00780 if ((y = *xb++)) { 00781 x = xa; 00782 xc = xc0; 00783 carry = 0; 00784 do { 00785 z = *x++ * (ULLong)y + *xc + carry; 00786 carry = z >> 32; 00787 *xc++ = z & FFFFFFFF; 00788 } 00789 while(x < xae); 00790 *xc = carry; 00791 } 00792 } 00793 #else 00794 #ifdef Pack_32 00795 for(; xb < xbe; xb++, xc0++) { 00796 if (y = *xb & 0xffff) { 00797 x = xa; 00798 xc = xc0; 00799 carry = 0; 00800 do { 00801 z = (*x & 0xffff) * y + (*xc & 0xffff) + carry; 00802 carry = z >> 16; 00803 z2 = (*x++ >> 16) * y + (*xc >> 16) + carry; 00804 carry = z2 >> 16; 00805 Storeinc(xc, z2, z); 00806 } 00807 while(x < xae); 00808 *xc = carry; 00809 } 00810 if (y = *xb >> 16) { 00811 x = xa; 00812 xc = xc0; 00813 carry = 0; 00814 z2 = *xc; 00815 do { 00816 z = (*x & 0xffff) * y + (*xc >> 16) + carry; 00817 carry = z >> 16; 00818 Storeinc(xc, z, z2); 00819 z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry; 00820 carry = z2 >> 16; 00821 } 00822 while(x < xae); 00823 *xc = z2; 00824 } 00825 } 00826 #else 00827 for(; xb < xbe; xc0++) { 00828 if (y = *xb++) { 00829 x = xa; 00830 xc = xc0; 00831 carry = 0; 00832 do { 00833 z = *x++ * y + *xc + carry; 00834 carry = z >> 16; 00835 *xc++ = z & 0xffff; 00836 } 00837 while(x < xae); 00838 *xc = carry; 00839 } 00840 } 00841 #endif 00842 #endif 00843 for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ; 00844 c->wds = wc; 00845 return c; 00846 } 00847 00848 static Bigint * 00849 pow5mult 00850 #ifdef KR_headers 00851 (b, k) Bigint *b; int k; 00852 #else 00853 (Bigint *b, int k) 00854 #endif 00855 { 00856 Bigint *b1, *p5, *p51; 00857 int i; 00858 static int CONST p05[3] = { 5, 25, 125 }; 00859 00860 if ((i = k & 3)) 00861 b = multadd(b, p05[i-1], 0); 00862 00863 if (!(k >>= 2)) 00864 return b; 00865 00866 p5 = i2b(625); 00867 for(;;) { 00868 if (k & 1) { 00869 b1 = mult(b, p5); 00870 Bfree(b); 00871 b = b1; 00872 } 00873 if (!(k >>= 1)) 00874 break; 00875 p51 = mult(p5,p5); 00876 Bfree(p5); 00877 p5 = p51; 00878 } 00879 Bfree(p5); 00880 return b; 00881 } 00882 00883 static Bigint * 00884 lshift 00885 #ifdef KR_headers 00886 (b, k) Bigint *b; int k; 00887 #else 00888 (Bigint *b, int k) 00889 #endif 00890 { 00891 int i, k1, n, n1; 00892 Bigint *b1; 00893 ULong *x, *x1, *xe, z; 00894 00895 #ifdef Pack_32 00896 n = k >> 5; 00897 #else 00898 n = k >> 4; 00899 #endif 00900 k1 = b->k; 00901 n1 = n + b->wds + 1; 00902 for(i = b->maxwds; n1 > i; i <<= 1) 00903 k1++; 00904 b1 = Balloc(k1); 00905 x1 = b1->x; 00906 for(i = 0; i < n; i++) 00907 *x1++ = 0; 00908 x = b->x; 00909 xe = x + b->wds; 00910 #ifdef Pack_32 00911 if (k &= 0x1f) { 00912 k1 = 32 - k; 00913 z = 0; 00914 do { 00915 *x1++ = *x << k | z; 00916 z = *x++ >> k1; 00917 } 00918 while(x < xe); 00919 if ((*x1 = z)) 00920 ++n1; 00921 } 00922 #else 00923 if (k &= 0xf) { 00924 k1 = 16 - k; 00925 z = 0; 00926 do { 00927 *x1++ = *x << k & 0xffff | z; 00928 z = *x++ >> k1; 00929 } 00930 while(x < xe); 00931 if (*x1 = z) 00932 ++n1; 00933 } 00934 #endif 00935 else do 00936 *x1++ = *x++; 00937 while(x < xe); 00938 b1->wds = n1 - 1; 00939 Bfree(b); 00940 return b1; 00941 } 00942 00943 static int 00944 cmp 00945 #ifdef KR_headers 00946 (a, b) Bigint *a, *b; 00947 #else 00948 (Bigint *a, Bigint *b) 00949 #endif 00950 { 00951 ULong *xa, *xa0, *xb, *xb0; 00952 int i, j; 00953 00954 i = a->wds; 00955 j = b->wds; 00956 #ifdef DEBUG 00957 if (i > 1 && !a->x[i-1]) 00958 Bug("cmp called with a->x[a->wds-1] == 0"); 00959 if (j > 1 && !b->x[j-1]) 00960 Bug("cmp called with b->x[b->wds-1] == 0"); 00961 #endif 00962 if (i -= j) 00963 return i; 00964 xa0 = a->x; 00965 xa = xa0 + j; 00966 xb0 = b->x; 00967 xb = xb0 + j; 00968 for(;;) { 00969 if (*--xa != *--xb) 00970 return *xa < *xb ? -1 : 1; 00971 if (xa <= xa0) 00972 break; 00973 } 00974 return 0; 00975 } 00976 00977 static Bigint * 00978 diff 00979 #ifdef KR_headers 00980 (a, b) Bigint *a, *b; 00981 #else 00982 (Bigint *a, Bigint *b) 00983 #endif 00984 { 00985 Bigint *c; 00986 int i, wa, wb; 00987 ULong *xa, *xae, *xb, *xbe, *xc; 00988 #ifdef ULLong 00989 ULLong borrow, y; 00990 #else 00991 ULong borrow, y; 00992 #ifdef Pack_32 00993 ULong z; 00994 #endif 00995 #endif 00996 00997 i = cmp(a,b); 00998 if (!i) { 00999 c = Balloc(0); 01000 c->wds = 1; 01001 c->x[0] = 0; 01002 return c; 01003 } 01004 if (i < 0) { 01005 c = a; 01006 a = b; 01007 b = c; 01008 i = 1; 01009 } 01010 else 01011 i = 0; 01012 c = Balloc(a->k); 01013 c->sign = i; 01014 wa = a->wds; 01015 xa = a->x; 01016 xae = xa + wa; 01017 wb = b->wds; 01018 xb = b->x; 01019 xbe = xb + wb; 01020 xc = c->x; 01021 borrow = 0; 01022 #ifdef ULLong 01023 do { 01024 y = (ULLong)*xa++ - *xb++ - borrow; 01025 borrow = y >> 32 & (ULong)1; 01026 *xc++ = y & FFFFFFFF; 01027 } 01028 while(xb < xbe); 01029 while(xa < xae) { 01030 y = *xa++ - borrow; 01031 borrow = y >> 32 & (ULong)1; 01032 *xc++ = y & FFFFFFFF; 01033 } 01034 #else 01035 #ifdef Pack_32 01036 do { 01037 y = (*xa & 0xffff) - (*xb & 0xffff) - borrow; 01038 borrow = (y & 0x10000) >> 16; 01039 z = (*xa++ >> 16) - (*xb++ >> 16) - borrow; 01040 borrow = (z & 0x10000) >> 16; 01041 Storeinc(xc, z, y); 01042 } 01043 while(xb < xbe); 01044 while(xa < xae) { 01045 y = (*xa & 0xffff) - borrow; 01046 borrow = (y & 0x10000) >> 16; 01047 z = (*xa++ >> 16) - borrow; 01048 borrow = (z & 0x10000) >> 16; 01049 Storeinc(xc, z, y); 01050 } 01051 #else 01052 do { 01053 y = *xa++ - *xb++ - borrow; 01054 borrow = (y & 0x10000) >> 16; 01055 *xc++ = y & 0xffff; 01056 } 01057 while(xb < xbe); 01058 while(xa < xae) { 01059 y = *xa++ - borrow; 01060 borrow = (y & 0x10000) >> 16; 01061 *xc++ = y & 0xffff; 01062 } 01063 #endif 01064 #endif 01065 while(!*--xc) 01066 wa--; 01067 c->wds = wa; 01068 return c; 01069 } 01070 01071 static double 01072 ulp 01073 #ifdef KR_headers 01074 (x) double x; 01075 #else 01076 (double x) 01077 #endif 01078 { 01079 register Long L; 01080 U a; 01081 01082 L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1; 01083 #ifndef Avoid_Underflow 01084 #ifndef Sudden_Underflow 01085 if (L > 0) { 01086 #endif 01087 #endif 01088 #ifdef IBM 01089 L |= Exp_msk1 >> 4; 01090 #endif 01091 word0(a) = L; 01092 word1(a) = 0; 01093 #ifndef Avoid_Underflow 01094 #ifndef Sudden_Underflow 01095 } 01096 else { 01097 L = -L >> Exp_shift; 01098 if (L < Exp_shift) { 01099 word0(a) = 0x80000 >> L; 01100 word1(a) = 0; 01101 } 01102 else { 01103 word0(a) = 0; 01104 L -= Exp_shift; 01105 word1(a) = L >= 31 ? 1 : 1 << 31 - L; 01106 } 01107 } 01108 #endif 01109 #endif 01110 return dval(a); 01111 } 01112 01113 static double 01114 b2d 01115 #ifdef KR_headers 01116 (a, e) Bigint *a; int *e; 01117 #else 01118 (Bigint *a, int *e) 01119 #endif 01120 { 01121 ULong *xa, *xa0, w, y, z; 01122 int k; 01123 U d; 01124 #ifdef VAX 01125 ULong d0, d1; 01126 #else 01127 #define d0 word0(d) 01128 #define d1 word1(d) 01129 #endif 01130 01131 xa0 = a->x; 01132 xa = xa0 + a->wds; 01133 y = *--xa; 01134 #ifdef DEBUG 01135 if (!y) Bug("zero y in b2d"); 01136 #endif 01137 k = hi0bits(y); 01138 *e = 32 - k; 01139 #ifdef Pack_32 01140 if (k < Ebits) { 01141 d0 = Exp_1 | y >> (Ebits - k); 01142 w = xa > xa0 ? *--xa : 0; 01143 d1 = y << ((32-Ebits) + k) | w >> (Ebits - k); 01144 goto ret_d; 01145 } 01146 z = xa > xa0 ? *--xa : 0; 01147 if (k -= Ebits) { 01148 d0 = Exp_1 | y << k | z >> (32 - k); 01149 y = xa > xa0 ? *--xa : 0; 01150 d1 = z << k | y >> (32 - k); 01151 } 01152 else { 01153 d0 = Exp_1 | y; 01154 d1 = z; 01155 } 01156 #else 01157 if (k < Ebits + 16) { 01158 z = xa > xa0 ? *--xa : 0; 01159 d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k; 01160 w = xa > xa0 ? *--xa : 0; 01161 y = xa > xa0 ? *--xa : 0; 01162 d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k; 01163 goto ret_d; 01164 } 01165 z = xa > xa0 ? *--xa : 0; 01166 w = xa > xa0 ? *--xa : 0; 01167 k -= Ebits + 16; 01168 d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k; 01169 y = xa > xa0 ? *--xa : 0; 01170 d1 = w << k + 16 | y << k; 01171 #endif 01172 ret_d: 01173 #ifdef VAX 01174 word0(d) = d0 >> 16 | d0 << 16; 01175 word1(d) = d1 >> 16 | d1 << 16; 01176 #else 01177 #undef d0 01178 #undef d1 01179 #endif 01180 return dval(d); 01181 } 01182 01183 static Bigint * 01184 d2b 01185 #ifdef KR_headers 01186 (d, e, bits) double d; int *e, *bits; 01187 #else 01188 (double _d, int *e, int *bits) 01189 #endif 01190 { 01191 Bigint *b; 01192 int de, k; 01193 ULong *x, y, z; 01194 U d; 01195 #ifndef Sudden_Underflow 01196 int i; 01197 #endif 01198 #ifdef VAX 01199 ULong d0, d1; 01200 d0 = word0(d) >> 16 | word0(d) << 16; 01201 d1 = word1(d) >> 16 | word1(d) << 16; 01202 #else 01203 #define d0 word0(d) 01204 #define d1 word1(d) 01205 #endif 01206 dval(d) = _d; 01207 01208 #ifdef Pack_32 01209 b = Balloc(1); 01210 #else 01211 b = Balloc(2); 01212 #endif 01213 x = b->x; 01214 01215 z = d0 & Frac_mask; 01216 d0 &= 0x7fffffff; /* clear sign bit, which we ignore */ 01217 #ifdef Sudden_Underflow 01218 de = (int)(d0 >> Exp_shift); 01219 #ifndef IBM 01220 z |= Exp_msk11; 01221 #endif 01222 #else 01223 if ((de = (int)(d0 >> Exp_shift))) 01224 z |= Exp_msk1; 01225 #endif 01226 #ifdef Pack_32 01227 if ((y = d1)) { 01228 if ((k = lo0bits(&y))) { 01229 x[0] = y | z << (32 - k); 01230 z >>= k; 01231 } 01232 else 01233 x[0] = y; 01234 #ifndef Sudden_Underflow 01235 i = 01236 #endif 01237 b->wds = (x[1] = z) ? 2 : 1; 01238 } 01239 else { 01240 #ifdef DEBUG 01241 if (!z) 01242 Bug("Zero passed to d2b"); 01243 #endif 01244 k = lo0bits(&z); 01245 x[0] = z; 01246 #ifndef Sudden_Underflow 01247 i = 01248 #endif 01249 b->wds = 1; 01250 k += 32; 01251 } 01252 #else 01253 if (y = d1) { 01254 if (k = lo0bits(&y)) 01255 if (k >= 16) { 01256 x[0] = y | z << 32 - k & 0xffff; 01257 x[1] = z >> k - 16 & 0xffff; 01258 x[2] = z >> k; 01259 i = 2; 01260 } 01261 else { 01262 x[0] = y & 0xffff; 01263 x[1] = y >> 16 | z << 16 - k & 0xffff; 01264 x[2] = z >> k & 0xffff; 01265 x[3] = z >> k+16; 01266 i = 3; 01267 } 01268 else { 01269 x[0] = y & 0xffff; 01270 x[1] = y >> 16; 01271 x[2] = z & 0xffff; 01272 x[3] = z >> 16; 01273 i = 3; 01274 } 01275 } 01276 else { 01277 #ifdef DEBUG 01278 if (!z) 01279 Bug("Zero passed to d2b"); 01280 #endif 01281 k = lo0bits(&z); 01282 if (k >= 16) { 01283 x[0] = z; 01284 i = 0; 01285 } 01286 else { 01287 x[0] = z & 0xffff; 01288 x[1] = z >> 16; 01289 i = 1; 01290 } 01291 k += 32; 01292 } 01293 while(!x[i]) 01294 --i; 01295 b->wds = i + 1; 01296 #endif 01297 #ifndef Sudden_Underflow 01298 if (de) { 01299 #endif 01300 #ifdef IBM 01301 *e = (de - Bias - (P-1) << 2) + k; 01302 *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask); 01303 #else 01304 *e = de - Bias - (P-1) + k; 01305 *bits = P - k; 01306 #endif 01307 #ifndef Sudden_Underflow 01308 } 01309 else { 01310 *e = de - Bias - (P-1) + 1 + k; 01311 #ifdef Pack_32 01312 *bits = 32*i - hi0bits(x[i-1]); 01313 #else 01314 *bits = (i+2)*16 - hi0bits(x[i]); 01315 #endif 01316 } 01317 #endif 01318 return b; 01319 } 01320 #undef d0 01321 #undef d1 01322 01323 static double 01324 ratio 01325 #ifdef KR_headers 01326 (a, b) Bigint *a, *b; 01327 #else 01328 (Bigint *a, Bigint *b) 01329 #endif 01330 { 01331 U da, db; 01332 int k, ka, kb; 01333 01334 dval(da) = b2d(a, &ka); 01335 dval(db) = b2d(b, &kb); 01336 #ifdef Pack_32 01337 k = ka - kb + 32*(a->wds - b->wds); 01338 #else 01339 k = ka - kb + 16*(a->wds - b->wds); 01340 #endif 01341 #ifdef IBM 01342 if (k > 0) { 01343 word0(da) += (k >> 2)*Exp_msk1; 01344 if (k &= 3) 01345 dval(da) *= 1 << k; 01346 } 01347 else { 01348 k = -k; 01349 word0(db) += (k >> 2)*Exp_msk1; 01350 if (k &= 3) 01351 dval(db) *= 1 << k; 01352 } 01353 #else 01354 if (k > 0) 01355 word0(da) += k*Exp_msk1; 01356 else { 01357 k = -k; 01358 word0(db) += k*Exp_msk1; 01359 } 01360 #endif 01361 return dval(da) / dval(db); 01362 } 01363 01364 static CONST double 01365 tens[] = { 01366 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 01367 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, 01368 1e20, 1e21, 1e22 01369 #ifdef VAX 01370 , 1e23, 1e24 01371 #endif 01372 }; 01373 01374 static CONST double 01375 #ifdef IEEE_Arith 01376 bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 }; 01377 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, 01378 #ifdef Avoid_Underflow 01379 9007199254740992.*9007199254740992.e-256 01380 /* = 2^106 * 1e-53 */ 01381 #else 01382 1e-256 01383 #endif 01384 }; 01385 /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */ 01386 /* flag unnecessarily. It leads to a song and dance at the end of strtod. */ 01387 #define Scale_Bit 0x10 01388 #define n_bigtens 5 01389 #else 01390 #ifdef IBM 01391 bigtens[] = { 1e16, 1e32, 1e64 }; 01392 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 }; 01393 #define n_bigtens 3 01394 #else 01395 bigtens[] = { 1e16, 1e32 }; 01396 static CONST double tinytens[] = { 1e-16, 1e-32 }; 01397 #define n_bigtens 2 01398 #endif 01399 #endif 01400 01401 #ifdef INFNAN_CHECK 01402 01403 #ifndef NAN_WORD0 01404 #define NAN_WORD0 0x7ff80000 01405 #endif 01406 01407 #ifndef NAN_WORD1 01408 #define NAN_WORD1 0 01409 #endif 01410 01411 static int 01412 match 01413 #ifdef KR_headers 01414 (sp, t) char **sp, *t; 01415 #else 01416 (CONST char **sp, char *t) 01417 #endif 01418 { 01419 int c, d; 01420 CONST char *s = *sp; 01421 01422 while((d = *t++)) { 01423 if ((c = *++s) >= 'A' && c <= 'Z') 01424 c += 'a' - 'A'; 01425 if (c != d) 01426 return 0; 01427 } 01428 *sp = s + 1; 01429 return 1; 01430 } 01431 01432 #ifndef No_Hex_NaN 01433 static void 01434 hexnan 01435 #ifdef KR_headers 01436 (rvp, sp) double *rvp; CONST char **sp; 01437 #else 01438 (U *rvp, CONST char **sp) 01439 #endif 01440 { 01441 ULong c, x[2]; 01442 CONST char *s; 01443 int havedig, udx0, xshift; 01444 01445 x[0] = x[1] = 0; 01446 havedig = xshift = 0; 01447 udx0 = 1; 01448 s = *sp; 01449 /* allow optional initial 0x or 0X */ 01450 while((c = *(CONST unsigned char*)(s+1)) && c <= ' ') 01451 ++s; 01452 if (s[1] == '0' && (s[2] == 'x' || s[2] == 'X')) 01453 s += 2; 01454 while((c = *(CONST unsigned char*)++s)) { 01455 if (c >= '0' && c <= '9') 01456 c -= '0'; 01457 else if (c >= 'a' && c <= 'f') 01458 c += 10 - 'a'; 01459 else if (c >= 'A' && c <= 'F') 01460 c += 10 - 'A'; 01461 else if (c <= ' ') { 01462 if (udx0 && havedig) { 01463 udx0 = 0; 01464 xshift = 1; 01465 } 01466 continue; 01467 } 01468 #ifdef GDTOA_NON_PEDANTIC_NANCHECK 01469 else if (/*(*/ c == ')' && havedig) { 01470 *sp = s + 1; 01471 break; 01472 } 01473 else 01474 return; /* invalid form: don't change *sp */ 01475 #else 01476 else { 01477 do { 01478 if (/*(*/ c == ')') { 01479 *sp = s + 1; 01480 break; 01481 } 01482 } while((c = *++s)); 01483 break; 01484 } 01485 #endif 01486 havedig = 1; 01487 if (xshift) { 01488 xshift = 0; 01489 x[0] = x[1]; 01490 x[1] = 0; 01491 } 01492 if (udx0) 01493 x[0] = (x[0] << 4) | (x[1] >> 28); 01494 x[1] = (x[1] << 4) | c; 01495 } 01496 if ((x[0] &= 0xfffff) || x[1]) { 01497 word0(*rvp) = Exp_mask | x[0]; 01498 word1(*rvp) = x[1]; 01499 } 01500 } 01501 #endif /*No_Hex_NaN*/ 01502 #endif /* INFNAN_CHECK */ 01503 01504 double 01505 sb_strtod 01506 #ifdef KR_headers 01507 (s00, se) CONST char *s00; char **se; 01508 #else 01509 (CONST char *s00, char **se) 01510 #endif 01511 { 01512 #ifdef Avoid_Underflow 01513 int scale; 01514 #endif 01515 int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign, 01516 e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign; 01517 CONST char *s, *s0, *s1; 01518 double aadj, adj; 01519 U rv, rv0, aadj1; 01520 Long L; 01521 ULong y, z; 01522 Bigint *bb, *bb1, *bd, *bd0, *bs, *delta; 01523 #ifdef SET_INEXACT 01524 int inexact, oldinexact; 01525 #endif 01526 #ifdef Honor_FLT_ROUNDS 01527 int rounding; 01528 #endif 01529 #ifdef USE_LOCALE 01530 CONST char *s2; 01531 #endif 01532 01533 sign = nz0 = nz = 0; 01534 dval(rv) = 0.; 01535 for(s = s00;;s++) switch(*s) { 01536 case '-': 01537 sign = 1; 01538 /* no break */ 01539 case '+': 01540 if (*++s) 01541 goto break2; 01542 /* no break */ 01543 case 0: 01544 goto ret0; 01545 case '\t': 01546 case '\n': 01547 case '\v': 01548 case '\f': 01549 case '\r': 01550 case ' ': 01551 continue; 01552 default: 01553 goto break2; 01554 } 01555 break2: 01556 if (*s == '0') { 01557 nz0 = 1; 01558 while(*++s == '0') ; 01559 if (!*s) 01560 goto ret; 01561 } 01562 s0 = s; 01563 y = z = 0; 01564 for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++) 01565 if (nd < 9) 01566 y = 10*y + c - '0'; 01567 else if (nd < 16) 01568 z = 10*z + c - '0'; 01569 nd0 = nd; 01570 #ifdef USE_LOCALE 01571 s1 = localeconv()->decimal_point; 01572 if (c == *s1) { 01573 c = '.'; 01574 if (*++s1) { 01575 s2 = s; 01576 for(;;) { 01577 if (*++s2 != *s1) { 01578 c = 0; 01579 break; 01580 } 01581 if (!*++s1) { 01582 s = s2; 01583 break; 01584 } 01585 } 01586 } 01587 } 01588 #endif 01589 if (c == '.') { 01590 c = *++s; 01591 if (!nd) { 01592 for(; c == '0'; c = *++s) 01593 nz++; 01594 if (c > '0' && c <= '9') { 01595 s0 = s; 01596 nf += nz; 01597 nz = 0; 01598 goto have_dig; 01599 } 01600 goto dig_done; 01601 } 01602 for(; c >= '0' && c <= '9'; c = *++s) { 01603 have_dig: 01604 nz++; 01605 if (c -= '0') { 01606 nf += nz; 01607 for(i = 1; i < nz; i++) 01608 if (nd++ < 9) 01609 y *= 10; 01610 else if (nd <= DBL_DIG + 1) 01611 z *= 10; 01612 if (nd++ < 9) 01613 y = 10*y + c; 01614 else if (nd <= DBL_DIG + 1) 01615 z = 10*z + c; 01616 nz = 0; 01617 } 01618 } 01619 } 01620 dig_done: 01621 e = 0; 01622 if (c == 'e' || c == 'E') { 01623 if (!nd && !nz && !nz0) { 01624 goto ret0; 01625 } 01626 s00 = s; 01627 esign = 0; 01628 switch(c = *++s) { 01629 case '-': 01630 esign = 1; 01631 case '+': 01632 c = *++s; 01633 } 01634 if (c >= '0' && c <= '9') { 01635 while(c == '0') 01636 c = *++s; 01637 if (c > '0' && c <= '9') { 01638 L = c - '0'; 01639 s1 = s; 01640 while((c = *++s) >= '0' && c <= '9') 01641 L = 10*L + c - '0'; 01642 if (s - s1 > 8 || L > 19999) 01643 /* Avoid confusion from exponents 01644 * so large that e might overflow. 01645 */ 01646 e = 19999; /* safe for 16 bit ints */ 01647 else 01648 e = (int)L; 01649 if (esign) 01650 e = -e; 01651 } 01652 else 01653 e = 0; 01654 } 01655 else 01656 s = s00; 01657 } 01658 if (!nd) { 01659 if (!nz && !nz0) { 01660 #ifdef INFNAN_CHECK 01661 /* Check for Nan and Infinity */ 01662 switch(c) { 01663 case 'i': 01664 case 'I': 01665 if (match(&s,"nf")) { 01666 --s; 01667 if (!match(&s,"inity")) 01668 ++s; 01669 word0(rv) = 0x7ff00000; 01670 word1(rv) = 0; 01671 goto ret; 01672 } 01673 break; 01674 case 'n': 01675 case 'N': 01676 if (match(&s, "an")) { 01677 word0(rv) = NAN_WORD0; 01678 word1(rv) = NAN_WORD1; 01679 #ifndef No_Hex_NaN 01680 if (*s == '(') /*)*/ 01681 hexnan(&rv, &s); 01682 #endif 01683 goto ret; 01684 } 01685 } 01686 #endif /* INFNAN_CHECK */ 01687 ret0: 01688 s = s00; 01689 sign = 0; 01690 } 01691 goto ret; 01692 } 01693 e1 = e -= nf; 01694 01695 /* Now we have nd0 digits, starting at s0, followed by a 01696 * decimal point, followed by nd-nd0 digits. The number we're 01697 * after is the integer represented by those digits times 01698 * 10**e */ 01699 01700 if (!nd0) 01701 nd0 = nd; 01702 k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1; 01703 dval(rv) = y; 01704 if (k > 9) { 01705 #ifdef SET_INEXACT 01706 if (k > DBL_DIG) 01707 oldinexact = get_inexact(); 01708 #endif 01709 dval(rv) = tens[k - 9] * dval(rv) + z; 01710 } 01711 bd0 = 0; 01712 if (nd <= DBL_DIG 01713 #ifndef RND_PRODQUOT 01714 #ifndef Honor_FLT_ROUNDS 01715 && Flt_Rounds == 1 01716 #endif 01717 #endif 01718 ) { 01719 if (!e) 01720 goto ret; 01721 if (e > 0) { 01722 if (e <= Ten_pmax) { 01723 #ifdef VAX 01724 goto vax_ovfl_check; 01725 #else 01726 #ifdef Honor_FLT_ROUNDS 01727 /* round correctly FLT_ROUNDS = 2 or 3 */ 01728 if (sign) { 01729 rv = -rv; 01730 sign = 0; 01731 } 01732 #endif 01733 /* rv = */ rounded_product(dval(rv), tens[e]); 01734 goto ret; 01735 #endif 01736 } 01737 i = DBL_DIG - nd; 01738 if (e <= Ten_pmax + i) { 01739 /* A fancier test would sometimes let us do 01740 * this for larger i values. 01741 */ 01742 #ifdef Honor_FLT_ROUNDS 01743 /* round correctly FLT_ROUNDS = 2 or 3 */ 01744 if (sign) { 01745 rv = -rv; 01746 sign = 0; 01747 } 01748 #endif 01749 e -= i; 01750 dval(rv) *= tens[i]; 01751 #ifdef VAX 01752 /* VAX exponent range is so narrow we must 01753 * worry about overflow here... 01754 */ 01755 vax_ovfl_check: 01756 word0(rv) -= P*Exp_msk1; 01757 /* rv = */ rounded_product(dval(rv), tens[e]); 01758 if ((word0(rv) & Exp_mask) 01759 > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) 01760 goto ovfl; 01761 word0(rv) += P*Exp_msk1; 01762 #else 01763 /* rv = */ rounded_product(dval(rv), tens[e]); 01764 #endif 01765 goto ret; 01766 } 01767 } 01768 #ifndef Inaccurate_Divide 01769 else if (e >= -Ten_pmax) { 01770 #ifdef Honor_FLT_ROUNDS 01771 /* round correctly FLT_ROUNDS = 2 or 3 */ 01772 if (sign) { 01773 rv = -rv; 01774 sign = 0; 01775 } 01776 #endif 01777 /* rv = */ rounded_quotient(dval(rv), tens[-e]); 01778 goto ret; 01779 } 01780 #endif 01781 } 01782 e1 += nd - k; 01783 01784 #ifdef IEEE_Arith 01785 #ifdef SET_INEXACT 01786 inexact = 1; 01787 if (k <= DBL_DIG) 01788 oldinexact = get_inexact(); 01789 #endif 01790 #ifdef Avoid_Underflow 01791 scale = 0; 01792 #endif 01793 #ifdef Honor_FLT_ROUNDS 01794 if ((rounding = Flt_Rounds) >= 2) { 01795 if (sign) 01796 rounding = rounding == 2 ? 0 : 2; 01797 else 01798 if (rounding != 2) 01799 rounding = 0; 01800 } 01801 #endif 01802 #endif /*IEEE_Arith*/ 01803 01804 /* Get starting approximation = rv * 10**e1 */ 01805 01806 if (e1 > 0) { 01807 if ((i = e1 & 15)) 01808 dval(rv) *= tens[i]; 01809 if (e1 &= ~15) { 01810 if (e1 > DBL_MAX_10_EXP) { 01811 ovfl: 01812 #ifndef NO_ERRNO 01813 errno = ERANGE; 01814 #endif 01815 /* Can't trust HUGE_VAL */ 01816 #ifdef IEEE_Arith 01817 #ifdef Honor_FLT_ROUNDS 01818 switch(rounding) { 01819 case 0: /* toward 0 */ 01820 case 3: /* toward -infinity */ 01821 word0(rv) = Big0; 01822 word1(rv) = Big1; 01823 break; 01824 default: 01825 word0(rv) = Exp_mask; 01826 word1(rv) = 0; 01827 } 01828 #else /*Honor_FLT_ROUNDS*/ 01829 word0(rv) = Exp_mask; 01830 word1(rv) = 0; 01831 #endif /*Honor_FLT_ROUNDS*/ 01832 #ifdef SET_INEXACT 01833 /* set overflow bit */ 01834 dval(rv0) = 1e300; 01835 dval(rv0) *= dval(rv0); 01836 #endif 01837 #else /*IEEE_Arith*/ 01838 word0(rv) = Big0; 01839 word1(rv) = Big1; 01840 #endif /*IEEE_Arith*/ 01841 if (bd0) 01842 goto retfree; 01843 goto ret; 01844 } 01845 e1 >>= 4; 01846 for(j = 0; e1 > 1; j++, e1 >>= 1) 01847 if (e1 & 1) 01848 dval(rv) *= bigtens[j]; 01849 /* The last multiplication could overflow. */ 01850 word0(rv) -= P*Exp_msk1; 01851 dval(rv) *= bigtens[j]; 01852 if ((z = word0(rv) & Exp_mask) 01853 > Exp_msk1*(DBL_MAX_EXP+Bias-P)) 01854 goto ovfl; 01855 if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) { 01856 /* set to largest number */ 01857 /* (Can't trust DBL_MAX) */ 01858 word0(rv) = Big0; 01859 word1(rv) = Big1; 01860 } 01861 else 01862 word0(rv) += P*Exp_msk1; 01863 } 01864 } 01865 else if (e1 < 0) { 01866 e1 = -e1; 01867 if ((i = e1 & 15)) 01868 dval(rv) /= tens[i]; 01869 if (e1 >>= 4) { 01870 if (e1 >= 1 << n_bigtens) 01871 goto undfl; 01872 #ifdef Avoid_Underflow 01873 if (e1 & Scale_Bit) 01874 scale = 2*P; 01875 for(j = 0; e1 > 0; j++, e1 >>= 1) 01876 if (e1 & 1) 01877 dval(rv) *= tinytens[j]; 01878 if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask) 01879 >> Exp_shift)) > 0) { 01880 /* scaled rv is denormal; zap j low bits */ 01881 if (j >= 32) { 01882 word1(rv) = 0; 01883 if (j >= 53) 01884 word0(rv) = (P+2)*Exp_msk1; 01885 else 01886 word0(rv) &= 0xffffffff << (j-32); 01887 } 01888 else 01889 word1(rv) &= 0xffffffff << j; 01890 } 01891 #else 01892 for(j = 0; e1 > 1; j++, e1 >>= 1) 01893 if (e1 & 1) 01894 dval(rv) *= tinytens[j]; 01895 /* The last multiplication could underflow. */ 01896 dval(rv0) = dval(rv); 01897 dval(rv) *= tinytens[j]; 01898 if (!dval(rv)) { 01899 dval(rv) = 2.*dval(rv0); 01900 dval(rv) *= tinytens[j]; 01901 #endif 01902 if (!dval(rv)) { 01903 undfl: 01904 dval(rv) = 0.; 01905 #ifndef NO_ERRNO 01906 errno = ERANGE; 01907 #endif 01908 if (bd0) 01909 goto retfree; 01910 goto ret; 01911 } 01912 #ifndef Avoid_Underflow 01913 word0(rv) = Tiny0; 01914 word1(rv) = Tiny1; 01915 /* The refinement below will clean 01916 * this approximation up. 01917 */ 01918 } 01919 #endif 01920 } 01921 } 01922 01923 /* Now the hard part -- adjusting rv to the correct value.*/ 01924 01925 /* Put digits into bd: true value = bd * 10^e */ 01926 01927 bd0 = s2b(s0, nd0, nd, y); 01928 01929 for(;;) { 01930 bd = Balloc(bd0->k); 01931 Bcopy(bd, bd0); 01932 bb = d2b(dval(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */ 01933 bs = i2b(1); 01934 01935 if (e >= 0) { 01936 bb2 = bb5 = 0; 01937 bd2 = bd5 = e; 01938 } 01939 else { 01940 bb2 = bb5 = -e; 01941 bd2 = bd5 = 0; 01942 } 01943 if (bbe >= 0) 01944 bb2 += bbe; 01945 else 01946 bd2 -= bbe; 01947 bs2 = bb2; 01948 #ifdef Honor_FLT_ROUNDS 01949 if (rounding != 1) 01950 bs2++; 01951 #endif 01952 #ifdef Avoid_Underflow 01953 j = bbe - scale; 01954 i = j + bbbits - 1; /* logb(rv) */ 01955 if (i < Emin) /* denormal */ 01956 j += P - Emin; 01957 else 01958 j = P + 1 - bbbits; 01959 #else /*Avoid_Underflow*/ 01960 #ifdef Sudden_Underflow 01961 #ifdef IBM 01962 j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3); 01963 #else 01964 j = P + 1 - bbbits; 01965 #endif 01966 #else /*Sudden_Underflow*/ 01967 j = bbe; 01968 i = j + bbbits - 1; /* logb(rv) */ 01969 if (i < Emin) /* denormal */ 01970 j += P - Emin; 01971 else 01972 j = P + 1 - bbbits; 01973 #endif /*Sudden_Underflow*/ 01974 #endif /*Avoid_Underflow*/ 01975 bb2 += j; 01976 bd2 += j; 01977 #ifdef Avoid_Underflow 01978 bd2 += scale; 01979 #endif 01980 i = bb2 < bd2 ? bb2 : bd2; 01981 if (i > bs2) 01982 i = bs2; 01983 if (i > 0) { 01984 bb2 -= i; 01985 bd2 -= i; 01986 bs2 -= i; 01987 } 01988 if (bb5 > 0) { 01989 bs = pow5mult(bs, bb5); 01990 bb1 = mult(bs, bb); 01991 Bfree(bb); 01992 bb = bb1; 01993 } 01994 if (bb2 > 0) 01995 bb = lshift(bb, bb2); 01996 if (bd5 > 0) 01997 bd = pow5mult(bd, bd5); 01998 if (bd2 > 0) 01999 bd = lshift(bd, bd2); 02000 if (bs2 > 0) 02001 bs = lshift(bs, bs2); 02002 delta = diff(bb, bd); 02003 dsign = delta->sign; 02004 delta->sign = 0; 02005 i = cmp(delta, bs); 02006 #ifdef Honor_FLT_ROUNDS 02007 if (rounding != 1) { 02008 if (i < 0) { 02009 /* Error is less than an ulp */ 02010 if (!delta->x[0] && delta->wds <= 1) { 02011 /* exact */ 02012 #ifdef SET_INEXACT 02013 inexact = 0; 02014 #endif 02015 break; 02016 } 02017 if (rounding) { 02018 if (dsign) { 02019 adj = 1.; 02020 goto apply_adj; 02021 } 02022 } 02023 else if (!dsign) { 02024 adj = -1.; 02025 if (!word1(rv) 02026 && !(word0(rv) & Frac_mask)) { 02027 y = word0(rv) & Exp_mask; 02028 #ifdef Avoid_Underflow 02029 if (!scale || y > 2*P*Exp_msk1) 02030 #else 02031 if (y) 02032 #endif 02033 { 02034 delta = lshift(delta,Log2P); 02035 if (cmp(delta, bs) <= 0) 02036 adj = -0.5; 02037 } 02038 } 02039 apply_adj: 02040 #ifdef Avoid_Underflow 02041 if (scale && (y = word0(rv) & Exp_mask) 02042 <= 2*P*Exp_msk1) 02043 word0(adj) += (2*P+1)*Exp_msk1 - y; 02044 #else 02045 #ifdef Sudden_Underflow 02046 if ((word0(rv) & Exp_mask) <= 02047 P*Exp_msk1) { 02048 word0(rv) += P*Exp_msk1; 02049 dval(rv) += adj*ulp(dval(rv)); 02050 word0(rv) -= P*Exp_msk1; 02051 } 02052 else 02053 #endif /*Sudden_Underflow*/ 02054 #endif /*Avoid_Underflow*/ 02055 dval(rv) += adj*ulp(dval(rv)); 02056 } 02057 break; 02058 } 02059 adj = ratio(delta, bs); 02060 if (adj < 1.) 02061 adj = 1.; 02062 if (adj <= 0x7ffffffe) { 02063 /* adj = rounding ? ceil(adj) : floor(adj); */ 02064 y = adj; 02065 if (y != adj) { 02066 if (!((rounding>>1) ^ dsign)) 02067 y++; 02068 adj = y; 02069 } 02070 } 02071 #ifdef Avoid_Underflow 02072 if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1) 02073 word0(adj) += (2*P+1)*Exp_msk1 - y; 02074 #else 02075 #ifdef Sudden_Underflow 02076 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) { 02077 word0(rv) += P*Exp_msk1; 02078 adj *= ulp(dval(rv)); 02079 if (dsign) 02080 dval(rv) += adj; 02081 else 02082 dval(rv) -= adj; 02083 word0(rv) -= P*Exp_msk1; 02084 goto cont; 02085 } 02086 #endif /*Sudden_Underflow*/ 02087 #endif /*Avoid_Underflow*/ 02088 adj *= ulp(dval(rv)); 02089 if (dsign) 02090 dval(rv) += adj; 02091 else 02092 dval(rv) -= adj; 02093 goto cont; 02094 } 02095 #endif /*Honor_FLT_ROUNDS*/ 02096 02097 if (i < 0) { 02098 /* Error is less than half an ulp -- check for 02099 * special case of mantissa a power of two. 02100 */ 02101 if (dsign || word1(rv) || word0(rv) & Bndry_mask 02102 #ifdef IEEE_Arith 02103 #ifdef Avoid_Underflow 02104 || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1 02105 #else 02106 || (word0(rv) & Exp_mask) <= Exp_msk1 02107 #endif 02108 #endif 02109 ) { 02110 #ifdef SET_INEXACT 02111 if (!delta->x[0] && delta->wds <= 1) 02112 inexact = 0; 02113 #endif 02114 break; 02115 } 02116 if (!delta->x[0] && delta->wds <= 1) { 02117 /* exact result */ 02118 #ifdef SET_INEXACT 02119 inexact = 0; 02120 #endif 02121 break; 02122 } 02123 delta = lshift(delta,Log2P); 02124 if (cmp(delta, bs) > 0) 02125 goto drop_down; 02126 break; 02127 } 02128 if (i == 0) { 02129 /* exactly half-way between */ 02130 if (dsign) { 02131 if ((word0(rv) & Bndry_mask1) == Bndry_mask1 02132 && word1(rv) == ( 02133 #ifdef Avoid_Underflow 02134 (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1) 02135 ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) : 02136 #endif 02137 0xffffffff)) { 02138 /*boundary case -- increment exponent*/ 02139 word0(rv) = (word0(rv) & Exp_mask) 02140 + Exp_msk1 02141 #ifdef IBM 02142 | Exp_msk1 >> 4 02143 #endif 02144 ; 02145 word1(rv) = 0; 02146 #ifdef Avoid_Underflow 02147 dsign = 0; 02148 #endif 02149 break; 02150 } 02151 } 02152 else if (!(word0(rv) & Bndry_mask) && !word1(rv)) { 02153 drop_down: 02154 /* boundary case -- decrement exponent */ 02155 #ifdef Sudden_Underflow /*{{*/ 02156 L = word0(rv) & Exp_mask; 02157 #ifdef IBM 02158 if (L < Exp_msk1) 02159 #else 02160 #ifdef Avoid_Underflow 02161 if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1)) 02162 #else 02163 if (L <= Exp_msk1) 02164 #endif /*Avoid_Underflow*/ 02165 #endif /*IBM*/ 02166 goto undfl; 02167 L -= Exp_msk1; 02168 #else /*Sudden_Underflow}{*/ 02169 #ifdef Avoid_Underflow 02170 if (scale) { 02171 L = word0(rv) & Exp_mask; 02172 if (L <= (2*P+1)*Exp_msk1) { 02173 if (L > (P+2)*Exp_msk1) 02174 /* round even ==> */ 02175 /* accept rv */ 02176 break; 02177 /* rv = smallest denormal */ 02178 goto undfl; 02179 } 02180 } 02181 #endif /*Avoid_Underflow*/ 02182 L = (word0(rv) & Exp_mask) - Exp_msk1; 02183 #endif /*Sudden_Underflow}}*/ 02184 word0(rv) = L | Bndry_mask1; 02185 word1(rv) = 0xffffffff; 02186 #ifdef IBM 02187 goto cont; 02188 #else 02189 break; 02190 #endif 02191 } 02192 #ifndef ROUND_BIASED 02193 if (!(word1(rv) & LSB)) 02194 break; 02195 #endif 02196 if (dsign) 02197 dval(rv) += ulp(dval(rv)); 02198 #ifndef ROUND_BIASED 02199 else { 02200 dval(rv) -= ulp(dval(rv)); 02201 #ifndef Sudden_Underflow 02202 if (!dval(rv)) 02203 goto undfl; 02204 #endif 02205 } 02206 #ifdef Avoid_Underflow 02207 dsign = 1 - dsign; 02208 #endif 02209 #endif 02210 break; 02211 } 02212 if ((aadj = ratio(delta, bs)) <= 2.) { 02213 if (dsign) 02214 aadj = dval(aadj1) = 1.; 02215 else if (word1(rv) || word0(rv) & Bndry_mask) { 02216 #ifndef Sudden_Underflow 02217 if (word1(rv) == Tiny1 && !word0(rv)) 02218 goto undfl; 02219 #endif 02220 aadj = 1.; 02221 dval(aadj1) = -1.; 02222 } 02223 else { 02224 /* special case -- power of FLT_RADIX to be */ 02225 /* rounded down... */ 02226 02227 if (aadj < 2./FLT_RADIX) 02228 aadj = 1./FLT_RADIX; 02229 else 02230 aadj *= 0.5; 02231 dval(aadj1) = -aadj; 02232 } 02233 } 02234 else { 02235 aadj *= 0.5; 02236 dval(aadj1) = dsign ? aadj : -aadj; 02237 #ifdef Check_FLT_ROUNDS 02238 switch(Rounding) { 02239 case 2: /* towards +infinity */ 02240 dval(aadj1) -= 0.5; 02241 break; 02242 case 0: /* towards 0 */ 02243 case 3: /* towards -infinity */ 02244 dval(aadj1) += 0.5; 02245 } 02246 #else 02247 if (Flt_Rounds == 0) 02248 dval(aadj1) += 0.5; 02249 #endif /*Check_FLT_ROUNDS*/ 02250 } 02251 y = word0(rv) & Exp_mask; 02252 02253 /* Check for overflow */ 02254 02255 if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) { 02256 dval(rv0) = dval(rv); 02257 word0(rv) -= P*Exp_msk1; 02258 adj = dval(aadj1) * ulp(dval(rv)); 02259 dval(rv) += adj; 02260 if ((word0(rv) & Exp_mask) >= 02261 Exp_msk1*(DBL_MAX_EXP+Bias-P)) { 02262 if (word0(rv0) == Big0 && word1(rv0) == Big1) 02263 goto ovfl; 02264 word0(rv) = Big0; 02265 word1(rv) = Big1; 02266 goto cont; 02267 } 02268 else 02269 word0(rv) += P*Exp_msk1; 02270 } 02271 else { 02272 #ifdef Avoid_Underflow 02273 if (scale && y <= 2*P*Exp_msk1) { 02274 if (aadj <= 0x7fffffff) { 02275 if ((z = (uint32)aadj) <= 0) 02276 z = 1; 02277 aadj = z; 02278 dval(aadj1) = dsign ? aadj : -aadj; 02279 } 02280 word0(aadj1) += (2*P+1)*Exp_msk1 - y; 02281 } 02282 adj = dval(aadj1) * ulp(dval(rv)); 02283 dval(rv) += adj; 02284 #else 02285 #ifdef Sudden_Underflow 02286 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) { 02287 dval(rv0) = dval(rv); 02288 word0(rv) += P*Exp_msk1; 02289 adj = aadj1 * ulp(dval(rv)); 02290 dval(rv) += adj; 02291 #ifdef IBM 02292 if ((word0(rv) & Exp_mask) < P*Exp_msk1) 02293 #else 02294 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) 02295 #endif 02296 { 02297 if (word0(rv0) == Tiny0 02298 && word1(rv0) == Tiny1) 02299 goto undfl; 02300 word0(rv) = Tiny0; 02301 word1(rv) = Tiny1; 02302 goto cont; 02303 } 02304 else 02305 word0(rv) -= P*Exp_msk1; 02306 } 02307 else { 02308 adj = aadj1 * ulp(dval(rv)); 02309 dval(rv) += adj; 02310 } 02311 #else /*Sudden_Underflow*/ 02312 /* Compute adj so that the IEEE rounding rules will 02313 * correctly round rv + adj in some half-way cases. 02314 * If rv * ulp(rv) is denormalized (i.e., 02315 * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid 02316 * trouble from bits lost to denormalization; 02317 * example: 1.2e-307 . 02318 */ 02319 if (y <= (P-1)*Exp_msk1 && aadj > 1.) { 02320 aadj1 = (double)(int)(aadj + 0.5); 02321 if (!dsign) 02322 aadj1 = -aadj1; 02323 } 02324 adj = aadj1 * ulp(dval(rv)); 02325 dval(rv) += adj; 02326 #endif /*Sudden_Underflow*/ 02327 #endif /*Avoid_Underflow*/ 02328 } 02329 z = word0(rv) & Exp_mask; 02330 #ifndef SET_INEXACT 02331 #ifdef Avoid_Underflow 02332 if (!scale) 02333 #endif 02334 if (y == z) { 02335 /* Can we stop now? */ 02336 L = (Long)aadj; 02337 aadj -= L; 02338 /* The tolerances below are conservative. */ 02339 if (dsign || word1(rv) || word0(rv) & Bndry_mask) { 02340 if (aadj < .4999999 || aadj > .5000001) 02341 break; 02342 } 02343 else if (aadj < .4999999/FLT_RADIX) 02344 break; 02345 } 02346 #endif 02347 cont: 02348 Bfree(bb); 02349 Bfree(bd); 02350 Bfree(bs); 02351 Bfree(delta); 02352 } 02353 #ifdef SET_INEXACT 02354 if (inexact) { 02355 if (!oldinexact) { 02356 word0(rv0) = Exp_1 + (70 << Exp_shift); 02357 word1(rv0) = 0; 02358 dval(rv0) += 1.; 02359 } 02360 } 02361 else if (!oldinexact) 02362 clear_inexact(); 02363 #endif 02364 #ifdef Avoid_Underflow 02365 if (scale) { 02366 word0(rv0) = Exp_1 - 2*P*Exp_msk1; 02367 word1(rv0) = 0; 02368 dval(rv) *= dval(rv0); 02369 #ifndef NO_ERRNO 02370 /* try to avoid the bug of testing an 8087 register value */ 02371 if (word0(rv) == 0 && word1(rv) == 0) 02372 errno = ERANGE; 02373 #endif 02374 } 02375 #endif /* Avoid_Underflow */ 02376 #ifdef SET_INEXACT 02377 if (inexact && !(word0(rv) & Exp_mask)) { 02378 /* set underflow bit */ 02379 dval(rv0) = 1e-300; 02380 dval(rv0) *= dval(rv0); 02381 } 02382 #endif 02383 retfree: 02384 Bfree(bb); 02385 Bfree(bd); 02386 Bfree(bs); 02387 Bfree(bd0); 02388 Bfree(delta); 02389 ret: 02390 if (se) 02391 *se = (char *)s; 02392 return sign ? -dval(rv) : dval(rv); 02393 }