dtoa.cpp
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 00021 David M. Gay 00022 Bell Laboratories, Room 2C-463 00023 600 Mountain Avenue 00024 Murray Hill, NJ 07974-0636 00025 U.S.A. 00026 dmg@bell-labs.com 00027 */ 00028 00029 /* On a machine with IEEE extended-precision registers, it is 00030 * necessary to specify double-precision (53-bit) rounding precision 00031 * before invoking strtod or dtoa. If the machine uses (the equivalent 00032 * of) Intel 80x87 arithmetic, the call 00033 * _control87(PC_53, MCW_PC); 00034 * does this with many compilers. Whether this or another call is 00035 * appropriate depends on the compiler; for this to work, it may be 00036 * necessary to #include "float.h" or another system-dependent header 00037 * file. 00038 */ 00039 00040 /* strtod for IEEE-, VAX-, and IBM-arithmetic machines. 00041 * 00042 * This strtod returns a nearest machine number to the input decimal 00043 * string (or sets errno to ERANGE). With IEEE arithmetic, ties are 00044 * broken by the IEEE round-even rule. Otherwise ties are broken by 00045 * biased rounding (add half and chop). 00046 * 00047 * Inspired loosely by William D. Clinger's paper "How to Read Floating 00048 * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101]. 00049 * 00050 * Modifications: 00051 * 00052 * 1. We only require IEEE, IBM, or VAX double-precision 00053 * arithmetic (not IEEE double-extended). 00054 * 2. We get by with floating-point arithmetic in a case that 00055 * Clinger missed -- when we're computing d * 10^n 00056 * for a small integer d and the integer n is not too 00057 * much larger than 22 (the maximum integer k for which 00058 * we can represent 10^k exactly), we may be able to 00059 * compute (d*10^k) * 10^(e-k) with just one roundoff. 00060 * 3. Rather than a bit-at-a-time adjustment of the binary 00061 * result in the hard case, we use floating-point 00062 * arithmetic to determine the adjustment to within 00063 * one bit; only in really hard cases do we need to 00064 * compute a second residual. 00065 * 4. Because of 3., we don't need a large table of powers of 10 00066 * for ten-to-e (just some small tables, e.g. of 10^k 00067 * for 0 <= k <= 22). 00068 */ 00069 00070 /* 00071 * #define IEEE_8087 for IEEE-arithmetic machines where the least 00072 * significant byte has the lowest address. 00073 * #define IEEE_MC68k for IEEE-arithmetic machines where the most 00074 * significant byte has the lowest address. 00075 * #define Long int on machines with 32-bit ints and 64-bit longs. 00076 * #define IBM for IBM mainframe-style floating-point arithmetic. 00077 * #define VAX for VAX-style floating-point arithmetic (D_floating). 00078 * #define No_leftright to omit left-right logic in fast floating-point 00079 * computation of dtoa. 00080 * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3 00081 * and strtod and dtoa should round accordingly. 00082 * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3 00083 * and Honor_FLT_ROUNDS is not #defined. 00084 * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines 00085 * that use extended-precision instructions to compute rounded 00086 * products and quotients) with IBM. 00087 * #define ROUND_BIASED for IEEE-format with biased rounding. 00088 * #define Inaccurate_Divide for IEEE-format with correctly rounded 00089 * products but inaccurate quotients, e.g., for Intel i860. 00090 * #define NO_LONG_LONG on machines that do not have a "long long" 00091 * integer type (of >= 64 bits). On such machines, you can 00092 * #define Just_16 to store 16 bits per 32-bit Long when doing 00093 * high-precision integer arithmetic. Whether this speeds things 00094 * up or slows things down depends on the machine and the number 00095 * being converted. If long long is available and the name is 00096 * something other than "long long", #define Llong to be the name, 00097 * and if "unsigned Llong" does not work as an unsigned version of 00098 * Llong, #define #ULLong to be the corresponding unsigned type. 00099 * #define KR_headers for old-style C function headers. 00100 * #define Bad_float_h if your system lacks a float.h or if it does not 00101 * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP, 00102 * FLT_RADIX, FLT_ROUNDS, and DBL_MAX. 00103 * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n) 00104 * if memory is available and otherwise does something you deem 00105 * appropriate. If MALLOC is undefined, malloc will be invoked 00106 * directly -- and assumed always to succeed. 00107 * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making 00108 * memory allocations from a private pool of memory when possible. 00109 * When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes, 00110 * unless #defined to be a different length. This default length 00111 * suffices to get rid of MALLOC calls except for unusual cases, 00112 * such as decimal-to-binary conversion of a very long string of 00113 * digits. The longest string dtoa can return is about 751 bytes 00114 * long. For conversions by strtod of strings of 800 digits and 00115 * all dtoa conversions in single-threaded executions with 8-byte 00116 * pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte 00117 * pointers, PRIVATE_MEM >= 7112 appears adequate. 00118 * #define INFNAN_CHECK on IEEE systems to cause strtod to check for 00119 * Infinity and NaN (case insensitively). On some systems (e.g., 00120 * some HP systems), it may be necessary to #define NAN_WORD0 00121 * appropriately -- to the most significant word of a quiet NaN. 00122 * (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.) 00123 * When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined, 00124 * strtod also accepts (case insensitively) strings of the form 00125 * NaN(x), where x is a string of hexadecimal digits and spaces; 00126 * if there is only one string of hexadecimal digits, it is taken 00127 * for the 52 fraction bits of the resulting NaN; if there are two 00128 * or more strings of hex digits, the first is for the high 20 bits, 00129 * the second and subsequent for the low 32 bits, with intervening 00130 * white space ignored; but if this results in none of the 52 00131 * fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0 00132 * and NAN_WORD1 are used instead. 00133 * #define MULTIPLE_THREADS if the system offers preemptively scheduled 00134 * multiple threads. In this case, you must provide (or suitably 00135 * #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed 00136 * by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed 00137 * in pow5mult, ensures lazy evaluation of only one copy of high 00138 * powers of 5; omitting this lock would introduce a small 00139 * probability of wasting memory, but would otherwise be harmless.) 00140 * You must also invoke freedtoa(s) to free the value s returned by 00141 * dtoa. You may do so whether or not MULTIPLE_THREADS is #defined. 00142 * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that 00143 * avoids underflows on inputs whose result does not underflow. 00144 * If you #define NO_IEEE_Scale on a machine that uses IEEE-format 00145 * floating-point numbers and flushes underflows to zero rather 00146 * than implementing gradual underflow, then you must also #define 00147 * Sudden_Underflow. 00148 * #define YES_ALIAS to permit aliasing certain double values with 00149 * arrays of ULongs. This leads to slightly better code with 00150 * some compilers and was always used prior to 19990916, but it 00151 * is not strictly legal and can cause trouble with aggressively 00152 * optimizing compilers (e.g., gcc 2.95.1 under -O2). 00153 * #define USE_LOCALE to use the current locale's decimal_point value. 00154 * #define SET_INEXACT if IEEE arithmetic is being used and extra 00155 * computation should be done to set the inexact flag when the 00156 * result is inexact and avoid setting inexact when the result 00157 * is exact. In this case, dtoa.c must be compiled in 00158 * an environment, perhaps provided by #include "dtoa.c" in a 00159 * suitable wrapper, that defines two functions, 00160 * int get_inexact(void); 00161 * void clear_inexact(void); 00162 * such that get_inexact() returns a nonzero value if the 00163 * inexact bit is already set, and clear_inexact() sets the 00164 * inexact bit to 0. When SET_INEXACT is #defined, strtod 00165 * also does extra computations to set the underflow and overflow 00166 * flags when appropriate (i.e., when the result is tiny and 00167 * inexact or when it is a numeric value rounded to +-infinity). 00168 * #define NO_ERRNO if strtod should not assign errno = ERANGE when 00169 * the result overflows to +-Infinity or underflows to 0. 00170 */ 00171 00172 #include "dtoa.h" 00173 #include <config.h> 00174 00175 #include "global.h" 00176 00177 // #if PLATFORM(BIG_ENDIAN) 00178 // #define IEEE_MC68k 00179 // #else 00180 #define IEEE_8087 00181 // #endif 00182 #define INFNAN_CHECK 00183 00184 00185 00186 #ifndef Long 00187 #define Long int 00188 #endif 00189 #ifndef ULong 00190 typedef unsigned Long ULong; 00191 #endif 00192 00193 #ifdef DEBUG 00194 #include <stdio.h> 00195 #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);} 00196 #endif 00197 00198 #include <stdlib.h> 00199 #include <string.h> 00200 00201 #ifdef USE_LOCALE 00202 #include <locale.h> 00203 #endif 00204 00205 #ifdef MALLOC 00206 extern void *MALLOC(size_t); 00207 #else 00208 #define MALLOC malloc 00209 #endif 00210 00211 #ifndef Omit_Private_Memory 00212 #ifndef PRIVATE_MEM 00213 #define PRIVATE_MEM 2304 00214 #endif 00215 #define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double)) 00216 static double private_mem[PRIVATE_mem], *pmem_next = private_mem; 00217 #endif 00218 00219 #undef IEEE_Arith 00220 #undef Avoid_Underflow 00221 #ifdef IEEE_MC68k 00222 #define IEEE_Arith 00223 #endif 00224 #ifdef IEEE_8087 00225 #define IEEE_Arith 00226 #endif 00227 00228 #include <errno.h> 00229 00230 #ifdef Bad_float_h 00231 00232 #ifdef IEEE_Arith 00233 #define DBL_DIG 15 00234 #define DBL_MAX_10_EXP 308 00235 #define DBL_MAX_EXP 1024 00236 #define FLT_RADIX 2 00237 #endif /*IEEE_Arith*/ 00238 00239 #ifdef IBM 00240 #define DBL_DIG 16 00241 #define DBL_MAX_10_EXP 75 00242 #define DBL_MAX_EXP 63 00243 #define FLT_RADIX 16 00244 #define DBL_MAX 7.2370055773322621e+75 00245 #endif 00246 00247 #ifdef VAX 00248 #define DBL_DIG 16 00249 #define DBL_MAX_10_EXP 38 00250 #define DBL_MAX_EXP 127 00251 #define FLT_RADIX 2 00252 #define DBL_MAX 1.7014118346046923e+38 00253 #endif 00254 00255 #ifndef LONG_MAX 00256 #define LONG_MAX 2147483647 00257 #endif 00258 00259 #else /* ifndef Bad_float_h */ 00260 #include <float.h> 00261 #endif /* Bad_float_h */ 00262 00263 #ifndef __MATH_H__ 00264 #include <math.h> 00265 #endif 00266 00267 #define strtod kjs_strtod 00268 #define dtoa kjs_dtoa 00269 #define freedtoa kjs_freedtoa 00270 00271 #ifdef __cplusplus 00272 extern "C" { 00273 #endif 00274 00275 // #ifndef CONST 00276 #define CONST const 00277 // #endif 00278 00279 #if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1 00280 Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined. 00281 #endif 00282 00283 typedef union { double d; ULong L[2]; } U; 00284 00285 #define dval(x) (x).d 00286 #ifdef IEEE_8087 00287 #define word0(x) (x).L[1] 00288 #define word1(x) (x).L[0] 00289 #else 00290 #define word0(x) (x).L[0] 00291 #define word1(x) (x).L[1] 00292 #endif 00293 00294 /* The following definition of Storeinc is appropriate for MIPS processors. 00295 * An alternative that might be better on some machines is 00296 */ 00297 #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff) 00298 00299 /* #define P DBL_MANT_DIG */ 00300 /* Ten_pmax = floor(P*log(2)/log(5)) */ 00301 /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */ 00302 /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */ 00303 /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */ 00304 00305 #ifdef IEEE_Arith 00306 #define Exp_shift 20 00307 #define Exp_shift1 20 00308 #define Exp_msk1 0x100000 00309 #define Exp_msk11 0x100000 00310 #define Exp_mask 0x7ff00000 00311 #define P 53 00312 #define Bias 1023 00313 #define Emin (-1022) 00314 #define Exp_1 0x3ff00000 00315 #define Exp_11 0x3ff00000 00316 #define Ebits 11 00317 #define Frac_mask 0xfffff 00318 #define Frac_mask1 0xfffff 00319 #define Ten_pmax 22 00320 #define Bletch 0x10 00321 #define Bndry_mask 0xfffff 00322 #define Bndry_mask1 0xfffff 00323 #define LSB 1 00324 #define Sign_bit 0x80000000 00325 #define Log2P 1 00326 #define Tiny0 0 00327 #define Tiny1 1 00328 #define Quick_max 14 00329 #define Int_max 14 00330 #ifndef NO_IEEE_Scale 00331 #define Avoid_Underflow 00332 #ifdef Flush_Denorm /* debugging option */ 00333 #undef Sudden_Underflow 00334 #endif 00335 #endif 00336 00337 #ifndef Flt_Rounds 00338 #ifdef FLT_ROUNDS 00339 #define Flt_Rounds FLT_ROUNDS 00340 #else 00341 #define Flt_Rounds 1 00342 #endif 00343 #endif /*Flt_Rounds*/ 00344 00345 #ifdef Honor_FLT_ROUNDS 00346 #define Rounding rounding 00347 #undef Check_FLT_ROUNDS 00348 #define Check_FLT_ROUNDS 00349 #else 00350 #define Rounding Flt_Rounds 00351 #endif 00352 00353 #else /* ifndef IEEE_Arith */ 00354 #undef Check_FLT_ROUNDS 00355 #undef Honor_FLT_ROUNDS 00356 #undef SET_INEXACT 00357 #undef Sudden_Underflow 00358 #define Sudden_Underflow 00359 #ifdef IBM 00360 #undef Flt_Rounds 00361 #define Flt_Rounds 0 00362 #define Exp_shift 24 00363 #define Exp_shift1 24 00364 #define Exp_msk1 0x1000000 00365 #define Exp_msk11 0x1000000 00366 #define Exp_mask 0x7f000000 00367 #define P 14 00368 #define Bias 65 00369 #define Exp_1 0x41000000 00370 #define Exp_11 0x41000000 00371 #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */ 00372 #define Frac_mask 0xffffff 00373 #define Frac_mask1 0xffffff 00374 #define Bletch 4 00375 #define Ten_pmax 22 00376 #define Bndry_mask 0xefffff 00377 #define Bndry_mask1 0xffffff 00378 #define LSB 1 00379 #define Sign_bit 0x80000000 00380 #define Log2P 4 00381 #define Tiny0 0x100000 00382 #define Tiny1 0 00383 #define Quick_max 14 00384 #define Int_max 15 00385 #else /* VAX */ 00386 #undef Flt_Rounds 00387 #define Flt_Rounds 1 00388 #define Exp_shift 23 00389 #define Exp_shift1 7 00390 #define Exp_msk1 0x80 00391 #define Exp_msk11 0x800000 00392 #define Exp_mask 0x7f80 00393 #define P 56 00394 #define Bias 129 00395 #define Exp_1 0x40800000 00396 #define Exp_11 0x4080 00397 #define Ebits 8 00398 #define Frac_mask 0x7fffff 00399 #define Frac_mask1 0xffff007f 00400 #define Ten_pmax 24 00401 #define Bletch 2 00402 #define Bndry_mask 0xffff007f 00403 #define Bndry_mask1 0xffff007f 00404 #define LSB 0x10000 00405 #define Sign_bit 0x8000 00406 #define Log2P 1 00407 #define Tiny0 0x80 00408 #define Tiny1 0 00409 #define Quick_max 15 00410 #define Int_max 15 00411 #endif /* IBM, VAX */ 00412 #endif /* IEEE_Arith */ 00413 00414 #ifndef IEEE_Arith 00415 #define ROUND_BIASED 00416 #endif 00417 00418 #ifdef RND_PRODQUOT 00419 #define rounded_product(a,b) a = rnd_prod(a, b) 00420 #define rounded_quotient(a,b) a = rnd_quot(a, b) 00421 extern double rnd_prod(double, double), rnd_quot(double, double); 00422 #else 00423 #define rounded_product(a,b) a *= b 00424 #define rounded_quotient(a,b) a /= b 00425 #endif 00426 00427 #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1)) 00428 #define Big1 0xffffffff 00429 00430 #ifndef Pack_32 00431 #define Pack_32 00432 #endif 00433 00434 #define FFFFFFFF 0xffffffffUL 00435 00436 #ifdef NO_LONG_LONG 00437 #undef ULLong 00438 #ifdef Just_16 00439 #undef Pack_32 00440 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long. 00441 * This makes some inner loops simpler and sometimes saves work 00442 * during multiplications, but it often seems to make things slightly 00443 * slower. Hence the default is now to store 32 bits per Long. 00444 */ 00445 #endif 00446 #else /* long long available */ 00447 #ifndef Llong 00448 #define Llong long long 00449 #endif 00450 #ifndef ULLong 00451 #define ULLong unsigned Llong 00452 #endif 00453 #endif /* NO_LONG_LONG */ 00454 00455 #ifndef MULTIPLE_THREADS 00456 #define ACQUIRE_DTOA_LOCK(n) /*nothing*/ 00457 #define FREE_DTOA_LOCK(n) /*nothing*/ 00458 #endif 00459 00460 #define Kmax (sizeof(size_t) << 3) 00461 00462 struct 00463 Bigint { 00464 struct Bigint *next; 00465 int k, maxwds, sign, wds; 00466 ULong x[1]; 00467 }; 00468 00469 typedef struct Bigint Bigint; 00470 00471 static Bigint *freelist[Kmax+1]; 00472 00473 static Bigint * 00474 Balloc 00475 (int k) 00476 { 00477 int x; 00478 Bigint *rv; 00479 #ifndef Omit_Private_Memory 00480 unsigned int len; 00481 #endif 00482 00483 ACQUIRE_DTOA_LOCK(0); 00484 if ((rv = freelist[k])) { 00485 freelist[k] = rv->next; 00486 } 00487 else { 00488 x = 1 << k; 00489 #ifdef Omit_Private_Memory 00490 rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong)); 00491 #else 00492 len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1) 00493 /sizeof(double); 00494 if (pmem_next - private_mem + len <= (unsigned)PRIVATE_mem) { 00495 rv = (Bigint*)pmem_next; 00496 pmem_next += len; 00497 } 00498 else 00499 rv = (Bigint*)MALLOC(len*sizeof(double)); 00500 #endif 00501 rv->k = k; 00502 rv->maxwds = x; 00503 } 00504 FREE_DTOA_LOCK(0); 00505 rv->sign = rv->wds = 0; 00506 return rv; 00507 } 00508 00509 static void 00510 Bfree 00511 (Bigint *v) 00512 { 00513 if (v) { 00514 ACQUIRE_DTOA_LOCK(0); 00515 v->next = freelist[v->k]; 00516 freelist[v->k] = v; 00517 FREE_DTOA_LOCK(0); 00518 } 00519 } 00520 00521 #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \ 00522 y->wds*sizeof(Long) + 2*sizeof(int)) 00523 00524 static Bigint * 00525 multadd 00526 (Bigint *b, int m, int a) /* multiply by m and add a */ 00527 { 00528 int i, wds; 00529 #ifdef ULLong 00530 ULong *x; 00531 ULLong carry, y; 00532 #else 00533 ULong carry, *x, y; 00534 #ifdef Pack_32 00535 ULong xi, z; 00536 #endif 00537 #endif 00538 Bigint *b1; 00539 00540 wds = b->wds; 00541 x = b->x; 00542 i = 0; 00543 carry = a; 00544 do { 00545 #ifdef ULLong 00546 y = *x * (ULLong)m + carry; 00547 carry = y >> 32; 00548 *x++ = (ULong)y & FFFFFFFF; 00549 #else 00550 #ifdef Pack_32 00551 xi = *x; 00552 y = (xi & 0xffff) * m + carry; 00553 z = (xi >> 16) * m + (y >> 16); 00554 carry = z >> 16; 00555 *x++ = (z << 16) + (y & 0xffff); 00556 #else 00557 y = *x * m + carry; 00558 carry = y >> 16; 00559 *x++ = y & 0xffff; 00560 #endif 00561 #endif 00562 } 00563 while(++i < wds); 00564 if (carry) { 00565 if (wds >= b->maxwds) { 00566 b1 = Balloc(b->k+1); 00567 Bcopy(b1, b); 00568 Bfree(b); 00569 b = b1; 00570 } 00571 b->x[wds++] = (ULong)carry; 00572 b->wds = wds; 00573 } 00574 return b; 00575 } 00576 00577 static Bigint * 00578 s2b 00579 (CONST char *s, int nd0, int nd, ULong y9) 00580 { 00581 Bigint *b; 00582 int i, k; 00583 Long x, y; 00584 00585 x = (nd + 8) / 9; 00586 for(k = 0, y = 1; x > y; y <<= 1, k++) ; 00587 #ifdef Pack_32 00588 b = Balloc(k); 00589 b->x[0] = y9; 00590 b->wds = 1; 00591 #else 00592 b = Balloc(k+1); 00593 b->x[0] = y9 & 0xffff; 00594 b->wds = (b->x[1] = y9 >> 16) ? 2 : 1; 00595 #endif 00596 00597 i = 9; 00598 if (9 < nd0) { 00599 s += 9; 00600 do b = multadd(b, 10, *s++ - '0'); 00601 while(++i < nd0); 00602 s++; 00603 } 00604 else 00605 s += 10; 00606 for(; i < nd; i++) 00607 b = multadd(b, 10, *s++ - '0'); 00608 return b; 00609 } 00610 00611 static int 00612 hi0bits 00613 (ULong x) 00614 { 00615 int k = 0; 00616 00617 if (!(x & 0xffff0000)) { 00618 k = 16; 00619 x <<= 16; 00620 } 00621 if (!(x & 0xff000000)) { 00622 k += 8; 00623 x <<= 8; 00624 } 00625 if (!(x & 0xf0000000)) { 00626 k += 4; 00627 x <<= 4; 00628 } 00629 if (!(x & 0xc0000000)) { 00630 k += 2; 00631 x <<= 2; 00632 } 00633 if (!(x & 0x80000000)) { 00634 k++; 00635 if (!(x & 0x40000000)) 00636 return 32; 00637 } 00638 return k; 00639 } 00640 00641 static int 00642 lo0bits 00643 (ULong *y) 00644 { 00645 int k; 00646 ULong x = *y; 00647 00648 if (x & 7) { 00649 if (x & 1) 00650 return 0; 00651 if (x & 2) { 00652 *y = x >> 1; 00653 return 1; 00654 } 00655 *y = x >> 2; 00656 return 2; 00657 } 00658 k = 0; 00659 if (!(x & 0xffff)) { 00660 k = 16; 00661 x >>= 16; 00662 } 00663 if (!(x & 0xff)) { 00664 k += 8; 00665 x >>= 8; 00666 } 00667 if (!(x & 0xf)) { 00668 k += 4; 00669 x >>= 4; 00670 } 00671 if (!(x & 0x3)) { 00672 k += 2; 00673 x >>= 2; 00674 } 00675 if (!(x & 1)) { 00676 k++; 00677 x >>= 1; 00678 if (!x & 1) 00679 return 32; 00680 } 00681 *y = x; 00682 return k; 00683 } 00684 00685 static Bigint * 00686 i2b 00687 (int i) 00688 { 00689 Bigint *b; 00690 00691 b = Balloc(1); 00692 b->x[0] = i; 00693 b->wds = 1; 00694 return b; 00695 } 00696 00697 static Bigint * 00698 mult 00699 (Bigint *a, Bigint *b) 00700 { 00701 Bigint *c; 00702 int k, wa, wb, wc; 00703 ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0; 00704 ULong y; 00705 #ifdef ULLong 00706 ULLong carry, z; 00707 #else 00708 ULong carry, z; 00709 #ifdef Pack_32 00710 ULong z2; 00711 #endif 00712 #endif 00713 00714 if (a->wds < b->wds) { 00715 c = a; 00716 a = b; 00717 b = c; 00718 } 00719 k = a->k; 00720 wa = a->wds; 00721 wb = b->wds; 00722 wc = wa + wb; 00723 if (wc > a->maxwds) 00724 k++; 00725 c = Balloc(k); 00726 for(x = c->x, xa = x + wc; x < xa; x++) 00727 *x = 0; 00728 xa = a->x; 00729 xae = xa + wa; 00730 xb = b->x; 00731 xbe = xb + wb; 00732 xc0 = c->x; 00733 #ifdef ULLong 00734 for(; xb < xbe; xc0++) { 00735 if ((y = *xb++)) { 00736 x = xa; 00737 xc = xc0; 00738 carry = 0; 00739 do { 00740 z = *x++ * (ULLong)y + *xc + carry; 00741 carry = z >> 32; 00742 *xc++ = (ULong)z & FFFFFFFF; 00743 } 00744 while(x < xae); 00745 *xc = (ULong)carry; 00746 } 00747 } 00748 #else 00749 #ifdef Pack_32 00750 for(; xb < xbe; xb++, xc0++) { 00751 if (y = *xb & 0xffff) { 00752 x = xa; 00753 xc = xc0; 00754 carry = 0; 00755 do { 00756 z = (*x & 0xffff) * y + (*xc & 0xffff) + carry; 00757 carry = z >> 16; 00758 z2 = (*x++ >> 16) * y + (*xc >> 16) + carry; 00759 carry = z2 >> 16; 00760 Storeinc(xc, z2, z); 00761 } 00762 while(x < xae); 00763 *xc = carry; 00764 } 00765 if (y = *xb >> 16) { 00766 x = xa; 00767 xc = xc0; 00768 carry = 0; 00769 z2 = *xc; 00770 do { 00771 z = (*x & 0xffff) * y + (*xc >> 16) + carry; 00772 carry = z >> 16; 00773 Storeinc(xc, z, z2); 00774 z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry; 00775 carry = z2 >> 16; 00776 } 00777 while(x < xae); 00778 *xc = z2; 00779 } 00780 } 00781 #else 00782 for(; xb < xbe; xc0++) { 00783 if (y = *xb++) { 00784 x = xa; 00785 xc = xc0; 00786 carry = 0; 00787 do { 00788 z = *x++ * y + *xc + carry; 00789 carry = z >> 16; 00790 *xc++ = z & 0xffff; 00791 } 00792 while(x < xae); 00793 *xc = carry; 00794 } 00795 } 00796 #endif 00797 #endif 00798 for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ; 00799 c->wds = wc; 00800 return c; 00801 } 00802 00803 static Bigint *p5s; 00804 00805 static Bigint * 00806 pow5mult 00807 (Bigint *b, int k) 00808 { 00809 Bigint *b1, *p5, *p51; 00810 int i; 00811 static int p05[3] = { 5, 25, 125 }; 00812 00813 if ((i = k & 3)) 00814 b = multadd(b, p05[i-1], 0); 00815 00816 if (!(k >>= 2)) 00817 return b; 00818 if (!(p5 = p5s)) { 00819 /* first time */ 00820 #ifdef MULTIPLE_THREADS 00821 ACQUIRE_DTOA_LOCK(1); 00822 if (!(p5 = p5s)) { 00823 p5 = p5s = i2b(625); 00824 p5->next = 0; 00825 } 00826 FREE_DTOA_LOCK(1); 00827 #else 00828 p5 = p5s = i2b(625); 00829 p5->next = 0; 00830 #endif 00831 } 00832 for(;;) { 00833 if (k & 1) { 00834 b1 = mult(b, p5); 00835 Bfree(b); 00836 b = b1; 00837 } 00838 if (!(k >>= 1)) 00839 break; 00840 if (!(p51 = p5->next)) { 00841 #ifdef MULTIPLE_THREADS 00842 ACQUIRE_DTOA_LOCK(1); 00843 if (!(p51 = p5->next)) { 00844 p51 = p5->next = mult(p5,p5); 00845 p51->next = 0; 00846 } 00847 FREE_DTOA_LOCK(1); 00848 #else 00849 p51 = p5->next = mult(p5,p5); 00850 p51->next = 0; 00851 #endif 00852 } 00853 p5 = p51; 00854 } 00855 return b; 00856 } 00857 00858 static Bigint * 00859 lshift 00860 (Bigint *b, int k) 00861 { 00862 int i, k1, n, n1; 00863 Bigint *b1; 00864 ULong *x, *x1, *xe, z; 00865 00866 #ifdef Pack_32 00867 n = k >> 5; 00868 #else 00869 n = k >> 4; 00870 #endif 00871 k1 = b->k; 00872 n1 = n + b->wds + 1; 00873 for(i = b->maxwds; n1 > i; i <<= 1) 00874 k1++; 00875 b1 = Balloc(k1); 00876 x1 = b1->x; 00877 for(i = 0; i < n; i++) 00878 *x1++ = 0; 00879 x = b->x; 00880 xe = x + b->wds; 00881 #ifdef Pack_32 00882 if (k &= 0x1f) { 00883 k1 = 32 - k; 00884 z = 0; 00885 do { 00886 *x1++ = *x << k | z; 00887 z = *x++ >> k1; 00888 } 00889 while(x < xe); 00890 if ((*x1 = z)) 00891 ++n1; 00892 } 00893 #else 00894 if (k &= 0xf) { 00895 k1 = 16 - k; 00896 z = 0; 00897 do { 00898 *x1++ = *x << k & 0xffff | z; 00899 z = *x++ >> k1; 00900 } 00901 while(x < xe); 00902 if (*x1 = z) 00903 ++n1; 00904 } 00905 #endif 00906 else do 00907 *x1++ = *x++; 00908 while(x < xe); 00909 b1->wds = n1 - 1; 00910 Bfree(b); 00911 return b1; 00912 } 00913 00914 static int 00915 cmp 00916 (Bigint *a, Bigint *b) 00917 { 00918 ULong *xa, *xa0, *xb, *xb0; 00919 int i, j; 00920 00921 i = a->wds; 00922 j = b->wds; 00923 #ifdef DEBUG 00924 if (i > 1 && !a->x[i-1]) 00925 Bug("cmp called with a->x[a->wds-1] == 0"); 00926 if (j > 1 && !b->x[j-1]) 00927 Bug("cmp called with b->x[b->wds-1] == 0"); 00928 #endif 00929 if (i -= j) 00930 return i; 00931 xa0 = a->x; 00932 xa = xa0 + j; 00933 xb0 = b->x; 00934 xb = xb0 + j; 00935 for(;;) { 00936 if (*--xa != *--xb) 00937 return *xa < *xb ? -1 : 1; 00938 if (xa <= xa0) 00939 break; 00940 } 00941 return 0; 00942 } 00943 00944 static Bigint * 00945 diff 00946 (Bigint *a, Bigint *b) 00947 { 00948 Bigint *c; 00949 int i, wa, wb; 00950 ULong *xa, *xae, *xb, *xbe, *xc; 00951 #ifdef ULLong 00952 ULLong borrow, y; 00953 #else 00954 ULong borrow, y; 00955 #ifdef Pack_32 00956 ULong z; 00957 #endif 00958 #endif 00959 00960 i = cmp(a,b); 00961 if (!i) { 00962 c = Balloc(0); 00963 c->wds = 1; 00964 c->x[0] = 0; 00965 return c; 00966 } 00967 if (i < 0) { 00968 c = a; 00969 a = b; 00970 b = c; 00971 i = 1; 00972 } 00973 else 00974 i = 0; 00975 c = Balloc(a->k); 00976 c->sign = i; 00977 wa = a->wds; 00978 xa = a->x; 00979 xae = xa + wa; 00980 wb = b->wds; 00981 xb = b->x; 00982 xbe = xb + wb; 00983 xc = c->x; 00984 borrow = 0; 00985 #ifdef ULLong 00986 do { 00987 y = (ULLong)*xa++ - *xb++ - borrow; 00988 borrow = y >> 32 & (ULong)1; 00989 *xc++ = (ULong)y & FFFFFFFF; 00990 } 00991 while(xb < xbe); 00992 while(xa < xae) { 00993 y = *xa++ - borrow; 00994 borrow = y >> 32 & (ULong)1; 00995 *xc++ = (ULong)y & FFFFFFFF; 00996 } 00997 #else 00998 #ifdef Pack_32 00999 do { 01000 y = (*xa & 0xffff) - (*xb & 0xffff) - borrow; 01001 borrow = (y & 0x10000) >> 16; 01002 z = (*xa++ >> 16) - (*xb++ >> 16) - borrow; 01003 borrow = (z & 0x10000) >> 16; 01004 Storeinc(xc, z, y); 01005 } 01006 while(xb < xbe); 01007 while(xa < xae) { 01008 y = (*xa & 0xffff) - borrow; 01009 borrow = (y & 0x10000) >> 16; 01010 z = (*xa++ >> 16) - borrow; 01011 borrow = (z & 0x10000) >> 16; 01012 Storeinc(xc, z, y); 01013 } 01014 #else 01015 do { 01016 y = *xa++ - *xb++ - borrow; 01017 borrow = (y & 0x10000) >> 16; 01018 *xc++ = y & 0xffff; 01019 } 01020 while(xb < xbe); 01021 while(xa < xae) { 01022 y = *xa++ - borrow; 01023 borrow = (y & 0x10000) >> 16; 01024 *xc++ = y & 0xffff; 01025 } 01026 #endif 01027 #endif 01028 while(!*--xc) 01029 wa--; 01030 c->wds = wa; 01031 return c; 01032 } 01033 01034 static double 01035 ulp 01036 (double dx) 01037 { 01038 Long L; 01039 U x, a; 01040 01041 dval(x) = dx; 01042 L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1; 01043 #ifndef Avoid_Underflow 01044 #ifndef Sudden_Underflow 01045 if (L > 0) { 01046 #endif 01047 #endif 01048 #ifdef IBM 01049 L |= Exp_msk1 >> 4; 01050 #endif 01051 word0(a) = L; 01052 word1(a) = 0; 01053 #ifndef Avoid_Underflow 01054 #ifndef Sudden_Underflow 01055 } 01056 else { 01057 L = -L >> Exp_shift; 01058 if (L < Exp_shift) { 01059 word0(a) = 0x80000 >> L; 01060 word1(a) = 0; 01061 } 01062 else { 01063 word0(a) = 0; 01064 L -= Exp_shift; 01065 word1(a) = L >= 31 ? 1 : 1 << 31 - L; 01066 } 01067 } 01068 #endif 01069 #endif 01070 return dval(a); 01071 } 01072 01073 static double 01074 b2d 01075 (Bigint *a, int *e) 01076 { 01077 ULong *xa, *xa0, w, y, z; 01078 int k; 01079 U d; 01080 #ifdef VAX 01081 ULong d0, d1; 01082 #else 01083 #define d0 word0(d) 01084 #define d1 word1(d) 01085 #endif 01086 01087 xa0 = a->x; 01088 xa = xa0 + a->wds; 01089 y = *--xa; 01090 #ifdef DEBUG 01091 if (!y) Bug("zero y in b2d"); 01092 #endif 01093 k = hi0bits(y); 01094 *e = 32 - k; 01095 #ifdef Pack_32 01096 if (k < Ebits) { 01097 d0 = Exp_1 | y >> Ebits - k; 01098 w = xa > xa0 ? *--xa : 0; 01099 d1 = y << (32-Ebits) + k | w >> Ebits - k; 01100 goto ret_d; 01101 } 01102 z = xa > xa0 ? *--xa : 0; 01103 if (k -= Ebits) { 01104 d0 = Exp_1 | y << k | z >> 32 - k; 01105 y = xa > xa0 ? *--xa : 0; 01106 d1 = z << k | y >> 32 - k; 01107 } 01108 else { 01109 d0 = Exp_1 | y; 01110 d1 = z; 01111 } 01112 #else 01113 if (k < Ebits + 16) { 01114 z = xa > xa0 ? *--xa : 0; 01115 d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k; 01116 w = xa > xa0 ? *--xa : 0; 01117 y = xa > xa0 ? *--xa : 0; 01118 d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k; 01119 goto ret_d; 01120 } 01121 z = xa > xa0 ? *--xa : 0; 01122 w = xa > xa0 ? *--xa : 0; 01123 k -= Ebits + 16; 01124 d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k; 01125 y = xa > xa0 ? *--xa : 0; 01126 d1 = w << k + 16 | y << k; 01127 #endif 01128 ret_d: 01129 #ifdef VAX 01130 word0(d) = d0 >> 16 | d0 << 16; 01131 word1(d) = d1 >> 16 | d1 << 16; 01132 #else 01133 #undef d0 01134 #undef d1 01135 #endif 01136 return dval(d); 01137 } 01138 01139 static Bigint * 01140 d2b 01141 (double dd, int *e, int *bits) 01142 { 01143 U d; 01144 Bigint *b; 01145 int de, k; 01146 ULong *x, y, z; 01147 #ifndef Sudden_Underflow 01148 int i; 01149 #endif 01150 #ifdef VAX 01151 ULong d0, d1; 01152 #endif 01153 dval(d) = dd; 01154 #ifdef VAX 01155 d0 = word0(d) >> 16 | word0(d) << 16; 01156 d1 = word1(d) >> 16 | word1(d) << 16; 01157 #else 01158 #define d0 word0(d) 01159 #define d1 word1(d) 01160 #endif 01161 01162 #ifdef Pack_32 01163 b = Balloc(1); 01164 #else 01165 b = Balloc(2); 01166 #endif 01167 x = b->x; 01168 01169 z = d0 & Frac_mask; 01170 d0 &= 0x7fffffff; /* clear sign bit, which we ignore */ 01171 #ifdef Sudden_Underflow 01172 de = (int)(d0 >> Exp_shift); 01173 #ifndef IBM 01174 z |= Exp_msk11; 01175 #endif 01176 #else 01177 if ((de = (int)(d0 >> Exp_shift))) 01178 z |= Exp_msk1; 01179 #endif 01180 #ifdef Pack_32 01181 if ((y = d1)) { 01182 if ((k = lo0bits(&y))) { 01183 x[0] = y | z << 32 - k; 01184 z >>= k; 01185 } 01186 else 01187 x[0] = y; 01188 #ifndef Sudden_Underflow 01189 i = 01190 #endif 01191 b->wds = (x[1] = z) ? 2 : 1; 01192 } 01193 else { 01194 #ifdef DEBUG 01195 if (!z) 01196 Bug("Zero passed to d2b"); 01197 #endif 01198 k = lo0bits(&z); 01199 x[0] = z; 01200 #ifndef Sudden_Underflow 01201 i = 01202 #endif 01203 b->wds = 1; 01204 k += 32; 01205 } 01206 #else 01207 if (y = d1) { 01208 if (k = lo0bits(&y)) 01209 if (k >= 16) { 01210 x[0] = y | z << 32 - k & 0xffff; 01211 x[1] = z >> k - 16 & 0xffff; 01212 x[2] = z >> k; 01213 i = 2; 01214 } 01215 else { 01216 x[0] = y & 0xffff; 01217 x[1] = y >> 16 | z << 16 - k & 0xffff; 01218 x[2] = z >> k & 0xffff; 01219 x[3] = z >> k+16; 01220 i = 3; 01221 } 01222 else { 01223 x[0] = y & 0xffff; 01224 x[1] = y >> 16; 01225 x[2] = z & 0xffff; 01226 x[3] = z >> 16; 01227 i = 3; 01228 } 01229 } 01230 else { 01231 #ifdef DEBUG 01232 if (!z) 01233 Bug("Zero passed to d2b"); 01234 #endif 01235 k = lo0bits(&z); 01236 if (k >= 16) { 01237 x[0] = z; 01238 i = 0; 01239 } 01240 else { 01241 x[0] = z & 0xffff; 01242 x[1] = z >> 16; 01243 i = 1; 01244 } 01245 k += 32; 01246 } 01247 while(!x[i]) 01248 --i; 01249 b->wds = i + 1; 01250 #endif 01251 #ifndef Sudden_Underflow 01252 if (de) { 01253 #endif 01254 #ifdef IBM 01255 *e = (de - Bias - (P-1) << 2) + k; 01256 *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask); 01257 #else 01258 *e = de - Bias - (P-1) + k; 01259 *bits = P - k; 01260 #endif 01261 #ifndef Sudden_Underflow 01262 } 01263 else { 01264 *e = de - Bias - (P-1) + 1 + k; 01265 #ifdef Pack_32 01266 *bits = 32*i - hi0bits(x[i-1]); 01267 #else 01268 *bits = (i+2)*16 - hi0bits(x[i]); 01269 #endif 01270 } 01271 #endif 01272 return b; 01273 } 01274 #undef d0 01275 #undef d1 01276 01277 static double 01278 ratio 01279 (Bigint *a, Bigint *b) 01280 { 01281 U da, db; 01282 int k, ka, kb; 01283 01284 dval(da) = b2d(a, &ka); 01285 dval(db) = b2d(b, &kb); 01286 #ifdef Pack_32 01287 k = ka - kb + 32*(a->wds - b->wds); 01288 #else 01289 k = ka - kb + 16*(a->wds - b->wds); 01290 #endif 01291 #ifdef IBM 01292 if (k > 0) { 01293 word0(da) += (k >> 2)*Exp_msk1; 01294 if (k &= 3) 01295 dval(da) *= 1 << k; 01296 } 01297 else { 01298 k = -k; 01299 word0(db) += (k >> 2)*Exp_msk1; 01300 if (k &= 3) 01301 dval(db) *= 1 << k; 01302 } 01303 #else 01304 if (k > 0) 01305 word0(da) += k*Exp_msk1; 01306 else { 01307 k = -k; 01308 word0(db) += k*Exp_msk1; 01309 } 01310 #endif 01311 return dval(da) / dval(db); 01312 } 01313 01314 static CONST double 01315 tens[] = { 01316 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 01317 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, 01318 1e20, 1e21, 1e22 01319 #ifdef VAX 01320 , 1e23, 1e24 01321 #endif 01322 }; 01323 01324 static CONST double 01325 #ifdef IEEE_Arith 01326 bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 }; 01327 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, 01328 #ifdef Avoid_Underflow 01329 9007199254740992.*9007199254740992.e-256 01330 /* = 2^106 * 1e-53 */ 01331 #else 01332 1e-256 01333 #endif 01334 }; 01335 /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */ 01336 /* flag unnecessarily. It leads to a song and dance at the end of strtod. */ 01337 #define Scale_Bit 0x10 01338 #define n_bigtens 5 01339 #else 01340 #ifdef IBM 01341 bigtens[] = { 1e16, 1e32, 1e64 }; 01342 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 }; 01343 #define n_bigtens 3 01344 #else 01345 bigtens[] = { 1e16, 1e32 }; 01346 static CONST double tinytens[] = { 1e-16, 1e-32 }; 01347 #define n_bigtens 2 01348 #endif 01349 #endif 01350 01351 #ifndef IEEE_Arith 01352 #undef INFNAN_CHECK 01353 #endif 01354 01355 #ifdef INFNAN_CHECK 01356 01357 #ifndef NAN_WORD0 01358 #define NAN_WORD0 0x7ff80000 01359 #endif 01360 01361 #ifndef NAN_WORD1 01362 #define NAN_WORD1 0 01363 #endif 01364 01365 static int 01366 match 01367 (CONST char **sp, CONST char *t) 01368 { 01369 int c, d; 01370 CONST char *s = *sp; 01371 01372 while((d = *t++)) { 01373 if ((c = *++s) >= 'A' && c <= 'Z') 01374 c += 'a' - 'A'; 01375 if (c != d) 01376 return 0; 01377 } 01378 *sp = s + 1; 01379 return 1; 01380 } 01381 01382 #ifndef No_Hex_NaN 01383 static void 01384 hexnan 01385 (U *rvp, CONST char **sp) 01386 { 01387 ULong c, x[2]; 01388 CONST char *s; 01389 int havedig, udx0, xshift; 01390 01391 x[0] = x[1] = 0; 01392 havedig = xshift = 0; 01393 udx0 = 1; 01394 s = *sp; 01395 while((c = *(CONST unsigned char*)++s)) { 01396 if (c >= '0' && c <= '9') 01397 c -= '0'; 01398 else if (c >= 'a' && c <= 'f') 01399 c += 10 - 'a'; 01400 else if (c >= 'A' && c <= 'F') 01401 c += 10 - 'A'; 01402 else if (c <= ' ') { 01403 if (udx0 && havedig) { 01404 udx0 = 0; 01405 xshift = 1; 01406 } 01407 continue; 01408 } 01409 else if (/*(*/ c == ')' && havedig) { 01410 *sp = s + 1; 01411 break; 01412 } 01413 else 01414 return; /* invalid form: don't change *sp */ 01415 havedig = 1; 01416 if (xshift) { 01417 xshift = 0; 01418 x[0] = x[1]; 01419 x[1] = 0; 01420 } 01421 if (udx0) 01422 x[0] = (x[0] << 4) | (x[1] >> 28); 01423 x[1] = (x[1] << 4) | c; 01424 } 01425 if ((x[0] &= 0xfffff) || x[1]) { 01426 word0(*rvp) = Exp_mask | x[0]; 01427 word1(*rvp) = x[1]; 01428 } 01429 } 01430 #endif /*No_Hex_NaN*/ 01431 #endif /* INFNAN_CHECK */ 01432 01433 double 01434 strtod 01435 (CONST char *s00, char **se) 01436 { 01437 #ifdef Avoid_Underflow 01438 int scale; 01439 #endif 01440 int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign, 01441 e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign; 01442 CONST char *s, *s0, *s1; 01443 double aadj, aadj1, adj; 01444 U aadj2, rv, rv0; 01445 Long L; 01446 ULong y, z; 01447 Bigint *bb = NULL, *bb1 = NULL, *bd = NULL, *bd0 = NULL, *bs = NULL, *delta = NULL; 01448 #ifdef SET_INEXACT 01449 int inexact, oldinexact; 01450 #endif 01451 #ifdef Honor_FLT_ROUNDS 01452 int rounding; 01453 #endif 01454 #ifdef USE_LOCALE 01455 CONST char *s2; 01456 #endif 01457 01458 sign = nz0 = nz = 0; 01459 dval(rv) = 0.; 01460 for(s = s00;;s++) switch(*s) { 01461 case '-': 01462 sign = 1; 01463 /* no break */ 01464 case '+': 01465 if (*++s) 01466 goto break2; 01467 /* no break */ 01468 case 0: 01469 goto ret0; 01470 case '\t': 01471 case '\n': 01472 case '\v': 01473 case '\f': 01474 case '\r': 01475 case ' ': 01476 continue; 01477 default: 01478 goto break2; 01479 } 01480 break2: 01481 if (*s == '0') { 01482 nz0 = 1; 01483 while(*++s == '0') ; 01484 if (!*s) 01485 goto ret; 01486 } 01487 s0 = s; 01488 y = z = 0; 01489 for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++) 01490 if (nd < 9) 01491 y = 10*y + c - '0'; 01492 else if (nd < 16) 01493 z = 10*z + c - '0'; 01494 nd0 = nd; 01495 #ifdef USE_LOCALE 01496 s1 = localeconv()->decimal_point; 01497 if (c == *s1) { 01498 c = '.'; 01499 if (*++s1) { 01500 s2 = s; 01501 for(;;) { 01502 if (*++s2 != *s1) { 01503 c = 0; 01504 break; 01505 } 01506 if (!*++s1) { 01507 s = s2; 01508 break; 01509 } 01510 } 01511 } 01512 } 01513 #endif 01514 if (c == '.') { 01515 c = *++s; 01516 if (!nd) { 01517 for(; c == '0'; c = *++s) 01518 nz++; 01519 if (c > '0' && c <= '9') { 01520 s0 = s; 01521 nf += nz; 01522 nz = 0; 01523 goto have_dig; 01524 } 01525 goto dig_done; 01526 } 01527 for(; c >= '0' && c <= '9'; c = *++s) { 01528 have_dig: 01529 nz++; 01530 if (c -= '0') { 01531 nf += nz; 01532 for(i = 1; i < nz; i++) 01533 if (nd++ < 9) 01534 y *= 10; 01535 else if (nd <= DBL_DIG + 1) 01536 z *= 10; 01537 if (nd++ < 9) 01538 y = 10*y + c; 01539 else if (nd <= DBL_DIG + 1) 01540 z = 10*z + c; 01541 nz = 0; 01542 } 01543 } 01544 } 01545 dig_done: 01546 e = 0; 01547 if (c == 'e' || c == 'E') { 01548 if (!nd && !nz && !nz0) { 01549 goto ret0; 01550 } 01551 s00 = s; 01552 esign = 0; 01553 switch(c = *++s) { 01554 case '-': 01555 esign = 1; 01556 case '+': 01557 c = *++s; 01558 } 01559 if (c >= '0' && c <= '9') { 01560 while(c == '0') 01561 c = *++s; 01562 if (c > '0' && c <= '9') { 01563 L = c - '0'; 01564 s1 = s; 01565 while((c = *++s) >= '0' && c <= '9') 01566 L = 10*L + c - '0'; 01567 if (s - s1 > 8 || L > 19999) 01568 /* Avoid confusion from exponents 01569 * so large that e might overflow. 01570 */ 01571 e = 19999; /* safe for 16 bit ints */ 01572 else 01573 e = (int)L; 01574 if (esign) 01575 e = -e; 01576 } 01577 else 01578 e = 0; 01579 } 01580 else 01581 s = s00; 01582 } 01583 if (!nd) { 01584 if (!nz && !nz0) { 01585 #ifdef INFNAN_CHECK 01586 /* Check for Nan and Infinity */ 01587 switch(c) { 01588 case 'i': 01589 case 'I': 01590 if (match(&s,"nf")) { 01591 --s; 01592 if (!match(&s,"inity")) 01593 ++s; 01594 word0(rv) = 0x7ff00000; 01595 word1(rv) = 0; 01596 goto ret; 01597 } 01598 break; 01599 case 'n': 01600 case 'N': 01601 if (match(&s, "an")) { 01602 word0(rv) = NAN_WORD0; 01603 word1(rv) = NAN_WORD1; 01604 #ifndef No_Hex_NaN 01605 if (*s == '(') /*)*/ 01606 hexnan(&rv, &s); 01607 #endif 01608 goto ret; 01609 } 01610 } 01611 #endif /* INFNAN_CHECK */ 01612 ret0: 01613 s = s00; 01614 sign = 0; 01615 } 01616 goto ret; 01617 } 01618 e1 = e -= nf; 01619 01620 /* Now we have nd0 digits, starting at s0, followed by a 01621 * decimal point, followed by nd-nd0 digits. The number we're 01622 * after is the integer represented by those digits times 01623 * 10**e */ 01624 01625 if (!nd0) 01626 nd0 = nd; 01627 k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1; 01628 dval(rv) = y; 01629 if (k > 9) { 01630 #ifdef SET_INEXACT 01631 if (k > DBL_DIG) 01632 oldinexact = get_inexact(); 01633 #endif 01634 dval(rv) = tens[k - 9] * dval(rv) + z; 01635 } 01636 bd0 = 0; 01637 if (nd <= DBL_DIG 01638 #ifndef RND_PRODQUOT 01639 #ifndef Honor_FLT_ROUNDS 01640 && Flt_Rounds == 1 01641 #endif 01642 #endif 01643 ) { 01644 if (!e) 01645 goto ret; 01646 if (e > 0) { 01647 if (e <= Ten_pmax) { 01648 #ifdef VAX 01649 goto vax_ovfl_check; 01650 #else 01651 #ifdef Honor_FLT_ROUNDS 01652 /* round correctly FLT_ROUNDS = 2 or 3 */ 01653 if (sign) { 01654 rv = -rv; 01655 sign = 0; 01656 } 01657 #endif 01658 /* rv = */ rounded_product(dval(rv), tens[e]); 01659 goto ret; 01660 #endif 01661 } 01662 i = DBL_DIG - nd; 01663 if (e <= Ten_pmax + i) { 01664 /* A fancier test would sometimes let us do 01665 * this for larger i values. 01666 */ 01667 #ifdef Honor_FLT_ROUNDS 01668 /* round correctly FLT_ROUNDS = 2 or 3 */ 01669 if (sign) { 01670 rv = -rv; 01671 sign = 0; 01672 } 01673 #endif 01674 e -= i; 01675 dval(rv) *= tens[i]; 01676 #ifdef VAX 01677 /* VAX exponent range is so narrow we must 01678 * worry about overflow here... 01679 */ 01680 vax_ovfl_check: 01681 word0(rv) -= P*Exp_msk1; 01682 /* rv = */ rounded_product(dval(rv), tens[e]); 01683 if ((word0(rv) & Exp_mask) 01684 > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) 01685 goto ovfl; 01686 word0(rv) += P*Exp_msk1; 01687 #else 01688 /* rv = */ rounded_product(dval(rv), tens[e]); 01689 #endif 01690 goto ret; 01691 } 01692 } 01693 #ifndef Inaccurate_Divide 01694 else if (e >= -Ten_pmax) { 01695 #ifdef Honor_FLT_ROUNDS 01696 /* round correctly FLT_ROUNDS = 2 or 3 */ 01697 if (sign) { 01698 rv = -rv; 01699 sign = 0; 01700 } 01701 #endif 01702 /* rv = */ rounded_quotient(dval(rv), tens[-e]); 01703 goto ret; 01704 } 01705 #endif 01706 } 01707 e1 += nd - k; 01708 01709 #ifdef IEEE_Arith 01710 #ifdef SET_INEXACT 01711 inexact = 1; 01712 if (k <= DBL_DIG) 01713 oldinexact = get_inexact(); 01714 #endif 01715 #ifdef Avoid_Underflow 01716 scale = 0; 01717 #endif 01718 #ifdef Honor_FLT_ROUNDS 01719 if ((rounding = Flt_Rounds) >= 2) { 01720 if (sign) 01721 rounding = rounding == 2 ? 0 : 2; 01722 else 01723 if (rounding != 2) 01724 rounding = 0; 01725 } 01726 #endif 01727 #endif /*IEEE_Arith*/ 01728 01729 /* Get starting approximation = rv * 10**e1 */ 01730 01731 if (e1 > 0) { 01732 if ((i = e1 & 15)) 01733 dval(rv) *= tens[i]; 01734 if (e1 &= ~15) { 01735 if (e1 > DBL_MAX_10_EXP) { 01736 ovfl: 01737 #ifndef NO_ERRNO 01738 errno = ERANGE; 01739 #endif 01740 /* Can't trust HUGE_VAL */ 01741 #ifdef IEEE_Arith 01742 #ifdef Honor_FLT_ROUNDS 01743 switch(rounding) { 01744 case 0: /* toward 0 */ 01745 case 3: /* toward -infinity */ 01746 word0(rv) = Big0; 01747 word1(rv) = Big1; 01748 break; 01749 default: 01750 word0(rv) = Exp_mask; 01751 word1(rv) = 0; 01752 } 01753 #else /*Honor_FLT_ROUNDS*/ 01754 word0(rv) = Exp_mask; 01755 word1(rv) = 0; 01756 #endif /*Honor_FLT_ROUNDS*/ 01757 #ifdef SET_INEXACT 01758 /* set overflow bit */ 01759 dval(rv0) = 1e300; 01760 dval(rv0) *= dval(rv0); 01761 #endif 01762 #else /*IEEE_Arith*/ 01763 word0(rv) = Big0; 01764 word1(rv) = Big1; 01765 #endif /*IEEE_Arith*/ 01766 if (bd0) 01767 goto retfree; 01768 goto ret; 01769 } 01770 e1 >>= 4; 01771 for(j = 0; e1 > 1; j++, e1 >>= 1) 01772 if (e1 & 1) 01773 dval(rv) *= bigtens[j]; 01774 /* The last multiplication could overflow. */ 01775 word0(rv) -= P*Exp_msk1; 01776 dval(rv) *= bigtens[j]; 01777 if ((z = word0(rv) & Exp_mask) 01778 > Exp_msk1*(DBL_MAX_EXP+Bias-P)) 01779 goto ovfl; 01780 if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) { 01781 /* set to largest number */ 01782 /* (Can't trust DBL_MAX) */ 01783 word0(rv) = Big0; 01784 word1(rv) = Big1; 01785 } 01786 else 01787 word0(rv) += P*Exp_msk1; 01788 } 01789 } 01790 else if (e1 < 0) { 01791 e1 = -e1; 01792 if ((i = e1 & 15)) 01793 dval(rv) /= tens[i]; 01794 if (e1 >>= 4) { 01795 if (e1 >= 1 << n_bigtens) 01796 goto undfl; 01797 #ifdef Avoid_Underflow 01798 if (e1 & Scale_Bit) 01799 scale = 2*P; 01800 for(j = 0; e1 > 0; j++, e1 >>= 1) 01801 if (e1 & 1) 01802 dval(rv) *= tinytens[j]; 01803 if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask) 01804 >> Exp_shift)) > 0) { 01805 /* scaled rv is denormal; zap j low bits */ 01806 if (j >= 32) { 01807 word1(rv) = 0; 01808 if (j >= 53) 01809 word0(rv) = (P+2)*Exp_msk1; 01810 else 01811 word0(rv) &= 0xffffffff << j-32; 01812 } 01813 else 01814 word1(rv) &= 0xffffffff << j; 01815 } 01816 #else 01817 for(j = 0; e1 > 1; j++, e1 >>= 1) 01818 if (e1 & 1) 01819 dval(rv) *= tinytens[j]; 01820 /* The last multiplication could underflow. */ 01821 dval(rv0) = dval(rv); 01822 dval(rv) *= tinytens[j]; 01823 if (!dval(rv)) { 01824 dval(rv) = 2.*dval(rv0); 01825 dval(rv) *= tinytens[j]; 01826 #endif 01827 if (!dval(rv)) { 01828 undfl: 01829 dval(rv) = 0.; 01830 #ifndef NO_ERRNO 01831 errno = ERANGE; 01832 #endif 01833 if (bd0) 01834 goto retfree; 01835 goto ret; 01836 } 01837 #ifndef Avoid_Underflow 01838 word0(rv) = Tiny0; 01839 word1(rv) = Tiny1; 01840 /* The refinement below will clean 01841 * this approximation up. 01842 */ 01843 } 01844 #endif 01845 } 01846 } 01847 01848 /* Now the hard part -- adjusting rv to the correct value.*/ 01849 01850 /* Put digits into bd: true value = bd * 10^e */ 01851 01852 bd0 = s2b(s0, nd0, nd, y); 01853 01854 for(;;) { 01855 bd = Balloc(bd0->k); 01856 Bcopy(bd, bd0); 01857 bb = d2b(dval(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */ 01858 bs = i2b(1); 01859 01860 if (e >= 0) { 01861 bb2 = bb5 = 0; 01862 bd2 = bd5 = e; 01863 } 01864 else { 01865 bb2 = bb5 = -e; 01866 bd2 = bd5 = 0; 01867 } 01868 if (bbe >= 0) 01869 bb2 += bbe; 01870 else 01871 bd2 -= bbe; 01872 bs2 = bb2; 01873 #ifdef Honor_FLT_ROUNDS 01874 if (rounding != 1) 01875 bs2++; 01876 #endif 01877 #ifdef Avoid_Underflow 01878 j = bbe - scale; 01879 i = j + bbbits - 1; /* logb(rv) */ 01880 if (i < Emin) /* denormal */ 01881 j += P - Emin; 01882 else 01883 j = P + 1 - bbbits; 01884 #else /*Avoid_Underflow*/ 01885 #ifdef Sudden_Underflow 01886 #ifdef IBM 01887 j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3); 01888 #else 01889 j = P + 1 - bbbits; 01890 #endif 01891 #else /*Sudden_Underflow*/ 01892 j = bbe; 01893 i = j + bbbits - 1; /* logb(rv) */ 01894 if (i < Emin) /* denormal */ 01895 j += P - Emin; 01896 else 01897 j = P + 1 - bbbits; 01898 #endif /*Sudden_Underflow*/ 01899 #endif /*Avoid_Underflow*/ 01900 bb2 += j; 01901 bd2 += j; 01902 #ifdef Avoid_Underflow 01903 bd2 += scale; 01904 #endif 01905 i = bb2 < bd2 ? bb2 : bd2; 01906 if (i > bs2) 01907 i = bs2; 01908 if (i > 0) { 01909 bb2 -= i; 01910 bd2 -= i; 01911 bs2 -= i; 01912 } 01913 if (bb5 > 0) { 01914 bs = pow5mult(bs, bb5); 01915 bb1 = mult(bs, bb); 01916 Bfree(bb); 01917 bb = bb1; 01918 } 01919 if (bb2 > 0) 01920 bb = lshift(bb, bb2); 01921 if (bd5 > 0) 01922 bd = pow5mult(bd, bd5); 01923 if (bd2 > 0) 01924 bd = lshift(bd, bd2); 01925 if (bs2 > 0) 01926 bs = lshift(bs, bs2); 01927 delta = diff(bb, bd); 01928 dsign = delta->sign; 01929 delta->sign = 0; 01930 i = cmp(delta, bs); 01931 #ifdef Honor_FLT_ROUNDS 01932 if (rounding != 1) { 01933 if (i < 0) { 01934 /* Error is less than an ulp */ 01935 if (!delta->x[0] && delta->wds <= 1) { 01936 /* exact */ 01937 #ifdef SET_INEXACT 01938 inexact = 0; 01939 #endif 01940 break; 01941 } 01942 if (rounding) { 01943 if (dsign) { 01944 adj = 1.; 01945 goto apply_adj; 01946 } 01947 } 01948 else if (!dsign) { 01949 adj = -1.; 01950 if (!word1(rv) 01951 && !(word0(rv) & Frac_mask)) { 01952 y = word0(rv) & Exp_mask; 01953 #ifdef Avoid_Underflow 01954 if (!scale || y > 2*P*Exp_msk1) 01955 #else 01956 if (y) 01957 #endif 01958 { 01959 delta = lshift(delta,Log2P); 01960 if (cmp(delta, bs) <= 0) 01961 adj = -0.5; 01962 } 01963 } 01964 apply_adj: 01965 #ifdef Avoid_Underflow 01966 if (scale && (y = word0(rv) & Exp_mask) 01967 <= 2*P*Exp_msk1) 01968 word0(adj) += (2*P+1)*Exp_msk1 - y; 01969 #else 01970 #ifdef Sudden_Underflow 01971 if ((word0(rv) & Exp_mask) <= 01972 P*Exp_msk1) { 01973 word0(rv) += P*Exp_msk1; 01974 dval(rv) += adj*ulp(dval(rv)); 01975 word0(rv) -= P*Exp_msk1; 01976 } 01977 else 01978 #endif /*Sudden_Underflow*/ 01979 #endif /*Avoid_Underflow*/ 01980 dval(rv) += adj*ulp(dval(rv)); 01981 } 01982 break; 01983 } 01984 adj = ratio(delta, bs); 01985 if (adj < 1.) 01986 adj = 1.; 01987 if (adj <= 0x7ffffffe) { 01988 /* adj = rounding ? ceil(adj) : floor(adj); */ 01989 y = adj; 01990 if (y != adj) { 01991 if (!((rounding>>1) ^ dsign)) 01992 y++; 01993 adj = y; 01994 } 01995 } 01996 #ifdef Avoid_Underflow 01997 if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1) 01998 word0(adj) += (2*P+1)*Exp_msk1 - y; 01999 #else 02000 #ifdef Sudden_Underflow 02001 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) { 02002 word0(rv) += P*Exp_msk1; 02003 adj *= ulp(dval(rv)); 02004 if (dsign) 02005 dval(rv) += adj; 02006 else 02007 dval(rv) -= adj; 02008 word0(rv) -= P*Exp_msk1; 02009 goto cont; 02010 } 02011 #endif /*Sudden_Underflow*/ 02012 #endif /*Avoid_Underflow*/ 02013 adj *= ulp(dval(rv)); 02014 if (dsign) 02015 dval(rv) += adj; 02016 else 02017 dval(rv) -= adj; 02018 goto cont; 02019 } 02020 #endif /*Honor_FLT_ROUNDS*/ 02021 02022 if (i < 0) { 02023 /* Error is less than half an ulp -- check for 02024 * special case of mantissa a power of two. 02025 */ 02026 if (dsign || word1(rv) || word0(rv) & Bndry_mask 02027 #ifdef IEEE_Arith 02028 #ifdef Avoid_Underflow 02029 || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1 02030 #else 02031 || (word0(rv) & Exp_mask) <= Exp_msk1 02032 #endif 02033 #endif 02034 ) { 02035 #ifdef SET_INEXACT 02036 if (!delta->x[0] && delta->wds <= 1) 02037 inexact = 0; 02038 #endif 02039 break; 02040 } 02041 if (!delta->x[0] && delta->wds <= 1) { 02042 /* exact result */ 02043 #ifdef SET_INEXACT 02044 inexact = 0; 02045 #endif 02046 break; 02047 } 02048 delta = lshift(delta,Log2P); 02049 if (cmp(delta, bs) > 0) 02050 goto drop_down; 02051 break; 02052 } 02053 if (i == 0) { 02054 /* exactly half-way between */ 02055 if (dsign) { 02056 if ((word0(rv) & Bndry_mask1) == Bndry_mask1 02057 && word1(rv) == ( 02058 #ifdef Avoid_Underflow 02059 (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1) 02060 ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) : 02061 #endif 02062 0xffffffff)) { 02063 /*boundary case -- increment exponent*/ 02064 word0(rv) = (word0(rv) & Exp_mask) 02065 + Exp_msk1 02066 #ifdef IBM 02067 | Exp_msk1 >> 4 02068 #endif 02069 ; 02070 word1(rv) = 0; 02071 #ifdef Avoid_Underflow 02072 dsign = 0; 02073 #endif 02074 break; 02075 } 02076 } 02077 else if (!(word0(rv) & Bndry_mask) && !word1(rv)) { 02078 drop_down: 02079 /* boundary case -- decrement exponent */ 02080 #ifdef Sudden_Underflow /*{{*/ 02081 L = word0(rv) & Exp_mask; 02082 #ifdef IBM 02083 if (L < Exp_msk1) 02084 #else 02085 #ifdef Avoid_Underflow 02086 if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1)) 02087 #else 02088 if (L <= Exp_msk1) 02089 #endif /*Avoid_Underflow*/ 02090 #endif /*IBM*/ 02091 goto undfl; 02092 L -= Exp_msk1; 02093 #else /*Sudden_Underflow}{*/ 02094 #ifdef Avoid_Underflow 02095 if (scale) { 02096 L = word0(rv) & Exp_mask; 02097 if (L <= (2*P+1)*Exp_msk1) { 02098 if (L > (P+2)*Exp_msk1) 02099 /* round even ==> */ 02100 /* accept rv */ 02101 break; 02102 /* rv = smallest denormal */ 02103 goto undfl; 02104 } 02105 } 02106 #endif /*Avoid_Underflow*/ 02107 L = (word0(rv) & Exp_mask) - Exp_msk1; 02108 #endif /*Sudden_Underflow}}*/ 02109 word0(rv) = L | Bndry_mask1; 02110 word1(rv) = 0xffffffff; 02111 #ifdef IBM 02112 goto cont; 02113 #else 02114 break; 02115 #endif 02116 } 02117 #ifndef ROUND_BIASED 02118 if (!(word1(rv) & LSB)) 02119 break; 02120 #endif 02121 if (dsign) 02122 dval(rv) += ulp(dval(rv)); 02123 #ifndef ROUND_BIASED 02124 else { 02125 dval(rv) -= ulp(dval(rv)); 02126 #ifndef Sudden_Underflow 02127 if (!dval(rv)) 02128 goto undfl; 02129 #endif 02130 } 02131 #ifdef Avoid_Underflow 02132 dsign = 1 - dsign; 02133 #endif 02134 #endif 02135 break; 02136 } 02137 if ((aadj = ratio(delta, bs)) <= 2.) { 02138 if (dsign) 02139 aadj = aadj1 = 1.; 02140 else if (word1(rv) || word0(rv) & Bndry_mask) { 02141 #ifndef Sudden_Underflow 02142 if (word1(rv) == Tiny1 && !word0(rv)) 02143 goto undfl; 02144 #endif 02145 aadj = 1.; 02146 aadj1 = -1.; 02147 } 02148 else { 02149 /* special case -- power of FLT_RADIX to be */ 02150 /* rounded down... */ 02151 02152 if (aadj < 2./FLT_RADIX) 02153 aadj = 1./FLT_RADIX; 02154 else 02155 aadj *= 0.5; 02156 aadj1 = -aadj; 02157 } 02158 } 02159 else { 02160 aadj *= 0.5; 02161 aadj1 = dsign ? aadj : -aadj; 02162 #ifdef Check_FLT_ROUNDS 02163 switch(Rounding) { 02164 case 2: /* towards +infinity */ 02165 aadj1 -= 0.5; 02166 break; 02167 case 0: /* towards 0 */ 02168 case 3: /* towards -infinity */ 02169 aadj1 += 0.5; 02170 } 02171 #else 02172 if (Flt_Rounds == 0) 02173 aadj1 += 0.5; 02174 #endif /*Check_FLT_ROUNDS*/ 02175 } 02176 y = word0(rv) & Exp_mask; 02177 02178 /* Check for overflow */ 02179 02180 if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) { 02181 dval(rv0) = dval(rv); 02182 word0(rv) -= P*Exp_msk1; 02183 adj = aadj1 * ulp(dval(rv)); 02184 dval(rv) += adj; 02185 if ((word0(rv) & Exp_mask) >= 02186 Exp_msk1*(DBL_MAX_EXP+Bias-P)) { 02187 if (word0(rv0) == Big0 && word1(rv0) == Big1) 02188 goto ovfl; 02189 word0(rv) = Big0; 02190 word1(rv) = Big1; 02191 goto cont; 02192 } 02193 else 02194 word0(rv) += P*Exp_msk1; 02195 } 02196 else { 02197 #ifdef Avoid_Underflow 02198 if (scale && y <= 2*P*Exp_msk1) { 02199 if (aadj <= 0x7fffffff) { 02200 if ((z = (ULong)aadj) <= 0) 02201 z = 1; 02202 aadj = z; 02203 aadj1 = dsign ? aadj : -aadj; 02204 } 02205 dval(aadj2) = aadj1; 02206 word0(aadj2) += (2*P+1)*Exp_msk1 - y; 02207 aadj1 = dval(aadj2); 02208 } 02209 adj = aadj1 * ulp(dval(rv)); 02210 dval(rv) += adj; 02211 #else 02212 #ifdef Sudden_Underflow 02213 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) { 02214 dval(rv0) = dval(rv); 02215 word0(rv) += P*Exp_msk1; 02216 adj = aadj1 * ulp(dval(rv)); 02217 dval(rv) += adj; 02218 #ifdef IBM 02219 if ((word0(rv) & Exp_mask) < P*Exp_msk1) 02220 #else 02221 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) 02222 #endif 02223 { 02224 if (word0(rv0) == Tiny0 02225 && word1(rv0) == Tiny1) 02226 goto undfl; 02227 word0(rv) = Tiny0; 02228 word1(rv) = Tiny1; 02229 goto cont; 02230 } 02231 else 02232 word0(rv) -= P*Exp_msk1; 02233 } 02234 else { 02235 adj = aadj1 * ulp(dval(rv)); 02236 dval(rv) += adj; 02237 } 02238 #else /*Sudden_Underflow*/ 02239 /* Compute adj so that the IEEE rounding rules will 02240 * correctly round rv + adj in some half-way cases. 02241 * If rv * ulp(rv) is denormalized (i.e., 02242 * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid 02243 * trouble from bits lost to denormalization; 02244 * example: 1.2e-307 . 02245 */ 02246 if (y <= (P-1)*Exp_msk1 && aadj > 1.) { 02247 aadj1 = (double)(int)(aadj + 0.5); 02248 if (!dsign) 02249 aadj1 = -aadj1; 02250 } 02251 adj = aadj1 * ulp(dval(rv)); 02252 dval(rv) += adj; 02253 #endif /*Sudden_Underflow*/ 02254 #endif /*Avoid_Underflow*/ 02255 } 02256 z = word0(rv) & Exp_mask; 02257 #ifndef SET_INEXACT 02258 #ifdef Avoid_Underflow 02259 if (!scale) 02260 #endif 02261 if (y == z) { 02262 /* Can we stop now? */ 02263 L = (Long)aadj; 02264 aadj -= L; 02265 /* The tolerances below are conservative. */ 02266 if (dsign || word1(rv) || word0(rv) & Bndry_mask) { 02267 if (aadj < .4999999 || aadj > .5000001) 02268 break; 02269 } 02270 else if (aadj < .4999999/FLT_RADIX) 02271 break; 02272 } 02273 #endif 02274 cont: 02275 Bfree(bb); 02276 Bfree(bd); 02277 Bfree(bs); 02278 Bfree(delta); 02279 } 02280 #ifdef SET_INEXACT 02281 if (inexact) { 02282 if (!oldinexact) { 02283 word0(rv0) = Exp_1 + (70 << Exp_shift); 02284 word1(rv0) = 0; 02285 dval(rv0) += 1.; 02286 } 02287 } 02288 else if (!oldinexact) 02289 clear_inexact(); 02290 #endif 02291 #ifdef Avoid_Underflow 02292 if (scale) { 02293 word0(rv0) = Exp_1 - 2*P*Exp_msk1; 02294 word1(rv0) = 0; 02295 dval(rv) *= dval(rv0); 02296 #ifndef NO_ERRNO 02297 /* try to avoid the bug of testing an 8087 register value */ 02298 if (word0(rv) == 0 && word1(rv) == 0) 02299 errno = ERANGE; 02300 #endif 02301 } 02302 #endif /* Avoid_Underflow */ 02303 #ifdef SET_INEXACT 02304 if (inexact && !(word0(rv) & Exp_mask)) { 02305 /* set underflow bit */ 02306 dval(rv0) = 1e-300; 02307 dval(rv0) *= dval(rv0); 02308 } 02309 #endif 02310 retfree: 02311 Bfree(bb); 02312 Bfree(bd); 02313 Bfree(bs); 02314 Bfree(bd0); 02315 Bfree(delta); 02316 ret: 02317 if (se) 02318 *se = (char *)s; 02319 return sign ? -dval(rv) : dval(rv); 02320 } 02321 02322 static int 02323 quorem 02324 (Bigint *b, Bigint *S) 02325 { 02326 int n; 02327 ULong *bx, *bxe, q, *sx, *sxe; 02328 #ifdef ULLong 02329 ULLong borrow, carry, y, ys; 02330 #else 02331 ULong borrow, carry, y, ys; 02332 #ifdef Pack_32 02333 ULong si, z, zs; 02334 #endif 02335 #endif 02336 02337 n = S->wds; 02338 #ifdef DEBUG 02339 /*debug*/ if (b->wds > n) 02340 /*debug*/ Bug("oversize b in quorem"); 02341 #endif 02342 if (b->wds < n) 02343 return 0; 02344 sx = S->x; 02345 sxe = sx + --n; 02346 bx = b->x; 02347 bxe = bx + n; 02348 q = *bxe / (*sxe + 1); /* ensure q <= true quotient */ 02349 #ifdef DEBUG 02350 /*debug*/ if (q > 9) 02351 /*debug*/ Bug("oversized quotient in quorem"); 02352 #endif 02353 if (q) { 02354 borrow = 0; 02355 carry = 0; 02356 do { 02357 #ifdef ULLong 02358 ys = *sx++ * (ULLong)q + carry; 02359 carry = ys >> 32; 02360 y = *bx - (ys & FFFFFFFF) - borrow; 02361 borrow = y >> 32 & (ULong)1; 02362 *bx++ = (ULong)y & FFFFFFFF; 02363 #else 02364 #ifdef Pack_32 02365 si = *sx++; 02366 ys = (si & 0xffff) * q + carry; 02367 zs = (si >> 16) * q + (ys >> 16); 02368 carry = zs >> 16; 02369 y = (*bx & 0xffff) - (ys & 0xffff) - borrow; 02370 borrow = (y & 0x10000) >> 16; 02371 z = (*bx >> 16) - (zs & 0xffff) - borrow; 02372 borrow = (z & 0x10000) >> 16; 02373 Storeinc(bx, z, y); 02374 #else 02375 ys = *sx++ * q + carry; 02376 carry = ys >> 16; 02377 y = *bx - (ys & 0xffff) - borrow; 02378 borrow = (y & 0x10000) >> 16; 02379 *bx++ = y & 0xffff; 02380 #endif 02381 #endif 02382 } 02383 while(sx <= sxe); 02384 if (!*bxe) { 02385 bx = b->x; 02386 while(--bxe > bx && !*bxe) 02387 --n; 02388 b->wds = n; 02389 } 02390 } 02391 if (cmp(b, S) >= 0) { 02392 q++; 02393 borrow = 0; 02394 carry = 0; 02395 bx = b->x; 02396 sx = S->x; 02397 do { 02398 #ifdef ULLong 02399 ys = *sx++ + carry; 02400 carry = ys >> 32; 02401 y = *bx - (ys & FFFFFFFF) - borrow; 02402 borrow = y >> 32 & (ULong)1; 02403 *bx++ = (ULong)y & FFFFFFFF; 02404 #else 02405 #ifdef Pack_32 02406 si = *sx++; 02407 ys = (si & 0xffff) + carry; 02408 zs = (si >> 16) + (ys >> 16); 02409 carry = zs >> 16; 02410 y = (*bx & 0xffff) - (ys & 0xffff) - borrow; 02411 borrow = (y & 0x10000) >> 16; 02412 z = (*bx >> 16) - (zs & 0xffff) - borrow; 02413 borrow = (z & 0x10000) >> 16; 02414 Storeinc(bx, z, y); 02415 #else 02416 ys = *sx++ + carry; 02417 carry = ys >> 16; 02418 y = *bx - (ys & 0xffff) - borrow; 02419 borrow = (y & 0x10000) >> 16; 02420 *bx++ = y & 0xffff; 02421 #endif 02422 #endif 02423 } 02424 while(sx <= sxe); 02425 bx = b->x; 02426 bxe = bx + n; 02427 if (!*bxe) { 02428 while(--bxe > bx && !*bxe) 02429 --n; 02430 b->wds = n; 02431 } 02432 } 02433 return q; 02434 } 02435 02436 #ifndef MULTIPLE_THREADS 02437 static char *dtoa_result; 02438 #endif 02439 02440 static char * 02441 rv_alloc(int i) 02442 { 02443 int j, k, *r; 02444 02445 j = sizeof(ULong); 02446 for(k = 0; 02447 sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= (unsigned)i; 02448 j <<= 1) 02449 k++; 02450 r = (int*)Balloc(k); 02451 *r = k; 02452 return 02453 #ifndef MULTIPLE_THREADS 02454 dtoa_result = 02455 #endif 02456 (char *)(r+1); 02457 } 02458 02459 static char * 02460 nrv_alloc(CONST char *s, char **rve, int n) 02461 { 02462 char *rv, *t; 02463 02464 t = rv = rv_alloc(n); 02465 while((*t = *s++)) t++; 02466 if (rve) 02467 *rve = t; 02468 return rv; 02469 } 02470 02471 /* freedtoa(s) must be used to free values s returned by dtoa 02472 * when MULTIPLE_THREADS is #defined. It should be used in all cases, 02473 * but for consistency with earlier versions of dtoa, it is optional 02474 * when MULTIPLE_THREADS is not defined. 02475 */ 02476 02477 void 02478 freedtoa(char *s) 02479 { 02480 Bigint *b = (Bigint *)((int *)s - 1); 02481 b->maxwds = 1 << (b->k = *(int*)b); 02482 Bfree(b); 02483 #ifndef MULTIPLE_THREADS 02484 if (s == dtoa_result) 02485 dtoa_result = 0; 02486 #endif 02487 } 02488 02489 /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string. 02490 * 02491 * Inspired by "How to Print Floating-Point Numbers Accurately" by 02492 * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101]. 02493 * 02494 * Modifications: 02495 * 1. Rather than iterating, we use a simple numeric overestimate 02496 * to determine k = floor(log10(d)). We scale relevant 02497 * quantities using O(log2(k)) rather than O(k) multiplications. 02498 * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't 02499 * try to generate digits strictly left to right. Instead, we 02500 * compute with fewer bits and propagate the carry if necessary 02501 * when rounding the final digit up. This is often faster. 02502 * 3. Under the assumption that input will be rounded nearest, 02503 * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22. 02504 * That is, we allow equality in stopping tests when the 02505 * round-nearest rule will give the same floating-point value 02506 * as would satisfaction of the stopping test with strict 02507 * inequality. 02508 * 4. We remove common factors of powers of 2 from relevant 02509 * quantities. 02510 * 5. When converting floating-point integers less than 1e16, 02511 * we use floating-point arithmetic rather than resorting 02512 * to multiple-precision integers. 02513 * 6. When asked to produce fewer than 15 digits, we first try 02514 * to get by with floating-point arithmetic; we resort to 02515 * multiple-precision integer arithmetic only if we cannot 02516 * guarantee that the floating-point calculation has given 02517 * the correctly rounded result. For k requested digits and 02518 * "uniformly" distributed input, the probability is 02519 * something like 10^(k-15) that we must resort to the Long 02520 * calculation. 02521 */ 02522 02523 char * 02524 dtoa 02525 (double dd, int mode, int ndigits, int *decpt, int *sign, char **rve) 02526 { 02527 /* Arguments ndigits, decpt, sign are similar to those 02528 of ecvt and fcvt; trailing zeros are suppressed from 02529 the returned string. If not null, *rve is set to point 02530 to the end of the return value. If d is +-Infinity or NaN, 02531 then *decpt is set to 9999. 02532 02533 mode: 02534 0 ==> shortest string that yields d when read in 02535 and rounded to nearest. 02536 1 ==> like 0, but with Steele & White stopping rule; 02537 e.g. with IEEE P754 arithmetic , mode 0 gives 02538 1e23 whereas mode 1 gives 9.999999999999999e22. 02539 2 ==> max(1,ndigits) significant digits. This gives a 02540 return value similar to that of ecvt, except 02541 that trailing zeros are suppressed. 02542 3 ==> through ndigits past the decimal point. This 02543 gives a return value similar to that from fcvt, 02544 except that trailing zeros are suppressed, and 02545 ndigits can be negative. 02546 4,5 ==> similar to 2 and 3, respectively, but (in 02547 round-nearest mode) with the tests of mode 0 to 02548 possibly return a shorter string that rounds to d. 02549 With IEEE arithmetic and compilation with 02550 -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same 02551 as modes 2 and 3 when FLT_ROUNDS != 1. 02552 6-9 ==> Debugging modes similar to mode - 4: don't try 02553 fast floating-point estimate (if applicable). 02554 02555 Values of mode other than 0-9 are treated as mode 0. 02556 02557 Sufficient space is allocated to the return value 02558 to hold the suppressed trailing zeros. 02559 */ 02560 02561 int bbits, b2, b5, be, dig, i, ieps, ilim = 0, ilim0, ilim1 = 0, 02562 j, j1, k, k0, k_check, leftright, m2, m5, s2, s5, 02563 spec_case, try_quick; 02564 Long L; 02565 #ifndef Sudden_Underflow 02566 int denorm; 02567 ULong x; 02568 #endif 02569 Bigint *b, *b1, *delta, *mlo = NULL, *mhi, *S; 02570 U d, d2, eps; 02571 double ds; 02572 char *s, *s0; 02573 #ifdef Honor_FLT_ROUNDS 02574 int rounding; 02575 #endif 02576 #ifdef SET_INEXACT 02577 int inexact, oldinexact; 02578 #endif 02579 02580 #ifndef MULTIPLE_THREADS 02581 if (dtoa_result) { 02582 freedtoa(dtoa_result); 02583 dtoa_result = 0; 02584 } 02585 #endif 02586 02587 dval(d) = dd; 02588 if (word0(d) & Sign_bit) { 02589 /* set sign for everything, including 0's and NaNs */ 02590 *sign = 1; 02591 word0(d) &= ~Sign_bit; /* clear sign bit */ 02592 } 02593 else 02594 *sign = 0; 02595 02596 #if defined(IEEE_Arith) + defined(VAX) 02597 #ifdef IEEE_Arith 02598 if ((word0(d) & Exp_mask) == Exp_mask) 02599 #else 02600 if (word0(d) == 0x8000) 02601 #endif 02602 { 02603 /* Infinity or NaN */ 02604 *decpt = 9999; 02605 #ifdef IEEE_Arith 02606 if (!word1(d) && !(word0(d) & 0xfffff)) 02607 return nrv_alloc("Infinity", rve, 8); 02608 #endif 02609 return nrv_alloc("NaN", rve, 3); 02610 } 02611 #endif 02612 #ifdef IBM 02613 dval(d) += 0; /* normalize */ 02614 #endif 02615 if (!dval(d)) { 02616 *decpt = 1; 02617 return nrv_alloc("0", rve, 1); 02618 } 02619 02620 #ifdef SET_INEXACT 02621 try_quick = oldinexact = get_inexact(); 02622 inexact = 1; 02623 #endif 02624 #ifdef Honor_FLT_ROUNDS 02625 if ((rounding = Flt_Rounds) >= 2) { 02626 if (*sign) 02627 rounding = rounding == 2 ? 0 : 2; 02628 else 02629 if (rounding != 2) 02630 rounding = 0; 02631 } 02632 #endif 02633 02634 b = d2b(dval(d), &be, &bbits); 02635 #ifdef Sudden_Underflow 02636 i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)); 02637 #else 02638 if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) { 02639 #endif 02640 dval(d2) = dval(d); 02641 word0(d2) &= Frac_mask1; 02642 word0(d2) |= Exp_11; 02643 #ifdef IBM 02644 if (j = 11 - hi0bits(word0(d2) & Frac_mask)) 02645 dval(d2) /= 1 << j; 02646 #endif 02647 02648 /* log(x) ~=~ log(1.5) + (x-1.5)/1.5 02649 * log10(x) = log(x) / log(10) 02650 * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10)) 02651 * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2) 02652 * 02653 * This suggests computing an approximation k to log10(d) by 02654 * 02655 * k = (i - Bias)*0.301029995663981 02656 * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 ); 02657 * 02658 * We want k to be too large rather than too small. 02659 * The error in the first-order Taylor series approximation 02660 * is in our favor, so we just round up the constant enough 02661 * to compensate for any error in the multiplication of 02662 * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077, 02663 * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14, 02664 * adding 1e-13 to the constant term more than suffices. 02665 * Hence we adjust the constant term to 0.1760912590558. 02666 * (We could get a more accurate k by invoking log10, 02667 * but this is probably not worthwhile.) 02668 */ 02669 02670 i -= Bias; 02671 #ifdef IBM 02672 i <<= 2; 02673 i += j; 02674 #endif 02675 #ifndef Sudden_Underflow 02676 denorm = 0; 02677 } 02678 else { 02679 /* d is denormalized */ 02680 02681 i = bbits + be + (Bias + (P-1) - 1); 02682 x = i > 32 ? word0(d) << 64 - i | word1(d) >> i - 32 02683 : word1(d) << 32 - i; 02684 dval(d2) = x; 02685 word0(d2) -= 31*Exp_msk1; /* adjust exponent */ 02686 i -= (Bias + (P-1) - 1) + 1; 02687 denorm = 1; 02688 } 02689 #endif 02690 ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981; 02691 k = (int)ds; 02692 if (ds < 0. && ds != k) 02693 k--; /* want k = floor(ds) */ 02694 k_check = 1; 02695 if (k >= 0 && k <= Ten_pmax) { 02696 if (dval(d) < tens[k]) 02697 k--; 02698 k_check = 0; 02699 } 02700 j = bbits - i - 1; 02701 if (j >= 0) { 02702 b2 = 0; 02703 s2 = j; 02704 } 02705 else { 02706 b2 = -j; 02707 s2 = 0; 02708 } 02709 if (k >= 0) { 02710 b5 = 0; 02711 s5 = k; 02712 s2 += k; 02713 } 02714 else { 02715 b2 -= k; 02716 b5 = -k; 02717 s5 = 0; 02718 } 02719 if (mode < 0 || mode > 9) 02720 mode = 0; 02721 02722 #ifndef SET_INEXACT 02723 #ifdef Check_FLT_ROUNDS 02724 try_quick = Rounding == 1; 02725 #else 02726 try_quick = 1; 02727 #endif 02728 #endif /*SET_INEXACT*/ 02729 02730 if (mode > 5) { 02731 mode -= 4; 02732 try_quick = 0; 02733 } 02734 leftright = 1; 02735 switch(mode) { 02736 case 0: 02737 case 1: 02738 ilim = ilim1 = -1; 02739 i = 18; 02740 ndigits = 0; 02741 break; 02742 case 2: 02743 leftright = 0; 02744 /* no break */ 02745 case 4: 02746 if (ndigits <= 0) 02747 ndigits = 1; 02748 ilim = ilim1 = i = ndigits; 02749 break; 02750 case 3: 02751 leftright = 0; 02752 /* no break */ 02753 case 5: 02754 i = ndigits + k + 1; 02755 ilim = i; 02756 ilim1 = i - 1; 02757 if (i <= 0) 02758 i = 1; 02759 } 02760 s = s0 = rv_alloc(i); 02761 02762 #ifdef Honor_FLT_ROUNDS 02763 if (mode > 1 && rounding != 1) 02764 leftright = 0; 02765 #endif 02766 02767 if (ilim >= 0 && ilim <= Quick_max && try_quick) { 02768 02769 /* Try to get by with floating-point arithmetic. */ 02770 02771 i = 0; 02772 dval(d2) = dval(d); 02773 k0 = k; 02774 ilim0 = ilim; 02775 ieps = 2; /* conservative */ 02776 if (k > 0) { 02777 ds = tens[k&0xf]; 02778 j = k >> 4; 02779 if (j & Bletch) { 02780 /* prevent overflows */ 02781 j &= Bletch - 1; 02782 dval(d) /= bigtens[n_bigtens-1]; 02783 ieps++; 02784 } 02785 for(; j; j >>= 1, i++) 02786 if (j & 1) { 02787 ieps++; 02788 ds *= bigtens[i]; 02789 } 02790 dval(d) /= ds; 02791 } 02792 else if ((j1 = -k)) { 02793 dval(d) *= tens[j1 & 0xf]; 02794 for(j = j1 >> 4; j; j >>= 1, i++) 02795 if (j & 1) { 02796 ieps++; 02797 dval(d) *= bigtens[i]; 02798 } 02799 } 02800 if (k_check && dval(d) < 1. && ilim > 0) { 02801 if (ilim1 <= 0) 02802 goto fast_failed; 02803 ilim = ilim1; 02804 k--; 02805 dval(d) *= 10.; 02806 ieps++; 02807 } 02808 dval(eps) = ieps*dval(d) + 7.; 02809 word0(eps) -= (P-1)*Exp_msk1; 02810 if (ilim == 0) { 02811 S = mhi = 0; 02812 dval(d) -= 5.; 02813 if (dval(d) > dval(eps)) 02814 goto one_digit; 02815 if (dval(d) < -dval(eps)) 02816 goto no_digits; 02817 goto fast_failed; 02818 } 02819 #ifndef No_leftright 02820 if (leftright) { 02821 /* Use Steele & White method of only 02822 * generating digits needed. 02823 */ 02824 dval(eps) = 0.5/tens[ilim-1] - dval(eps); 02825 for(i = 0;;) { 02826 L = (long int)dval(d); 02827 dval(d) -= L; 02828 *s++ = '0' + (int)L; 02829 if (dval(d) < dval(eps)) 02830 goto ret1; 02831 if (1. - dval(d) < dval(eps)) 02832 goto bump_up; 02833 if (++i >= ilim) 02834 break; 02835 dval(eps) *= 10.; 02836 dval(d) *= 10.; 02837 } 02838 } 02839 else { 02840 #endif 02841 /* Generate ilim digits, then fix them up. */ 02842 dval(eps) *= tens[ilim-1]; 02843 for(i = 1;; i++, dval(d) *= 10.) { 02844 L = (Long)(dval(d)); 02845 if (!(dval(d) -= L)) 02846 ilim = i; 02847 *s++ = '0' + (int)L; 02848 if (i == ilim) { 02849 if (dval(d) > 0.5 + dval(eps)) 02850 goto bump_up; 02851 else if (dval(d) < 0.5 - dval(eps)) { 02852 while(*--s == '0') 02853 ; 02854 s++; 02855 goto ret1; 02856 } 02857 break; 02858 } 02859 } 02860 #ifndef No_leftright 02861 } 02862 #endif 02863 fast_failed: 02864 s = s0; 02865 dval(d) = dval(d2); 02866 k = k0; 02867 ilim = ilim0; 02868 } 02869 02870 /* Do we have a "small" integer? */ 02871 02872 if (be >= 0 && k <= Int_max) { 02873 /* Yes. */ 02874 ds = tens[k]; 02875 if (ndigits < 0 && ilim <= 0) { 02876 S = mhi = 0; 02877 if (ilim < 0 || dval(d) <= 5*ds) 02878 goto no_digits; 02879 goto one_digit; 02880 } 02881 for(i = 1;; i++, dval(d) *= 10.) { 02882 L = (Long)(dval(d) / ds); 02883 dval(d) -= L*ds; 02884 #ifdef Check_FLT_ROUNDS 02885 /* If FLT_ROUNDS == 2, L will usually be high by 1 */ 02886 if (dval(d) < 0) { 02887 L--; 02888 dval(d) += ds; 02889 } 02890 #endif 02891 *s++ = '0' + (int)L; 02892 if (!dval(d)) { 02893 #ifdef SET_INEXACT 02894 inexact = 0; 02895 #endif 02896 break; 02897 } 02898 if (i == ilim) { 02899 #ifdef Honor_FLT_ROUNDS 02900 if (mode > 1) 02901 switch(rounding) { 02902 case 0: goto ret1; 02903 case 2: goto bump_up; 02904 } 02905 #endif 02906 dval(d) += dval(d); 02907 if (dval(d) > ds || dval(d) == ds && L & 1) { 02908 bump_up: 02909 while(*--s == '9') 02910 if (s == s0) { 02911 k++; 02912 *s = '0'; 02913 break; 02914 } 02915 ++*s++; 02916 } 02917 break; 02918 } 02919 } 02920 goto ret1; 02921 } 02922 02923 m2 = b2; 02924 m5 = b5; 02925 mhi = mlo = 0; 02926 if (leftright) { 02927 i = 02928 #ifndef Sudden_Underflow 02929 denorm ? be + (Bias + (P-1) - 1 + 1) : 02930 #endif 02931 #ifdef IBM 02932 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3); 02933 #else 02934 1 + P - bbits; 02935 #endif 02936 b2 += i; 02937 s2 += i; 02938 mhi = i2b(1); 02939 } 02940 if (m2 > 0 && s2 > 0) { 02941 i = m2 < s2 ? m2 : s2; 02942 b2 -= i; 02943 m2 -= i; 02944 s2 -= i; 02945 } 02946 if (b5 > 0) { 02947 if (leftright) { 02948 if (m5 > 0) { 02949 mhi = pow5mult(mhi, m5); 02950 b1 = mult(mhi, b); 02951 Bfree(b); 02952 b = b1; 02953 } 02954 if ((j = b5 - m5)) 02955 b = pow5mult(b, j); 02956 } 02957 else 02958 b = pow5mult(b, b5); 02959 } 02960 S = i2b(1); 02961 if (s5 > 0) 02962 S = pow5mult(S, s5); 02963 02964 /* Check for special case that d is a normalized power of 2. */ 02965 02966 spec_case = 0; 02967 if ((mode < 2 || leftright) 02968 #ifdef Honor_FLT_ROUNDS 02969 && rounding == 1 02970 #endif 02971 ) { 02972 if (!word1(d) && !(word0(d) & Bndry_mask) 02973 #ifndef Sudden_Underflow 02974 && word0(d) & (Exp_mask & ~Exp_msk1) 02975 #endif 02976 ) { 02977 /* The special case */ 02978 b2 += Log2P; 02979 s2 += Log2P; 02980 spec_case = 1; 02981 } 02982 } 02983 02984 /* Arrange for convenient computation of quotients: 02985 * shift left if necessary so divisor has 4 leading 0 bits. 02986 * 02987 * Perhaps we should just compute leading 28 bits of S once 02988 * and for all and pass them and a shift to quorem, so it 02989 * can do shifts and ors to compute the numerator for q. 02990 */ 02991 #ifdef Pack_32 02992 if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f)) 02993 i = 32 - i; 02994 #else 02995 if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf) 02996 i = 16 - i; 02997 #endif 02998 if (i > 4) { 02999 i -= 4; 03000 b2 += i; 03001 m2 += i; 03002 s2 += i; 03003 } 03004 else if (i < 4) { 03005 i += 28; 03006 b2 += i; 03007 m2 += i; 03008 s2 += i; 03009 } 03010 if (b2 > 0) 03011 b = lshift(b, b2); 03012 if (s2 > 0) 03013 S = lshift(S, s2); 03014 if (k_check) { 03015 if (cmp(b,S) < 0) { 03016 k--; 03017 b = multadd(b, 10, 0); /* we botched the k estimate */ 03018 if (leftright) 03019 mhi = multadd(mhi, 10, 0); 03020 ilim = ilim1; 03021 } 03022 } 03023 if (ilim <= 0 && (mode == 3 || mode == 5)) { 03024 if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) { 03025 /* no digits, fcvt style */ 03026 no_digits: 03027 k = -1 - ndigits; 03028 goto ret; 03029 } 03030 one_digit: 03031 *s++ = '1'; 03032 k++; 03033 goto ret; 03034 } 03035 if (leftright) { 03036 if (m2 > 0) 03037 mhi = lshift(mhi, m2); 03038 03039 /* Compute mlo -- check for special case 03040 * that d is a normalized power of 2. 03041 */ 03042 03043 mlo = mhi; 03044 if (spec_case) { 03045 mhi = Balloc(mhi->k); 03046 Bcopy(mhi, mlo); 03047 mhi = lshift(mhi, Log2P); 03048 } 03049 03050 for(i = 1;;i++) { 03051 dig = quorem(b,S) + '0'; 03052 /* Do we yet have the shortest decimal string 03053 * that will round to d? 03054 */ 03055 j = cmp(b, mlo); 03056 delta = diff(S, mhi); 03057 j1 = delta->sign ? 1 : cmp(b, delta); 03058 Bfree(delta); 03059 #ifndef ROUND_BIASED 03060 if (j1 == 0 && mode != 1 && !(word1(d) & 1) 03061 #ifdef Honor_FLT_ROUNDS 03062 && rounding >= 1 03063 #endif 03064 ) { 03065 if (dig == '9') 03066 goto round_9_up; 03067 if (j > 0) 03068 dig++; 03069 #ifdef SET_INEXACT 03070 else if (!b->x[0] && b->wds <= 1) 03071 inexact = 0; 03072 #endif 03073 *s++ = dig; 03074 goto ret; 03075 } 03076 #endif 03077 if (j < 0 || j == 0 && mode != 1 03078 #ifndef ROUND_BIASED 03079 && !(word1(d) & 1) 03080 #endif 03081 ) { 03082 if (!b->x[0] && b->wds <= 1) { 03083 #ifdef SET_INEXACT 03084 inexact = 0; 03085 #endif 03086 goto accept_dig; 03087 } 03088 #ifdef Honor_FLT_ROUNDS 03089 if (mode > 1) 03090 switch(rounding) { 03091 case 0: goto accept_dig; 03092 case 2: goto keep_dig; 03093 } 03094 #endif /*Honor_FLT_ROUNDS*/ 03095 if (j1 > 0) { 03096 b = lshift(b, 1); 03097 j1 = cmp(b, S); 03098 if ((j1 > 0 || j1 == 0 && dig & 1) 03099 && dig++ == '9') 03100 goto round_9_up; 03101 } 03102 accept_dig: 03103 *s++ = dig; 03104 goto ret; 03105 } 03106 if (j1 > 0) { 03107 #ifdef Honor_FLT_ROUNDS 03108 if (!rounding) 03109 goto accept_dig; 03110 #endif 03111 if (dig == '9') { /* possible if i == 1 */ 03112 round_9_up: 03113 *s++ = '9'; 03114 goto roundoff; 03115 } 03116 *s++ = dig + 1; 03117 goto ret; 03118 } 03119 #ifdef Honor_FLT_ROUNDS 03120 keep_dig: 03121 #endif 03122 *s++ = dig; 03123 if (i == ilim) 03124 break; 03125 b = multadd(b, 10, 0); 03126 if (mlo == mhi) 03127 mlo = mhi = multadd(mhi, 10, 0); 03128 else { 03129 mlo = multadd(mlo, 10, 0); 03130 mhi = multadd(mhi, 10, 0); 03131 } 03132 } 03133 } 03134 else 03135 for(i = 1;; i++) { 03136 *s++ = dig = quorem(b,S) + '0'; 03137 if (!b->x[0] && b->wds <= 1) { 03138 #ifdef SET_INEXACT 03139 inexact = 0; 03140 #endif 03141 goto ret; 03142 } 03143 if (i >= ilim) 03144 break; 03145 b = multadd(b, 10, 0); 03146 } 03147 03148 /* Round off last digit */ 03149 03150 #ifdef Honor_FLT_ROUNDS 03151 switch(rounding) { 03152 case 0: goto trimzeros; 03153 case 2: goto roundoff; 03154 } 03155 #endif 03156 b = lshift(b, 1); 03157 j = cmp(b, S); 03158 if (j > 0 || j == 0 && dig & 1) { 03159 roundoff: 03160 while(*--s == '9') 03161 if (s == s0) { 03162 k++; 03163 *s++ = '1'; 03164 goto ret; 03165 } 03166 ++*s++; 03167 } 03168 else { 03169 #ifdef Honor_FLT_ROUNDS 03170 trimzeros: 03171 #endif 03172 while(*--s == '0') 03173 ; 03174 s++; 03175 } 03176 ret: 03177 Bfree(S); 03178 if (mhi) { 03179 if (mlo && mlo != mhi) 03180 Bfree(mlo); 03181 Bfree(mhi); 03182 } 03183 ret1: 03184 #ifdef SET_INEXACT 03185 if (inexact) { 03186 if (!oldinexact) { 03187 word0(d) = Exp_1 + (70 << Exp_shift); 03188 word1(d) = 0; 03189 dval(d) += 1.; 03190 } 03191 } 03192 else if (!oldinexact) 03193 clear_inexact(); 03194 #endif 03195 Bfree(b); 03196 *s = 0; 03197 *decpt = k + 1; 03198 if (rve) 03199 *rve = s; 03200 return s0; 03201 } 03202 #ifdef __cplusplus 03203 } 03204 #endif