1 | /**************************************************************** |
2 | * |
3 | * The author of this software is David M. Gay. |
4 | * |
5 | * Copyright (c) 1991, 2000, 2001 by Lucent Technologies. |
6 | * |
7 | * Permission to use, copy, modify, and distribute this software for any |
8 | * purpose without fee is hereby granted, provided that this entire notice |
9 | * is included in all copies of any software which is or includes a copy |
10 | * or modification of this software and in all copies of the supporting |
11 | * documentation for such software. |
12 | * |
13 | * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED |
14 | * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY |
15 | * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY |
16 | * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE. |
17 | * |
18 | ***************************************************************/ |
19 | |
20 | /* Please send bug reports to |
21 | David M. Gay |
22 | Bell Laboratories, Room 2C-463 |
23 | 600 Mountain Avenue |
24 | Murray Hill, NJ 07974-0636 |
25 | U.S.A. |
26 | dmg@bell-labs.com |
27 | */ |
28 | |
29 | /* On a machine with IEEE extended-precision registers, it is |
30 | * necessary to specify double-precision (53-bit) rounding precision |
31 | * before invoking strtod or dtoa. If the machine uses (the equivalent |
32 | * of) Intel 80x87 arithmetic, the call |
33 | * _control87(PC_53, MCW_PC); |
34 | * does this with many compilers. Whether this or another call is |
35 | * appropriate depends on the compiler; for this to work, it may be |
36 | * necessary to #include "float.h" or another system-dependent header |
37 | * file. |
38 | */ |
39 | |
40 | /* strtod for IEEE-, VAX-, and IBM-arithmetic machines. |
41 | * |
42 | * This strtod returns a nearest machine number to the input decimal |
43 | * string (or sets errno to ERANGE). With IEEE arithmetic, ties are |
44 | * broken by the IEEE round-even rule. Otherwise ties are broken by |
45 | * biased rounding (add half and chop). |
46 | * |
47 | * Inspired loosely by William D. Clinger's paper "How to Read Floating |
48 | * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101]. |
49 | * |
50 | * Modifications: |
51 | * |
52 | * 1. We only require IEEE, IBM, or VAX double-precision |
53 | * arithmetic (not IEEE double-extended). |
54 | * 2. We get by with floating-point arithmetic in a case that |
55 | * Clinger missed -- when we're computing d * 10^n |
56 | * for a small integer d and the integer n is not too |
57 | * much larger than 22 (the maximum integer k for which |
58 | * we can represent 10^k exactly), we may be able to |
59 | * compute (d*10^k) * 10^(e-k) with just one roundoff. |
60 | * 3. Rather than a bit-at-a-time adjustment of the binary |
61 | * result in the hard case, we use floating-point |
62 | * arithmetic to determine the adjustment to within |
63 | * one bit; only in really hard cases do we need to |
64 | * compute a second residual. |
65 | * 4. Because of 3., we don't need a large table of powers of 10 |
66 | * for ten-to-e (just some small tables, e.g. of 10^k |
67 | * for 0 <= k <= 22). |
68 | */ |
69 | |
70 | /* |
71 | * #define IEEE_8087 for IEEE-arithmetic machines where the least |
72 | * significant byte has the lowest address. |
73 | * #define IEEE_MC68k for IEEE-arithmetic machines where the most |
74 | * significant byte has the lowest address. |
75 | * #define Long int on machines with 32-bit ints and 64-bit longs. |
76 | * #define IBM for IBM mainframe-style floating-point arithmetic. |
77 | * #define VAX for VAX-style floating-point arithmetic (D_floating). |
78 | * #define No_leftright to omit left-right logic in fast floating-point |
79 | * computation of dtoa. |
80 | * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3 |
81 | * and strtod and dtoa should round accordingly. |
82 | * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3 |
83 | * and Honor_FLT_ROUNDS is not #defined. |
84 | * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines |
85 | * that use extended-precision instructions to compute rounded |
86 | * products and quotients) with IBM. |
87 | * #define ROUND_BIASED for IEEE-format with biased rounding. |
88 | * #define Inaccurate_Divide for IEEE-format with correctly rounded |
89 | * products but inaccurate quotients, e.g., for Intel i860. |
90 | * #define NO_LONG_LONG on machines that do not have a "long long" |
91 | * integer type (of >= 64 bits). On such machines, you can |
92 | * #define Just_16 to store 16 bits per 32-bit Long when doing |
93 | * high-precision integer arithmetic. Whether this speeds things |
94 | * up or slows things down depends on the machine and the number |
95 | * being converted. If long long is available and the name is |
96 | * something other than "long long", #define Llong to be the name, |
97 | * and if "unsigned Llong" does not work as an unsigned version of |
98 | * Llong, #define #ULLong to be the corresponding unsigned type. |
99 | * #define KR_headers for old-style C function headers. |
100 | * #define Bad_float_h if your system lacks a float.h or if it does not |
101 | * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP, |
102 | * FLT_RADIX, FLT_ROUNDS, and DBL_MAX. |
103 | * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n) |
104 | * if memory is available and otherwise does something you deem |
105 | * appropriate. If MALLOC is undefined, malloc will be invoked |
106 | * directly -- and assumed always to succeed. |
107 | * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making |
108 | * memory allocations from a private pool of memory when possible. |
109 | * When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes, |
110 | * unless #defined to be a different length. This default length |
111 | * suffices to get rid of MALLOC calls except for unusual cases, |
112 | * such as decimal-to-binary conversion of a very long string of |
113 | * digits. The longest string dtoa can return is about 751 bytes |
114 | * long. For conversions by strtod of strings of 800 digits and |
115 | * all dtoa conversions in single-threaded executions with 8-byte |
116 | * pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte |
117 | * pointers, PRIVATE_MEM >= 7112 appears adequate. |
118 | * #define INFNAN_CHECK on IEEE systems to cause strtod to check for |
119 | * Infinity and NaN (case insensitively). On some systems (e.g., |
120 | * some HP systems), it may be necessary to #define NAN_WORD0 |
121 | * appropriately -- to the most significant word of a quiet NaN. |
122 | * (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.) |
123 | * When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined, |
124 | * strtod also accepts (case insensitively) strings of the form |
125 | * NaN(x), where x is a string of hexadecimal digits and spaces; |
126 | * if there is only one string of hexadecimal digits, it is taken |
127 | * for the 52 fraction bits of the resulting NaN; if there are two |
128 | * or more strings of hex digits, the first is for the high 20 bits, |
129 | * the second and subsequent for the low 32 bits, with intervening |
130 | * white space ignored; but if this results in none of the 52 |
131 | * fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0 |
132 | * and NAN_WORD1 are used instead. |
133 | * #define MULTIPLE_THREADS if the system offers preemptively scheduled |
134 | * multiple threads. In this case, you must provide (or suitably |
135 | * #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed |
136 | * by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed |
137 | * in pow5mult, ensures lazy evaluation of only one copy of high |
138 | * powers of 5; omitting this lock would introduce a small |
139 | * probability of wasting memory, but would otherwise be harmless.) |
140 | * You must also invoke freedtoa(s) to free the value s returned by |
141 | * dtoa. You may do so whether or not MULTIPLE_THREADS is #defined. |
142 | * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that |
143 | * avoids underflows on inputs whose result does not underflow. |
144 | * If you #define NO_IEEE_Scale on a machine that uses IEEE-format |
145 | * floating-point numbers and flushes underflows to zero rather |
146 | * than implementing gradual underflow, then you must also #define |
147 | * Sudden_Underflow. |
148 | * #define YES_ALIAS to permit aliasing certain double values with |
149 | * arrays of ULongs. This leads to slightly better code with |
150 | * some compilers and was always used prior to 19990916, but it |
151 | * is not strictly legal and can cause trouble with aggressively |
152 | * optimizing compilers (e.g., gcc 2.95.1 under -O2). |
153 | * #define USE_LOCALE to use the current locale's decimal_point value. |
154 | * #define SET_INEXACT if IEEE arithmetic is being used and extra |
155 | * computation should be done to set the inexact flag when the |
156 | * result is inexact and avoid setting inexact when the result |
157 | * is exact. In this case, dtoa.c must be compiled in |
158 | * an environment, perhaps provided by #include "dtoa.c" in a |
159 | * suitable wrapper, that defines two functions, |
160 | * int get_inexact(void); |
161 | * void clear_inexact(void); |
162 | * such that get_inexact() returns a nonzero value if the |
163 | * inexact bit is already set, and clear_inexact() sets the |
164 | * inexact bit to 0. When SET_INEXACT is #defined, strtod |
165 | * also does extra computations to set the underflow and overflow |
166 | * flags when appropriate (i.e., when the result is tiny and |
167 | * inexact or when it is a numeric value rounded to +-infinity). |
168 | * #define NO_ERRNO if strtod should not assign errno = ERANGE when |
169 | * the result overflows to +-Infinity or underflows to 0. |
170 | */ |
171 | |
172 | #include "dtoa.h" |
173 | #include <config-kjs.h> |
174 | |
175 | #include "global.h" |
176 | |
177 | #if PLATFORM(BIG_ENDIAN) |
178 | #define IEEE_MC68k |
179 | #else |
180 | #define IEEE_8087 |
181 | #endif |
182 | #define INFNAN_CHECK |
183 | |
184 | |
185 | |
186 | #ifndef Long |
187 | #define Long int |
188 | #endif |
189 | #ifndef ULong |
190 | typedef unsigned Long ULong; |
191 | #endif |
192 | |
193 | #ifdef DEBUG |
194 | #include <stdio.h> |
195 | #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);} |
196 | #endif |
197 | |
198 | #include <stdlib.h> |
199 | #include <string.h> |
200 | |
201 | #ifdef USE_LOCALE |
202 | #include <locale.h> |
203 | #endif |
204 | |
205 | #ifdef MALLOC |
206 | extern void *MALLOC(size_t); |
207 | #else |
208 | #define MALLOC malloc |
209 | #endif |
210 | |
211 | #ifndef Omit_Private_Memory |
212 | #ifndef PRIVATE_MEM |
213 | #define PRIVATE_MEM 2304 |
214 | #endif |
215 | #define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double)) |
216 | static double private_mem[PRIVATE_mem], *pmem_next = private_mem; |
217 | #endif |
218 | |
219 | #undef IEEE_Arith |
220 | #undef Avoid_Underflow |
221 | #ifdef IEEE_MC68k |
222 | #define IEEE_Arith |
223 | #endif |
224 | #ifdef IEEE_8087 |
225 | #define IEEE_Arith |
226 | #endif |
227 | |
228 | #include <errno.h> |
229 | |
230 | #ifdef Bad_float_h |
231 | |
232 | #ifdef IEEE_Arith |
233 | #define DBL_DIG 15 |
234 | #define DBL_MAX_10_EXP 308 |
235 | #define DBL_MAX_EXP 1024 |
236 | #define FLT_RADIX 2 |
237 | #endif /*IEEE_Arith*/ |
238 | |
239 | #ifdef IBM |
240 | #define DBL_DIG 16 |
241 | #define DBL_MAX_10_EXP 75 |
242 | #define DBL_MAX_EXP 63 |
243 | #define FLT_RADIX 16 |
244 | #define DBL_MAX 7.2370055773322621e+75 |
245 | #endif |
246 | |
247 | #ifdef VAX |
248 | #define DBL_DIG 16 |
249 | #define DBL_MAX_10_EXP 38 |
250 | #define DBL_MAX_EXP 127 |
251 | #define FLT_RADIX 2 |
252 | #define DBL_MAX 1.7014118346046923e+38 |
253 | #endif |
254 | |
255 | #ifndef LONG_MAX |
256 | #define LONG_MAX 2147483647 |
257 | #endif |
258 | |
259 | #else /* ifndef Bad_float_h */ |
260 | #include <float.h> |
261 | #endif /* Bad_float_h */ |
262 | |
263 | #ifndef __MATH_H__ |
264 | #include <math.h> |
265 | #endif |
266 | |
267 | #define strtod kjs_strtod |
268 | #define dtoa kjs_dtoa |
269 | #define freedtoa kjs_freedtoa |
270 | |
271 | #ifdef __cplusplus |
272 | extern "C" { |
273 | #endif |
274 | |
275 | #ifndef CONST |
276 | #define CONST const |
277 | #endif |
278 | |
279 | #if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1 |
280 | Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined. |
281 | #endif |
282 | |
283 | typedef union { double d; ULong L[2]; } U; |
284 | |
285 | #define dval(x) (x).d |
286 | #ifdef IEEE_8087 |
287 | #define word0(x) (x).L[1] |
288 | #define word1(x) (x).L[0] |
289 | #else |
290 | #define word0(x) (x).L[0] |
291 | #define word1(x) (x).L[1] |
292 | #endif |
293 | |
294 | /* The following definition of Storeinc is appropriate for MIPS processors. |
295 | * An alternative that might be better on some machines is |
296 | */ |
297 | #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff) |
298 | |
299 | /* #define P DBL_MANT_DIG */ |
300 | /* Ten_pmax = floor(P*log(2)/log(5)) */ |
301 | /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */ |
302 | /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */ |
303 | /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */ |
304 | |
305 | #ifdef IEEE_Arith |
306 | #define Exp_shift 20 |
307 | #define Exp_shift1 20 |
308 | #define Exp_msk1 0x100000 |
309 | #define Exp_msk11 0x100000 |
310 | #define Exp_mask 0x7ff00000 |
311 | #define P 53 |
312 | #define Bias 1023 |
313 | #define Emin (-1022) |
314 | #define Exp_1 0x3ff00000 |
315 | #define Exp_11 0x3ff00000 |
316 | #define Ebits 11 |
317 | #define Frac_mask 0xfffff |
318 | #define Frac_mask1 0xfffff |
319 | #define Ten_pmax 22 |
320 | #define Bletch 0x10 |
321 | #define Bndry_mask 0xfffff |
322 | #define Bndry_mask1 0xfffff |
323 | #define LSB 1 |
324 | #define Sign_bit 0x80000000 |
325 | #define Log2P 1 |
326 | #define Tiny0 0 |
327 | #define Tiny1 1 |
328 | #define Quick_max 14 |
329 | #define Int_max 14 |
330 | #ifndef NO_IEEE_Scale |
331 | #define Avoid_Underflow |
332 | #ifdef Flush_Denorm /* debugging option */ |
333 | #undef Sudden_Underflow |
334 | #endif |
335 | #endif |
336 | |
337 | #ifndef Flt_Rounds |
338 | #ifdef FLT_ROUNDS |
339 | #define Flt_Rounds FLT_ROUNDS |
340 | #else |
341 | #define Flt_Rounds 1 |
342 | #endif |
343 | #endif /*Flt_Rounds*/ |
344 | |
345 | #ifdef Honor_FLT_ROUNDS |
346 | #define Rounding rounding |
347 | #undef Check_FLT_ROUNDS |
348 | #define Check_FLT_ROUNDS |
349 | #else |
350 | #define Rounding Flt_Rounds |
351 | #endif |
352 | |
353 | #else /* ifndef IEEE_Arith */ |
354 | #undef Check_FLT_ROUNDS |
355 | #undef Honor_FLT_ROUNDS |
356 | #undef SET_INEXACT |
357 | #undef Sudden_Underflow |
358 | #define Sudden_Underflow |
359 | #ifdef IBM |
360 | #undef Flt_Rounds |
361 | #define Flt_Rounds 0 |
362 | #define Exp_shift 24 |
363 | #define Exp_shift1 24 |
364 | #define Exp_msk1 0x1000000 |
365 | #define Exp_msk11 0x1000000 |
366 | #define Exp_mask 0x7f000000 |
367 | #define P 14 |
368 | #define Bias 65 |
369 | #define Exp_1 0x41000000 |
370 | #define Exp_11 0x41000000 |
371 | #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */ |
372 | #define Frac_mask 0xffffff |
373 | #define Frac_mask1 0xffffff |
374 | #define Bletch 4 |
375 | #define Ten_pmax 22 |
376 | #define Bndry_mask 0xefffff |
377 | #define Bndry_mask1 0xffffff |
378 | #define LSB 1 |
379 | #define Sign_bit 0x80000000 |
380 | #define Log2P 4 |
381 | #define Tiny0 0x100000 |
382 | #define Tiny1 0 |
383 | #define Quick_max 14 |
384 | #define Int_max 15 |
385 | #else /* VAX */ |
386 | #undef Flt_Rounds |
387 | #define Flt_Rounds 1 |
388 | #define Exp_shift 23 |
389 | #define Exp_shift1 7 |
390 | #define Exp_msk1 0x80 |
391 | #define Exp_msk11 0x800000 |
392 | #define Exp_mask 0x7f80 |
393 | #define P 56 |
394 | #define Bias 129 |
395 | #define Exp_1 0x40800000 |
396 | #define Exp_11 0x4080 |
397 | #define Ebits 8 |
398 | #define Frac_mask 0x7fffff |
399 | #define Frac_mask1 0xffff007f |
400 | #define Ten_pmax 24 |
401 | #define Bletch 2 |
402 | #define Bndry_mask 0xffff007f |
403 | #define Bndry_mask1 0xffff007f |
404 | #define LSB 0x10000 |
405 | #define Sign_bit 0x8000 |
406 | #define Log2P 1 |
407 | #define Tiny0 0x80 |
408 | #define Tiny1 0 |
409 | #define Quick_max 15 |
410 | #define Int_max 15 |
411 | #endif /* IBM, VAX */ |
412 | #endif /* IEEE_Arith */ |
413 | |
414 | #ifndef IEEE_Arith |
415 | #define ROUND_BIASED |
416 | #endif |
417 | |
418 | #ifdef RND_PRODQUOT |
419 | #define rounded_product(a,b) a = rnd_prod(a, b) |
420 | #define rounded_quotient(a,b) a = rnd_quot(a, b) |
421 | extern double rnd_prod(double, double), rnd_quot(double, double); |
422 | #else |
423 | #define rounded_product(a,b) a *= b |
424 | #define rounded_quotient(a,b) a /= b |
425 | #endif |
426 | |
427 | #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1)) |
428 | #define Big1 0xffffffff |
429 | |
430 | #ifndef Pack_32 |
431 | #define Pack_32 |
432 | #endif |
433 | |
434 | #define FFFFFFFF 0xffffffffUL |
435 | |
436 | #ifdef NO_LONG_LONG |
437 | #undef ULLong |
438 | #ifdef Just_16 |
439 | #undef Pack_32 |
440 | /* When Pack_32 is not defined, we store 16 bits per 32-bit Long. |
441 | * This makes some inner loops simpler and sometimes saves work |
442 | * during multiplications, but it often seems to make things slightly |
443 | * slower. Hence the default is now to store 32 bits per Long. |
444 | */ |
445 | #endif |
446 | #else /* long long available */ |
447 | #ifndef Llong |
448 | #define Llong long long |
449 | #endif |
450 | #ifndef ULLong |
451 | #define ULLong unsigned Llong |
452 | #endif |
453 | #endif /* NO_LONG_LONG */ |
454 | |
455 | #ifndef MULTIPLE_THREADS |
456 | #define ACQUIRE_DTOA_LOCK(n) /*nothing*/ |
457 | #define FREE_DTOA_LOCK(n) /*nothing*/ |
458 | #endif |
459 | |
460 | #define Kmax (sizeof(size_t) << 3) |
461 | |
462 | struct |
463 | Bigint { |
464 | struct Bigint *next; |
465 | int k, maxwds, sign, wds; |
466 | ULong x[1]; |
467 | }; |
468 | |
469 | typedef struct Bigint Bigint; |
470 | |
471 | static Bigint *freelist[Kmax+1]; |
472 | |
473 | static Bigint * |
474 | Balloc |
475 | (int k) |
476 | { |
477 | int x; |
478 | Bigint *rv; |
479 | #ifndef Omit_Private_Memory |
480 | unsigned int len; |
481 | #endif |
482 | |
483 | ACQUIRE_DTOA_LOCK(0); |
484 | if ((rv = freelist[k])) { |
485 | freelist[k] = rv->next; |
486 | } |
487 | else { |
488 | x = 1 << k; |
489 | #ifdef Omit_Private_Memory |
490 | rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong)); |
491 | #else |
492 | len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1) |
493 | /sizeof(double); |
494 | if (pmem_next - private_mem + len <= (unsigned)PRIVATE_mem) { |
495 | rv = (Bigint*)pmem_next; |
496 | pmem_next += len; |
497 | } |
498 | else |
499 | rv = (Bigint*)MALLOC(len*sizeof(double)); |
500 | #endif |
501 | rv->k = k; |
502 | rv->maxwds = x; |
503 | } |
504 | FREE_DTOA_LOCK(0); |
505 | rv->sign = rv->wds = 0; |
506 | return rv; |
507 | } |
508 | |
509 | static void |
510 | Bfree |
511 | (Bigint *v) |
512 | { |
513 | if (v) { |
514 | ACQUIRE_DTOA_LOCK(0); |
515 | v->next = freelist[v->k]; |
516 | freelist[v->k] = v; |
517 | FREE_DTOA_LOCK(0); |
518 | } |
519 | } |
520 | |
521 | #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \ |
522 | y->wds*sizeof(Long) + 2*sizeof(int)) |
523 | |
524 | static Bigint * |
525 | multadd |
526 | (Bigint *b, int m, int a) /* multiply by m and add a */ |
527 | { |
528 | int i, wds; |
529 | #ifdef ULLong |
530 | ULong *x; |
531 | ULLong carry, y; |
532 | #else |
533 | ULong carry, *x, y; |
534 | #ifdef Pack_32 |
535 | ULong xi, z; |
536 | #endif |
537 | #endif |
538 | Bigint *b1; |
539 | |
540 | wds = b->wds; |
541 | x = b->x; |
542 | i = 0; |
543 | carry = a; |
544 | do { |
545 | #ifdef ULLong |
546 | y = *x * (ULLong)m + carry; |
547 | carry = y >> 32; |
548 | *x++ = (ULong)y & FFFFFFFF; |
549 | #else |
550 | #ifdef Pack_32 |
551 | xi = *x; |
552 | y = (xi & 0xffff) * m + carry; |
553 | z = (xi >> 16) * m + (y >> 16); |
554 | carry = z >> 16; |
555 | *x++ = (z << 16) + (y & 0xffff); |
556 | #else |
557 | y = *x * m + carry; |
558 | carry = y >> 16; |
559 | *x++ = y & 0xffff; |
560 | #endif |
561 | #endif |
562 | } |
563 | while(++i < wds); |
564 | if (carry) { |
565 | if (wds >= b->maxwds) { |
566 | b1 = Balloc(b->k+1); |
567 | Bcopy(b1, b); |
568 | Bfree(b); |
569 | b = b1; |
570 | } |
571 | b->x[wds++] = (ULong)carry; |
572 | b->wds = wds; |
573 | } |
574 | return b; |
575 | } |
576 | |
577 | static Bigint * |
578 | s2b |
579 | (CONST char *s, int nd0, int nd, ULong y9) |
580 | { |
581 | Bigint *b; |
582 | int i, k; |
583 | Long x, y; |
584 | |
585 | x = (nd + 8) / 9; |
586 | for(k = 0, y = 1; x > y; y <<= 1, k++) ; |
587 | #ifdef Pack_32 |
588 | b = Balloc(k); |
589 | b->x[0] = y9; |
590 | b->wds = 1; |
591 | #else |
592 | b = Balloc(k+1); |
593 | b->x[0] = y9 & 0xffff; |
594 | b->wds = (b->x[1] = y9 >> 16) ? 2 : 1; |
595 | #endif |
596 | |
597 | i = 9; |
598 | if (9 < nd0) { |
599 | s += 9; |
600 | do b = multadd(b, 10, *s++ - '0'); |
601 | while(++i < nd0); |
602 | s++; |
603 | } |
604 | else |
605 | s += 10; |
606 | for(; i < nd; i++) |
607 | b = multadd(b, 10, *s++ - '0'); |
608 | return b; |
609 | } |
610 | |
611 | static int |
612 | hi0bits |
613 | (register ULong x) |
614 | { |
615 | register int k = 0; |
616 | |
617 | if (!(x & 0xffff0000)) { |
618 | k = 16; |
619 | x <<= 16; |
620 | } |
621 | if (!(x & 0xff000000)) { |
622 | k += 8; |
623 | x <<= 8; |
624 | } |
625 | if (!(x & 0xf0000000)) { |
626 | k += 4; |
627 | x <<= 4; |
628 | } |
629 | if (!(x & 0xc0000000)) { |
630 | k += 2; |
631 | x <<= 2; |
632 | } |
633 | if (!(x & 0x80000000)) { |
634 | k++; |
635 | if (!(x & 0x40000000)) |
636 | return 32; |
637 | } |
638 | return k; |
639 | } |
640 | |
641 | static int |
642 | lo0bits |
643 | (ULong *y) |
644 | { |
645 | register int k; |
646 | register ULong x = *y; |
647 | |
648 | if (x & 7) { |
649 | if (x & 1) |
650 | return 0; |
651 | if (x & 2) { |
652 | *y = x >> 1; |
653 | return 1; |
654 | } |
655 | *y = x >> 2; |
656 | return 2; |
657 | } |
658 | k = 0; |
659 | if (!(x & 0xffff)) { |
660 | k = 16; |
661 | x >>= 16; |
662 | } |
663 | if (!(x & 0xff)) { |
664 | k += 8; |
665 | x >>= 8; |
666 | } |
667 | if (!(x & 0xf)) { |
668 | k += 4; |
669 | x >>= 4; |
670 | } |
671 | if (!(x & 0x3)) { |
672 | k += 2; |
673 | x >>= 2; |
674 | } |
675 | if (!(x & 1)) { |
676 | k++; |
677 | x >>= 1; |
678 | if (!x & 1) |
679 | return 32; |
680 | } |
681 | *y = x; |
682 | return k; |
683 | } |
684 | |
685 | static Bigint * |
686 | i2b |
687 | (int i) |
688 | { |
689 | Bigint *b; |
690 | |
691 | b = Balloc(1); |
692 | b->x[0] = i; |
693 | b->wds = 1; |
694 | return b; |
695 | } |
696 | |
697 | static Bigint * |
698 | mult |
699 | (Bigint *a, Bigint *b) |
700 | { |
701 | Bigint *c; |
702 | int k, wa, wb, wc; |
703 | ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0; |
704 | ULong y; |
705 | #ifdef ULLong |
706 | ULLong carry, z; |
707 | #else |
708 | ULong carry, z; |
709 | #ifdef Pack_32 |
710 | ULong z2; |
711 | #endif |
712 | #endif |
713 | |
714 | if (a->wds < b->wds) { |
715 | c = a; |
716 | a = b; |
717 | b = c; |
718 | } |
719 | k = a->k; |
720 | wa = a->wds; |
721 | wb = b->wds; |
722 | wc = wa + wb; |
723 | if (wc > a->maxwds) |
724 | k++; |
725 | c = Balloc(k); |
726 | for(x = c->x, xa = x + wc; x < xa; x++) |
727 | *x = 0; |
728 | xa = a->x; |
729 | xae = xa + wa; |
730 | xb = b->x; |
731 | xbe = xb + wb; |
732 | xc0 = c->x; |
733 | #ifdef ULLong |
734 | for(; xb < xbe; xc0++) { |
735 | if ((y = *xb++)) { |
736 | x = xa; |
737 | xc = xc0; |
738 | carry = 0; |
739 | do { |
740 | z = *x++ * (ULLong)y + *xc + carry; |
741 | carry = z >> 32; |
742 | *xc++ = (ULong)z & FFFFFFFF; |
743 | } |
744 | while(x < xae); |
745 | *xc = (ULong)carry; |
746 | } |
747 | } |
748 | #else |
749 | #ifdef Pack_32 |
750 | for(; xb < xbe; xb++, xc0++) { |
751 | if (y = *xb & 0xffff) { |
752 | x = xa; |
753 | xc = xc0; |
754 | carry = 0; |
755 | do { |
756 | z = (*x & 0xffff) * y + (*xc & 0xffff) + carry; |
757 | carry = z >> 16; |
758 | z2 = (*x++ >> 16) * y + (*xc >> 16) + carry; |
759 | carry = z2 >> 16; |
760 | Storeinc(xc, z2, z); |
761 | } |
762 | while(x < xae); |
763 | *xc = carry; |
764 | } |
765 | if (y = *xb >> 16) { |
766 | x = xa; |
767 | xc = xc0; |
768 | carry = 0; |
769 | z2 = *xc; |
770 | do { |
771 | z = (*x & 0xffff) * y + (*xc >> 16) + carry; |
772 | carry = z >> 16; |
773 | Storeinc(xc, z, z2); |
774 | z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry; |
775 | carry = z2 >> 16; |
776 | } |
777 | while(x < xae); |
778 | *xc = z2; |
779 | } |
780 | } |
781 | #else |
782 | for(; xb < xbe; xc0++) { |
783 | if (y = *xb++) { |
784 | x = xa; |
785 | xc = xc0; |
786 | carry = 0; |
787 | do { |
788 | z = *x++ * y + *xc + carry; |
789 | carry = z >> 16; |
790 | *xc++ = z & 0xffff; |
791 | } |
792 | while(x < xae); |
793 | *xc = carry; |
794 | } |
795 | } |
796 | #endif |
797 | #endif |
798 | for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ; |
799 | c->wds = wc; |
800 | return c; |
801 | } |
802 | |
803 | static Bigint *p5s; |
804 | |
805 | static Bigint * |
806 | pow5mult |
807 | (Bigint *b, int k) |
808 | { |
809 | Bigint *b1, *p5, *p51; |
810 | int i; |
811 | static int p05[3] = { 5, 25, 125 }; |
812 | |
813 | if ((i = k & 3)) |
814 | b = multadd(b, p05[i-1], 0); |
815 | |
816 | if (!(k >>= 2)) |
817 | return b; |
818 | if (!(p5 = p5s)) { |
819 | /* first time */ |
820 | #ifdef MULTIPLE_THREADS |
821 | ACQUIRE_DTOA_LOCK(1); |
822 | if (!(p5 = p5s)) { |
823 | p5 = p5s = i2b(625); |
824 | p5->next = 0; |
825 | } |
826 | FREE_DTOA_LOCK(1); |
827 | #else |
828 | p5 = p5s = i2b(625); |
829 | p5->next = 0; |
830 | #endif |
831 | } |
832 | for(;;) { |
833 | if (k & 1) { |
834 | b1 = mult(b, p5); |
835 | Bfree(b); |
836 | b = b1; |
837 | } |
838 | if (!(k >>= 1)) |
839 | break; |
840 | if (!(p51 = p5->next)) { |
841 | #ifdef MULTIPLE_THREADS |
842 | ACQUIRE_DTOA_LOCK(1); |
843 | if (!(p51 = p5->next)) { |
844 | p51 = p5->next = mult(p5,p5); |
845 | p51->next = 0; |
846 | } |
847 | FREE_DTOA_LOCK(1); |
848 | #else |
849 | p51 = p5->next = mult(p5,p5); |
850 | p51->next = 0; |
851 | #endif |
852 | } |
853 | p5 = p51; |
854 | } |
855 | return b; |
856 | } |
857 | |
858 | static Bigint * |
859 | lshift |
860 | (Bigint *b, int k) |
861 | { |
862 | int i, k1, n, n1; |
863 | Bigint *b1; |
864 | ULong *x, *x1, *xe, z; |
865 | |
866 | #ifdef Pack_32 |
867 | n = k >> 5; |
868 | #else |
869 | n = k >> 4; |
870 | #endif |
871 | k1 = b->k; |
872 | n1 = n + b->wds + 1; |
873 | for(i = b->maxwds; n1 > i; i <<= 1) |
874 | k1++; |
875 | b1 = Balloc(k1); |
876 | x1 = b1->x; |
877 | for(i = 0; i < n; i++) |
878 | *x1++ = 0; |
879 | x = b->x; |
880 | xe = x + b->wds; |
881 | #ifdef Pack_32 |
882 | if (k &= 0x1f) { |
883 | k1 = 32 - k; |
884 | z = 0; |
885 | do { |
886 | *x1++ = *x << k | z; |
887 | z = *x++ >> k1; |
888 | } |
889 | while(x < xe); |
890 | if ((*x1 = z)) |
891 | ++n1; |
892 | } |
893 | #else |
894 | if (k &= 0xf) { |
895 | k1 = 16 - k; |
896 | z = 0; |
897 | do { |
898 | *x1++ = *x << k & 0xffff | z; |
899 | z = *x++ >> k1; |
900 | } |
901 | while(x < xe); |
902 | if (*x1 = z) |
903 | ++n1; |
904 | } |
905 | #endif |
906 | else do |
907 | *x1++ = *x++; |
908 | while(x < xe); |
909 | b1->wds = n1 - 1; |
910 | Bfree(b); |
911 | return b1; |
912 | } |
913 | |
914 | static int |
915 | cmp |
916 | (Bigint *a, Bigint *b) |
917 | { |
918 | ULong *xa, *xa0, *xb, *xb0; |
919 | int i, j; |
920 | |
921 | i = a->wds; |
922 | j = b->wds; |
923 | #ifdef DEBUG |
924 | if (i > 1 && !a->x[i-1]) |
925 | Bug("cmp called with a->x[a->wds-1] == 0" ); |
926 | if (j > 1 && !b->x[j-1]) |
927 | Bug("cmp called with b->x[b->wds-1] == 0" ); |
928 | #endif |
929 | if (i -= j) |
930 | return i; |
931 | xa0 = a->x; |
932 | xa = xa0 + j; |
933 | xb0 = b->x; |
934 | xb = xb0 + j; |
935 | for(;;) { |
936 | if (*--xa != *--xb) |
937 | return *xa < *xb ? -1 : 1; |
938 | if (xa <= xa0) |
939 | break; |
940 | } |
941 | return 0; |
942 | } |
943 | |
944 | static Bigint * |
945 | diff |
946 | (Bigint *a, Bigint *b) |
947 | { |
948 | Bigint *c; |
949 | int i, wa, wb; |
950 | ULong *xa, *xae, *xb, *xbe, *xc; |
951 | #ifdef ULLong |
952 | ULLong borrow, y; |
953 | #else |
954 | ULong borrow, y; |
955 | #ifdef Pack_32 |
956 | ULong z; |
957 | #endif |
958 | #endif |
959 | |
960 | i = cmp(a,b); |
961 | if (!i) { |
962 | c = Balloc(0); |
963 | c->wds = 1; |
964 | c->x[0] = 0; |
965 | return c; |
966 | } |
967 | if (i < 0) { |
968 | c = a; |
969 | a = b; |
970 | b = c; |
971 | i = 1; |
972 | } |
973 | else |
974 | i = 0; |
975 | c = Balloc(a->k); |
976 | c->sign = i; |
977 | wa = a->wds; |
978 | xa = a->x; |
979 | xae = xa + wa; |
980 | wb = b->wds; |
981 | xb = b->x; |
982 | xbe = xb + wb; |
983 | xc = c->x; |
984 | borrow = 0; |
985 | #ifdef ULLong |
986 | do { |
987 | y = (ULLong)*xa++ - *xb++ - borrow; |
988 | borrow = y >> 32 & (ULong)1; |
989 | *xc++ = (ULong)y & FFFFFFFF; |
990 | } |
991 | while(xb < xbe); |
992 | while(xa < xae) { |
993 | y = *xa++ - borrow; |
994 | borrow = y >> 32 & (ULong)1; |
995 | *xc++ = (ULong)y & FFFFFFFF; |
996 | } |
997 | #else |
998 | #ifdef Pack_32 |
999 | do { |
1000 | y = (*xa & 0xffff) - (*xb & 0xffff) - borrow; |
1001 | borrow = (y & 0x10000) >> 16; |
1002 | z = (*xa++ >> 16) - (*xb++ >> 16) - borrow; |
1003 | borrow = (z & 0x10000) >> 16; |
1004 | Storeinc(xc, z, y); |
1005 | } |
1006 | while(xb < xbe); |
1007 | while(xa < xae) { |
1008 | y = (*xa & 0xffff) - borrow; |
1009 | borrow = (y & 0x10000) >> 16; |
1010 | z = (*xa++ >> 16) - borrow; |
1011 | borrow = (z & 0x10000) >> 16; |
1012 | Storeinc(xc, z, y); |
1013 | } |
1014 | #else |
1015 | do { |
1016 | y = *xa++ - *xb++ - borrow; |
1017 | borrow = (y & 0x10000) >> 16; |
1018 | *xc++ = y & 0xffff; |
1019 | } |
1020 | while(xb < xbe); |
1021 | while(xa < xae) { |
1022 | y = *xa++ - borrow; |
1023 | borrow = (y & 0x10000) >> 16; |
1024 | *xc++ = y & 0xffff; |
1025 | } |
1026 | #endif |
1027 | #endif |
1028 | while(!*--xc) |
1029 | wa--; |
1030 | c->wds = wa; |
1031 | return c; |
1032 | } |
1033 | |
1034 | static double |
1035 | ulp |
1036 | (double dx) |
1037 | { |
1038 | register Long L; |
1039 | U x, a; |
1040 | |
1041 | dval(x) = dx; |
1042 | L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1; |
1043 | #ifndef Avoid_Underflow |
1044 | #ifndef Sudden_Underflow |
1045 | if (L > 0) { |
1046 | #endif |
1047 | #endif |
1048 | #ifdef IBM |
1049 | L |= Exp_msk1 >> 4; |
1050 | #endif |
1051 | word0(a) = L; |
1052 | word1(a) = 0; |
1053 | #ifndef Avoid_Underflow |
1054 | #ifndef Sudden_Underflow |
1055 | } |
1056 | else { |
1057 | L = -L >> Exp_shift; |
1058 | if (L < Exp_shift) { |
1059 | word0(a) = 0x80000 >> L; |
1060 | word1(a) = 0; |
1061 | } |
1062 | else { |
1063 | word0(a) = 0; |
1064 | L -= Exp_shift; |
1065 | word1(a) = L >= 31 ? 1 : 1 << 31 - L; |
1066 | } |
1067 | } |
1068 | #endif |
1069 | #endif |
1070 | return dval(a); |
1071 | } |
1072 | |
1073 | static double |
1074 | b2d |
1075 | (Bigint *a, int *e) |
1076 | { |
1077 | ULong *xa, *xa0, w, y, z; |
1078 | int k; |
1079 | U d; |
1080 | #ifdef VAX |
1081 | ULong d0, d1; |
1082 | #else |
1083 | #define d0 word0(d) |
1084 | #define d1 word1(d) |
1085 | #endif |
1086 | |
1087 | xa0 = a->x; |
1088 | xa = xa0 + a->wds; |
1089 | y = *--xa; |
1090 | #ifdef DEBUG |
1091 | if (!y) Bug("zero y in b2d" ); |
1092 | #endif |
1093 | k = hi0bits(y); |
1094 | *e = 32 - k; |
1095 | #ifdef Pack_32 |
1096 | if (k < Ebits) { |
1097 | d0 = Exp_1 | y >> (Ebits - k); |
1098 | w = xa > xa0 ? *--xa : 0; |
1099 | d1 = y << (32-Ebits + k) | w >> (Ebits - k); |
1100 | goto ret_d; |
1101 | } |
1102 | z = xa > xa0 ? *--xa : 0; |
1103 | if (k -= Ebits) { |
1104 | d0 = Exp_1 | y << k | z >> (32 - k); |
1105 | y = xa > xa0 ? *--xa : 0; |
1106 | d1 = z << k | y >> (32 - k); |
1107 | } |
1108 | else { |
1109 | d0 = Exp_1 | y; |
1110 | d1 = z; |
1111 | } |
1112 | #else |
1113 | if (k < Ebits + 16) { |
1114 | z = xa > xa0 ? *--xa : 0; |
1115 | d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k; |
1116 | w = xa > xa0 ? *--xa : 0; |
1117 | y = xa > xa0 ? *--xa : 0; |
1118 | d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k; |
1119 | goto ret_d; |
1120 | } |
1121 | z = xa > xa0 ? *--xa : 0; |
1122 | w = xa > xa0 ? *--xa : 0; |
1123 | k -= Ebits + 16; |
1124 | d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k; |
1125 | y = xa > xa0 ? *--xa : 0; |
1126 | d1 = w << k + 16 | y << k; |
1127 | #endif |
1128 | ret_d: |
1129 | #ifdef VAX |
1130 | word0(d) = d0 >> 16 | d0 << 16; |
1131 | word1(d) = d1 >> 16 | d1 << 16; |
1132 | #else |
1133 | #undef d0 |
1134 | #undef d1 |
1135 | #endif |
1136 | return dval(d); |
1137 | } |
1138 | |
1139 | static Bigint * |
1140 | d2b |
1141 | (double dd, int *e, int *bits) |
1142 | { |
1143 | U d; |
1144 | Bigint *b; |
1145 | int de, k; |
1146 | ULong *x, y, z; |
1147 | #ifndef Sudden_Underflow |
1148 | int i; |
1149 | #endif |
1150 | #ifdef VAX |
1151 | ULong d0, d1; |
1152 | #endif |
1153 | dval(d) = dd; |
1154 | #ifdef VAX |
1155 | d0 = word0(d) >> 16 | word0(d) << 16; |
1156 | d1 = word1(d) >> 16 | word1(d) << 16; |
1157 | #else |
1158 | #define d0 word0(d) |
1159 | #define d1 word1(d) |
1160 | #endif |
1161 | |
1162 | #ifdef Pack_32 |
1163 | b = Balloc(1); |
1164 | #else |
1165 | b = Balloc(2); |
1166 | #endif |
1167 | x = b->x; |
1168 | |
1169 | z = d0 & Frac_mask; |
1170 | d0 &= 0x7fffffff; /* clear sign bit, which we ignore */ |
1171 | #ifdef Sudden_Underflow |
1172 | de = (int)(d0 >> Exp_shift); |
1173 | #ifndef IBM |
1174 | z |= Exp_msk11; |
1175 | #endif |
1176 | #else |
1177 | if ((de = (int)(d0 >> Exp_shift))) |
1178 | z |= Exp_msk1; |
1179 | #endif |
1180 | #ifdef Pack_32 |
1181 | if ((y = d1)) { |
1182 | if ((k = lo0bits(&y))) { |
1183 | x[0] = y | z << (32 - k); |
1184 | z >>= k; |
1185 | } |
1186 | else |
1187 | x[0] = y; |
1188 | #ifndef Sudden_Underflow |
1189 | i = |
1190 | #endif |
1191 | b->wds = (x[1] = z) ? 2 : 1; |
1192 | } |
1193 | else { |
1194 | #ifdef DEBUG |
1195 | if (!z) |
1196 | Bug("Zero passed to d2b" ); |
1197 | #endif |
1198 | k = lo0bits(&z); |
1199 | x[0] = z; |
1200 | #ifndef Sudden_Underflow |
1201 | i = |
1202 | #endif |
1203 | b->wds = 1; |
1204 | k += 32; |
1205 | } |
1206 | #else |
1207 | if (y = d1) { |
1208 | if (k = lo0bits(&y)) |
1209 | if (k >= 16) { |
1210 | x[0] = y | z << 32 - k & 0xffff; |
1211 | x[1] = z >> k - 16 & 0xffff; |
1212 | x[2] = z >> k; |
1213 | i = 2; |
1214 | } |
1215 | else { |
1216 | x[0] = y & 0xffff; |
1217 | x[1] = y >> 16 | z << 16 - k & 0xffff; |
1218 | x[2] = z >> k & 0xffff; |
1219 | x[3] = z >> k+16; |
1220 | i = 3; |
1221 | } |
1222 | else { |
1223 | x[0] = y & 0xffff; |
1224 | x[1] = y >> 16; |
1225 | x[2] = z & 0xffff; |
1226 | x[3] = z >> 16; |
1227 | i = 3; |
1228 | } |
1229 | } |
1230 | else { |
1231 | #ifdef DEBUG |
1232 | if (!z) |
1233 | Bug("Zero passed to d2b" ); |
1234 | #endif |
1235 | k = lo0bits(&z); |
1236 | if (k >= 16) { |
1237 | x[0] = z; |
1238 | i = 0; |
1239 | } |
1240 | else { |
1241 | x[0] = z & 0xffff; |
1242 | x[1] = z >> 16; |
1243 | i = 1; |
1244 | } |
1245 | k += 32; |
1246 | } |
1247 | while(!x[i]) |
1248 | --i; |
1249 | b->wds = i + 1; |
1250 | #endif |
1251 | #ifndef Sudden_Underflow |
1252 | if (de) { |
1253 | #endif |
1254 | #ifdef IBM |
1255 | *e = (de - Bias - (P-1) << 2) + k; |
1256 | *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask); |
1257 | #else |
1258 | *e = de - Bias - (P-1) + k; |
1259 | *bits = P - k; |
1260 | #endif |
1261 | #ifndef Sudden_Underflow |
1262 | } |
1263 | else { |
1264 | *e = de - Bias - (P-1) + 1 + k; |
1265 | #ifdef Pack_32 |
1266 | *bits = 32*i - hi0bits(x[i-1]); |
1267 | #else |
1268 | *bits = (i+2)*16 - hi0bits(x[i]); |
1269 | #endif |
1270 | } |
1271 | #endif |
1272 | return b; |
1273 | } |
1274 | #undef d0 |
1275 | #undef d1 |
1276 | |
1277 | static double |
1278 | ratio |
1279 | (Bigint *a, Bigint *b) |
1280 | { |
1281 | U da, db; |
1282 | int k, ka, kb; |
1283 | |
1284 | dval(da) = b2d(a, &ka); |
1285 | dval(db) = b2d(b, &kb); |
1286 | #ifdef Pack_32 |
1287 | k = ka - kb + 32*(a->wds - b->wds); |
1288 | #else |
1289 | k = ka - kb + 16*(a->wds - b->wds); |
1290 | #endif |
1291 | #ifdef IBM |
1292 | if (k > 0) { |
1293 | word0(da) += (k >> 2)*Exp_msk1; |
1294 | if (k &= 3) |
1295 | dval(da) *= 1 << k; |
1296 | } |
1297 | else { |
1298 | k = -k; |
1299 | word0(db) += (k >> 2)*Exp_msk1; |
1300 | if (k &= 3) |
1301 | dval(db) *= 1 << k; |
1302 | } |
1303 | #else |
1304 | if (k > 0) |
1305 | word0(da) += k*Exp_msk1; |
1306 | else { |
1307 | k = -k; |
1308 | word0(db) += k*Exp_msk1; |
1309 | } |
1310 | #endif |
1311 | return dval(da) / dval(db); |
1312 | } |
1313 | |
1314 | static CONST double |
1315 | tens[] = { |
1316 | 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, |
1317 | 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, |
1318 | 1e20, 1e21, 1e22 |
1319 | #ifdef VAX |
1320 | , 1e23, 1e24 |
1321 | #endif |
1322 | }; |
1323 | |
1324 | static CONST double |
1325 | #ifdef IEEE_Arith |
1326 | bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 }; |
1327 | static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, |
1328 | #ifdef Avoid_Underflow |
1329 | 9007199254740992.*9007199254740992.e-256 |
1330 | /* = 2^106 * 1e-53 */ |
1331 | #else |
1332 | 1e-256 |
1333 | #endif |
1334 | }; |
1335 | /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */ |
1336 | /* flag unnecessarily. It leads to a song and dance at the end of strtod. */ |
1337 | #define Scale_Bit 0x10 |
1338 | #define n_bigtens 5 |
1339 | #else |
1340 | #ifdef IBM |
1341 | bigtens[] = { 1e16, 1e32, 1e64 }; |
1342 | static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 }; |
1343 | #define n_bigtens 3 |
1344 | #else |
1345 | bigtens[] = { 1e16, 1e32 }; |
1346 | static CONST double tinytens[] = { 1e-16, 1e-32 }; |
1347 | #define n_bigtens 2 |
1348 | #endif |
1349 | #endif |
1350 | |
1351 | #ifndef IEEE_Arith |
1352 | #undef INFNAN_CHECK |
1353 | #endif |
1354 | |
1355 | #ifdef INFNAN_CHECK |
1356 | |
1357 | #ifndef NAN_WORD0 |
1358 | #define NAN_WORD0 0x7ff80000 |
1359 | #endif |
1360 | |
1361 | #ifndef NAN_WORD1 |
1362 | #define NAN_WORD1 0 |
1363 | #endif |
1364 | |
1365 | static int |
1366 | match |
1367 | (CONST char **sp, CONST char *t) |
1368 | { |
1369 | int c, d; |
1370 | CONST char *s = *sp; |
1371 | |
1372 | while((d = *t++)) { |
1373 | if ((c = *++s) >= 'A' && c <= 'Z') |
1374 | c += 'a' - 'A'; |
1375 | if (c != d) |
1376 | return 0; |
1377 | } |
1378 | *sp = s + 1; |
1379 | return 1; |
1380 | } |
1381 | |
1382 | #ifndef No_Hex_NaN |
1383 | static void |
1384 | hexnan |
1385 | (U *rvp, CONST char **sp) |
1386 | { |
1387 | ULong c, x[2]; |
1388 | CONST char *s; |
1389 | int havedig, udx0, xshift; |
1390 | |
1391 | x[0] = x[1] = 0; |
1392 | havedig = xshift = 0; |
1393 | udx0 = 1; |
1394 | s = *sp; |
1395 | while((c = *(CONST unsigned char*)++s)) { |
1396 | if (c >= '0' && c <= '9') |
1397 | c -= '0'; |
1398 | else if (c >= 'a' && c <= 'f') |
1399 | c += 10 - 'a'; |
1400 | else if (c >= 'A' && c <= 'F') |
1401 | c += 10 - 'A'; |
1402 | else if (c <= ' ') { |
1403 | if (udx0 && havedig) { |
1404 | udx0 = 0; |
1405 | xshift = 1; |
1406 | } |
1407 | continue; |
1408 | } |
1409 | else if (/*(*/ c == ')' && havedig) { |
1410 | *sp = s + 1; |
1411 | break; |
1412 | } |
1413 | else |
1414 | return; /* invalid form: don't change *sp */ |
1415 | havedig = 1; |
1416 | if (xshift) { |
1417 | xshift = 0; |
1418 | x[0] = x[1]; |
1419 | x[1] = 0; |
1420 | } |
1421 | if (udx0) |
1422 | x[0] = (x[0] << 4) | (x[1] >> 28); |
1423 | x[1] = (x[1] << 4) | c; |
1424 | } |
1425 | if ((x[0] &= 0xfffff) || x[1]) { |
1426 | word0(*rvp) = Exp_mask | x[0]; |
1427 | word1(*rvp) = x[1]; |
1428 | } |
1429 | } |
1430 | #endif /*No_Hex_NaN*/ |
1431 | #endif /* INFNAN_CHECK */ |
1432 | |
1433 | double |
1434 | strtod |
1435 | (CONST char *s00, char **se) |
1436 | { |
1437 | #ifdef Avoid_Underflow |
1438 | int scale; |
1439 | #endif |
1440 | int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign, |
1441 | e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign; |
1442 | CONST char *s, *s0, *s1; |
1443 | double aadj, aadj1, adj; |
1444 | U aadj2, rv, rv0; |
1445 | Long L; |
1446 | ULong y, z; |
1447 | Bigint *bb = NULL, *bb1 = NULL, *bd = NULL, *bd0 = NULL, *bs = NULL, *delta = NULL; |
1448 | #ifdef SET_INEXACT |
1449 | int inexact, oldinexact; |
1450 | #endif |
1451 | #ifdef Honor_FLT_ROUNDS |
1452 | int rounding; |
1453 | #endif |
1454 | #ifdef USE_LOCALE |
1455 | CONST char *s2; |
1456 | #endif |
1457 | |
1458 | sign = nz0 = nz = 0; |
1459 | dval(rv) = 0.; |
1460 | for(s = s00;;s++) switch(*s) { |
1461 | case '-': |
1462 | sign = 1; |
1463 | /* no break */ |
1464 | case '+': |
1465 | if (*++s) |
1466 | goto break2; |
1467 | /* no break */ |
1468 | case 0: |
1469 | goto ret0; |
1470 | case '\t': |
1471 | case '\n': |
1472 | case '\v': |
1473 | case '\f': |
1474 | case '\r': |
1475 | case ' ': |
1476 | continue; |
1477 | default: |
1478 | goto break2; |
1479 | } |
1480 | break2: |
1481 | if (*s == '0') { |
1482 | nz0 = 1; |
1483 | while(*++s == '0') ; |
1484 | if (!*s) |
1485 | goto ret; |
1486 | } |
1487 | s0 = s; |
1488 | y = z = 0; |
1489 | for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++) |
1490 | if (nd < 9) |
1491 | y = 10*y + c - '0'; |
1492 | else if (nd < 16) |
1493 | z = 10*z + c - '0'; |
1494 | nd0 = nd; |
1495 | #ifdef USE_LOCALE |
1496 | s1 = localeconv()->decimal_point; |
1497 | if (c == *s1) { |
1498 | c = '.'; |
1499 | if (*++s1) { |
1500 | s2 = s; |
1501 | for(;;) { |
1502 | if (*++s2 != *s1) { |
1503 | c = 0; |
1504 | break; |
1505 | } |
1506 | if (!*++s1) { |
1507 | s = s2; |
1508 | break; |
1509 | } |
1510 | } |
1511 | } |
1512 | } |
1513 | #endif |
1514 | if (c == '.') { |
1515 | c = *++s; |
1516 | if (!nd) { |
1517 | for(; c == '0'; c = *++s) |
1518 | nz++; |
1519 | if (c > '0' && c <= '9') { |
1520 | s0 = s; |
1521 | nf += nz; |
1522 | nz = 0; |
1523 | goto have_dig; |
1524 | } |
1525 | goto dig_done; |
1526 | } |
1527 | for(; c >= '0' && c <= '9'; c = *++s) { |
1528 | have_dig: |
1529 | nz++; |
1530 | if (c -= '0') { |
1531 | nf += nz; |
1532 | for(i = 1; i < nz; i++) |
1533 | if (nd++ < 9) |
1534 | y *= 10; |
1535 | else if (nd <= DBL_DIG + 1) |
1536 | z *= 10; |
1537 | if (nd++ < 9) |
1538 | y = 10*y + c; |
1539 | else if (nd <= DBL_DIG + 1) |
1540 | z = 10*z + c; |
1541 | nz = 0; |
1542 | } |
1543 | } |
1544 | } |
1545 | dig_done: |
1546 | e = 0; |
1547 | if (c == 'e' || c == 'E') { |
1548 | if (!nd && !nz && !nz0) { |
1549 | goto ret0; |
1550 | } |
1551 | s00 = s; |
1552 | esign = 0; |
1553 | switch(c = *++s) { |
1554 | case '-': |
1555 | esign = 1; |
1556 | case '+': |
1557 | c = *++s; |
1558 | } |
1559 | if (c >= '0' && c <= '9') { |
1560 | while(c == '0') |
1561 | c = *++s; |
1562 | if (c > '0' && c <= '9') { |
1563 | L = c - '0'; |
1564 | s1 = s; |
1565 | while((c = *++s) >= '0' && c <= '9') |
1566 | L = 10*L + c - '0'; |
1567 | if (s - s1 > 8 || L > 19999) |
1568 | /* Avoid confusion from exponents |
1569 | * so large that e might overflow. |
1570 | */ |
1571 | e = 19999; /* safe for 16 bit ints */ |
1572 | else |
1573 | e = (int)L; |
1574 | if (esign) |
1575 | e = -e; |
1576 | } |
1577 | else |
1578 | e = 0; |
1579 | } |
1580 | else |
1581 | s = s00; |
1582 | } |
1583 | if (!nd) { |
1584 | if (!nz && !nz0) { |
1585 | #ifdef INFNAN_CHECK |
1586 | /* Check for Nan and Infinity */ |
1587 | switch(c) { |
1588 | case 'i': |
1589 | case 'I': |
1590 | if (match(&s,"nf" )) { |
1591 | --s; |
1592 | if (!match(&s,"inity" )) |
1593 | ++s; |
1594 | word0(rv) = 0x7ff00000; |
1595 | word1(rv) = 0; |
1596 | goto ret; |
1597 | } |
1598 | break; |
1599 | case 'n': |
1600 | case 'N': |
1601 | if (match(&s, "an" )) { |
1602 | word0(rv) = NAN_WORD0; |
1603 | word1(rv) = NAN_WORD1; |
1604 | #ifndef No_Hex_NaN |
1605 | if (*s == '(') /*)*/ |
1606 | hexnan(&rv, &s); |
1607 | #endif |
1608 | goto ret; |
1609 | } |
1610 | } |
1611 | #endif /* INFNAN_CHECK */ |
1612 | ret0: |
1613 | s = s00; |
1614 | sign = 0; |
1615 | } |
1616 | goto ret; |
1617 | } |
1618 | e1 = e -= nf; |
1619 | |
1620 | /* Now we have nd0 digits, starting at s0, followed by a |
1621 | * decimal point, followed by nd-nd0 digits. The number we're |
1622 | * after is the integer represented by those digits times |
1623 | * 10**e */ |
1624 | |
1625 | if (!nd0) |
1626 | nd0 = nd; |
1627 | k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1; |
1628 | dval(rv) = y; |
1629 | if (k > 9) { |
1630 | #ifdef SET_INEXACT |
1631 | if (k > DBL_DIG) |
1632 | oldinexact = get_inexact(); |
1633 | #endif |
1634 | dval(rv) = tens[k - 9] * dval(rv) + z; |
1635 | } |
1636 | bd0 = 0; |
1637 | if (nd <= DBL_DIG |
1638 | #ifndef RND_PRODQUOT |
1639 | #ifndef Honor_FLT_ROUNDS |
1640 | && Flt_Rounds == 1 |
1641 | #endif |
1642 | #endif |
1643 | ) { |
1644 | if (!e) |
1645 | goto ret; |
1646 | if (e > 0) { |
1647 | if (e <= Ten_pmax) { |
1648 | #ifdef VAX |
1649 | goto vax_ovfl_check; |
1650 | #else |
1651 | #ifdef Honor_FLT_ROUNDS |
1652 | /* round correctly FLT_ROUNDS = 2 or 3 */ |
1653 | if (sign) { |
1654 | rv = -rv; |
1655 | sign = 0; |
1656 | } |
1657 | #endif |
1658 | /* rv = */ rounded_product(dval(rv), tens[e]); |
1659 | goto ret; |
1660 | #endif |
1661 | } |
1662 | i = DBL_DIG - nd; |
1663 | if (e <= Ten_pmax + i) { |
1664 | /* A fancier test would sometimes let us do |
1665 | * this for larger i values. |
1666 | */ |
1667 | #ifdef Honor_FLT_ROUNDS |
1668 | /* round correctly FLT_ROUNDS = 2 or 3 */ |
1669 | if (sign) { |
1670 | rv = -rv; |
1671 | sign = 0; |
1672 | } |
1673 | #endif |
1674 | e -= i; |
1675 | dval(rv) *= tens[i]; |
1676 | #ifdef VAX |
1677 | /* VAX exponent range is so narrow we must |
1678 | * worry about overflow here... |
1679 | */ |
1680 | vax_ovfl_check: |
1681 | word0(rv) -= P*Exp_msk1; |
1682 | /* rv = */ rounded_product(dval(rv), tens[e]); |
1683 | if ((word0(rv) & Exp_mask) |
1684 | > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) |
1685 | goto ovfl; |
1686 | word0(rv) += P*Exp_msk1; |
1687 | #else |
1688 | /* rv = */ rounded_product(dval(rv), tens[e]); |
1689 | #endif |
1690 | goto ret; |
1691 | } |
1692 | } |
1693 | #ifndef Inaccurate_Divide |
1694 | else if (e >= -Ten_pmax) { |
1695 | #ifdef Honor_FLT_ROUNDS |
1696 | /* round correctly FLT_ROUNDS = 2 or 3 */ |
1697 | if (sign) { |
1698 | rv = -rv; |
1699 | sign = 0; |
1700 | } |
1701 | #endif |
1702 | /* rv = */ rounded_quotient(dval(rv), tens[-e]); |
1703 | goto ret; |
1704 | } |
1705 | #endif |
1706 | } |
1707 | e1 += nd - k; |
1708 | |
1709 | #ifdef IEEE_Arith |
1710 | #ifdef SET_INEXACT |
1711 | inexact = 1; |
1712 | if (k <= DBL_DIG) |
1713 | oldinexact = get_inexact(); |
1714 | #endif |
1715 | #ifdef Avoid_Underflow |
1716 | scale = 0; |
1717 | #endif |
1718 | #ifdef Honor_FLT_ROUNDS |
1719 | if ((rounding = Flt_Rounds) >= 2) { |
1720 | if (sign) |
1721 | rounding = rounding == 2 ? 0 : 2; |
1722 | else |
1723 | if (rounding != 2) |
1724 | rounding = 0; |
1725 | } |
1726 | #endif |
1727 | #endif /*IEEE_Arith*/ |
1728 | |
1729 | /* Get starting approximation = rv * 10**e1 */ |
1730 | |
1731 | if (e1 > 0) { |
1732 | if ((i = e1 & 15)) |
1733 | dval(rv) *= tens[i]; |
1734 | if (e1 &= ~15) { |
1735 | if (e1 > DBL_MAX_10_EXP) { |
1736 | ovfl: |
1737 | #ifndef NO_ERRNO |
1738 | errno = ERANGE; |
1739 | #endif |
1740 | /* Can't trust HUGE_VAL */ |
1741 | #ifdef IEEE_Arith |
1742 | #ifdef Honor_FLT_ROUNDS |
1743 | switch(rounding) { |
1744 | case 0: /* toward 0 */ |
1745 | case 3: /* toward -infinity */ |
1746 | word0(rv) = Big0; |
1747 | word1(rv) = Big1; |
1748 | break; |
1749 | default: |
1750 | word0(rv) = Exp_mask; |
1751 | word1(rv) = 0; |
1752 | } |
1753 | #else /*Honor_FLT_ROUNDS*/ |
1754 | word0(rv) = Exp_mask; |
1755 | word1(rv) = 0; |
1756 | #endif /*Honor_FLT_ROUNDS*/ |
1757 | #ifdef SET_INEXACT |
1758 | /* set overflow bit */ |
1759 | dval(rv0) = 1e300; |
1760 | dval(rv0) *= dval(rv0); |
1761 | #endif |
1762 | #else /*IEEE_Arith*/ |
1763 | word0(rv) = Big0; |
1764 | word1(rv) = Big1; |
1765 | #endif /*IEEE_Arith*/ |
1766 | if (bd0) |
1767 | goto retfree; |
1768 | goto ret; |
1769 | } |
1770 | e1 >>= 4; |
1771 | for(j = 0; e1 > 1; j++, e1 >>= 1) |
1772 | if (e1 & 1) |
1773 | dval(rv) *= bigtens[j]; |
1774 | /* The last multiplication could overflow. */ |
1775 | word0(rv) -= P*Exp_msk1; |
1776 | dval(rv) *= bigtens[j]; |
1777 | if ((z = word0(rv) & Exp_mask) |
1778 | > Exp_msk1*(DBL_MAX_EXP+Bias-P)) |
1779 | goto ovfl; |
1780 | if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) { |
1781 | /* set to largest number */ |
1782 | /* (Can't trust DBL_MAX) */ |
1783 | word0(rv) = Big0; |
1784 | word1(rv) = Big1; |
1785 | } |
1786 | else |
1787 | word0(rv) += P*Exp_msk1; |
1788 | } |
1789 | } |
1790 | else if (e1 < 0) { |
1791 | e1 = -e1; |
1792 | if ((i = e1 & 15)) |
1793 | dval(rv) /= tens[i]; |
1794 | if (e1 >>= 4) { |
1795 | if (e1 >= 1 << n_bigtens) |
1796 | goto undfl; |
1797 | #ifdef Avoid_Underflow |
1798 | if (e1 & Scale_Bit) |
1799 | scale = 2*P; |
1800 | for(j = 0; e1 > 0; j++, e1 >>= 1) |
1801 | if (e1 & 1) |
1802 | dval(rv) *= tinytens[j]; |
1803 | if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask) |
1804 | >> Exp_shift)) > 0) { |
1805 | /* scaled rv is denormal; zap j low bits */ |
1806 | if (j >= 32) { |
1807 | word1(rv) = 0; |
1808 | if (j >= 53) |
1809 | word0(rv) = (P+2)*Exp_msk1; |
1810 | else |
1811 | word0(rv) &= 0xffffffff << (j-32); |
1812 | } |
1813 | else |
1814 | word1(rv) &= 0xffffffff << j; |
1815 | } |
1816 | #else |
1817 | for(j = 0; e1 > 1; j++, e1 >>= 1) |
1818 | if (e1 & 1) |
1819 | dval(rv) *= tinytens[j]; |
1820 | /* The last multiplication could underflow. */ |
1821 | dval(rv0) = dval(rv); |
1822 | dval(rv) *= tinytens[j]; |
1823 | if (!dval(rv)) { |
1824 | dval(rv) = 2.*dval(rv0); |
1825 | dval(rv) *= tinytens[j]; |
1826 | #endif |
1827 | if (!dval(rv)) { |
1828 | undfl: |
1829 | dval(rv) = 0.; |
1830 | #ifndef NO_ERRNO |
1831 | errno = ERANGE; |
1832 | #endif |
1833 | if (bd0) |
1834 | goto retfree; |
1835 | goto ret; |
1836 | } |
1837 | #ifndef Avoid_Underflow |
1838 | word0(rv) = Tiny0; |
1839 | word1(rv) = Tiny1; |
1840 | /* The refinement below will clean |
1841 | * this approximation up. |
1842 | */ |
1843 | } |
1844 | #endif |
1845 | } |
1846 | } |
1847 | |
1848 | /* Now the hard part -- adjusting rv to the correct value.*/ |
1849 | |
1850 | /* Put digits into bd: true value = bd * 10^e */ |
1851 | |
1852 | bd0 = s2b(s0, nd0, nd, y); |
1853 | |
1854 | for(;;) { |
1855 | bd = Balloc(bd0->k); |
1856 | Bcopy(bd, bd0); |
1857 | bb = d2b(dval(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */ |
1858 | bs = i2b(1); |
1859 | |
1860 | if (e >= 0) { |
1861 | bb2 = bb5 = 0; |
1862 | bd2 = bd5 = e; |
1863 | } |
1864 | else { |
1865 | bb2 = bb5 = -e; |
1866 | bd2 = bd5 = 0; |
1867 | } |
1868 | if (bbe >= 0) |
1869 | bb2 += bbe; |
1870 | else |
1871 | bd2 -= bbe; |
1872 | bs2 = bb2; |
1873 | #ifdef Honor_FLT_ROUNDS |
1874 | if (rounding != 1) |
1875 | bs2++; |
1876 | #endif |
1877 | #ifdef Avoid_Underflow |
1878 | j = bbe - scale; |
1879 | i = j + bbbits - 1; /* logb(rv) */ |
1880 | if (i < Emin) /* denormal */ |
1881 | j += P - Emin; |
1882 | else |
1883 | j = P + 1 - bbbits; |
1884 | #else /*Avoid_Underflow*/ |
1885 | #ifdef Sudden_Underflow |
1886 | #ifdef IBM |
1887 | j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3); |
1888 | #else |
1889 | j = P + 1 - bbbits; |
1890 | #endif |
1891 | #else /*Sudden_Underflow*/ |
1892 | j = bbe; |
1893 | i = j + bbbits - 1; /* logb(rv) */ |
1894 | if (i < Emin) /* denormal */ |
1895 | j += P - Emin; |
1896 | else |
1897 | j = P + 1 - bbbits; |
1898 | #endif /*Sudden_Underflow*/ |
1899 | #endif /*Avoid_Underflow*/ |
1900 | bb2 += j; |
1901 | bd2 += j; |
1902 | #ifdef Avoid_Underflow |
1903 | bd2 += scale; |
1904 | #endif |
1905 | i = bb2 < bd2 ? bb2 : bd2; |
1906 | if (i > bs2) |
1907 | i = bs2; |
1908 | if (i > 0) { |
1909 | bb2 -= i; |
1910 | bd2 -= i; |
1911 | bs2 -= i; |
1912 | } |
1913 | if (bb5 > 0) { |
1914 | bs = pow5mult(bs, bb5); |
1915 | bb1 = mult(bs, bb); |
1916 | Bfree(bb); |
1917 | bb = bb1; |
1918 | } |
1919 | if (bb2 > 0) |
1920 | bb = lshift(bb, bb2); |
1921 | if (bd5 > 0) |
1922 | bd = pow5mult(bd, bd5); |
1923 | if (bd2 > 0) |
1924 | bd = lshift(bd, bd2); |
1925 | if (bs2 > 0) |
1926 | bs = lshift(bs, bs2); |
1927 | delta = diff(bb, bd); |
1928 | dsign = delta->sign; |
1929 | delta->sign = 0; |
1930 | i = cmp(delta, bs); |
1931 | #ifdef Honor_FLT_ROUNDS |
1932 | if (rounding != 1) { |
1933 | if (i < 0) { |
1934 | /* Error is less than an ulp */ |
1935 | if (!delta->x[0] && delta->wds <= 1) { |
1936 | /* exact */ |
1937 | #ifdef SET_INEXACT |
1938 | inexact = 0; |
1939 | #endif |
1940 | break; |
1941 | } |
1942 | if (rounding) { |
1943 | if (dsign) { |
1944 | adj = 1.; |
1945 | goto apply_adj; |
1946 | } |
1947 | } |
1948 | else if (!dsign) { |
1949 | adj = -1.; |
1950 | if (!word1(rv) |
1951 | && !(word0(rv) & Frac_mask)) { |
1952 | y = word0(rv) & Exp_mask; |
1953 | #ifdef Avoid_Underflow |
1954 | if (!scale || y > 2*P*Exp_msk1) |
1955 | #else |
1956 | if (y) |
1957 | #endif |
1958 | { |
1959 | delta = lshift(delta,Log2P); |
1960 | if (cmp(delta, bs) <= 0) |
1961 | adj = -0.5; |
1962 | } |
1963 | } |
1964 | apply_adj: |
1965 | #ifdef Avoid_Underflow |
1966 | if (scale && (y = word0(rv) & Exp_mask) |
1967 | <= 2*P*Exp_msk1) |
1968 | word0(adj) += (2*P+1)*Exp_msk1 - y; |
1969 | #else |
1970 | #ifdef Sudden_Underflow |
1971 | if ((word0(rv) & Exp_mask) <= |
1972 | P*Exp_msk1) { |
1973 | word0(rv) += P*Exp_msk1; |
1974 | dval(rv) += adj*ulp(dval(rv)); |
1975 | word0(rv) -= P*Exp_msk1; |
1976 | } |
1977 | else |
1978 | #endif /*Sudden_Underflow*/ |
1979 | #endif /*Avoid_Underflow*/ |
1980 | dval(rv) += adj*ulp(dval(rv)); |
1981 | } |
1982 | break; |
1983 | } |
1984 | adj = ratio(delta, bs); |
1985 | if (adj < 1.) |
1986 | adj = 1.; |
1987 | if (adj <= 0x7ffffffe) { |
1988 | /* adj = rounding ? ceil(adj) : floor(adj); */ |
1989 | y = adj; |
1990 | if (y != adj) { |
1991 | if (!((rounding>>1) ^ dsign)) |
1992 | y++; |
1993 | adj = y; |
1994 | } |
1995 | } |
1996 | #ifdef Avoid_Underflow |
1997 | if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1) |
1998 | word0(adj) += (2*P+1)*Exp_msk1 - y; |
1999 | #else |
2000 | #ifdef Sudden_Underflow |
2001 | if ((word0(rv) & Exp_mask) <= P*Exp_msk1) { |
2002 | word0(rv) += P*Exp_msk1; |
2003 | adj *= ulp(dval(rv)); |
2004 | if (dsign) |
2005 | dval(rv) += adj; |
2006 | else |
2007 | dval(rv) -= adj; |
2008 | word0(rv) -= P*Exp_msk1; |
2009 | goto cont; |
2010 | } |
2011 | #endif /*Sudden_Underflow*/ |
2012 | #endif /*Avoid_Underflow*/ |
2013 | adj *= ulp(dval(rv)); |
2014 | if (dsign) |
2015 | dval(rv) += adj; |
2016 | else |
2017 | dval(rv) -= adj; |
2018 | goto cont; |
2019 | } |
2020 | #endif /*Honor_FLT_ROUNDS*/ |
2021 | |
2022 | if (i < 0) { |
2023 | /* Error is less than half an ulp -- check for |
2024 | * special case of mantissa a power of two. |
2025 | */ |
2026 | if (dsign || word1(rv) || word0(rv) & Bndry_mask |
2027 | #ifdef IEEE_Arith |
2028 | #ifdef Avoid_Underflow |
2029 | || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1 |
2030 | #else |
2031 | || (word0(rv) & Exp_mask) <= Exp_msk1 |
2032 | #endif |
2033 | #endif |
2034 | ) { |
2035 | #ifdef SET_INEXACT |
2036 | if (!delta->x[0] && delta->wds <= 1) |
2037 | inexact = 0; |
2038 | #endif |
2039 | break; |
2040 | } |
2041 | if (!delta->x[0] && delta->wds <= 1) { |
2042 | /* exact result */ |
2043 | #ifdef SET_INEXACT |
2044 | inexact = 0; |
2045 | #endif |
2046 | break; |
2047 | } |
2048 | delta = lshift(delta,Log2P); |
2049 | if (cmp(delta, bs) > 0) |
2050 | goto drop_down; |
2051 | break; |
2052 | } |
2053 | if (i == 0) { |
2054 | /* exactly half-way between */ |
2055 | if (dsign) { |
2056 | if ((word0(rv) & Bndry_mask1) == Bndry_mask1 |
2057 | && word1(rv) == ( |
2058 | #ifdef Avoid_Underflow |
2059 | (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1) |
2060 | ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) : |
2061 | #endif |
2062 | 0xffffffff)) { |
2063 | /*boundary case -- increment exponent*/ |
2064 | word0(rv) = (word0(rv) & Exp_mask) |
2065 | + Exp_msk1 |
2066 | #ifdef IBM |
2067 | | Exp_msk1 >> 4 |
2068 | #endif |
2069 | ; |
2070 | word1(rv) = 0; |
2071 | #ifdef Avoid_Underflow |
2072 | dsign = 0; |
2073 | #endif |
2074 | break; |
2075 | } |
2076 | } |
2077 | else if (!(word0(rv) & Bndry_mask) && !word1(rv)) { |
2078 | drop_down: |
2079 | /* boundary case -- decrement exponent */ |
2080 | #ifdef Sudden_Underflow /*{{*/ |
2081 | L = word0(rv) & Exp_mask; |
2082 | #ifdef IBM |
2083 | if (L < Exp_msk1) |
2084 | #else |
2085 | #ifdef Avoid_Underflow |
2086 | if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1)) |
2087 | #else |
2088 | if (L <= Exp_msk1) |
2089 | #endif /*Avoid_Underflow*/ |
2090 | #endif /*IBM*/ |
2091 | goto undfl; |
2092 | L -= Exp_msk1; |
2093 | #else /*Sudden_Underflow}{*/ |
2094 | #ifdef Avoid_Underflow |
2095 | if (scale) { |
2096 | L = word0(rv) & Exp_mask; |
2097 | if (L <= (2*P+1)*Exp_msk1) { |
2098 | if (L > (P+2)*Exp_msk1) |
2099 | /* round even ==> */ |
2100 | /* accept rv */ |
2101 | break; |
2102 | /* rv = smallest denormal */ |
2103 | goto undfl; |
2104 | } |
2105 | } |
2106 | #endif /*Avoid_Underflow*/ |
2107 | L = (word0(rv) & Exp_mask) - Exp_msk1; |
2108 | #endif /*Sudden_Underflow}}*/ |
2109 | word0(rv) = L | Bndry_mask1; |
2110 | word1(rv) = 0xffffffff; |
2111 | #ifdef IBM |
2112 | goto cont; |
2113 | #else |
2114 | break; |
2115 | #endif |
2116 | } |
2117 | #ifndef ROUND_BIASED |
2118 | if (!(word1(rv) & LSB)) |
2119 | break; |
2120 | #endif |
2121 | if (dsign) |
2122 | dval(rv) += ulp(dval(rv)); |
2123 | #ifndef ROUND_BIASED |
2124 | else { |
2125 | dval(rv) -= ulp(dval(rv)); |
2126 | #ifndef Sudden_Underflow |
2127 | if (!dval(rv)) |
2128 | goto undfl; |
2129 | #endif |
2130 | } |
2131 | #ifdef Avoid_Underflow |
2132 | dsign = 1 - dsign; |
2133 | #endif |
2134 | #endif |
2135 | break; |
2136 | } |
2137 | if ((aadj = ratio(delta, bs)) <= 2.) { |
2138 | if (dsign) |
2139 | aadj = aadj1 = 1.; |
2140 | else if (word1(rv) || word0(rv) & Bndry_mask) { |
2141 | #ifndef Sudden_Underflow |
2142 | if (word1(rv) == Tiny1 && !word0(rv)) |
2143 | goto undfl; |
2144 | #endif |
2145 | aadj = 1.; |
2146 | aadj1 = -1.; |
2147 | } |
2148 | else { |
2149 | /* special case -- power of FLT_RADIX to be */ |
2150 | /* rounded down... */ |
2151 | |
2152 | if (aadj < 2./FLT_RADIX) |
2153 | aadj = 1./FLT_RADIX; |
2154 | else |
2155 | aadj *= 0.5; |
2156 | aadj1 = -aadj; |
2157 | } |
2158 | } |
2159 | else { |
2160 | aadj *= 0.5; |
2161 | aadj1 = dsign ? aadj : -aadj; |
2162 | #ifdef Check_FLT_ROUNDS |
2163 | switch(Rounding) { |
2164 | case 2: /* towards +infinity */ |
2165 | aadj1 -= 0.5; |
2166 | break; |
2167 | case 0: /* towards 0 */ |
2168 | case 3: /* towards -infinity */ |
2169 | aadj1 += 0.5; |
2170 | } |
2171 | #else |
2172 | if (Flt_Rounds == 0) |
2173 | aadj1 += 0.5; |
2174 | #endif /*Check_FLT_ROUNDS*/ |
2175 | } |
2176 | y = word0(rv) & Exp_mask; |
2177 | |
2178 | /* Check for overflow */ |
2179 | |
2180 | if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) { |
2181 | dval(rv0) = dval(rv); |
2182 | word0(rv) -= P*Exp_msk1; |
2183 | adj = aadj1 * ulp(dval(rv)); |
2184 | dval(rv) += adj; |
2185 | if ((word0(rv) & Exp_mask) >= |
2186 | Exp_msk1*(DBL_MAX_EXP+Bias-P)) { |
2187 | if (word0(rv0) == Big0 && word1(rv0) == Big1) |
2188 | goto ovfl; |
2189 | word0(rv) = Big0; |
2190 | word1(rv) = Big1; |
2191 | goto cont; |
2192 | } |
2193 | else |
2194 | word0(rv) += P*Exp_msk1; |
2195 | } |
2196 | else { |
2197 | #ifdef Avoid_Underflow |
2198 | if (scale && y <= 2*P*Exp_msk1) { |
2199 | if (aadj <= 0x7fffffff) { |
2200 | if ((z = (ULong)aadj) <= 0) |
2201 | z = 1; |
2202 | aadj = z; |
2203 | aadj1 = dsign ? aadj : -aadj; |
2204 | } |
2205 | dval(aadj2) = aadj1; |
2206 | word0(aadj2) += (2*P+1)*Exp_msk1 - y; |
2207 | aadj1 = dval(aadj2); |
2208 | } |
2209 | adj = aadj1 * ulp(dval(rv)); |
2210 | dval(rv) += adj; |
2211 | #else |
2212 | #ifdef Sudden_Underflow |
2213 | if ((word0(rv) & Exp_mask) <= P*Exp_msk1) { |
2214 | dval(rv0) = dval(rv); |
2215 | word0(rv) += P*Exp_msk1; |
2216 | adj = aadj1 * ulp(dval(rv)); |
2217 | dval(rv) += adj; |
2218 | #ifdef IBM |
2219 | if ((word0(rv) & Exp_mask) < P*Exp_msk1) |
2220 | #else |
2221 | if ((word0(rv) & Exp_mask) <= P*Exp_msk1) |
2222 | #endif |
2223 | { |
2224 | if (word0(rv0) == Tiny0 |
2225 | && word1(rv0) == Tiny1) |
2226 | goto undfl; |
2227 | word0(rv) = Tiny0; |
2228 | word1(rv) = Tiny1; |
2229 | goto cont; |
2230 | } |
2231 | else |
2232 | word0(rv) -= P*Exp_msk1; |
2233 | } |
2234 | else { |
2235 | adj = aadj1 * ulp(dval(rv)); |
2236 | dval(rv) += adj; |
2237 | } |
2238 | #else /*Sudden_Underflow*/ |
2239 | /* Compute adj so that the IEEE rounding rules will |
2240 | * correctly round rv + adj in some half-way cases. |
2241 | * If rv * ulp(rv) is denormalized (i.e., |
2242 | * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid |
2243 | * trouble from bits lost to denormalization; |
2244 | * example: 1.2e-307 . |
2245 | */ |
2246 | if (y <= (P-1)*Exp_msk1 && aadj > 1.) { |
2247 | aadj1 = (double)(int)(aadj + 0.5); |
2248 | if (!dsign) |
2249 | aadj1 = -aadj1; |
2250 | } |
2251 | adj = aadj1 * ulp(dval(rv)); |
2252 | dval(rv) += adj; |
2253 | #endif /*Sudden_Underflow*/ |
2254 | #endif /*Avoid_Underflow*/ |
2255 | } |
2256 | z = word0(rv) & Exp_mask; |
2257 | #ifndef SET_INEXACT |
2258 | #ifdef Avoid_Underflow |
2259 | if (!scale) |
2260 | #endif |
2261 | if (y == z) { |
2262 | /* Can we stop now? */ |
2263 | L = (Long)aadj; |
2264 | aadj -= L; |
2265 | /* The tolerances below are conservative. */ |
2266 | if (dsign || word1(rv) || word0(rv) & Bndry_mask) { |
2267 | if (aadj < .4999999 || aadj > .5000001) |
2268 | break; |
2269 | } |
2270 | else if (aadj < .4999999/FLT_RADIX) |
2271 | break; |
2272 | } |
2273 | #endif |
2274 | cont: |
2275 | Bfree(bb); |
2276 | Bfree(bd); |
2277 | Bfree(bs); |
2278 | Bfree(delta); |
2279 | } |
2280 | #ifdef SET_INEXACT |
2281 | if (inexact) { |
2282 | if (!oldinexact) { |
2283 | word0(rv0) = Exp_1 + (70 << Exp_shift); |
2284 | word1(rv0) = 0; |
2285 | dval(rv0) += 1.; |
2286 | } |
2287 | } |
2288 | else if (!oldinexact) |
2289 | clear_inexact(); |
2290 | #endif |
2291 | #ifdef Avoid_Underflow |
2292 | if (scale) { |
2293 | word0(rv0) = Exp_1 - 2*P*Exp_msk1; |
2294 | word1(rv0) = 0; |
2295 | dval(rv) *= dval(rv0); |
2296 | #ifndef NO_ERRNO |
2297 | /* try to avoid the bug of testing an 8087 register value */ |
2298 | if (word0(rv) == 0 && word1(rv) == 0) |
2299 | errno = ERANGE; |
2300 | #endif |
2301 | } |
2302 | #endif /* Avoid_Underflow */ |
2303 | #ifdef SET_INEXACT |
2304 | if (inexact && !(word0(rv) & Exp_mask)) { |
2305 | /* set underflow bit */ |
2306 | dval(rv0) = 1e-300; |
2307 | dval(rv0) *= dval(rv0); |
2308 | } |
2309 | #endif |
2310 | retfree: |
2311 | Bfree(bb); |
2312 | Bfree(bd); |
2313 | Bfree(bs); |
2314 | Bfree(bd0); |
2315 | Bfree(delta); |
2316 | ret: |
2317 | if (se) |
2318 | *se = (char *)s; |
2319 | return sign ? -dval(rv) : dval(rv); |
2320 | } |
2321 | |
2322 | static int |
2323 | quorem |
2324 | (Bigint *b, Bigint *S) |
2325 | { |
2326 | int n; |
2327 | ULong *bx, *bxe, q, *sx, *sxe; |
2328 | #ifdef ULLong |
2329 | ULLong borrow, carry, y, ys; |
2330 | #else |
2331 | ULong borrow, carry, y, ys; |
2332 | #ifdef Pack_32 |
2333 | ULong si, z, zs; |
2334 | #endif |
2335 | #endif |
2336 | |
2337 | n = S->wds; |
2338 | #ifdef DEBUG |
2339 | /*debug*/ if (b->wds > n) |
2340 | /*debug*/ Bug("oversize b in quorem" ); |
2341 | #endif |
2342 | if (b->wds < n) |
2343 | return 0; |
2344 | sx = S->x; |
2345 | sxe = sx + --n; |
2346 | bx = b->x; |
2347 | bxe = bx + n; |
2348 | q = *bxe / (*sxe + 1); /* ensure q <= true quotient */ |
2349 | #ifdef DEBUG |
2350 | /*debug*/ if (q > 9) |
2351 | /*debug*/ Bug("oversized quotient in quorem" ); |
2352 | #endif |
2353 | if (q) { |
2354 | borrow = 0; |
2355 | carry = 0; |
2356 | do { |
2357 | #ifdef ULLong |
2358 | ys = *sx++ * (ULLong)q + carry; |
2359 | carry = ys >> 32; |
2360 | y = *bx - (ys & FFFFFFFF) - borrow; |
2361 | borrow = y >> 32 & (ULong)1; |
2362 | *bx++ = (ULong)y & FFFFFFFF; |
2363 | #else |
2364 | #ifdef Pack_32 |
2365 | si = *sx++; |
2366 | ys = (si & 0xffff) * q + carry; |
2367 | zs = (si >> 16) * q + (ys >> 16); |
2368 | carry = zs >> 16; |
2369 | y = (*bx & 0xffff) - (ys & 0xffff) - borrow; |
2370 | borrow = (y & 0x10000) >> 16; |
2371 | z = (*bx >> 16) - (zs & 0xffff) - borrow; |
2372 | borrow = (z & 0x10000) >> 16; |
2373 | Storeinc(bx, z, y); |
2374 | #else |
2375 | ys = *sx++ * q + carry; |
2376 | carry = ys >> 16; |
2377 | y = *bx - (ys & 0xffff) - borrow; |
2378 | borrow = (y & 0x10000) >> 16; |
2379 | *bx++ = y & 0xffff; |
2380 | #endif |
2381 | #endif |
2382 | } |
2383 | while(sx <= sxe); |
2384 | if (!*bxe) { |
2385 | bx = b->x; |
2386 | while(--bxe > bx && !*bxe) |
2387 | --n; |
2388 | b->wds = n; |
2389 | } |
2390 | } |
2391 | if (cmp(b, S) >= 0) { |
2392 | q++; |
2393 | borrow = 0; |
2394 | carry = 0; |
2395 | bx = b->x; |
2396 | sx = S->x; |
2397 | do { |
2398 | #ifdef ULLong |
2399 | ys = *sx++ + carry; |
2400 | carry = ys >> 32; |
2401 | y = *bx - (ys & FFFFFFFF) - borrow; |
2402 | borrow = y >> 32 & (ULong)1; |
2403 | *bx++ = (ULong)y & FFFFFFFF; |
2404 | #else |
2405 | #ifdef Pack_32 |
2406 | si = *sx++; |
2407 | ys = (si & 0xffff) + carry; |
2408 | zs = (si >> 16) + (ys >> 16); |
2409 | carry = zs >> 16; |
2410 | y = (*bx & 0xffff) - (ys & 0xffff) - borrow; |
2411 | borrow = (y & 0x10000) >> 16; |
2412 | z = (*bx >> 16) - (zs & 0xffff) - borrow; |
2413 | borrow = (z & 0x10000) >> 16; |
2414 | Storeinc(bx, z, y); |
2415 | #else |
2416 | ys = *sx++ + carry; |
2417 | carry = ys >> 16; |
2418 | y = *bx - (ys & 0xffff) - borrow; |
2419 | borrow = (y & 0x10000) >> 16; |
2420 | *bx++ = y & 0xffff; |
2421 | #endif |
2422 | #endif |
2423 | } |
2424 | while(sx <= sxe); |
2425 | bx = b->x; |
2426 | bxe = bx + n; |
2427 | if (!*bxe) { |
2428 | while(--bxe > bx && !*bxe) |
2429 | --n; |
2430 | b->wds = n; |
2431 | } |
2432 | } |
2433 | return q; |
2434 | } |
2435 | |
2436 | #ifndef MULTIPLE_THREADS |
2437 | static char *dtoa_result; |
2438 | #endif |
2439 | |
2440 | static char * |
2441 | rv_alloc(int i) |
2442 | { |
2443 | int j, k, *r; |
2444 | |
2445 | j = sizeof(ULong); |
2446 | for(k = 0; |
2447 | sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= (unsigned)i; |
2448 | j <<= 1) |
2449 | k++; |
2450 | r = (int*)Balloc(k); |
2451 | *r = k; |
2452 | return |
2453 | #ifndef MULTIPLE_THREADS |
2454 | dtoa_result = |
2455 | #endif |
2456 | (char *)(r+1); |
2457 | } |
2458 | |
2459 | static char * |
2460 | nrv_alloc(CONST char *s, char **rve, int n) |
2461 | { |
2462 | char *rv, *t; |
2463 | |
2464 | t = rv = rv_alloc(n); |
2465 | while((*t = *s++)) t++; |
2466 | if (rve) |
2467 | *rve = t; |
2468 | return rv; |
2469 | } |
2470 | |
2471 | /* freedtoa(s) must be used to free values s returned by dtoa |
2472 | * when MULTIPLE_THREADS is #defined. It should be used in all cases, |
2473 | * but for consistency with earlier versions of dtoa, it is optional |
2474 | * when MULTIPLE_THREADS is not defined. |
2475 | */ |
2476 | |
2477 | void |
2478 | freedtoa(char *s) |
2479 | { |
2480 | Bigint *b = (Bigint *)((int *)s - 1); |
2481 | b->maxwds = 1 << (b->k = *(int*)b); |
2482 | Bfree(b); |
2483 | #ifndef MULTIPLE_THREADS |
2484 | if (s == dtoa_result) |
2485 | dtoa_result = 0; |
2486 | #endif |
2487 | } |
2488 | |
2489 | /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string. |
2490 | * |
2491 | * Inspired by "How to Print Floating-Point Numbers Accurately" by |
2492 | * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101]. |
2493 | * |
2494 | * Modifications: |
2495 | * 1. Rather than iterating, we use a simple numeric overestimate |
2496 | * to determine k = floor(log10(d)). We scale relevant |
2497 | * quantities using O(log2(k)) rather than O(k) multiplications. |
2498 | * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't |
2499 | * try to generate digits strictly left to right. Instead, we |
2500 | * compute with fewer bits and propagate the carry if necessary |
2501 | * when rounding the final digit up. This is often faster. |
2502 | * 3. Under the assumption that input will be rounded nearest, |
2503 | * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22. |
2504 | * That is, we allow equality in stopping tests when the |
2505 | * round-nearest rule will give the same floating-point value |
2506 | * as would satisfaction of the stopping test with strict |
2507 | * inequality. |
2508 | * 4. We remove common factors of powers of 2 from relevant |
2509 | * quantities. |
2510 | * 5. When converting floating-point integers less than 1e16, |
2511 | * we use floating-point arithmetic rather than resorting |
2512 | * to multiple-precision integers. |
2513 | * 6. When asked to produce fewer than 15 digits, we first try |
2514 | * to get by with floating-point arithmetic; we resort to |
2515 | * multiple-precision integer arithmetic only if we cannot |
2516 | * guarantee that the floating-point calculation has given |
2517 | * the correctly rounded result. For k requested digits and |
2518 | * "uniformly" distributed input, the probability is |
2519 | * something like 10^(k-15) that we must resort to the Long |
2520 | * calculation. |
2521 | */ |
2522 | |
2523 | char * |
2524 | dtoa |
2525 | (double dd, int mode, int ndigits, int *decpt, int *sign, char **rve) |
2526 | { |
2527 | /* Arguments ndigits, decpt, sign are similar to those |
2528 | of ecvt and fcvt; trailing zeros are suppressed from |
2529 | the returned string. If not null, *rve is set to point |
2530 | to the end of the return value. If d is +-Infinity or NaN, |
2531 | then *decpt is set to 9999. |
2532 | |
2533 | mode: |
2534 | 0 ==> shortest string that yields d when read in |
2535 | and rounded to nearest. |
2536 | 1 ==> like 0, but with Steele & White stopping rule; |
2537 | e.g. with IEEE P754 arithmetic , mode 0 gives |
2538 | 1e23 whereas mode 1 gives 9.999999999999999e22. |
2539 | 2 ==> max(1,ndigits) significant digits. This gives a |
2540 | return value similar to that of ecvt, except |
2541 | that trailing zeros are suppressed. |
2542 | 3 ==> through ndigits past the decimal point. This |
2543 | gives a return value similar to that from fcvt, |
2544 | except that trailing zeros are suppressed, and |
2545 | ndigits can be negative. |
2546 | 4,5 ==> similar to 2 and 3, respectively, but (in |
2547 | round-nearest mode) with the tests of mode 0 to |
2548 | possibly return a shorter string that rounds to d. |
2549 | With IEEE arithmetic and compilation with |
2550 | -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same |
2551 | as modes 2 and 3 when FLT_ROUNDS != 1. |
2552 | 6-9 ==> Debugging modes similar to mode - 4: don't try |
2553 | fast floating-point estimate (if applicable). |
2554 | |
2555 | Values of mode other than 0-9 are treated as mode 0. |
2556 | |
2557 | Sufficient space is allocated to the return value |
2558 | to hold the suppressed trailing zeros. |
2559 | */ |
2560 | |
2561 | int bbits, b2, b5, be, dig, i, ieps, ilim = 0, ilim0, ilim1 = 0, |
2562 | j, j1, k, k0, k_check, leftright, m2, m5, s2, s5, |
2563 | spec_case, try_quick; |
2564 | Long L; |
2565 | #ifndef Sudden_Underflow |
2566 | int denorm; |
2567 | ULong x; |
2568 | #endif |
2569 | Bigint *b, *b1, *delta, *mlo = NULL, *mhi, *S; |
2570 | U d, d2, eps; |
2571 | double ds; |
2572 | char *s, *s0; |
2573 | #ifdef Honor_FLT_ROUNDS |
2574 | int rounding; |
2575 | #endif |
2576 | #ifdef SET_INEXACT |
2577 | int inexact, oldinexact; |
2578 | #endif |
2579 | |
2580 | #ifndef MULTIPLE_THREADS |
2581 | if (dtoa_result) { |
2582 | freedtoa(dtoa_result); |
2583 | dtoa_result = 0; |
2584 | } |
2585 | #endif |
2586 | |
2587 | dval(d) = dd; |
2588 | if (word0(d) & Sign_bit) { |
2589 | /* set sign for everything, including 0's and NaNs */ |
2590 | *sign = 1; |
2591 | word0(d) &= ~Sign_bit; /* clear sign bit */ |
2592 | } |
2593 | else |
2594 | *sign = 0; |
2595 | |
2596 | #if defined(IEEE_Arith) + defined(VAX) |
2597 | #ifdef IEEE_Arith |
2598 | if ((word0(d) & Exp_mask) == Exp_mask) |
2599 | #else |
2600 | if (word0(d) == 0x8000) |
2601 | #endif |
2602 | { |
2603 | /* Infinity or NaN */ |
2604 | *decpt = 9999; |
2605 | #ifdef IEEE_Arith |
2606 | if (!word1(d) && !(word0(d) & 0xfffff)) |
2607 | return nrv_alloc("Infinity" , rve, 8); |
2608 | #endif |
2609 | return nrv_alloc("NaN" , rve, 3); |
2610 | } |
2611 | #endif |
2612 | #ifdef IBM |
2613 | dval(d) += 0; /* normalize */ |
2614 | #endif |
2615 | if (!dval(d)) { |
2616 | *decpt = 1; |
2617 | return nrv_alloc("0" , rve, 1); |
2618 | } |
2619 | |
2620 | #ifdef SET_INEXACT |
2621 | try_quick = oldinexact = get_inexact(); |
2622 | inexact = 1; |
2623 | #endif |
2624 | #ifdef Honor_FLT_ROUNDS |
2625 | if ((rounding = Flt_Rounds) >= 2) { |
2626 | if (*sign) |
2627 | rounding = rounding == 2 ? 0 : 2; |
2628 | else |
2629 | if (rounding != 2) |
2630 | rounding = 0; |
2631 | } |
2632 | #endif |
2633 | |
2634 | b = d2b(dval(d), &be, &bbits); |
2635 | #ifdef Sudden_Underflow |
2636 | i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)); |
2637 | #else |
2638 | if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) { |
2639 | #endif |
2640 | dval(d2) = dval(d); |
2641 | word0(d2) &= Frac_mask1; |
2642 | word0(d2) |= Exp_11; |
2643 | #ifdef IBM |
2644 | if (j = 11 - hi0bits(word0(d2) & Frac_mask)) |
2645 | dval(d2) /= 1 << j; |
2646 | #endif |
2647 | |
2648 | /* log(x) ~=~ log(1.5) + (x-1.5)/1.5 |
2649 | * log10(x) = log(x) / log(10) |
2650 | * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10)) |
2651 | * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2) |
2652 | * |
2653 | * This suggests computing an approximation k to log10(d) by |
2654 | * |
2655 | * k = (i - Bias)*0.301029995663981 |
2656 | * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 ); |
2657 | * |
2658 | * We want k to be too large rather than too small. |
2659 | * The error in the first-order Taylor series approximation |
2660 | * is in our favor, so we just round up the constant enough |
2661 | * to compensate for any error in the multiplication of |
2662 | * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077, |
2663 | * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14, |
2664 | * adding 1e-13 to the constant term more than suffices. |
2665 | * Hence we adjust the constant term to 0.1760912590558. |
2666 | * (We could get a more accurate k by invoking log10, |
2667 | * but this is probably not worthwhile.) |
2668 | */ |
2669 | |
2670 | i -= Bias; |
2671 | #ifdef IBM |
2672 | i <<= 2; |
2673 | i += j; |
2674 | #endif |
2675 | #ifndef Sudden_Underflow |
2676 | denorm = 0; |
2677 | } |
2678 | else { |
2679 | /* d is denormalized */ |
2680 | |
2681 | i = bbits + be + (Bias + (P-1) - 1); |
2682 | x = i > 32 ? word0(d) << (64 - i) | word1(d) >> (i - 32) |
2683 | : word1(d) << (32 - i); |
2684 | dval(d2) = x; |
2685 | word0(d2) -= 31*Exp_msk1; /* adjust exponent */ |
2686 | i -= (Bias + (P-1) - 1) + 1; |
2687 | denorm = 1; |
2688 | } |
2689 | #endif |
2690 | ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981; |
2691 | k = (int)ds; |
2692 | if (ds < 0. && ds != k) |
2693 | k--; /* want k = floor(ds) */ |
2694 | k_check = 1; |
2695 | if (k >= 0 && k <= Ten_pmax) { |
2696 | if (dval(d) < tens[k]) |
2697 | k--; |
2698 | k_check = 0; |
2699 | } |
2700 | j = bbits - i - 1; |
2701 | if (j >= 0) { |
2702 | b2 = 0; |
2703 | s2 = j; |
2704 | } |
2705 | else { |
2706 | b2 = -j; |
2707 | s2 = 0; |
2708 | } |
2709 | if (k >= 0) { |
2710 | b5 = 0; |
2711 | s5 = k; |
2712 | s2 += k; |
2713 | } |
2714 | else { |
2715 | b2 -= k; |
2716 | b5 = -k; |
2717 | s5 = 0; |
2718 | } |
2719 | if (mode < 0 || mode > 9) |
2720 | mode = 0; |
2721 | |
2722 | #ifndef SET_INEXACT |
2723 | #ifdef Check_FLT_ROUNDS |
2724 | try_quick = Rounding == 1; |
2725 | #else |
2726 | try_quick = 1; |
2727 | #endif |
2728 | #endif /*SET_INEXACT*/ |
2729 | |
2730 | if (mode > 5) { |
2731 | mode -= 4; |
2732 | try_quick = 0; |
2733 | } |
2734 | leftright = 1; |
2735 | switch(mode) { |
2736 | case 0: |
2737 | case 1: |
2738 | ilim = ilim1 = -1; |
2739 | i = 18; |
2740 | ndigits = 0; |
2741 | break; |
2742 | case 2: |
2743 | leftright = 0; |
2744 | /* no break */ |
2745 | case 4: |
2746 | if (ndigits <= 0) |
2747 | ndigits = 1; |
2748 | ilim = ilim1 = i = ndigits; |
2749 | break; |
2750 | case 3: |
2751 | leftright = 0; |
2752 | /* no break */ |
2753 | case 5: |
2754 | i = ndigits + k + 1; |
2755 | ilim = i; |
2756 | ilim1 = i - 1; |
2757 | if (i <= 0) |
2758 | i = 1; |
2759 | } |
2760 | s = s0 = rv_alloc(i); |
2761 | |
2762 | #ifdef Honor_FLT_ROUNDS |
2763 | if (mode > 1 && rounding != 1) |
2764 | leftright = 0; |
2765 | #endif |
2766 | |
2767 | if (ilim >= 0 && ilim <= Quick_max && try_quick) { |
2768 | |
2769 | /* Try to get by with floating-point arithmetic. */ |
2770 | |
2771 | i = 0; |
2772 | dval(d2) = dval(d); |
2773 | k0 = k; |
2774 | ilim0 = ilim; |
2775 | ieps = 2; /* conservative */ |
2776 | if (k > 0) { |
2777 | ds = tens[k&0xf]; |
2778 | j = k >> 4; |
2779 | if (j & Bletch) { |
2780 | /* prevent overflows */ |
2781 | j &= Bletch - 1; |
2782 | dval(d) /= bigtens[n_bigtens-1]; |
2783 | ieps++; |
2784 | } |
2785 | for(; j; j >>= 1, i++) |
2786 | if (j & 1) { |
2787 | ieps++; |
2788 | ds *= bigtens[i]; |
2789 | } |
2790 | dval(d) /= ds; |
2791 | } |
2792 | else if ((j1 = -k)) { |
2793 | dval(d) *= tens[j1 & 0xf]; |
2794 | for(j = j1 >> 4; j; j >>= 1, i++) |
2795 | if (j & 1) { |
2796 | ieps++; |
2797 | dval(d) *= bigtens[i]; |
2798 | } |
2799 | } |
2800 | if (k_check && dval(d) < 1. && ilim > 0) { |
2801 | if (ilim1 <= 0) |
2802 | goto fast_failed; |
2803 | ilim = ilim1; |
2804 | k--; |
2805 | dval(d) *= 10.; |
2806 | ieps++; |
2807 | } |
2808 | dval(eps) = ieps*dval(d) + 7.; |
2809 | word0(eps) -= (P-1)*Exp_msk1; |
2810 | if (ilim == 0) { |
2811 | S = mhi = 0; |
2812 | dval(d) -= 5.; |
2813 | if (dval(d) > dval(eps)) |
2814 | goto one_digit; |
2815 | if (dval(d) < -dval(eps)) |
2816 | goto no_digits; |
2817 | goto fast_failed; |
2818 | } |
2819 | #ifndef No_leftright |
2820 | if (leftright) { |
2821 | /* Use Steele & White method of only |
2822 | * generating digits needed. |
2823 | */ |
2824 | dval(eps) = 0.5/tens[ilim-1] - dval(eps); |
2825 | for(i = 0;;) { |
2826 | L = (long int)dval(d); |
2827 | dval(d) -= L; |
2828 | *s++ = '0' + (int)L; |
2829 | if (dval(d) < dval(eps)) |
2830 | goto ret1; |
2831 | if (1. - dval(d) < dval(eps)) |
2832 | goto bump_up; |
2833 | if (++i >= ilim) |
2834 | break; |
2835 | dval(eps) *= 10.; |
2836 | dval(d) *= 10.; |
2837 | } |
2838 | } |
2839 | else { |
2840 | #endif |
2841 | /* Generate ilim digits, then fix them up. */ |
2842 | dval(eps) *= tens[ilim-1]; |
2843 | for(i = 1;; i++, dval(d) *= 10.) { |
2844 | L = (Long)(dval(d)); |
2845 | if (!(dval(d) -= L)) |
2846 | ilim = i; |
2847 | *s++ = '0' + (int)L; |
2848 | if (i == ilim) { |
2849 | if (dval(d) > 0.5 + dval(eps)) |
2850 | goto bump_up; |
2851 | else if (dval(d) < 0.5 - dval(eps)) { |
2852 | while(*--s == '0') |
2853 | ; |
2854 | s++; |
2855 | goto ret1; |
2856 | } |
2857 | break; |
2858 | } |
2859 | } |
2860 | #ifndef No_leftright |
2861 | } |
2862 | #endif |
2863 | fast_failed: |
2864 | s = s0; |
2865 | dval(d) = dval(d2); |
2866 | k = k0; |
2867 | ilim = ilim0; |
2868 | } |
2869 | |
2870 | /* Do we have a "small" integer? */ |
2871 | |
2872 | if (be >= 0 && k <= Int_max) { |
2873 | /* Yes. */ |
2874 | ds = tens[k]; |
2875 | if (ndigits < 0 && ilim <= 0) { |
2876 | S = mhi = 0; |
2877 | if (ilim < 0 || dval(d) <= 5*ds) |
2878 | goto no_digits; |
2879 | goto one_digit; |
2880 | } |
2881 | for(i = 1;; i++, dval(d) *= 10.) { |
2882 | L = (Long)(dval(d) / ds); |
2883 | dval(d) -= L*ds; |
2884 | #ifdef Check_FLT_ROUNDS |
2885 | /* If FLT_ROUNDS == 2, L will usually be high by 1 */ |
2886 | if (dval(d) < 0) { |
2887 | L--; |
2888 | dval(d) += ds; |
2889 | } |
2890 | #endif |
2891 | *s++ = '0' + (int)L; |
2892 | if (!dval(d)) { |
2893 | #ifdef SET_INEXACT |
2894 | inexact = 0; |
2895 | #endif |
2896 | break; |
2897 | } |
2898 | if (i == ilim) { |
2899 | #ifdef Honor_FLT_ROUNDS |
2900 | if (mode > 1) |
2901 | switch(rounding) { |
2902 | case 0: goto ret1; |
2903 | case 2: goto bump_up; |
2904 | } |
2905 | #endif |
2906 | dval(d) += dval(d); |
2907 | if (dval(d) > ds || (dval(d) == ds && L & 1)) { |
2908 | bump_up: |
2909 | while(*--s == '9') |
2910 | if (s == s0) { |
2911 | k++; |
2912 | *s = '0'; |
2913 | break; |
2914 | } |
2915 | ++*s++; |
2916 | } |
2917 | break; |
2918 | } |
2919 | } |
2920 | goto ret1; |
2921 | } |
2922 | |
2923 | m2 = b2; |
2924 | m5 = b5; |
2925 | mhi = mlo = 0; |
2926 | if (leftright) { |
2927 | i = |
2928 | #ifndef Sudden_Underflow |
2929 | denorm ? be + (Bias + (P-1) - 1 + 1) : |
2930 | #endif |
2931 | #ifdef IBM |
2932 | 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3); |
2933 | #else |
2934 | 1 + P - bbits; |
2935 | #endif |
2936 | b2 += i; |
2937 | s2 += i; |
2938 | mhi = i2b(1); |
2939 | } |
2940 | if (m2 > 0 && s2 > 0) { |
2941 | i = m2 < s2 ? m2 : s2; |
2942 | b2 -= i; |
2943 | m2 -= i; |
2944 | s2 -= i; |
2945 | } |
2946 | if (b5 > 0) { |
2947 | if (leftright) { |
2948 | if (m5 > 0) { |
2949 | mhi = pow5mult(mhi, m5); |
2950 | b1 = mult(mhi, b); |
2951 | Bfree(b); |
2952 | b = b1; |
2953 | } |
2954 | if ((j = b5 - m5)) |
2955 | b = pow5mult(b, j); |
2956 | } |
2957 | else |
2958 | b = pow5mult(b, b5); |
2959 | } |
2960 | S = i2b(1); |
2961 | if (s5 > 0) |
2962 | S = pow5mult(S, s5); |
2963 | |
2964 | /* Check for special case that d is a normalized power of 2. */ |
2965 | |
2966 | spec_case = 0; |
2967 | if ((mode < 2 || leftright) |
2968 | #ifdef Honor_FLT_ROUNDS |
2969 | && rounding == 1 |
2970 | #endif |
2971 | ) { |
2972 | if (!word1(d) && !(word0(d) & Bndry_mask) |
2973 | #ifndef Sudden_Underflow |
2974 | && word0(d) & (Exp_mask & ~Exp_msk1) |
2975 | #endif |
2976 | ) { |
2977 | /* The special case */ |
2978 | b2 += Log2P; |
2979 | s2 += Log2P; |
2980 | spec_case = 1; |
2981 | } |
2982 | } |
2983 | |
2984 | /* Arrange for convenient computation of quotients: |
2985 | * shift left if necessary so divisor has 4 leading 0 bits. |
2986 | * |
2987 | * Perhaps we should just compute leading 28 bits of S once |
2988 | * and for all and pass them and a shift to quorem, so it |
2989 | * can do shifts and ors to compute the numerator for q. |
2990 | */ |
2991 | #ifdef Pack_32 |
2992 | if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f)) |
2993 | i = 32 - i; |
2994 | #else |
2995 | if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf) |
2996 | i = 16 - i; |
2997 | #endif |
2998 | if (i > 4) { |
2999 | i -= 4; |
3000 | b2 += i; |
3001 | m2 += i; |
3002 | s2 += i; |
3003 | } |
3004 | else if (i < 4) { |
3005 | i += 28; |
3006 | b2 += i; |
3007 | m2 += i; |
3008 | s2 += i; |
3009 | } |
3010 | if (b2 > 0) |
3011 | b = lshift(b, b2); |
3012 | if (s2 > 0) |
3013 | S = lshift(S, s2); |
3014 | if (k_check) { |
3015 | if (cmp(b,S) < 0) { |
3016 | k--; |
3017 | b = multadd(b, 10, 0); /* we botched the k estimate */ |
3018 | if (leftright) |
3019 | mhi = multadd(mhi, 10, 0); |
3020 | ilim = ilim1; |
3021 | } |
3022 | } |
3023 | if (ilim <= 0 && (mode == 3 || mode == 5)) { |
3024 | if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) { |
3025 | /* no digits, fcvt style */ |
3026 | no_digits: |
3027 | k = -1 - ndigits; |
3028 | goto ret; |
3029 | } |
3030 | one_digit: |
3031 | *s++ = '1'; |
3032 | k++; |
3033 | goto ret; |
3034 | } |
3035 | if (leftright) { |
3036 | if (m2 > 0) |
3037 | mhi = lshift(mhi, m2); |
3038 | |
3039 | /* Compute mlo -- check for special case |
3040 | * that d is a normalized power of 2. |
3041 | */ |
3042 | |
3043 | mlo = mhi; |
3044 | if (spec_case) { |
3045 | mhi = Balloc(mhi->k); |
3046 | Bcopy(mhi, mlo); |
3047 | mhi = lshift(mhi, Log2P); |
3048 | } |
3049 | |
3050 | for(i = 1;;i++) { |
3051 | dig = quorem(b,S) + '0'; |
3052 | /* Do we yet have the shortest decimal string |
3053 | * that will round to d? |
3054 | */ |
3055 | j = cmp(b, mlo); |
3056 | delta = diff(S, mhi); |
3057 | j1 = delta->sign ? 1 : cmp(b, delta); |
3058 | Bfree(delta); |
3059 | #ifndef ROUND_BIASED |
3060 | if (j1 == 0 && mode != 1 && !(word1(d) & 1) |
3061 | #ifdef Honor_FLT_ROUNDS |
3062 | && rounding >= 1 |
3063 | #endif |
3064 | ) { |
3065 | if (dig == '9') |
3066 | goto round_9_up; |
3067 | if (j > 0) |
3068 | dig++; |
3069 | #ifdef SET_INEXACT |
3070 | else if (!b->x[0] && b->wds <= 1) |
3071 | inexact = 0; |
3072 | #endif |
3073 | *s++ = dig; |
3074 | goto ret; |
3075 | } |
3076 | #endif |
3077 | if (j < 0 || (j == 0 && mode != 1 |
3078 | #ifndef ROUND_BIASED |
3079 | && !(word1(d) & 1) |
3080 | #endif |
3081 | )) { |
3082 | if (!b->x[0] && b->wds <= 1) { |
3083 | #ifdef SET_INEXACT |
3084 | inexact = 0; |
3085 | #endif |
3086 | goto accept_dig; |
3087 | } |
3088 | #ifdef Honor_FLT_ROUNDS |
3089 | if (mode > 1) |
3090 | switch(rounding) { |
3091 | case 0: goto accept_dig; |
3092 | case 2: goto keep_dig; |
3093 | } |
3094 | #endif /*Honor_FLT_ROUNDS*/ |
3095 | if (j1 > 0) { |
3096 | b = lshift(b, 1); |
3097 | j1 = cmp(b, S); |
3098 | if ((j1 > 0 || (j1 == 0 && dig & 1)) |
3099 | && dig++ == '9') |
3100 | goto round_9_up; |
3101 | } |
3102 | accept_dig: |
3103 | *s++ = dig; |
3104 | goto ret; |
3105 | } |
3106 | if (j1 > 0) { |
3107 | #ifdef Honor_FLT_ROUNDS |
3108 | if (!rounding) |
3109 | goto accept_dig; |
3110 | #endif |
3111 | if (dig == '9') { /* possible if i == 1 */ |
3112 | round_9_up: |
3113 | *s++ = '9'; |
3114 | goto roundoff; |
3115 | } |
3116 | *s++ = dig + 1; |
3117 | goto ret; |
3118 | } |
3119 | #ifdef Honor_FLT_ROUNDS |
3120 | keep_dig: |
3121 | #endif |
3122 | *s++ = dig; |
3123 | if (i == ilim) |
3124 | break; |
3125 | b = multadd(b, 10, 0); |
3126 | if (mlo == mhi) |
3127 | mlo = mhi = multadd(mhi, 10, 0); |
3128 | else { |
3129 | mlo = multadd(mlo, 10, 0); |
3130 | mhi = multadd(mhi, 10, 0); |
3131 | } |
3132 | } |
3133 | } |
3134 | else |
3135 | for(i = 1;; i++) { |
3136 | *s++ = dig = quorem(b,S) + '0'; |
3137 | if (!b->x[0] && b->wds <= 1) { |
3138 | #ifdef SET_INEXACT |
3139 | inexact = 0; |
3140 | #endif |
3141 | goto ret; |
3142 | } |
3143 | if (i >= ilim) |
3144 | break; |
3145 | b = multadd(b, 10, 0); |
3146 | } |
3147 | |
3148 | /* Round off last digit */ |
3149 | |
3150 | #ifdef Honor_FLT_ROUNDS |
3151 | switch(rounding) { |
3152 | case 0: goto trimzeros; |
3153 | case 2: goto roundoff; |
3154 | } |
3155 | #endif |
3156 | b = lshift(b, 1); |
3157 | j = cmp(b, S); |
3158 | if (j > 0 || (j == 0 && dig & 1)) { |
3159 | roundoff: |
3160 | while(*--s == '9') |
3161 | if (s == s0) { |
3162 | k++; |
3163 | *s++ = '1'; |
3164 | goto ret; |
3165 | } |
3166 | ++*s++; |
3167 | } |
3168 | else { |
3169 | #ifdef Honor_FLT_ROUNDS |
3170 | trimzeros: |
3171 | #endif |
3172 | while(*--s == '0') |
3173 | ; |
3174 | s++; |
3175 | } |
3176 | ret: |
3177 | Bfree(S); |
3178 | if (mhi) { |
3179 | if (mlo && mlo != mhi) |
3180 | Bfree(mlo); |
3181 | Bfree(mhi); |
3182 | } |
3183 | ret1: |
3184 | #ifdef SET_INEXACT |
3185 | if (inexact) { |
3186 | if (!oldinexact) { |
3187 | word0(d) = Exp_1 + (70 << Exp_shift); |
3188 | word1(d) = 0; |
3189 | dval(d) += 1.; |
3190 | } |
3191 | } |
3192 | else if (!oldinexact) |
3193 | clear_inexact(); |
3194 | #endif |
3195 | Bfree(b); |
3196 | *s = 0; |
3197 | *decpt = k + 1; |
3198 | if (rve) |
3199 | *rve = s; |
3200 | return s0; |
3201 | } |
3202 | #ifdef __cplusplus |
3203 | } |
3204 | #endif |
3205 | |