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1.1 misho 1: /****************************************************************
2: *
3: * The author of this software is David M. Gay.
4: *
5: * Copyright (c) 1991 by AT&T.
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 AT&T 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: AT&T Bell Laboratories, Room 2C-463
23: 600 Mountain Avenue
24: Murray Hill, NJ 07974-2070
25: U.S.A.
26: dmg@research.att.com or research!dmg
27: */
28:
29: /* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
30: *
31: * This strtod returns a nearest machine number to the input decimal
32: * string (or sets errno to ERANGE). With IEEE arithmetic, ties are
33: * broken by the IEEE round-even rule. Otherwise ties are broken by
34: * biased rounding (add half and chop).
35: *
36: * Inspired loosely by William D. Clinger's paper "How to Read Floating
37: * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
38: *
39: * Modifications:
40: *
41: * 1. We only require IEEE, IBM, or VAX double-precision
42: * arithmetic (not IEEE double-extended).
43: * 2. We get by with floating-point arithmetic in a case that
44: * Clinger missed -- when we're computing d * 10^n
45: * for a small integer d and the integer n is not too
46: * much larger than 22 (the maximum integer k for which
47: * we can represent 10^k exactly), we may be able to
48: * compute (d*10^k) * 10^(e-k) with just one roundoff.
49: * 3. Rather than a bit-at-a-time adjustment of the binary
50: * result in the hard case, we use floating-point
51: * arithmetic to determine the adjustment to within
52: * one bit; only in really hard cases do we need to
53: * compute a second residual.
54: * 4. Because of 3., we don't need a large table of powers of 10
55: * for ten-to-e (just some small tables, e.g. of 10^k
56: * for 0 <= k <= 22).
57: */
58:
59: /*
60: * #define IEEE_LITTLE_ENDIAN for IEEE-arithmetic machines where the least
61: * significant byte has the lowest address.
62: * #define IEEE_BIG_ENDIAN for IEEE-arithmetic machines where the most
63: * significant byte has the lowest address.
64: * #define Long int on machines with 32-bit ints and 64-bit longs.
65: * #define Sudden_Underflow for IEEE-format machines without gradual
66: * underflow (i.e., that flush to zero on underflow).
67: * #define IBM for IBM mainframe-style floating-point arithmetic.
68: * #define VAX for VAX-style floating-point arithmetic.
69: * #define Unsigned_Shifts if >> does treats its left operand as unsigned.
70: * #define No_leftright to omit left-right logic in fast floating-point
71: * computation of dtoa.
72: * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3.
73: * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
74: * that use extended-precision instructions to compute rounded
75: * products and quotients) with IBM.
76: * #define ROUND_BIASED for IEEE-format with biased rounding.
77: * #define Inaccurate_Divide for IEEE-format with correctly rounded
78: * products but inaccurate quotients, e.g., for Intel i860.
79: * #define Just_16 to store 16 bits per 32-bit Long when doing high-precision
80: * integer arithmetic. Whether this speeds things up or slows things
81: * down depends on the machine and the number being converted.
82: * #define KR_headers for old-style C function headers.
83: * #define Bad_float_h if your system lacks a float.h or if it does not
84: * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
85: * FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
86: * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
87: * if memory is available and otherwise does something you deem
88: * appropriate. If MALLOC is undefined, malloc will be invoked
89: * directly -- and assumed always to succeed.
90: */
91:
1.1.1.2 misho 92: /* $Id$ */
1.1 misho 93:
94: #include <zend_operators.h>
95: #include <zend_strtod.h>
96:
97: #ifdef ZTS
98: #include <TSRM.h>
99: #endif
100:
101: #include <stddef.h>
102: #include <stdio.h>
103: #include <ctype.h>
104: #include <stdarg.h>
105: #include <string.h>
106: #include <stdlib.h>
107: #include <math.h>
108:
109: #ifdef HAVE_LOCALE_H
110: #include <locale.h>
111: #endif
112:
113: #ifdef HAVE_SYS_TYPES_H
114: #include <sys/types.h>
115: #endif
116:
117: #if defined(HAVE_INTTYPES_H)
118: #include <inttypes.h>
119: #elif defined(HAVE_STDINT_H)
120: #include <stdint.h>
121: #endif
122:
123: #ifndef HAVE_INT32_T
124: # if SIZEOF_INT == 4
125: typedef int int32_t;
126: # elif SIZEOF_LONG == 4
127: typedef long int int32_t;
128: # endif
129: #endif
130:
131: #ifndef HAVE_UINT32_T
132: # if SIZEOF_INT == 4
133: typedef unsigned int uint32_t;
134: # elif SIZEOF_LONG == 4
135: typedef unsigned long int uint32_t;
136: # endif
137: #endif
138:
139: #if (defined(__APPLE__) || defined(__APPLE_CC__)) && (defined(__BIG_ENDIAN__) || defined(__LITTLE_ENDIAN__))
140: # if defined(__LITTLE_ENDIAN__)
141: # undef WORDS_BIGENDIAN
142: # else
143: # if defined(__BIG_ENDIAN__)
144: # define WORDS_BIGENDIAN
145: # endif
146: # endif
147: #endif
148:
149: #ifdef WORDS_BIGENDIAN
150: #define IEEE_BIG_ENDIAN
151: #else
152: #define IEEE_LITTLE_ENDIAN
153: #endif
154:
155: #if defined(__arm__) && !defined(__VFP_FP__)
156: /*
157: * * Although the CPU is little endian the FP has different
158: * * byte and word endianness. The byte order is still little endian
159: * * but the word order is big endian.
160: * */
161: #define IEEE_BIG_ENDIAN
162: #undef IEEE_LITTLE_ENDIAN
163: #endif
164:
165: #ifdef __vax__
166: #define VAX
167: #undef IEEE_LITTLE_ENDIAN
168: #endif
169:
170: #if defined(_MSC_VER)
171: #define int32_t __int32
172: #define uint32_t unsigned __int32
173: #define IEEE_LITTLE_ENDIAN
174: #endif
175:
176: #define Long int32_t
177: #define ULong uint32_t
178:
179: #ifdef __cplusplus
180: #include "malloc.h"
181: #include "memory.h"
182: #else
183: #ifndef KR_headers
184: #include "stdlib.h"
185: #include "string.h"
186: #include "locale.h"
187: #else
188: #include "malloc.h"
189: #include "memory.h"
190: #endif
191: #endif
192:
193: #ifdef MALLOC
194: #ifdef KR_headers
195: extern char *MALLOC();
196: #else
197: extern void *MALLOC(size_t);
198: #endif
199: #else
200: #define MALLOC malloc
201: #endif
202:
203: #include "ctype.h"
204: #include "errno.h"
205:
206: #ifdef Bad_float_h
207: #ifdef IEEE_BIG_ENDIAN
208: #define IEEE_ARITHMETIC
209: #endif
210: #ifdef IEEE_LITTLE_ENDIAN
211: #define IEEE_ARITHMETIC
212: #endif
213:
214: #ifdef IEEE_ARITHMETIC
215: #define DBL_DIG 15
216: #define DBL_MAX_10_EXP 308
217: #define DBL_MAX_EXP 1024
218: #define FLT_RADIX 2
219: #define FLT_ROUNDS 1
220: #define DBL_MAX 1.7976931348623157e+308
221: #endif
222:
223: #ifdef IBM
224: #define DBL_DIG 16
225: #define DBL_MAX_10_EXP 75
226: #define DBL_MAX_EXP 63
227: #define FLT_RADIX 16
228: #define FLT_ROUNDS 0
229: #define DBL_MAX 7.2370055773322621e+75
230: #endif
231:
232: #ifdef VAX
233: #define DBL_DIG 16
234: #define DBL_MAX_10_EXP 38
235: #define DBL_MAX_EXP 127
236: #define FLT_RADIX 2
237: #define FLT_ROUNDS 1
238: #define DBL_MAX 1.7014118346046923e+38
239: #endif
240:
241:
242: #ifndef LONG_MAX
243: #define LONG_MAX 2147483647
244: #endif
245: #else
246: #include "float.h"
247: #endif
248: #ifndef __MATH_H__
249: #include "math.h"
250: #endif
251:
252: BEGIN_EXTERN_C()
253:
254: #ifndef CONST
255: #ifdef KR_headers
256: #define CONST /* blank */
257: #else
258: #define CONST const
259: #endif
260: #endif
261:
262: #ifdef Unsigned_Shifts
263: #define Sign_Extend(a,b) if (b < 0) a |= 0xffff0000;
264: #else
265: #define Sign_Extend(a,b) /*no-op*/
266: #endif
267:
268: #if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) + defined(VAX) + \
269: defined(IBM) != 1
1.1.1.3 ! misho 270: #error "Exactly one of IEEE_LITTLE_ENDIAN IEEE_BIG_ENDIAN, VAX, or IBM should be defined."
1.1 misho 271: #endif
272:
273: typedef union {
274: double d;
275: ULong ul[2];
276: } _double;
277: #define value(x) ((x).d)
278: #ifdef IEEE_LITTLE_ENDIAN
279: #define word0(x) ((x).ul[1])
280: #define word1(x) ((x).ul[0])
281: #else
282: #define word0(x) ((x).ul[0])
283: #define word1(x) ((x).ul[1])
284: #endif
285:
286: /* The following definition of Storeinc is appropriate for MIPS processors.
287: * An alternative that might be better on some machines is
288: * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
289: */
290: #if defined(IEEE_LITTLE_ENDIAN) + defined(VAX) + defined(__arm__)
291: #define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
292: ((unsigned short *)a)[0] = (unsigned short)c, a++)
293: #else
294: #define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
295: ((unsigned short *)a)[1] = (unsigned short)c, a++)
296: #endif
297:
298: /* #define P DBL_MANT_DIG */
299: /* Ten_pmax = floor(P*log(2)/log(5)) */
300: /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
301: /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
302: /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
303:
304: #if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN)
305: #define Exp_shift 20
306: #define Exp_shift1 20
307: #define Exp_msk1 0x100000
308: #define Exp_msk11 0x100000
309: #define Exp_mask 0x7ff00000
310: #define P 53
311: #define Bias 1023
312: #define IEEE_Arith
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: #define Infinite(x) (word0(x) == 0x7ff00000) /* sufficient test for here */
331: #else
332: #undef Sudden_Underflow
333: #define Sudden_Underflow
334: #ifdef IBM
335: #define Exp_shift 24
336: #define Exp_shift1 24
337: #define Exp_msk1 0x1000000
338: #define Exp_msk11 0x1000000
339: #define Exp_mask 0x7f000000
340: #define P 14
341: #define Bias 65
342: #define Exp_1 0x41000000
343: #define Exp_11 0x41000000
344: #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
345: #define Frac_mask 0xffffff
346: #define Frac_mask1 0xffffff
347: #define Bletch 4
348: #define Ten_pmax 22
349: #define Bndry_mask 0xefffff
350: #define Bndry_mask1 0xffffff
351: #define LSB 1
352: #define Sign_bit 0x80000000
353: #define Log2P 4
354: #define Tiny0 0x100000
355: #define Tiny1 0
356: #define Quick_max 14
357: #define Int_max 15
358: #else /* VAX */
359: #define Exp_shift 23
360: #define Exp_shift1 7
361: #define Exp_msk1 0x80
362: #define Exp_msk11 0x800000
363: #define Exp_mask 0x7f80
364: #define P 56
365: #define Bias 129
366: #define Exp_1 0x40800000
367: #define Exp_11 0x4080
368: #define Ebits 8
369: #define Frac_mask 0x7fffff
370: #define Frac_mask1 0xffff007f
371: #define Ten_pmax 24
372: #define Bletch 2
373: #define Bndry_mask 0xffff007f
374: #define Bndry_mask1 0xffff007f
375: #define LSB 0x10000
376: #define Sign_bit 0x8000
377: #define Log2P 1
378: #define Tiny0 0x80
379: #define Tiny1 0
380: #define Quick_max 15
381: #define Int_max 15
382: #endif
383: #endif
384:
385: #ifndef IEEE_Arith
386: #define ROUND_BIASED
387: #endif
388:
389: #ifdef RND_PRODQUOT
390: #define rounded_product(a,b) a = rnd_prod(a, b)
391: #define rounded_quotient(a,b) a = rnd_quot(a, b)
392: #ifdef KR_headers
393: extern double rnd_prod(), rnd_quot();
394: #else
395: extern double rnd_prod(double, double), rnd_quot(double, double);
396: #endif
397: #else
398: #define rounded_product(a,b) a *= b
399: #define rounded_quotient(a,b) a /= b
400: #endif
401:
402: #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
403: #define Big1 0xffffffff
404:
405: #ifndef Just_16
406: /* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
407: * * This makes some inner loops simpler and sometimes saves work
408: * * during multiplications, but it often seems to make things slightly
409: * * slower. Hence the default is now to store 32 bits per Long.
410: * */
411: #ifndef Pack_32
412: #define Pack_32
413: #endif
414: #endif
415:
416: #define Kmax 15
417:
418: struct Bigint {
419: struct Bigint *next;
420: int k, maxwds, sign, wds;
421: ULong x[1];
422: };
423:
424: typedef struct Bigint Bigint;
425:
426: /* static variables, multithreading fun! */
427: static Bigint *freelist[Kmax+1];
428: static Bigint *p5s;
429:
430: static void destroy_freelist(void);
431:
432: #ifdef ZTS
433:
434: static MUTEX_T dtoa_mutex;
435: static MUTEX_T pow5mult_mutex;
436:
437: #define _THREAD_PRIVATE_MUTEX_LOCK(x) tsrm_mutex_lock(x);
438: #define _THREAD_PRIVATE_MUTEX_UNLOCK(x) tsrm_mutex_unlock(x);
439:
440: #else
441:
442: #define _THREAD_PRIVATE_MUTEX_LOCK(x)
443: #define _THREAD_PRIVATE_MUTEX_UNLOCK(x)
444:
445: #endif /* ZTS */
446:
447: #ifdef DEBUG
448: static void Bug(const char *message) {
449: fprintf(stderr, "%s\n", message);
450: }
451: #endif
452:
453: ZEND_API int zend_startup_strtod(void) /* {{{ */
454: {
455: #ifdef ZTS
456: dtoa_mutex = tsrm_mutex_alloc();
457: pow5mult_mutex = tsrm_mutex_alloc();
458: #endif
459: return 1;
460: }
461: /* }}} */
462: ZEND_API int zend_shutdown_strtod(void) /* {{{ */
463: {
464: destroy_freelist();
465: #ifdef ZTS
466: tsrm_mutex_free(dtoa_mutex);
467: dtoa_mutex = NULL;
468:
469: tsrm_mutex_free(pow5mult_mutex);
470: pow5mult_mutex = NULL;
471: #endif
472: return 1;
473: }
474: /* }}} */
475:
476: static Bigint * Balloc(int k)
477: {
478: int x;
479: Bigint *rv;
480:
481: if (k > Kmax) {
482: zend_error(E_ERROR, "Balloc() allocation exceeds list boundary");
483: }
484:
485: _THREAD_PRIVATE_MUTEX_LOCK(dtoa_mutex);
486: if ((rv = freelist[k])) {
487: freelist[k] = rv->next;
488: } else {
489: x = 1 << k;
490: rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(Long));
491: if (!rv) {
492: _THREAD_PRIVATE_MUTEX_UNLOCK(dtoa_mutex);
493: zend_error(E_ERROR, "Balloc() failed to allocate memory");
494: }
495: rv->k = k;
496: rv->maxwds = x;
497: }
498: _THREAD_PRIVATE_MUTEX_UNLOCK(dtoa_mutex);
499: rv->sign = rv->wds = 0;
500: return rv;
501: }
502:
503: static void Bfree(Bigint *v)
504: {
505: if (v) {
506: _THREAD_PRIVATE_MUTEX_LOCK(dtoa_mutex);
507: v->next = freelist[v->k];
508: freelist[v->k] = v;
509: _THREAD_PRIVATE_MUTEX_UNLOCK(dtoa_mutex);
510: }
511: }
512:
513: #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
514: y->wds*sizeof(Long) + 2*sizeof(int))
515:
516: /* return value is only used as a simple string, so mis-aligned parts
517: * inside the Bigint are not at risk on strict align architectures
518: */
519: static char * rv_alloc(int i) {
520: int j, k, *r;
521:
522: j = sizeof(ULong);
523: for(k = 0;
524: sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= i;
525: j <<= 1) {
526: k++;
527: }
528: r = (int*)Balloc(k);
529: *r = k;
530: return (char *)(r+1);
531: }
532:
533:
534: static char * nrv_alloc(char *s, char **rve, int n)
535: {
536: char *rv, *t;
537:
538: t = rv = rv_alloc(n);
539: while((*t = *s++) !=0) {
540: t++;
541: }
542: if (rve) {
543: *rve = t;
544: }
545: return rv;
546: }
547:
548: static Bigint * multadd(Bigint *b, int m, int a) /* multiply by m and add a */
549: {
550: int i, wds;
551: ULong *x, y;
552: #ifdef Pack_32
553: ULong xi, z;
554: #endif
555: Bigint *b1;
556:
557: wds = b->wds;
558: x = b->x;
559: i = 0;
560: do {
561: #ifdef Pack_32
562: xi = *x;
563: y = (xi & 0xffff) * m + a;
564: z = (xi >> 16) * m + (y >> 16);
565: a = (int)(z >> 16);
566: *x++ = (z << 16) + (y & 0xffff);
567: #else
568: y = *x * m + a;
569: a = (int)(y >> 16);
570: *x++ = y & 0xffff;
571: #endif
572: }
573: while(++i < wds);
574: if (a) {
575: if (wds >= b->maxwds) {
576: b1 = Balloc(b->k+1);
577: Bcopy(b1, b);
578: Bfree(b);
579: b = b1;
580: }
581: b->x[wds++] = a;
582: b->wds = wds;
583: }
584: return b;
585: }
586:
587: static int hi0bits(ULong x)
588: {
589: int k = 0;
590:
591: if (!(x & 0xffff0000)) {
592: k = 16;
593: x <<= 16;
594: }
595: if (!(x & 0xff000000)) {
596: k += 8;
597: x <<= 8;
598: }
599: if (!(x & 0xf0000000)) {
600: k += 4;
601: x <<= 4;
602: }
603: if (!(x & 0xc0000000)) {
604: k += 2;
605: x <<= 2;
606: }
607: if (!(x & 0x80000000)) {
608: k++;
609: if (!(x & 0x40000000)) {
610: return 32;
611: }
612: }
613: return k;
614: }
615:
616: static int lo0bits(ULong *y)
617: {
618: int k;
619: ULong x = *y;
620:
621: if (x & 7) {
622: if (x & 1) {
623: return 0;
624: }
625: if (x & 2) {
626: *y = x >> 1;
627: return 1;
628: }
629: *y = x >> 2;
630: return 2;
631: }
632: k = 0;
633: if (!(x & 0xffff)) {
634: k = 16;
635: x >>= 16;
636: }
637: if (!(x & 0xff)) {
638: k += 8;
639: x >>= 8;
640: }
641: if (!(x & 0xf)) {
642: k += 4;
643: x >>= 4;
644: }
645: if (!(x & 0x3)) {
646: k += 2;
647: x >>= 2;
648: }
649: if (!(x & 1)) {
650: k++;
651: x >>= 1;
652: if (!(x & 1)) {
653: return 32;
654: }
655: }
656: *y = x;
657: return k;
658: }
659:
660: static Bigint * i2b(int i)
661: {
662: Bigint *b;
663:
664: b = Balloc(1);
665: b->x[0] = i;
666: b->wds = 1;
667: return b;
668: }
669:
670: static Bigint * mult(Bigint *a, Bigint *b)
671: {
672: Bigint *c;
673: int k, wa, wb, wc;
674: ULong carry, y, z;
675: ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
676: #ifdef Pack_32
677: ULong z2;
678: #endif
679:
680: if (a->wds < b->wds) {
681: c = a;
682: a = b;
683: b = c;
684: }
685: k = a->k;
686: wa = a->wds;
687: wb = b->wds;
688: wc = wa + wb;
689: if (wc > a->maxwds) {
690: k++;
691: }
692: c = Balloc(k);
693: for(x = c->x, xa = x + wc; x < xa; x++) {
694: *x = 0;
695: }
696: xa = a->x;
697: xae = xa + wa;
698: xb = b->x;
699: xbe = xb + wb;
700: xc0 = c->x;
701: #ifdef Pack_32
702: for(; xb < xbe; xb++, xc0++) {
703: if ((y = *xb & 0xffff)) {
704: x = xa;
705: xc = xc0;
706: carry = 0;
707: do {
708: z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
709: carry = z >> 16;
710: z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
711: carry = z2 >> 16;
712: Storeinc(xc, z2, z);
713: }
714: while(x < xae);
715: *xc = carry;
716: }
717: if ((y = *xb >> 16)) {
718: x = xa;
719: xc = xc0;
720: carry = 0;
721: z2 = *xc;
722: do {
723: z = (*x & 0xffff) * y + (*xc >> 16) + carry;
724: carry = z >> 16;
725: Storeinc(xc, z, z2);
726: z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
727: carry = z2 >> 16;
728: }
729: while(x < xae);
730: *xc = z2;
731: }
732: }
733: #else
734: for(; xb < xbe; xc0++) {
735: if (y = *xb++) {
736: x = xa;
737: xc = xc0;
738: carry = 0;
739: do {
740: z = *x++ * y + *xc + carry;
741: carry = z >> 16;
742: *xc++ = z & 0xffff;
743: }
744: while(x < xae);
745: *xc = carry;
746: }
747: }
748: #endif
749: for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
750: c->wds = wc;
751: return c;
752: }
753:
754: static Bigint * s2b (CONST char *s, int nd0, int nd, ULong y9)
755: {
756: Bigint *b;
757: int i, k;
758: Long x, y;
759:
760: x = (nd + 8) / 9;
761: for(k = 0, y = 1; x > y; y <<= 1, k++) ;
762: #ifdef Pack_32
763: b = Balloc(k);
764: b->x[0] = y9;
765: b->wds = 1;
766: #else
767: b = Balloc(k+1);
768: b->x[0] = y9 & 0xffff;
769: b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
770: #endif
771:
772: i = 9;
773: if (9 < nd0) {
774: s += 9;
775: do b = multadd(b, 10, *s++ - '0');
776: while(++i < nd0);
777: s++;
778: } else {
779: s += 10;
780: }
781: for(; i < nd; i++) {
782: b = multadd(b, 10, *s++ - '0');
783: }
784: return b;
785: }
786:
787: static Bigint * pow5mult(Bigint *b, int k)
788: {
789: Bigint *b1, *p5, *p51;
790: int i;
791: static int p05[3] = { 5, 25, 125 };
792:
793: _THREAD_PRIVATE_MUTEX_LOCK(pow5mult_mutex);
794: if ((i = k & 3)) {
795: b = multadd(b, p05[i-1], 0);
796: }
797:
798: if (!(k >>= 2)) {
799: _THREAD_PRIVATE_MUTEX_UNLOCK(pow5mult_mutex);
800: return b;
801: }
802: if (!(p5 = p5s)) {
803: /* first time */
804: p5 = p5s = i2b(625);
805: p5->next = 0;
806: }
807: for(;;) {
808: if (k & 1) {
809: b1 = mult(b, p5);
810: Bfree(b);
811: b = b1;
812: }
813: if (!(k >>= 1)) {
814: break;
815: }
816: if (!(p51 = p5->next)) {
817: if (!(p51 = p5->next)) {
818: p51 = p5->next = mult(p5,p5);
819: p51->next = 0;
820: }
821: }
822: p5 = p51;
823: }
824: _THREAD_PRIVATE_MUTEX_UNLOCK(pow5mult_mutex);
825: return b;
826: }
827:
828:
829: static Bigint *lshift(Bigint *b, int k)
830: {
831: int i, k1, n, n1;
832: Bigint *b1;
833: ULong *x, *x1, *xe, z;
834:
835: #ifdef Pack_32
836: n = k >> 5;
837: #else
838: n = k >> 4;
839: #endif
840: k1 = b->k;
841: n1 = n + b->wds + 1;
842: for(i = b->maxwds; n1 > i; i <<= 1) {
843: k1++;
844: }
845: b1 = Balloc(k1);
846: x1 = b1->x;
847: for(i = 0; i < n; i++) {
848: *x1++ = 0;
849: }
850: x = b->x;
851: xe = x + b->wds;
852: #ifdef Pack_32
853: if (k &= 0x1f) {
854: k1 = 32 - k;
855: z = 0;
856: do {
857: *x1++ = *x << k | z;
858: z = *x++ >> k1;
859: }
860: while(x < xe);
861: if ((*x1 = z)) {
862: ++n1;
863: }
864: }
865: #else
866: if (k &= 0xf) {
867: k1 = 16 - k;
868: z = 0;
869: do {
870: *x1++ = *x << k & 0xffff | z;
871: z = *x++ >> k1;
872: }
873: while(x < xe);
874: if (*x1 = z) {
875: ++n1;
876: }
877: }
878: #endif
879: else do
880: *x1++ = *x++;
881: while(x < xe);
882: b1->wds = n1 - 1;
883: Bfree(b);
884: return b1;
885: }
886:
887: static int cmp(Bigint *a, Bigint *b)
888: {
889: ULong *xa, *xa0, *xb, *xb0;
890: int i, j;
891:
892: i = a->wds;
893: j = b->wds;
894: #ifdef DEBUG
895: if (i > 1 && !a->x[i-1])
896: Bug("cmp called with a->x[a->wds-1] == 0");
897: if (j > 1 && !b->x[j-1])
898: Bug("cmp called with b->x[b->wds-1] == 0");
899: #endif
900: if (i -= j)
901: return i;
902: xa0 = a->x;
903: xa = xa0 + j;
904: xb0 = b->x;
905: xb = xb0 + j;
906: for(;;) {
907: if (*--xa != *--xb)
908: return *xa < *xb ? -1 : 1;
909: if (xa <= xa0)
910: break;
911: }
912: return 0;
913: }
914:
915:
916: static Bigint * diff(Bigint *a, Bigint *b)
917: {
918: Bigint *c;
919: int i, wa, wb;
920: Long borrow, y; /* We need signed shifts here. */
921: ULong *xa, *xae, *xb, *xbe, *xc;
922: #ifdef Pack_32
923: Long z;
924: #endif
925:
926: i = cmp(a,b);
927: if (!i) {
928: c = Balloc(0);
929: c->wds = 1;
930: c->x[0] = 0;
931: return c;
932: }
933: if (i < 0) {
934: c = a;
935: a = b;
936: b = c;
937: i = 1;
938: } else {
939: i = 0;
940: }
941: c = Balloc(a->k);
942: c->sign = i;
943: wa = a->wds;
944: xa = a->x;
945: xae = xa + wa;
946: wb = b->wds;
947: xb = b->x;
948: xbe = xb + wb;
949: xc = c->x;
950: borrow = 0;
951: #ifdef Pack_32
952: do {
953: y = (*xa & 0xffff) - (*xb & 0xffff) + borrow;
954: borrow = y >> 16;
955: Sign_Extend(borrow, y);
956: z = (*xa++ >> 16) - (*xb++ >> 16) + borrow;
957: borrow = z >> 16;
958: Sign_Extend(borrow, z);
959: Storeinc(xc, z, y);
960: } while(xb < xbe);
961: while(xa < xae) {
962: y = (*xa & 0xffff) + borrow;
963: borrow = y >> 16;
964: Sign_Extend(borrow, y);
965: z = (*xa++ >> 16) + borrow;
966: borrow = z >> 16;
967: Sign_Extend(borrow, z);
968: Storeinc(xc, z, y);
969: }
970: #else
971: do {
972: y = *xa++ - *xb++ + borrow;
973: borrow = y >> 16;
974: Sign_Extend(borrow, y);
975: *xc++ = y & 0xffff;
976: } while(xb < xbe);
977: while(xa < xae) {
978: y = *xa++ + borrow;
979: borrow = y >> 16;
980: Sign_Extend(borrow, y);
981: *xc++ = y & 0xffff;
982: }
983: #endif
984: while(!*--xc) {
985: wa--;
986: }
987: c->wds = wa;
988: return c;
989: }
990:
991: static double ulp (double _x)
992: {
993: volatile _double x;
994: register Long L;
995: volatile _double a;
996:
997: value(x) = _x;
998: L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
999: #ifndef Sudden_Underflow
1000: if (L > 0) {
1001: #endif
1002: #ifdef IBM
1003: L |= Exp_msk1 >> 4;
1004: #endif
1005: word0(a) = L;
1006: word1(a) = 0;
1007: #ifndef Sudden_Underflow
1008: }
1009: else {
1010: L = -L >> Exp_shift;
1011: if (L < Exp_shift) {
1012: word0(a) = 0x80000 >> L;
1013: word1(a) = 0;
1014: }
1015: else {
1016: word0(a) = 0;
1017: L -= Exp_shift;
1018: word1(a) = L >= 31 ? 1 : 1 << (31 - L);
1019: }
1020: }
1021: #endif
1022: return value(a);
1023: }
1024:
1025: static double
1026: b2d
1027: #ifdef KR_headers
1028: (a, e) Bigint *a; int *e;
1029: #else
1030: (Bigint *a, int *e)
1031: #endif
1032: {
1033: ULong *xa, *xa0, w, y, z;
1034: int k;
1035: volatile _double d;
1036: #ifdef VAX
1037: ULong d0, d1;
1038: #else
1039: #define d0 word0(d)
1040: #define d1 word1(d)
1041: #endif
1042:
1043: xa0 = a->x;
1044: xa = xa0 + a->wds;
1045: y = *--xa;
1046: #ifdef DEBUG
1047: if (!y) Bug("zero y in b2d");
1048: #endif
1049: k = hi0bits(y);
1050: *e = 32 - k;
1051: #ifdef Pack_32
1052: if (k < Ebits) {
1053: d0 = Exp_1 | y >> (Ebits - k);
1054: w = xa > xa0 ? *--xa : 0;
1055: d1 = y << ((32-Ebits) + k) | w >> (Ebits - k);
1056: goto ret_d;
1057: }
1058: z = xa > xa0 ? *--xa : 0;
1059: if (k -= Ebits) {
1060: d0 = Exp_1 | y << k | z >> (32 - k);
1061: y = xa > xa0 ? *--xa : 0;
1062: d1 = z << k | y >> (32 - k);
1063: }
1064: else {
1065: d0 = Exp_1 | y;
1066: d1 = z;
1067: }
1068: #else
1069: if (k < Ebits + 16) {
1070: z = xa > xa0 ? *--xa : 0;
1071: d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
1072: w = xa > xa0 ? *--xa : 0;
1073: y = xa > xa0 ? *--xa : 0;
1074: d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
1075: goto ret_d;
1076: }
1077: z = xa > xa0 ? *--xa : 0;
1078: w = xa > xa0 ? *--xa : 0;
1079: k -= Ebits + 16;
1080: d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
1081: y = xa > xa0 ? *--xa : 0;
1082: d1 = w << k + 16 | y << k;
1083: #endif
1084: ret_d:
1085: #ifdef VAX
1086: word0(d) = d0 >> 16 | d0 << 16;
1087: word1(d) = d1 >> 16 | d1 << 16;
1088: #else
1089: #undef d0
1090: #undef d1
1091: #endif
1092: return value(d);
1093: }
1094:
1095:
1096: static Bigint * d2b(double _d, int *e, int *bits)
1097: {
1098: Bigint *b;
1099: int de, i, k;
1100: ULong *x, y, z;
1101: volatile _double d;
1102: #ifdef VAX
1103: ULong d0, d1;
1104: #endif
1105:
1106: value(d) = _d;
1107: #ifdef VAX
1108: d0 = word0(d) >> 16 | word0(d) << 16;
1109: d1 = word1(d) >> 16 | word1(d) << 16;
1110: #else
1111: #define d0 word0(d)
1112: #define d1 word1(d)
1113: #endif
1114:
1115: #ifdef Pack_32
1116: b = Balloc(1);
1117: #else
1118: b = Balloc(2);
1119: #endif
1120: x = b->x;
1121:
1122: z = d0 & Frac_mask;
1123: d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
1124: #ifdef Sudden_Underflow
1125: de = (int)(d0 >> Exp_shift);
1126: #ifndef IBM
1127: z |= Exp_msk11;
1128: #endif
1129: #else
1130: if ((de = (int)(d0 >> Exp_shift)))
1131: z |= Exp_msk1;
1132: #endif
1133: #ifdef Pack_32
1134: if ((y = d1)) {
1135: if ((k = lo0bits(&y))) {
1136: x[0] = y | (z << (32 - k));
1137: z >>= k;
1138: } else {
1139: x[0] = y;
1140: }
1141: i = b->wds = (x[1] = z) ? 2 : 1;
1142: } else {
1143: #ifdef DEBUG
1144: if (!z)
1145: Bug("Zero passed to d2b");
1146: #endif
1147: k = lo0bits(&z);
1148: x[0] = z;
1149: i = b->wds = 1;
1150: k += 32;
1151: }
1152: #else
1153: if (y = d1) {
1154: if (k = lo0bits(&y)) {
1155: if (k >= 16) {
1156: x[0] = y | z << 32 - k & 0xffff;
1157: x[1] = z >> k - 16 & 0xffff;
1158: x[2] = z >> k;
1159: i = 2;
1160: } else {
1161: x[0] = y & 0xffff;
1162: x[1] = y >> 16 | z << 16 - k & 0xffff;
1163: x[2] = z >> k & 0xffff;
1164: x[3] = z >> k+16;
1165: i = 3;
1166: }
1167: } else {
1168: x[0] = y & 0xffff;
1169: x[1] = y >> 16;
1170: x[2] = z & 0xffff;
1171: x[3] = z >> 16;
1172: i = 3;
1173: }
1174: } else {
1175: #ifdef DEBUG
1176: if (!z)
1177: Bug("Zero passed to d2b");
1178: #endif
1179: k = lo0bits(&z);
1180: if (k >= 16) {
1181: x[0] = z;
1182: i = 0;
1183: } else {
1184: x[0] = z & 0xffff;
1185: x[1] = z >> 16;
1186: i = 1;
1187: }
1188: k += 32;
1189: }
1190: while(!x[i])
1191: --i;
1192: b->wds = i + 1;
1193: #endif
1194: #ifndef Sudden_Underflow
1195: if (de) {
1196: #endif
1197: #ifdef IBM
1198: *e = (de - Bias - (P-1) << 2) + k;
1199: *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
1200: #else
1201: *e = de - Bias - (P-1) + k;
1202: *bits = P - k;
1203: #endif
1204: #ifndef Sudden_Underflow
1205: } else {
1206: *e = de - Bias - (P-1) + 1 + k;
1207: #ifdef Pack_32
1208: *bits = 32*i - hi0bits(x[i-1]);
1209: #else
1210: *bits = (i+2)*16 - hi0bits(x[i]);
1211: #endif
1212: }
1213: #endif
1214: return b;
1215: }
1216: #undef d0
1217: #undef d1
1218:
1219:
1220: static double ratio (Bigint *a, Bigint *b)
1221: {
1222: volatile _double da, db;
1223: int k, ka, kb;
1224:
1225: value(da) = b2d(a, &ka);
1226: value(db) = b2d(b, &kb);
1227: #ifdef Pack_32
1228: k = ka - kb + 32*(a->wds - b->wds);
1229: #else
1230: k = ka - kb + 16*(a->wds - b->wds);
1231: #endif
1232: #ifdef IBM
1233: if (k > 0) {
1234: word0(da) += (k >> 2)*Exp_msk1;
1235: if (k &= 3) {
1236: da *= 1 << k;
1237: }
1238: } else {
1239: k = -k;
1240: word0(db) += (k >> 2)*Exp_msk1;
1241: if (k &= 3)
1242: db *= 1 << k;
1243: }
1244: #else
1245: if (k > 0) {
1246: word0(da) += k*Exp_msk1;
1247: } else {
1248: k = -k;
1249: word0(db) += k*Exp_msk1;
1250: }
1251: #endif
1252: return value(da) / value(db);
1253: }
1254:
1255: static CONST double
1256: tens[] = {
1257: 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1258: 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1259: 1e20, 1e21, 1e22
1260: #ifdef VAX
1261: , 1e23, 1e24
1262: #endif
1263: };
1264:
1265: #ifdef IEEE_Arith
1266: static CONST double bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
1267: static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, 1e-256 };
1268: #define n_bigtens 5
1269: #else
1270: #ifdef IBM
1271: static CONST double bigtens[] = { 1e16, 1e32, 1e64 };
1272: static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
1273: #define n_bigtens 3
1274: #else
1275: static CONST double bigtens[] = { 1e16, 1e32 };
1276: static CONST double tinytens[] = { 1e-16, 1e-32 };
1277: #define n_bigtens 2
1278: #endif
1279: #endif
1280:
1281:
1282: static int quorem(Bigint *b, Bigint *S)
1283: {
1284: int n;
1285: Long borrow, y;
1286: ULong carry, q, ys;
1287: ULong *bx, *bxe, *sx, *sxe;
1288: #ifdef Pack_32
1289: Long z;
1290: ULong si, zs;
1291: #endif
1292:
1293: n = S->wds;
1294: #ifdef DEBUG
1295: /*debug*/ if (b->wds > n)
1296: /*debug*/ Bug("oversize b in quorem");
1297: #endif
1298: if (b->wds < n)
1299: return 0;
1300: sx = S->x;
1301: sxe = sx + --n;
1302: bx = b->x;
1303: bxe = bx + n;
1304: q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
1305: #ifdef DEBUG
1306: /*debug*/ if (q > 9)
1307: /*debug*/ Bug("oversized quotient in quorem");
1308: #endif
1309: if (q) {
1310: borrow = 0;
1311: carry = 0;
1312: do {
1313: #ifdef Pack_32
1314: si = *sx++;
1315: ys = (si & 0xffff) * q + carry;
1316: zs = (si >> 16) * q + (ys >> 16);
1317: carry = zs >> 16;
1318: y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
1319: borrow = y >> 16;
1320: Sign_Extend(borrow, y);
1321: z = (*bx >> 16) - (zs & 0xffff) + borrow;
1322: borrow = z >> 16;
1323: Sign_Extend(borrow, z);
1324: Storeinc(bx, z, y);
1325: #else
1326: ys = *sx++ * q + carry;
1327: carry = ys >> 16;
1328: y = *bx - (ys & 0xffff) + borrow;
1329: borrow = y >> 16;
1330: Sign_Extend(borrow, y);
1331: *bx++ = y & 0xffff;
1332: #endif
1333: }
1334: while(sx <= sxe);
1335: if (!*bxe) {
1336: bx = b->x;
1337: while(--bxe > bx && !*bxe)
1338: --n;
1339: b->wds = n;
1340: }
1341: }
1342: if (cmp(b, S) >= 0) {
1343: q++;
1344: borrow = 0;
1345: carry = 0;
1346: bx = b->x;
1347: sx = S->x;
1348: do {
1349: #ifdef Pack_32
1350: si = *sx++;
1351: ys = (si & 0xffff) + carry;
1352: zs = (si >> 16) + (ys >> 16);
1353: carry = zs >> 16;
1354: y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
1355: borrow = y >> 16;
1356: Sign_Extend(borrow, y);
1357: z = (*bx >> 16) - (zs & 0xffff) + borrow;
1358: borrow = z >> 16;
1359: Sign_Extend(borrow, z);
1360: Storeinc(bx, z, y);
1361: #else
1362: ys = *sx++ + carry;
1363: carry = ys >> 16;
1364: y = *bx - (ys & 0xffff) + borrow;
1365: borrow = y >> 16;
1366: Sign_Extend(borrow, y);
1367: *bx++ = y & 0xffff;
1368: #endif
1369: }
1370: while(sx <= sxe);
1371: bx = b->x;
1372: bxe = bx + n;
1373: if (!*bxe) {
1374: while(--bxe > bx && !*bxe)
1375: --n;
1376: b->wds = n;
1377: }
1378: }
1379: return q;
1380: }
1381:
1382: static void destroy_freelist(void)
1383: {
1384: int i;
1385: Bigint *tmp;
1386:
1387: _THREAD_PRIVATE_MUTEX_LOCK(dtoa_mutex);
1388: for (i = 0; i <= Kmax; i++) {
1389: Bigint **listp = &freelist[i];
1390: while ((tmp = *listp) != NULL) {
1391: *listp = tmp->next;
1392: free(tmp);
1393: }
1394: freelist[i] = NULL;
1395: }
1396: _THREAD_PRIVATE_MUTEX_UNLOCK(dtoa_mutex);
1397:
1398: }
1399:
1400:
1401: ZEND_API void zend_freedtoa(char *s)
1402: {
1403: Bigint *b = (Bigint *)((int *)s - 1);
1404: b->maxwds = 1 << (b->k = *(int*)b);
1405: Bfree(b);
1406: }
1407:
1408: /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
1409: *
1410: * Inspired by "How to Print Floating-Point Numbers Accurately" by
1411: * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101].
1412: *
1413: * Modifications:
1414: * 1. Rather than iterating, we use a simple numeric overestimate
1415: * to determine k = floor(log10(d)). We scale relevant
1416: * quantities using O(log2(k)) rather than O(k) multiplications.
1417: * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
1418: * try to generate digits strictly left to right. Instead, we
1419: * compute with fewer bits and propagate the carry if necessary
1420: * when rounding the final digit up. This is often faster.
1421: * 3. Under the assumption that input will be rounded nearest,
1422: * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
1423: * That is, we allow equality in stopping tests when the
1424: * round-nearest rule will give the same floating-point value
1425: * as would satisfaction of the stopping test with strict
1426: * inequality.
1427: * 4. We remove common factors of powers of 2 from relevant
1428: * quantities.
1429: * 5. When converting floating-point integers less than 1e16,
1430: * we use floating-point arithmetic rather than resorting
1431: * to multiple-precision integers.
1432: * 6. When asked to produce fewer than 15 digits, we first try
1433: * to get by with floating-point arithmetic; we resort to
1434: * multiple-precision integer arithmetic only if we cannot
1435: * guarantee that the floating-point calculation has given
1436: * the correctly rounded result. For k requested digits and
1437: * "uniformly" distributed input, the probability is
1438: * something like 10^(k-15) that we must resort to the Long
1439: * calculation.
1440: */
1441:
1442: ZEND_API char * zend_dtoa(double _d, int mode, int ndigits, int *decpt, int *sign, char **rve)
1443: {
1444: /* Arguments ndigits, decpt, sign are similar to those
1445: of ecvt and fcvt; trailing zeros are suppressed from
1446: the returned string. If not null, *rve is set to point
1447: to the end of the return value. If d is +-Infinity or NaN,
1448: then *decpt is set to 9999.
1449:
1450: mode:
1451: 0 ==> shortest string that yields d when read in
1452: and rounded to nearest.
1453: 1 ==> like 0, but with Steele & White stopping rule;
1454: e.g. with IEEE P754 arithmetic , mode 0 gives
1455: 1e23 whereas mode 1 gives 9.999999999999999e22.
1456: 2 ==> max(1,ndigits) significant digits. This gives a
1457: return value similar to that of ecvt, except
1458: that trailing zeros are suppressed.
1459: 3 ==> through ndigits past the decimal point. This
1460: gives a return value similar to that from fcvt,
1461: except that trailing zeros are suppressed, and
1462: ndigits can be negative.
1463: 4-9 should give the same return values as 2-3, i.e.,
1464: 4 <= mode <= 9 ==> same return as mode
1465: 2 + (mode & 1). These modes are mainly for
1466: debugging; often they run slower but sometimes
1467: faster than modes 2-3.
1468: 4,5,8,9 ==> left-to-right digit generation.
1469: 6-9 ==> don't try fast floating-point estimate
1470: (if applicable).
1471:
1472: Values of mode other than 0-9 are treated as mode 0.
1473:
1474: Sufficient space is allocated to the return value
1475: to hold the suppressed trailing zeros.
1476: */
1477:
1478: int bbits, b2, b5, be, dig, i, ieps, ilim = 0, ilim0, ilim1,
1479: j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
1480: spec_case = 0, try_quick;
1481: Long L;
1482: #ifndef Sudden_Underflow
1483: int denorm;
1484: ULong x;
1485: #endif
1486: Bigint *b, *b1, *delta, *mlo, *mhi, *S, *tmp;
1487: double ds;
1488: char *s, *s0;
1489: volatile _double d, d2, eps;
1490:
1491: value(d) = _d;
1492:
1493: if (word0(d) & Sign_bit) {
1494: /* set sign for everything, including 0's and NaNs */
1495: *sign = 1;
1496: word0(d) &= ~Sign_bit; /* clear sign bit */
1497: }
1498: else
1499: *sign = 0;
1500:
1501: #if defined(IEEE_Arith) + defined(VAX)
1502: #ifdef IEEE_Arith
1503: if ((word0(d) & Exp_mask) == Exp_mask)
1504: #else
1505: if (word0(d) == 0x8000)
1506: #endif
1507: {
1508: /* Infinity or NaN */
1509: *decpt = 9999;
1510: #ifdef IEEE_Arith
1511: if (!word1(d) && !(word0(d) & 0xfffff))
1512: return nrv_alloc("Infinity", rve, 8);
1513: #endif
1514: return nrv_alloc("NaN", rve, 3);
1515: }
1516: #endif
1517: #ifdef IBM
1518: value(d) += 0; /* normalize */
1519: #endif
1520: if (!value(d)) {
1521: *decpt = 1;
1522: return nrv_alloc("0", rve, 1);
1523: }
1524:
1525: b = d2b(value(d), &be, &bbits);
1526: #ifdef Sudden_Underflow
1527: i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
1528: #else
1529: if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) {
1530: #endif
1531: value(d2) = value(d);
1532: word0(d2) &= Frac_mask1;
1533: word0(d2) |= Exp_11;
1534: #ifdef IBM
1535: if (j = 11 - hi0bits(word0(d2) & Frac_mask))
1536: value(d2) /= 1 << j;
1537: #endif
1538:
1539: /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
1540: * log10(x) = log(x) / log(10)
1541: * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
1542: * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
1543: *
1544: * This suggests computing an approximation k to log10(d) by
1545: *
1546: * k = (i - Bias)*0.301029995663981
1547: * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
1548: *
1549: * We want k to be too large rather than too small.
1550: * The error in the first-order Taylor series approximation
1551: * is in our favor, so we just round up the constant enough
1552: * to compensate for any error in the multiplication of
1553: * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
1554: * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
1555: * adding 1e-13 to the constant term more than suffices.
1556: * Hence we adjust the constant term to 0.1760912590558.
1557: * (We could get a more accurate k by invoking log10,
1558: * but this is probably not worthwhile.)
1559: */
1560:
1561: i -= Bias;
1562: #ifdef IBM
1563: i <<= 2;
1564: i += j;
1565: #endif
1566: #ifndef Sudden_Underflow
1567: denorm = 0;
1568: }
1569: else {
1570: /* d is denormalized */
1571:
1572: i = bbits + be + (Bias + (P-1) - 1);
1573: x = i > 32 ? (word0(d) << (64 - i)) | (word1(d) >> (i - 32))
1574: : (word1(d) << (32 - i));
1575: value(d2) = x;
1576: word0(d2) -= 31*Exp_msk1; /* adjust exponent */
1577: i -= (Bias + (P-1) - 1) + 1;
1578: denorm = 1;
1579: }
1580: #endif
1581: ds = (value(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
1582: k = (int)ds;
1583: if (ds < 0. && ds != k)
1584: k--; /* want k = floor(ds) */
1585: k_check = 1;
1586: if (k >= 0 && k <= Ten_pmax) {
1587: if (value(d) < tens[k])
1588: k--;
1589: k_check = 0;
1590: }
1591: j = bbits - i - 1;
1592: if (j >= 0) {
1593: b2 = 0;
1594: s2 = j;
1595: }
1596: else {
1597: b2 = -j;
1598: s2 = 0;
1599: }
1600: if (k >= 0) {
1601: b5 = 0;
1602: s5 = k;
1603: s2 += k;
1604: }
1605: else {
1606: b2 -= k;
1607: b5 = -k;
1608: s5 = 0;
1609: }
1610: if (mode < 0 || mode > 9)
1611: mode = 0;
1612: try_quick = 1;
1613: if (mode > 5) {
1614: mode -= 4;
1615: try_quick = 0;
1616: }
1617: leftright = 1;
1618: switch(mode) {
1619: case 0:
1620: case 1:
1621: ilim = ilim1 = -1;
1622: i = 18;
1623: ndigits = 0;
1624: break;
1625: case 2:
1626: leftright = 0;
1627: /* no break */
1628: case 4:
1629: if (ndigits <= 0)
1630: ndigits = 1;
1631: ilim = ilim1 = i = ndigits;
1632: break;
1633: case 3:
1634: leftright = 0;
1635: /* no break */
1636: case 5:
1637: i = ndigits + k + 1;
1638: ilim = i;
1639: ilim1 = i - 1;
1640: if (i <= 0)
1641: i = 1;
1642: }
1643: s = s0 = rv_alloc(i);
1644:
1645: if (ilim >= 0 && ilim <= Quick_max && try_quick) {
1646:
1647: /* Try to get by with floating-point arithmetic. */
1648:
1649: i = 0;
1650: value(d2) = value(d);
1651: k0 = k;
1652: ilim0 = ilim;
1653: ieps = 2; /* conservative */
1654: if (k > 0) {
1655: ds = tens[k&0xf];
1656: j = k >> 4;
1657: if (j & Bletch) {
1658: /* prevent overflows */
1659: j &= Bletch - 1;
1660: value(d) /= bigtens[n_bigtens-1];
1661: ieps++;
1662: }
1663: for(; j; j >>= 1, i++)
1664: if (j & 1) {
1665: ieps++;
1666: ds *= bigtens[i];
1667: }
1668: value(d) /= ds;
1669: }
1670: else if ((j1 = -k)) {
1671: value(d) *= tens[j1 & 0xf];
1672: for(j = j1 >> 4; j; j >>= 1, i++)
1673: if (j & 1) {
1674: ieps++;
1675: value(d) *= bigtens[i];
1676: }
1677: }
1678: if (k_check && value(d) < 1. && ilim > 0) {
1679: if (ilim1 <= 0)
1680: goto fast_failed;
1681: ilim = ilim1;
1682: k--;
1683: value(d) *= 10.;
1684: ieps++;
1685: }
1686: value(eps) = ieps*value(d) + 7.;
1687: word0(eps) -= (P-1)*Exp_msk1;
1688: if (ilim == 0) {
1689: S = mhi = 0;
1690: value(d) -= 5.;
1691: if (value(d) > value(eps))
1692: goto one_digit;
1693: if (value(d) < -value(eps))
1694: goto no_digits;
1695: goto fast_failed;
1696: }
1697: #ifndef No_leftright
1698: if (leftright) {
1699: /* Use Steele & White method of only
1700: * generating digits needed.
1701: */
1702: value(eps) = 0.5/tens[ilim-1] - value(eps);
1703: for(i = 0;;) {
1704: L = value(d);
1705: value(d) -= L;
1706: *s++ = '0' + (int)L;
1707: if (value(d) < value(eps))
1708: goto ret1;
1709: if (1. - value(d) < value(eps))
1710: goto bump_up;
1711: if (++i >= ilim)
1712: break;
1713: value(eps) *= 10.;
1714: value(d) *= 10.;
1715: }
1716: }
1717: else {
1718: #endif
1719: /* Generate ilim digits, then fix them up. */
1720: value(eps) *= tens[ilim-1];
1721: for(i = 1;; i++, value(d) *= 10.) {
1722: L = value(d);
1723: value(d) -= L;
1724: *s++ = '0' + (int)L;
1725: if (i == ilim) {
1726: if (value(d) > 0.5 + value(eps))
1727: goto bump_up;
1728: else if (value(d) < 0.5 - value(eps)) {
1729: while(*--s == '0');
1730: s++;
1731: goto ret1;
1732: }
1733: break;
1734: }
1735: }
1736: #ifndef No_leftright
1737: }
1738: #endif
1739: fast_failed:
1740: s = s0;
1741: value(d) = value(d2);
1742: k = k0;
1743: ilim = ilim0;
1744: }
1745:
1746: /* Do we have a "small" integer? */
1747:
1748: if (be >= 0 && k <= Int_max) {
1749: /* Yes. */
1750: ds = tens[k];
1751: if (ndigits < 0 && ilim <= 0) {
1752: S = mhi = 0;
1753: if (ilim < 0 || value(d) <= 5*ds)
1754: goto no_digits;
1755: goto one_digit;
1756: }
1757: for(i = 1;; i++) {
1758: L = value(d) / ds;
1759: value(d) -= L*ds;
1760: #ifdef Check_FLT_ROUNDS
1761: /* If FLT_ROUNDS == 2, L will usually be high by 1 */
1762: if (value(d) < 0) {
1763: L--;
1764: value(d) += ds;
1765: }
1766: #endif
1767: *s++ = '0' + (int)L;
1768: if (i == ilim) {
1769: value(d) += value(d);
1770: if (value(d) > ds || (value(d) == ds && (L & 1))) {
1771: bump_up:
1772: while(*--s == '9')
1773: if (s == s0) {
1774: k++;
1775: *s = '0';
1776: break;
1777: }
1778: ++*s++;
1779: }
1780: break;
1781: }
1782: if (!(value(d) *= 10.))
1783: break;
1784: }
1785: goto ret1;
1786: }
1787:
1788: m2 = b2;
1789: m5 = b5;
1790: mhi = mlo = 0;
1791: if (leftright) {
1792: if (mode < 2) {
1793: i =
1794: #ifndef Sudden_Underflow
1795: denorm ? be + (Bias + (P-1) - 1 + 1) :
1796: #endif
1797: #ifdef IBM
1798: 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
1799: #else
1800: 1 + P - bbits;
1801: #endif
1802: }
1803: else {
1804: j = ilim - 1;
1805: if (m5 >= j)
1806: m5 -= j;
1807: else {
1808: s5 += j -= m5;
1809: b5 += j;
1810: m5 = 0;
1811: }
1812: if ((i = ilim) < 0) {
1813: m2 -= i;
1814: i = 0;
1815: }
1816: }
1817: b2 += i;
1818: s2 += i;
1819: mhi = i2b(1);
1820: }
1821: if (m2 > 0 && s2 > 0) {
1822: i = m2 < s2 ? m2 : s2;
1823: b2 -= i;
1824: m2 -= i;
1825: s2 -= i;
1826: }
1827: if (b5 > 0) {
1828: if (leftright) {
1829: if (m5 > 0) {
1830: mhi = pow5mult(mhi, m5);
1831: b1 = mult(mhi, b);
1832: Bfree(b);
1833: b = b1;
1834: }
1835: if ((j = b5 - m5)) {
1836: b = pow5mult(b, j);
1837: }
1838: } else {
1839: b = pow5mult(b, b5);
1840: }
1841: }
1842: S = i2b(1);
1843: if (s5 > 0)
1844: S = pow5mult(S, s5);
1845: /* Check for special case that d is a normalized power of 2. */
1846:
1847: if (mode < 2) {
1848: if (!word1(d) && !(word0(d) & Bndry_mask)
1849: #ifndef Sudden_Underflow
1850: && word0(d) & Exp_mask
1851: #endif
1852: ) {
1853: /* The special case */
1854: b2 += Log2P;
1855: s2 += Log2P;
1856: spec_case = 1;
1857: } else {
1858: spec_case = 0;
1859: }
1860: }
1861:
1862: /* Arrange for convenient computation of quotients:
1863: * shift left if necessary so divisor has 4 leading 0 bits.
1864: *
1865: * Perhaps we should just compute leading 28 bits of S once
1866: * and for all and pass them and a shift to quorem, so it
1867: * can do shifts and ors to compute the numerator for q.
1868: */
1869: #ifdef Pack_32
1870: if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f))
1871: i = 32 - i;
1872: #else
1873: if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf))
1874: i = 16 - i;
1875: #endif
1876: if (i > 4) {
1877: i -= 4;
1878: b2 += i;
1879: m2 += i;
1880: s2 += i;
1881: }
1882: else if (i < 4) {
1883: i += 28;
1884: b2 += i;
1885: m2 += i;
1886: s2 += i;
1887: }
1888: if (b2 > 0)
1889: b = lshift(b, b2);
1890: if (s2 > 0)
1891: S = lshift(S, s2);
1892: if (k_check) {
1893: if (cmp(b,S) < 0) {
1894: k--;
1895: b = multadd(b, 10, 0); /* we botched the k estimate */
1896: if (leftright)
1897: mhi = multadd(mhi, 10, 0);
1898: ilim = ilim1;
1899: }
1900: }
1901: if (ilim <= 0 && mode > 2) {
1902: if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
1903: /* no digits, fcvt style */
1904: no_digits:
1905: k = -1 - ndigits;
1906: goto ret;
1907: }
1908: one_digit:
1909: *s++ = '1';
1910: k++;
1911: goto ret;
1912: }
1913: if (leftright) {
1914: if (m2 > 0)
1915: mhi = lshift(mhi, m2);
1916:
1917: /* Compute mlo -- check for special case
1918: * that d is a normalized power of 2.
1919: */
1920:
1921: mlo = mhi;
1922: if (spec_case) {
1923: mhi = Balloc(mhi->k);
1924: Bcopy(mhi, mlo);
1925: mhi = lshift(mhi, Log2P);
1926: }
1927:
1928: for(i = 1;;i++) {
1929: dig = quorem(b,S) + '0';
1930: /* Do we yet have the shortest decimal string
1931: * that will round to d?
1932: */
1933: j = cmp(b, mlo);
1934: delta = diff(S, mhi);
1935: j1 = delta->sign ? 1 : cmp(b, delta);
1936: Bfree(delta);
1937: #ifndef ROUND_BIASED
1938: if (j1 == 0 && !mode && !(word1(d) & 1)) {
1939: if (dig == '9')
1940: goto round_9_up;
1941: if (j > 0)
1942: dig++;
1943: *s++ = dig;
1944: goto ret;
1945: }
1946: #endif
1947: if (j < 0 || (j == 0 && !mode
1948: #ifndef ROUND_BIASED
1949: && !(word1(d) & 1)
1950: #endif
1951: )) {
1952: if (j1 > 0) {
1953: b = lshift(b, 1);
1954: j1 = cmp(b, S);
1955: if ((j1 > 0 || (j1 == 0 && (dig & 1)))
1956: && dig++ == '9')
1957: goto round_9_up;
1958: }
1959: *s++ = dig;
1960: goto ret;
1961: }
1962: if (j1 > 0) {
1963: if (dig == '9') { /* possible if i == 1 */
1964: round_9_up:
1965: *s++ = '9';
1966: goto roundoff;
1967: }
1968: *s++ = dig + 1;
1969: goto ret;
1970: }
1971: *s++ = dig;
1972: if (i == ilim)
1973: break;
1974: b = multadd(b, 10, 0);
1975: if (mlo == mhi)
1976: mlo = mhi = multadd(mhi, 10, 0);
1977: else {
1978: mlo = multadd(mlo, 10, 0);
1979: mhi = multadd(mhi, 10, 0);
1980: }
1981: }
1982: }
1983: else
1984: for(i = 1;; i++) {
1985: *s++ = dig = quorem(b,S) + '0';
1986: if (i >= ilim)
1987: break;
1988: b = multadd(b, 10, 0);
1989: }
1990:
1991: /* Round off last digit */
1992:
1993: b = lshift(b, 1);
1994: j = cmp(b, S);
1995: if (j > 0 || (j == 0 && (dig & 1))) {
1996: roundoff:
1997: while(*--s == '9')
1998: if (s == s0) {
1999: k++;
2000: *s++ = '1';
2001: goto ret;
2002: }
2003: ++*s++;
2004: }
2005: else {
2006: while(*--s == '0');
2007: s++;
2008: }
2009: ret:
2010: Bfree(S);
2011: if (mhi) {
2012: if (mlo && mlo != mhi)
2013: Bfree(mlo);
2014: Bfree(mhi);
2015: }
2016: ret1:
2017:
2018: _THREAD_PRIVATE_MUTEX_LOCK(pow5mult_mutex);
2019: while (p5s) {
2020: tmp = p5s;
2021: p5s = p5s->next;
2022: free(tmp);
2023: }
2024: _THREAD_PRIVATE_MUTEX_UNLOCK(pow5mult_mutex);
2025:
2026: Bfree(b);
2027:
2028: if (s == s0) { /* don't return empty string */
2029: *s++ = '0';
2030: k = 0;
2031: }
2032: *s = 0;
2033: *decpt = k + 1;
2034: if (rve)
2035: *rve = s;
2036: return s0;
2037: }
2038:
1.1.1.2 misho 2039: ZEND_API double zend_strtod (CONST char *s00, CONST char **se)
1.1 misho 2040: {
2041: int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
2042: e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
2043: CONST char *s, *s0, *s1;
2044: volatile double aadj, aadj1, adj;
2045: volatile _double rv, rv0;
2046: Long L;
2047: ULong y, z;
2048: Bigint *bb, *bb1, *bd, *bd0, *bs, *delta, *tmp;
2049: double result;
2050:
2051: CONST char decimal_point = '.';
2052:
2053: sign = nz0 = nz = 0;
2054: value(rv) = 0.;
2055:
2056:
2057: for(s = s00; isspace((unsigned char) *s); s++)
2058: ;
2059:
2060: if (*s == '-') {
2061: sign = 1;
2062: s++;
2063: } else if (*s == '+') {
2064: s++;
2065: }
2066:
2067: if (*s == '\0') {
2068: s = s00;
2069: goto ret;
2070: }
2071:
2072: if (*s == '0') {
2073: nz0 = 1;
2074: while(*++s == '0') ;
2075: if (!*s)
2076: goto ret;
2077: }
2078: s0 = s;
2079: y = z = 0;
2080: for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
2081: if (nd < 9)
2082: y = 10*y + c - '0';
2083: else if (nd < 16)
2084: z = 10*z + c - '0';
2085: nd0 = nd;
2086: if (c == decimal_point) {
2087: c = *++s;
2088: if (!nd) {
2089: for(; c == '0'; c = *++s)
2090: nz++;
2091: if (c > '0' && c <= '9') {
2092: s0 = s;
2093: nf += nz;
2094: nz = 0;
2095: goto have_dig;
2096: }
2097: goto dig_done;
2098: }
2099: for(; c >= '0' && c <= '9'; c = *++s) {
2100: have_dig:
2101: nz++;
2102: if (c -= '0') {
2103: nf += nz;
2104: for(i = 1; i < nz; i++)
2105: if (nd++ < 9)
2106: y *= 10;
2107: else if (nd <= DBL_DIG + 1)
2108: z *= 10;
2109: if (nd++ < 9)
2110: y = 10*y + c;
2111: else if (nd <= DBL_DIG + 1)
2112: z = 10*z + c;
2113: nz = 0;
2114: }
2115: }
2116: }
2117: dig_done:
2118: e = 0;
2119: if (c == 'e' || c == 'E') {
2120: if (!nd && !nz && !nz0) {
2121: s = s00;
2122: goto ret;
2123: }
2124: s00 = s;
2125: esign = 0;
2126: switch(c = *++s) {
2127: case '-':
2128: esign = 1;
2129: case '+':
2130: c = *++s;
2131: }
2132: if (c >= '0' && c <= '9') {
2133: while(c == '0')
2134: c = *++s;
2135: if (c > '0' && c <= '9') {
2136: L = c - '0';
2137: s1 = s;
2138: while((c = *++s) >= '0' && c <= '9')
2139: L = 10*L + c - '0';
2140: if (s - s1 > 8 || L > 19999)
2141: /* Avoid confusion from exponents
2142: * so large that e might overflow.
2143: */
2144: e = 19999; /* safe for 16 bit ints */
2145: else
2146: e = (int)L;
2147: if (esign)
2148: e = -e;
2149: }
2150: else
2151: e = 0;
2152: }
2153: else
2154: s = s00;
2155: }
2156: if (!nd) {
2157: if (!nz && !nz0)
2158: s = s00;
2159: goto ret;
2160: }
2161: e1 = e -= nf;
2162:
2163: /* Now we have nd0 digits, starting at s0, followed by a
2164: * decimal point, followed by nd-nd0 digits. The number we're
2165: * after is the integer represented by those digits times
2166: * 10**e */
2167:
2168: if (!nd0)
2169: nd0 = nd;
2170: k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
2171: value(rv) = y;
2172: if (k > 9)
2173: value(rv) = tens[k - 9] * value(rv) + z;
2174: bd0 = 0;
2175: if (nd <= DBL_DIG
2176: #ifndef RND_PRODQUOT
2177: && FLT_ROUNDS == 1
2178: #endif
2179: ) {
2180: if (!e)
2181: goto ret;
2182: if (e > 0) {
2183: if (e <= Ten_pmax) {
2184: #ifdef VAX
2185: goto vax_ovfl_check;
2186: #else
2187: /* value(rv) = */ rounded_product(value(rv),
2188: tens[e]);
2189: goto ret;
2190: #endif
2191: }
2192: i = DBL_DIG - nd;
2193: if (e <= Ten_pmax + i) {
2194: /* A fancier test would sometimes let us do
2195: * this for larger i values.
2196: */
2197: e -= i;
2198: value(rv) *= tens[i];
2199: #ifdef VAX
2200: /* VAX exponent range is so narrow we must
2201: * worry about overflow here...
2202: */
2203: vax_ovfl_check:
2204: word0(rv) -= P*Exp_msk1;
2205: /* value(rv) = */ rounded_product(value(rv),
2206: tens[e]);
2207: if ((word0(rv) & Exp_mask)
2208: > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
2209: goto ovfl;
2210: word0(rv) += P*Exp_msk1;
2211: #else
2212: /* value(rv) = */ rounded_product(value(rv),
2213: tens[e]);
2214: #endif
2215: goto ret;
2216: }
2217: }
2218: #ifndef Inaccurate_Divide
2219: else if (e >= -Ten_pmax) {
2220: /* value(rv) = */ rounded_quotient(value(rv),
2221: tens[-e]);
2222: goto ret;
2223: }
2224: #endif
2225: }
2226: e1 += nd - k;
2227:
2228: /* Get starting approximation = rv * 10**e1 */
2229:
2230: if (e1 > 0) {
2231: if ((i = e1 & 15))
2232: value(rv) *= tens[i];
2233: if (e1 &= ~15) {
2234: if (e1 > DBL_MAX_10_EXP) {
2235: ovfl:
2236: errno = ERANGE;
2237: #ifndef Bad_float_h
2238: value(rv) = HUGE_VAL;
2239: #else
2240: /* Can't trust HUGE_VAL */
2241: #ifdef IEEE_Arith
2242: word0(rv) = Exp_mask;
2243: word1(rv) = 0;
2244: #else
2245: word0(rv) = Big0;
2246: word1(rv) = Big1;
2247: #endif
2248: #endif
2249: if (bd0)
2250: goto retfree;
2251: goto ret;
2252: }
2253: if (e1 >>= 4) {
2254: for(j = 0; e1 > 1; j++, e1 >>= 1)
2255: if (e1 & 1)
2256: value(rv) *= bigtens[j];
2257: /* The last multiplication could overflow. */
2258: word0(rv) -= P*Exp_msk1;
2259: value(rv) *= bigtens[j];
2260: if ((z = word0(rv) & Exp_mask)
2261: > Exp_msk1*(DBL_MAX_EXP+Bias-P))
2262: goto ovfl;
2263: if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
2264: /* set to largest number */
2265: /* (Can't trust DBL_MAX) */
2266: word0(rv) = Big0;
2267: word1(rv) = Big1;
2268: }
2269: else
2270: word0(rv) += P*Exp_msk1;
2271: }
2272:
2273: }
2274: }
2275: else if (e1 < 0) {
2276: e1 = -e1;
2277: if ((i = e1 & 15))
2278: value(rv) /= tens[i];
2279: if (e1 &= ~15) {
2280: e1 >>= 4;
2281: if (e1 >= 1 << n_bigtens)
2282: goto undfl;
2283: for(j = 0; e1 > 1; j++, e1 >>= 1)
2284: if (e1 & 1)
2285: value(rv) *= tinytens[j];
2286: /* The last multiplication could underflow. */
2287: value(rv0) = value(rv);
2288: value(rv) *= tinytens[j];
2289: if (!value(rv)) {
2290: value(rv) = 2.*value(rv0);
2291: value(rv) *= tinytens[j];
2292: if (!value(rv)) {
2293: undfl:
2294: value(rv) = 0.;
2295: errno = ERANGE;
2296: if (bd0)
2297: goto retfree;
2298: goto ret;
2299: }
2300: word0(rv) = Tiny0;
2301: word1(rv) = Tiny1;
2302: /* The refinement below will clean
2303: * this approximation up.
2304: */
2305: }
2306: }
2307: }
2308:
2309: /* Now the hard part -- adjusting rv to the correct value.*/
2310:
2311: /* Put digits into bd: true value = bd * 10^e */
2312:
2313: bd0 = s2b(s0, nd0, nd, y);
2314:
2315: for(;;) {
2316: bd = Balloc(bd0->k);
2317: Bcopy(bd, bd0);
2318: bb = d2b(value(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */
2319: bs = i2b(1);
2320:
2321: if (e >= 0) {
2322: bb2 = bb5 = 0;
2323: bd2 = bd5 = e;
2324: }
2325: else {
2326: bb2 = bb5 = -e;
2327: bd2 = bd5 = 0;
2328: }
2329: if (bbe >= 0)
2330: bb2 += bbe;
2331: else
2332: bd2 -= bbe;
2333: bs2 = bb2;
2334: #ifdef Sudden_Underflow
2335: #ifdef IBM
2336: j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
2337: #else
2338: j = P + 1 - bbbits;
2339: #endif
2340: #else
2341: i = bbe + bbbits - 1; /* logb(rv) */
2342: if (i < Emin) /* denormal */
2343: j = bbe + (P-Emin);
2344: else
2345: j = P + 1 - bbbits;
2346: #endif
2347: bb2 += j;
2348: bd2 += j;
2349: i = bb2 < bd2 ? bb2 : bd2;
2350: if (i > bs2)
2351: i = bs2;
2352: if (i > 0) {
2353: bb2 -= i;
2354: bd2 -= i;
2355: bs2 -= i;
2356: }
2357: if (bb5 > 0) {
2358: bs = pow5mult(bs, bb5);
2359: bb1 = mult(bs, bb);
2360: Bfree(bb);
2361: bb = bb1;
2362: }
2363: if (bb2 > 0)
2364: bb = lshift(bb, bb2);
2365: if (bd5 > 0)
2366: bd = pow5mult(bd, bd5);
2367: if (bd2 > 0)
2368: bd = lshift(bd, bd2);
2369: if (bs2 > 0)
2370: bs = lshift(bs, bs2);
2371: delta = diff(bb, bd);
2372: dsign = delta->sign;
2373: delta->sign = 0;
2374: i = cmp(delta, bs);
2375: if (i < 0) {
2376: /* Error is less than half an ulp -- check for
2377: * special case of mantissa a power of two.
2378: */
2379: if (dsign || word1(rv) || word0(rv) & Bndry_mask)
2380: break;
2381: delta = lshift(delta,Log2P);
2382: if (cmp(delta, bs) > 0)
2383: goto drop_down;
2384: break;
2385: }
2386: if (i == 0) {
2387: /* exactly half-way between */
2388: if (dsign) {
2389: if ((word0(rv) & Bndry_mask1) == Bndry_mask1
2390: && word1(rv) == 0xffffffff) {
2391: /*boundary case -- increment exponent*/
2392: word0(rv) = (word0(rv) & Exp_mask)
2393: + Exp_msk1
2394: #ifdef IBM
2395: | Exp_msk1 >> 4
2396: #endif
2397: ;
2398: word1(rv) = 0;
2399: break;
2400: }
2401: }
2402: else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
2403: drop_down:
2404: /* boundary case -- decrement exponent */
2405: #ifdef Sudden_Underflow
2406: L = word0(rv) & Exp_mask;
2407: #ifdef IBM
2408: if (L < Exp_msk1)
2409: #else
2410: if (L <= Exp_msk1)
2411: #endif
2412: goto undfl;
2413: L -= Exp_msk1;
2414: #else
2415: L = (word0(rv) & Exp_mask) - Exp_msk1;
2416: #endif
2417: word0(rv) = L | Bndry_mask1;
2418: word1(rv) = 0xffffffff;
2419: #ifdef IBM
2420: goto cont;
2421: #else
2422: break;
2423: #endif
2424: }
2425: #ifndef ROUND_BIASED
2426: if (!(word1(rv) & LSB))
2427: break;
2428: #endif
2429: if (dsign)
2430: value(rv) += ulp(value(rv));
2431: #ifndef ROUND_BIASED
2432: else {
2433: value(rv) -= ulp(value(rv));
2434: #ifndef Sudden_Underflow
2435: if (!value(rv))
2436: goto undfl;
2437: #endif
2438: }
2439: #endif
2440: break;
2441: }
2442: if ((aadj = ratio(delta, bs)) <= 2.) {
2443: if (dsign)
2444: aadj = aadj1 = 1.;
2445: else if (word1(rv) || word0(rv) & Bndry_mask) {
2446: #ifndef Sudden_Underflow
2447: if (word1(rv) == Tiny1 && !word0(rv))
2448: goto undfl;
2449: #endif
2450: aadj = 1.;
2451: aadj1 = -1.;
2452: }
2453: else {
2454: /* special case -- power of FLT_RADIX to be */
2455: /* rounded down... */
2456:
2457: if (aadj < 2./FLT_RADIX)
2458: aadj = 1./FLT_RADIX;
2459: else
2460: aadj *= 0.5;
2461: aadj1 = -aadj;
2462: }
2463: }
2464: else {
2465: aadj *= 0.5;
2466: aadj1 = dsign ? aadj : -aadj;
2467: #ifdef Check_FLT_ROUNDS
2468: switch(FLT_ROUNDS) {
2469: case 2: /* towards +infinity */
2470: aadj1 -= 0.5;
2471: break;
2472: case 0: /* towards 0 */
2473: case 3: /* towards -infinity */
2474: aadj1 += 0.5;
2475: }
2476: #else
2477: if (FLT_ROUNDS == 0)
2478: aadj1 += 0.5;
2479: #endif
2480: }
2481: y = word0(rv) & Exp_mask;
2482:
2483: /* Check for overflow */
2484:
2485: if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
2486: value(rv0) = value(rv);
2487: word0(rv) -= P*Exp_msk1;
2488: adj = aadj1 * ulp(value(rv));
2489: value(rv) += adj;
2490: if ((word0(rv) & Exp_mask) >=
2491: Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
2492: if (word0(rv0) == Big0 && word1(rv0) == Big1)
2493: goto ovfl;
2494: word0(rv) = Big0;
2495: word1(rv) = Big1;
2496: goto cont;
2497: }
2498: else
2499: word0(rv) += P*Exp_msk1;
2500: }
2501: else {
2502: #ifdef Sudden_Underflow
2503: if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2504: value(rv0) = value(rv);
2505: word0(rv) += P*Exp_msk1;
2506: adj = aadj1 * ulp(value(rv));
2507: value(rv) += adj;
2508: #ifdef IBM
2509: if ((word0(rv) & Exp_mask) < P*Exp_msk1)
2510: #else
2511: if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
2512: #endif
2513: {
2514: if (word0(rv0) == Tiny0
2515: && word1(rv0) == Tiny1)
2516: goto undfl;
2517: word0(rv) = Tiny0;
2518: word1(rv) = Tiny1;
2519: goto cont;
2520: }
2521: else
2522: word0(rv) -= P*Exp_msk1;
2523: }
2524: else {
2525: adj = aadj1 * ulp(value(rv));
2526: value(rv) += adj;
2527: }
2528: #else
2529: /* Compute adj so that the IEEE rounding rules will
2530: * correctly round rv + adj in some half-way cases.
2531: * If rv * ulp(rv) is denormalized (i.e.,
2532: * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
2533: * trouble from bits lost to denormalization;
2534: * example: 1.2e-307 .
2535: */
2536: if (y <= (P-1)*Exp_msk1 && aadj >= 1.) {
2537: aadj1 = (double)(int)(aadj + 0.5);
2538: if (!dsign)
2539: aadj1 = -aadj1;
2540: }
2541: adj = aadj1 * ulp(value(rv));
2542: value(rv) += adj;
2543: #endif
2544: }
2545: z = word0(rv) & Exp_mask;
2546: if (y == z) {
2547: /* Can we stop now? */
2548: L = aadj;
2549: aadj -= L;
2550: /* The tolerances below are conservative. */
2551: if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
2552: if (aadj < .4999999 || aadj > .5000001)
2553: break;
2554: }
2555: else if (aadj < .4999999/FLT_RADIX)
2556: break;
2557: }
2558: cont:
2559: Bfree(bb);
2560: Bfree(bd);
2561: Bfree(bs);
2562: Bfree(delta);
2563: }
2564: retfree:
2565: Bfree(bb);
2566: Bfree(bd);
2567: Bfree(bs);
2568: Bfree(bd0);
2569: Bfree(delta);
2570: ret:
2571: if (se)
1.1.1.2 misho 2572: *se = s;
1.1 misho 2573: result = sign ? -value(rv) : value(rv);
2574:
2575: _THREAD_PRIVATE_MUTEX_LOCK(pow5mult_mutex);
2576: while (p5s) {
2577: tmp = p5s;
2578: p5s = p5s->next;
2579: free(tmp);
2580: }
2581: _THREAD_PRIVATE_MUTEX_UNLOCK(pow5mult_mutex);
2582:
2583: return result;
2584: }
2585:
1.1.1.2 misho 2586: ZEND_API double zend_hex_strtod(const char *str, const char **endptr)
1.1 misho 2587: {
2588: const char *s = str;
2589: char c;
2590: int any = 0;
2591: double value = 0;
2592:
1.1.1.2 misho 2593: if (strlen(str) < 2) {
2594: *endptr = str;
2595: return 0.0;
2596: }
2597:
1.1 misho 2598: if (*s == '0' && (s[1] == 'x' || s[1] == 'X')) {
2599: s += 2;
2600: }
2601:
2602: while ((c = *s++)) {
2603: if (c >= '0' && c <= '9') {
2604: c -= '0';
2605: } else if (c >= 'A' && c <= 'F') {
2606: c -= 'A' - 10;
2607: } else if (c >= 'a' && c <= 'f') {
2608: c -= 'a' - 10;
2609: } else {
2610: break;
2611: }
2612:
2613: any = 1;
2614: value = value * 16 + c;
2615: }
2616:
2617: if (endptr != NULL) {
1.1.1.2 misho 2618: *endptr = any ? s - 1 : str;
1.1 misho 2619: }
2620:
2621: return value;
2622: }
2623:
1.1.1.2 misho 2624: ZEND_API double zend_oct_strtod(const char *str, const char **endptr)
1.1 misho 2625: {
2626: const char *s = str;
2627: char c;
2628: double value = 0;
2629: int any = 0;
2630:
1.1.1.2 misho 2631: if (strlen(str) < 1) {
2632: *endptr = str;
2633: return 0.0;
2634: }
2635:
1.1 misho 2636: /* skip leading zero */
2637: s++;
2638:
2639: while ((c = *s++)) {
2640: if (c < '0' || c > '7') {
2641: /* break and return the current value if the number is not well-formed
2642: * that's what Linux strtol() does
2643: */
2644: break;
2645: }
2646: value = value * 8 + c - '0';
2647: any = 1;
2648: }
2649:
2650: if (endptr != NULL) {
1.1.1.2 misho 2651: *endptr = any ? s - 1 : str;
2652: }
2653:
2654: return value;
2655: }
2656:
2657: ZEND_API double zend_bin_strtod(const char *str, const char **endptr)
2658: {
2659: const char *s = str;
2660: char c;
2661: double value = 0;
2662: int any = 0;
2663:
2664: if (strlen(str) < 2) {
2665: *endptr = str;
2666: return 0.0;
2667: }
2668:
2669: if ('0' == *s && ('b' == s[1] || 'B' == s[1])) {
2670: s += 2;
2671: }
2672:
2673: while ((c = *s++)) {
2674: /*
2675: * Verify the validity of the current character as a base-2 digit. In
2676: * the event that an invalid digit is found, halt the conversion and
2677: * return the portion which has been converted thus far.
2678: */
2679: if ('0' == c || '1' == c)
2680: value = value * 2 + c - '0';
2681: else
2682: break;
2683:
2684: any = 1;
2685: }
2686:
2687: /*
2688: * As with many strtoX implementations, should the subject sequence be
2689: * empty or not well-formed, no conversion is performed and the original
2690: * value of str is stored in *endptr, provided that endptr is not a null
2691: * pointer.
2692: */
2693: if (NULL != endptr) {
1.1 misho 2694: *endptr = (char *)(any ? s - 1 : str);
2695: }
2696:
2697: return value;
2698: }
2699:
2700: /*
2701: * Local variables:
2702: * tab-width: 4
2703: * c-basic-offset: 4
2704: * End:
2705: * vim600: sw=4 ts=4 fdm=marker
2706: * vim<600: sw=4 ts=4
2707: */