xref: /PHP-5.5/Zend/zend_strtod.c (revision c062c18d)
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 
92 /* $Id$ */
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
270 #error "Exactly one of IEEE_LITTLE_ENDIAN IEEE_BIG_ENDIAN, VAX, or IBM should be defined."
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
Bug(const char * message)448 static void Bug(const char *message) {
449 	fprintf(stderr, "%s\n", message);
450 }
451 #endif
452 
zend_startup_strtod(void)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 /* }}} */
zend_shutdown_strtod(void)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 
Balloc(int k)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 
Bfree(Bigint * v)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  */
rv_alloc(int i)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 
nrv_alloc(char * s,char ** rve,int n)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 
multadd(Bigint * b,int m,int a)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 
hi0bits(ULong x)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 
lo0bits(ULong * y)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 
i2b(int i)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 
mult(Bigint * a,Bigint * b)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 
s2b(CONST char * s,int nd0,int nd,ULong y9)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 
pow5mult(Bigint * b,int k)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 
lshift(Bigint * b,int k)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 
cmp(Bigint * a,Bigint * b)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 
diff(Bigint * a,Bigint * b)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 
ulp(double _x)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
b2d(a,e)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 
d2b(double _d,int * e,int * bits)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 
ratio(Bigint * a,Bigint * b)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 
quorem(Bigint * b,Bigint * S)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 
destroy_freelist(void)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 
zend_freedtoa(char * s)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 
zend_dtoa(double _d,int mode,int ndigits,int * decpt,int * sign,char ** rve)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 
zend_strtod(CONST char * s00,CONST char ** se)2039 ZEND_API double zend_strtod (CONST char *s00, CONST char **se)
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)
2572 		*se = s;
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 
zend_hex_strtod(const char * str,const char ** endptr)2586 ZEND_API double zend_hex_strtod(const char *str, const char **endptr)
2587 {
2588 	const char *s = str;
2589 	char c;
2590 	int any = 0;
2591 	double value = 0;
2592 
2593 	if (strlen(str) < 2) {
2594 		*endptr = str;
2595 		return 0.0;
2596 	}
2597 
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) {
2618 		*endptr = any ? s - 1 : str;
2619 	}
2620 
2621 	return value;
2622 }
2623 
zend_oct_strtod(const char * str,const char ** endptr)2624 ZEND_API double zend_oct_strtod(const char *str, const char **endptr)
2625 {
2626 	const char *s = str;
2627 	char c;
2628 	double value = 0;
2629 	int any = 0;
2630 
2631 	if (strlen(str) < 1) {
2632 		*endptr = str;
2633 		return 0.0;
2634 	}
2635 
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) {
2651 		*endptr = any ? s - 1 : str;
2652 	}
2653 
2654 	return value;
2655 }
2656 
zend_bin_strtod(const char * str,const char ** endptr)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) {
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  */
2708