hphp/zend/zend-strtod.cpp

   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 #include "hphp/zend/zend-strtod.h"
  93
  94 #include "hphp/util/assertions.h"
  95 #include "hphp/util/rds-local.h"
  96
  97 #include <new>
  98 #include <stdint.h>
  99 #include <stdlib.h>
 100 #include <string.h>
 101
 102 namespace HPHP {
 103 ///////////////////////////////////////////////////////////////////////////////
 104
 105 #if (defined(__APPLE__) || defined(__APPLE_CC__)) && (defined(__BIG_ENDIAN__) || defined(__LITTLE_ENDIAN__))
 106 # if defined(__LITTLE_ENDIAN__)
 107 #  undef WORDS_BIGENDIAN
 108 # else
 109 #  if defined(__BIG_ENDIAN__)
 110 #   define WORDS_BIGENDIAN
 111 #  endif
 112 # endif
 113 #endif
 114
 115 #ifdef WORDS_BIGENDIAN
 116 #define IEEE_BIG_ENDIAN
 117 #else
 118 #define IEEE_LITTLE_ENDIAN
 119 #endif
 120
 121 #if defined(__arm__) && !defined(__VFP_FP__)
 122 /*
 123  *  * Although the CPU is little endian the FP has different
 124  *   * byte and word endianness. The byte order is still little endian
 125  *    * but the word order is big endian.
 126  *     */
 127 #define IEEE_BIG_ENDIAN
 128 #undef IEEE_LITTLE_ENDIAN
 129 #endif
 130
 131 #ifdef __vax__
 132 #define VAX
 133 #endif
 134
 135 #if defined(_MSC_VER)
 136 #define int32_t __int32
 137 #define uint32_t unsigned __int32
 138 #define IEEE_LITTLE_ENDIAN
 139 #endif
 140
 141 #define Long    int32_t
 142 #define ULong   uint32_t
 143
 144 #ifdef MALLOC
 145 #ifdef KR_headers
 146 extern char *MALLOC();
 147 #else
 148 extern void *MALLOC(size_t);
 149 #endif
 150 #else
 151 #define MALLOC malloc
 152 #endif
 153
 154 } // namespace HPHP
 155
 156 #include <ctype.h>
 157 #include <errno.h>
 158
 159 namespace HPHP {
 160
 161 #ifdef Bad_float_h
 162 #ifdef IEEE_BIG_ENDIAN
 163 #define IEEE_ARITHMETIC
 164 #endif
 165 #ifdef IEEE_LITTLE_ENDIAN
 166 #define IEEE_ARITHMETIC
 167 #endif
 168
 169 #ifdef IEEE_ARITHMETIC
 170 #define DBL_DIG 15
 171 #define DBL_MAX_10_EXP 308
 172 #define DBL_MAX_EXP 1024
 173 #define FLT_RADIX 2
 174 #define FLT_ROUNDS 1
 175 #define DBL_MAX 1.7976931348623157e+308
 176 #endif
 177
 178 #ifdef IBM
 179 #define DBL_DIG 16
 180 #define DBL_MAX_10_EXP 75
 181 #define DBL_MAX_EXP 63
 182 #define FLT_RADIX 16
 183 #define FLT_ROUNDS 0
 184 #define DBL_MAX 7.2370055773322621e+75
 185 #endif
 186
 187 #ifdef VAX
 188 #define DBL_DIG 16
 189 #define DBL_MAX_10_EXP 38
 190 #define DBL_MAX_EXP 127
 191 #define FLT_RADIX 2
 192 #define FLT_ROUNDS 1
 193 #define DBL_MAX 1.7014118346046923e+38
 194 #endif
 195
 196
 197 #ifndef LONG_MAX
 198 #define LONG_MAX 2147483647
 199 #endif
 200 #else
 201 } // namespace HPHP
 202
 203 #include <float.h>
 204
 205 namespace HPHP {
 206 #endif
 207 #ifndef __MATH_H__
 208 } // namespace HPHP
 209
 210 #include <math.h>
 211
 212 namespace HPHP {
 213 #endif
 214
 215 #ifndef CONST
 216 #ifdef KR_headers
 217 #define CONST /* blank */
 218 #else
 219 #define CONST const
 220 #endif
 221 #endif
 222
 223 #ifdef Unsigned_Shifts
 224 #define Sign_Extend(a,b) if (b < 0) a |= 0xffff0000;
 225 #else
 226 #define Sign_Extend(a,b) /*no-op*/
 227 #endif
 228
 229 #if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) + defined(VAX) + \
 230         defined(IBM) != 1
 231 #error Exactly one of IEEE_LITTLE_ENDIAN, IEEE_BIG_ENDIAN, VAX, or IBM \
 232        should be defined.
 233 #endif
 234
 235   typedef union {
 236         double d;
 237           ULong ul[2];
 238   } _double;
 239 #define value(x) ((x).d)
 240 #ifdef IEEE_LITTLE_ENDIAN
 241 #define word0(x) ((x).ul[1])
 242 #define word1(x) ((x).ul[0])
 243 #else
 244 #define word0(x) ((x).ul[0])
 245 #define word1(x) ((x).ul[1])
 246 #endif
 247
 248 /* The following definition of Storeinc is appropriate for MIPS processors.
 249  * An alternative that might be better on some machines is
 250  * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
 251  */
 252 #if defined(IEEE_LITTLE_ENDIAN) + defined(VAX) + defined(__arm__)
 253 #define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
 254     ((unsigned short *)a)[0] = (unsigned short)c, a++)
 255 #else
 256 #define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
 257     ((unsigned short *)a)[1] = (unsigned short)c, a++)
 258 #endif
 259
 260 /* #define P DBL_MANT_DIG */
 261 /* Ten_pmax = floor(P*log(2)/log(5)) */
 262 /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
 263 /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
 264 /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
 265
 266 #if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN)
 267 #define Exp_shift  20
 268 #define Exp_shift1 20
 269 #define Exp_msk1    0x100000
 270 #define Exp_msk11   0x100000
 271 #define Exp_mask  0x7ff00000
 272 #define P 53
 273 #define Bias 1023
 274 #define IEEE_Arith
 275 #define Emin (-1022)
 276 #define Exp_1  0x3ff00000
 277 #define Exp_11 0x3ff00000
 278 #define Ebits 11
 279 #define Frac_mask  0xfffff
 280 #define Frac_mask1 0xfffff
 281 #define Ten_pmax 22
 282 #define Bletch 0x10
 283 #define Bndry_mask  0xfffff
 284 #define Bndry_mask1 0xfffff
 285 #define LSB 1
 286 #define Sign_bit 0x80000000
 287 #define Log2P 1
 288 #define Tiny0 0
 289 #define Tiny1 1
 290 #define Quick_max 14
 291 #define Int_max 14
 292 #define Infinite(x) (word0(x) == 0x7ff00000) /* sufficient test for here */
 293 #else
 294 #undef  Sudden_Underflow
 295 #define Sudden_Underflow
 296 #ifdef IBM
 297 #define Exp_shift  24
 298 #define Exp_shift1 24
 299 #define Exp_msk1   0x1000000
 300 #define Exp_msk11  0x1000000
 301 #define Exp_mask  0x7f000000
 302 #define P 14
 303 #define Bias 65
 304 #define Exp_1  0x41000000
 305 #define Exp_11 0x41000000
 306 #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
 307 #define Frac_mask  0xffffff
 308 #define Frac_mask1 0xffffff
 309 #define Bletch 4
 310 #define Ten_pmax 22
 311 #define Bndry_mask  0xefffff
 312 #define Bndry_mask1 0xffffff
 313 #define LSB 1
 314 #define Sign_bit 0x80000000
 315 #define Log2P 4
 316 #define Tiny0 0x100000
 317 #define Tiny1 0
 318 #define Quick_max 14
 319 #define Int_max 15
 320 #else /* VAX */
 321 #define Exp_shift  23
 322 #define Exp_shift1 7
 323 #define Exp_msk1    0x80
 324 #define Exp_msk11   0x800000
 325 #define Exp_mask  0x7f80
 326 #define P 56
 327 #define Bias 129
 328 #define Exp_1  0x40800000
 329 #define Exp_11 0x4080
 330 #define Ebits 8
 331 #define Frac_mask  0x7fffff
 332 #define Frac_mask1 0xffff007f
 333 #define Ten_pmax 24
 334 #define Bletch 2
 335 #define Bndry_mask  0xffff007f
 336 #define Bndry_mask1 0xffff007f
 337 #define LSB 0x10000
 338 #define Sign_bit 0x8000
 339 #define Log2P 1
 340 #define Tiny0 0x80
 341 #define Tiny1 0
 342 #define Quick_max 15
 343 #define Int_max 15
 344 #endif
 345 #endif
 346
 347 #ifndef IEEE_Arith
 348 #define ROUND_BIASED
 349 #endif
 350
 351 #ifdef RND_PRODQUOT
 352 #define rounded_product(a,b) a = rnd_prod(a, b)
 353 #define rounded_quotient(a,b) a = rnd_quot(a, b)
 354 #ifdef KR_headers
 355 extern double rnd_prod(), rnd_quot();
 356 #else
 357 extern double rnd_prod(double, double), rnd_quot(double, double);
 358 #endif
 359 #else
 360 #define rounded_product(a,b) a *= b
 361 #define rounded_quotient(a,b) a /= b
 362 #endif
 363
 364 #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
 365 #define Big1 0xffffffff
 366
 367 #ifndef Just_16
 368 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
 369  *  * This makes some inner loops simpler and sometimes saves work
 370  *   * during multiplications, but it often seems to make things slightly
 371  *    * slower.  Hence the default is now to store 32 bits per Long.
 372  *     */
 373 #ifndef Pack_32
 374 #define Pack_32
 375 #endif
 376 #endif
 377
 378 #define Kmax 15
 379
 380 namespace {
 381
 382 struct Bigint {
 383   struct Bigint *next;
 384   int k, maxwds, sign, wds;
 385   ULong x[1];
 386 };
 387
 388 typedef struct Bigint Bigint;
 389
 390 } // namespace
 391
 392 void destroy_freelist(Bigint** freelist);
 393
 394 struct BigintData {
 395   BigintData() : p5s(nullptr) {
 396     freelist = (Bigint **)calloc(Kmax + 1, sizeof(Bigint *));
 397   }
 398   ~BigintData() {
 399     destroy_freelist(freelist);
 400     free(freelist);
 401   }
 402
 403   Bigint **freelist;
 404   Bigint *p5s;
 405 };
 406 static RDS_LOCAL_NO_CHECK(BigintData, s_bigint_data);
 407
 408 // NOTE: If this has not been called, various functions in this file,
 409 // and in other files (e.g. "zend-printf.cpp"), will crash when called.
 410 void zend_get_bigint_data() {
 411   s_bigint_data.getCheck();
 412 }
 413
 414 static Bigint * Balloc(int k)
 415 {
 416   int x;
 417   Bigint *rv;
 418
 419   assertx(k <= Kmax);
 420
 421   Bigint **&freelist = s_bigint_data->freelist;
 422   if ((rv = freelist[k])) {
 423     freelist[k] = rv->next;
 424   } else {
 425     x = 1 << k;
 426     rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(Long));
 427     assertx(rv != nullptr);
 428     rv->k = k;
 429     rv->maxwds = x;
 430   }
 431   rv->sign = rv->wds = 0;
 432   return rv;
 433 }
 434
 435 static void Bfree(Bigint *v)
 436 {
 437   if (v) {
 438     Bigint **&freelist = s_bigint_data->freelist;
 439     v->next = freelist[v->k];
 440     freelist[v->k] = v;
 441   }
 442 }
 443
 444 #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
 445     y->wds*sizeof(Long) + 2*sizeof(int))
 446
 447 /* return value is only used as a simple string, so mis-aligned parts
 448  * inside the Bigint are not at risk on strict align architectures
 449  */
 450 static char * rv_alloc(int i) {
 451   int j, k, *r;
 452
 453   j = sizeof(ULong);
 454   for(k = 0;
 455       (int)(sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j) <= i;
 456       j <<= 1) {
 457     k++;
 458   }
 459   r = (int*)Balloc(k);
 460   *r = k;
 461   return (char *)(r+1);
 462 }
 463
 464
 465 static char * nrv_alloc(const char *s, char **rve, int n)
 466 {
 467   char *rv, *t;
 468
 469   t = rv = rv_alloc(n);
 470   while((*t = *s++) !=0) {
 471     t++;
 472   }
 473   if (rve) {
 474     *rve = t;
 475   }
 476   return rv;
 477 }
 478
 479 static Bigint * multadd(Bigint *b, int m, int a) /* multiply by m and add a */
 480 {
 481   int i, wds;
 482   ULong *x, y;
 483 #ifdef Pack_32
 484   ULong xi, z;
 485 #endif
 486   Bigint *b1;
 487
 488   wds = b->wds;
 489   x = b->x;
 490   i = 0;
 491   do {
 492 #ifdef Pack_32
 493     xi = *x;
 494     y = (xi & 0xffff) * m + a;
 495     z = (xi >> 16) * m + (y >> 16);
 496     a = (int)(z >> 16);
 497     *x++ = (z << 16) + (y & 0xffff);
 498 #else
 499     y = *x * m + a;
 500     a = (int)(y >> 16);
 501     *x++ = y & 0xffff;
 502 #endif
 503   }
 504   while(++i < wds);
 505   if (a) {
 506     if (wds >= b->maxwds) {
 507       b1 = Balloc(b->k+1);
 508       Bcopy(b1, b);
 509       Bfree(b);
 510       b = b1;
 511     }
 512     b->x[wds++] = a;
 513     b->wds = wds;
 514   }
 515   return b;
 516 }
 517
 518 static int hi0bits(ULong x)
 519 {
 520   int k = 0;
 521
 522   if (!(x & 0xffff0000)) {
 523     k = 16;
 524     x <<= 16;
 525   }
 526   if (!(x & 0xff000000)) {
 527     k += 8;
 528     x <<= 8;
 529   }
 530   if (!(x & 0xf0000000)) {
 531     k += 4;
 532     x <<= 4;
 533   }
 534   if (!(x & 0xc0000000)) {
 535     k += 2;
 536     x <<= 2;
 537   }
 538   if (!(x & 0x80000000)) {
 539     k++;
 540     if (!(x & 0x40000000)) {
 541       return 32;
 542     }
 543   }
 544   return k;
 545 }
 546
 547 static int lo0bits(ULong *y)
 548 {
 549   int k;
 550   ULong x = *y;
 551
 552   if (x & 7) {
 553     if (x & 1) {
 554       return 0;
 555     }
 556     if (x & 2) {
 557       *y = x >> 1;
 558       return 1;
 559     }
 560     *y = x >> 2;
 561     return 2;
 562   }
 563   k = 0;
 564   if (!(x & 0xffff)) {
 565     k = 16;
 566     x >>= 16;
 567   }
 568   if (!(x & 0xff)) {
 569     k += 8;
 570     x >>= 8;
 571   }
 572   if (!(x & 0xf)) {
 573     k += 4;
 574     x >>= 4;
 575   }
 576   if (!(x & 0x3)) {
 577     k += 2;
 578     x >>= 2;
 579   }
 580   if (!(x & 1)) {
 581     k++;
 582     x >>= 1;
 583     if (!(x & 1)) {
 584       return 32;
 585     }
 586   }
 587   *y = x;
 588   return k;
 589 }
 590
 591 static Bigint * i2b(int i)
 592 {
 593   Bigint *b;
 594
 595   b = Balloc(1);
 596   b->x[0] = i;
 597   b->wds = 1;
 598   return b;
 599 }
 600
 601 static Bigint * mult(Bigint *a, Bigint *b)
 602 {
 603   Bigint *c;
 604   int k, wa, wb, wc;
 605   ULong carry, y, z;
 606   ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
 607 #ifdef Pack_32
 608   ULong z2;
 609 #endif
 610
 611   if (a->wds < b->wds) {
 612     c = a;
 613     a = b;
 614     b = c;
 615   }
 616   k = a->k;
 617   wa = a->wds;
 618   wb = b->wds;
 619   wc = wa + wb;
 620   if (wc > a->maxwds) {
 621     k++;
 622   }
 623   c = Balloc(k);
 624   for(x = c->x, xa = x + wc; x < xa; x++) {
 625     *x = 0;
 626   }
 627   xa = a->x;
 628   xae = xa + wa;
 629   xb = b->x;
 630   xbe = xb + wb;
 631   xc0 = c->x;
 632 #ifdef Pack_32
 633   for(; xb < xbe; xb++, xc0++) {
 634     if ((y = *xb & 0xffff)) {
 635       x = xa;
 636       xc = xc0;
 637       carry = 0;
 638       do {
 639         z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
 640         carry = z >> 16;
 641         z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
 642         carry = z2 >> 16;
 643         Storeinc(xc, z2, z);
 644       }
 645       while(x < xae);
 646       *xc = carry;
 647     }
 648     if ((y = *xb >> 16)) {
 649       x = xa;
 650       xc = xc0;
 651       carry = 0;
 652       z2 = *xc;
 653       do {
 654         z = (*x & 0xffff) * y + (*xc >> 16) + carry;
 655         carry = z >> 16;
 656         Storeinc(xc, z, z2);
 657         z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
 658         carry = z2 >> 16;
 659       }
 660       while(x < xae);
 661       *xc = z2;
 662     }
 663   }
 664 #else
 665   for(; xb < xbe; xc0++) {
 666     if (y = *xb++) {
 667       x = xa;
 668       xc = xc0;
 669       carry = 0;
 670       do {
 671         z = *x++ * y + *xc + carry;
 672         carry = z >> 16;
 673         *xc++ = z & 0xffff;
 674       }
 675       while(x < xae);
 676       *xc = carry;
 677     }
 678   }
 679 #endif
 680   for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
 681   c->wds = wc;
 682   return c;
 683 }
 684
 685 static Bigint * s2b (CONST char *s, int nd0, int nd, ULong y9)
 686 {
 687   Bigint *b;
 688   int i, k;
 689   Long x, y;
 690
 691   x = (nd + 8) / 9;
 692   for(k = 0, y = 1; x > y; y <<= 1, k++) ;
 693 #ifdef Pack_32
 694   b = Balloc(k);
 695   b->x[0] = y9;
 696   b->wds = 1;
 697 #else
 698   b = Balloc(k+1);
 699   b->x[0] = y9 & 0xffff;
 700   b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
 701 #endif
 702
 703   i = 9;
 704   if (9 < nd0) {
 705     s += 9;
 706     do b = multadd(b, 10, *s++ - '0');
 707     while(++i < nd0);
 708     s++;
 709   } else {
 710     s += 10;
 711   }
 712   for(; i < nd; i++) {
 713     b = multadd(b, 10, *s++ - '0');
 714   }
 715   return b;
 716 }
 717
 718 static Bigint * pow5mult(Bigint *b, int k)
 719 {
 720   Bigint *b1, *p5, *p51;
 721   int i;
 722   static int p05[3] = { 5, 25, 125 };
 723
 724   Bigint *&p5s = s_bigint_data->p5s;
 725   if ((i = k & 3)) {
 726     b = multadd(b, p05[i-1], 0);
 727   }
 728
 729   if (!(k >>= 2)) {
 730     return b;
 731   }
 732   if (!(p5 = p5s)) {
 733     /* first time */
 734     p5 = p5s = i2b(625);
 735     p5->next = 0;
 736   }
 737   for(;;) {
 738     if (k & 1) {
 739       b1 = mult(b, p5);
 740       Bfree(b);
 741       b = b1;
 742     }
 743     if (!(k >>= 1)) {
 744       break;
 745     }
 746     if (!(p51 = p5->next)) {
 747       if (!(p51 = p5->next)) {
 748         p51 = p5->next = mult(p5,p5);
 749         p51->next = 0;
 750       }
 751     }
 752     p5 = p51;
 753   }
 754   return b;
 755 }
 756
 757
 758 static Bigint *lshift(Bigint *b, int k)
 759 {
 760   int i, k1, n, n1;
 761   Bigint *b1;
 762   ULong *x, *x1, *xe, z;
 763
 764 #ifdef Pack_32
 765   n = k >> 5;
 766 #else
 767   n = k >> 4;
 768 #endif
 769   k1 = b->k;
 770   n1 = n + b->wds + 1;
 771   for(i = b->maxwds; n1 > i; i <<= 1) {
 772     k1++;
 773   }
 774   b1 = Balloc(k1);
 775   x1 = b1->x;
 776   for(i = 0; i < n; i++) {
 777     *x1++ = 0;
 778   }
 779   x = b->x;
 780   xe = x + b->wds;
 781 #ifdef Pack_32
 782   if (k &= 0x1f) {
 783     k1 = 32 - k;
 784     z = 0;
 785     do {
 786       *x1++ = *x << k | z;
 787       z = *x++ >> k1;
 788     }
 789     while(x < xe);
 790     if ((*x1 = z)) {
 791       ++n1;
 792     }
 793   }
 794 #else
 795   if (k &= 0xf) {
 796     k1 = 16 - k;
 797     z = 0;
 798     do {
 799       *x1++ = *x << k  & 0xffff | z;
 800       z = *x++ >> k1;
 801     }
 802     while(x < xe);
 803     if (*x1 = z) {
 804       ++n1;
 805     }
 806   }
 807 #endif
 808   else do
 809     *x1++ = *x++;
 810   while(x < xe);
 811   b1->wds = n1 - 1;
 812   Bfree(b);
 813   return b1;
 814 }
 815
 816 static int cmp(Bigint *a, Bigint *b)
 817 {
 818   ULong *xa, *xa0, *xb, *xb0;
 819   int i, j;
 820
 821   i = a->wds;
 822   j = b->wds;
 823   if (i -= j)
 824     return i;
 825   xa0 = a->x;
 826   xa = xa0 + j;
 827   xb0 = b->x;
 828   xb = xb0 + j;
 829   for(;;) {
 830     if (*--xa != *--xb)
 831       return *xa < *xb ? -1 : 1;
 832     if (xa <= xa0)
 833       break;
 834   }
 835   return 0;
 836 }
 837
 838
 839 static Bigint * diff(Bigint *a, Bigint *b)
 840 {
 841   Bigint *c;
 842   int i, wa, wb;
 843   Long borrow, y; /* We need signed shifts here. */
 844   ULong *xa, *xae, *xb, *xbe, *xc;
 845 #ifdef Pack_32
 846   Long z;
 847 #endif
 848
 849   i = cmp(a,b);
 850   if (!i) {
 851     c = Balloc(0);
 852     c->wds = 1;
 853     c->x[0] = 0;
 854     return c;
 855   }
 856   if (i < 0) {
 857     c = a;
 858     a = b;
 859     b = c;
 860     i = 1;
 861   } else {
 862     i = 0;
 863   }
 864   c = Balloc(a->k);
 865   c->sign = i;
 866   wa = a->wds;
 867   xa = a->x;
 868   xae = xa + wa;
 869   wb = b->wds;
 870   xb = b->x;
 871   xbe = xb + wb;
 872   xc = c->x;
 873   borrow = 0;
 874 #ifdef Pack_32
 875   do {
 876     y = (*xa & 0xffff) - (*xb & 0xffff) + borrow;
 877     borrow = y >> 16;
 878     Sign_Extend(borrow, y);
 879     z = (*xa++ >> 16) - (*xb++ >> 16) + borrow;
 880     borrow = z >> 16;
 881     Sign_Extend(borrow, z);
 882     Storeinc(xc, z, y);
 883   } while(xb < xbe);
 884   while(xa < xae) {
 885     y = (*xa & 0xffff) + borrow;
 886     borrow = y >> 16;
 887     Sign_Extend(borrow, y);
 888     z = (*xa++ >> 16) + borrow;
 889     borrow = z >> 16;
 890     Sign_Extend(borrow, z);
 891     Storeinc(xc, z, y);
 892   }
 893 #else
 894   do {
 895     y = *xa++ - *xb++ + borrow;
 896     borrow = y >> 16;
 897     Sign_Extend(borrow, y);
 898     *xc++ = y & 0xffff;
 899   } while(xb < xbe);
 900   while(xa < xae) {
 901     y = *xa++ + borrow;
 902     borrow = y >> 16;
 903     Sign_Extend(borrow, y);
 904     *xc++ = y & 0xffff;
 905   }
 906 #endif
 907   while(!*--xc) {
 908     wa--;
 909   }
 910   c->wds = wa;
 911   return c;
 912 }
 913
 914 static double ulp (double _x)
 915 {
 916   _double x;
 917   register Long L;
 918   _double a;
 919
 920   value(x) = _x;
 921   L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
 922 #ifndef Sudden_Underflow
 923   if (L > 0) {
 924 #endif
 925 #ifdef IBM
 926     L |= Exp_msk1 >> 4;
 927 #endif
 928     word0(a) = L;
 929     word1(a) = 0;
 930 #ifndef Sudden_Underflow
 931   }
 932   else {
 933     L = -L >> Exp_shift;
 934     if (L < Exp_shift) {
 935       word0(a) = 0x80000 >> L;
 936       word1(a) = 0;
 937     }
 938     else {
 939       word0(a) = 0;
 940       L -= Exp_shift;
 941       word1(a) = L >= 31 ? 1 : 1 << (31 - L);
 942     }
 943   }
 944 #endif
 945   return value(a);
 946 }
 947
 948 static double
 949 b2d
 950 #ifdef KR_headers
 951 (a, e) Bigint *a; int *e;
 952 #else
 953 (Bigint *a, int *e)
 954 #endif
 955 {
 956   ULong *xa, *xa0, w, y, z;
 957   int k;
 958   _double d;
 959 #ifdef VAX
 960   ULong d0, d1;
 961 #else
 962 #define d0 word0(d)
 963 #define d1 word1(d)
 964 #endif
 965
 966   xa0 = a->x;
 967   xa = xa0 + a->wds;
 968   y = *--xa;
 969   k = hi0bits(y);
 970   *e = 32 - k;
 971 #ifdef Pack_32
 972   if (k < Ebits) {
 973     d0 = Exp_1 | y >> (Ebits - k);
 974     w = xa > xa0 ? *--xa : 0;
 975     d1 = y << ((32-Ebits) + k) | w >> (Ebits - k);
 976     goto ret_d;
 977   }
 978   z = xa > xa0 ? *--xa : 0;
 979   if (k -= Ebits) {
 980     d0 = Exp_1 | y << k | z >> (32 - k);
 981     y = xa > xa0 ? *--xa : 0;
 982     d1 = z << k | y >> (32 - k);
 983   }
 984   else {
 985     d0 = Exp_1 | y;
 986     d1 = z;
 987   }
 988 #else
 989   if (k < Ebits + 16) {
 990     z = xa > xa0 ? *--xa : 0;
 991     d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
 992     w = xa > xa0 ? *--xa : 0;
 993     y = xa > xa0 ? *--xa : 0;
 994     d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
 995     goto ret_d;
 996   }
 997   z = xa > xa0 ? *--xa : 0;
 998   w = xa > xa0 ? *--xa : 0;
 999   k -= Ebits + 16;
1000   d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
1001   y = xa > xa0 ? *--xa : 0;
1002   d1 = w << k + 16 | y << k;
1003 #endif
1004 ret_d:
1005 #ifdef VAX
1006   word0(d) = d0 >> 16 | d0 << 16;
1007   word1(d) = d1 >> 16 | d1 << 16;
1008 #else
1009 #undef d0
1010 #undef d1
1011 #endif
1012   return value(d);
1013 }
1014
1015
1016 static Bigint * d2b(double _d, int *e, int *bits)
1017 {
1018   Bigint *b;
1019   int de, i, k;
1020   ULong *x, y, z;
1021   _double d;
1022 #ifdef VAX
1023   ULong d0, d1;
1024 #endif
1025
1026   value(d) = _d;
1027 #ifdef VAX
1028   d0 = word0(d) >> 16 | word0(d) << 16;
1029   d1 = word1(d) >> 16 | word1(d) << 16;
1030 #else
1031 #define d0 word0(d)
1032 #define d1 word1(d)
1033 #endif
1034
1035 #ifdef Pack_32
1036   b = Balloc(1);
1037 #else
1038   b = Balloc(2);
1039 #endif
1040   x = b->x;
1041
1042   z = d0 & Frac_mask;
1043   d0 &= 0x7fffffff;   /* clear sign bit, which we ignore */
1044 #ifdef Sudden_Underflow
1045   de = (int)(d0 >> Exp_shift);
1046 #ifndef IBM
1047   z |= Exp_msk11;
1048 #endif
1049 #else
1050   if ((de = (int)(d0 >> Exp_shift)))
1051     z |= Exp_msk1;
1052 #endif
1053 #ifdef Pack_32
1054   if ((y = d1)) {
1055     if ((k = lo0bits(&y))) {
1056       x[0] = y | (z << (32 - k));
1057       z >>= k;
1058     } else {
1059       x[0] = y;
1060     }
1061     i = b->wds = (x[1] = z) ? 2 : 1;
1062   } else {
1063     k = lo0bits(&z);
1064     x[0] = z;
1065     i = b->wds = 1;
1066     k += 32;
1067   }
1068 #else
1069   if (y = d1) {
1070     if (k = lo0bits(&y)) {
1071       if (k >= 16) {
1072         x[0] = y | z << 32 - k & 0xffff;
1073         x[1] = z >> k - 16 & 0xffff;
1074         x[2] = z >> k;
1075         i = 2;
1076       } else {
1077         x[0] = y & 0xffff;
1078         x[1] = y >> 16 | z << 16 - k & 0xffff;
1079         x[2] = z >> k & 0xffff;
1080         x[3] = z >> k+16;
1081         i = 3;
1082       }
1083     } else {
1084       x[0] = y & 0xffff;
1085       x[1] = y >> 16;
1086       x[2] = z & 0xffff;
1087       x[3] = z >> 16;
1088       i = 3;
1089     }
1090   } else {
1091     k = lo0bits(&z);
1092     if (k >= 16) {
1093       x[0] = z;
1094       i = 0;
1095     } else {
1096       x[0] = z & 0xffff;
1097       x[1] = z >> 16;
1098       i = 1;
1099     }
1100     k += 32;
1101   }
1102   while(!x[i])
1103     --i;
1104   b->wds = i + 1;
1105 #endif
1106 #ifndef Sudden_Underflow
1107   if (de) {
1108 #endif
1109 #ifdef IBM
1110     *e = (de - Bias - (P-1) << 2) + k;
1111     *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
1112 #else
1113     *e = de - Bias - (P-1) + k;
1114     *bits = P - k;
1115 #endif
1116 #ifndef Sudden_Underflow
1117   } else {
1118     *e = de - Bias - (P-1) + 1 + k;
1119 #ifdef Pack_32
1120     *bits = 32*i - hi0bits(x[i-1]);
1121 #else
1122     *bits = (i+2)*16 - hi0bits(x[i]);
1123 #endif
1124   }
1125 #endif
1126   return b;
1127 }
1128 #undef d0
1129 #undef d1
1130
1131
1132 static double ratio (Bigint *a, Bigint *b)
1133 {
1134   _double da, db;
1135   int k, ka, kb;
1136
1137   value(da) = b2d(a, &ka);
1138   value(db) = b2d(b, &kb);
1139 #ifdef Pack_32
1140   k = ka - kb + 32*(a->wds - b->wds);
1141 #else
1142   k = ka - kb + 16*(a->wds - b->wds);
1143 #endif
1144 #ifdef IBM
1145   if (k > 0) {
1146     word0(da) += (k >> 2)*Exp_msk1;
1147     if (k &= 3) {
1148       da *= 1 << k;
1149     }
1150   } else {
1151     k = -k;
1152     word0(db) += (k >> 2)*Exp_msk1;
1153     if (k &= 3)
1154       db *= 1 << k;
1155   }
1156 #else
1157   if (k > 0) {
1158     word0(da) += k*Exp_msk1;
1159   } else {
1160     k = -k;
1161     word0(db) += k*Exp_msk1;
1162   }
1163 #endif
1164   return value(da) / value(db);
1165 }
1166
1167 static CONST double
1168 tens[] = {
1169   1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1170   1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1171   1e20, 1e21, 1e22
1172 #ifdef VAX
1173     , 1e23, 1e24
1174 #endif
1175 };
1176
1177 #ifdef IEEE_Arith
1178 static CONST double bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
1179 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, 1e-256 };
1180 #define n_bigtens 5
1181 #else
1182 #ifdef IBM
1183 static CONST double bigtens[] = { 1e16, 1e32, 1e64 };
1184 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
1185 #define n_bigtens 3
1186 #else
1187 static CONST double bigtens[] = { 1e16, 1e32 };
1188 static CONST double tinytens[] = { 1e-16, 1e-32 };
1189 #define n_bigtens 2
1190 #endif
1191 #endif
1192
1193
1194 static int quorem(Bigint *b, Bigint *S)
1195 {
1196   int n;
1197   Long borrow, y;
1198   ULong carry, q, ys;
1199   ULong *bx, *bxe, *sx, *sxe;
1200 #ifdef Pack_32
1201   Long z;
1202   ULong si, zs;
1203 #endif
1204
1205   n = S->wds;
1206   if (b->wds < n)
1207     return 0;
1208   sx = S->x;
1209   sxe = sx + --n;
1210   bx = b->x;
1211   bxe = bx + n;
1212   q = *bxe / (*sxe + 1);  /* ensure q <= true quotient */
1213   if (q) {
1214     borrow = 0;
1215     carry = 0;
1216     do {
1217 #ifdef Pack_32
1218       si = *sx++;
1219       ys = (si & 0xffff) * q + carry;
1220       zs = (si >> 16) * q + (ys >> 16);
1221       carry = zs >> 16;
1222       y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
1223       borrow = y >> 16;
1224       Sign_Extend(borrow, y);
1225       z = (*bx >> 16) - (zs & 0xffff) + borrow;
1226       borrow = z >> 16;
1227       Sign_Extend(borrow, z);
1228       Storeinc(bx, z, y);
1229 #else
1230       ys = *sx++ * q + carry;
1231       carry = ys >> 16;
1232       y = *bx - (ys & 0xffff) + borrow;
1233       borrow = y >> 16;
1234       Sign_Extend(borrow, y);
1235       *bx++ = y & 0xffff;
1236 #endif
1237     }
1238     while(sx <= sxe);
1239     if (!*bxe) {
1240       bx = b->x;
1241       while(--bxe > bx && !*bxe)
1242         --n;
1243       b->wds = n;
1244     }
1245   }
1246   if (cmp(b, S) >= 0) {
1247     q++;
1248     borrow = 0;
1249     carry = 0;
1250     bx = b->x;
1251     sx = S->x;
1252     do {
1253 #ifdef Pack_32
1254       si = *sx++;
1255       ys = (si & 0xffff) + carry;
1256       zs = (si >> 16) + (ys >> 16);
1257       carry = zs >> 16;
1258       y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
1259       borrow = y >> 16;
1260       Sign_Extend(borrow, y);
1261       z = (*bx >> 16) - (zs & 0xffff) + borrow;
1262       borrow = z >> 16;
1263       Sign_Extend(borrow, z);
1264       Storeinc(bx, z, y);
1265 #else
1266       ys = *sx++ + carry;
1267       carry = ys >> 16;
1268       y = *bx - (ys & 0xffff) + borrow;
1269       borrow = y >> 16;
1270       Sign_Extend(borrow, y);
1271       *bx++ = y & 0xffff;
1272 #endif
1273     }
1274     while(sx <= sxe);
1275     bx = b->x;
1276     bxe = bx + n;
1277     if (!*bxe) {
1278       while(--bxe > bx && !*bxe)
1279         --n;
1280       b->wds = n;
1281     }
1282   }
1283   return q;
1284 }
1285
1286 void destroy_freelist(Bigint** freelist)
1287 {
1288   int i;
1289   Bigint *tmp;
1290
1291   for (i = 0; i <= Kmax; i++) {
1292     Bigint **listp = &freelist[i];
1293     while ((tmp = *listp) != nullptr) {
1294       *listp = tmp->next;
1295       free(tmp);
1296     }
1297     freelist[i] = nullptr;
1298   }
1299
1300 }
1301
1302
1303 void zend_freedtoa(char *s)
1304 {
1305   Bigint *b = (Bigint *)((int *)s - 1);
1306   b->maxwds = 1 << (b->k = *(int*)b);
1307   Bfree(b);
1308 }
1309
1310 /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
1311  *
1312  * Inspired by "How to Print Floating-Point Numbers Accurately" by
1313  * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101].
1314  *
1315  * Modifications:
1316  *  1. Rather than iterating, we use a simple numeric overestimate
1317  *     to determine k = floor(log10(d)).  We scale relevant
1318  *     quantities using O(log2(k)) rather than O(k) multiplications.
1319  *  2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
1320  *     try to generate digits strictly left to right.  Instead, we
1321  *     compute with fewer bits and propagate the carry if necessary
1322  *     when rounding the final digit up.  This is often faster.
1323  *  3. Under the assumption that input will be rounded nearest,
1324  *     mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
1325  *     That is, we allow equality in stopping tests when the
1326  *     round-nearest rule will give the same floating-point value
1327  *     as would satisfaction of the stopping test with strict
1328  *     inequality.
1329  *  4. We remove common factors of powers of 2 from relevant
1330  *     quantities.
1331  *  5. When converting floating-point integers less than 1e16,
1332  *     we use floating-point arithmetic rather than resorting
1333  *     to multiple-precision integers.
1334  *  6. When asked to produce fewer than 15 digits, we first try
1335  *     to get by with floating-point arithmetic; we resort to
1336  *     multiple-precision integer arithmetic only if we cannot
1337  *     guarantee that the floating-point calculation has given
1338  *     the correctly rounded result.  For k requested digits and
1339  *     "uniformly" distributed input, the probability is
1340  *     something like 10^(k-15) that we must resort to the Long
1341  *     calculation.
1342  */
1343
1344 char * zend_dtoa(double _d, int mode, int ndigits, int *decpt, int *sign, char **rve)
1345 {
1346  /* Arguments ndigits, decpt, sign are similar to those
1347     of ecvt and fcvt; trailing zeros are suppressed from
1348     the returned string.  If not null, *rve is set to point
1349     to the end of the return value.  If d is +-Infinity or NaN,
1350     then *decpt is set to 9999.
1351
1352     mode:
1353         0 ==> shortest string that yields d when read in
1354             and rounded to nearest.
1355         1 ==> like 0, but with Steele & White stopping rule;
1356             e.g. with IEEE P754 arithmetic , mode 0 gives
1357             1e23 whereas mode 1 gives 9.999999999999999e22.
1358         2 ==> max(1,ndigits) significant digits.  This gives a
1359             return value similar to that of ecvt, except
1360             that trailing zeros are suppressed.
1361         3 ==> through ndigits past the decimal point.  This
1362             gives a return value similar to that from fcvt,
1363             except that trailing zeros are suppressed, and
1364             ndigits can be negative.
1365         4-9 should give the same return values as 2-3, i.e.,
1366             4 <= mode <= 9 ==> same return as mode
1367             2 + (mode & 1).  These modes are mainly for
1368             debugging; often they run slower but sometimes
1369             faster than modes 2-3.
1370         4,5,8,9 ==> left-to-right digit generation.
1371         6-9 ==> don't try fast floating-point estimate
1372             (if applicable).
1373
1374         Values of mode other than 0-9 are treated as mode 0.
1375
1376         Sufficient space is allocated to the return value
1377         to hold the suppressed trailing zeros.
1378     */
1379
1380   int bbits, b2, b5, be, dig, i, ieps, ilim = 0, ilim0, ilim1 = 0,
1381     j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
1382     spec_case = 0, try_quick;
1383   Long L;
1384 #ifndef Sudden_Underflow
1385   int denorm;
1386   ULong x;
1387 #endif
1388   Bigint *b, *b1, *delta, *mlo = 0, *mhi, *S, *tmp;
1389   double ds;
1390   char *s, *s0;
1391   _double d, d2, eps;
1392
1393   value(d) = _d;
1394
1395   if (word0(d) & Sign_bit) {
1396     /* set sign for everything, including 0's and NaNs */
1397     *sign = 1;
1398     word0(d) &= ~Sign_bit;  /* clear sign bit */
1399   }
1400   else
1401     *sign = 0;
1402
1403 #if defined(IEEE_Arith) + defined(VAX)
1404 #ifdef IEEE_Arith
1405   if ((word0(d) & Exp_mask) == Exp_mask)
1406 #else
1407     if (word0(d)  == 0x8000)
1408 #endif
1409     {
1410       /* Infinity or NaN */
1411       *decpt = 9999;
1412 #ifdef IEEE_Arith
1413       if (!word1(d) && !(word0(d) & 0xfffff))
1414         return nrv_alloc("Infinity", rve, 8);
1415 #endif
1416       return nrv_alloc("NaN", rve, 3);
1417     }
1418 #endif
1419 #ifdef IBM
1420   value(d) += 0; /* normalize */
1421 #endif
1422   if (!value(d)) {
1423     *decpt = 1;
1424     return nrv_alloc("0", rve, 1);
1425   }
1426
1427   b = d2b(value(d), &be, &bbits);
1428 #ifdef Sudden_Underflow
1429   i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
1430 #else
1431   if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) {
1432 #endif
1433     value(d2) = value(d);
1434     word0(d2) &= Frac_mask1;
1435     word0(d2) |= Exp_11;
1436 #ifdef IBM
1437     if (j = 11 - hi0bits(word0(d2) & Frac_mask))
1438       value(d2) /= 1 << j;
1439 #endif
1440
1441     /* log(x)   ~=~ log(1.5) + (x-1.5)/1.5
1442      * log10(x)  =  log(x) / log(10)
1443      *      ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
1444      * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
1445      *
1446      * This suggests computing an approximation k to log10(d) by
1447      *
1448      * k = (i - Bias)*0.301029995663981
1449      *  + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
1450      *
1451      * We want k to be too large rather than too small.
1452      * The error in the first-order Taylor series approximation
1453      * is in our favor, so we just round up the constant enough
1454      * to compensate for any error in the multiplication of
1455      * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
1456      * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
1457      * adding 1e-13 to the constant term more than suffices.
1458      * Hence we adjust the constant term to 0.1760912590558.
1459      * (We could get a more accurate k by invoking log10,
1460      *  but this is probably not worthwhile.)
1461      */
1462
1463     i -= Bias;
1464 #ifdef IBM
1465     i <<= 2;
1466     i += j;
1467 #endif
1468 #ifndef Sudden_Underflow
1469     denorm = 0;
1470   }
1471   else {
1472     /* d is denormalized */
1473
1474     i = bbits + be + (Bias + (P-1) - 1);
1475     x = i > 32  ? (word0(d) << (64 - i)) | (word1(d) >> (i - 32))
1476       : (word1(d) << (32 - i));
1477     value(d2) = x;
1478     word0(d2) -= 31*Exp_msk1; /* adjust exponent */
1479     i -= (Bias + (P-1) - 1) + 1;
1480     denorm = 1;
1481   }
1482 #endif
1483   ds = (value(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
1484   k = (int)ds;
1485   if (ds < 0. && ds != k)
1486     k--;    /* want k = floor(ds) */
1487   k_check = 1;
1488   if (k >= 0 && k <= Ten_pmax) {
1489     if (value(d) < tens[k])
1490       k--;
1491     k_check = 0;
1492   }
1493   j = bbits - i - 1;
1494   if (j >= 0) {
1495     b2 = 0;
1496     s2 = j;
1497   }
1498   else {
1499     b2 = -j;
1500     s2 = 0;
1501   }
1502   if (k >= 0) {
1503     b5 = 0;
1504     s5 = k;
1505     s2 += k;
1506   }
1507   else {
1508     b2 -= k;
1509     b5 = -k;
1510     s5 = 0;
1511   }
1512   if (mode < 0 || mode > 9)
1513     mode = 0;
1514   try_quick = 1;
1515   if (mode > 5) {
1516     mode -= 4;
1517     try_quick = 0;
1518   }
1519   leftright = 1;
1520   switch(mode) {
1521     case 0:
1522     case 1:
1523       ilim = ilim1 = -1;
1524       i = 18;
1525       ndigits = 0;
1526       break;
1527     case 2:
1528       leftright = 0;
1529       /* no break */
1530     case 4:
1531       if (ndigits <= 0)
1532         ndigits = 1;
1533       ilim = ilim1 = i = ndigits;
1534       break;
1535     case 3:
1536       leftright = 0;
1537       /* no break */
1538     case 5:
1539       i = ndigits + k + 1;
1540       ilim = i;
1541       ilim1 = i - 1;
1542       if (i <= 0)
1543         i = 1;
1544   }
1545   s = s0 = rv_alloc(i);
1546
1547   if (ilim >= 0 && ilim <= Quick_max && try_quick) {
1548
1549     /* Try to get by with floating-point arithmetic. */
1550
1551     i = 0;
1552     value(d2) = value(d);
1553     k0 = k;
1554     ilim0 = ilim;
1555     ieps = 2; /* conservative */
1556     if (k > 0) {
1557       ds = tens[k&0xf];
1558       j = k >> 4;
1559       if (j & Bletch) {
1560         /* prevent overflows */
1561         j &= Bletch - 1;
1562         value(d) /= bigtens[n_bigtens-1];
1563         ieps++;
1564       }
1565       for(; j; j >>= 1, i++)
1566         if (j & 1) {
1567           ieps++;
1568           ds *= bigtens[i];
1569         }
1570       value(d) /= ds;
1571     }
1572     else if ((j1 = -k)) {
1573       value(d) *= tens[j1 & 0xf];
1574       for(j = j1 >> 4; j; j >>= 1, i++)
1575         if (j & 1) {
1576           ieps++;
1577           value(d) *= bigtens[i];
1578         }
1579     }
1580     if (k_check && value(d) < 1. && ilim > 0) {
1581       if (ilim1 <= 0)
1582         goto fast_failed;
1583       ilim = ilim1;
1584       k--;
1585       value(d) *= 10.;
1586       ieps++;
1587     }
1588     value(eps) = ieps*value(d) + 7.;
1589     word0(eps) -= (P-1)*Exp_msk1;
1590     if (ilim == 0) {
1591       S = mhi = 0;
1592       value(d) -= 5.;
1593       if (value(d) > value(eps))
1594         goto one_digit;
1595       if (value(d) < -value(eps))
1596         goto no_digits;
1597       goto fast_failed;
1598     }
1599 #ifndef No_leftright
1600     if (leftright) {
1601       /* Use Steele & White method of only
1602        * generating digits needed.
1603        */
1604       value(eps) = 0.5/tens[ilim-1] - value(eps);
1605       for(i = 0;;) {
1606         L = (int32_t)value(d);
1607         value(d) -= L;
1608         *s++ = '0' + (int)L;
1609         if (value(d) < value(eps))
1610           goto ret1;
1611         if (1. - value(d) < value(eps))
1612           goto bump_up;
1613         if (++i >= ilim)
1614           break;
1615         value(eps) *= 10.;
1616         value(d) *= 10.;
1617       }
1618     }
1619     else {
1620 #endif
1621       /* Generate ilim digits, then fix them up. */
1622       value(eps) *= tens[ilim-1];
1623       for(i = 1;; i++, value(d) *= 10.) {
1624         L = (int32_t)value(d);
1625         value(d) -= L;
1626         *s++ = '0' + (int)L;
1627         if (i == ilim) {
1628           if (value(d) > 0.5 + value(eps))
1629             goto bump_up;
1630           else if (value(d) < 0.5 - value(eps)) {
1631             /* cut ALL traling zeros only if the number of chars is greater than precision
1632              * otherwise cut only extra zeros
1633              */
1634             if (k < ndigits) {
1635               while(*--s == '0' && (s - s0) > k);
1636             } else {
1637               while(*--s == '0');
1638             }
1639             s++;
1640             goto ret1;
1641           }
1642           break;
1643         }
1644       }
1645 #ifndef No_leftright
1646     }
1647 #endif
1648 fast_failed:
1649     s = s0;
1650     value(d) = value(d2);
1651     k = k0;
1652     ilim = ilim0;
1653   }
1654
1655   /* Do we have a "small" integer? */
1656
1657   if (be >= 0 && k <= Int_max) {
1658     /* Yes. */
1659     ds = tens[k];
1660     if (ndigits < 0 && ilim <= 0) {
1661       S = mhi = 0;
1662       if (ilim < 0 || value(d) <= 5*ds)
1663         goto no_digits;
1664       goto one_digit;
1665     }
1666     for(i = 1;; i++) {
1667       L = (int32_t)(value(d) / ds);
1668       value(d) -= L*ds;
1669 #ifdef Check_FLT_ROUNDS
1670       /* If FLT_ROUNDS == 2, L will usually be high by 1 */
1671       if (value(d) < 0) {
1672         L--;
1673         value(d) += ds;
1674       }
1675 #endif
1676       *s++ = '0' + (int)L;
1677       if (i == ilim) {
1678         value(d) += value(d);
1679         if (value(d) > ds || (value(d) == ds && (L & 1))) {
1680 bump_up:
1681           while(*--s == '9')
1682             if (s == s0) {
1683               k++;
1684               *s = '0';
1685               break;
1686             }
1687           ++*s++;
1688         }
1689         break;
1690       }
1691       if (!(value(d) *= 10.))
1692         break;
1693     }
1694     goto ret1;
1695   }
1696
1697   m2 = b2;
1698   m5 = b5;
1699   mhi = mlo = 0;
1700   if (leftright) {
1701     if (mode < 2) {
1702       i =
1703 #ifndef Sudden_Underflow
1704         denorm ? be + (Bias + (P-1) - 1 + 1) :
1705 #endif
1706 #ifdef IBM
1707         1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
1708 #else
1709       1 + P - bbits;
1710 #endif
1711     }
1712     else {
1713       j = ilim - 1;
1714       if (m5 >= j)
1715         m5 -= j;
1716       else {
1717         s5 += j -= m5;
1718         b5 += j;
1719         m5 = 0;
1720       }
1721       if ((i = ilim) < 0) {
1722         m2 -= i;
1723         i = 0;
1724       }
1725     }
1726     b2 += i;
1727     s2 += i;
1728     mhi = i2b(1);
1729   }
1730   if (m2 > 0 && s2 > 0) {
1731     i = m2 < s2 ? m2 : s2;
1732     b2 -= i;
1733     m2 -= i;
1734     s2 -= i;
1735   }
1736   if (b5 > 0) {
1737     if (leftright) {
1738       if (m5 > 0) {
1739         mhi = pow5mult(mhi, m5);
1740         b1 = mult(mhi, b);
1741         Bfree(b);
1742         b = b1;
1743       }
1744       if ((j = b5 - m5)) {
1745         b = pow5mult(b, j);
1746       }
1747     } else {
1748       b = pow5mult(b, b5);
1749     }
1750   }
1751   S = i2b(1);
1752   if (s5 > 0)
1753     S = pow5mult(S, s5);
1754   /* Check for special case that d is a normalized power of 2. */
1755
1756   if (mode < 2) {
1757     if (!word1(d) && !(word0(d) & Bndry_mask)
1758 #ifndef Sudden_Underflow
1759         && word0(d) & Exp_mask
1760 #endif
1761        ) {
1762       /* The special case */
1763       b2 += Log2P;
1764       s2 += Log2P;
1765       spec_case = 1;
1766     } else {
1767       spec_case = 0;
1768     }
1769   }
1770
1771   /* Arrange for convenient computation of quotients:
1772    * shift left if necessary so divisor has 4 leading 0 bits.
1773    *
1774    * Perhaps we should just compute leading 28 bits of S once
1775    * and for all and pass them and a shift to quorem, so it
1776    * can do shifts and ors to compute the numerator for q.
1777    */
1778 #ifdef Pack_32
1779   if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f))
1780     i = 32 - i;
1781 #else
1782   if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf))
1783     i = 16 - i;
1784 #endif
1785   if (i > 4) {
1786     i -= 4;
1787     b2 += i;
1788     m2 += i;
1789     s2 += i;
1790   }
1791   else if (i < 4) {
1792     i += 28;
1793     b2 += i;
1794     m2 += i;
1795     s2 += i;
1796   }
1797   if (b2 > 0)
1798     b = lshift(b, b2);
1799   if (s2 > 0)
1800     S = lshift(S, s2);
1801   if (k_check) {
1802     if (cmp(b,S) < 0) {
1803       k--;
1804       b = multadd(b, 10, 0);  /* we botched the k estimate */
1805       if (leftright)
1806         mhi = multadd(mhi, 10, 0);
1807       ilim = ilim1;
1808     }
1809   }
1810   if (ilim <= 0 && mode > 2) {
1811     if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
1812       /* no digits, fcvt style */
1813 no_digits:
1814       k = -1 - ndigits;
1815       goto ret;
1816     }
1817 one_digit:
1818     *s++ = '1';
1819     k++;
1820     goto ret;
1821   }
1822   if (leftright) {
1823     if (m2 > 0)
1824       mhi = lshift(mhi, m2);
1825
1826     /* Compute mlo -- check for special case
1827      * that d is a normalized power of 2.
1828      */
1829
1830     mlo = mhi;
1831     if (spec_case) {
1832       mhi = Balloc(mhi->k);
1833       Bcopy(mhi, mlo);
1834       mhi = lshift(mhi, Log2P);
1835     }
1836
1837     for(i = 1;;i++) {
1838       dig = quorem(b,S) + '0';
1839       /* Do we yet have the shortest decimal string
1840        * that will round to d?
1841        */
1842       j = cmp(b, mlo);
1843       delta = diff(S, mhi);
1844       j1 = delta->sign ? 1 : cmp(b, delta);
1845       Bfree(delta);
1846 #ifndef ROUND_BIASED
1847       if (j1 == 0 && !mode && !(word1(d) & 1)) {
1848         if (dig == '9')
1849           goto round_9_up;
1850         if (j > 0)
1851           dig++;
1852         *s++ = dig;
1853         goto ret;
1854       }
1855 #endif
1856       if (j < 0 || (j == 0 && !mode
1857 #ifndef ROUND_BIASED
1858             && !(word1(d) & 1)
1859 #endif
1860             )) {
1861         if (j1 > 0) {
1862           b = lshift(b, 1);
1863           j1 = cmp(b, S);
1864           if ((j1 > 0 || (j1 == 0 && (dig & 1)))
1865               && dig++ == '9')
1866             goto round_9_up;
1867         }
1868         *s++ = dig;
1869         goto ret;
1870       }
1871       if (j1 > 0) {
1872         if (dig == '9') { /* possible if i == 1 */
1873 round_9_up:
1874           *s++ = '9';
1875           goto roundoff;
1876         }
1877         *s++ = dig + 1;
1878         goto ret;
1879       }
1880       *s++ = dig;
1881       if (i == ilim)
1882         break;
1883       b = multadd(b, 10, 0);
1884       if (mlo == mhi)
1885         mlo = mhi = multadd(mhi, 10, 0);
1886       else {
1887         mlo = multadd(mlo, 10, 0);
1888         mhi = multadd(mhi, 10, 0);
1889       }
1890     }
1891   }
1892   else
1893     for(i = 1;; i++) {
1894       *s++ = dig = quorem(b,S) + '0';
1895       if (i >= ilim)
1896         break;
1897       b = multadd(b, 10, 0);
1898     }
1899
1900   /* Round off last digit */
1901
1902   b = lshift(b, 1);
1903   j = cmp(b, S);
1904   if (j > 0 || (j == 0 && (dig & 1))) {
1905 roundoff:
1906     while(*--s == '9')
1907       if (s == s0) {
1908         k++;
1909         *s++ = '1';
1910         goto ret;
1911       }
1912     ++*s++;
1913   }
1914   else {
1915     while(*--s == '0');
1916     s++;
1917   }
1918 ret:
1919   Bfree(S);
1920   if (mhi) {
1921     if (mlo && mlo != mhi)
1922       Bfree(mlo);
1923     Bfree(mhi);
1924   }
1925 ret1:
1926
1927   {
1928     Bigint *&p5s = s_bigint_data->p5s;
1929     while (p5s) {
1930       tmp = p5s;
1931       p5s = p5s->next;
1932       free(tmp);
1933     }
1934   }
1935
1936   Bfree(b);
1937
1938   if (s == s0) {              /* don't return empty string */
1939     *s++ = '0';
1940     k = 0;
1941   }
1942   *s = 0;
1943   *decpt = k + 1;
1944   if (rve)
1945     *rve = s;
1946   return s0;
1947 }
1948
1949 double zend_strtod (CONST char *s00, const char **se)
1950 {
1951   int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
1952     e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
1953   CONST char *s, *s0, *s1;
1954   double aadj, aadj1, adj;
1955   _double rv, rv0;
1956   ULong L;
1957   ULong y, z;
1958   Bigint *bb = 0, *bb1, *bd = 0, *bd0, *bs = 0, *delta = 0, *tmp;
1959   double result;
1960
1961   CONST char decimal_point = '.';
1962
1963   sign = nz0 = nz = 0;
1964   value(rv) = 0.;
1965
1966
1967   for(s = s00; isspace((unsigned char) *s); s++)
1968     ;
1969
1970   if (*s == '-') {
1971     sign = 1;
1972     s++;
1973   } else if (*s == '+') {
1974     s++;
1975   }
1976
1977   if (*s == '\0') {
1978     s = s00;
1979     goto ret;
1980   }
1981
1982   if (*s == '0') {
1983     nz0 = 1;
1984     while(*++s == '0') ;
1985     if (!*s)
1986       goto ret;
1987   }
1988   s0 = s;
1989   y = z = 0;
1990   for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
1991     if (nd < 9)
1992       y = 10*y + c - '0';
1993     else if (nd < 16)
1994       z = 10*z + c - '0';
1995   nd0 = nd;
1996   if (c == decimal_point) {
1997     c = *++s;
1998     if (!nd) {
1999       for(; c == '0'; c = *++s)
2000         nz++;
2001       if (c > '0' && c <= '9') {
2002         s0 = s;
2003         nf += nz;
2004         nz = 0;
2005         goto have_dig;
2006       }
2007       goto dig_done;
2008     }
2009     for(; c >= '0' && c <= '9'; c = *++s) {
2010 have_dig:
2011       nz++;
2012       if (c -= '0') {
2013         nf += nz;
2014         for(i = 1; i < nz; i++)
2015           if (nd++ < 9)
2016             y *= 10;
2017           else if (nd <= DBL_DIG + 1)
2018             z *= 10;
2019         if (nd++ < 9)
2020           y = 10*y + c;
2021         else if (nd <= DBL_DIG + 1)
2022           z = 10*z + c;
2023         nz = 0;
2024       }
2025     }
2026   }
2027 dig_done:
2028   e = 0;
2029   if (c == 'e' || c == 'E') {
2030     if (!nd && !nz && !nz0) {
2031       s = s00;
2032       goto ret;
2033     }
2034     s00 = s;
2035     esign = 0;
2036     switch(c = *++s) {
2037       case '-':
2038         esign = 1;
2039       case '+':
2040         c = *++s;
2041     }
2042     if (c >= '0' && c <= '9') {
2043       while(c == '0')
2044         c = *++s;
2045       if (c > '0' && c <= '9') {
2046         L = c - '0';
2047         s1 = s;
2048         while((c = *++s) >= '0' && c <= '9')
2049           L = 10*L + c - '0';
2050         if (s - s1 > 8 || L > 19999)
2051           /* Avoid confusion from exponents
2052            * so large that e might overflow.
2053            */
2054           e = 19999; /* safe for 16 bit ints */
2055         else
2056           e = (int)L;
2057         if (esign)
2058           e = -e;
2059       }
2060       else
2061         e = 0;
2062     }
2063     else
2064       s = s00;
2065   }
2066   if (!nd) {
2067     if (!nz && !nz0)
2068       s = s00;
2069     goto ret;
2070   }
2071   e1 = e -= nf;
2072
2073   /* Now we have nd0 digits, starting at s0, followed by a
2074    * decimal point, followed by nd-nd0 digits.  The number we're
2075    * after is the integer represented by those digits times
2076    * 10**e */
2077
2078   if (!nd0)
2079     nd0 = nd;
2080   k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
2081   value(rv) = y;
2082   if (k > 9)
2083     value(rv) = tens[k - 9] * value(rv) + z;
2084   bd0 = 0;
2085   if (nd <= DBL_DIG
2086 #ifndef RND_PRODQUOT
2087       && FLT_ROUNDS == 1
2088 #endif
2089      ) {
2090     if (!e)
2091       goto ret;
2092     if (e > 0) {
2093       if (e <= Ten_pmax) {
2094 #ifdef VAX
2095         goto vax_ovfl_check;
2096 #else
2097         /* value(rv) = */ rounded_product(value(rv),
2098             tens[e]);
2099         goto ret;
2100 #endif
2101       }
2102       i = DBL_DIG - nd;
2103       if (e <= Ten_pmax + i) {
2104         /* A fancier test would sometimes let us do
2105          * this for larger i values.
2106          */
2107         e -= i;
2108         value(rv) *= tens[i];
2109 #ifdef VAX
2110         /* VAX exponent range is so narrow we must
2111          * worry about overflow here...
2112          */
2113 vax_ovfl_check:
2114         word0(rv) -= P*Exp_msk1;
2115         /* value(rv) = */ rounded_product(value(rv),
2116             tens[e]);
2117         if ((word0(rv) & Exp_mask)
2118             > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
2119           goto ovfl;
2120         word0(rv) += P*Exp_msk1;
2121 #else
2122         /* value(rv) = */ rounded_product(value(rv),
2123             tens[e]);
2124 #endif
2125         goto ret;
2126       }
2127     }
2128 #ifndef Inaccurate_Divide
2129     else if (e >= -Ten_pmax) {
2130       /* value(rv) = */ rounded_quotient(value(rv),
2131           tens[-e]);
2132       goto ret;
2133     }
2134 #endif
2135   }
2136   e1 += nd - k;
2137
2138   /* Get starting approximation = rv * 10**e1 */
2139
2140   if (e1 > 0) {
2141     if ((i = e1 & 15))
2142       value(rv) *= tens[i];
2143     if (e1 &= ~15) {
2144       if (e1 > DBL_MAX_10_EXP) {
2145 ovfl:
2146         errno = ERANGE;
2147 #ifndef Bad_float_h
2148         value(rv) = HUGE_VAL;
2149 #else
2150         /* Can't trust HUGE_VAL */
2151 #ifdef IEEE_Arith
2152         word0(rv) = Exp_mask;
2153         word1(rv) = 0;
2154 #else
2155         word0(rv) = Big0;
2156         word1(rv) = Big1;
2157 #endif
2158 #endif
2159         if (bd0)
2160           goto retfree;
2161         goto ret;
2162       }
2163       if (e1 >>= 4) {
2164         for(j = 0; e1 > 1; j++, e1 >>= 1)
2165           if (e1 & 1)
2166             value(rv) *= bigtens[j];
2167         /* The last multiplication could overflow. */
2168         word0(rv) -= P*Exp_msk1;
2169         value(rv) *= bigtens[j];
2170         if ((z = word0(rv) & Exp_mask)
2171             > Exp_msk1*(DBL_MAX_EXP+Bias-P))
2172           goto ovfl;
2173         if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
2174           /* set to largest number */
2175           /* (Can't trust DBL_MAX) */
2176           word0(rv) = Big0;
2177           word1(rv) = Big1;
2178         }
2179         else
2180           word0(rv) += P*Exp_msk1;
2181       }
2182
2183     }
2184   }
2185   else if (e1 < 0) {
2186     e1 = -e1;
2187     if ((i = e1 & 15))
2188       value(rv) /= tens[i];
2189     if (e1 &= ~15) {
2190       e1 >>= 4;
2191       if (e1 >= 1 << n_bigtens)
2192         goto undfl;
2193       for(j = 0; e1 > 1; j++, e1 >>= 1)
2194         if (e1 & 1)
2195           value(rv) *= tinytens[j];
2196       /* The last multiplication could underflow. */
2197       value(rv0) = value(rv);
2198       value(rv) *= tinytens[j];
2199       if (!value(rv)) {
2200         value(rv) = 2.*value(rv0);
2201         value(rv) *= tinytens[j];
2202         if (!value(rv)) {
2203 undfl:
2204           value(rv) = 0.;
2205           errno = ERANGE;
2206           if (bd0)
2207             goto retfree;
2208           goto ret;
2209         }
2210         word0(rv) = Tiny0;
2211         word1(rv) = Tiny1;
2212         /* The refinement below will clean
2213          * this approximation up.
2214          */
2215       }
2216     }
2217   }
2218
2219   /* Now the hard part -- adjusting rv to the correct value.*/
2220
2221   /* Put digits into bd: true value = bd * 10^e */
2222
2223   bd0 = s2b(s0, nd0, nd, y);
2224
2225   for(;;) {
2226     bd = Balloc(bd0->k);
2227     Bcopy(bd, bd0);
2228     bb = d2b(value(rv), &bbe, &bbbits);  /* rv = bb * 2^bbe */
2229     bs = i2b(1);
2230
2231     if (e >= 0) {
2232       bb2 = bb5 = 0;
2233       bd2 = bd5 = e;
2234     }
2235     else {
2236       bb2 = bb5 = -e;
2237       bd2 = bd5 = 0;
2238     }
2239     if (bbe >= 0)
2240       bb2 += bbe;
2241     else
2242       bd2 -= bbe;
2243     bs2 = bb2;
2244 #ifdef Sudden_Underflow
2245 #ifdef IBM
2246     j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
2247 #else
2248     j = P + 1 - bbbits;
2249 #endif
2250 #else
2251     i = bbe + bbbits - 1;  /* logb(rv) */
2252     if (i < Emin)  /* denormal */
2253       j = bbe + (P-Emin);
2254     else
2255       j = P + 1 - bbbits;
2256 #endif
2257     bb2 += j;
2258     bd2 += j;
2259     i = bb2 < bd2 ? bb2 : bd2;
2260     if (i > bs2)
2261       i = bs2;
2262     if (i > 0) {
2263       bb2 -= i;
2264       bd2 -= i;
2265       bs2 -= i;
2266     }
2267     if (bb5 > 0) {
2268       bs = pow5mult(bs, bb5);
2269       bb1 = mult(bs, bb);
2270       Bfree(bb);
2271       bb = bb1;
2272     }
2273     if (bb2 > 0)
2274       bb = lshift(bb, bb2);
2275     if (bd5 > 0)
2276       bd = pow5mult(bd, bd5);
2277     if (bd2 > 0)
2278       bd = lshift(bd, bd2);
2279     if (bs2 > 0)
2280       bs = lshift(bs, bs2);
2281     delta = diff(bb, bd);
2282     dsign = delta->sign;
2283     delta->sign = 0;
2284     i = cmp(delta, bs);
2285     if (i < 0) {
2286       /* Error is less than half an ulp -- check for
2287        * special case of mantissa a power of two.
2288        */
2289       if (dsign || word1(rv) || word0(rv) & Bndry_mask)
2290         break;
2291       delta = lshift(delta,Log2P);
2292       if (cmp(delta, bs) > 0)
2293         goto drop_down;
2294       break;
2295     }
2296     if (i == 0) {
2297       /* exactly half-way between */
2298       if (dsign) {
2299         if ((word0(rv) & Bndry_mask1) == Bndry_mask1
2300             &&  word1(rv) == 0xffffffff) {
2301           /*boundary case -- increment exponent*/
2302           word0(rv) = (word0(rv) & Exp_mask)
2303             + Exp_msk1
2304 #ifdef IBM
2305             | Exp_msk1 >> 4
2306 #endif
2307             ;
2308           word1(rv) = 0;
2309           break;
2310         }
2311       }
2312       else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
2313 drop_down:
2314         /* boundary case -- decrement exponent */
2315 #ifdef Sudden_Underflow
2316         L = word0(rv) & Exp_mask;
2317 #ifdef IBM
2318         if (L <  Exp_msk1)
2319 #else
2320           if (L <= Exp_msk1)
2321 #endif
2322             goto undfl;
2323         L -= Exp_msk1;
2324 #else
2325         L = (word0(rv) & Exp_mask) - Exp_msk1;
2326 #endif
2327         word0(rv) = L | Bndry_mask1;
2328         word1(rv) = 0xffffffff;
2329 #ifdef IBM
2330         goto cont;
2331 #else
2332         break;
2333 #endif
2334       }
2335 #ifndef ROUND_BIASED
2336       if (!(word1(rv) & LSB))
2337         break;
2338 #endif
2339       if (dsign)
2340         value(rv) += ulp(value(rv));
2341 #ifndef ROUND_BIASED
2342       else {
2343         value(rv) -= ulp(value(rv));
2344 #ifndef Sudden_Underflow
2345         if (!value(rv))
2346           goto undfl;
2347 #endif
2348       }
2349 #endif
2350       break;
2351     }
2352     if ((aadj = ratio(delta, bs)) <= 2.) {
2353       if (dsign)
2354         aadj = aadj1 = 1.;
2355       else if (word1(rv) || word0(rv) & Bndry_mask) {
2356 #ifndef Sudden_Underflow
2357         if (word1(rv) == Tiny1 && !word0(rv))
2358           goto undfl;
2359 #endif
2360         aadj = 1.;
2361         aadj1 = -1.;
2362       }
2363       else {
2364         /* special case -- power of FLT_RADIX to be */
2365         /* rounded down... */
2366
2367         if (aadj < 2./FLT_RADIX)
2368           aadj = 1./FLT_RADIX;
2369         else
2370           aadj *= 0.5;
2371         aadj1 = -aadj;
2372       }
2373     }
2374     else {
2375       aadj *= 0.5;
2376       aadj1 = dsign ? aadj : -aadj;
2377 #ifdef Check_FLT_ROUNDS
2378       switch(FLT_ROUNDS) {
2379         case 2: /* towards +infinity */
2380           aadj1 -= 0.5;
2381           break;
2382         case 0: /* towards 0 */
2383         case 3: /* towards -infinity */
2384           aadj1 += 0.5;
2385       }
2386 #else
2387       if (FLT_ROUNDS == 0)
2388         aadj1 += 0.5;
2389 #endif
2390     }
2391     y = word0(rv) & Exp_mask;
2392
2393     /* Check for overflow */
2394
2395     if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
2396       value(rv0) = value(rv);
2397       word0(rv) -= P*Exp_msk1;
2398       adj = aadj1 * ulp(value(rv));
2399       value(rv) += adj;
2400       if ((word0(rv) & Exp_mask) >=
2401           Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
2402         if (word0(rv0) == Big0 && word1(rv0) == Big1)
2403           goto ovfl;
2404         word0(rv) = Big0;
2405         word1(rv) = Big1;
2406         goto cont;
2407       }
2408       else
2409         word0(rv) += P*Exp_msk1;
2410     }
2411     else {
2412 #ifdef Sudden_Underflow
2413       if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2414         value(rv0) = value(rv);
2415         word0(rv) += P*Exp_msk1;
2416         adj = aadj1 * ulp(value(rv));
2417         value(rv) += adj;
2418 #ifdef IBM
2419         if ((word0(rv) & Exp_mask) <  P*Exp_msk1)
2420 #else
2421           if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
2422 #endif
2423           {
2424             if (word0(rv0) == Tiny0
2425                 && word1(rv0) == Tiny1)
2426               goto undfl;
2427             word0(rv) = Tiny0;
2428             word1(rv) = Tiny1;
2429             goto cont;
2430           }
2431           else
2432             word0(rv) -= P*Exp_msk1;
2433       }
2434       else {
2435         adj = aadj1 * ulp(value(rv));
2436         value(rv) += adj;
2437       }
2438 #else
2439       /* Compute adj so that the IEEE rounding rules will
2440        * correctly round rv + adj in some half-way cases.
2441        * If rv * ulp(rv) is denormalized (i.e.,
2442        * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
2443        * trouble from bits lost to denormalization;
2444        * example: 1.2e-307 .
2445        */
2446       if (y <= (P-1)*Exp_msk1 && aadj >= 1.) {
2447         aadj1 = (double)(int)(aadj + 0.5);
2448         if (!dsign)
2449           aadj1 = -aadj1;
2450       }
2451       adj = aadj1 * ulp(value(rv));
2452       value(rv) += adj;
2453 #endif
2454     }
2455     z = word0(rv) & Exp_mask;
2456     if (y == z) {
2457       /* Can we stop now? */
2458       L = (int32_t)aadj;
2459       aadj -= L;
2460       /* The tolerances below are conservative. */
2461       if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
2462         if (aadj < .4999999 || aadj > .5000001)
2463           break;
2464       }
2465       else if (aadj < .4999999/FLT_RADIX)
2466         break;
2467     }
2468 cont:
2469     Bfree(bb);
2470     Bfree(bd);
2471     Bfree(bs);
2472     Bfree(delta);
2473   }
2474 retfree:
2475   Bfree(bb);
2476   Bfree(bd);
2477   Bfree(bs);
2478   Bfree(bd0);
2479   Bfree(delta);
2480 ret:
2481   if (se)
2482     *se = (char *)s;
2483   result = sign ? -value(rv) : value(rv);
2484
2485   if (s_bigint_data.isNull()) {
2486     return result;
2487   }
2488
2489   Bigint *&p5s = s_bigint_data->p5s;
2490   while (p5s) {
2491     tmp = p5s;
2492     p5s = p5s->next;
2493     free(tmp);
2494   }
2495
2496   return result;
2497 }
2498
2499 double zend_hex_strtod(const char *str, const char **endptr)
2500 {
2501   const char *s = str;
2502   char c;
2503   int any = 0;
2504   double value = 0;
2505
2506   if (*s == '0' && (s[1] == 'x' || s[1] == 'X')) {
2507     s += 2;
2508   }
2509
2510   while ((c = *s++)) {
2511     if (c >= '0' && c <= '9') {
2512       c -= '0';
2513     } else if (c >= 'A' && c <= 'F') {
2514       c -= 'A' - 10;
2515     } else if (c >= 'a' && c <= 'f') {
2516       c -= 'a' - 10;
2517     } else {
2518       break;
2519     }
2520
2521     any = 1;
2522     value = value * 16 + c;
2523   }
2524
2525   if (endptr != nullptr) {
2526     *endptr = (char *)(any ? s - 1 : str);
2527   }
2528
2529   return value;
2530 }
2531
2532 double zend_oct_strtod(const char *str, const char **endptr)
2533 {
2534   const char *s = str;
2535   char c;
2536   double value = 0;
2537   int any = 0;
2538
2539   /* skip leading zero */
2540   s++;
2541
2542   while ((c = *s++)) {
2543     if (c > '7') {
2544       /* break and return the current value if the number is not well-formed
2545        * that's what Linux strtol() does
2546        */
2547       break;
2548     }
2549     // Note parentheses: convert digit into integer before adding as a double
2550     // in order to avoid accumulating floating point inaccuracies
2551     value = value * 8 + (c - '0');
2552     any = 1;
2553   }
2554
2555   if (endptr != nullptr) {
2556     *endptr = (char *)(any ? s - 1 : str);
2557   }
2558
2559   return value;
2560 }
2561
2562 double zend_bin_strtod(const char *str, const char **endptr)
2563 {
2564   const char *s = str;
2565   char    c;
2566   double  value = 0;
2567   int     any = 0;
2568
2569   if (strlen(str) < 2) {
2570     *endptr = str;
2571     return 0.0;
2572   }
2573
2574   if ('0' == *s && ('b' == s[1] || 'B' == s[1])) {
2575     s += 2;
2576   }
2577
2578   while ((c = *s++)) {
2579     /*
2580      * Verify the validity of the current character as a base-2 digit.  In
2581      * the event that an invalid digit is found, halt the conversion and
2582      * return the portion which has been converted thus far.
2583      */
2584     if ('0' == c || '1' == c)
2585       // Note parentheses: convert digit into integer before adding as a double
2586       // in order to avoid accumulating floating point inaccuracies
2587       value = value * 2 + (c - '0');
2588     else
2589       break;
2590
2591     any = 1;
2592   }
2593
2594   /*
2595    * As with many strtoX implementations, should the subject sequence be
2596    * empty or not well-formed, no conversion is performed and the original
2597    * value of str is stored in *endptr, provided that endptr is not a null
2598    * pointer.
2599    */
2600   if (nullptr != endptr) {
2601     *endptr = (char *)(any ? s - 1 : str);
2602   }
2603
2604   return value;
2605 }
2606
2607 ///////////////////////////////////////////////////////////////////////////////
2608 }