src/system/libroot/posix/stdlib/strtod.c

   1 /* [zooey]:
   2  * This implementation is broken, as e.g. strtod("1.7E+064", ...) yields an
   3  * incorrect (inaccurate) result.
   4  * For libroot, we use the glibc version instead.
   5  * This file is still used in the kernel, however, since I didn't dare
   6  * introducing a glibc-based source into the kernel.
   7  * So, currently we have to live with the fact that strtod() in our kernel
   8  * gives somewhat inaccurate results.
   9  */
  10
  11 /*-
  12  * Copyright (c) 1993
  13  *      The Regents of the University of California.  All rights reserved.
  14  *
  15  * Redistribution and use in source and binary forms, with or without
  16  * modification, are permitted provided that the following conditions
  17  * are met:
  18  * 1. Redistributions of source code must retain the above copyright
  19  *    notice, this list of conditions and the following disclaimer.
  20  * 2. Redistributions in binary form must reproduce the above copyright
  21  *    notice, this list of conditions and the following disclaimer in the
  22  *    documentation and/or other materials provided with the distribution.
  23  * 3. All advertising materials mentioning features or use of this software
  24  *    must display the following acknowledgement:
  25  *      This product includes software developed by the University of
  26  *      California, Berkeley and its contributors.
  27  * 4. Neither the name of the University nor the names of its contributors
  28  *    may be used to endorse or promote products derived from this software
  29  *    without specific prior written permission.
  30  *
  31  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
  32  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  33  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  34  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
  35  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  36  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  37  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  38  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  39  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  40  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  41  * SUCH DAMAGE.
  42  */
  43
  44
  45 /****************************************************************
  46  *
  47  * The author of this software is David M. Gay.
  48  *
  49  * Copyright (c) 1991 by AT&T.
  50  *
  51  * Permission to use, copy, modify, and distribute this software for any
  52  * purpose without fee is hereby granted, provided that this entire notice
  53  * is included in all copies of any software which is or includes a copy
  54  * or modification of this software and in all copies of the supporting
  55  * documentation for such software.
  56  *
  57  * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
  58  * WARRANTY.  IN PARTICULAR, NEITHER THE AUTHOR NOR AT&T MAKES ANY
  59  * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
  60  * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
  61  *
  62  ***************************************************************/
  63
  64 /* Please send bug reports to
  65         David M. Gay
  66         AT&T Bell Laboratories, Room 2C-463
  67         600 Mountain Avenue
  68         Murray Hill, NJ 07974-2070
  69         U.S.A.
  70         dmg@research.att.com or research!dmg
  71  */
  72
  73 /* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
  74  *
  75  * This strtod returns a nearest machine number to the input decimal
  76  * string (or sets errno to ERANGE).  With IEEE arithmetic, ties are
  77  * broken by the IEEE round-even rule.  Otherwise ties are broken by
  78  * biased rounding (add half and chop).
  79  *
  80  * Inspired loosely by William D. Clinger's paper "How to Read Floating
  81  * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
  82  *
  83  * Modifications:
  84  *
  85  *      1. We only require IEEE, IBM, or VAX double-precision
  86  *              arithmetic (not IEEE double-extended).
  87  *      2. We get by with floating-point arithmetic in a case that
  88  *              Clinger missed -- when we're computing d * 10^n
  89  *              for a small integer d and the integer n is not too
  90  *              much larger than 22 (the maximum integer k for which
  91  *              we can represent 10^k exactly), we may be able to
  92  *              compute (d*10^k) * 10^(e-k) with just one roundoff.
  93  *      3. Rather than a bit-at-a-time adjustment of the binary
  94  *              result in the hard case, we use floating-point
  95  *              arithmetic to determine the adjustment to within
  96  *              one bit; only in really hard cases do we need to
  97  *              compute a second residual.
  98  *      4. Because of 3., we don't need a large table of powers of 10
  99  *              for ten-to-e (just some small tables, e.g. of 10^k
 100  *              for 0 <= k <= 22).
 101  */
 102
 103 /*
 104  * #define Sudden_Underflow for IEEE-format machines without gradual
 105  *      underflow (i.e., that flush to zero on underflow).
 106  * #define IBM for IBM mainframe-style floating-point arithmetic.
 107  * #define VAX for VAX-style floating-point arithmetic.
 108  * #define Unsigned_Shifts if >> does treats its left operand as unsigned.
 109  * #define No_leftright to omit left-right logic in fast floating-point
 110  *      computation of dtoa.
 111  * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3.
 112  * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
 113  *      that use extended-precision instructions to compute rounded
 114  *      products and quotients) with IBM.
 115  * #define ROUND_BIASED for IEEE-format with biased rounding.
 116  * #define Inaccurate_Divide for IEEE-format with correctly rounded
 117  *      products but inaccurate quotients, e.g., for Intel i860.
 118  * #define Just_16 to store 16 bits per 32-bit Long when doing high-precision
 119  *      integer arithmetic.  Whether this speeds things up or slows things
 120  *      down depends on the machine and the number being converted.
 121  * #define Bad_float_h if your system lacks a float.h or if it does not
 122  *      define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
 123  *      FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
 124  */
 125
 126 #if defined(__i386__) || defined(__ia64__) || defined(__alpha__) || \
 127     defined(__sparc64__) || defined(__powerpc__) || defined(__POWERPC__) || \
 128     defined(__m68k__) || defined(__M68K__) || defined(__arm__) || \
 129     defined(__ARM__) || defined(__mipsel__) || defined(__MIPSEL__) || \
 130     defined(__x86_64__)
 131 #       include <sys/types.h>
 132 #       if BYTE_ORDER == BIG_ENDIAN
 133 #               define IEEE_BIG_ENDIAN
 134 #       else
 135 #               define IEEE_LITTLE_ENDIAN
 136 #       endif
 137 #endif /* defined(__i386__) ... */
 138
 139 #include <inttypes.h>
 140
 141 typedef int32_t   Long;
 142 typedef u_int32_t ULong;
 143
 144 #ifdef DEBUG
 145 #       if      _KERNEL_MODE
 146 #               include <KernelExport.h>
 147 #               define Bug(x) {dprintf("%s\n", x);}
 148 #       else
 149 #               include <stdio.h>
 150 #               define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
 151 #       endif
 152 #endif
 153
 154 #include <locale.h>
 155 #include <stdlib.h>
 156 #include <string.h>
 157
 158 #include <errno.h>
 159 #include <ctype.h>
 160
 161 #include <errno_private.h>
 162
 163 #ifdef Bad_float_h
 164 #undef __STDC__
 165 #ifdef IEEE_BIG_ENDIAN
 166 #       define IEEE_ARITHMETIC
 167 #endif
 168 #ifdef IEEE_LITTLE_ENDIAN
 169 #       define IEEE_ARITHMETIC
 170 #endif
 171 #ifdef IEEE_ARITHMETIC
 172 #       define DBL_DIG 15
 173 #       define DBL_MAX_10_EXP 308
 174 #       define DBL_MAX_EXP 1024
 175 #       define FLT_RADIX 2
 176 #       define FLT_ROUNDS 1
 177 #       define DBL_MAX 1.7976931348623157e+308
 178 #endif
 179
 180 #ifdef IBM
 181 #       define DBL_DIG 16
 182 #       define DBL_MAX_10_EXP 75
 183 #       define DBL_MAX_EXP 63
 184 #       define FLT_RADIX 16
 185 #       define FLT_ROUNDS 0
 186 #       define DBL_MAX 7.2370055773322621e+75
 187 #endif
 188
 189 #ifdef VAX
 190 #       define DBL_DIG 16
 191 #       define DBL_MAX_10_EXP 38
 192 #       define DBL_MAX_EXP 127
 193 #       define FLT_RADIX 2
 194 #       define FLT_ROUNDS 1
 195 #       define DBL_MAX 1.7014118346046923e+38
 196 #endif
 197
 198 #ifndef LONG_MAX
 199 #       define LONG_MAX 2147483647
 200 #endif
 201 #else
 202 #       include "float.h"
 203 #endif
 204 #ifndef __MATH_H__
 205 #       include "math.h"
 206 #endif
 207
 208 #ifdef __cplusplus
 209 extern "C" {
 210 #endif
 211
 212 #ifdef Unsigned_Shifts
 213 #       define Sign_Extend(a,b) if (b < 0) a |= 0xffff0000;
 214 #else
 215 #       define Sign_Extend(a,b) /*no-op*/
 216 #endif
 217
 218 #if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) + defined(VAX) + \
 219     defined(IBM) != 1
 220 #error Only one of IEEE_LITTLE_ENDIAN, IEEE_BIG_ENDIAN, VAX, or IBM should be defined.
 221 #endif
 222
 223 union doubleasulongs {
 224         double x;
 225         ULong w[2];
 226 };
 227
 228 #ifdef IEEE_LITTLE_ENDIAN
 229 #       define word0(x) (((union doubleasulongs *)&x)->w)[1]
 230 #       define word1(x) (((union doubleasulongs *)&x)->w)[0]
 231 #else
 232 #       define word0(x) (((union doubleasulongs *)&x)->w)[0]
 233 #       define word1(x) (((union doubleasulongs *)&x)->w)[1]
 234 #endif
 235
 236 /* The following definition of Storeinc is appropriate for MIPS processors.
 237  * An alternative that might be better on some machines is
 238  * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
 239  */
 240 #if defined(IEEE_LITTLE_ENDIAN) + defined(VAX)
 241 #       define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
 242                 ((unsigned short *)a)[0] = (unsigned short)c, a++)
 243 #else
 244 #       define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
 245                 ((unsigned short *)a)[1] = (unsigned short)c, a++)
 246 #endif
 247
 248 /* #define P DBL_MANT_DIG */
 249 /* Ten_pmax = floor(P*log(2)/log(5)) */
 250 /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
 251 /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
 252 /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
 253
 254 #if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN)
 255 #define Exp_shift  20
 256 #define Exp_shift1 20
 257 #define Exp_msk1    0x100000
 258 #define Exp_msk11   0x100000
 259 #define Exp_mask  0x7ff00000
 260 #define P 53
 261 #define Bias 1023
 262 #define IEEE_Arith
 263 #define Emin (-1022)
 264 #define Exp_1  0x3ff00000
 265 #define Exp_11 0x3ff00000
 266 #define Ebits 11
 267 #define Frac_mask  0xfffff
 268 #define Frac_mask1 0xfffff
 269 #define Ten_pmax 22
 270 #define Bletch 0x10
 271 #define Bndry_mask  0xfffff
 272 #define Bndry_mask1 0xfffff
 273 #define LSB 1
 274 #define Sign_bit 0x80000000
 275 #define Log2P 1
 276 #define Tiny0 0
 277 #define Tiny1 1
 278 #define Quick_max 14
 279 #define Int_max 14
 280 #define Infinite(x) (word0(x) == 0x7ff00000) /* sufficient test for here */
 281 #else
 282 #undef  Sudden_Underflow
 283 #define Sudden_Underflow
 284 #ifdef IBM
 285 #define Exp_shift  24
 286 #define Exp_shift1 24
 287 #define Exp_msk1   0x1000000
 288 #define Exp_msk11  0x1000000
 289 #define Exp_mask  0x7f000000
 290 #define P 14
 291 #define Bias 65
 292 #define Exp_1  0x41000000
 293 #define Exp_11 0x41000000
 294 #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
 295 #define Frac_mask  0xffffff
 296 #define Frac_mask1 0xffffff
 297 #define Bletch 4
 298 #define Ten_pmax 22
 299 #define Bndry_mask  0xefffff
 300 #define Bndry_mask1 0xffffff
 301 #define LSB 1
 302 #define Sign_bit 0x80000000
 303 #define Log2P 4
 304 #define Tiny0 0x100000
 305 #define Tiny1 0
 306 #define Quick_max 14
 307 #define Int_max 15
 308 #else /* VAX */
 309 #define Exp_shift  23
 310 #define Exp_shift1 7
 311 #define Exp_msk1    0x80
 312 #define Exp_msk11   0x800000
 313 #define Exp_mask  0x7f80
 314 #define P 56
 315 #define Bias 129
 316 #define Exp_1  0x40800000
 317 #define Exp_11 0x4080
 318 #define Ebits 8
 319 #define Frac_mask  0x7fffff
 320 #define Frac_mask1 0xffff007f
 321 #define Ten_pmax 24
 322 #define Bletch 2
 323 #define Bndry_mask  0xffff007f
 324 #define Bndry_mask1 0xffff007f
 325 #define LSB 0x10000
 326 #define Sign_bit 0x8000
 327 #define Log2P 1
 328 #define Tiny0 0x80
 329 #define Tiny1 0
 330 #define Quick_max 15
 331 #define Int_max 15
 332 #endif
 333 #endif
 334
 335 #ifndef IEEE_Arith
 336 #define ROUND_BIASED
 337 #endif
 338
 339 #ifdef RND_PRODQUOT
 340 #define rounded_product(a,b) a = rnd_prod(a, b)
 341 #define rounded_quotient(a,b) a = rnd_quot(a, b)
 342 extern double rnd_prod(double, double), rnd_quot(double, double);
 343 #else
 344 #define rounded_product(a,b) a *= b
 345 #define rounded_quotient(a,b) a /= b
 346 #endif
 347
 348 #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
 349 #define Big1 0xffffffff
 350
 351 #ifndef Just_16
 352 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
 353  * This makes some inner loops simpler and sometimes saves work
 354  * during multiplications, but it often seems to make things slightly
 355  * slower.  Hence the default is now to store 32 bits per Long.
 356  */
 357 #ifndef Pack_32
 358 #define Pack_32
 359 #endif
 360 #endif
 361
 362 #define Kmax 15
 363
 364 #ifdef __cplusplus
 365 extern "C" double strtod(const char *s00, char **se);
 366 extern "C" char *__dtoa(double d, int mode, int ndigits,
 367                         int *decpt, int *sign, char **rve, char **resultp);
 368 #endif
 369
 370 struct
 371 Bigint {
 372         struct Bigint *next;
 373         int k, maxwds, sign, wds;
 374         ULong x[1];
 375 };
 376
 377 typedef struct Bigint Bigint;
 378
 379 static Bigint *
 380 Balloc(int k)
 381 {
 382         int x;
 383         Bigint *rv;
 384
 385         x = 1 << k;
 386         rv = (Bigint *)malloc(sizeof(Bigint) + (x-1)*sizeof(Long));
 387         rv->k = k;
 388         rv->maxwds = x;
 389         rv->sign = rv->wds = 0;
 390         return rv;
 391 }
 392
 393
 394 static void
 395 Bfree(Bigint *v)
 396 {
 397         free(v);
 398 }
 399
 400
 401 #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
 402         y->wds*sizeof(Long) + 2*sizeof(int))
 403
 404
 405 static Bigint *
 406 multadd(Bigint *b, int m, int a)        /* multiply by m and add a */
 407 {
 408         int i, wds;
 409         ULong *x, y;
 410 #ifdef Pack_32
 411         ULong xi, z;
 412 #endif
 413         Bigint *b1;
 414
 415         wds = b->wds;
 416         x = b->x;
 417         i = 0;
 418         do {
 419 #ifdef Pack_32
 420                 xi = *x;
 421                 y = (xi & 0xffff) * m + a;
 422                 z = (xi >> 16) * m + (y >> 16);
 423                 a = (int)(z >> 16);
 424                 *x++ = (z << 16) + (y & 0xffff);
 425 #else
 426                 y = *x * m + a;
 427                 a = (int)(y >> 16);
 428                 *x++ = y & 0xffff;
 429 #endif
 430         } while (++i < wds);
 431         if (a) {
 432                 if (wds >= b->maxwds) {
 433                         b1 = Balloc(b->k+1);
 434                         Bcopy(b1, b);
 435                         Bfree(b);
 436                         b = b1;
 437                         }
 438                 b->x[wds++] = a;
 439                 b->wds = wds;
 440         }
 441         return b;
 442 }
 443
 444
 445 static Bigint *
 446 s2b(const char *s, int nd0, int nd, ULong y9)
 447 {
 448         Bigint *b;
 449         int i, k;
 450         Long x, y;
 451
 452         x = (nd + 8) / 9;
 453         for (k = 0, y = 1; x > y; y <<= 1, k++) ;
 454 #ifdef Pack_32
 455         b = Balloc(k);
 456         b->x[0] = y9;
 457         b->wds = 1;
 458 #else
 459         b = Balloc(k+1);
 460         b->x[0] = y9 & 0xffff;
 461         b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
 462 #endif
 463
 464         i = 9;
 465         if (9 < nd0) {
 466                 s += 9;
 467                 do
 468                         b = multadd(b, 10, *s++ - '0');
 469                 while (++i < nd0);
 470                 s++;
 471         } else
 472                 s += 10;
 473         for (; i < nd; i++)
 474                 b = multadd(b, 10, *s++ - '0');
 475         return b;
 476 }
 477
 478
 479 static int
 480 hi0bits(ULong x)
 481 {
 482         int k = 0;
 483
 484         if (!(x & 0xffff0000)) {
 485                 k = 16;
 486                 x <<= 16;
 487         }
 488         if (!(x & 0xff000000)) {
 489                 k += 8;
 490                 x <<= 8;
 491         }
 492         if (!(x & 0xf0000000)) {
 493                 k += 4;
 494                 x <<= 4;
 495         }
 496         if (!(x & 0xc0000000)) {
 497                 k += 2;
 498                 x <<= 2;
 499         }
 500         if (!(x & 0x80000000)) {
 501                 k++;
 502                 if (!(x & 0x40000000))
 503                         return 32;
 504         }
 505         return k;
 506 }
 507
 508
 509 static int
 510 lo0bits(ULong *y)
 511 {
 512         int k;
 513         ULong x = *y;
 514
 515         if (x & 7) {
 516                 if (x & 1)
 517                         return 0;
 518                 if (x & 2) {
 519                         *y = x >> 1;
 520                         return 1;
 521                 }
 522                 *y = x >> 2;
 523                 return 2;
 524         }
 525         k = 0;
 526         if (!(x & 0xffff)) {
 527                 k = 16;
 528                 x >>= 16;
 529         }
 530         if (!(x & 0xff)) {
 531                 k += 8;
 532                 x >>= 8;
 533         }
 534         if (!(x & 0xf)) {
 535                 k += 4;
 536                 x >>= 4;
 537         }
 538         if (!(x & 0x3)) {
 539                 k += 2;
 540                 x >>= 2;
 541         }
 542         if (!(x & 1)) {
 543                 k++;
 544                 x >>= 1;
 545                 if (!x & 1)
 546                         return 32;
 547         }
 548         *y = x;
 549         return k;
 550 }
 551
 552
 553 static Bigint *
 554 i2b(int i)
 555 {
 556         Bigint *b;
 557
 558         b = Balloc(1);
 559         b->x[0] = i;
 560         b->wds = 1;
 561         return b;
 562 }
 563
 564
 565 static Bigint *
 566 mult(Bigint *a, Bigint *b)
 567 {
 568         Bigint *c;
 569         int k, wa, wb, wc;
 570         ULong carry, y, z;
 571         ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
 572 #ifdef Pack_32
 573         ULong z2;
 574 #endif
 575
 576         if (a->wds < b->wds) {
 577                 c = a;
 578                 a = b;
 579                 b = c;
 580         }
 581         k = a->k;
 582         wa = a->wds;
 583         wb = b->wds;
 584         wc = wa + wb;
 585         if (wc > a->maxwds)
 586                 k++;
 587         c = Balloc(k);
 588         for (x = c->x, xa = x + wc; x < xa; x++)
 589                 *x = 0;
 590         xa = a->x;
 591         xae = xa + wa;
 592         xb = b->x;
 593         xbe = xb + wb;
 594         xc0 = c->x;
 595 #ifdef Pack_32
 596         for (; xb < xbe; xb++, xc0++) {
 597                 if ( (y = *xb & 0xffff) ) {
 598                         x = xa;
 599                         xc = xc0;
 600                         carry = 0;
 601                         do {
 602                                 z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
 603                                 carry = z >> 16;
 604                                 z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
 605                                 carry = z2 >> 16;
 606                                 Storeinc(xc, z2, z);
 607                         } while (x < xae);
 608                         *xc = carry;
 609                 }
 610                 if ( (y = *xb >> 16) ) {
 611                         x = xa;
 612                         xc = xc0;
 613                         carry = 0;
 614                         z2 = *xc;
 615                         do {
 616                                 z = (*x & 0xffff) * y + (*xc >> 16) + carry;
 617                                 carry = z >> 16;
 618                                 Storeinc(xc, z, z2);
 619                                 z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
 620                                 carry = z2 >> 16;
 621                         } while (x < xae);
 622                         *xc = z2;
 623                 }
 624         }
 625 #else
 626         for (; xb < xbe; xc0++) {
 627                 if (y = *xb++) {
 628                         x = xa;
 629                         xc = xc0;
 630                         carry = 0;
 631                         do {
 632                                 z = *x++ * y + *xc + carry;
 633                                 carry = z >> 16;
 634                                 *xc++ = z & 0xffff;
 635                         } while (x < xae);
 636                         *xc = carry;
 637                 }
 638         }
 639 #endif
 640         for (xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
 641         c->wds = wc;
 642         return c;
 643 }
 644
 645
 646 static Bigint *p5s;
 647
 648
 649 static Bigint *
 650 pow5mult(Bigint *b, int k)
 651 {
 652         Bigint *b1, *p5, *p51;
 653         int i;
 654         static int p05[3] = { 5, 25, 125 };
 655
 656         if ( (i = k & 3) )
 657                 b = multadd(b, p05[i-1], 0);
 658
 659         if (!(k >>= 2))
 660                 return b;
 661         if (!(p5 = p5s)) {
 662                 /* first time */
 663                 p5 = p5s = i2b(625);
 664                 p5->next = 0;
 665         }
 666         for (;;) {
 667                 if (k & 1) {
 668                         b1 = mult(b, p5);
 669                         Bfree(b);
 670                         b = b1;
 671                 }
 672                 if (!(k >>= 1))
 673                         break;
 674                 if (!(p51 = p5->next)) {
 675                         p51 = p5->next = mult(p5,p5);
 676                         p51->next = 0;
 677                 }
 678                 p5 = p51;
 679         }
 680         return b;
 681 }
 682
 683
 684 static Bigint *
 685 lshift(Bigint *b, int k)
 686 {
 687         int i, k1, n, n1;
 688         Bigint *b1;
 689         ULong *x, *x1, *xe, z;
 690
 691 #ifdef Pack_32
 692         n = k >> 5;
 693 #else
 694         n = k >> 4;
 695 #endif
 696         k1 = b->k;
 697         n1 = n + b->wds + 1;
 698         for (i = b->maxwds; n1 > i; i <<= 1)
 699                 k1++;
 700         b1 = Balloc(k1);
 701         x1 = b1->x;
 702         for (i = 0; i < n; i++)
 703                 *x1++ = 0;
 704         x = b->x;
 705         xe = x + b->wds;
 706 #ifdef Pack_32
 707         if (k &= 0x1f) {
 708                 k1 = 32 - k;
 709                 z = 0;
 710                 do {
 711                         *x1++ = *x << k | z;
 712                         z = *x++ >> k1;
 713                 } while (x < xe);
 714                 if ( (*x1 = z) )
 715                         ++n1;
 716         }
 717 #else
 718         if (k &= 0xf) {
 719                 k1 = 16 - k;
 720                 z = 0;
 721                 do {
 722                         *x1++ = *x << k  & 0xffff | z;
 723                         z = *x++ >> k1;
 724                 } while (x < xe);
 725                 if (*x1 = z)
 726                         ++n1;
 727         }
 728 #endif
 729         else
 730                 do
 731                         *x1++ = *x++;
 732                 while (x < xe);
 733         b1->wds = n1 - 1;
 734         Bfree(b);
 735         return b1;
 736 }
 737
 738
 739 static int
 740 cmp(Bigint *a, Bigint *b)
 741 {
 742         ULong *xa, *xa0, *xb, *xb0;
 743         int i, j;
 744
 745         i = a->wds;
 746         j = b->wds;
 747 #ifdef DEBUG
 748         if (i > 1 && !a->x[i-1])
 749                 Bug("cmp called with a->x[a->wds-1] == 0");
 750         if (j > 1 && !b->x[j-1])
 751                 Bug("cmp called with b->x[b->wds-1] == 0");
 752 #endif
 753         if (i -= j)
 754                 return i;
 755         xa0 = a->x;
 756         xa = xa0 + j;
 757         xb0 = b->x;
 758         xb = xb0 + j;
 759         for (;;) {
 760                 if (*--xa != *--xb)
 761                         return *xa < *xb ? -1 : 1;
 762                 if (xa <= xa0)
 763                         break;
 764         }
 765         return 0;
 766 }
 767
 768
 769 static Bigint *
 770 diff(Bigint *a, Bigint *b)
 771 {
 772         Bigint *c;
 773         int i, wa, wb;
 774         Long borrow, y; /* We need signed shifts here. */
 775         ULong *xa, *xae, *xb, *xbe, *xc;
 776 #ifdef Pack_32
 777         Long z;
 778 #endif
 779
 780         i = cmp(a,b);
 781         if (!i) {
 782                 c = Balloc(0);
 783                 c->wds = 1;
 784                 c->x[0] = 0;
 785                 return c;
 786         }
 787         if (i < 0) {
 788                 c = a;
 789                 a = b;
 790                 b = c;
 791                 i = 1;
 792         } else
 793                 i = 0;
 794         c = Balloc(a->k);
 795         c->sign = i;
 796         wa = a->wds;
 797         xa = a->x;
 798         xae = xa + wa;
 799         wb = b->wds;
 800         xb = b->x;
 801         xbe = xb + wb;
 802         xc = c->x;
 803         borrow = 0;
 804 #ifdef Pack_32
 805         do {
 806                 y = (*xa & 0xffff) - (*xb & 0xffff) + borrow;
 807                 borrow = y >> 16;
 808                 Sign_Extend(borrow, y);
 809                 z = (*xa++ >> 16) - (*xb++ >> 16) + borrow;
 810                 borrow = z >> 16;
 811                 Sign_Extend(borrow, z);
 812                 Storeinc(xc, z, y);
 813         } while (xb < xbe);
 814         while (xa < xae) {
 815                 y = (*xa & 0xffff) + borrow;
 816                 borrow = y >> 16;
 817                 Sign_Extend(borrow, y);
 818                 z = (*xa++ >> 16) + borrow;
 819                 borrow = z >> 16;
 820                 Sign_Extend(borrow, z);
 821                 Storeinc(xc, z, y);
 822         }
 823 #else
 824         do {
 825                 y = *xa++ - *xb++ + borrow;
 826                 borrow = y >> 16;
 827                 Sign_Extend(borrow, y);
 828                 *xc++ = y & 0xffff;
 829         } while (xb < xbe);
 830         while (xa < xae) {
 831                 y = *xa++ + borrow;
 832                 borrow = y >> 16;
 833                 Sign_Extend(borrow, y);
 834                 *xc++ = y & 0xffff;
 835         }
 836 #endif
 837         while (!*--xc)
 838                 wa--;
 839         c->wds = wa;
 840         return c;
 841 }
 842
 843
 844 static double
 845 ulp(double x)
 846 {
 847         Long L;
 848         double a;
 849
 850         L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
 851 #ifndef Sudden_Underflow
 852         if (L > 0) {
 853 #endif
 854 #ifdef IBM
 855                 L |= Exp_msk1 >> 4;
 856 #endif
 857                 word0(a) = L;
 858                 word1(a) = 0;
 859 #ifndef Sudden_Underflow
 860         } else {
 861                 L = -L >> Exp_shift;
 862                 if (L < Exp_shift) {
 863                         word0(a) = 0x80000 >> L;
 864                         word1(a) = 0;
 865                 } else {
 866                         word0(a) = 0;
 867                         L -= Exp_shift;
 868                         word1(a) = L >= 31 ? 1 : 1 << (31 - L);
 869                 }
 870         }
 871 #endif
 872         return a;
 873 }
 874
 875
 876 static double
 877 b2d(Bigint *a, int *e)
 878 {
 879         ULong *xa, *xa0, w, y, z;
 880         int k;
 881         double d;
 882 #ifdef VAX
 883         ULong d0, d1;
 884 #else
 885 #define d0 word0(d)
 886 #define d1 word1(d)
 887 #endif
 888
 889         xa0 = a->x;
 890         xa = xa0 + a->wds;
 891         y = *--xa;
 892 #ifdef DEBUG
 893         if (!y) Bug("zero y in b2d");
 894 #endif
 895         k = hi0bits(y);
 896         *e = 32 - k;
 897 #ifdef Pack_32
 898         if (k < Ebits) {
 899                 d0 = Exp_1 | (y >> (Ebits - k));
 900                 w = xa > xa0 ? *--xa : 0;
 901                 d1 = (y << ((32-Ebits) + k)) | (w >> (Ebits - k));
 902                 goto ret_d;
 903                 }
 904         z = xa > xa0 ? *--xa : 0;
 905         if (k -= Ebits) {
 906                 d0 = Exp_1 | (y << k) | (z >> (32 - k));
 907                 y = xa > xa0 ? *--xa : 0;
 908                 d1 = (z << k) | (y >> (32 - k));
 909         } else {
 910                 d0 = Exp_1 | y;
 911                 d1 = z;
 912         }
 913 #else
 914         if (k < Ebits + 16) {
 915                 z = xa > xa0 ? *--xa : 0;
 916                 d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
 917                 w = xa > xa0 ? *--xa : 0;
 918                 y = xa > xa0 ? *--xa : 0;
 919                 d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
 920                 goto ret_d;
 921         }
 922         z = xa > xa0 ? *--xa : 0;
 923         w = xa > xa0 ? *--xa : 0;
 924         k -= Ebits + 16;
 925         d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
 926         y = xa > xa0 ? *--xa : 0;
 927         d1 = w << k + 16 | y << k;
 928 #endif
 929  ret_d:
 930 #ifdef VAX
 931         word0(d) = d0 >> 16 | d0 << 16;
 932         word1(d) = d1 >> 16 | d1 << 16;
 933 #else
 934 #undef d0
 935 #undef d1
 936 #endif
 937         return d;
 938 }
 939
 940
 941 static Bigint *
 942 d2b(double d, int *e, int *bits)
 943 {
 944         Bigint *b;
 945         int de, i, k;
 946         ULong *x, y, z;
 947 #ifdef VAX
 948         ULong d0, d1;
 949         d0 = word0(d) >> 16 | word0(d) << 16;
 950         d1 = word1(d) >> 16 | word1(d) << 16;
 951 #else
 952 #define d0 word0(d)
 953 #define d1 word1(d)
 954 #endif
 955
 956 #ifdef Pack_32
 957         b = Balloc(1);
 958 #else
 959         b = Balloc(2);
 960 #endif
 961         x = b->x;
 962
 963         z = d0 & Frac_mask;
 964         d0 &= 0x7fffffff;       /* clear sign bit, which we ignore */
 965 #ifdef Sudden_Underflow
 966         de = (int)(d0 >> Exp_shift);
 967 #ifndef IBM
 968         z |= Exp_msk11;
 969 #endif
 970 #else
 971         if ( (de = (int)(d0 >> Exp_shift)) )
 972                 z |= Exp_msk1;
 973 #endif
 974 #ifdef Pack_32
 975         if ( (y = d1) ) {
 976                 if ( (k = lo0bits(&y)) ) {
 977                         x[0] = y | (z << (32 - k));
 978                         z >>= k;
 979                         }
 980                 else
 981                         x[0] = y;
 982                 i = b->wds = (x[1] = z) ? 2 : 1;
 983         } else {
 984 #ifdef DEBUG
 985                 if (!z)
 986                         Bug("Zero passed to d2b");
 987 #endif
 988                 k = lo0bits(&z);
 989                 x[0] = z;
 990                 i = b->wds = 1;
 991                 k += 32;
 992         }
 993 #else
 994         if (y = d1) {
 995                 if (k = lo0bits(&y))
 996                         if (k >= 16) {
 997                                 x[0] = y | z << 32 - k & 0xffff;
 998                                 x[1] = z >> k - 16 & 0xffff;
 999                                 x[2] = z >> k;
1000                                 i = 2;
1001                         } else {
1002                                 x[0] = y & 0xffff;
1003                                 x[1] = y >> 16 | z << 16 - k & 0xffff;
1004                                 x[2] = z >> k & 0xffff;
1005                                 x[3] = z >> k+16;
1006                                 i = 3;
1007                         }
1008                 else {
1009                         x[0] = y & 0xffff;
1010                         x[1] = y >> 16;
1011                         x[2] = z & 0xffff;
1012                         x[3] = z >> 16;
1013                         i = 3;
1014                 }
1015         } else {
1016 #ifdef DEBUG
1017                 if (!z)
1018                         Bug("Zero passed to d2b");
1019 #endif
1020                 k = lo0bits(&z);
1021                 if (k >= 16) {
1022                         x[0] = z;
1023                         i = 0;
1024                 } else {
1025                         x[0] = z & 0xffff;
1026                         x[1] = z >> 16;
1027                         i = 1;
1028                 }
1029                 k += 32;
1030         }
1031         while (!x[i])
1032                 --i;
1033         b->wds = i + 1;
1034 #endif
1035 #ifndef Sudden_Underflow
1036         if (de) {
1037 #endif
1038 #ifdef IBM
1039                 *e = (de - Bias - (P-1) << 2) + k;
1040                 *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
1041 #else
1042                 *e = de - Bias - (P-1) + k;
1043                 *bits = P - k;
1044 #endif
1045 #ifndef Sudden_Underflow
1046         } else {
1047                 *e = de - Bias - (P-1) + 1 + k;
1048 #ifdef Pack_32
1049                 *bits = 32*i - hi0bits(x[i-1]);
1050 #else
1051                 *bits = (i+2)*16 - hi0bits(x[i]);
1052 #endif
1053         }
1054 #endif
1055         return b;
1056 }
1057 #undef d0
1058 #undef d1
1059
1060
1061 static double
1062 ratio(Bigint *a, Bigint *b)
1063 {
1064         double da, db;
1065         int k, ka, kb;
1066
1067         da = b2d(a, &ka);
1068         db = b2d(b, &kb);
1069 #ifdef Pack_32
1070         k = ka - kb + 32*(a->wds - b->wds);
1071 #else
1072         k = ka - kb + 16*(a->wds - b->wds);
1073 #endif
1074 #ifdef IBM
1075         if (k > 0) {
1076                 word0(da) += (k >> 2)*Exp_msk1;
1077                 if (k &= 3)
1078                         da *= 1 << k;
1079         } else {
1080                 k = -k;
1081                 word0(db) += (k >> 2)*Exp_msk1;
1082                 if (k &= 3)
1083                         db *= 1 << k;
1084         }
1085 #else
1086         if (k > 0)
1087                 word0(da) += k*Exp_msk1;
1088         else {
1089                 k = -k;
1090                 word0(db) += k*Exp_msk1;
1091         }
1092 #endif
1093         return da / db;
1094 }
1095
1096 static double
1097 tens[] = {
1098                 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1099                 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1100                 1e20, 1e21, 1e22
1101 #ifdef VAX
1102                 , 1e23, 1e24
1103 #endif
1104                 };
1105
1106 static double
1107 #ifdef IEEE_Arith
1108 bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
1109 static double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, 1e-256 };
1110 #define n_bigtens 5
1111 #else
1112 #ifdef IBM
1113 bigtens[] = { 1e16, 1e32, 1e64 };
1114 static double tinytens[] = { 1e-16, 1e-32, 1e-64 };
1115 #define n_bigtens 3
1116 #else
1117 bigtens[] = { 1e16, 1e32 };
1118 static double tinytens[] = { 1e-16, 1e-32 };
1119 #define n_bigtens 2
1120 #endif
1121 #endif
1122
1123
1124 double
1125 strtod(const char * __restrict s00, char ** __restrict se)
1126 {
1127         int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
1128                  e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
1129         const char *s, *s0, *s1;
1130         double aadj, aadj1, adj, rv, rv0;
1131         Long L;
1132         ULong y, z;
1133         Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
1134         char decimal_point = localeconv()->decimal_point[0];
1135
1136         sign = nz0 = nz = 0;
1137         rv = 0.;
1138         for (s = s00;;s++) switch(*s) {
1139                 case '-':
1140                         sign = 1;
1141                         /* no break */
1142                 case '+':
1143                         if (*++s)
1144                                 goto break2;
1145                         /* no break */
1146                 case 0:
1147                         s = s00;
1148                         goto ret;
1149                 default:
1150                         if (isspace((unsigned char)*s))
1151                                 continue;
1152                         goto break2;
1153         }
1154  break2:
1155         if (*s == '0') {
1156                 nz0 = 1;
1157                 while (*++s == '0') ;
1158                 if (!*s)
1159                         goto ret;
1160         }
1161         s0 = s;
1162         y = z = 0;
1163         for (nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
1164                 if (nd < 9)
1165                         y = 10*y + c - '0';
1166                 else if (nd < 16)
1167                         z = 10*z + c - '0';
1168         nd0 = nd;
1169         if ((char)c == decimal_point) {
1170                 c = *++s;
1171                 if (!nd) {
1172                         for (; c == '0'; c = *++s)
1173                                 nz++;
1174                         if (c > '0' && c <= '9') {
1175                                 s0 = s;
1176                                 nf += nz;
1177                                 nz = 0;
1178                                 goto have_dig;
1179                         }
1180                         goto dig_done;
1181                 }
1182                 for (; c >= '0' && c <= '9'; c = *++s) {
1183  have_dig:
1184                         nz++;
1185                         if (c - '0' > 0) {
1186                                 nf += nz;
1187                                 for (i = 1; i < nz; i++)
1188                                         if (nd++ < 9)
1189                                                 y *= 10;
1190                                         else if (nd <= DBL_DIG + 1)
1191                                                 z *= 10;
1192                                 if (nd++ < 9)
1193                                         y = 10*y + c - '0';
1194                                 else if (nd <= DBL_DIG + 1)
1195                                         z = 10*z + c - '0';
1196                                 nz = 0;
1197                         }
1198                 }
1199         }
1200  dig_done:
1201         e = 0;
1202         if (c == 'e' || c == 'E') {
1203                 if (!nd && !nz && !nz0) {
1204                         s = s00;
1205                         goto ret;
1206                 }
1207                 s00 = s;
1208                 esign = 0;
1209                 switch(c = *++s) {
1210                         case '-':
1211                                 esign = 1;
1212                         case '+':
1213                                 c = *++s;
1214                 }
1215                 if (c >= '0' && c <= '9') {
1216                         while (c == '0')
1217                                 c = *++s;
1218                         if (c > '0' && c <= '9') {
1219                                 L = c - '0';
1220                                 s1 = s;
1221                                 while ((c = *++s) >= '0' && c <= '9')
1222                                         L = 10*L + c - '0';
1223                                 if (s - s1 > 8 || L > 19999)
1224                                         /* Avoid confusion from exponents
1225                                          * so large that e might overflow.
1226                                          */
1227                                         e = 19999; /* safe for 16 bit ints */
1228                                 else
1229                                         e = (int)L;
1230                                 if (esign)
1231                                         e = -e;
1232                         } else
1233                                 e = 0;
1234                 } else
1235                         s = s00;
1236         }
1237         if (!nd) {
1238                 if (!nz && !nz0)
1239                         s = s00;
1240                 goto ret;
1241         }
1242         e1 = e -= nf;
1243
1244         /* Now we have nd0 digits, starting at s0, followed by a
1245          * decimal point, followed by nd-nd0 digits.  The number we're
1246          * after is the integer represented by those digits times
1247          * 10**e */
1248
1249         if (!nd0)
1250                 nd0 = nd;
1251         k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
1252         rv = y;
1253         if (k > 9)
1254                 rv = tens[k - 9] * rv + z;
1255         if (nd <= DBL_DIG
1256 #ifndef RND_PRODQUOT
1257                 && FLT_ROUNDS == 1
1258 #endif
1259                         ) {
1260                 if (!e)
1261                         goto ret;
1262                 if (e > 0) {
1263                         if (e <= Ten_pmax) {
1264 #ifdef VAX
1265                                 goto vax_ovfl_check;
1266 #else
1267                                 /* rv = */ rounded_product(rv, tens[e]);
1268                                 goto ret;
1269 #endif
1270                                 }
1271                         i = DBL_DIG - nd;
1272                         if (e <= Ten_pmax + i) {
1273                                 /* A fancier test would sometimes let us do
1274                                  * this for larger i values.
1275                                  */
1276                                 e -= i;
1277                                 rv *= tens[i];
1278 #ifdef VAX
1279                                 /* VAX exponent range is so narrow we must
1280                                  * worry about overflow here...
1281                                  */
1282  vax_ovfl_check:
1283                                 word0(rv) -= P*Exp_msk1;
1284                                 /* rv = */ rounded_product(rv, tens[e]);
1285                                 if ((word0(rv) & Exp_mask)
1286                                  > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
1287                                         goto ovfl;
1288                                 word0(rv) += P*Exp_msk1;
1289 #else
1290                                 /* rv = */ rounded_product(rv, tens[e]);
1291 #endif
1292                                 goto ret;
1293                         }
1294                 }
1295 #ifndef Inaccurate_Divide
1296                 else if (e >= -Ten_pmax) {
1297                         /* rv = */ rounded_quotient(rv, tens[-e]);
1298                         goto ret;
1299                 }
1300 #endif
1301         }
1302         e1 += nd - k;
1303
1304         /* Get starting approximation = rv * 10**e1 */
1305
1306         if (e1 > 0) {
1307                 if ( (i = e1 & 15) )
1308                         rv *= tens[i];
1309                 if ( (e1 &= ~15) ) {
1310                         if (e1 > DBL_MAX_10_EXP) {
1311  ovfl:
1312                                 __set_errno(ERANGE);
1313                                 rv = HUGE_VAL;
1314                                 goto ret;
1315                         }
1316                         if (e1 >>= 4) {
1317                                 for (j = 0; e1 > 1; j++, e1 >>= 1)
1318                                         if (e1 & 1)
1319                                                 rv *= bigtens[j];
1320                         /* The last multiplication could overflow. */
1321                                 word0(rv) -= P*Exp_msk1;
1322                                 rv *= bigtens[j];
1323                                 if ((z = word0(rv) & Exp_mask)
1324                                  > Exp_msk1*(DBL_MAX_EXP+Bias-P))
1325                                         goto ovfl;
1326                                 if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
1327                                         /* set to largest number */
1328                                         /* (Can't trust DBL_MAX) */
1329                                         word0(rv) = Big0;
1330                                         word1(rv) = Big1;
1331                                         }
1332                                 else
1333                                         word0(rv) += P*Exp_msk1;
1334                         }
1335                 }
1336         } else if (e1 < 0) {
1337                 e1 = -e1;
1338                 if ( (i = e1 & 15) )
1339                         rv /= tens[i];
1340                 if ( (e1 &= ~15) ) {
1341                         e1 >>= 4;
1342                         for (j = 0; e1 > 1; j++, e1 >>= 1)
1343                                 if (e1 & 1)
1344                                         rv *= tinytens[j];
1345                         /* The last multiplication could underflow. */
1346                         rv0 = rv;
1347                         rv *= tinytens[j];
1348                         if (!rv) {
1349                                 rv = 2.*rv0;
1350                                 rv *= tinytens[j];
1351                                 if (!rv) {
1352  undfl:
1353                                         rv = 0.;
1354                                         __set_errno(ERANGE);
1355                                         goto ret;
1356                                         }
1357                                 word0(rv) = Tiny0;
1358                                 word1(rv) = Tiny1;
1359                                 /* The refinement below will clean
1360                                  * this approximation up.
1361                                  */
1362                         }
1363                 }
1364         }
1365
1366         /* Now the hard part -- adjusting rv to the correct value.*/
1367
1368         /* Put digits into bd: true value = bd * 10^e */
1369
1370         bd0 = s2b(s0, nd0, nd, y);
1371
1372         for (;;) {
1373                 bd = Balloc(bd0->k);
1374                 Bcopy(bd, bd0);
1375                 bb = d2b(rv, &bbe, &bbbits);    /* rv = bb * 2^bbe */
1376                 bs = i2b(1);
1377
1378                 if (e >= 0) {
1379                         bb2 = bb5 = 0;
1380                         bd2 = bd5 = e;
1381                 } else {
1382                         bb2 = bb5 = -e;
1383                         bd2 = bd5 = 0;
1384                 }
1385                 if (bbe >= 0)
1386                         bb2 += bbe;
1387                 else
1388                         bd2 -= bbe;
1389                 bs2 = bb2;
1390 #ifdef Sudden_Underflow
1391 #ifdef IBM
1392                 j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
1393 #else
1394                 j = P + 1 - bbbits;
1395 #endif
1396 #else
1397                 i = bbe + bbbits - 1;   /* logb(rv) */
1398                 if (i < Emin)   /* denormal */
1399                         j = bbe + (P-Emin);
1400                 else
1401                         j = P + 1 - bbbits;
1402 #endif
1403                 bb2 += j;
1404                 bd2 += j;
1405                 i = bb2 < bd2 ? bb2 : bd2;
1406                 if (i > bs2)
1407                         i = bs2;
1408                 if (i > 0) {
1409                         bb2 -= i;
1410                         bd2 -= i;
1411                         bs2 -= i;
1412                         }
1413                 if (bb5 > 0) {
1414                         bs = pow5mult(bs, bb5);
1415                         bb1 = mult(bs, bb);
1416                         Bfree(bb);
1417                         bb = bb1;
1418                         }
1419                 if (bb2 > 0)
1420                         bb = lshift(bb, bb2);
1421                 if (bd5 > 0)
1422                         bd = pow5mult(bd, bd5);
1423                 if (bd2 > 0)
1424                         bd = lshift(bd, bd2);
1425                 if (bs2 > 0)
1426                         bs = lshift(bs, bs2);
1427                 delta = diff(bb, bd);
1428                 dsign = delta->sign;
1429                 delta->sign = 0;
1430                 i = cmp(delta, bs);
1431                 if (i < 0) {
1432                         /* Error is less than half an ulp -- check for
1433                          * special case of mantissa a power of two.
1434                          */
1435                         if (dsign || word1(rv) || word0(rv) & Bndry_mask)
1436                                 break;
1437                         delta = lshift(delta,Log2P);
1438                         if (cmp(delta, bs) > 0)
1439                                 goto drop_down;
1440                         break;
1441                 }
1442                 if (i == 0) {
1443                         /* exactly half-way between */
1444                         if (dsign) {
1445                                 if ((word0(rv) & Bndry_mask1) == Bndry_mask1
1446                                  &&  word1(rv) == 0xffffffff) {
1447                                         /*boundary case -- increment exponent*/
1448                                         word0(rv) = (word0(rv) & Exp_mask)
1449                                                 + Exp_msk1
1450 #ifdef IBM
1451                                                 | Exp_msk1 >> 4
1452 #endif
1453                                                 ;
1454                                         word1(rv) = 0;
1455                                         break;
1456                                 }
1457                         } else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
1458  drop_down:
1459                                 /* boundary case -- decrement exponent */
1460 #ifdef Sudden_Underflow
1461                                 L = word0(rv) & Exp_mask;
1462 #ifdef IBM
1463                                 if (L <  Exp_msk1)
1464 #else
1465                                 if (L <= Exp_msk1)
1466 #endif
1467                                         goto undfl;
1468                                 L -= Exp_msk1;
1469 #else
1470                                 L = (word0(rv) & Exp_mask) - Exp_msk1;
1471 #endif
1472                                 word0(rv) = L | Bndry_mask1;
1473                                 word1(rv) = 0xffffffff;
1474 #ifdef IBM
1475                                 goto cont;
1476 #else
1477                                 break;
1478 #endif
1479                         }
1480 #ifndef ROUND_BIASED
1481                         if (!(word1(rv) & LSB))
1482                                 break;
1483 #endif
1484                         if (dsign)
1485                                 rv += ulp(rv);
1486 #ifndef ROUND_BIASED
1487                         else {
1488                                 rv -= ulp(rv);
1489 #ifndef Sudden_Underflow
1490                                 if (!rv)
1491                                         goto undfl;
1492 #endif
1493                         }
1494 #endif
1495                         break;
1496                 }
1497                 if ((aadj = ratio(delta, bs)) <= 2.) {
1498                         if (dsign)
1499                                 aadj = aadj1 = 1.;
1500                         else if (word1(rv) || word0(rv) & Bndry_mask) {
1501 #ifndef Sudden_Underflow
1502                                 if (word1(rv) == Tiny1 && !word0(rv))
1503                                         goto undfl;
1504 #endif
1505                                 aadj = 1.;
1506                                 aadj1 = -1.;
1507                         } else {
1508                                 /* special case -- power of FLT_RADIX to be */
1509                                 /* rounded down... */
1510
1511                                 if (aadj < 2./FLT_RADIX)
1512                                         aadj = 1./FLT_RADIX;
1513                                 else
1514                                         aadj *= 0.5;
1515                                 aadj1 = -aadj;
1516                         }
1517                 } else {
1518                         aadj *= 0.5;
1519                         aadj1 = dsign ? aadj : -aadj;
1520 #ifdef Check_FLT_ROUNDS
1521                         switch(FLT_ROUNDS) {
1522                                 case 2: /* towards +infinity */
1523                                         aadj1 -= 0.5;
1524                                         break;
1525                                 case 0: /* towards 0 */
1526                                 case 3: /* towards -infinity */
1527                                         aadj1 += 0.5;
1528                         }
1529 #else
1530                         if (FLT_ROUNDS == 0)
1531                                 aadj1 += 0.5;
1532 #endif
1533                 }
1534                 y = word0(rv) & Exp_mask;
1535
1536                 /* Check for overflow */
1537
1538                 if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
1539                         rv0 = rv;
1540                         word0(rv) -= P*Exp_msk1;
1541                         adj = aadj1 * ulp(rv);
1542                         rv += adj;
1543                         if ((word0(rv) & Exp_mask) >=
1544                                         Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
1545                                 if (word0(rv0) == Big0 && word1(rv0) == Big1)
1546                                         goto ovfl;
1547                                 word0(rv) = Big0;
1548                                 word1(rv) = Big1;
1549                                 goto cont;
1550                         } else
1551                                 word0(rv) += P*Exp_msk1;
1552                 } else {
1553 #ifdef Sudden_Underflow
1554                         if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
1555                                 rv0 = rv;
1556                                 word0(rv) += P*Exp_msk1;
1557                                 adj = aadj1 * ulp(rv);
1558                                 rv += adj;
1559 #ifdef IBM
1560                                 if ((word0(rv) & Exp_mask) <  P*Exp_msk1)
1561 #else
1562                                 if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
1563 #endif
1564                                 {
1565                                         if (word0(rv0) == Tiny0
1566                                          && word1(rv0) == Tiny1)
1567                                                 goto undfl;
1568                                         word0(rv) = Tiny0;
1569                                         word1(rv) = Tiny1;
1570                                         goto cont;
1571                                 } else
1572                                         word0(rv) -= P*Exp_msk1;
1573                         } else {
1574                                 adj = aadj1 * ulp(rv);
1575                                 rv += adj;
1576                         }
1577 #else
1578                         /* Compute adj so that the IEEE rounding rules will
1579                          * correctly round rv + adj in some half-way cases.
1580                          * If rv * ulp(rv) is denormalized (i.e.,
1581                          * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
1582                          * trouble from bits lost to denormalization;
1583                          * example: 1.2e-307 .
1584                          */
1585                         if (y <= (P-1)*Exp_msk1 && aadj >= 1.) {
1586                                 aadj1 = (double)(int)(aadj + 0.5);
1587                                 if (!dsign)
1588                                         aadj1 = -aadj1;
1589                         }
1590                         adj = aadj1 * ulp(rv);
1591                         rv += adj;
1592 #endif
1593                 }
1594                 z = word0(rv) & Exp_mask;
1595                 if (y == z) {
1596                         /* Can we stop now? */
1597                         L = aadj;
1598                         aadj -= L;
1599                         /* The tolerances below are conservative. */
1600                         if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
1601                                 if (aadj < .4999999 || aadj > .5000001)
1602                                         break;
1603                         } else if (aadj < .4999999/FLT_RADIX)
1604                                 break;
1605                 }
1606  cont:
1607                 Bfree(bb);
1608                 Bfree(bd);
1609                 Bfree(bs);
1610                 Bfree(delta);
1611         }
1612         Bfree(bb);
1613         Bfree(bd);
1614         Bfree(bs);
1615         Bfree(bd0);
1616         Bfree(delta);
1617  ret:
1618         if (se)
1619                 *se = (char *)s;
1620         return sign ? -rv : rv;
1621 }
1622
1623
1624 double __strtod_internal(const char *number, char **_end, int group);
1625
1626 double
1627 __strtod_internal(const char *number, char **_end, int group)
1628 {
1629         // ToDo: group is currently not supported!
1630         (void)group;
1631
1632         return strtod(number, _end);
1633 }
1634
1635 // XXX this is not correct
1636
1637 long double __strtold_internal(const char *number, char **_end, int group);
1638
1639 long double
1640 __strtold_internal(const char *number, char **_end, int group)
1641 {
1642         return __strtod_internal(number, _end, group);
1643 }
1644
1645 float __strtof_internal(const char *number, char **_end, int group);
1646
1647 float
1648 __strtof_internal(const char *number, char **_end, int group)
1649 {
1650         return __strtod_internal(number, _end, group);
1651 }
1652
1653
1654 /* removed from the build, is only used by __dtoa() */
1655 #if 0
1656 static int
1657 quorem(Bigint *b, Bigint *S)
1658 {
1659         int n;
1660         Long borrow, y;
1661         ULong carry, q, ys;
1662         ULong *bx, *bxe, *sx, *sxe;
1663 #ifdef Pack_32
1664         Long z;
1665         ULong si, zs;
1666 #endif
1667
1668         n = S->wds;
1669 #ifdef DEBUG
1670         /*debug*/ if (b->wds > n)
1671         /*debug*/       Bug("oversize b in quorem");
1672 #endif
1673         if (b->wds < n)
1674                 return 0;
1675         sx = S->x;
1676         sxe = sx + --n;
1677         bx = b->x;
1678         bxe = bx + n;
1679         q = *bxe / (*sxe + 1);  /* ensure q <= true quotient */
1680 #ifdef DEBUG
1681         /*debug*/ if (q > 9)
1682         /*debug*/       Bug("oversized quotient in quorem");
1683 #endif
1684         if (q) {
1685                 borrow = 0;
1686                 carry = 0;
1687                 do {
1688 #ifdef Pack_32
1689                         si = *sx++;
1690                         ys = (si & 0xffff) * q + carry;
1691                         zs = (si >> 16) * q + (ys >> 16);
1692                         carry = zs >> 16;
1693                         y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
1694                         borrow = y >> 16;
1695                         Sign_Extend(borrow, y);
1696                         z = (*bx >> 16) - (zs & 0xffff) + borrow;
1697                         borrow = z >> 16;
1698                         Sign_Extend(borrow, z);
1699                         Storeinc(bx, z, y);
1700 #else
1701                         ys = *sx++ * q + carry;
1702                         carry = ys >> 16;
1703                         y = *bx - (ys & 0xffff) + borrow;
1704                         borrow = y >> 16;
1705                         Sign_Extend(borrow, y);
1706                         *bx++ = y & 0xffff;
1707 #endif
1708                 } while (sx <= sxe);
1709                 if (!*bxe) {
1710                         bx = b->x;
1711                         while (--bxe > bx && !*bxe)
1712                                 --n;
1713                         b->wds = n;
1714                 }
1715         }
1716         if (cmp(b, S) >= 0) {
1717                 q++;
1718                 borrow = 0;
1719                 carry = 0;
1720                 bx = b->x;
1721                 sx = S->x;
1722                 do {
1723 #ifdef Pack_32
1724                         si = *sx++;
1725                         ys = (si & 0xffff) + carry;
1726                         zs = (si >> 16) + (ys >> 16);
1727                         carry = zs >> 16;
1728                         y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
1729                         borrow = y >> 16;
1730                         Sign_Extend(borrow, y);
1731                         z = (*bx >> 16) - (zs & 0xffff) + borrow;
1732                         borrow = z >> 16;
1733                         Sign_Extend(borrow, z);
1734                         Storeinc(bx, z, y);
1735 #else
1736                         ys = *sx++ + carry;
1737                         carry = ys >> 16;
1738                         y = *bx - (ys & 0xffff) + borrow;
1739                         borrow = y >> 16;
1740                         Sign_Extend(borrow, y);
1741                         *bx++ = y & 0xffff;
1742 #endif
1743                 } while (sx <= sxe);
1744                 bx = b->x;
1745                 bxe = bx + n;
1746                 if (!*bxe) {
1747                         while (--bxe > bx && !*bxe)
1748                                 --n;
1749                         b->wds = n;
1750                 }
1751         }
1752         return q;
1753 }
1754 #endif  /* removed from the build, is only used by __dtoa() */
1755
1756 /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
1757  *
1758  * Inspired by "How to Print Floating-Point Numbers Accurately" by
1759  * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101].
1760  *
1761  * Modifications:
1762  *      1. Rather than iterating, we use a simple numeric overestimate
1763  *         to determine k = floor(log10(d)).  We scale relevant
1764  *         quantities using O(log2(k)) rather than O(k) multiplications.
1765  *      2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
1766  *         try to generate digits strictly left to right.  Instead, we
1767  *         compute with fewer bits and propagate the carry if necessary
1768  *         when rounding the final digit up.  This is often faster.
1769  *      3. Under the assumption that input will be rounded nearest,
1770  *         mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
1771  *         That is, we allow equality in stopping tests when the
1772  *         round-nearest rule will give the same floating-point value
1773  *         as would satisfaction of the stopping test with strict
1774  *         inequality.
1775  *      4. We remove common factors of powers of 2 from relevant
1776  *         quantities.
1777  *      5. When converting floating-point integers less than 1e16,
1778  *         we use floating-point arithmetic rather than resorting
1779  *         to multiple-precision integers.
1780  *      6. When asked to produce fewer than 15 digits, we first try
1781  *         to get by with floating-point arithmetic; we resort to
1782  *         multiple-precision integer arithmetic only if we cannot
1783  *         guarantee that the floating-point calculation has given
1784  *         the correctly rounded result.  For k requested digits and
1785  *         "uniformly" distributed input, the probability is
1786  *         something like 10^(k-15) that we must resort to the Long
1787  *         calculation.
1788  */
1789
1790 #if 0
1791 char *
1792 __dtoa(double d, int mode, int ndigits, int *decpt, int *sign, char **rve,
1793          char **resultp)
1794 {
1795  /*     Arguments ndigits, decpt, sign are similar to those
1796         of ecvt and fcvt; trailing zeros are suppressed from
1797         the returned string.  If not null, *rve is set to point
1798         to the end of the return value.  If d is +-Infinity or NaN,
1799         then *decpt is set to 9999.
1800
1801         mode:
1802                 0 ==> shortest string that yields d when read in
1803                         and rounded to nearest.
1804                 1 ==> like 0, but with Steele & White stopping rule;
1805                         e.g. with IEEE P754 arithmetic , mode 0 gives
1806                         1e23 whereas mode 1 gives 9.999999999999999e22.
1807                 2 ==> max(1,ndigits) significant digits.  This gives a
1808                         return value similar to that of ecvt, except
1809                         that trailing zeros are suppressed.
1810                 3 ==> through ndigits past the decimal point.  This
1811                         gives a return value similar to that from fcvt,
1812                         except that trailing zeros are suppressed, and
1813                         ndigits can be negative.
1814                 4-9 should give the same return values as 2-3, i.e.,
1815                         4 <= mode <= 9 ==> same return as mode
1816                         2 + (mode & 1).  These modes are mainly for
1817                         debugging; often they run slower but sometimes
1818                         faster than modes 2-3.
1819                 4,5,8,9 ==> left-to-right digit generation.
1820                 6-9 ==> don't try fast floating-point estimate
1821                         (if applicable).
1822
1823                 Values of mode other than 0-9 are treated as mode 0.
1824
1825                 Sufficient space is allocated to the return value
1826                 to hold the suppressed trailing zeros.
1827         */
1828
1829         int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
1830                 j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
1831                 spec_case, try_quick;
1832         Long L;
1833 #ifndef Sudden_Underflow
1834         int denorm;
1835         ULong x;
1836 #endif
1837         Bigint *b, *b1, *delta, *mlo, *mhi, *S;
1838         double d2, ds, eps;
1839         char *s, *s0;
1840
1841         if (word0(d) & Sign_bit) {
1842                 /* set sign for everything, including 0's and NaNs */
1843                 *sign = 1;
1844                 word0(d) &= ~Sign_bit;  /* clear sign bit */
1845         }
1846         else
1847                 *sign = 0;
1848
1849 #if defined(IEEE_Arith) + defined(VAX)
1850 #ifdef IEEE_Arith
1851         if ((word0(d) & Exp_mask) == Exp_mask)
1852 #else
1853         if (word0(d)  == 0x8000)
1854 #endif
1855         {
1856                 /* Infinity or NaN */
1857                 *decpt = 9999;
1858                 s =
1859 #ifdef IEEE_Arith
1860                         !word1(d) && !(word0(d) & 0xfffff) ? "Infinity" :
1861 #endif
1862                                 "NaN";
1863                 if (rve)
1864                         *rve =
1865 #ifdef IEEE_Arith
1866                                 s[3] ? s + 8 :
1867 #endif
1868                                                 s + 3;
1869                 return s;
1870         }
1871 #endif
1872 #ifdef IBM
1873         d += 0; /* normalize */
1874 #endif
1875         if (!d) {
1876                 *decpt = 1;
1877                 s = "0";
1878                 if (rve)
1879                         *rve = s + 1;
1880                 return s;
1881         }
1882
1883         b = d2b(d, &be, &bbits);
1884 #ifdef Sudden_Underflow
1885         i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
1886 #else
1887         if ( (i = (int)((word0(d) >> Exp_shift1) & (Exp_mask>>Exp_shift1))) ) {
1888 #endif
1889                 d2 = d;
1890                 word0(d2) &= Frac_mask1;
1891                 word0(d2) |= Exp_11;
1892 #ifdef IBM
1893                 if ( (j = 11 - hi0bits(word0(d2) & Frac_mask)) )
1894                         d2 /= 1 << j;
1895 #endif
1896
1897                 /* log(x)       ~=~ log(1.5) + (x-1.5)/1.5
1898                  * log10(x)      =  log(x) / log(10)
1899                  *              ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
1900                  * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
1901                  *
1902                  * This suggests computing an approximation k to log10(d) by
1903                  *
1904                  * k = (i - Bias)*0.301029995663981
1905                  *      + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
1906                  *
1907                  * We want k to be too large rather than too small.
1908                  * The error in the first-order Taylor series approximation
1909                  * is in our favor, so we just round up the constant enough
1910                  * to compensate for any error in the multiplication of
1911                  * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
1912                  * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
1913                  * adding 1e-13 to the constant term more than suffices.
1914                  * Hence we adjust the constant term to 0.1760912590558.
1915                  * (We could get a more accurate k by invoking log10,
1916                  *  but this is probably not worthwhile.)
1917                  */
1918
1919                 i -= Bias;
1920 #ifdef IBM
1921                 i <<= 2;
1922                 i += j;
1923 #endif
1924 #ifndef Sudden_Underflow
1925                 denorm = 0;
1926         } else {
1927                 /* d is denormalized */
1928
1929                 i = bbits + be + (Bias + (P-1) - 1);
1930                 x = i > 32  ? ((word0(d) << (64 - i)) | (word1(d) >> (i - 32)))
1931                             : (word1(d) << (32 - i));
1932                 d2 = x;
1933                 word0(d2) -= 31*Exp_msk1; /* adjust exponent */
1934                 i -= (Bias + (P-1) - 1) + 1;
1935                 denorm = 1;
1936         }
1937 #endif
1938         ds = (d2-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
1939         k = (int)ds;
1940         if (ds < 0. && ds != k)
1941                 k--;    /* want k = floor(ds) */
1942         k_check = 1;
1943         if (k >= 0 && k <= Ten_pmax) {
1944                 if (d < tens[k])
1945                         k--;
1946                 k_check = 0;
1947         }
1948         j = bbits - i - 1;
1949         if (j >= 0) {
1950                 b2 = 0;
1951                 s2 = j;
1952         } else {
1953                 b2 = -j;
1954                 s2 = 0;
1955         }
1956         if (k >= 0) {
1957                 b5 = 0;
1958                 s5 = k;
1959                 s2 += k;
1960         } else {
1961                 b2 -= k;
1962                 b5 = -k;
1963                 s5 = 0;
1964         }
1965         if (mode < 0 || mode > 9)
1966                 mode = 0;
1967         try_quick = 1;
1968         if (mode > 5) {
1969                 mode -= 4;
1970                 try_quick = 0;
1971         }
1972         leftright = 1;
1973         switch(mode) {
1974                 case 0:
1975                 case 1:
1976                         ilim = ilim1 = -1;
1977                         i = 18;
1978                         ndigits = 0;
1979                         break;
1980                 case 2:
1981                         leftright = 0;
1982                         /* no break */
1983                 case 4:
1984                         if (ndigits <= 0)
1985                                 ndigits = 1;
1986                         ilim = ilim1 = i = ndigits;
1987                         break;
1988                 case 3:
1989                         leftright = 0;
1990                         /* no break */
1991                 case 5:
1992                         i = ndigits + k + 1;
1993                         ilim = i;
1994                         ilim1 = i - 1;
1995                         if (i <= 0)
1996                                 i = 1;
1997         }
1998         *resultp = (char *) malloc(i + 1);
1999         s = s0 = *resultp;
2000
2001         if (ilim >= 0 && ilim <= Quick_max && try_quick) {
2002
2003                 /* Try to get by with floating-point arithmetic. */
2004
2005                 i = 0;
2006                 d2 = d;
2007                 k0 = k;
2008                 ilim0 = ilim;
2009                 ieps = 2; /* conservative */
2010                 if (k > 0) {
2011                         ds = tens[k&0xf];
2012                         j = k >> 4;
2013                         if (j & Bletch) {
2014                                 /* prevent overflows */
2015                                 j &= Bletch - 1;
2016                                 d /= bigtens[n_bigtens-1];
2017                                 ieps++;
2018                         }
2019                         for (; j; j >>= 1, i++)
2020                                 if (j & 1) {
2021                                         ieps++;
2022                                         ds *= bigtens[i];
2023                                 }
2024                         d /= ds;
2025                 } else if ( (j1 = -k) ) {
2026                         d *= tens[j1 & 0xf];
2027                         for (j = j1 >> 4; j; j >>= 1, i++)
2028                                 if (j & 1) {
2029                                         ieps++;
2030                                         d *= bigtens[i];
2031                                 }
2032                 }
2033                 if (k_check && d < 1. && ilim > 0) {
2034                         if (ilim1 <= 0)
2035                                 goto fast_failed;
2036                         ilim = ilim1;
2037                         k--;
2038                         d *= 10.;
2039                         ieps++;
2040                 }
2041                 eps = ieps*d + 7.;
2042                 word0(eps) -= (P-1)*Exp_msk1;
2043                 if (ilim == 0) {
2044                         S = mhi = 0;
2045                         d -= 5.;
2046                         if (d > eps)
2047                                 goto one_digit;
2048                         if (d < -eps)
2049                                 goto no_digits;
2050                         goto fast_failed;
2051                 }
2052 #ifndef No_leftright
2053                 if (leftright) {
2054                         /* Use Steele & White method of only
2055                          * generating digits needed.
2056                          */
2057                         eps = 0.5/tens[ilim-1] - eps;
2058                         for (i = 0;;) {
2059                                 L = d;
2060                                 d -= L;
2061                                 *s++ = '0' + (int)L;
2062                                 if (d < eps)
2063                                         goto ret1;
2064                                 if (1. - d < eps)
2065                                         goto bump_up;
2066                                 if (++i >= ilim)
2067                                         break;
2068                                 eps *= 10.;
2069                                 d *= 10.;
2070                         }
2071                 } else {
2072 #endif
2073                         /* Generate ilim digits, then fix them up. */
2074                         eps *= tens[ilim-1];
2075                         for (i = 1;; i++, d *= 10.) {
2076                                 L = d;
2077                                 d -= L;
2078                                 *s++ = '0' + (int)L;
2079                                 if (i == ilim) {
2080                                         if (d > 0.5 + eps)
2081                                                 goto bump_up;
2082                                         else if (d < 0.5 - eps) {
2083                                                 while (*--s == '0');
2084                                                 s++;
2085                                                 goto ret1;
2086                                         }
2087                                         break;
2088                                 }
2089                         }
2090 #ifndef No_leftright
2091                 }
2092 #endif
2093  fast_failed:
2094                 s = s0;
2095                 d = d2;
2096                 k = k0;
2097                 ilim = ilim0;
2098         }
2099
2100         /* Do we have a "small" integer? */
2101
2102         if (be >= 0 && k <= Int_max) {
2103                 /* Yes. */
2104                 ds = tens[k];
2105                 if (ndigits < 0 && ilim <= 0) {
2106                         S = mhi = 0;
2107                         if (ilim < 0 || d <= 5*ds)
2108                                 goto no_digits;
2109                         goto one_digit;
2110                 }
2111                 for (i = 1;; i++) {
2112                         L = d / ds;
2113                         d -= L*ds;
2114 #ifdef Check_FLT_ROUNDS
2115                         /* If FLT_ROUNDS == 2, L will usually be high by 1 */
2116                         if (d < 0) {
2117                                 L--;
2118                                 d += ds;
2119                         }
2120 #endif
2121                         *s++ = '0' + (int)L;
2122                         if (i == ilim) {
2123                                 d += d;
2124                                 if (d > ds || (d == ds && L & 1)) {
2125  bump_up:
2126                                         while (*--s == '9')
2127                                                 if (s == s0) {
2128                                                         k++;
2129                                                         *s = '0';
2130                                                         break;
2131                                                 }
2132                                         ++*s++;
2133                                 }
2134                                 break;
2135                         }
2136                         if (!(d *= 10.))
2137                                 break;
2138                 }
2139                 goto ret1;
2140         }
2141
2142         m2 = b2;
2143         m5 = b5;
2144         mhi = mlo = 0;
2145         if (leftright) {
2146                 if (mode < 2) {
2147                         i =
2148 #ifndef Sudden_Underflow
2149                                 denorm ? be + (Bias + (P-1) - 1 + 1) :
2150 #endif
2151 #ifdef IBM
2152                                 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
2153 #else
2154                                 1 + P - bbits;
2155 #endif
2156                 } else {
2157                         j = ilim - 1;
2158                         if (m5 >= j)
2159                                 m5 -= j;
2160                         else {
2161                                 s5 += j -= m5;
2162                                 b5 += j;
2163                                 m5 = 0;
2164                         }
2165                         if ((i = ilim) < 0) {
2166                                 m2 -= i;
2167                                 i = 0;
2168                         }
2169                 }
2170                 b2 += i;
2171                 s2 += i;
2172                 mhi = i2b(1);
2173         }
2174         if (m2 > 0 && s2 > 0) {
2175                 i = m2 < s2 ? m2 : s2;
2176                 b2 -= i;
2177                 m2 -= i;
2178                 s2 -= i;
2179         }
2180         if (b5 > 0) {
2181                 if (leftright) {
2182                         if (m5 > 0) {
2183                                 mhi = pow5mult(mhi, m5);
2184                                 b1 = mult(mhi, b);
2185                                 Bfree(b);
2186                                 b = b1;
2187                                 }
2188                         if ( (j = b5 - m5) )
2189                                 b = pow5mult(b, j);
2190                 } else
2191                         b = pow5mult(b, b5);
2192         }
2193         S = i2b(1);
2194         if (s5 > 0)
2195                 S = pow5mult(S, s5);
2196
2197         /* Check for special case that d is a normalized power of 2. */
2198
2199         if (mode < 2) {
2200                 if (!word1(d) && !(word0(d) & Bndry_mask)
2201 #ifndef Sudden_Underflow
2202                  && word0(d) & Exp_mask
2203 #endif
2204                                 ) {
2205                         /* The special case */
2206                         b2 += Log2P;
2207                         s2 += Log2P;
2208                         spec_case = 1;
2209                 } else
2210                         spec_case = 0;
2211         }
2212
2213         /* Arrange for convenient computation of quotients:
2214          * shift left if necessary so divisor has 4 leading 0 bits.
2215          *
2216          * Perhaps we should just compute leading 28 bits of S once
2217          * and for all and pass them and a shift to quorem, so it
2218          * can do shifts and ors to compute the numerator for q.
2219          */
2220 #ifdef Pack_32
2221         if ( (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f) )
2222                 i = 32 - i;
2223 #else
2224         if ( (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf) )
2225                 i = 16 - i;
2226 #endif
2227         if (i > 4) {
2228                 i -= 4;
2229                 b2 += i;
2230                 m2 += i;
2231                 s2 += i;
2232         } else if (i < 4) {
2233                 i += 28;
2234                 b2 += i;
2235                 m2 += i;
2236                 s2 += i;
2237         }
2238         if (b2 > 0)
2239                 b = lshift(b, b2);
2240         if (s2 > 0)
2241                 S = lshift(S, s2);
2242         if (k_check) {
2243                 if (cmp(b,S) < 0) {
2244                         k--;
2245                         b = multadd(b, 10, 0);  /* we botched the k estimate */
2246                         if (leftright)
2247                                 mhi = multadd(mhi, 10, 0);
2248                         ilim = ilim1;
2249                 }
2250         }
2251         if (ilim <= 0 && mode > 2) {
2252                 if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
2253                         /* no digits, fcvt style */
2254  no_digits:
2255                         k = -1 - ndigits;
2256                         goto ret;
2257                 }
2258  one_digit:
2259                 *s++ = '1';
2260                 k++;
2261                 goto ret;
2262         }
2263         if (leftright) {
2264                 if (m2 > 0)
2265                         mhi = lshift(mhi, m2);
2266
2267                 /* Compute mlo -- check for special case
2268                  * that d is a normalized power of 2.
2269                  */
2270
2271                 mlo = mhi;
2272                 if (spec_case) {
2273                         mhi = Balloc(mhi->k);
2274                         Bcopy(mhi, mlo);
2275                         mhi = lshift(mhi, Log2P);
2276                 }
2277
2278                 for (i = 1;;i++) {
2279                         dig = quorem(b,S) + '0';
2280                         /* Do we yet have the shortest decimal string
2281                          * that will round to d?
2282                          */
2283                         j = cmp(b, mlo);
2284                         delta = diff(S, mhi);
2285                         j1 = delta->sign ? 1 : cmp(b, delta);
2286                         Bfree(delta);
2287 #ifndef ROUND_BIASED
2288                         if (j1 == 0 && !mode && !(word1(d) & 1)) {
2289                                 if (dig == '9')
2290                                         goto round_9_up;
2291                                 if (j > 0)
2292                                         dig++;
2293                                 *s++ = dig;
2294                                 goto ret;
2295                         }
2296 #endif
2297                         if (j < 0 || (j == 0 && !mode
2298 #ifndef ROUND_BIASED
2299                                                         && !(word1(d) & 1)
2300 #endif
2301                                         )) {
2302                                 if (j1 > 0) {
2303                                         b = lshift(b, 1);
2304                                         j1 = cmp(b, S);
2305                                         if ((j1 > 0 || (j1 == 0 && dig & 1))
2306                                         && dig++ == '9')
2307                                                 goto round_9_up;
2308                                 }
2309                                 *s++ = dig;
2310                                 goto ret;
2311                         }
2312                         if (j1 > 0) {
2313                                 if (dig == '9') { /* possible if i == 1 */
2314  round_9_up:
2315                                         *s++ = '9';
2316                                         goto roundoff;
2317                                 }
2318                                 *s++ = dig + 1;
2319                                 goto ret;
2320                         }
2321                         *s++ = dig;
2322                         if (i == ilim)
2323                                 break;
2324                         b = multadd(b, 10, 0);
2325                         if (mlo == mhi)
2326                                 mlo = mhi = multadd(mhi, 10, 0);
2327                         else {
2328                                 mlo = multadd(mlo, 10, 0);
2329                                 mhi = multadd(mhi, 10, 0);
2330                         }
2331                 }
2332         } else
2333                 for (i = 1;; i++) {
2334                         *s++ = dig = quorem(b,S) + '0';
2335                         if (i >= ilim)
2336                                 break;
2337                         b = multadd(b, 10, 0);
2338                 }
2339
2340         /* Round off last digit */
2341
2342         b = lshift(b, 1);
2343         j = cmp(b, S);
2344         if (j > 0 || (j == 0 && dig & 1)) {
2345  roundoff:
2346                 while (*--s == '9')
2347                         if (s == s0) {
2348                                 k++;
2349                                 *s++ = '1';
2350                                 goto ret;
2351                         }
2352                 ++*s++;
2353         } else {
2354                 while (*--s == '0');
2355                 s++;
2356         }
2357  ret:
2358         Bfree(S);
2359         if (mhi) {
2360                 if (mlo && mlo != mhi)
2361                         Bfree(mlo);
2362                 Bfree(mhi);
2363         }
2364  ret1:
2365         Bfree(b);
2366         if (s == s0) {  /* don't return empty string */
2367                 *s++ = '0';
2368                 k = 0;
2369         }
2370         *s = 0;
2371         *decpt = k + 1;
2372         if (rve)
2373                 *rve = s;
2374         return s0;
2375 }
2376 #endif  // 0 -> __dtoa() is removed from the build
2377
2378 #ifdef __cplusplus
2379 }
2380 #endif