js/src/dtoa.c

   1 /* -*- Mode: C; tab-width: 8; indent-tabs-mode: t; c-basic-offset: 8 -*- */
   2 /****************************************************************
   3  *
   4  * The author of this software is David M. Gay.
   5  *
   6  * Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
   7  *
   8  * Permission to use, copy, modify, and distribute this software for any
   9  * purpose without fee is hereby granted, provided that this entire notice
  10  * is included in all copies of any software which is or includes a copy
  11  * or modification of this software and in all copies of the supporting
  12  * documentation for such software.
  13  *
  14  * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
  15  * WARRANTY.  IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY
  16  * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
  17  * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
  18  *
  19  ***************************************************************/
  20
  21 /* Please send bug reports to David M. Gay (dmg at acm dot org,
  22  * with " at " changed at "@" and " dot " changed to ".").      */
  23
  24 /* On a machine with IEEE extended-precision registers, it is
  25  * necessary to specify double-precision (53-bit) rounding precision
  26  * before invoking strtod or dtoa.  If the machine uses (the equivalent
  27  * of) Intel 80x87 arithmetic, the call
  28  *      _control87(PC_53, MCW_PC);
  29  * does this with many compilers.  Whether this or another call is
  30  * appropriate depends on the compiler; for this to work, it may be
  31  * necessary to #include "float.h" or another system-dependent header
  32  * file.
  33  */
  34
  35 /* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
  36  *
  37  * This strtod returns a nearest machine number to the input decimal
  38  * string (or sets errno to ERANGE).  With IEEE arithmetic, ties are
  39  * broken by the IEEE round-even rule.  Otherwise ties are broken by
  40  * biased rounding (add half and chop).
  41  *
  42  * Inspired loosely by William D. Clinger's paper "How to Read Floating
  43  * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
  44  *
  45  * Modifications:
  46  *
  47  *      1. We only require IEEE, IBM, or VAX double-precision
  48  *              arithmetic (not IEEE double-extended).
  49  *      2. We get by with floating-point arithmetic in a case that
  50  *              Clinger missed -- when we're computing d * 10^n
  51  *              for a small integer d and the integer n is not too
  52  *              much larger than 22 (the maximum integer k for which
  53  *              we can represent 10^k exactly), we may be able to
  54  *              compute (d*10^k) * 10^(e-k) with just one roundoff.
  55  *      3. Rather than a bit-at-a-time adjustment of the binary
  56  *              result in the hard case, we use floating-point
  57  *              arithmetic to determine the adjustment to within
  58  *              one bit; only in really hard cases do we need to
  59  *              compute a second residual.
  60  *      4. Because of 3., we don't need a large table of powers of 10
  61  *              for ten-to-e (just some small tables, e.g. of 10^k
  62  *              for 0 <= k <= 22).
  63  */
  64
  65 /*
  66  * #define IEEE_8087 for IEEE-arithmetic machines where the least
  67  *      significant byte has the lowest address.
  68  * #define IEEE_MC68k for IEEE-arithmetic machines where the most
  69  *      significant byte has the lowest address.
  70  * #define Long int on machines with 32-bit ints and 64-bit longs.
  71  * #define IBM for IBM mainframe-style floating-point arithmetic.
  72  * #define VAX for VAX-style floating-point arithmetic (D_floating).
  73  * #define No_leftright to omit left-right logic in fast floating-point
  74  *      computation of dtoa.
  75  * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
  76  *      and strtod and dtoa should round accordingly.
  77  * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
  78  *      and Honor_FLT_ROUNDS is not #defined.
  79  * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
  80  *      that use extended-precision instructions to compute rounded
  81  *      products and quotients) with IBM.
  82  * #define ROUND_BIASED for IEEE-format with biased rounding.
  83  * #define Inaccurate_Divide for IEEE-format with correctly rounded
  84  *      products but inaccurate quotients, e.g., for Intel i860.
  85  * #define NO_LONG_LONG on machines that do not have a "long long"
  86  *      integer type (of >= 64 bits).  On such machines, you can
  87  *      #define Just_16 to store 16 bits per 32-bit Long when doing
  88  *      high-precision integer arithmetic.  Whether this speeds things
  89  *      up or slows things down depends on the machine and the number
  90  *      being converted.  If long long is available and the name is
  91  *      something other than "long long", #define Llong to be the name,
  92  *      and if "unsigned Llong" does not work as an unsigned version of
  93  *      Llong, #define #ULLong to be the corresponding unsigned type.
  94  * #define KR_headers for old-style C function headers.
  95  * #define Bad_float_h if your system lacks a float.h or if it does not
  96  *      define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
  97  *      FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
  98  * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
  99  *      if memory is available and otherwise does something you deem
 100  *      appropriate.  If MALLOC is undefined, malloc will be invoked
 101  *      directly -- and assumed always to succeed.  Similarly, if you
 102  *      want something other than the system's free() to be called to
 103  *      recycle memory acquired from MALLOC, #define FREE to be the
 104  *      name of the alternate routine.  (Unless you #define
 105  *      NO_GLOBAL_STATE and call destroydtoa, FREE or free is only
 106  *      called in pathological cases, e.g., in a dtoa call after a dtoa
 107  *      return in mode 3 with thousands of digits requested.)
 108  * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
 109  *      memory allocations from a private pool of memory when possible.
 110  *      When used, the private pool is PRIVATE_MEM bytes long:  2304 bytes,
 111  *      unless #defined to be a different length.  This default length
 112  *      suffices to get rid of MALLOC calls except for unusual cases,
 113  *      such as decimal-to-binary conversion of a very long string of
 114  *      digits.  The longest string dtoa can return is about 751 bytes
 115  *      long.  For conversions by strtod of strings of 800 digits and
 116  *      all dtoa conversions in single-threaded executions with 8-byte
 117  *      pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte
 118  *      pointers, PRIVATE_MEM >= 7112 appears adequate.
 119  * #define MULTIPLE_THREADS if the system offers preemptively scheduled
 120  *      multiple threads.  In this case, you must provide (or suitably
 121  *      #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
 122  *      by FREE_DTOA_LOCK(n) for n = 0 or 1.  (The second lock, accessed
 123  *      in pow5mult, ensures lazy evaluation of only one copy of high
 124  *      powers of 5; omitting this lock would introduce a small
 125  *      probability of wasting memory, but would otherwise be harmless.)
 126  *      You must also invoke freedtoa(s) to free the value s returned by
 127  *      dtoa.  You may do so whether or not MULTIPLE_THREADS is #defined.
 128  * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
 129  *      avoids underflows on inputs whose result does not underflow.
 130  *      If you #define NO_IEEE_Scale on a machine that uses IEEE-format
 131  *      floating-point numbers and flushes underflows to zero rather
 132  *      than implementing gradual underflow, then you must also #define
 133  *      Sudden_Underflow.
 134  * #define USE_LOCALE to use the current locale's decimal_point value.
 135  * #define SET_INEXACT if IEEE arithmetic is being used and extra
 136  *      computation should be done to set the inexact flag when the
 137  *      result is inexact and avoid setting inexact when the result
 138  *      is exact.  In this case, dtoa.c must be compiled in
 139  *      an environment, perhaps provided by #include "dtoa.c" in a
 140  *      suitable wrapper, that defines two functions,
 141  *              int get_inexact(void);
 142  *              void clear_inexact(void);
 143  *      such that get_inexact() returns a nonzero value if the
 144  *      inexact bit is already set, and clear_inexact() sets the
 145  *      inexact bit to 0.  When SET_INEXACT is #defined, strtod
 146  *      also does extra computations to set the underflow and overflow
 147  *      flags when appropriate (i.e., when the result is tiny and
 148  *      inexact or when it is a numeric value rounded to +-infinity).
 149  * #define NO_ERRNO if strtod should not assign errno = ERANGE when
 150  *      the result overflows to +-Infinity or underflows to 0.
 151  * #define NO_GLOBAL_STATE to avoid defining any non-const global or
 152  *      static variables. Instead the necessary state is stored in an
 153  *      opaque struct, DtoaState, a pointer to which must be passed to
 154  *      every entry point. Two new functions are added to the API:
 155  *              DtoaState *newdtoa(void);
 156  *              void destroydtoa(DtoaState *);
 157  */
 158
 159 #ifndef Long
 160 #define Long long
 161 #endif
 162 #ifndef ULong
 163 typedef unsigned Long ULong;
 164 #endif
 165
 166 #ifdef DEBUG
 167 #include "stdio.h"
 168 #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
 169 #endif
 170
 171 #include "stdlib.h"
 172 #include "string.h"
 173
 174 #ifdef USE_LOCALE
 175 #include "locale.h"
 176 #endif
 177
 178 #ifdef MALLOC
 179 #ifdef KR_headers
 180 extern char *MALLOC();
 181 #else
 182 extern void *MALLOC(size_t);
 183 #endif
 184 #else
 185 #define MALLOC malloc
 186 #endif
 187
 188 #ifndef FREE
 189 #define FREE free
 190 #endif
 191
 192 #ifndef Omit_Private_Memory
 193 #ifndef PRIVATE_MEM
 194 #define PRIVATE_MEM 2304
 195 #endif
 196 #define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
 197 #endif
 198
 199 #undef IEEE_Arith
 200 #undef Avoid_Underflow
 201 #ifdef IEEE_MC68k
 202 #define IEEE_Arith
 203 #endif
 204 #ifdef IEEE_8087
 205 #define IEEE_Arith
 206 #endif
 207
 208 #include "errno.h"
 209
 210 #ifdef Bad_float_h
 211
 212 #ifdef IEEE_Arith
 213 #define DBL_DIG 15
 214 #define DBL_MAX_10_EXP 308
 215 #define DBL_MAX_EXP 1024
 216 #define FLT_RADIX 2
 217 #endif /*IEEE_Arith*/
 218
 219 #ifdef IBM
 220 #define DBL_DIG 16
 221 #define DBL_MAX_10_EXP 75
 222 #define DBL_MAX_EXP 63
 223 #define FLT_RADIX 16
 224 #define DBL_MAX 7.2370055773322621e+75
 225 #endif
 226
 227 #ifdef VAX
 228 #define DBL_DIG 16
 229 #define DBL_MAX_10_EXP 38
 230 #define DBL_MAX_EXP 127
 231 #define FLT_RADIX 2
 232 #define DBL_MAX 1.7014118346046923e+38
 233 #endif
 234
 235 #ifndef LONG_MAX
 236 #define LONG_MAX 2147483647
 237 #endif
 238
 239 #else /* ifndef Bad_float_h */
 240 #include "float.h"
 241 #endif /* Bad_float_h */
 242
 243 #ifndef __MATH_H__
 244 #include "math.h"
 245 #endif
 246
 247 #ifdef __cplusplus
 248 extern "C" {
 249 #endif
 250
 251 #ifndef CONST
 252 #ifdef KR_headers
 253 #define CONST /* blank */
 254 #else
 255 #define CONST const
 256 #endif
 257 #endif
 258
 259 #if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
 260 Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
 261 #endif
 262
 263 typedef union { double d; ULong L[2]; } U;
 264
 265 #define dval(x) ((x).d)
 266 #ifdef IEEE_8087
 267 #define word0(x) ((x).L[1])
 268 #define word1(x) ((x).L[0])
 269 #else
 270 #define word0(x) ((x).L[0])
 271 #define word1(x) ((x).L[1])
 272 #endif
 273
 274 /* The following definition of Storeinc is appropriate for MIPS processors.
 275  * An alternative that might be better on some machines is
 276  * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
 277  */
 278 #if defined(IEEE_8087) + defined(VAX)
 279 #define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
 280 ((unsigned short *)a)[0] = (unsigned short)c, a++)
 281 #else
 282 #define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
 283 ((unsigned short *)a)[1] = (unsigned short)c, a++)
 284 #endif
 285
 286 /* #define P DBL_MANT_DIG */
 287 /* Ten_pmax = floor(P*log(2)/log(5)) */
 288 /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
 289 /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
 290 /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
 291
 292 #ifdef IEEE_Arith
 293 #define Exp_shift  20
 294 #define Exp_shift1 20
 295 #define Exp_msk1    0x100000
 296 #define Exp_msk11   0x100000
 297 #define Exp_mask  0x7ff00000
 298 #define P 53
 299 #define Bias 1023
 300 #define Emin (-1022)
 301 #define Exp_1  0x3ff00000
 302 #define Exp_11 0x3ff00000
 303 #define Ebits 11
 304 #define Frac_mask  0xfffff
 305 #define Frac_mask1 0xfffff
 306 #define Ten_pmax 22
 307 #define Bletch 0x10
 308 #define Bndry_mask  0xfffff
 309 #define Bndry_mask1 0xfffff
 310 #define LSB 1
 311 #define Sign_bit 0x80000000
 312 #define Log2P 1
 313 #define Tiny0 0
 314 #define Tiny1 1
 315 #define Quick_max 14
 316 #define Int_max 14
 317 #ifndef NO_IEEE_Scale
 318 #define Avoid_Underflow
 319 #ifdef Flush_Denorm     /* debugging option */
 320 #undef Sudden_Underflow
 321 #endif
 322 #endif
 323
 324 #ifndef Flt_Rounds
 325 #ifdef FLT_ROUNDS
 326 #define Flt_Rounds FLT_ROUNDS
 327 #else
 328 #define Flt_Rounds 1
 329 #endif
 330 #endif /*Flt_Rounds*/
 331
 332 #ifdef Honor_FLT_ROUNDS
 333 #define Rounding rounding
 334 #undef Check_FLT_ROUNDS
 335 #define Check_FLT_ROUNDS
 336 #else
 337 #define Rounding Flt_Rounds
 338 #endif
 339
 340 #else /* ifndef IEEE_Arith */
 341 #undef Check_FLT_ROUNDS
 342 #undef Honor_FLT_ROUNDS
 343 #undef SET_INEXACT
 344 #undef  Sudden_Underflow
 345 #define Sudden_Underflow
 346 #ifdef IBM
 347 #undef Flt_Rounds
 348 #define Flt_Rounds 0
 349 #define Exp_shift  24
 350 #define Exp_shift1 24
 351 #define Exp_msk1   0x1000000
 352 #define Exp_msk11  0x1000000
 353 #define Exp_mask  0x7f000000
 354 #define P 14
 355 #define Bias 65
 356 #define Exp_1  0x41000000
 357 #define Exp_11 0x41000000
 358 #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
 359 #define Frac_mask  0xffffff
 360 #define Frac_mask1 0xffffff
 361 #define Bletch 4
 362 #define Ten_pmax 22
 363 #define Bndry_mask  0xefffff
 364 #define Bndry_mask1 0xffffff
 365 #define LSB 1
 366 #define Sign_bit 0x80000000
 367 #define Log2P 4
 368 #define Tiny0 0x100000
 369 #define Tiny1 0
 370 #define Quick_max 14
 371 #define Int_max 15
 372 #else /* VAX */
 373 #undef Flt_Rounds
 374 #define Flt_Rounds 1
 375 #define Exp_shift  23
 376 #define Exp_shift1 7
 377 #define Exp_msk1    0x80
 378 #define Exp_msk11   0x800000
 379 #define Exp_mask  0x7f80
 380 #define P 56
 381 #define Bias 129
 382 #define Exp_1  0x40800000
 383 #define Exp_11 0x4080
 384 #define Ebits 8
 385 #define Frac_mask  0x7fffff
 386 #define Frac_mask1 0xffff007f
 387 #define Ten_pmax 24
 388 #define Bletch 2
 389 #define Bndry_mask  0xffff007f
 390 #define Bndry_mask1 0xffff007f
 391 #define LSB 0x10000
 392 #define Sign_bit 0x8000
 393 #define Log2P 1
 394 #define Tiny0 0x80
 395 #define Tiny1 0
 396 #define Quick_max 15
 397 #define Int_max 15
 398 #endif /* IBM, VAX */
 399 #endif /* IEEE_Arith */
 400
 401 #ifndef IEEE_Arith
 402 #define ROUND_BIASED
 403 #endif
 404
 405 #ifdef RND_PRODQUOT
 406 #define rounded_product(a,b) a = rnd_prod(a, b)
 407 #define rounded_quotient(a,b) a = rnd_quot(a, b)
 408 #ifdef KR_headers
 409 extern double rnd_prod(), rnd_quot();
 410 #else
 411 extern double rnd_prod(double, double), rnd_quot(double, double);
 412 #endif
 413 #else
 414 #define rounded_product(a,b) a *= b
 415 #define rounded_quotient(a,b) a /= b
 416 #endif
 417
 418 #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
 419 #define Big1 0xffffffff
 420
 421 #ifndef Pack_32
 422 #define Pack_32
 423 #endif
 424
 425 #ifdef KR_headers
 426 #define FFFFFFFF ((((unsigned long)0xffff)<<16)|(unsigned long)0xffff)
 427 #else
 428 #define FFFFFFFF 0xffffffffUL
 429 #endif
 430
 431 #ifdef NO_LONG_LONG
 432 #undef ULLong
 433 #ifdef Just_16
 434 #undef Pack_32
 435 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
 436  * This makes some inner loops simpler and sometimes saves work
 437  * during multiplications, but it often seems to make things slightly
 438  * slower.  Hence the default is now to store 32 bits per Long.
 439  */
 440 #endif
 441 #else   /* long long available */
 442 #ifndef Llong
 443 #define Llong long long
 444 #endif
 445 #ifndef ULLong
 446 #define ULLong unsigned Llong
 447 #endif
 448 #endif /* NO_LONG_LONG */
 449
 450 #ifndef MULTIPLE_THREADS
 451 #define ACQUIRE_DTOA_LOCK(n)    /*nothing*/
 452 #define FREE_DTOA_LOCK(n)       /*nothing*/
 453 #endif
 454
 455 #define Kmax 7
 456
 457  struct
 458 Bigint {
 459         struct Bigint *next;
 460         int k, maxwds, sign, wds;
 461         ULong x[1];
 462         };
 463
 464  typedef struct Bigint Bigint;
 465
 466 #ifdef NO_GLOBAL_STATE
 467 #ifdef MULTIPLE_THREADS
 468 #error "cannot have both NO_GLOBAL_STATE and MULTIPLE_THREADS"
 469 #endif
 470  struct
 471 DtoaState {
 472 #define DECLARE_GLOBAL_STATE  /* nothing */
 473 #else
 474 #define DECLARE_GLOBAL_STATE static
 475 #endif
 476
 477         DECLARE_GLOBAL_STATE Bigint *freelist[Kmax+1];
 478         DECLARE_GLOBAL_STATE Bigint *p5s;
 479 #ifndef Omit_Private_Memory
 480         DECLARE_GLOBAL_STATE double private_mem[PRIVATE_mem];
 481         DECLARE_GLOBAL_STATE double *pmem_next
 482 #ifndef NO_GLOBAL_STATE
 483                                                = private_mem
 484 #endif
 485                                                             ;
 486 #endif
 487 #ifdef NO_GLOBAL_STATE
 488         };
 489  typedef struct DtoaState DtoaState;
 490 #ifdef KR_headers
 491 #define STATE_PARAM state,
 492 #define STATE_PARAM_DECL DtoaState *state;
 493 #else
 494 #define STATE_PARAM DtoaState *state,
 495 #endif
 496 #define PASS_STATE state,
 497 #define GET_STATE(field) (state->field)
 498
 499  static DtoaState *
 500 newdtoa(void)
 501 {
 502         DtoaState *state = (DtoaState *) MALLOC(sizeof(DtoaState));
 503         if (state) {
 504                 memset(state, 0, sizeof(DtoaState));
 505 #ifndef Omit_Private_Memory
 506                 state->pmem_next = state->private_mem;
 507 #endif
 508                 }
 509         return state;
 510 }
 511
 512  static void
 513 destroydtoa
 514 #ifdef KR_headers
 515         (state) STATE_PARAM_DECL
 516 #else
 517         (DtoaState *state)
 518 #endif
 519 {
 520         int i;
 521         Bigint *v, *next;
 522
 523         for (i = 0; i <= Kmax; i++) {
 524                 for (v = GET_STATE(freelist)[i]; v; v = next) {
 525                         next = v->next;
 526 #ifndef Omit_Private_Memory
 527                         if ((double*)v < GET_STATE(private_mem) ||
 528                             (double*)v >= GET_STATE(private_mem) + PRIVATE_mem)
 529 #endif
 530                                 FREE((void*)v);
 531                         }
 532                 }
 533         FREE((void *)state);
 534 }
 535
 536 #else
 537 #define STATE_PARAM      /* nothing */
 538 #define STATE_PARAM_DECL /* nothing */
 539 #define PASS_STATE       /* nothing */
 540 #define GET_STATE(name) name
 541 #endif
 542
 543  static Bigint *
 544 Balloc
 545 #ifdef KR_headers
 546         (STATE_PARAM k) STATE_PARAM_DECL int k;
 547 #else
 548         (STATE_PARAM int k)
 549 #endif
 550 {
 551         int x;
 552         Bigint *rv;
 553 #ifndef Omit_Private_Memory
 554         size_t len;
 555 #endif
 556
 557         ACQUIRE_DTOA_LOCK(0);
 558         /* The k > Kmax case does not need ACQUIRE_DTOA_LOCK(0), */
 559         /* but this case seems very unlikely. */
 560         if (k <= Kmax && (rv = GET_STATE(freelist)[k]))
 561                 GET_STATE(freelist)[k] = rv->next;
 562         else {
 563                 x = 1 << k;
 564 #ifdef Omit_Private_Memory
 565                 rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
 566 #else
 567                 len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
 568                         /sizeof(double);
 569                 if (k <= Kmax && GET_STATE(pmem_next) - GET_STATE(private_mem) + len <= PRIVATE_mem) {
 570                         rv = (Bigint*)GET_STATE(pmem_next);
 571                         GET_STATE(pmem_next) += len;
 572                         }
 573                 else
 574                         rv = (Bigint*)MALLOC(len*sizeof(double));
 575 #endif
 576                 rv->k = k;
 577                 rv->maxwds = x;
 578                 }
 579         FREE_DTOA_LOCK(0);
 580         rv->sign = rv->wds = 0;
 581         return rv;
 582         }
 583
 584  static void
 585 Bfree
 586 #ifdef KR_headers
 587         (STATE_PARAM v) STATE_PARAM_DECL Bigint *v;
 588 #else
 589         (STATE_PARAM Bigint *v)
 590 #endif
 591 {
 592         if (v) {
 593                 if (v->k > Kmax)
 594                         FREE((void*)v);
 595                 else {
 596                         ACQUIRE_DTOA_LOCK(0);
 597                         v->next = GET_STATE(freelist)[v->k];
 598                         GET_STATE(freelist)[v->k] = v;
 599                         FREE_DTOA_LOCK(0);
 600                         }
 601                 }
 602         }
 603
 604 #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
 605 y->wds*sizeof(Long) + 2*sizeof(int))
 606
 607  static Bigint *
 608 multadd
 609 #ifdef KR_headers
 610         (STATE_PARAM b, m, a) STATE_PARAM_DECL Bigint *b; int m, a;
 611 #else
 612         (STATE_PARAM Bigint *b, int m, int a)   /* multiply by m and add a */
 613 #endif
 614 {
 615         int i, wds;
 616 #ifdef ULLong
 617         ULong *x;
 618         ULLong carry, y;
 619 #else
 620         ULong carry, *x, y;
 621 #ifdef Pack_32
 622         ULong xi, z;
 623 #endif
 624 #endif
 625         Bigint *b1;
 626
 627         wds = b->wds;
 628         x = b->x;
 629         i = 0;
 630         carry = a;
 631         do {
 632 #ifdef ULLong
 633                 y = *x * (ULLong)m + carry;
 634                 carry = y >> 32;
 635                 *x++ = (ULong) y & FFFFFFFF;
 636 #else
 637 #ifdef Pack_32
 638                 xi = *x;
 639                 y = (xi & 0xffff) * m + carry;
 640                 z = (xi >> 16) * m + (y >> 16);
 641                 carry = z >> 16;
 642                 *x++ = (z << 16) + (y & 0xffff);
 643 #else
 644                 y = *x * m + carry;
 645                 carry = y >> 16;
 646                 *x++ = y & 0xffff;
 647 #endif
 648 #endif
 649                 }
 650                 while(++i < wds);
 651         if (carry) {
 652                 if (wds >= b->maxwds) {
 653                         b1 = Balloc(PASS_STATE b->k+1);
 654                         Bcopy(b1, b);
 655                         Bfree(PASS_STATE b);
 656                         b = b1;
 657                         }
 658                 b->x[wds++] = (ULong) carry;
 659                 b->wds = wds;
 660                 }
 661         return b;
 662         }
 663
 664  static Bigint *
 665 s2b
 666 #ifdef KR_headers
 667         (STATE_PARAM s, nd0, nd, y9) STATE_PARAM_DECL CONST char *s; int nd0, nd; ULong y9;
 668 #else
 669         (STATE_PARAM CONST char *s, int nd0, int nd, ULong y9)
 670 #endif
 671 {
 672         Bigint *b;
 673         int i, k;
 674         Long x, y;
 675
 676         x = (nd + 8) / 9;
 677         for(k = 0, y = 1; x > y; y <<= 1, k++) ;
 678 #ifdef Pack_32
 679         b = Balloc(PASS_STATE k);
 680         b->x[0] = y9;
 681         b->wds = 1;
 682 #else
 683         b = Balloc(PASS_STATE k+1);
 684         b->x[0] = y9 & 0xffff;
 685         b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
 686 #endif
 687
 688         i = 9;
 689         if (9 < nd0) {
 690                 s += 9;
 691                 do b = multadd(PASS_STATE b, 10, *s++ - '0');
 692                         while(++i < nd0);
 693                 s++;
 694                 }
 695         else
 696                 s += 10;
 697         for(; i < nd; i++)
 698                 b = multadd(PASS_STATE b, 10, *s++ - '0');
 699         return b;
 700         }
 701
 702  static int
 703 hi0bits
 704 #ifdef KR_headers
 705         (x) register ULong x;
 706 #else
 707         (register ULong x)
 708 #endif
 709 {
 710         register int k = 0;
 711
 712         if (!(x & 0xffff0000)) {
 713                 k = 16;
 714                 x <<= 16;
 715                 }
 716         if (!(x & 0xff000000)) {
 717                 k += 8;
 718                 x <<= 8;
 719                 }
 720         if (!(x & 0xf0000000)) {
 721                 k += 4;
 722                 x <<= 4;
 723                 }
 724         if (!(x & 0xc0000000)) {
 725                 k += 2;
 726                 x <<= 2;
 727                 }
 728         if (!(x & 0x80000000)) {
 729                 k++;
 730                 if (!(x & 0x40000000))
 731                         return 32;
 732                 }
 733         return k;
 734         }
 735
 736  static int
 737 lo0bits
 738 #ifdef KR_headers
 739         (y) ULong *y;
 740 #else
 741         (ULong *y)
 742 #endif
 743 {
 744         register int k;
 745         register ULong x = *y;
 746
 747         if (x & 7) {
 748                 if (x & 1)
 749                         return 0;
 750                 if (x & 2) {
 751                         *y = x >> 1;
 752                         return 1;
 753                         }
 754                 *y = x >> 2;
 755                 return 2;
 756                 }
 757         k = 0;
 758         if (!(x & 0xffff)) {
 759                 k = 16;
 760                 x >>= 16;
 761                 }
 762         if (!(x & 0xff)) {
 763                 k += 8;
 764                 x >>= 8;
 765                 }
 766         if (!(x & 0xf)) {
 767                 k += 4;
 768                 x >>= 4;
 769                 }
 770         if (!(x & 0x3)) {
 771                 k += 2;
 772                 x >>= 2;
 773                 }
 774         if (!(x & 1)) {
 775                 k++;
 776                 x >>= 1;
 777                 if (!x)
 778                         return 32;
 779                 }
 780         *y = x;
 781         return k;
 782         }
 783
 784  static Bigint *
 785 i2b
 786 #ifdef KR_headers
 787         (STATE_PARAM i) STATE_PARAM_DECL int i;
 788 #else
 789         (STATE_PARAM int i)
 790 #endif
 791 {
 792         Bigint *b;
 793
 794         b = Balloc(PASS_STATE 1);
 795         b->x[0] = i;
 796         b->wds = 1;
 797         return b;
 798         }
 799
 800  static Bigint *
 801 mult
 802 #ifdef KR_headers
 803         (STATE_PARAM a, b) STATE_PARAM_DECL Bigint *a, *b;
 804 #else
 805         (STATE_PARAM Bigint *a, Bigint *b)
 806 #endif
 807 {
 808         Bigint *c;
 809         int k, wa, wb, wc;
 810         ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
 811         ULong y;
 812 #ifdef ULLong
 813         ULLong carry, z;
 814 #else
 815         ULong carry, z;
 816 #ifdef Pack_32
 817         ULong z2;
 818 #endif
 819 #endif
 820
 821         if (a->wds < b->wds) {
 822                 c = a;
 823                 a = b;
 824                 b = c;
 825                 }
 826         k = a->k;
 827         wa = a->wds;
 828         wb = b->wds;
 829         wc = wa + wb;
 830         if (wc > a->maxwds)
 831                 k++;
 832         c = Balloc(PASS_STATE k);
 833         for(x = c->x, xa = x + wc; x < xa; x++)
 834                 *x = 0;
 835         xa = a->x;
 836         xae = xa + wa;
 837         xb = b->x;
 838         xbe = xb + wb;
 839         xc0 = c->x;
 840 #ifdef ULLong
 841         for(; xb < xbe; xc0++) {
 842                 if ((y = *xb++)) {
 843                         x = xa;
 844                         xc = xc0;
 845                         carry = 0;
 846                         do {
 847                                 z = *x++ * (ULLong)y + *xc + carry;
 848                                 carry = z >> 32;
 849                                 *xc++ = (ULong) z & FFFFFFFF;
 850                                 }
 851                                 while(x < xae);
 852                         *xc = (ULong) carry;
 853                         }
 854                 }
 855 #else
 856 #ifdef Pack_32
 857         for(; xb < xbe; xb++, xc0++) {
 858                 if (y = *xb & 0xffff) {
 859                         x = xa;
 860                         xc = xc0;
 861                         carry = 0;
 862                         do {
 863                                 z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
 864                                 carry = z >> 16;
 865                                 z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
 866                                 carry = z2 >> 16;
 867                                 Storeinc(xc, z2, z);
 868                                 }
 869                                 while(x < xae);
 870                         *xc = carry;
 871                         }
 872                 if (y = *xb >> 16) {
 873                         x = xa;
 874                         xc = xc0;
 875                         carry = 0;
 876                         z2 = *xc;
 877                         do {
 878                                 z = (*x & 0xffff) * y + (*xc >> 16) + carry;
 879                                 carry = z >> 16;
 880                                 Storeinc(xc, z, z2);
 881                                 z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
 882                                 carry = z2 >> 16;
 883                                 }
 884                                 while(x < xae);
 885                         *xc = z2;
 886                         }
 887                 }
 888 #else
 889         for(; xb < xbe; xc0++) {
 890                 if (y = *xb++) {
 891                         x = xa;
 892                         xc = xc0;
 893                         carry = 0;
 894                         do {
 895                                 z = *x++ * y + *xc + carry;
 896                                 carry = z >> 16;
 897                                 *xc++ = z & 0xffff;
 898                                 }
 899                                 while(x < xae);
 900                         *xc = carry;
 901                         }
 902                 }
 903 #endif
 904 #endif
 905         for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
 906         c->wds = wc;
 907         return c;
 908         }
 909
 910  static Bigint *
 911 pow5mult
 912 #ifdef KR_headers
 913         (STATE_PARAM b, k) STATE_PARAM_DECL Bigint *b; int k;
 914 #else
 915         (STATE_PARAM Bigint *b, int k)
 916 #endif
 917 {
 918         Bigint *b1, *p5, *p51;
 919         int i;
 920         static CONST int p05[3] = { 5, 25, 125 };
 921
 922         if ((i = k & 3))
 923                 b = multadd(PASS_STATE b, p05[i-1], 0);
 924
 925         if (!(k >>= 2))
 926                 return b;
 927         if (!(p5 = GET_STATE(p5s))) {
 928                 /* first time */
 929 #ifdef MULTIPLE_THREADS
 930                 ACQUIRE_DTOA_LOCK(1);
 931                 if (!(p5 = p5s)) {
 932                         p5 = p5s = i2b(625);
 933                         p5->next = 0;
 934                         }
 935                 FREE_DTOA_LOCK(1);
 936 #else
 937                 p5 = GET_STATE(p5s) = i2b(PASS_STATE 625);
 938                 p5->next = 0;
 939 #endif
 940                 }
 941         for(;;) {
 942                 if (k & 1) {
 943                         b1 = mult(PASS_STATE b, p5);
 944                         Bfree(PASS_STATE b);
 945                         b = b1;
 946                         }
 947                 if (!(k >>= 1))
 948                         break;
 949                 if (!(p51 = p5->next)) {
 950 #ifdef MULTIPLE_THREADS
 951                         ACQUIRE_DTOA_LOCK(1);
 952                         if (!(p51 = p5->next)) {
 953                                 p51 = p5->next = mult(p5,p5);
 954                                 p51->next = 0;
 955                                 }
 956                         FREE_DTOA_LOCK(1);
 957 #else
 958                         p51 = p5->next = mult(PASS_STATE p5,p5);
 959                         p51->next = 0;
 960 #endif
 961                         }
 962                 p5 = p51;
 963                 }
 964         return b;
 965         }
 966
 967  static Bigint *
 968 lshift
 969 #ifdef KR_headers
 970         (STATE_PARAM b, k) STATE_PARAM_DECL Bigint *b; int k;
 971 #else
 972         (STATE_PARAM Bigint *b, int k)
 973 #endif
 974 {
 975         int i, k1, n, n1;
 976         Bigint *b1;
 977         ULong *x, *x1, *xe, z;
 978
 979 #ifdef Pack_32
 980         n = k >> 5;
 981 #else
 982         n = k >> 4;
 983 #endif
 984         k1 = b->k;
 985         n1 = n + b->wds + 1;
 986         for(i = b->maxwds; n1 > i; i <<= 1)
 987                 k1++;
 988         b1 = Balloc(PASS_STATE k1);
 989         x1 = b1->x;
 990         for(i = 0; i < n; i++)
 991                 *x1++ = 0;
 992         x = b->x;
 993         xe = x + b->wds;
 994 #ifdef Pack_32
 995         if (k &= 0x1f) {
 996                 k1 = 32 - k;
 997                 z = 0;
 998                 do {
 999                         *x1++ = *x << k | z;
1000                         z = *x++ >> k1;
1001                         }
1002                         while(x < xe);
1003                 if ((*x1 = z))
1004                         ++n1;
1005                 }
1006 #else
1007         if (k &= 0xf) {
1008                 k1 = 16 - k;
1009                 z = 0;
1010                 do {
1011                         *x1++ = *x << k  & 0xffff | z;
1012                         z = *x++ >> k1;
1013                         }
1014                         while(x < xe);
1015                 if (*x1 = z)
1016                         ++n1;
1017                 }
1018 #endif
1019         else do
1020                 *x1++ = *x++;
1021                 while(x < xe);
1022         b1->wds = n1 - 1;
1023         Bfree(PASS_STATE b);
1024         return b1;
1025         }
1026
1027  static int
1028 cmp
1029 #ifdef KR_headers
1030         (a, b) Bigint *a, *b;
1031 #else
1032         (Bigint *a, Bigint *b)
1033 #endif
1034 {
1035         ULong *xa, *xa0, *xb, *xb0;
1036         int i, j;
1037
1038         i = a->wds;
1039         j = b->wds;
1040 #ifdef DEBUG
1041         if (i > 1 && !a->x[i-1])
1042                 Bug("cmp called with a->x[a->wds-1] == 0");
1043         if (j > 1 && !b->x[j-1])
1044                 Bug("cmp called with b->x[b->wds-1] == 0");
1045 #endif
1046         if (i -= j)
1047                 return i;
1048         xa0 = a->x;
1049         xa = xa0 + j;
1050         xb0 = b->x;
1051         xb = xb0 + j;
1052         for(;;) {
1053                 if (*--xa != *--xb)
1054                         return *xa < *xb ? -1 : 1;
1055                 if (xa <= xa0)
1056                         break;
1057                 }
1058         return 0;
1059         }
1060
1061  static Bigint *
1062 diff
1063 #ifdef KR_headers
1064         (STATE_PARAM a, b) STATE_PARAM_DECL Bigint *a, *b;
1065 #else
1066         (STATE_PARAM Bigint *a, Bigint *b)
1067 #endif
1068 {
1069         Bigint *c;
1070         int i, wa, wb;
1071         ULong *xa, *xae, *xb, *xbe, *xc;
1072 #ifdef ULLong
1073         ULLong borrow, y;
1074 #else
1075         ULong borrow, y;
1076 #ifdef Pack_32
1077         ULong z;
1078 #endif
1079 #endif
1080
1081         i = cmp(a,b);
1082         if (!i) {
1083                 c = Balloc(PASS_STATE 0);
1084                 c->wds = 1;
1085                 c->x[0] = 0;
1086                 return c;
1087                 }
1088         if (i < 0) {
1089                 c = a;
1090                 a = b;
1091                 b = c;
1092                 i = 1;
1093                 }
1094         else
1095                 i = 0;
1096         c = Balloc(PASS_STATE a->k);
1097         c->sign = i;
1098         wa = a->wds;
1099         xa = a->x;
1100         xae = xa + wa;
1101         wb = b->wds;
1102         xb = b->x;
1103         xbe = xb + wb;
1104         xc = c->x;
1105         borrow = 0;
1106 #ifdef ULLong
1107         do {
1108                 y = (ULLong)*xa++ - *xb++ - borrow;
1109                 borrow = y >> 32 & (ULong)1;
1110                 *xc++ = (ULong) y & FFFFFFFF;
1111                 }
1112                 while(xb < xbe);
1113         while(xa < xae) {
1114                 y = *xa++ - borrow;
1115                 borrow = y >> 32 & (ULong)1;
1116                 *xc++ = (ULong) y & FFFFFFFF;
1117                 }
1118 #else
1119 #ifdef Pack_32
1120         do {
1121                 y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
1122                 borrow = (y & 0x10000) >> 16;
1123                 z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
1124                 borrow = (z & 0x10000) >> 16;
1125                 Storeinc(xc, z, y);
1126                 }
1127                 while(xb < xbe);
1128         while(xa < xae) {
1129                 y = (*xa & 0xffff) - borrow;
1130                 borrow = (y & 0x10000) >> 16;
1131                 z = (*xa++ >> 16) - borrow;
1132                 borrow = (z & 0x10000) >> 16;
1133                 Storeinc(xc, z, y);
1134                 }
1135 #else
1136         do {
1137                 y = *xa++ - *xb++ - borrow;
1138                 borrow = (y & 0x10000) >> 16;
1139                 *xc++ = y & 0xffff;
1140                 }
1141                 while(xb < xbe);
1142         while(xa < xae) {
1143                 y = *xa++ - borrow;
1144                 borrow = (y & 0x10000) >> 16;
1145                 *xc++ = y & 0xffff;
1146                 }
1147 #endif
1148 #endif
1149         while(!*--xc)
1150                 wa--;
1151         c->wds = wa;
1152         return c;
1153         }
1154
1155  static double
1156 ulp
1157 #ifdef KR_headers
1158         (x) U x;
1159 #else
1160         (U x)
1161 #endif
1162 {
1163         register Long L;
1164         U a;
1165
1166         L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
1167 #ifndef Avoid_Underflow
1168 #ifndef Sudden_Underflow
1169         if (L > 0) {
1170 #endif
1171 #endif
1172 #ifdef IBM
1173                 L |= Exp_msk1 >> 4;
1174 #endif
1175                 word0(a) = L;
1176                 word1(a) = 0;
1177 #ifndef Avoid_Underflow
1178 #ifndef Sudden_Underflow
1179                 }
1180         else {
1181                 L = -L >> Exp_shift;
1182                 if (L < Exp_shift) {
1183                         word0(a) = 0x80000 >> L;
1184                         word1(a) = 0;
1185                         }
1186                 else {
1187                         word0(a) = 0;
1188                         L -= Exp_shift;
1189                         word1(a) = L >= 31 ? 1 : 1 << 31 - L;
1190                         }
1191                 }
1192 #endif
1193 #endif
1194         return dval(a);
1195         }
1196
1197  static double
1198 b2d
1199 #ifdef KR_headers
1200         (a, e) Bigint *a; int *e;
1201 #else
1202         (Bigint *a, int *e)
1203 #endif
1204 {
1205         ULong *xa, *xa0, w, y, z;
1206         int k;
1207         U d;
1208 #ifdef VAX
1209         ULong d0, d1;
1210 #else
1211 #define d0 word0(d)
1212 #define d1 word1(d)
1213 #endif
1214
1215         xa0 = a->x;
1216         xa = xa0 + a->wds;
1217         y = *--xa;
1218 #ifdef DEBUG
1219         if (!y) Bug("zero y in b2d");
1220 #endif
1221         k = hi0bits(y);
1222         *e = 32 - k;
1223 #ifdef Pack_32
1224         if (k < Ebits) {
1225                 d0 = Exp_1 | y >> (Ebits - k);
1226                 w = xa > xa0 ? *--xa : 0;
1227                 d1 = y << ((32-Ebits) + k) | w >> (Ebits - k);
1228                 goto ret_d;
1229                 }
1230         z = xa > xa0 ? *--xa : 0;
1231         if (k -= Ebits) {
1232                 d0 = Exp_1 | y << k | z >> (32 - k);
1233                 y = xa > xa0 ? *--xa : 0;
1234                 d1 = z << k | y >> (32 - k);
1235                 }
1236         else {
1237                 d0 = Exp_1 | y;
1238                 d1 = z;
1239                 }
1240 #else
1241         if (k < Ebits + 16) {
1242                 z = xa > xa0 ? *--xa : 0;
1243                 d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
1244                 w = xa > xa0 ? *--xa : 0;
1245                 y = xa > xa0 ? *--xa : 0;
1246                 d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
1247                 goto ret_d;
1248                 }
1249         z = xa > xa0 ? *--xa : 0;
1250         w = xa > xa0 ? *--xa : 0;
1251         k -= Ebits + 16;
1252         d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
1253         y = xa > xa0 ? *--xa : 0;
1254         d1 = w << k + 16 | y << k;
1255 #endif
1256  ret_d:
1257 #ifdef VAX
1258         word0(d) = d0 >> 16 | d0 << 16;
1259         word1(d) = d1 >> 16 | d1 << 16;
1260 #else
1261 #undef d0
1262 #undef d1
1263 #endif
1264         return dval(d);
1265         }
1266
1267  static Bigint *
1268 d2b
1269 #ifdef KR_headers
1270         (STATE_PARAM d, e, bits) STATE_PARAM_DECL U d; int *e, *bits;
1271 #else
1272         (STATE_PARAM U d, int *e, int *bits)
1273 #endif
1274 {
1275         Bigint *b;
1276         int de, k;
1277         ULong *x, y, z;
1278 #ifndef Sudden_Underflow
1279         int i;
1280 #endif
1281 #ifdef VAX
1282         ULong d0, d1;
1283         d0 = word0(d) >> 16 | word0(d) << 16;
1284         d1 = word1(d) >> 16 | word1(d) << 16;
1285 #else
1286 #define d0 word0(d)
1287 #define d1 word1(d)
1288 #endif
1289
1290 #ifdef Pack_32
1291         b = Balloc(PASS_STATE 1);
1292 #else
1293         b = Balloc(PASS_STATE 2);
1294 #endif
1295         x = b->x;
1296
1297         z = d0 & Frac_mask;
1298         d0 &= 0x7fffffff;       /* clear sign bit, which we ignore */
1299 #ifdef Sudden_Underflow
1300         de = (int)(d0 >> Exp_shift);
1301 #ifndef IBM
1302         z |= Exp_msk11;
1303 #endif
1304 #else
1305         if ((de = (int)(d0 >> Exp_shift)))
1306                 z |= Exp_msk1;
1307 #endif
1308 #ifdef Pack_32
1309         if ((y = d1)) {
1310                 if ((k = lo0bits(&y))) {
1311                         x[0] = y | z << (32 - k);
1312                         z >>= k;
1313                         }
1314                 else
1315                         x[0] = y;
1316 #ifndef Sudden_Underflow
1317                 i =
1318 #endif
1319                     b->wds = (x[1] = z) ? 2 : 1;
1320                 }
1321         else {
1322                 k = lo0bits(&z);
1323                 x[0] = z;
1324 #ifndef Sudden_Underflow
1325                 i =
1326 #endif
1327                     b->wds = 1;
1328                 k += 32;
1329                 }
1330 #else
1331         if (y = d1) {
1332                 if (k = lo0bits(&y))
1333                         if (k >= 16) {
1334                                 x[0] = y | z << 32 - k & 0xffff;
1335                                 x[1] = z >> k - 16 & 0xffff;
1336                                 x[2] = z >> k;
1337                                 i = 2;
1338                                 }
1339                         else {
1340                                 x[0] = y & 0xffff;
1341                                 x[1] = y >> 16 | z << 16 - k & 0xffff;
1342                                 x[2] = z >> k & 0xffff;
1343                                 x[3] = z >> k+16;
1344                                 i = 3;
1345                                 }
1346                 else {
1347                         x[0] = y & 0xffff;
1348                         x[1] = y >> 16;
1349                         x[2] = z & 0xffff;
1350                         x[3] = z >> 16;
1351                         i = 3;
1352                         }
1353                 }
1354         else {
1355 #ifdef DEBUG
1356                 if (!z)
1357                         Bug("Zero passed to d2b");
1358 #endif
1359                 k = lo0bits(&z);
1360                 if (k >= 16) {
1361                         x[0] = z;
1362                         i = 0;
1363                         }
1364                 else {
1365                         x[0] = z & 0xffff;
1366                         x[1] = z >> 16;
1367                         i = 1;
1368                         }
1369                 k += 32;
1370                 }
1371         while(!x[i])
1372                 --i;
1373         b->wds = i + 1;
1374 #endif
1375 #ifndef Sudden_Underflow
1376         if (de) {
1377 #endif
1378 #ifdef IBM
1379                 *e = (de - Bias - (P-1) << 2) + k;
1380                 *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
1381 #else
1382                 *e = de - Bias - (P-1) + k;
1383                 *bits = P - k;
1384 #endif
1385 #ifndef Sudden_Underflow
1386                 }
1387         else {
1388                 *e = de - Bias - (P-1) + 1 + k;
1389 #ifdef Pack_32
1390                 *bits = 32*i - hi0bits(x[i-1]);
1391 #else
1392                 *bits = (i+2)*16 - hi0bits(x[i]);
1393 #endif
1394                 }
1395 #endif
1396         return b;
1397         }
1398 #undef d0
1399 #undef d1
1400
1401  static double
1402 ratio
1403 #ifdef KR_headers
1404         (a, b) Bigint *a, *b;
1405 #else
1406         (Bigint *a, Bigint *b)
1407 #endif
1408 {
1409         U da, db;
1410         int k, ka, kb;
1411
1412         dval(da) = b2d(a, &ka);
1413         dval(db) = b2d(b, &kb);
1414 #ifdef Pack_32
1415         k = ka - kb + 32*(a->wds - b->wds);
1416 #else
1417         k = ka - kb + 16*(a->wds - b->wds);
1418 #endif
1419 #ifdef IBM
1420         if (k > 0) {
1421                 word0(da) += (k >> 2)*Exp_msk1;
1422                 if (k &= 3)
1423                         dval(da) *= 1 << k;
1424                 }
1425         else {
1426                 k = -k;
1427                 word0(db) += (k >> 2)*Exp_msk1;
1428                 if (k &= 3)
1429                         dval(db) *= 1 << k;
1430                 }
1431 #else
1432         if (k > 0)
1433                 word0(da) += k*Exp_msk1;
1434         else {
1435                 k = -k;
1436                 word0(db) += k*Exp_msk1;
1437                 }
1438 #endif
1439         return dval(da) / dval(db);
1440         }
1441
1442  static CONST double
1443 tens[] = {
1444                 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1445                 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1446                 1e20, 1e21, 1e22
1447 #ifdef VAX
1448                 , 1e23, 1e24
1449 #endif
1450                 };
1451
1452  static CONST double
1453 #ifdef IEEE_Arith
1454 bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
1455 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
1456 #ifdef Avoid_Underflow
1457                 9007199254740992.*9007199254740992.e-256
1458                 /* = 2^106 * 1e-53 */
1459 #else
1460                 1e-256
1461 #endif
1462                 };
1463 /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
1464 /* flag unnecessarily.  It leads to a song and dance at the end of strtod. */
1465 #define Scale_Bit 0x10
1466 #define n_bigtens 5
1467 #else
1468 #ifdef IBM
1469 bigtens[] = { 1e16, 1e32, 1e64 };
1470 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
1471 #define n_bigtens 3
1472 #else
1473 bigtens[] = { 1e16, 1e32 };
1474 static CONST double tinytens[] = { 1e-16, 1e-32 };
1475 #define n_bigtens 2
1476 #endif
1477 #endif
1478
1479  static double
1480 _strtod
1481 #ifdef KR_headers
1482         (STATE_PARAM s00, se) STATE_PARAM_DECL CONST char *s00; char **se;
1483 #else
1484         (STATE_PARAM CONST char *s00, char **se)
1485 #endif
1486 {
1487 #ifdef Avoid_Underflow
1488         int scale;
1489 #endif
1490         int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
1491                  e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
1492         CONST char *s, *s0, *s1;
1493         double aadj, adj;
1494         U aadj1, rv, rv0;
1495         Long L;
1496         ULong y, z;
1497         Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
1498 #ifdef SET_INEXACT
1499         int inexact, oldinexact;
1500 #endif
1501 #ifdef Honor_FLT_ROUNDS
1502         int rounding;
1503 #endif
1504 #ifdef USE_LOCALE
1505         CONST char *s2;
1506 #endif
1507
1508 #ifdef __GNUC__
1509         delta = bb = bd = bs = 0;
1510 #endif
1511
1512         sign = nz0 = nz = 0;
1513         dval(rv) = 0.;
1514         for(s = s00;;s++) switch(*s) {
1515                 case '-':
1516                         sign = 1;
1517                         /* no break */
1518                 case '+':
1519                         if (*++s)
1520                                 goto break2;
1521                         /* no break */
1522                 case 0:
1523                         goto ret0;
1524                 case '\t':
1525                 case '\n':
1526                 case '\v':
1527                 case '\f':
1528                 case '\r':
1529                 case ' ':
1530                         continue;
1531                 default:
1532                         goto break2;
1533                 }
1534  break2:
1535         if (*s == '0') {
1536                 nz0 = 1;
1537                 while(*++s == '0') ;
1538                 if (!*s)
1539                         goto ret;
1540                 }
1541         s0 = s;
1542         y = z = 0;
1543         for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
1544                 if (nd < 9)
1545                         y = 10*y + c - '0';
1546                 else if (nd < 16)
1547                         z = 10*z + c - '0';
1548         nd0 = nd;
1549 #ifdef USE_LOCALE
1550         s1 = localeconv()->decimal_point;
1551         if (c == *s1) {
1552                 c = '.';
1553                 if (*++s1) {
1554                         s2 = s;
1555                         for(;;) {
1556                                 if (*++s2 != *s1) {
1557                                         c = 0;
1558                                         break;
1559                                         }
1560                                 if (!*++s1) {
1561                                         s = s2;
1562                                         break;
1563                                         }
1564                                 }
1565                         }
1566                 }
1567 #endif
1568         if (c == '.') {
1569                 c = *++s;
1570                 if (!nd) {
1571                         for(; c == '0'; c = *++s)
1572                                 nz++;
1573                         if (c > '0' && c <= '9') {
1574                                 s0 = s;
1575                                 nf += nz;
1576                                 nz = 0;
1577                                 goto have_dig;
1578                                 }
1579                         goto dig_done;
1580                         }
1581                 for(; c >= '0' && c <= '9'; c = *++s) {
1582  have_dig:
1583                         nz++;
1584                         if (c -= '0') {
1585                                 nf += nz;
1586                                 for(i = 1; i < nz; i++)
1587                                         if (nd++ < 9)
1588                                                 y *= 10;
1589                                         else if (nd <= DBL_DIG + 1)
1590                                                 z *= 10;
1591                                 if (nd++ < 9)
1592                                         y = 10*y + c;
1593                                 else if (nd <= DBL_DIG + 1)
1594                                         z = 10*z + c;
1595                                 nz = 0;
1596                                 }
1597                         }
1598                 }
1599  dig_done:
1600         e = 0;
1601         if (c == 'e' || c == 'E') {
1602                 if (!nd && !nz && !nz0) {
1603                         goto ret0;
1604                         }
1605                 s00 = s;
1606                 esign = 0;
1607                 switch(c = *++s) {
1608                         case '-':
1609                                 esign = 1;
1610                         case '+':
1611                                 c = *++s;
1612                         }
1613                 if (c >= '0' && c <= '9') {
1614                         while(c == '0')
1615                                 c = *++s;
1616                         if (c > '0' && c <= '9') {
1617                                 L = c - '0';
1618                                 s1 = s;
1619                                 while((c = *++s) >= '0' && c <= '9')
1620                                         L = 10*L + c - '0';
1621                                 if (s - s1 > 8 || L > 19999)
1622                                         /* Avoid confusion from exponents
1623                                          * so large that e might overflow.
1624                                          */
1625                                         e = 19999; /* safe for 16 bit ints */
1626                                 else
1627                                         e = (int)L;
1628                                 if (esign)
1629                                         e = -e;
1630                                 }
1631                         else
1632                                 e = 0;
1633                         }
1634                 else
1635                         s = s00;
1636                 }
1637         if (!nd) {
1638                 if (!nz && !nz0) {
1639  ret0:
1640                         s = s00;
1641                         sign = 0;
1642                         }
1643                 goto ret;
1644                 }
1645         e1 = e -= nf;
1646
1647         /* Now we have nd0 digits, starting at s0, followed by a
1648          * decimal point, followed by nd-nd0 digits.  The number we're
1649          * after is the integer represented by those digits times
1650          * 10**e */
1651
1652         if (!nd0)
1653                 nd0 = nd;
1654         k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
1655         dval(rv) = y;
1656         if (k > 9) {
1657 #ifdef SET_INEXACT
1658                 if (k > DBL_DIG)
1659                         oldinexact = get_inexact();
1660 #endif
1661                 dval(rv) = tens[k - 9] * dval(rv) + z;
1662                 }
1663         bd0 = 0;
1664         if (nd <= DBL_DIG
1665 #ifndef RND_PRODQUOT
1666 #ifndef Honor_FLT_ROUNDS
1667                 && Flt_Rounds == 1
1668 #endif
1669 #endif
1670                         ) {
1671                 if (!e)
1672                         goto ret;
1673                 if (e > 0) {
1674                         if (e <= Ten_pmax) {
1675 #ifdef VAX
1676                                 goto vax_ovfl_check;
1677 #else
1678 #ifdef Honor_FLT_ROUNDS
1679                                 /* round correctly FLT_ROUNDS = 2 or 3 */
1680                                 if (sign) {
1681                                         rv = -rv;
1682                                         sign = 0;
1683                                         }
1684 #endif
1685                                 /* rv = */ rounded_product(dval(rv), tens[e]);
1686                                 goto ret;
1687 #endif
1688                                 }
1689                         i = DBL_DIG - nd;
1690                         if (e <= Ten_pmax + i) {
1691                                 /* A fancier test would sometimes let us do
1692                                  * this for larger i values.
1693                                  */
1694 #ifdef Honor_FLT_ROUNDS
1695                                 /* round correctly FLT_ROUNDS = 2 or 3 */
1696                                 if (sign) {
1697                                         rv = -rv;
1698                                         sign = 0;
1699                                         }
1700 #endif
1701                                 e -= i;
1702                                 dval(rv) *= tens[i];
1703 #ifdef VAX
1704                                 /* VAX exponent range is so narrow we must
1705                                  * worry about overflow here...
1706                                  */
1707  vax_ovfl_check:
1708                                 word0(rv) -= P*Exp_msk1;
1709                                 /* rv = */ rounded_product(dval(rv), tens[e]);
1710                                 if ((word0(rv) & Exp_mask)
1711                                  > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
1712                                         goto ovfl;
1713                                 word0(rv) += P*Exp_msk1;
1714 #else
1715                                 /* rv = */ rounded_product(dval(rv), tens[e]);
1716 #endif
1717                                 goto ret;
1718                                 }
1719                         }
1720 #ifndef Inaccurate_Divide
1721                 else if (e >= -Ten_pmax) {
1722 #ifdef Honor_FLT_ROUNDS
1723                         /* round correctly FLT_ROUNDS = 2 or 3 */
1724                         if (sign) {
1725                                 rv = -rv;
1726                                 sign = 0;
1727                                 }
1728 #endif
1729                         /* rv = */ rounded_quotient(dval(rv), tens[-e]);
1730                         goto ret;
1731                         }
1732 #endif
1733                 }
1734         e1 += nd - k;
1735
1736 #ifdef IEEE_Arith
1737 #ifdef SET_INEXACT
1738         inexact = 1;
1739         if (k <= DBL_DIG)
1740                 oldinexact = get_inexact();
1741 #endif
1742 #ifdef Avoid_Underflow
1743         scale = 0;
1744 #endif
1745 #ifdef Honor_FLT_ROUNDS
1746         if ((rounding = Flt_Rounds) >= 2) {
1747                 if (sign)
1748                         rounding = rounding == 2 ? 0 : 2;
1749                 else
1750                         if (rounding != 2)
1751                                 rounding = 0;
1752                 }
1753 #endif
1754 #endif /*IEEE_Arith*/
1755
1756         /* Get starting approximation = rv * 10**e1 */
1757
1758         if (e1 > 0) {
1759                 if ((i = e1 & 15))
1760                         dval(rv) *= tens[i];
1761                 if (e1 &= ~15) {
1762                         if (e1 > DBL_MAX_10_EXP) {
1763  ovfl:
1764 #ifndef NO_ERRNO
1765                                 errno = ERANGE;
1766 #endif
1767                                 /* Can't trust HUGE_VAL */
1768 #ifdef IEEE_Arith
1769 #ifdef Honor_FLT_ROUNDS
1770                                 switch(rounding) {
1771                                   case 0: /* toward 0 */
1772                                   case 3: /* toward -infinity */
1773                                         word0(rv) = Big0;
1774                                         word1(rv) = Big1;
1775                                         break;
1776                                   default:
1777                                         word0(rv) = Exp_mask;
1778                                         word1(rv) = 0;
1779                                   }
1780 #else /*Honor_FLT_ROUNDS*/
1781                                 word0(rv) = Exp_mask;
1782                                 word1(rv) = 0;
1783 #endif /*Honor_FLT_ROUNDS*/
1784 #ifdef SET_INEXACT
1785                                 /* set overflow bit */
1786                                 dval(rv0) = 1e300;
1787                                 dval(rv0) *= dval(rv0);
1788 #endif
1789 #else /*IEEE_Arith*/
1790                                 word0(rv) = Big0;
1791                                 word1(rv) = Big1;
1792 #endif /*IEEE_Arith*/
1793                                 if (bd0)
1794                                         goto retfree;
1795                                 goto ret;
1796                                 }
1797                         e1 >>= 4;
1798                         for(j = 0; e1 > 1; j++, e1 >>= 1)
1799                                 if (e1 & 1)
1800                                         dval(rv) *= bigtens[j];
1801                 /* The last multiplication could overflow. */
1802                         word0(rv) -= P*Exp_msk1;
1803                         dval(rv) *= bigtens[j];
1804                         if ((z = word0(rv) & Exp_mask)
1805                          > Exp_msk1*(DBL_MAX_EXP+Bias-P))
1806                                 goto ovfl;
1807                         if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
1808                                 /* set to largest number */
1809                                 /* (Can't trust DBL_MAX) */
1810                                 word0(rv) = Big0;
1811                                 word1(rv) = Big1;
1812                                 }
1813                         else
1814                                 word0(rv) += P*Exp_msk1;
1815                         }
1816                 }
1817         else if (e1 < 0) {
1818                 e1 = -e1;
1819                 if ((i = e1 & 15))
1820                         dval(rv) /= tens[i];
1821                 if (e1 >>= 4) {
1822                         if (e1 >= 1 << n_bigtens)
1823                                 goto undfl;
1824 #ifdef Avoid_Underflow
1825                         if (e1 & Scale_Bit)
1826                                 scale = 2*P;
1827                         for(j = 0; e1 > 0; j++, e1 >>= 1)
1828                                 if (e1 & 1)
1829                                         dval(rv) *= tinytens[j];
1830                         if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
1831                                                 >> Exp_shift)) > 0) {
1832                                 /* scaled rv is denormal; zap j low bits */
1833                                 if (j >= 32) {
1834                                         word1(rv) = 0;
1835                                         if (j >= 53)
1836                                          word0(rv) = (P+2)*Exp_msk1;
1837                                         else
1838                                          word0(rv) &= 0xffffffff << (j-32);
1839                                         }
1840                                 else
1841                                         word1(rv) &= 0xffffffff << j;
1842                                 }
1843 #else
1844                         for(j = 0; e1 > 1; j++, e1 >>= 1)
1845                                 if (e1 & 1)
1846                                         dval(rv) *= tinytens[j];
1847                         /* The last multiplication could underflow. */
1848                         dval(rv0) = dval(rv);
1849                         dval(rv) *= tinytens[j];
1850                         if (!dval(rv)) {
1851                                 dval(rv) = 2.*dval(rv0);
1852                                 dval(rv) *= tinytens[j];
1853 #endif
1854                                 if (!dval(rv)) {
1855  undfl:
1856                                         dval(rv) = 0.;
1857 #ifndef NO_ERRNO
1858                                         errno = ERANGE;
1859 #endif
1860                                         if (bd0)
1861                                                 goto retfree;
1862                                         goto ret;
1863                                         }
1864 #ifndef Avoid_Underflow
1865                                 word0(rv) = Tiny0;
1866                                 word1(rv) = Tiny1;
1867                                 /* The refinement below will clean
1868                                  * this approximation up.
1869                                  */
1870                                 }
1871 #endif
1872                         }
1873                 }
1874
1875         /* Now the hard part -- adjusting rv to the correct value.*/
1876
1877         /* Put digits into bd: true value = bd * 10^e */
1878
1879         bd0 = s2b(PASS_STATE s0, nd0, nd, y);
1880
1881         for(;;) {
1882                 bd = Balloc(PASS_STATE bd0->k);
1883                 Bcopy(bd, bd0);
1884                 bb = d2b(PASS_STATE rv, &bbe, &bbbits); /* rv = bb * 2^bbe */
1885                 bs = i2b(PASS_STATE 1);
1886
1887                 if (e >= 0) {
1888                         bb2 = bb5 = 0;
1889                         bd2 = bd5 = e;
1890                         }
1891                 else {
1892                         bb2 = bb5 = -e;
1893                         bd2 = bd5 = 0;
1894                         }
1895                 if (bbe >= 0)
1896                         bb2 += bbe;
1897                 else
1898                         bd2 -= bbe;
1899                 bs2 = bb2;
1900 #ifdef Honor_FLT_ROUNDS
1901                 if (rounding != 1)
1902                         bs2++;
1903 #endif
1904 #ifdef Avoid_Underflow
1905                 j = bbe - scale;
1906                 i = j + bbbits - 1;     /* logb(rv) */
1907                 if (i < Emin)   /* denormal */
1908                         j += P - Emin;
1909                 else
1910                         j = P + 1 - bbbits;
1911 #else /*Avoid_Underflow*/
1912 #ifdef Sudden_Underflow
1913 #ifdef IBM
1914                 j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
1915 #else
1916                 j = P + 1 - bbbits;
1917 #endif
1918 #else /*Sudden_Underflow*/
1919                 j = bbe;
1920                 i = j + bbbits - 1;     /* logb(rv) */
1921                 if (i < Emin)   /* denormal */
1922                         j += P - Emin;
1923                 else
1924                         j = P + 1 - bbbits;
1925 #endif /*Sudden_Underflow*/
1926 #endif /*Avoid_Underflow*/
1927                 bb2 += j;
1928                 bd2 += j;
1929 #ifdef Avoid_Underflow
1930                 bd2 += scale;
1931 #endif
1932                 i = bb2 < bd2 ? bb2 : bd2;
1933                 if (i > bs2)
1934                         i = bs2;
1935                 if (i > 0) {
1936                         bb2 -= i;
1937                         bd2 -= i;
1938                         bs2 -= i;
1939                         }
1940                 if (bb5 > 0) {
1941                         bs = pow5mult(PASS_STATE bs, bb5);
1942                         bb1 = mult(PASS_STATE bs, bb);
1943                         Bfree(PASS_STATE bb);
1944                         bb = bb1;
1945                         }
1946                 if (bb2 > 0)
1947                         bb = lshift(PASS_STATE bb, bb2);
1948                 if (bd5 > 0)
1949                         bd = pow5mult(PASS_STATE bd, bd5);
1950                 if (bd2 > 0)
1951                         bd = lshift(PASS_STATE bd, bd2);
1952                 if (bs2 > 0)
1953                         bs = lshift(PASS_STATE bs, bs2);
1954                 delta = diff(PASS_STATE bb, bd);
1955                 dsign = delta->sign;
1956                 delta->sign = 0;
1957                 i = cmp(delta, bs);
1958 #ifdef Honor_FLT_ROUNDS
1959                 if (rounding != 1) {
1960                         if (i < 0) {
1961                                 /* Error is less than an ulp */
1962                                 if (!delta->x[0] && delta->wds <= 1) {
1963                                         /* exact */
1964 #ifdef SET_INEXACT
1965                                         inexact = 0;
1966 #endif
1967                                         break;
1968                                         }
1969                                 if (rounding) {
1970                                         if (dsign) {
1971                                                 adj = 1.;
1972                                                 goto apply_adj;
1973                                                 }
1974                                         }
1975                                 else if (!dsign) {
1976                                         adj = -1.;
1977                                         if (!word1(rv)
1978                                          && !(word0(rv) & Frac_mask)) {
1979                                                 y = word0(rv) & Exp_mask;
1980 #ifdef Avoid_Underflow
1981                                                 if (!scale || y > 2*P*Exp_msk1)
1982 #else
1983                                                 if (y)
1984 #endif
1985                                                   {
1986                                                   delta = lshift(PASS_STATE delta,Log2P);
1987                                                   if (cmp(delta, bs) <= 0)
1988                                                         adj = -0.5;
1989                                                   }
1990                                                 }
1991  apply_adj:
1992 #ifdef Avoid_Underflow
1993                                         if (scale && (y = word0(rv) & Exp_mask)
1994                                                 <= 2*P*Exp_msk1)
1995                                           word0(adj) += (2*P+1)*Exp_msk1 - y;
1996 #else
1997 #ifdef Sudden_Underflow
1998                                         if ((word0(rv) & Exp_mask) <=
1999                                                         P*Exp_msk1) {
2000                                                 word0(rv) += P*Exp_msk1;
2001                                                 dval(rv) += adj*ulp(rv);
2002                                                 word0(rv) -= P*Exp_msk1;
2003                                                 }
2004                                         else
2005 #endif /*Sudden_Underflow*/
2006 #endif /*Avoid_Underflow*/
2007                                         dval(rv) += adj*ulp(rv);
2008                                         }
2009                                 break;
2010                                 }
2011                         adj = ratio(delta, bs);
2012                         if (adj < 1.)
2013                                 adj = 1.;
2014                         if (adj <= 0x7ffffffe) {
2015                                 /* adj = rounding ? ceil(adj) : floor(adj); */
2016                                 y = adj;
2017                                 if (y != adj) {
2018                                         if (!((rounding>>1) ^ dsign))
2019                                                 y++;
2020                                         adj = y;
2021                                         }
2022                                 }
2023 #ifdef Avoid_Underflow
2024                         if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2025                                 word0(adj) += (2*P+1)*Exp_msk1 - y;
2026 #else
2027 #ifdef Sudden_Underflow
2028                         if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2029                                 word0(rv) += P*Exp_msk1;
2030                                 adj *= ulp(rv);
2031                                 if (dsign)
2032                                         dval(rv) += adj;
2033                                 else
2034                                         dval(rv) -= adj;
2035                                 word0(rv) -= P*Exp_msk1;
2036                                 goto cont;
2037                                 }
2038 #endif /*Sudden_Underflow*/
2039 #endif /*Avoid_Underflow*/
2040                         adj *= ulp(rv);
2041                         if (dsign)
2042                                 dval(rv) += adj;
2043                         else
2044                                 dval(rv) -= adj;
2045                         goto cont;
2046                         }
2047 #endif /*Honor_FLT_ROUNDS*/
2048
2049                 if (i < 0) {
2050                         /* Error is less than half an ulp -- check for
2051                          * special case of mantissa a power of two.
2052                          */
2053                         if (dsign || word1(rv) || word0(rv) & Bndry_mask
2054 #ifdef IEEE_Arith
2055 #ifdef Avoid_Underflow
2056                          || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
2057 #else
2058                          || (word0(rv) & Exp_mask) <= Exp_msk1
2059 #endif
2060 #endif
2061                                 ) {
2062 #ifdef SET_INEXACT
2063                                 if (!delta->x[0] && delta->wds <= 1)
2064                                         inexact = 0;
2065 #endif
2066                                 break;
2067                                 }
2068                         if (!delta->x[0] && delta->wds <= 1) {
2069                                 /* exact result */
2070 #ifdef SET_INEXACT
2071                                 inexact = 0;
2072 #endif
2073                                 break;
2074                                 }
2075                         delta = lshift(PASS_STATE delta,Log2P);
2076                         if (cmp(delta, bs) > 0)
2077                                 goto drop_down;
2078                         break;
2079                         }
2080                 if (i == 0) {
2081                         /* exactly half-way between */
2082                         if (dsign) {
2083                                 if ((word0(rv) & Bndry_mask1) == Bndry_mask1
2084                                  &&  word1(rv) == (
2085 #ifdef Avoid_Underflow
2086                         (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2087                 ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
2088 #endif
2089                                                    0xffffffff)) {
2090                                         /*boundary case -- increment exponent*/
2091                                         word0(rv) = (word0(rv) & Exp_mask)
2092                                                 + Exp_msk1
2093 #ifdef IBM
2094                                                 | Exp_msk1 >> 4
2095 #endif
2096                                                 ;
2097                                         word1(rv) = 0;
2098 #ifdef Avoid_Underflow
2099                                         dsign = 0;
2100 #endif
2101                                         break;
2102                                         }
2103                                 }
2104                         else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
2105  drop_down:
2106                                 /* boundary case -- decrement exponent */
2107 #ifdef Sudden_Underflow /*{{*/
2108                                 L = word0(rv) & Exp_mask;
2109 #ifdef IBM
2110                                 if (L <  Exp_msk1)
2111 #else
2112 #ifdef Avoid_Underflow
2113                                 if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
2114 #else
2115                                 if (L <= Exp_msk1)
2116 #endif /*Avoid_Underflow*/
2117 #endif /*IBM*/
2118                                         goto undfl;
2119                                 L -= Exp_msk1;
2120 #else /*Sudden_Underflow}{*/
2121 #ifdef Avoid_Underflow
2122                                 if (scale) {
2123                                         L = word0(rv) & Exp_mask;
2124                                         if (L <= (2*P+1)*Exp_msk1) {
2125                                                 if (L > (P+2)*Exp_msk1)
2126                                                         /* round even ==> */
2127                                                         /* accept rv */
2128                                                         break;
2129                                                 /* rv = smallest denormal */
2130                                                 goto undfl;
2131                                                 }
2132                                         }
2133 #endif /*Avoid_Underflow*/
2134                                 L = (word0(rv) & Exp_mask) - Exp_msk1;
2135 #endif /*Sudden_Underflow}}*/
2136                                 word0(rv) = L | Bndry_mask1;
2137                                 word1(rv) = 0xffffffff;
2138 #ifdef IBM
2139                                 goto cont;
2140 #else
2141                                 break;
2142 #endif
2143                                 }
2144 #ifndef ROUND_BIASED
2145                         if (!(word1(rv) & LSB))
2146                                 break;
2147 #endif
2148                         if (dsign)
2149                                 dval(rv) += ulp(rv);
2150 #ifndef ROUND_BIASED
2151                         else {
2152                                 dval(rv) -= ulp(rv);
2153 #ifndef Sudden_Underflow
2154                                 if (!dval(rv))
2155                                         goto undfl;
2156 #endif
2157                                 }
2158 #ifdef Avoid_Underflow
2159                         dsign = 1 - dsign;
2160 #endif
2161 #endif
2162                         break;
2163                         }
2164                 if ((aadj = ratio(delta, bs)) <= 2.) {
2165                         if (dsign)
2166                                 aadj = dval(aadj1) = 1.;
2167                         else if (word1(rv) || word0(rv) & Bndry_mask) {
2168 #ifndef Sudden_Underflow
2169                                 if (word1(rv) == Tiny1 && !word0(rv))
2170                                         goto undfl;
2171 #endif
2172                                 aadj = 1.;
2173                                 dval(aadj1) = -1.;
2174                                 }
2175                         else {
2176                                 /* special case -- power of FLT_RADIX to be */
2177                                 /* rounded down... */
2178
2179                                 if (aadj < 2./FLT_RADIX)
2180                                         aadj = 1./FLT_RADIX;
2181                                 else
2182                                         aadj *= 0.5;
2183                                 dval(aadj1) = -aadj;
2184                                 }
2185                         }
2186                 else {
2187                         aadj *= 0.5;
2188                         dval(aadj1) = dsign ? aadj : -aadj;
2189 #ifdef Check_FLT_ROUNDS
2190                         switch(Rounding) {
2191                                 case 2: /* towards +infinity */
2192                                         dval(aadj1) -= 0.5;
2193                                         break;
2194                                 case 0: /* towards 0 */
2195                                 case 3: /* towards -infinity */
2196                                         dval(aadj1) += 0.5;
2197                                 }
2198 #else
2199                         if (Flt_Rounds == 0)
2200                                 dval(aadj1) += 0.5;
2201 #endif /*Check_FLT_ROUNDS*/
2202                         }
2203                 y = word0(rv) & Exp_mask;
2204
2205                 /* Check for overflow */
2206
2207                 if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
2208                         dval(rv0) = dval(rv);
2209                         word0(rv) -= P*Exp_msk1;
2210                         adj = dval(aadj1) * ulp(rv);
2211                         dval(rv) += adj;
2212                         if ((word0(rv) & Exp_mask) >=
2213                                         Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
2214                                 if (word0(rv0) == Big0 && word1(rv0) == Big1)
2215                                         goto ovfl;
2216                                 word0(rv) = Big0;
2217                                 word1(rv) = Big1;
2218                                 goto cont;
2219                                 }
2220                         else
2221                                 word0(rv) += P*Exp_msk1;
2222                         }
2223                 else {
2224 #ifdef Avoid_Underflow
2225                         if (scale && y <= 2*P*Exp_msk1) {
2226                                 if (aadj <= 0x7fffffff) {
2227                                         if ((z = (ULong) aadj) <= 0)
2228                                                 z = 1;
2229                                         aadj = z;
2230                                         dval(aadj1) = dsign ? aadj : -aadj;
2231                                         }
2232                                 word0(aadj1) += (2*P+1)*Exp_msk1 - y;
2233                                 }
2234                         adj = dval(aadj1) * ulp(rv);
2235                         dval(rv) += adj;
2236 #else
2237 #ifdef Sudden_Underflow
2238                         if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2239                                 dval(rv0) = dval(rv);
2240                                 word0(rv) += P*Exp_msk1;
2241                                 adj = dval(aadj1) * ulp(rv);
2242                                 dval(rv) += adj;
2243 #ifdef IBM
2244                                 if ((word0(rv) & Exp_mask) <  P*Exp_msk1)
2245 #else
2246                                 if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
2247 #endif
2248                                         {
2249                                         if (word0(rv0) == Tiny0
2250                                          && word1(rv0) == Tiny1)
2251                                                 goto undfl;
2252                                         word0(rv) = Tiny0;
2253                                         word1(rv) = Tiny1;
2254                                         goto cont;
2255                                         }
2256                                 else
2257                                         word0(rv) -= P*Exp_msk1;
2258                                 }
2259                         else {
2260                                 adj = dval(aadj1) * ulp(rv);
2261                                 dval(rv) += adj;
2262                                 }
2263 #else /*Sudden_Underflow*/
2264                         /* Compute adj so that the IEEE rounding rules will
2265                          * correctly round rv + adj in some half-way cases.
2266                          * If rv * ulp(rv) is denormalized (i.e.,
2267                          * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
2268                          * trouble from bits lost to denormalization;
2269                          * example: 1.2e-307 .
2270                          */
2271                         if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
2272                                 dval(aadj1) = (double)(int)(aadj + 0.5);
2273                                 if (!dsign)
2274                                         dval(aadj1) = -dval(aadj1);
2275                                 }
2276                         adj = dval(aadj1) * ulp(rv);
2277                         dval(rv) += adj;
2278 #endif /*Sudden_Underflow*/
2279 #endif /*Avoid_Underflow*/
2280                         }
2281                 z = word0(rv) & Exp_mask;
2282 #ifndef SET_INEXACT
2283 #ifdef Avoid_Underflow
2284                 if (!scale)
2285 #endif
2286                 if (y == z) {
2287                         /* Can we stop now? */
2288                         L = (Long)aadj;
2289                         aadj -= L;
2290                         /* The tolerances below are conservative. */
2291                         if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
2292                                 if (aadj < .4999999 || aadj > .5000001)
2293                                         break;
2294                                 }
2295                         else if (aadj < .4999999/FLT_RADIX)
2296                                 break;
2297                         }
2298 #endif
2299  cont:
2300                 Bfree(PASS_STATE bb);
2301                 Bfree(PASS_STATE bd);
2302                 Bfree(PASS_STATE bs);
2303                 Bfree(PASS_STATE delta);
2304                 }
2305 #ifdef SET_INEXACT
2306         if (inexact) {
2307                 if (!oldinexact) {
2308                         word0(rv0) = Exp_1 + (70 << Exp_shift);
2309                         word1(rv0) = 0;
2310                         dval(rv0) += 1.;
2311                         }
2312                 }
2313         else if (!oldinexact)
2314                 clear_inexact();
2315 #endif
2316 #ifdef Avoid_Underflow
2317         if (scale) {
2318                 word0(rv0) = Exp_1 - 2*P*Exp_msk1;
2319                 word1(rv0) = 0;
2320                 dval(rv) *= dval(rv0);
2321 #ifndef NO_ERRNO
2322                 /* try to avoid the bug of testing an 8087 register value */
2323                 if (word0(rv) == 0 && word1(rv) == 0)
2324                         errno = ERANGE;
2325 #endif
2326                 }
2327 #endif /* Avoid_Underflow */
2328 #ifdef SET_INEXACT
2329         if (inexact && !(word0(rv) & Exp_mask)) {
2330                 /* set underflow bit */
2331                 dval(rv0) = 1e-300;
2332                 dval(rv0) *= dval(rv0);
2333                 }
2334 #endif
2335  retfree:
2336         Bfree(PASS_STATE bb);
2337         Bfree(PASS_STATE bd);
2338         Bfree(PASS_STATE bs);
2339         Bfree(PASS_STATE bd0);
2340         Bfree(PASS_STATE delta);
2341  ret:
2342         if (se)
2343                 *se = (char *)s;
2344         return sign ? -dval(rv) : dval(rv);
2345         }
2346
2347  static int
2348 quorem
2349 #ifdef KR_headers
2350         (b, S) Bigint *b, *S;
2351 #else
2352         (Bigint *b, Bigint *S)
2353 #endif
2354 {
2355         int n;
2356         ULong *bx, *bxe, q, *sx, *sxe;
2357 #ifdef ULLong
2358         ULLong borrow, carry, y, ys;
2359 #else
2360         ULong borrow, carry, y, ys;
2361 #ifdef Pack_32
2362         ULong si, z, zs;
2363 #endif
2364 #endif
2365
2366         n = S->wds;
2367 #ifdef DEBUG
2368         /*debug*/ if (b->wds > n)
2369         /*debug*/       Bug("oversize b in quorem");
2370 #endif
2371         if (b->wds < n)
2372                 return 0;
2373         sx = S->x;
2374         sxe = sx + --n;
2375         bx = b->x;
2376         bxe = bx + n;
2377         q = *bxe / (*sxe + 1);  /* ensure q <= true quotient */
2378 #ifdef DEBUG
2379         /*debug*/ if (q > 9)
2380         /*debug*/       Bug("oversized quotient in quorem");
2381 #endif
2382         if (q) {
2383                 borrow = 0;
2384                 carry = 0;
2385                 do {
2386 #ifdef ULLong
2387                         ys = *sx++ * (ULLong)q + carry;
2388                         carry = ys >> 32;
2389                         y = *bx - (ys & FFFFFFFF) - borrow;
2390                         borrow = y >> 32 & (ULong)1;
2391                         *bx++ = (ULong) y & FFFFFFFF;
2392 #else
2393 #ifdef Pack_32
2394                         si = *sx++;
2395                         ys = (si & 0xffff) * q + carry;
2396                         zs = (si >> 16) * q + (ys >> 16);
2397                         carry = zs >> 16;
2398                         y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2399                         borrow = (y & 0x10000) >> 16;
2400                         z = (*bx >> 16) - (zs & 0xffff) - borrow;
2401                         borrow = (z & 0x10000) >> 16;
2402                         Storeinc(bx, z, y);
2403 #else
2404                         ys = *sx++ * q + carry;
2405                         carry = ys >> 16;
2406                         y = *bx - (ys & 0xffff) - borrow;
2407                         borrow = (y & 0x10000) >> 16;
2408                         *bx++ = y & 0xffff;
2409 #endif
2410 #endif
2411                         }
2412                         while(sx <= sxe);
2413                 if (!*bxe) {
2414                         bx = b->x;
2415                         while(--bxe > bx && !*bxe)
2416                                 --n;
2417                         b->wds = n;
2418                         }
2419                 }
2420         if (cmp(b, S) >= 0) {
2421                 q++;
2422                 borrow = 0;
2423                 carry = 0;
2424                 bx = b->x;
2425                 sx = S->x;
2426                 do {
2427 #ifdef ULLong
2428                         ys = *sx++ + carry;
2429                         carry = ys >> 32;
2430                         y = *bx - (ys & FFFFFFFF) - borrow;
2431                         borrow = y >> 32 & (ULong)1;
2432                         *bx++ = (ULong) y & FFFFFFFF;
2433 #else
2434 #ifdef Pack_32
2435                         si = *sx++;
2436                         ys = (si & 0xffff) + carry;
2437                         zs = (si >> 16) + (ys >> 16);
2438                         carry = zs >> 16;
2439                         y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2440                         borrow = (y & 0x10000) >> 16;
2441                         z = (*bx >> 16) - (zs & 0xffff) - borrow;
2442                         borrow = (z & 0x10000) >> 16;
2443                         Storeinc(bx, z, y);
2444 #else
2445                         ys = *sx++ + carry;
2446                         carry = ys >> 16;
2447                         y = *bx - (ys & 0xffff) - borrow;
2448                         borrow = (y & 0x10000) >> 16;
2449                         *bx++ = y & 0xffff;
2450 #endif
2451 #endif
2452                         }
2453                         while(sx <= sxe);
2454                 bx = b->x;
2455                 bxe = bx + n;
2456                 if (!*bxe) {
2457                         while(--bxe > bx && !*bxe)
2458                                 --n;
2459                         b->wds = n;
2460                         }
2461                 }
2462         return q;
2463         }
2464
2465 #if !defined(MULTIPLE_THREADS) && !defined(NO_GLOBAL_STATE)
2466 #define USE_DTOA_RESULT 1
2467  static char *dtoa_result;
2468 #endif
2469
2470  static char *
2471 #ifdef KR_headers
2472 rv_alloc(STATE_PARAM i) STATE_PARAM_DECL int i;
2473 #else
2474 rv_alloc(STATE_PARAM int i)
2475 #endif
2476 {
2477         int j, k, *r;
2478
2479         j = sizeof(ULong);
2480         for(k = 0;
2481                 sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= (unsigned) i;
2482                 j <<= 1)
2483                         k++;
2484         r = (int*)Balloc(PASS_STATE k);
2485         *r = k;
2486         return
2487 #ifdef USE_DTOA_RESULT
2488         dtoa_result =
2489 #endif
2490                 (char *)(r+1);
2491         }
2492
2493  static char *
2494 #ifdef KR_headers
2495 nrv_alloc(STATE_PARAM s, rve, n) STATE_PARAM_DECL char *s, **rve; int n;
2496 #else
2497 nrv_alloc(STATE_PARAM CONST char *s, char **rve, int n)
2498 #endif
2499 {
2500         char *rv, *t;
2501
2502         t = rv = rv_alloc(PASS_STATE n);
2503         while((*t = *s++)) t++;
2504         if (rve)
2505                 *rve = t;
2506         return rv;
2507         }
2508
2509 /* freedtoa(s) must be used to free values s returned by dtoa
2510  * when MULTIPLE_THREADS is #defined.  It should be used in all cases,
2511  * but for consistency with earlier versions of dtoa, it is optional
2512  * when MULTIPLE_THREADS is not defined.
2513  */
2514
2515  static void
2516 #ifdef KR_headers
2517 freedtoa(STATE_PARAM s) STATE_PARAM_DECL char *s;
2518 #else
2519 freedtoa(STATE_PARAM char *s)
2520 #endif
2521 {
2522         Bigint *b = (Bigint *)((int *)s - 1);
2523         b->maxwds = 1 << (b->k = *(int*)b);
2524         Bfree(PASS_STATE b);
2525 #ifdef USE_DTOA_RESULT
2526         if (s == dtoa_result)
2527                 dtoa_result = 0;
2528 #endif
2529         }
2530
2531 /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
2532  *
2533  * Inspired by "How to Print Floating-Point Numbers Accurately" by
2534  * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
2535  *
2536  * Modifications:
2537  *      1. Rather than iterating, we use a simple numeric overestimate
2538  *         to determine k = floor(log10(d)).  We scale relevant
2539  *         quantities using O(log2(k)) rather than O(k) multiplications.
2540  *      2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
2541  *         try to generate digits strictly left to right.  Instead, we
2542  *         compute with fewer bits and propagate the carry if necessary
2543  *         when rounding the final digit up.  This is often faster.
2544  *      3. Under the assumption that input will be rounded nearest,
2545  *         mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
2546  *         That is, we allow equality in stopping tests when the
2547  *         round-nearest rule will give the same floating-point value
2548  *         as would satisfaction of the stopping test with strict
2549  *         inequality.
2550  *      4. We remove common factors of powers of 2 from relevant
2551  *         quantities.
2552  *      5. When converting floating-point integers less than 1e16,
2553  *         we use floating-point arithmetic rather than resorting
2554  *         to multiple-precision integers.
2555  *      6. When asked to produce fewer than 15 digits, we first try
2556  *         to get by with floating-point arithmetic; we resort to
2557  *         multiple-precision integer arithmetic only if we cannot
2558  *         guarantee that the floating-point calculation has given
2559  *         the correctly rounded result.  For k requested digits and
2560  *         "uniformly" distributed input, the probability is
2561  *         something like 10^(k-15) that we must resort to the Long
2562  *         calculation.
2563  */
2564
2565  static char *
2566 dtoa
2567 #ifdef KR_headers
2568         (STATE_PARAM d, mode, ndigits, decpt, sign, rve)
2569         STATE_PARAM_DECL U d; int mode, ndigits, *decpt, *sign; char **rve;
2570 #else
2571         (STATE_PARAM U d, int mode, int ndigits, int *decpt, int *sign, char **rve)
2572 #endif
2573 {
2574  /*     Arguments ndigits, decpt, sign are similar to those
2575         of ecvt and fcvt; trailing zeros are suppressed from
2576         the returned string.  If not null, *rve is set to point
2577         to the end of the return value.  If d is +-Infinity or NaN,
2578         then *decpt is set to 9999.
2579
2580         mode:
2581                 0 ==> shortest string that yields d when read in
2582                         and rounded to nearest.
2583                 1 ==> like 0, but with Steele & White stopping rule;
2584                         e.g. with IEEE P754 arithmetic , mode 0 gives
2585                         1e23 whereas mode 1 gives 9.999999999999999e22.
2586                 2 ==> max(1,ndigits) significant digits.  This gives a
2587                         return value similar to that of ecvt, except
2588                         that trailing zeros are suppressed.
2589                 3 ==> through ndigits past the decimal point.  This
2590                         gives a return value similar to that from fcvt,
2591                         except that trailing zeros are suppressed, and
2592                         ndigits can be negative.
2593                 4,5 ==> similar to 2 and 3, respectively, but (in
2594                         round-nearest mode) with the tests of mode 0 to
2595                         possibly return a shorter string that rounds to d.
2596                         With IEEE arithmetic and compilation with
2597                         -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
2598                         as modes 2 and 3 when FLT_ROUNDS != 1.
2599                 6-9 ==> Debugging modes similar to mode - 4:  don't try
2600                         fast floating-point estimate (if applicable).
2601
2602                 Values of mode other than 0-9 are treated as mode 0.
2603
2604                 Sufficient space is allocated to the return value
2605                 to hold the suppressed trailing zeros.
2606         */
2607
2608         int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
2609                 j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
2610                 spec_case, try_quick;
2611         Long L;
2612 #ifndef Sudden_Underflow
2613         int denorm;
2614         ULong x;
2615 #endif
2616         Bigint *b, *b1, *delta, *mlo, *mhi, *S;
2617         U d2, eps;
2618         double ds;
2619         char *s, *s0;
2620 #ifdef Honor_FLT_ROUNDS
2621         int rounding;
2622 #endif
2623 #ifdef SET_INEXACT
2624         int inexact, oldinexact;
2625 #endif
2626
2627 #ifdef __GNUC__
2628         ilim = ilim1 = 0;
2629         mlo = NULL;
2630 #endif
2631
2632 #ifdef USE_DTOA_RESULT
2633         if (dtoa_result) {
2634                 freedtoa(PASS_STATE dtoa_result);
2635                 dtoa_result = 0;
2636                 }
2637 #endif
2638
2639         if (word0(d) & Sign_bit) {
2640                 /* set sign for everything, including 0's and NaNs */
2641                 *sign = 1;
2642                 word0(d) &= ~Sign_bit;  /* clear sign bit */
2643                 }
2644         else
2645                 *sign = 0;
2646
2647 #if defined(IEEE_Arith) + defined(VAX)
2648 #ifdef IEEE_Arith
2649         if ((word0(d) & Exp_mask) == Exp_mask)
2650 #else
2651         if (word0(d)  == 0x8000)
2652 #endif
2653                 {
2654                 /* Infinity or NaN */
2655                 *decpt = 9999;
2656 #ifdef IEEE_Arith
2657                 if (!word1(d) && !(word0(d) & 0xfffff))
2658                         return nrv_alloc(PASS_STATE "Infinity", rve, 8);
2659 #endif
2660                 return nrv_alloc(PASS_STATE "NaN", rve, 3);
2661                 }
2662 #endif
2663 #ifdef IBM
2664         dval(d) += 0; /* normalize */
2665 #endif
2666         if (!dval(d)) {
2667                 *decpt = 1;
2668                 return nrv_alloc(PASS_STATE "0", rve, 1);
2669                 }
2670
2671 #ifdef SET_INEXACT
2672         try_quick = oldinexact = get_inexact();
2673         inexact = 1;
2674 #endif
2675 #ifdef Honor_FLT_ROUNDS
2676         if ((rounding = Flt_Rounds) >= 2) {
2677                 if (*sign)
2678                         rounding = rounding == 2 ? 0 : 2;
2679                 else
2680                         if (rounding != 2)
2681                                 rounding = 0;
2682                 }
2683 #endif
2684
2685         b = d2b(PASS_STATE d, &be, &bbits);
2686 #ifdef Sudden_Underflow
2687         i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
2688 #else
2689         if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) {
2690 #endif
2691                 dval(d2) = dval(d);
2692                 word0(d2) &= Frac_mask1;
2693                 word0(d2) |= Exp_11;
2694 #ifdef IBM
2695                 if (j = 11 - hi0bits(word0(d2) & Frac_mask))
2696                         dval(d2) /= 1 << j;
2697 #endif
2698
2699                 /* log(x)       ~=~ log(1.5) + (x-1.5)/1.5
2700                  * log10(x)      =  log(x) / log(10)
2701                  *              ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
2702                  * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
2703                  *
2704                  * This suggests computing an approximation k to log10(d) by
2705                  *
2706                  * k = (i - Bias)*0.301029995663981
2707                  *      + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
2708                  *
2709                  * We want k to be too large rather than too small.
2710                  * The error in the first-order Taylor series approximation
2711                  * is in our favor, so we just round up the constant enough
2712                  * to compensate for any error in the multiplication of
2713                  * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
2714                  * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
2715                  * adding 1e-13 to the constant term more than suffices.
2716                  * Hence we adjust the constant term to 0.1760912590558.
2717                  * (We could get a more accurate k by invoking log10,
2718                  *  but this is probably not worthwhile.)
2719                  */
2720
2721                 i -= Bias;
2722 #ifdef IBM
2723                 i <<= 2;
2724                 i += j;
2725 #endif
2726 #ifndef Sudden_Underflow
2727                 denorm = 0;
2728                 }
2729         else {
2730                 /* d is denormalized */
2731
2732                 i = bbits + be + (Bias + (P-1) - 1);
2733                 x = i > 32  ? word0(d) << (64 - i) | word1(d) >> (i - 32)
2734                             : word1(d) << (32 - i);
2735                 dval(d2) = x;
2736                 word0(d2) -= 31*Exp_msk1; /* adjust exponent */
2737                 i -= (Bias + (P-1) - 1) + 1;
2738                 denorm = 1;
2739                 }
2740 #endif
2741         ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
2742         k = (int)ds;
2743         if (ds < 0. && ds != k)
2744                 k--;    /* want k = floor(ds) */
2745         k_check = 1;
2746         if (k >= 0 && k <= Ten_pmax) {
2747                 if (dval(d) < tens[k])
2748                         k--;
2749                 k_check = 0;
2750                 }
2751         j = bbits - i - 1;
2752         if (j >= 0) {
2753                 b2 = 0;
2754                 s2 = j;
2755                 }
2756         else {
2757                 b2 = -j;
2758                 s2 = 0;
2759                 }
2760         if (k >= 0) {
2761                 b5 = 0;
2762                 s5 = k;
2763                 s2 += k;
2764                 }
2765         else {
2766                 b2 -= k;
2767                 b5 = -k;
2768                 s5 = 0;
2769                 }
2770         if (mode < 0 || mode > 9)
2771                 mode = 0;
2772
2773 #ifndef SET_INEXACT
2774 #ifdef Check_FLT_ROUNDS
2775         try_quick = Rounding == 1;
2776 #else
2777         try_quick = 1;
2778 #endif
2779 #endif /*SET_INEXACT*/
2780
2781         if (mode > 5) {
2782                 mode -= 4;
2783                 try_quick = 0;
2784                 }
2785         leftright = 1;
2786         switch(mode) {
2787                 case 0:
2788                 case 1:
2789                         ilim = ilim1 = -1;
2790                         i = 18;
2791                         ndigits = 0;
2792                         break;
2793                 case 2:
2794                         leftright = 0;
2795                         /* no break */
2796                 case 4:
2797                         if (ndigits <= 0)
2798                                 ndigits = 1;
2799                         ilim = ilim1 = i = ndigits;
2800                         break;
2801                 case 3:
2802                         leftright = 0;
2803                         /* no break */
2804                 case 5:
2805                         i = ndigits + k + 1;
2806                         ilim = i;
2807                         ilim1 = i - 1;
2808                         if (i <= 0)
2809                                 i = 1;
2810                 }
2811         s = s0 = rv_alloc(PASS_STATE i);
2812
2813 #ifdef Honor_FLT_ROUNDS
2814         if (mode > 1 && rounding != 1)
2815                 leftright = 0;
2816 #endif
2817
2818         if (ilim >= 0 && ilim <= Quick_max && try_quick) {
2819
2820                 /* Try to get by with floating-point arithmetic. */
2821
2822                 i = 0;
2823                 dval(d2) = dval(d);
2824                 k0 = k;
2825                 ilim0 = ilim;
2826                 ieps = 2; /* conservative */
2827                 if (k > 0) {
2828                         ds = tens[k&0xf];
2829                         j = k >> 4;
2830                         if (j & Bletch) {
2831                                 /* prevent overflows */
2832                                 j &= Bletch - 1;
2833                                 dval(d) /= bigtens[n_bigtens-1];
2834                                 ieps++;
2835                                 }
2836                         for(; j; j >>= 1, i++)
2837                                 if (j & 1) {
2838                                         ieps++;
2839                                         ds *= bigtens[i];
2840                                         }
2841                         dval(d) /= ds;
2842                         }
2843                 else if ((j1 = -k)) {
2844                         dval(d) *= tens[j1 & 0xf];
2845                         for(j = j1 >> 4; j; j >>= 1, i++)
2846                                 if (j & 1) {
2847                                         ieps++;
2848                                         dval(d) *= bigtens[i];
2849                                         }
2850                         }
2851                 if (k_check && dval(d) < 1. && ilim > 0) {
2852                         if (ilim1 <= 0)
2853                                 goto fast_failed;
2854                         ilim = ilim1;
2855                         k--;
2856                         dval(d) *= 10.;
2857                         ieps++;
2858                         }
2859                 dval(eps) = ieps*dval(d) + 7.;
2860                 word0(eps) -= (P-1)*Exp_msk1;
2861                 if (ilim == 0) {
2862                         S = mhi = 0;
2863                         dval(d) -= 5.;
2864                         if (dval(d) > dval(eps))
2865                                 goto one_digit;
2866                         if (dval(d) < -dval(eps))
2867                                 goto no_digits;
2868                         goto fast_failed;
2869                         }
2870 #ifndef No_leftright
2871                 if (leftright) {
2872                         /* Use Steele & White method of only
2873                          * generating digits needed.
2874                          */
2875                         dval(eps) = 0.5/tens[ilim-1] - dval(eps);
2876                         for(i = 0;;) {
2877                                 L = (ULong) dval(d);
2878                                 dval(d) -= L;
2879                                 *s++ = '0' + (int)L;
2880                                 if (dval(d) < dval(eps))
2881                                         goto ret1;
2882                                 if (1. - dval(d) < dval(eps))
2883                                         goto bump_up;
2884                                 if (++i >= ilim)
2885                                         break;
2886                                 dval(eps) *= 10.;
2887                                 dval(d) *= 10.;
2888                                 }
2889                         }
2890                 else {
2891 #endif
2892                         /* Generate ilim digits, then fix them up. */
2893                         dval(eps) *= tens[ilim-1];
2894                         for(i = 1;; i++, dval(d) *= 10.) {
2895                                 L = (Long)(dval(d));
2896                                 if (!(dval(d) -= L))
2897                                         ilim = i;
2898                                 *s++ = '0' + (int)L;
2899                                 if (i == ilim) {
2900                                         if (dval(d) > 0.5 + dval(eps))
2901                                                 goto bump_up;
2902                                         else if (dval(d) < 0.5 - dval(eps)) {
2903                                                 while(*--s == '0');
2904                                                 s++;
2905                                                 goto ret1;
2906                                                 }
2907                                         break;
2908                                         }
2909                                 }
2910 #ifndef No_leftright
2911                         }
2912 #endif
2913  fast_failed:
2914                 s = s0;
2915                 dval(d) = dval(d2);
2916                 k = k0;
2917                 ilim = ilim0;
2918                 }
2919
2920         /* Do we have a "small" integer? */
2921
2922         if (be >= 0 && k <= Int_max) {
2923                 /* Yes. */
2924                 ds = tens[k];
2925                 if (ndigits < 0 && ilim <= 0) {
2926                         S = mhi = 0;
2927                         if (ilim < 0 || dval(d) < 5*ds)
2928                                 goto no_digits;
2929                         goto one_digit;
2930                         }
2931                 for(i = 1;; i++, dval(d) *= 10.) {
2932                         L = (Long)(dval(d) / ds);
2933                         dval(d) -= L*ds;
2934 #ifdef Check_FLT_ROUNDS
2935                         /* If FLT_ROUNDS == 2, L will usually be high by 1 */
2936                         if (dval(d) < 0) {
2937                                 L--;
2938                                 dval(d) += ds;
2939                                 }
2940 #endif
2941                         *s++ = '0' + (int)L;
2942                         if (!dval(d)) {
2943 #ifdef SET_INEXACT
2944                                 inexact = 0;
2945 #endif
2946                                 break;
2947                                 }
2948                         if (i == ilim) {
2949 #ifdef Honor_FLT_ROUNDS
2950                                 if (mode > 1)
2951                                 switch(rounding) {
2952                                   case 0: goto ret1;
2953                                   case 2: goto bump_up;
2954                                   }
2955 #endif
2956                                 dval(d) += dval(d);
2957                                 if (dval(d) > ds || (dval(d) == ds && L & 1)) {
2958  bump_up:
2959                                         while(*--s == '9')
2960                                                 if (s == s0) {
2961                                                         k++;
2962                                                         *s = '0';
2963                                                         break;
2964                                                         }
2965                                         ++*s++;
2966                                         }
2967                                 break;
2968                                 }
2969                         }
2970                 goto ret1;
2971                 }
2972
2973         m2 = b2;
2974         m5 = b5;
2975         mhi = mlo = 0;
2976         if (leftright) {
2977                 i =
2978 #ifndef Sudden_Underflow
2979                         denorm ? be + (Bias + (P-1) - 1 + 1) :
2980 #endif
2981 #ifdef IBM
2982                         1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
2983 #else
2984                         1 + P - bbits;
2985 #endif
2986                 b2 += i;
2987                 s2 += i;
2988                 mhi = i2b(PASS_STATE 1);
2989                 }
2990         if (m2 > 0 && s2 > 0) {
2991                 i = m2 < s2 ? m2 : s2;
2992                 b2 -= i;
2993                 m2 -= i;
2994                 s2 -= i;
2995                 }
2996         if (b5 > 0) {
2997                 if (leftright) {
2998                         if (m5 > 0) {
2999                                 mhi = pow5mult(PASS_STATE mhi, m5);
3000                                 b1 = mult(PASS_STATE mhi, b);
3001                                 Bfree(PASS_STATE b);
3002                                 b = b1;
3003                                 }
3004                         if ((j = b5 - m5))
3005                                 b = pow5mult(PASS_STATE b, j);
3006                         }
3007                 else
3008                         b = pow5mult(PASS_STATE b, b5);
3009                 }
3010         S = i2b(PASS_STATE 1);
3011         if (s5 > 0)
3012                 S = pow5mult(PASS_STATE S, s5);
3013
3014         /* Check for special case that d is a normalized power of 2. */
3015
3016         spec_case = 0;
3017         if ((mode < 2 || leftright)
3018 #ifdef Honor_FLT_ROUNDS
3019                         && rounding == 1
3020 #endif
3021                                 ) {
3022                 if (!word1(d) && !(word0(d) & Bndry_mask)
3023 #ifndef Sudden_Underflow
3024                  && word0(d) & (Exp_mask & ~Exp_msk1)
3025 #endif
3026                                 ) {
3027                         /* The special case */
3028                         b2 += Log2P;
3029                         s2 += Log2P;
3030                         spec_case = 1;
3031                         }
3032                 }
3033
3034         /* Arrange for convenient computation of quotients:
3035          * shift left if necessary so divisor has 4 leading 0 bits.
3036          *
3037          * Perhaps we should just compute leading 28 bits of S once
3038          * and for all and pass them and a shift to quorem, so it
3039          * can do shifts and ors to compute the numerator for q.
3040          */
3041 #ifdef Pack_32
3042         if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f))
3043                 i = 32 - i;
3044 #else
3045         if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf)
3046                 i = 16 - i;
3047 #endif
3048         if (i > 4) {
3049                 i -= 4;
3050                 b2 += i;
3051                 m2 += i;
3052                 s2 += i;
3053                 }
3054         else if (i < 4) {
3055                 i += 28;
3056                 b2 += i;
3057                 m2 += i;
3058                 s2 += i;
3059                 }
3060         if (b2 > 0)
3061                 b = lshift(PASS_STATE b, b2);
3062         if (s2 > 0)
3063                 S = lshift(PASS_STATE S, s2);
3064         if (k_check) {
3065                 if (cmp(b,S) < 0) {
3066                         k--;
3067                         b = multadd(PASS_STATE b, 10, 0);       /* we botched the k estimate */
3068                         if (leftright)
3069                                 mhi = multadd(PASS_STATE mhi, 10, 0);
3070                         ilim = ilim1;
3071                         }
3072                 }
3073         if (ilim <= 0 && (mode == 3 || mode == 5)) {
3074                 if (ilim < 0 || cmp(b,S = multadd(PASS_STATE S,5,0)) < 0) {
3075                         /* no digits, fcvt style */
3076  no_digits:
3077                         /* MOZILLA CHANGE: Always return a non-empty string. */
3078                         *s++ = '0';
3079                         k = 0;
3080                         goto ret;
3081                         }
3082  one_digit:
3083                 *s++ = '1';
3084                 k++;
3085                 goto ret;
3086                 }
3087         if (leftright) {
3088                 if (m2 > 0)
3089                         mhi = lshift(PASS_STATE mhi, m2);
3090
3091                 /* Compute mlo -- check for special case
3092                  * that d is a normalized power of 2.
3093                  */
3094
3095                 mlo = mhi;
3096                 if (spec_case) {
3097                         mhi = Balloc(PASS_STATE mhi->k);
3098                         Bcopy(mhi, mlo);
3099                         mhi = lshift(PASS_STATE mhi, Log2P);
3100                         }
3101
3102                 for(i = 1;;i++) {
3103                         dig = quorem(b,S) + '0';
3104                         /* Do we yet have the shortest decimal string
3105                          * that will round to d?
3106                          */
3107                         j = cmp(b, mlo);
3108                         delta = diff(PASS_STATE S, mhi);
3109                         j1 = delta->sign ? 1 : cmp(b, delta);
3110                         Bfree(PASS_STATE delta);
3111 #ifndef ROUND_BIASED
3112                         if (j1 == 0 && mode != 1 && !(word1(d) & 1)
3113 #ifdef Honor_FLT_ROUNDS
3114                                 && rounding >= 1
3115 #endif
3116                                                                    ) {
3117                                 if (dig == '9')
3118                                         goto round_9_up;
3119                                 if (j > 0)
3120                                         dig++;
3121 #ifdef SET_INEXACT
3122                                 else if (!b->x[0] && b->wds <= 1)
3123                                         inexact = 0;
3124 #endif
3125                                 *s++ = dig;
3126                                 goto ret;
3127                                 }
3128 #endif
3129                         if (j < 0 || (j == 0 && mode != 1
3130 #ifndef ROUND_BIASED
3131                                                         && !(word1(d) & 1)
3132 #endif
3133                                         )) {
3134                                 if (!b->x[0] && b->wds <= 1) {
3135 #ifdef SET_INEXACT
3136                                         inexact = 0;
3137 #endif
3138                                         goto accept_dig;
3139                                         }
3140 #ifdef Honor_FLT_ROUNDS
3141                                 if (mode > 1)
3142                                  switch(rounding) {
3143                                   case 0: goto accept_dig;
3144                                   case 2: goto keep_dig;
3145                                   }
3146 #endif /*Honor_FLT_ROUNDS*/
3147                                 if (j1 > 0) {
3148                                         b = lshift(PASS_STATE b, 1);
3149                                         j1 = cmp(b, S);
3150                                         if ((j1 > 0 || (j1 == 0 && dig & 1))
3151                                         && dig++ == '9')
3152                                                 goto round_9_up;
3153                                         }
3154  accept_dig:
3155                                 *s++ = dig;
3156                                 goto ret;
3157                                 }
3158                         if (j1 > 0) {
3159 #ifdef Honor_FLT_ROUNDS
3160                                 if (!rounding)
3161                                         goto accept_dig;
3162 #endif
3163                                 if (dig == '9') { /* possible if i == 1 */
3164  round_9_up:
3165                                         *s++ = '9';
3166                                         goto roundoff;
3167                                         }
3168                                 *s++ = dig + 1;
3169                                 goto ret;
3170                                 }
3171 #ifdef Honor_FLT_ROUNDS
3172  keep_dig:
3173 #endif
3174                         *s++ = dig;
3175                         if (i == ilim)
3176                                 break;
3177                         b = multadd(PASS_STATE b, 10, 0);
3178                         if (mlo == mhi)
3179                                 mlo = mhi = multadd(PASS_STATE mhi, 10, 0);
3180                         else {
3181                                 mlo = multadd(PASS_STATE mlo, 10, 0);
3182                                 mhi = multadd(PASS_STATE mhi, 10, 0);
3183                                 }
3184                         }
3185                 }
3186         else
3187                 for(i = 1;; i++) {
3188                         *s++ = dig = quorem(b,S) + '0';
3189                         if (!b->x[0] && b->wds <= 1) {
3190 #ifdef SET_INEXACT
3191                                 inexact = 0;
3192 #endif
3193                                 goto ret;
3194                                 }
3195                         if (i >= ilim)
3196                                 break;
3197                         b = multadd(PASS_STATE b, 10, 0);
3198                         }
3199
3200         /* Round off last digit */
3201
3202 #ifdef Honor_FLT_ROUNDS
3203         switch(rounding) {
3204           case 0: goto trimzeros;
3205           case 2: goto roundoff;
3206           }
3207 #endif
3208         b = lshift(PASS_STATE b, 1);
3209         j = cmp(b, S);
3210         if (j >= 0) {  /* ECMA compatible rounding needed by Spidermonkey */
3211  roundoff:
3212                 while(*--s == '9')
3213                         if (s == s0) {
3214                                 k++;
3215                                 *s++ = '1';
3216                                 goto ret;
3217                                 }
3218                 ++*s++;
3219                 }
3220         else {
3221 #ifdef Honor_FLT_ROUNDS
3222  trimzeros:
3223 #endif
3224                 while(*--s == '0');
3225                 s++;
3226                 }
3227  ret:
3228         Bfree(PASS_STATE S);
3229         if (mhi) {
3230                 if (mlo && mlo != mhi)
3231                         Bfree(PASS_STATE mlo);
3232                 Bfree(PASS_STATE mhi);
3233                 }
3234  ret1:
3235 #ifdef SET_INEXACT
3236         if (inexact) {
3237                 if (!oldinexact) {
3238                         word0(d) = Exp_1 + (70 << Exp_shift);
3239                         word1(d) = 0;
3240                         dval(d) += 1.;
3241                         }
3242                 }
3243         else if (!oldinexact)
3244                 clear_inexact();
3245 #endif
3246         Bfree(PASS_STATE b);
3247         *s = 0;
3248         *decpt = k + 1;
3249         if (rve)
3250                 *rve = s;
3251         return s0;
3252         }
3253 #ifdef __cplusplus
3254 }
3255 #endif