libjava/java/lang/dtoa.c

   1 /****************************************************************
   2  *
   3  * The author of this software is David M. Gay.
   4  *
   5  * Copyright (c) 1991 by AT&T.
   6  *
   7  * Permission to use, copy, modify, and distribute this software for any
   8  * purpose without fee is hereby granted, provided that this entire notice
   9  * is included in all copies of any software which is or includes a copy
  10  * or modification of this software and in all copies of the supporting
  11  * documentation for such software.
  12  *
  13  * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
  14  * WARRANTY.  IN PARTICULAR, NEITHER THE AUTHOR NOR AT&T MAKES ANY
  15  * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
  16  * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
  17  *
  18  ***************************************************************/
  19
  20 /* Please send bug reports to
  21         David M. Gay
  22         AT&T Bell Laboratories, Room 2C-463
  23         600 Mountain Avenue
  24         Murray Hill, NJ 07974-2070
  25         U.S.A.
  26         dmg@research.att.com or research!dmg
  27  */
  28
  29 #include "mprec.h"
  30 #include <string.h>
  31
  32 static int
  33 _DEFUN (quorem,
  34         (b, S),
  35         _Jv_Bigint * b _AND _Jv_Bigint * S)
  36 {
  37   int n;
  38   long borrow, y;
  39   unsigned long carry, q, ys;
  40   unsigned long *bx, *bxe, *sx, *sxe;
  41 #ifdef Pack_32
  42   long z;
  43   unsigned long si, zs;
  44 #endif
  45
  46   n = S->_wds;
  47 #ifdef DEBUG
  48   /*debug*/ if (b->_wds > n)
  49     /*debug*/ Bug ("oversize b in quorem");
  50 #endif
  51   if (b->_wds < n)
  52     return 0;
  53   sx = S->_x;
  54   sxe = sx + --n;
  55   bx = b->_x;
  56   bxe = bx + n;
  57   q = *bxe / (*sxe + 1);        /* ensure q <= true quotient */
  58 #ifdef DEBUG
  59   /*debug*/ if (q > 9)
  60     /*debug*/ Bug ("oversized quotient in quorem");
  61 #endif
  62   if (q)
  63     {
  64       borrow = 0;
  65       carry = 0;
  66       do
  67         {
  68 #ifdef Pack_32
  69           si = *sx++;
  70           ys = (si & 0xffff) * q + carry;
  71           zs = (si >> 16) * q + (ys >> 16);
  72           carry = zs >> 16;
  73           y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
  74           borrow = y >> 16;
  75           Sign_Extend (borrow, y);
  76           z = (*bx >> 16) - (zs & 0xffff) + borrow;
  77           borrow = z >> 16;
  78           Sign_Extend (borrow, z);
  79           Storeinc (bx, z, y);
  80 #else
  81           ys = *sx++ * q + carry;
  82           carry = ys >> 16;
  83           y = *bx - (ys & 0xffff) + borrow;
  84           borrow = y >> 16;
  85           Sign_Extend (borrow, y);
  86           *bx++ = y & 0xffff;
  87 #endif
  88         }
  89       while (sx <= sxe);
  90       if (!*bxe)
  91         {
  92           bx = b->_x;
  93           while (--bxe > bx && !*bxe)
  94             --n;
  95           b->_wds = n;
  96         }
  97     }
  98   if (cmp (b, S) >= 0)
  99     {
 100       q++;
 101       borrow = 0;
 102       carry = 0;
 103       bx = b->_x;
 104       sx = S->_x;
 105       do
 106         {
 107 #ifdef Pack_32
 108           si = *sx++;
 109           ys = (si & 0xffff) + carry;
 110           zs = (si >> 16) + (ys >> 16);
 111           carry = zs >> 16;
 112           y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
 113           borrow = y >> 16;
 114           Sign_Extend (borrow, y);
 115           z = (*bx >> 16) - (zs & 0xffff) + borrow;
 116           borrow = z >> 16;
 117           Sign_Extend (borrow, z);
 118           Storeinc (bx, z, y);
 119 #else
 120           ys = *sx++ + carry;
 121           carry = ys >> 16;
 122           y = *bx - (ys & 0xffff) + borrow;
 123           borrow = y >> 16;
 124           Sign_Extend (borrow, y);
 125           *bx++ = y & 0xffff;
 126 #endif
 127         }
 128       while (sx <= sxe);
 129       bx = b->_x;
 130       bxe = bx + n;
 131       if (!*bxe)
 132         {
 133           while (--bxe > bx && !*bxe)
 134             --n;
 135           b->_wds = n;
 136         }
 137     }
 138   return q;
 139 }
 140
 141 #ifdef DEBUG
 142 #include <stdio.h>
 143
 144 void
 145 print (_Jv_Bigint * b)
 146 {
 147   int i, wds;
 148   unsigned long *x, y;
 149   wds = b->_wds;
 150   x = b->_x+wds;
 151   i = 0;
 152   do
 153     {
 154       x--;
 155       fprintf (stderr, "%08x", *x);
 156     }
 157   while (++i < wds);
 158   fprintf (stderr, "\n");
 159 }
 160 #endif
 161
 162 /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
 163  *
 164  * Inspired by "How to Print Floating-Point Numbers Accurately" by
 165  * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101].
 166  *
 167  * Modifications:
 168  *      1. Rather than iterating, we use a simple numeric overestimate
 169  *         to determine k = floor(log10(d)).  We scale relevant
 170  *         quantities using O(log2(k)) rather than O(k) multiplications.
 171  *      2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
 172  *         try to generate digits strictly left to right.  Instead, we
 173  *         compute with fewer bits and propagate the carry if necessary
 174  *         when rounding the final digit up.  This is often faster.
 175  *      3. Under the assumption that input will be rounded nearest,
 176  *         mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
 177  *         That is, we allow equality in stopping tests when the
 178  *         round-nearest rule will give the same floating-point value
 179  *         as would satisfaction of the stopping test with strict
 180  *         inequality.
 181  *      4. We remove common factors of powers of 2 from relevant
 182  *         quantities.
 183  *      5. When converting floating-point integers less than 1e16,
 184  *         we use floating-point arithmetic rather than resorting
 185  *         to multiple-precision integers.
 186  *      6. When asked to produce fewer than 15 digits, we first try
 187  *         to get by with floating-point arithmetic; we resort to
 188  *         multiple-precision integer arithmetic only if we cannot
 189  *         guarantee that the floating-point calculation has given
 190  *         the correctly rounded result.  For k requested digits and
 191  *         "uniformly" distributed input, the probability is
 192  *         something like 10^(k-15) that we must resort to the long
 193  *         calculation.
 194  */
 195
 196
 197 char *
 198 _DEFUN (_dtoa_r,
 199         (ptr, _d, mode, ndigits, decpt, sign, rve, float_type),
 200         struct _Jv_reent *ptr _AND
 201         double _d _AND
 202         int mode _AND
 203         int ndigits _AND
 204         int *decpt _AND
 205         int *sign _AND
 206         char **rve _AND
 207         int float_type)
 208 {
 209   /*
 210         float_type == 0 for double precision, 1 for float.
 211
 212         Arguments ndigits, decpt, sign are similar to those
 213         of ecvt and fcvt; trailing zeros are suppressed from
 214         the returned string.  If not null, *rve is set to point
 215         to the end of the return value.  If d is +-Infinity or NaN,
 216         then *decpt is set to 9999.
 217
 218         mode:
 219                 0 ==> shortest string that yields d when read in
 220                         and rounded to nearest.
 221                 1 ==> like 0, but with Steele & White stopping rule;
 222                         e.g. with IEEE P754 arithmetic , mode 0 gives
 223                         1e23 whereas mode 1 gives 9.999999999999999e22.
 224                 2 ==> max(1,ndigits) significant digits.  This gives a
 225                         return value similar to that of ecvt, except
 226                         that trailing zeros are suppressed.
 227                 3 ==> through ndigits past the decimal point.  This
 228                         gives a return value similar to that from fcvt,
 229                         except that trailing zeros are suppressed, and
 230                         ndigits can be negative.
 231                 4-9 should give the same return values as 2-3, i.e.,
 232                         4 <= mode <= 9 ==> same return as mode
 233                         2 + (mode & 1).  These modes are mainly for
 234                         debugging; often they run slower but sometimes
 235                         faster than modes 2-3.
 236                 4,5,8,9 ==> left-to-right digit generation.
 237                 6-9 ==> don't try fast floating-point estimate
 238                         (if applicable).
 239
 240                 > 16 ==> Floating-point arg is treated as single precision.
 241
 242                 Values of mode other than 0-9 are treated as mode 0.
 243
 244                 Sufficient space is allocated to the return value
 245                 to hold the suppressed trailing zeros.
 246         */
 247
 248   int bbits, b2, b5, be, dig, i, ieps, ilim0, j, j1, k, k0,
 249     k_check, leftright, m2, m5, s2, s5, try_quick;
 250   int ilim = 0, ilim1 = 0, spec_case = 0;
 251   union double_union d, d2, eps;
 252   long L;
 253 #ifndef Sudden_Underflow
 254   int denorm;
 255   unsigned long x;
 256 #endif
 257   _Jv_Bigint *b, *b1, *delta, *mlo = NULL, *mhi, *S;
 258   double ds;
 259   char *s, *s0;
 260
 261   d.d = _d;
 262
 263   if (ptr->_result)
 264     {
 265       ptr->_result->_k = ptr->_result_k;
 266       ptr->_result->_maxwds = 1 << ptr->_result_k;
 267       Bfree (ptr, ptr->_result);
 268       ptr->_result = 0;
 269     }
 270
 271   if (word0 (d) & Sign_bit)
 272     {
 273       /* set sign for everything, including 0's and NaNs */
 274       *sign = 1;
 275       word0 (d) &= ~Sign_bit;   /* clear sign bit */
 276     }
 277   else
 278     *sign = 0;
 279
 280 #if defined(IEEE_Arith) + defined(VAX)
 281 #ifdef IEEE_Arith
 282   if ((word0 (d) & Exp_mask) == Exp_mask)
 283 #else
 284   if (word0 (d) == 0x8000)
 285 #endif
 286     {
 287       /* Infinity or NaN */
 288       *decpt = 9999;
 289       s =
 290 #ifdef IEEE_Arith
 291         !word1 (d) && !(word0 (d) & 0xfffff) ? "Infinity" :
 292 #endif
 293         "NaN";
 294       if (rve)
 295         *rve =
 296 #ifdef IEEE_Arith
 297           s[3] ? s + 8 :
 298 #endif
 299           s + 3;
 300       return s;
 301     }
 302 #endif
 303 #ifdef IBM
 304   d.d += 0;                     /* normalize */
 305 #endif
 306   if (!d.d)
 307     {
 308       *decpt = 1;
 309       s = "0";
 310       if (rve)
 311         *rve = s + 1;
 312       return s;
 313     }
 314
 315   b = d2b (ptr, d.d, &be, &bbits);
 316 #ifdef Sudden_Underflow
 317   i = (int) (word0 (d) >> Exp_shift1 & (Exp_mask >> Exp_shift1));
 318 #else
 319   if ((i = (int) (word0 (d) >> Exp_shift1 & (Exp_mask >> Exp_shift1))))
 320     {
 321 #endif
 322       d2.d = d.d;
 323       word0 (d2) &= Frac_mask1;
 324       word0 (d2) |= Exp_11;
 325 #ifdef IBM
 326       if (j = 11 - hi0bits (word0 (d2) & Frac_mask))
 327         d2.d /= 1 << j;
 328 #endif
 329
 330       /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
 331                  * log10(x)      =  log(x) / log(10)
 332                  *              ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
 333                  * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
 334                  *
 335                  * This suggests computing an approximation k to log10(d) by
 336                  *
 337                  * k = (i - Bias)*0.301029995663981
 338                  *      + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
 339                  *
 340                  * We want k to be too large rather than too small.
 341                  * The error in the first-order Taylor series approximation
 342                  * is in our favor, so we just round up the constant enough
 343                  * to compensate for any error in the multiplication of
 344                  * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
 345                  * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
 346                  * adding 1e-13 to the constant term more than suffices.
 347                  * Hence we adjust the constant term to 0.1760912590558.
 348                  * (We could get a more accurate k by invoking log10,
 349                  *  but this is probably not worthwhile.)
 350                  */
 351
 352       i -= Bias;
 353 #ifdef IBM
 354       i <<= 2;
 355       i += j;
 356 #endif
 357 #ifndef Sudden_Underflow
 358       denorm = 0;
 359     }
 360   else
 361     {
 362       /* d is denormalized */
 363
 364       i = bbits + be + (Bias + (P - 1) - 1);
 365       x = i > 32 ? word0 (d) << (64 - i) | word1 (d) >> (i - 32)
 366         : word1 (d) << (32 - i);
 367       d2.d = x;
 368       word0 (d2) -= 31 * Exp_msk1;      /* adjust exponent */
 369       i -= (Bias + (P - 1) - 1) + 1;
 370       denorm = 1;
 371     }
 372 #endif
 373   ds = (d2.d - 1.5) * 0.289529654602168 + 0.1760912590558 + i * 0.301029995663981;
 374   k = (int) ds;
 375   if (ds < 0. && ds != k)
 376     k--;                        /* want k = floor(ds) */
 377   k_check = 1;
 378   if (k >= 0 && k <= Ten_pmax)
 379     {
 380       if (d.d < tens[k])
 381         k--;
 382       k_check = 0;
 383     }
 384   j = bbits - i - 1;
 385   if (j >= 0)
 386     {
 387       b2 = 0;
 388       s2 = j;
 389     }
 390   else
 391     {
 392       b2 = -j;
 393       s2 = 0;
 394     }
 395   if (k >= 0)
 396     {
 397       b5 = 0;
 398       s5 = k;
 399       s2 += k;
 400     }
 401   else
 402     {
 403       b2 -= k;
 404       b5 = -k;
 405       s5 = 0;
 406     }
 407   if (mode < 0 || mode > 9)
 408     mode = 0;
 409   try_quick = 1;
 410   if (mode > 5)
 411     {
 412       mode -= 4;
 413       try_quick = 0;
 414     }
 415   leftright = 1;
 416   switch (mode)
 417     {
 418     case 0:
 419     case 1:
 420       ilim = ilim1 = -1;
 421       i = 18;
 422       ndigits = 0;
 423       break;
 424     case 2:
 425       leftright = 0;
 426       /* no break */
 427     case 4:
 428       if (ndigits <= 0)
 429         ndigits = 1;
 430       ilim = ilim1 = i = ndigits;
 431       break;
 432     case 3:
 433       leftright = 0;
 434       /* no break */
 435     case 5:
 436       i = ndigits + k + 1;
 437       ilim = i;
 438       ilim1 = i - 1;
 439       if (i <= 0)
 440         i = 1;
 441     }
 442   j = sizeof (unsigned long);
 443   for (ptr->_result_k = 0; (int) (sizeof (_Jv_Bigint) - sizeof (unsigned long)) + j <= i;
 444        j <<= 1)
 445     ptr->_result_k++;
 446   ptr->_result = Balloc (ptr, ptr->_result_k);
 447   s = s0 = (char *) ptr->_result;
 448
 449   if (ilim >= 0 && ilim <= Quick_max && try_quick)
 450     {
 451       /* Try to get by with floating-point arithmetic. */
 452
 453       i = 0;
 454       d2.d = d.d;
 455       k0 = k;
 456       ilim0 = ilim;
 457       ieps = 2;                 /* conservative */
 458       if (k > 0)
 459         {
 460           ds = tens[k & 0xf];
 461           j = k >> 4;
 462           if (j & Bletch)
 463             {
 464               /* prevent overflows */
 465               j &= Bletch - 1;
 466               d.d /= bigtens[n_bigtens - 1];
 467               ieps++;
 468             }
 469           for (; j; j >>= 1, i++)
 470             if (j & 1)
 471               {
 472                 ieps++;
 473                 ds *= bigtens[i];
 474               }
 475           d.d /= ds;
 476         }
 477       else if ((j1 = -k))
 478         {
 479           d.d *= tens[j1 & 0xf];
 480           for (j = j1 >> 4; j; j >>= 1, i++)
 481             if (j & 1)
 482               {
 483                 ieps++;
 484                 d.d *= bigtens[i];
 485               }
 486         }
 487       if (k_check && d.d < 1. && ilim > 0)
 488         {
 489           if (ilim1 <= 0)
 490             goto fast_failed;
 491           ilim = ilim1;
 492           k--;
 493           d.d *= 10.;
 494           ieps++;
 495         }
 496       eps.d = ieps * d.d + 7.;
 497       word0 (eps) -= (P - 1) * Exp_msk1;
 498       if (ilim == 0)
 499         {
 500           S = mhi = 0;
 501           d.d -= 5.;
 502           if (d.d > eps.d)
 503             goto one_digit;
 504           if (d.d < -eps.d)
 505             goto no_digits;
 506           goto fast_failed;
 507         }
 508 #ifndef No_leftright
 509       if (leftright)
 510         {
 511           /* Use Steele & White method of only
 512            * generating digits needed.
 513            */
 514           eps.d = 0.5 / tens[ilim - 1] - eps.d;
 515           for (i = 0;;)
 516             {
 517               L = d.d;
 518               d.d -= L;
 519               *s++ = '0' + (int) L;
 520               if (d.d < eps.d)
 521                 goto ret1;
 522               if (1. - d.d < eps.d)
 523                 goto bump_up;
 524               if (++i >= ilim)
 525                 break;
 526               eps.d *= 10.;
 527               d.d *= 10.;
 528             }
 529         }
 530       else
 531         {
 532 #endif
 533           /* Generate ilim digits, then fix them up. */
 534           eps.d *= tens[ilim - 1];
 535           for (i = 1;; i++, d.d *= 10.)
 536             {
 537               L = d.d;
 538               d.d -= L;
 539               *s++ = '0' + (int) L;
 540               if (i == ilim)
 541                 {
 542                   if (d.d > 0.5 + eps.d)
 543                     goto bump_up;
 544                   else if (d.d < 0.5 - eps.d)
 545                     {
 546                       while (*--s == '0');
 547                       s++;
 548                       goto ret1;
 549                     }
 550                   break;
 551                 }
 552             }
 553 #ifndef No_leftright
 554         }
 555 #endif
 556     fast_failed:
 557       s = s0;
 558       d.d = d2.d;
 559       k = k0;
 560       ilim = ilim0;
 561     }
 562
 563   /* Do we have a "small" integer? */
 564
 565   if (be >= 0 && k <= Int_max)
 566     {
 567       /* Yes. */
 568       ds = tens[k];
 569       if (ndigits < 0 && ilim <= 0)
 570         {
 571           S = mhi = 0;
 572           if (ilim < 0 || d.d <= 5 * ds)
 573             goto no_digits;
 574           goto one_digit;
 575         }
 576       for (i = 1;; i++)
 577         {
 578           L = d.d / ds;
 579           d.d -= L * ds;
 580 #ifdef Check_FLT_ROUNDS
 581           /* If FLT_ROUNDS == 2, L will usually be high by 1 */
 582           if (d.d < 0)
 583             {
 584               L--;
 585               d.d += ds;
 586             }
 587 #endif
 588           *s++ = '0' + (int) L;
 589           if (i == ilim)
 590             {
 591               d.d += d.d;
 592               if (d.d > ds || (d.d == ds && L & 1))
 593                 {
 594                 bump_up:
 595                   while (*--s == '9')
 596                     if (s == s0)
 597                       {
 598                         k++;
 599                         *s = '0';
 600                         break;
 601                       }
 602                   ++*s++;
 603                 }
 604               break;
 605             }
 606           if (!(d.d *= 10.))
 607             break;
 608         }
 609       goto ret1;
 610     }
 611
 612   m2 = b2;
 613   m5 = b5;
 614   mhi = mlo = 0;
 615   if (leftright)
 616     {
 617       if (mode < 2)
 618         {
 619           i =
 620 #ifndef Sudden_Underflow
 621             denorm ? be + (Bias + (P - 1) - 1 + 1) :
 622 #endif
 623 #ifdef IBM
 624             1 + 4 * P - 3 - bbits + ((bbits + be - 1) & 3);
 625 #else
 626             1 + P - bbits;
 627 #endif
 628         }
 629       else
 630         {
 631           j = ilim - 1;
 632           if (m5 >= j)
 633             m5 -= j;
 634           else
 635             {
 636               s5 += j -= m5;
 637               b5 += j;
 638               m5 = 0;
 639             }
 640           if ((i = ilim) < 0)
 641             {
 642               m2 -= i;
 643               i = 0;
 644             }
 645         }
 646       b2 += i;
 647       s2 += i;
 648       mhi = i2b (ptr, 1);
 649     }
 650   if (m2 > 0 && s2 > 0)
 651     {
 652       i = m2 < s2 ? m2 : s2;
 653       b2 -= i;
 654       m2 -= i;
 655       s2 -= i;
 656     }
 657   if (b5 > 0)
 658     {
 659       if (leftright)
 660         {
 661           if (m5 > 0)
 662             {
 663               mhi = pow5mult (ptr, mhi, m5);
 664               b1 = mult (ptr, mhi, b);
 665               Bfree (ptr, b);
 666               b = b1;
 667             }
 668           if ((j = b5 - m5))
 669             b = pow5mult (ptr, b, j);
 670         }
 671       else
 672         b = pow5mult (ptr, b, b5);
 673     }
 674   S = i2b (ptr, 1);
 675   if (s5 > 0)
 676     S = pow5mult (ptr, S, s5);
 677
 678   /* Check for special case that d is a normalized power of 2. */
 679
 680   if (mode < 2)
 681     {
 682       if (!word1 (d) && !(word0 (d) & Bndry_mask)
 683 #ifndef Sudden_Underflow
 684           && word0(d) & Exp_mask
 685 #endif
 686         )
 687         {
 688           /* The special case */
 689           b2 += Log2P;
 690           s2 += Log2P;
 691           spec_case = 1;
 692         }
 693       else
 694         spec_case = 0;
 695     }
 696
 697   /* Arrange for convenient computation of quotients:
 698    * shift left if necessary so divisor has 4 leading 0 bits.
 699    *
 700    * Perhaps we should just compute leading 28 bits of S once
 701    * and for all and pass them and a shift to quorem, so it
 702    * can do shifts and ors to compute the numerator for q.
 703    */
 704
 705 #ifdef Pack_32
 706   if ((i = ((s5 ? 32 - hi0bits (S->_x[S->_wds - 1]) : 1) + s2) & 0x1f))
 707     i = 32 - i;
 708 #else
 709   if ((i = ((s5 ? 32 - hi0bits (S->_x[S->_wds - 1]) : 1) + s2) & 0xf))
 710     i = 16 - i;
 711 #endif
 712   if (i > 4)
 713     {
 714       i -= 4;
 715       b2 += i;
 716       m2 += i;
 717       s2 += i;
 718     }
 719   else if (i < 4)
 720     {
 721       i += 28;
 722       b2 += i;
 723       m2 += i;
 724       s2 += i;
 725     }
 726   if (b2 > 0)
 727     b = lshift (ptr, b, b2);
 728   if (s2 > 0)
 729     S = lshift (ptr, S, s2);
 730   if (k_check)
 731     {
 732       if (cmp (b, S) < 0)
 733         {
 734           k--;
 735           b = multadd (ptr, b, 10, 0);  /* we botched the k estimate */
 736           if (leftright)
 737             mhi = multadd (ptr, mhi, 10, 0);
 738           ilim = ilim1;
 739         }
 740     }
 741   if (ilim <= 0 && mode > 2)
 742     {
 743       if (ilim < 0 || cmp (b, S = multadd (ptr, S, 5, 0)) <= 0)
 744         {
 745           /* no digits, fcvt style */
 746         no_digits:
 747           k = -1 - ndigits;
 748           goto ret;
 749         }
 750     one_digit:
 751       *s++ = '1';
 752       k++;
 753       goto ret;
 754     }
 755   if (leftright)
 756     {
 757       if (m2 > 0)
 758         mhi = lshift (ptr, mhi, m2);
 759
 760       /* Single precision case, */
 761       if (float_type)
 762         mhi = lshift (ptr, mhi, 29);
 763
 764       /* Compute mlo -- check for special case
 765        * that d is a normalized power of 2.
 766        */
 767
 768       mlo = mhi;
 769       if (spec_case)
 770         {
 771           mhi = Balloc (ptr, mhi->_k);
 772           Bcopy (mhi, mlo);
 773           mhi = lshift (ptr, mhi, Log2P);
 774         }
 775
 776       for (i = 1;; i++)
 777         {
 778           dig = quorem (b, S) + '0';
 779           /* Do we yet have the shortest decimal string
 780            * that will round to d?
 781            */
 782           j = cmp (b, mlo);
 783           delta = diff (ptr, S, mhi);
 784           j1 = delta->_sign ? 1 : cmp (b, delta);
 785           Bfree (ptr, delta);
 786 #ifndef ROUND_BIASED
 787           if (j1 == 0 && !mode && !(word1 (d) & 1))
 788             {
 789               if (dig == '9')
 790                 goto round_9_up;
 791               if (j > 0)
 792                 dig++;
 793               *s++ = dig;
 794               goto ret;
 795             }
 796 #endif
 797           if (j < 0 || (j == 0 && !mode
 798 #ifndef ROUND_BIASED
 799               && !(word1 (d) & 1)
 800 #endif
 801             ))
 802             {
 803               if (j1 > 0)
 804                 {
 805                   b = lshift (ptr, b, 1);
 806                   j1 = cmp (b, S);
 807                   if ((j1 > 0 || (j1 == 0 && dig & 1))
 808                       && dig++ == '9')
 809                     goto round_9_up;
 810                 }
 811               *s++ = dig;
 812               goto ret;
 813             }
 814           if (j1 > 0)
 815             {
 816               if (dig == '9')
 817                 {               /* possible if i == 1 */
 818                 round_9_up:
 819                   *s++ = '9';
 820                   goto roundoff;
 821                 }
 822               *s++ = dig + 1;
 823               goto ret;
 824             }
 825           *s++ = dig;
 826           if (i == ilim)
 827             break;
 828           b = multadd (ptr, b, 10, 0);
 829           if (mlo == mhi)
 830             mlo = mhi = multadd (ptr, mhi, 10, 0);
 831           else
 832             {
 833               mlo = multadd (ptr, mlo, 10, 0);
 834               mhi = multadd (ptr, mhi, 10, 0);
 835             }
 836         }
 837     }
 838   else
 839     for (i = 1;; i++)
 840       {
 841         *s++ = dig = quorem (b, S) + '0';
 842         if (i >= ilim)
 843           break;
 844         b = multadd (ptr, b, 10, 0);
 845       }
 846
 847   /* Round off last digit */
 848
 849   b = lshift (ptr, b, 1);
 850   j = cmp (b, S);
 851   if (j > 0 || (j == 0 && dig & 1))
 852     {
 853     roundoff:
 854       while (*--s == '9')
 855         if (s == s0)
 856           {
 857             k++;
 858             *s++ = '1';
 859             goto ret;
 860           }
 861       ++*s++;
 862     }
 863   else
 864     {
 865       while (*--s == '0');
 866       s++;
 867     }
 868 ret:
 869   Bfree (ptr, S);
 870   if (mhi)
 871     {
 872       if (mlo && mlo != mhi)
 873         Bfree (ptr, mlo);
 874       Bfree (ptr, mhi);
 875     }
 876 ret1:
 877   Bfree (ptr, b);
 878   *s = 0;
 879   *decpt = k + 1;
 880   if (rve)
 881     *rve = s;
 882   return s0;
 883 }
 884
 885
 886 _VOID
 887 _DEFUN (_dtoa,
 888         (_d, mode, ndigits, decpt, sign, rve, buf, float_type),
 889         double _d _AND
 890         int mode _AND
 891         int ndigits _AND
 892         int *decpt _AND
 893         int *sign _AND
 894         char **rve _AND
 895         char *buf _AND
 896         int float_type)
 897 {
 898   struct _Jv_reent reent;
 899   char *p;
 900   memset (&reent, 0, sizeof reent);
 901
 902   p = _dtoa_r (&reent, _d, mode, ndigits, decpt, sign, rve, float_type);
 903   strcpy (buf, p);
 904
 905   return;
 906 }