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, ilim, ilim0, ilim1, j, j1, k, k0,
 249     k_check, leftright, m2, m5, s2, s5, spec_case, try_quick;
 250   union double_union d, d2, eps;
 251   long L;
 252 #ifndef Sudden_Underflow
 253   int denorm;
 254   unsigned long x;
 255 #endif
 256   _Jv_Bigint *b, *b1, *delta, *mlo, *mhi, *S;
 257   double ds;
 258   char *s, *s0;
 259
 260   d.d = _d;
 261
 262   if (ptr->_result)
 263     {
 264       ptr->_result->_k = ptr->_result_k;
 265       ptr->_result->_maxwds = 1 << ptr->_result_k;
 266       Bfree (ptr, ptr->_result);
 267       ptr->_result = 0;
 268     }
 269
 270   if (word0 (d) & Sign_bit)
 271     {
 272       /* set sign for everything, including 0's and NaNs */
 273       *sign = 1;
 274       word0 (d) &= ~Sign_bit;   /* clear sign bit */
 275     }
 276   else
 277     *sign = 0;
 278
 279 #if defined(IEEE_Arith) + defined(VAX)
 280 #ifdef IEEE_Arith
 281   if ((word0 (d) & Exp_mask) == Exp_mask)
 282 #else
 283   if (word0 (d) == 0x8000)
 284 #endif
 285     {
 286       /* Infinity or NaN */
 287       *decpt = 9999;
 288       s =
 289 #ifdef IEEE_Arith
 290         !word1 (d) && !(word0 (d) & 0xfffff) ? "Infinity" :
 291 #endif
 292         "NaN";
 293       if (rve)
 294         *rve =
 295 #ifdef IEEE_Arith
 296           s[3] ? s + 8 :
 297 #endif
 298           s + 3;
 299       return s;
 300     }
 301 #endif
 302 #ifdef IBM
 303   d.d += 0;                     /* normalize */
 304 #endif
 305   if (!d.d)
 306     {
 307       *decpt = 1;
 308       s = "0";
 309       if (rve)
 310         *rve = s + 1;
 311       return s;
 312     }
 313
 314   b = d2b (ptr, d.d, &be, &bbits);
 315 #ifdef Sudden_Underflow
 316   i = (int) (word0 (d) >> Exp_shift1 & (Exp_mask >> Exp_shift1));
 317 #else
 318   if ((i = (int) (word0 (d) >> Exp_shift1 & (Exp_mask >> Exp_shift1))))
 319     {
 320 #endif
 321       d2.d = d.d;
 322       word0 (d2) &= Frac_mask1;
 323       word0 (d2) |= Exp_11;
 324 #ifdef IBM
 325       if (j = 11 - hi0bits (word0 (d2) & Frac_mask))
 326         d2.d /= 1 << j;
 327 #endif
 328
 329       /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
 330                  * log10(x)      =  log(x) / log(10)
 331                  *              ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
 332                  * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
 333                  *
 334                  * This suggests computing an approximation k to log10(d) by
 335                  *
 336                  * k = (i - Bias)*0.301029995663981
 337                  *      + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
 338                  *
 339                  * We want k to be too large rather than too small.
 340                  * The error in the first-order Taylor series approximation
 341                  * is in our favor, so we just round up the constant enough
 342                  * to compensate for any error in the multiplication of
 343                  * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
 344                  * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
 345                  * adding 1e-13 to the constant term more than suffices.
 346                  * Hence we adjust the constant term to 0.1760912590558.
 347                  * (We could get a more accurate k by invoking log10,
 348                  *  but this is probably not worthwhile.)
 349                  */
 350
 351       i -= Bias;
 352 #ifdef IBM
 353       i <<= 2;
 354       i += j;
 355 #endif
 356 #ifndef Sudden_Underflow
 357       denorm = 0;
 358     }
 359   else
 360     {
 361       /* d is denormalized */
 362
 363       i = bbits + be + (Bias + (P - 1) - 1);
 364       x = i > 32 ? word0 (d) << (64 - i) | word1 (d) >> (i - 32)
 365         : word1 (d) << (32 - i);
 366       d2.d = x;
 367       word0 (d2) -= 31 * Exp_msk1;      /* adjust exponent */
 368       i -= (Bias + (P - 1) - 1) + 1;
 369       denorm = 1;
 370     }
 371 #endif
 372   ds = (d2.d - 1.5) * 0.289529654602168 + 0.1760912590558 + i * 0.301029995663981;
 373   k = (int) ds;
 374   if (ds < 0. && ds != k)
 375     k--;                        /* want k = floor(ds) */
 376   k_check = 1;
 377   if (k >= 0 && k <= Ten_pmax)
 378     {
 379       if (d.d < tens[k])
 380         k--;
 381       k_check = 0;
 382     }
 383   j = bbits - i - 1;
 384   if (j >= 0)
 385     {
 386       b2 = 0;
 387       s2 = j;
 388     }
 389   else
 390     {
 391       b2 = -j;
 392       s2 = 0;
 393     }
 394   if (k >= 0)
 395     {
 396       b5 = 0;
 397       s5 = k;
 398       s2 += k;
 399     }
 400   else
 401     {
 402       b2 -= k;
 403       b5 = -k;
 404       s5 = 0;
 405     }
 406   if (mode < 0 || mode > 9)
 407     mode = 0;
 408   try_quick = 1;
 409   if (mode > 5)
 410     {
 411       mode -= 4;
 412       try_quick = 0;
 413     }
 414   leftright = 1;
 415   switch (mode)
 416     {
 417     case 0:
 418     case 1:
 419       ilim = ilim1 = -1;
 420       i = 18;
 421       ndigits = 0;
 422       break;
 423     case 2:
 424       leftright = 0;
 425       /* no break */
 426     case 4:
 427       if (ndigits <= 0)
 428         ndigits = 1;
 429       ilim = ilim1 = i = ndigits;
 430       break;
 431     case 3:
 432       leftright = 0;
 433       /* no break */
 434     case 5:
 435       i = ndigits + k + 1;
 436       ilim = i;
 437       ilim1 = i - 1;
 438       if (i <= 0)
 439         i = 1;
 440     }
 441   j = sizeof (unsigned long);
 442   for (ptr->_result_k = 0; (int) (sizeof (_Jv_Bigint) - sizeof (unsigned long)) + j <= i;
 443        j <<= 1)
 444     ptr->_result_k++;
 445   ptr->_result = Balloc (ptr, ptr->_result_k);
 446   s = s0 = (char *) ptr->_result;
 447
 448   if (ilim >= 0 && ilim <= Quick_max && try_quick)
 449     {
 450       /* Try to get by with floating-point arithmetic. */
 451
 452       i = 0;
 453       d2.d = d.d;
 454       k0 = k;
 455       ilim0 = ilim;
 456       ieps = 2;                 /* conservative */
 457       if (k > 0)
 458         {
 459           ds = tens[k & 0xf];
 460           j = k >> 4;
 461           if (j & Bletch)
 462             {
 463               /* prevent overflows */
 464               j &= Bletch - 1;
 465               d.d /= bigtens[n_bigtens - 1];
 466               ieps++;
 467             }
 468           for (; j; j >>= 1, i++)
 469             if (j & 1)
 470               {
 471                 ieps++;
 472                 ds *= bigtens[i];
 473               }
 474           d.d /= ds;
 475         }
 476       else if ((j1 = -k))
 477         {
 478           d.d *= tens[j1 & 0xf];
 479           for (j = j1 >> 4; j; j >>= 1, i++)
 480             if (j & 1)
 481               {
 482                 ieps++;
 483                 d.d *= bigtens[i];
 484               }
 485         }
 486       if (k_check && d.d < 1. && ilim > 0)
 487         {
 488           if (ilim1 <= 0)
 489             goto fast_failed;
 490           ilim = ilim1;
 491           k--;
 492           d.d *= 10.;
 493           ieps++;
 494         }
 495       eps.d = ieps * d.d + 7.;
 496       word0 (eps) -= (P - 1) * Exp_msk1;
 497       if (ilim == 0)
 498         {
 499           S = mhi = 0;
 500           d.d -= 5.;
 501           if (d.d > eps.d)
 502             goto one_digit;
 503           if (d.d < -eps.d)
 504             goto no_digits;
 505           goto fast_failed;
 506         }
 507 #ifndef No_leftright
 508       if (leftright)
 509         {
 510           /* Use Steele & White method of only
 511            * generating digits needed.
 512            */
 513           eps.d = 0.5 / tens[ilim - 1] - eps.d;
 514           for (i = 0;;)
 515             {
 516               L = d.d;
 517               d.d -= L;
 518               *s++ = '0' + (int) L;
 519               if (d.d < eps.d)
 520                 goto ret1;
 521               if (1. - d.d < eps.d)
 522                 goto bump_up;
 523               if (++i >= ilim)
 524                 break;
 525               eps.d *= 10.;
 526               d.d *= 10.;
 527             }
 528         }
 529       else
 530         {
 531 #endif
 532           /* Generate ilim digits, then fix them up. */
 533           eps.d *= tens[ilim - 1];
 534           for (i = 1;; i++, d.d *= 10.)
 535             {
 536               L = d.d;
 537               d.d -= L;
 538               *s++ = '0' + (int) L;
 539               if (i == ilim)
 540                 {
 541                   if (d.d > 0.5 + eps.d)
 542                     goto bump_up;
 543                   else if (d.d < 0.5 - eps.d)
 544                     {
 545                       while (*--s == '0');
 546                       s++;
 547                       goto ret1;
 548                     }
 549                   break;
 550                 }
 551             }
 552 #ifndef No_leftright
 553         }
 554 #endif
 555     fast_failed:
 556       s = s0;
 557       d.d = d2.d;
 558       k = k0;
 559       ilim = ilim0;
 560     }
 561
 562   /* Do we have a "small" integer? */
 563
 564   if (be >= 0 && k <= Int_max)
 565     {
 566       /* Yes. */
 567       ds = tens[k];
 568       if (ndigits < 0 && ilim <= 0)
 569         {
 570           S = mhi = 0;
 571           if (ilim < 0 || d.d <= 5 * ds)
 572             goto no_digits;
 573           goto one_digit;
 574         }
 575       for (i = 1;; i++)
 576         {
 577           L = d.d / ds;
 578           d.d -= L * ds;
 579 #ifdef Check_FLT_ROUNDS
 580           /* If FLT_ROUNDS == 2, L will usually be high by 1 */
 581           if (d.d < 0)
 582             {
 583               L--;
 584               d.d += ds;
 585             }
 586 #endif
 587           *s++ = '0' + (int) L;
 588           if (i == ilim)
 589             {
 590               d.d += d.d;
 591               if (d.d > ds || (d.d == ds && L & 1))
 592                 {
 593                 bump_up:
 594                   while (*--s == '9')
 595                     if (s == s0)
 596                       {
 597                         k++;
 598                         *s = '0';
 599                         break;
 600                       }
 601                   ++*s++;
 602                 }
 603               break;
 604             }
 605           if (!(d.d *= 10.))
 606             break;
 607         }
 608       goto ret1;
 609     }
 610
 611   m2 = b2;
 612   m5 = b5;
 613   mhi = mlo = 0;
 614   if (leftright)
 615     {
 616       if (mode < 2)
 617         {
 618           i =
 619 #ifndef Sudden_Underflow
 620             denorm ? be + (Bias + (P - 1) - 1 + 1) :
 621 #endif
 622 #ifdef IBM
 623             1 + 4 * P - 3 - bbits + ((bbits + be - 1) & 3);
 624 #else
 625             1 + P - bbits;
 626 #endif
 627         }
 628       else
 629         {
 630           j = ilim - 1;
 631           if (m5 >= j)
 632             m5 -= j;
 633           else
 634             {
 635               s5 += j -= m5;
 636               b5 += j;
 637               m5 = 0;
 638             }
 639           if ((i = ilim) < 0)
 640             {
 641               m2 -= i;
 642               i = 0;
 643             }
 644         }
 645       b2 += i;
 646       s2 += i;
 647       mhi = i2b (ptr, 1);
 648     }
 649   if (m2 > 0 && s2 > 0)
 650     {
 651       i = m2 < s2 ? m2 : s2;
 652       b2 -= i;
 653       m2 -= i;
 654       s2 -= i;
 655     }
 656   if (b5 > 0)
 657     {
 658       if (leftright)
 659         {
 660           if (m5 > 0)
 661             {
 662               mhi = pow5mult (ptr, mhi, m5);
 663               b1 = mult (ptr, mhi, b);
 664               Bfree (ptr, b);
 665               b = b1;
 666             }
 667           if ((j = b5 - m5))
 668             b = pow5mult (ptr, b, j);
 669         }
 670       else
 671         b = pow5mult (ptr, b, b5);
 672     }
 673   S = i2b (ptr, 1);
 674   if (s5 > 0)
 675     S = pow5mult (ptr, S, s5);
 676
 677   /* Check for special case that d is a normalized power of 2. */
 678
 679   if (mode < 2)
 680     {
 681       if (!word1 (d) && !(word0 (d) & Bndry_mask)
 682 #ifndef Sudden_Underflow
 683           && word0(d) & Exp_mask
 684 #endif
 685         )
 686         {
 687           /* The special case */
 688           b2 += Log2P;
 689           s2 += Log2P;
 690           spec_case = 1;
 691         }
 692       else
 693         spec_case = 0;
 694     }
 695
 696   /* Arrange for convenient computation of quotients:
 697    * shift left if necessary so divisor has 4 leading 0 bits.
 698    *
 699    * Perhaps we should just compute leading 28 bits of S once
 700    * and for all and pass them and a shift to quorem, so it
 701    * can do shifts and ors to compute the numerator for q.
 702    */
 703
 704 #ifdef Pack_32
 705   if ((i = ((s5 ? 32 - hi0bits (S->_x[S->_wds - 1]) : 1) + s2) & 0x1f))
 706     i = 32 - i;
 707 #else
 708   if ((i = ((s5 ? 32 - hi0bits (S->_x[S->_wds - 1]) : 1) + s2) & 0xf))
 709     i = 16 - i;
 710 #endif
 711   if (i > 4)
 712     {
 713       i -= 4;
 714       b2 += i;
 715       m2 += i;
 716       s2 += i;
 717     }
 718   else if (i < 4)
 719     {
 720       i += 28;
 721       b2 += i;
 722       m2 += i;
 723       s2 += i;
 724     }
 725   if (b2 > 0)
 726     b = lshift (ptr, b, b2);
 727   if (s2 > 0)
 728     S = lshift (ptr, S, s2);
 729   if (k_check)
 730     {
 731       if (cmp (b, S) < 0)
 732         {
 733           k--;
 734           b = multadd (ptr, b, 10, 0);  /* we botched the k estimate */
 735           if (leftright)
 736             mhi = multadd (ptr, mhi, 10, 0);
 737           ilim = ilim1;
 738         }
 739     }
 740   if (ilim <= 0 && mode > 2)
 741     {
 742       if (ilim < 0 || cmp (b, S = multadd (ptr, S, 5, 0)) <= 0)
 743         {
 744           /* no digits, fcvt style */
 745         no_digits:
 746           k = -1 - ndigits;
 747           goto ret;
 748         }
 749     one_digit:
 750       *s++ = '1';
 751       k++;
 752       goto ret;
 753     }
 754   if (leftright)
 755     {
 756       if (m2 > 0)
 757         mhi = lshift (ptr, mhi, m2);
 758
 759       /* Single precision case, */
 760       if (float_type)
 761         mhi = lshift (ptr, mhi, 29);
 762
 763       /* Compute mlo -- check for special case
 764        * that d is a normalized power of 2.
 765        */
 766
 767       mlo = mhi;
 768       if (spec_case)
 769         {
 770           mhi = Balloc (ptr, mhi->_k);
 771           Bcopy (mhi, mlo);
 772           mhi = lshift (ptr, mhi, Log2P);
 773         }
 774
 775       for (i = 1;; i++)
 776         {
 777           dig = quorem (b, S) + '0';
 778           /* Do we yet have the shortest decimal string
 779            * that will round to d?
 780            */
 781           j = cmp (b, mlo);
 782           delta = diff (ptr, S, mhi);
 783           j1 = delta->_sign ? 1 : cmp (b, delta);
 784           Bfree (ptr, delta);
 785 #ifndef ROUND_BIASED
 786           if (j1 == 0 && !mode && !(word1 (d) & 1))
 787             {
 788               if (dig == '9')
 789                 goto round_9_up;
 790               if (j > 0)
 791                 dig++;
 792               *s++ = dig;
 793               goto ret;
 794             }
 795 #endif
 796           if (j < 0 || (j == 0 && !mode
 797 #ifndef ROUND_BIASED
 798               && !(word1 (d) & 1)
 799 #endif
 800             ))
 801             {
 802               if (j1 > 0)
 803                 {
 804                   b = lshift (ptr, b, 1);
 805                   j1 = cmp (b, S);
 806                   if ((j1 > 0 || (j1 == 0 && dig & 1))
 807                       && dig++ == '9')
 808                     goto round_9_up;
 809                 }
 810               *s++ = dig;
 811               goto ret;
 812             }
 813           if (j1 > 0)
 814             {
 815               if (dig == '9')
 816                 {               /* possible if i == 1 */
 817                 round_9_up:
 818                   *s++ = '9';
 819                   goto roundoff;
 820                 }
 821               *s++ = dig + 1;
 822               goto ret;
 823             }
 824           *s++ = dig;
 825           if (i == ilim)
 826             break;
 827           b = multadd (ptr, b, 10, 0);
 828           if (mlo == mhi)
 829             mlo = mhi = multadd (ptr, mhi, 10, 0);
 830           else
 831             {
 832               mlo = multadd (ptr, mlo, 10, 0);
 833               mhi = multadd (ptr, mhi, 10, 0);
 834             }
 835         }
 836     }
 837   else
 838     for (i = 1;; i++)
 839       {
 840         *s++ = dig = quorem (b, S) + '0';
 841         if (i >= ilim)
 842           break;
 843         b = multadd (ptr, b, 10, 0);
 844       }
 845
 846   /* Round off last digit */
 847
 848   b = lshift (ptr, b, 1);
 849   j = cmp (b, S);
 850   if (j > 0 || (j == 0 && dig & 1))
 851     {
 852     roundoff:
 853       while (*--s == '9')
 854         if (s == s0)
 855           {
 856             k++;
 857             *s++ = '1';
 858             goto ret;
 859           }
 860       ++*s++;
 861     }
 862   else
 863     {
 864       while (*--s == '0');
 865       s++;
 866     }
 867 ret:
 868   Bfree (ptr, S);
 869   if (mhi)
 870     {
 871       if (mlo && mlo != mhi)
 872         Bfree (ptr, mlo);
 873       Bfree (ptr, mhi);
 874     }
 875 ret1:
 876   Bfree (ptr, b);
 877   *s = 0;
 878   *decpt = k + 1;
 879   if (rve)
 880     *rve = s;
 881   return s0;
 882 }
 883
 884
 885 _VOID
 886 _DEFUN (_dtoa,
 887         (_d, mode, ndigits, decpt, sign, rve, buf, float_type),
 888         double _d _AND
 889         int mode _AND
 890         int ndigits _AND
 891         int *decpt _AND
 892         int *sign _AND
 893         char **rve _AND
 894         char *buf _AND
 895         int float_type)
 896 {
 897   struct _Jv_reent reent;
 898   char *p;
 899   memset (&reent, 0, sizeof reent);
 900
 901   p = _dtoa_r (&reent, _d, mode, ndigits, decpt, sign, rve, float_type);
 902   strcpy (buf, p);
 903
 904   return;
 905 }