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755 lines
16 KiB
C
755 lines
16 KiB
C
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/****************************************************************
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The author of this software is David M. Gay.
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Copyright (C) 1998, 1999 by Lucent Technologies
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All Rights Reserved
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Permission to use, copy, modify, and distribute this software and
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its documentation for any purpose and without fee is hereby
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granted, provided that the above copyright notice appear in all
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copies and that both that the copyright notice and this
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permission notice and warranty disclaimer appear in supporting
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documentation, and that the name of Lucent or any of its entities
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not be used in advertising or publicity pertaining to
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distribution of the software without specific, written prior
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permission.
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LUCENT DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE,
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INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS.
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IN NO EVENT SHALL LUCENT OR ANY OF ITS ENTITIES BE LIABLE FOR ANY
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SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
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WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER
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IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION,
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ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF
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THIS SOFTWARE.
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****************************************************************/
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/* Please send bug reports to David M. Gay (dmg at acm dot org,
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* with " at " changed at "@" and " dot " changed to "."). */
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#include "gdtoaimp.h"
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#include <limits.h>
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/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
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*
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* Inspired by "How to Print Floating-Point Numbers Accurately" by
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* Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
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*
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* Modifications:
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* 1. Rather than iterating, we use a simple numeric overestimate
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* to determine k = floor(log10(d)). We scale relevant
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* quantities using O(log2(k)) rather than O(k) multiplications.
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* 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
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* try to generate digits strictly left to right. Instead, we
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* compute with fewer bits and propagate the carry if necessary
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* when rounding the final digit up. This is often faster.
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* 3. Under the assumption that input will be rounded nearest,
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* mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
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* That is, we allow equality in stopping tests when the
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* round-nearest rule will give the same floating-point value
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* as would satisfaction of the stopping test with strict
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* inequality.
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* 4. We remove common factors of powers of 2 from relevant
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* quantities.
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* 5. When converting floating-point integers less than 1e16,
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* we use floating-point arithmetic rather than resorting
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* to multiple-precision integers.
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* 6. When asked to produce fewer than 15 digits, we first try
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* to get by with floating-point arithmetic; we resort to
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* multiple-precision integer arithmetic only if we cannot
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* guarantee that the floating-point calculation has given
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* the correctly rounded result. For k requested digits and
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* "uniformly" distributed input, the probability is
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* something like 10^(k-15) that we must resort to the Long
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* calculation.
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*/
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#ifdef Honor_FLT_ROUNDS
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#define Rounding rounding
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#undef Check_FLT_ROUNDS
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#define Check_FLT_ROUNDS
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#else
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#define Rounding Flt_Rounds
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#endif
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char *
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dtoa
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#ifdef KR_headers
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(d, mode, ndigits, decpt, sign, rve)
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double d; int mode, ndigits, *decpt, *sign; char **rve;
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#else
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(double d, int mode, int ndigits, int *decpt, int *sign, char **rve)
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#endif
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{
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/* Arguments ndigits, decpt, sign are similar to those
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of ecvt and fcvt; trailing zeros are suppressed from
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the returned string. If not null, *rve is set to point
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to the end of the return value. If d is +-Infinity or NaN,
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then *decpt is set to INT_MAX.
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mode:
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0 ==> shortest string that yields d when read in
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and rounded to nearest.
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1 ==> like 0, but with Steele & White stopping rule;
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e.g. with IEEE P754 arithmetic , mode 0 gives
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1e23 whereas mode 1 gives 9.999999999999999e22.
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2 ==> max(1,ndigits) significant digits. This gives a
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return value similar to that of ecvt, except
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that trailing zeros are suppressed.
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3 ==> through ndigits past the decimal point. This
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gives a return value similar to that from fcvt,
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except that trailing zeros are suppressed, and
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ndigits can be negative.
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4,5 ==> similar to 2 and 3, respectively, but (in
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round-nearest mode) with the tests of mode 0 to
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possibly return a shorter string that rounds to d.
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With IEEE arithmetic and compilation with
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-DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
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as modes 2 and 3 when FLT_ROUNDS != 1.
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6-9 ==> Debugging modes similar to mode - 4: don't try
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fast floating-point estimate (if applicable).
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Values of mode other than 0-9 are treated as mode 0.
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Sufficient space is allocated to the return value
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to hold the suppressed trailing zeros.
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*/
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int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
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j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
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spec_case, try_quick;
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Long L;
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#ifndef Sudden_Underflow
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int denorm;
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ULong x;
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#endif
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Bigint *b, *b1, *delta, *mlo, *mhi, *S;
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double d2, ds, eps;
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char *s, *s0;
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#ifdef Honor_FLT_ROUNDS
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int rounding;
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#endif
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#ifdef SET_INEXACT
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int inexact, oldinexact;
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#endif
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#ifndef MULTIPLE_THREADS
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if (dtoa_result) {
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freedtoa(dtoa_result);
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dtoa_result = 0;
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}
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#endif
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if (word0(d) & Sign_bit) {
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/* set sign for everything, including 0's and NaNs */
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*sign = 1;
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word0(d) &= ~Sign_bit; /* clear sign bit */
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}
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else
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*sign = 0;
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#if defined(IEEE_Arith) + defined(VAX)
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#ifdef IEEE_Arith
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if ((word0(d) & Exp_mask) == Exp_mask)
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#else
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if (word0(d) == 0x8000)
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#endif
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{
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/* Infinity or NaN */
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*decpt = INT_MAX;
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#ifdef IEEE_Arith
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if (!word1(d) && !(word0(d) & 0xfffff))
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return nrv_alloc("Infinity", rve, 8);
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#endif
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return nrv_alloc("NaN", rve, 3);
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}
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#endif
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#ifdef IBM
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dval(d) += 0; /* normalize */
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#endif
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if (!dval(d)) {
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*decpt = 1;
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return nrv_alloc("0", rve, 1);
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}
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#ifdef SET_INEXACT
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try_quick = oldinexact = get_inexact();
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inexact = 1;
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#endif
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#ifdef Honor_FLT_ROUNDS
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if ((rounding = Flt_Rounds) >= 2) {
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if (*sign)
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rounding = rounding == 2 ? 0 : 2;
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else
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if (rounding != 2)
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rounding = 0;
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}
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#endif
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b = d2b(dval(d), &be, &bbits);
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#ifdef Sudden_Underflow
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i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
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#else
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if (( i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)) )!=0) {
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#endif
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dval(d2) = dval(d);
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word0(d2) &= Frac_mask1;
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word0(d2) |= Exp_11;
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#ifdef IBM
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if (( j = 11 - hi0bits(word0(d2) & Frac_mask) )!=0)
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dval(d2) /= 1 << j;
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#endif
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/* log(x) ~=~ log(1.5) + (x-1.5)/1.5
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* log10(x) = log(x) / log(10)
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* ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
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* log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
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*
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* This suggests computing an approximation k to log10(d) by
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*
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* k = (i - Bias)*0.301029995663981
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* + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
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*
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* We want k to be too large rather than too small.
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* The error in the first-order Taylor series approximation
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* is in our favor, so we just round up the constant enough
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* to compensate for any error in the multiplication of
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* (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
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* and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
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* adding 1e-13 to the constant term more than suffices.
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* Hence we adjust the constant term to 0.1760912590558.
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* (We could get a more accurate k by invoking log10,
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* but this is probably not worthwhile.)
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*/
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i -= Bias;
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#ifdef IBM
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i <<= 2;
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i += j;
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#endif
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#ifndef Sudden_Underflow
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denorm = 0;
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}
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else {
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/* d is denormalized */
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i = bbits + be + (Bias + (P-1) - 1);
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x = i > 32 ? word0(d) << 64 - i | word1(d) >> i - 32
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: word1(d) << 32 - i;
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dval(d2) = x;
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word0(d2) -= 31*Exp_msk1; /* adjust exponent */
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i -= (Bias + (P-1) - 1) + 1;
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denorm = 1;
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}
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#endif
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ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
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k = (int)ds;
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if (ds < 0. && ds != k)
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k--; /* want k = floor(ds) */
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k_check = 1;
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if (k >= 0 && k <= Ten_pmax) {
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if (dval(d) < tens[k])
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k--;
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k_check = 0;
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}
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j = bbits - i - 1;
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if (j >= 0) {
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b2 = 0;
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s2 = j;
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}
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else {
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b2 = -j;
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s2 = 0;
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}
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if (k >= 0) {
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b5 = 0;
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s5 = k;
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s2 += k;
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}
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else {
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b2 -= k;
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b5 = -k;
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s5 = 0;
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}
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if (mode < 0 || mode > 9)
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mode = 0;
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#ifndef SET_INEXACT
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#ifdef Check_FLT_ROUNDS
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try_quick = Rounding == 1;
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#else
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try_quick = 1;
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#endif
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#endif /*SET_INEXACT*/
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if (mode > 5) {
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mode -= 4;
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try_quick = 0;
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}
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leftright = 1;
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switch(mode) {
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case 0:
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case 1:
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ilim = ilim1 = -1;
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i = 18;
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ndigits = 0;
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break;
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case 2:
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leftright = 0;
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/* no break */
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case 4:
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if (ndigits <= 0)
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ndigits = 1;
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ilim = ilim1 = i = ndigits;
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break;
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case 3:
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leftright = 0;
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/* no break */
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case 5:
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i = ndigits + k + 1;
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ilim = i;
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ilim1 = i - 1;
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if (i <= 0)
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i = 1;
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}
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s = s0 = rv_alloc(i);
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#ifdef Honor_FLT_ROUNDS
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if (mode > 1 && rounding != 1)
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leftright = 0;
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#endif
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if (ilim >= 0 && ilim <= Quick_max && try_quick) {
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/* Try to get by with floating-point arithmetic. */
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i = 0;
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dval(d2) = dval(d);
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k0 = k;
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ilim0 = ilim;
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ieps = 2; /* conservative */
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if (k > 0) {
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ds = tens[k&0xf];
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j = k >> 4;
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if (j & Bletch) {
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/* prevent overflows */
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j &= Bletch - 1;
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dval(d) /= bigtens[n_bigtens-1];
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ieps++;
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}
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for(; j; j >>= 1, i++)
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if (j & 1) {
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ieps++;
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ds *= bigtens[i];
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}
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dval(d) /= ds;
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}
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else if (( j1 = -k )!=0) {
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dval(d) *= tens[j1 & 0xf];
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for(j = j1 >> 4; j; j >>= 1, i++)
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if (j & 1) {
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ieps++;
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dval(d) *= bigtens[i];
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}
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}
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if (k_check && dval(d) < 1. && ilim > 0) {
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if (ilim1 <= 0)
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goto fast_failed;
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ilim = ilim1;
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k--;
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dval(d) *= 10.;
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ieps++;
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}
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dval(eps) = ieps*dval(d) + 7.;
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word0(eps) -= (P-1)*Exp_msk1;
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|
|
if (ilim == 0) {
|
||
|
|
S = mhi = 0;
|
||
|
|
dval(d) -= 5.;
|
||
|
|
if (dval(d) > dval(eps))
|
||
|
|
goto one_digit;
|
||
|
|
if (dval(d) < -dval(eps))
|
||
|
|
goto no_digits;
|
||
|
|
goto fast_failed;
|
||
|
|
}
|
||
|
|
#ifndef No_leftright
|
||
|
|
if (leftright) {
|
||
|
|
/* Use Steele & White method of only
|
||
|
|
* generating digits needed.
|
||
|
|
*/
|
||
|
|
dval(eps) = 0.5/tens[ilim-1] - dval(eps);
|
||
|
|
for(i = 0;;) {
|
||
|
|
L = (Long)dval(d);
|
||
|
|
dval(d) -= L;
|
||
|
|
*s++ = '0' + (int)L;
|
||
|
|
if (dval(d) < dval(eps))
|
||
|
|
goto ret1;
|
||
|
|
if (1. - dval(d) < dval(eps))
|
||
|
|
goto bump_up;
|
||
|
|
if (++i >= ilim)
|
||
|
|
break;
|
||
|
|
dval(eps) *= 10.;
|
||
|
|
dval(d) *= 10.;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
else {
|
||
|
|
#endif
|
||
|
|
/* Generate ilim digits, then fix them up. */
|
||
|
|
dval(eps) *= tens[ilim-1];
|
||
|
|
for(i = 1;; i++, dval(d) *= 10.) {
|
||
|
|
L = (Long)(dval(d));
|
||
|
|
if (!(dval(d) -= L))
|
||
|
|
ilim = i;
|
||
|
|
*s++ = '0' + (int)L;
|
||
|
|
if (i == ilim) {
|
||
|
|
if (dval(d) > 0.5 + dval(eps))
|
||
|
|
goto bump_up;
|
||
|
|
else if (dval(d) < 0.5 - dval(eps)) {
|
||
|
|
while(*--s == '0');
|
||
|
|
s++;
|
||
|
|
goto ret1;
|
||
|
|
}
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
#ifndef No_leftright
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
fast_failed:
|
||
|
|
s = s0;
|
||
|
|
dval(d) = dval(d2);
|
||
|
|
k = k0;
|
||
|
|
ilim = ilim0;
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Do we have a "small" integer? */
|
||
|
|
|
||
|
|
if (be >= 0 && k <= Int_max) {
|
||
|
|
/* Yes. */
|
||
|
|
ds = tens[k];
|
||
|
|
if (ndigits < 0 && ilim <= 0) {
|
||
|
|
S = mhi = 0;
|
||
|
|
if (ilim < 0 || dval(d) <= 5*ds)
|
||
|
|
goto no_digits;
|
||
|
|
goto one_digit;
|
||
|
|
}
|
||
|
|
for(i = 1;; i++, dval(d) *= 10.) {
|
||
|
|
L = (Long)(dval(d) / ds);
|
||
|
|
dval(d) -= L*ds;
|
||
|
|
#ifdef Check_FLT_ROUNDS
|
||
|
|
/* If FLT_ROUNDS == 2, L will usually be high by 1 */
|
||
|
|
if (dval(d) < 0) {
|
||
|
|
L--;
|
||
|
|
dval(d) += ds;
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
*s++ = '0' + (int)L;
|
||
|
|
if (!dval(d)) {
|
||
|
|
#ifdef SET_INEXACT
|
||
|
|
inexact = 0;
|
||
|
|
#endif
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
if (i == ilim) {
|
||
|
|
#ifdef Honor_FLT_ROUNDS
|
||
|
|
if (mode > 1)
|
||
|
|
switch(rounding) {
|
||
|
|
case 0: goto ret1;
|
||
|
|
case 2: goto bump_up;
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
dval(d) += dval(d);
|
||
|
|
if (dval(d) > ds || dval(d) == ds && L & 1) {
|
||
|
|
bump_up:
|
||
|
|
while(*--s == '9')
|
||
|
|
if (s == s0) {
|
||
|
|
k++;
|
||
|
|
*s = '0';
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
++*s++;
|
||
|
|
}
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
goto ret1;
|
||
|
|
}
|
||
|
|
|
||
|
|
m2 = b2;
|
||
|
|
m5 = b5;
|
||
|
|
mhi = mlo = 0;
|
||
|
|
if (leftright) {
|
||
|
|
i =
|
||
|
|
#ifndef Sudden_Underflow
|
||
|
|
denorm ? be + (Bias + (P-1) - 1 + 1) :
|
||
|
|
#endif
|
||
|
|
#ifdef IBM
|
||
|
|
1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
|
||
|
|
#else
|
||
|
|
1 + P - bbits;
|
||
|
|
#endif
|
||
|
|
b2 += i;
|
||
|
|
s2 += i;
|
||
|
|
mhi = i2b(1);
|
||
|
|
}
|
||
|
|
if (m2 > 0 && s2 > 0) {
|
||
|
|
i = m2 < s2 ? m2 : s2;
|
||
|
|
b2 -= i;
|
||
|
|
m2 -= i;
|
||
|
|
s2 -= i;
|
||
|
|
}
|
||
|
|
if (b5 > 0) {
|
||
|
|
if (leftright) {
|
||
|
|
if (m5 > 0) {
|
||
|
|
mhi = pow5mult(mhi, m5);
|
||
|
|
b1 = mult(mhi, b);
|
||
|
|
Bfree(b);
|
||
|
|
b = b1;
|
||
|
|
}
|
||
|
|
if (( j = b5 - m5 )!=0)
|
||
|
|
b = pow5mult(b, j);
|
||
|
|
}
|
||
|
|
else
|
||
|
|
b = pow5mult(b, b5);
|
||
|
|
}
|
||
|
|
S = i2b(1);
|
||
|
|
if (s5 > 0)
|
||
|
|
S = pow5mult(S, s5);
|
||
|
|
|
||
|
|
/* Check for special case that d is a normalized power of 2. */
|
||
|
|
|
||
|
|
spec_case = 0;
|
||
|
|
if ((mode < 2 || leftright)
|
||
|
|
#ifdef Honor_FLT_ROUNDS
|
||
|
|
&& rounding == 1
|
||
|
|
#endif
|
||
|
|
) {
|
||
|
|
if (!word1(d) && !(word0(d) & Bndry_mask)
|
||
|
|
#ifndef Sudden_Underflow
|
||
|
|
&& word0(d) & (Exp_mask & ~Exp_msk1)
|
||
|
|
#endif
|
||
|
|
) {
|
||
|
|
/* The special case */
|
||
|
|
b2 += Log2P;
|
||
|
|
s2 += Log2P;
|
||
|
|
spec_case = 1;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Arrange for convenient computation of quotients:
|
||
|
|
* shift left if necessary so divisor has 4 leading 0 bits.
|
||
|
|
*
|
||
|
|
* Perhaps we should just compute leading 28 bits of S once
|
||
|
|
* and for all and pass them and a shift to quorem, so it
|
||
|
|
* can do shifts and ors to compute the numerator for q.
|
||
|
|
*/
|
||
|
|
#ifdef Pack_32
|
||
|
|
if (( i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f )!=0)
|
||
|
|
i = 32 - i;
|
||
|
|
#else
|
||
|
|
if (( i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf )!=0)
|
||
|
|
i = 16 - i;
|
||
|
|
#endif
|
||
|
|
if (i > 4) {
|
||
|
|
i -= 4;
|
||
|
|
b2 += i;
|
||
|
|
m2 += i;
|
||
|
|
s2 += i;
|
||
|
|
}
|
||
|
|
else if (i < 4) {
|
||
|
|
i += 28;
|
||
|
|
b2 += i;
|
||
|
|
m2 += i;
|
||
|
|
s2 += i;
|
||
|
|
}
|
||
|
|
if (b2 > 0)
|
||
|
|
b = lshift(b, b2);
|
||
|
|
if (s2 > 0)
|
||
|
|
S = lshift(S, s2);
|
||
|
|
if (k_check) {
|
||
|
|
if (cmp(b,S) < 0) {
|
||
|
|
k--;
|
||
|
|
b = multadd(b, 10, 0); /* we botched the k estimate */
|
||
|
|
if (leftright)
|
||
|
|
mhi = multadd(mhi, 10, 0);
|
||
|
|
ilim = ilim1;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
if (ilim <= 0 && (mode == 3 || mode == 5)) {
|
||
|
|
if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
|
||
|
|
/* no digits, fcvt style */
|
||
|
|
no_digits:
|
||
|
|
k = -1 - ndigits;
|
||
|
|
goto ret;
|
||
|
|
}
|
||
|
|
one_digit:
|
||
|
|
*s++ = '1';
|
||
|
|
k++;
|
||
|
|
goto ret;
|
||
|
|
}
|
||
|
|
if (leftright) {
|
||
|
|
if (m2 > 0)
|
||
|
|
mhi = lshift(mhi, m2);
|
||
|
|
|
||
|
|
/* Compute mlo -- check for special case
|
||
|
|
* that d is a normalized power of 2.
|
||
|
|
*/
|
||
|
|
|
||
|
|
mlo = mhi;
|
||
|
|
if (spec_case) {
|
||
|
|
mhi = Balloc(mhi->k);
|
||
|
|
Bcopy(mhi, mlo);
|
||
|
|
mhi = lshift(mhi, Log2P);
|
||
|
|
}
|
||
|
|
|
||
|
|
for(i = 1;;i++) {
|
||
|
|
dig = quorem(b,S) + '0';
|
||
|
|
/* Do we yet have the shortest decimal string
|
||
|
|
* that will round to d?
|
||
|
|
*/
|
||
|
|
j = cmp(b, mlo);
|
||
|
|
delta = diff(S, mhi);
|
||
|
|
j1 = delta->sign ? 1 : cmp(b, delta);
|
||
|
|
Bfree(delta);
|
||
|
|
#ifndef ROUND_BIASED
|
||
|
|
if (j1 == 0 && mode != 1 && !(word1(d) & 1)
|
||
|
|
#ifdef Honor_FLT_ROUNDS
|
||
|
|
&& rounding >= 1
|
||
|
|
#endif
|
||
|
|
) {
|
||
|
|
if (dig == '9')
|
||
|
|
goto round_9_up;
|
||
|
|
if (j > 0)
|
||
|
|
dig++;
|
||
|
|
#ifdef SET_INEXACT
|
||
|
|
else if (!b->x[0] && b->wds <= 1)
|
||
|
|
inexact = 0;
|
||
|
|
#endif
|
||
|
|
*s++ = dig;
|
||
|
|
goto ret;
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
if (j < 0 || j == 0 && mode != 1
|
||
|
|
#ifndef ROUND_BIASED
|
||
|
|
&& !(word1(d) & 1)
|
||
|
|
#endif
|
||
|
|
) {
|
||
|
|
if (!b->x[0] && b->wds <= 1) {
|
||
|
|
#ifdef SET_INEXACT
|
||
|
|
inexact = 0;
|
||
|
|
#endif
|
||
|
|
goto accept_dig;
|
||
|
|
}
|
||
|
|
#ifdef Honor_FLT_ROUNDS
|
||
|
|
if (mode > 1)
|
||
|
|
switch(rounding) {
|
||
|
|
case 0: goto accept_dig;
|
||
|
|
case 2: goto keep_dig;
|
||
|
|
}
|
||
|
|
#endif /*Honor_FLT_ROUNDS*/
|
||
|
|
if (j1 > 0) {
|
||
|
|
b = lshift(b, 1);
|
||
|
|
j1 = cmp(b, S);
|
||
|
|
if ((j1 > 0 || j1 == 0 && dig & 1)
|
||
|
|
&& dig++ == '9')
|
||
|
|
goto round_9_up;
|
||
|
|
}
|
||
|
|
accept_dig:
|
||
|
|
*s++ = dig;
|
||
|
|
goto ret;
|
||
|
|
}
|
||
|
|
if (j1 > 0) {
|
||
|
|
#ifdef Honor_FLT_ROUNDS
|
||
|
|
if (!rounding)
|
||
|
|
goto accept_dig;
|
||
|
|
#endif
|
||
|
|
if (dig == '9') { /* possible if i == 1 */
|
||
|
|
round_9_up:
|
||
|
|
*s++ = '9';
|
||
|
|
goto roundoff;
|
||
|
|
}
|
||
|
|
*s++ = dig + 1;
|
||
|
|
goto ret;
|
||
|
|
}
|
||
|
|
#ifdef Honor_FLT_ROUNDS
|
||
|
|
keep_dig:
|
||
|
|
#endif
|
||
|
|
*s++ = dig;
|
||
|
|
if (i == ilim)
|
||
|
|
break;
|
||
|
|
b = multadd(b, 10, 0);
|
||
|
|
if (mlo == mhi)
|
||
|
|
mlo = mhi = multadd(mhi, 10, 0);
|
||
|
|
else {
|
||
|
|
mlo = multadd(mlo, 10, 0);
|
||
|
|
mhi = multadd(mhi, 10, 0);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
else
|
||
|
|
for(i = 1;; i++) {
|
||
|
|
*s++ = dig = quorem(b,S) + '0';
|
||
|
|
if (!b->x[0] && b->wds <= 1) {
|
||
|
|
#ifdef SET_INEXACT
|
||
|
|
inexact = 0;
|
||
|
|
#endif
|
||
|
|
goto ret;
|
||
|
|
}
|
||
|
|
if (i >= ilim)
|
||
|
|
break;
|
||
|
|
b = multadd(b, 10, 0);
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Round off last digit */
|
||
|
|
|
||
|
|
#ifdef Honor_FLT_ROUNDS
|
||
|
|
switch(rounding) {
|
||
|
|
case 0: goto trimzeros;
|
||
|
|
case 2: goto roundoff;
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
b = lshift(b, 1);
|
||
|
|
j = cmp(b, S);
|
||
|
|
if (j > 0 || j == 0 && dig & 1) {
|
||
|
|
roundoff:
|
||
|
|
while(*--s == '9')
|
||
|
|
if (s == s0) {
|
||
|
|
k++;
|
||
|
|
*s++ = '1';
|
||
|
|
goto ret;
|
||
|
|
}
|
||
|
|
++*s++;
|
||
|
|
}
|
||
|
|
else {
|
||
|
|
trimzeros:
|
||
|
|
while(*--s == '0');
|
||
|
|
s++;
|
||
|
|
}
|
||
|
|
ret:
|
||
|
|
Bfree(S);
|
||
|
|
if (mhi) {
|
||
|
|
if (mlo && mlo != mhi)
|
||
|
|
Bfree(mlo);
|
||
|
|
Bfree(mhi);
|
||
|
|
}
|
||
|
|
ret1:
|
||
|
|
#ifdef SET_INEXACT
|
||
|
|
if (inexact) {
|
||
|
|
if (!oldinexact) {
|
||
|
|
word0(d) = Exp_1 + (70 << Exp_shift);
|
||
|
|
word1(d) = 0;
|
||
|
|
dval(d) += 1.;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
else if (!oldinexact)
|
||
|
|
clear_inexact();
|
||
|
|
#endif
|
||
|
|
Bfree(b);
|
||
|
|
*s = 0;
|
||
|
|
*decpt = k + 1;
|
||
|
|
if (rve)
|
||
|
|
*rve = s;
|
||
|
|
return s0;
|
||
|
|
}
|