765 lines
17 KiB
C
765 lines
17 KiB
C
/****************************************************************
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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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static Bigint *
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#ifdef KR_headers
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bitstob(bits, nbits, bbits) ULong *bits; int nbits; int *bbits;
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#else
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bitstob(ULong *bits, int nbits, int *bbits)
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#endif
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{
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int i, k;
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Bigint *b;
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ULong *be, *x, *x0;
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i = ULbits;
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k = 0;
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while(i < nbits) {
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i <<= 1;
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k++;
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}
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#ifndef Pack_32
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if (!k)
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k = 1;
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#endif
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b = Balloc(k);
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be = bits + ((nbits - 1) >> kshift);
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x = x0 = b->x;
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do {
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*x++ = *bits & ALL_ON;
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#ifdef Pack_16
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*x++ = (*bits >> 16) & ALL_ON;
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#endif
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} while(++bits <= be);
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i = x - x0;
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while(!x0[--i])
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if (!i) {
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b->wds = 0;
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*bbits = 0;
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goto ret;
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}
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b->wds = i + 1;
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*bbits = i*ULbits + 32 - hi0bits(b->x[i]);
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ret:
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return b;
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}
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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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char *
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gdtoa
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#ifdef KR_headers
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(fpi, be, bits, kindp, mode, ndigits, decpt, rve)
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FPI *fpi; int be; ULong *bits;
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int *kindp, mode, ndigits, *decpt; char **rve;
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#else
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(FPI *fpi, int be, ULong *bits, int *kindp, int mode, int ndigits, int *decpt, char **rve)
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#endif
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{
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/* Arguments ndigits and decpt are similar to the second and third
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arguments 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 9999.
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be = exponent: value = (integer represented by bits) * (2 to the power of be).
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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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4-9 should give the same return values as 2-3, i.e.,
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4 <= mode <= 9 ==> same return as mode
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2 + (mode & 1). These modes are mainly for
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debugging; often they run slower but sometimes
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faster than modes 2-3.
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4,5,8,9 ==> left-to-right digit generation.
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6-9 ==> don't try fast floating-point estimate
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(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, be0, dig, i, ieps, ilim, ilim0, ilim1, inex;
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int j, j1, k, k0, k_check, kind, leftright, m2, m5, nbits;
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int rdir, s2, s5, spec_case, try_quick;
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Long L;
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Bigint *b, *b1, *delta, *mlo, *mhi, *mhi1, *S;
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double d2, ds;
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char *s, *s0;
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U d, eps;
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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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inex = 0;
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kind = *kindp &= ~STRTOG_Inexact;
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switch(kind & STRTOG_Retmask) {
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case STRTOG_Zero:
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goto ret_zero;
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case STRTOG_Normal:
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case STRTOG_Denormal:
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break;
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case STRTOG_Infinite:
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*decpt = -32768;
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return nrv_alloc("Infinity", rve, 8);
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case STRTOG_NaN:
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*decpt = -32768;
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return nrv_alloc("NaN", rve, 3);
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default:
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return 0;
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}
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b = bitstob(bits, nbits = fpi->nbits, &bbits);
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be0 = be;
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if ( (i = trailz(b)) !=0) {
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rshift(b, i);
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be += i;
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bbits -= i;
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}
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if (!b->wds) {
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Bfree(b);
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ret_zero:
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*decpt = 1;
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return nrv_alloc("0", rve, 1);
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}
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dval(&d) = b2d(b, &i);
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i = be + bbits - 1;
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word0(&d) &= Frac_mask1;
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word0(&d) |= Exp_11;
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#ifdef IBM
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if ( (j = 11 - hi0bits(word0(&d) & Frac_mask)) !=0)
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dval(&d) /= 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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#ifdef IBM
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i <<= 2;
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i += j;
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#endif
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ds = (dval(&d)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
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/* correct assumption about exponent range */
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if ((j = i) < 0)
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j = -j;
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if ((j -= 1077) > 0)
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ds += j * 7e-17;
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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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#ifdef IBM
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j = be + bbits - 1;
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if ( (j1 = j & 3) !=0)
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dval(&d) *= 1 << j1;
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word0(&d) += j << Exp_shift - 2 & Exp_mask;
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#else
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word0(&d) += (be + bbits - 1) << Exp_shift;
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#endif
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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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try_quick = 1;
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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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else if (i >= -4 - Emin || i < Emin)
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try_quick = 0;
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leftright = 1;
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ilim = ilim1 = -1; /* Values for cases 0 and 1; done here to */
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/* silence erroneous "gcc -Wall" warning. */
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switch(mode) {
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case 0:
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case 1:
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i = (int)(nbits * .30103) + 3;
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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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if ( (rdir = fpi->rounding - 1) !=0) {
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if (rdir < 0)
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rdir = 2;
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if (kind & STRTOG_Neg)
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rdir = 3 - rdir;
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}
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/* Now rdir = 0 ==> round near, 1 ==> round up, 2 ==> round down. */
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if (ilim >= 0 && ilim <= Quick_max && try_quick && !rdir
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#ifndef IMPRECISE_INEXACT
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&& k == 0
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#endif
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) {
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/* Try to get by with floating-point arithmetic. */
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i = 0;
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d2 = dval(&d);
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#ifdef IBM
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if ( (j = 11 - hi0bits(word0(&d) & Frac_mask)) !=0)
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dval(&d) /= 1 << j;
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#endif
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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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}
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else {
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ds = 1.;
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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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}
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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) {
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S = mhi = 0;
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dval(&d) -= 5.;
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if (dval(&d) > dval(&eps))
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goto one_digit;
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if (dval(&d) < -dval(&eps))
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goto no_digits;
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goto fast_failed;
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}
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#ifndef No_leftright
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if (leftright) {
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/* Use Steele & White method of only
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* generating digits needed.
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*/
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dval(&eps) = ds*0.5/tens[ilim-1] - dval(&eps);
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for(i = 0;;) {
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L = (Long)(dval(&d)/ds);
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dval(&d) -= L*ds;
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*s++ = '0' + (int)L;
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if (dval(&d) < dval(&eps)) {
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if (dval(&d))
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inex = STRTOG_Inexlo;
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goto ret1;
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}
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if (ds - dval(&d) < dval(&eps))
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goto bump_up;
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if (++i >= ilim)
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break;
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dval(&eps) *= 10.;
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dval(&d) *= 10.;
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}
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}
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else {
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#endif
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/* Generate ilim digits, then fix them up. */
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dval(&eps) *= tens[ilim-1];
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for(i = 1;; i++, dval(&d) *= 10.) {
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if ( (L = (Long)(dval(&d)/ds)) !=0)
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dval(&d) -= L*ds;
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*s++ = '0' + (int)L;
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if (i == ilim) {
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ds *= 0.5;
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if (dval(&d) > ds + dval(&eps))
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goto bump_up;
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else if (dval(&d) < ds - dval(&eps)) {
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if (dval(&d))
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inex = STRTOG_Inexlo;
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goto clear_trailing0;
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}
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break;
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}
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}
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#ifndef No_leftright
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}
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#endif
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fast_failed:
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s = s0;
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dval(&d) = d2;
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k = k0;
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ilim = ilim0;
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}
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/* Do we have a "small" integer? */
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if (be >= 0 && k <= Int_max) {
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/* Yes. */
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ds = tens[k];
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if (ndigits < 0 && ilim <= 0) {
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S = mhi = 0;
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if (ilim < 0 || dval(&d) <= 5*ds)
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goto no_digits;
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goto one_digit;
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}
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for(i = 1;; i++, dval(&d) *= 10.) {
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L = dval(&d) / ds;
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dval(&d) -= L*ds;
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#ifdef Check_FLT_ROUNDS
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/* If FLT_ROUNDS == 2, L will usually be high by 1 */
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if (dval(&d) < 0) {
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L--;
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dval(&d) += ds;
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}
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#endif
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*s++ = '0' + (int)L;
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if (dval(&d) == 0.)
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break;
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if (i == ilim) {
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if (rdir) {
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if (rdir == 1)
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goto bump_up;
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inex = STRTOG_Inexlo;
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goto ret1;
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}
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dval(&d) += dval(&d);
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#ifdef ROUND_BIASED
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if (dval(&d) >= ds)
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#else
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if (dval(&d) > ds || (dval(&d) == ds && L & 1))
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#endif
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{
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bump_up:
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inex = STRTOG_Inexhi;
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while(*--s == '9')
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if (s == s0) {
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k++;
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*s = '0';
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break;
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}
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++*s++;
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}
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else {
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inex = STRTOG_Inexlo;
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clear_trailing0:
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while(*--s == '0'){}
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++s;
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}
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break;
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}
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}
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goto ret1;
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}
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m2 = b2;
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m5 = b5;
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mhi = mlo = 0;
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if (leftright) {
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i = nbits - bbits;
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if (be - i++ < fpi->emin && mode != 3 && mode != 5) {
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/* denormal */
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i = be - fpi->emin + 1;
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if (mode >= 2 && ilim > 0 && ilim < i)
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goto small_ilim;
|
|
}
|
|
else if (mode >= 2) {
|
|
small_ilim:
|
|
j = ilim - 1;
|
|
if (m5 >= j)
|
|
m5 -= j;
|
|
else {
|
|
s5 += j -= m5;
|
|
b5 += j;
|
|
m5 = 0;
|
|
}
|
|
if ((i = ilim) < 0) {
|
|
m2 -= i;
|
|
i = 0;
|
|
}
|
|
}
|
|
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) {
|
|
if (bbits == 1 && be0 > fpi->emin + 1) {
|
|
/* The special case */
|
|
b2++;
|
|
s2++;
|
|
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.
|
|
*/
|
|
i = ((s5 ? hi0bits(S->x[S->wds-1]) : ULbits - 1) - s2 - 4) & kmask;
|
|
m2 += i;
|
|
if ((b2 += i) > 0)
|
|
b = lshift(b, b2);
|
|
if ((s2 += i) > 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 > 2) {
|
|
if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
|
|
/* no digits, fcvt style */
|
|
no_digits:
|
|
k = -1 - ndigits;
|
|
inex = STRTOG_Inexlo;
|
|
goto ret;
|
|
}
|
|
one_digit:
|
|
inex = STRTOG_Inexhi;
|
|
*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, 1);
|
|
}
|
|
|
|
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 && !(bits[0] & 1) && !rdir) {
|
|
if (dig == '9')
|
|
goto round_9_up;
|
|
if (j <= 0) {
|
|
if (b->wds > 1 || b->x[0])
|
|
inex = STRTOG_Inexlo;
|
|
}
|
|
else {
|
|
dig++;
|
|
inex = STRTOG_Inexhi;
|
|
}
|
|
*s++ = dig;
|
|
goto ret;
|
|
}
|
|
#endif
|
|
if (j < 0 || (j == 0 && !mode
|
|
#ifndef ROUND_BIASED
|
|
&& !(bits[0] & 1)
|
|
#endif
|
|
)) {
|
|
if (rdir && (b->wds > 1 || b->x[0])) {
|
|
if (rdir == 2) {
|
|
inex = STRTOG_Inexlo;
|
|
goto accept;
|
|
}
|
|
while (cmp(S,mhi) > 0) {
|
|
*s++ = dig;
|
|
mhi1 = multadd(mhi, 10, 0);
|
|
if (mlo == mhi)
|
|
mlo = mhi1;
|
|
mhi = mhi1;
|
|
b = multadd(b, 10, 0);
|
|
dig = quorem(b,S) + '0';
|
|
}
|
|
if (dig++ == '9')
|
|
goto round_9_up;
|
|
inex = STRTOG_Inexhi;
|
|
goto accept;
|
|
}
|
|
if (j1 > 0) {
|
|
b = lshift(b, 1);
|
|
j1 = cmp(b, S);
|
|
#ifdef ROUND_BIASED
|
|
if (j1 >= 0 /*)*/
|
|
#else
|
|
if ((j1 > 0 || (j1 == 0 && dig & 1))
|
|
#endif
|
|
&& dig++ == '9')
|
|
goto round_9_up;
|
|
inex = STRTOG_Inexhi;
|
|
}
|
|
if (b->wds > 1 || b->x[0])
|
|
inex = STRTOG_Inexlo;
|
|
accept:
|
|
*s++ = dig;
|
|
goto ret;
|
|
}
|
|
if (j1 > 0 && rdir != 2) {
|
|
if (dig == '9') { /* possible if i == 1 */
|
|
round_9_up:
|
|
*s++ = '9';
|
|
inex = STRTOG_Inexhi;
|
|
goto roundoff;
|
|
}
|
|
inex = STRTOG_Inexhi;
|
|
*s++ = dig + 1;
|
|
goto ret;
|
|
}
|
|
*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 (i >= ilim)
|
|
break;
|
|
b = multadd(b, 10, 0);
|
|
}
|
|
|
|
/* Round off last digit */
|
|
|
|
if (rdir) {
|
|
if (rdir == 2 || (b->wds <= 1 && !b->x[0]))
|
|
goto chopzeros;
|
|
goto roundoff;
|
|
}
|
|
b = lshift(b, 1);
|
|
j = cmp(b, S);
|
|
#ifdef ROUND_BIASED
|
|
if (j >= 0)
|
|
#else
|
|
if (j > 0 || (j == 0 && dig & 1))
|
|
#endif
|
|
{
|
|
roundoff:
|
|
inex = STRTOG_Inexhi;
|
|
while(*--s == '9')
|
|
if (s == s0) {
|
|
k++;
|
|
*s++ = '1';
|
|
goto ret;
|
|
}
|
|
++*s++;
|
|
}
|
|
else {
|
|
chopzeros:
|
|
if (b->wds > 1 || b->x[0])
|
|
inex = STRTOG_Inexlo;
|
|
while(*--s == '0'){}
|
|
++s;
|
|
}
|
|
ret:
|
|
Bfree(S);
|
|
if (mhi) {
|
|
if (mlo && mlo != mhi)
|
|
Bfree(mlo);
|
|
Bfree(mhi);
|
|
}
|
|
ret1:
|
|
Bfree(b);
|
|
*s = 0;
|
|
*decpt = k + 1;
|
|
if (rve)
|
|
*rve = s;
|
|
*kindp |= inex;
|
|
return s0;
|
|
}
|