983 lines
20 KiB
C
983 lines
20 KiB
C
/****************************************************************
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The author of this software is David M. Gay.
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Copyright (C) 1998-2001 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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#ifndef NO_FENV_H
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#include <fenv.h>
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#endif
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#ifdef USE_LOCALE
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#include "locale.h"
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#endif
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#ifdef IEEE_Arith
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#ifndef NO_IEEE_Scale
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#define Avoid_Underflow
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#undef tinytens
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/* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
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/* flag unnecessarily. It leads to a song and dance at the end of strtod. */
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static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
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9007199254740992.e-256
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};
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#endif
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#endif
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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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double
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strtod
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#ifdef KR_headers
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(s00, se) CONST char *s00; char **se;
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#else
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(CONST char *s00, char **se)
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#endif
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{
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#ifdef Avoid_Underflow
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int scale;
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#endif
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int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, decpt, dsign,
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e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
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CONST char *s, *s0, *s1;
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double aadj, aadj1, adj, rv, rv0;
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Long L;
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ULong y, z;
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Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
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#ifdef SET_INEXACT
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int inexact, oldinexact;
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#endif
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#ifdef Honor_FLT_ROUNDS
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int rounding;
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#endif
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sign = nz0 = nz = decpt = 0;
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dval(rv) = 0.;
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for(s = s00;;s++) switch(*s) {
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case '-':
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sign = 1;
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/* no break */
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case '+':
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if (*++s)
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goto break2;
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/* no break */
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case 0:
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goto ret0;
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case '\t':
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case '\n':
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case '\v':
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case '\f':
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case '\r':
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case ' ':
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continue;
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default:
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goto break2;
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}
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break2:
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if (*s == '0') {
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#ifndef NO_HEX_FP
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{
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static FPI fpi = { 53, 1-1023-53+1, 2046-1023-53+1, 1, SI };
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Long exp;
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ULong bits[2];
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switch(s[1]) {
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case 'x':
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case 'X':
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{
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#if defined(FE_DOWNWARD) && defined(FE_TONEAREST) && defined(FE_TOWARDZERO) && defined(FE_UPWARD)
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FPI fpi1 = fpi;
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switch(fegetround()) {
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case FE_TOWARDZERO: fpi1.rounding = 0; break;
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case FE_UPWARD: fpi1.rounding = 2; break;
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case FE_DOWNWARD: fpi1.rounding = 3;
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}
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#else
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#define fpi1 fpi
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#endif
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switch((i = gethex(&s, &fpi1, &exp, &bb, sign)) & STRTOG_Retmask) {
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case STRTOG_NoNumber:
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s = s00;
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sign = 0;
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case STRTOG_Zero:
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break;
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default:
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if (bb) {
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copybits(bits, fpi.nbits, bb);
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Bfree(bb);
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}
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ULtod(((U*)&rv)->L, bits, exp, i);
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}}
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goto ret;
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}
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}
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#endif
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nz0 = 1;
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while(*++s == '0') ;
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if (!*s)
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goto ret;
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}
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s0 = s;
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y = z = 0;
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for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
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if (nd < 9)
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y = 10*y + c - '0';
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else if (nd < 16)
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z = 10*z + c - '0';
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nd0 = nd;
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#ifdef USE_LOCALE
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if (c == *localeconv()->decimal_point)
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#else
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if (c == '.')
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#endif
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{
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decpt = 1;
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c = *++s;
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if (!nd) {
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for(; c == '0'; c = *++s)
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nz++;
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if (c > '0' && c <= '9') {
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s0 = s;
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nf += nz;
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nz = 0;
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goto have_dig;
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}
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goto dig_done;
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}
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for(; c >= '0' && c <= '9'; c = *++s) {
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have_dig:
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nz++;
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if (c -= '0') {
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nf += nz;
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for(i = 1; i < nz; i++)
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if (nd++ < 9)
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y *= 10;
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else if (nd <= DBL_DIG + 1)
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z *= 10;
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if (nd++ < 9)
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y = 10*y + c;
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else if (nd <= DBL_DIG + 1)
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z = 10*z + c;
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nz = 0;
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}
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}
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}
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dig_done:
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e = 0;
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if (c == 'e' || c == 'E') {
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if (!nd && !nz && !nz0) {
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goto ret0;
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}
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s00 = s;
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esign = 0;
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switch(c = *++s) {
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case '-':
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esign = 1;
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case '+':
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c = *++s;
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}
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if (c >= '0' && c <= '9') {
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while(c == '0')
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c = *++s;
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if (c > '0' && c <= '9') {
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L = c - '0';
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s1 = s;
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while((c = *++s) >= '0' && c <= '9')
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L = 10*L + c - '0';
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if (s - s1 > 8 || L > 19999)
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/* Avoid confusion from exponents
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* so large that e might overflow.
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*/
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e = 19999; /* safe for 16 bit ints */
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else
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e = (int)L;
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if (esign)
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e = -e;
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}
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else
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e = 0;
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}
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else
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s = s00;
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}
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if (!nd) {
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if (!nz && !nz0) {
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#ifdef INFNAN_CHECK
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/* Check for Nan and Infinity */
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ULong bits[2];
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static FPI fpinan = /* only 52 explicit bits */
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{ 52, 1-1023-53+1, 2046-1023-53+1, 1, SI };
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if (!decpt)
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switch(c) {
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case 'i':
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case 'I':
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if (match(&s,"nf")) {
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--s;
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if (!match(&s,"inity"))
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++s;
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word0(rv) = 0x7ff00000;
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word1(rv) = 0;
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goto ret;
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}
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break;
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case 'n':
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case 'N':
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if (match(&s, "an")) {
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#ifndef No_Hex_NaN
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if (*s == '(' /*)*/
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&& hexnan(&s, &fpinan, bits)
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== STRTOG_NaNbits) {
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word0(rv) = 0x7ff00000 | bits[1];
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word1(rv) = bits[0];
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}
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else {
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#endif
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word0(rv) = NAN_WORD0;
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word1(rv) = NAN_WORD1;
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#ifndef No_Hex_NaN
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}
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#endif
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goto ret;
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}
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}
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#endif /* INFNAN_CHECK */
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ret0:
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s = s00;
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sign = 0;
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}
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goto ret;
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}
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e1 = e -= nf;
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/* Now we have nd0 digits, starting at s0, followed by a
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* decimal point, followed by nd-nd0 digits. The number we're
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* after is the integer represented by those digits times
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* 10**e */
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if (!nd0)
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nd0 = nd;
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k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
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dval(rv) = y;
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if (k > 9) {
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#ifdef SET_INEXACT
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if (k > DBL_DIG)
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oldinexact = get_inexact();
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#endif
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dval(rv) = tens[k - 9] * dval(rv) + z;
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}
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bd0 = 0;
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if (nd <= DBL_DIG
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#ifndef RND_PRODQUOT
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#ifndef Honor_FLT_ROUNDS
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&& Flt_Rounds == 1
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#endif
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#endif
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) {
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if (!e)
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goto ret;
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if (e > 0) {
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if (e <= Ten_pmax) {
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#ifdef VAX
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goto vax_ovfl_check;
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#else
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#ifdef Honor_FLT_ROUNDS
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/* round correctly FLT_ROUNDS = 2 or 3 */
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if (sign) {
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rv = -rv;
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sign = 0;
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}
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#endif
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/* rv = */ rounded_product(dval(rv), tens[e]);
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goto ret;
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#endif
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}
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i = DBL_DIG - nd;
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if (e <= Ten_pmax + i) {
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/* A fancier test would sometimes let us do
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* this for larger i values.
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*/
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#ifdef Honor_FLT_ROUNDS
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/* round correctly FLT_ROUNDS = 2 or 3 */
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if (sign) {
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rv = -rv;
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sign = 0;
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}
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#endif
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e -= i;
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dval(rv) *= tens[i];
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#ifdef VAX
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/* VAX exponent range is so narrow we must
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* worry about overflow here...
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*/
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vax_ovfl_check:
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word0(rv) -= P*Exp_msk1;
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/* rv = */ rounded_product(dval(rv), tens[e]);
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if ((word0(rv) & Exp_mask)
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> Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
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goto ovfl;
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word0(rv) += P*Exp_msk1;
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#else
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/* rv = */ rounded_product(dval(rv), tens[e]);
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#endif
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goto ret;
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}
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}
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#ifndef Inaccurate_Divide
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else if (e >= -Ten_pmax) {
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#ifdef Honor_FLT_ROUNDS
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/* round correctly FLT_ROUNDS = 2 or 3 */
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if (sign) {
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rv = -rv;
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sign = 0;
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}
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#endif
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/* rv = */ rounded_quotient(dval(rv), tens[-e]);
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goto ret;
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}
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#endif
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}
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e1 += nd - k;
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|
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#ifdef IEEE_Arith
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#ifdef SET_INEXACT
|
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inexact = 1;
|
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if (k <= DBL_DIG)
|
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oldinexact = get_inexact();
|
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#endif
|
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#ifdef Avoid_Underflow
|
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scale = 0;
|
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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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#endif /*IEEE_Arith*/
|
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|
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/* Get starting approximation = rv * 10**e1 */
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|
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if (e1 > 0) {
|
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if ( (i = e1 & 15) !=0)
|
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dval(rv) *= tens[i];
|
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if (e1 &= ~15) {
|
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if (e1 > DBL_MAX_10_EXP) {
|
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ovfl:
|
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#ifndef NO_ERRNO
|
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errno = ERANGE;
|
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#endif
|
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/* Can't trust HUGE_VAL */
|
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#ifdef IEEE_Arith
|
|
#ifdef Honor_FLT_ROUNDS
|
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switch(rounding) {
|
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case 0: /* toward 0 */
|
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case 3: /* toward -infinity */
|
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word0(rv) = Big0;
|
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word1(rv) = Big1;
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break;
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default:
|
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word0(rv) = Exp_mask;
|
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word1(rv) = 0;
|
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}
|
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#else /*Honor_FLT_ROUNDS*/
|
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word0(rv) = Exp_mask;
|
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word1(rv) = 0;
|
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#endif /*Honor_FLT_ROUNDS*/
|
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#ifdef SET_INEXACT
|
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/* set overflow bit */
|
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dval(rv0) = 1e300;
|
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dval(rv0) *= dval(rv0);
|
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#endif
|
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#else /*IEEE_Arith*/
|
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word0(rv) = Big0;
|
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word1(rv) = Big1;
|
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#endif /*IEEE_Arith*/
|
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if (bd0)
|
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goto retfree;
|
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goto ret;
|
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}
|
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e1 >>= 4;
|
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for(j = 0; e1 > 1; j++, e1 >>= 1)
|
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if (e1 & 1)
|
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dval(rv) *= bigtens[j];
|
|
/* The last multiplication could overflow. */
|
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word0(rv) -= P*Exp_msk1;
|
|
dval(rv) *= bigtens[j];
|
|
if ((z = word0(rv) & Exp_mask)
|
|
> Exp_msk1*(DBL_MAX_EXP+Bias-P))
|
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goto ovfl;
|
|
if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
|
|
/* set to largest number */
|
|
/* (Can't trust DBL_MAX) */
|
|
word0(rv) = Big0;
|
|
word1(rv) = Big1;
|
|
}
|
|
else
|
|
word0(rv) += P*Exp_msk1;
|
|
}
|
|
}
|
|
else if (e1 < 0) {
|
|
e1 = -e1;
|
|
if ( (i = e1 & 15) !=0)
|
|
dval(rv) /= tens[i];
|
|
if (e1 >>= 4) {
|
|
if (e1 >= 1 << n_bigtens)
|
|
goto undfl;
|
|
#ifdef Avoid_Underflow
|
|
if (e1 & Scale_Bit)
|
|
scale = 2*P;
|
|
for(j = 0; e1 > 0; j++, e1 >>= 1)
|
|
if (e1 & 1)
|
|
dval(rv) *= tinytens[j];
|
|
if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
|
|
>> Exp_shift)) > 0) {
|
|
/* scaled rv is denormal; zap j low bits */
|
|
if (j >= 32) {
|
|
word1(rv) = 0;
|
|
if (j >= 53)
|
|
word0(rv) = (P+2)*Exp_msk1;
|
|
else
|
|
word0(rv) &= 0xffffffff << j-32;
|
|
}
|
|
else
|
|
word1(rv) &= 0xffffffff << j;
|
|
}
|
|
#else
|
|
for(j = 0; e1 > 1; j++, e1 >>= 1)
|
|
if (e1 & 1)
|
|
dval(rv) *= tinytens[j];
|
|
/* The last multiplication could underflow. */
|
|
dval(rv0) = dval(rv);
|
|
dval(rv) *= tinytens[j];
|
|
if (!dval(rv)) {
|
|
dval(rv) = 2.*dval(rv0);
|
|
dval(rv) *= tinytens[j];
|
|
#endif
|
|
if (!dval(rv)) {
|
|
undfl:
|
|
dval(rv) = 0.;
|
|
#ifndef NO_ERRNO
|
|
errno = ERANGE;
|
|
#endif
|
|
if (bd0)
|
|
goto retfree;
|
|
goto ret;
|
|
}
|
|
#ifndef Avoid_Underflow
|
|
word0(rv) = Tiny0;
|
|
word1(rv) = Tiny1;
|
|
/* The refinement below will clean
|
|
* this approximation up.
|
|
*/
|
|
}
|
|
#endif
|
|
}
|
|
}
|
|
|
|
/* Now the hard part -- adjusting rv to the correct value.*/
|
|
|
|
/* Put digits into bd: true value = bd * 10^e */
|
|
|
|
bd0 = s2b(s0, nd0, nd, y);
|
|
|
|
for(;;) {
|
|
bd = Balloc(bd0->k);
|
|
Bcopy(bd, bd0);
|
|
bb = d2b(dval(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */
|
|
bs = i2b(1);
|
|
|
|
if (e >= 0) {
|
|
bb2 = bb5 = 0;
|
|
bd2 = bd5 = e;
|
|
}
|
|
else {
|
|
bb2 = bb5 = -e;
|
|
bd2 = bd5 = 0;
|
|
}
|
|
if (bbe >= 0)
|
|
bb2 += bbe;
|
|
else
|
|
bd2 -= bbe;
|
|
bs2 = bb2;
|
|
#ifdef Honor_FLT_ROUNDS
|
|
if (rounding != 1)
|
|
bs2++;
|
|
#endif
|
|
#ifdef Avoid_Underflow
|
|
j = bbe - scale;
|
|
i = j + bbbits - 1; /* logb(rv) */
|
|
if (i < Emin) /* denormal */
|
|
j += P - Emin;
|
|
else
|
|
j = P + 1 - bbbits;
|
|
#else /*Avoid_Underflow*/
|
|
#ifdef Sudden_Underflow
|
|
#ifdef IBM
|
|
j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
|
|
#else
|
|
j = P + 1 - bbbits;
|
|
#endif
|
|
#else /*Sudden_Underflow*/
|
|
j = bbe;
|
|
i = j + bbbits - 1; /* logb(rv) */
|
|
if (i < Emin) /* denormal */
|
|
j += P - Emin;
|
|
else
|
|
j = P + 1 - bbbits;
|
|
#endif /*Sudden_Underflow*/
|
|
#endif /*Avoid_Underflow*/
|
|
bb2 += j;
|
|
bd2 += j;
|
|
#ifdef Avoid_Underflow
|
|
bd2 += scale;
|
|
#endif
|
|
i = bb2 < bd2 ? bb2 : bd2;
|
|
if (i > bs2)
|
|
i = bs2;
|
|
if (i > 0) {
|
|
bb2 -= i;
|
|
bd2 -= i;
|
|
bs2 -= i;
|
|
}
|
|
if (bb5 > 0) {
|
|
bs = pow5mult(bs, bb5);
|
|
bb1 = mult(bs, bb);
|
|
Bfree(bb);
|
|
bb = bb1;
|
|
}
|
|
if (bb2 > 0)
|
|
bb = lshift(bb, bb2);
|
|
if (bd5 > 0)
|
|
bd = pow5mult(bd, bd5);
|
|
if (bd2 > 0)
|
|
bd = lshift(bd, bd2);
|
|
if (bs2 > 0)
|
|
bs = lshift(bs, bs2);
|
|
delta = diff(bb, bd);
|
|
dsign = delta->sign;
|
|
delta->sign = 0;
|
|
i = cmp(delta, bs);
|
|
#ifdef Honor_FLT_ROUNDS
|
|
if (rounding != 1) {
|
|
if (i < 0) {
|
|
/* Error is less than an ulp */
|
|
if (!delta->x[0] && delta->wds <= 1) {
|
|
/* exact */
|
|
#ifdef SET_INEXACT
|
|
inexact = 0;
|
|
#endif
|
|
break;
|
|
}
|
|
if (rounding) {
|
|
if (dsign) {
|
|
adj = 1.;
|
|
goto apply_adj;
|
|
}
|
|
}
|
|
else if (!dsign) {
|
|
adj = -1.;
|
|
if (!word1(rv)
|
|
&& !(word0(rv) & Frac_mask)) {
|
|
y = word0(rv) & Exp_mask;
|
|
#ifdef Avoid_Underflow
|
|
if (!scale || y > 2*P*Exp_msk1)
|
|
#else
|
|
if (y)
|
|
#endif
|
|
{
|
|
delta = lshift(delta,Log2P);
|
|
if (cmp(delta, bs) <= 0)
|
|
adj = -0.5;
|
|
}
|
|
}
|
|
apply_adj:
|
|
#ifdef Avoid_Underflow
|
|
if (scale && (y = word0(rv) & Exp_mask)
|
|
<= 2*P*Exp_msk1)
|
|
word0(adj) += (2*P+1)*Exp_msk1 - y;
|
|
#else
|
|
#ifdef Sudden_Underflow
|
|
if ((word0(rv) & Exp_mask) <=
|
|
P*Exp_msk1) {
|
|
word0(rv) += P*Exp_msk1;
|
|
dval(rv) += adj*ulp(dval(rv));
|
|
word0(rv) -= P*Exp_msk1;
|
|
}
|
|
else
|
|
#endif /*Sudden_Underflow*/
|
|
#endif /*Avoid_Underflow*/
|
|
dval(rv) += adj*ulp(dval(rv));
|
|
}
|
|
break;
|
|
}
|
|
adj = ratio(delta, bs);
|
|
if (adj < 1.)
|
|
adj = 1.;
|
|
if (adj <= 0x7ffffffe) {
|
|
/* adj = rounding ? ceil(adj) : floor(adj); */
|
|
y = adj;
|
|
if (y != adj) {
|
|
if (!((rounding>>1) ^ dsign))
|
|
y++;
|
|
adj = y;
|
|
}
|
|
}
|
|
#ifdef Avoid_Underflow
|
|
if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
|
|
word0(adj) += (2*P+1)*Exp_msk1 - y;
|
|
#else
|
|
#ifdef Sudden_Underflow
|
|
if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
|
|
word0(rv) += P*Exp_msk1;
|
|
adj *= ulp(dval(rv));
|
|
if (dsign)
|
|
dval(rv) += adj;
|
|
else
|
|
dval(rv) -= adj;
|
|
word0(rv) -= P*Exp_msk1;
|
|
goto cont;
|
|
}
|
|
#endif /*Sudden_Underflow*/
|
|
#endif /*Avoid_Underflow*/
|
|
adj *= ulp(dval(rv));
|
|
if (dsign)
|
|
dval(rv) += adj;
|
|
else
|
|
dval(rv) -= adj;
|
|
goto cont;
|
|
}
|
|
#endif /*Honor_FLT_ROUNDS*/
|
|
|
|
if (i < 0) {
|
|
/* Error is less than half an ulp -- check for
|
|
* special case of mantissa a power of two.
|
|
*/
|
|
if (dsign || word1(rv) || word0(rv) & Bndry_mask
|
|
#ifdef IEEE_Arith
|
|
#ifdef Avoid_Underflow
|
|
|| (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
|
|
#else
|
|
|| (word0(rv) & Exp_mask) <= Exp_msk1
|
|
#endif
|
|
#endif
|
|
) {
|
|
#ifdef SET_INEXACT
|
|
if (!delta->x[0] && delta->wds <= 1)
|
|
inexact = 0;
|
|
#endif
|
|
break;
|
|
}
|
|
if (!delta->x[0] && delta->wds <= 1) {
|
|
/* exact result */
|
|
#ifdef SET_INEXACT
|
|
inexact = 0;
|
|
#endif
|
|
break;
|
|
}
|
|
delta = lshift(delta,Log2P);
|
|
if (cmp(delta, bs) > 0)
|
|
goto drop_down;
|
|
break;
|
|
}
|
|
if (i == 0) {
|
|
/* exactly half-way between */
|
|
if (dsign) {
|
|
if ((word0(rv) & Bndry_mask1) == Bndry_mask1
|
|
&& word1(rv) == (
|
|
#ifdef Avoid_Underflow
|
|
(scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
|
|
? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
|
|
#endif
|
|
0xffffffff)) {
|
|
/*boundary case -- increment exponent*/
|
|
word0(rv) = (word0(rv) & Exp_mask)
|
|
+ Exp_msk1
|
|
#ifdef IBM
|
|
| Exp_msk1 >> 4
|
|
#endif
|
|
;
|
|
word1(rv) = 0;
|
|
#ifdef Avoid_Underflow
|
|
dsign = 0;
|
|
#endif
|
|
break;
|
|
}
|
|
}
|
|
else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
|
|
drop_down:
|
|
/* boundary case -- decrement exponent */
|
|
#ifdef Sudden_Underflow /*{{*/
|
|
L = word0(rv) & Exp_mask;
|
|
#ifdef IBM
|
|
if (L < Exp_msk1)
|
|
#else
|
|
#ifdef Avoid_Underflow
|
|
if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
|
|
#else
|
|
if (L <= Exp_msk1)
|
|
#endif /*Avoid_Underflow*/
|
|
#endif /*IBM*/
|
|
goto undfl;
|
|
L -= Exp_msk1;
|
|
#else /*Sudden_Underflow}{*/
|
|
#ifdef Avoid_Underflow
|
|
if (scale) {
|
|
L = word0(rv) & Exp_mask;
|
|
if (L <= (2*P+1)*Exp_msk1) {
|
|
if (L > (P+2)*Exp_msk1)
|
|
/* round even ==> */
|
|
/* accept rv */
|
|
break;
|
|
/* rv = smallest denormal */
|
|
goto undfl;
|
|
}
|
|
}
|
|
#endif /*Avoid_Underflow*/
|
|
L = (word0(rv) & Exp_mask) - Exp_msk1;
|
|
#endif /*Sudden_Underflow}*/
|
|
word0(rv) = L | Bndry_mask1;
|
|
word1(rv) = 0xffffffff;
|
|
#ifdef IBM
|
|
goto cont;
|
|
#else
|
|
break;
|
|
#endif
|
|
}
|
|
#ifndef ROUND_BIASED
|
|
if (!(word1(rv) & LSB))
|
|
break;
|
|
#endif
|
|
if (dsign)
|
|
dval(rv) += ulp(dval(rv));
|
|
#ifndef ROUND_BIASED
|
|
else {
|
|
dval(rv) -= ulp(dval(rv));
|
|
#ifndef Sudden_Underflow
|
|
if (!dval(rv))
|
|
goto undfl;
|
|
#endif
|
|
}
|
|
#ifdef Avoid_Underflow
|
|
dsign = 1 - dsign;
|
|
#endif
|
|
#endif
|
|
break;
|
|
}
|
|
if ((aadj = ratio(delta, bs)) <= 2.) {
|
|
if (dsign)
|
|
aadj = aadj1 = 1.;
|
|
else if (word1(rv) || word0(rv) & Bndry_mask) {
|
|
#ifndef Sudden_Underflow
|
|
if (word1(rv) == Tiny1 && !word0(rv))
|
|
goto undfl;
|
|
#endif
|
|
aadj = 1.;
|
|
aadj1 = -1.;
|
|
}
|
|
else {
|
|
/* special case -- power of FLT_RADIX to be */
|
|
/* rounded down... */
|
|
|
|
if (aadj < 2./FLT_RADIX)
|
|
aadj = 1./FLT_RADIX;
|
|
else
|
|
aadj *= 0.5;
|
|
aadj1 = -aadj;
|
|
}
|
|
}
|
|
else {
|
|
aadj *= 0.5;
|
|
aadj1 = dsign ? aadj : -aadj;
|
|
#ifdef Check_FLT_ROUNDS
|
|
switch(Rounding) {
|
|
case 2: /* towards +infinity */
|
|
aadj1 -= 0.5;
|
|
break;
|
|
case 0: /* towards 0 */
|
|
case 3: /* towards -infinity */
|
|
aadj1 += 0.5;
|
|
}
|
|
#else
|
|
if (Flt_Rounds == 0)
|
|
aadj1 += 0.5;
|
|
#endif /*Check_FLT_ROUNDS*/
|
|
}
|
|
y = word0(rv) & Exp_mask;
|
|
|
|
/* Check for overflow */
|
|
|
|
if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
|
|
dval(rv0) = dval(rv);
|
|
word0(rv) -= P*Exp_msk1;
|
|
adj = aadj1 * ulp(dval(rv));
|
|
dval(rv) += adj;
|
|
if ((word0(rv) & Exp_mask) >=
|
|
Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
|
|
if (word0(rv0) == Big0 && word1(rv0) == Big1)
|
|
goto ovfl;
|
|
word0(rv) = Big0;
|
|
word1(rv) = Big1;
|
|
goto cont;
|
|
}
|
|
else
|
|
word0(rv) += P*Exp_msk1;
|
|
}
|
|
else {
|
|
#ifdef Avoid_Underflow
|
|
if (scale && y <= 2*P*Exp_msk1) {
|
|
if (aadj <= 0x7fffffff) {
|
|
if ((z = aadj) <= 0)
|
|
z = 1;
|
|
aadj = z;
|
|
aadj1 = dsign ? aadj : -aadj;
|
|
}
|
|
word0(aadj1) += (2*P+1)*Exp_msk1 - y;
|
|
}
|
|
adj = aadj1 * ulp(dval(rv));
|
|
dval(rv) += adj;
|
|
#else
|
|
#ifdef Sudden_Underflow
|
|
if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
|
|
dval(rv0) = dval(rv);
|
|
word0(rv) += P*Exp_msk1;
|
|
adj = aadj1 * ulp(dval(rv));
|
|
dval(rv) += adj;
|
|
#ifdef IBM
|
|
if ((word0(rv) & Exp_mask) < P*Exp_msk1)
|
|
#else
|
|
if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
|
|
#endif
|
|
{
|
|
if (word0(rv0) == Tiny0
|
|
&& word1(rv0) == Tiny1)
|
|
goto undfl;
|
|
word0(rv) = Tiny0;
|
|
word1(rv) = Tiny1;
|
|
goto cont;
|
|
}
|
|
else
|
|
word0(rv) -= P*Exp_msk1;
|
|
}
|
|
else {
|
|
adj = aadj1 * ulp(dval(rv));
|
|
dval(rv) += adj;
|
|
}
|
|
#else /*Sudden_Underflow*/
|
|
/* Compute adj so that the IEEE rounding rules will
|
|
* correctly round rv + adj in some half-way cases.
|
|
* If rv * ulp(rv) is denormalized (i.e.,
|
|
* y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
|
|
* trouble from bits lost to denormalization;
|
|
* example: 1.2e-307 .
|
|
*/
|
|
if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
|
|
aadj1 = (double)(int)(aadj + 0.5);
|
|
if (!dsign)
|
|
aadj1 = -aadj1;
|
|
}
|
|
adj = aadj1 * ulp(dval(rv));
|
|
dval(rv) += adj;
|
|
#endif /*Sudden_Underflow*/
|
|
#endif /*Avoid_Underflow*/
|
|
}
|
|
z = word0(rv) & Exp_mask;
|
|
#ifndef SET_INEXACT
|
|
#ifdef Avoid_Underflow
|
|
if (!scale)
|
|
#endif
|
|
if (y == z) {
|
|
/* Can we stop now? */
|
|
L = (Long)aadj;
|
|
aadj -= L;
|
|
/* The tolerances below are conservative. */
|
|
if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
|
|
if (aadj < .4999999 || aadj > .5000001)
|
|
break;
|
|
}
|
|
else if (aadj < .4999999/FLT_RADIX)
|
|
break;
|
|
}
|
|
#endif
|
|
cont:
|
|
Bfree(bb);
|
|
Bfree(bd);
|
|
Bfree(bs);
|
|
Bfree(delta);
|
|
}
|
|
#ifdef SET_INEXACT
|
|
if (inexact) {
|
|
if (!oldinexact) {
|
|
word0(rv0) = Exp_1 + (70 << Exp_shift);
|
|
word1(rv0) = 0;
|
|
dval(rv0) += 1.;
|
|
}
|
|
}
|
|
else if (!oldinexact)
|
|
clear_inexact();
|
|
#endif
|
|
#ifdef Avoid_Underflow
|
|
if (scale) {
|
|
word0(rv0) = Exp_1 - 2*P*Exp_msk1;
|
|
word1(rv0) = 0;
|
|
dval(rv) *= dval(rv0);
|
|
#ifndef NO_ERRNO
|
|
/* try to avoid the bug of testing an 8087 register value */
|
|
if (word0(rv) == 0 && word1(rv) == 0)
|
|
errno = ERANGE;
|
|
#endif
|
|
}
|
|
#endif /* Avoid_Underflow */
|
|
#ifdef SET_INEXACT
|
|
if (inexact && !(word0(rv) & Exp_mask)) {
|
|
/* set underflow bit */
|
|
dval(rv0) = 1e-300;
|
|
dval(rv0) *= dval(rv0);
|
|
}
|
|
#endif
|
|
retfree:
|
|
Bfree(bb);
|
|
Bfree(bd);
|
|
Bfree(bs);
|
|
Bfree(bd0);
|
|
Bfree(delta);
|
|
ret:
|
|
if (se)
|
|
*se = (char *)s;
|
|
return sign ? -dval(rv) : dval(rv);
|
|
}
|
|
|