1013 lines
19 KiB
C
1013 lines
19 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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#ifdef USE_LOCALE
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#include "locale.h"
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#endif
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static CONST int
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fivesbits[] = { 0, 3, 5, 7, 10, 12, 14, 17, 19, 21,
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24, 26, 28, 31, 33, 35, 38, 40, 42, 45,
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47, 49, 52
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#ifdef VAX
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, 54, 56
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#endif
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};
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Bigint *
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#ifdef KR_headers
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increment(b) Bigint *b;
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#else
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increment(Bigint *b)
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#endif
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{
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ULong *x, *xe;
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Bigint *b1;
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#ifdef Pack_16
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ULong carry = 1, y;
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#endif
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x = b->x;
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xe = x + b->wds;
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#ifdef Pack_32
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do {
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if (*x < (ULong)0xffffffffL) {
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++*x;
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return b;
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}
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*x++ = 0;
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} while(x < xe);
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#else
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do {
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y = *x + carry;
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carry = y >> 16;
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*x++ = y & 0xffff;
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if (!carry)
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return b;
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} while(x < xe);
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if (carry)
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#endif
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{
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if (b->wds >= b->maxwds) {
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b1 = Balloc(b->k+1);
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Bcopy(b1,b);
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Bfree(b);
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b = b1;
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}
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b->x[b->wds++] = 1;
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}
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return b;
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}
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int
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#ifdef KR_headers
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decrement(b) Bigint *b;
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#else
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decrement(Bigint *b)
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#endif
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{
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ULong *x, *xe;
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#ifdef Pack_16
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ULong borrow = 1, y;
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#endif
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x = b->x;
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xe = x + b->wds;
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#ifdef Pack_32
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do {
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if (*x) {
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--*x;
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break;
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}
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*x++ = 0xffffffffL;
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}
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while(x < xe);
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#else
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do {
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y = *x - borrow;
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borrow = (y & 0x10000) >> 16;
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*x++ = y & 0xffff;
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} while(borrow && x < xe);
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#endif
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return STRTOG_Inexlo;
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}
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static int
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#ifdef KR_headers
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all_on(b, n) Bigint *b; int n;
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#else
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all_on(Bigint *b, int n)
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#endif
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{
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ULong *x, *xe;
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x = b->x;
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xe = x + (n >> kshift);
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while(x < xe)
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if ((*x++ & ALL_ON) != ALL_ON)
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return 0;
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if (n &= kmask)
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return ((*x | (ALL_ON << n)) & ALL_ON) == ALL_ON;
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return 1;
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}
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Bigint *
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#ifdef KR_headers
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set_ones(b, n) Bigint *b; int n;
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#else
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set_ones(Bigint *b, int n)
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#endif
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{
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int k;
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ULong *x, *xe;
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k = (n + ((1 << kshift) - 1)) >> kshift;
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if (b->k < k) {
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Bfree(b);
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b = Balloc(k);
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}
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k = n >> kshift;
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if (n &= kmask)
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k++;
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b->wds = k;
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x = b->x;
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xe = x + k;
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while(x < xe)
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*x++ = ALL_ON;
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if (n)
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x[-1] >>= ULbits - n;
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return b;
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}
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static int
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rvOK
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#ifdef KR_headers
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(d, fpi, exp, bits, exact, rd, irv)
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double d; FPI *fpi; Long *exp; ULong *bits; int exact, rd, *irv;
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#else
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(double d, FPI *fpi, Long *exp, ULong *bits, int exact, int rd, int *irv)
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#endif
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{
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Bigint *b;
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ULong carry, inex, lostbits;
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int bdif, e, j, k, k1, nb, rv;
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carry = rv = 0;
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b = d2b(d, &e, &bdif);
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bdif -= nb = fpi->nbits;
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e += bdif;
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if (bdif <= 0) {
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if (exact)
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goto trunc;
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goto ret;
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}
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if (P == nb) {
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if (
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#ifndef IMPRECISE_INEXACT
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exact &&
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#endif
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fpi->rounding ==
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#ifdef RND_PRODQUOT
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FPI_Round_near
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#else
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Flt_Rounds
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#endif
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) goto trunc;
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goto ret;
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}
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switch(rd) {
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case 1:
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goto trunc;
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case 2:
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break;
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default: /* round near */
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k = bdif - 1;
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if (k < 0)
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goto trunc;
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if (!k) {
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if (!exact)
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goto ret;
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if (b->x[0] & 2)
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break;
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goto trunc;
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}
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if (b->x[k>>kshift] & ((ULong)1 << (k & kmask)))
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break;
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goto trunc;
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}
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/* "break" cases: round up 1 bit, then truncate; bdif > 0 */
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carry = 1;
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trunc:
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inex = lostbits = 0;
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if (bdif > 0) {
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if ( (lostbits = any_on(b, bdif)) !=0)
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inex = STRTOG_Inexlo;
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rshift(b, bdif);
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if (carry) {
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inex = STRTOG_Inexhi;
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b = increment(b);
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if ( (j = nb & kmask) !=0)
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j = ULbits - j;
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if (hi0bits(b->x[b->wds - 1]) != j) {
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if (!lostbits)
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lostbits = b->x[0] & 1;
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rshift(b, 1);
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e++;
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}
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}
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}
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else if (bdif < 0)
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b = lshift(b, -bdif);
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if (e < fpi->emin) {
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k = fpi->emin - e;
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e = fpi->emin;
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if (k > nb || fpi->sudden_underflow) {
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b->wds = inex = 0;
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*irv = STRTOG_Underflow | STRTOG_Inexlo;
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}
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else {
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k1 = k - 1;
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if (k1 > 0 && !lostbits)
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lostbits = any_on(b, k1);
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if (!lostbits && !exact)
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goto ret;
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lostbits |=
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carry = b->x[k1>>kshift] & (1 << (k1 & kmask));
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rshift(b, k);
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*irv = STRTOG_Denormal;
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if (carry) {
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b = increment(b);
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inex = STRTOG_Inexhi | STRTOG_Underflow;
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}
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else if (lostbits)
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inex = STRTOG_Inexlo | STRTOG_Underflow;
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}
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}
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else if (e > fpi->emax) {
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e = fpi->emax + 1;
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*irv = STRTOG_Infinite | STRTOG_Overflow | STRTOG_Inexhi;
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#ifndef NO_ERRNO
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errno = ERANGE;
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#endif
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b->wds = inex = 0;
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}
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*exp = e;
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copybits(bits, nb, b);
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*irv |= inex;
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rv = 1;
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ret:
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Bfree(b);
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return rv;
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}
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static int
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#ifdef KR_headers
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mantbits(d) double d;
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#else
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mantbits(double d)
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#endif
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{
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ULong L;
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#ifdef VAX
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L = word1(d) << 16 | word1(d) >> 16;
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if (L)
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#else
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if ( (L = word1(d)) !=0)
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#endif
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return P - lo0bits(&L);
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#ifdef VAX
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L = word0(d) << 16 | word0(d) >> 16 | Exp_msk11;
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#else
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L = word0(d) | Exp_msk1;
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#endif
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return P - 32 - lo0bits(&L);
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}
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int
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strtodg
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#ifdef KR_headers
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(s00, se, fpi, exp, bits)
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CONST char *s00; char **se; FPI *fpi; Long *exp; ULong *bits;
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#else
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(CONST char *s00, char **se, FPI *fpi, Long *exp, ULong *bits)
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#endif
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{
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int abe, abits, asub;
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int bb0, bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, decpt, denorm;
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int dsign, e, e1, e2, emin, esign, finished, i, inex, irv;
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int j, k, nbits, nd, nd0, nf, nz, nz0, rd, rvbits, rve, rve1, sign;
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int sudden_underflow;
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CONST char *s, *s0, *s1;
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double adj, adj0, rv, tol;
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Long L;
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ULong y, z;
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Bigint *ab, *bb, *bb1, *bd, *bd0, *bs, *delta, *rvb, *rvb0;
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irv = STRTOG_Zero;
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denorm = sign = nz0 = nz = 0;
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dval(rv) = 0.;
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rvb = 0;
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nbits = fpi->nbits;
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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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sign = 0;
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irv = STRTOG_NoNumber;
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s = s00;
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goto ret;
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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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switch(s[1]) {
|
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case 'x':
|
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case 'X':
|
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irv = gethex(&s, fpi, exp, &rvb, sign);
|
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if (irv == STRTOG_NoNumber) {
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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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}
|
|
#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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sudden_underflow = fpi->sudden_underflow;
|
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s0 = s;
|
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y = z = 0;
|
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for(decpt = nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
|
|
if (nd < 9)
|
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y = 10*y + c - '0';
|
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else if (nd < 16)
|
|
z = 10*z + c - '0';
|
|
nd0 = nd;
|
|
#ifdef USE_LOCALE
|
|
if (c == *localeconv()->decimal_point)
|
|
#else
|
|
if (c == '.')
|
|
#endif
|
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{
|
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decpt = 1;
|
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c = *++s;
|
|
if (!nd) {
|
|
for(; c == '0'; c = *++s)
|
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nz++;
|
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if (c > '0' && c <= '9') {
|
|
s0 = s;
|
|
nf += nz;
|
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nz = 0;
|
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goto have_dig;
|
|
}
|
|
goto dig_done;
|
|
}
|
|
for(; c >= '0' && c <= '9'; c = *++s) {
|
|
have_dig:
|
|
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)
|
|
z *= 10;
|
|
if (nd++ < 9)
|
|
y = 10*y + c;
|
|
else if (nd <= DBL_DIG + 1)
|
|
z = 10*z + c;
|
|
nz = 0;
|
|
}
|
|
}
|
|
}
|
|
dig_done:
|
|
e = 0;
|
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if (c == 'e' || c == 'E') {
|
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if (!nd && !nz && !nz0) {
|
|
irv = STRTOG_NoNumber;
|
|
s = s00;
|
|
goto ret;
|
|
}
|
|
s00 = s;
|
|
esign = 0;
|
|
switch(c = *++s) {
|
|
case '-':
|
|
esign = 1;
|
|
case '+':
|
|
c = *++s;
|
|
}
|
|
if (c >= '0' && c <= '9') {
|
|
while(c == '0')
|
|
c = *++s;
|
|
if (c > '0' && c <= '9') {
|
|
L = c - '0';
|
|
s1 = s;
|
|
while((c = *++s) >= '0' && c <= '9')
|
|
L = 10*L + c - '0';
|
|
if (s - s1 > 8 || L > 19999)
|
|
/* Avoid confusion from exponents
|
|
* so large that e might overflow.
|
|
*/
|
|
e = 19999; /* safe for 16 bit ints */
|
|
else
|
|
e = (int)L;
|
|
if (esign)
|
|
e = -e;
|
|
}
|
|
else
|
|
e = 0;
|
|
}
|
|
else
|
|
s = s00;
|
|
}
|
|
if (!nd) {
|
|
if (!nz && !nz0) {
|
|
#ifdef INFNAN_CHECK
|
|
/* Check for Nan and Infinity */
|
|
if (!decpt)
|
|
switch(c) {
|
|
case 'i':
|
|
case 'I':
|
|
if (match(&s,"nf")) {
|
|
--s;
|
|
if (!match(&s,"inity"))
|
|
++s;
|
|
irv = STRTOG_Infinite;
|
|
goto infnanexp;
|
|
}
|
|
break;
|
|
case 'n':
|
|
case 'N':
|
|
if (match(&s, "an")) {
|
|
irv = STRTOG_NaN;
|
|
*exp = fpi->emax + 1;
|
|
#ifndef No_Hex_NaN
|
|
if (*s == '(') /*)*/
|
|
irv = hexnan(&s, fpi, bits);
|
|
#endif
|
|
goto infnanexp;
|
|
}
|
|
}
|
|
#endif /* INFNAN_CHECK */
|
|
irv = STRTOG_NoNumber;
|
|
s = s00;
|
|
}
|
|
goto ret;
|
|
}
|
|
|
|
irv = STRTOG_Normal;
|
|
e1 = e -= nf;
|
|
rd = 0;
|
|
switch(fpi->rounding & 3) {
|
|
case FPI_Round_up:
|
|
rd = 2 - sign;
|
|
break;
|
|
case FPI_Round_zero:
|
|
rd = 1;
|
|
break;
|
|
case FPI_Round_down:
|
|
rd = 1 + sign;
|
|
}
|
|
|
|
/* Now we have nd0 digits, starting at s0, followed by a
|
|
* decimal point, followed by nd-nd0 digits. The number we're
|
|
* after is the integer represented by those digits times
|
|
* 10**e */
|
|
|
|
if (!nd0)
|
|
nd0 = nd;
|
|
k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
|
|
dval(rv) = y;
|
|
if (k > 9)
|
|
dval(rv) = tens[k - 9] * dval(rv) + z;
|
|
bd0 = 0;
|
|
if (nbits <= P && nd <= DBL_DIG) {
|
|
if (!e) {
|
|
if (rvOK(dval(rv), fpi, exp, bits, 1, rd, &irv))
|
|
goto ret;
|
|
}
|
|
else if (e > 0) {
|
|
if (e <= Ten_pmax) {
|
|
#ifdef VAX
|
|
goto vax_ovfl_check;
|
|
#else
|
|
i = fivesbits[e] + mantbits(dval(rv)) <= P;
|
|
/* rv = */ rounded_product(dval(rv), tens[e]);
|
|
if (rvOK(dval(rv), fpi, exp, bits, i, rd, &irv))
|
|
goto ret;
|
|
e1 -= e;
|
|
goto rv_notOK;
|
|
#endif
|
|
}
|
|
i = DBL_DIG - nd;
|
|
if (e <= Ten_pmax + i) {
|
|
/* A fancier test would sometimes let us do
|
|
* this for larger i values.
|
|
*/
|
|
e2 = e - i;
|
|
e1 -= i;
|
|
dval(rv) *= tens[i];
|
|
#ifdef VAX
|
|
/* VAX exponent range is so narrow we must
|
|
* worry about overflow here...
|
|
*/
|
|
vax_ovfl_check:
|
|
dval(adj) = dval(rv);
|
|
word0(adj) -= P*Exp_msk1;
|
|
/* adj = */ rounded_product(dval(adj), tens[e2]);
|
|
if ((word0(adj) & Exp_mask)
|
|
> Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
|
|
goto rv_notOK;
|
|
word0(adj) += P*Exp_msk1;
|
|
dval(rv) = dval(adj);
|
|
#else
|
|
/* rv = */ rounded_product(dval(rv), tens[e2]);
|
|
#endif
|
|
if (rvOK(dval(rv), fpi, exp, bits, 0, rd, &irv))
|
|
goto ret;
|
|
e1 -= e2;
|
|
}
|
|
}
|
|
#ifndef Inaccurate_Divide
|
|
else if (e >= -Ten_pmax) {
|
|
/* rv = */ rounded_quotient(dval(rv), tens[-e]);
|
|
if (rvOK(dval(rv), fpi, exp, bits, 0, rd, &irv))
|
|
goto ret;
|
|
e1 -= e;
|
|
}
|
|
#endif
|
|
}
|
|
rv_notOK:
|
|
e1 += nd - k;
|
|
|
|
/* Get starting approximation = rv * 10**e1 */
|
|
|
|
e2 = 0;
|
|
if (e1 > 0) {
|
|
if ( (i = e1 & 15) !=0)
|
|
dval(rv) *= tens[i];
|
|
if (e1 &= ~15) {
|
|
e1 >>= 4;
|
|
while(e1 >= (1 << n_bigtens-1)) {
|
|
e2 += ((word0(rv) & Exp_mask)
|
|
>> Exp_shift1) - Bias;
|
|
word0(rv) &= ~Exp_mask;
|
|
word0(rv) |= Bias << Exp_shift1;
|
|
dval(rv) *= bigtens[n_bigtens-1];
|
|
e1 -= 1 << n_bigtens-1;
|
|
}
|
|
e2 += ((word0(rv) & Exp_mask) >> Exp_shift1) - Bias;
|
|
word0(rv) &= ~Exp_mask;
|
|
word0(rv) |= Bias << Exp_shift1;
|
|
for(j = 0; e1 > 0; j++, e1 >>= 1)
|
|
if (e1 & 1)
|
|
dval(rv) *= bigtens[j];
|
|
}
|
|
}
|
|
else if (e1 < 0) {
|
|
e1 = -e1;
|
|
if ( (i = e1 & 15) !=0)
|
|
dval(rv) /= tens[i];
|
|
if (e1 &= ~15) {
|
|
e1 >>= 4;
|
|
while(e1 >= (1 << n_bigtens-1)) {
|
|
e2 += ((word0(rv) & Exp_mask)
|
|
>> Exp_shift1) - Bias;
|
|
word0(rv) &= ~Exp_mask;
|
|
word0(rv) |= Bias << Exp_shift1;
|
|
dval(rv) *= tinytens[n_bigtens-1];
|
|
e1 -= 1 << n_bigtens-1;
|
|
}
|
|
e2 += ((word0(rv) & Exp_mask) >> Exp_shift1) - Bias;
|
|
word0(rv) &= ~Exp_mask;
|
|
word0(rv) |= Bias << Exp_shift1;
|
|
for(j = 0; e1 > 0; j++, e1 >>= 1)
|
|
if (e1 & 1)
|
|
dval(rv) *= tinytens[j];
|
|
}
|
|
}
|
|
#ifdef IBM
|
|
/* e2 is a correction to the (base 2) exponent of the return
|
|
* value, reflecting adjustments above to avoid overflow in the
|
|
* native arithmetic. For native IBM (base 16) arithmetic, we
|
|
* must multiply e2 by 4 to change from base 16 to 2.
|
|
*/
|
|
e2 <<= 2;
|
|
#endif
|
|
rvb = d2b(dval(rv), &rve, &rvbits); /* rv = rvb * 2^rve */
|
|
rve += e2;
|
|
if ((j = rvbits - nbits) > 0) {
|
|
rshift(rvb, j);
|
|
rvbits = nbits;
|
|
rve += j;
|
|
}
|
|
bb0 = 0; /* trailing zero bits in rvb */
|
|
e2 = rve + rvbits - nbits;
|
|
if (e2 > fpi->emax + 1)
|
|
goto huge;
|
|
rve1 = rve + rvbits - nbits;
|
|
if (e2 < (emin = fpi->emin)) {
|
|
denorm = 1;
|
|
j = rve - emin;
|
|
if (j > 0) {
|
|
rvb = lshift(rvb, j);
|
|
rvbits += j;
|
|
}
|
|
else if (j < 0) {
|
|
rvbits += j;
|
|
if (rvbits <= 0) {
|
|
if (rvbits < -1) {
|
|
ufl:
|
|
rvb->wds = 0;
|
|
rvb->x[0] = 0;
|
|
*exp = emin;
|
|
irv = STRTOG_Underflow | STRTOG_Inexlo;
|
|
goto ret;
|
|
}
|
|
rvb->x[0] = rvb->wds = rvbits = 1;
|
|
}
|
|
else
|
|
rshift(rvb, -j);
|
|
}
|
|
rve = rve1 = emin;
|
|
if (sudden_underflow && e2 + 1 < emin)
|
|
goto ufl;
|
|
}
|
|
|
|
/* 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 = Balloc(rvb->k);
|
|
Bcopy(bb, rvb);
|
|
bbbits = rvbits - bb0;
|
|
bbe = rve + bb0;
|
|
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;
|
|
j = nbits + 1 - bbbits;
|
|
i = bbe + bbbits - nbits;
|
|
if (i < emin) /* denormal */
|
|
j += i - emin;
|
|
bb2 += j;
|
|
bd2 += j;
|
|
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;
|
|
}
|
|
bb2 -= bb0;
|
|
if (bb2 > 0)
|
|
bb = lshift(bb, bb2);
|
|
else if (bb2 < 0)
|
|
rshift(bb, -bb2);
|
|
if (bd5 > 0)
|
|
bd = pow5mult(bd, bd5);
|
|
if (bd2 > 0)
|
|
bd = lshift(bd, bd2);
|
|
if (bs2 > 0)
|
|
bs = lshift(bs, bs2);
|
|
asub = 1;
|
|
inex = STRTOG_Inexhi;
|
|
delta = diff(bb, bd);
|
|
if (delta->wds <= 1 && !delta->x[0])
|
|
break;
|
|
dsign = delta->sign;
|
|
delta->sign = finished = 0;
|
|
L = 0;
|
|
i = cmp(delta, bs);
|
|
if (rd && i <= 0) {
|
|
irv = STRTOG_Normal;
|
|
if ( (finished = dsign ^ (rd&1)) !=0) {
|
|
if (dsign != 0) {
|
|
irv |= STRTOG_Inexhi;
|
|
goto adj1;
|
|
}
|
|
irv |= STRTOG_Inexlo;
|
|
if (rve1 == emin)
|
|
goto adj1;
|
|
for(i = 0, j = nbits; j >= ULbits;
|
|
i++, j -= ULbits) {
|
|
if (rvb->x[i] & ALL_ON)
|
|
goto adj1;
|
|
}
|
|
if (j > 1 && lo0bits(rvb->x + i) < j - 1)
|
|
goto adj1;
|
|
rve = rve1 - 1;
|
|
rvb = set_ones(rvb, rvbits = nbits);
|
|
break;
|
|
}
|
|
irv |= dsign ? STRTOG_Inexlo : STRTOG_Inexhi;
|
|
break;
|
|
}
|
|
if (i < 0) {
|
|
/* Error is less than half an ulp -- check for
|
|
* special case of mantissa a power of two.
|
|
*/
|
|
irv = dsign
|
|
? STRTOG_Normal | STRTOG_Inexlo
|
|
: STRTOG_Normal | STRTOG_Inexhi;
|
|
if (dsign || bbbits > 1 || denorm || rve1 == emin)
|
|
break;
|
|
delta = lshift(delta,1);
|
|
if (cmp(delta, bs) > 0) {
|
|
irv = STRTOG_Normal | STRTOG_Inexlo;
|
|
goto drop_down;
|
|
}
|
|
break;
|
|
}
|
|
if (i == 0) {
|
|
/* exactly half-way between */
|
|
if (dsign) {
|
|
if (denorm && all_on(rvb, rvbits)) {
|
|
/*boundary case -- increment exponent*/
|
|
rvb->wds = 1;
|
|
rvb->x[0] = 1;
|
|
rve = emin + nbits - (rvbits = 1);
|
|
irv = STRTOG_Normal | STRTOG_Inexhi;
|
|
denorm = 0;
|
|
break;
|
|
}
|
|
irv = STRTOG_Normal | STRTOG_Inexlo;
|
|
}
|
|
else if (bbbits == 1) {
|
|
irv = STRTOG_Normal;
|
|
drop_down:
|
|
/* boundary case -- decrement exponent */
|
|
if (rve1 == emin) {
|
|
irv = STRTOG_Normal | STRTOG_Inexhi;
|
|
if (rvb->wds == 1 && rvb->x[0] == 1)
|
|
sudden_underflow = 1;
|
|
break;
|
|
}
|
|
rve -= nbits;
|
|
rvb = set_ones(rvb, rvbits = nbits);
|
|
break;
|
|
}
|
|
else
|
|
irv = STRTOG_Normal | STRTOG_Inexhi;
|
|
if (bbbits < nbits && !denorm || !(rvb->x[0] & 1))
|
|
break;
|
|
if (dsign) {
|
|
rvb = increment(rvb);
|
|
if ( (j = rvbits & kmask) !=0)
|
|
j = ULbits - j;
|
|
if (hi0bits(rvb->x[(rvb->wds - 1) >> kshift])
|
|
!= j)
|
|
rvbits++;
|
|
irv = STRTOG_Normal | STRTOG_Inexhi;
|
|
}
|
|
else {
|
|
if (bbbits == 1)
|
|
goto undfl;
|
|
decrement(rvb);
|
|
irv = STRTOG_Normal | STRTOG_Inexlo;
|
|
}
|
|
break;
|
|
}
|
|
if ((dval(adj) = ratio(delta, bs)) <= 2.) {
|
|
adj1:
|
|
inex = STRTOG_Inexlo;
|
|
if (dsign) {
|
|
asub = 0;
|
|
inex = STRTOG_Inexhi;
|
|
}
|
|
else if (denorm && bbbits <= 1) {
|
|
undfl:
|
|
rvb->wds = 0;
|
|
rve = emin;
|
|
irv = STRTOG_Underflow | STRTOG_Inexlo;
|
|
break;
|
|
}
|
|
adj0 = dval(adj) = 1.;
|
|
}
|
|
else {
|
|
adj0 = dval(adj) *= 0.5;
|
|
if (dsign) {
|
|
asub = 0;
|
|
inex = STRTOG_Inexlo;
|
|
}
|
|
if (dval(adj) < 2147483647.) {
|
|
L = adj0;
|
|
adj0 -= L;
|
|
switch(rd) {
|
|
case 0:
|
|
if (adj0 >= .5)
|
|
goto inc_L;
|
|
break;
|
|
case 1:
|
|
if (asub && adj0 > 0.)
|
|
goto inc_L;
|
|
break;
|
|
case 2:
|
|
if (!asub && adj0 > 0.) {
|
|
inc_L:
|
|
L++;
|
|
inex = STRTOG_Inexact - inex;
|
|
}
|
|
}
|
|
dval(adj) = L;
|
|
}
|
|
}
|
|
y = rve + rvbits;
|
|
|
|
/* adj *= ulp(dval(rv)); */
|
|
/* if (asub) rv -= adj; else rv += adj; */
|
|
|
|
if (!denorm && rvbits < nbits) {
|
|
rvb = lshift(rvb, j = nbits - rvbits);
|
|
rve -= j;
|
|
rvbits = nbits;
|
|
}
|
|
ab = d2b(dval(adj), &abe, &abits);
|
|
if (abe < 0)
|
|
rshift(ab, -abe);
|
|
else if (abe > 0)
|
|
ab = lshift(ab, abe);
|
|
rvb0 = rvb;
|
|
if (asub) {
|
|
/* rv -= adj; */
|
|
j = hi0bits(rvb->x[rvb->wds-1]);
|
|
rvb = diff(rvb, ab);
|
|
k = rvb0->wds - 1;
|
|
if (denorm)
|
|
/* do nothing */;
|
|
else if (rvb->wds <= k
|
|
|| hi0bits( rvb->x[k]) >
|
|
hi0bits(rvb0->x[k])) {
|
|
/* unlikely; can only have lost 1 high bit */
|
|
if (rve1 == emin) {
|
|
--rvbits;
|
|
denorm = 1;
|
|
}
|
|
else {
|
|
rvb = lshift(rvb, 1);
|
|
--rve;
|
|
--rve1;
|
|
L = finished = 0;
|
|
}
|
|
}
|
|
}
|
|
else {
|
|
rvb = sum(rvb, ab);
|
|
k = rvb->wds - 1;
|
|
if (k >= rvb0->wds
|
|
|| hi0bits(rvb->x[k]) < hi0bits(rvb0->x[k])) {
|
|
if (denorm) {
|
|
if (++rvbits == nbits)
|
|
denorm = 0;
|
|
}
|
|
else {
|
|
rshift(rvb, 1);
|
|
rve++;
|
|
rve1++;
|
|
L = 0;
|
|
}
|
|
}
|
|
}
|
|
Bfree(ab);
|
|
Bfree(rvb0);
|
|
if (finished)
|
|
break;
|
|
|
|
z = rve + rvbits;
|
|
if (y == z && L) {
|
|
/* Can we stop now? */
|
|
tol = dval(adj) * 5e-16; /* > max rel error */
|
|
dval(adj) = adj0 - .5;
|
|
if (dval(adj) < -tol) {
|
|
if (adj0 > tol) {
|
|
irv |= inex;
|
|
break;
|
|
}
|
|
}
|
|
else if (dval(adj) > tol && adj0 < 1. - tol) {
|
|
irv |= inex;
|
|
break;
|
|
}
|
|
}
|
|
bb0 = denorm ? 0 : trailz(rvb);
|
|
Bfree(bb);
|
|
Bfree(bd);
|
|
Bfree(bs);
|
|
Bfree(delta);
|
|
}
|
|
if (!denorm && (j = nbits - rvbits)) {
|
|
if (j > 0)
|
|
rvb = lshift(rvb, j);
|
|
else
|
|
rshift(rvb, -j);
|
|
rve -= j;
|
|
}
|
|
*exp = rve;
|
|
Bfree(bb);
|
|
Bfree(bd);
|
|
Bfree(bs);
|
|
Bfree(bd0);
|
|
Bfree(delta);
|
|
if (rve > fpi->emax) {
|
|
huge:
|
|
rvb->wds = 0;
|
|
irv = STRTOG_Infinite | STRTOG_Overflow | STRTOG_Inexhi;
|
|
#ifndef NO_ERRNO
|
|
errno = ERANGE;
|
|
#endif
|
|
infnanexp:
|
|
*exp = fpi->emax + 1;
|
|
}
|
|
ret:
|
|
if (denorm) {
|
|
if (sudden_underflow) {
|
|
rvb->wds = 0;
|
|
irv = STRTOG_Underflow | STRTOG_Inexlo;
|
|
}
|
|
else {
|
|
irv = (irv & ~STRTOG_Retmask) |
|
|
(rvb->wds > 0 ? STRTOG_Denormal : STRTOG_Zero);
|
|
if (irv & STRTOG_Inexact)
|
|
irv |= STRTOG_Underflow;
|
|
}
|
|
}
|
|
if (se)
|
|
*se = (char *)s;
|
|
if (sign)
|
|
irv |= STRTOG_Neg;
|
|
if (rvb) {
|
|
copybits(bits, nbits, rvb);
|
|
Bfree(rvb);
|
|
}
|
|
return irv;
|
|
}
|