732 lines
14 KiB
C
732 lines
14 KiB
C
#include "fconv.h"
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/* strtod for IEEE-, VAX-, and IBM-arithmetic machines (dmg).
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*
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* This strtod returns a nearest machine number to the input decimal
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* string (or sets errno to ERANGE). With IEEE arithmetic, ties are
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* broken by the IEEE round-even rule. Otherwise ties are broken by
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* biased rounding (add half and chop).
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*
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* Inspired loosely by William D. Clinger's paper "How to Read Floating
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* Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
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*
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* Modifications:
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*
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* 1. We only require IEEE, IBM, or VAX double-precision
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* arithmetic (not IEEE double-extended).
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* 2. We get by with floating-point arithmetic in a case that
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* Clinger missed -- when we're computing d * 10^n
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* for a small integer d and the integer n is not too
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* much larger than 22 (the maximum integer k for which
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* we can represent 10^k exactly), we may be able to
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* compute (d*10^k) * 10^(e-k) with just one roundoff.
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* 3. Rather than a bit-at-a-time adjustment of the binary
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* result in the hard case, we use floating-point
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* arithmetic to determine the adjustment to within
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* one bit; only in really hard cases do we need to
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* compute a second residual.
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* 4. Because of 3., we don't need a large table of powers of 10
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* for ten-to-e (just some small tables, e.g. of 10^k
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* for 0 <= k <= 22).
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*/
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#ifdef RND_PRODQUOT
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#define rounded_product(a,b) a = rnd_prod(a, b)
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#define rounded_quotient(a,b) a = rnd_quot(a, b)
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extern double rnd_prod(double, double), rnd_quot(double, double);
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#else
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#define rounded_product(a,b) a *= b
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#define rounded_quotient(a,b) a /= b
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#endif
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static double
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ulp(double xarg)
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{
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register long L;
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Dul a;
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Dul x;
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x.d = xarg;
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L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
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#ifndef Sudden_Underflow
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if (L > 0) {
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#endif
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#ifdef IBM
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L |= Exp_msk1 >> 4;
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#endif
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word0(a) = L;
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word1(a) = 0;
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#ifndef Sudden_Underflow
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}
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else {
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L = -L >> Exp_shift;
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if (L < Exp_shift) {
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word0(a) = 0x80000 >> L;
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word1(a) = 0;
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}
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else {
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word0(a) = 0;
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L -= Exp_shift;
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word1(a) = L >= 31 ? 1 : 1 << 31 - L;
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}
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}
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#endif
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return a.d;
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}
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static Bigint *
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s2b(CONST char *s, int nd0, int nd, unsigned long y9)
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{
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Bigint *b;
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int i, k;
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long x, y;
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x = (nd + 8) / 9;
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for(k = 0, y = 1; x > y; y <<= 1, k++) ;
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#ifdef Pack_32
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b = Balloc(k);
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b->x[0] = y9;
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b->wds = 1;
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#else
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b = Balloc(k+1);
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b->x[0] = y9 & 0xffff;
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b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
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#endif
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i = 9;
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if (9 < nd0) {
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s += 9;
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do b = multadd(b, 10, *s++ - '0');
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while(++i < nd0);
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s++;
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}
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else
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s += 10;
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for(; i < nd; i++)
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b = multadd(b, 10, *s++ - '0');
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return b;
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}
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static double
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b2d(Bigint *a, int *e)
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{
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unsigned long *xa, *xa0, w, y, z;
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int k;
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Dul d;
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#ifdef VAX
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unsigned long d0, d1;
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#else
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#define d0 word0(d)
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#define d1 word1(d)
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#endif
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xa0 = a->x;
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xa = xa0 + a->wds;
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y = *--xa;
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#ifdef DEBUG
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if (!y) Bug("zero y in b2d");
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#endif
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k = hi0bits(y);
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*e = 32 - k;
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#ifdef Pack_32
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if (k < Ebits) {
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d0 = Exp_1 | y >> Ebits - k;
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w = xa > xa0 ? *--xa : 0;
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d1 = y << (32-Ebits) + k | w >> Ebits - k;
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goto ret_d;
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}
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z = xa > xa0 ? *--xa : 0;
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if (k -= Ebits) {
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d0 = Exp_1 | y << k | z >> 32 - k;
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y = xa > xa0 ? *--xa : 0;
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d1 = z << k | y >> 32 - k;
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}
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else {
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d0 = Exp_1 | y;
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d1 = z;
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}
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#else
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if (k < Ebits + 16) {
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z = xa > xa0 ? *--xa : 0;
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d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
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w = xa > xa0 ? *--xa : 0;
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y = xa > xa0 ? *--xa : 0;
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d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
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goto ret_d;
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}
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z = xa > xa0 ? *--xa : 0;
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w = xa > xa0 ? *--xa : 0;
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k -= Ebits + 16;
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d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
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y = xa > xa0 ? *--xa : 0;
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d1 = w << k + 16 | y << k;
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#endif
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ret_d:
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#ifdef VAX
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word0(d) = d0 >> 16 | d0 << 16;
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word1(d) = d1 >> 16 | d1 << 16;
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#else
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#undef d0
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#undef d1
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#endif
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return d.d;
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}
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static double
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ratio(Bigint *a, Bigint *b)
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{
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Dul da, db;
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int k, ka, kb;
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da.d = b2d(a, &ka);
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db.d = b2d(b, &kb);
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#ifdef Pack_32
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k = ka - kb + 32*(a->wds - b->wds);
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#else
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k = ka - kb + 16*(a->wds - b->wds);
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#endif
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#ifdef IBM
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if (k > 0) {
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word0(da) += (k >> 2)*Exp_msk1;
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if (k &= 3)
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da *= 1 << k;
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}
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else {
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k = -k;
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word0(db) += (k >> 2)*Exp_msk1;
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if (k &= 3)
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db *= 1 << k;
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}
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#else
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if (k > 0)
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word0(da) += k*Exp_msk1;
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else {
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k = -k;
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word0(db) += k*Exp_msk1;
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}
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#endif
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return da.d / db.d;
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}
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double
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strtod(CONST char *s00, char **se)
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{
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int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, 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;
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Dul rv, rv0;
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long L;
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unsigned long y, z;
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Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
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sign = nz0 = nz = 0;
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rv.d = 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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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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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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if (c == '.') {
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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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s = s00;
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goto ret;
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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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e = c - '0';
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s1 = s;
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while((c = *++s) >= '0' && c <= '9')
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e = 10*e + c - '0';
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if (s - s1 > 8)
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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 = 9999999;
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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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s = s00;
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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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rv.d = y;
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if (k > 9)
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rv.d = tens[k - 9] * rv.d + z;
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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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&& FLT_ROUNDS == 1
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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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/* rv = */ rounded_product(rv.d, 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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e -= i;
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rv.d *= 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(rv.d, 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(rv.d, 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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else if (e >= -Ten_pmax) {
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/* rv = */ rounded_quotient(rv.d, tens[-e]);
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goto ret;
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}
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}
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e1 += nd - k;
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/* Get starting approximation = rv * 10**e1 */
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if (e1 > 0) {
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if (nd0 + e1 - 1 > DBL_MAX_10_EXP)
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goto ovfl;
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if (i = e1 & 15)
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rv.d *= 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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errno = ERANGE;
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rv.d = HUGE_VAL;
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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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if (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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rv.d *= bigtens[j];
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/* The last multiplication could overflow. */
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word0(rv) -= P*Exp_msk1;
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rv.d *= bigtens[j];
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if ((z = word0(rv) & Exp_mask)
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> Exp_msk1*(DBL_MAX_EXP+Bias-P))
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goto ovfl;
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if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
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/* set to largest number */
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/* (Can't trust DBL_MAX) */
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word0(rv) = Big0;
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word1(rv) = Big1;
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}
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else
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word0(rv) += P*Exp_msk1;
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}
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}
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}
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else if (e1 < 0) {
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e1 = -e1;
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if (i = e1 & 15)
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rv.d /= tens[i];
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if (e1 &= ~15) {
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e1 >>= 4;
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if (e1 >= 1 << n_bigtens)
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goto undfl;
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for(j = 0; e1 > 1; j++, e1 >>= 1)
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if (e1 & 1)
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rv.d *= tinytens[j];
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/* The last multiplication could underflow. */
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rv0.d = rv.d;
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rv.d *= tinytens[j];
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if (rv.d == 0) {
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rv.d = 2.*rv0.d;
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rv.d *= tinytens[j];
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if (rv.d == 0) {
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undfl:
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rv.d = 0.;
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errno = ERANGE;
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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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word0(rv) = Tiny0;
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word1(rv) = Tiny1;
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/* The refinement below will clean
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* this approximation up.
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*/
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}
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}
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}
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/* Now the hard part -- adjusting rv to the correct value.*/
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/* Put digits into bd: true value = bd * 10^e */
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bd0 = s2b(s0, nd0, nd, y);
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for(;;) {
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bd = Balloc(bd0->k);
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Bcopy(bd, bd0);
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bb = d2b(rv.d, &bbe, &bbbits); /* rv = bb * 2^bbe */
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bs = i2b(1);
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if (e >= 0) {
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bb2 = bb5 = 0;
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bd2 = bd5 = e;
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}
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else {
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bb2 = bb5 = -e;
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bd2 = bd5 = 0;
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}
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if (bbe >= 0)
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bb2 += bbe;
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else
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bd2 -= bbe;
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bs2 = bb2;
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#ifdef Sudden_Underflow
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#ifdef IBM
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j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
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#else
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j = P + 1 - bbbits;
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#endif
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#else
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i = bbe + bbbits - 1; /* logb(rv) */
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if (i < Emin) /* denormal */
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j = bbe + (P-Emin);
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else
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j = P + 1 - bbbits;
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#endif
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bb2 += j;
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bd2 += j;
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i = bb2 < bd2 ? bb2 : bd2;
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if (i > bs2)
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i = bs2;
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if (i > 0) {
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bb2 -= i;
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bd2 -= i;
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bs2 -= i;
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}
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if (bb5 > 0) {
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bs = pow5mult(bs, bb5);
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bb1 = mult(bs, bb);
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Bfree(bb);
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bb = bb1;
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}
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if (bb2 > 0)
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bb = lshift(bb, bb2);
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if (bd5 > 0)
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bd = pow5mult(bd, bd5);
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if (bd2 > 0)
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bd = lshift(bd, bd2);
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if (bs2 > 0)
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bs = lshift(bs, bs2);
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delta = diff(bb, bd);
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dsign = delta->sign;
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delta->sign = 0;
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i = cmp(delta, bs);
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if (i < 0) {
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/* Error is less than half an ulp -- check for
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* special case of mantissa a power of two.
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*/
|
|
if (dsign || word1(rv) || word0(rv) & Bndry_mask)
|
|
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) == 0xffffffff) {
|
|
/*boundary case -- increment exponent*/
|
|
word0(rv) = (word0(rv) & Exp_mask)
|
|
+ Exp_msk1
|
|
#ifdef IBM
|
|
| Exp_msk1 >> 4
|
|
#endif
|
|
;
|
|
word1(rv) = 0;
|
|
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
|
|
if (L <= Exp_msk1)
|
|
#endif
|
|
goto undfl;
|
|
L -= Exp_msk1;
|
|
#else
|
|
L = (word0(rv) & Exp_mask) - Exp_msk1;
|
|
#endif
|
|
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)
|
|
rv.d += ulp(rv.d);
|
|
#ifndef ROUND_BIASED
|
|
else {
|
|
rv.d -= ulp(rv.d);
|
|
#ifndef Sudden_Underflow
|
|
if (rv.d == 0)
|
|
goto undfl;
|
|
#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(FLT_ROUNDS) {
|
|
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
|
|
}
|
|
y = word0(rv) & Exp_mask;
|
|
|
|
/* Check for overflow */
|
|
|
|
if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
|
|
rv0.d = rv.d;
|
|
word0(rv) -= P*Exp_msk1;
|
|
adj = aadj1 * ulp(rv.d);
|
|
rv.d += 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 Sudden_Underflow
|
|
if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
|
|
rv0.d = rv.d;
|
|
word0(rv) += P*Exp_msk1;
|
|
adj = aadj1 * ulp(rv.d);
|
|
rv.d += 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(rv.d);
|
|
rv.d += adj;
|
|
}
|
|
#else
|
|
/* 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(rv.d);
|
|
rv.d += adj;
|
|
#endif
|
|
}
|
|
z = word0(rv) & Exp_mask;
|
|
if (y == z) {
|
|
/* Can we stop now? */
|
|
L = 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;
|
|
}
|
|
cont:
|
|
Bfree(bb);
|
|
Bfree(bd);
|
|
Bfree(bs);
|
|
Bfree(delta);
|
|
}
|
|
retfree:
|
|
Bfree(bb);
|
|
Bfree(bd);
|
|
Bfree(bs);
|
|
Bfree(bd0);
|
|
Bfree(delta);
|
|
ret:
|
|
if (se)
|
|
*se = (char *)s;
|
|
return sign ? -rv.d : rv.d;
|
|
}
|