707 lines
14 KiB
C
707 lines
14 KiB
C
/*
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(c) copyright 1988 by the Vrije Universiteit, Amsterdam, The Netherlands.
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See the copyright notice in the ACK home directory, in the file "Copyright".
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*/
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/* $Header$ */
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/* extended precision arithmetic for the strtod() and cvt() routines */
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/* This may require some more work when long doubles get bigger than 8
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bytes. In this case, these routines may become obsolete. ???
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*/
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static int b64_add();
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static int b64_sft();
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#include <ctype.h>
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struct mantissa {
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unsigned long h_32;
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unsigned long l_32;
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};
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struct EXTEND {
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short sign;
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short exp;
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struct mantissa mantissa;
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#define m1 mantissa.h_32
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#define m2 mantissa.l_32
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};
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static
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mul_ext(e1,e2,e3)
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struct EXTEND *e1,*e2,*e3;
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{
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/* Multiply the extended numbers e1 and e2, and put the
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result in e3.
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*/
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register int i,j; /* loop control */
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unsigned short mp[4];
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unsigned short mc[4];
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unsigned short result[8]; /* result */
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register unsigned short *pres;
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/* first save the sign (XOR) */
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e3->sign = e1->sign ^ e2->sign;
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/* compute new exponent */
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e3->exp = e1->exp + e2->exp + 1;
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/* check for overflow/underflow ??? */
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/* 128 bit multiply of mantissas */
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/* assign unknown long formats */
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/* to known unsigned word formats */
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mp[0] = e1->m1 >> 16;
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mp[1] = (unsigned short) e1->m1;
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mp[2] = e1->m2 >> 16;
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mp[3] = (unsigned short) e1->m2;
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mc[0] = e2->m1 >> 16;
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mc[1] = (unsigned short) e2->m1;
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mc[2] = e2->m2 >> 16;
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mc[3] = (unsigned short) e2->m2;
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for (i = 8; i--;) {
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result[i] = 0;
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}
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/*
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* fill registers with their components
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*/
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for(i=4, pres = &result[4];i--;pres--) if (mp[i]) {
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unsigned short k = 0;
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unsigned long mpi = mp[i];
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for(j=4;j--;) {
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unsigned long tmp = (unsigned long)pres[j] + k;
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if (mc[j]) tmp += mpi * mc[j];
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pres[j] = tmp;
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k = tmp >> 16;
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}
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pres[-1] = k;
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}
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if (! (result[0] & 0x8000)) {
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e3->exp--;
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for (i = 0; i <= 3; i++) {
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result[i] <<= 1;
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if (result[i+1]&0x8000) result[i] |= 1;
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}
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result[4] <<= 1;
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}
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/*
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* combine the registers to a total
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*/
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e3->m1 = ((unsigned long)(result[0]) << 16) + result[1];
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e3->m2 = ((unsigned long)(result[2]) << 16) + result[3];
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if (result[4] & 0x8000) {
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if (++e3->m2 == 0) {
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if (++e3->m1 == 0) {
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e3->m1 = 0x80000000;
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e3->exp++;
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}
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}
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}
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}
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static
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add_ext(e1,e2,e3)
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struct EXTEND *e1,*e2,*e3;
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{
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/* Add two extended numbers e1 and e2, and put the result
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in e3
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*/
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struct EXTEND ce2;
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int diff;
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if ((e2->m1 | e2->m2) == 0L) {
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*e3 = *e1;
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return;
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}
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if ((e1->m1 | e1->m2) == 0L) {
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*e3 = *e2;
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return;
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}
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ce2 = *e2;
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*e3 = *e1;
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e1 = &ce2;
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/* adjust mantissas to equal power */
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diff = e3->exp - e1->exp;
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if (diff < 0) {
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diff = -diff;
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e3->exp += diff;
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b64_sft(&(e3->mantissa), diff);
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}
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else if (diff > 0) {
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e1->exp += diff;
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b64_sft(&(e1->mantissa), diff);
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}
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if (e1->sign != e3->sign) {
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/* e3 + e1 = e3 - (-e1) */
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if (e1->m1 > e3->m1 ||
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(e1->m1 == e3->m1 && e1->m2 > e3->m2)) {
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/* abs(e1) > abs(e3) */
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if (e3->m2 > e1->m2) {
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e1->m1 -= 1; /* carry in */
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}
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e1->m1 -= e3->m1;
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e1->m2 -= e3->m2;
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*e3 = *e1;
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}
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else {
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if (e1->m2 > e3->m2)
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e3->m1 -= 1; /* carry in */
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e3->m1 -= e1->m1;
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e3->m2 -= e1->m2;
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}
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}
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else {
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if (b64_add(&e3->mantissa,&e1->mantissa)) {/* addition carry */
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b64_sft(&e3->mantissa,1);/* shift mantissa one bit RIGHT */
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e3->m1 |= 0x80000000L; /* set max bit */
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e3->exp++; /* increase the exponent */
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}
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}
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if ((e3->m2 | e3->m1) != 0L) {
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/* normalize */
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if (e3->m1 == 0L) {
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e3->m1 = e3->m2; e3->m2 = 0L; e3->exp -= 32;
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}
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if (!(e3->m1 & 0x80000000)) {
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unsigned long l = 0x40000000;
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int cnt = -1;
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while (! (l & e3->m1)) {
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l >>= 1; cnt--;
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}
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e3->exp += cnt;
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b64_sft(&(e3->mantissa), cnt);
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}
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}
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}
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static int
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cmp_ext(e1, e2)
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struct EXTEND *e1, *e2;
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{
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struct EXTEND tmp;
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e2->sign = ! e2->sign;
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add_ext(e1, e2, &tmp);
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e2->sign = ! e2->sign;
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if (tmp.m1 == 0 && tmp.m2 == 0) return 0;
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if (tmp.sign) return -1;
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return 1;
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}
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static
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b64_sft(e1,n)
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struct mantissa *e1;
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int n;
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{
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if (n > 0) {
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if (n > 63) {
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e1->l_32 = 0;
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e1->h_32 = 0;
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return;
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}
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if (n >= 32) {
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e1->l_32 = e1->h_32;
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e1->h_32 = 0;
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n -= 32;
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}
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if (n > 0) {
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e1->l_32 >>= n;
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if (e1->h_32 != 0) {
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e1->l_32 |= (e1->h_32 << (32 - n));
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e1->h_32 >>= n;
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}
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}
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return;
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}
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n = -n;
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if (n > 0) {
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if (n > 63) {
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e1->l_32 = 0;
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e1->h_32 = 0;
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return;
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}
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if (n >= 32) {
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e1->h_32 = e1->l_32;
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e1->l_32 = 0;
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n -= 32;
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}
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if (n > 0) {
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e1->h_32 <<= n;
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if (e1->l_32 != 0) {
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e1->h_32 |= (e1->l_32 >> (32 - n));
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e1->l_32 <<= n;
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}
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}
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}
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}
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static int
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b64_add(e1,e2)
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/*
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* pointers to 64 bit 'registers'
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*/
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struct mantissa *e1,*e2;
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{
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register int overflow;
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int carry;
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/* add higher pair of 32 bits */
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overflow = ((unsigned long) 0xFFFFFFFF - e1->h_32 < e2->h_32);
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e1->h_32 += e2->h_32;
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/* add lower pair of 32 bits */
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carry = ((unsigned long) 0xFFFFFFFF - e1->l_32 < e2->l_32);
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e1->l_32 += e2->l_32;
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if ((carry) && (++e1->h_32 == 0))
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return(1); /* had a 64 bit overflow */
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else
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return(overflow); /* return status from higher add */
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}
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/* The following tables can be computed with the following bc(1)
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program:
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obase=16
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scale=0
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define t(x){
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auto a, b, c
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a=2;b=1;c=2^32;n=1
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while(a<x) {
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b=a;n+=n;a*=a
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}
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n/=2
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a=b
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while(b<x) {
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a=b;b*=c;n+=32
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}
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n-=32
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b=a
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while(a<x) {
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b=a;a+=a;n+=1
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}
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n-=1
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x*=16^16
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b=x%a
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x/=a
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if(a<=(2*b)) x+=1
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obase=10
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n
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obase=16
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return(x)
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}
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for (i=1;i<28;i++) {
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t(10^i)
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}
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0
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for (i=1;i<20;i++) {
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t(10^(28*i))
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}
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0
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define r(x){
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auto a, b, c
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a=2;b=1;c=2^32;n=1
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while(a<x) {
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b=a;n+=n;a*=a
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}
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n/=2
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a=b
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while(b<x) {
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a=b;b*=c;n+=32
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}
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n-=32
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b=a
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while(a<x) {
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b=a;a+=a;n+=1
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}
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a=b
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a*=16^16
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b=a%x
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a/=x
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if(x<=(2*b)) a+=1
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obase=10
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-n
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obase=16
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return(a)
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}
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for (i=1;i<28;i++) {
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r(10^i)
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}
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0
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for (i=1;i<20;i++) {
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r(10^(28*i))
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}
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0
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*/
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static struct EXTEND ten_powers[] = { /* representation of 10 ** i */
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{ 0, 0, 0x80000000, 0 },
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{ 0, 3, 0xA0000000, 0 },
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{ 0, 6, 0xC8000000, 0 },
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{ 0, 9, 0xFA000000, 0 },
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{ 0, 13, 0x9C400000, 0 },
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{ 0, 16, 0xC3500000, 0 },
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{ 0, 19, 0xF4240000, 0 },
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{ 0, 23, 0x98968000, 0 },
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{ 0, 26, 0xBEBC2000, 0 },
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{ 0, 29, 0xEE6B2800, 0 },
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{ 0, 33, 0x9502F900, 0 },
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{ 0, 36, 0xBA43B740, 0 },
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{ 0, 39, 0xE8D4A510, 0 },
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{ 0, 43, 0x9184E72A, 0 },
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{ 0, 46, 0xB5E620F4, 0x80000000 },
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{ 0, 49, 0xE35FA931, 0xA0000000 },
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{ 0, 53, 0x8E1BC9BF, 0x04000000 },
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{ 0, 56, 0xB1A2BC2E, 0xC5000000 },
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{ 0, 59, 0xDE0B6B3A, 0x76400000 },
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{ 0, 63, 0x8AC72304, 0x89E80000 },
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{ 0, 66, 0xAD78EBC5, 0xAC620000 },
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{ 0, 69, 0xD8D726B7, 0x177A8000 },
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{ 0, 73, 0x87867832, 0x6EAC9000 },
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{ 0, 76, 0xA968163F, 0x0A57B400 },
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{ 0, 79, 0xD3C21BCE, 0xCCEDA100 },
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{ 0, 83, 0x84595161, 0x401484A0 },
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{ 0, 86, 0xA56FA5B9, 0x9019A5C8 },
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{ 0, 89, 0xCECB8F27, 0xF4200F3A }
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};
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static struct EXTEND big_ten_powers[] = { /* representation of 10 ** (28*i) */
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{ 0, 0, 0x80000000, 0 },
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{ 0, 93, 0x813F3978, 0xF8940984 },
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{ 0, 186, 0x82818F12, 0x81ED44A0 },
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{ 0, 279, 0x83C7088E, 0x1AAB65DB },
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{ 0, 372, 0x850FADC0, 0x9923329E },
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{ 0, 465, 0x865B8692, 0x5B9BC5C2 },
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{ 0, 558, 0x87AA9AFF, 0x79042287 },
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{ 0, 651, 0x88FCF317, 0xF22241E2 },
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{ 0, 744, 0x8A5296FF, 0xE33CC930 },
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{ 0, 837, 0x8BAB8EEF, 0xB6409C1A },
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{ 0, 930, 0x8D07E334, 0x55637EB3 },
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{ 0, 1023, 0x8E679C2F, 0x5E44FF8F },
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{ 0, 1116, 0x8FCAC257, 0x558EE4E6 },
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{ 0, 1209, 0x91315E37, 0xDB165AA9 },
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{ 0, 1302, 0x929B7871, 0xDE7F22B9 },
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{ 0, 1395, 0x940919BB, 0xD4620B6D },
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{ 0, 1488, 0x957A4AE1, 0xEBF7F3D4 },
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{ 0, 1581, 0x96EF14C6, 0x454AA840 },
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{ 0, 1674, 0x98678061, 0x27ECE4F5 },
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{ 0, 1767, 0x99E396C1, 0x3A3ACFF2 }
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};
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static struct EXTEND r_ten_powers[] = { /* representation of 10 ** -i */
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{ 0, 0, 0x80000000, 0 },
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{ 0, -4, 0xCCCCCCCC, 0xCCCCCCCD },
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{ 0, -7, 0xA3D70A3D, 0x70A3D70A },
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{ 0, -10, 0x83126E97, 0x8D4FDF3B },
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{ 0, -14, 0xD1B71758, 0xE219652C },
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{ 0, -17, 0xA7C5AC47, 0x1B478423 },
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{ 0, -20, 0x8637BD05, 0xAF6C69B6 },
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{ 0, -24, 0xD6BF94D5, 0xE57A42BC },
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{ 0, -27, 0xABCC7711, 0x8461CEFD },
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{ 0, -30, 0x89705F41, 0x36B4A597 },
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{ 0, -34, 0xDBE6FECE, 0xBDEDD5BF },
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{ 0, -37, 0xAFEBFF0B, 0xCB24AAFF },
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{ 0, -40, 0x8CBCCC09, 0x6F5088CC },
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{ 0, -44, 0xE12E1342, 0x4BB40E13 },
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{ 0, -47, 0xB424DC35, 0x095CD80F },
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{ 0, -50, 0x901D7CF7, 0x3AB0ACD9 },
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{ 0, -54, 0xE69594BE, 0xC44DE15B },
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{ 0, -57, 0xB877AA32, 0x36A4B449 },
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{ 0, -60, 0x9392EE8E, 0x921D5D07 },
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{ 0, -64, 0xEC1E4A7D, 0xB69561A5 },
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{ 0, -67, 0xBCE50864, 0x92111AEB },
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{ 0, -70, 0x971DA050, 0x74DA7BEF },
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{ 0, -74, 0xF1C90080, 0xBAF72CB1 },
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{ 0, -77, 0xC16D9A00, 0x95928A27 },
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{ 0, -80, 0x9ABE14CD, 0x44753B53 },
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{ 0, -84, 0xF79687AE, 0xD3EEC551 },
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{ 0, -87, 0xC6120625, 0x76589DDB },
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{ 0, -90, 0x9E74D1B7, 0x91E07E48 }
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};
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static struct EXTEND r_big_ten_powers[] = { /* representation of 10 ** -(28*i) */
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{ 0, 0, 0x80000000, 0 },
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{ 0, -94, 0xFD87B5F2, 0x8300CA0E },
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{ 0, -187, 0xFB158592, 0xBE068D2F },
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{ 0, -280, 0xF8A95FCF, 0x88747D94 },
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{ 0, -373, 0xF64335BC, 0xF065D37D },
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{ 0, -466, 0xF3E2F893, 0xDEC3F126 },
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{ 0, -559, 0xF18899B1, 0xBC3F8CA2 },
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{ 0, -652, 0xEF340A98, 0x172AACE5 },
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{ 0, -745, 0xECE53CEC, 0x4A314EBE },
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{ 0, -838, 0xEA9C2277, 0x23EE8BCB },
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{ 0, -931, 0xE858AD24, 0x8F5C22CA },
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{ 0, -1024, 0xE61ACF03, 0x3D1A45DF },
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{ 0, -1117, 0xE3E27A44, 0x4D8D98B8 },
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{ 0, -1210, 0xE1AFA13A, 0xFBD14D6E },
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{ 0, -1303, 0xDF82365C, 0x497B5454 },
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{ 0, -1396, 0xDD5A2C3E, 0xAB3097CC },
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{ 0, -1489, 0xDB377599, 0xB6074245 },
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{ 0, -1582, 0xD91A0545, 0xCDB51186 },
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{ 0, -1675, 0xD701CE3B, 0xD387BF48 },
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{ 0, -1768, 0xD4EEC394, 0xD6258BF8 }
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};
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static
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add_exponent(e, exp)
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struct EXTEND *e;
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{
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int neg = exp < 0;
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int divsz, modsz;
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struct EXTEND x;
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if (neg) exp = -exp;
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divsz = exp / (sizeof(ten_powers)/sizeof(ten_powers[0]));
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modsz = exp % (sizeof(ten_powers)/sizeof(ten_powers[0]));
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if (neg) {
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mul_ext(e, &r_ten_powers[modsz], &x);
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mul_ext(&x, &r_big_ten_powers[divsz], e);
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}
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else {
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mul_ext(e, &ten_powers[modsz], &x);
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mul_ext(&x, &big_ten_powers[divsz], e);
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}
|
|
}
|
|
|
|
_str_ext_cvt(s, ss, e)
|
|
char *s, **ss;
|
|
struct EXTEND *e;
|
|
{
|
|
/* Like strtod, but for extended precision */
|
|
register int c;
|
|
int dotseen = 0;
|
|
int digitseen = 0;
|
|
int exp = 0;
|
|
|
|
if (ss) *ss = s;
|
|
while (isspace(*s)) s++;
|
|
|
|
e->sign = 0;
|
|
e->exp = 0;
|
|
e->m1 = e->m2 = 0;
|
|
|
|
c = *s;
|
|
switch(c) {
|
|
case '-':
|
|
e->sign = 1;
|
|
case '+':
|
|
s++;
|
|
}
|
|
while (c = *s++, isdigit(c) || (c == '.' && ! dotseen++)) {
|
|
if (c == '.') continue;
|
|
digitseen = 1;
|
|
if (e->m1 <= (unsigned long)(0xFFFFFFFF)/10) {
|
|
struct mantissa a1;
|
|
|
|
a1 = e->mantissa;
|
|
b64_sft(&(e->mantissa), -3);
|
|
b64_sft(&a1, -1);
|
|
b64_add(&(e->mantissa), &a1);
|
|
a1.h_32 = 0;
|
|
a1.l_32 = c - '0';
|
|
b64_add(&(e->mantissa), &a1);
|
|
}
|
|
else exp++;
|
|
if (dotseen) exp--;
|
|
}
|
|
if (! digitseen) return;
|
|
|
|
if (ss) *ss = s - 1;
|
|
|
|
if (c == 'E' || c == 'e') {
|
|
int exp1 = 0;
|
|
int sign = 1;
|
|
|
|
switch(*s) {
|
|
case '-':
|
|
sign = -1;
|
|
case '+':
|
|
s++;
|
|
}
|
|
if (c = *s, isdigit(c)) {
|
|
do {
|
|
exp1 = 10 * exp1 + (c - '0');
|
|
} while (c = *++s, isdigit(c));
|
|
if (ss) *ss = s;
|
|
}
|
|
exp += sign * exp1;
|
|
}
|
|
if (e->m1 == 0 && e->m2 == 0) return;
|
|
e->exp = 63;
|
|
while (! (e->m1 & 0x80000000)) {
|
|
b64_sft(&(e->mantissa),-1);
|
|
e->exp--;
|
|
}
|
|
add_exponent(e, exp);
|
|
}
|
|
|
|
extern double ldexp(), frexp(), modf();
|
|
|
|
#define NDIGITS 128
|
|
|
|
char *
|
|
_ext_str_cvt(e, ndigit, decpt, sign, ecvtflag)
|
|
struct EXTEND *e;
|
|
int ndigit, *decpt, *sign;
|
|
{
|
|
/* Like cvt(), but for extended precision */
|
|
|
|
static char buf[NDIGITS+1];
|
|
register char *p = buf;
|
|
register char *pe;
|
|
int findex = 0;
|
|
|
|
if (ndigit < 0) ndigit = 0;
|
|
if (ndigit > NDIGITS) ndigit = NDIGITS;
|
|
pe = &buf[ndigit];
|
|
buf[0] = '\0';
|
|
|
|
*sign = 0;
|
|
if (e->sign) {
|
|
*sign = 1;
|
|
e->sign = 0;
|
|
}
|
|
|
|
*decpt = 0;
|
|
if (e->m1 != 0) {
|
|
register struct EXTEND *pp = &big_ten_powers[1];
|
|
|
|
while(cmp_ext(e,pp) >= 0) pp++;
|
|
pp--;
|
|
findex = pp - big_ten_powers;
|
|
mul_ext(e,&r_big_ten_powers[findex],e);
|
|
*decpt += findex * (sizeof(ten_powers)/sizeof(ten_powers[0]));
|
|
pp = &ten_powers[1];
|
|
while(pp<&ten_powers[(sizeof(ten_powers)/sizeof(ten_powers[0]))] &&
|
|
cmp_ext(e, pp) >= 0) pp++;
|
|
pp--;
|
|
findex = pp - ten_powers;
|
|
*decpt += findex;
|
|
|
|
if (cmp_ext(e, &ten_powers[0]) < 0) {
|
|
pp = &r_big_ten_powers[1];
|
|
while(cmp_ext(e,pp) < 0) pp++;
|
|
pp--;
|
|
findex = pp - r_big_ten_powers;
|
|
mul_ext(e,&big_ten_powers[findex],e);
|
|
*decpt -= findex *
|
|
(sizeof(ten_powers)/sizeof(ten_powers[0]));
|
|
/* here, value >= 10 ** -28 */
|
|
mul_ext(e, &ten_powers[1], e);
|
|
(*decpt)--;
|
|
pp = &r_ten_powers[0];
|
|
while(cmp_ext(e, pp) < 0) pp++;
|
|
findex = -(pp - r_ten_powers);
|
|
mul_ext(e, &ten_powers[-findex], e);
|
|
*decpt += findex;
|
|
findex = 0;
|
|
}
|
|
(*decpt)++; /* because now value in [1.0, 10.0) */
|
|
}
|
|
if (! ecvtflag) {
|
|
/* for fcvt() we need ndigit digits behind the dot */
|
|
pe += *decpt;
|
|
if (pe > &buf[NDIGITS]) pe = &buf[NDIGITS];
|
|
}
|
|
while (p <= pe) {
|
|
if (findex) {
|
|
struct EXTEND tc, oldtc;
|
|
int count = 0;
|
|
|
|
oldtc.exp = 0;
|
|
oldtc.sign = 0;
|
|
oldtc.m1 = 0;
|
|
oldtc.m2 = 0;
|
|
tc = ten_powers[findex];
|
|
while (cmp_ext(e, &tc) >= 0) {
|
|
oldtc = tc;
|
|
add_ext(&tc, &ten_powers[findex], &tc);
|
|
count++;
|
|
}
|
|
*p++ = count + '0';
|
|
oldtc.sign = 1;
|
|
add_ext(e, &oldtc, e);
|
|
findex--;
|
|
continue;
|
|
}
|
|
if (e->exp >= 0 && e->m1 != 0) {
|
|
struct EXTEND x;
|
|
|
|
x.m2 = 0; x.exp = e->exp;
|
|
x.sign = 1;
|
|
x.m1 = e->m1>>(31-e->exp);
|
|
*p++ = (x.m1) + '0';
|
|
if (x.m1) {
|
|
x.m1 = x.m1 << (31-e->exp);
|
|
add_ext(e, &x, e);
|
|
}
|
|
}
|
|
else *p++ = '0';
|
|
if (e->m1) mul_ext(e, &ten_powers[1], e);
|
|
}
|
|
if (pe >= buf) {
|
|
p = pe;
|
|
*p += 5; /* round of at the end */
|
|
while (*p > '9') {
|
|
*p = '0';
|
|
if (p > buf) ++*--p;
|
|
else {
|
|
*p = '1';
|
|
++*decpt;
|
|
if (! ecvtflag) {
|
|
/* maybe add another digit at the end,
|
|
because the point was shifted right
|
|
*/
|
|
if (pe > buf) *pe = '0';
|
|
pe++;
|
|
}
|
|
}
|
|
}
|
|
*pe = '\0';
|
|
}
|
|
return buf;
|
|
}
|
|
|
|
_dbl_ext_cvt(value, e)
|
|
double value;
|
|
struct EXTEND *e;
|
|
{
|
|
/* Convert double to extended
|
|
*/
|
|
int exponent;
|
|
register int i;
|
|
|
|
value = frexp(value, &exponent);
|
|
e->sign = value < 0.0;
|
|
if (e->sign) value = -value;
|
|
e->exp = exponent - 1;
|
|
e->m1 = 0;
|
|
e->m2 = 0;
|
|
for (i = 64; i > 0 && value != 0; i--) {
|
|
double ipart;
|
|
|
|
b64_sft(&(e->mantissa),-1);
|
|
value = modf(2.0*value, &ipart);
|
|
if (ipart) {
|
|
e->m2 |= 1;
|
|
}
|
|
}
|
|
if (i > 0) b64_sft(&(e->mantissa),-i);
|
|
}
|
|
|
|
double
|
|
_ext_dbl_cvt(e)
|
|
struct EXTEND *e;
|
|
{
|
|
/* Convert extended to double
|
|
*/
|
|
double f = ldexp(ldexp((double)e->m1, 32) + (double)e->m2, e->exp-63);
|
|
if (e->sign) f = -f;
|
|
return f;
|
|
}
|