876 lines
14 KiB
C
876 lines
14 KiB
C
/****************************************************************
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The author of this software is David M. Gay.
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Copyright (C) 1998, 1999 by Lucent Technologies
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All Rights Reserved
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Permission to use, copy, modify, and distribute this software and
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its documentation for any purpose and without fee is hereby
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granted, provided that the above copyright notice appear in all
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copies and that both that the copyright notice and this
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permission notice and warranty disclaimer appear in supporting
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documentation, and that the name of Lucent or any of its entities
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not be used in advertising or publicity pertaining to
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distribution of the software without specific, written prior
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permission.
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LUCENT DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE,
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INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS.
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IN NO EVENT SHALL LUCENT OR ANY OF ITS ENTITIES BE LIABLE FOR ANY
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SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
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WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER
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IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION,
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ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF
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THIS SOFTWARE.
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****************************************************************/
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/* Please send bug reports to David M. Gay (dmg at acm dot org,
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* with " at " changed at "@" and " dot " changed to "."). */
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#include "gdtoaimp.h"
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static Bigint *freelist[Kmax+1];
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#ifndef Omit_Private_Memory
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#ifndef PRIVATE_MEM
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#define PRIVATE_MEM 2304
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#endif
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#define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
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static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
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#endif
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Bigint *
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Balloc
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#ifdef KR_headers
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(k) int k;
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#else
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(int k)
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#endif
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{
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int x;
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Bigint *rv;
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#ifndef Omit_Private_Memory
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unsigned int len;
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#endif
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ACQUIRE_DTOA_LOCK(0);
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/* The k > Kmax case does not need ACQUIRE_DTOA_LOCK(0), */
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/* but this case seems very unlikely. */
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if (k <= Kmax && (rv = freelist[k]) !=0) {
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freelist[k] = rv->next;
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}
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else {
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x = 1 << k;
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#ifdef Omit_Private_Memory
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rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
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#else
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len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
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/sizeof(double);
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if (k <= Kmax && pmem_next - private_mem + len <= PRIVATE_mem) {
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rv = (Bigint*)pmem_next;
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pmem_next += len;
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}
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else
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rv = (Bigint*)MALLOC(len*sizeof(double));
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#endif
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rv->k = k;
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rv->maxwds = x;
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}
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FREE_DTOA_LOCK(0);
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rv->sign = rv->wds = 0;
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return rv;
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}
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void
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Bfree
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#ifdef KR_headers
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(v) Bigint *v;
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#else
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(Bigint *v)
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#endif
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{
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if (v) {
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if (v->k > Kmax)
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#ifdef FREE
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FREE((void*)v);
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#else
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free((void*)v);
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#endif
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else {
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ACQUIRE_DTOA_LOCK(0);
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v->next = freelist[v->k];
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freelist[v->k] = v;
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FREE_DTOA_LOCK(0);
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}
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}
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}
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int
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lo0bits
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#ifdef KR_headers
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(y) ULong *y;
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#else
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(ULong *y)
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#endif
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{
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int k;
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ULong x = *y;
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if (x & 7) {
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if (x & 1)
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return 0;
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if (x & 2) {
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*y = x >> 1;
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return 1;
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}
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*y = x >> 2;
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return 2;
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}
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k = 0;
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if (!(x & 0xffff)) {
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k = 16;
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x >>= 16;
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}
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if (!(x & 0xff)) {
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k += 8;
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x >>= 8;
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}
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if (!(x & 0xf)) {
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k += 4;
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x >>= 4;
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}
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if (!(x & 0x3)) {
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k += 2;
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x >>= 2;
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}
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if (!(x & 1)) {
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k++;
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x >>= 1;
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if (!x)
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return 32;
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}
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*y = x;
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return k;
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}
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Bigint *
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multadd
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#ifdef KR_headers
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(b, m, a) Bigint *b; int m, a;
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#else
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(Bigint *b, int m, int a) /* multiply by m and add a */
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#endif
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{
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int i, wds;
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#ifdef ULLong
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ULong *x;
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ULLong carry, y;
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#else
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ULong carry, *x, y;
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#ifdef Pack_32
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ULong xi, z;
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#endif
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#endif
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Bigint *b1;
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wds = b->wds;
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x = b->x;
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i = 0;
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carry = a;
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do {
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#ifdef ULLong
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y = *x * (ULLong)m + carry;
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carry = y >> 32;
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*x++ = y & 0xffffffffUL;
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#else
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#ifdef Pack_32
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xi = *x;
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y = (xi & 0xffff) * m + carry;
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z = (xi >> 16) * m + (y >> 16);
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carry = z >> 16;
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*x++ = (z << 16) + (y & 0xffff);
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#else
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y = *x * m + carry;
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carry = y >> 16;
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*x++ = y & 0xffff;
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#endif
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#endif
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}
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while(++i < wds);
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if (carry) {
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if (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[wds++] = carry;
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b->wds = wds;
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}
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return b;
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}
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int
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hi0bits_D2A
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#ifdef KR_headers
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(x) ULong x;
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#else
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(ULong x)
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#endif
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{
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int k = 0;
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if (!(x & 0xffff0000)) {
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k = 16;
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x <<= 16;
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}
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if (!(x & 0xff000000)) {
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k += 8;
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x <<= 8;
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}
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if (!(x & 0xf0000000)) {
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k += 4;
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x <<= 4;
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}
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if (!(x & 0xc0000000)) {
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k += 2;
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x <<= 2;
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}
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if (!(x & 0x80000000)) {
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k++;
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if (!(x & 0x40000000))
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return 32;
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}
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return k;
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}
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Bigint *
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i2b
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#ifdef KR_headers
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(i) int i;
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#else
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(int i)
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#endif
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{
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Bigint *b;
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b = Balloc(1);
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b->x[0] = i;
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b->wds = 1;
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return b;
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}
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Bigint *
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mult
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#ifdef KR_headers
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(a, b) Bigint *a, *b;
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#else
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(Bigint *a, Bigint *b)
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#endif
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{
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Bigint *c;
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int k, wa, wb, wc;
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ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
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ULong y;
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#ifdef ULLong
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ULLong carry, z;
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#else
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ULong carry, z;
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#ifdef Pack_32
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ULong z2;
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#endif
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#endif
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if (a->wds < b->wds) {
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c = a;
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a = b;
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b = c;
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}
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k = a->k;
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wa = a->wds;
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wb = b->wds;
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wc = wa + wb;
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if (wc > a->maxwds)
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k++;
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c = Balloc(k);
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for(x = c->x, xa = x + wc; x < xa; x++)
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*x = 0;
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xa = a->x;
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xae = xa + wa;
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xb = b->x;
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xbe = xb + wb;
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xc0 = c->x;
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#ifdef ULLong
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for(; xb < xbe; xc0++) {
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if ( (y = *xb++) !=0) {
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x = xa;
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xc = xc0;
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carry = 0;
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do {
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z = *x++ * (ULLong)y + *xc + carry;
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carry = z >> 32;
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*xc++ = z & 0xffffffffUL;
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}
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while(x < xae);
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*xc = carry;
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}
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}
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#else
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#ifdef Pack_32
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for(; xb < xbe; xb++, xc0++) {
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if ( (y = *xb & 0xffff) !=0) {
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x = xa;
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xc = xc0;
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carry = 0;
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do {
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z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
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carry = z >> 16;
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z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
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carry = z2 >> 16;
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Storeinc(xc, z2, z);
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}
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while(x < xae);
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*xc = carry;
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}
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if ( (y = *xb >> 16) !=0) {
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x = xa;
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xc = xc0;
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carry = 0;
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z2 = *xc;
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do {
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z = (*x & 0xffff) * y + (*xc >> 16) + carry;
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carry = z >> 16;
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Storeinc(xc, z, z2);
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z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
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carry = z2 >> 16;
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}
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while(x < xae);
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*xc = z2;
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}
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}
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#else
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for(; xb < xbe; xc0++) {
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if ( (y = *xb++) !=0) {
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x = xa;
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xc = xc0;
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carry = 0;
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do {
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z = *x++ * y + *xc + carry;
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carry = z >> 16;
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*xc++ = z & 0xffff;
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}
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while(x < xae);
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*xc = carry;
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}
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}
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#endif
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#endif
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for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
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c->wds = wc;
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return c;
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}
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static Bigint *p5s;
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Bigint *
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pow5mult
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#ifdef KR_headers
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(b, k) Bigint *b; int k;
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#else
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(Bigint *b, int k)
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#endif
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{
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Bigint *b1, *p5, *p51;
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int i;
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static int p05[3] = { 5, 25, 125 };
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if ( (i = k & 3) !=0)
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b = multadd(b, p05[i-1], 0);
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if (!(k >>= 2))
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return b;
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if ((p5 = p5s) == 0) {
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/* first time */
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#ifdef MULTIPLE_THREADS
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ACQUIRE_DTOA_LOCK(1);
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if (!(p5 = p5s)) {
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p5 = p5s = i2b(625);
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p5->next = 0;
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}
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FREE_DTOA_LOCK(1);
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#else
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p5 = p5s = i2b(625);
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p5->next = 0;
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#endif
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}
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for(;;) {
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if (k & 1) {
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b1 = mult(b, p5);
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Bfree(b);
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b = b1;
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}
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if (!(k >>= 1))
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break;
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if ((p51 = p5->next) == 0) {
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#ifdef MULTIPLE_THREADS
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ACQUIRE_DTOA_LOCK(1);
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if (!(p51 = p5->next)) {
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p51 = p5->next = mult(p5,p5);
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p51->next = 0;
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}
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FREE_DTOA_LOCK(1);
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#else
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p51 = p5->next = mult(p5,p5);
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p51->next = 0;
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#endif
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}
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p5 = p51;
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}
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return b;
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}
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Bigint *
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lshift
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#ifdef KR_headers
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(b, k) Bigint *b; int k;
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#else
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(Bigint *b, int k)
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#endif
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{
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int i, k1, n, n1;
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Bigint *b1;
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ULong *x, *x1, *xe, z;
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n = k >> kshift;
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k1 = b->k;
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n1 = n + b->wds + 1;
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for(i = b->maxwds; n1 > i; i <<= 1)
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k1++;
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b1 = Balloc(k1);
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x1 = b1->x;
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for(i = 0; i < n; i++)
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*x1++ = 0;
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x = b->x;
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xe = x + b->wds;
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if (k &= kmask) {
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#ifdef Pack_32
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k1 = 32 - k;
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z = 0;
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do {
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*x1++ = *x << k | z;
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z = *x++ >> k1;
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}
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while(x < xe);
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if ((*x1 = z) !=0)
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++n1;
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#else
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k1 = 16 - k;
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z = 0;
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do {
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*x1++ = *x << k & 0xffff | z;
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z = *x++ >> k1;
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}
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while(x < xe);
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if (*x1 = z)
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++n1;
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#endif
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}
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else do
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*x1++ = *x++;
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while(x < xe);
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b1->wds = n1 - 1;
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Bfree(b);
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return b1;
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}
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int
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cmp
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#ifdef KR_headers
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(a, b) Bigint *a, *b;
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#else
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(Bigint *a, Bigint *b)
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#endif
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{
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ULong *xa, *xa0, *xb, *xb0;
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int i, j;
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i = a->wds;
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j = b->wds;
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#ifdef DEBUG
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if (i > 1 && !a->x[i-1])
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Bug("cmp called with a->x[a->wds-1] == 0");
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if (j > 1 && !b->x[j-1])
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Bug("cmp called with b->x[b->wds-1] == 0");
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#endif
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if (i -= j)
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return i;
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xa0 = a->x;
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xa = xa0 + j;
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xb0 = b->x;
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xb = xb0 + j;
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for(;;) {
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if (*--xa != *--xb)
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return *xa < *xb ? -1 : 1;
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if (xa <= xa0)
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break;
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}
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return 0;
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}
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Bigint *
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diff
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#ifdef KR_headers
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(a, b) Bigint *a, *b;
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#else
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(Bigint *a, Bigint *b)
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#endif
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{
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Bigint *c;
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int i, wa, wb;
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ULong *xa, *xae, *xb, *xbe, *xc;
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#ifdef ULLong
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ULLong borrow, y;
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#else
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ULong borrow, y;
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#ifdef Pack_32
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ULong z;
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#endif
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#endif
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i = cmp(a,b);
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if (!i) {
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c = Balloc(0);
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c->wds = 1;
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c->x[0] = 0;
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return c;
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}
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if (i < 0) {
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c = a;
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a = b;
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b = c;
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i = 1;
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}
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else
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i = 0;
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c = Balloc(a->k);
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c->sign = i;
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wa = a->wds;
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xa = a->x;
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xae = xa + wa;
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wb = b->wds;
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xb = b->x;
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xbe = xb + wb;
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xc = c->x;
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borrow = 0;
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#ifdef ULLong
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do {
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y = (ULLong)*xa++ - *xb++ - borrow;
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borrow = y >> 32 & 1UL;
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*xc++ = y & 0xffffffffUL;
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}
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while(xb < xbe);
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while(xa < xae) {
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y = *xa++ - borrow;
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borrow = y >> 32 & 1UL;
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*xc++ = y & 0xffffffffUL;
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}
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#else
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#ifdef Pack_32
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do {
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y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
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borrow = (y & 0x10000) >> 16;
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z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
|
|
borrow = (z & 0x10000) >> 16;
|
|
Storeinc(xc, z, y);
|
|
}
|
|
while(xb < xbe);
|
|
while(xa < xae) {
|
|
y = (*xa & 0xffff) - borrow;
|
|
borrow = (y & 0x10000) >> 16;
|
|
z = (*xa++ >> 16) - borrow;
|
|
borrow = (z & 0x10000) >> 16;
|
|
Storeinc(xc, z, y);
|
|
}
|
|
#else
|
|
do {
|
|
y = *xa++ - *xb++ - borrow;
|
|
borrow = (y & 0x10000) >> 16;
|
|
*xc++ = y & 0xffff;
|
|
}
|
|
while(xb < xbe);
|
|
while(xa < xae) {
|
|
y = *xa++ - borrow;
|
|
borrow = (y & 0x10000) >> 16;
|
|
*xc++ = y & 0xffff;
|
|
}
|
|
#endif
|
|
#endif
|
|
while(!*--xc)
|
|
wa--;
|
|
c->wds = wa;
|
|
return c;
|
|
}
|
|
|
|
double
|
|
b2d
|
|
#ifdef KR_headers
|
|
(a, e) Bigint *a; int *e;
|
|
#else
|
|
(Bigint *a, int *e)
|
|
#endif
|
|
{
|
|
ULong *xa, *xa0, w, y, z;
|
|
int k;
|
|
U d;
|
|
#ifdef VAX
|
|
ULong d0, d1;
|
|
#else
|
|
#define d0 word0(&d)
|
|
#define d1 word1(&d)
|
|
#endif
|
|
|
|
xa0 = a->x;
|
|
xa = xa0 + a->wds;
|
|
y = *--xa;
|
|
#ifdef DEBUG
|
|
if (!y) Bug("zero y in b2d");
|
|
#endif
|
|
k = hi0bits(y);
|
|
*e = 32 - k;
|
|
#ifdef Pack_32
|
|
if (k < Ebits) {
|
|
d0 = Exp_1 | y >> (Ebits - k);
|
|
w = xa > xa0 ? *--xa : 0;
|
|
d1 = y << ((32-Ebits) + k) | w >> (Ebits - k);
|
|
goto ret_d;
|
|
}
|
|
z = xa > xa0 ? *--xa : 0;
|
|
if (k -= Ebits) {
|
|
d0 = Exp_1 | y << k | z >> (32 - k);
|
|
y = xa > xa0 ? *--xa : 0;
|
|
d1 = z << k | y >> (32 - k);
|
|
}
|
|
else {
|
|
d0 = Exp_1 | y;
|
|
d1 = z;
|
|
}
|
|
#else
|
|
if (k < Ebits + 16) {
|
|
z = xa > xa0 ? *--xa : 0;
|
|
d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
|
|
w = xa > xa0 ? *--xa : 0;
|
|
y = xa > xa0 ? *--xa : 0;
|
|
d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
|
|
goto ret_d;
|
|
}
|
|
z = xa > xa0 ? *--xa : 0;
|
|
w = xa > xa0 ? *--xa : 0;
|
|
k -= Ebits + 16;
|
|
d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
|
|
y = xa > xa0 ? *--xa : 0;
|
|
d1 = w << k + 16 | y << k;
|
|
#endif
|
|
ret_d:
|
|
#ifdef VAX
|
|
word0(&d) = d0 >> 16 | d0 << 16;
|
|
word1(&d) = d1 >> 16 | d1 << 16;
|
|
#endif
|
|
return dval(&d);
|
|
}
|
|
#undef d0
|
|
#undef d1
|
|
|
|
Bigint *
|
|
d2b
|
|
#ifdef KR_headers
|
|
(dd, e, bits) double dd; int *e, *bits;
|
|
#else
|
|
(double dd, int *e, int *bits)
|
|
#endif
|
|
{
|
|
Bigint *b;
|
|
U d;
|
|
#ifndef Sudden_Underflow
|
|
int i;
|
|
#endif
|
|
int de, k;
|
|
ULong *x, y, z;
|
|
#ifdef VAX
|
|
ULong d0, d1;
|
|
#else
|
|
#define d0 word0(&d)
|
|
#define d1 word1(&d)
|
|
#endif
|
|
d.d = dd;
|
|
#ifdef VAX
|
|
d0 = word0(&d) >> 16 | word0(&d) << 16;
|
|
d1 = word1(&d) >> 16 | word1(&d) << 16;
|
|
#endif
|
|
|
|
#ifdef Pack_32
|
|
b = Balloc(1);
|
|
#else
|
|
b = Balloc(2);
|
|
#endif
|
|
x = b->x;
|
|
|
|
z = d0 & Frac_mask;
|
|
d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
|
|
#ifdef Sudden_Underflow
|
|
de = (int)(d0 >> Exp_shift);
|
|
#ifndef IBM
|
|
z |= Exp_msk11;
|
|
#endif
|
|
#else
|
|
if ( (de = (int)(d0 >> Exp_shift)) !=0)
|
|
z |= Exp_msk1;
|
|
#endif
|
|
#ifdef Pack_32
|
|
if ( (y = d1) !=0) {
|
|
if ( (k = lo0bits(&y)) !=0) {
|
|
x[0] = y | z << (32 - k);
|
|
z >>= k;
|
|
}
|
|
else
|
|
x[0] = y;
|
|
#ifndef Sudden_Underflow
|
|
i =
|
|
#endif
|
|
b->wds = (x[1] = z) !=0 ? 2 : 1;
|
|
}
|
|
else {
|
|
k = lo0bits(&z);
|
|
x[0] = z;
|
|
#ifndef Sudden_Underflow
|
|
i =
|
|
#endif
|
|
b->wds = 1;
|
|
k += 32;
|
|
}
|
|
#else
|
|
if ( (y = d1) !=0) {
|
|
if ( (k = lo0bits(&y)) !=0)
|
|
if (k >= 16) {
|
|
x[0] = y | z << 32 - k & 0xffff;
|
|
x[1] = z >> k - 16 & 0xffff;
|
|
x[2] = z >> k;
|
|
i = 2;
|
|
}
|
|
else {
|
|
x[0] = y & 0xffff;
|
|
x[1] = y >> 16 | z << 16 - k & 0xffff;
|
|
x[2] = z >> k & 0xffff;
|
|
x[3] = z >> k+16;
|
|
i = 3;
|
|
}
|
|
else {
|
|
x[0] = y & 0xffff;
|
|
x[1] = y >> 16;
|
|
x[2] = z & 0xffff;
|
|
x[3] = z >> 16;
|
|
i = 3;
|
|
}
|
|
}
|
|
else {
|
|
#ifdef DEBUG
|
|
if (!z)
|
|
Bug("Zero passed to d2b");
|
|
#endif
|
|
k = lo0bits(&z);
|
|
if (k >= 16) {
|
|
x[0] = z;
|
|
i = 0;
|
|
}
|
|
else {
|
|
x[0] = z & 0xffff;
|
|
x[1] = z >> 16;
|
|
i = 1;
|
|
}
|
|
k += 32;
|
|
}
|
|
while(!x[i])
|
|
--i;
|
|
b->wds = i + 1;
|
|
#endif
|
|
#ifndef Sudden_Underflow
|
|
if (de) {
|
|
#endif
|
|
#ifdef IBM
|
|
*e = (de - Bias - (P-1) << 2) + k;
|
|
*bits = 4*P + 8 - k - hi0bits(word0(&d) & Frac_mask);
|
|
#else
|
|
*e = de - Bias - (P-1) + k;
|
|
*bits = P - k;
|
|
#endif
|
|
#ifndef Sudden_Underflow
|
|
}
|
|
else {
|
|
*e = de - Bias - (P-1) + 1 + k;
|
|
#ifdef Pack_32
|
|
*bits = 32*i - hi0bits(x[i-1]);
|
|
#else
|
|
*bits = (i+2)*16 - hi0bits(x[i]);
|
|
#endif
|
|
}
|
|
#endif
|
|
return b;
|
|
}
|
|
#undef d0
|
|
#undef d1
|
|
|
|
CONST double
|
|
#ifdef IEEE_Arith
|
|
bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
|
|
CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, 1e-256
|
|
};
|
|
#else
|
|
#ifdef IBM
|
|
bigtens[] = { 1e16, 1e32, 1e64 };
|
|
CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
|
|
#else
|
|
bigtens[] = { 1e16, 1e32 };
|
|
CONST double tinytens[] = { 1e-16, 1e-32 };
|
|
#endif
|
|
#endif
|
|
|
|
CONST double
|
|
tens[] = {
|
|
1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
|
|
1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
|
|
1e20, 1e21, 1e22
|
|
#ifdef VAX
|
|
, 1e23, 1e24
|
|
#endif
|
|
};
|
|
|
|
char *
|
|
#ifdef KR_headers
|
|
strcp_D2A(a, b) char *a; char *b;
|
|
#else
|
|
strcp_D2A(char *a, CONST char *b)
|
|
#endif
|
|
{
|
|
while((*a = *b++))
|
|
a++;
|
|
return a;
|
|
}
|
|
|
|
#ifdef NO_STRING_H
|
|
|
|
Char *
|
|
#ifdef KR_headers
|
|
memcpy_D2A(a, b, len) Char *a; Char *b; size_t len;
|
|
#else
|
|
memcpy_D2A(void *a1, void *b1, size_t len)
|
|
#endif
|
|
{
|
|
char *a = (char*)a1, *ae = a + len;
|
|
char *b = (char*)b1, *a0 = a;
|
|
while(a < ae)
|
|
*a++ = *b++;
|
|
return a0;
|
|
}
|
|
|
|
#endif /* NO_STRING_H */
|