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@@ -1,1181 +0,0 @@
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-/*
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- * This file is part of the UCB release of Plan 9. It is subject to the license
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- * terms in the LICENSE file found in the top-level directory of this
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- * distribution and at http://akaros.cs.berkeley.edu/files/Plan9License. No
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- * part of the UCB release of Plan 9, including this file, may be copied,
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- * modified, propagated, or distributed except according to the terms contained
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- * in the LICENSE file.
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- */
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-
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-/* derived from /netlib/fp/dtoa.c assuming IEEE, Standard C */
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-/* kudos to dmg@bell-labs.com, gripes to ehg@bell-labs.com */
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-
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-/* Let x be the exact mathematical number defined by a decimal
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- * string s. Then atof(s) is the round-nearest-even IEEE
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- * floating point value.
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- * Let y be an IEEE floating point value and let s be the string
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- * printed as %.17g. Then atof(s) is exactly y.
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- */
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-#include <u.h>
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-#include <lib9.h>
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-
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-static Lock _dtoalk[2];
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-#define ACQUIRE_DTOA_LOCK(n) jehanne_lock(&_dtoalk[n])
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-#define FREE_DTOA_LOCK(n) jehanne_unlock(&_dtoalk[n])
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-
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-#define PRIVATE_mem ((2000+sizeof(double)-1)/sizeof(double))
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-static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
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-
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-#define FLT_ROUNDS 1
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-#define DBL_DIG 15
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-#define DBL_MAX_10_EXP 308
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-#define DBL_MAX_EXP 1024
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-#define FLT_RADIX 2
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-#define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
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-
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-/* Ten_pmax = floor(P*log(2)/log(5)) */
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-/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
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-/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
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-/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
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-
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-#define Exp_shift 20
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-#define Exp_shift1 20
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-#define Exp_msk1 0x100000
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-#define Exp_msk11 0x100000
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-#define Exp_mask 0x7ff00000
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-#define P 53
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-#define Bias 1023
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-#define Emin (-1022)
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-#define Exp_1 0x3ff00000
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-#define Exp_11 0x3ff00000
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-#define Ebits 11
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-#define Frac_mask 0xfffff
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-#define Frac_mask1 0xfffff
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-#define Ten_pmax 22
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-#define Bletch 0x10
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-#define Bndry_mask 0xfffff
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-#define Bndry_mask1 0xfffff
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-#define LSB 1
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-#define Sign_bit 0x80000000
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-#define Log2P 1
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-#define Tiny0 0
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-#define Tiny1 1
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-#define Quick_max 14
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-#define Int_max 14
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-#define Avoid_Underflow
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-
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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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-
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-#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
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-#define Big1 0xffffffff
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-
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-#define FFFFFFFF 0xffffffffUL
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-
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-#define Kmax 15
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-
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-typedef struct Bigint Bigint;
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-typedef struct Ulongs Ulongs;
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-
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-struct Bigint {
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- Bigint *next;
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- int k, maxwds, sign, wds;
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- unsigned x[1];
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-};
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-
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-struct Ulongs {
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- uint32_t hi;
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- uint32_t lo;
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-};
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-
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-static Bigint *freelist[Kmax+1];
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-
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-Ulongs
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-double2ulongs(double d)
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-{
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- FPdbleword dw;
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- Ulongs uls;
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-
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- dw.x = d;
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- uls.hi = dw.hi;
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- uls.lo = dw.lo;
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- return uls;
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-}
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-
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-double
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-ulongs2double(Ulongs uls)
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-{
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- FPdbleword dw;
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-
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- dw.hi = uls.hi;
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- dw.lo = uls.lo;
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- return dw.x;
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-}
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-
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-static Bigint *
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-Balloc(int k)
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-{
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- int x;
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- Bigint * rv;
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- unsigned int len;
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-
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- ACQUIRE_DTOA_LOCK(0);
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- if (rv = freelist[k]) {
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- freelist[k] = rv->next;
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- } else {
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- x = 1 << k;
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- len = (sizeof(Bigint) + (x - 1) * sizeof(unsigned int) + sizeof(double) -1)
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- / sizeof(double);
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- if (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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- } else
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- rv = (Bigint * )malloc(len * sizeof(double));
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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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-
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-static void
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-Bfree(Bigint *v)
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-{
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- if (v) {
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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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-#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
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-y->wds*sizeof(int) + 2*sizeof(int))
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-
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-static Bigint *
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-multadd(Bigint *b, int m, int a) /* multiply by m and add a */
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-{
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- int i, wds;
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- unsigned int carry, *x, y;
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- unsigned int xi, z;
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- Bigint * b1;
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-
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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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- 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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- } 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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-
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-static int
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-hi0bits(register unsigned int x)
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-{
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- register int k = 0;
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-
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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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-
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-static int
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-lo0bits(unsigned int *y)
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-{
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- register int k;
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- register unsigned int x = *y;
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-
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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 & 1)
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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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-
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-static Bigint *
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-i2b(int i)
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-{
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- Bigint * b;
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-
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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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-
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-static Bigint *
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-mult(Bigint *a, Bigint *b)
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-{
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- Bigint * c;
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- int k, wa, wb, wc;
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- unsigned int * x, *xa, *xae, *xb, *xbe, *xc, *xc0;
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- unsigned int y;
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- unsigned int carry, z;
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- unsigned int z2;
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-
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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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- for (; xb < xbe; xb++, xc0++) {
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- if (y = *xb & 0xffff) {
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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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- } while (x < xae);
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- *xc = carry;
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- }
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- if (y = *xb >> 16) {
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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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- } while (x < xae);
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- *xc = z2;
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- }
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- }
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- for (xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc)
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- ;
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- c->wds = wc;
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- return c;
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-}
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-
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-static Bigint *p5s;
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-
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-static Bigint *
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-pow5mult(Bigint *b, int k)
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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] = {
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- 5, 25, 125 };
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-
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- if (i = k & 3)
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- b = multadd(b, p05[i-1], 0);
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-
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- if (!(k >>= 2))
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- return b;
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- if (!(p5 = p5s)) {
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- /* first time */
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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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- }
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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)) {
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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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- }
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- p5 = p51;
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- }
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- return b;
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-}
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-
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-static Bigint *
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-lshift(Bigint *b, int k)
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-{
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- int i, k1, n, n1;
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- Bigint * b1;
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- unsigned int * x, *x1, *xe, z;
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-
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- n = k >> 5;
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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 &= 0x1f) {
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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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- } while (x < xe);
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- if (*x1 = z)
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- ++n1;
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- } else
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- 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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-
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-static int
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-cmp(Bigint *a, Bigint *b)
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-{
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- unsigned int * xa, *xa0, *xb, *xb0;
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- int i, j;
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-
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- i = a->wds;
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- j = b->wds;
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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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|
|
-}
|
|
|
-
|
|
|
-static Bigint *
|
|
|
-diff(Bigint *a, Bigint *b)
|
|
|
-{
|
|
|
- Bigint * c;
|
|
|
- int i, wa, wb;
|
|
|
- unsigned int * xa, *xae, *xb, *xbe, *xc;
|
|
|
- unsigned int borrow, y;
|
|
|
- unsigned int z;
|
|
|
-
|
|
|
- i = cmp(a, b);
|
|
|
- if (!i) {
|
|
|
- c = Balloc(0);
|
|
|
- c->wds = 1;
|
|
|
- c->x[0] = 0;
|
|
|
- return c;
|
|
|
- }
|
|
|
- if (i < 0) {
|
|
|
- c = a;
|
|
|
- a = b;
|
|
|
- b = c;
|
|
|
- i = 1;
|
|
|
- } else
|
|
|
- i = 0;
|
|
|
- c = Balloc(a->k);
|
|
|
- c->sign = i;
|
|
|
- wa = a->wds;
|
|
|
- xa = a->x;
|
|
|
- xae = xa + wa;
|
|
|
- wb = b->wds;
|
|
|
- xb = b->x;
|
|
|
- xbe = xb + wb;
|
|
|
- xc = c->x;
|
|
|
- borrow = 0;
|
|
|
- do {
|
|
|
- y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
|
|
|
- borrow = (y & 0x10000) >> 16;
|
|
|
- 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);
|
|
|
- }
|
|
|
- while (!*--xc)
|
|
|
- wa--;
|
|
|
- c->wds = wa;
|
|
|
- return c;
|
|
|
-}
|
|
|
-
|
|
|
-static Bigint *
|
|
|
-d2b(double d, int *e, int *bits)
|
|
|
-{
|
|
|
- Bigint * b;
|
|
|
- int de, i, k;
|
|
|
- unsigned *x, y, z;
|
|
|
- Ulongs uls;
|
|
|
-
|
|
|
- b = Balloc(1);
|
|
|
- x = b->x;
|
|
|
-
|
|
|
- uls = double2ulongs(d);
|
|
|
- z = uls.hi & Frac_mask;
|
|
|
- uls.hi &= 0x7fffffff; /* clear sign bit, which we ignore */
|
|
|
- de = (int)(uls.hi >> Exp_shift);
|
|
|
- z |= Exp_msk11;
|
|
|
- if (y = uls.lo) { /* assignment = */
|
|
|
- if (k = lo0bits(&y)) { /* assignment = */
|
|
|
- x[0] = y | z << 32 - k;
|
|
|
- z >>= k;
|
|
|
- } else
|
|
|
- x[0] = y;
|
|
|
- i = b->wds = (x[1] = z) ? 2 : 1;
|
|
|
- } else {
|
|
|
- k = lo0bits(&z);
|
|
|
- x[0] = z;
|
|
|
- i = b->wds = 1;
|
|
|
- k += 32;
|
|
|
- }
|
|
|
- USED(i);
|
|
|
- *e = de - Bias - (P - 1) + k;
|
|
|
- *bits = P - k;
|
|
|
- return b;
|
|
|
-}
|
|
|
-
|
|
|
-static 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
|
|
|
-};
|
|
|
-
|
|
|
-static const double
|
|
|
-bigtens[] = {
|
|
|
- 1e16, 1e32, 1e64, 1e128, 1e256 };
|
|
|
-/*
|
|
|
-static const double tinytens[] = {
|
|
|
- 1e-16, 1e-32, 1e-64, 1e-128,
|
|
|
- 9007199254740992.e-256
|
|
|
-};
|
|
|
-*/
|
|
|
-/* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
|
|
|
-/* flag unnecessarily. It leads to a song and dance at the end of strtod. */
|
|
|
-#define Scale_Bit 0x10
|
|
|
-#define n_bigtens 5
|
|
|
-
|
|
|
-#define NAN_WORD0 0x7ff80000
|
|
|
-
|
|
|
-#define NAN_WORD1 0
|
|
|
-
|
|
|
-static int
|
|
|
-quorem(Bigint *b, Bigint *S)
|
|
|
-{
|
|
|
- int n;
|
|
|
- unsigned int * bx, *bxe, q, *sx, *sxe;
|
|
|
- unsigned int borrow, carry, y, ys;
|
|
|
- unsigned int si, z, zs;
|
|
|
-
|
|
|
- n = S->wds;
|
|
|
- if (b->wds < n)
|
|
|
- return 0;
|
|
|
- sx = S->x;
|
|
|
- sxe = sx + --n;
|
|
|
- bx = b->x;
|
|
|
- bxe = bx + n;
|
|
|
- q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
|
|
|
- if (q) {
|
|
|
- borrow = 0;
|
|
|
- carry = 0;
|
|
|
- do {
|
|
|
- si = *sx++;
|
|
|
- ys = (si & 0xffff) * q + carry;
|
|
|
- zs = (si >> 16) * q + (ys >> 16);
|
|
|
- carry = zs >> 16;
|
|
|
- y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
|
|
|
- borrow = (y & 0x10000) >> 16;
|
|
|
- z = (*bx >> 16) - (zs & 0xffff) - borrow;
|
|
|
- borrow = (z & 0x10000) >> 16;
|
|
|
- Storeinc(bx, z, y);
|
|
|
- } while (sx <= sxe);
|
|
|
- if (!*bxe) {
|
|
|
- bx = b->x;
|
|
|
- while (--bxe > bx && !*bxe)
|
|
|
- --n;
|
|
|
- b->wds = n;
|
|
|
- }
|
|
|
- }
|
|
|
- if (cmp(b, S) >= 0) {
|
|
|
- q++;
|
|
|
- borrow = 0;
|
|
|
- carry = 0;
|
|
|
- bx = b->x;
|
|
|
- sx = S->x;
|
|
|
- do {
|
|
|
- si = *sx++;
|
|
|
- ys = (si & 0xffff) + carry;
|
|
|
- zs = (si >> 16) + (ys >> 16);
|
|
|
- carry = zs >> 16;
|
|
|
- y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
|
|
|
- borrow = (y & 0x10000) >> 16;
|
|
|
- z = (*bx >> 16) - (zs & 0xffff) - borrow;
|
|
|
- borrow = (z & 0x10000) >> 16;
|
|
|
- Storeinc(bx, z, y);
|
|
|
- } while (sx <= sxe);
|
|
|
- bx = b->x;
|
|
|
- bxe = bx + n;
|
|
|
- if (!*bxe) {
|
|
|
- while (--bxe > bx && !*bxe)
|
|
|
- --n;
|
|
|
- b->wds = n;
|
|
|
- }
|
|
|
- }
|
|
|
- return q;
|
|
|
-}
|
|
|
-
|
|
|
-static char *
|
|
|
-rv_alloc(int i)
|
|
|
-{
|
|
|
- int j, k, *r;
|
|
|
-
|
|
|
- j = sizeof(unsigned int);
|
|
|
- for (k = 0;
|
|
|
- sizeof(Bigint) - sizeof(unsigned int) - sizeof(int) + j <= i;
|
|
|
- j <<= 1)
|
|
|
- k++;
|
|
|
- r = (int * )Balloc(k);
|
|
|
- *r = k;
|
|
|
- return
|
|
|
- (char *)(r + 1);
|
|
|
-}
|
|
|
-
|
|
|
-static char *
|
|
|
-nrv_alloc(char *s, char **rve, int n)
|
|
|
-{
|
|
|
- char *rv, *t;
|
|
|
-
|
|
|
- t = rv = rv_alloc(n);
|
|
|
- while (*t = *s++)
|
|
|
- t++;
|
|
|
- if (rve)
|
|
|
- *rve = t;
|
|
|
- return rv;
|
|
|
-}
|
|
|
-
|
|
|
-/* freedtoa(s) must be used to free values s returned by dtoa
|
|
|
- * when MULTIPLE_THREADS is #defined. It should be used in all cases,
|
|
|
- * but for consistency with earlier versions of dtoa, it is optional
|
|
|
- * when MULTIPLE_THREADS is not defined.
|
|
|
- */
|
|
|
-
|
|
|
-void
|
|
|
-freedtoa(char *s)
|
|
|
-{
|
|
|
- Bigint * b = (Bigint * )((int *)s - 1);
|
|
|
- b->maxwds = 1 << (b->k = *(int * )b);
|
|
|
- Bfree(b);
|
|
|
-}
|
|
|
-
|
|
|
-/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
|
|
|
- *
|
|
|
- * Inspired by "How to Print Floating-Point Numbers Accurately" by
|
|
|
- * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101].
|
|
|
- *
|
|
|
- * Modifications:
|
|
|
- * 1. Rather than iterating, we use a simple numeric overestimate
|
|
|
- * to determine k = floor(log10(d)). We scale relevant
|
|
|
- * quantities using O(log2(k)) rather than O(k) multiplications.
|
|
|
- * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
|
|
|
- * try to generate digits strictly left to right. Instead, we
|
|
|
- * compute with fewer bits and propagate the carry if necessary
|
|
|
- * when rounding the final digit up. This is often faster.
|
|
|
- * 3. Under the assumption that input will be rounded nearest,
|
|
|
- * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
|
|
|
- * That is, we allow equality in stopping tests when the
|
|
|
- * round-nearest rule will give the same floating-point value
|
|
|
- * as would satisfaction of the stopping test with strict
|
|
|
- * inequality.
|
|
|
- * 4. We remove common factors of powers of 2 from relevant
|
|
|
- * quantities.
|
|
|
- * 5. When converting floating-point integers less than 1e16,
|
|
|
- * we use floating-point arithmetic rather than resorting
|
|
|
- * to multiple-precision integers.
|
|
|
- * 6. When asked to produce fewer than 15 digits, we first try
|
|
|
- * to get by with floating-point arithmetic; we resort to
|
|
|
- * multiple-precision integer arithmetic only if we cannot
|
|
|
- * guarantee that the floating-point calculation has given
|
|
|
- * the correctly rounded result. For k requested digits and
|
|
|
- * "uniformly" distributed input, the probability is
|
|
|
- * something like 10^(k-15) that we must resort to the int
|
|
|
- * calculation.
|
|
|
- */
|
|
|
-
|
|
|
-char *
|
|
|
-dtoa(double d, int mode, int ndigits, int *decpt, int *sign, char **rve)
|
|
|
-{
|
|
|
- /* Arguments ndigits, decpt, sign are similar to those
|
|
|
- of ecvt and fcvt; trailing zeros are suppressed from
|
|
|
- the returned string. If not null, *rve is set to point
|
|
|
- to the end of the return value. If d is +-Infinity or NaN,
|
|
|
- then *decpt is set to 9999.
|
|
|
-
|
|
|
- mode:
|
|
|
- 0 ==> shortest string that yields d when read in
|
|
|
- and rounded to nearest.
|
|
|
- 1 ==> like 0, but with Steele & White stopping rule;
|
|
|
- e.g. with IEEE P754 arithmetic , mode 0 gives
|
|
|
- 1e23 whereas mode 1 gives 9.999999999999999e22.
|
|
|
- 2 ==> max(1,ndigits) significant digits. This gives a
|
|
|
- return value similar to that of ecvt, except
|
|
|
- that trailing zeros are suppressed.
|
|
|
- 3 ==> through ndigits past the decimal point. This
|
|
|
- gives a return value similar to that from fcvt,
|
|
|
- except that trailing zeros are suppressed, and
|
|
|
- ndigits can be negative.
|
|
|
- 4-9 should give the same return values as 2-3, i.e.,
|
|
|
- 4 <= mode <= 9 ==> same return as mode
|
|
|
- 2 + (mode & 1). These modes are mainly for
|
|
|
- debugging; often they run slower but sometimes
|
|
|
- faster than modes 2-3.
|
|
|
- 4,5,8,9 ==> left-to-right digit generation.
|
|
|
- 6-9 ==> don't try fast floating-point estimate
|
|
|
- (if applicable).
|
|
|
-
|
|
|
- Values of mode other than 0-9 are treated as mode 0.
|
|
|
-
|
|
|
- Sufficient space is allocated to the return value
|
|
|
- to hold the suppressed trailing zeros.
|
|
|
- */
|
|
|
-
|
|
|
- int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
|
|
|
- j, j1, k, k0, k_check, L, leftright, m2, m5, s2, s5,
|
|
|
- spec_case, try_quick;
|
|
|
- Bigint * b, *b1, *delta, *mlo=nil, *mhi, *S;
|
|
|
- double d2, ds, eps;
|
|
|
- char *s, *s0;
|
|
|
- Ulongs ulsd, ulsd2;
|
|
|
-
|
|
|
- ulsd = double2ulongs(d);
|
|
|
- if (ulsd.hi & Sign_bit) {
|
|
|
- /* set sign for everything, including 0's and NaNs */
|
|
|
- *sign = 1;
|
|
|
- ulsd.hi &= ~Sign_bit; /* clear sign bit */
|
|
|
- } else
|
|
|
- *sign = 0;
|
|
|
-
|
|
|
- if ((ulsd.hi & Exp_mask) == Exp_mask) {
|
|
|
- /* Infinity or NaN */
|
|
|
- *decpt = 9999;
|
|
|
- if (!ulsd.lo && !(ulsd.hi & 0xfffff))
|
|
|
- return nrv_alloc("Infinity", rve, 8);
|
|
|
- return nrv_alloc("NaN", rve, 3);
|
|
|
- }
|
|
|
- d = ulongs2double(ulsd);
|
|
|
-
|
|
|
- if (!d) {
|
|
|
- *decpt = 1;
|
|
|
- return nrv_alloc("0", rve, 1);
|
|
|
- }
|
|
|
-
|
|
|
- b = d2b(d, &be, &bbits);
|
|
|
- i = (int)(ulsd.hi >> Exp_shift1 & (Exp_mask >> Exp_shift1));
|
|
|
-
|
|
|
- ulsd2 = ulsd;
|
|
|
- ulsd2.hi &= Frac_mask1;
|
|
|
- ulsd2.hi |= Exp_11;
|
|
|
- d2 = ulongs2double(ulsd2);
|
|
|
-
|
|
|
- /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
|
|
|
- * log10(x) = log(x) / log(10)
|
|
|
- * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
|
|
|
- * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
|
|
|
- *
|
|
|
- * This suggests computing an approximation k to log10(d) by
|
|
|
- *
|
|
|
- * k = (i - Bias)*0.301029995663981
|
|
|
- * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
|
|
|
- *
|
|
|
- * We want k to be too large rather than too small.
|
|
|
- * The error in the first-order Taylor series approximation
|
|
|
- * is in our favor, so we just round up the constant enough
|
|
|
- * to compensate for any error in the multiplication of
|
|
|
- * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
|
|
|
- * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
|
|
|
- * adding 1e-13 to the constant term more than suffices.
|
|
|
- * Hence we adjust the constant term to 0.1760912590558.
|
|
|
- * (We could get a more accurate k by invoking log10,
|
|
|
- * but this is probably not worthwhile.)
|
|
|
- */
|
|
|
-
|
|
|
- i -= Bias;
|
|
|
- ds = (d2 - 1.5) * 0.289529654602168 + 0.1760912590558 + i * 0.301029995663981;
|
|
|
- k = (int)ds;
|
|
|
- if (ds < 0. && ds != k)
|
|
|
- k--; /* want k = floor(ds) */
|
|
|
- k_check = 1;
|
|
|
- if (k >= 0 && k <= Ten_pmax) {
|
|
|
- if (d < tens[k])
|
|
|
- k--;
|
|
|
- k_check = 0;
|
|
|
- }
|
|
|
- j = bbits - i - 1;
|
|
|
- if (j >= 0) {
|
|
|
- b2 = 0;
|
|
|
- s2 = j;
|
|
|
- } else {
|
|
|
- b2 = -j;
|
|
|
- s2 = 0;
|
|
|
- }
|
|
|
- if (k >= 0) {
|
|
|
- b5 = 0;
|
|
|
- s5 = k;
|
|
|
- s2 += k;
|
|
|
- } else {
|
|
|
- b2 -= k;
|
|
|
- b5 = -k;
|
|
|
- s5 = 0;
|
|
|
- }
|
|
|
- if (mode < 0 || mode > 9)
|
|
|
- mode = 0;
|
|
|
- try_quick = 1;
|
|
|
- if (mode > 5) {
|
|
|
- mode -= 4;
|
|
|
- try_quick = 0;
|
|
|
- }
|
|
|
- leftright = 1;
|
|
|
- switch (mode) {
|
|
|
- case 0:
|
|
|
- case 1:
|
|
|
- default:
|
|
|
- ilim = ilim1 = -1;
|
|
|
- i = 18;
|
|
|
- ndigits = 0;
|
|
|
- break;
|
|
|
- case 2:
|
|
|
- leftright = 0;
|
|
|
- /* no break */
|
|
|
- case 4:
|
|
|
- if (ndigits <= 0)
|
|
|
- ndigits = 1;
|
|
|
- ilim = ilim1 = i = ndigits;
|
|
|
- break;
|
|
|
- case 3:
|
|
|
- leftright = 0;
|
|
|
- /* no break */
|
|
|
- case 5:
|
|
|
- i = ndigits + k + 1;
|
|
|
- ilim = i;
|
|
|
- ilim1 = i - 1;
|
|
|
- if (i <= 0)
|
|
|
- i = 1;
|
|
|
- }
|
|
|
- s = s0 = rv_alloc(i);
|
|
|
-
|
|
|
- if (ilim >= 0 && ilim <= Quick_max && try_quick) {
|
|
|
-
|
|
|
- /* Try to get by with floating-point arithmetic. */
|
|
|
-
|
|
|
- i = 0;
|
|
|
- d2 = d;
|
|
|
- k0 = k;
|
|
|
- ilim0 = ilim;
|
|
|
- ieps = 2; /* conservative */
|
|
|
- if (k > 0) {
|
|
|
- ds = tens[k&0xf];
|
|
|
- j = k >> 4;
|
|
|
- if (j & Bletch) {
|
|
|
- /* prevent overflows */
|
|
|
- j &= Bletch - 1;
|
|
|
- d /= bigtens[n_bigtens-1];
|
|
|
- ieps++;
|
|
|
- }
|
|
|
- for (; j; j >>= 1, i++)
|
|
|
- if (j & 1) {
|
|
|
- ieps++;
|
|
|
- ds *= bigtens[i];
|
|
|
- }
|
|
|
- d /= ds;
|
|
|
- } else if (j1 = -k) {
|
|
|
- d *= tens[j1 & 0xf];
|
|
|
- for (j = j1 >> 4; j; j >>= 1, i++)
|
|
|
- if (j & 1) {
|
|
|
- ieps++;
|
|
|
- d *= bigtens[i];
|
|
|
- }
|
|
|
- }
|
|
|
- if (k_check && d < 1. && ilim > 0) {
|
|
|
- if (ilim1 <= 0)
|
|
|
- goto fast_failed;
|
|
|
- ilim = ilim1;
|
|
|
- k--;
|
|
|
- d *= 10.;
|
|
|
- ieps++;
|
|
|
- }
|
|
|
- eps = ieps * d + 7.;
|
|
|
-
|
|
|
- ulsd = double2ulongs(eps);
|
|
|
- ulsd.hi -= (P - 1) * Exp_msk1;
|
|
|
- eps = ulongs2double(ulsd);
|
|
|
-
|
|
|
- if (ilim == 0) {
|
|
|
- S = mhi = 0;
|
|
|
- d -= 5.;
|
|
|
- if (d > eps)
|
|
|
- goto one_digit;
|
|
|
- if (d < -eps)
|
|
|
- goto no_digits;
|
|
|
- goto fast_failed;
|
|
|
- }
|
|
|
- /* Generate ilim digits, then fix them up. */
|
|
|
- eps *= tens[ilim-1];
|
|
|
- for (i = 1; ; i++, d *= 10.) {
|
|
|
- L = d;
|
|
|
- // assert(L < 10);
|
|
|
- d -= L;
|
|
|
- *s++ = '0' + (int)L;
|
|
|
- if (i == ilim) {
|
|
|
- if (d > 0.5 + eps)
|
|
|
- goto bump_up;
|
|
|
- else if (d < 0.5 - eps) {
|
|
|
- while (*--s == '0')
|
|
|
- ;
|
|
|
- s++;
|
|
|
- goto ret1;
|
|
|
- }
|
|
|
- break;
|
|
|
- }
|
|
|
- }
|
|
|
-fast_failed:
|
|
|
- s = s0;
|
|
|
- d = d2;
|
|
|
- k = k0;
|
|
|
- ilim = ilim0;
|
|
|
- }
|
|
|
-
|
|
|
- /* Do we have a "small" integer? */
|
|
|
-
|
|
|
- if (be >= 0 && k <= Int_max) {
|
|
|
- /* Yes. */
|
|
|
- ds = tens[k];
|
|
|
- if (ndigits < 0 && ilim <= 0) {
|
|
|
- S = mhi = 0;
|
|
|
- if (ilim < 0 || d <= 5 * ds)
|
|
|
- goto no_digits;
|
|
|
- goto one_digit;
|
|
|
- }
|
|
|
- for (i = 1; ; i++) {
|
|
|
- L = d / ds;
|
|
|
- d -= L * ds;
|
|
|
- *s++ = '0' + (int)L;
|
|
|
- if (i == ilim) {
|
|
|
- d += d;
|
|
|
- if (d > ds || d == ds && L & 1) {
|
|
|
-bump_up:
|
|
|
- while (*--s == '9')
|
|
|
- if (s == s0) {
|
|
|
- k++;
|
|
|
- *s = '0';
|
|
|
- break;
|
|
|
- }
|
|
|
- ++ * s++;
|
|
|
- }
|
|
|
- break;
|
|
|
- }
|
|
|
- if (!(d *= 10.))
|
|
|
- break;
|
|
|
- }
|
|
|
- goto ret1;
|
|
|
- }
|
|
|
-
|
|
|
- m2 = b2;
|
|
|
- m5 = b5;
|
|
|
- mhi = mlo = 0;
|
|
|
- if (leftright) {
|
|
|
- if (mode < 2) {
|
|
|
- i =
|
|
|
- 1 + P - bbits;
|
|
|
- } else {
|
|
|
- j = ilim - 1;
|
|
|
- if (m5 >= j)
|
|
|
- m5 -= j;
|
|
|
- else {
|
|
|
- s5 += j -= m5;
|
|
|
- b5 += j;
|
|
|
- m5 = 0;
|
|
|
- }
|
|
|
- if ((i = ilim) < 0) {
|
|
|
- m2 -= i;
|
|
|
- i = 0;
|
|
|
- }
|
|
|
- }
|
|
|
- b2 += i;
|
|
|
- s2 += i;
|
|
|
- mhi = i2b(1);
|
|
|
- }
|
|
|
- if (m2 > 0 && s2 > 0) {
|
|
|
- i = m2 < s2 ? m2 : s2;
|
|
|
- b2 -= i;
|
|
|
- m2 -= i;
|
|
|
- s2 -= i;
|
|
|
- }
|
|
|
- if (b5 > 0) {
|
|
|
- if (leftright) {
|
|
|
- if (m5 > 0) {
|
|
|
- mhi = pow5mult(mhi, m5);
|
|
|
- b1 = mult(mhi, b);
|
|
|
- Bfree(b);
|
|
|
- b = b1;
|
|
|
- }
|
|
|
- if (j = b5 - m5)
|
|
|
- b = pow5mult(b, j);
|
|
|
- } else
|
|
|
- b = pow5mult(b, b5);
|
|
|
- }
|
|
|
- S = i2b(1);
|
|
|
- if (s5 > 0)
|
|
|
- S = pow5mult(S, s5);
|
|
|
-
|
|
|
- /* Check for special case that d is a normalized power of 2. */
|
|
|
-
|
|
|
- spec_case = 0;
|
|
|
- if (mode < 2) {
|
|
|
- ulsd = double2ulongs(d);
|
|
|
- if (!ulsd.lo && !(ulsd.hi & Bndry_mask)) {
|
|
|
- /* The special case */
|
|
|
- b2 += Log2P;
|
|
|
- s2 += Log2P;
|
|
|
- spec_case = 1;
|
|
|
- }
|
|
|
- }
|
|
|
-
|
|
|
- /* Arrange for convenient computation of quotients:
|
|
|
- * shift left if necessary so divisor has 4 leading 0 bits.
|
|
|
- *
|
|
|
- * Perhaps we should just compute leading 28 bits of S once
|
|
|
- * and for all and pass them and a shift to quorem, so it
|
|
|
- * can do shifts and ors to compute the numerator for q.
|
|
|
- */
|
|
|
- if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f)
|
|
|
- i = 32 - i;
|
|
|
- if (i > 4) {
|
|
|
- i -= 4;
|
|
|
- b2 += i;
|
|
|
- m2 += i;
|
|
|
- s2 += i;
|
|
|
- } else if (i < 4) {
|
|
|
- i += 28;
|
|
|
- b2 += i;
|
|
|
- m2 += i;
|
|
|
- s2 += i;
|
|
|
- }
|
|
|
- if (b2 > 0)
|
|
|
- b = lshift(b, b2);
|
|
|
- if (s2 > 0)
|
|
|
- S = lshift(S, s2);
|
|
|
- if (k_check) {
|
|
|
- if (cmp(b, S) < 0) {
|
|
|
- k--;
|
|
|
- b = multadd(b, 10, 0); /* we botched the k estimate */
|
|
|
- if (leftright)
|
|
|
- mhi = multadd(mhi, 10, 0);
|
|
|
- ilim = ilim1;
|
|
|
- }
|
|
|
- }
|
|
|
- if (ilim <= 0 && mode > 2) {
|
|
|
- if (ilim < 0 || cmp(b, S = multadd(S, 5, 0)) <= 0) {
|
|
|
- /* no digits, fcvt style */
|
|
|
-no_digits:
|
|
|
- k = -1 - ndigits;
|
|
|
- goto ret;
|
|
|
- }
|
|
|
-one_digit:
|
|
|
- *s++ = '1';
|
|
|
- k++;
|
|
|
- goto ret;
|
|
|
- }
|
|
|
- if (leftright) {
|
|
|
- if (m2 > 0)
|
|
|
- mhi = lshift(mhi, m2);
|
|
|
-
|
|
|
- /* Compute mlo -- check for special case
|
|
|
- * that d is a normalized power of 2.
|
|
|
- */
|
|
|
-
|
|
|
- mlo = mhi;
|
|
|
- if (spec_case) {
|
|
|
- mhi = Balloc(mhi->k);
|
|
|
- Bcopy(mhi, mlo);
|
|
|
- mhi = lshift(mhi, Log2P);
|
|
|
- }
|
|
|
-
|
|
|
- for (i = 1; ; i++) {
|
|
|
- dig = quorem(b, S) + '0';
|
|
|
- /* Do we yet have the shortest decimal string
|
|
|
- * that will round to d?
|
|
|
- */
|
|
|
- j = cmp(b, mlo);
|
|
|
- delta = diff(S, mhi);
|
|
|
- j1 = delta->sign ? 1 : cmp(b, delta);
|
|
|
- Bfree(delta);
|
|
|
- ulsd = double2ulongs(d);
|
|
|
- if (j1 == 0 && !mode && !(ulsd.lo & 1)) {
|
|
|
- if (dig == '9')
|
|
|
- goto round_9_up;
|
|
|
- if (j > 0)
|
|
|
- dig++;
|
|
|
- *s++ = dig;
|
|
|
- goto ret;
|
|
|
- }
|
|
|
- if (j < 0 || j == 0 && !mode && !(ulsd.lo & 1)) {
|
|
|
- if (j1 > 0) {
|
|
|
- b = lshift(b, 1);
|
|
|
- j1 = cmp(b, S);
|
|
|
- if ((j1 > 0 || j1 == 0 && dig & 1)
|
|
|
- && dig++ == '9')
|
|
|
- goto round_9_up;
|
|
|
- }
|
|
|
- *s++ = dig;
|
|
|
- goto ret;
|
|
|
- }
|
|
|
- if (j1 > 0) {
|
|
|
- if (dig == '9') { /* possible if i == 1 */
|
|
|
-round_9_up:
|
|
|
- *s++ = '9';
|
|
|
- goto roundoff;
|
|
|
- }
|
|
|
- *s++ = dig + 1;
|
|
|
- goto ret;
|
|
|
- }
|
|
|
- *s++ = dig;
|
|
|
- if (i == ilim)
|
|
|
- break;
|
|
|
- b = multadd(b, 10, 0);
|
|
|
- if (mlo == mhi)
|
|
|
- mlo = mhi = multadd(mhi, 10, 0);
|
|
|
- else {
|
|
|
- mlo = multadd(mlo, 10, 0);
|
|
|
- mhi = multadd(mhi, 10, 0);
|
|
|
- }
|
|
|
- }
|
|
|
- } else
|
|
|
- for (i = 1; ; i++) {
|
|
|
- *s++ = dig = quorem(b, S) + '0';
|
|
|
- if (i >= ilim)
|
|
|
- break;
|
|
|
- b = multadd(b, 10, 0);
|
|
|
- }
|
|
|
-
|
|
|
- /* Round off last digit */
|
|
|
-
|
|
|
- b = lshift(b, 1);
|
|
|
- j = cmp(b, S);
|
|
|
- if (j > 0 || j == 0 && dig & 1) {
|
|
|
-roundoff:
|
|
|
- while (*--s == '9')
|
|
|
- if (s == s0) {
|
|
|
- k++;
|
|
|
- *s++ = '1';
|
|
|
- goto ret;
|
|
|
- }
|
|
|
- ++ * s++;
|
|
|
- } else {
|
|
|
- while (*--s == '0')
|
|
|
- ;
|
|
|
- s++;
|
|
|
- }
|
|
|
-ret:
|
|
|
- Bfree(S);
|
|
|
- if (mhi) {
|
|
|
- if (mlo && mlo != mhi)
|
|
|
- Bfree(mlo);
|
|
|
- Bfree(mhi);
|
|
|
- }
|
|
|
-ret1:
|
|
|
- Bfree(b);
|
|
|
- *s = 0;
|
|
|
- *decpt = k + 1;
|
|
|
- if (rve)
|
|
|
- *rve = s;
|
|
|
- return s0;
|
|
|
-}
|