+++ /dev/null
-/*
- * Copyright (c) 1999 Apple Computer, Inc. All rights reserved.
- *
- * @APPLE_LICENSE_HEADER_START@
- *
- * Copyright (c) 1999-2003 Apple Computer, Inc. All Rights Reserved.
- *
- * This file contains Original Code and/or Modifications of Original Code
- * as defined in and that are subject to the Apple Public Source License
- * Version 2.0 (the 'License'). You may not use this file except in
- * compliance with the License. Please obtain a copy of the License at
- * http://www.opensource.apple.com/apsl/ and read it before using this
- * file.
- *
- * The Original Code and all software distributed under the License are
- * distributed on an 'AS IS' basis, WITHOUT WARRANTY OF ANY KIND, EITHER
- * EXPRESS OR IMPLIED, AND APPLE HEREBY DISCLAIMS ALL SUCH WARRANTIES,
- * INCLUDING WITHOUT LIMITATION, ANY WARRANTIES OF MERCHANTABILITY,
- * FITNESS FOR A PARTICULAR PURPOSE, QUIET ENJOYMENT OR NON-INFRINGEMENT.
- * Please see the License for the specific language governing rights and
- * limitations under the License.
- *
- * @APPLE_LICENSE_HEADER_END@
- */
-/****************************************************************
- *
- * The author of this software is David M. Gay.
- *
- * Copyright (c) 1991 by AT&T.
- *
- * Permission to use, copy, modify, and distribute this software for any
- * purpose without fee is hereby granted, provided that this entire notice
- * is included in all copies of any software which is or includes a copy
- * or modification of this software and in all copies of the supporting
- * documentation for such software.
- *
- * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
- * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR AT&T MAKES ANY
- * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
- * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
- *
- ***************************************************************/
-
-/* Please send bug reports to
- David M. Gay
- AT&T Bell Laboratories, Room 2C-463
- 600 Mountain Avenue
- Murray Hill, NJ 07974-2070
- U.S.A.
- dmg@research.att.com or research!dmg
- */
-
-/* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
- *
- * This strtod returns a nearest machine number to the input decimal
- * string (or sets errno to ERANGE). With IEEE arithmetic, ties are
- * broken by the IEEE round-even rule. Otherwise ties are broken by
- * biased rounding (add half and chop).
- *
- * Inspired loosely by William D. Clinger's paper "How to Read Floating
- * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
- *
- * Modifications:
- *
- * 1. We only require IEEE, IBM, or VAX double-precision
- * arithmetic (not IEEE double-extended).
- * 2. We get by with floating-point arithmetic in a case that
- * Clinger missed -- when we're computing d * 10^n
- * for a small integer d and the integer n is not too
- * much larger than 22 (the maximum integer k for which
- * we can represent 10^k exactly), we may be able to
- * compute (d*10^k) * 10^(e-k) with just one roundoff.
- * 3. Rather than a bit-at-a-time adjustment of the binary
- * result in the hard case, we use floating-point
- * arithmetic to determine the adjustment to within
- * one bit; only in really hard cases do we need to
- * compute a second residual.
- * 4. Because of 3., we don't need a large table of powers of 10
- * for ten-to-e (just some small tables, e.g. of 10^k
- * for 0 <= k <= 22).
- */
-
-/*
- * #define IEEE_LITTLE_ENDIAN for IEEE-arithmetic machines where the least
- * significant byte has the lowest address.
- * #define IEEE_BIG_ENDIAN for IEEE-arithmetic machines where the most
- * significant byte has the lowest address.
- * #define Long int on machines with 32-bit ints and 64-bit longs.
- * #define Sudden_Underflow for IEEE-format machines without gradual
- * underflow (i.e., that flush to zero on underflow).
- * #define IBM for IBM mainframe-style floating-point arithmetic.
- * #define VAX for VAX-style floating-point arithmetic.
- * #define Unsigned_Shifts if >> does treats its left operand as unsigned.
- * #define No_leftright to omit left-right logic in fast floating-point
- * computation of dtoa.
- * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3.
- * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
- * that use extended-precision instructions to compute rounded
- * products and quotients) with IBM.
- * #define ROUND_BIASED for IEEE-format with biased rounding.
- * #define Inaccurate_Divide for IEEE-format with correctly rounded
- * products but inaccurate quotients, e.g., for Intel i860.
- * #define Just_16 to store 16 bits per 32-bit Long when doing high-precision
- * integer arithmetic. Whether this speeds things up or slows things
- * down depends on the machine and the number being converted.
- * #define KR_headers for old-style C function headers.
- * #define Bad_float_h if your system lacks a float.h or if it does not
- * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
- * FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
- * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
- * if memory is available and otherwise does something you deem
- * appropriate. If MALLOC is undefined, malloc will be invoked
- * directly -- and assumed always to succeed.
- */
-
-#if defined(LIBC_SCCS) && !defined(lint)
-static char *rcsid = "$OpenBSD: strtod.c,v 1.9 1997/03/25 17:07:30 rahnds Exp $";
-#endif /* LIBC_SCCS and not lint */
-
-#if defined(__m68k__) || defined(__sparc__) || defined(__i386__) || \
- defined(__mips__) || defined(__ns32k__) || defined(__alpha__) || \
- defined(__powerpc__) || defined(__m88k__) || defined(__ppc__)
-#include <sys/types.h>
-#if BYTE_ORDER == BIG_ENDIAN
-#define IEEE_BIG_ENDIAN
-#else
-#define IEEE_LITTLE_ENDIAN
-#endif
-#endif
-
-#ifdef __arm32__
-/*
- * Although the CPU is little endian the FP has different
- * byte and word endianness. The byte order is still little endian
- * but the word order is big endian.
- */
-#define IEEE_BIG_ENDIAN
-#endif
-
-#ifdef vax
-#define VAX
-#endif
-
-#define Long int32_t
-#define ULong u_int32_t
-
-#ifdef DEBUG
-#include "stdio.h"
-#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
-#endif
-
-#ifdef __cplusplus
-#include "malloc.h"
-#include "memory.h"
-#else
-#ifndef KR_headers
-#include "stdlib.h"
-#include "string.h"
-#include "locale.h"
-#else
-#include "malloc.h"
-#include "memory.h"
-#endif
-#endif
-
-#ifdef MALLOC
-#ifdef KR_headers
-extern char *MALLOC();
-#else
-extern void *MALLOC(size_t);
-#endif
-#else
-#define MALLOC malloc
-#endif
-
-#include "ctype.h"
-#include "errno.h"
-
-#if defined(__APPLE__)
-/*
- * Temporarily define this, so we avoid pulling in symbols from libm
- */
-#define Bad_float_h
-#endif
-
-#ifdef Bad_float_h
-#undef __STDC__
-#ifdef IEEE_BIG_ENDIAN
-#define IEEE_ARITHMETIC
-#endif
-#ifdef IEEE_LITTLE_ENDIAN
-#define IEEE_ARITHMETIC
-#endif
-
-#ifdef IEEE_ARITHMETIC
-#define DBL_DIG 15
-#define DBL_MAX_10_EXP 308
-#define DBL_MAX_EXP 1024
-#define FLT_RADIX 2
-#define FLT_ROUNDS 1
-#define DBL_MAX 1.7976931348623157e+308
-#endif
-
-#ifdef IBM
-#define DBL_DIG 16
-#define DBL_MAX_10_EXP 75
-#define DBL_MAX_EXP 63
-#define FLT_RADIX 16
-#define FLT_ROUNDS 0
-#define DBL_MAX 7.2370055773322621e+75
-#endif
-
-#ifdef VAX
-#define DBL_DIG 16
-#define DBL_MAX_10_EXP 38
-#define DBL_MAX_EXP 127
-#define FLT_RADIX 2
-#define FLT_ROUNDS 1
-#define DBL_MAX 1.7014118346046923e+38
-#endif
-
-#ifndef LONG_MAX
-#define LONG_MAX 2147483647
-#endif
-#else
-#include "float.h"
-#endif
-#ifndef __MATH_H__
-#include "math.h"
-#endif
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-#ifndef CONST
-#ifdef KR_headers
-#define CONST /* blank */
-#else
-#define CONST const
-#endif
-#endif
-
-#ifdef Unsigned_Shifts
-#define Sign_Extend(a,b) if (b < 0) a |= 0xffff0000;
-#else
-#define Sign_Extend(a,b) /*no-op*/
-#endif
-
-#if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) + defined(VAX) + \
- defined(IBM) != 1
-Exactly one of IEEE_LITTLE_ENDIAN IEEE_BIG_ENDIAN, VAX, or
-IBM should be defined.
-#endif
-
-#ifdef IEEE_LITTLE_ENDIAN
-#define word0(x) ((ULong *)&x)[1]
-#define word1(x) ((ULong *)&x)[0]
-#else
-#define word0(x) ((ULong *)&x)[0]
-#define word1(x) ((ULong *)&x)[1]
-#endif
-
-/* The following definition of Storeinc is appropriate for MIPS processors.
- * An alternative that might be better on some machines is
- * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
- */
-#if defined(IEEE_LITTLE_ENDIAN) + defined(VAX) + defined(__arm32__)
-#define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
-((unsigned short *)a)[0] = (unsigned short)c, a++)
-#else
-#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
-((unsigned short *)a)[1] = (unsigned short)c, a++)
-#endif
-
-/* #define P DBL_MANT_DIG */
-/* Ten_pmax = floor(P*log(2)/log(5)) */
-/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
-/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
-/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
-
-#if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN)
-#define Exp_shift 20
-#define Exp_shift1 20
-#define Exp_msk1 0x100000
-#define Exp_msk11 0x100000
-#define Exp_mask 0x7ff00000
-#define P 53
-#define Bias 1023
-#define IEEE_Arith
-#define Emin (-1022)
-#define Exp_1 0x3ff00000
-#define Exp_11 0x3ff00000
-#define Ebits 11
-#define Frac_mask 0xfffff
-#define Frac_mask1 0xfffff
-#define Ten_pmax 22
-#define Bletch 0x10
-#define Bndry_mask 0xfffff
-#define Bndry_mask1 0xfffff
-#define LSB 1
-#define Sign_bit 0x80000000
-#define Log2P 1
-#define Tiny0 0
-#define Tiny1 1
-#define Quick_max 14
-#define Int_max 14
-#define Infinite(x) (word0(x) == 0x7ff00000) /* sufficient test for here */
-#else
-#undef Sudden_Underflow
-#define Sudden_Underflow
-#ifdef IBM
-#define Exp_shift 24
-#define Exp_shift1 24
-#define Exp_msk1 0x1000000
-#define Exp_msk11 0x1000000
-#define Exp_mask 0x7f000000
-#define P 14
-#define Bias 65
-#define Exp_1 0x41000000
-#define Exp_11 0x41000000
-#define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
-#define Frac_mask 0xffffff
-#define Frac_mask1 0xffffff
-#define Bletch 4
-#define Ten_pmax 22
-#define Bndry_mask 0xefffff
-#define Bndry_mask1 0xffffff
-#define LSB 1
-#define Sign_bit 0x80000000
-#define Log2P 4
-#define Tiny0 0x100000
-#define Tiny1 0
-#define Quick_max 14
-#define Int_max 15
-#else /* VAX */
-#define Exp_shift 23
-#define Exp_shift1 7
-#define Exp_msk1 0x80
-#define Exp_msk11 0x800000
-#define Exp_mask 0x7f80
-#define P 56
-#define Bias 129
-#define Exp_1 0x40800000
-#define Exp_11 0x4080
-#define Ebits 8
-#define Frac_mask 0x7fffff
-#define Frac_mask1 0xffff007f
-#define Ten_pmax 24
-#define Bletch 2
-#define Bndry_mask 0xffff007f
-#define Bndry_mask1 0xffff007f
-#define LSB 0x10000
-#define Sign_bit 0x8000
-#define Log2P 1
-#define Tiny0 0x80
-#define Tiny1 0
-#define Quick_max 15
-#define Int_max 15
-#endif
-#endif
-
-#ifndef IEEE_Arith
-#define ROUND_BIASED
-#endif
-
-#ifdef RND_PRODQUOT
-#define rounded_product(a,b) a = rnd_prod(a, b)
-#define rounded_quotient(a,b) a = rnd_quot(a, b)
-#ifdef KR_headers
-extern double rnd_prod(), rnd_quot();
-#else
-extern double rnd_prod(double, double), rnd_quot(double, double);
-#endif
-#else
-#define rounded_product(a,b) a *= b
-#define rounded_quotient(a,b) a /= b
-#endif
-
-#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
-#define Big1 0xffffffff
-
-#ifndef Just_16
-/* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
- * This makes some inner loops simpler and sometimes saves work
- * during multiplications, but it often seems to make things slightly
- * slower. Hence the default is now to store 32 bits per Long.
- */
-#ifndef Pack_32
-#define Pack_32
-#endif
-#endif
-
-#define Kmax 15
-
-#ifdef __cplusplus
-extern "C" double strtod(const char *s00, char **se);
-extern "C" char *__dtoa(double d, int mode, int ndigits,
- int *decpt, int *sign, char **rve, char **resultp);
-#endif
-
- struct
-Bigint {
- struct Bigint *next;
- int k, maxwds, sign, wds;
- ULong x[1];
- };
-
- typedef struct Bigint Bigint;
-
- static Bigint *
-Balloc
-#ifdef KR_headers
- (k) int k;
-#else
- (int k)
-#endif
-{
- int x;
- Bigint *rv;
-
- x = 1 << k;
- rv = (Bigint *)malloc(sizeof(Bigint) + (x-1)*sizeof(Long));
- rv->k = k;
- rv->maxwds = x;
- rv->sign = rv->wds = 0;
- return rv;
-}
-
- static void
-Bfree
-#ifdef KR_headers
- (v) Bigint *v;
-#else
- (Bigint *v)
-#endif
-{
- free(v);
-}
-
-#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
-y->wds*sizeof(Long) + 2*sizeof(int))
-
- static Bigint *
-multadd
-#ifdef KR_headers
- (b, m, a) Bigint *b; int m, a;
-#else
- (Bigint *b, int m, int a) /* multiply by m and add a */
-#endif
-{
- int i, wds;
- ULong *x, y;
-#ifdef Pack_32
- ULong xi, z;
-#endif
- Bigint *b1;
-
- wds = b->wds;
- x = b->x;
- i = 0;
- do {
-#ifdef Pack_32
- xi = *x;
- y = (xi & 0xffff) * m + a;
- z = (xi >> 16) * m + (y >> 16);
- a = (int)(z >> 16);
- *x++ = (z << 16) + (y & 0xffff);
-#else
- y = *x * m + a;
- a = (int)(y >> 16);
- *x++ = y & 0xffff;
-#endif
- }
- while(++i < wds);
- if (a) {
- if (wds >= b->maxwds) {
- b1 = Balloc(b->k+1);
- Bcopy(b1, b);
- Bfree(b);
- b = b1;
- }
- b->x[wds++] = a;
- b->wds = wds;
- }
- return b;
- }
-
- static Bigint *
-s2b
-#ifdef KR_headers
- (s, nd0, nd, y9) CONST char *s; int nd0, nd; ULong y9;
-#else
- (CONST char *s, int nd0, int nd, ULong y9)
-#endif
-{
- Bigint *b;
- int i, k;
- Long x, y;
-
- x = (nd + 8) / 9;
- for(k = 0, y = 1; x > y; y <<= 1, k++) ;
-#ifdef Pack_32
- b = Balloc(k);
- b->x[0] = y9;
- b->wds = 1;
-#else
- b = Balloc(k+1);
- b->x[0] = y9 & 0xffff;
- b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
-#endif
-
- i = 9;
- if (9 < nd0) {
- s += 9;
- do b = multadd(b, 10, *s++ - '0');
- while(++i < nd0);
- s++;
- }
- else
- s += 10;
- for(; i < nd; i++)
- b = multadd(b, 10, *s++ - '0');
- return b;
- }
-
- static int
-hi0bits
-#ifdef KR_headers
- (x) register ULong x;
-#else
- (register ULong x)
-#endif
-{
- register int k = 0;
-
- if (!(x & 0xffff0000)) {
- k = 16;
- x <<= 16;
- }
- if (!(x & 0xff000000)) {
- k += 8;
- x <<= 8;
- }
- if (!(x & 0xf0000000)) {
- k += 4;
- x <<= 4;
- }
- if (!(x & 0xc0000000)) {
- k += 2;
- x <<= 2;
- }
- if (!(x & 0x80000000)) {
- k++;
- if (!(x & 0x40000000))
- return 32;
- }
- return k;
- }
-
- static int
-lo0bits
-#ifdef KR_headers
- (y) ULong *y;
-#else
- (ULong *y)
-#endif
-{
- register int k;
- register ULong x = *y;
-
- if (x & 7) {
- if (x & 1)
- return 0;
- if (x & 2) {
- *y = x >> 1;
- return 1;
- }
- *y = x >> 2;
- return 2;
- }
- k = 0;
- if (!(x & 0xffff)) {
- k = 16;
- x >>= 16;
- }
- if (!(x & 0xff)) {
- k += 8;
- x >>= 8;
- }
- if (!(x & 0xf)) {
- k += 4;
- x >>= 4;
- }
- if (!(x & 0x3)) {
- k += 2;
- x >>= 2;
- }
- if (!(x & 1)) {
- k++;
- x >>= 1;
- if (!x & 1)
- return 32;
- }
- *y = x;
- return k;
- }
-
- static Bigint *
-i2b
-#ifdef KR_headers
- (i) int i;
-#else
- (int i)
-#endif
-{
- Bigint *b;
-
- b = Balloc(1);
- b->x[0] = i;
- b->wds = 1;
- return b;
- }
-
- static Bigint *
-mult
-#ifdef KR_headers
- (a, b) Bigint *a, *b;
-#else
- (Bigint *a, Bigint *b)
-#endif
-{
- Bigint *c;
- int k, wa, wb, wc;
- ULong carry, y, z;
- ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
-#ifdef Pack_32
- ULong z2;
-#endif
-
- if (a->wds < b->wds) {
- c = a;
- a = b;
- b = c;
- }
- k = a->k;
- wa = a->wds;
- wb = b->wds;
- wc = wa + wb;
- if (wc > a->maxwds)
- k++;
- c = Balloc(k);
- for(x = c->x, xa = x + wc; x < xa; x++)
- *x = 0;
- xa = a->x;
- xae = xa + wa;
- xb = b->x;
- xbe = xb + wb;
- xc0 = c->x;
-#ifdef Pack_32
- for(; xb < xbe; xb++, xc0++) {
- if (y = *xb & 0xffff) {
- x = xa;
- xc = xc0;
- carry = 0;
- do {
- z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
- carry = z >> 16;
- z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
- carry = z2 >> 16;
- Storeinc(xc, z2, z);
- }
- while(x < xae);
- *xc = carry;
- }
- if (y = *xb >> 16) {
- x = xa;
- xc = xc0;
- carry = 0;
- z2 = *xc;
- do {
- z = (*x & 0xffff) * y + (*xc >> 16) + carry;
- carry = z >> 16;
- Storeinc(xc, z, z2);
- z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
- carry = z2 >> 16;
- }
- while(x < xae);
- *xc = z2;
- }
- }
-#else
- for(; xb < xbe; xc0++) {
- if (y = *xb++) {
- x = xa;
- xc = xc0;
- carry = 0;
- do {
- z = *x++ * y + *xc + carry;
- carry = z >> 16;
- *xc++ = z & 0xffff;
- }
- while(x < xae);
- *xc = carry;
- }
- }
-#endif
- for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
- c->wds = wc;
- return c;
- }
-
- static Bigint *p5s;
-
- static Bigint *
-pow5mult
-#ifdef KR_headers
- (b, k) Bigint *b; int k;
-#else
- (Bigint *b, int k)
-#endif
-{
- Bigint *b1, *p5, *p51;
- int i;
- static int p05[3] = { 5, 25, 125 };
-
- if (i = k & 3)
- b = multadd(b, p05[i-1], 0);
-
- if (!(k >>= 2))
- return b;
- if (!(p5 = p5s)) {
- /* first time */
- p5 = p5s = i2b(625);
- p5->next = 0;
- }
- for(;;) {
- if (k & 1) {
- b1 = mult(b, p5);
- Bfree(b);
- b = b1;
- }
- if (!(k >>= 1))
- break;
- if (!(p51 = p5->next)) {
- p51 = p5->next = mult(p5,p5);
- p51->next = 0;
- }
- p5 = p51;
- }
- return b;
- }
-
- static Bigint *
-lshift
-#ifdef KR_headers
- (b, k) Bigint *b; int k;
-#else
- (Bigint *b, int k)
-#endif
-{
- int i, k1, n, n1;
- Bigint *b1;
- ULong *x, *x1, *xe, z;
-
-#ifdef Pack_32
- n = k >> 5;
-#else
- n = k >> 4;
-#endif
- k1 = b->k;
- n1 = n + b->wds + 1;
- for(i = b->maxwds; n1 > i; i <<= 1)
- k1++;
- b1 = Balloc(k1);
- x1 = b1->x;
- for(i = 0; i < n; i++)
- *x1++ = 0;
- x = b->x;
- xe = x + b->wds;
-#ifdef Pack_32
- if (k &= 0x1f) {
- k1 = 32 - k;
- z = 0;
- do {
- *x1++ = *x << k | z;
- z = *x++ >> k1;
- }
- while(x < xe);
- if (*x1 = z)
- ++n1;
- }
-#else
- if (k &= 0xf) {
- k1 = 16 - k;
- z = 0;
- do {
- *x1++ = *x << k & 0xffff | z;
- z = *x++ >> k1;
- }
- while(x < xe);
- if (*x1 = z)
- ++n1;
- }
-#endif
- else do
- *x1++ = *x++;
- while(x < xe);
- b1->wds = n1 - 1;
- Bfree(b);
- return b1;
- }
-
- static int
-cmp
-#ifdef KR_headers
- (a, b) Bigint *a, *b;
-#else
- (Bigint *a, Bigint *b)
-#endif
-{
- ULong *xa, *xa0, *xb, *xb0;
- int i, j;
-
- i = a->wds;
- j = b->wds;
-#ifdef DEBUG
- if (i > 1 && !a->x[i-1])
- Bug("cmp called with a->x[a->wds-1] == 0");
- if (j > 1 && !b->x[j-1])
- Bug("cmp called with b->x[b->wds-1] == 0");
-#endif
- if (i -= j)
- return i;
- xa0 = a->x;
- xa = xa0 + j;
- xb0 = b->x;
- xb = xb0 + j;
- for(;;) {
- if (*--xa != *--xb)
- return *xa < *xb ? -1 : 1;
- if (xa <= xa0)
- break;
- }
- return 0;
- }
-
- static Bigint *
-diff
-#ifdef KR_headers
- (a, b) Bigint *a, *b;
-#else
- (Bigint *a, Bigint *b)
-#endif
-{
- Bigint *c;
- int i, wa, wb;
- Long borrow, y; /* We need signed shifts here. */
- ULong *xa, *xae, *xb, *xbe, *xc;
-#ifdef Pack_32
- Long z;
-#endif
-
- 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;
-#ifdef Pack_32
- do {
- y = (*xa & 0xffff) - (*xb & 0xffff) + borrow;
- borrow = y >> 16;
- Sign_Extend(borrow, y);
- z = (*xa++ >> 16) - (*xb++ >> 16) + borrow;
- borrow = z >> 16;
- Sign_Extend(borrow, z);
- Storeinc(xc, z, y);
- }
- while(xb < xbe);
- while(xa < xae) {
- y = (*xa & 0xffff) + borrow;
- borrow = y >> 16;
- Sign_Extend(borrow, y);
- z = (*xa++ >> 16) + borrow;
- borrow = z >> 16;
- Sign_Extend(borrow, z);
- Storeinc(xc, z, y);
- }
-#else
- do {
- y = *xa++ - *xb++ + borrow;
- borrow = y >> 16;
- Sign_Extend(borrow, y);
- *xc++ = y & 0xffff;
- }
- while(xb < xbe);
- while(xa < xae) {
- y = *xa++ + borrow;
- borrow = y >> 16;
- Sign_Extend(borrow, y);
- *xc++ = y & 0xffff;
- }
-#endif
- while(!*--xc)
- wa--;
- c->wds = wa;
- return c;
- }
-
- static double
-ulp
-#ifdef KR_headers
- (x) double x;
-#else
- (double x)
-#endif
-{
- register Long L;
- double a;
-
- L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
-#ifndef Sudden_Underflow
- if (L > 0) {
-#endif
-#ifdef IBM
- L |= Exp_msk1 >> 4;
-#endif
- word0(a) = L;
- word1(a) = 0;
-#ifndef Sudden_Underflow
- }
- else {
- L = -L >> Exp_shift;
- if (L < Exp_shift) {
- word0(a) = 0x80000 >> L;
- word1(a) = 0;
- }
- else {
- word0(a) = 0;
- L -= Exp_shift;
- word1(a) = L >= 31 ? 1 : 1 << 31 - L;
- }
- }
-#endif
- return a;
- }
-
- static 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;
- double 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;
-#else
-#undef d0
-#undef d1
-#endif
- return d;
- }
-
- static Bigint *
-d2b
-#ifdef KR_headers
- (d, e, bits) double d; int *e, *bits;
-#else
- (double d, int *e, int *bits)
-#endif
-{
- Bigint *b;
- int de, i, k;
- ULong *x, y, z;
-#ifdef VAX
- ULong d0, d1;
- d0 = word0(d) >> 16 | word0(d) << 16;
- d1 = word1(d) >> 16 | word1(d) << 16;
-#else
-#define d0 word0(d)
-#define d1 word1(d)
-#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))
- z |= Exp_msk1;
-#endif
-#ifdef Pack_32
- if (y = d1) {
- if (k = lo0bits(&y)) {
- x[0] = y | z << 32 - k;
- z >>= k;
- }
- else
- x[0] = y;
- i = b->wds = (x[1] = z) ? 2 : 1;
- }
- else {
-#ifdef DEBUG
- if (!z)
- Bug("Zero passed to d2b");
-#endif
- k = lo0bits(&z);
- x[0] = z;
- i = b->wds = 1;
- k += 32;
- }
-#else
- if (y = d1) {
- if (k = lo0bits(&y))
- 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
-
- static double
-ratio
-#ifdef KR_headers
- (a, b) Bigint *a, *b;
-#else
- (Bigint *a, Bigint *b)
-#endif
-{
- double da, db;
- int k, ka, kb;
-
- da = b2d(a, &ka);
- db = b2d(b, &kb);
-#ifdef Pack_32
- k = ka - kb + 32*(a->wds - b->wds);
-#else
- k = ka - kb + 16*(a->wds - b->wds);
-#endif
-#ifdef IBM
- if (k > 0) {
- word0(da) += (k >> 2)*Exp_msk1;
- if (k &= 3)
- da *= 1 << k;
- }
- else {
- k = -k;
- word0(db) += (k >> 2)*Exp_msk1;
- if (k &= 3)
- db *= 1 << k;
- }
-#else
- if (k > 0)
- word0(da) += k*Exp_msk1;
- else {
- k = -k;
- word0(db) += k*Exp_msk1;
- }
-#endif
- return da / db;
- }
-
-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
-#ifdef VAX
- , 1e23, 1e24
-#endif
- };
-
-#ifdef IEEE_Arith
-static CONST double bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
-static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, 1e-256 };
-#define n_bigtens 5
-#else
-#ifdef IBM
-static CONST double bigtens[] = { 1e16, 1e32, 1e64 };
-static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
-#define n_bigtens 3
-#else
-static CONST double bigtens[] = { 1e16, 1e32 };
-static CONST double tinytens[] = { 1e-16, 1e-32 };
-#define n_bigtens 2
-#endif
-#endif
-
- double
-strtod
-#ifdef KR_headers
- (s00, se) CONST char *s00; char **se;
-#else
- (CONST char *s00, char **se)
-#endif
-{
- int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
- e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
- CONST char *s, *s0, *s1;
- double aadj, aadj1, adj, rv, rv0;
- Long L;
- ULong y, z;
- Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
-
-#ifndef KR_headers
- CONST char decimal_point = localeconv()->decimal_point[0];
-#else
- CONST char decimal_point = '.';
-#endif
-
- sign = nz0 = nz = 0;
- rv = 0.;
-
-
- for(s = s00; isspace((unsigned char) *s); s++)
- ;
-
- if (*s == '-') {
- sign = 1;
- s++;
- } else if (*s == '+') {
- s++;
- }
-
- if (*s == '\0') {
- s = s00;
- goto ret;
- }
-
- if (*s == '0') {
- nz0 = 1;
- while(*++s == '0') ;
- if (!*s)
- goto ret;
- }
- s0 = s;
- y = z = 0;
- for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
- if (nd < 9)
- y = 10*y + c - '0';
- else if (nd < 16)
- z = 10*z + c - '0';
- nd0 = nd;
- if (c == decimal_point) {
- c = *++s;
- if (!nd) {
- for(; c == '0'; c = *++s)
- nz++;
- if (c > '0' && c <= '9') {
- s0 = s;
- nf += nz;
- nz = 0;
- goto have_dig;
- }
- goto dig_done;
- }
- for(; c >= '0' && c <= '9'; c = *++s) {
- have_dig:
- nz++;
- if (c -= '0') {
- nf += nz;
- for(i = 1; i < nz; i++)
- if (nd++ < 9)
- y *= 10;
- else if (nd <= DBL_DIG + 1)
- z *= 10;
- if (nd++ < 9)
- y = 10*y + c;
- else if (nd <= DBL_DIG + 1)
- z = 10*z + c;
- nz = 0;
- }
- }
- }
- dig_done:
- e = 0;
- if (c == 'e' || c == 'E') {
- if (!nd && !nz && !nz0) {
- s = s00;
- goto ret;
- }
- s00 = s;
- esign = 0;
- switch(c = *++s) {
- case '-':
- esign = 1;
- case '+':
- c = *++s;
- }
- if (c >= '0' && c <= '9') {
- while(c == '0')
- c = *++s;
- if (c > '0' && c <= '9') {
- L = c - '0';
- s1 = s;
- while((c = *++s) >= '0' && c <= '9')
- L = 10*L + c - '0';
- if (s - s1 > 8 || L > 19999)
- /* Avoid confusion from exponents
- * so large that e might overflow.
- */
- e = 19999; /* safe for 16 bit ints */
- else
- e = (int)L;
- if (esign)
- e = -e;
- }
- else
- e = 0;
- }
- else
- s = s00;
- }
- if (!nd) {
- if (!nz && !nz0)
- s = s00;
- goto ret;
- }
- e1 = e -= nf;
-
- /* Now we have nd0 digits, starting at s0, followed by a
- * decimal point, followed by nd-nd0 digits. The number we're
- * after is the integer represented by those digits times
- * 10**e */
-
- if (!nd0)
- nd0 = nd;
- k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
- rv = y;
- if (k > 9)
- rv = tens[k - 9] * rv + z;
- bd0 = 0;
- if (nd <= DBL_DIG
-#ifndef RND_PRODQUOT
- && FLT_ROUNDS == 1
-#endif
- ) {
- if (!e)
- goto ret;
- if (e > 0) {
- if (e <= Ten_pmax) {
-#ifdef VAX
- goto vax_ovfl_check;
-#else
- /* rv = */ rounded_product(rv, tens[e]);
- goto ret;
-#endif
- }
- i = DBL_DIG - nd;
- if (e <= Ten_pmax + i) {
- /* A fancier test would sometimes let us do
- * this for larger i values.
- */
- e -= i;
- rv *= tens[i];
-#ifdef VAX
- /* VAX exponent range is so narrow we must
- * worry about overflow here...
- */
- vax_ovfl_check:
- word0(rv) -= P*Exp_msk1;
- /* rv = */ rounded_product(rv, tens[e]);
- if ((word0(rv) & Exp_mask)
- > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
- goto ovfl;
- word0(rv) += P*Exp_msk1;
-#else
- /* rv = */ rounded_product(rv, tens[e]);
-#endif
- goto ret;
- }
- }
-#ifndef Inaccurate_Divide
- else if (e >= -Ten_pmax) {
- /* rv = */ rounded_quotient(rv, tens[-e]);
- goto ret;
- }
-#endif
- }
- e1 += nd - k;
-
- /* Get starting approximation = rv * 10**e1 */
-
- if (e1 > 0) {
- if (i = e1 & 15)
- rv *= tens[i];
- if (e1 &= ~15) {
- if (e1 > DBL_MAX_10_EXP) {
- ovfl:
- errno = ERANGE;
-#ifdef __STDC__
- rv = HUGE_VAL;
-#else
- /* Can't trust HUGE_VAL */
-#ifdef IEEE_Arith
- word0(rv) = Exp_mask;
- word1(rv) = 0;
-#else
- word0(rv) = Big0;
- word1(rv) = Big1;
-#endif
-#endif
- if (bd0)
- goto retfree;
- goto ret;
- }
- if (e1 >>= 4) {
- for(j = 0; e1 > 1; j++, e1 >>= 1)
- if (e1 & 1)
- rv *= bigtens[j];
- /* The last multiplication could overflow. */
- word0(rv) -= P*Exp_msk1;
- rv *= bigtens[j];
- if ((z = word0(rv) & Exp_mask)
- > Exp_msk1*(DBL_MAX_EXP+Bias-P))
- goto ovfl;
- if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
- /* set to largest number */
- /* (Can't trust DBL_MAX) */
- word0(rv) = Big0;
- word1(rv) = Big1;
- }
- else
- word0(rv) += P*Exp_msk1;
- }
-
- }
- }
- else if (e1 < 0) {
- e1 = -e1;
- if (i = e1 & 15)
- rv /= tens[i];
- if (e1 &= ~15) {
- e1 >>= 4;
- if (e1 >= 1 << n_bigtens)
- goto undfl;
- for(j = 0; e1 > 1; j++, e1 >>= 1)
- if (e1 & 1)
- rv *= tinytens[j];
- /* The last multiplication could underflow. */
- rv0 = rv;
- rv *= tinytens[j];
- if (!rv) {
- rv = 2.*rv0;
- rv *= tinytens[j];
- if (!rv) {
- undfl:
- rv = 0.;
- errno = ERANGE;
- if (bd0)
- goto retfree;
- goto ret;
- }
- word0(rv) = Tiny0;
- word1(rv) = Tiny1;
- /* The refinement below will clean
- * this approximation up.
- */
- }
- }
- }
-
- /* Now the hard part -- adjusting rv to the correct value.*/
-
- /* Put digits into bd: true value = bd * 10^e */
-
- bd0 = s2b(s0, nd0, nd, y);
-
- for(;;) {
- bd = Balloc(bd0->k);
- Bcopy(bd, bd0);
- bb = d2b(rv, &bbe, &bbbits); /* rv = bb * 2^bbe */
- bs = i2b(1);
-
- if (e >= 0) {
- bb2 = bb5 = 0;
- bd2 = bd5 = e;
- }
- else {
- bb2 = bb5 = -e;
- bd2 = bd5 = 0;
- }
- if (bbe >= 0)
- bb2 += bbe;
- else
- bd2 -= bbe;
- bs2 = bb2;
-#ifdef Sudden_Underflow
-#ifdef IBM
- j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
-#else
- j = P + 1 - bbbits;
-#endif
-#else
- i = bbe + bbbits - 1; /* logb(rv) */
- if (i < Emin) /* denormal */
- j = bbe + (P-Emin);
- else
- j = P + 1 - bbbits;
-#endif
- bb2 += j;
- bd2 += j;
- i = bb2 < bd2 ? bb2 : bd2;
- if (i > bs2)
- i = bs2;
- if (i > 0) {
- bb2 -= i;
- bd2 -= i;
- bs2 -= i;
- }
- if (bb5 > 0) {
- bs = pow5mult(bs, bb5);
- bb1 = mult(bs, bb);
- Bfree(bb);
- bb = bb1;
- }
- if (bb2 > 0)
- bb = lshift(bb, bb2);
- if (bd5 > 0)
- bd = pow5mult(bd, bd5);
- if (bd2 > 0)
- bd = lshift(bd, bd2);
- if (bs2 > 0)
- bs = lshift(bs, bs2);
- delta = diff(bb, bd);
- dsign = delta->sign;
- delta->sign = 0;
- i = cmp(delta, bs);
- if (i < 0) {
- /* Error is less than half an ulp -- check for
- * special case of mantissa a power of two.
- */
- if (dsign || word1(rv) || word0(rv) & Bndry_mask)
- break;
- delta = lshift(delta,Log2P);
- if (cmp(delta, bs) > 0)
- goto drop_down;
- break;
- }
- if (i == 0) {
- /* exactly half-way between */
- if (dsign) {
- if ((word0(rv) & Bndry_mask1) == Bndry_mask1
- && word1(rv) == 0xffffffff) {
- /*boundary case -- increment exponent*/
- word0(rv) = (word0(rv) & Exp_mask)
- + Exp_msk1
-#ifdef IBM
- | Exp_msk1 >> 4
-#endif
- ;
- word1(rv) = 0;
- break;
- }
- }
- else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
- drop_down:
- /* boundary case -- decrement exponent */
-#ifdef Sudden_Underflow
- L = word0(rv) & Exp_mask;
-#ifdef IBM
- if (L < Exp_msk1)
-#else
- if (L <= Exp_msk1)
-#endif
- goto undfl;
- L -= Exp_msk1;
-#else
- L = (word0(rv) & Exp_mask) - Exp_msk1;
-#endif
- word0(rv) = L | Bndry_mask1;
- word1(rv) = 0xffffffff;
-#ifdef IBM
- goto cont;
-#else
- break;
-#endif
- }
-#ifndef ROUND_BIASED
- if (!(word1(rv) & LSB))
- break;
-#endif
- if (dsign)
- rv += ulp(rv);
-#ifndef ROUND_BIASED
- else {
- rv -= ulp(rv);
-#ifndef Sudden_Underflow
- if (!rv)
- goto undfl;
-#endif
- }
-#endif
- break;
- }
- if ((aadj = ratio(delta, bs)) <= 2.) {
- if (dsign)
- aadj = aadj1 = 1.;
- else if (word1(rv) || word0(rv) & Bndry_mask) {
-#ifndef Sudden_Underflow
- if (word1(rv) == Tiny1 && !word0(rv))
- goto undfl;
-#endif
- aadj = 1.;
- aadj1 = -1.;
- }
- else {
- /* special case -- power of FLT_RADIX to be */
- /* rounded down... */
-
- if (aadj < 2./FLT_RADIX)
- aadj = 1./FLT_RADIX;
- else
- aadj *= 0.5;
- aadj1 = -aadj;
- }
- }
- else {
- aadj *= 0.5;
- aadj1 = dsign ? aadj : -aadj;
-#ifdef Check_FLT_ROUNDS
- switch(FLT_ROUNDS) {
- case 2: /* towards +infinity */
- aadj1 -= 0.5;
- break;
- case 0: /* towards 0 */
- case 3: /* towards -infinity */
- aadj1 += 0.5;
- }
-#else
- if (FLT_ROUNDS == 0)
- aadj1 += 0.5;
-#endif
- }
- y = word0(rv) & Exp_mask;
-
- /* Check for overflow */
-
- if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
- rv0 = rv;
- word0(rv) -= P*Exp_msk1;
- adj = aadj1 * ulp(rv);
- rv += adj;
- if ((word0(rv) & Exp_mask) >=
- Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
- if (word0(rv0) == Big0 && word1(rv0) == Big1)
- goto ovfl;
- word0(rv) = Big0;
- word1(rv) = Big1;
- goto cont;
- }
- else
- word0(rv) += P*Exp_msk1;
- }
- else {
-#ifdef Sudden_Underflow
- if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
- rv0 = rv;
- word0(rv) += P*Exp_msk1;
- adj = aadj1 * ulp(rv);
- rv += adj;
-#ifdef IBM
- if ((word0(rv) & Exp_mask) < P*Exp_msk1)
-#else
- if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
-#endif
- {
- if (word0(rv0) == Tiny0
- && word1(rv0) == Tiny1)
- goto undfl;
- word0(rv) = Tiny0;
- word1(rv) = Tiny1;
- goto cont;
- }
- else
- word0(rv) -= P*Exp_msk1;
- }
- else {
- adj = aadj1 * ulp(rv);
- rv += adj;
- }
-#else
- /* Compute adj so that the IEEE rounding rules will
- * correctly round rv + adj in some half-way cases.
- * If rv * ulp(rv) is denormalized (i.e.,
- * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
- * trouble from bits lost to denormalization;
- * example: 1.2e-307 .
- */
- if (y <= (P-1)*Exp_msk1 && aadj >= 1.) {
- aadj1 = (double)(int)(aadj + 0.5);
- if (!dsign)
- aadj1 = -aadj1;
- }
- adj = aadj1 * ulp(rv);
- rv += adj;
-#endif
- }
- z = word0(rv) & Exp_mask;
- if (y == z) {
- /* Can we stop now? */
- L = aadj;
- aadj -= L;
- /* The tolerances below are conservative. */
- if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
- if (aadj < .4999999 || aadj > .5000001)
- break;
- }
- else if (aadj < .4999999/FLT_RADIX)
- break;
- }
- cont:
- Bfree(bb);
- Bfree(bd);
- Bfree(bs);
- Bfree(delta);
- }
- retfree:
- Bfree(bb);
- Bfree(bd);
- Bfree(bs);
- Bfree(bd0);
- Bfree(delta);
- ret:
- if (se)
- *se = (char *)s;
- return sign ? -rv : rv;
- }
-
- static int
-quorem
-#ifdef KR_headers
- (b, S) Bigint *b, *S;
-#else
- (Bigint *b, Bigint *S)
-#endif
-{
- int n;
- Long borrow, y;
- ULong carry, q, ys;
- ULong *bx, *bxe, *sx, *sxe;
-#ifdef Pack_32
- Long z;
- ULong si, zs;
-#endif
-
- n = S->wds;
-#ifdef DEBUG
- /*debug*/ if (b->wds > n)
- /*debug*/ Bug("oversize b in quorem");
-#endif
- 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 */
-#ifdef DEBUG
- /*debug*/ if (q > 9)
- /*debug*/ Bug("oversized quotient in quorem");
-#endif
- if (q) {
- borrow = 0;
- carry = 0;
- do {
-#ifdef Pack_32
- si = *sx++;
- ys = (si & 0xffff) * q + carry;
- zs = (si >> 16) * q + (ys >> 16);
- carry = zs >> 16;
- y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
- borrow = y >> 16;
- Sign_Extend(borrow, y);
- z = (*bx >> 16) - (zs & 0xffff) + borrow;
- borrow = z >> 16;
- Sign_Extend(borrow, z);
- Storeinc(bx, z, y);
-#else
- ys = *sx++ * q + carry;
- carry = ys >> 16;
- y = *bx - (ys & 0xffff) + borrow;
- borrow = y >> 16;
- Sign_Extend(borrow, y);
- *bx++ = y & 0xffff;
-#endif
- }
- 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 {
-#ifdef Pack_32
- si = *sx++;
- ys = (si & 0xffff) + carry;
- zs = (si >> 16) + (ys >> 16);
- carry = zs >> 16;
- y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
- borrow = y >> 16;
- Sign_Extend(borrow, y);
- z = (*bx >> 16) - (zs & 0xffff) + borrow;
- borrow = z >> 16;
- Sign_Extend(borrow, z);
- Storeinc(bx, z, y);
-#else
- ys = *sx++ + carry;
- carry = ys >> 16;
- y = *bx - (ys & 0xffff) + borrow;
- borrow = y >> 16;
- Sign_Extend(borrow, y);
- *bx++ = y & 0xffff;
-#endif
- }
- while(sx <= sxe);
- bx = b->x;
- bxe = bx + n;
- if (!*bxe) {
- while(--bxe > bx && !*bxe)
- --n;
- b->wds = n;
- }
- }
- return q;
- }
-
-/* 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 Long
- * calculation.
- */
-
- char *
-__dtoa
-#ifdef KR_headers
- (d, mode, ndigits, decpt, sign, rve)
- double d; int mode, ndigits, *decpt, *sign; char **rve, char **resultp;
-#else
- (double d, int mode, int ndigits, int *decpt, int *sign, char **rve, char **resultp)
-#endif
-{
- /* 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, leftright, m2, m5, s2, s5,
- spec_case, try_quick;
- Long L;
-#ifndef Sudden_Underflow
- int denorm;
- ULong x;
-#endif
- Bigint *b, *b1, *delta, *mlo, *mhi, *S;
- double d2, ds, eps;
- char *s, *s0;
-
- if (word0(d) & Sign_bit) {
- /* set sign for everything, including 0's and NaNs */
- *sign = 1;
- word0(d) &= ~Sign_bit; /* clear sign bit */
- }
- else
- *sign = 0;
-
-#if defined(IEEE_Arith) + defined(VAX)
-#ifdef IEEE_Arith
- if ((word0(d) & Exp_mask) == Exp_mask)
-#else
- if (word0(d) == 0x8000)
-#endif
- {
- /* Infinity or NaN */
- *decpt = 9999;
- s =
-#ifdef IEEE_Arith
- !word1(d) && !(word0(d) & 0xfffff) ? "Infinity" :
-#endif
- "NaN";
- if (rve)
- *rve =
-#ifdef IEEE_Arith
- s[3] ? s + 8 :
-#endif
- s + 3;
- return s;
- }
-#endif
-#ifdef IBM
- d += 0; /* normalize */
-#endif
- if (!d) {
- *decpt = 1;
- s = "0";
- if (rve)
- *rve = s + 1;
- return s;
- }
-
- b = d2b(d, &be, &bbits);
-#ifdef Sudden_Underflow
- i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
-#else
- if (i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1))) {
-#endif
- d2 = d;
- word0(d2) &= Frac_mask1;
- word0(d2) |= Exp_11;
-#ifdef IBM
- if (j = 11 - hi0bits(word0(d2) & Frac_mask))
- d2 /= 1 << j;
-#endif
-
- /* 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;
-#ifdef IBM
- i <<= 2;
- i += j;
-#endif
-#ifndef Sudden_Underflow
- denorm = 0;
- }
- else {
- /* d is denormalized */
-
- i = bbits + be + (Bias + (P-1) - 1);
- x = i > 32 ? word0(d) << 64 - i | word1(d) >> i - 32
- : word1(d) << 32 - i;
- d2 = x;
- word0(d2) -= 31*Exp_msk1; /* adjust exponent */
- i -= (Bias + (P-1) - 1) + 1;
- denorm = 1;
- }
-#endif
- 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:
- 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;
- }
- *resultp = (char *) malloc(i + 1);
- s = s0 = *resultp;
-
- 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.;
- word0(eps) -= (P-1)*Exp_msk1;
- if (ilim == 0) {
- S = mhi = 0;
- d -= 5.;
- if (d > eps)
- goto one_digit;
- if (d < -eps)
- goto no_digits;
- goto fast_failed;
- }
-#ifndef No_leftright
- if (leftright) {
- /* Use Steele & White method of only
- * generating digits needed.
- */
- eps = 0.5/tens[ilim-1] - eps;
- for(i = 0;;) {
- L = d;
- d -= L;
- *s++ = '0' + (int)L;
- if (d < eps)
- goto ret1;
- if (1. - d < eps)
- goto bump_up;
- if (++i >= ilim)
- break;
- eps *= 10.;
- d *= 10.;
- }
- }
- else {
-#endif
- /* Generate ilim digits, then fix them up. */
- eps *= tens[ilim-1];
- for(i = 1;; i++, d *= 10.) {
- L = d;
- 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;
- }
- }
-#ifndef No_leftright
- }
-#endif
- 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;
-#ifdef Check_FLT_ROUNDS
- /* If FLT_ROUNDS == 2, L will usually be high by 1 */
- if (d < 0) {
- L--;
- d += ds;
- }
-#endif
- *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 =
-#ifndef Sudden_Underflow
- denorm ? be + (Bias + (P-1) - 1 + 1) :
-#endif
-#ifdef IBM
- 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
-#else
- 1 + P - bbits;
-#endif
- }
- 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. */
-
- if (mode < 2) {
- if (!word1(d) && !(word0(d) & Bndry_mask)
-#ifndef Sudden_Underflow
- && word0(d) & Exp_mask
-#endif
- ) {
- /* The special case */
- b2 += Log2P;
- s2 += Log2P;
- spec_case = 1;
- }
- else
- spec_case = 0;
- }
-
- /* 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.
- */
-#ifdef Pack_32
- if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f)
- i = 32 - i;
-#else
- if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf)
- i = 16 - i;
-#endif
- 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);
-#ifndef ROUND_BIASED
- if (j1 == 0 && !mode && !(word1(d) & 1)) {
- if (dig == '9')
- goto round_9_up;
- if (j > 0)
- dig++;
- *s++ = dig;
- goto ret;
- }
-#endif
- if (j < 0 || j == 0 && !mode
-#ifndef ROUND_BIASED
- && !(word1(d) & 1)
-#endif
- ) {
- 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);
- if (s == s0) { /* don't return empty string */
- *s++ = '0';
- k = 0;
- }
- *s = 0;
- *decpt = k + 1;
- if (rve)
- *rve = s;
- return s0;
- }
-#ifdef __cplusplus
-}
-#endif
projects / apple / libc.git / blobdiff