1994-05-27 05:00:24 +00:00
|
|
|
/*-
|
|
|
|
* Copyright (c) 1993
|
|
|
|
* The Regents of the University of California. All rights reserved.
|
|
|
|
*
|
|
|
|
* Redistribution and use in source and binary forms, with or without
|
|
|
|
* modification, are permitted provided that the following conditions
|
|
|
|
* are met:
|
|
|
|
* 1. Redistributions of source code must retain the above copyright
|
|
|
|
* notice, this list of conditions and the following disclaimer.
|
|
|
|
* 2. Redistributions in binary form must reproduce the above copyright
|
|
|
|
* notice, this list of conditions and the following disclaimer in the
|
|
|
|
* documentation and/or other materials provided with the distribution.
|
|
|
|
* 3. All advertising materials mentioning features or use of this software
|
|
|
|
* must display the following acknowledgement:
|
|
|
|
* This product includes software developed by the University of
|
|
|
|
* California, Berkeley and its contributors.
|
|
|
|
* 4. Neither the name of the University nor the names of its contributors
|
|
|
|
* may be used to endorse or promote products derived from this software
|
|
|
|
* without specific prior written permission.
|
|
|
|
*
|
|
|
|
* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
|
|
|
|
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
|
|
|
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
|
|
|
* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
|
|
|
|
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
|
|
|
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
|
|
|
|
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
|
|
|
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
|
|
|
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
|
|
|
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
|
|
|
* SUCH DAMAGE.
|
2001-02-08 20:22:28 +00:00
|
|
|
*
|
|
|
|
* $FreeBSD$
|
1994-05-27 05:00:24 +00:00
|
|
|
*/
|
|
|
|
|
|
|
|
#if defined(LIBC_SCCS) && !defined(lint)
|
|
|
|
static char sccsid[] = "@(#)strtod.c 8.1 (Berkeley) 6/4/93";
|
|
|
|
#endif /* LIBC_SCCS and not lint */
|
|
|
|
|
|
|
|
/****************************************************************
|
|
|
|
*
|
|
|
|
* 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_8087 for IEEE-arithmetic machines where the least
|
|
|
|
* significant byte has the lowest address.
|
|
|
|
* #define IEEE_MC68k for IEEE-arithmetic machines where the most
|
|
|
|
* significant byte has the lowest address.
|
|
|
|
* #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.
|
|
|
|
*/
|
|
|
|
|
|
|
|
#if defined(i386) || defined(mips) && defined(MIPSEL)
|
|
|
|
#define IEEE_8087
|
|
|
|
#else
|
|
|
|
#define IEEE_MC68k
|
|
|
|
#endif
|
|
|
|
|
|
|
|
#ifdef DEBUG
|
|
|
|
#include "stdio.h"
|
|
|
|
#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
|
|
|
|
#endif
|
|
|
|
|
2001-02-10 05:05:09 +00:00
|
|
|
#include <locale.h>
|
1994-05-27 05:00:24 +00:00
|
|
|
#ifdef __cplusplus
|
|
|
|
#include "malloc.h"
|
|
|
|
#include "memory.h"
|
|
|
|
#else
|
|
|
|
#ifndef KR_headers
|
|
|
|
#include "stdlib.h"
|
|
|
|
#include "string.h"
|
|
|
|
#else
|
|
|
|
#include "malloc.h"
|
|
|
|
#include "memory.h"
|
|
|
|
#endif
|
|
|
|
#endif
|
|
|
|
|
|
|
|
#include "errno.h"
|
1995-08-01 22:20:16 +00:00
|
|
|
#include <ctype.h>
|
1994-05-27 05:00:24 +00:00
|
|
|
#ifdef Bad_float_h
|
|
|
|
#undef __STDC__
|
|
|
|
#ifdef IEEE_MC68k
|
|
|
|
#define IEEE_ARITHMETIC
|
|
|
|
#endif
|
|
|
|
#ifdef IEEE_8087
|
|
|
|
#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_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
|
|
|
|
Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
|
|
|
|
#endif
|
|
|
|
|
|
|
|
#ifdef IEEE_8087
|
|
|
|
#define word0(x) ((unsigned long *)&x)[1]
|
|
|
|
#define word1(x) ((unsigned long *)&x)[0]
|
|
|
|
#else
|
|
|
|
#define word0(x) ((unsigned long *)&x)[0]
|
|
|
|
#define word1(x) ((unsigned long *)&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_8087) + defined(VAX)
|
|
|
|
#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_8087) + defined(IEEE_MC68k)
|
|
|
|
#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);
|
|
|
|
#endif
|
|
|
|
|
|
|
|
struct
|
|
|
|
Bigint {
|
|
|
|
struct Bigint *next;
|
|
|
|
int k, maxwds, sign, wds;
|
|
|
|
unsigned long x[1];
|
|
|
|
};
|
|
|
|
|
|
|
|
typedef struct Bigint Bigint;
|
|
|
|
|
|
|
|
static Bigint *freelist[Kmax+1];
|
|
|
|
|
|
|
|
static Bigint *
|
|
|
|
Balloc
|
|
|
|
#ifdef KR_headers
|
|
|
|
(k) int k;
|
|
|
|
#else
|
|
|
|
(int k)
|
|
|
|
#endif
|
|
|
|
{
|
|
|
|
int x;
|
|
|
|
Bigint *rv;
|
|
|
|
|
1996-07-12 18:57:58 +00:00
|
|
|
if ( (rv = freelist[k]) ) {
|
1994-05-27 05:00:24 +00:00
|
|
|
freelist[k] = rv->next;
|
|
|
|
} else {
|
|
|
|
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
|
|
|
|
{
|
|
|
|
if (v) {
|
|
|
|
v->next = freelist[v->k];
|
|
|
|
freelist[v->k] = 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;
|
|
|
|
unsigned long *x, y;
|
|
|
|
#ifdef Pack_32
|
|
|
|
unsigned long 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; unsigned long y9;
|
|
|
|
#else
|
|
|
|
(CONST char *s, int nd0, int nd, unsigned long 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 unsigned long x;
|
|
|
|
#else
|
|
|
|
(register unsigned long 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) unsigned long *y;
|
|
|
|
#else
|
|
|
|
(unsigned long *y)
|
|
|
|
#endif
|
|
|
|
{
|
|
|
|
register int k;
|
|
|
|
register unsigned long 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;
|
|
|
|
unsigned long carry, y, z;
|
|
|
|
unsigned long *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
|
|
|
|
#ifdef Pack_32
|
|
|
|
unsigned long 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++) {
|
1996-07-12 18:57:58 +00:00
|
|
|
if ( (y = *xb & 0xffff) ) {
|
1994-05-27 05:00:24 +00:00
|
|
|
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;
|
|
|
|
}
|
1996-07-12 18:57:58 +00:00
|
|
|
if ( (y = *xb >> 16) ) {
|
1994-05-27 05:00:24 +00:00
|
|
|
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 };
|
|
|
|
|
1996-07-12 18:57:58 +00:00
|
|
|
if ( (i = k & 3) )
|
1994-05-27 05:00:24 +00:00
|
|
|
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;
|
|
|
|
unsigned long *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);
|
1996-07-12 18:57:58 +00:00
|
|
|
if ( (*x1 = z) )
|
1994-05-27 05:00:24 +00:00
|
|
|
++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
|
|
|
|
{
|
|
|
|
unsigned long *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. */
|
|
|
|
unsigned long *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;
|
1996-07-12 18:57:58 +00:00
|
|
|
word1(a) = L >= 31 ? 1 : 1 << (31 - L);
|
1994-05-27 05:00:24 +00:00
|
|
|
}
|
|
|
|
}
|
|
|
|
#endif
|
|
|
|
return a;
|
|
|
|
}
|
|
|
|
|
|
|
|
static double
|
|
|
|
b2d
|
|
|
|
#ifdef KR_headers
|
|
|
|
(a, e) Bigint *a; int *e;
|
|
|
|
#else
|
|
|
|
(Bigint *a, int *e)
|
|
|
|
#endif
|
|
|
|
{
|
|
|
|
unsigned long *xa, *xa0, w, y, z;
|
|
|
|
int k;
|
|
|
|
double d;
|
|
|
|
#ifdef VAX
|
|
|
|
unsigned long 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) {
|
1996-07-12 18:57:58 +00:00
|
|
|
d0 = Exp_1 | (y >> (Ebits - k));
|
1994-05-27 05:00:24 +00:00
|
|
|
w = xa > xa0 ? *--xa : 0;
|
1996-07-12 18:57:58 +00:00
|
|
|
d1 = (y << ((32-Ebits) + k)) | (w >> (Ebits - k));
|
1994-05-27 05:00:24 +00:00
|
|
|
goto ret_d;
|
|
|
|
}
|
|
|
|
z = xa > xa0 ? *--xa : 0;
|
|
|
|
if (k -= Ebits) {
|
1996-07-12 18:57:58 +00:00
|
|
|
d0 = Exp_1 | (y << k) | (z >> (32 - k));
|
1994-05-27 05:00:24 +00:00
|
|
|
y = xa > xa0 ? *--xa : 0;
|
1996-07-12 18:57:58 +00:00
|
|
|
d1 = (z << k) | (y >> (32 - k));
|
1994-05-27 05:00:24 +00:00
|
|
|
} 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;
|
|
|
|
unsigned long *x, y, z;
|
|
|
|
#ifdef VAX
|
|
|
|
unsigned long 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
|
1996-07-12 18:57:58 +00:00
|
|
|
if ( (de = (int)(d0 >> Exp_shift)) )
|
1994-05-27 05:00:24 +00:00
|
|
|
z |= Exp_msk1;
|
|
|
|
#endif
|
|
|
|
#ifdef Pack_32
|
1996-07-12 18:57:58 +00:00
|
|
|
if ( (y = d1) ) {
|
|
|
|
if ( (k = lo0bits(&y)) ) {
|
|
|
|
x[0] = y | (z << (32 - k));
|
1994-05-27 05:00:24 +00:00
|
|
|
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 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
|
|
|
|
};
|
|
|
|
|
|
|
|
static double
|
|
|
|
#ifdef IEEE_Arith
|
|
|
|
bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
|
|
|
|
static double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, 1e-256 };
|
|
|
|
#define n_bigtens 5
|
|
|
|
#else
|
|
|
|
#ifdef IBM
|
|
|
|
bigtens[] = { 1e16, 1e32, 1e64 };
|
|
|
|
static double tinytens[] = { 1e-16, 1e-32, 1e-64 };
|
|
|
|
#define n_bigtens 3
|
|
|
|
#else
|
|
|
|
bigtens[] = { 1e16, 1e32 };
|
|
|
|
static 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;
|
|
|
|
unsigned long y, z;
|
|
|
|
Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
|
2001-02-10 05:05:09 +00:00
|
|
|
char decimal_point = localeconv()->decimal_point[0];
|
|
|
|
|
1994-05-27 05:00:24 +00:00
|
|
|
sign = nz0 = nz = 0;
|
|
|
|
rv = 0.;
|
|
|
|
for (s = s00;;s++) switch(*s) {
|
|
|
|
case '-':
|
|
|
|
sign = 1;
|
|
|
|
/* no break */
|
|
|
|
case '+':
|
|
|
|
if (*++s)
|
|
|
|
goto break2;
|
|
|
|
/* no break */
|
|
|
|
case 0:
|
|
|
|
s = s00;
|
|
|
|
goto ret;
|
|
|
|
default:
|
1995-08-01 22:20:16 +00:00
|
|
|
if (isspace((unsigned char)*s))
|
|
|
|
continue;
|
1994-05-27 05:00:24 +00:00
|
|
|
goto break2;
|
|
|
|
}
|
|
|
|
break2:
|
|
|
|
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;
|
2001-02-10 05:05:09 +00:00
|
|
|
if ((char)c == decimal_point) {
|
1994-05-27 05:00:24 +00:00
|
|
|
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;
|
|
|
|
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) {
|
1996-07-12 18:57:58 +00:00
|
|
|
if ( (i = e1 & 15) )
|
1994-05-27 05:00:24 +00:00
|
|
|
rv *= tens[i];
|
1996-07-12 18:57:58 +00:00
|
|
|
if ( (e1 &= ~15) ) {
|
1994-05-27 05:00:24 +00:00
|
|
|
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
|
|
|
|
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;
|
1996-07-12 18:57:58 +00:00
|
|
|
if ( (i = e1 & 15) )
|
1994-05-27 05:00:24 +00:00
|
|
|
rv /= tens[i];
|
1996-07-12 18:57:58 +00:00
|
|
|
if ( (e1 &= ~15) ) {
|
1994-05-27 05:00:24 +00:00
|
|
|
e1 >>= 4;
|
|
|
|
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;
|
|
|
|
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);
|
|
|
|
}
|
|
|
|
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;
|
|
|
|
unsigned long carry, q, ys;
|
|
|
|
unsigned long *bx, *bxe, *sx, *sxe;
|
|
|
|
#ifdef Pack_32
|
|
|
|
long z;
|
|
|
|
unsigned long 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
|
2001-02-09 20:31:48 +00:00
|
|
|
(d, mode, ndigits, decpt, sign, rve)
|
|
|
|
double d; int mode, ndigits, *decpt, *sign; char **rve;
|
1994-05-27 05:00:24 +00:00
|
|
|
#else
|
2001-02-09 20:31:48 +00:00
|
|
|
(double d, int mode, int ndigits, int *decpt, int *sign, char **rve)
|
1994-05-27 05:00:24 +00:00
|
|
|
#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;
|
|
|
|
unsigned long x;
|
|
|
|
#endif
|
|
|
|
Bigint *b, *b1, *delta, *mlo, *mhi, *S;
|
|
|
|
double d2, ds, eps;
|
|
|
|
char *s, *s0;
|
2001-02-09 20:31:48 +00:00
|
|
|
static Bigint *result;
|
|
|
|
static int result_k;
|
|
|
|
|
|
|
|
if (result) {
|
|
|
|
result->k = result_k;
|
|
|
|
result->maxwds = 1 << result_k;
|
|
|
|
Bfree(result);
|
|
|
|
result = 0;
|
|
|
|
}
|
1994-05-27 05:00:24 +00:00
|
|
|
|
|
|
|
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
|
1996-07-12 18:57:58 +00:00
|
|
|
if ( (i = (int)((word0(d) >> Exp_shift1) & (Exp_mask>>Exp_shift1))) ) {
|
1994-05-27 05:00:24 +00:00
|
|
|
#endif
|
|
|
|
d2 = d;
|
|
|
|
word0(d2) &= Frac_mask1;
|
|
|
|
word0(d2) |= Exp_11;
|
|
|
|
#ifdef IBM
|
1996-07-12 18:57:58 +00:00
|
|
|
if ( (j = 11 - hi0bits(word0(d2) & Frac_mask)) )
|
1994-05-27 05:00:24 +00:00
|
|
|
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);
|
1996-07-12 18:57:58 +00:00
|
|
|
x = i > 32 ? ((word0(d) << (64 - i)) | (word1(d) >> (i - 32)))
|
|
|
|
: (word1(d) << (32 - i));
|
1994-05-27 05:00:24 +00:00
|
|
|
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;
|
|
|
|
}
|
2001-02-09 20:31:48 +00:00
|
|
|
j = sizeof(unsigned long);
|
|
|
|
for (result_k = 0; sizeof(Bigint) - sizeof(unsigned long) + j < i;
|
|
|
|
j <<= 1) result_k++;
|
|
|
|
result = Balloc(result_k);
|
|
|
|
s = s0 = (char *)result;
|
1994-05-27 05:00:24 +00:00
|
|
|
|
|
|
|
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;
|
1996-07-12 18:57:58 +00:00
|
|
|
} else if ( (j1 = -k) ) {
|
1994-05-27 05:00:24 +00:00
|
|
|
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;
|
1996-07-12 18:57:58 +00:00
|
|
|
if (d > ds || (d == ds && L & 1)) {
|
1994-05-27 05:00:24 +00:00
|
|
|
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;
|
|
|
|
}
|
1996-07-12 18:57:58 +00:00
|
|
|
if ( (j = b5 - m5) )
|
1994-05-27 05:00:24 +00:00
|
|
|
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
|
1996-07-12 18:57:58 +00:00
|
|
|
if ( (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f) )
|
1994-05-27 05:00:24 +00:00
|
|
|
i = 32 - i;
|
|
|
|
#else
|
1996-07-12 18:57:58 +00:00
|
|
|
if ( (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf) )
|
1994-05-27 05:00:24 +00:00
|
|
|
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
|
1996-07-12 18:57:58 +00:00
|
|
|
if (j < 0 || (j == 0 && !mode
|
1994-05-27 05:00:24 +00:00
|
|
|
#ifndef ROUND_BIASED
|
|
|
|
&& !(word1(d) & 1)
|
|
|
|
#endif
|
1996-07-12 18:57:58 +00:00
|
|
|
)) {
|
1994-05-27 05:00:24 +00:00
|
|
|
if (j1 > 0) {
|
|
|
|
b = lshift(b, 1);
|
|
|
|
j1 = cmp(b, S);
|
1996-07-12 18:57:58 +00:00
|
|
|
if ((j1 > 0 || (j1 == 0 && dig & 1))
|
1994-05-27 05:00:24 +00:00
|
|
|
&& 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);
|
1996-07-12 18:57:58 +00:00
|
|
|
if (j > 0 || (j == 0 && dig & 1)) {
|
1994-05-27 05:00:24 +00:00
|
|
|
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
|