aboutsummaryrefslogtreecommitdiff
path: root/contrib/libio/floatconv.c
diff options
context:
space:
mode:
Diffstat (limited to 'contrib/libio/floatconv.c')
-rw-r--r--contrib/libio/floatconv.c2375
1 files changed, 0 insertions, 2375 deletions
diff --git a/contrib/libio/floatconv.c b/contrib/libio/floatconv.c
deleted file mode 100644
index 9503187b5d57..000000000000
--- a/contrib/libio/floatconv.c
+++ /dev/null
@@ -1,2375 +0,0 @@
-/*
-Copyright (C) 1993, 1994 Free Software Foundation
-
-This file is part of the GNU IO Library. This library is free
-software; you can redistribute it and/or modify it under the
-terms of the GNU General Public License as published by the
-Free Software Foundation; either version 2, or (at your option)
-any later version.
-
-This library is distributed in the hope that it will be useful,
-but WITHOUT ANY WARRANTY; without even the implied warranty of
-MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-GNU General Public License for more details.
-
-You should have received a copy of the GNU General Public License
-along with this library; see the file COPYING. If not, write to the Free
-Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
-
-As a special exception, if you link this library with files
-compiled with a GNU compiler to produce an executable, this does not cause
-the resulting executable to be covered by the GNU General Public License.
-This exception does not however invalidate any other reasons why
-the executable file might be covered by the GNU General Public License. */
-
-#include <libioP.h>
-#ifdef _IO_USE_DTOA
-/****************************************************************
- *
- * 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.
- *
- ***************************************************************/
-
-/* Some cleaning up by Per Bothner, bothner@cygnus.com, 1992, 1993.
- Re-written to not need static variables
- (except result, result_k, HIWORD, LOWORD). */
-
-/* Note that the checking of _DOUBLE_IS_32BITS is for use with the
- cross targets that employ the newlib ieeefp.h header. -- brendan */
-
-/* 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 KR_headers for old-style C function headers.
- */
-
-#ifdef DEBUG
-#include <stdio.h>
-#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
-#endif
-
-#ifdef __STDC__
-#include <stdlib.h>
-#include <string.h>
-#include <float.h>
-#define CONST const
-#else
-#define CONST
-#define KR_headers
-
-/* In this case, we assume IEEE floats. */
-#define FLT_ROUNDS 1
-#define FLT_RADIX 2
-#define DBL_MANT_DIG 53
-#define DBL_DIG 15
-#define DBL_MAX_10_EXP 308
-#define DBL_MAX_EXP 1024
-#endif
-
-#include <errno.h>
-#ifndef __MATH_H__
-#include <math.h>
-#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(__i386__) || defined(__i860__) || defined(clipper)
-#define IEEE_8087
-#endif
-#if defined(MIPSEL) || defined(__alpha__)
-#define IEEE_8087
-#endif
-#if defined(__sparc__) || defined(sparc) || defined(MIPSEB)
-#define IEEE_MC68k
-#endif
-
-#if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
-
-#ifndef _DOUBLE_IS_32BITS
-#if FLT_RADIX==16
-#define IBM
-#else
-#if DBL_MANT_DIG==56
-#define VAX
-#else
-#if DBL_MANT_DIG==53 && DBL_MAX_10_EXP==308
-#define IEEE_Unknown
-#else
-Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
-#endif
-#endif
-#endif
-#endif /* !_DOUBLE_IS_32BITS */
-#endif
-
-typedef _G_uint32_t unsigned32;
-
-union doubleword {
- double d;
- unsigned32 u[2];
-};
-
-#ifdef IEEE_8087
-#define HIWORD 1
-#define LOWORD 0
-#define TEST_ENDIANNESS /* nothing */
-#else
-#if defined(IEEE_MC68k)
-#define HIWORD 0
-#define LOWORD 1
-#define TEST_ENDIANNESS /* nothing */
-#else
-static int HIWORD = -1, LOWORD;
-static void test_endianness()
-{
- union doubleword dw;
- dw.d = 10;
- if (dw.u[0] != 0) /* big-endian */
- HIWORD=0, LOWORD=1;
- else
- HIWORD=1, LOWORD=0;
-}
-#define TEST_ENDIANNESS if (HIWORD<0) test_endianness();
-#endif
-#endif
-
-#if 0
-union doubleword _temp;
-#endif
-#if defined(__GNUC__) && !defined(_DOUBLE_IS_32BITS)
-#define word0(x) ({ union doubleword _du; _du.d = (x); _du.u[HIWORD]; })
-#define word1(x) ({ union doubleword _du; _du.d = (x); _du.u[LOWORD]; })
-#define setword0(D,W) \
- ({ union doubleword _du; _du.d = (D); _du.u[HIWORD]=(W); (D)=_du.d; })
-#define setword1(D,W) \
- ({ union doubleword _du; _du.d = (D); _du.u[LOWORD]=(W); (D)=_du.d; })
-#define setwords(D,W0,W1) ({ union doubleword _du; \
- _du.u[HIWORD]=(W0); _du.u[LOWORD]=(W1); (D)=_du.d; })
-#define addword0(D,W) \
- ({ union doubleword _du; _du.d = (D); _du.u[HIWORD]+=(W); (D)=_du.d; })
-#else
-#define word0(x) ((unsigned32 *)&x)[HIWORD]
-#ifndef _DOUBLE_IS_32BITS
-#define word1(x) ((unsigned32 *)&x)[LOWORD]
-#else
-#define word1(x) 0
-#endif
-#define setword0(D,W) word0(D) = (W)
-#ifndef _DOUBLE_IS_32BITS
-#define setword1(D,W) word1(D) = (W)
-#define setwords(D,W0,W1) (setword0(D,W0),setword1(D,W1))
-#else
-#define setword1(D,W)
-#define setwords(D,W0,W1) (setword0(D,W0))
-#endif
-#define addword0(D,X) (word0(D) += (X))
-#endif
-
-/* The following definition of Storeinc is appropriate for MIPS processors. */
-#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
-#if defined(IEEE_MC68k)
-#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
-((unsigned short *)a)[1] = (unsigned short)c, a++)
-#else
-#define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
-#endif
-#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) + defined(IEEE_Unknown)
-#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)
-extern double rnd_prod(double, double), rnd_quot(double, double);
-#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
-
-#define Kmax 15
-
-/* (1<<BIGINT_MINIMUM_K) is the minimum number of words to allocate
- in a Bigint. dtoa usually manages with 1<<2, and has not been
- known to need more than 1<<3. */
-
-#define BIGINT_MINIMUM_K 3
-
-struct Bigint {
- struct Bigint *next;
- int k; /* Parameter given to Balloc(k) */
- int maxwds; /* Allocated space: equals 1<<k. */
- short on_stack; /* 1 if stack-allocated. */
- short sign; /* 0 if value is positive or zero; 1 if negative. */
- int wds; /* Current length. */
- unsigned32 x[1<<BIGINT_MINIMUM_K]; /* Actually: x[maxwds] */
-};
-
-#define BIGINT_HEADER_SIZE \
- (sizeof(Bigint) - (1<<BIGINT_MINIMUM_K) * sizeof(unsigned32))
-
-typedef struct Bigint Bigint;
-
-/* Initialize a stack-allocated Bigint. */
-
-static Bigint *
-Binit
-#ifdef KR_headers
- (v) Bigint *v;
-#else
- (Bigint *v)
-#endif
-{
- v->on_stack = 1;
- v->k = BIGINT_MINIMUM_K;
- v->maxwds = 1 << BIGINT_MINIMUM_K;
- v->sign = v->wds = 0;
- return v;
-}
-
-/* Allocate a Bigint with '1<<k' big digits. */
-
-static Bigint *
-Balloc
-#ifdef KR_headers
- (k) int k;
-#else
- (int k)
-#endif
-{
- int x;
- Bigint *rv;
-
- if (k < BIGINT_MINIMUM_K)
- k = BIGINT_MINIMUM_K;
-
- x = 1 << k;
- rv = (Bigint *)
- malloc(BIGINT_HEADER_SIZE + x * sizeof(unsigned32));
- rv->k = k;
- rv->maxwds = x;
- rv->sign = rv->wds = 0;
- rv->on_stack = 0;
- return rv;
-}
-
-static void
-Bfree
-#ifdef KR_headers
- (v) Bigint *v;
-#else
- (Bigint *v)
-#endif
-{
- if (v && !v->on_stack)
- free (v);
-}
-
-static void
-Bcopy
-#ifdef KR_headers
- (x, y) Bigint *x, *y;
-#else
- (Bigint *x, Bigint *y)
-#endif
-{
- register unsigned32 *xp, *yp;
- register int i = y->wds;
- x->sign = y->sign;
- x->wds = i;
- for (xp = x->x, yp = y->x; --i >= 0; )
- *xp++ = *yp++;
-}
-
-/* Make sure b has room for at least 1<<k big digits. */
-
-static Bigint *
-Brealloc
-#ifdef KR_headers
- (b, k) Bigint *b; int k;
-#else
- (Bigint * b, int k)
-#endif
-{
- if (b == NULL)
- return Balloc(k);
- if (b->k >= k)
- return b;
- else
- {
- Bigint *rv = Balloc (k);
- Bcopy(rv, b);
- Bfree(b);
- return rv;
- }
-}
-
-/* Return b*m+a. b is modified.
- Assumption: 0xFFFF*m+a fits in 32 bits. */
-
-static Bigint *
-multadd
-#ifdef KR_headers
- (b, m, a) Bigint *b; int m, a;
-#else
- (Bigint *b, int m, int a)
-#endif
-{
- int i, wds;
- unsigned32 *x, y;
- unsigned32 xi, z;
-
- wds = b->wds;
- x = b->x;
- i = 0;
- do {
- xi = *x;
- y = (xi & 0xffff) * m + a;
- z = (xi >> 16) * m + (y >> 16);
- a = (int)(z >> 16);
- *x++ = (z << 16) + (y & 0xffff);
- }
- while(++i < wds);
- if (a) {
- if (wds >= b->maxwds)
- b = Brealloc(b, b->k+1);
- b->x[wds++] = a;
- b->wds = wds;
- }
- return b;
- }
-
-static Bigint *
-s2b
-#ifdef KR_headers
- (result, s, nd0, nd, y9)
- Bigint *result; CONST char *s; int nd0, nd; unsigned32 y9;
-#else
- (Bigint *result, CONST char *s, int nd0, int nd, unsigned32 y9)
-#endif
-{
- int i, k;
- _G_int32_t x, y;
-
- x = (nd + 8) / 9;
- for(k = 0, y = 1; x > y; y <<= 1, k++) ;
- result = Brealloc(result, k);
- result->x[0] = y9;
- result->wds = 1;
-
- i = 9;
- if (9 < nd0)
- {
- s += 9;
- do
- result = multadd(result, 10, *s++ - '0');
- while (++i < nd0);
- s++;
- }
- else
- s += 10;
- for(; i < nd; i++)
- result = multadd(result, 10, *s++ - '0');
- return result;
-}
-
-static int
-hi0bits
-#ifdef KR_headers
- (x) register unsigned32 x;
-#else
- (register unsigned32 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) unsigned32 *y;
-#else
- (unsigned32 *y)
-#endif
-{
- register int k;
- register unsigned32 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
- (result, i) Bigint *result; int i;
-#else
- (Bigint* result, int i)
-#endif
-{
- result = Brealloc(result, 1);
- result->x[0] = i;
- result->wds = 1;
- return result;
-}
-
-/* Do: c = a * b. */
-
-static Bigint *
-mult
-#ifdef KR_headers
- (c, a, b) Bigint *a, *b, *c;
-#else
- (Bigint *c, Bigint *a, Bigint *b)
-#endif
-{
- int k, wa, wb, wc;
- unsigned32 carry, y, z;
- unsigned32 *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
- unsigned32 z2;
- if (a->wds < b->wds) {
- Bigint *tmp = a;
- a = b;
- b = tmp;
- }
- k = a->k;
- wa = a->wds;
- wb = b->wds;
- wc = wa + wb;
- if (wc > a->maxwds)
- k++;
- c = Brealloc(c, 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;
- 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;
- }
- }
- for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
- c->wds = wc;
- return c;
- }
-
-/* Returns b*(5**k). b is modified. */
-/* Re-written by Per Bothner to not need a static list. */
-
-static Bigint *
-pow5mult
-#ifdef KR_headers
- (b, k) Bigint *b; int k;
-#else
- (Bigint *b, int k)
-#endif
-{
- static int p05[6] = { 5, 25, 125, 625, 3125, 15625 };
-
- for (; k > 6; k -= 6)
- b = multadd(b, 15625, 0); /* b *= 5**6 */
- if (k == 0)
- return b;
- else
- return multadd(b, p05[k-1], 0);
-}
-
-/* Re-written by Per Bothner so shift can be in place. */
-
-static Bigint *
-lshift
-#ifdef KR_headers
- (b, k) Bigint *b; int k;
-#else
- (Bigint *b, int k)
-#endif
-{
- int i;
- unsigned32 *x, *x1, *xe;
- int old_wds = b->wds;
- int n = k >> 5;
- int k1 = b->k;
- int n1 = n + old_wds + 1;
-
- if (k == 0)
- return b;
-
- for(i = b->maxwds; n1 > i; i <<= 1)
- k1++;
- b = Brealloc(b, k1);
-
- xe = b->x; /* Source limit */
- x = xe + old_wds; /* Source pointer */
- x1 = x + n; /* Destination pointer */
- if (k &= 0x1f) {
- int k1 = 32 - k;
- unsigned32 z = *--x;
- if ((*x1 = (z >> k1)) != 0) {
- ++n1;
- }
- while (x > xe) {
- unsigned32 w = *--x;
- *--x1 = (z << k) | (w >> k1);
- z = w;
- }
- *--x1 = z << k;
- }
- else
- do {
- *--x1 = *--x;
- } while(x > xe);
- while (x1 > xe)
- *--x1 = 0;
- b->wds = n1 - 1;
- return b;
-}
-
-static int
-cmp
-#ifdef KR_headers
- (a, b) Bigint *a, *b;
-#else
- (Bigint *a, Bigint *b)
-#endif
-{
- unsigned32 *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;
- }
-
-/* Do: c = a-b. */
-
-static Bigint *
-diff
-#ifdef KR_headers
- (c, a, b) Bigint *c, *a, *b;
-#else
- (Bigint *c, Bigint *a, Bigint *b)
-#endif
-{
- int i, wa, wb;
- _G_int32_t borrow, y; /* We need signed shifts here. */
- unsigned32 *xa, *xae, *xb, *xbe, *xc;
- _G_int32_t z;
-
- i = cmp(a,b);
- if (!i) {
- c = Brealloc(c, 0);
- c->wds = 1;
- c->x[0] = 0;
- return c;
- }
- if (i < 0) {
- Bigint *tmp = a;
- a = b;
- b = tmp;
- i = 1;
- }
- else
- i = 0;
- c = Brealloc(c, a->k);
- c->sign = i;
- wa = a->wds;
- xa = a->x;
- xae = xa + wa;
- wb = b->wds;
- xb = b->x;
- xbe = xb + wb;
- xc = c->x;
- borrow = 0;
- do {
- y = (*xa & 0xffff) - (*xb & 0xffff) + borrow;
- borrow = y >> 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);
- }
- while(!*--xc)
- wa--;
- c->wds = wa;
- return c;
- }
-
-static double
-ulp
-#ifdef KR_headers
- (x) double x;
-#else
- (double x)
-#endif
-{
- register _G_int32_t 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
- setwords(a, L, 0);
-#ifndef Sudden_Underflow
- }
- else {
- L = -L >> Exp_shift;
- if (L < Exp_shift)
- setwords(a, 0x80000 >> L, 0);
- else {
- L -= Exp_shift;
- setwords(a, 0, 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
-{
- unsigned32 *xa, *xa0, w, y, z;
- int k;
- double d;
- unsigned32 d0, d1;
-
- 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;
- if (k < Ebits) {
- d0 = Exp_1 | y >> (Ebits - k);
- w = xa > xa0 ? *--xa : 0;
-#ifndef _DOUBLE_IS_32BITS
- d1 = y << ((32-Ebits) + k) | w >> (Ebits - k);
-#endif
- goto ret_d;
- }
- z = xa > xa0 ? *--xa : 0;
- if (k -= Ebits) {
- d0 = Exp_1 | y << k | z >> (32 - k);
- y = xa > xa0 ? *--xa : 0;
-#ifndef _DOUBLE_IS_32BITS
- d1 = z << k | y >> (32 - k);
-#endif
- }
- else {
- d0 = Exp_1 | y;
-#ifndef _DOUBLE_IS_32BITS
- d1 = z;
-#endif
- }
- ret_d:
-#ifdef VAX
- setwords(d, d0 >> 16 | d0 << 16, d1 >> 16 | d1 << 16);
-#else
- setwords (d, d0, d1);
-#endif
- return d;
- }
-
-static Bigint *
-d2b
-#ifdef KR_headers
- (result, d, e, bits) Bigint *result; double d; _G_int32_t *e, *bits;
-#else
- (Bigint *result, double d, _G_int32_t *e, _G_int32_t *bits)
-#endif
-{
- int de, i, k;
- unsigned32 *x, y, z;
- unsigned32 d0, d1;
-#ifdef VAX
- d0 = word0(d) >> 16 | word0(d) << 16;
- d1 = word1(d) >> 16 | word1(d) << 16;
-#else
- d0 = word0(d);
- d1 = word1(d);
-#endif
-
- result = Brealloc(result, 1);
- x = result->x;
-
- z = d0 & Frac_mask;
- d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
-
- de = (int)(d0 >> Exp_shift); /* The exponent part of d. */
-
- /* Put back the suppressed high-order bit, if normalized. */
-#ifndef IBM
-#ifndef Sudden_Underflow
- if (de)
-#endif
- z |= Exp_msk11;
-#endif
-
-#ifndef _DOUBLE_IS_32BITS
- if ((y = d1)) {
- if ((k = lo0bits(&y))) {
- x[0] = y | z << (32 - k);
- z >>= k;
- }
- else
- x[0] = y;
- i = result->wds = (x[1] = z) ? 2 : 1;
- }
- else {
-#endif /* !_DOUBLE_IS_32BITS */
-#ifdef DEBUG
- if (!z)
- Bug("Zero passed to d2b");
-#endif
- k = lo0bits(&z);
- x[0] = z;
- i = result->wds = 1;
-#ifndef _DOUBLE_IS_32BITS
- k += 32;
- }
-#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;
- *bits = 32*i - hi0bits(x[i-1]);
- }
-#endif
- return result;
- }
-
-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);
- k = ka - kb + 32*(a->wds - b->wds);
-#ifdef IBM
- if (k > 0) {
- addword0(da, (k >> 2)*Exp_msk1);
- if (k &= 3)
- da *= 1 << k;
- }
- else {
- k = -k;
- addword0(db,(k >> 2)*Exp_msk1);
- if (k &= 3)
- db *= 1 << k;
- }
-#else
- if (k > 0)
- addword0(da, k*Exp_msk1);
- else {
- k = -k;
- addword0(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
-/* Also used for the case when !_DOUBLE_IS_32BITS. */
-static CONST double bigtens[] = { 1e16, 1e32 };
-static CONST double tinytens[] = { 1e-16, 1e-32 };
-#define n_bigtens 2
-#endif
-#endif
-
- double
-_IO_strtod
-#ifdef KR_headers
- (s00, se) CONST char *s00; char **se;
-#else
- (CONST char *s00, char **se)
-#endif
-{
- _G_int32_t 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;
- _G_int32_t L;
- unsigned32 y, z;
- Bigint _bb, _b_avail, _bd, _bd0, _bs, _delta;
- Bigint *bb = Binit(&_bb);
- Bigint *bd = Binit(&_bd);
- Bigint *bd0 = Binit(&_bd0);
- Bigint *bs = Binit(&_bs);
- Bigint *b_avail = Binit(&_b_avail);
- Bigint *delta = Binit(&_delta);
-
- TEST_ENDIANNESS;
- sign = nz0 = nz = 0;
- rv = 0.;
- (void)&rv; /* Force rv into the stack */
- for(s = s00;;s++) switch(*s) {
- case '-':
- sign = 1;
- /* no break */
- case '+':
- if (*++s)
- goto break2;
- /* no break */
- case 0:
- /* "+" and "-" should be reported as an error? */
- sign = 0;
- s = s00;
- goto ret;
- case '\t':
- case '\n':
- case '\v':
- case '\f':
- case '\r':
- case ' ':
- continue;
- default:
- 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;
- if (c == '.') {
- 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') {
- e = c - '0';
- s1 = s;
- while((c = *++s) >= '0' && c <= '9')
- e = 10*e + c - '0';
- if (s - s1 > 8)
- /* Avoid confusion from exponents
- * so large that e might overflow.
- */
- e = 9999999;
- 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:
- addword0(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;
- addword0(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;
-#if defined(sun) && !defined(__svr4__)
-/* SunOS defines HUGE_VAL as __infinity(), which is in libm. */
-#undef HUGE_VAL
-#endif
-#ifndef HUGE_VAL
-#define HUGE_VAL 1.7976931348623157E+308
-#endif
- rv = HUGE_VAL;
- goto ret;
- }
- if (e1 >>= 4) {
- for(j = 0; e1 > 1; j++, e1 >>= 1)
- if (e1 & 1)
- rv *= bigtens[j];
- /* The last multiplication could overflow. */
- addword0(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) */
- setwords(rv, Big0, Big1);
- }
- else
- addword0(rv, P*Exp_msk1);
- }
-
- }
- }
- else if (e1 < 0) {
- e1 = -e1;
- if ((i = e1 & 15))
- rv /= tens[i];
- if (e1 &= ~15) {
- 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;
- }
- setwords(rv, Tiny0, 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(bd0, s0, nd0, nd, y);
- bd = Brealloc(bd, bd0->k);
-
- for(;;) {
- Bcopy(bd, bd0);
- bb = d2b(bb, rv, &bbe, &bbbits); /* rv = bb * 2^bbe */
- bs = i2b(bs, 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) {
- Bigint *b_tmp;
- bs = pow5mult(bs, bb5);
- b_tmp = mult(b_avail, bs, bb);
- b_avail = bb;
- bb = b_tmp;
- }
- 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(delta, 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*/
- setword0(rv, (word0(rv) & Exp_mask)
- + Exp_msk1);
-#ifdef IBM
- setword0 (rv,
- word0(rv) | (Exp_msk1 >> 4));
-#endif
- setword1(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
- setwords(rv, L | Bndry_mask1, 0xffffffff);
-#ifdef IBM
- continue;
-#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;
- addword0(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;
- setwords(rv, Big0, Big1);
- continue;
- }
- else
- addword0(rv, P*Exp_msk1);
- }
- else {
-#ifdef Sudden_Underflow
- if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
- rv0 = rv;
- addword0(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;
- setwords(rv, Tiny0, Tiny1);
- continue;
- }
- else
- addword0(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 = (_G_int32_t)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;
- }
- }
- Bfree(bb);
- Bfree(bd);
- Bfree(bs);
- Bfree(bd0);
- Bfree(delta);
- Bfree(b_avail);
- 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;
- _G_int32_t borrow, y;
- unsigned32 carry, q, ys;
- unsigned32 *bx, *bxe, *sx, *sxe;
- _G_int32_t z;
- unsigned32 si, zs;
-
- 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 {
- 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);
- }
- while(sx <= sxe);
- if (!*bxe) {
- bx = b->x;
- while(--bxe > bx && !*bxe)
- --n;
- b->wds = n;
- }
- }
- if (cmp(b, S) >= 0) {
- q++;
- borrow = 0;
- carry = 0;
- bx = b->x;
- sx = S->x;
- do {
- si = *sx++;
- ys = (si & 0xffff) + carry;
- zs = (si >> 16) + (ys >> 16);
- carry = zs >> 16;
- y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
- borrow = y >> 16;
- Sign_Extend(borrow, y);
- z = (*bx >> 16) - (zs & 0xffff) + borrow;
- borrow = z >> 16;
- Sign_Extend(borrow, z);
- Storeinc(bx, z, y);
- }
- while(sx <= sxe);
- bx = b->x;
- bxe = bx + n;
- if (!*bxe) {
- while(--bxe > bx && !*bxe)
- --n;
- b->wds = n;
- }
- }
- return q;
- }
-
-/* 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 *
-_IO_dtoa
-#ifdef KR_headers
- (d, mode, ndigits, decpt, sign, rve)
- double d; int mode, ndigits, *decpt, *sign; char **rve;
-#else
- (double d, int mode, int ndigits, int *decpt, int *sign, char **rve)
-#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.
- */
-
- _G_int32_t 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;
- _G_int32_t L;
-#ifndef Sudden_Underflow
- int denorm;
-#endif
- Bigint _b_avail, _b, _mhi, _mlo, _S;
- Bigint *b_avail = Binit(&_b_avail);
- Bigint *b = Binit(&_b);
- Bigint *S = Binit(&_S);
- /* mhi and mlo are only set and used if leftright. */
- Bigint *mhi = NULL, *mlo = NULL;
- double d2, ds, eps;
- char *s, *s0;
- static Bigint *result = NULL;
- static int result_k;
-
- TEST_ENDIANNESS;
- if (result) {
- /* result is contains a string, so its fields (interpreted
- as a Bigint have been trashed. Restore them.
- This is a really ugly interface - result should
- not be static, since that is not thread-safe. FIXME. */
- result->k = result_k;
- result->maxwds = 1 << result_k;
- result->on_stack = 0;
- }
-
- if (word0(d) & Sign_bit) {
- /* set sign for everything, including 0's and NaNs */
- *sign = 1;
- setword0(d, 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;
-#ifdef IEEE_Arith
- if (!word1(d) && !(word0(d) & 0xfffff))
- {
- s = "Infinity";
- if (rve)
- *rve = s + 8;
- }
- else
-#endif
- {
- s = "NaN";
- if (rve)
- *rve = 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(b, d, &be, &bbits);
- i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
-#ifndef Sudden_Underflow
- if (i) {
-#endif
- d2 = d;
- setword0(d2, (word0(d2) & Frac_mask1) | Exp_11);
-#ifdef IBM
- if (j = 11 - hi0bits(word0(d2) & Frac_mask))
- d2 /= 1 << j;
-#endif
-
- i -= Bias;
-#ifdef IBM
- i <<= 2;
- i += j;
-#endif
-#ifndef Sudden_Underflow
- denorm = 0;
- }
- else {
- /* d is denormalized */
- unsigned32 x;
-
- i = bbits + be + (Bias + (P-1) - 1);
- x = i > 32 ? word0(d) << (64 - i) | word1(d) >> (i - 32)
- : word1(d) << (32 - i);
- d2 = x;
- addword0(d2, - 31*Exp_msk1); /* adjust exponent */
- i -= (Bias + (P-1) - 1) + 1;
- denorm = 1;
- }
-#endif
-
- /* Now i is the unbiased base-2 exponent. */
-
- /* 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*log(2)/log(10) + log10(d2)
- *
- * This suggests computing an approximation k to log10(d) by
- *
- * k = i*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) by 0.301029995663981; since |i| <= 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.)
- */
-
- 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;
- }
- /* i is now an upper bound of the number of digits to generate. */
- j = sizeof(unsigned32) * (1<<BIGINT_MINIMUM_K);
- /* The test is <= so as to allow room for the final '\0'. */
- for(result_k = BIGINT_MINIMUM_K; BIGINT_HEADER_SIZE + j <= i;
- j <<= 1) result_k++;
- if (!result || result_k > result->k)
- {
- Bfree (result);
- result = Balloc(result_k);
- }
- s = s0 = (char *)result;
-
- 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.;
- addword0(eps, - (P-1)*Exp_msk1);
- if (ilim == 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 = (_G_int32_t)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 = (_G_int32_t)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) {
- if (ilim < 0 || d <= 5*ds)
- goto no_digits;
- goto one_digit;
- }
- for(i = 1;; i++) {
- L = (_G_int32_t)(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;
- 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(Binit(&_mhi), 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) {
- Bigint *b_tmp;
- mhi = pow5mult(mhi, m5);
- b_tmp = mult(b_avail, mhi, b);
- b_avail = b;
- b = b_tmp;
- }
- if ((j = b5 - m5))
- b = pow5mult(b, j);
- }
- else
- b = pow5mult(b, b5);
- }
- S = i2b(S, 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.
- */
- if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f))
- i = 32 - i;
- if (i > 4) {
- i -= 4;
- b2 += i;
- m2 += i;
- s2 += i;
- }
- else if (i < 4) {
- i += 28;
- b2 += i;
- m2 += i;
- s2 += i;
- }
- if (b2 > 0)
- b = lshift(b, b2);
- if (s2 > 0)
- S = lshift(S, s2);
- if (k_check) {
- if (cmp(b,S) < 0) {
- k--;
- b = multadd(b, 10, 0); /* we botched the k estimate */
- if (leftright)
- mhi = multadd(mhi, 10, 0);
- ilim = ilim1;
- }
- }
- if (ilim <= 0 && mode > 2) {
- if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
- /* no digits, fcvt style */
- no_digits:
- k = -1 - ndigits;
- goto ret;
- }
- one_digit:
- *s++ = '1';
- k++;
- goto ret;
- }
- if (leftright) {
- if (m2 > 0)
- mhi = lshift(mhi, m2);
-
- /* Compute mlo -- check for special case
- * that d is a normalized power of 2.
- */
-
- if (spec_case) {
- mlo = Brealloc(Binit(&_mlo), mhi->k);
- Bcopy(mlo, mhi);
- mhi = lshift(mhi, Log2P);
- }
- else
- mlo = mhi;
-
- 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);
- b_avail = diff(b_avail, S, mhi); /* b_avail = S - mi */
- j1 = b_avail->sign ? 1 : cmp(b, b_avail);
-#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(b_avail);
- Bfree(S);
- if (mhi) {
- if (mlo && mlo != mhi)
- Bfree(mlo);
- Bfree(mhi);
- }
- ret1:
- Bfree(b);
- *s = 0;
- *decpt = k + 1;
- if (rve)
- *rve = s;
- return s0;
- }
-#endif /* _IO_USE_DTOA */
generated by cgit v1.2.3 (git 2.25.1) at 2025-10-31 18:05:34 +0000