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-rw-r--r--libio/floatconv.c2375
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diff --git a/libio/floatconv.c b/libio/floatconv.c
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--- /dev/null
+++ b/libio/floatconv.c
@@ -0,0 +1,2375 @@
+/*
+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 2024-07-18 16:29:37 +0000