Add FreeBSD strtod
authorMiguel de Icaza <miguel@gnome.org>
Mon, 13 May 2002 22:43:03 +0000 (22:43 -0000)
committerMiguel de Icaza <miguel@gnome.org>
Mon, 13 May 2002 22:43:03 +0000 (22:43 -0000)
svn path=/trunk/mono/; revision=4611

mono/utils/Makefile.am
mono/utils/strtod.c [new file with mode: 0644]
mono/utils/strtod.h [new file with mode: 0644]

index 5851b34b28e7635b32fbc0625dfe28d9296a1244..a25980c22bd45afdee2d2deabae481a1ba57f795 100644 (file)
@@ -6,7 +6,8 @@ libmonoutils_a_SOURCES = \
        mono-hash.c     \
        mono-hash.h     \
        monobitset.h    \
-       monobitset.c
+       monobitset.c    \
+       strtod.c
 
 libmonoutilsincludedir = $(includedir)/mono/utils
 
diff --git a/mono/utils/strtod.c b/mono/utils/strtod.c
new file mode 100644 (file)
index 0000000..437a704
--- /dev/null
@@ -0,0 +1,2443 @@
+/*
+ * This strtod has been modified to not use values from the locale,
+ * but to hardcode the `.' as the separator.  Our class libraries will
+ * make sure that only the dot is passed.
+ *
+ * This is so we do not call `setlocale' from our runtime before doing
+ * a strtod, because this could have unwanted effects in code that is
+ * co-hosted with the Mono runtime
+ *
+ * The entry point has been renamed `bsd_strtod'.
+ *
+ * Taken from the FreeBSD distribution.
+ */
+#include "strtod.h"
+
+/*-
+ * Copyright (c) 1993
+ *     The Regents of the University of California.  All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *     This product includes software developed by the University of
+ *     California, Berkeley and its contributors.
+ * 4. Neither the name of the University nor the names of its contributors
+ *    may be used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ *
+ * $FreeBSD: src/lib/libc/stdlib/strtod.c,v 1.3.8.3 2002/04/17 12:01:21 ache Exp $
+ */
+
+#if defined(LIBC_SCCS) && !defined(lint)
+static char sccsid[] = "@(#)strtod.c   8.1 (Berkeley) 6/4/93";
+#endif /* LIBC_SCCS and not lint */
+
+/****************************************************************
+ *
+ * The author of this software is David M. Gay.
+ *
+ * Copyright (c) 1991 by AT&T.
+ *
+ * Permission to use, copy, modify, and distribute this software for any
+ * purpose without fee is hereby granted, provided that this entire notice
+ * is included in all copies of any software which is or includes a copy
+ * or modification of this software and in all copies of the supporting
+ * documentation for such software.
+ *
+ * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
+ * WARRANTY.  IN PARTICULAR, NEITHER THE AUTHOR NOR AT&T MAKES ANY
+ * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
+ * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
+ *
+ ***************************************************************/
+
+/* Please send bug reports to
+       David M. Gay
+       AT&T Bell Laboratories, Room 2C-463
+       600 Mountain Avenue
+       Murray Hill, NJ 07974-2070
+       U.S.A.
+       dmg@research.att.com or research!dmg
+ */
+
+/* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
+ *
+ * This strtod returns a nearest machine number to the input decimal
+ * string (or sets errno to ERANGE).  With IEEE arithmetic, ties are
+ * broken by the IEEE round-even rule.  Otherwise ties are broken by
+ * biased rounding (add half and chop).
+ *
+ * Inspired loosely by William D. Clinger's paper "How to Read Floating
+ * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
+ *
+ * Modifications:
+ *
+ *     1. We only require IEEE, IBM, or VAX double-precision
+ *             arithmetic (not IEEE double-extended).
+ *     2. We get by with floating-point arithmetic in a case that
+ *             Clinger missed -- when we're computing d * 10^n
+ *             for a small integer d and the integer n is not too
+ *             much larger than 22 (the maximum integer k for which
+ *             we can represent 10^k exactly), we may be able to
+ *             compute (d*10^k) * 10^(e-k) with just one roundoff.
+ *     3. Rather than a bit-at-a-time adjustment of the binary
+ *             result in the hard case, we use floating-point
+ *             arithmetic to determine the adjustment to within
+ *             one bit; only in really hard cases do we need to
+ *             compute a second residual.
+ *     4. Because of 3., we don't need a large table of powers of 10
+ *             for ten-to-e (just some small tables, e.g. of 10^k
+ *             for 0 <= k <= 22).
+ */
+
+/*
+ * #define IEEE_8087 for IEEE-arithmetic machines where the least
+ *     significant byte has the lowest address.
+ * #define IEEE_MC68k for IEEE-arithmetic machines where the most
+ *     significant byte has the lowest address.
+ * #define Sudden_Underflow for IEEE-format machines without gradual
+ *     underflow (i.e., that flush to zero on underflow).
+ * #define IBM for IBM mainframe-style floating-point arithmetic.
+ * #define VAX for VAX-style floating-point arithmetic.
+ * #define Unsigned_Shifts if >> does treats its left operand as unsigned.
+ * #define No_leftright to omit left-right logic in fast floating-point
+ *     computation of dtoa.
+ * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3.
+ * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
+ *     that use extended-precision instructions to compute rounded
+ *     products and quotients) with IBM.
+ * #define ROUND_BIASED for IEEE-format with biased rounding.
+ * #define Inaccurate_Divide for IEEE-format with correctly rounded
+ *     products but inaccurate quotients, e.g., for Intel i860.
+ * #define Just_16 to store 16 bits per 32-bit long when doing high-precision
+ *     integer arithmetic.  Whether this speeds things up or slows things
+ *     down depends on the machine and the number being converted.
+ * #define KR_headers for old-style C function headers.
+ * #define Bad_float_h if your system lacks a float.h or if it does not
+ *     define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
+ *     FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
+ */
+
+#if defined(i386) || defined(mips) && defined(MIPSEL)
+#define IEEE_8087
+#else
+#define IEEE_MC68k
+#endif
+
+#ifdef DEBUG
+#include "stdio.h"
+#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
+#endif
+
+#include <locale.h>
+#ifdef __cplusplus
+#include "malloc.h"
+#include "memory.h"
+#else
+#ifndef KR_headers
+#include "stdlib.h"
+#include "string.h"
+#else
+#include "malloc.h"
+#include "memory.h"
+#endif
+#endif
+
+#include "errno.h"
+#include <ctype.h>
+#ifdef Bad_float_h
+#undef __STDC__
+#ifdef IEEE_MC68k
+#define IEEE_ARITHMETIC
+#endif
+#ifdef IEEE_8087
+#define IEEE_ARITHMETIC
+#endif
+#ifdef IEEE_ARITHMETIC
+#define DBL_DIG 15
+#define DBL_MAX_10_EXP 308
+#define DBL_MAX_EXP 1024
+#define FLT_RADIX 2
+#define FLT_ROUNDS 1
+#define DBL_MAX 1.7976931348623157e+308
+#endif
+
+#ifdef IBM
+#define DBL_DIG 16
+#define DBL_MAX_10_EXP 75
+#define DBL_MAX_EXP 63
+#define FLT_RADIX 16
+#define FLT_ROUNDS 0
+#define DBL_MAX 7.2370055773322621e+75
+#endif
+
+#ifdef VAX
+#define DBL_DIG 16
+#define DBL_MAX_10_EXP 38
+#define DBL_MAX_EXP 127
+#define FLT_RADIX 2
+#define FLT_ROUNDS 1
+#define DBL_MAX 1.7014118346046923e+38
+#endif
+
+#ifndef LONG_MAX
+#define LONG_MAX 2147483647
+#endif
+#else
+#include "float.h"
+#endif
+#ifndef __MATH_H__
+#include "math.h"
+#endif
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#ifndef CONST
+#ifdef KR_headers
+#define CONST /* blank */
+#else
+#define CONST const
+#endif
+#endif
+
+#ifdef Unsigned_Shifts
+#define Sign_Extend(a,b) if (b < 0) a |= 0xffff0000;
+#else
+#define Sign_Extend(a,b) /*no-op*/
+#endif
+
+#if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
+Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
+#endif
+
+#ifdef IEEE_8087
+#define word0(x) ((unsigned long *)&x)[1]
+#define word1(x) ((unsigned long *)&x)[0]
+#else
+#define word0(x) ((unsigned long *)&x)[0]
+#define word1(x) ((unsigned long *)&x)[1]
+#endif
+
+/* The following definition of Storeinc is appropriate for MIPS processors.
+ * An alternative that might be better on some machines is
+ * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
+ */
+#if defined(IEEE_8087) + defined(VAX)
+#define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
+((unsigned short *)a)[0] = (unsigned short)c, a++)
+#else
+#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
+((unsigned short *)a)[1] = (unsigned short)c, a++)
+#endif
+
+/* #define P DBL_MANT_DIG */
+/* Ten_pmax = floor(P*log(2)/log(5)) */
+/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
+/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
+/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
+
+#if defined(IEEE_8087) + defined(IEEE_MC68k)
+#define Exp_shift  20
+#define Exp_shift1 20
+#define Exp_msk1    0x100000
+#define Exp_msk11   0x100000
+#define Exp_mask  0x7ff00000
+#define P 53
+#define Bias 1023
+#define IEEE_Arith
+#define Emin (-1022)
+#define Exp_1  0x3ff00000
+#define Exp_11 0x3ff00000
+#define Ebits 11
+#define Frac_mask  0xfffff
+#define Frac_mask1 0xfffff
+#define Ten_pmax 22
+#define Bletch 0x10
+#define Bndry_mask  0xfffff
+#define Bndry_mask1 0xfffff
+#define LSB 1
+#define Sign_bit 0x80000000
+#define Log2P 1
+#define Tiny0 0
+#define Tiny1 1
+#define Quick_max 14
+#define Int_max 14
+#define Infinite(x) (word0(x) == 0x7ff00000) /* sufficient test for here */
+#else
+#undef  Sudden_Underflow
+#define Sudden_Underflow
+#ifdef IBM
+#define Exp_shift  24
+#define Exp_shift1 24
+#define Exp_msk1   0x1000000
+#define Exp_msk11  0x1000000
+#define Exp_mask  0x7f000000
+#define P 14
+#define Bias 65
+#define Exp_1  0x41000000
+#define Exp_11 0x41000000
+#define Ebits 8        /* exponent has 7 bits, but 8 is the right value in b2d */
+#define Frac_mask  0xffffff
+#define Frac_mask1 0xffffff
+#define Bletch 4
+#define Ten_pmax 22
+#define Bndry_mask  0xefffff
+#define Bndry_mask1 0xffffff
+#define LSB 1
+#define Sign_bit 0x80000000
+#define Log2P 4
+#define Tiny0 0x100000
+#define Tiny1 0
+#define Quick_max 14
+#define Int_max 15
+#else /* VAX */
+#define Exp_shift  23
+#define Exp_shift1 7
+#define Exp_msk1    0x80
+#define Exp_msk11   0x800000
+#define Exp_mask  0x7f80
+#define P 56
+#define Bias 129
+#define Exp_1  0x40800000
+#define Exp_11 0x4080
+#define Ebits 8
+#define Frac_mask  0x7fffff
+#define Frac_mask1 0xffff007f
+#define Ten_pmax 24
+#define Bletch 2
+#define Bndry_mask  0xffff007f
+#define Bndry_mask1 0xffff007f
+#define LSB 0x10000
+#define Sign_bit 0x8000
+#define Log2P 1
+#define Tiny0 0x80
+#define Tiny1 0
+#define Quick_max 15
+#define Int_max 15
+#endif
+#endif
+
+#ifndef IEEE_Arith
+#define ROUND_BIASED
+#endif
+
+#ifdef RND_PRODQUOT
+#define rounded_product(a,b) a = rnd_prod(a, b)
+#define rounded_quotient(a,b) a = rnd_quot(a, b)
+#ifdef KR_headers
+extern double rnd_prod(), rnd_quot();
+#else
+extern double rnd_prod(double, double), rnd_quot(double, double);
+#endif
+#else
+#define rounded_product(a,b) a *= b
+#define rounded_quotient(a,b) a /= b
+#endif
+
+#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
+#define Big1 0xffffffff
+
+#ifndef Just_16
+/* When Pack_32 is not defined, we store 16 bits per 32-bit long.
+ * This makes some inner loops simpler and sometimes saves work
+ * during multiplications, but it often seems to make things slightly
+ * slower.  Hence the default is now to store 32 bits per long.
+ */
+#ifndef Pack_32
+#define Pack_32
+#endif
+#endif
+
+#define Kmax 15
+
+#ifdef __cplusplus
+extern "C" double bsd_strtod(const char *s00, char **se);
+extern "C" char *__dtoa(double d, int mode, int ndigits,
+                       int *decpt, int *sign, char **rve, char **resultp);
+#endif
+
+ struct
+Bigint {
+       struct Bigint *next;
+       int k, maxwds, sign, wds;
+       unsigned long x[1];
+};
+
+ typedef struct Bigint Bigint;
+
+ static Bigint *
+Balloc
+#ifdef KR_headers
+       (k) int k;
+#else
+       (int k)
+#endif
+{
+       int x;
+       Bigint *rv;
+
+       x = 1 << k;
+       rv = (Bigint *)malloc(sizeof(Bigint) + (x-1)*sizeof(long));
+       rv->k = k;
+       rv->maxwds = x;
+       rv->sign = rv->wds = 0;
+       return rv;
+}
+
+ static void
+Bfree
+#ifdef KR_headers
+       (v) Bigint *v;
+#else
+       (Bigint *v)
+#endif
+{
+       free(v);
+}
+
+#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
+y->wds*sizeof(long) + 2*sizeof(int))
+
+ static Bigint *
+multadd
+#ifdef KR_headers
+       (b, m, a) Bigint *b; int m, a;
+#else
+       (Bigint *b, int m, int a)       /* multiply by m and add a */
+#endif
+{
+       int i, wds;
+       unsigned long *x, y;
+#ifdef Pack_32
+       unsigned long xi, z;
+#endif
+       Bigint *b1;
+
+       wds = b->wds;
+       x = b->x;
+       i = 0;
+       do {
+#ifdef Pack_32
+               xi = *x;
+               y = (xi & 0xffff) * m + a;
+               z = (xi >> 16) * m + (y >> 16);
+               a = (int)(z >> 16);
+               *x++ = (z << 16) + (y & 0xffff);
+#else
+               y = *x * m + a;
+               a = (int)(y >> 16);
+               *x++ = y & 0xffff;
+#endif
+       } while (++i < wds);
+       if (a) {
+               if (wds >= b->maxwds) {
+                       b1 = Balloc(b->k+1);
+                       Bcopy(b1, b);
+                       Bfree(b);
+                       b = b1;
+                       }
+               b->x[wds++] = a;
+               b->wds = wds;
+       }
+       return b;
+}
+
+ static Bigint *
+s2b
+#ifdef KR_headers
+       (s, nd0, nd, y9) CONST char *s; int nd0, nd; unsigned long y9;
+#else
+       (CONST char *s, int nd0, int nd, unsigned long y9)
+#endif
+{
+       Bigint *b;
+       int i, k;
+       long x, y;
+
+       x = (nd + 8) / 9;
+       for (k = 0, y = 1; x > y; y <<= 1, k++) ;
+#ifdef Pack_32
+       b = Balloc(k);
+       b->x[0] = y9;
+       b->wds = 1;
+#else
+       b = Balloc(k+1);
+       b->x[0] = y9 & 0xffff;
+       b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
+#endif
+
+       i = 9;
+       if (9 < nd0) {
+               s += 9;
+               do
+                       b = multadd(b, 10, *s++ - '0');
+               while (++i < nd0);
+               s++;
+       } else
+               s += 10;
+       for (; i < nd; i++)
+               b = multadd(b, 10, *s++ - '0');
+       return b;
+}
+
+ static int
+hi0bits
+#ifdef KR_headers
+       (x) register unsigned long x;
+#else
+       (register unsigned long x)
+#endif
+{
+       register int k = 0;
+
+       if (!(x & 0xffff0000)) {
+               k = 16;
+               x <<= 16;
+       }
+       if (!(x & 0xff000000)) {
+               k += 8;
+               x <<= 8;
+       }
+       if (!(x & 0xf0000000)) {
+               k += 4;
+               x <<= 4;
+       }
+       if (!(x & 0xc0000000)) {
+               k += 2;
+               x <<= 2;
+       }
+       if (!(x & 0x80000000)) {
+               k++;
+               if (!(x & 0x40000000))
+                       return 32;
+       }
+       return k;
+}
+
+ static int
+lo0bits
+#ifdef KR_headers
+       (y) unsigned long *y;
+#else
+       (unsigned long *y)
+#endif
+{
+       register int k;
+       register unsigned long x = *y;
+
+       if (x & 7) {
+               if (x & 1)
+                       return 0;
+               if (x & 2) {
+                       *y = x >> 1;
+                       return 1;
+               }
+               *y = x >> 2;
+               return 2;
+       }
+       k = 0;
+       if (!(x & 0xffff)) {
+               k = 16;
+               x >>= 16;
+       }
+       if (!(x & 0xff)) {
+               k += 8;
+               x >>= 8;
+       }
+       if (!(x & 0xf)) {
+               k += 4;
+               x >>= 4;
+       }
+       if (!(x & 0x3)) {
+               k += 2;
+               x >>= 2;
+       }
+       if (!(x & 1)) {
+               k++;
+               x >>= 1;
+               if (!x & 1)
+                       return 32;
+       }
+       *y = x;
+       return k;
+}
+
+ static Bigint *
+i2b
+#ifdef KR_headers
+       (i) int i;
+#else
+       (int i)
+#endif
+{
+       Bigint *b;
+
+       b = Balloc(1);
+       b->x[0] = i;
+       b->wds = 1;
+       return b;
+       }
+
+ static Bigint *
+mult
+#ifdef KR_headers
+       (a, b) Bigint *a, *b;
+#else
+       (Bigint *a, Bigint *b)
+#endif
+{
+       Bigint *c;
+       int k, wa, wb, wc;
+       unsigned long carry, y, z;
+       unsigned long *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
+#ifdef Pack_32
+       unsigned long z2;
+#endif
+
+       if (a->wds < b->wds) {
+               c = a;
+               a = b;
+               b = c;
+       }
+       k = a->k;
+       wa = a->wds;
+       wb = b->wds;
+       wc = wa + wb;
+       if (wc > a->maxwds)
+               k++;
+       c = Balloc(k);
+       for (x = c->x, xa = x + wc; x < xa; x++)
+               *x = 0;
+       xa = a->x;
+       xae = xa + wa;
+       xb = b->x;
+       xbe = xb + wb;
+       xc0 = c->x;
+#ifdef Pack_32
+       for (; xb < xbe; xb++, xc0++) {
+               if ( (y = *xb & 0xffff) ) {
+                       x = xa;
+                       xc = xc0;
+                       carry = 0;
+                       do {
+                               z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
+                               carry = z >> 16;
+                               z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
+                               carry = z2 >> 16;
+                               Storeinc(xc, z2, z);
+                       } while (x < xae);
+                       *xc = carry;
+               }
+               if ( (y = *xb >> 16) ) {
+                       x = xa;
+                       xc = xc0;
+                       carry = 0;
+                       z2 = *xc;
+                       do {
+                               z = (*x & 0xffff) * y + (*xc >> 16) + carry;
+                               carry = z >> 16;
+                               Storeinc(xc, z, z2);
+                               z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
+                               carry = z2 >> 16;
+                       } while (x < xae);
+                       *xc = z2;
+               }
+       }
+#else
+       for (; xb < xbe; xc0++) {
+               if (y = *xb++) {
+                       x = xa;
+                       xc = xc0;
+                       carry = 0;
+                       do {
+                               z = *x++ * y + *xc + carry;
+                               carry = z >> 16;
+                               *xc++ = z & 0xffff;
+                       } while (x < xae);
+                       *xc = carry;
+               }
+       }
+#endif
+       for (xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
+       c->wds = wc;
+       return c;
+}
+
+ static Bigint *p5s;
+
+ static Bigint *
+pow5mult
+#ifdef KR_headers
+       (b, k) Bigint *b; int k;
+#else
+       (Bigint *b, int k)
+#endif
+{
+       Bigint *b1, *p5, *p51;
+       int i;
+       static int p05[3] = { 5, 25, 125 };
+
+       if ( (i = k & 3) )
+               b = multadd(b, p05[i-1], 0);
+
+       if (!(k >>= 2))
+               return b;
+       if (!(p5 = p5s)) {
+               /* first time */
+               p5 = p5s = i2b(625);
+               p5->next = 0;
+       }
+       for (;;) {
+               if (k & 1) {
+                       b1 = mult(b, p5);
+                       Bfree(b);
+                       b = b1;
+               }
+               if (!(k >>= 1))
+                       break;
+               if (!(p51 = p5->next)) {
+                       p51 = p5->next = mult(p5,p5);
+                       p51->next = 0;
+               }
+               p5 = p51;
+       }
+       return b;
+}
+
+ static Bigint *
+lshift
+#ifdef KR_headers
+       (b, k) Bigint *b; int k;
+#else
+       (Bigint *b, int k)
+#endif
+{
+       int i, k1, n, n1;
+       Bigint *b1;
+       unsigned long *x, *x1, *xe, z;
+
+#ifdef Pack_32
+       n = k >> 5;
+#else
+       n = k >> 4;
+#endif
+       k1 = b->k;
+       n1 = n + b->wds + 1;
+       for (i = b->maxwds; n1 > i; i <<= 1)
+               k1++;
+       b1 = Balloc(k1);
+       x1 = b1->x;
+       for (i = 0; i < n; i++)
+               *x1++ = 0;
+       x = b->x;
+       xe = x + b->wds;
+#ifdef Pack_32
+       if (k &= 0x1f) {
+               k1 = 32 - k;
+               z = 0;
+               do {
+                       *x1++ = *x << k | z;
+                       z = *x++ >> k1;
+               } while (x < xe);
+               if ( (*x1 = z) )
+                       ++n1;
+       }
+#else
+       if (k &= 0xf) {
+               k1 = 16 - k;
+               z = 0;
+               do {
+                       *x1++ = *x << k  & 0xffff | z;
+                       z = *x++ >> k1;
+               } while (x < xe);
+               if (*x1 = z)
+                       ++n1;
+       }
+#endif
+       else
+               do
+                       *x1++ = *x++;
+               while (x < xe);
+       b1->wds = n1 - 1;
+       Bfree(b);
+       return b1;
+}
+
+ static int
+cmp
+#ifdef KR_headers
+       (a, b) Bigint *a, *b;
+#else
+       (Bigint *a, Bigint *b)
+#endif
+{
+       unsigned long *xa, *xa0, *xb, *xb0;
+       int i, j;
+
+       i = a->wds;
+       j = b->wds;
+#ifdef DEBUG
+       if (i > 1 && !a->x[i-1])
+               Bug("cmp called with a->x[a->wds-1] == 0");
+       if (j > 1 && !b->x[j-1])
+               Bug("cmp called with b->x[b->wds-1] == 0");
+#endif
+       if (i -= j)
+               return i;
+       xa0 = a->x;
+       xa = xa0 + j;
+       xb0 = b->x;
+       xb = xb0 + j;
+       for (;;) {
+               if (*--xa != *--xb)
+                       return *xa < *xb ? -1 : 1;
+               if (xa <= xa0)
+                       break;
+       }
+       return 0;
+}
+
+ static Bigint *
+diff
+#ifdef KR_headers
+       (a, b) Bigint *a, *b;
+#else
+       (Bigint *a, Bigint *b)
+#endif
+{
+       Bigint *c;
+       int i, wa, wb;
+       long borrow, y; /* We need signed shifts here. */
+       unsigned long *xa, *xae, *xb, *xbe, *xc;
+#ifdef Pack_32
+       long z;
+#endif
+
+       i = cmp(a,b);
+       if (!i) {
+               c = Balloc(0);
+               c->wds = 1;
+               c->x[0] = 0;
+               return c;
+       }
+       if (i < 0) {
+               c = a;
+               a = b;
+               b = c;
+               i = 1;
+       } else
+               i = 0;
+       c = Balloc(a->k);
+       c->sign = i;
+       wa = a->wds;
+       xa = a->x;
+       xae = xa + wa;
+       wb = b->wds;
+       xb = b->x;
+       xbe = xb + wb;
+       xc = c->x;
+       borrow = 0;
+#ifdef Pack_32
+       do {
+               y = (*xa & 0xffff) - (*xb & 0xffff) + borrow;
+               borrow = y >> 16;
+               Sign_Extend(borrow, y);
+               z = (*xa++ >> 16) - (*xb++ >> 16) + borrow;
+               borrow = z >> 16;
+               Sign_Extend(borrow, z);
+               Storeinc(xc, z, y);
+       } while (xb < xbe);
+       while (xa < xae) {
+               y = (*xa & 0xffff) + borrow;
+               borrow = y >> 16;
+               Sign_Extend(borrow, y);
+               z = (*xa++ >> 16) + borrow;
+               borrow = z >> 16;
+               Sign_Extend(borrow, z);
+               Storeinc(xc, z, y);
+       }
+#else
+       do {
+               y = *xa++ - *xb++ + borrow;
+               borrow = y >> 16;
+               Sign_Extend(borrow, y);
+               *xc++ = y & 0xffff;
+       } while (xb < xbe);
+       while (xa < xae) {
+               y = *xa++ + borrow;
+               borrow = y >> 16;
+               Sign_Extend(borrow, y);
+               *xc++ = y & 0xffff;
+       }
+#endif
+       while (!*--xc)
+               wa--;
+       c->wds = wa;
+       return c;
+}
+
+ static double
+ulp
+#ifdef KR_headers
+       (x) double x;
+#else
+       (double x)
+#endif
+{
+       register long L;
+       double a;
+
+       L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
+#ifndef Sudden_Underflow
+       if (L > 0) {
+#endif
+#ifdef IBM
+               L |= Exp_msk1 >> 4;
+#endif
+               word0(a) = L;
+               word1(a) = 0;
+#ifndef Sudden_Underflow
+       } else {
+               L = -L >> Exp_shift;
+               if (L < Exp_shift) {
+                       word0(a) = 0x80000 >> L;
+                       word1(a) = 0;
+               } else {
+                       word0(a) = 0;
+                       L -= Exp_shift;
+                       word1(a) = L >= 31 ? 1 : 1 << (31 - L);
+               }
+       }
+#endif
+       return a;
+}
+
+ static double
+b2d
+#ifdef KR_headers
+       (a, e) Bigint *a; int *e;
+#else
+       (Bigint *a, int *e)
+#endif
+{
+       unsigned long *xa, *xa0, w, y, z;
+       int k;
+       double d;
+#ifdef VAX
+       unsigned long d0, d1;
+#else
+#define d0 word0(d)
+#define d1 word1(d)
+#endif
+
+       xa0 = a->x;
+       xa = xa0 + a->wds;
+       y = *--xa;
+#ifdef DEBUG
+       if (!y) Bug("zero y in b2d");
+#endif
+       k = hi0bits(y);
+       *e = 32 - k;
+#ifdef Pack_32
+       if (k < Ebits) {
+               d0 = Exp_1 | (y >> (Ebits - k));
+               w = xa > xa0 ? *--xa : 0;
+               d1 = (y << ((32-Ebits) + k)) | (w >> (Ebits - k));
+               goto ret_d;
+               }
+       z = xa > xa0 ? *--xa : 0;
+       if (k -= Ebits) {
+               d0 = Exp_1 | (y << k) | (z >> (32 - k));
+               y = xa > xa0 ? *--xa : 0;
+               d1 = (z << k) | (y >> (32 - k));
+       } else {
+               d0 = Exp_1 | y;
+               d1 = z;
+       }
+#else
+       if (k < Ebits + 16) {
+               z = xa > xa0 ? *--xa : 0;
+               d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
+               w = xa > xa0 ? *--xa : 0;
+               y = xa > xa0 ? *--xa : 0;
+               d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
+               goto ret_d;
+       }
+       z = xa > xa0 ? *--xa : 0;
+       w = xa > xa0 ? *--xa : 0;
+       k -= Ebits + 16;
+       d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
+       y = xa > xa0 ? *--xa : 0;
+       d1 = w << k + 16 | y << k;
+#endif
+ ret_d:
+#ifdef VAX
+       word0(d) = d0 >> 16 | d0 << 16;
+       word1(d) = d1 >> 16 | d1 << 16;
+#else
+#undef d0
+#undef d1
+#endif
+       return d;
+}
+
+ static Bigint *
+d2b
+#ifdef KR_headers
+       (d, e, bits) double d; int *e, *bits;
+#else
+       (double d, int *e, int *bits)
+#endif
+{
+       Bigint *b;
+       int de, i, k;
+       unsigned long *x, y, z;
+#ifdef VAX
+       unsigned long d0, d1;
+       d0 = word0(d) >> 16 | word0(d) << 16;
+       d1 = word1(d) >> 16 | word1(d) << 16;
+#else
+#define d0 word0(d)
+#define d1 word1(d)
+#endif
+
+#ifdef Pack_32
+       b = Balloc(1);
+#else
+       b = Balloc(2);
+#endif
+       x = b->x;
+
+       z = d0 & Frac_mask;
+       d0 &= 0x7fffffff;       /* clear sign bit, which we ignore */
+#ifdef Sudden_Underflow
+       de = (int)(d0 >> Exp_shift);
+#ifndef IBM
+       z |= Exp_msk11;
+#endif
+#else
+       if ( (de = (int)(d0 >> Exp_shift)) )
+               z |= Exp_msk1;
+#endif
+#ifdef Pack_32
+       if ( (y = d1) ) {
+               if ( (k = lo0bits(&y)) ) {
+                       x[0] = y | (z << (32 - k));
+                       z >>= k;
+                       }
+               else
+                       x[0] = y;
+               i = b->wds = (x[1] = z) ? 2 : 1;
+       } else {
+#ifdef DEBUG
+               if (!z)
+                       Bug("Zero passed to d2b");
+#endif
+               k = lo0bits(&z);
+               x[0] = z;
+               i = b->wds = 1;
+               k += 32;
+       }
+#else
+       if (y = d1) {
+               if (k = lo0bits(&y))
+                       if (k >= 16) {
+                               x[0] = y | z << 32 - k & 0xffff;
+                               x[1] = z >> k - 16 & 0xffff;
+                               x[2] = z >> k;
+                               i = 2;
+                       } else {
+                               x[0] = y & 0xffff;
+                               x[1] = y >> 16 | z << 16 - k & 0xffff;
+                               x[2] = z >> k & 0xffff;
+                               x[3] = z >> k+16;
+                               i = 3;
+                       }
+               else {
+                       x[0] = y & 0xffff;
+                       x[1] = y >> 16;
+                       x[2] = z & 0xffff;
+                       x[3] = z >> 16;
+                       i = 3;
+               }
+       } else {
+#ifdef DEBUG
+               if (!z)
+                       Bug("Zero passed to d2b");
+#endif
+               k = lo0bits(&z);
+               if (k >= 16) {
+                       x[0] = z;
+                       i = 0;
+               } else {
+                       x[0] = z & 0xffff;
+                       x[1] = z >> 16;
+                       i = 1;
+               }
+               k += 32;
+       }
+       while (!x[i])
+               --i;
+       b->wds = i + 1;
+#endif
+#ifndef Sudden_Underflow
+       if (de) {
+#endif
+#ifdef IBM
+               *e = (de - Bias - (P-1) << 2) + k;
+               *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
+#else
+               *e = de - Bias - (P-1) + k;
+               *bits = P - k;
+#endif
+#ifndef Sudden_Underflow
+       } else {
+               *e = de - Bias - (P-1) + 1 + k;
+#ifdef Pack_32
+               *bits = 32*i - hi0bits(x[i-1]);
+#else
+               *bits = (i+2)*16 - hi0bits(x[i]);
+#endif
+       }
+#endif
+       return b;
+}
+#undef d0
+#undef d1
+
+ static double
+ratio
+#ifdef KR_headers
+       (a, b) Bigint *a, *b;
+#else
+       (Bigint *a, Bigint *b)
+#endif
+{
+       double da, db;
+       int k, ka, kb;
+
+       da = b2d(a, &ka);
+       db = b2d(b, &kb);
+#ifdef Pack_32
+       k = ka - kb + 32*(a->wds - b->wds);
+#else
+       k = ka - kb + 16*(a->wds - b->wds);
+#endif
+#ifdef IBM
+       if (k > 0) {
+               word0(da) += (k >> 2)*Exp_msk1;
+               if (k &= 3)
+                       da *= 1 << k;
+       } else {
+               k = -k;
+               word0(db) += (k >> 2)*Exp_msk1;
+               if (k &= 3)
+                       db *= 1 << k;
+       }
+#else
+       if (k > 0)
+               word0(da) += k*Exp_msk1;
+       else {
+               k = -k;
+               word0(db) += k*Exp_msk1;
+       }
+#endif
+       return da / db;
+}
+
+ static double
+tens[] = {
+               1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
+               1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
+               1e20, 1e21, 1e22
+#ifdef VAX
+               , 1e23, 1e24
+#endif
+               };
+
+ static double
+#ifdef IEEE_Arith
+bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
+static double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, 1e-256 };
+#define n_bigtens 5
+#else
+#ifdef IBM
+bigtens[] = { 1e16, 1e32, 1e64 };
+static double tinytens[] = { 1e-16, 1e-32, 1e-64 };
+#define n_bigtens 3
+#else
+bigtens[] = { 1e16, 1e32 };
+static double tinytens[] = { 1e-16, 1e-32 };
+#define n_bigtens 2
+#endif
+#endif
+
+ double
+bsd_strtod
+#ifdef KR_headers
+       (s00, se) CONST char *s00; char **se;
+#else
+       (CONST char *s00, char **se)
+#endif
+{
+       int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
+                e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
+       CONST char *s, *s0, *s1;
+       double aadj, aadj1, adj, rv, rv0;
+       long L;
+       unsigned long y, z;
+       Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
+       char decimal_point = '.';
+
+       sign = nz0 = nz = 0;
+       rv = 0.;
+       for (s = s00;;s++) switch(*s) {
+               case '-':
+                       sign = 1;
+                       /* no break */
+               case '+':
+                       if (*++s)
+                               goto break2;
+                       /* no break */
+               case 0:
+                       s = s00;
+                       goto ret;
+               default:
+                       if (isspace((unsigned char)*s))
+                               continue;
+                       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 ((char)c == decimal_point) {
+               c = *++s;
+               if (!nd) {
+                       for (; c == '0'; c = *++s)
+                               nz++;
+                       if (c > '0' && c <= '9') {
+                               s0 = s;
+                               nf += nz;
+                               nz = 0;
+                               goto have_dig;
+                       }
+                       goto dig_done;
+               }
+               for (; c >= '0' && c <= '9'; c = *++s) {
+ have_dig:
+                       nz++;
+                       if (c -= '0') {
+                               nf += nz;
+                               for (i = 1; i < nz; i++)
+                                       if (nd++ < 9)
+                                               y *= 10;
+                                       else if (nd <= DBL_DIG + 1)
+                                               z *= 10;
+                               if (nd++ < 9)
+                                       y = 10*y + c;
+                               else if (nd <= DBL_DIG + 1)
+                                       z = 10*z + c;
+                               nz = 0;
+                       }
+               }
+       }
+ dig_done:
+       e = 0;
+       if (c == 'e' || c == 'E') {
+               if (!nd && !nz && !nz0) {
+                       s = s00;
+                       goto ret;
+               }
+               s00 = s;
+               esign = 0;
+               switch(c = *++s) {
+                       case '-':
+                               esign = 1;
+                       case '+':
+                               c = *++s;
+               }
+               if (c >= '0' && c <= '9') {
+                       while (c == '0')
+                               c = *++s;
+                       if (c > '0' && c <= '9') {
+                               L = c - '0';
+                               s1 = s;
+                               while ((c = *++s) >= '0' && c <= '9')
+                                       L = 10*L + c - '0';
+                               if (s - s1 > 8 || L > 19999)
+                                       /* Avoid confusion from exponents
+                                        * so large that e might overflow.
+                                        */
+                                       e = 19999; /* safe for 16 bit ints */
+                               else
+                                       e = (int)L;
+                               if (esign)
+                                       e = -e;
+                       } else
+                               e = 0;
+               } else
+                       s = s00;
+       }
+       if (!nd) {
+               if (!nz && !nz0)
+                       s = s00;
+               goto ret;
+       }
+       e1 = e -= nf;
+
+       /* Now we have nd0 digits, starting at s0, followed by a
+        * decimal point, followed by nd-nd0 digits.  The number we're
+        * after is the integer represented by those digits times
+        * 10**e */
+
+       if (!nd0)
+               nd0 = nd;
+       k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
+       rv = y;
+       if (k > 9)
+               rv = tens[k - 9] * rv + z;
+       if (nd <= DBL_DIG
+#ifndef RND_PRODQUOT
+               && FLT_ROUNDS == 1
+#endif
+                       ) {
+               if (!e)
+                       goto ret;
+               if (e > 0) {
+                       if (e <= Ten_pmax) {
+#ifdef VAX
+                               goto vax_ovfl_check;
+#else
+                               /* rv = */ rounded_product(rv, tens[e]);
+                               goto ret;
+#endif
+                               }
+                       i = DBL_DIG - nd;
+                       if (e <= Ten_pmax + i) {
+                               /* A fancier test would sometimes let us do
+                                * this for larger i values.
+                                */
+                               e -= i;
+                               rv *= tens[i];
+#ifdef VAX
+                               /* VAX exponent range is so narrow we must
+                                * worry about overflow here...
+                                */
+ vax_ovfl_check:
+                               word0(rv) -= P*Exp_msk1;
+                               /* rv = */ rounded_product(rv, tens[e]);
+                               if ((word0(rv) & Exp_mask)
+                                > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
+                                       goto ovfl;
+                               word0(rv) += P*Exp_msk1;
+#else
+                               /* rv = */ rounded_product(rv, tens[e]);
+#endif
+                               goto ret;
+                       }
+               }
+#ifndef Inaccurate_Divide
+               else if (e >= -Ten_pmax) {
+                       /* rv = */ rounded_quotient(rv, tens[-e]);
+                       goto ret;
+               }
+#endif
+       }
+       e1 += nd - k;
+
+       /* Get starting approximation = rv * 10**e1 */
+
+       if (e1 > 0) {
+               if ( (i = e1 & 15) )
+                       rv *= tens[i];
+               if ( (e1 &= ~15) ) {
+                       if (e1 > DBL_MAX_10_EXP) {
+ ovfl:
+                               errno = ERANGE;
+#ifdef __STDC__
+                               rv = HUGE_VAL;
+#else
+                               /* Can't trust HUGE_VAL */
+#ifdef IEEE_Arith
+                               word0(rv) = Exp_mask;
+                               word1(rv) = 0;
+#else
+                               word0(rv) = Big0;
+                               word1(rv) = Big1;
+#endif
+#endif
+                               goto ret;
+                       }
+                       if (e1 >>= 4) {
+                               for (j = 0; e1 > 1; j++, e1 >>= 1)
+                                       if (e1 & 1)
+                                               rv *= bigtens[j];
+                       /* The last multiplication could overflow. */
+                               word0(rv) -= P*Exp_msk1;
+                               rv *= bigtens[j];
+                               if ((z = word0(rv) & Exp_mask)
+                                > Exp_msk1*(DBL_MAX_EXP+Bias-P))
+                                       goto ovfl;
+                               if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
+                                       /* set to largest number */
+                                       /* (Can't trust DBL_MAX) */
+                                       word0(rv) = Big0;
+                                       word1(rv) = Big1;
+                                       }
+                               else
+                                       word0(rv) += P*Exp_msk1;
+                       }
+               }
+       } else if (e1 < 0) {
+               e1 = -e1;
+               if ( (i = e1 & 15) )
+                       rv /= tens[i];
+               if ( (e1 &= ~15) ) {
+                       e1 >>= 4;
+                       for (j = 0; e1 > 1; j++, e1 >>= 1)
+                               if (e1 & 1)
+                                       rv *= tinytens[j];
+                       /* The last multiplication could underflow. */
+                       rv0 = rv;
+                       rv *= tinytens[j];
+                       if (!rv) {
+                               rv = 2.*rv0;
+                               rv *= tinytens[j];
+                               if (!rv) {
+ undfl:
+                                       rv = 0.;
+                                       errno = ERANGE;
+                                       goto ret;
+                                       }
+                               word0(rv) = Tiny0;
+                               word1(rv) = Tiny1;
+                               /* The refinement below will clean
+                                * this approximation up.
+                                */
+                       }
+               }
+       }
+
+       /* Now the hard part -- adjusting rv to the correct value.*/
+
+       /* Put digits into bd: true value = bd * 10^e */
+
+       bd0 = s2b(s0, nd0, nd, y);
+
+       for (;;) {
+               bd = Balloc(bd0->k);
+               Bcopy(bd, bd0);
+               bb = d2b(rv, &bbe, &bbbits);    /* rv = bb * 2^bbe */
+               bs = i2b(1);
+
+               if (e >= 0) {
+                       bb2 = bb5 = 0;
+                       bd2 = bd5 = e;
+               } else {
+                       bb2 = bb5 = -e;
+                       bd2 = bd5 = 0;
+               }
+               if (bbe >= 0)
+                       bb2 += bbe;
+               else
+                       bd2 -= bbe;
+               bs2 = bb2;
+#ifdef Sudden_Underflow
+#ifdef IBM
+               j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
+#else
+               j = P + 1 - bbbits;
+#endif
+#else
+               i = bbe + bbbits - 1;   /* logb(rv) */
+               if (i < Emin)   /* denormal */
+                       j = bbe + (P-Emin);
+               else
+                       j = P + 1 - bbbits;
+#endif
+               bb2 += j;
+               bd2 += j;
+               i = bb2 < bd2 ? bb2 : bd2;
+               if (i > bs2)
+                       i = bs2;
+               if (i > 0) {
+                       bb2 -= i;
+                       bd2 -= i;
+                       bs2 -= i;
+                       }
+               if (bb5 > 0) {
+                       bs = pow5mult(bs, bb5);
+                       bb1 = mult(bs, bb);
+                       Bfree(bb);
+                       bb = bb1;
+                       }
+               if (bb2 > 0)
+                       bb = lshift(bb, bb2);
+               if (bd5 > 0)
+                       bd = pow5mult(bd, bd5);
+               if (bd2 > 0)
+                       bd = lshift(bd, bd2);
+               if (bs2 > 0)
+                       bs = lshift(bs, bs2);
+               delta = diff(bb, bd);
+               dsign = delta->sign;
+               delta->sign = 0;
+               i = cmp(delta, bs);
+               if (i < 0) {
+                       /* Error is less than half an ulp -- check for
+                        * special case of mantissa a power of two.
+                        */
+                       if (dsign || word1(rv) || word0(rv) & Bndry_mask)
+                               break;
+                       delta = lshift(delta,Log2P);
+                       if (cmp(delta, bs) > 0)
+                               goto drop_down;
+                       break;
+               }
+               if (i == 0) {
+                       /* exactly half-way between */
+                       if (dsign) {
+                               if ((word0(rv) & Bndry_mask1) == Bndry_mask1
+                                &&  word1(rv) == 0xffffffff) {
+                                       /*boundary case -- increment exponent*/
+                                       word0(rv) = (word0(rv) & Exp_mask)
+                                               + Exp_msk1
+#ifdef IBM
+                                               | Exp_msk1 >> 4
+#endif
+                                               ;
+                                       word1(rv) = 0;
+                                       break;
+                               }
+                       } else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
+ drop_down:
+                               /* boundary case -- decrement exponent */
+#ifdef Sudden_Underflow
+                               L = word0(rv) & Exp_mask;
+#ifdef IBM
+                               if (L <  Exp_msk1)
+#else
+                               if (L <= Exp_msk1)
+#endif
+                                       goto undfl;
+                               L -= Exp_msk1;
+#else
+                               L = (word0(rv) & Exp_mask) - Exp_msk1;
+#endif
+                               word0(rv) = L | Bndry_mask1;
+                               word1(rv) = 0xffffffff;
+#ifdef IBM
+                               goto cont;
+#else
+                               break;
+#endif
+                       }
+#ifndef ROUND_BIASED
+                       if (!(word1(rv) & LSB))
+                               break;
+#endif
+                       if (dsign)
+                               rv += ulp(rv);
+#ifndef ROUND_BIASED
+                       else {
+                               rv -= ulp(rv);
+#ifndef Sudden_Underflow
+                               if (!rv)
+                                       goto undfl;
+#endif
+                       }
+#endif
+                       break;
+               }
+               if ((aadj = ratio(delta, bs)) <= 2.) {
+                       if (dsign)
+                               aadj = aadj1 = 1.;
+                       else if (word1(rv) || word0(rv) & Bndry_mask) {
+#ifndef Sudden_Underflow
+                               if (word1(rv) == Tiny1 && !word0(rv))
+                                       goto undfl;
+#endif
+                               aadj = 1.;
+                               aadj1 = -1.;
+                       } else {
+                               /* special case -- power of FLT_RADIX to be */
+                               /* rounded down... */
+
+                               if (aadj < 2./FLT_RADIX)
+                                       aadj = 1./FLT_RADIX;
+                               else
+                                       aadj *= 0.5;
+                               aadj1 = -aadj;
+                       }
+               } else {
+                       aadj *= 0.5;
+                       aadj1 = dsign ? aadj : -aadj;
+#ifdef Check_FLT_ROUNDS
+                       switch(FLT_ROUNDS) {
+                               case 2: /* towards +infinity */
+                                       aadj1 -= 0.5;
+                                       break;
+                               case 0: /* towards 0 */
+                               case 3: /* towards -infinity */
+                                       aadj1 += 0.5;
+                       }
+#else
+                       if (FLT_ROUNDS == 0)
+                               aadj1 += 0.5;
+#endif
+               }
+               y = word0(rv) & Exp_mask;
+
+               /* Check for overflow */
+
+               if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
+                       rv0 = rv;
+                       word0(rv) -= P*Exp_msk1;
+                       adj = aadj1 * ulp(rv);
+                       rv += adj;
+                       if ((word0(rv) & Exp_mask) >=
+                                       Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
+                               if (word0(rv0) == Big0 && word1(rv0) == Big1)
+                                       goto ovfl;
+                               word0(rv) = Big0;
+                               word1(rv) = Big1;
+                               goto cont;
+                       } else
+                               word0(rv) += P*Exp_msk1;
+               } else {
+#ifdef Sudden_Underflow
+                       if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
+                               rv0 = rv;
+                               word0(rv) += P*Exp_msk1;
+                               adj = aadj1 * ulp(rv);
+                               rv += adj;
+#ifdef IBM
+                               if ((word0(rv) & Exp_mask) <  P*Exp_msk1)
+#else
+                               if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
+#endif
+                               {
+                                       if (word0(rv0) == Tiny0
+                                        && word1(rv0) == Tiny1)
+                                               goto undfl;
+                                       word0(rv) = Tiny0;
+                                       word1(rv) = Tiny1;
+                                       goto cont;
+                               } else
+                                       word0(rv) -= P*Exp_msk1;
+                       } else {
+                               adj = aadj1 * ulp(rv);
+                               rv += adj;
+                       }
+#else
+                       /* Compute adj so that the IEEE rounding rules will
+                        * correctly round rv + adj in some half-way cases.
+                        * If rv * ulp(rv) is denormalized (i.e.,
+                        * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
+                        * trouble from bits lost to denormalization;
+                        * example: 1.2e-307 .
+                        */
+                       if (y <= (P-1)*Exp_msk1 && aadj >= 1.) {
+                               aadj1 = (double)(int)(aadj + 0.5);
+                               if (!dsign)
+                                       aadj1 = -aadj1;
+                       }
+                       adj = aadj1 * ulp(rv);
+                       rv += adj;
+#endif
+               }
+               z = word0(rv) & Exp_mask;
+               if (y == z) {
+                       /* Can we stop now? */
+                       L = aadj;
+                       aadj -= L;
+                       /* The tolerances below are conservative. */
+                       if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
+                               if (aadj < .4999999 || aadj > .5000001)
+                                       break;
+                       } else if (aadj < .4999999/FLT_RADIX)
+                               break;
+               }
+ cont:
+               Bfree(bb);
+               Bfree(bd);
+               Bfree(bs);
+               Bfree(delta);
+       }
+       Bfree(bb);
+       Bfree(bd);
+       Bfree(bs);
+       Bfree(bd0);
+       Bfree(delta);
+ ret:
+       if (se)
+               *se = (char *)s;
+       return sign ? -rv : rv;
+}
+
+ static int
+quorem
+#ifdef KR_headers
+       (b, S) Bigint *b, *S;
+#else
+       (Bigint *b, Bigint *S)
+#endif
+{
+       int n;
+       long borrow, y;
+       unsigned long carry, q, ys;
+       unsigned long *bx, *bxe, *sx, *sxe;
+#ifdef Pack_32
+       long z;
+       unsigned long si, zs;
+#endif
+
+       n = S->wds;
+#ifdef DEBUG
+       /*debug*/ if (b->wds > n)
+       /*debug*/       Bug("oversize b in quorem");
+#endif
+       if (b->wds < n)
+               return 0;
+       sx = S->x;
+       sxe = sx + --n;
+       bx = b->x;
+       bxe = bx + n;
+       q = *bxe / (*sxe + 1);  /* ensure q <= true quotient */
+#ifdef DEBUG
+       /*debug*/ if (q > 9)
+       /*debug*/       Bug("oversized quotient in quorem");
+#endif
+       if (q) {
+               borrow = 0;
+               carry = 0;
+               do {
+#ifdef Pack_32
+                       si = *sx++;
+                       ys = (si & 0xffff) * q + carry;
+                       zs = (si >> 16) * q + (ys >> 16);
+                       carry = zs >> 16;
+                       y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
+                       borrow = y >> 16;
+                       Sign_Extend(borrow, y);
+                       z = (*bx >> 16) - (zs & 0xffff) + borrow;
+                       borrow = z >> 16;
+                       Sign_Extend(borrow, z);
+                       Storeinc(bx, z, y);
+#else
+                       ys = *sx++ * q + carry;
+                       carry = ys >> 16;
+                       y = *bx - (ys & 0xffff) + borrow;
+                       borrow = y >> 16;
+                       Sign_Extend(borrow, y);
+                       *bx++ = y & 0xffff;
+#endif
+               } while (sx <= sxe);
+               if (!*bxe) {
+                       bx = b->x;
+                       while (--bxe > bx && !*bxe)
+                               --n;
+                       b->wds = n;
+               }
+       }
+       if (cmp(b, S) >= 0) {
+               q++;
+               borrow = 0;
+               carry = 0;
+               bx = b->x;
+               sx = S->x;
+               do {
+#ifdef Pack_32
+                       si = *sx++;
+                       ys = (si & 0xffff) + carry;
+                       zs = (si >> 16) + (ys >> 16);
+                       carry = zs >> 16;
+                       y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
+                       borrow = y >> 16;
+                       Sign_Extend(borrow, y);
+                       z = (*bx >> 16) - (zs & 0xffff) + borrow;
+                       borrow = z >> 16;
+                       Sign_Extend(borrow, z);
+                       Storeinc(bx, z, y);
+#else
+                       ys = *sx++ + carry;
+                       carry = ys >> 16;
+                       y = *bx - (ys & 0xffff) + borrow;
+                       borrow = y >> 16;
+                       Sign_Extend(borrow, y);
+                       *bx++ = y & 0xffff;
+#endif
+               } while (sx <= sxe);
+               bx = b->x;
+               bxe = bx + n;
+               if (!*bxe) {
+                       while (--bxe > bx && !*bxe)
+                               --n;
+                       b->wds = n;
+               }
+       }
+       return q;
+}
+
+/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
+ *
+ * Inspired by "How to Print Floating-Point Numbers Accurately" by
+ * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101].
+ *
+ * Modifications:
+ *     1. Rather than iterating, we use a simple numeric overestimate
+ *        to determine k = floor(log10(d)).  We scale relevant
+ *        quantities using O(log2(k)) rather than O(k) multiplications.
+ *     2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
+ *        try to generate digits strictly left to right.  Instead, we
+ *        compute with fewer bits and propagate the carry if necessary
+ *        when rounding the final digit up.  This is often faster.
+ *     3. Under the assumption that input will be rounded nearest,
+ *        mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
+ *        That is, we allow equality in stopping tests when the
+ *        round-nearest rule will give the same floating-point value
+ *        as would satisfaction of the stopping test with strict
+ *        inequality.
+ *     4. We remove common factors of powers of 2 from relevant
+ *        quantities.
+ *     5. When converting floating-point integers less than 1e16,
+ *        we use floating-point arithmetic rather than resorting
+ *        to multiple-precision integers.
+ *     6. When asked to produce fewer than 15 digits, we first try
+ *        to get by with floating-point arithmetic; we resort to
+ *        multiple-precision integer arithmetic only if we cannot
+ *        guarantee that the floating-point calculation has given
+ *        the correctly rounded result.  For k requested digits and
+ *        "uniformly" distributed input, the probability is
+ *        something like 10^(k-15) that we must resort to the long
+ *        calculation.
+ */
+
+char *
+__bsd_dtoa
+#ifdef KR_headers
+       (d, mode, ndigits, decpt, sign, rve, resultp)
+       double d; int mode, ndigits, *decpt, *sign; char **rve, **resultp;
+#else
+       (double d, int mode, int ndigits, int *decpt, int *sign, char **rve,
+        char **resultp)
+#endif
+{
+ /*    Arguments ndigits, decpt, sign are similar to those
+       of ecvt and fcvt; trailing zeros are suppressed from
+       the returned string.  If not null, *rve is set to point
+       to the end of the return value.  If d is +-Infinity or NaN,
+       then *decpt is set to 9999.
+
+       mode:
+               0 ==> shortest string that yields d when read in
+                       and rounded to nearest.
+               1 ==> like 0, but with Steele & White stopping rule;
+                       e.g. with IEEE P754 arithmetic , mode 0 gives
+                       1e23 whereas mode 1 gives 9.999999999999999e22.
+               2 ==> max(1,ndigits) significant digits.  This gives a
+                       return value similar to that of ecvt, except
+                       that trailing zeros are suppressed.
+               3 ==> through ndigits past the decimal point.  This
+                       gives a return value similar to that from fcvt,
+                       except that trailing zeros are suppressed, and
+                       ndigits can be negative.
+               4-9 should give the same return values as 2-3, i.e.,
+                       4 <= mode <= 9 ==> same return as mode
+                       2 + (mode & 1).  These modes are mainly for
+                       debugging; often they run slower but sometimes
+                       faster than modes 2-3.
+               4,5,8,9 ==> left-to-right digit generation.
+               6-9 ==> don't try fast floating-point estimate
+                       (if applicable).
+
+               Values of mode other than 0-9 are treated as mode 0.
+
+               Sufficient space is allocated to the return value
+               to hold the suppressed trailing zeros.
+       */
+
+       int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
+               j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
+               spec_case, try_quick;
+       long L;
+#ifndef Sudden_Underflow
+       int denorm;
+       unsigned long x;
+#endif
+       Bigint *b, *b1, *delta, *mlo, *mhi, *S;
+       double d2, ds, eps;
+       char *s, *s0;
+
+       if (word0(d) & Sign_bit) {
+               /* set sign for everything, including 0's and NaNs */
+               *sign = 1;
+               word0(d) &= ~Sign_bit;  /* clear sign bit */
+       }
+       else
+               *sign = 0;
+
+#if defined(IEEE_Arith) + defined(VAX)
+#ifdef IEEE_Arith
+       if ((word0(d) & Exp_mask) == Exp_mask)
+#else
+       if (word0(d)  == 0x8000)
+#endif
+       {
+               /* Infinity or NaN */
+               *decpt = 9999;
+               s =
+#ifdef IEEE_Arith
+                       !word1(d) && !(word0(d) & 0xfffff) ? "Infinity" :
+#endif
+                               "NaN";
+               if (rve)
+                       *rve =
+#ifdef IEEE_Arith
+                               s[3] ? s + 8 :
+#endif
+                                               s + 3;
+               return s;
+       }
+#endif
+#ifdef IBM
+       d += 0; /* normalize */
+#endif
+       if (!d) {
+               *decpt = 1;
+               s = "0";
+               if (rve)
+                       *rve = s + 1;
+               return s;
+       }
+
+       b = d2b(d, &be, &bbits);
+#ifdef Sudden_Underflow
+       i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
+#else
+       if ( (i = (int)((word0(d) >> Exp_shift1) & (Exp_mask>>Exp_shift1))) ) {
+#endif
+               d2 = d;
+               word0(d2) &= Frac_mask1;
+               word0(d2) |= Exp_11;
+#ifdef IBM
+               if ( (j = 11 - hi0bits(word0(d2) & Frac_mask)) )
+                       d2 /= 1 << j;
+#endif
+
+               /* log(x)       ~=~ log(1.5) + (x-1.5)/1.5
+                * log10(x)      =  log(x) / log(10)
+                *              ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
+                * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
+                *
+                * This suggests computing an approximation k to log10(d) by
+                *
+                * k = (i - Bias)*0.301029995663981
+                *      + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
+                *
+                * We want k to be too large rather than too small.
+                * The error in the first-order Taylor series approximation
+                * is in our favor, so we just round up the constant enough
+                * to compensate for any error in the multiplication of
+                * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
+                * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
+                * adding 1e-13 to the constant term more than suffices.
+                * Hence we adjust the constant term to 0.1760912590558.
+                * (We could get a more accurate k by invoking log10,
+                *  but this is probably not worthwhile.)
+                */
+
+               i -= Bias;
+#ifdef IBM
+               i <<= 2;
+               i += j;
+#endif
+#ifndef Sudden_Underflow
+               denorm = 0;
+       } else {
+               /* d is denormalized */
+
+               i = bbits + be + (Bias + (P-1) - 1);
+               x = i > 32  ? ((word0(d) << (64 - i)) | (word1(d) >> (i - 32)))
+                           : (word1(d) << (32 - i));
+               d2 = x;
+               word0(d2) -= 31*Exp_msk1; /* adjust exponent */
+               i -= (Bias + (P-1) - 1) + 1;
+               denorm = 1;
+       }
+#endif
+       ds = (d2-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
+       k = (int)ds;
+       if (ds < 0. && ds != k)
+               k--;    /* want k = floor(ds) */
+       k_check = 1;
+       if (k >= 0 && k <= Ten_pmax) {
+               if (d < tens[k])
+                       k--;
+               k_check = 0;
+       }
+       j = bbits - i - 1;
+       if (j >= 0) {
+               b2 = 0;
+               s2 = j;
+       } else {
+               b2 = -j;
+               s2 = 0;
+       }
+       if (k >= 0) {
+               b5 = 0;
+               s5 = k;
+               s2 += k;
+       } else {
+               b2 -= k;
+               b5 = -k;
+               s5 = 0;
+       }
+       if (mode < 0 || mode > 9)
+               mode = 0;
+       try_quick = 1;
+       if (mode > 5) {
+               mode -= 4;
+               try_quick = 0;
+       }
+       leftright = 1;
+       switch(mode) {
+               case 0:
+               case 1:
+                       ilim = ilim1 = -1;
+                       i = 18;
+                       ndigits = 0;
+                       break;
+               case 2:
+                       leftright = 0;
+                       /* no break */
+               case 4:
+                       if (ndigits <= 0)
+                               ndigits = 1;
+                       ilim = ilim1 = i = ndigits;
+                       break;
+               case 3:
+                       leftright = 0;
+                       /* no break */
+               case 5:
+                       i = ndigits + k + 1;
+                       ilim = i;
+                       ilim1 = i - 1;
+                       if (i <= 0)
+                               i = 1;
+       }
+       *resultp = (char *) malloc(i + 1);
+       s = s0 = *resultp;
+
+       if (ilim >= 0 && ilim <= Quick_max && try_quick) {
+
+               /* Try to get by with floating-point arithmetic. */
+
+               i = 0;
+               d2 = d;
+               k0 = k;
+               ilim0 = ilim;
+               ieps = 2; /* conservative */
+               if (k > 0) {
+                       ds = tens[k&0xf];
+                       j = k >> 4;
+                       if (j & Bletch) {
+                               /* prevent overflows */
+                               j &= Bletch - 1;
+                               d /= bigtens[n_bigtens-1];
+                               ieps++;
+                       }
+                       for (; j; j >>= 1, i++)
+                               if (j & 1) {
+                                       ieps++;
+                                       ds *= bigtens[i];
+                               }
+                       d /= ds;
+               } else if ( (j1 = -k) ) {
+                       d *= tens[j1 & 0xf];
+                       for (j = j1 >> 4; j; j >>= 1, i++)
+                               if (j & 1) {
+                                       ieps++;
+                                       d *= bigtens[i];
+                               }
+               }
+               if (k_check && d < 1. && ilim > 0) {
+                       if (ilim1 <= 0)
+                               goto fast_failed;
+                       ilim = ilim1;
+                       k--;
+                       d *= 10.;
+                       ieps++;
+               }
+               eps = ieps*d + 7.;
+               word0(eps) -= (P-1)*Exp_msk1;
+               if (ilim == 0) {
+                       S = mhi = 0;
+                       d -= 5.;
+                       if (d > eps)
+                               goto one_digit;
+                       if (d < -eps)
+                               goto no_digits;
+                       goto fast_failed;
+               }
+#ifndef No_leftright
+               if (leftright) {
+                       /* Use Steele & White method of only
+                        * generating digits needed.
+                        */
+                       eps = 0.5/tens[ilim-1] - eps;
+                       for (i = 0;;) {
+                               L = d;
+                               d -= L;
+                               *s++ = '0' + (int)L;
+                               if (d < eps)
+                                       goto ret1;
+                               if (1. - d < eps)
+                                       goto bump_up;
+                               if (++i >= ilim)
+                                       break;
+                               eps *= 10.;
+                               d *= 10.;
+                       }
+               } else {
+#endif
+                       /* Generate ilim digits, then fix them up. */
+                       eps *= tens[ilim-1];
+                       for (i = 1;; i++, d *= 10.) {
+                               L = d;
+                               d -= L;
+                               *s++ = '0' + (int)L;
+                               if (i == ilim) {
+                                       if (d > 0.5 + eps)
+                                               goto bump_up;
+                                       else if (d < 0.5 - eps) {
+                                               while (*--s == '0');
+                                               s++;
+                                               goto ret1;
+                                       }
+                                       break;
+                               }
+                       }
+#ifndef No_leftright
+               }
+#endif
+ fast_failed:
+               s = s0;
+               d = d2;
+               k = k0;
+               ilim = ilim0;
+       }
+
+       /* Do we have a "small" integer? */
+
+       if (be >= 0 && k <= Int_max) {
+               /* Yes. */
+               ds = tens[k];
+               if (ndigits < 0 && ilim <= 0) {
+                       S = mhi = 0;
+                       if (ilim < 0 || d <= 5*ds)
+                               goto no_digits;
+                       goto one_digit;
+               }
+               for (i = 1;; i++) {
+                       L = d / ds;
+                       d -= L*ds;
+#ifdef Check_FLT_ROUNDS
+                       /* If FLT_ROUNDS == 2, L will usually be high by 1 */
+                       if (d < 0) {
+                               L--;
+                               d += ds;
+                       }
+#endif
+                       *s++ = '0' + (int)L;
+                       if (i == ilim) {
+                               d += d;
+                               if (d > ds || (d == ds && L & 1)) {
+ bump_up:
+                                       while (*--s == '9')
+                                               if (s == s0) {
+                                                       k++;
+                                                       *s = '0';
+                                                       break;
+                                               }
+                                       ++*s++;
+                               }
+                               break;
+                       }
+                       if (!(d *= 10.))
+                               break;
+               }
+               goto ret1;
+       }
+
+       m2 = b2;
+       m5 = b5;
+       mhi = mlo = 0;
+       if (leftright) {
+               if (mode < 2) {
+                       i =
+#ifndef Sudden_Underflow
+                               denorm ? be + (Bias + (P-1) - 1 + 1) :
+#endif
+#ifdef IBM
+                               1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
+#else
+                               1 + P - bbits;
+#endif
+               } else {
+                       j = ilim - 1;
+                       if (m5 >= j)
+                               m5 -= j;
+                       else {
+                               s5 += j -= m5;
+                               b5 += j;
+                               m5 = 0;
+                       }
+                       if ((i = ilim) < 0) {
+                               m2 -= i;
+                               i = 0;
+                       }
+               }
+               b2 += i;
+               s2 += i;
+               mhi = i2b(1);
+       }
+       if (m2 > 0 && s2 > 0) {
+               i = m2 < s2 ? m2 : s2;
+               b2 -= i;
+               m2 -= i;
+               s2 -= i;
+       }
+       if (b5 > 0) {
+               if (leftright) {
+                       if (m5 > 0) {
+                               mhi = pow5mult(mhi, m5);
+                               b1 = mult(mhi, b);
+                               Bfree(b);
+                               b = b1;
+                               }
+                       if ( (j = b5 - m5) )
+                               b = pow5mult(b, j);
+               } else
+                       b = pow5mult(b, b5);
+       }
+       S = i2b(1);
+       if (s5 > 0)
+               S = pow5mult(S, s5);
+
+       /* Check for special case that d is a normalized power of 2. */
+
+       if (mode < 2) {
+               if (!word1(d) && !(word0(d) & Bndry_mask)
+#ifndef Sudden_Underflow
+                && word0(d) & Exp_mask
+#endif
+                               ) {
+                       /* The special case */
+                       b2 += Log2P;
+                       s2 += Log2P;
+                       spec_case = 1;
+               } else
+                       spec_case = 0;
+       }
+
+       /* Arrange for convenient computation of quotients:
+        * shift left if necessary so divisor has 4 leading 0 bits.
+        *
+        * Perhaps we should just compute leading 28 bits of S once
+        * and for all and pass them and a shift to quorem, so it
+        * can do shifts and ors to compute the numerator for q.
+        */
+#ifdef Pack_32
+       if ( (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f) )
+               i = 32 - i;
+#else
+       if ( (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf) )
+               i = 16 - i;
+#endif
+       if (i > 4) {
+               i -= 4;
+               b2 += i;
+               m2 += i;
+               s2 += i;
+       } else if (i < 4) {
+               i += 28;
+               b2 += i;
+               m2 += i;
+               s2 += i;
+       }
+       if (b2 > 0)
+               b = lshift(b, b2);
+       if (s2 > 0)
+               S = lshift(S, s2);
+       if (k_check) {
+               if (cmp(b,S) < 0) {
+                       k--;
+                       b = multadd(b, 10, 0);  /* we botched the k estimate */
+                       if (leftright)
+                               mhi = multadd(mhi, 10, 0);
+                       ilim = ilim1;
+               }
+       }
+       if (ilim <= 0 && mode > 2) {
+               if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
+                       /* no digits, fcvt style */
+ no_digits:
+                       k = -1 - ndigits;
+                       goto ret;
+               }
+ one_digit:
+               *s++ = '1';
+               k++;
+               goto ret;
+       }
+       if (leftright) {
+               if (m2 > 0)
+                       mhi = lshift(mhi, m2);
+
+               /* Compute mlo -- check for special case
+                * that d is a normalized power of 2.
+                */
+
+               mlo = mhi;
+               if (spec_case) {
+                       mhi = Balloc(mhi->k);
+                       Bcopy(mhi, mlo);
+                       mhi = lshift(mhi, Log2P);
+               }
+
+               for (i = 1;;i++) {
+                       dig = quorem(b,S) + '0';
+                       /* Do we yet have the shortest decimal string
+                        * that will round to d?
+                        */
+                       j = cmp(b, mlo);
+                       delta = diff(S, mhi);
+                       j1 = delta->sign ? 1 : cmp(b, delta);
+                       Bfree(delta);
+#ifndef ROUND_BIASED
+                       if (j1 == 0 && !mode && !(word1(d) & 1)) {
+                               if (dig == '9')
+                                       goto round_9_up;
+                               if (j > 0)
+                                       dig++;
+                               *s++ = dig;
+                               goto ret;
+                       }
+#endif
+                       if (j < 0 || (j == 0 && !mode
+#ifndef ROUND_BIASED
+                                                       && !(word1(d) & 1)
+#endif
+                                       )) {
+                               if (j1 > 0) {
+                                       b = lshift(b, 1);
+                                       j1 = cmp(b, S);
+                                       if ((j1 > 0 || (j1 == 0 && dig & 1))
+                                       && dig++ == '9')
+                                               goto round_9_up;
+                               }
+                               *s++ = dig;
+                               goto ret;
+                       }
+                       if (j1 > 0) {
+                               if (dig == '9') { /* possible if i == 1 */
+ round_9_up:
+                                       *s++ = '9';
+                                       goto roundoff;
+                               }
+                               *s++ = dig + 1;
+                               goto ret;
+                       }
+                       *s++ = dig;
+                       if (i == ilim)
+                               break;
+                       b = multadd(b, 10, 0);
+                       if (mlo == mhi)
+                               mlo = mhi = multadd(mhi, 10, 0);
+                       else {
+                               mlo = multadd(mlo, 10, 0);
+                               mhi = multadd(mhi, 10, 0);
+                       }
+               }
+       } else
+               for (i = 1;; i++) {
+                       *s++ = dig = quorem(b,S) + '0';
+                       if (i >= ilim)
+                               break;
+                       b = multadd(b, 10, 0);
+               }
+
+       /* Round off last digit */
+
+       b = lshift(b, 1);
+       j = cmp(b, S);
+       if (j > 0 || (j == 0 && dig & 1)) {
+ roundoff:
+               while (*--s == '9')
+                       if (s == s0) {
+                               k++;
+                               *s++ = '1';
+                               goto ret;
+                       }
+               ++*s++;
+       } else {
+               while (*--s == '0');
+               s++;
+       }
+ ret:
+       Bfree(S);
+       if (mhi) {
+               if (mlo && mlo != mhi)
+                       Bfree(mlo);
+               Bfree(mhi);
+       }
+ ret1:
+       Bfree(b);
+       if (s == s0) {  /* don't return empty string */
+               *s++ = '0';
+               k = 0;
+       }
+       *s = 0;
+       *decpt = k + 1;
+       if (rve)
+               *rve = s;
+       return s0;
+       }
+#ifdef __cplusplus
+}
+#endif
diff --git a/mono/utils/strtod.h b/mono/utils/strtod.h
new file mode 100644 (file)
index 0000000..54f40f7
--- /dev/null
@@ -0,0 +1,7 @@
+#ifndef MONO_STRTOD_H
+#define MONO_STRTOD_H 1
+
+double bsd_strtod (const char *s00, char **se);
+char *__bsd_dtoa  (double d, int mode, int ndigits, int *decpt, int *sign, char **rve, char **resultp);
+
+#endif