2 files changed, 2528 insertions, 2 deletions

diff --git a/lib/libc/stdlib/Makefile.inc b/lib/libc/stdlib/Makefile.inc
index 6ad404ef7976..0d7ae27093ad 100644
--- a/lib/libc/stdlib/Makefile.inc
+++ b/lib/libc/stdlib/Makefile.inc
@@ -1,5 +1,5 @@
 #	from @(#)Makefile.inc	8.3 (Berkeley) 2/4/95
-#	$Id: Makefile.inc,v 1.13 1997/10/21 08:41:13 bde Exp $
+#	$Id: Makefile.inc,v 1.14 1998/02/20 08:41:46 jb Exp $
 
 # machine-independent stdlib sources
 .PATH: ${.CURDIR}/../libc/${MACHINE_ARCH}/stdlib ${.CURDIR}/../libc/stdlib
@@ -7,9 +7,18 @@
 MISRCS+=abort.c abs.c atexit.c atof.c atoi.c atol.c bsearch.c calloc.c div.c \
 	exit.c getenv.c getopt.c getsubopt.c heapsort.c labs.c ldiv.c \
 	malloc.c merge.c putenv.c qsort.c radixsort.c rand.c random.c \
-	realpath.c setenv.c strhash.c strtod.c strtol.c strtoq.c strtoul.c \
+	realpath.c setenv.c strhash.c strtol.c strtoq.c strtoul.c \
 	strtouq.c system.c
 
+.if ${MACHINE_ARCH} == "alpha"
+#  XXX Temporary until the assumption that a long is 32-bits is resolved
+#  XXX FreeBSD's code. NetBSD kludged this with Long = int32_t and
+#  XXX ULong = u_int32_t
+SRCS+=	netbsd_strtod.c
+.else
+SRCS+=	strtod.c
+.endif
+
 # machine-dependent stdlib sources
 .include "${.CURDIR}/../libc/${MACHINE_ARCH}/stdlib/Makefile.inc"
 
diff --git a/lib/libc/stdlib/netbsd_strtod.c b/lib/libc/stdlib/netbsd_strtod.c
new file mode 100644
index 000000000000..72cd366ff8db
--- /dev/null
+++ b/lib/libc/stdlib/netbsd_strtod.c
@@ -0,0 +1,2517 @@
+/*	From: NetBSD: strtod.c,v 1.26 1998/02/03 18:44:21 perry Exp */
+/*	$Id$	*/
+
+/****************************************************************
+ *
+ * The author of this software is David M. Gay.
+ *
+ * Copyright (c) 1991 by AT&T.
+ *
+ * Permission to use, copy, modify, and distribute this software for any
+ * purpose without fee is hereby granted, provided that this entire notice
+ * is included in all copies of any software which is or includes a copy
+ * or modification of this software and in all copies of the supporting
+ * documentation for such software.
+ *
+ * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
+ * WARRANTY.  IN PARTICULAR, NEITHER THE AUTHOR NOR AT&T MAKES ANY
+ * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
+ * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
+ *
+ ***************************************************************/
+
+/* Please send bug reports to
+	David M. Gay
+	AT&T Bell Laboratories, Room 2C-463
+	600 Mountain Avenue
+	Murray Hill, NJ 07974-2070
+	U.S.A.
+	dmg@research.att.com or research!dmg
+ */
+
+/* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
+ *
+ * This strtod returns a nearest machine number to the input decimal
+ * string (or sets errno to ERANGE).  With IEEE arithmetic, ties are
+ * broken by the IEEE round-even rule.  Otherwise ties are broken by
+ * biased rounding (add half and chop).
+ *
+ * Inspired loosely by William D. Clinger's paper "How to Read Floating
+ * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
+ *
+ * Modifications:
+ *
+ *	1. We only require IEEE, IBM, or VAX double-precision
+ *		arithmetic (not IEEE double-extended).
+ *	2. We get by with floating-point arithmetic in a case that
+ *		Clinger missed -- when we're computing d * 10^n
+ *		for a small integer d and the integer n is not too
+ *		much larger than 22 (the maximum integer k for which
+ *		we can represent 10^k exactly), we may be able to
+ *		compute (d*10^k) * 10^(e-k) with just one roundoff.
+ *	3. Rather than a bit-at-a-time adjustment of the binary
+ *		result in the hard case, we use floating-point
+ *		arithmetic to determine the adjustment to within
+ *		one bit; only in really hard cases do we need to
+ *		compute a second residual.
+ *	4. Because of 3., we don't need a large table of powers of 10
+ *		for ten-to-e (just some small tables, e.g. of 10^k
+ *		for 0 <= k <= 22).
+ */
+
+/*
+ * #define IEEE_LITTLE_ENDIAN for IEEE-arithmetic machines where the least
+ *	significant byte has the lowest address.
+ * #define IEEE_BIG_ENDIAN for IEEE-arithmetic machines where the most
+ *	significant byte has the lowest address.
+ * #define Long int on machines with 32-bit ints and 64-bit longs.
+ * #define Sudden_Underflow for IEEE-format machines without gradual
+ *	underflow (i.e., that flush to zero on underflow).
+ * #define IBM for IBM mainframe-style floating-point arithmetic.
+ * #define VAX for VAX-style floating-point arithmetic.
+ * #define Unsigned_Shifts if >> does treats its left operand as unsigned.
+ * #define No_leftright to omit left-right logic in fast floating-point
+ *	computation of dtoa.
+ * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3.
+ * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
+ *	that use extended-precision instructions to compute rounded
+ *	products and quotients) with IBM.
+ * #define ROUND_BIASED for IEEE-format with biased rounding.
+ * #define Inaccurate_Divide for IEEE-format with correctly rounded
+ *	products but inaccurate quotients, e.g., for Intel i860.
+ * #define Just_16 to store 16 bits per 32-bit Long when doing high-precision
+ *	integer arithmetic.  Whether this speeds things up or slows things
+ *	down depends on the machine and the number being converted.
+ * #define KR_headers for old-style C function headers.
+ * #define Bad_float_h if your system lacks a float.h or if it does not
+ *	define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
+ *	FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
+ * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
+ *	if memory is available and otherwise does something you deem
+ *	appropriate.  If MALLOC is undefined, malloc will be invoked
+ *	directly -- and assumed always to succeed.
+ */
+
+#include <sys/cdefs.h>
+#if defined(LIBC_SCCS) && !defined(lint)
+__RCSID("$NetBSD: strtod.c,v 1.26 1998/02/03 18:44:21 perry Exp $");
+#endif /* LIBC_SCCS and not lint */
+
+#if defined(__m68k__) || defined(__sparc__) || defined(__i386__) || \
+    defined(__mips__) || defined(__ns32k__) || defined(__alpha__) || \
+    defined(__powerpc__)
+#include <sys/types.h>
+#if BYTE_ORDER == BIG_ENDIAN
+#define IEEE_BIG_ENDIAN
+#else
+#define IEEE_LITTLE_ENDIAN
+#endif
+#endif
+
+#ifdef __arm32__
+/*
+ * Although the CPU is little endian the FP has different
+ * byte and word endianness. The byte order is still little endian
+ * but the word order is big endian.
+ */
+#define IEEE_BIG_ENDIAN
+#endif
+
+#ifdef vax
+#define VAX
+#endif
+
+#define Long	int32_t
+#define ULong	u_int32_t
+
+#ifdef DEBUG
+#include "stdio.h"
+#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
+#endif
+
+#ifdef __cplusplus
+#include "malloc.h"
+#include "memory.h"
+#else
+#ifndef KR_headers
+#include "stdlib.h"
+#include "string.h"
+#include "locale.h"
+#else
+#include "malloc.h"
+#include "memory.h"
+#endif
+#endif
+char *__dtoa __P((double, int, int, int *, int *, char **));
+
+#ifdef MALLOC
+#ifdef KR_headers
+extern char *MALLOC();
+#else
+extern void *MALLOC(size_t);
+#endif
+#else
+#define MALLOC malloc
+#endif
+
+#include "ctype.h"
+#include "errno.h"
+
+#ifdef Bad_float_h
+#undef __STDC__
+#ifdef IEEE_BIG_ENDIAN
+#define IEEE_ARITHMETIC
+#endif
+#ifdef IEEE_LITTLE_ENDIAN
+#define IEEE_ARITHMETIC
+#endif
+
+#ifdef IEEE_ARITHMETIC
+#define DBL_DIG 15
+#define DBL_MAX_10_EXP 308
+#define DBL_MAX_EXP 1024
+#define FLT_RADIX 2
+#define FLT_ROUNDS 1
+#define DBL_MAX 1.7976931348623157e+308
+#endif
+
+#ifdef IBM
+#define DBL_DIG 16
+#define DBL_MAX_10_EXP 75
+#define DBL_MAX_EXP 63
+#define FLT_RADIX 16
+#define FLT_ROUNDS 0
+#define DBL_MAX 7.2370055773322621e+75
+#endif
+
+#ifdef VAX
+#define DBL_DIG 16
+#define DBL_MAX_10_EXP 38
+#define DBL_MAX_EXP 127
+#define FLT_RADIX 2
+#define FLT_ROUNDS 1
+#define DBL_MAX 1.7014118346046923e+38
+#endif
+
+#ifndef LONG_MAX
+#define LONG_MAX 2147483647
+#endif
+#else
+#include "float.h"
+#endif
+#ifndef __MATH_H__
+#include "math.h"
+#endif
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#ifndef CONST
+#ifdef KR_headers
+#define CONST /* blank */
+#else
+#define CONST const
+#endif
+#endif
+
+#ifdef Unsigned_Shifts
+#define Sign_Extend(a,b) if (b < 0) a |= 0xffff0000;
+#else
+#define Sign_Extend(a,b) /*no-op*/
+#endif
+
+#if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) + defined(VAX) + \
+    defined(IBM) != 1
+Exactly one of IEEE_LITTLE_ENDIAN IEEE_BIG_ENDIAN, VAX, or
+IBM should be defined.
+#endif
+
+#ifdef IEEE_LITTLE_ENDIAN
+#define word0(x) ((ULong *)&x)[1]
+#define word1(x) ((ULong *)&x)[0]
+#else
+#define word0(x) ((ULong *)&x)[0]
+#define word1(x) ((ULong *)&x)[1]
+#endif
+
+/* The following definition of Storeinc is appropriate for MIPS processors.
+ * An alternative that might be better on some machines is
+ * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
+ */
+#if defined(IEEE_LITTLE_ENDIAN) + defined(VAX) + defined(__arm32__)
+#define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
+((unsigned short *)a)[0] = (unsigned short)c, a++)
+#else
+#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
+((unsigned short *)a)[1] = (unsigned short)c, a++)
+#endif
+
+/* #define P DBL_MANT_DIG */
+/* Ten_pmax = floor(P*log(2)/log(5)) */
+/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
+/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
+/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
+
+#if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN)
+#define Exp_shift  20
+#define Exp_shift1 20
+#define Exp_msk1    0x100000
+#define Exp_msk11   0x100000
+#define Exp_mask  0x7ff00000
+#define P 53
+#define Bias 1023
+#define IEEE_Arith
+#define Emin (-1022)
+#define Exp_1  0x3ff00000
+#define Exp_11 0x3ff00000
+#define Ebits 11
+#define Frac_mask  0xfffff
+#define Frac_mask1 0xfffff
+#define Ten_pmax 22
+#define Bletch 0x10
+#define Bndry_mask  0xfffff
+#define Bndry_mask1 0xfffff
+#define LSB 1
+#define Sign_bit 0x80000000
+#define Log2P 1
+#define Tiny0 0
+#define Tiny1 1
+#define Quick_max 14
+#define Int_max 14
+#define Infinite(x) (word0(x) == 0x7ff00000) /* sufficient test for here */
+#else
+#undef  Sudden_Underflow
+#define Sudden_Underflow
+#ifdef IBM
+#define Exp_shift  24
+#define Exp_shift1 24
+#define Exp_msk1   0x1000000
+#define Exp_msk11  0x1000000
+#define Exp_mask  0x7f000000
+#define P 14
+#define Bias 65
+#define Exp_1  0x41000000
+#define Exp_11 0x41000000
+#define Ebits 8	/* exponent has 7 bits, but 8 is the right value in b2d */
+#define Frac_mask  0xffffff
+#define Frac_mask1 0xffffff
+#define Bletch 4
+#define Ten_pmax 22
+#define Bndry_mask  0xefffff
+#define Bndry_mask1 0xffffff
+#define LSB 1
+#define Sign_bit 0x80000000
+#define Log2P 4
+#define Tiny0 0x100000
+#define Tiny1 0
+#define Quick_max 14
+#define Int_max 15
+#else /* VAX */
+#define Exp_shift  23
+#define Exp_shift1 7
+#define Exp_msk1    0x80
+#define Exp_msk11   0x800000
+#define Exp_mask  0x7f80
+#define P 56
+#define Bias 129
+#define Exp_1  0x40800000
+#define Exp_11 0x4080
+#define Ebits 8
+#define Frac_mask  0x7fffff
+#define Frac_mask1 0xffff007f
+#define Ten_pmax 24
+#define Bletch 2
+#define Bndry_mask  0xffff007f
+#define Bndry_mask1 0xffff007f
+#define LSB 0x10000
+#define Sign_bit 0x8000
+#define Log2P 1
+#define Tiny0 0x80
+#define Tiny1 0
+#define Quick_max 15
+#define Int_max 15
+#endif
+#endif
+
+#ifndef IEEE_Arith
+#define ROUND_BIASED
+#endif
+
+#ifdef RND_PRODQUOT
+#define rounded_product(a,b) a = rnd_prod(a, b)
+#define rounded_quotient(a,b) a = rnd_quot(a, b)
+#ifdef KR_headers
+extern double rnd_prod(), rnd_quot();
+#else
+extern double rnd_prod(double, double), rnd_quot(double, double);
+#endif
+#else
+#define rounded_product(a,b) a *= b
+#define rounded_quotient(a,b) a /= b
+#endif
+
+#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
+#define Big1 0xffffffff
+
+#ifndef Just_16
+/* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
+ * This makes some inner loops simpler and sometimes saves work
+ * during multiplications, but it often seems to make things slightly
+ * slower.  Hence the default is now to store 32 bits per Long.
+ */
+#ifndef Pack_32
+#define Pack_32
+#endif
+#endif
+
+#define Kmax 15
+
+#ifdef __cplusplus
+extern "C" double strtod(const char *s00, char **se);
+extern "C" char *__dtoa(double d, int mode, int ndigits,
+			int *decpt, int *sign, char **rve);
+#endif
+
+ struct
+Bigint {
+	struct Bigint *next;
+	int k, maxwds, sign, wds;
+	ULong x[1];
+	};
+
+ typedef struct Bigint Bigint;
+
+ static Bigint *freelist[Kmax+1];
+
+ static Bigint *
+Balloc
+#ifdef KR_headers
+	(k) int k;
+#else
+	(int k)
+#endif
+{
+	int x;
+	Bigint *rv;
+
+	if ((rv = freelist[k]) != NULL) {
+		freelist[k] = rv->next;
+		}
+	else {
+		x = 1 << k;
+		rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(Long));
+		rv->k = k;
+		rv->maxwds = x;
+		}
+	rv->sign = rv->wds = 0;
+	return rv;
+	}
+
+ static void
+Bfree
+#ifdef KR_headers
+	(v) Bigint *v;
+#else
+	(Bigint *v)
+#endif
+{
+	if (v) {
+		v->next = freelist[v->k];
+		freelist[v->k] = v;
+		}
+	}
+
+#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
+y->wds*sizeof(Long) + 2*sizeof(int))
+
+ static Bigint *
+multadd
+#ifdef KR_headers
+	(b, m, a) Bigint *b; int m, a;
+#else
+	(Bigint *b, int m, int a)	/* multiply by m and add a */
+#endif
+{
+	int i, wds;
+	ULong *x, y;
+#ifdef Pack_32
+	ULong xi, z;
+#endif
+	Bigint *b1;
+
+	wds = b->wds;
+	x = b->x;
+	i = 0;
+	do {
+#ifdef Pack_32
+		xi = *x;
+		y = (xi & 0xffff) * m + a;
+		z = (xi >> 16) * m + (y >> 16);
+		a = (int)(z >> 16);
+		*x++ = (z << 16) + (y & 0xffff);
+#else
+		y = *x * m + a;
+		a = (int)(y >> 16);
+		*x++ = y & 0xffff;
+#endif
+		}
+		while(++i < wds);
+	if (a) {
+		if (wds >= b->maxwds) {
+			b1 = Balloc(b->k+1);
+			Bcopy(b1, b);
+			Bfree(b);
+			b = b1;
+			}
+		b->x[wds++] = a;
+		b->wds = wds;
+		}
+	return b;
+	}
+
+ static Bigint *
+s2b
+#ifdef KR_headers
+	(s, nd0, nd, y9) CONST char *s; int nd0, nd; ULong y9;
+#else
+	(CONST char *s, int nd0, int nd, ULong y9)
+#endif
+{
+	Bigint *b;
+	int i, k;
+	Long x, y;
+
+	x = (nd + 8) / 9;
+	for(k = 0, y = 1; x > y; y <<= 1, k++) ;
+#ifdef Pack_32
+	b = Balloc(k);
+	b->x[0] = y9;
+	b->wds = 1;
+#else
+	b = Balloc(k+1);
+	b->x[0] = y9 & 0xffff;
+	b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
+#endif
+
+	i = 9;
+	if (9 < nd0) {
+		s += 9;
+		do b = multadd(b, 10, *s++ - '0');
+			while(++i < nd0);
+		s++;
+		}
+	else
+		s += 10;
+	for(; i < nd; i++)
+		b = multadd(b, 10, *s++ - '0');
+	return b;
+	}
+
+ static int
+hi0bits
+#ifdef KR_headers
+	(x) ULong x;
+#else
+	(ULong x)
+#endif
+{
+	int k = 0;
+
+	if (!(x & 0xffff0000)) {
+		k = 16;
+		x <<= 16;
+		}
+	if (!(x & 0xff000000)) {
+		k += 8;
+		x <<= 8;
+		}
+	if (!(x & 0xf0000000)) {
+		k += 4;
+		x <<= 4;
+		}
+	if (!(x & 0xc0000000)) {
+		k += 2;
+		x <<= 2;
+		}
+	if (!(x & 0x80000000)) {
+		k++;
+		if (!(x & 0x40000000))
+			return 32;
+		}
+	return k;
+	}
+
+ static int
+lo0bits
+#ifdef KR_headers
+	(y) ULong *y;
+#else
+	(ULong *y)
+#endif
+{
+	int k;
+	ULong x = *y;
+
+	if (x & 7) {
+		if (x & 1)
+			return 0;
+		if (x & 2) {
+			*y = x >> 1;
+			return 1;
+			}
+		*y = x >> 2;
+		return 2;
+		}
+	k = 0;
+	if (!(x & 0xffff)) {
+		k = 16;
+		x >>= 16;
+		}
+	if (!(x & 0xff)) {
+		k += 8;
+		x >>= 8;
+		}
+	if (!(x & 0xf)) {
+		k += 4;
+		x >>= 4;
+		}
+	if (!(x & 0x3)) {
+		k += 2;
+		x >>= 2;
+		}
+	if (!(x & 1)) {
+		k++;
+		x >>= 1;
+		if (!x & 1)
+			return 32;
+		}
+	*y = x;
+	return k;
+	}
+
+ static Bigint *
+i2b
+#ifdef KR_headers
+	(i) int i;
+#else
+	(int i)
+#endif
+{
+	Bigint *b;
+
+	b = Balloc(1);
+	b->x[0] = i;
+	b->wds = 1;
+	return b;
+	}
+
+ static Bigint *
+mult
+#ifdef KR_headers
+	(a, b) Bigint *a, *b;
+#else
+	(Bigint *a, Bigint *b)
+#endif
+{
+	Bigint *c;
+	int k, wa, wb, wc;
+	ULong carry, y, z;
+	ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
+#ifdef Pack_32
+	ULong z2;
+#endif
+
+	if (a->wds < b->wds) {
+		c = a;
+		a = b;
+		b = c;
+		}
+	k = a->k;
+	wa = a->wds;
+	wb = b->wds;
+	wc = wa + wb;
+	if (wc > a->maxwds)
+		k++;
+	c = Balloc(k);
+	for(x = c->x, xa = x + wc; x < xa; x++)
+		*x = 0;
+	xa = a->x;
+	xae = xa + wa;
+	xb = b->x;
+	xbe = xb + wb;
+	xc0 = c->x;
+#ifdef Pack_32
+	for(; xb < xbe; xb++, xc0++) {
+		if ((y = *xb & 0xffff) != 0) {
+			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) != 0) {
+			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) != 0)
+		b = multadd(b, p05[i-1], 0);
+
+	if (!(k >>= 2))
+		return b;
+	if (!(p5 = p5s)) {
+		/* first time */
+		p5 = p5s = i2b(625);
+		p5->next = 0;
+		}
+	for(;;) {
+		if (k & 1) {
+			b1 = mult(b, p5);
+			Bfree(b);
+			b = b1;
+			}
+		if (!(k >>= 1))
+			break;
+		if (!(p51 = p5->next)) {
+			p51 = p5->next = mult(p5,p5);
+			p51->next = 0;
+			}
+		p5 = p51;
+		}
+	return b;
+	}
+
+ static Bigint *
+lshift
+#ifdef KR_headers
+	(b, k) Bigint *b; int k;
+#else
+	(Bigint *b, int k)
+#endif
+{
+	int i, k1, n, n1;
+	Bigint *b1;
+	ULong *x, *x1, *xe, z;
+
+#ifdef Pack_32
+	n = k >> 5;
+#else
+	n = k >> 4;
+#endif
+	k1 = b->k;
+	n1 = n + b->wds + 1;
+	for(i = b->maxwds; n1 > i; i <<= 1)
+		k1++;
+	b1 = Balloc(k1);
+	x1 = b1->x;
+	for(i = 0; i < n; i++)
+		*x1++ = 0;
+	x = b->x;
+	xe = x + b->wds;
+#ifdef Pack_32
+	if (k &= 0x1f) {
+		k1 = 32 - k;
+		z = 0;
+		do {
+			*x1++ = *x << k | z;
+			z = *x++ >> k1;
+			}
+			while(x < xe);
+		if ((*x1 = z) != 0)
+			++n1;
+		}
+#else
+	if (k &= 0xf) {
+		k1 = 16 - k;
+		z = 0;
+		do {
+			*x1++ = *x << k  & 0xffff | z;
+			z = *x++ >> k1;
+			}
+			while(x < xe);
+		if (*x1 = z)
+			++n1;
+		}
+#endif
+	else do
+		*x1++ = *x++;
+		while(x < xe);
+	b1->wds = n1 - 1;
+	Bfree(b);
+	return b1;
+	}
+
+ static int
+cmp
+#ifdef KR_headers
+	(a, b) Bigint *a, *b;
+#else
+	(Bigint *a, Bigint *b)
+#endif
+{
+	ULong *xa, *xa0, *xb, *xb0;
+	int i, j;
+
+	i = a->wds;
+	j = b->wds;
+#ifdef DEBUG
+	if (i > 1 && !a->x[i-1])
+		Bug("cmp called with a->x[a->wds-1] == 0");
+	if (j > 1 && !b->x[j-1])
+		Bug("cmp called with b->x[b->wds-1] == 0");
+#endif
+	if (i -= j)
+		return i;
+	xa0 = a->x;
+	xa = xa0 + j;
+	xb0 = b->x;
+	xb = xb0 + j;
+	for(;;) {
+		if (*--xa != *--xb)
+			return *xa < *xb ? -1 : 1;
+		if (xa <= xa0)
+			break;
+		}
+	return 0;
+	}
+
+ static Bigint *
+diff
+#ifdef KR_headers
+	(a, b) Bigint *a, *b;
+#else
+	(Bigint *a, Bigint *b)
+#endif
+{
+	Bigint *c;
+	int i, wa, wb;
+	Long borrow, y;	/* We need signed shifts here. */
+	ULong *xa, *xae, *xb, *xbe, *xc;
+#ifdef Pack_32
+	Long z;
+#endif
+
+	i = cmp(a,b);
+	if (!i) {
+		c = Balloc(0);
+		c->wds = 1;
+		c->x[0] = 0;
+		return c;
+		}
+	if (i < 0) {
+		c = a;
+		a = b;
+		b = c;
+		i = 1;
+		}
+	else
+		i = 0;
+	c = Balloc(a->k);
+	c->sign = i;
+	wa = a->wds;
+	xa = a->x;
+	xae = xa + wa;
+	wb = b->wds;
+	xb = b->x;
+	xbe = xb + wb;
+	xc = c->x;
+	borrow = 0;
+#ifdef Pack_32
+	do {
+		y = (*xa & 0xffff) - (*xb & 0xffff) + borrow;
+		borrow = y >> 16;
+		Sign_Extend(borrow, y);
+		z = (*xa++ >> 16) - (*xb++ >> 16) + borrow;
+		borrow = z >> 16;
+		Sign_Extend(borrow, z);
+		Storeinc(xc, z, y);
+		}
+		while(xb < xbe);
+	while(xa < xae) {
+		y = (*xa & 0xffff) + borrow;
+		borrow = y >> 16;
+		Sign_Extend(borrow, y);
+		z = (*xa++ >> 16) + borrow;
+		borrow = z >> 16;
+		Sign_Extend(borrow, z);
+		Storeinc(xc, z, y);
+		}
+#else
+	do {
+		y = *xa++ - *xb++ + borrow;
+		borrow = y >> 16;
+		Sign_Extend(borrow, y);
+		*xc++ = y & 0xffff;
+		}
+		while(xb < xbe);
+	while(xa < xae) {
+		y = *xa++ + borrow;
+		borrow = y >> 16;
+		Sign_Extend(borrow, y);
+		*xc++ = y & 0xffff;
+		}
+#endif
+	while(!*--xc)
+		wa--;
+	c->wds = wa;
+	return c;
+	}
+
+ static double
+ulp
+#ifdef KR_headers
+	(x) double x;
+#else
+	(double x)
+#endif
+{
+	Long L;
+	double a;
+
+	L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
+#ifndef Sudden_Underflow
+	if (L > 0) {
+#endif
+#ifdef IBM
+		L |= Exp_msk1 >> 4;
+#endif
+		word0(a) = L;
+		word1(a) = 0;
+#ifndef Sudden_Underflow
+		}
+	else {
+		L = -L >> Exp_shift;
+		if (L < Exp_shift) {
+			word0(a) = 0x80000 >> L;
+			word1(a) = 0;
+			}
+		else {
+			word0(a) = 0;
+			L -= Exp_shift;
+			word1(a) = L >= 31 ? 1 : 1 << (31 - L);
+			}
+		}
+#endif
+	return a;
+	}
+
+ static double
+b2d
+#ifdef KR_headers
+	(a, e) Bigint *a; int *e;
+#else
+	(Bigint *a, int *e)
+#endif
+{
+	ULong *xa, *xa0, w, y, z;
+	int k;
+	double d;
+#ifdef VAX
+	ULong d0, d1;
+#else
+#define d0 word0(d)
+#define d1 word1(d)
+#endif
+
+	xa0 = a->x;
+	xa = xa0 + a->wds;
+	y = *--xa;
+#ifdef DEBUG
+	if (!y) Bug("zero y in b2d");
+#endif
+	k = hi0bits(y);
+	*e = 32 - k;
+#ifdef Pack_32
+	if (k < Ebits) {
+		d0 = Exp_1 | y >> (Ebits - k);
+		w = xa > xa0 ? *--xa : 0;
+		d1 = y << ((32-Ebits) + k) | w >> (Ebits - k);
+		goto ret_d;
+		}
+	z = xa > xa0 ? *--xa : 0;
+	if (k -= Ebits) {
+		d0 = Exp_1 | y << k | z >> (32 - k);
+		y = xa > xa0 ? *--xa : 0;
+		d1 = z << k | y >> (32 - k);
+		}
+	else {
+		d0 = Exp_1 | y;
+		d1 = z;
+		}
+#else
+	if (k < Ebits + 16) {
+		z = xa > xa0 ? *--xa : 0;
+		d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
+		w = xa > xa0 ? *--xa : 0;
+		y = xa > xa0 ? *--xa : 0;
+		d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
+		goto ret_d;
+		}
+	z = xa > xa0 ? *--xa : 0;
+	w = xa > xa0 ? *--xa : 0;
+	k -= Ebits + 16;
+	d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
+	y = xa > xa0 ? *--xa : 0;
+	d1 = w << k + 16 | y << k;
+#endif
+ ret_d:
+#ifdef VAX
+	word0(d) = d0 >> 16 | d0 << 16;
+	word1(d) = d1 >> 16 | d1 << 16;
+#else
+#undef d0
+#undef d1
+#endif
+	return d;
+	}
+
+ static Bigint *
+d2b
+#ifdef KR_headers
+	(d, e, bits) double d; int *e, *bits;
+#else
+	(double d, int *e, int *bits)
+#endif
+{
+	Bigint *b;
+	int de, i, k;
+	ULong *x, y, z;
+#ifdef VAX
+	ULong d0, d1;
+	d0 = word0(d) >> 16 | word0(d) << 16;
+	d1 = word1(d) >> 16 | word1(d) << 16;
+#else
+#define d0 word0(d)
+#define d1 word1(d)
+#endif
+
+#ifdef Pack_32
+	b = Balloc(1);
+#else
+	b = Balloc(2);
+#endif
+	x = b->x;
+
+	z = d0 & Frac_mask;
+	d0 &= 0x7fffffff;	/* clear sign bit, which we ignore */
+#ifdef Sudden_Underflow
+	de = (int)(d0 >> Exp_shift);
+#ifndef IBM
+	z |= Exp_msk11;
+#endif
+#else
+	if ((de = (int)(d0 >> Exp_shift)) != 0)
+		z |= Exp_msk1;
+#endif
+#ifdef Pack_32
+	if ((y = d1) != 0) {
+		if ((k = lo0bits(&y)) != 0) {
+			x[0] = y | z << (32 - k);
+			z >>= k;
+			}
+		else
+			x[0] = y;
+		i = b->wds = (x[1] = z) ? 2 : 1;
+		}
+	else {
+#ifdef DEBUG
+		if (!z)
+			Bug("Zero passed to d2b");
+#endif
+		k = lo0bits(&z);
+		x[0] = z;
+		i = b->wds = 1;
+		k += 32;
+		}
+#else
+	if (y = d1) {
+		if (k = lo0bits(&y))
+			if (k >= 16) {
+				x[0] = y | z << 32 - k & 0xffff;
+				x[1] = z >> k - 16 & 0xffff;
+				x[2] = z >> k;
+				i = 2;
+				}
+			else {
+				x[0] = y & 0xffff;
+				x[1] = y >> 16 | z << 16 - k & 0xffff;
+				x[2] = z >> k & 0xffff;
+				x[3] = z >> k+16;
+				i = 3;
+				}
+		else {
+			x[0] = y & 0xffff;
+			x[1] = y >> 16;
+			x[2] = z & 0xffff;
+			x[3] = z >> 16;
+			i = 3;
+			}
+		}
+	else {
+#ifdef DEBUG
+		if (!z)
+			Bug("Zero passed to d2b");
+#endif
+		k = lo0bits(&z);
+		if (k >= 16) {
+			x[0] = z;
+			i = 0;
+			}
+		else {
+			x[0] = z & 0xffff;
+			x[1] = z >> 16;
+			i = 1;
+			}
+		k += 32;
+		}
+	while(!x[i])
+		--i;
+	b->wds = i + 1;
+#endif
+#ifndef Sudden_Underflow
+	if (de) {
+#endif
+#ifdef IBM
+		*e = (de - Bias - (P-1) << 2) + k;
+		*bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
+#else
+		*e = de - Bias - (P-1) + k;
+		*bits = P - k;
+#endif
+#ifndef Sudden_Underflow
+		}
+	else {
+		*e = de - Bias - (P-1) + 1 + k;
+#ifdef Pack_32
+		*bits = 32*i - hi0bits(x[i-1]);
+#else
+		*bits = (i+2)*16 - hi0bits(x[i]);
+#endif
+		}
+#endif
+	return b;
+	}
+#undef d0
+#undef d1
+
+ static double
+ratio
+#ifdef KR_headers
+	(a, b) Bigint *a, *b;
+#else
+	(Bigint *a, Bigint *b)
+#endif
+{
+	double da, db;
+	int k, ka, kb;
+
+	da = b2d(a, &ka);
+	db = b2d(b, &kb);
+#ifdef Pack_32
+	k = ka - kb + 32*(a->wds - b->wds);
+#else
+	k = ka - kb + 16*(a->wds - b->wds);
+#endif
+#ifdef IBM
+	if (k > 0) {
+		word0(da) += (k >> 2)*Exp_msk1;
+		if (k &= 3)
+			da *= 1 << k;
+		}
+	else {
+		k = -k;
+		word0(db) += (k >> 2)*Exp_msk1;
+		if (k &= 3)
+			db *= 1 << k;
+		}
+#else
+	if (k > 0)
+		word0(da) += k*Exp_msk1;
+	else {
+		k = -k;
+		word0(db) += k*Exp_msk1;
+		}
+#endif
+	return da / db;
+	}
+
+static CONST double
+tens[] = {
+		1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
+		1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
+		1e20, 1e21, 1e22
+#ifdef VAX
+		, 1e23, 1e24
+#endif
+		};
+
+#ifdef IEEE_Arith
+static CONST double bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
+static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, 1e-256 };
+#define n_bigtens 5
+#else
+#ifdef IBM
+static CONST double bigtens[] = { 1e16, 1e32, 1e64 };
+static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
+#define n_bigtens 3
+#else
+static CONST double bigtens[] = { 1e16, 1e32 };
+static CONST double tinytens[] = { 1e-16, 1e-32 };
+#define n_bigtens 2
+#endif
+#endif
+
+ double
+strtod
+#ifdef KR_headers
+	(s00, se) CONST char *s00; char **se;
+#else
+	(CONST char *s00, char **se)
+#endif
+{
+	int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
+		 e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
+	CONST char *s, *s0, *s1;
+	double aadj, aadj1, adj, rv, rv0;
+	Long L;
+	ULong y, z;
+	Bigint *bb1, *bd0;
+	Bigint *bb = NULL, *bd = NULL, *bs = NULL, *delta = NULL;/* pacify gcc */
+
+#ifndef KR_headers
+	CONST char decimal_point = localeconv()->decimal_point[0];
+#else
+	CONST char decimal_point = '.';
+#endif
+
+	sign = nz0 = nz = 0;
+	rv = 0.;
+
+
+	for(s = s00; isspace((unsigned char) *s); s++)
+		;
+
+	if (*s == '-') {
+		sign = 1;
+		s++;
+	} else if (*s == '+') {
+		s++;
+	}
+
+	if (*s == '\0') {
+		s = s00;
+		goto ret;
+	}
+
+	if (*s == '0') {
+		nz0 = 1;
+		while(*++s == '0') ;
+		if (!*s)
+			goto ret;
+		}
+	s0 = s;
+	y = z = 0;
+	for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
+		if (nd < 9)
+			y = 10*y + c - '0';
+		else if (nd < 16)
+			z = 10*z + c - '0';
+	nd0 = nd;
+	if (c == decimal_point) {
+		c = *++s;
+		if (!nd) {
+			for(; c == '0'; c = *++s)
+				nz++;
+			if (c > '0' && c <= '9') {
+				s0 = s;
+				nf += nz;
+				nz = 0;
+				goto have_dig;
+				}
+			goto dig_done;
+			}
+		for(; c >= '0' && c <= '9'; c = *++s) {
+ have_dig:
+			nz++;
+			if (c -= '0') {
+				nf += nz;
+				for(i = 1; i < nz; i++)
+					if (nd++ < 9)
+						y *= 10;
+					else if (nd <= DBL_DIG + 1)
+						z *= 10;
+				if (nd++ < 9)
+					y = 10*y + c;
+				else if (nd <= DBL_DIG + 1)
+					z = 10*z + c;
+				nz = 0;
+				}
+			}
+		}
+ dig_done:
+	e = 0;
+	if (c == 'e' || c == 'E') {
+		if (!nd && !nz && !nz0) {
+			s = s00;
+			goto ret;
+			}
+		s00 = s;
+		esign = 0;
+		switch(c = *++s) {
+			case '-':
+				esign = 1;
+			case '+':
+				c = *++s;
+			}
+		if (c >= '0' && c <= '9') {
+			while(c == '0')
+				c = *++s;
+			if (c > '0' && c <= '9') {
+				L = c - '0';
+				s1 = s;
+				while((c = *++s) >= '0' && c <= '9')
+					L = 10*L + c - '0';
+				if (s - s1 > 8 || L > 19999)
+					/* Avoid confusion from exponents
+					 * so large that e might overflow.
+					 */
+					e = 19999; /* safe for 16 bit ints */
+				else
+					e = (int)L;
+				if (esign)
+					e = -e;
+				}
+			else
+				e = 0;
+			}
+		else
+			s = s00;
+		}
+	if (!nd) {
+		if (!nz && !nz0)
+			s = s00;
+		goto ret;
+		}
+	e1 = e -= nf;
+
+	/* Now we have nd0 digits, starting at s0, followed by a
+	 * decimal point, followed by nd-nd0 digits.  The number we're
+	 * after is the integer represented by those digits times
+	 * 10**e */
+
+	if (!nd0)
+		nd0 = nd;
+	k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
+	rv = y;
+	if (k > 9)
+		rv = tens[k - 9] * rv + z;
+	bd0 = 0;
+	if (nd <= DBL_DIG
+#ifndef RND_PRODQUOT
+		&& FLT_ROUNDS == 1
+#endif
+			) {
+		if (!e)
+			goto ret;
+		if (e > 0) {
+			if (e <= Ten_pmax) {
+#ifdef VAX
+				goto vax_ovfl_check;
+#else
+				/* rv = */ rounded_product(rv, tens[e]);
+				goto ret;
+#endif
+				}
+			i = DBL_DIG - nd;
+			if (e <= Ten_pmax + i) {
+				/* A fancier test would sometimes let us do
+				 * this for larger i values.
+				 */
+				e -= i;
+				rv *= tens[i];
+#ifdef VAX
+				/* VAX exponent range is so narrow we must
+				 * worry about overflow here...
+				 */
+ vax_ovfl_check:
+				word0(rv) -= P*Exp_msk1;
+				/* rv = */ rounded_product(rv, tens[e]);
+				if ((word0(rv) & Exp_mask)
+				 > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
+					goto ovfl;
+				word0(rv) += P*Exp_msk1;
+#else
+				/* rv = */ rounded_product(rv, tens[e]);
+#endif
+				goto ret;
+				}
+			}
+#ifndef Inaccurate_Divide
+		else if (e >= -Ten_pmax) {
+			/* rv = */ rounded_quotient(rv, tens[-e]);
+			goto ret;
+			}
+#endif
+		}
+	e1 += nd - k;
+
+	/* Get starting approximation = rv * 10**e1 */
+
+	if (e1 > 0) {
+		if ((i = e1 & 15) != 0)
+			rv *= tens[i];
+		if (e1 &= ~15) {
+			if (e1 > DBL_MAX_10_EXP) {
+ ovfl:
+				errno = ERANGE;
+#ifdef __STDC__
+				rv = HUGE_VAL;
+#else
+				/* Can't trust HUGE_VAL */
+#ifdef IEEE_Arith
+				word0(rv) = Exp_mask;
+				word1(rv) = 0;
+#else
+				word0(rv) = Big0;
+				word1(rv) = Big1;
+#endif
+#endif
+				if (bd0)
+					goto retfree;
+				goto ret;
+				}
+			if (e1 >>= 4) {
+				for(j = 0; e1 > 1; j++, e1 >>= 1)
+					if (e1 & 1)
+						rv *= bigtens[j];
+			/* The last multiplication could overflow. */
+				word0(rv) -= P*Exp_msk1;
+				rv *= bigtens[j];
+				if ((z = word0(rv) & Exp_mask)
+				 > Exp_msk1*(DBL_MAX_EXP+Bias-P))
+					goto ovfl;
+				if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
+					/* set to largest number */
+					/* (Can't trust DBL_MAX) */
+					word0(rv) = Big0;
+					word1(rv) = Big1;
+					}
+				else
+					word0(rv) += P*Exp_msk1;
+				}
+
+			}
+		}
+	else if (e1 < 0) {
+		e1 = -e1;
+		if ((i = e1 & 15) != 0)
+			rv /= tens[i];
+		if (e1 &= ~15) {
+			e1 >>= 4;
+			if (e1 >= 1 << n_bigtens)
+				goto undfl;
+			for(j = 0; e1 > 1; j++, e1 >>= 1)
+				if (e1 & 1)
+					rv *= tinytens[j];
+			/* The last multiplication could underflow. */
+			rv0 = rv;
+			rv *= tinytens[j];
+			if (!rv) {
+				rv = 2.*rv0;
+				rv *= tinytens[j];
+				if (!rv) {
+ undfl:
+					rv = 0.;
+					errno = ERANGE;
+					if (bd0)
+						goto retfree;
+					goto ret;
+					}
+				word0(rv) = Tiny0;
+				word1(rv) = Tiny1;
+				/* The refinement below will clean
+				 * this approximation up.
+				 */
+				}
+			}
+		}
+
+	/* Now the hard part -- adjusting rv to the correct value.*/
+
+	/* Put digits into bd: true value = bd * 10^e */
+
+	bd0 = s2b(s0, nd0, nd, y);
+
+	for(;;) {
+		bd = Balloc(bd0->k);
+		Bcopy(bd, bd0);
+		bb = d2b(rv, &bbe, &bbbits);	/* rv = bb * 2^bbe */
+		bs = i2b(1);
+
+		if (e >= 0) {
+			bb2 = bb5 = 0;
+			bd2 = bd5 = e;
+			}
+		else {
+			bb2 = bb5 = -e;
+			bd2 = bd5 = 0;
+			}
+		if (bbe >= 0)
+			bb2 += bbe;
+		else
+			bd2 -= bbe;
+		bs2 = bb2;
+#ifdef Sudden_Underflow
+#ifdef IBM
+		j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
+#else
+		j = P + 1 - bbbits;
+#endif
+#else
+		i = bbe + bbbits - 1;	/* logb(rv) */
+		if (i < Emin)	/* denormal */
+			j = bbe + (P-Emin);
+		else
+			j = P + 1 - bbbits;
+#endif
+		bb2 += j;
+		bd2 += j;
+		i = bb2 < bd2 ? bb2 : bd2;
+		if (i > bs2)
+			i = bs2;
+		if (i > 0) {
+			bb2 -= i;
+			bd2 -= i;
+			bs2 -= i;
+			}
+		if (bb5 > 0) {
+			bs = pow5mult(bs, bb5);
+			bb1 = mult(bs, bb);
+			Bfree(bb);
+			bb = bb1;
+			}
+		if (bb2 > 0)
+			bb = lshift(bb, bb2);
+		if (bd5 > 0)
+			bd = pow5mult(bd, bd5);
+		if (bd2 > 0)
+			bd = lshift(bd, bd2);
+		if (bs2 > 0)
+			bs = lshift(bs, bs2);
+		delta = diff(bb, bd);
+		dsign = delta->sign;
+		delta->sign = 0;
+		i = cmp(delta, bs);
+		if (i < 0) {
+			/* Error is less than half an ulp -- check for
+			 * special case of mantissa a power of two.
+			 */
+			if (dsign || word1(rv) || word0(rv) & Bndry_mask)
+				break;
+			delta = lshift(delta,Log2P);
+			if (cmp(delta, bs) > 0)
+				goto drop_down;
+			break;
+			}
+		if (i == 0) {
+			/* exactly half-way between */
+			if (dsign) {
+				if ((word0(rv) & Bndry_mask1) == Bndry_mask1
+				 &&  word1(rv) == 0xffffffff) {
+					/*boundary case -- increment exponent*/
+					word0(rv) = (word0(rv) & Exp_mask)
+						+ Exp_msk1
+#ifdef IBM
+						| Exp_msk1 >> 4
+#endif
+						;
+					word1(rv) = 0;
+					break;
+					}
+				}
+			else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
+ drop_down:
+				/* boundary case -- decrement exponent */
+#ifdef Sudden_Underflow
+				L = word0(rv) & Exp_mask;
+#ifdef IBM
+				if (L <  Exp_msk1)
+#else
+				if (L <= Exp_msk1)
+#endif
+					goto undfl;
+				L -= Exp_msk1;
+#else
+				L = (word0(rv) & Exp_mask) - Exp_msk1;
+#endif
+				word0(rv) = L | Bndry_mask1;
+				word1(rv) = 0xffffffff;
+#ifdef IBM
+				goto cont;
+#else
+				break;
+#endif
+				}
+#ifndef ROUND_BIASED
+			if (!(word1(rv) & LSB))
+				break;
+#endif
+			if (dsign)
+				rv += ulp(rv);
+#ifndef ROUND_BIASED
+			else {
+				rv -= ulp(rv);
+#ifndef Sudden_Underflow
+				if (!rv)
+					goto undfl;
+#endif
+				}
+#endif
+			break;
+			}
+		if ((aadj = ratio(delta, bs)) <= 2.) {
+			if (dsign)
+				aadj = aadj1 = 1.;
+			else if (word1(rv) || word0(rv) & Bndry_mask) {
+#ifndef Sudden_Underflow
+				if (word1(rv) == Tiny1 && !word0(rv))
+					goto undfl;
+#endif
+				aadj = 1.;
+				aadj1 = -1.;
+				}
+			else {
+				/* special case -- power of FLT_RADIX to be */
+				/* rounded down... */
+
+				if (aadj < 2./FLT_RADIX)
+					aadj = 1./FLT_RADIX;
+				else
+					aadj *= 0.5;
+				aadj1 = -aadj;
+				}
+			}
+		else {
+			aadj *= 0.5;
+			aadj1 = dsign ? aadj : -aadj;
+#ifdef Check_FLT_ROUNDS
+			switch(FLT_ROUNDS) {
+				case 2: /* towards +infinity */
+					aadj1 -= 0.5;
+					break;
+				case 0: /* towards 0 */
+				case 3: /* towards -infinity */
+					aadj1 += 0.5;
+				}
+#else
+			if (FLT_ROUNDS == 0)
+				aadj1 += 0.5;
+#endif
+			}
+		y = word0(rv) & Exp_mask;
+
+		/* Check for overflow */
+
+		if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
+			rv0 = rv;
+			word0(rv) -= P*Exp_msk1;
+			adj = aadj1 * ulp(rv);
+			rv += adj;
+			if ((word0(rv) & Exp_mask) >=
+					Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
+				if (word0(rv0) == Big0 && word1(rv0) == Big1)
+					goto ovfl;
+				word0(rv) = Big0;
+				word1(rv) = Big1;
+				goto cont;
+				}
+			else
+				word0(rv) += P*Exp_msk1;
+			}
+		else {
+#ifdef Sudden_Underflow
+			if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
+				rv0 = rv;
+				word0(rv) += P*Exp_msk1;
+				adj = aadj1 * ulp(rv);
+				rv += adj;
+#ifdef IBM
+				if ((word0(rv) & Exp_mask) <  P*Exp_msk1)
+#else
+				if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
+#endif
+					{
+					if (word0(rv0) == Tiny0
+					 && word1(rv0) == Tiny1)
+						goto undfl;
+					word0(rv) = Tiny0;
+					word1(rv) = Tiny1;
+					goto cont;
+					}
+				else
+					word0(rv) -= P*Exp_msk1;
+				}
+			else {
+				adj = aadj1 * ulp(rv);
+				rv += adj;
+				}
+#else
+			/* Compute adj so that the IEEE rounding rules will
+			 * correctly round rv + adj in some half-way cases.
+			 * If rv * ulp(rv) is denormalized (i.e.,
+			 * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
+			 * trouble from bits lost to denormalization;
+			 * example: 1.2e-307 .
+			 */
+			if (y <= (P-1)*Exp_msk1 && aadj >= 1.) {
+				aadj1 = (double)(int)(aadj + 0.5);
+				if (!dsign)
+					aadj1 = -aadj1;
+				}
+			adj = aadj1 * ulp(rv);
+			rv += adj;
+#endif
+			}
+		z = word0(rv) & Exp_mask;
+		if (y == z) {
+			/* Can we stop now? */
+			L = aadj;
+			aadj -= L;
+			/* The tolerances below are conservative. */
+			if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
+				if (aadj < .4999999 || aadj > .5000001)
+					break;
+				}
+			else if (aadj < .4999999/FLT_RADIX)
+				break;
+			}
+ cont:
+		Bfree(bb);
+		Bfree(bd);
+		Bfree(bs);
+		Bfree(delta);
+		}
+ retfree:
+	Bfree(bb);
+	Bfree(bd);
+	Bfree(bs);
+	Bfree(bd0);
+	Bfree(delta);
+ ret:
+	if (se)
+		*se = (char *)s;
+	return sign ? -rv : rv;
+	}
+
+ static int
+quorem
+#ifdef KR_headers
+	(b, S) Bigint *b, *S;
+#else
+	(Bigint *b, Bigint *S)
+#endif
+{
+	int n;
+	Long borrow, y;
+	ULong carry, q, ys;
+	ULong *bx, *bxe, *sx, *sxe;
+#ifdef Pack_32
+	Long z;
+	ULong si, zs;
+#endif
+
+	n = S->wds;
+#ifdef DEBUG
+	/*debug*/ if (b->wds > n)
+	/*debug*/	Bug("oversize b in quorem");
+#endif
+	if (b->wds < n)
+		return 0;
+	sx = S->x;
+	sxe = sx + --n;
+	bx = b->x;
+	bxe = bx + n;
+	q = *bxe / (*sxe + 1);	/* ensure q <= true quotient */
+#ifdef DEBUG
+	/*debug*/ if (q > 9)
+	/*debug*/	Bug("oversized quotient in quorem");
+#endif
+	if (q) {
+		borrow = 0;
+		carry = 0;
+		do {
+#ifdef Pack_32
+			si = *sx++;
+			ys = (si & 0xffff) * q + carry;
+			zs = (si >> 16) * q + (ys >> 16);
+			carry = zs >> 16;
+			y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
+			borrow = y >> 16;
+			Sign_Extend(borrow, y);
+			z = (*bx >> 16) - (zs & 0xffff) + borrow;
+			borrow = z >> 16;
+			Sign_Extend(borrow, z);
+			Storeinc(bx, z, y);
+#else
+			ys = *sx++ * q + carry;
+			carry = ys >> 16;
+			y = *bx - (ys & 0xffff) + borrow;
+			borrow = y >> 16;
+			Sign_Extend(borrow, y);
+			*bx++ = y & 0xffff;
+#endif
+			}
+			while(sx <= sxe);
+		if (!*bxe) {
+			bx = b->x;
+			while(--bxe > bx && !*bxe)
+				--n;
+			b->wds = n;
+			}
+		}
+	if (cmp(b, S) >= 0) {
+		q++;
+		borrow = 0;
+		carry = 0;
+		bx = b->x;
+		sx = S->x;
+		do {
+#ifdef Pack_32
+			si = *sx++;
+			ys = (si & 0xffff) + carry;
+			zs = (si >> 16) + (ys >> 16);
+			carry = zs >> 16;
+			y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
+			borrow = y >> 16;
+			Sign_Extend(borrow, y);
+			z = (*bx >> 16) - (zs & 0xffff) + borrow;
+			borrow = z >> 16;
+			Sign_Extend(borrow, z);
+			Storeinc(bx, z, y);
+#else
+			ys = *sx++ + carry;
+			carry = ys >> 16;
+			y = *bx - (ys & 0xffff) + borrow;
+			borrow = y >> 16;
+			Sign_Extend(borrow, y);
+			*bx++ = y & 0xffff;
+#endif
+			}
+			while(sx <= sxe);
+		bx = b->x;
+		bxe = bx + n;
+		if (!*bxe) {
+			while(--bxe > bx && !*bxe)
+				--n;
+			b->wds = n;
+			}
+		}
+	return q;
+	}
+
+/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
+ *
+ * Inspired by "How to Print Floating-Point Numbers Accurately" by
+ * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101].
+ *
+ * Modifications:
+ *	1. Rather than iterating, we use a simple numeric overestimate
+ *	   to determine k = floor(log10(d)).  We scale relevant
+ *	   quantities using O(log2(k)) rather than O(k) multiplications.
+ *	2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
+ *	   try to generate digits strictly left to right.  Instead, we
+ *	   compute with fewer bits and propagate the carry if necessary
+ *	   when rounding the final digit up.  This is often faster.
+ *	3. Under the assumption that input will be rounded nearest,
+ *	   mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
+ *	   That is, we allow equality in stopping tests when the
+ *	   round-nearest rule will give the same floating-point value
+ *	   as would satisfaction of the stopping test with strict
+ *	   inequality.
+ *	4. We remove common factors of powers of 2 from relevant
+ *	   quantities.
+ *	5. When converting floating-point integers less than 1e16,
+ *	   we use floating-point arithmetic rather than resorting
+ *	   to multiple-precision integers.
+ *	6. When asked to produce fewer than 15 digits, we first try
+ *	   to get by with floating-point arithmetic; we resort to
+ *	   multiple-precision integer arithmetic only if we cannot
+ *	   guarantee that the floating-point calculation has given
+ *	   the correctly rounded result.  For k requested digits and
+ *	   "uniformly" distributed input, the probability is
+ *	   something like 10^(k-15) that we must resort to the Long
+ *	   calculation.
+ */
+
+ char *
+__dtoa
+#ifdef KR_headers
+	(d, mode, ndigits, decpt, sign, rve)
+	double d; int mode, ndigits, *decpt, *sign; char **rve;
+#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.
+	*/
+
+	int bbits, b2, b5, be, dig, i, ieps, ilim0,
+		j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
+		try_quick;
+	int ilim = 0, ilim1 = 0, spec_case = 0;	/* pacify gcc */
+	Long L;
+#ifndef Sudden_Underflow
+	int denorm;
+	ULong x;
+#endif
+	Bigint *b, *b1, *delta, *mhi, *S;
+	Bigint *mlo = NULL; /* pacify gcc */
+	double d2, ds, eps;
+	char *s, *s0;
+	static Bigint *result;
+	static int result_k;
+
+	if (result) {
+		result->k = result_k;
+		result->maxwds = 1 << result_k;
+		Bfree(result);
+		result = 0;
+		}
+
+	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))) != 0) {
+#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;
+		}
+	j = sizeof(ULong);
+	for(result_k = 0; sizeof(Bigint) - sizeof(ULong) + j <= i;
+		j <<= 1) result_k++;
+	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) != 0) {
+			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) != 0)
+				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) != 0)
+		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