This is a hack to workaround source that is coded to use long variables

but also assumes that they are 32-bits. This is one place where I don't
think it is appropriate to change 'long' to 'int'. I don't see why the
code couldn't be fixed so that using natural long variables does the
right thing. It's spaggetti code so it'll take some effort. Obviously
NetBSD thought so too because they change 'long' to 'int32_t' etc
and left it at that. As a temporary measure FreeBSD/Alpha can use the
NetBSD code and put this on the list of things to fix.

2 files changed, 2528 insertions, 2 deletions

diff --git a/lib/libc/stdlib/Makefile.inc b/lib/libc/stdlib/Makefile.inc
index 6ad404e..0d7ae27 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 0000000..72cd366
--- /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