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ruby-changes:4848

From: ko1@a...
Date: Sat, 10 May 2008 09:18:50 +0900 (JST)
Subject: [ruby-changes:4848] matz - Ruby:r16342 (ruby_1_8): * util.c (ruby_strtod): backported from 1.9. a patch from Satoshi

matz	2008-05-10 09:18:32 +0900 (Sat, 10 May 2008)

  New Revision: 16342

  Modified files:
    branches/ruby_1_8/ChangeLog
    branches/ruby_1_8/util.c
    branches/ruby_1_8/version.h

  Log:
    * util.c (ruby_strtod): backported from 1.9.  a patch from Satoshi
      Nakagawa <psychs at limechat.net> in [ruby-dev:34625]. 
      fixed: [ruby-dev:34623]

  http://svn.ruby-lang.org/cgi-bin/viewvc.cgi/branches/ruby_1_8/ChangeLog?r1=16342&r2=16341&diff_format=u
  http://svn.ruby-lang.org/cgi-bin/viewvc.cgi/branches/ruby_1_8/util.c?r1=16342&r2=16341&diff_format=u
  http://svn.ruby-lang.org/cgi-bin/viewvc.cgi/branches/ruby_1_8/version.h?r1=16342&r2=16341&diff_format=u

Index: ruby_1_8/util.c
===================================================================
--- ruby_1_8/util.c	(revision 16341)
+++ ruby_1_8/util.c	(revision 16342)
@@ -664,288 +664,3193 @@
     return buf;
 }
 
-/* copyright notice for strtod implementation --
+
+/****************************************************************
  *
- * Copyright (c) 1988-1993 The Regents of the University of California.
- * Copyright (c) 1994 Sun Microsystems, Inc.
+ * The author of this software is David M. Gay.
  *
- * Permission to use, copy, modify, and distribute this
- * software and its documentation for any purpose and without
- * fee is hereby granted, provided that the above copyright
- * notice appear in all copies.  The University of California
- * makes no representations about the suitability of this
- * software for any purpose.  It is provided "as is" without
- * express or implied warranty.
+ * Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
  *
- */
+ * 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 LUCENT MAKES ANY
+ * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
+ * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
+ *
+ ***************************************************************/
 
-#define MDMINEXPT DBL_MIN_10_EXP
-#define MDMAXEXPT DBL_MAX_10_EXP
+/* Please send bug reports to David M. Gay (dmg at acm dot org,
+ * with " at " changed at "@" and " dot " changed to ".").	*/
 
-static const
-double powersOf10[] = { 	/* Table giving binary powers of 10.  Entry */
-    10.0,			/* is 10^2^i.  Used to convert decimal */
-    100.0,			/* exponents into floating-point numbers. */
-    1.0e4,
-    1.0e8,
-    1.0e16,
-    1.0e32,
-    1.0e64,
-    1.0e128,
-    1.0e256
-};
+/* On a machine with IEEE extended-precision registers, it is
+ * necessary to specify double-precision (53-bit) rounding precision
+ * before invoking strtod or dtoa.  If the machine uses (the equivalent
+ * of) Intel 80x87 arithmetic, the call
+ *	_control87(PC_53, MCW_PC);
+ * does this with many compilers.  Whether this or another call is
+ * appropriate depends on the compiler; for this to work, it may be
+ * necessary to #include "float.h" or another system-dependent header
+ * file.
+ */
 
-/*
- *----------------------------------------------------------------------
+/* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
  *
- * strtod --
+ * 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).
  *
- *	This procedure converts a floating-point number from an ASCII
- *	decimal representation to internal double-precision format.
+ * Inspired loosely by William D. Clinger's paper "How to Read Floating
+ * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
  *
- * Results:
- *	The return value is the double-precision floating-point
- *	representation of the characters in string.  If endPtr isn't
- *	NULL, then *endPtr is filled in with the address of the
- *	next character after the last one that was part of the
- *	floating-point number.
+ * Modifications:
  *
- * Side effects:
- *	None.
- *
- *----------------------------------------------------------------------
+ *	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 IBM for IBM mainframe-style floating-point arithmetic.
+ * #define VAX for VAX-style floating-point arithmetic (D_floating).
+ * #define No_leftright to omit left-right logic in fast floating-point
+ *	computation of dtoa.
+ * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
+ *	and strtod and dtoa should round accordingly.
+ * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
+ *	and Honor_FLT_ROUNDS is not #defined.
+ * #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 NO_LONG_LONG on machines that do not have a "long long"
+ *	integer type (of >= 64 bits).  On such machines, you can
+ *	#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.  If long long is available and the name is
+ *	something other than "long long", #define Llong to be the name,
+ *	and if "unsigned Llong" does not work as an unsigned version of
+ *	Llong, #define #ULLong to be the corresponding unsigned type.
+ * #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.
+ * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
+ *	memory allocations from a private pool of memory when possible.
+ *	When used, the private pool is PRIVATE_MEM bytes long:  2304 bytes,
+ *	unless #defined to be a different length.  This default length
+ *	suffices to get rid of MALLOC calls except for unusual cases,
+ *	such as decimal-to-binary conversion of a very long string of
+ *	digits.  The longest string dtoa can return is about 751 bytes
+ *	long.  For conversions by strtod of strings of 800 digits and
+ *	all dtoa conversions in single-threaded executions with 8-byte
+ *	pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte
+ *	pointers, PRIVATE_MEM >= 7112 appears adequate.
+ * #define INFNAN_CHECK on IEEE systems to cause strtod to check for
+ *	Infinity and NaN (case insensitively).  On some systems (e.g.,
+ *	some HP systems), it may be necessary to #define NAN_WORD0
+ *	appropriately -- to the most significant word of a quiet NaN.
+ *	(On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
+ *	When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
+ *	strtod also accepts (case insensitively) strings of the form
+ *	NaN(x), where x is a string of hexadecimal digits and spaces;
+ *	if there is only one string of hexadecimal digits, it is taken
+ *	for the 52 fraction bits of the resulting NaN; if there are two
+ *	or more strings of hex digits, the first is for the high 20 bits,
+ *	the second and subsequent for the low 32 bits, with intervening
+ *	white space ignored; but if this results in none of the 52
+ *	fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0
+ *	and NAN_WORD1 are used instead.
+ * #define MULTIPLE_THREADS if the system offers preemptively scheduled
+ *	multiple threads.  In this case, you must provide (or suitably
+ *	#define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
+ *	by FREE_DTOA_LOCK(n) for n = 0 or 1.  (The second lock, accessed
+ *	in pow5mult, ensures lazy evaluation of only one copy of high
+ *	powers of 5; omitting this lock would introduce a small
+ *	probability of wasting memory, but would otherwise be harmless.)
+ *	You must also invoke freedtoa(s) to free the value s returned by
+ *	dtoa.  You may do so whether or not MULTIPLE_THREADS is #defined.
+ * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
+ *	avoids underflows on inputs whose result does not underflow.
+ *	If you #define NO_IEEE_Scale on a machine that uses IEEE-format
+ *	floating-point numbers and flushes underflows to zero rather
+ *	than implementing gradual underflow, then you must also #define
+ *	Sudden_Underflow.
+ * #define YES_ALIAS to permit aliasing certain double values with
+ *	arrays of ULongs.  This leads to slightly better code with
+ *	some compilers and was always used prior to 19990916, but it
+ *	is not strictly legal and can cause trouble with aggressively
+ *	optimizing compilers (e.g., gcc 2.95.1 under -O2).
+ * #define USE_LOCALE to use the current locale's decimal_point value.
+ * #define SET_INEXACT if IEEE arithmetic is being used and extra
+ *	computation should be done to set the inexact flag when the
+ *	result is inexact and avoid setting inexact when the result
+ *	is exact.  In this case, dtoa.c must be compiled in
+ *	an environment, perhaps provided by #include "dtoa.c" in a
+ *	suitable wrapper, that defines two functions,
+ *		int get_inexact(void);
+ *		void clear_inexact(void);
+ *	such that get_inexact() returns a nonzero value if the
+ *	inexact bit is already set, and clear_inexact() sets the
+ *	inexact bit to 0.  When SET_INEXACT is #defined, strtod
+ *	also does extra computations to set the underflow and overflow
+ *	flags when appropriate (i.e., when the result is tiny and
+ *	inexact or when it is a numeric value rounded to +-infinity).
+ * #define NO_ERRNO if strtod should not assign errno = ERANGE when
+ *	the result overflows to +-Infinity or underflows to 0.
+ */
+
+#ifdef WORDS_BIGENDIAN
+#define IEEE_BIG_ENDIAN
+#else
+#define IEEE_LITTLE_ENDIAN
+#endif
+
+#ifdef __vax__
+#define VAX
+#undef IEEE_BIG_ENDIAN
+#undef IEEE_LITTLE_ENDIAN
+#endif
+
+#if defined(__arm__) && !defined(__VFP_FP__)
+#define IEEE_BIG_ENDIAN
+#undef IEEE_LITTLE_ENDIAN
+#endif
+
+#undef Long
+#undef ULong
+
+#if SIZEOF_INT == 4
+#define Long int
+#define ULong unsigned int
+#elif SIZEOF_LONG == 4
+#define Long long int
+#define ULong unsigned long int
+#endif
+
+#if HAVE_LONG_LONG
+#define Llong LONG_LONG
+#endif
+
+#ifdef DEBUG
+#include "stdio.h"
+#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
+#endif
+
+#include "stdlib.h"
+#include "string.h"
+
+#ifdef USE_LOCALE
+#include "locale.h"
+#endif
+
+#ifdef MALLOC
+extern void *MALLOC(size_t);
+#else
+#define MALLOC malloc
+#endif
+
+#ifndef Omit_Private_Memory
+#ifndef PRIVATE_MEM
+#define PRIVATE_MEM 2304
+#endif
+#define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
+static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
+#endif
+
+#undef IEEE_Arith
+#undef Avoid_Underflow
+#ifdef IEEE_BIG_ENDIAN
+#define IEEE_Arith
+#endif
+#ifdef IEEE_LITTLE_ENDIAN
+#define IEEE_Arith
+#endif
+
+#include "errno.h"
+
+#ifdef Bad_float_h
+
+#ifdef IEEE_Arith
+#define DBL_DIG 15
+#define DBL_MAX_10_EXP 308
+#define DBL_MAX_EXP 1024
+#define FLT_RADIX 2
+#endif /*IEEE_Arith*/
+
+#ifdef IBM
+#define DBL_DIG 16
+#define DBL_MAX_10_EXP 75
+#define DBL_MAX_EXP 63
+#define FLT_RADIX 16
+#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 DBL_MAX 1.7014118346046923e+38
+#endif
+
+#ifndef LONG_MAX
+#define LONG_MAX 2147483647
+#endif
+
+#else /* ifndef Bad_float_h */
+#include "float.h"
+#endif /* Bad_float_h */
+
+#ifndef __MATH_H__
+#include "math.h"
+#endif
+
+#ifdef __cplusplus
+extern "C" {
+#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
+
+typedef union { double d; ULong L[2]; } U;
+
+#ifdef YES_ALIAS
+#define dval(x) x
+#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
+#else
+#ifdef IEEE_LITTLE_ENDIAN
+#define word0(x) ((U*)&x)->L[1]
+#define word1(x) ((U*)&x)->L[0]
+#else
+#define word0(x) ((U*)&x)->L[0]
+#define word1(x) ((U*)&x)->L[1]
+#endif
+#define dval(x) ((U*)&x)->d
+#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(__arm__)
+#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) */
+
+#ifdef IEEE_Arith
+#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 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
+#ifndef NO_IEEE_Scale
+#define Avoid_Underflow
+#ifdef Flush_Denorm	/* debugging option */
+#undef Sudden_Underflow
+#endif
+#endif
+
+#ifndef Flt_Rounds
+#ifdef FLT_ROUNDS
+#define Flt_Rounds FLT_ROUNDS
+#else
+#define Flt_Rounds 1
+#endif
+#endif /*Flt_Rounds*/
+
+#ifdef Honor_FLT_ROUNDS
+#define Rounding rounding
+#undef Check_FLT_ROUNDS
+#define Check_FLT_ROUNDS
+#else
+#define Rounding Flt_Rounds
+#endif
+
+#else /* ifndef IEEE_Arith */
+#undef Check_FLT_ROUNDS
+#undef Honor_FLT_ROUNDS
+#undef SET_INEXACT
+#undef  Sudden_Underflow
+#define Sudden_Underflow
+#ifdef IBM
+#undef Flt_Rounds
+#define Flt_Rounds 0
+#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 */
+#undef Flt_Rounds
+#define Flt_Rounds 1
+#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 /* IBM, VAX */
+#endif /* IEEE_Arith */
+
+#ifndef IEEE_Arith
+#define ROUND_BIASED
+#endif
+
+#ifdef RND_PRODQUOT
+#define rounded_product(a,b) a = rnd_prod(a, b)
+#define rounded_quotient(a,b) a = rnd_quot(a, b)
+extern double rnd_prod(double, double), rnd_quot(double, double);
+#else
+#define rounded_product(a,b) a *= b
+#define rounded_quotient(a,b) a /= b
+#endif
+
+#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
+#define Big1 0xffffffff
+
+#ifndef Pack_32
+#define Pack_32
+#endif
+
+#define FFFFFFFF 0xffffffffUL
+
+#ifdef NO_LONG_LONG
+#undef ULLong
+#ifdef Just_16
+#undef Pack_32
+/* 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.
+ */
+#endif
+#else	/* long long available */
+#ifndef Llong
+#define Llong long long
+#endif
+#ifndef ULLong
+#define ULLong unsigned Llong
+#endif
+#endif /* NO_LONG_LONG */
+
+#ifndef MULTIPLE_THREADS
+#define ACQUIRE_DTOA_LOCK(n)	/*nothing*/
+#define FREE_DTOA_LOCK(n)	/*nothing*/
+#endif
+
+#define Kmax 15
+
+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(int k)
+{
+    int x;
+    Bigint *rv;
+#ifndef Omit_Private_Memory
+    unsigned int len;
+#endif
+
+    ACQUIRE_DTOA_LOCK(0);
+    if ((rv = freelist[k]) != 0) {
+        freelist[k] = rv->next;
+    }
+    else {
+        x = 1 << k;
+#ifdef Omit_Private_Memory
+        rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
+#else
+        len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
+                /sizeof(double);
+        if (pmem_next - private_mem + len <= PRIVATE_mem) {
+            rv = (Bigint*)pmem_next;
+            pmem_next += len;
+        }
+        else
+            rv = (Bigint*)MALLOC(len*sizeof(double));
+#endif
+        rv->k = k;
+        rv->maxwds = x;
+    }
+    FREE_DTOA_LOCK(0);
+    rv->sign = rv->wds = 0;
+    return rv;
+}
+
+static void
+Bfree(Bigint *v)
+{
+    if (v) {
+        ACQUIRE_DTOA_LOCK(0);
+        v->next = freelist[v->k];
+        freelist[v->k] = v;
+        FREE_DTOA_LOCK(0);
+    }
+}
+
+#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
+y->wds*sizeof(Long) + 2*sizeof(int))
+
+static Bigint *
+multadd(Bigint *b, int m, int a)   /* multiply by m and add a */
+{
+    int i, wds;
+#ifdef ULLong
+    ULong *x;
+    ULLong carry, y;
+#else
+    ULong carry, *x, y;
+#ifdef Pack_32
+    ULong xi, z;
+#endif
+#endif
+    Bigint *b1;
+
+    wds = b->wds;
+    x = b->x;
+    i = 0;
+    carry = a;
+    do {
+#ifdef ULLong
+        y = *x * (ULLong)m + carry;
+        carry = y >> 32;
+        *x++ = y & FFFFFFFF;
+#else
+#ifdef Pack_32
+        xi = *x;
+        y = (xi & 0xffff) * m + carry;
+        z = (xi >> 16) * m + (y >> 16);
+        carry = z >> 16;
+        *x++ = (z << 16) + (y & 0xffff);
+#else
+        y = *x * m + carry;
+        carry = y >> 16;
+        *x++ = y & 0xffff;
+#endif
+#endif
+    } while (++i < wds);
+    if (carry) {
+        if (wds >= b->maxwds) {
+            b1 = Balloc(b->k+1);
+            Bcopy(b1, b);
+            Bfree(b);
+            b = b1;
+        }
+        b->x[wds++] = carry;
+        b->wds = wds;
+    }
+    return b;
+}
+
+static Bigint *
+s2b(const char *s, int nd0, int nd, ULong y9)
+{
+    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(register ULong x)
+{
+    register int k = 0;
+
+    if (!(x & 0xffff0000)) {
+        k = 16;
+        x <<= 16;
+    }
+    if (!(x & 0xff000000)) {
+        k += 8;
+        x <<= 8;
+    }
+    if (!(x & 0xf0000000)) {
+        k += 4;
+        x <<= 4;
+    }
+    if (!(x & 0xc0000000)) {
+        k += 2;
+        x <<= 2;
+    }
+    if (!(x & 0x80000000)) {
+        k++;
+        if (!(x & 0x40000000))
+            return 32;
+    }
+    return k;
+}
+
+static int
+lo0bits(ULong *y)
+{
+    register int k;
+    register 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)
+            return 32;
+    }
+    *y = x;
+    return k;
+}
+
+static Bigint *
+i2b(int i)
+{
+    Bigint *b;
+
+    b = Balloc(1);
+    b->x[0] = i;
+    b->wds = 1;
+    return b;
+}
+
+static Bigint *
+mult(Bigint *a, Bigint *b)
+{
+    Bigint *c;
+    int k, wa, wb, wc;
+    ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
+    ULong y;
+#ifdef ULLong
+    ULLong carry, z;
+#else
+    ULong carry, z;
+#ifdef Pack_32
+    ULong z2;
+#endif
+#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 ULLong
+    for (; xb < xbe; xc0++) {
+        if ((y = *xb++) != 0) {
+            x = xa;
+            xc = xc0;
+            carry = 0;
+            do {
+                z = *x++ * (ULLong)y + *xc + carry;
+                carry = z >> 32;
+                *xc++ = z & FFFFFFFF;
+            } while (x < xae);
+            *xc = carry;
+        }
+    }
+#else
+#ifdef Pack_32
+    for (; xb < xbe; xb++, xc0++) {
+        if (y = *xb & 0xffff) {
+            x = xa;
+            xc = xc0;
+            carry = 0;
+            do {
+                z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
+                carry = z >> 16;
+                z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
+                carry = z2 >> 16;
+                Storeinc(xc, z2, z);
+            } while (x < xae);
+            *xc = carry;
+        }
+        if (y = *xb >> 16) {
+            x = xa;
+            xc = xc0;
+            carry = 0;
+            z2 = *xc;
+            do {
+                z = (*x & 0xffff) * y + (*xc >> 16) + carry;
+                carry = z >> 16;
+                Storeinc(xc, z, z2);
+                z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
+                carry = z2 >> 16;
+            } while (x < xae);
+            *xc = z2;
+        }
+    }
+#else
+    for (; xb < xbe; xc0++) {
+        if (y = *xb++) {
+            x = xa;
+            xc = xc0;
+            carry = 0;
+            do {
+                z = *x++ * y + *xc + carry;
+                carry = z >> 16;
+                *xc++ = z & 0xffff;
+            } while (x < xae);
+            *xc = carry;
+        }
+    }
+#endif
+#endif
+    for (xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
+    c->wds = wc;
+    return c;
+}
+
+static Bigint *p5s;
+
+static Bigint *
+pow5mult(Bigint *b, int k)
+{
+    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 */
+#ifdef MULTIPLE_THREADS
+        ACQUIRE_DTOA_LOCK(1);
+        if (!(p5 = p5s)) {
+            p5 = p5s = i2b(625);
+            p5->next = 0;
+        }
+        FREE_DTOA_LOCK(1);
+#else
+        p5 = p5s = i2b(625);
+        p5->next = 0;
+#endif
+    }
+    for (;;) {
+        if (k & 1) {
+            b1 = mult(b, p5);
+            Bfree(b);
+            b = b1;
+        }
+        if (!(k >>= 1))
+            break;
+        if (!(p51 = p5->next)) {
+#ifdef MULTIPLE_THREADS
+            ACQUIRE_DTOA_LOCK(1);
+            if (!(p51 = p5->next)) {
+                p51 = p5->next = mult(p5,p5);
+                p51->next = 0;
+            }
+            FREE_DTOA_LOCK(1);
+#else
+            p51 = p5->next = mult(p5,p5);
+            p51->next = 0;
+#endif
+        }
+        p5 = p51;
+    }
+    return b;
+}
+
+static Bigint *
+lshift(Bigint *b, int k)
+{
+    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(Bigint *a, Bigint *b)
+{
+    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(Bigint *a, Bigint *b)
+{
+    Bigint *c;
+    int i, wa, wb;
+    ULong *xa, *xae, *xb, *xbe, *xc;
+#ifdef ULLong
+    ULLong borrow, y;
+#else
+    ULong borrow, y;
+#ifdef Pack_32
+    ULong z;
+#endif
+#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 ULLong
+    do {
+        y = (ULLong)*xa++ - *xb++ - borrow;
+        borrow = y >> 32 & (ULong)1;
+        *xc++ = y & FFFFFFFF;
+    } while (xb < xbe);
+    while (xa < xae) {
+        y = *xa++ - borrow;
+        borrow = y >> 32 & (ULong)1;
+        *xc++ = y & FFFFFFFF;
+    }
+#else
+#ifdef Pack_32
+    do {
+        y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
+        borrow = (y & 0x10000) >> 16;
+        z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
+        borrow = (z & 0x10000) >> 16;
+        Storeinc(xc, z, y);
+    } while (xb < xbe);
+    while (xa < xae) {
+        y = (*xa & 0xffff) - borrow;
+        borrow = (y & 0x10000) >> 16;
+        z = (*xa++ >> 16) - borrow;
+        borrow = (z & 0x10000) >> 16;
+        Storeinc(xc, z, y);
+    }
+#else
+    do {
+        y = *xa++ - *xb++ - borrow;
+        borrow = (y & 0x10000) >> 16;
+        *xc++ = y & 0xffff;
+    } while (xb < xbe);
+    while (xa < xae) {
+        y = *xa++ - borrow;
+        borrow = (y & 0x10000) >> 16;
+        *xc++ = y & 0xffff;
+    }
+#endif
+#endif
+    while (!*--xc)
+        wa--;
+    c->wds = wa;
+    return c;
+}
+
+static double
+ulp(double x)
+{
+    register Long L;
+    double a;
+
+    L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
+#ifndef Avoid_Underflow
+#ifndef Sudden_Underflow
+    if (L > 0) {
+#endif
+#endif
+#ifdef IBM
+        L |= Exp_msk1 >> 4;
+#endif
+        word0(a) = L;
+        word1(a) = 0;
+#ifndef Avoid_Underflow
+#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
+#endif
+    return dval(a);
+}
+
+static double
+b2d(Bigint *a, int *e)
+{
+    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 dval(d);
+}
+
+static Bigint *
+d2b(double d, int *e, int *bits)
+{
+    Bigint *b;
+    int de, k;
+    ULong *x, y, z;
+#ifndef Sudden_Underflow
+    int i;
+#endif
+#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;
+#ifndef Sudden_Underflow
+        i =
+#endif
+        b->wds = (x[1] = z) ? 2 : 1;
+    }
+    else {
+#ifdef DEBUG
+        if (!z)
+            Bug("Zero passed to d2b");
+#endif
+        k = lo0bits(&z);
+        x[0] = z;
+#ifndef Sudden_Underflow
+        i =
+#endif
+        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(Bigint *a, Bigint *b)
+{
+    double da, db;
+    int k, ka, kb;
+
+    dval(da) = b2d(a, &ka);
+    dval(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)
+            dval(da) *= 1 << k;
+    }
+    else {
+        k = -k;
+        word0(db) += (k >> 2)*Exp_msk1;
+        if (k &= 3)
+            dval(db) *= 1 << k;
+    }
+#else
+    if (k > 0)
+        word0(da) += k*Exp_msk1;
+    else {
+        k = -k;
+        word0(db) += k*Exp_msk1;
+    }
+#endif
+    return dval(da) / dval(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
+};
+
+static const double
+#ifdef IEEE_Arith
+bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
+static const double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
+#ifdef Avoid_Underflow
+    9007199254740992.*9007199254740992.e-256
+    /* = 2^106 * 1e-53 */
+#else
+    1e-256
+#endif
+};
+/* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
+/* flag unnecessarily.  It leads to a song and dance at the end of strtod. */
+#define Scale_Bit 0x10
+#define n_bigtens 5
+#else
+#ifdef IBM
+bigtens[] = { 1e16, 1e32, 1e64 };
+static const double tinytens[] = { 1e-16, 1e-32, 1e-64 };
+#define n_bigtens 3
+#else
+bigtens[] = { 1e16, 1e32 };
+static const double tinytens[] = { 1e-16, 1e-32 };
+#define n_bigtens 2
+#endif
+#endif
+
+#ifndef IEEE_Arith
+#undef INFNAN_CHECK
+#endif
+
+#ifdef INFNAN_CHECK
+
+#ifndef NAN_WORD0
+#define NAN_WORD0 0x7ff80000
+#endif
+
+#ifndef NAN_WORD1
+#define NAN_WORD1 0
+#endif
+
+static int
+match(const char **sp, char *t)
+{
+    int c, d;
+    const char *s = *sp;
+
+    while (d = *t++) {
+        if ((c = *++s) >= 'A' && c <= 'Z')
+            c += 'a' - 'A';
+        if (c != d)
+            return 0;
+    }
+    *sp = s + 1;
+    return 1;
+}
+
+#ifndef No_Hex_NaN
+static void
+hexnan(double *rvp, const char **sp)
+{
+    ULong c, x[2];
+    const char *s;
+    int havedig, udx0, xshift;
+
+    x[0] = x[1] = 0;
+    havedig = xshift = 0;
+    udx0 = 1;
+    s = *sp;
+    while (c = *(const unsigned char*)++s) {
+        if (c >= '0' && c <= '9')
+            c -= '0';
+        else if (c >= 'a' && c <= 'f')
+            c += 10 - 'a';
+        else if (c >= 'A' && c <= 'F')
+            c += 10 - 'A';
+        else if (c <= ' ') {
+            if (udx0 && havedig) {
+                udx0 = 0;
+                xshift = 1;
+            }
+            continue;
+        }
+        else if (/*(*/ c == ')' && havedig) {
+            *sp = s + 1;
+            break;
+        }
+        else
+            return; /* invalid form: don't change *sp */
+        havedig = 1;
+        if (xshift) {
+            xshift = 0;
+            x[0] = x[1];
+            x[1] = 0;
+        }
+        if (udx0)
+            x[0] = (x[0] << 4) | (x[1] >> 28);
+        x[1] = (x[1] << 4) | c;
+    }
+    if ((x[0] &= 0xfffff) || x[1]) {
+        word0(*rvp) = Exp_mask | x[0];
+        word1(*rvp) = x[1];
+    }
+}
+#endif /*No_Hex_NaN*/
+#endif /* INFNAN_CHECK */
+
 double
-ruby_strtod(string, endPtr)
-    const char *string;		/* A decimal ASCII floating-point number,
-				 * optionally preceded by white space.
-				 * Must have form "-I.FE-X", where I is the
-				 * integer part of the mantissa, F is the
-				 * fractional part of the mantissa, and X
-				 * is the exponent.  Either of the signs
-				 * may be "+", "-", or omitted.  Either I
-				 * or F may be omitted, but both cannot be
-				 * ommitted at once. The decimal
-				 * point isn't necessary unless F is present.
-				 * The "E" may actually be an "e".  E and X
-				 * may both be omitted (but not just one).
-				 */
-    char **endPtr;		/* If non-NULL, store terminating character's
-				 * address here. */
+ruby_strtod(const char *s00, char **se)
 {
-    int sign, expSign = Qfalse;
-    double fraction = 0.0, dblExp;
-    const double *d;
-    register const char *p;
-    register int c;
-    int exp = 0;		/* Exponent read from "EX" field. */
-    int fracExp = 0;		/* Exponent that derives from the fractional
-				 * part.  Under normal circumstatnces, it is
-				 * the negative of the number of digits in F.
-				 * However, if I is very long, the last digits
-				 * of I get dropped (otherwise a long I with a
-				 * large negative exponent could cause an
-				 * unnecessary overflow on I alone).  In this
-				 * case, fracExp is incremented one for each
-				 * dropped digit. */
-    int mantSize = 0;		/* Number of digits in mantissa. */
-    int hasPoint = Qfalse;	/* Decimal point exists. */
-    int hasDigit = Qfalse;	/* I or F exists. */
-    const char *pMant;		/* Temporarily holds location of mantissa
-				 * in string. */
-    const char *pExp;		/* Temporarily holds location of exponent
-				 * in string. */
+#ifdef Avoid_Underflow
+    int scale;
+#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 *bb, *bb1, *bd, *bd0, *bs, *delta;
+#ifdef SET_INEXACT
+    int inexact, oldinexact;
+#endif
+#ifdef Honor_FLT_ROUNDS
+    int rounding;
+#endif
+#ifdef USE_LOCALE
+    const char *s2;
+#endif
 
-    /*
-     * Strip off leading blanks and check for a sign.
-     */
+    sign = nz0 = nz = 0;
+    dval(rv) = 0.;
+    for (s = s00;;s++)
+        switch (*s) {
+          case '-':
+            sign = 1;
+            /* no break */
+          case '+':
+            if (*++s)
+                goto break2;
+            /* no break */
+          case 0:
+            goto ret0;
+          case '\t':
+          case '\n':
+          case '\v':
+          case '\f':
+          case '\r':
+          case ' ':
+            continue;
+          default:
+            goto break2;
+        }
+break2:
+    if (*s == '0') {
+        nz0 = 1;
+        while (*++s == '0') ;
+        if (!*s)
+            goto ret;
+    }
+    s0 = s;
+    y = z = 0;
+    for (nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
+        if (nd < 9)
+            y = 10*y + c - '0';
+        else if (nd < 16)
+            z = 10*z + c - '0';
+    nd0 = nd;
+#ifdef USE_LOCALE
+    s1 = localeconv()->decimal_point;
+    if (c == *s1) {
+        c = '.';
+        if (*++s1) {
+            s2 = s;
+            for (;;) {
+                if (*++s2 != *s1) {
+                    c = 0;
+                    break;
+                }
+                if (!*++s1) {
+                    s = s2;
+                    break;
+                }
+            }
+        }
+    }
+#endif
+    if (c == '.') {
+        c = *++s;
+        if (!nd) {
+            for (; c == '0'; c = *++s)
+                nz++;
+            if (c > '0' && c <= '9') {
+                s0 = s;
+                nf += nz;
+                nz = 0;
+                goto have_dig;
+            }
+            goto dig_done;
+        }
+        for (; c >= '0' && c <= '9'; c = *++s) {
+have_dig:
+            nz++;
+            if (c -= '0') {
+                nf += nz;
+                for (i = 1; i < nz; i++)
+                    if (nd++ < 9)
+                        y *= 10;
+                    else if (nd <= DBL_DIG + 1)
+                        z *= 10;
+                if (nd++ < 9)
+                    y = 10*y + c;
+                else if (nd <= DBL_DIG + 1)
+                    z = 10*z + c;
+                nz = 0;
+            }
+        }
+    }
+dig_done:
+    e = 0;
+    if (c == 'e' || c == 'E') {
+        if (!nd && !nz && !nz0) {
+            goto ret0;
+        }
+        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) {
+#ifdef INFNAN_CHECK
+            /* Check for Nan and Infinity */
+            switch (c) {
+              case 'i':
+              case 'I':
+                if (match(&s,"nf")) {
+                    --s;
+                    if (!match(&s,"inity"))
+                        ++s;
+                    word0(rv) = 0x7ff00000;
+                    word1(rv) = 0;
+                    goto ret;
+                }
+                break;
+              case 'n':
+              case 'N':
+                if (match(&s, "an")) {
+                    word0(rv) = NAN_WORD0;
+                    word1(rv) = NAN_WORD1;
+#ifndef No_Hex_NaN
+                    if (*s == '(') /*)*/
+                        hexnan(&rv, &s);
+#endif
+                    goto ret;
+                }
+            }
+#endif /* INFNAN_CHECK */
+ret0:
+            s = s00;
+            sign = 0;
+        }
+        goto ret;
+    }
+    e1 = e -= nf;
 
-    errno = 0;
-    p = string;
-    while (ISSPACE(*p)) p++;
-    if (*p == '-') {
-	sign = Qtrue;
-	p++;
+    /* 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;
+    dval(rv) = y;
+    if (k > 9) {
+#ifdef SET_INEXACT
+        if (k > DBL_DIG)
+            oldinexact = get_inexact();
+#endif
+        dval(rv) = tens[k - 9] * dval(rv) + z;
     }
+    bd0 = 0;
+    if (nd <= DBL_DIG
+#ifndef RND_PRODQUOT
+#ifndef Honor_FLT_ROUNDS
+        && Flt_Rounds == 1
+#endif
+#endif
+    ) {
+        if (!e)
+            goto ret;
+        if (e > 0) {
+            if (e <= Ten_pmax) {
+#ifdef VAX
+                goto vax_ovfl_check;
+#else
+#ifdef Honor_FLT_ROUNDS
+                /* round correctly FLT_ROUNDS = 2 or 3 */
+                if (sign) {
+                    rv = -rv;
+                    sign = 0;
+                }
+#endif
+                /* rv = */ rounded_product(dval(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.
+                 */
+#ifdef Honor_FLT_ROUNDS
+                /* round correctly FLT_ROUNDS = 2 or 3 */
+                if (sign) {
+                    rv = -rv;
+                    sign = 0;
+                }
+#endif
+                e -= i;
+                dval(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(dval(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(dval(rv), tens[e]);
+#endif
+                goto ret;
+            }
+        }
+#ifndef Inaccurate_Divide
+        else if (e >= -Ten_pmax) {
+#ifdef Honor_FLT_ROUNDS
+            /* round correctly FLT_ROUNDS = 2 or 3 */
+            if (sign) {
+                rv = -rv;
+                sign = 0;
+            }
+#endif
+            /* rv = */ rounded_quotient(dval(rv), tens[-e]);
+            goto ret;
+        }
+#endif
+    }
+    e1 += nd - k;
+
+#ifdef IEEE_Arith
+#ifdef SET_INEXACT
+    inexact = 1;
+    if (k <= DBL_DIG)
+        oldinexact = get_inexact();
+#endif
+#ifdef Avoid_Underflow
+    scale = 0;
+#endif
+#ifdef Honor_FLT_ROUNDS
+    if ((rounding = Flt_Rounds) >= 2) {
+        if (sign)
+            rounding = rounding == 2 ? 0 : 2;
+        else
+            if (rounding != 2)
+                rounding = 0;
+    }
+#endif
+#endif /*IEEE_Arith*/
+
+    /* Get starting approximation = rv * 10**e1 */
+
+    if (e1 > 0) {
+        if ((i = e1 & 15) != 0)
+            dval(rv) *= tens[i];
+        if (e1 &= ~15) {
+            if (e1 > DBL_MAX_10_EXP) {
+ovfl:
+#ifndef NO_ERRNO
+                errno = ERANGE;
+#endif
+                /* Can't trust HUGE_VAL */
+#ifdef IEEE_Arith
+#ifdef Honor_FLT_ROUNDS
+                switch (rounding) {
+                  case 0: /* toward 0 */
+                  case 3: /* toward -infinity */
+                    word0(rv) = Big0;
+                    word1(rv) = Big1;
+                    break;
+                  default:
+                    word0(rv) = Exp_mask;
+                    word1(rv) = 0;
+                }
+#else /*Honor_FLT_ROUNDS*/
+                word0(rv) = Exp_mask;
+                word1(rv) = 0;
+#endif /*Honor_FLT_ROUNDS*/
+#ifdef SET_INEXACT
+                /* set overflow bit */
+                dval(rv0) = 1e300;
+                dval(rv0) *= dval(rv0);
+#endif
+#else /*IEEE_Arith*/
+                word0(rv) = Big0;
+                word1(rv) = Big1;
+#endif /*IEEE_Arith*/
+                if (bd0)
+                    goto retfree;
+                goto ret;
+            }
+            e1 >>= 4;
+            for (j = 0; e1 > 1; j++, e1 >>= 1)
+                if (e1 & 1)
+                    dval(rv) *= bigtens[j];
+            /* The last multiplication could overflow. */
+            word0(rv) -= P*Exp_msk1;
+            dval(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)
+            dval(rv) /= tens[i];
+        if (e1 >>= 4) {
+            if (e1 >= 1 << n_bigtens)
+                goto undfl;
+#ifdef Avoid_Underflow
+            if (e1 & Scale_Bit)
+                scale = 2*P;
+            for (j = 0; e1 > 0; j++, e1 >>= 1)
+                if (e1 & 1)
+                    dval(rv) *= tinytens[j];
+            if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
+                    >> Exp_shift)) > 0) {
+                /* scaled rv is denormal; zap j low bits */
+                if (j >= 32) {
+                    word1(rv) = 0;
+                    if (j >= 53)
+                        word0(rv) = (P+2)*Exp_msk1;
+                    else
+                        word0(rv) &= 0xffffffff << (j-32);
+                }
+                else
+                    word1(rv) &= 0xffffffff << j;
+            }
+#else
+            for (j = 0; e1 > 1; j++, e1 >>= 1)
+                if (e1 & 1)
+                    dval(rv) *= tinytens[j];
+            /* The last multiplication could underflow. */
+            dval(rv0) = dval(rv);
+            dval(rv) *= tinytens[j];
+            if (!dval(rv)) {
+                dval(rv) = 2.*dval(rv0);
+                dval(rv) *= tinytens[j];
+#endif
+                if (!dval(rv)) {
+undfl:
+                    dval(rv) = 0.;
+#ifndef NO_ERRNO
+                    errno = ERANGE;
+#endif
+                    if (bd0)
+                        goto retfree;
+                    goto ret;
+                }
+#ifndef Avoid_Underflow
+                word0(rv) = Tiny0;
+                word1(rv) = Tiny1;
+                /* The refinement below will clean
+                 * this approximation up.
+                 */
+            }
+#endif
+        }
+    }
+
+    /* 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(dval(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 Honor_FLT_ROUNDS
+        if (rounding != 1)
+            bs2++;
+#endif
+#ifdef Avoid_Underflow
+        j = bbe - scale;
+        i = j + bbbits - 1; /* logb(rv) */
+        if (i < Emin)   /* denormal */
+            j += P - Emin;
+        else
+            j = P + 1 - bbbits;
+#else /*Avoid_Underflow*/
+#ifdef Sudden_Underflow
+#ifdef IBM
+        j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
+#else
+        j = P + 1 - bbbits;
+#endif
+#else /*Sudden_Underflow*/
+        j = bbe;
+        i = j + bbbits - 1; /* logb(rv) */
+        if (i < Emin)   /* denormal */
+            j += P - Emin;
+        else
+            j = P + 1 - bbbits;
+#endif /*Sudden_Underflow*/
+#endif /*Avoid_Underflow*/
+        bb2 += j;
+        bd2 += j;
+#ifdef Avoid_Underflow
+        bd2 += scale;
+#endif
+        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);
+#ifdef Honor_FLT_ROUNDS
+        if (rounding != 1) {
+            if (i < 0) {
+                /* Error is less than an ulp */
+                if (!delta->x[0] && delta->wds <= 1) {
+                    /* exact */
+#ifdef SET_INEXACT
+                    inexact = 0;
+#endif
+                    break;
+                }
+                if (rounding) {
+                    if (dsign) {
+                        adj = 1.;
+                        goto apply_adj;
+                    }
+                }
+                else if (!dsign) {
+                    adj = -1.;
+                    if (!word1(rv)
+                     && !(word0(rv) & Frac_mask)) {
+                        y = word0(rv) & Exp_mask;
+#ifdef Avoid_Underflow
+                        if (!scale || y > 2*P*Exp_msk1)
+#else
+                        if (y)
+#endif
+                        {
+                            delta = lshift(delta,Log2P);
+                            if (cmp(delta, bs) <= 0)
+                                adj = -0.5;
+                        }
+                    }
+apply_adj:
+#ifdef Avoid_Underflow
+                    if (scale && (y = word0(rv) & Exp_mask)
+                            <= 2*P*Exp_msk1)
+                        word0(adj) += (2*P+1)*Exp_msk1 - y;
+#else
+#ifdef Sudden_Underflow
+                    if ((word0(rv) & Exp_mask) <=
+                            P*Exp_msk1) {
+                        word0(rv) += P*Exp_msk1;
+                        dval(rv) += adj*ulp(dval(rv));
+                        word0(rv) -= P*Exp_msk1;
+                    }
+                    else
+#endif /*Sudden_Underflow*/
+#endif /*Avoid_Underflow*/
+                    dval(rv) += adj*ulp(dval(rv));
+                }
+                break;
+            }
+            adj = ratio(delta, bs);
+            if (adj < 1.)
+                adj = 1.;
+            if (adj <= 0x7ffffffe) {
+                /* adj = rounding ? ceil(adj) : floor(adj); */
+                y = adj;
+                if (y != adj) {
+                    if (!((rounding>>1) ^ dsign))
+                        y++;
+                    adj = y;
+                }
+            }
+#ifdef Avoid_Underflow
+            if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
+                word0(adj) += (2*P+1)*Exp_msk1 - y;
+#else
+#ifdef Sudden_Underflow
+            if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
+                word0(rv) += P*Exp_msk1;
+                adj *= ulp(dval(rv));
+                if (dsign)
+                    dval(rv) += adj;
+                else
+                    dval(rv) -= adj;
+                word0(rv) -= P*Exp_msk1;
+                goto cont;
+            }
+#endif /*Sudden_Underflow*/
+#endif /*Avoid_Underflow*/
+            adj *= ulp(dval(rv));
+            if (dsign)
+                dval(rv) += adj;
+            else
+                dval(rv) -= adj;
+            goto cont;
+        }
+#endif /*Honor_FLT_ROUNDS*/
+
+        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
+#ifdef IEEE_Arith
+#ifdef Avoid_Underflow
+                || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
+#else
+                || (word0(rv) & Exp_mask) <= Exp_msk1
+#endif
+#endif
+            ) {
+#ifdef SET_INEXACT
+                if (!delta->x[0] && delta->wds <= 1)
+                    inexact = 0;
+#endif
+                break;
+            }
+            if (!delta->x[0] && delta->wds <= 1) {
+                /* exact result */
+#ifdef SET_INEXACT
+                inexact = 0;
+#endif
+                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) == (
+#ifdef Avoid_Underflow
+                        (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
+                        ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
+#endif
+                        0xffffffff)) {
+                    /*boundary case -- increment exponent*/
+                    word0(rv) = (word0(rv) & Exp_mask)
+                                + Exp_msk1
+#ifdef IBM
+                                | Exp_msk1 >> 4
+#endif
+                    ;
+                    word1(rv) = 0;
+#ifdef Avoid_Underflow
+                    dsign = 0;
+#endif
+                    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
+#ifdef Avoid_Underflow
+                if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
+#else
+                if (L <= Exp_msk1)
+#endif /*Avoid_Underflow*/
+#endif /*IBM*/
+                    goto undfl;
+                L -= Exp_msk1;
+#else /*Sudden_Underflow}{*/
+#ifdef Avoid_Underflow
+                if (scale) {
+                    L = word0(rv) & Exp_mask;
+                    if (L <= (2*P+1)*Exp_msk1) {
+                        if (L > (P+2)*Exp_msk1)
+                            /* round even ==> */
+                            /* accept rv */
+                            break;
+                        /* rv = smallest denormal */
+                        goto undfl;
+                    }
+                }
+#endif /*Avoid_Underflow*/
+                L = (word0(rv) & Exp_mask) - Exp_msk1;
+#endif /*Sudden_Underflow}}*/
+                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)
+                dval(rv) += ulp(dval(rv));
+#ifndef ROUND_BIASED
+            else {
+                dval(rv) -= ulp(dval(rv));
+#ifndef Sudden_Underflow
+                if (!dval(rv))
+                    goto undfl;
+#endif
+            }
+#ifdef Avoid_Underflow
+            dsign = 1 - dsign;
+#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 (Rounding) {
+              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 /*Check_FLT_ROUNDS*/
+        }
+        y = word0(rv) & Exp_mask;
+
+        /* Check for overflow */
+
+        if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
+            dval(rv0) = dval(rv);
+            word0(rv) -= P*Exp_msk1;
+            adj = aadj1 * ulp(dval(rv));
+            dval(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 Avoid_Underflow
+            if (scale && y <= 2*P*Exp_msk1) {
+                if (aadj <= 0x7fffffff) {
+                    if ((z = aadj) <= 0)
+                        z = 1;
+                    aadj = z;
+                    aadj1 = dsign ? aadj : -aadj;
+                }
+                word0(aadj1) += (2*P+1)*Exp_msk1 - y;
+            }
+            adj = aadj1 * ulp(dval(rv));
+            dval(rv) += adj;
+#else
+#ifdef Sudden_Underflow
+            if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
+                dval(rv0) = dval(rv);
+                word0(rv) += P*Exp_msk1;
+                adj = aadj1 * ulp(dval(rv));
+                dval(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(dval(rv));
+                dval(rv) += adj;
+            }
+#else /*Sudden_Underflow*/
+            /* 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(dval(rv));
+            dval(rv) += adj;
+#endif /*Sudden_Underflow*/
+#endif /*Avoid_Underflow*/
+        }
+        z = word0(rv) & Exp_mask;
+#ifndef SET_INEXACT
+#ifdef Avoid_Underflow
+        if (!scale)
+#endif
+        if (y == z) {
+            /* Can we stop now? */
+            L = (Long)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;
+        }
+#endif
+cont:
+        Bfree(bb);
+        Bfree(bd);
+        Bfree(bs);
+        Bfree(delta);
+    }
+#ifdef SET_INEXACT
+    if (inexact) {
+        if (!oldinexact) {
+            word0(rv0) = Exp_1 + (70 << Exp_shift);
+            word1(rv0) = 0;
+            dval(rv0) += 1.;
+        }
+    }
+    else if (!oldinexact)
+        clear_inexact();
+#endif
+#ifdef Avoid_Underflow
+    if (scale) {
+        word0(rv0) = Exp_1 - 2*P*Exp_msk1;
+        word1(rv0) = 0;
+        dval(rv) *= dval(rv0);
+#ifndef NO_ERRNO
+        /* try to avoid the bug of testing an 8087 register value */
+        if (word0(rv) == 0 && word1(rv) == 0)
+            errno = ERANGE;
+#endif
+    }
+#endif /* Avoid_Underflow */
+#ifdef SET_INEXACT
+    if (inexact && !(word0(rv) & Exp_mask)) {
+        /* set underflow bit */
+        dval(rv0) = 1e-300;
+        dval(rv0) *= dval(rv0);
+    }
+#endif
+retfree:
+    Bfree(bb);
+    Bfree(bd);
+    Bfree(bs);
+    Bfree(bd0);
+    Bfree(delta);
+ret:
+    if (se)
+        *se = (char *)s;
+    return sign ? -dval(rv) : dval(rv);
+}
+
+static int
+quorem(Bigint *b, Bigint *S)
+{
+    int n;
+    ULong *bx, *bxe, q, *sx, *sxe;
+#ifdef ULLong
+    ULLong borrow, carry, y, ys;
+#else
+    ULong borrow, carry, y, ys;
+#ifdef Pack_32
+    ULong si, z, zs;
+#endif
+#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 ULLong
+            ys = *sx++ * (ULLong)q + carry;
+            carry = ys >> 32;
+            y = *bx - (ys & FFFFFFFF) - borrow;
+            borrow = y >> 32 & (ULong)1;
+            *bx++ = y & FFFFFFFF;
+#else
+#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 & 0x10000) >> 16;
+            z = (*bx >> 16) - (zs & 0xffff) - borrow;
+            borrow = (z & 0x10000) >> 16;
+            Storeinc(bx, z, y);
+#else
+            ys = *sx++ * q + carry;
+            carry = ys >> 16;
+            y = *bx - (ys & 0xffff) - borrow;
+            borrow = (y & 0x10000) >> 16;
+            *bx++ = y & 0xffff;
+#endif
+#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 ULLong
+            ys = *sx++ + carry;
+            carry = ys >> 32;
+            y = *bx - (ys & FFFFFFFF) - borrow;
+            borrow = y >> 32 & (ULong)1;
+            *bx++ = y & FFFFFFFF;
+#else
+#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 & 0x10000) >> 16;
+            z = (*bx >> 16) - (zs & 0xffff) - borrow;
+            borrow = (z & 0x10000) >> 16;
+            Storeinc(bx, z, y);
+#else
+            ys = *sx++ + carry;
+            carry = ys >> 16;
+            y = *bx - (ys & 0xffff) - borrow;
+            borrow = (y & 0x10000) >> 16;
+            *bx++ = y & 0xffff;
+#endif
+#endif
+        } while (sx <= sxe);
+        bx = b->x;
+        bxe = bx + n;
+        if (!*bxe) {
+            while (--bxe > bx && !*bxe)
+                --n;
+            b->wds = n;
+        }
+    }
+    return q;
+}
+
+#ifndef MULTIPLE_THREADS
+static char *dtoa_result;
+#endif
+
+static char *
+rv_alloc(int i)
+{
+    int j, k, *r;
+
+    j = sizeof(ULong);
+    for (k = 0;
+            sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= i;
+            j <<= 1)
+        k++;
+    r = (int*)Balloc(k);
+    *r = k;
+    return
+#ifndef MULTIPLE_THREADS
+        dtoa_result =
+#endif
+        (char *)(r+1);
+}
+
+static char *
+nrv_alloc(char *s, char **rve, int n)
+{
+    char *rv, *t;
+
+    t = rv = rv_alloc(n);
+    while ((*t = *s++) != 0) t++;
+    if (rve)
+        *rve = t;
+    return rv;
+}
+
+/* freedtoa(s) must be used to free values s returned by dtoa
+ * when MULTIPLE_THREADS is #defined.  It should be used in all cases,
+ * but for consistency with earlier versions of dtoa, it is optional
+ * when MULTIPLE_THREADS is not defined.
+ */
+
+void
+freedtoa(char *s)
+{
+    Bigint *b = (Bigint *)((int *)s - 1);
+    b->maxwds = 1 << (b->k = *(int*)b);
+    Bfree(b);
+#ifndef MULTIPLE_THREADS
+    if (s == dtoa_result)
+        dtoa_result = 0;
+#endif
+}
+
+/* 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. 112-126].
+ *
+ * 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(double d, int mode, int ndigits, int *decpt, int *sign, char **rve)
+{
+ /* 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.
+        4,5 ==> similar to 2 and 3, respectively, but (in
+            round-nearest mode) with the tests of mode 0 to
+            possibly return a shorter string that rounds to d.
+            With IEEE arithmetic and compilation with
+            -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
+            as modes 2 and 3 when FLT_ROUNDS != 1.
+        6-9 ==> Debugging modes similar to mode - 4:  don't try
+            fast floating-point estimate (if applicable).
+
+        Values of mode other than 0-9 are treated as mode 0.
+
+        Sufficient space is allocated to the return value
+        to hold the suppressed trailing zeros.
+    */
+
+    int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
+        j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
+        spec_case, try_quick;
+    Long L;
+#ifndef Sudden_Underflow
+    int denorm;
+    ULong x;
+#endif
+    Bigint *b, *b1, *delta, *mlo, *mhi, *S;
+    double d2, ds, eps;
+    char *s, *s0;
+#ifdef Honor_FLT_ROUNDS
+    int rounding;
+#endif
+#ifdef SET_INEXACT
+    int inexact, oldinexact;
+#endif
+
+#ifndef MULTIPLE_THREADS
+    if (dtoa_result) {
+        freedtoa(dtoa_result);
+        dtoa_result = 0;
+    }
+#endif
+
+    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;
+#ifdef IEEE_Arith
+        if (!word1(d) && !(word0(d) & 0xfffff))
+            return nrv_alloc("Infinity", rve, 8);
+#endif
+        return nrv_alloc("NaN", rve, 3);
+    }
+#endif
+#ifdef IBM
+    dval(d) += 0; /* normalize */
+#endif
+    if (!dval(d)) {
+        *decpt = 1;
+        return nrv_alloc("0", rve, 1);
+    }
+
+#ifdef SET_INEXACT
+    try_quick = oldinexact = get_inexact();
+    inexact = 1;
+#endif
+#ifdef Honor_FLT_ROUNDS
+    if ((rounding = Flt_Rounds) >= 2) {
+        if (*sign)
+            rounding = rounding == 2 ? 0 : 2;
+        else
+            if (rounding != 2)
+                rounding = 0;
+    }
+#endif
+
+    b = d2b(dval(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
+        dval(d2) = dval(d);
+        word0(d2) &= Frac_mask1;
+        word0(d2) |= Exp_11;
+#ifdef IBM
+        if (j = 11 - hi0bits(word0(d2) & Frac_mask))
+            dval(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 {
-	if (*p == '+') p++;
-	sign = Qfalse;
+        /* 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);
+        dval(d2) = x;
+        word0(d2) -= 31*Exp_msk1; /* adjust exponent */
+        i -= (Bias + (P-1) - 1) + 1;
+        denorm = 1;
     }
+#endif
+    ds = (dval(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 (dval(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;
 
-    fraction = 0.;
-    exp = 0;
+#ifndef SET_INEXACT
+#ifdef Check_FLT_ROUNDS
+    try_quick = Rounding == 1;
+#else
+    try_quick = 1;
+#endif
+#endif /*SET_INEXACT*/
 
-    /*
-     * Count the number of digits in the mantissa
-     * and also locate the decimal point.
-     */
+    if (mode > 5) {
+        mode -= 4;
+        try_quick = 0;
+    }
+    leftright = 1;
+    ilim = ilim1 = -1;
+    switch (mode) {
+      case 0:
+      case 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;
+    }
+    s = s0 = rv_alloc(i);
 
-    for ( ; (c = *p) != '\0'; p++) {
-	if (!ISDIGIT(c)) {
-	    if (c != '.' || hasPoint || !ISDIGIT(p[1])) {
-		break;
-	    }
-	    hasPoint = Qtrue;
-	}
-	else {
-	    if (hasPoint) { /* already in fractional part */
-		fracExp--;
-	    }
-	    if (mantSize) { /* already in mantissa */
-		mantSize++;
-	    }
-	    else if (c != '0') { /* have entered mantissa */
-		mantSize++;
-		pMant = p;
-	    }
-	    hasDigit = Qtrue;
-	}
+#ifdef Honor_FLT_ROUNDS
+    if (mode > 1 && rounding != 1)
+        leftright = 0;
+#endif
+
+    if (ilim >= 0 && ilim <= Quick_max && try_quick) {
+
+        /* Try to get by with floating-point arithmetic. */
+
+        i = 0;
+        dval(d2) = dval(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;
+                dval(d) /= bigtens[n_bigtens-1];
+                ieps++;
+            }
+            for (; j; j >>= 1, i++)
+                if (j & 1) {
+                    ieps++;
+                    ds *= bigtens[i];
+                }
+            dval(d) /= ds;
+        }
+        else if ((j1 = -k) != 0) {
+            dval(d) *= tens[j1 & 0xf];
+            for (j = j1 >> 4; j; j >>= 1, i++)
+                if (j & 1) {
+                    ieps++;
+                    dval(d) *= bigtens[i];
+                }
+        }
+        if (k_check && dval(d) < 1. && ilim > 0) {
+            if (ilim1 <= 0)
+                goto fast_failed;
+            ilim = ilim1;
+            k--;
+            dval(d) *= 10.;
+            ieps++;
+        }
+        dval(eps) = ieps*dval(d) + 7.;
+        word0(eps) -= (P-1)*Exp_msk1;
+        if (ilim == 0) {
+            S = mhi = 0;
+            dval(d) -= 5.;
+            if (dval(d) > dval(eps))
+                goto one_digit;
+            if (dval(d) < -dval(eps))
+                goto no_digits;
+            goto fast_failed;
+        }
+#ifndef No_leftright
+        if (leftright) {
+            /* Use Steele & White method of only
+             * generating digits needed.
+             */
+            dval(eps) = 0.5/tens[ilim-1] - dval(eps);
+            for (i = 0;;) {
+                L = dval(d);
+                dval(d) -= L;
+                *s++ = '0' + (int)L;
+                if (dval(d) < dval(eps))
+                    goto ret1;
+                if (1. - dval(d) < dval(eps))
+                    goto bump_up;
+                if (++i >= ilim)
+                    break;
+                dval(eps) *= 10.;
+                dval(d) *= 10.;
+            }
+        }
+        else {
+#endif
+            /* Generate ilim digits, then fix them up. */
+            dval(eps) *= tens[ilim-1];
+            for (i = 1;; i++, dval(d) *= 10.) {
+                L = (Long)(dval(d));
+                if (!(dval(d) -= L))
+                    ilim = i;
+                *s++ = '0' + (int)L;
+                if (i == ilim) {
+                    if (dval(d) > 0.5 + dval(eps))
+                        goto bump_up;
+                    else if (dval(d) < 0.5 - dval(eps)) {
+                        while (*--s == '0') ;
+                        s++;
+                        goto ret1;
+                    }
+                    break;
+                }
+            }
+#ifndef No_leftright
+        }
+#endif
+fast_failed:
+        s = s0;
+        dval(d) = dval(d2);
+        k = k0;
+        ilim = ilim0;
     }
 
-    /*
-     * Now suck up the digits in the mantissa.  Use two integers to
-     * collect 9 digits each (this is faster than using floating-point).
-     * If the mantissa has more than 18 digits, ignore the extras, since
-     * they can't affect the value anyway.
+    /* 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 || dval(d) <= 5*ds)
+                goto no_digits;
+            goto one_digit;
+        }
+        for (i = 1;; i++, dval(d) *= 10.) {
+            L = (Long)(dval(d) / ds);
+            dval(d) -= L*ds;
+#ifdef Check_FLT_ROUNDS
+            /* If FLT_ROUNDS == 2, L will usually be high by 1 */
+            if (dval(d) < 0) {
+                L--;
+                dval(d) += ds;
+            }
+#endif
+            *s++ = '0' + (int)L;
+            if (!dval(d)) {
+#ifdef SET_INEXACT
+                inexact = 0;
+#endif
+                break;
+            }
+            if (i == ilim) {
+#ifdef Honor_FLT_ROUNDS
+                if (mode > 1)
+                switch (rounding) {
+                  case 0: goto ret1;
+                  case 2: goto bump_up;
+                }
+#endif
+                dval(d) += dval(d);
+                if (dval(d) > ds || (dval(d) == ds && (L & 1))) {
+bump_up:
+                    while (*--s == '9')
+                        if (s == s0) {
+                            k++;
+                            *s = '0';
+                            break;
+                        }
+                    ++*s++;
+                }
+                break;
+            }
+        }
+        goto ret1;
+    }
+
+    m2 = b2;
+    m5 = b5;
+    mhi = mlo = 0;
+    if (leftright) {
+        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
+        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. */
+
+    spec_case = 0;
+    if ((mode < 2 || leftright)
+#ifdef Honor_FLT_ROUNDS
+            && rounding == 1
+#endif
+    ) {
+        if (!word1(d) && !(word0(d) & Bndry_mask)
+#ifndef Sudden_Underflow
+            && word0(d) & (Exp_mask & ~Exp_msk1)
+#endif
+        ) {
+            /* The special case */
+            b2 += Log2P;
+            s2 += Log2P;
+            spec_case = 1;
+        }
+    }
+
+    /* 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.
      */
-    
-    pExp = p;
-    if (mantSize) {
-	p = pMant;
+#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) != 0)
+        i = 16 - i;
+#endif
+    if (i > 4) {
+        i -= 4;
+        b2 += i;
+        m2 += i;
+        s2 += i;
     }
-    if (mantSize > 18) {
-	fracExp += (mantSize - 18);
-	mantSize = 18;
+    else if (i < 4) {
+        i += 28;
+        b2 += i;
+        m2 += i;
+        s2 += i;
     }
-    if (!hasDigit) {
-	fraction = 0.0;
-	p = string;
+    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;
+        }
     }
-    else {
-	double frac1, frac2;
-	frac1 = 0;
-	for ( ; mantSize > 9; mantSize -= 1) {
-	    c = *p;
-	    p += 1;
-	    if (c == '.') {
-		c = *p;
-		p += 1;
-	    }
-	    frac1 = 10*frac1 + (c - '0');
-	}
-	frac2 = 0;
-	for (; mantSize > 0; mantSize -= 1) {
-	    c = *p;
-	    p += 1;
-	    if (c == '.') {
-		c = *p;
-		p += 1;
-	    }
-	    frac2 = 10*frac2 + (c - '0');
-	}
+    if (ilim <= 0 && (mode == 3 || mode == 5)) {
+        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);
 
-	/*
-	 * Skim off the exponent.
-	 */
+        /* Compute mlo -- check for special case
+         * that d is a normalized power of 2.
+         */
 
-	p = pExp;
-	if ((*p == 'E') || (*p == 'e')) {
-	    p++;
-	    if (*p == '-') {
-		expSign = Qtrue;
-		p++;
-	    }
-	    else {
-		if (*p == '+') {
-		    p++;
-		}
-		expSign = Qfalse;
-	    }
-	    if (ISDIGIT(*p)) {
-		do {
-		    exp = exp * 10 + (*p++ - '0');
-		}
-		while (ISDIGIT(*p));
-	    }
-	    else {
-		p = pExp;
-	    }
-	}
-	if (expSign) {
-	    exp = fracExp - exp;
-	}
-	else {
-	    exp = fracExp + exp;
-	}
+        mlo = mhi;
+        if (spec_case) {
+            mhi = Balloc(mhi->k);
+            Bcopy(mhi, mlo);
+            mhi = lshift(mhi, Log2P);
+        }
 
-	/*
-	 * Generate a floating-point number that represents the exponent.
-	 * Do this by processing the exponent one bit at a time to combine
-	 * many powers of 2 of 10. Then combine the exponent with the
-	 * fraction.
-	 */
-    
-	if (exp >= MDMAXEXPT) {
-	    errno = ERANGE;
-	    fraction = HUGE_VAL;
-	    goto ret;
-	}
-	else if (exp < MDMINEXPT) {
-	    errno = ERANGE;
-	    fraction = 0.0;
-	    goto ret;
-	}
-	fracExp = exp;
-	exp += 9;
-	if (exp < 0) {
-	    expSign = Qtrue;
-	    exp = -exp;
-	}
-	else {
-	    expSign = Qfalse;
-	}
-	dblExp = 1.0;
-	for (d = powersOf10; exp != 0; exp >>= 1, d += 1) {
-	    if (exp & 01) {
-		dblExp *= *d;
-	    }
-	}
-	if (expSign) {
-	    frac1 /= dblExp;
-	}
-	else {
-	    frac1 *= dblExp;
-	}
-	exp = fracExp;
-	if (exp < 0) {
-	    expSign = Qtrue;
-	    exp = -exp;
-	}
-	else {
-	    expSign = Qfalse;
-	}
-	dblExp = 1.0;
-	for (d = powersOf10; exp != 0; exp >>= 1, d += 1) {
-	    if (exp & 01) {
-		dblExp *= *d;
-	    }
-	}
-	if (expSign) {
-	    frac2 /= dblExp;
-	}
-	else {
-	    frac2 *= dblExp;
-	}
-	fraction = frac1 + frac2;
+        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 != 1 && !(word1(d) & 1)
+#ifdef Honor_FLT_ROUNDS
+                && rounding >= 1
+#endif
+            ) {
+                if (dig == '9')
+                    goto round_9_up;
+                if (j > 0)
+                    dig++;
+#ifdef SET_INEXACT
+                else if (!b->x[0] && b->wds <= 1)
+                    inexact = 0;
+#endif
+                *s++ = dig;
+                goto ret;
+            }
+#endif
+            if (j < 0 || (j == 0 && mode != 1
+#ifndef ROUND_BIASED
+                && !(word1(d) & 1)
+#endif
+            )) {
+                if (!b->x[0] && b->wds <= 1) {
+#ifdef SET_INEXACT
+                    inexact = 0;
+#endif
+                    goto accept_dig;
+                }
+#ifdef Honor_FLT_ROUNDS
+                if (mode > 1)
+                    switch (rounding) {
+                      case 0: goto accept_dig;
+                      case 2: goto keep_dig;
+                    }
+#endif /*Honor_FLT_ROUNDS*/
+                if (j1 > 0) {
+                    b = lshift(b, 1);
+                    j1 = cmp(b, S);
+                    if ((j1 > 0 || (j1 == 0 && (dig & 1))) && dig++ == '9')
+                        goto round_9_up;
+                }
+accept_dig:
+                *s++ = dig;
+                goto ret;
+            }
+            if (j1 > 0) {
+#ifdef Honor_FLT_ROUNDS
+                if (!rounding)
+                    goto accept_dig;
+#endif
+                if (dig == '9') { /* possible if i == 1 */
+round_9_up:
+                    *s++ = '9';
+                    goto roundoff;
+                }
+                *s++ = dig + 1;
+                goto ret;
+            }
+#ifdef Honor_FLT_ROUNDS
+keep_dig:
+#endif
+            *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 (!b->x[0] && b->wds <= 1) {
+#ifdef SET_INEXACT
+                inexact = 0;
+#endif
+                goto ret;
+            }
+            if (i >= ilim)
+                break;
+            b = multadd(b, 10, 0);
+        }
 
-  ret:
-    if (endPtr != NULL) {
-	*endPtr = (char *)p;
+    /* Round off last digit */
+
+#ifdef Honor_FLT_ROUNDS
+    switch (rounding) {
+      case 0: goto trimzeros;
+      case 2: goto roundoff;
     }
-    if (sign) {
-	return -fraction;
+#endif
+    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++;
     }
-    return fraction;
+    else {
+        while (*--s == '0') ;
+        s++;
+    }
+ret:
+    Bfree(S);
+    if (mhi) {
+        if (mlo && mlo != mhi)
+            Bfree(mlo);
+        Bfree(mhi);
+    }
+ret1:
+#ifdef SET_INEXACT
+    if (inexact) {
+        if (!oldinexact) {
+            word0(d) = Exp_1 + (70 << Exp_shift);
+            word1(d) = 0;
+            dval(d) += 1.;
+        }
+    }
+    else if (!oldinexact)
+        clear_inexact();
+#endif
+    Bfree(b);
+    *s = 0;
+    *decpt = k + 1;
+    if (rve)
+        *rve = s;
+    return s0;
 }
+
+void
+ruby_each_words(const char *str, void (*func)(const char*, int, void*), void *arg)
+{
+    const char *end;
+    int len;
+
+    if (!str) return;
+    for (; *str; str = end) {
+	while (ISSPACE(*str) || *str == ',') str++;
+	if (!*str) break;
+	end = str;
+	while (*end && !ISSPACE(*end) && *end != ',') end++;
+	len = end - str;
+	(*func)(str, len, arg);
+    }
+}
+
+#ifdef __cplusplus
+}
+#endif
Index: ruby_1_8/ChangeLog
===================================================================
--- ruby_1_8/ChangeLog	(revision 16341)
+++ ruby_1_8/ChangeLog	(revision 16342)
@@ -1,3 +1,9 @@
+Sat May 10 09:16:13 2008  Yukihiro Matsumoto  <matz@r...>
+
+	* util.c (ruby_strtod): backported from 1.9.  a patch from Satoshi
+	  Nakagawa <psychs at limechat.net> in [ruby-dev:34625]. 
+	  fixed: [ruby-dev:34623]
+
 Fri May  9 23:33:25 2008  Hidetoshi NAGAI  <nagai@a...>
 
 	* ext/tk/lib/tk/wm.rb: methods of Tk::Wm_for_General module cannot
Index: ruby_1_8/version.h
===================================================================
--- ruby_1_8/version.h	(revision 16341)
+++ ruby_1_8/version.h	(revision 16342)
@@ -1,7 +1,7 @@
 #define RUBY_VERSION "1.8.7"
-#define RUBY_RELEASE_DATE "2008-05-07"
+#define RUBY_RELEASE_DATE "2008-05-10"
 #define RUBY_VERSION_CODE 187
-#define RUBY_RELEASE_CODE 20080507
+#define RUBY_RELEASE_CODE 20080510
 #define RUBY_PATCHLEVEL 5000
 
 #define RUBY_VERSION_MAJOR 1
@@ -9,7 +9,7 @@
 #define RUBY_VERSION_TEENY 7
 #define RUBY_RELEASE_YEAR 2008
 #define RUBY_RELEASE_MONTH 5
-#define RUBY_RELEASE_DAY 7
+#define RUBY_RELEASE_DAY 10
 
 #ifdef RUBY_EXTERN
 RUBY_EXTERN const char ruby_version[];

--
ML: ruby-changes@q...
Info: http://www.atdot.net/~ko1/quickml/

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