src/third_party/dtoa/dtoa.c

説明を見る。

/****************************************************************
 *
 * The author of this software is David M. Gay.
 *
 * 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.
 *
 ***************************************************************/

/* Please send bug reports to David M. Gay (dmg at acm dot org,
 * with " at " changed at "@" and " dot " changed to ".").      */

/* 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.
 *
 * This strtod returns a nearest machine number to the input decimal
 * string (or sets errno to ERANGE).  With IEEE arithmetic, ties are
 * broken by the IEEE round-even rule.  Otherwise ties are broken by
 * biased rounding (add half and chop).
 *
 * Inspired loosely by William D. Clinger's paper "How to Read Floating
 * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
 *
 * Modifications:
 *
 *      1. We only require IEEE, IBM, or VAX double-precision
 *              arithmetic (not IEEE double-extended).
 *      2. We get by with floating-point arithmetic in a case that
 *              Clinger missed -- when we're computing d * 10^n
 *              for a small integer d and the integer n is not too
 *              much larger than 22 (the maximum integer k for which
 *              we can represent 10^k exactly), we may be able to
 *              compute (d*10^k) * 10^(e-k) with just one roundoff.
 *      3. Rather than a bit-at-a-time adjustment of the binary
 *              result in the hard case, we use floating-point
 *              arithmetic to determine the adjustment to within
 *              one bit; only in really hard cases do we need to
 *              compute a second residual.
 *      4. Because of 3., we don't need a large table of powers of 10
 *              for ten-to-e (just some small tables, e.g. of 10^k
 *              for 0 <= k <= 22).
 */

/*
 * #define IEEE_8087 for IEEE-arithmetic machines where the least
 *      significant byte has the lowest address.
 * #define IEEE_MC68k for IEEE-arithmetic machines where the most
 *      significant byte has the lowest address.
 * #define 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.
 */

#ifndef Long
#define Long long
#endif
#ifndef ULong
typedef unsigned Long ULong;
#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
#ifdef KR_headers
extern char *MALLOC();
#else
extern void *MALLOC(size_t);
#endif
#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_MC68k
#define IEEE_Arith
#endif
#ifdef IEEE_8087
#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

#ifndef CONST
#ifdef KR_headers
#define CONST /* blank */
#else
#define CONST const
#endif
#endif

#if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
#endif

typedef union { double d; ULong L[2]; } U;

#ifdef YES_ALIAS
#define dval(x) x
#ifdef IEEE_8087
#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_8087
#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_8087) + defined(VAX)
#define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
((unsigned short *)a)[0] = (unsigned short)c, a++)
#else
#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
((unsigned short *)a)[1] = (unsigned short)c, a++)
#endif

/* #define P DBL_MANT_DIG */
/* Ten_pmax = floor(P*log(2)/log(5)) */
/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */

#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)
#ifdef KR_headers
extern double rnd_prod(), rnd_quot();
#else
extern double rnd_prod(double, double), rnd_quot(double, double);
#endif
#else
#define rounded_product(a,b) a *= b
#define rounded_quotient(a,b) a /= b
#endif

#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
#define Big1 0xffffffff

#ifndef Pack_32
#define Pack_32
#endif

#ifdef KR_headers
#define FFFFFFFF ((((unsigned long)0xffff)<<16)|(unsigned long)0xffff)
#else
#define FFFFFFFF 0xffffffffUL
#endif

#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

#ifdef __cplusplus
extern "C" double strtod(const char *s00, char **se);
extern "C" char *dtoa(double d, int mode, int ndigits,
                        int *decpt, int *sign, char **rve);
#endif

 struct
Bigint {
        struct Bigint *next;
        int k, maxwds, sign, wds;
        ULong x[1];
        };

 typedef struct Bigint Bigint;

 static Bigint *freelist[Kmax+1];

 static Bigint *
Balloc
#ifdef KR_headers
        (k) int k;
#else
        (int k)
#endif
{
        int x;
        Bigint *rv;
#ifndef Omit_Private_Memory
        unsigned int len;
#endif

        ACQUIRE_DTOA_LOCK(0);
        if ((rv = freelist[k])) {
                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
#ifdef KR_headers
        (v) Bigint *v;
#else
        (Bigint *v)
#endif
{
        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
#ifdef KR_headers
        (b, m, a) Bigint *b; int m, a;
#else
        (Bigint *b, int m, int a)       /* multiply by m and add a */
#endif
{
        int i, wds;
#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
#ifdef KR_headers
        (s, nd0, nd, y9) CONST char *s; int nd0, nd; ULong y9;
#else
        (CONST char *s, int nd0, int nd, ULong y9)
#endif
{
        Bigint *b;
        int i, k;
        Long x, y;

        x = (nd + 8) / 9;
        for(k = 0, y = 1; x > y; y <<= 1, k++) ;
#ifdef Pack_32
        b = Balloc(k);
        b->x[0] = y9;
        b->wds = 1;
#else
        b = Balloc(k+1);
        b->x[0] = y9 & 0xffff;
        b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
#endif

        i = 9;
        if (9 < nd0) {
                s += 9;
                do b = multadd(b, 10, *s++ - '0');
                        while(++i < nd0);
                s++;
                }
        else
                s += 10;
        for(; i < nd; i++)
                b = multadd(b, 10, *s++ - '0');
        return b;
        }

 static int
hi0bits
#ifdef KR_headers
        (x) register ULong x;
#else
        (register ULong x)
#endif
{
        register int k = 0;

        if (!(x & 0xffff0000)) {
                k = 16;
                x <<= 16;
                }
        if (!(x & 0xff000000)) {
                k += 8;
                x <<= 8;
                }
        if (!(x & 0xf0000000)) {
                k += 4;
                x <<= 4;
                }
        if (!(x & 0xc0000000)) {
                k += 2;
                x <<= 2;
                }
        if (!(x & 0x80000000)) {
                k++;
                if (!(x & 0x40000000))
                        return 32;
                }
        return k;
        }

 static int
lo0bits
#ifdef KR_headers
        (y) ULong *y;
#else
        (ULong *y)
#endif
{
        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
#ifdef KR_headers
        (i) int i;
#else
        (int i)
#endif
{
        Bigint *b;

        b = Balloc(1);
        b->x[0] = i;
        b->wds = 1;
        return b;
        }

 static Bigint *
mult
#ifdef KR_headers
        (a, b) Bigint *a, *b;
#else
        (Bigint *a, Bigint *b)
#endif
{
        Bigint *c;
        int k, wa, wb, wc;
        ULong *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++)) {
                        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
#ifdef KR_headers
        (b, k) Bigint *b; int k;
#else
        (Bigint *b, int k)
#endif
{
        Bigint *b1, *p5, *p51;
        int i;
        static int p05[3] = { 5, 25, 125 };

        if ((i = k & 3))
                b = multadd(b, p05[i-1], 0);

        if (!(k >>= 2))
                return b;
        if (!(p5 = p5s)) {
                /* first time */
#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
#ifdef KR_headers
        (b, k) Bigint *b; int k;
#else
        (Bigint *b, int k)
#endif
{
        int i, k1, n, n1;
        Bigint *b1;
        ULong *x, *x1, *xe, z;

#ifdef Pack_32
        n = k >> 5;
#else
        n = k >> 4;
#endif
        k1 = b->k;
        n1 = n + b->wds + 1;
        for(i = b->maxwds; n1 > i; i <<= 1)
                k1++;
        b1 = Balloc(k1);
        x1 = b1->x;
        for(i = 0; i < n; i++)
                *x1++ = 0;
        x = b->x;
        xe = x + b->wds;
#ifdef Pack_32
        if (k &= 0x1f) {
                k1 = 32 - k;
                z = 0;
                do {
                        *x1++ = *x << k | z;
                        z = *x++ >> k1;
                        }
                        while(x < xe);
                if ((*x1 = z))
                        ++n1;
                }
#else
        if (k &= 0xf) {
                k1 = 16 - k;
                z = 0;
                do {
                        *x1++ = *x << k  & 0xffff | z;
                        z = *x++ >> k1;
                        }
                        while(x < xe);
                if (*x1 = z)
                        ++n1;
                }
#endif
        else do
                *x1++ = *x++;
                while(x < xe);
        b1->wds = n1 - 1;
        Bfree(b);
        return b1;
        }

 static int
cmp
#ifdef KR_headers
        (a, b) Bigint *a, *b;
#else
        (Bigint *a, Bigint *b)
#endif
{
        ULong *xa, *xa0, *xb, *xb0;
        int i, j;

        i = a->wds;
        j = b->wds;
#ifdef DEBUG
        if (i > 1 && !a->x[i-1])
                Bug("cmp called with a->x[a->wds-1] == 0");
        if (j > 1 && !b->x[j-1])
                Bug("cmp called with b->x[b->wds-1] == 0");
#endif
        if (i -= j)
                return i;
        xa0 = a->x;
        xa = xa0 + j;
        xb0 = b->x;
        xb = xb0 + j;
        for(;;) {
                if (*--xa != *--xb)
                        return *xa < *xb ? -1 : 1;
                if (xa <= xa0)
                        break;
                }
        return 0;
        }

 static Bigint *
diff
#ifdef KR_headers
        (a, b) Bigint *a, *b;
#else
        (Bigint *a, Bigint *b)
#endif
{
        Bigint *c;
        int i, wa, wb;
        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
#ifdef KR_headers
        (x) double x;
#else
        (double x)
#endif
{
        register Long L;
        double a;

        L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
#ifndef 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
#ifdef KR_headers
        (a, e) Bigint *a; int *e;
#else
        (Bigint *a, int *e)
#endif
{
        ULong *xa, *xa0, w, y, z;
        int k;
        double d;
#ifdef VAX
        ULong d0, d1;
#else
#define d0 word0(d)
#define d1 word1(d)
#endif

        xa0 = a->x;
        xa = xa0 + a->wds;
        y = *--xa;
#ifdef DEBUG
        if (!y) Bug("zero y in b2d");
#endif
        k = hi0bits(y);
        *e = 32 - k;
#ifdef Pack_32
        if (k < Ebits) {
                d0 = Exp_1 | (y >> (Ebits - k));
                w = xa > xa0 ? *--xa : 0;
                d1 = (y << ((32-Ebits) + k)) | (w >> (Ebits - k));
                goto ret_d;
                }
        z = xa > xa0 ? *--xa : 0;
        if (k -= Ebits) {
                d0 = Exp_1 | (y << k) | (z >> (32 - k));
                y = xa > xa0 ? *--xa : 0;
                d1 = (z << k) | (y >> (32 - k));
                }
        else {
                d0 = Exp_1 | y;
                d1 = z;
                }
#else
        if (k < Ebits + 16) {
                z = xa > xa0 ? *--xa : 0;
                d0 = Exp_1 | (y << (k - Ebits)) | (z >> (Ebits + 16 - k));
                w = xa > xa0 ? *--xa : 0;
                y = xa > xa0 ? *--xa : 0;
                d1 = (z << (k + 16 - Ebits)) | (w << (k - Ebits)) | (y >> (16 + Ebits - k));
                goto ret_d;
                }
        z = xa > xa0 ? *--xa : 0;
        w = xa > xa0 ? *--xa : 0;
        k -= Ebits + 16;
        d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
        y = xa > xa0 ? *--xa : 0;
        d1 = w << k + 16 | y << k;
#endif
 ret_d:
#ifdef VAX
        word0(d) = d0 >> 16 | d0 << 16;
        word1(d) = d1 >> 16 | d1 << 16;
#else
#undef d0
#undef d1
#endif
        return dval(d);
        }

 static Bigint *
d2b
#ifdef KR_headers
        (d, e, bits) double d; int *e, *bits;
#else
        (double d, int *e, int *bits)
#endif
{
        Bigint *b;
        int de, 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)))
                z |= Exp_msk1;
#endif
#ifdef Pack_32
        if ((y = d1)) {
                if ((k = lo0bits(&y))) {
                        x[0] = y | (z << (32 - k));
                        z >>= k;
                        }
                else
                        x[0] = y;
#ifndef Sudden_Underflow
                i =
#endif
                    b->wds = (x[1] = z) ? 2 : 1;
                }
        else {
               /* This assertion fails for "1e-500" and other very 
                * small numbers.  It provides the right result (0) 
                * though. This assert has also been removed from KJS's
                * version of dtoa.c.
                *
                * #ifdef DEBUG
                *     if (!z) Bug("zero z in b2d");
                * #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
#ifdef KR_headers
        (a, b) Bigint *a, *b;
#else
        (Bigint *a, Bigint *b)
#endif
{
        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
#ifdef KR_headers
        (sp, t) char **sp, *t;
#else
        (CONST char **sp, char *t)
#endif
{
        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
#ifdef KR_headers
        (rvp, sp) double *rvp; CONST char **sp;
#else
        (double *rvp, CONST char **sp)
#endif
{
        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
strtod
#ifdef KR_headers
        (s00, se) CONST char *s00; char **se;
#else
        (CONST char *s00, char **se)
#endif
{
#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

        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;

        /* 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))
                        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))
                        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
#ifdef KR_headers
        (b, S) Bigint *b, *S;
#else
        (Bigint *b, Bigint *S)
#endif
{
        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 *
#ifdef KR_headers
rv_alloc(i) int i;
#else
rv_alloc(int i)
#endif
{
        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 *
#ifdef KR_headers
nrv_alloc(s, rve, n) char *s, **rve; int n;
#else
nrv_alloc(const char *s, char **rve, int n)
#endif
{
        char *rv, *t;

        t = rv = rv_alloc(n);
        while ((*t = *s++)) 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
#ifdef KR_headers
freedtoa(s) char *s;
#else
freedtoa(char *s)
#endif
{
        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
#ifdef KR_headers
        (d, mode, ndigits, decpt, sign, rve)
        double d; int mode, ndigits, *decpt, *sign; char **rve;
#else
        (double d, int mode, int ndigits, int *decpt, int *sign, char **rve)
#endif
{
 /*     Arguments ndigits, decpt, sign are similar to those
        of ecvt and fcvt; trailing zeros are suppressed from
        the returned string.  If not null, *rve is set to point
        to the end of the return value.  If d is +-Infinity or NaN,
        then *decpt is set to 9999.

        mode:
                0 ==> shortest string that yields d when read in
                        and rounded to nearest.
                1 ==> like 0, but with Steele & White stopping rule;
                        e.g. with IEEE P754 arithmetic , mode 0 gives
                        1e23 whereas mode 1 gives 9.999999999999999e22.
                2 ==> max(1,ndigits) significant digits.  This gives a
                        return value similar to that of ecvt, except
                        that trailing zeros are suppressed.
                3 ==> through ndigits past the decimal point.  This
                        gives a return value similar to that from fcvt,
                        except that trailing zeros are suppressed, and
                        ndigits can be negative.
                4,5 ==> 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, bias_round_up;
        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

        /* In mode 2 and 3 we bias rounding up when there are ties. */
        bias_round_up = mode == 2 || mode == 3;

        ilim = ilim1 = 0; /* to avoid Google3 compiler warnings */

#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)))) {
#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 {
                /* 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;

#ifndef SET_INEXACT
#ifdef Check_FLT_ROUNDS
        try_quick = Rounding == 1;
#else
        try_quick = 1;
#endif
#endif /*SET_INEXACT*/

        if (mode > 5) {
                mode -= 4;
                try_quick = 0;
                }
        leftright = 1;
        switch(mode) {
                case 0:
                case 1:
                        ilim = ilim1 = -1;
                        i = 18;
                        ndigits = 0;
                        break;
                case 2:
                        leftright = 0;
                        /* no break */
                case 4:
                        if (ndigits <= 0)
                                ndigits = 1;
                        ilim = ilim1 = i = ndigits;
                        break;
                case 3:
                        leftright = 0;
                        /* no break */
                case 5:
                        i = ndigits + k + 1;
                        ilim = i;
                        ilim1 = i - 1;
                        if (i <= 0)
                                i = 1;
                }
        s = s0 = rv_alloc(i);

#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)) {
                        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;
                }

        /* 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 || ((dval(d) == 5*ds) && !bias_round_up))
                                goto no_digits;
                        goto one_digit;
                        }

                /* Limit looping by the number of digits to produce.
                 * Firefox had a crash bug because some plugins reduce
                 * the precision of double arithmetic.  With reduced
                 * precision "dval(d) -= L*ds" might be imprecise and
                 * d might not become zero and the loop might not
                 * terminate.
                 *
                 * See https://bugzilla.mozilla.org/show_bug.cgi?id=358569
                 */
                for(i = 1; i <= k+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) || bias_round_up))) {
 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))
                                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.
         */
#ifdef Pack_32
        if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f))
                i = 32 - i;
#else
        if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf))
                i = 16 - i;
#endif
        if (i > 4) {
                i -= 4;
                b2 += i;
                m2 += i;
                s2 += i;
                }
        else if (i < 4) {
                i += 28;
                b2 += i;
                m2 += i;
                s2 += i;
                }
        if (b2 > 0)
                b = lshift(b, b2);
        if (s2 > 0)
                S = lshift(S, s2);
        if (k_check) {
                if (cmp(b,S) < 0) {
                        k--;
                        b = multadd(b, 10, 0);  /* we botched the k estimate */
                        if (leftright)
                                mhi = multadd(mhi, 10, 0);
                        ilim = ilim1;
                        }
                }
        if (ilim <= 0 && (mode == 3 || mode == 5)) {
                S = multadd(S, 5, 0);
                if (ilim < 0 || cmp(b, S) < 0 || ((cmp(b, S) == 0) && !bias_round_up)) {
                        /* no digits, fcvt style */
 no_digits:
                        k = -1 - ndigits;
                        goto ret;
                        }
 one_digit:
                *s++ = '1';
                k++;
                goto ret;
                }
        if (leftright) {
                if (m2 > 0)
                        mhi = lshift(mhi, m2);

                /* Compute mlo -- check for special case
                 * that d is a normalized power of 2.
                 */

                mlo = mhi;
                if (spec_case) {
                        mhi = Balloc(mhi->k);
                        Bcopy(mhi, mlo);
                        mhi = lshift(mhi, Log2P);
                        }

                for(i = 1;;i++) {
                        dig = quorem(b,S) + '0';
                        /* Do we yet have the shortest decimal string
                         * that will round to d?
                         */
                        j = cmp(b, mlo);
                        delta = diff(S, mhi);
                        j1 = delta->sign ? 1 : cmp(b, delta);
                        Bfree(delta);
#ifndef ROUND_BIASED
                        if (j1 == 0 && mode != 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) || bias_round_up)))
                                            && 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);
                        }

        /* Round off last digit */

#ifdef Honor_FLT_ROUNDS
        switch(rounding) {
          case 0: goto trimzeros;
          case 2: goto roundoff;
          }
#endif
        b = lshift(b, 1);
        j = cmp(b, S);
        if (j > 0 || (j == 0 && ((dig & 1) || bias_round_up))) {
 roundoff:
                while(*--s == '9')
                        if (s == s0) {
                                k++;
                                *s++ = '1';
                                goto ret;
                                }
                ++*s++;
                }
        else {
/* trimzeros:  (never used) */
                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;
        }
#ifdef __cplusplus
}
#endif