/src/brpc/src/butil/third_party/dmg_fp/dtoa.cc

Source (jump to first uncovered line)
/****************************************************************
 *
 * 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.  Unless Trust_FLT_ROUNDS
 *  is also #defined, fegetround() will be queried for the rounding mode.
 *  Note that both FLT_ROUNDS and fegetround() are specified by the C99
 *  standard (and are specified to be consistent, with fesetround()
 *  affecting the value of FLT_ROUNDS), but that some (Linux) systems
 *  do not work correctly in this regard, so using fegetround() is more
 *  portable than using FLT_FOUNDS directly.
 * #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.  Similarly, if you
 *  want something other than the system's free() to be called to
 *  recycle memory acquired from MALLOC, #define FREE to be the
 *  name of the alternate routine.  (FREE or free is only called in
 *  pathological cases, e.g., in a dtoa call after a dtoa return in
 *  mode 3 with thousands of digits requested.)
 * #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 NO_INFNAN_CHECK if you do not wish to have INFNAN_CHECK
 *  #defined automatically on IEEE systems.  On such systems,
 *  when INFNAN_CHECK is #defined, strtod checks
 *  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 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.
 * #define NO_HEX_FP to omit recognition of hexadecimal floating-point
 *  values by strtod.
 * #define NO_STRTOD_BIGCOMP (on IEEE-arithmetic systems only for now)
 *  to disable logic for "fast" testing of very long input strings
 *  to strtod.  This testing proceeds by initially truncating the
 *  input string, then if necessary comparing the whole string with
 *  a decimal expansion to decide close cases. This logic is only
 *  used for input more than STRTOD_DIGLIM digits long (default 40).
 */

#define IEEE_8087
#define NO_HEX_FP

#ifndef Long
#if __LP64__
#define Long int
#else
#define Long long
#endif
#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 Honor_FLT_ROUNDS
#ifndef Trust_FLT_ROUNDS
#include <fenv.h>
#endif
#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 ((unsigned)((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

#ifdef IEEE_Arith
#ifndef NO_INFNAN_CHECK
#undef INFNAN_CHECK
#define INFNAN_CHECK
#endif
#else
#undef INFNAN_CHECK
#define NO_STRTOD_BIGCOMP
#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

namespace dmg_fp {

#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 IEEE_8087
#define word0(x) (x)->L[1]
#define word1(x) (x)->L[0]
#else
#define word0(x) (x)->L[0]
#define word1(x) (x)->L[1]
#endif
#define dval(x) (x)->d

#ifndef STRTOD_DIGLIM
#define STRTOD_DIGLIM 40
#endif

#ifdef DIGLIM_DEBUG
extern int strtod_diglim;
#else
#define strtod_diglim STRTOD_DIGLIM
#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 Nbits 53
#define Bias 1023
#define Emax 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
#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 Nbits 56
#define Bias 65
#define Emax 248
#define Emin (-260)
#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 Nbits 56
#define Bias 129
#define Emax 126
#define Emin (-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

typedef struct BCinfo BCinfo;
 struct
BCinfo { int dp0, dp1, dplen, dsign, e0, inexact, nd, nd0, rounding, scale, uflchk; };

#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 7

double strtod(const char *s00, char **se);
char *dtoa(double d, int mode, int ndigits,
      int *decpt, int *sign, char **rve);

 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);
  /* The k > Kmax case does not need ACQUIRE_DTOA_LOCK(0), */
  /* but this case seems very unlikely. */
  if (k <= Kmax && (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 (k <= Kmax && 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) {
    if (v->k > Kmax)
#ifdef FREE
      FREE((void*)v);
#else
      free((void*)v);
#endif
    else {
      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, dplen) CONST char *s; int nd0, nd, dplen; ULong y9;
#else
  (CONST char *s, int nd0, int nd, ULong y9, int dplen)
#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 += dplen;
    }
  else
    s += dplen + 9;
  for(; i < nd; i++)
    b = multadd(b, 10, *s++ - '0');
  return b;
  }

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

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

 static int
lo0bits
#ifdef KR_headers
  (y) ULong *y;
#else
  (ULong *y)
#endif
{
  int k;
  ULong x = *y;

  if (x & 7) {
    if (x & 1)
      return 0;
    if (x & 2) {
      *y = x >> 1;
      return 1;
      }
    *y = x >> 2;
    return 2;
    }
  k = 0;
  if (!(x & 0xffff)) {
    k = 16;
    x >>= 16;
    }
  if (!(x & 0xff)) {
    k += 8;
    x >>= 8;
    }
  if (!(x & 0xf)) {
    k += 4;
    x >>= 4;
    }
  if (!(x & 0x3)) {
    k += 2;
    x >>= 2;
    }
  if (!(x & 1)) {
    k++;
    x >>= 1;
    if (!x)
      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) U *x;
#else
  (U *x)
#endif
{
  Long L;
  U u;

  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(&u) = L;
    word1(&u) = 0;
#ifndef Avoid_Underflow
#ifndef Sudden_Underflow
    }
  else {
    L = -L >> Exp_shift;
    if (L < Exp_shift) {
      word0(&u) = 0x80000 >> L;
      word1(&u) = 0;
      }
    else {
      word0(&u) = 0;
      L -= Exp_shift;
      word1(&u) = L >= 31 ? 1 : 1 << 31 - L;
      }
    }
#endif
#endif
  return dval(&u);
  }

 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;
  U 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) U *d; int *e, *bits;
#else
  (U *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 {
    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
{
  U 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-256 */
#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

#undef Need_Hexdig
#ifdef INFNAN_CHECK
#ifndef No_Hex_NaN
#define Need_Hexdig
#endif
#endif

#ifndef Need_Hexdig
#ifndef NO_HEX_FP
#define Need_Hexdig
#endif
#endif

#ifdef Need_Hexdig /*{*/
static unsigned char hexdig[256];

 static void
#ifdef KR_headers
htinit(h, s, inc) unsigned char *h; unsigned char *s; int inc;
#else
htinit(unsigned char *h, unsigned char *s, int inc)
#endif
{
  int i, j;
  for(i = 0; (j = s[i]) !=0; i++)
    h[j] = i + inc;
  }

 static void
#ifdef KR_headers
hexdig_init()
#else
hexdig_init(void)
#endif
{
#define USC (unsigned char *)
  htinit(hexdig, USC "0123456789", 0x10);
  htinit(hexdig, USC "abcdef", 0x10 + 10);
  htinit(hexdig, USC "ABCDEF", 0x10 + 10);
  }
#endif /* } Need_Hexdig */

#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, CONST 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) U *rvp; CONST char **sp;
#else
  (U *rvp, CONST char **sp)
#endif
{
  ULong c, x[2];
  CONST char *s;
  int c1, havedig, udx0, xshift;

  if (!hexdig[(int)'0'])
    hexdig_init();
  x[0] = x[1] = 0;
  havedig = xshift = 0;
  udx0 = 1;
  s = *sp;
  /* allow optional initial 0x or 0X */
  while((c = *(CONST unsigned char*)(s+1)) && c <= ' ')
    ++s;
  if (s[1] == '0' && (s[2] == 'x' || s[2] == 'X'))
    s += 2;
  while((c = *(CONST unsigned char*)++s)) {
    if ((c1 = hexdig[c]))
      c  = c1 & 0xf;
    else if (c <= ' ') {
      if (udx0 && havedig) {
        udx0 = 0;
        xshift = 1;
        }
      continue;
      }
#ifdef GDTOA_NON_PEDANTIC_NANCHECK
    else if (/*(*/ c == ')' && havedig) {
      *sp = s + 1;
      break;
      }
    else
      return; /* invalid form: don't change *sp */
#else
    else {
      do {
        if (/*(*/ c == ')') {
          *sp = s + 1;
          break;
          }
        } while((c = *++s));
      break;
      }
#endif
    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 */

#ifdef Pack_32
#define ULbits 32
#define kshift 5
#define kmask 31
#else
#define ULbits 16
#define kshift 4
#define kmask 15
#endif
#ifndef NO_HEX_FP /*{*/

 static void
#ifdef KR_headers
rshift(b, k) Bigint *b; int k;
#else
rshift(Bigint *b, int k)
#endif
{
  ULong *x, *x1, *xe, y;
  int n;

  x = x1 = b->x;
  n = k >> kshift;
  if (n < b->wds) {
    xe = x + b->wds;
    x += n;
    if (k &= kmask) {
      n = 32 - k;
      y = *x++ >> k;
      while(x < xe) {
        *x1++ = (y | (*x << n)) & 0xffffffff;
        y = *x++ >> k;
        }
      if ((*x1 = y) !=0)
        x1++;
      }
    else
      while(x < xe)
        *x1++ = *x++;
    }
  if ((b->wds = x1 - b->x) == 0)
    b->x[0] = 0;
  }

 static ULong
#ifdef KR_headers
any_on(b, k) Bigint *b; int k;
#else
any_on(Bigint *b, int k)
#endif
{
  int n, nwds;
  ULong *x, *x0, x1, x2;

  x = b->x;
  nwds = b->wds;
  n = k >> kshift;
  if (n > nwds)
    n = nwds;
  else if (n < nwds && (k &= kmask)) {
    x1 = x2 = x[n];
    x1 >>= k;
    x1 <<= k;
    if (x1 != x2)
      return 1;
    }
  x0 = x;
  x += n;
  while(x > x0)
    if (*--x)
      return 1;
  return 0;
  }

enum {  /* rounding values: same as FLT_ROUNDS */
  Round_zero = 0,
  Round_near = 1,
  Round_up = 2,
  Round_down = 3
  };

 static Bigint *
#ifdef KR_headers
increment(b) Bigint *b;
#else
increment(Bigint *b)
#endif
{
  ULong *x, *xe;
  Bigint *b1;

  x = b->x;
  xe = x + b->wds;
  do {
    if (*x < (ULong)0xffffffffL) {
      ++*x;
      return b;
      }
    *x++ = 0;
    } while(x < xe);
  {
    if (b->wds >= b->maxwds) {
      b1 = Balloc(b->k+1);
      Bcopy(b1,b);
      Bfree(b);
      b = b1;
      }
    b->x[b->wds++] = 1;
    }
  return b;
  }

 void
#ifdef KR_headers
gethex(sp, rvp, rounding, sign)
  CONST char **sp; U *rvp; int rounding, sign;
#else
gethex( CONST char **sp, U *rvp, int rounding, int sign)
#endif
{
  Bigint *b;
  CONST unsigned char *decpt, *s0, *s, *s1;
  Long e, e1;
  ULong L, lostbits, *x;
  int big, denorm, esign, havedig, k, n, nbits, up, zret;
#ifdef IBM
  int j;
#endif
  enum {
#ifdef IEEE_Arith /*{{*/
    emax = 0x7fe - Bias - P + 1,
    emin = Emin - P + 1
#else /*}{*/
    emin = Emin - P,
#ifdef VAX
    emax = 0x7ff - Bias - P + 1
#endif
#ifdef IBM
    emax = 0x7f - Bias - P
#endif
#endif /*}}*/
    };
#ifdef USE_LOCALE
  int i;
#ifdef NO_LOCALE_CACHE
  const unsigned char *decimalpoint = (unsigned char*)
    localeconv()->decimal_point;
#else
  const unsigned char *decimalpoint;
  static unsigned char *decimalpoint_cache;
  if (!(s0 = decimalpoint_cache)) {
    s0 = (unsigned char*)localeconv()->decimal_point;
    if ((decimalpoint_cache = (unsigned char*)
        MALLOC(strlen((CONST char*)s0) + 1))) {
      strcpy((char*)decimalpoint_cache, (CONST char*)s0);
      s0 = decimalpoint_cache;
      }
    }
  decimalpoint = s0;
#endif
#endif

  if (!hexdig['0'])
    hexdig_init();
  havedig = 0;
  s0 = *(CONST unsigned char **)sp + 2;
  while(s0[havedig] == '0')
    havedig++;
  s0 += havedig;
  s = s0;
  decpt = 0;
  zret = 0;
  e = 0;
  if (hexdig[*s])
    havedig++;
  else {
    zret = 1;
#ifdef USE_LOCALE
    for(i = 0; decimalpoint[i]; ++i) {
      if (s[i] != decimalpoint[i])
        goto pcheck;
      }
    decpt = s += i;
#else
    if (*s != '.')
      goto pcheck;
    decpt = ++s;
#endif
    if (!hexdig[*s])
      goto pcheck;
    while(*s == '0')
      s++;
    if (hexdig[*s])
      zret = 0;
    havedig = 1;
    s0 = s;
    }
  while(hexdig[*s])
    s++;
#ifdef USE_LOCALE
  if (*s == *decimalpoint && !decpt) {
    for(i = 1; decimalpoint[i]; ++i) {
      if (s[i] != decimalpoint[i])
        goto pcheck;
      }
    decpt = s += i;
#else
  if (*s == '.' && !decpt) {
    decpt = ++s;
#endif
    while(hexdig[*s])
      s++;
    }/*}*/
  if (decpt)
    e = -(((Long)(s-decpt)) << 2);
 pcheck:
  s1 = s;
  big = esign = 0;
  switch(*s) {
    case 'p':
    case 'P':
    switch(*++s) {
      case '-':
      esign = 1;
      // fall through
      case '+':
      s++;
      }
    if ((n = hexdig[*s]) == 0 || n > 0x19) {
      s = s1;
      break;
      }
    e1 = n - 0x10;
    while((n = hexdig[*++s]) !=0 && n <= 0x19) {
      if (e1 & 0xf8000000)
        big = 1;
      e1 = 10*e1 + n - 0x10;
      }
    if (esign)
      e1 = -e1;
    e += e1;
    }
  *sp = (char*)s;
  if (!havedig)
    *sp = (char*)s0 - 1;
  if (zret)
    goto retz1;
  if (big) {
    if (esign) {
#ifdef IEEE_Arith
      switch(rounding) {
        case Round_up:
        if (sign)
          break;
        goto ret_tiny;
        case Round_down:
        if (!sign)
          break;
        goto ret_tiny;
        }
#endif
      goto retz;
#ifdef IEEE_Arith
 ret_tiny:
#ifndef NO_ERRNO
      errno = ERANGE;
#endif
      word0(rvp) = 0;
      word1(rvp) = 1;
      return;
#endif /* IEEE_Arith */
      }
    switch(rounding) {
      case Round_near:
      goto ovfl1;
      case Round_up:
      if (!sign)
        goto ovfl1;
      goto ret_big;
      case Round_down:
      if (sign)
        goto ovfl1;
      goto ret_big;
      }
 ret_big:
    word0(rvp) = Big0;
    word1(rvp) = Big1;
    return;
    }
  n = s1 - s0 - 1;
  for(k = 0; n > (1 << (kshift-2)) - 1; n >>= 1)
    k++;
  b = Balloc(k);
  x = b->x;
  n = 0;
  L = 0;
#ifdef USE_LOCALE
  for(i = 0; decimalpoint[i+1]; ++i);
#endif
  while(s1 > s0) {
#ifdef USE_LOCALE
    if (*--s1 == decimalpoint[i]) {
      s1 -= i;
      continue;
      }
#else
    if (*--s1 == '.')
      continue;
#endif
    if (n == ULbits) {
      *x++ = L;
      L = 0;
      n = 0;
      }
    L |= (hexdig[*s1] & 0x0f) << n;
    n += 4;
    }
  *x++ = L;
  b->wds = n = x - b->x;
  n = ULbits*n - hi0bits(L);
  nbits = Nbits;
  lostbits = 0;
  x = b->x;
  if (n > nbits) {
    n -= nbits;
    if (any_on(b,n)) {
      lostbits = 1;
      k = n - 1;
      if (x[k>>kshift] & 1 << (k & kmask)) {
        lostbits = 2;
        if (k > 0 && any_on(b,k))
          lostbits = 3;
        }
      }
    rshift(b, n);
    e += n;
    }
  else if (n < nbits) {
    n = nbits - n;
    b = lshift(b, n);
    e -= n;
    x = b->x;
    }
  if (e > Emax) {
 ovfl:
    Bfree(b);
 ovfl1:
#ifndef NO_ERRNO
    errno = ERANGE;
#endif
    word0(rvp) = Exp_mask;
    word1(rvp) = 0;
    return;
    }
  denorm = 0;
  if (e < emin) {
    denorm = 1;
    n = emin - e;
    if (n >= nbits) {
#ifdef IEEE_Arith /*{*/
      switch (rounding) {
        case Round_near:
        if (n == nbits && (n < 2 || any_on(b,n-1)))
          goto ret_tiny;
        break;
        case Round_up:
        if (!sign)
          goto ret_tiny;
        break;
        case Round_down:
        if (sign)
          goto ret_tiny;
        }
#endif /* } IEEE_Arith */
      Bfree(b);
 retz:
#ifndef NO_ERRNO
      errno = ERANGE;
#endif
 retz1:
      rvp->d = 0.;
      return;
      }
    k = n - 1;
    if (lostbits)
      lostbits = 1;
    else if (k > 0)
      lostbits = any_on(b,k);
    if (x[k>>kshift] & 1 << (k & kmask))
      lostbits |= 2;
    nbits -= n;
    rshift(b,n);
    e = emin;
    }
  if (lostbits) {
    up = 0;
    switch(rounding) {
      case Round_zero:
      break;
      case Round_near:
      if (lostbits & 2
       && (lostbits & 1) | (x[0] & 1))
        up = 1;
      break;
      case Round_up:
      up = 1 - sign;
      break;
      case Round_down:
      up = sign;
      }
    if (up) {
      k = b->wds;
      b = increment(b);
      x = b->x;
      if (denorm) {
#if 0
        if (nbits == Nbits - 1
         && x[nbits >> kshift] & 1 << (nbits & kmask))
          denorm = 0; /* not currently used */
#endif
        }
      else if (b->wds > k
       || ((n = nbits & kmask) !=0
           && hi0bits(x[k-1]) < 32-n)) {
        rshift(b,1);
        if (++e > Emax)
          goto ovfl;
        }
      }
    }
#ifdef IEEE_Arith
  if (denorm)
    word0(rvp) = b->wds > 1 ? b->x[1] & ~0x100000 : 0;
  else
    word0(rvp) = (b->x[1] & ~0x100000) | ((e + 0x3ff + 52) << 20);
  word1(rvp) = b->x[0];
#endif
#ifdef IBM
  if ((j = e & 3)) {
    k = b->x[0] & ((1 << j) - 1);
    rshift(b,j);
    if (k) {
      switch(rounding) {
        case Round_up:
        if (!sign)
          increment(b);
        break;
        case Round_down:
        if (sign)
          increment(b);
        break;
        case Round_near:
        j = 1 << (j-1);
        if (k & j && ((k & (j-1)) | lostbits))
          increment(b);
        }
      }
    }
  e >>= 2;
  word0(rvp) = b->x[1] | ((e + 65 + 13) << 24);
  word1(rvp) = b->x[0];
#endif
#ifdef VAX
  /* The next two lines ignore swap of low- and high-order 2 bytes. */
  /* word0(rvp) = (b->x[1] & ~0x800000) | ((e + 129 + 55) << 23); */
  /* word1(rvp) = b->x[0]; */
  word0(rvp) = ((b->x[1] & ~0x800000) >> 16) | ((e + 129 + 55) << 7) | (b->x[1] << 16);
  word1(rvp) = (b->x[0] >> 16) | (b->x[0] << 16);
#endif
  Bfree(b);
  }
#endif /*}!NO_HEX_FP*/

 static int
#ifdef KR_headers
dshift(b, p2) Bigint *b; int p2;
#else
dshift(Bigint *b, int p2)
#endif
{
  int rv = hi0bits(b->x[b->wds-1]) - 4;
  if (p2 > 0)
    rv -= p2;
  return rv & kmask;
  }

 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 NO_STRTOD_BIGCOMP

 static void
bigcomp
#ifdef KR_headers
  (rv, s0, bc)
  U *rv; CONST char *s0; BCinfo *bc;
#else
  (U *rv, CONST char *s0, BCinfo *bc)
#endif
{
  Bigint *b, *d;
  int b2, bbits, d2, dd, dig, dsign, i, j, nd, nd0, p2, p5, speccase;

  dsign = bc->dsign;
  nd = bc->nd;
  nd0 = bc->nd0;
  p5 = nd + bc->e0 - 1;
  dd = speccase = 0;
#ifndef Sudden_Underflow
  if (rv->d == 0.) { /* special case: value near underflow-to-zero */
        /* threshold was rounded to zero */
    b = i2b(1);
    p2 = Emin - P + 1;
    bbits = 1;
#ifdef Avoid_Underflow
    word0(rv) = (P+2) << Exp_shift;
#else
    word1(rv) = 1;
#endif
    i = 0;
#ifdef Honor_FLT_ROUNDS
    if (bc->rounding == 1)
#endif
      {
      speccase = 1;
      --p2;
      dsign = 0;
      goto have_i;
      }
    }
  else
#endif
    b = d2b(rv, &p2, &bbits);
#ifdef Avoid_Underflow
  p2 -= bc->scale;
#endif
  /* floor(log2(rv)) == bbits - 1 + p2 */
  /* Check for denormal case. */
  i = P - bbits;
  if (i > (j = P - Emin - 1 + p2)) {
#ifdef Sudden_Underflow
    Bfree(b);
    b = i2b(1);
    p2 = Emin;
    i = P - 1;
#ifdef Avoid_Underflow
    word0(rv) = (1 + bc->scale) << Exp_shift;
#else
    word0(rv) = Exp_msk1;
#endif
    word1(rv) = 0;
#else
    i = j;
#endif
    }
#ifdef Honor_FLT_ROUNDS
  if (bc->rounding != 1) {
    if (i > 0)
      b = lshift(b, i);
    if (dsign)
      b = increment(b);
    }
  else
#endif
    {
    b = lshift(b, ++i);
    b->x[0] |= 1;
    }
#ifndef Sudden_Underflow
 have_i:
#endif
  p2 -= p5 + i;
  d = i2b(1);
  /* Arrange for convenient computation of quotients:
   * shift left if necessary so divisor has 4 leading 0 bits.
   */
  if (p5 > 0)
    d = pow5mult(d, p5);
  else if (p5 < 0)
    b = pow5mult(b, -p5);
  if (p2 > 0) {
    b2 = p2;
    d2 = 0;
    }
  else {
    b2 = 0;
    d2 = -p2;
    }
  i = dshift(d, d2);
  if ((b2 += i) > 0)
    b = lshift(b, b2);
  if ((d2 += i) > 0)
    d = lshift(d, d2);

  /* Now b/d = exactly half-way between the two floating-point values */
  /* on either side of the input string.  Compute first digit of b/d. */

  if (!(dig = quorem(b,d))) {
    b = multadd(b, 10, 0);  /* very unlikely */
    dig = quorem(b,d);
    }

  /* Compare b/d with s0 */

  for(i = 0; i < nd0; ) {
    if ((dd = s0[i++] - '0' - dig))
      goto ret;
    if (!b->x[0] && b->wds == 1) {
      if (i < nd)
        dd = 1;
      goto ret;
      }
    b = multadd(b, 10, 0);
    dig = quorem(b,d);
    }
  for(j = bc->dp1; i++ < nd;) {
    if ((dd = s0[j++] - '0' - dig))
      goto ret;
    if (!b->x[0] && b->wds == 1) {
      if (i < nd)
        dd = 1;
      goto ret;
      }
    b = multadd(b, 10, 0);
    dig = quorem(b,d);
    }
  if (b->x[0] || b->wds > 1)
    dd = -1;
 ret:
  Bfree(b);
  Bfree(d);
#ifdef Honor_FLT_ROUNDS
  if (bc->rounding != 1) {
    if (dd < 0) {
      if (bc->rounding == 0) {
        if (!dsign)
          goto retlow1;
        }
      else if (dsign)
        goto rethi1;
      }
    else if (dd > 0) {
      if (bc->rounding == 0) {
        if (dsign)
          goto rethi1;
        goto ret1;
        }
      if (!dsign)
        goto rethi1;
      dval(rv) += 2.*ulp(rv);
      }
    else {
      bc->inexact = 0;
      if (dsign)
        goto rethi1;
      }
    }
  else
#endif
  if (speccase) {
    if (dd <= 0)
      rv->d = 0.;
    }
  else if (dd < 0) {
    if (!dsign) /* does not happen for round-near */
retlow1:
      dval(rv) -= ulp(rv);
    }
  else if (dd > 0) {
    if (dsign) {
 rethi1:
      dval(rv) += ulp(rv);
      }
    }
  else {
    /* Exact half-way case:  apply round-even rule. */
    if (word1(rv) & 1) {
      if (dsign)
        goto rethi1;
      goto retlow1;
      }
    }

#ifdef Honor_FLT_ROUNDS
 ret1:
#endif
  return;
  }
#endif /* NO_STRTOD_BIGCOMP */

 double
strtod
#ifdef KR_headers
  (s00, se) CONST char *s00; char **se;
#else
  (CONST char *s00, char **se)
#endif
{
  int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, e, e1;
  int esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
  CONST char *s, *s0, *s1;
  double aadj, aadj1;
  Long L;
  U aadj2, adj, rv, rv0;
  ULong y, z;
  BCinfo bc;
  Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
#ifdef SET_INEXACT
  int oldinexact;
#endif
#ifdef Honor_FLT_ROUNDS /*{*/
#ifdef Trust_FLT_ROUNDS /*{{ only define this if FLT_ROUNDS really works! */
  bc.rounding = Flt_Rounds;
#else /*}{*/
  bc.rounding = 1;
  switch(fegetround()) {
    case FE_TOWARDZERO: bc.rounding = 0; break;
    case FE_UPWARD: bc.rounding = 2; break;
    case FE_DOWNWARD: bc.rounding = 3;
    }
#endif /*}}*/
#endif /*}*/
#ifdef USE_LOCALE
  CONST char *s2;
#endif

  sign = nz0 = nz = bc.dplen = bc.uflchk = 0;
  dval(&rv) = 0.;
  for(s = s00;;s++) switch(*s) {
    case '-':
      sign = 1;
      // fall through
    case '+':
      if (*++s)
        goto break2;
      // fall through
    case 0:
      goto ret0;
    case '\t':
    case '\n':
    case '\v':
    case '\f':
    case '\r':
    case ' ':
      continue;
    default:
      goto break2;
    }
 break2:
  if (*s == '0') {
#ifndef NO_HEX_FP /*{*/
    switch(s[1]) {
      case 'x':
      case 'X':
#ifdef Honor_FLT_ROUNDS
      gethex(&s, &rv, bc.rounding, sign);
#else
      gethex(&s, &rv, 1, sign);
#endif
      goto ret;
      }
#endif /*}*/
    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;
  bc.dp0 = bc.dp1 = s - s0;
#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;
    bc.dp1 = s - s0;
    bc.dplen = bc.dp1 - bc.dp0;
    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;
        // fall through
      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 */
      if (!bc.dplen)
       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;
    }
  bc.e0 = 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.d = -rv.d;
          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.d = -rv.d;
          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.d = -rv.d;
        sign = 0;
        }
#endif
      /* rv = */ rounded_quotient(dval(&rv), tens[-e]);
      goto ret;
      }
#endif
    }
  e1 += nd - k;

#ifdef IEEE_Arith
#ifdef SET_INEXACT
  bc.inexact = 1;
  if (k <= DBL_DIG)
    oldinexact = get_inexact();
#endif
#ifdef Avoid_Underflow
  bc.scale = 0;
#endif
#ifdef Honor_FLT_ROUNDS
  if (bc.rounding >= 2) {
    if (sign)
      bc.rounding = bc.rounding == 2 ? 0 : 2;
    else
      if (bc.rounding != 2)
        bc.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(bc.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*/
        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)
        bc.scale = 2*P;
      for(j = 0; e1 > 0; j++, e1 >>= 1)
        if (e1 & 1)
          dval(&rv) *= tinytens[j];
      if (bc.scale && (j = 2*P + 1 - ((word0(&rv) & Exp_mask)
            >> Exp_shift)) > 0) {
        /* scaled rv is denormal; clear 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
          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 */

  bc.nd = nd;
#ifndef NO_STRTOD_BIGCOMP
  bc.nd0 = nd0; /* Only needed if nd > strtod_diglim, but done here */
      /* to silence an erroneous warning about bc.nd0 */
      /* possibly not being initialized. */
  if (nd > strtod_diglim) {
    /* ASSERT(strtod_diglim >= 18); 18 == one more than the */
    /* minimum number of decimal digits to distinguish double values */
    /* in IEEE arithmetic. */
    i = j = 18;
    if (i > nd0)
      j += bc.dplen;
    for(;;) {
      if (--j <= bc.dp1 && j >= bc.dp0)
        j = bc.dp0 - 1;
      if (s0[j] != '0')
        break;
      --i;
      }
    e += nd - i;
    nd = i;
    if (nd0 > nd)
      nd0 = nd;
    if (nd < 9) { /* must recompute y */
      y = 0;
      for(i = 0; i < nd0; ++i)
        y = 10*y + s0[i] - '0';
      for(j = bc.dp1; i < nd; ++i)
        y = 10*y + s0[j++] - '0';
      }
    }
#endif
  bd0 = s2b(s0, nd0, nd, y, bc.dplen);

  for(;;) {
    bd = Balloc(bd0->k);
    Bcopy(bd, bd0);
    bb = d2b(&rv, &bbe, &bbbits); /* rv = bb * 2^bbe */
    bs = i2b(1);

    if (e >= 0) {
      bb2 = bb5 = 0;
      bd2 = bd5 = e;
      }
    else {
      bb2 = bb5 = -e;
      bd2 = bd5 = 0;
      }
    if (bbe >= 0)
      bb2 += bbe;
    else
      bd2 -= bbe;
    bs2 = bb2;
#ifdef Honor_FLT_ROUNDS
    if (bc.rounding != 1)
      bs2++;
#endif
#ifdef Avoid_Underflow
    j = bbe - bc.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 += bc.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);
    bc.dsign = delta->sign;
    delta->sign = 0;
    i = cmp(delta, bs);
#ifndef NO_STRTOD_BIGCOMP
    if (bc.nd > nd && i <= 0) {
      if (bc.dsign)
        break; /* Must use bigcomp(). */
#ifdef Honor_FLT_ROUNDS
      if (bc.rounding != 1) {
        if (i < 0)
          break;
        }
      else
#endif
        {
        bc.nd = nd;
        i = -1; /* Discarded digits make delta smaller. */
        }
      }
#endif
#ifdef Honor_FLT_ROUNDS
    if (bc.rounding != 1) {
      if (i < 0) {
        /* Error is less than an ulp */
        if (!delta->x[0] && delta->wds <= 1) {
          /* exact */
#ifdef SET_INEXACT
          bc.inexact = 0;
#endif
          break;
          }
        if (bc.rounding) {
          if (bc.dsign) {
            adj.d = 1.;
            goto apply_adj;
            }
          }
        else if (!bc.dsign) {
          adj.d = -1.;
          if (!word1(&rv)
           && !(word0(&rv) & Frac_mask)) {
            y = word0(&rv) & Exp_mask;
#ifdef Avoid_Underflow
            if (!bc.scale || y > 2*P*Exp_msk1)
#else
            if (y)
#endif
              {
              delta = lshift(delta,Log2P);
              if (cmp(delta, bs) <= 0)
              adj.d = -0.5;
              }
            }
 apply_adj:
#ifdef Avoid_Underflow
          if (bc.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.d*ulp(dval(&rv));
            word0(&rv) -= P*Exp_msk1;
            }
          else
#endif /*Sudden_Underflow*/
#endif /*Avoid_Underflow*/
          dval(&rv) += adj.d*ulp(&rv);
          }
        break;
        }
      adj.d = ratio(delta, bs);
      if (adj.d < 1.)
        adj.d = 1.;
      if (adj.d <= 0x7ffffffe) {
        /* adj = rounding ? ceil(adj) : floor(adj); */
        y = adj.d;
        if (y != adj.d) {
          if (!((bc.rounding>>1) ^ bc.dsign))
            y++;
          adj.d = y;
          }
        }
#ifdef Avoid_Underflow
      if (bc.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.d *= ulp(dval(&rv));
        if (bc.dsign)
          dval(&rv) += adj.d;
        else
          dval(&rv) -= adj.d;
        word0(&rv) -= P*Exp_msk1;
        goto cont;
        }
#endif /*Sudden_Underflow*/
#endif /*Avoid_Underflow*/
      adj.d *= ulp(&rv);
      if (bc.dsign) {
        if (word0(&rv) == Big0 && word1(&rv) == Big1)
          goto ovfl;
        dval(&rv) += adj.d;
        }
      else
        dval(&rv) -= adj.d;
      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 (bc.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)
          bc.inexact = 0;
#endif
        break;
        }
      if (!delta->x[0] && delta->wds <= 1) {
        /* exact result */
#ifdef SET_INEXACT
        bc.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 (bc.dsign) {
        if ((word0(&rv) & Bndry_mask1) == Bndry_mask1
         &&  word1(&rv) == (
#ifdef Avoid_Underflow
      (bc.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
          bc.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 <= (bc.scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
#else
        if (L <= Exp_msk1)
#endif /*Avoid_Underflow*/
#endif /*IBM*/
          {
          if (bc.nd >nd) {
            bc.uflchk = 1;
            break;
            }
          goto undfl;
          }
        L -= Exp_msk1;
#else /*Sudden_Underflow}{*/
#ifdef Avoid_Underflow
        if (bc.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 */
            if (bc.nd >nd) {
              bc.uflchk = 1;
              break;
              }
            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 (bc.dsign)
        dval(&rv) += ulp(&rv);
#ifndef ROUND_BIASED
      else {
        dval(&rv) -= ulp(&rv);
#ifndef Sudden_Underflow
        if (!dval(&rv)) {
          if (bc.nd >nd) {
            bc.uflchk = 1;
            break;
            }
          goto undfl;
          }
#endif
        }
#ifdef Avoid_Underflow
      bc.dsign = 1 - bc.dsign;
#endif
#endif
      break;
      }
    if ((aadj = ratio(delta, bs)) <= 2.) {
      if (bc.dsign)
        aadj = aadj1 = 1.;
      else if (word1(&rv) || word0(&rv) & Bndry_mask) {
#ifndef Sudden_Underflow
        if (word1(&rv) == Tiny1 && !word0(&rv)) {
          if (bc.nd >nd) {
            bc.uflchk = 1;
            break;
            }
          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 = bc.dsign ? aadj : -aadj;
#ifdef Check_FLT_ROUNDS
      switch(bc.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.d = aadj1 * ulp(&rv);
      dval(&rv) += adj.d;
      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 (bc.scale && y <= 2*P*Exp_msk1) {
        if (aadj <= 0x7fffffff) {
                                    if ((z = (ULong)aadj) <= 0)
            z = 1;
          aadj = z;
          aadj1 = bc.dsign ? aadj : -aadj;
          }
        dval(&aadj2) = aadj1;
        word0(&aadj2) += (2*P+1)*Exp_msk1 - y;
        aadj1 = dval(&aadj2);
        }
      adj.d = aadj1 * ulp(&rv);
      dval(&rv) += adj.d;
#else
#ifdef Sudden_Underflow
      if ((word0(&rv) & Exp_mask) <= P*Exp_msk1) {
        dval(&rv0) = dval(&rv);
        word0(&rv) += P*Exp_msk1;
        adj.d = aadj1 * ulp(&rv);
        dval(&rv) += adj.d;
#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) {
            if (bc.nd >nd) {
              bc.uflchk = 1;
              break;
              }
            goto undfl;
            }
          word0(&rv) = Tiny0;
          word1(&rv) = Tiny1;
          goto cont;
          }
        else
          word0(&rv) -= P*Exp_msk1;
        }
      else {
        adj.d = aadj1 * ulp(&rv);
        dval(&rv) += adj.d;
        }
#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 (!bc.dsign)
          aadj1 = -aadj1;
        }
      adj.d = aadj1 * ulp(&rv);
      dval(&rv) += adj.d;
#endif /*Sudden_Underflow*/
#endif /*Avoid_Underflow*/
      }
    z = word0(&rv) & Exp_mask;
#ifndef SET_INEXACT
    if (bc.nd == nd) {
#ifdef Avoid_Underflow
    if (!bc.scale)
#endif
    if (y == z) {
      /* Can we stop now? */
      L = (Long)aadj;
      aadj -= L;
      /* The tolerances below are conservative. */
      if (bc.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);
    }
  Bfree(bb);
  Bfree(bd);
  Bfree(bs);
  Bfree(bd0);
  Bfree(delta);
#ifndef NO_STRTOD_BIGCOMP
  if (bc.nd > nd)
    bigcomp(&rv, s0, &bc);
#endif
#ifdef SET_INEXACT
  if (bc.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 (bc.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 */
#ifdef IEEE_Arith
    if (!(word0(&rv) & Exp_mask))
#else
    if (word0(&rv) == 0 && word1(&rv) == 0)
#endif
      errno = ERANGE;
#endif
    }
#endif /* Avoid_Underflow */
#ifdef SET_INEXACT
  if (bc.inexact && !(word0(&rv) & Exp_mask)) {
    /* set underflow bit */
    dval(&rv0) = 1e-300;
    dval(&rv0) *= dval(&rv0);
    }
#endif
 ret:
  if (se)
    *se = (char *)s;
  return sign ? -dval(&rv) : dval(&rv);
  }

#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 <= (size_t)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
  (dd, mode, ndigits, decpt, sign, rve)
  double dd; int mode, ndigits, *decpt, *sign; char **rve;
#else
  (double dd, 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;
  Long L;
#ifndef Sudden_Underflow
  int denorm;
  ULong x;
#endif
  Bigint *b, *b1, *delta, *mlo = NULL, *mhi, *S;
  U d2, eps, u;
  double ds;
  char *s, *s0;
#ifdef SET_INEXACT
  int inexact, oldinexact;
#endif
#ifdef Honor_FLT_ROUNDS /*{*/
  int Rounding;
#ifdef Trust_FLT_ROUNDS /*{{ only define this if FLT_ROUNDS really works! */
  Rounding = Flt_Rounds;
#else /*}{*/
  Rounding = 1;
  switch(fegetround()) {
    case FE_TOWARDZERO: Rounding = 0; break;
    case FE_UPWARD: Rounding = 2; break;
    case FE_DOWNWARD: Rounding = 3;
    }
#endif /*}}*/
#endif /*}*/

#ifndef MULTIPLE_THREADS
  if (dtoa_result) {
    freedtoa(dtoa_result);
    dtoa_result = 0;
    }
#endif

  u.d = dd;
  if (word0(&u) & Sign_bit) {
    /* set sign for everything, including 0's and NaNs */
    *sign = 1;
    word0(&u) &= ~Sign_bit; /* clear sign bit */
    }
  else
    *sign = 0;

#if defined(IEEE_Arith) + defined(VAX)
#ifdef IEEE_Arith
  if ((word0(&u) & Exp_mask) == Exp_mask)
#else
  if (word0(&u)  == 0x8000)
#endif
    {
    /* Infinity or NaN */
    *decpt = 9999;
#ifdef IEEE_Arith
    if (!word1(&u) && !(word0(&u) & 0xfffff))
      return nrv_alloc("Infinity", rve, 8);
#endif
    return nrv_alloc("NaN", rve, 3);
    }
#endif
#ifdef IBM
  dval(&u) += 0; /* normalize */
#endif
  if (!dval(&u)) {
    *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 >= 2) {
    if (*sign)
      Rounding = Rounding == 2 ? 0 : 2;
    else
      if (Rounding != 2)
        Rounding = 0;
    }
#endif

  b = d2b(&u, &be, &bbits);
#ifdef Sudden_Underflow
  i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
#else
  if ((i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) {
#endif
    dval(&d2) = dval(&u);
    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(&u) << (64 - i) | word1(&u) >> (i - 32)
          : word1(&u) << (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(&u) < 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;
  ilim = ilim1 = -1;  /* Values for cases 0 and 1; done here to */
        /* silence erroneous "gcc -Wall" warning. */
  switch(mode) {
    case 0:
    case 1:
      i = 18;
      ndigits = 0;
      break;
    case 2:
      leftright = 0;
      // fall through
    case 4:
      if (ndigits <= 0)
        ndigits = 1;
      ilim = ilim1 = i = ndigits;
      break;
    case 3:
      leftright = 0;
      // fall through
    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(&u);
    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(&u) /= bigtens[n_bigtens-1];
        ieps++;
        }
      for(; j; j >>= 1, i++)
        if (j & 1) {
          ieps++;
          ds *= bigtens[i];
          }
      dval(&u) /= ds;
      }
    else if ((j1 = -k)) {
      dval(&u) *= tens[j1 & 0xf];
      for(j = j1 >> 4; j; j >>= 1, i++)
        if (j & 1) {
          ieps++;
          dval(&u) *= bigtens[i];
          }
      }
    if (k_check && dval(&u) < 1. && ilim > 0) {
      if (ilim1 <= 0)
        goto fast_failed;
      ilim = ilim1;
      k--;
      dval(&u) *= 10.;
      ieps++;
      }
    dval(&eps) = ieps*dval(&u) + 7.;
    word0(&eps) -= (P-1)*Exp_msk1;
    if (ilim == 0) {
      S = mhi = 0;
      dval(&u) -= 5.;
      if (dval(&u) > dval(&eps))
        goto one_digit;
      if (dval(&u) < -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 = (Long)dval(&u);
        dval(&u) -= L;
        *s++ = '0' + (int)L;
        if (dval(&u) < dval(&eps))
          goto ret1;
        if (1. - dval(&u) < dval(&eps))
          goto bump_up;
        if (++i >= ilim)
          break;
        dval(&eps) *= 10.;
        dval(&u) *= 10.;
        }
      }
    else {
#endif
      /* Generate ilim digits, then fix them up. */
      dval(&eps) *= tens[ilim-1];
      for(i = 1;; i++, dval(&u) *= 10.) {
        L = (Long)(dval(&u));
        if (!(dval(&u) -= L))
          ilim = i;
        *s++ = '0' + (int)L;
        if (i == ilim) {
          if (dval(&u) > 0.5 + dval(&eps))
            goto bump_up;
          else if (dval(&u) < 0.5 - dval(&eps)) {
            while(*--s == '0') {}
            s++;
            goto ret1;
            }
          break;
          }
        }
#ifndef No_leftright
      }
#endif
 fast_failed:
    s = s0;
    dval(&u) = 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(&u) <= 5*ds)
        goto no_digits;
      goto one_digit;
      }
    for(i = 1; i <= k + 1; i++, dval(&u) *= 10.) {
      L = (Long)(dval(&u) / ds);
      dval(&u) -= L*ds;
#ifdef Check_FLT_ROUNDS
      /* If FLT_ROUNDS == 2, L will usually be high by 1 */
      if (dval(&u) < 0) {
        L--;
        dval(&u) += ds;
        }
#endif
      *s++ = '0' + (int)L;
      if (!dval(&u)) {
#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(&u) += dval(&u);
        if (dval(&u) > ds || (dval(&u) == ds && L & 1)) {
 bump_up:
          while(*--s == '9')
            if (s == s0) {
              k++;
              *s = '0';
              break;
              }
          ++*s++;
          }
        break;
        }
      }
    goto ret1;
    }

  m2 = b2;
  m5 = b5;
  mhi = mlo = 0;
  if (leftright) {
    i =
#ifndef Sudden_Underflow
      denorm ? be + (Bias + (P-1) - 1 + 1) :
#endif
#ifdef IBM
      1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
#else
      1 + P - bbits;
#endif
    b2 += i;
    s2 += i;
    mhi = i2b(1);
    }
  if (m2 > 0 && s2 > 0) {
    i = m2 < s2 ? m2 : s2;
    b2 -= i;
    m2 -= i;
    s2 -= i;
    }
  if (b5 > 0) {
    if (leftright) {
      if (m5 > 0) {
        mhi = pow5mult(mhi, m5);
        b1 = mult(mhi, b);
        Bfree(b);
        b = b1;
        }
      if ((j = b5 - m5))
        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(&u) && !(word0(&u) & Bndry_mask)
#ifndef Sudden_Underflow
     && word0(&u) & (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;
#define iInc 28
#else
  if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf)
    i = 16 - i;
#define iInc 12
#endif
  i = dshift(S, s2);
  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)) {
    if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
      /* no digits, fcvt style */
 no_digits:
      k = -1 - ndigits;
      goto ret;
      }
 one_digit:
    *s++ = '1';
    k++;
    goto ret;
    }
  if (leftright) {
    if (m2 > 0)
      mhi = lshift(mhi, m2);

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

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

    for(i = 1;;i++) {
      dig = quorem(b,S) + '0';
      /* Do we yet have the shortest decimal string
       * that will round to d?
       */
      j = cmp(b, mlo);
      delta = diff(S, mhi);
      j1 = delta->sign ? 1 : cmp(b, delta);
      Bfree(delta);
#ifndef ROUND_BIASED
      if (j1 == 0 && mode != 1 && !(word1(&u) & 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(&u) & 1)
#endif
          )) {
        if (!b->x[0] && b->wds <= 1) {
#ifdef SET_INEXACT
          inexact = 0;
#endif
          goto accept_dig;
          }
#ifdef Honor_FLT_ROUNDS
        if (mode > 1)
         switch(Rounding) {
          case 0: goto accept_dig;
          case 2: goto keep_dig;
          }
#endif /*Honor_FLT_ROUNDS*/
        if (j1 > 0) {
          b = lshift(b, 1);
          j1 = cmp(b, S);
          if ((j1 > 0 || (j1 == 0 && dig & 1))
          && dig++ == '9')
            goto round_9_up;
          }
 accept_dig:
        *s++ = dig;
        goto ret;
        }
      if (j1 > 0) {
#ifdef Honor_FLT_ROUNDS
        if (!Rounding)
          goto accept_dig;
#endif
        if (dig == '9') { /* possible if i == 1 */
 round_9_up:
          *s++ = '9';
          goto roundoff;
          }
        *s++ = dig + 1;
        goto ret;
        }
#ifdef Honor_FLT_ROUNDS
 keep_dig:
#endif
      *s++ = dig;
      if (i == ilim)
        break;
      b = multadd(b, 10, 0);
      if (mlo == mhi)
        mlo = mhi = multadd(mhi, 10, 0);
      else {
        mlo = multadd(mlo, 10, 0);
        mhi = multadd(mhi, 10, 0);
        }
      }
    }
  else
    for(i = 1;; i++) {
      *s++ = dig = quorem(b,S) + '0';
      if (!b->x[0] && b->wds <= 1) {
#ifdef SET_INEXACT
        inexact = 0;
#endif
        goto ret;
        }
      if (i >= ilim)
        break;
      b = multadd(b, 10, 0);
      }

  /* 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)) {
 roundoff:
    while(*--s == '9')
      if (s == s0) {
        k++;
        *s++ = '1';
        goto ret;
        }
    ++*s++;
    }
  else {
#ifdef Honor_FLT_ROUNDS
 trimzeros:
#endif
    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(&u) = Exp_1 + (70 << Exp_shift);
      word1(&u) = 0;
      dval(&u) += 1.;
      }
    }
  else if (!oldinexact)
    clear_inexact();
#endif
  Bfree(b);
  *s = 0;
  *decpt = k + 1;
  if (rve)
    *rve = s;
  return s0;
  }

}  // namespace dmg_fp

Coverage Report

Created: 2024-09-03 06:23