File indexing completed on 2024-05-12 15:43:19

 /****************************************************************
  *
  * 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
     Bell Laboratories, Room 2C-463
     600 Mountain Avenue
     Murray Hill, NJ 07974-0636
     U.S.A.
     dmg@bell-labs.com
  */
 
 /* On a machine with IEEE extended-precision registers, it is
  * necessary to specify double-precision (53-bit) rounding precision
  * before invoking strtod or dtoa.  If the machine uses (the equivalent
  * of) Intel 80x87 arithmetic, the call
  *  _control87(PC_53, MCW_PC);
  * does this with many compilers.  Whether this or another call is
  * appropriate depends on the compiler; for this to work, it may be
  * necessary to #include "float.h" or another system-dependent header
  * file.
  */
 
 /* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
  *
  * This strtod returns a nearest machine number to the input decimal
  * string (or sets errno to ERANGE).  With IEEE arithmetic, ties are
  * broken by the IEEE round-even rule.  Otherwise ties are broken by
  * biased rounding (add half and chop).
  *
  * Inspired loosely by William D. Clinger's paper "How to Read Floating
  * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
  *
  * Modifications:
  *
  *  1. We only require IEEE, IBM, or VAX double-precision
  *      arithmetic (not IEEE double-extended).
  *  2. We get by with floating-point arithmetic in a case that
  *      Clinger missed -- when we're computing d * 10^n
  *      for a small integer d and the integer n is not too
  *      much larger than 22 (the maximum integer k for which
  *      we can represent 10^k exactly), we may be able to
  *      compute (d*10^k) * 10^(e-k) with just one roundoff.
  *  3. Rather than a bit-at-a-time adjustment of the binary
  *      result in the hard case, we use floating-point
  *      arithmetic to determine the adjustment to within
  *      one bit; only in really hard cases do we need to
  *      compute a second residual.
  *  4. Because of 3., we don't need a large table of powers of 10
  *      for ten-to-e (just some small tables, e.g. of 10^k
  *      for 0 <= k <= 22).
  */
 
 /*
  * #define IEEE_8087 for IEEE-arithmetic machines where the least
  *  significant byte has the lowest address.
  * #define IEEE_MC68k for IEEE-arithmetic machines where the most
  *  significant byte has the lowest address.
  * #define Long int on machines with 32-bit ints and 64-bit longs.
  * #define IBM for IBM mainframe-style floating-point arithmetic.
  * #define VAX for VAX-style floating-point arithmetic (D_floating).
  * #define No_leftright to omit left-right logic in fast floating-point
  *  computation of dtoa.
  * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
  *  and strtod and dtoa should round accordingly.
  * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
  *  and Honor_FLT_ROUNDS is not #defined.
  * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
  *  that use extended-precision instructions to compute rounded
  *  products and quotients) with IBM.
  * #define ROUND_BIASED for IEEE-format with biased rounding.
  * #define Inaccurate_Divide for IEEE-format with correctly rounded
  *  products but inaccurate quotients, e.g., for Intel i860.
  * #define NO_LONG_LONG on machines that do not have a "long long"
  *  integer type (of >= 64 bits).  On such machines, you can
  *  #define Just_16 to store 16 bits per 32-bit Long when doing
  *  high-precision integer arithmetic.  Whether this speeds things
  *  up or slows things down depends on the machine and the number
  *  being converted.  If long long is available and the name is
  *  something other than "long long", #define Llong to be the name,
  *  and if "unsigned Llong" does not work as an unsigned version of
  *  Llong, #define #ULLong to be the corresponding unsigned type.
  * #define KR_headers for old-style C function headers.
  * #define Bad_float_h if your system lacks a float.h or if it does not
  *  define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
  *  FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
  * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
  *  if memory is available and otherwise does something you deem
  *  appropriate.  If MALLOC is undefined, malloc will be invoked
  *  directly -- and assumed always to succeed.
  * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
  *  memory allocations from a private pool of memory when possible.
  *  When used, the private pool is PRIVATE_MEM bytes long:  2304 bytes,
  *  unless #defined to be a different length.  This default length
  *  suffices to get rid of MALLOC calls except for unusual cases,
  *  such as decimal-to-binary conversion of a very long string of
  *  digits.  The longest string dtoa can return is about 751 bytes
  *  long.  For conversions by strtod of strings of 800 digits and
  *  all dtoa conversions in single-threaded executions with 8-byte
  *  pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte
  *  pointers, PRIVATE_MEM >= 7112 appears adequate.
  * #define INFNAN_CHECK on IEEE systems to cause strtod to check for
  *  Infinity and NaN (case insensitively).  On some systems (e.g.,
  *  some HP systems), it may be necessary to #define NAN_WORD0
  *  appropriately -- to the most significant word of a quiet NaN.
  *  (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
  *  When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
  *  strtod also accepts (case insensitively) strings of the form
  *  NaN(x), where x is a string of hexadecimal digits and spaces;
  *  if there is only one string of hexadecimal digits, it is taken
  *  for the 52 fraction bits of the resulting NaN; if there are two
  *  or more strings of hex digits, the first is for the high 20 bits,
  *  the second and subsequent for the low 32 bits, with intervening
  *  white space ignored; but if this results in none of the 52
  *  fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0
  *  and NAN_WORD1 are used instead.
  * #define MULTIPLE_THREADS if the system offers preemptively scheduled
  *  multiple threads.  In this case, you must provide (or suitably
  *  #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
  *  by FREE_DTOA_LOCK(n) for n = 0 or 1.  (The second lock, accessed
  *  in pow5mult, ensures lazy evaluation of only one copy of high
  *  powers of 5; omitting this lock would introduce a small
  *  probability of wasting memory, but would otherwise be harmless.)
  *  You must also invoke freedtoa(s) to free the value s returned by
  *  dtoa.  You may do so whether or not MULTIPLE_THREADS is #defined.
  * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
  *  avoids underflows on inputs whose result does not underflow.
  *  If you #define NO_IEEE_Scale on a machine that uses IEEE-format
  *  floating-point numbers and flushes underflows to zero rather
  *  than implementing gradual underflow, then you must also #define
  *  Sudden_Underflow.
  * #define YES_ALIAS to permit aliasing certain double values with
  *  arrays of ULongs.  This leads to slightly better code with
  *  some compilers and was always used prior to 19990916, but it
  *  is not strictly legal and can cause trouble with aggressively
  *  optimizing compilers (e.g., gcc 2.95.1 under -O2).
  * #define USE_LOCALE to use the current locale's decimal_point value.
  * #define SET_INEXACT if IEEE arithmetic is being used and extra
  *  computation should be done to set the inexact flag when the
  *  result is inexact and avoid setting inexact when the result
  *  is exact.  In this case, dtoa.c must be compiled in
  *  an environment, perhaps provided by #include "dtoa.c" in a
  *  suitable wrapper, that defines two functions,
  *      int get_inexact(void);
  *      void clear_inexact(void);
  *  such that get_inexact() returns a nonzero value if the
  *  inexact bit is already set, and clear_inexact() sets the
  *  inexact bit to 0.  When SET_INEXACT is #defined, strtod
  *  also does extra computations to set the underflow and overflow
  *  flags when appropriate (i.e., when the result is tiny and
  *  inexact or when it is a numeric value rounded to +-infinity).
  * #define NO_ERRNO if strtod should not assign errno = ERANGE when
  *  the result overflows to +-Infinity or underflows to 0.
  */
 
 #include "dtoa.h"
 
 #include "global.h"
 
 #if PLATFORM(BIG_ENDIAN)
 #define IEEE_MC68k
 #else
 #define IEEE_8087
 #endif
 #define INFNAN_CHECK
 
 #ifndef Long
 #define Long int
 #endif
 #ifndef ULong
 typedef unsigned Long ULong;
 #endif
 
 #ifdef DEBUG
 #include <stdio.h>
 #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
 #endif
 
 #include <stdlib.h>
 #include <string.h>
 
 #ifdef USE_LOCALE
 #include <locale.h>
 #endif
 
 #ifdef MALLOC
 extern void *MALLOC(size_t);
 #else
 #define MALLOC malloc
 #endif
 
 #ifndef Omit_Private_Memory
 #ifndef PRIVATE_MEM
 #define PRIVATE_MEM 2304
 #endif
 #define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
 static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
 #endif
 
 #undef IEEE_Arith
 #undef Avoid_Underflow
 #ifdef IEEE_MC68k
 #define IEEE_Arith
 #endif
 #ifdef IEEE_8087
 #define IEEE_Arith
 #endif
 
 #if HAVE_ERRNO_H
 #include <errno.h>
 #endif
 
 #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
 
 #define strtod kjs_strtod
 #define dtoa kjs_dtoa
 #define freedtoa kjs_freedtoa
 
 #ifdef __cplusplus
 extern "C" {
 #endif
 
 #ifndef CONST
 #define CONST const
 #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;
 
 #define dval(x) (x).d
 #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
 
 /* 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)
 
 /* #define P DBL_MANT_DIG */
 /* Ten_pmax = floor(P*log(2)/log(5)) */
 /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
 /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
 /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
 
 #ifdef IEEE_Arith
 #define Exp_shift  20
 #define Exp_shift1 20
 #define Exp_msk1    0x100000
 #define Exp_msk11   0x100000
 #define Exp_mask  0x7ff00000
 #define P 53
 #define Bias 1023
 #define Emin (-1022)
 #define Exp_1  0x3ff00000
 #define Exp_11 0x3ff00000
 #define Ebits 11
 #define Frac_mask  0xfffff
 #define Frac_mask1 0xfffff
 #define Ten_pmax 22
 #define Bletch 0x10
 #define Bndry_mask  0xfffff
 #define Bndry_mask1 0xfffff
 #define LSB 1
 #define Sign_bit 0x80000000
 #define Log2P 1
 #define Tiny0 0
 #define Tiny1 1
 #define Quick_max 14
 #define Int_max 14
 #ifndef NO_IEEE_Scale
 #define Avoid_Underflow
 #ifdef Flush_Denorm /* debugging option */
 #undef Sudden_Underflow
 #endif
 #endif
 
 #ifndef Flt_Rounds
 #ifdef FLT_ROUNDS
 #define Flt_Rounds FLT_ROUNDS
 #else
 #define Flt_Rounds 1
 #endif
 #endif /*Flt_Rounds*/
 
 #ifdef Honor_FLT_ROUNDS
 #define Rounding rounding
 #undef Check_FLT_ROUNDS
 #define Check_FLT_ROUNDS
 #else
 #define Rounding Flt_Rounds
 #endif
 
 #else /* ifndef IEEE_Arith */
 #undef Check_FLT_ROUNDS
 #undef Honor_FLT_ROUNDS
 #undef SET_INEXACT
 #undef  Sudden_Underflow
 #define Sudden_Underflow
 #ifdef IBM
 #undef Flt_Rounds
 #define Flt_Rounds 0
 #define Exp_shift  24
 #define Exp_shift1 24
 #define Exp_msk1   0x1000000
 #define Exp_msk11  0x1000000
 #define Exp_mask  0x7f000000
 #define P 14
 #define Bias 65
 #define Exp_1  0x41000000
 #define Exp_11 0x41000000
 #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
 #define Frac_mask  0xffffff
 #define Frac_mask1 0xffffff
 #define Bletch 4
 #define Ten_pmax 22
 #define Bndry_mask  0xefffff
 #define Bndry_mask1 0xffffff
 #define LSB 1
 #define Sign_bit 0x80000000
 #define Log2P 4
 #define Tiny0 0x100000
 #define Tiny1 0
 #define Quick_max 14
 #define Int_max 15
 #else /* VAX */
 #undef Flt_Rounds
 #define Flt_Rounds 1
 #define Exp_shift  23
 #define Exp_shift1 7
 #define Exp_msk1    0x80
 #define Exp_msk11   0x800000
 #define Exp_mask  0x7f80
 #define P 56
 #define Bias 129
 #define Exp_1  0x40800000
 #define Exp_11 0x4080
 #define Ebits 8
 #define Frac_mask  0x7fffff
 #define Frac_mask1 0xffff007f
 #define Ten_pmax 24
 #define Bletch 2
 #define Bndry_mask  0xffff007f
 #define Bndry_mask1 0xffff007f
 #define LSB 0x10000
 #define Sign_bit 0x8000
 #define Log2P 1
 #define Tiny0 0x80
 #define Tiny1 0
 #define Quick_max 15
 #define Int_max 15
 #endif /* IBM, VAX */
 #endif /* IEEE_Arith */
 
 #ifndef IEEE_Arith
 #define ROUND_BIASED
 #endif
 
 #ifdef RND_PRODQUOT
 #define rounded_product(a,b) a = rnd_prod(a, b)
 #define rounded_quotient(a,b) a = rnd_quot(a, b)
 extern double rnd_prod(double, double), rnd_quot(double, double);
 #else
 #define rounded_product(a,b) a *= b
 #define rounded_quotient(a,b) a /= b
 #endif
 
 #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
 #define Big1 0xffffffff
 
 #ifndef Pack_32
 #define Pack_32
 #endif
 
 #define FFFFFFFF 0xffffffffUL
 
 #ifdef NO_LONG_LONG
 #undef ULLong
 #ifdef Just_16
 #undef Pack_32
 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
  * This makes some inner loops simpler and sometimes saves work
  * during multiplications, but it often seems to make things slightly
  * slower.  Hence the default is now to store 32 bits per Long.
  */
 #endif
 #else   /* long long available */
 #ifndef Llong
 #define Llong long long
 #endif
 #ifndef ULLong
 #define ULLong unsigned Llong
 #endif
 #endif /* NO_LONG_LONG */
 
 #ifndef MULTIPLE_THREADS
 #define ACQUIRE_DTOA_LOCK(n)    /*nothing*/
 #define FREE_DTOA_LOCK(n)   /*nothing*/
 #endif
 
 #define Kmax (sizeof(size_t) << 3)
 
 struct
         Bigint {
     struct Bigint *next;
     int k, maxwds, sign, wds;
     ULong x[1];
 };
 
 typedef struct Bigint Bigint;
 
 static Bigint *freelist[Kmax + 1];
 
 static Bigint *
 Balloc
 (int k)
 {
     int x;
     Bigint *rv;
 #ifndef Omit_Private_Memory
     unsigned int len;
 #endif
 
     ACQUIRE_DTOA_LOCK(0);
     if ((rv = freelist[k])) {
         freelist[k] = rv->next;
     } else {
         x = 1 << k;
 #ifdef Omit_Private_Memory
         rv = (Bigint *)MALLOC(sizeof(Bigint) + (x - 1) * sizeof(ULong));
 #else
         len = (sizeof(Bigint) + (x - 1) * sizeof(ULong) + sizeof(double) - 1)
               / sizeof(double);
         if (pmem_next - private_mem + len <= (unsigned)PRIVATE_mem) {
             rv = (Bigint *)pmem_next;
             pmem_next += len;
         } else {
             rv = (Bigint *)MALLOC(len * sizeof(double));
         }
 #endif
         rv->k = k;
         rv->maxwds = x;
     }
     FREE_DTOA_LOCK(0);
     rv->sign = rv->wds = 0;
     return rv;
 }
 
 static void
 Bfree
 (Bigint *v)
 {
     if (v) {
         ACQUIRE_DTOA_LOCK(0);
         v->next = freelist[v->k];
         freelist[v->k] = v;
         FREE_DTOA_LOCK(0);
     }
 }
 
 #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
                           y->wds*sizeof(Long) + 2*sizeof(int))
 
 static Bigint *
 multadd
 (Bigint *b, int m, int a)   /* multiply by m and add a */
 {
     int i, wds;
 #ifdef ULLong
     ULong *x;
     ULLong carry, y;
 #else
     ULong carry, *x, y;
 #ifdef Pack_32
     ULong xi, z;
 #endif
 #endif
     Bigint *b1;
 
     wds = b->wds;
     x = b->x;
     i = 0;
     carry = a;
     do {
 #ifdef ULLong
         y = *x * (ULLong)m + carry;
         carry = y >> 32;
         *x++ = (ULong)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++] = (ULong)carry;
         b->wds = wds;
     }
     return b;
 }
 
 static Bigint *
 s2b
 (CONST char *s, int nd0, int nd, ULong y9)
 {
     Bigint *b;
     int i, k;
     Long x, y;
 
     x = (nd + 8) / 9;
     for (k = 0, y = 1; x > y; y <<= 1, k++);
 #ifdef Pack_32
     b = Balloc(k);
     b->x[0] = y9;
     b->wds = 1;
 #else
     b = Balloc(k + 1);
     b->x[0] = y9 & 0xffff;
     b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
 #endif
 
     i = 9;
     if (9 < nd0) {
         s += 9;
         do {
             b = multadd(b, 10, *s++ - '0');
         } while (++i < nd0);
         s++;
     } else {
         s += 10;
     }
     for (; i < nd; i++) {
         b = multadd(b, 10, *s++ - '0');
     }
     return b;
 }
 
 static int
 hi0bits
 (ULong x)
 {
     int k = 0;
 
     if (!(x & 0xffff0000)) {
         k = 16;
         x <<= 16;
     }
     if (!(x & 0xff000000)) {
         k += 8;
         x <<= 8;
     }
     if (!(x & 0xf0000000)) {
         k += 4;
         x <<= 4;
     }
     if (!(x & 0xc0000000)) {
         k += 2;
         x <<= 2;
     }
     if (!(x & 0x80000000)) {
         k++;
         if (!(x & 0x40000000)) {
             return 32;
         }
     }
     return k;
 }
 
 static int
 lo0bits
 (ULong *y)
 {
     int k;
     ULong x = *y;
 
     if (x & 7) {
         if (x & 1) {
             return 0;
         }
         if (x & 2) {
             *y = x >> 1;
             return 1;
         }
         *y = x >> 2;
         return 2;
     }
     k = 0;
     if (!(x & 0xffff)) {
         k = 16;
         x >>= 16;
     }
     if (!(x & 0xff)) {
         k += 8;
         x >>= 8;
     }
     if (!(x & 0xf)) {
         k += 4;
         x >>= 4;
     }
     if (!(x & 0x3)) {
         k += 2;
         x >>= 2;
     }
     if (!(x & 1)) {
         k++;
         x >>= 1;
         if (!x & 1) {
             return 32;
         }
     }
     *y = x;
     return k;
 }
 
 static Bigint *
 i2b
 (int i)
 {
     Bigint *b;
 
     b = Balloc(1);
     b->x[0] = i;
     b->wds = 1;
     return b;
 }
 
 static Bigint *
 mult
 (Bigint *a, Bigint *b)
 {
     Bigint *c;
     int k, wa, wb, wc;
     ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
     ULong y;
 #ifdef ULLong
     ULLong carry, z;
 #else
     ULong carry, z;
 #ifdef Pack_32
     ULong z2;
 #endif
 #endif
 
     if (a->wds < b->wds) {
         c = a;
         a = b;
         b = c;
     }
     k = a->k;
     wa = a->wds;
     wb = b->wds;
     wc = wa + wb;
     if (wc > a->maxwds) {
         k++;
     }
     c = Balloc(k);
     for (x = c->x, xa = x + wc; x < xa; x++) {
         *x = 0;
     }
     xa = a->x;
     xae = xa + wa;
     xb = b->x;
     xbe = xb + wb;
     xc0 = c->x;
 #ifdef ULLong
     for (; xb < xbe; xc0++) {
         if ((y = *xb++)) {
             x = xa;
             xc = xc0;
             carry = 0;
             do {
                 z = *x++ * (ULLong)y + *xc + carry;
                 carry = z >> 32;
                 *xc++ = (ULong)z & FFFFFFFF;
             } while (x < xae);
             *xc = (ULong)carry;
         }
     }
 #else
 #ifdef Pack_32
     for (; xb < xbe; xb++, xc0++) {
         if (y = *xb & 0xffff) {
             x = xa;
             xc = xc0;
             carry = 0;
             do {
                 z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
                 carry = z >> 16;
                 z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
                 carry = z2 >> 16;
                 Storeinc(xc, z2, z);
             } while (x < xae);
             *xc = carry;
         }
         if (y = *xb >> 16) {
             x = xa;
             xc = xc0;
             carry = 0;
             z2 = *xc;
             do {
                 z = (*x & 0xffff) * y + (*xc >> 16) + carry;
                 carry = z >> 16;
                 Storeinc(xc, z, z2);
                 z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
                 carry = z2 >> 16;
             } while (x < xae);
             *xc = z2;
         }
     }
 #else
     for (; xb < xbe; xc0++) {
         if (y = *xb++) {
             x = xa;
             xc = xc0;
             carry = 0;
             do {
                 z = *x++ * y + *xc + carry;
                 carry = z >> 16;
                 *xc++ = z & 0xffff;
             } while (x < xae);
             *xc = carry;
         }
     }
 #endif
 #endif
     for (xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc);
     c->wds = wc;
     return c;
 }
 
 static Bigint *p5s;
 
 static Bigint *
 pow5mult
 (Bigint *b, int k)
 {
     Bigint *b1, *p5, *p51;
     int i;
     static int p05[3] = { 5, 25, 125 };
 
     if ((i = k & 3)) {
         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 = nullptr;
 #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 = nullptr;
 #endif
         }
         p5 = p51;
     }
     return b;
 }
 
 static Bigint *
 lshift
 (Bigint *b, int k)
 {
     int i, k1, n, n1;
     Bigint *b1;
     ULong *x, *x1, *xe, z;
 
 #ifdef Pack_32
     n = k >> 5;
 #else
     n = k >> 4;
 #endif
     k1 = b->k;
     n1 = n + b->wds + 1;
     for (i = b->maxwds; n1 > i; i <<= 1) {
         k1++;
     }
     b1 = Balloc(k1);
     x1 = b1->x;
     for (i = 0; i < n; i++) {
         *x1++ = 0;
     }
     x = b->x;
     xe = x + b->wds;
 #ifdef Pack_32
     if (k &= 0x1f) {
         k1 = 32 - k;
         z = 0;
         do {
             *x1++ = *x << k | z;
             z = *x++ >> k1;
         } while (x < xe);
         if ((*x1 = z)) {
             ++n1;
         }
     }
 #else
     if (k &= 0xf) {
         k1 = 16 - k;
         z = 0;
         do {
             *x1++ = *x << k  & 0xffff | z;
             z = *x++ >> k1;
         } while (x < xe);
         if (*x1 = z) {
             ++n1;
         }
     }
 #endif
     else do {
             *x1++ = *x++;
         } while (x < xe);
     b1->wds = n1 - 1;
     Bfree(b);
     return b1;
 }
 
 static int
 cmp
 (Bigint *a, Bigint *b)
 {
     ULong *xa, *xa0, *xb, *xb0;
     int i, j;
 
     i = a->wds;
     j = b->wds;
 #ifdef DEBUG
     if (i > 1 && !a->x[i - 1]) {
         Bug("cmp called with a->x[a->wds-1] == 0");
     }
     if (j > 1 && !b->x[j - 1]) {
         Bug("cmp called with b->x[b->wds-1] == 0");
     }
 #endif
     if (i -= j) {
         return i;
     }
     xa0 = a->x;
     xa = xa0 + j;
     xb0 = b->x;
     xb = xb0 + j;
     for (;;) {
         if (*--xa != *--xb) {
             return *xa < *xb ? -1 : 1;
         }
         if (xa <= xa0) {
             break;
         }
     }
     return 0;
 }
 
 static Bigint *
 diff
 (Bigint *a, Bigint *b)
 {
     Bigint *c;
     int i, wa, wb;
     ULong *xa, *xae, *xb, *xbe, *xc;
 #ifdef ULLong
     ULLong borrow, y;
 #else
     ULong borrow, y;
 #ifdef Pack_32
     ULong z;
 #endif
 #endif
 
     i = cmp(a, b);
     if (!i) {
         c = Balloc(0);
         c->wds = 1;
         c->x[0] = 0;
         return c;
     }
     if (i < 0) {
         c = a;
         a = b;
         b = c;
         i = 1;
     } else {
         i = 0;
     }
     c = Balloc(a->k);
     c->sign = i;
     wa = a->wds;
     xa = a->x;
     xae = xa + wa;
     wb = b->wds;
     xb = b->x;
     xbe = xb + wb;
     xc = c->x;
     borrow = 0;
 #ifdef ULLong
     do {
         y = (ULLong) * xa++ - *xb++ - borrow;
         borrow = y >> 32 & (ULong)1;
         *xc++ = (ULong)y & FFFFFFFF;
     } while (xb < xbe);
     while (xa < xae) {
         y = *xa++ - borrow;
         borrow = y >> 32 & (ULong)1;
         *xc++ = (ULong)y & FFFFFFFF;
     }
 #else
 #ifdef Pack_32
     do {
         y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
         borrow = (y & 0x10000) >> 16;
         z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
         borrow = (z & 0x10000) >> 16;
         Storeinc(xc, z, y);
     } while (xb < xbe);
     while (xa < xae) {
         y = (*xa & 0xffff) - borrow;
         borrow = (y & 0x10000) >> 16;
         z = (*xa++ >> 16) - borrow;
         borrow = (z & 0x10000) >> 16;
         Storeinc(xc, z, y);
     }
 #else
     do {
         y = *xa++ - *xb++ - borrow;
         borrow = (y & 0x10000) >> 16;
         *xc++ = y & 0xffff;
     } while (xb < xbe);
     while (xa < xae) {
         y = *xa++ - borrow;
         borrow = (y & 0x10000) >> 16;
         *xc++ = y & 0xffff;
     }
 #endif
 #endif
     while (!*--xc) {
         wa--;
     }
     c->wds = wa;
     return c;
 }
 
 static double
 ulp
 (double dx)
 {
     Long L;
     U x, a;
 
     dval(x) = dx;
     L = (word0(x) & Exp_mask) - (P - 1) * Exp_msk1;
 #ifndef Avoid_Underflow
 #ifndef Sudden_Underflow
     if (L > 0) {
 #endif
 #endif
 #ifdef IBM
         L |= Exp_msk1 >> 4;
 #endif
         word0(a) = L;
         word1(a) = 0;
 #ifndef Avoid_Underflow
 #ifndef Sudden_Underflow
     } else {
         L = -L >> Exp_shift;
         if (L < Exp_shift) {
             word0(a) = 0x80000 >> L;
             word1(a) = 0;
         } else {
             word0(a) = 0;
             L -= Exp_shift;
             word1(a) = L >= 31 ? 1 : 1 << 31 - L;
         }
     }
 #endif
 #endif
     return dval(a);
 }
 
 static double
 b2d
 (Bigint *a, int *e)
 {
     ULong *xa, *xa0, w, y, z;
     int k;
     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
 (double dd, int *e, int *bits)
 {
     U d;
     Bigint *b;
     int de, k;
     ULong *x, y, z;
 #ifndef Sudden_Underflow
     int i;
 #endif
 #ifdef VAX
     ULong d0, d1;
 #endif
     dval(d) = dd;
 #ifdef VAX
     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 {
 #ifdef DEBUG
         if (!z) {
             Bug("Zero passed to d2b");
         }
 #endif
         k = lo0bits(&z);
         x[0] = z;
 #ifndef Sudden_Underflow
         i =
 #endif
             b->wds = 1;
         k += 32;
     }
 #else
     if (y = d1) {
         if (k = lo0bits(&y))
             if (k >= 16) {
                 x[0] = y | z << 32 - k & 0xffff;
                 x[1] = z >> k - 16 & 0xffff;
                 x[2] = z >> k;
                 i = 2;
             } else {
                 x[0] = y & 0xffff;
                 x[1] = y >> 16 | z << 16 - k & 0xffff;
                 x[2] = z >> k & 0xffff;
                 x[3] = z >> k + 16;
                 i = 3;
             }
         else {
             x[0] = y & 0xffff;
             x[1] = y >> 16;
             x[2] = z & 0xffff;
             x[3] = z >> 16;
             i = 3;
         }
     } else {
 #ifdef DEBUG
         if (!z) {
             Bug("Zero passed to d2b");
         }
 #endif
         k = lo0bits(&z);
         if (k >= 16) {
             x[0] = z;
             i = 0;
         } else {
             x[0] = z & 0xffff;
             x[1] = z >> 16;
             i = 1;
         }
         k += 32;
     }
     while (!x[i]) {
         --i;
     }
     b->wds = i + 1;
 #endif
 #ifndef Sudden_Underflow
     if (de) {
 #endif
 #ifdef IBM
         *e = (de - Bias - (P - 1) << 2) + k;
         *bits = 4 * P + 8 - k - hi0bits(word0(d) & Frac_mask);
 #else
         *e = de - Bias - (P - 1) + k;
         *bits = P - k;
 #endif
 #ifndef Sudden_Underflow
     } else {
         *e = de - Bias - (P - 1) + 1 + k;
 #ifdef Pack_32
         *bits = 32 * i - hi0bits(x[i - 1]);
 #else
         *bits = (i + 2) * 16 - hi0bits(x[i]);
 #endif
     }
 #endif
     return b;
 }
 #undef d0
 #undef d1
 
 static double
 ratio
 (Bigint *a, Bigint *b)
 {
     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-53 */
 #else
                                    1e-256
 #endif
                                  };
 /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
 /* flag unnecessarily.  It leads to a song and dance at the end of strtod. */
 #define Scale_Bit 0x10
 #define n_bigtens 5
 #else
 #ifdef IBM
 bigtens[] = { 1e16, 1e32, 1e64 };
 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
 #define n_bigtens 3
 #else
 bigtens[] = { 1e16, 1e32 };
 static CONST double tinytens[] = { 1e-16, 1e-32 };
 #define n_bigtens 2
 #endif
 #endif
 
 #ifndef IEEE_Arith
 #undef INFNAN_CHECK
 #endif
 
 #ifdef INFNAN_CHECK
 
 #ifndef NAN_WORD0
 #define NAN_WORD0 0x7ff80000
 #endif
 
 #ifndef NAN_WORD1
 #define NAN_WORD1 0
 #endif
 
 static int
 match
 (CONST char **sp, CONST char *t)
 {
     int c, d;
     CONST char *s = *sp;
 
     while ((d = *t++)) {
         if ((c = *++s) >= 'A' && c <= 'Z') {
             c += 'a' - 'A';
         }
         if (c != d) {
             return 0;
         }
     }
     *sp = s + 1;
     return 1;
 }
 
 #ifndef No_Hex_NaN
 static void
 hexnan
 (U *rvp, CONST char **sp)
 {
     ULong c, x[2];
     CONST char *s;
     int havedig, udx0, xshift;
 
     x[0] = x[1] = 0;
     havedig = xshift = 0;
     udx0 = 1;
     s = *sp;
     while ((c = *(CONST unsigned char *)++s)) {
         if (c >= '0' && c <= '9') {
             c -= '0';
         } else if (c >= 'a' && c <= 'f') {
             c += 10 - 'a';
         } else if (c >= 'A' && c <= 'F') {
             c += 10 - 'A';
         } else if (c <= ' ') {
             if (udx0 && havedig) {
                 udx0 = 0;
                 xshift = 1;
             }
             continue;
         } else if (/*(*/ c == ')' && havedig) {
             *sp = s + 1;
             break;
         } else {
             return;    /* invalid form: don't change *sp */
         }
         havedig = 1;
         if (xshift) {
             xshift = 0;
             x[0] = x[1];
             x[1] = 0;
         }
         if (udx0) {
             x[0] = (x[0] << 4) | (x[1] >> 28);
         }
         x[1] = (x[1] << 4) | c;
     }
     if ((x[0] &= 0xfffff) || x[1]) {
         word0(*rvp) = Exp_mask | x[0];
         word1(*rvp) = x[1];
     }
 }
 #endif /*No_Hex_NaN*/
 #endif /* INFNAN_CHECK */
 
 double
 strtod
 (CONST char *s00, char **se)
 {
 #ifdef Avoid_Underflow
     int scale;
 #endif
     int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
         e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
     CONST char *s, *s0, *s1;
     double aadj, aadj1, adj;
     U aadj2, rv, rv0;
     Long L;
     ULong y, z;
     Bigint *bb = nullptr, *bb1 = nullptr, *bd = nullptr, *bd0 = nullptr, *bs = nullptr, *delta = nullptr;
 #ifdef SET_INEXACT
     int inexact, oldinexact;
 #endif
 #ifdef Honor_FLT_ROUNDS
     int rounding;
 #endif
 #ifdef USE_LOCALE
     CONST char *s2;
 #endif
 
     sign = nz0 = nz = 0;
     dval(rv) = 0.;
     for (s = s00;; s++) switch (*s) {
         case '-':
             sign = 1;
         /* no break */
         case '+':
             if (*++s) {
                 goto break2;
             }
         /* no break */
         case 0:
             goto ret0;
         case '\t':
         case '\n':
         case '\v':
         case '\f':
         case '\r':
         case ' ':
             continue;
         default:
             goto break2;
         }
 break2:
     if (*s == '0') {
         nz0 = 1;
         while (*++s == '0');
         if (!*s) {
             goto ret;
         }
     }
     s0 = s;
     y = z = 0;
     for (nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
         if (nd < 9) {
             y = 10 * y + c - '0';
         } else if (nd < 16) {
             z = 10 * z + c - '0';
         }
     nd0 = nd;
 #ifdef USE_LOCALE
     s1 = localeconv()->decimal_point;
     if (c == *s1) {
         c = '.';
         if (*++s1) {
             s2 = s;
             for (;;) {
                 if (*++s2 != *s1) {
                     c = 0;
                     break;
                 }
                 if (!*++s1) {
                     s = s2;
                     break;
                 }
             }
         }
     }
 #endif
     if (c == '.') {
         c = *++s;
         if (!nd) {
             for (; c == '0'; c = *++s) {
                 nz++;
             }
             if (c > '0' && c <= '9') {
                 s0 = s;
                 nf += nz;
                 nz = 0;
                 goto have_dig;
             }
             goto dig_done;
         }
         for (; c >= '0' && c <= '9'; c = *++s) {
         have_dig:
             nz++;
             if (c -= '0') {
                 nf += nz;
                 for (i = 1; i < nz; i++)
                     if (nd++ < 9) {
                         y *= 10;
                     } else if (nd <= DBL_DIG + 1) {
                         z *= 10;
                     }
                 if (nd++ < 9) {
                     y = 10 * y + c;
                 } else if (nd <= DBL_DIG + 1) {
                     z = 10 * z + c;
                 }
                 nz = 0;
             }
         }
     }
 dig_done:
     e = 0;
     if (c == 'e' || c == 'E') {
         if (!nd && !nz && !nz0) {
             goto ret0;
         }
         s00 = s;
         esign = 0;
         switch (c = *++s) {
         case '-':
             esign = 1;
         case '+':
             c = *++s;
         }
         if (c >= '0' && c <= '9') {
             while (c == '0') {
                 c = *++s;
             }
             if (c > '0' && c <= '9') {
                 L = c - '0';
                 s1 = s;
                 while ((c = *++s) >= '0' && c <= '9') {
                     L = 10 * L + c - '0';
                 }
                 if (s - s1 > 8 || L > 19999)
                     /* Avoid confusion from exponents
                      * so large that e might overflow.
                      */
                 {
                     e = 19999;    /* safe for 16 bit ints */
                 } else {
                     e = (int)L;
                 }
                 if (esign) {
                     e = -e;
                 }
             } else {
                 e = 0;
             }
         } else {
             s = s00;
         }
     }
     if (!nd) {
         if (!nz && !nz0) {
 #ifdef INFNAN_CHECK
             /* Check for Nan and Infinity */
             switch (c) {
             case 'i':
             case 'I':
                 if (match(&s, "nf")) {
                     --s;
                     if (!match(&s, "inity")) {
                         ++s;
                     }
                     word0(rv) = 0x7ff00000;
                     word1(rv) = 0;
                     goto ret;
                 }
                 break;
             case 'n':
             case 'N':
                 if (match(&s, "an")) {
                     word0(rv) = NAN_WORD0;
                     word1(rv) = NAN_WORD1;
 #ifndef No_Hex_NaN
                     if (*s == '(') { /*)*/
                         hexnan(&rv, &s);
                     }
 #endif
                     goto ret;
                 }
             }
 #endif /* INFNAN_CHECK */
         ret0:
             s = s00;
             sign = 0;
         }
         goto ret;
     }
     e1 = e -= nf;
 
     /* Now we have nd0 digits, starting at s0, followed by a
      * decimal point, followed by nd-nd0 digits.  The number we're
      * after is the integer represented by those digits times
      * 10**e */
 
     if (!nd0) {
         nd0 = nd;
     }
     k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
     dval(rv) = y;
     if (k > 9) {
 #ifdef SET_INEXACT
         if (k > DBL_DIG) {
             oldinexact = get_inexact();
         }
 #endif
         dval(rv) = tens[k - 9] * dval(rv) + z;
     }
     bd0 = nullptr;
     if (nd <= DBL_DIG
 #ifndef RND_PRODQUOT
 #ifndef Honor_FLT_ROUNDS
             && Flt_Rounds == 1
 #endif
 #endif
        ) {
         if (!e) {
             goto ret;
         }
         if (e > 0) {
             if (e <= Ten_pmax) {
 #ifdef VAX
                 goto vax_ovfl_check;
 #else
 #ifdef Honor_FLT_ROUNDS
                 /* round correctly FLT_ROUNDS = 2 or 3 */
                 if (sign) {
                     rv = -rv;
                     sign = 0;
                 }
 #endif
                 /* rv = */ rounded_product(dval(rv), tens[e]);
                 goto ret;
 #endif
             }
             i = DBL_DIG - nd;
             if (e <= Ten_pmax + i) {
                 /* A fancier test would sometimes let us do
                  * this for larger i values.
                  */
 #ifdef Honor_FLT_ROUNDS
                 /* round correctly FLT_ROUNDS = 2 or 3 */
                 if (sign) {
                     rv = -rv;
                     sign = 0;
                 }
 #endif
                 e -= i;
                 dval(rv) *= tens[i];
 #ifdef VAX
                 /* VAX exponent range is so narrow we must
                  * worry about overflow here...
                  */
             vax_ovfl_check:
                 word0(rv) -= P * Exp_msk1;
                 /* rv = */ rounded_product(dval(rv), tens[e]);
                 if ((word0(rv) & Exp_mask)
                         > Exp_msk1 * (DBL_MAX_EXP + Bias - 1 - P)) {
                     goto ovfl;
                 }
                 word0(rv) += P * Exp_msk1;
 #else
                 /* rv = */ rounded_product(dval(rv), tens[e]);
 #endif
                 goto ret;
             }
         }
 #ifndef Inaccurate_Divide
         else if (e >= -Ten_pmax) {
 #ifdef Honor_FLT_ROUNDS
             /* round correctly FLT_ROUNDS = 2 or 3 */
             if (sign) {
                 rv = -rv;
                 sign = 0;
             }
 #endif
             /* rv = */ rounded_quotient(dval(rv), tens[-e]);
             goto ret;
         }
 #endif
     }
     e1 += nd - k;
 
 #ifdef IEEE_Arith
 #ifdef SET_INEXACT
     inexact = 1;
     if (k <= DBL_DIG) {
         oldinexact = get_inexact();
     }
 #endif
 #ifdef Avoid_Underflow
     scale = 0;
 #endif
 #ifdef Honor_FLT_ROUNDS
     if ((rounding = Flt_Rounds) >= 2) {
         if (sign) {
             rounding = rounding == 2 ? 0 : 2;
         } else if (rounding != 2) {
             rounding = 0;
         }
     }
 #endif
 #endif /*IEEE_Arith*/
 
     /* Get starting approximation = rv * 10**e1 */
 
     if (e1 > 0) {
         if ((i = e1 & 15)) {
             dval(rv) *= tens[i];
         }
         if (e1 &= ~15) {
             if (e1 > DBL_MAX_10_EXP) {
             ovfl:
 #if HAVE_ERRNO_H
                 errno = ERANGE;
 #endif
                 /* Can't trust HUGE_VAL */
 #ifdef IEEE_Arith
 #ifdef Honor_FLT_ROUNDS
                 switch (rounding) {
                 case 0: /* toward 0 */
                 case 3: /* toward -infinity */
                     word0(rv) = Big0;
                     word1(rv) = Big1;
                     break;
                 default:
                     word0(rv) = Exp_mask;
                     word1(rv) = 0;
                 }
 #else /*Honor_FLT_ROUNDS*/
                 word0(rv) = Exp_mask;
                 word1(rv) = 0;
 #endif /*Honor_FLT_ROUNDS*/
 #ifdef SET_INEXACT
                 /* set overflow bit */
                 dval(rv0) = 1e300;
                 dval(rv0) *= dval(rv0);
 #endif
 #else /*IEEE_Arith*/
                 word0(rv) = Big0;
                 word1(rv) = Big1;
 #endif /*IEEE_Arith*/
                 if (bd0) {
                     goto retfree;
                 }
                 goto ret;
             }
             e1 >>= 4;
             for (j = 0; e1 > 1; j++, e1 >>= 1)
                 if (e1 & 1) {
                     dval(rv) *= bigtens[j];
                 }
             /* The last multiplication could overflow. */
             word0(rv) -= P * Exp_msk1;
             dval(rv) *= bigtens[j];
             if ((z = word0(rv) & Exp_mask)
                     > Exp_msk1 * (DBL_MAX_EXP + Bias - P)) {
                 goto ovfl;
             }
             if (z > Exp_msk1 * (DBL_MAX_EXP + Bias - 1 - P)) {
                 /* set to largest number */
                 /* (Can't trust DBL_MAX) */
                 word0(rv) = Big0;
                 word1(rv) = Big1;
             } else {
                 word0(rv) += P * Exp_msk1;
             }
         }
     } else if (e1 < 0) {
         e1 = -e1;
         if ((i = e1 & 15)) {
             dval(rv) /= tens[i];
         }
         if (e1 >>= 4) {
             if (e1 >= 1 << n_bigtens) {
                 goto undfl;
             }
 #ifdef Avoid_Underflow
             if (e1 & Scale_Bit) {
                 scale = 2 * P;
             }
             for (j = 0; e1 > 0; j++, e1 >>= 1)
                 if (e1 & 1) {
                     dval(rv) *= tinytens[j];
                 }
             if (scale && (j = 2 * P + 1 - ((word0(rv) & Exp_mask)
                                            >> Exp_shift)) > 0) {
                 /* scaled rv is denormal; zap j low bits */
                 if (j >= 32) {
                     word1(rv) = 0;
                     if (j >= 53) {
                         word0(rv) = (P + 2) * Exp_msk1;
                     } else {
                         word0(rv) &= 0xffffffff << (j - 32);
                     }
                 } else {
                     word1(rv) &= 0xffffffff << j;
                 }
             }
 #else
             for (j = 0; e1 > 1; j++, e1 >>= 1)
                 if (e1 & 1) {
                     dval(rv) *= tinytens[j];
                 }
             /* The last multiplication could underflow. */
             dval(rv0) = dval(rv);
             dval(rv) *= tinytens[j];
             if (!dval(rv)) {
                 dval(rv) = 2.*dval(rv0);
                 dval(rv) *= tinytens[j];
 #endif
             if (!dval(rv)) {
             undfl:
                 dval(rv) = 0.;
 #if HAVE_ERRNO_H
                 errno = ERANGE;
 #endif
                 if (bd0) {
                     goto retfree;
                 }
                 goto ret;
             }
 #ifndef Avoid_Underflow
             word0(rv) = Tiny0;
             word1(rv) = Tiny1;
             /* The refinement below will clean
              * this approximation up.
              */
         }
 #endif
     }
 }
 
 /* Now the hard part -- adjusting rv to the correct value.*/
 
 /* Put digits into bd: true value = bd * 10^e */
 
 bd0 = s2b(s0, nd0, nd, y);
 
 for (;;) {
     bd = Balloc(bd0->k);
     Bcopy(bd, bd0);
     bb = d2b(dval(rv), &bbe, &bbbits);  /* rv = bb * 2^bbe */
     bs = i2b(1);
 
     if (e >= 0) {
         bb2 = bb5 = 0;
         bd2 = bd5 = e;
     } else {
         bb2 = bb5 = -e;
         bd2 = bd5 = 0;
     }
     if (bbe >= 0) {
         bb2 += bbe;
     } else {
         bd2 -= bbe;
     }
     bs2 = bb2;
 #ifdef Honor_FLT_ROUNDS
     if (rounding != 1) {
         bs2++;
     }
 #endif
 #ifdef Avoid_Underflow
     j = bbe - scale;
     i = j + bbbits - 1; /* logb(rv) */
     if (i < Emin) { /* denormal */
         j += P - Emin;
     } else {
         j = P + 1 - bbbits;
     }
 #else /*Avoid_Underflow*/
 #ifdef Sudden_Underflow
 #ifdef IBM
     j = 1 + 4 * P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
 #else
     j = P + 1 - bbbits;
 #endif
 #else /*Sudden_Underflow*/
     j = bbe;
     i = j + bbbits - 1; /* logb(rv) */
     if (i < Emin) { /* denormal */
         j += P - Emin;
     } else {
         j = P + 1 - bbbits;
     }
 #endif /*Sudden_Underflow*/
 #endif /*Avoid_Underflow*/
     bb2 += j;
     bd2 += j;
 #ifdef Avoid_Underflow
     bd2 += scale;
 #endif
     i = bb2 < bd2 ? bb2 : bd2;
     if (i > bs2) {
         i = bs2;
     }
     if (i > 0) {
         bb2 -= i;
         bd2 -= i;
         bs2 -= i;
     }
     if (bb5 > 0) {
         bs = pow5mult(bs, bb5);
         bb1 = mult(bs, bb);
         Bfree(bb);
         bb = bb1;
     }
     if (bb2 > 0) {
         bb = lshift(bb, bb2);
     }
     if (bd5 > 0) {
         bd = pow5mult(bd, bd5);
     }
     if (bd2 > 0) {
         bd = lshift(bd, bd2);
     }
     if (bs2 > 0) {
         bs = lshift(bs, bs2);
     }
     delta = diff(bb, bd);
     dsign = delta->sign;
     delta->sign = 0;
     i = cmp(delta, bs);
 #ifdef Honor_FLT_ROUNDS
     if (rounding != 1) {
         if (i < 0) {
             /* Error is less than an ulp */
             if (!delta->x[0] && delta->wds <= 1) {
                 /* exact */
 #ifdef SET_INEXACT
                 inexact = 0;
 #endif
                 break;
             }
             if (rounding) {
                 if (dsign) {
                     adj = 1.;
                     goto apply_adj;
                 }
             } else if (!dsign) {
                 adj = -1.;
                 if (!word1(rv)
                         && !(word0(rv) & Frac_mask)) {
                     y = word0(rv) & Exp_mask;
 #ifdef Avoid_Underflow
                     if (!scale || y > 2 * P * Exp_msk1)
 #else
                     if (y)
 #endif
                     {
                         delta = lshift(delta, Log2P);
                         if (cmp(delta, bs) <= 0) {
                             adj = -0.5;
                         }
                     }
                 }
             apply_adj:
 #ifdef Avoid_Underflow
                 if (scale && (y = word0(rv) & Exp_mask)
                         <= 2 * P * Exp_msk1) {
                     word0(adj) += (2 * P + 1) * Exp_msk1 - y;
                 }
 #else
 #ifdef Sudden_Underflow
                 if ((word0(rv) & Exp_mask) <=
                         P * Exp_msk1) {
                     word0(rv) += P * Exp_msk1;
                     dval(rv) += adj * ulp(dval(rv));
                     word0(rv) -= P * Exp_msk1;
                 } else
 #endif /*Sudden_Underflow*/
 #endif /*Avoid_Underflow*/
                 dval(rv) += adj * ulp(dval(rv));
             }
             break;
         }
         adj = ratio(delta, bs);
         if (adj < 1.) {
             adj = 1.;
         }
         if (adj <= 0x7ffffffe) {
             /* adj = rounding ? ceil(adj) : floor(adj); */
             y = adj;
             if (y != adj) {
                 if (!((rounding >> 1) ^ dsign)) {
                     y++;
                 }
                 adj = y;
             }
         }
 #ifdef Avoid_Underflow
         if (scale && (y = word0(rv) & Exp_mask) <= 2 * P * Exp_msk1) {
             word0(adj) += (2 * P + 1) * Exp_msk1 - y;
         }
 #else
 #ifdef Sudden_Underflow
         if ((word0(rv) & Exp_mask) <= P * Exp_msk1) {
             word0(rv) += P * Exp_msk1;
             adj *= ulp(dval(rv));
             if (dsign) {
                 dval(rv) += adj;
             } else {
                 dval(rv) -= adj;
             }
             word0(rv) -= P * Exp_msk1;
             goto cont;
         }
 #endif /*Sudden_Underflow*/
 #endif /*Avoid_Underflow*/
         adj *= ulp(dval(rv));
         if (dsign) {
             dval(rv) += adj;
         } else {
             dval(rv) -= adj;
         }
         goto cont;
     }
 #endif /*Honor_FLT_ROUNDS*/
 
     if (i < 0) {
         /* Error is less than half an ulp -- check for
          * special case of mantissa a power of two.
          */
         if (dsign || word1(rv) || word0(rv) & Bndry_mask
 #ifdef IEEE_Arith
 #ifdef Avoid_Underflow
                 || (word0(rv) & Exp_mask) <= (2 * P + 1)*Exp_msk1
 #else
                 || (word0(rv) & Exp_mask) <= Exp_msk1
 #endif
 #endif
            ) {
 #ifdef SET_INEXACT
             if (!delta->x[0] && delta->wds <= 1) {
                 inexact = 0;
             }
 #endif
             break;
         }
         if (!delta->x[0] && delta->wds <= 1) {
             /* exact result */
 #ifdef SET_INEXACT
             inexact = 0;
 #endif
             break;
         }
         delta = lshift(delta, Log2P);
         if (cmp(delta, bs) > 0) {
             goto drop_down;
         }
         break;
     }
     if (i == 0) {
         /* exactly half-way between */
         if (dsign) {
             if ((word0(rv) & Bndry_mask1) == Bndry_mask1
                     &&  word1(rv) == (
 #ifdef Avoid_Underflow
                         (scale && (y = word0(rv) & Exp_mask) <= 2 * P * Exp_msk1)
                         ? (0xffffffff & (0xffffffff << (2 * P + 1 - (y >> Exp_shift)))) :
 #endif
                         0xffffffff)) {
                 /*boundary case -- increment exponent*/
                 word0(rv) = (word0(rv) & Exp_mask)
                             + Exp_msk1
 #ifdef IBM
                             | Exp_msk1 >> 4
 #endif
                             ;
                 word1(rv) = 0;
 #ifdef Avoid_Underflow
                 dsign = 0;
 #endif
                 break;
             }
         } else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
         drop_down:
             /* boundary case -- decrement exponent */
 #ifdef Sudden_Underflow /*{{*/
             L = word0(rv) & Exp_mask;
 #ifdef IBM
             if (L <  Exp_msk1)
 #else
 #ifdef Avoid_Underflow
             if (L <= (scale ? (2 * P + 1)*Exp_msk1 : Exp_msk1))
 #else
             if (L <= Exp_msk1)
 #endif /*Avoid_Underflow*/
 #endif /*IBM*/
                 goto undfl;
             L -= Exp_msk1;
 #else /*Sudden_Underflow}{*/
 #ifdef Avoid_Underflow
             if (scale) {
                 L = word0(rv) & Exp_mask;
                 if (L <= (2 * P + 1)*Exp_msk1) {
                     if (L > (P + 2)*Exp_msk1)
                         /* round even ==> */
                         /* accept rv */
                     {
                         break;
                     }
                     /* rv = smallest denormal */
                     goto undfl;
                 }
             }
 #endif /*Avoid_Underflow*/
             L = (word0(rv) & Exp_mask) - Exp_msk1;
 #endif /*Sudden_Underflow}}*/
             word0(rv) = L | Bndry_mask1;
             word1(rv) = 0xffffffff;
 #ifdef IBM
             goto cont;
 #else
             break;
 #endif
         }
 #ifndef ROUND_BIASED
         if (!(word1(rv) & LSB)) {
             break;
         }
 #endif
         if (dsign) {
             dval(rv) += ulp(dval(rv));
         }
 #ifndef ROUND_BIASED
         else {
             dval(rv) -= ulp(dval(rv));
 #ifndef Sudden_Underflow
             if (!dval(rv)) {
                 goto undfl;
             }
 #endif
         }
 #ifdef Avoid_Underflow
         dsign = 1 - dsign;
 #endif
 #endif
         break;
     }
     if ((aadj = ratio(delta, bs)) <= 2.) {
         if (dsign) {
             aadj = aadj1 = 1.;
         } else if (word1(rv) || word0(rv) & Bndry_mask) {
 #ifndef Sudden_Underflow
             if (word1(rv) == Tiny1 && !word0(rv)) {
                 goto undfl;
             }
 #endif
             aadj = 1.;
             aadj1 = -1.;
         } else {
             /* special case -- power of FLT_RADIX to be */
             /* rounded down... */
 
             if (aadj < 2. / FLT_RADIX) {
                 aadj = 1. / FLT_RADIX;
             } else {
                 aadj *= 0.5;
             }
             aadj1 = -aadj;
         }
     } else {
         aadj *= 0.5;
         aadj1 = dsign ? aadj : -aadj;
 #ifdef Check_FLT_ROUNDS
         switch (Rounding) {
         case 2: /* towards +infinity */
             aadj1 -= 0.5;
             break;
         case 0: /* towards 0 */
         case 3: /* towards -infinity */
             aadj1 += 0.5;
         }
 #else
         if (Flt_Rounds == 0) {
             aadj1 += 0.5;
         }
 #endif /*Check_FLT_ROUNDS*/
     }
     y = word0(rv) & Exp_mask;
 
     /* Check for overflow */
 
     if (y == Exp_msk1 * (DBL_MAX_EXP + Bias - 1)) {
         dval(rv0) = dval(rv);
         word0(rv) -= P * Exp_msk1;
         adj = aadj1 * ulp(dval(rv));
         dval(rv) += adj;
         if ((word0(rv) & Exp_mask) >=
                 Exp_msk1 * (DBL_MAX_EXP + Bias - P)) {
             if (word0(rv0) == Big0 && word1(rv0) == Big1) {
                 goto ovfl;
             }
             word0(rv) = Big0;
             word1(rv) = Big1;
             goto cont;
         } else {
             word0(rv) += P * Exp_msk1;
         }
     } else {
 #ifdef Avoid_Underflow
         if (scale && y <= 2 * P * Exp_msk1) {
             if (aadj <= 0x7fffffff) {
                 if ((z = (ULong)aadj) <= 0) {
                     z = 1;
                 }
                 aadj = z;
                 aadj1 = dsign ? aadj : -aadj;
             }
             dval(aadj2) = aadj1;
             word0(aadj2) += (2 * P + 1) * Exp_msk1 - y;
             aadj1 = dval(aadj2);
         }
         adj = aadj1 * ulp(dval(rv));
         dval(rv) += adj;
 #else
 #ifdef Sudden_Underflow
         if ((word0(rv) & Exp_mask) <= P * Exp_msk1) {
             dval(rv0) = dval(rv);
             word0(rv) += P * Exp_msk1;
             adj = aadj1 * ulp(dval(rv));
             dval(rv) += adj;
 #ifdef IBM
             if ((word0(rv) & Exp_mask) <  P * Exp_msk1)
 #else
             if ((word0(rv) & Exp_mask) <= P * Exp_msk1)
 #endif
             {
                 if (word0(rv0) == Tiny0
                         && word1(rv0) == Tiny1) {
                     goto undfl;
                 }
                 word0(rv) = Tiny0;
                 word1(rv) = Tiny1;
                 goto cont;
             } else {
                 word0(rv) -= P * Exp_msk1;
             }
         } else {
             adj = aadj1 * ulp(dval(rv));
             dval(rv) += adj;
         }
 #else /*Sudden_Underflow*/
         /* Compute adj so that the IEEE rounding rules will
          * correctly round rv + adj in some half-way cases.
          * If rv * ulp(rv) is denormalized (i.e.,
          * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
          * trouble from bits lost to denormalization;
          * example: 1.2e-307 .
          */
         if (y <= (P - 1)*Exp_msk1 && aadj > 1.) {
             aadj1 = (double)(int)(aadj + 0.5);
             if (!dsign) {
                 aadj1 = -aadj1;
             }
         }
         adj = aadj1 * ulp(dval(rv));
         dval(rv) += adj;
 #endif /*Sudden_Underflow*/
 #endif /*Avoid_Underflow*/
     }
     z = word0(rv) & Exp_mask;
 #ifndef SET_INEXACT
 #ifdef Avoid_Underflow
     if (!scale)
 #endif
         if (y == z) {
             /* Can we stop now? */
             L = (Long)aadj;
             aadj -= L;
             /* The tolerances below are conservative. */
             if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
                 if (aadj < .4999999 || aadj > .5000001) {
                     break;
                 }
             } else if (aadj < .4999999 / FLT_RADIX) {
                 break;
             }
         }
 #endif
 cont:
     Bfree(bb);
     Bfree(bd);
     Bfree(bs);
     Bfree(delta);
 }
 #ifdef SET_INEXACT
 if (inexact) {
     if (!oldinexact) {
         word0(rv0) = Exp_1 + (70 << Exp_shift);
         word1(rv0) = 0;
         dval(rv0) += 1.;
     }
 } else if (!oldinexact) {
     clear_inexact();
 }
 #endif
 #ifdef Avoid_Underflow
 if (scale) {
     word0(rv0) = Exp_1 - 2 * P * Exp_msk1;
     word1(rv0) = 0;
     dval(rv) *= dval(rv0);
 #if HAVE_ERRNO_H
     /* try to avoid the bug of testing an 8087 register value */
     if (word0(rv) == 0 && word1(rv) == 0) {
         errno = ERANGE;
     }
 #endif
 }
 #endif /* Avoid_Underflow */
 #ifdef SET_INEXACT
 if (inexact && !(word0(rv) & Exp_mask)) {
     /* set underflow bit */
     dval(rv0) = 1e-300;
     dval(rv0) *= dval(rv0);
 }
 #endif
 retfree:
 Bfree(bb);
 Bfree(bd);
 Bfree(bs);
 Bfree(bd0);
 Bfree(delta);
 ret:
 if (se) {
     *se = (char *)s;
 }
 return sign ? -dval(rv) : dval(rv);
 }
 
 static int
 quorem
 (Bigint *b, Bigint *S)
 {
     int n;
     ULong *bx, *bxe, q, *sx, *sxe;
 #ifdef ULLong
     ULLong borrow, carry, y, ys;
 #else
     ULong borrow, carry, y, ys;
 #ifdef Pack_32
     ULong si, z, zs;
 #endif
 #endif
 
     n = S->wds;
 #ifdef DEBUG
     /*debug*/ if (b->wds > n)
         /*debug*/{
         Bug("oversize b in quorem");
     }
 #endif
     if (b->wds < n) {
         return 0;
     }
     sx = S->x;
     sxe = sx + --n;
     bx = b->x;
     bxe = bx + n;
     q = *bxe / (*sxe + 1);  /* ensure q <= true quotient */
 #ifdef DEBUG
     /*debug*/ if (q > 9)
         /*debug*/{
         Bug("oversized quotient in quorem");
     }
 #endif
     if (q) {
         borrow = 0;
         carry = 0;
         do {
 #ifdef ULLong
             ys = *sx++ * (ULLong)q + carry;
             carry = ys >> 32;
             y = *bx - (ys & FFFFFFFF) - borrow;
             borrow = y >> 32 & (ULong)1;
             *bx++ = (ULong)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++ = (ULong)y & FFFFFFFF;
 #else
 #ifdef Pack_32
             si = *sx++;
             ys = (si & 0xffff) + carry;
             zs = (si >> 16) + (ys >> 16);
             carry = zs >> 16;
             y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
             borrow = (y & 0x10000) >> 16;
             z = (*bx >> 16) - (zs & 0xffff) - borrow;
             borrow = (z & 0x10000) >> 16;
             Storeinc(bx, z, y);
 #else
             ys = *sx++ + carry;
             carry = ys >> 16;
             y = *bx - (ys & 0xffff) - borrow;
             borrow = (y & 0x10000) >> 16;
             *bx++ = y & 0xffff;
 #endif
 #endif
         } while (sx <= sxe);
         bx = b->x;
         bxe = bx + n;
         if (!*bxe) {
             while (--bxe > bx && !*bxe) {
                 --n;
             }
             b->wds = n;
         }
     }
     return q;
 }
 
 #ifndef MULTIPLE_THREADS
 static char *dtoa_result;
 #endif
 
 static char *
 rv_alloc(int i)
 {
     int j, k, *r;
 
     j = sizeof(ULong);
     for (k = 0;
             sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= (unsigned)i;
             j <<= 1) {
         k++;
     }
     r = (int *)Balloc(k);
     *r = k;
     return
 #ifndef MULTIPLE_THREADS
         dtoa_result =
 #endif
             (char *)(r + 1);
 }
 
 static char *
 nrv_alloc(CONST char *s, char **rve, int n)
 {
     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
 freedtoa(char *s)
 {
     Bigint *b = (Bigint *)((int *)s - 1);
     b->maxwds = 1 << (b->k = *(int *)b);
     Bfree(b);
 #ifndef MULTIPLE_THREADS
     if (s == dtoa_result) {
         dtoa_result = nullptr;
     }
 #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. 92-101].
  *
  * Modifications:
  *  1. Rather than iterating, we use a simple numeric overestimate
  *     to determine k = floor(log10(d)).  We scale relevant
  *     quantities using O(log2(k)) rather than O(k) multiplications.
  *  2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
  *     try to generate digits strictly left to right.  Instead, we
  *     compute with fewer bits and propagate the carry if necessary
  *     when rounding the final digit up.  This is often faster.
  *  3. Under the assumption that input will be rounded nearest,
  *     mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
  *     That is, we allow equality in stopping tests when the
  *     round-nearest rule will give the same floating-point value
  *     as would satisfaction of the stopping test with strict
  *     inequality.
  *  4. We remove common factors of powers of 2 from relevant
  *     quantities.
  *  5. When converting floating-point integers less than 1e16,
  *     we use floating-point arithmetic rather than resorting
  *     to multiple-precision integers.
  *  6. When asked to produce fewer than 15 digits, we first try
  *     to get by with floating-point arithmetic; we resort to
  *     multiple-precision integer arithmetic only if we cannot
  *     guarantee that the floating-point calculation has given
  *     the correctly rounded result.  For k requested digits and
  *     "uniformly" distributed input, the probability is
  *     something like 10^(k-15) that we must resort to the Long
  *     calculation.
  */
 
 char *
 dtoa
 (double dd, int mode, int ndigits, int *decpt, int *sign, char **rve)
 {
     /* Arguments ndigits, decpt, sign are similar to those
     of ecvt and fcvt; trailing zeros are suppressed from
     the returned string.  If not null, *rve is set to point
     to the end of the return value.  If d is +-Infinity or NaN,
     then *decpt is set to 9999.
 
     mode:
        0 ==> shortest string that yields d when read in
            and rounded to nearest.
        1 ==> like 0, but with Steele & White stopping rule;
            e.g. with IEEE P754 arithmetic , mode 0 gives
            1e23 whereas mode 1 gives 9.999999999999999e22.
        2 ==> max(1,ndigits) significant digits.  This gives a
            return value similar to that of ecvt, except
            that trailing zeros are suppressed.
        3 ==> through ndigits past the decimal point.  This
            gives a return value similar to that from fcvt,
            except that trailing zeros are suppressed, and
            ndigits can be negative.
        4,5 ==> similar to 2 and 3, respectively, but (in
            round-nearest mode) with the tests of mode 0 to
            possibly return a shorter string that rounds to d.
            With IEEE arithmetic and compilation with
            -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
            as modes 2 and 3 when FLT_ROUNDS != 1.
        6-9 ==> Debugging modes similar to mode - 4:  don't try
            fast floating-point estimate (if applicable).
 
        Values of mode other than 0-9 are treated as mode 0.
 
        Sufficient space is allocated to the return value
        to hold the suppressed trailing zeros.
     */
 
     int bbits, b2, b5, be, dig, i, ieps, ilim = 0, ilim0, ilim1 = 0,
                                          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 = nullptr, *mhi, *S;
     U d, d2, eps;
     double ds;
     char *s, *s0;
 #ifdef Honor_FLT_ROUNDS
     int rounding;
 #endif
 #ifdef SET_INEXACT
     int inexact, oldinexact;
 #endif
 
 #ifndef MULTIPLE_THREADS
     if (dtoa_result) {
         freedtoa(dtoa_result);
         dtoa_result = nullptr;
     }
 #endif
 
     dval(d) = dd;
     if (word0(d) & Sign_bit) {
         /* set sign for everything, including 0's and NaNs */
         *sign = 1;
         word0(d) &= ~Sign_bit;  /* clear sign bit */
     } else {
         *sign = 0;
     }
 
 #if defined(IEEE_Arith) + defined(VAX)
 #ifdef IEEE_Arith
     if ((word0(d) & Exp_mask) == Exp_mask)
 #else
     if (word0(d)  == 0x8000)
 #endif
     {
         /* Infinity or NaN */
         *decpt = 9999;
 #ifdef IEEE_Arith
         if (!word1(d) && !(word0(d) & 0xfffff)) {
             return nrv_alloc("Infinity", rve, 8);
         }
 #endif
         return nrv_alloc("NaN", rve, 3);
     }
 #endif
 #ifdef IBM
     dval(d) += 0; /* normalize */
 #endif
     if (!dval(d)) {
         *decpt = 1;
         return nrv_alloc("0", rve, 1);
     }
 
 #ifdef SET_INEXACT
     try_quick = oldinexact = get_inexact();
     inexact = 1;
 #endif
 #ifdef Honor_FLT_ROUNDS
     if ((rounding = Flt_Rounds) >= 2) {
         if (*sign) {
             rounding = rounding == 2 ? 0 : 2;
         } else if (rounding != 2) {
             rounding = 0;
         }
     }
 #endif
 
     b = d2b(dval(d), &be, &bbits);
 #ifdef Sudden_Underflow
     i = (int)(word0(d) >> Exp_shift1 & (Exp_mask >> Exp_shift1));
 #else
     if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask >> Exp_shift1)))) {
 #endif
     dval(d2) = dval(d);
     word0(d2) &= Frac_mask1;
     word0(d2) |= Exp_11;
 #ifdef IBM
     if (j = 11 - hi0bits(word0(d2) & Frac_mask)) {
         dval(d2) /= 1 << j;
     }
 #endif
 
     /* log(x)   ~=~ log(1.5) + (x-1.5)/1.5
      * log10(x)  =  log(x) / log(10)
      *      ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
      * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
      *
      * This suggests computing an approximation k to log10(d) by
      *
      * k = (i - Bias)*0.301029995663981
      *  + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
      *
      * We want k to be too large rather than too small.
      * The error in the first-order Taylor series approximation
      * is in our favor, so we just round up the constant enough
      * to compensate for any error in the multiplication of
      * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
      * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
      * adding 1e-13 to the constant term more than suffices.
      * Hence we adjust the constant term to 0.1760912590558.
      * (We could get a more accurate k by invoking log10,
      *  but this is probably not worthwhile.)
      */
 
     i -= Bias;
 #ifdef IBM
     i <<= 2;
     i += j;
 #endif
 #ifndef Sudden_Underflow
     denorm = 0;
 } else {
     /* d is denormalized */
 
     i = bbits + be + (Bias + (P - 1) - 1);
     x = i > 32  ? word0(d) << (64 - i) | word1(d) >> (i - 32)
         : word1(d) << (32 - i);
     dval(d2) = x;
     word0(d2) -= 31 * Exp_msk1; /* adjust exponent */
     i -= (Bias + (P - 1) - 1) + 1;
     denorm = 1;
 }
 #endif
 ds = (dval(d2) - 1.5) * 0.289529654602168 + 0.1760912590558 + i * 0.301029995663981;
 k = (int)ds;
 if (ds < 0. && ds != k) {
     k--;    /* want k = floor(ds) */
 }
 k_check = 1;
 if (k >= 0 && k <= Ten_pmax) {
     if (dval(d) < tens[k]) {
         k--;
     }
     k_check = 0;
 }
 j = bbits - i - 1;
 if (j >= 0) {
     b2 = 0;
     s2 = j;
 } else {
     b2 = -j;
     s2 = 0;
 }
 if (k >= 0) {
     b5 = 0;
     s5 = k;
     s2 += k;
 } else {
     b2 -= k;
     b5 = -k;
     s5 = 0;
 }
 if (mode < 0 || mode > 9) {
     mode = 0;
 }
 
 #ifndef SET_INEXACT
 #ifdef Check_FLT_ROUNDS
 try_quick = Rounding == 1;
 #else
 try_quick = 1;
 #endif
 #endif /*SET_INEXACT*/
 
 if (mode > 5) {
     mode -= 4;
     try_quick = 0;
 }
 leftright = 1;
 switch (mode) {
 case 0:
 case 1:
     ilim = ilim1 = -1;
     i = 18;
     ndigits = 0;
     break;
 case 2:
     leftright = 0;
 /* no break */
 case 4:
     if (ndigits <= 0) {
         ndigits = 1;
     }
     ilim = ilim1 = i = ndigits;
     break;
 case 3:
     leftright = 0;
 /* no break */
 case 5:
     i = ndigits + k + 1;
     ilim = i;
     ilim1 = i - 1;
     if (i <= 0) {
         i = 1;
     }
 }
 s = s0 = rv_alloc(i);
 
 #ifdef Honor_FLT_ROUNDS
 if (mode > 1 && rounding != 1) {
     leftright = 0;
 }
 #endif
 
 if (ilim >= 0 && ilim <= Quick_max && try_quick) {
 
     /* Try to get by with floating-point arithmetic. */
 
     i = 0;
     dval(d2) = dval(d);
     k0 = k;
     ilim0 = ilim;
     ieps = 2; /* conservative */
     if (k > 0) {
         ds = tens[k & 0xf];
         j = k >> 4;
         if (j & Bletch) {
             /* prevent overflows */
             j &= Bletch - 1;
             dval(d) /= bigtens[n_bigtens - 1];
             ieps++;
         }
         for (; j; j >>= 1, i++)
             if (j & 1) {
                 ieps++;
                 ds *= bigtens[i];
             }
         dval(d) /= ds;
     } else if ((j1 = -k)) {
         dval(d) *= tens[j1 & 0xf];
         for (j = j1 >> 4; j; j >>= 1, i++)
             if (j & 1) {
                 ieps++;
                 dval(d) *= bigtens[i];
             }
     }
     if (k_check && dval(d) < 1. && ilim > 0) {
         if (ilim1 <= 0) {
             goto fast_failed;
         }
         ilim = ilim1;
         k--;
         dval(d) *= 10.;
         ieps++;
     }
     dval(eps) = ieps * dval(d) + 7.;
     word0(eps) -= (P - 1) * Exp_msk1;
     if (ilim == 0) {
         S = mhi = nullptr;
         dval(d) -= 5.;
         if (dval(d) > dval(eps)) {
             goto one_digit;
         }
         if (dval(d) < -dval(eps)) {
             goto no_digits;
         }
         goto fast_failed;
     }
 #ifndef No_leftright
     if (leftright) {
         /* Use Steele & White method of only
          * generating digits needed.
          */
         dval(eps) = 0.5 / tens[ilim - 1] - dval(eps);
         for (i = 0;;) {
             L = (long int)dval(d);
             dval(d) -= L;
             *s++ = '0' + (int)L;
             if (dval(d) < dval(eps)) {
                 goto ret1;
             }
             if (1. - dval(d) < dval(eps)) {
                 goto bump_up;
             }
             if (++i >= ilim) {
                 break;
             }
             dval(eps) *= 10.;
             dval(d) *= 10.;
         }
     } else {
 #endif
         /* Generate ilim digits, then fix them up. */
         dval(eps) *= tens[ilim - 1];
         for (i = 1;; i++, dval(d) *= 10.) {
             L = (Long)(dval(d));
             if (!(dval(d) -= L)) {
                 ilim = i;
             }
             *s++ = '0' + (int)L;
             if (i == ilim) {
                 if (dval(d) > 0.5 + dval(eps)) {
                     goto bump_up;
                 } else if (dval(d) < 0.5 - dval(eps)) {
                     while (*--s == '0')
                         ;
                     s++;
                     goto ret1;
                 }
                 break;
             }
         }
 #ifndef No_leftright
     }
 #endif
 fast_failed:
     s = s0;
     dval(d) = dval(d2);
     k = k0;
     ilim = ilim0;
 }
 
 /* Do we have a "small" integer? */
 
 if (be >= 0 && k <= Int_max) {
     /* Yes. */
     ds = tens[k];
     if (ndigits < 0 && ilim <= 0) {
         S = mhi = nullptr;
         if (ilim < 0 || dval(d) <= 5 * ds) {
             goto no_digits;
         }
         goto one_digit;
     }
     for (i = 1;; i++, dval(d) *= 10.) {
         L = (Long)(dval(d) / ds);
         dval(d) -= L * ds;
 #ifdef Check_FLT_ROUNDS
         /* If FLT_ROUNDS == 2, L will usually be high by 1 */
         if (dval(d) < 0) {
             L--;
             dval(d) += ds;
         }
 #endif
         *s++ = '0' + (int)L;
         if (!dval(d)) {
 #ifdef SET_INEXACT
             inexact = 0;
 #endif
             break;
         }
         if (i == ilim) {
 #ifdef Honor_FLT_ROUNDS
             if (mode > 1)
                 switch (rounding) {
                 case 0: goto ret1;
                 case 2: goto bump_up;
                 }
 #endif
             dval(d) += dval(d);
             if (dval(d) > ds || (dval(d) == ds && L & 1)) {
             bump_up:
                 while (*--s == '9')
                     if (s == s0) {
                         k++;
                         *s = '0';
                         break;
                     }
                 ++*s++;
             }
             break;
         }
     }
     goto ret1;
 }
 
 m2 = b2;
 m5 = b5;
 mhi = mlo = nullptr;
 if (leftright) {
     i =
 #ifndef Sudden_Underflow
         denorm ? be + (Bias + (P - 1) - 1 + 1) :
 #endif
 #ifdef IBM
         1 + 4 * P - 3 - bbits + ((bbits + be - 1) & 3);
 #else
         1 + P - bbits;
 #endif
     b2 += i;
     s2 += i;
     mhi = i2b(1);
 }
 if (m2 > 0 && s2 > 0) {
     i = m2 < s2 ? m2 : s2;
     b2 -= i;
     m2 -= i;
     s2 -= i;
 }
 if (b5 > 0) {
     if (leftright) {
         if (m5 > 0) {
             mhi = pow5mult(mhi, m5);
             b1 = mult(mhi, b);
             Bfree(b);
             b = b1;
         }
         if ((j = b5 - m5)) {
             b = pow5mult(b, j);
         }
     } else {
         b = pow5mult(b, b5);
     }
 }
 S = i2b(1);
 if (s5 > 0) {
     S = pow5mult(S, s5);
 }
 
 /* Check for special case that d is a normalized power of 2. */
 
 spec_case = 0;
 if ((mode < 2 || leftright)
 #ifdef Honor_FLT_ROUNDS
         && rounding == 1
 #endif
    ) {
     if (!word1(d) && !(word0(d) & Bndry_mask)
 #ifndef Sudden_Underflow
             && word0(d) & (Exp_mask & ~Exp_msk1)
 #endif
        ) {
         /* The special case */
         b2 += Log2P;
         s2 += Log2P;
         spec_case = 1;
     }
 }
 
 /* Arrange for convenient computation of quotients:
  * shift left if necessary so divisor has 4 leading 0 bits.
  *
  * Perhaps we should just compute leading 28 bits of S once
  * and for all and pass them and a shift to quorem, so it
  * can do shifts and ors to compute the numerator for q.
  */
 #ifdef Pack_32
 if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds - 1]) : 1) + s2) & 0x1f)) {
     i = 32 - i;
 }
 #else
 if (i = ((s5 ? 32 - hi0bits(S->x[S->wds - 1]) : 1) + s2) & 0xf) {
     i = 16 - i;
 }
 #endif
 if (i > 4) {
     i -= 4;
     b2 += i;
     m2 += i;
     s2 += i;
 } else if (i < 4) {
     i += 28;
     b2 += i;
     m2 += i;
     s2 += i;
 }
 if (b2 > 0) {
     b = lshift(b, b2);
 }
 if (s2 > 0) {
     S = lshift(S, s2);
 }
 if (k_check) {
     if (cmp(b, S) < 0) {
         k--;
         b = multadd(b, 10, 0);  /* we botched the k estimate */
         if (leftright) {
             mhi = multadd(mhi, 10, 0);
         }
         ilim = ilim1;
     }
 }
 if (ilim <= 0 && (mode == 3 || mode == 5)) {
     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(d) & 1)
 #ifdef Honor_FLT_ROUNDS
                 && rounding >= 1
 #endif
            ) {
             if (dig == '9') {
                 goto round_9_up;
             }
             if (j > 0) {
                 dig++;
             }
 #ifdef SET_INEXACT
             else if (!b->x[0] && b->wds <= 1) {
                 inexact = 0;
             }
 #endif
             *s++ = dig;
             goto ret;
         }
 #endif
         if (j < 0 || (j == 0 && mode != 1
 #ifndef ROUND_BIASED
                       && !(word1(d) & 1)
 #endif
                      )) {
             if (!b->x[0] && b->wds <= 1) {
 #ifdef SET_INEXACT
                 inexact = 0;
 #endif
                 goto accept_dig;
             }
 #ifdef Honor_FLT_ROUNDS
             if (mode > 1)
                 switch (rounding) {
                 case 0: goto accept_dig;
                 case 2: goto keep_dig;
                 }
 #endif /*Honor_FLT_ROUNDS*/
             if (j1 > 0) {
                 b = lshift(b, 1);
                 j1 = cmp(b, S);
                 if ((j1 > 0 || (j1 == 0 && dig & 1))
                         && dig++ == '9') {
                     goto round_9_up;
                 }
             }
         accept_dig:
             *s++ = dig;
             goto ret;
         }
         if (j1 > 0) {
 #ifdef Honor_FLT_ROUNDS
             if (!rounding) {
                 goto accept_dig;
             }
 #endif
             if (dig == '9') { /* possible if i == 1 */
             round_9_up:
                 *s++ = '9';
                 goto roundoff;
             }
             *s++ = dig + 1;
             goto ret;
         }
 #ifdef Honor_FLT_ROUNDS
     keep_dig:
 #endif
         *s++ = dig;
         if (i == ilim) {
             break;
         }
         b = multadd(b, 10, 0);
         if (mlo == mhi) {
             mlo = mhi = multadd(mhi, 10, 0);
         } else {
             mlo = multadd(mlo, 10, 0);
             mhi = multadd(mhi, 10, 0);
         }
     }
 } else
     for (i = 1;; i++) {
         *s++ = dig = quorem(b, S) + '0';
         if (!b->x[0] && b->wds <= 1) {
 #ifdef SET_INEXACT
             inexact = 0;
 #endif
             goto ret;
         }
         if (i >= ilim) {
             break;
         }
         b = multadd(b, 10, 0);
     }
 
 /* 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(d) = Exp_1 + (70 << Exp_shift);
         word1(d) = 0;
         dval(d) += 1.;
     }
 } else if (!oldinexact) {
     clear_inexact();
 }
 #endif
 Bfree(b);
 *s = 0;
 *decpt = k + 1;
 if (rve) {
     *rve = s;
 }
 return s0;
 }
 #ifdef __cplusplus
 }
 #endif