Make unit_tests pass with pt_BR.UTF-8 locale.

third_party/dmg_fp/dtoa.cc

+/****************************************************************
+ *
+ * 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.
+ * #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 YES_ALIAS to permit aliasing certain double values with
+ *      arrays of ULongs.  This leads to slightly better code with
+ *      some compilers and was always used prior to 19990916, but it
+ *      is not strictly legal and can cause trouble with aggressively
+ *      optimizing compilers (e.g., gcc 2.95.1 under -O2).
+ * #define USE_LOCALE to use the current locale's decimal_point value.
+ * #define SET_INEXACT if IEEE arithmetic is being used and extra
+ *      computation should be done to set the inexact flag when the
+ *      result is inexact and avoid setting inexact when the result
+ *      is exact.  In this case, dtoa.c must be compiled in
+ *      an environment, perhaps provided by #include "dtoa.c" in a
+ *      suitable wrapper, that defines two functions,
+ *              int get_inexact(void);
+ *              void clear_inexact(void);
+ *      such that get_inexact() returns a nonzero value if the
+ *      inexact bit is already set, and clear_inexact() sets the
+ *      inexact bit to 0.  When SET_INEXACT is #defined, strtod
+ *      also does extra computations to set the underflow and overflow
+ *      flags when appropriate (i.e., when the result is tiny and
+ *      inexact or when it is a numeric value rounded to +-infinity).
+ * #define NO_ERRNO if strtod should not assign errno = ERANGE when
+ *      the result overflows to +-Infinity or underflows to 0.
+ */
+
+#ifndef Long
+#define Long long
+#endif
+#ifndef ULong
+typedef unsigned Long ULong;
+#endif
+
+#ifdef DEBUG
+#include "stdio.h"
+#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
+#endif
+
+#include "stdlib.h"
+#include "string.h"
+
+#ifdef USE_LOCALE
+#include "locale.h"
+#endif
+
+#ifdef MALLOC
+#ifdef KR_headers
+extern char *MALLOC();
+#else
+extern void *MALLOC(size_t);
+#endif
+#else
+#define MALLOC malloc
+#endif
+
+#ifndef Omit_Private_Memory
+#ifndef PRIVATE_MEM
+#define PRIVATE_MEM 2304
+#endif
+#define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
+static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
+#endif
+
+#undef IEEE_Arith
+#undef Avoid_Underflow
+#ifdef IEEE_MC68k
+#define IEEE_Arith
+#endif
+#ifdef IEEE_8087
+#define IEEE_Arith
+#endif
+
+#ifdef IEEE_Arith
+#ifndef NO_INFNAN_CHECK
+#undef INFNAN_CHECK
+#define INFNAN_CHECK
+#endif
+#else
+#undef INFNAN_CHECK
+#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 YES_ALIAS
+#define dval(x) x
+#ifdef IEEE_8087
+#define word0(x) ((ULong *)&x)[1]
+#define word1(x) ((ULong *)&x)[0]
+#else
+#define word0(x) ((ULong *)&x)[0]
+#define word1(x) ((ULong *)&x)[1]
+#endif
+#else
+#ifdef IEEE_8087
+#define word0(x) ((U*)&x)->L[1]
+#define word1(x) ((U*)&x)->L[0]
+#else
+#define word0(x) ((U*)&x)->L[0]
+#define word1(x) ((U*)&x)->L[1]
+#endif
+#define dval(x) ((U*)&x)->d
+#endif
+
+/* The following definition of Storeinc is appropriate for MIPS processors.
+ * An alternative that might be better on some machines is
+ * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
+ */
+#if defined(IEEE_8087) + defined(VAX)
+#define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
+((unsigned short *)a)[0] = (unsigned short)c, a++)
+#else
+#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
+((unsigned short *)a)[1] = (unsigned short)c, a++)
+#endif
+
+/* #define P DBL_MANT_DIG */
+/* Ten_pmax = floor(P*log(2)/log(5)) */
+/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
+/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
+/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
+
+#ifdef IEEE_Arith
+#define Exp_shift  20
+#define Exp_shift1 20
+#define Exp_msk1    0x100000
+#define Exp_msk11   0x100000
+#define Exp_mask  0x7ff00000
+#define P 53
+#define Bias 1023
+#define Emin (-1022)
+#define Exp_1  0x3ff00000
+#define Exp_11 0x3ff00000
+#define Ebits 11
+#define Frac_mask  0xfffff
+#define Frac_mask1 0xfffff
+#define Ten_pmax 22
+#define Bletch 0x10
+#define Bndry_mask  0xfffff
+#define Bndry_mask1 0xfffff
+#define LSB 1
+#define Sign_bit 0x80000000
+#define Log2P 1
+#define Tiny0 0
+#define Tiny1 1
+#define Quick_max 14
+#define Int_max 14
+#ifndef NO_IEEE_Scale
+#define Avoid_Underflow
+#ifdef Flush_Denorm     /* debugging option */
+#undef Sudden_Underflow
+#endif
+#endif
+
+#ifndef Flt_Rounds
+#ifdef FLT_ROUNDS
+#define Flt_Rounds FLT_ROUNDS
+#else
+#define Flt_Rounds 1
+#endif
+#endif /*Flt_Rounds*/
+
+#ifdef Honor_FLT_ROUNDS
+#undef Check_FLT_ROUNDS
+#define Check_FLT_ROUNDS
+#else
+#define Rounding Flt_Rounds
+#endif
+
+#else /* ifndef IEEE_Arith */
+#undef Check_FLT_ROUNDS
+#undef Honor_FLT_ROUNDS
+#undef SET_INEXACT
+#undef  Sudden_Underflow
+#define Sudden_Underflow
+#ifdef IBM
+#undef Flt_Rounds
+#define Flt_Rounds 0
+#define Exp_shift  24
+#define Exp_shift1 24
+#define Exp_msk1   0x1000000
+#define Exp_msk11  0x1000000
+#define Exp_mask  0x7f000000
+#define P 14
+#define Bias 65
+#define Exp_1  0x41000000
+#define Exp_11 0x41000000
+#define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
+#define Frac_mask  0xffffff
+#define Frac_mask1 0xffffff
+#define Bletch 4
+#define Ten_pmax 22
+#define Bndry_mask  0xefffff
+#define Bndry_mask1 0xffffff
+#define LSB 1
+#define Sign_bit 0x80000000
+#define Log2P 4
+#define Tiny0 0x100000
+#define Tiny1 0
+#define Quick_max 14
+#define Int_max 15
+#else /* VAX */
+#undef Flt_Rounds
+#define Flt_Rounds 1
+#define Exp_shift  23
+#define Exp_shift1 7
+#define Exp_msk1    0x80
+#define Exp_msk11   0x800000
+#define Exp_mask  0x7f80
+#define P 56
+#define Bias 129
+#define Exp_1  0x40800000
+#define Exp_11 0x4080
+#define Ebits 8
+#define Frac_mask  0x7fffff
+#define Frac_mask1 0xffff007f
+#define Ten_pmax 24
+#define Bletch 2
+#define Bndry_mask  0xffff007f
+#define Bndry_mask1 0xffff007f
+#define LSB 0x10000
+#define Sign_bit 0x8000
+#define Log2P 1
+#define Tiny0 0x80
+#define Tiny1 0
+#define Quick_max 15
+#define Int_max 15
+#endif /* IBM, VAX */
+#endif /* IEEE_Arith */
+
+#ifndef IEEE_Arith
+#define ROUND_BIASED
+#endif
+
+#ifdef RND_PRODQUOT
+#define rounded_product(a,b) a = rnd_prod(a, b)
+#define rounded_quotient(a,b) a = rnd_quot(a, b)
+#ifdef KR_headers
+extern double rnd_prod(), rnd_quot();
+#else
+extern double rnd_prod(double, double), rnd_quot(double, double);
+#endif
+#else
+#define rounded_product(a,b) a *= b
+#define rounded_quotient(a,b) a /= b
+#endif
+
+#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
+#define Big1 0xffffffff
+
+#ifndef Pack_32
+#define Pack_32
+#endif
+
+#ifdef KR_headers
+#define FFFFFFFF ((((unsigned long)0xffff)<<16)|(unsigned long)0xffff)
+#else
+#define FFFFFFFF 0xffffffffUL
+#endif
+
+#ifdef NO_LONG_LONG
+#undef ULLong
+#ifdef Just_16
+#undef Pack_32
+/* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
+ * This makes some inner loops simpler and sometimes saves work
+ * during multiplications, but it often seems to make things slightly
+ * slower.  Hence the default is now to store 32 bits per Long.
+ */
+#endif
+#else   /* long long available */
+#ifndef Llong
+#define Llong long long
+#endif
+#ifndef ULLong
+#define ULLong unsigned Llong
+#endif
+#endif /* NO_LONG_LONG */
+
+#ifndef MULTIPLE_THREADS
+#define ACQUIRE_DTOA_LOCK(n)    /*nothing*/
+#define FREE_DTOA_LOCK(n)       /*nothing*/
+#endif
+
+#define Kmax 15
+
+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);
+        if (rv = freelist[k]) {
+                freelist[k] = rv->next;
+                }
+        else {
+                x = 1 << k;
+#ifdef Omit_Private_Memory
+                rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
+#else
+                len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
+                        /sizeof(double);
+                if (pmem_next - private_mem + len <= PRIVATE_mem) {
+                        rv = (Bigint*)pmem_next;
+                        pmem_next += len;
+                        }
+                else
+                        rv = (Bigint*)MALLOC(len*sizeof(double));
+#endif
+                rv->k = k;
+                rv->maxwds = x;
+                }
+        FREE_DTOA_LOCK(0);
+        rv->sign = rv->wds = 0;
+        return rv;
+        }
+
+ static void
+Bfree
+#ifdef KR_headers
+        (v) Bigint *v;
+#else
+        (Bigint *v)
+#endif
+{
+        if (v) {
+                ACQUIRE_DTOA_LOCK(0);
+                v->next = freelist[v->k];
+                freelist[v->k] = v;
+                FREE_DTOA_LOCK(0);
+                }
+        }
+
+#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
+y->wds*sizeof(Long) + 2*sizeof(int))
+
+ static Bigint *
+multadd
+#ifdef KR_headers
+        (b, m, a) Bigint *b; int m, a;
+#else
+        (Bigint *b, int m, int a)       /* multiply by m and add a */
+#endif
+{
+        int i, wds;
+#ifdef ULLong
+        ULong *x;
+        ULLong carry, y;
+#else
+        ULong carry, *x, y;
+#ifdef Pack_32
+        ULong xi, z;
+#endif
+#endif
+        Bigint *b1;
+
+        wds = b->wds;
+        x = b->x;
+        i = 0;
+        carry = a;
+        do {
+#ifdef ULLong
+                y = *x * (ULLong)m + carry;
+                carry = y >> 32;
+                *x++ = y & FFFFFFFF;
+#else
+#ifdef Pack_32
+                xi = *x;
+                y = (xi & 0xffff) * m + carry;
+                z = (xi >> 16) * m + (y >> 16);
+                carry = z >> 16;
+                *x++ = (z << 16) + (y & 0xffff);
+#else
+                y = *x * m + carry;
+                carry = y >> 16;
+                *x++ = y & 0xffff;
+#endif
+#endif
+                }
+                while(++i < wds);
+        if (carry) {
+                if (wds >= b->maxwds) {
+                        b1 = Balloc(b->k+1);
+                        Bcopy(b1, b);
+                        Bfree(b);
+                        b = b1;
+                        }
+                b->x[wds++] = carry;
+                b->wds = wds;
+                }
+        return b;
+        }
+
+ static Bigint *
+s2b
+#ifdef KR_headers
+        (s, nd0, nd, y9) CONST char *s; int nd0, nd; ULong y9;
+#else
+        (CONST char *s, int nd0, int nd, ULong y9)
+#endif
+{
+        Bigint *b;
+        int i, k;
+        Long x, y;
+
+        x = (nd + 8) / 9;
+        for(k = 0, y = 1; x > y; y <<= 1, k++) ;
+#ifdef Pack_32
+        b = Balloc(k);
+        b->x[0] = y9;
+        b->wds = 1;
+#else
+        b = Balloc(k+1);
+        b->x[0] = y9 & 0xffff;
+        b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
+#endif
+
+        i = 9;
+        if (9 < nd0) {
+                s += 9;
+                do b = multadd(b, 10, *s++ - '0');
+                        while(++i < nd0);
+                s++;
+                }
+        else
+                s += 10;
+        for(; i < nd; i++)
+                b = multadd(b, 10, *s++ - '0');
+        return b;
+        }
+
+ static int
+hi0bits
+#ifdef KR_headers
+        (x) register ULong x;
+#else
+        (register ULong x)
+#endif
+{
+        register int k = 0;
+
+        if (!(x & 0xffff0000)) {
+                k = 16;
+                x <<= 16;
+                }
+        if (!(x & 0xff000000)) {
+                k += 8;
+                x <<= 8;
+                }
+        if (!(x & 0xf0000000)) {
+                k += 4;
+                x <<= 4;
+                }
+        if (!(x & 0xc0000000)) {
+                k += 2;
+                x <<= 2;
+                }
+        if (!(x & 0x80000000)) {
+                k++;
+                if (!(x & 0x40000000))
+                        return 32;
+                }
+        return k;
+        }
+
+ static int
+lo0bits
+#ifdef KR_headers
+        (y) ULong *y;
+#else
+        (ULong *y)
+#endif
+{
+        register int k;
+        register ULong x = *y;
+
+        if (x & 7) {
+                if (x & 1)
+                        return 0;
+                if (x & 2) {
+                        *y = x >> 1;
+                        return 1;
+                        }
+                *y = x >> 2;
+                return 2;
+                }
+        k = 0;
+        if (!(x & 0xffff)) {
+                k = 16;
+                x >>= 16;
+                }
+        if (!(x & 0xff)) {
+                k += 8;
+                x >>= 8;
+                }
+        if (!(x & 0xf)) {
+                k += 4;
+                x >>= 4;
+                }
+        if (!(x & 0x3)) {
+                k += 2;
+                x >>= 2;
+                }
+        if (!(x & 1)) {
+                k++;
+                x >>= 1;
+                if (!x)
+                        return 32;
+                }
+        *y = x;
+        return k;
+        }
+
+ static Bigint *
+i2b
+#ifdef KR_headers
+        (i) int i;
+#else
+        (int i)
+#endif
+{
+        Bigint *b;
+
+        b = Balloc(1);
+        b->x[0] = i;
+        b->wds = 1;
+        return b;
+        }
+
+ static Bigint *
+mult
+#ifdef KR_headers
+        (a, b) Bigint *a, *b;
+#else
+        (Bigint *a, Bigint *b)
+#endif
+{
+        Bigint *c;
+        int k, wa, wb, wc;
+        ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
+        ULong y;
+#ifdef ULLong
+        ULLong carry, z;
+#else
+        ULong carry, z;
+#ifdef Pack_32
+        ULong z2;
+#endif
+#endif
+
+        if (a->wds < b->wds) {
+                c = a;
+                a = b;
+                b = c;
+                }
+        k = a->k;
+        wa = a->wds;
+        wb = b->wds;
+        wc = wa + wb;
+        if (wc > a->maxwds)
+                k++;
+        c = Balloc(k);
+        for(x = c->x, xa = x + wc; x < xa; x++)
+                *x = 0;
+        xa = a->x;
+        xae = xa + wa;
+        xb = b->x;
+        xbe = xb + wb;
+        xc0 = c->x;
+#ifdef ULLong
+        for(; xb < xbe; xc0++) {
+                if (y = *xb++) {
+                        x = xa;
+                        xc = xc0;
+                        carry = 0;
+                        do {
+                                z = *x++ * (ULLong)y + *xc + carry;
+                                carry = z >> 32;
+                                *xc++ = z & FFFFFFFF;
+                                }
+                                while(x < xae);
+                        *xc = carry;
+                        }
+                }
+#else
+#ifdef Pack_32
+        for(; xb < xbe; xb++, xc0++) {
+                if (y = *xb & 0xffff) {
+                        x = xa;
+                        xc = xc0;
+                        carry = 0;
+                        do {
+                                z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
+                                carry = z >> 16;
+                                z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
+                                carry = z2 >> 16;
+                                Storeinc(xc, z2, z);
+                                }
+                                while(x < xae);
+                        *xc = carry;
+                        }
+                if (y = *xb >> 16) {
+                        x = xa;
+                        xc = xc0;
+                        carry = 0;
+                        z2 = *xc;
+                        do {
+                                z = (*x & 0xffff) * y + (*xc >> 16) + carry;
+                                carry = z >> 16;
+                                Storeinc(xc, z, z2);
+                                z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
+                                carry = z2 >> 16;
+                                }
+                                while(x < xae);
+                        *xc = z2;
+                        }
+                }
+#else
+        for(; xb < xbe; xc0++) {
+                if (y = *xb++) {
+                        x = xa;
+                        xc = xc0;
+                        carry = 0;
+                        do {
+                                z = *x++ * y + *xc + carry;
+                                carry = z >> 16;
+                                *xc++ = z & 0xffff;
+                                }
+                                while(x < xae);
+                        *xc = carry;
+                        }
+                }
+#endif
+#endif
+        for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
+        c->wds = wc;
+        return c;
+        }
+
+ static Bigint *p5s;
+
+ static Bigint *
+pow5mult
+#ifdef KR_headers
+        (b, k) Bigint *b; int k;
+#else
+        (Bigint *b, int k)
+#endif
+{
+        Bigint *b1, *p5, *p51;
+        int i;
+        static int p05[3] = { 5, 25, 125 };
+
+        if (i = k & 3)
+                b = multadd(b, p05[i-1], 0);
+
+        if (!(k >>= 2))
+                return b;
+        if (!(p5 = p5s)) {
+                /* first time */
+#ifdef MULTIPLE_THREADS
+                ACQUIRE_DTOA_LOCK(1);
+                if (!(p5 = p5s)) {
+                        p5 = p5s = i2b(625);
+                        p5->next = 0;
+                        }
+                FREE_DTOA_LOCK(1);
+#else
+                p5 = p5s = i2b(625);
+                p5->next = 0;
+#endif
+                }
+        for(;;) {
+                if (k & 1) {
+                        b1 = mult(b, p5);
+                        Bfree(b);
+                        b = b1;
+                        }
+                if (!(k >>= 1))
+                        break;
+                if (!(p51 = p5->next)) {
+#ifdef MULTIPLE_THREADS
+                        ACQUIRE_DTOA_LOCK(1);
+                        if (!(p51 = p5->next)) {
+                                p51 = p5->next = mult(p5,p5);
+                                p51->next = 0;
+                                }
+                        FREE_DTOA_LOCK(1);
+#else
+                        p51 = p5->next = mult(p5,p5);
+                        p51->next = 0;
+#endif
+                        }
+                p5 = p51;
+                }
+        return b;
+        }
+
+ static Bigint *
+lshift
+#ifdef KR_headers
+        (b, k) Bigint *b; int k;
+#else
+        (Bigint *b, int k)
+#endif
+{
+        int i, k1, n, n1;
+        Bigint *b1;
+        ULong *x, *x1, *xe, z;
+
+#ifdef Pack_32
+        n = k >> 5;
+#else
+        n = k >> 4;
+#endif
+        k1 = b->k;
+        n1 = n + b->wds + 1;
+        for(i = b->maxwds; n1 > i; i <<= 1)
+                k1++;
+        b1 = Balloc(k1);
+        x1 = b1->x;
+        for(i = 0; i < n; i++)
+                *x1++ = 0;
+        x = b->x;
+        xe = x + b->wds;
+#ifdef Pack_32
+        if (k &= 0x1f) {
+                k1 = 32 - k;
+                z = 0;
+                do {
+                        *x1++ = *x << k | z;
+                        z = *x++ >> k1;
+                        }
+                        while(x < xe);
+                if (*x1 = z)
+                        ++n1;
+                }
+#else
+        if (k &= 0xf) {
+                k1 = 16 - k;
+                z = 0;
+                do {
+                        *x1++ = *x << k  & 0xffff | z;
+                        z = *x++ >> k1;
+                        }
+                        while(x < xe);
+                if (*x1 = z)
+                        ++n1;
+                }
+#endif
+        else do
+                *x1++ = *x++;
+                while(x < xe);
+        b1->wds = n1 - 1;
+        Bfree(b);
+        return b1;
+        }
+
+ static int
+cmp
+#ifdef KR_headers
+        (a, b) Bigint *a, *b;
+#else
+        (Bigint *a, Bigint *b)
+#endif
+{
+        ULong *xa, *xa0, *xb, *xb0;
+        int i, j;
+
+        i = a->wds;
+        j = b->wds;
+#ifdef DEBUG
+        if (i > 1 && !a->x[i-1])
+                Bug("cmp called with a->x[a->wds-1] == 0");
+        if (j > 1 && !b->x[j-1])
+                Bug("cmp called with b->x[b->wds-1] == 0");
+#endif
+        if (i -= j)
+                return i;
+        xa0 = a->x;
+        xa = xa0 + j;
+        xb0 = b->x;
+        xb = xb0 + j;
+        for(;;) {
+                if (*--xa != *--xb)
+                        return *xa < *xb ? -1 : 1;
+                if (xa <= xa0)
+                        break;
+                }
+        return 0;
+        }
+
+ static Bigint *
+diff
+#ifdef KR_headers
+        (a, b) Bigint *a, *b;
+#else
+        (Bigint *a, Bigint *b)
+#endif
+{
+        Bigint *c;
+        int i, wa, wb;
+        ULong *xa, *xae, *xb, *xbe, *xc;
+#ifdef ULLong
+        ULLong borrow, y;
+#else
+        ULong borrow, y;
+#ifdef Pack_32
+        ULong z;
+#endif
+#endif
+
+        i = cmp(a,b);
+        if (!i) {
+                c = Balloc(0);
+                c->wds = 1;
+                c->x[0] = 0;
+                return c;
+                }
+        if (i < 0) {
+                c = a;
+                a = b;
+                b = c;
+                i = 1;
+                }
+        else
+                i = 0;
+        c = Balloc(a->k);
+        c->sign = i;
+        wa = a->wds;
+        xa = a->x;
+        xae = xa + wa;
+        wb = b->wds;
+        xb = b->x;
+        xbe = xb + wb;
+        xc = c->x;
+        borrow = 0;
+#ifdef ULLong
+        do {
+                y = (ULLong)*xa++ - *xb++ - borrow;
+                borrow = y >> 32 & (ULong)1;
+                *xc++ = y & FFFFFFFF;
+                }
+                while(xb < xbe);
+        while(xa < xae) {
+                y = *xa++ - borrow;
+                borrow = y >> 32 & (ULong)1;
+                *xc++ = y & FFFFFFFF;
+                }
+#else
+#ifdef Pack_32
+        do {
+                y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
+                borrow = (y & 0x10000) >> 16;
+                z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
+                borrow = (z & 0x10000) >> 16;
+                Storeinc(xc, z, y);
+                }
+                while(xb < xbe);
+        while(xa < xae) {
+                y = (*xa & 0xffff) - borrow;
+                borrow = (y & 0x10000) >> 16;
+                z = (*xa++ >> 16) - borrow;
+                borrow = (z & 0x10000) >> 16;
+                Storeinc(xc, z, y);
+                }
+#else
+        do {
+                y = *xa++ - *xb++ - borrow;
+                borrow = (y & 0x10000) >> 16;
+                *xc++ = y & 0xffff;
+                }
+                while(xb < xbe);
+        while(xa < xae) {
+                y = *xa++ - borrow;
+                borrow = (y & 0x10000) >> 16;
+                *xc++ = y & 0xffff;
+                }
+#endif
+#endif
+        while(!*--xc)
+                wa--;
+        c->wds = wa;
+        return c;
+        }
+
+ static double
+ulp
+#ifdef KR_headers
+        (x) double x;
+#else
+        (double x)
+#endif
+{
+        register Long L;
+        double a;
+
+        L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
+#ifndef Avoid_Underflow
+#ifndef Sudden_Underflow
+        if (L > 0) {
+#endif
+#endif
+#ifdef IBM
+                L |= Exp_msk1 >> 4;
+#endif
+                word0(a) = L;
+                word1(a) = 0;
+#ifndef Avoid_Underflow
+#ifndef Sudden_Underflow
+                }
+        else {
+                L = -L >> Exp_shift;
+                if (L < Exp_shift) {
+                        word0(a) = 0x80000 >> L;
+                        word1(a) = 0;
+                        }
+                else {
+                        word0(a) = 0;
+                        L -= Exp_shift;
+                        word1(a) = L >= 31 ? 1 : 1 << 31 - L;
+                        }
+                }
+#endif
+#endif
+        return dval(a);
+        }
+
+ static double
+b2d
+#ifdef KR_headers
+        (a, e) Bigint *a; int *e;
+#else
+        (Bigint *a, int *e)
+#endif
+{
+        ULong *xa, *xa0, w, y, z;
+        int k;
+        double d;
+#ifdef VAX
+        ULong d0, d1;
+#else
+#define d0 word0(d)
+#define d1 word1(d)
+#endif
+
+        xa0 = a->x;
+        xa = xa0 + a->wds;
+        y = *--xa;
+#ifdef DEBUG
+        if (!y) Bug("zero y in b2d");
+#endif
+        k = hi0bits(y);
+        *e = 32 - k;
+#ifdef Pack_32
+        if (k < Ebits) {
+                d0 = Exp_1 | y >> Ebits - k;
+                w = xa > xa0 ? *--xa : 0;
+                d1 = y << (32-Ebits) + k | w >> Ebits - k;
+                goto ret_d;
+                }
+        z = xa > xa0 ? *--xa : 0;
+        if (k -= Ebits) {
+                d0 = Exp_1 | y << k | z >> 32 - k;
+                y = xa > xa0 ? *--xa : 0;
+                d1 = z << k | y >> 32 - k;
+                }
+        else {
+                d0 = Exp_1 | y;
+                d1 = z;
+                }
+#else
+        if (k < Ebits + 16) {
+                z = xa > xa0 ? *--xa : 0;
+                d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
+                w = xa > xa0 ? *--xa : 0;
+                y = xa > xa0 ? *--xa : 0;
+                d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
+                goto ret_d;
+                }
+        z = xa > xa0 ? *--xa : 0;
+        w = xa > xa0 ? *--xa : 0;
+        k -= Ebits + 16;
+        d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
+        y = xa > xa0 ? *--xa : 0;
+        d1 = w << k + 16 | y << k;
+#endif
+ ret_d:
+#ifdef VAX
+        word0(d) = d0 >> 16 | d0 << 16;
+        word1(d) = d1 >> 16 | d1 << 16;
+#else
+#undef d0
+#undef d1
+#endif
+        return dval(d);
+        }
+
+ static Bigint *
+d2b
+#ifdef KR_headers
+        (d, e, bits) double d; int *e, *bits;
+#else
+        (double d, int *e, int *bits)
+#endif
+{
+        Bigint *b;
+        int de, k;
+        ULong *x, y, z;
+#ifndef Sudden_Underflow
+        int i;
+#endif
+#ifdef VAX
+        ULong d0, d1;
+        d0 = word0(d) >> 16 | word0(d) << 16;
+        d1 = word1(d) >> 16 | word1(d) << 16;
+#else
+#define d0 word0(d)
+#define d1 word1(d)
+#endif
+
+#ifdef Pack_32
+        b = Balloc(1);
+#else
+        b = Balloc(2);
+#endif
+        x = b->x;
+
+        z = d0 & Frac_mask;
+        d0 &= 0x7fffffff;       /* clear sign bit, which we ignore */
+#ifdef Sudden_Underflow
+        de = (int)(d0 >> Exp_shift);
+#ifndef IBM
+        z |= Exp_msk11;
+#endif
+#else
+        if (de = (int)(d0 >> Exp_shift))
+                z |= Exp_msk1;
+#endif
+#ifdef Pack_32
+        if (y = d1) {
+                if (k = lo0bits(&y)) {
+                        x[0] = y | z << 32 - k;
+                        z >>= k;
+                        }
+                else
+                        x[0] = y;
+#ifndef Sudden_Underflow
+                i =
+#endif
+                    b->wds = (x[1] = z) ? 2 : 1;
+                }
+        else {
+#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
+#ifdef KR_headers
+        (a, b) Bigint *a, *b;
+#else
+        (Bigint *a, Bigint *b)
+#endif
+{
+        double da, db;
+        int k, ka, kb;
+
+        dval(da) = b2d(a, &ka);
+        dval(db) = b2d(b, &kb);
+#ifdef Pack_32
+        k = ka - kb + 32*(a->wds - b->wds);
+#else
+        k = ka - kb + 16*(a->wds - b->wds);
+#endif
+#ifdef IBM
+        if (k > 0) {
+                word0(da) += (k >> 2)*Exp_msk1;
+                if (k &= 3)
+                        dval(da) *= 1 << k;
+                }
+        else {
+                k = -k;
+                word0(db) += (k >> 2)*Exp_msk1;
+                if (k &= 3)
+                        dval(db) *= 1 << k;
+                }
+#else
+        if (k > 0)
+                word0(da) += k*Exp_msk1;
+        else {
+                k = -k;
+                word0(db) += k*Exp_msk1;
+                }
+#endif
+        return dval(da) / dval(db);
+        }
+
+ static CONST double
+tens[] = {
+                1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
+                1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
+                1e20, 1e21, 1e22
+#ifdef VAX
+                , 1e23, 1e24
+#endif
+                };
+
+ static CONST double
+#ifdef IEEE_Arith
+bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
+static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
+#ifdef Avoid_Underflow
+                9007199254740992.*9007199254740992.e-256
+                /* = 2^106 * 1e-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
+
+#ifdef INFNAN_CHECK
+
+#ifndef NAN_WORD0
+#define NAN_WORD0 0x7ff80000
+#endif
+
+#ifndef NAN_WORD1
+#define NAN_WORD1 0
+#endif
+
+ static int
+match
+#ifdef KR_headers
+        (sp, t) char **sp, *t;
+#else
+        (CONST char **sp, char *t)
+#endif
+{
+        int c, d;
+        CONST char *s = *sp;
+
+        while(d = *t++) {
+                if ((c = *++s) >= 'A' && c <= 'Z')
+                        c += 'a' - 'A';
+                if (c != d)
+                        return 0;
+                }
+        *sp = s + 1;
+        return 1;
+        }
+
+#ifndef No_Hex_NaN
+ static void
+hexnan
+#ifdef KR_headers
+        (rvp, sp) double *rvp; CONST char **sp;
+#else
+        (double *rvp, CONST char **sp)
+#endif
+{
+        ULong c, x[2];
+        CONST char *s;
+        int havedig, udx0, xshift;
+
+        x[0] = x[1] = 0;
+        havedig = xshift = 0;
+        udx0 = 1;
+        s = *sp;
+        /* 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 (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;
+                        }
+#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 */
+
+ double
+strtod
+#ifdef KR_headers
+        (s00, se) CONST char *s00; char **se;
+#else
+        (CONST char *s00, char **se)
+#endif
+{
+#ifdef Avoid_Underflow
+        int scale;
+#endif
+        int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
+                 e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
+        CONST char *s, *s0, *s1;
+        double aadj, aadj1, adj, rv, rv0;
+        Long L;
+        ULong y, z;
+        Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
+#ifdef SET_INEXACT
+        int inexact, oldinexact;
+#endif
+#ifdef Honor_FLT_ROUNDS /*{*/
+        int Rounding;
+#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 /*}*/
+#ifdef USE_LOCALE
+        CONST char *s2;
+#endif
+
+        sign = nz0 = nz = 0;
+        dval(rv) = 0.;
+        for(s = s00;;s++) switch(*s) {
+                case '-':
+                        sign = 1;
+                        /* no break */
+                case '+':
+                        if (*++s)
+                                goto break2;
+                        /* no break */
+                case 0:
+                        goto ret0;
+                case '\t':
+                case '\n':
+                case '\v':
+                case '\f':
+                case '\r':
+                case ' ':
+                        continue;
+                default:
+                        goto break2;
+                }
+ break2:
+        if (*s == '0') {
+                nz0 = 1;
+                while(*++s == '0') ;
+                if (!*s)
+                        goto ret;
+                }
+        s0 = s;
+        y = z = 0;
+        for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
+                if (nd < 9)
+                        y = 10*y + c - '0';
+                else if (nd < 16)
+                        z = 10*z + c - '0';
+        nd0 = nd;
+#ifdef USE_LOCALE
+        s1 = localeconv()->decimal_point;
+        if (c == *s1) {
+                c = '.';
+                if (*++s1) {
+                        s2 = s;
+                        for(;;) {
+                                if (*++s2 != *s1) {
+                                        c = 0;
+                                        break;
+                                        }
+                                if (!*++s1) {
+                                        s = s2;
+                                        break;
+                                        }
+                                }
+                        }
+                }
+#endif
+        if (c == '.') {
+                c = *++s;
+                if (!nd) {
+                        for(; c == '0'; c = *++s)
+                                nz++;
+                        if (c > '0' && c <= '9') {
+                                s0 = s;
+                                nf += nz;
+                                nz = 0;
+                                goto have_dig;
+                                }
+                        goto dig_done;
+                        }
+                for(; c >= '0' && c <= '9'; c = *++s) {
+ have_dig:
+                        nz++;
+                        if (c -= '0') {
+                                nf += nz;
+                                for(i = 1; i < nz; i++)
+                                        if (nd++ < 9)
+                                                y *= 10;
+                                        else if (nd <= DBL_DIG + 1)
+                                                z *= 10;
+                                if (nd++ < 9)
+                                        y = 10*y + c;
+                                else if (nd <= DBL_DIG + 1)
+                                        z = 10*z + c;
+                                nz = 0;
+                                }
+                        }
+                }
+ dig_done:
+        e = 0;
+        if (c == 'e' || c == 'E') {
+                if (!nd && !nz && !nz0) {
+                        goto ret0;
+                        }
+                s00 = s;
+                esign = 0;
+                switch(c = *++s) {
+                        case '-':
+                                esign = 1;
+                        case '+':
+                                c = *++s;
+                        }
+                if (c >= '0' && c <= '9') {
+                        while(c == '0')
+                                c = *++s;
+                        if (c > '0' && c <= '9') {
+                                L = c - '0';
+                                s1 = s;
+                                while((c = *++s) >= '0' && c <= '9')
+                                        L = 10*L + c - '0';
+                                if (s - s1 > 8 || L > 19999)
+                                        /* Avoid confusion from exponents
+                                         * so large that e might overflow.
+                                         */
+                                        e = 19999; /* safe for 16 bit ints */
+                                else
+                                        e = (int)L;
+                                if (esign)
+                                        e = -e;
+                                }
+                        else
+                                e = 0;
+                        }
+                else
+                        s = s00;
+                }
+        if (!nd) {
+                if (!nz && !nz0) {
+#ifdef INFNAN_CHECK
+                        /* Check for Nan and Infinity */
+                        switch(c) {
+                          case 'i':
+                          case 'I':
+                                if (match(&s,"nf")) {
+                                        --s;
+                                        if (!match(&s,"inity"))
+                                                ++s;
+                                        word0(rv) = 0x7ff00000;
+                                        word1(rv) = 0;
+                                        goto ret;
+                                        }
+                                break;
+                          case 'n':
+                          case 'N':
+                                if (match(&s, "an")) {
+                                        word0(rv) = NAN_WORD0;
+                                        word1(rv) = NAN_WORD1;
+#ifndef No_Hex_NaN
+                                        if (*s == '(') /*)*/
+                                                hexnan(&rv, &s);
+#endif
+                                        goto ret;
+                                        }
+                          }
+#endif /* INFNAN_CHECK */
+ ret0:
+                        s = s00;
+                        sign = 0;
+                        }
+                goto ret;
+                }
+        e1 = e -= nf;
+
+        /* Now we have nd0 digits, starting at s0, followed by a
+         * decimal point, followed by nd-nd0 digits.  The number we're
+         * after is the integer represented by those digits times
+         * 10**e */
+
+        if (!nd0)
+                nd0 = nd;
+        k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
+        dval(rv) = y;
+        if (k > 9) {
+#ifdef SET_INEXACT
+                if (k > DBL_DIG)
+                        oldinexact = get_inexact();
+#endif
+                dval(rv) = tens[k - 9] * dval(rv) + z;
+                }
+        bd0 = 0;
+        if (nd <= DBL_DIG
+#ifndef RND_PRODQUOT
+#ifndef Honor_FLT_ROUNDS
+                && Flt_Rounds == 1
+#endif
+#endif
+                        ) {
+                if (!e)
+                        goto ret;
+                if (e > 0) {
+                        if (e <= Ten_pmax) {
+#ifdef VAX
+                                goto vax_ovfl_check;
+#else
+#ifdef Honor_FLT_ROUNDS
+                                /* round correctly FLT_ROUNDS = 2 or 3 */
+                                if (sign) {
+                                        rv = -rv;
+                                        sign = 0;
+                                        }
+#endif
+                                /* rv = */ rounded_product(dval(rv), tens[e]);
+                                goto ret;
+#endif
+                                }
+                        i = DBL_DIG - nd;
+                        if (e <= Ten_pmax + i) {
+                                /* A fancier test would sometimes let us do
+                                 * this for larger i values.
+                                 */
+#ifdef Honor_FLT_ROUNDS
+                                /* round correctly FLT_ROUNDS = 2 or 3 */
+                                if (sign) {
+                                        rv = -rv;
+                                        sign = 0;
+                                        }
+#endif
+                                e -= i;
+                                dval(rv) *= tens[i];
+#ifdef VAX
+                                /* VAX exponent range is so narrow we must
+                                 * worry about overflow here...
+                                 */
+ vax_ovfl_check:
+                                word0(rv) -= P*Exp_msk1;
+                                /* rv = */ rounded_product(dval(rv), tens[e]);
+                                if ((word0(rv) & Exp_mask)
+                                 > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
+                                        goto ovfl;
+                                word0(rv) += P*Exp_msk1;
+#else
+                                /* rv = */ rounded_product(dval(rv), tens[e]);
+#endif
+                                goto ret;
+                                }
+                        }
+#ifndef Inaccurate_Divide
+                else if (e >= -Ten_pmax) {
+#ifdef Honor_FLT_ROUNDS
+                        /* round correctly FLT_ROUNDS = 2 or 3 */
+                        if (sign) {
+                                rv = -rv;
+                                sign = 0;
+                                }
+#endif
+                        /* rv = */ rounded_quotient(dval(rv), tens[-e]);
+                        goto ret;
+                        }
+#endif
+                }
+        e1 += nd - k;
+
+#ifdef IEEE_Arith
+#ifdef SET_INEXACT
+        inexact = 1;
+        if (k <= DBL_DIG)
+                oldinexact = get_inexact();
+#endif
+#ifdef Avoid_Underflow
+        scale = 0;
+#endif
+#ifdef Honor_FLT_ROUNDS
+        if (Rounding >= 2) {
+                if (sign)
+                        Rounding = Rounding == 2 ? 0 : 2;
+                else
+                        if (Rounding != 2)
+                                Rounding = 0;
+                }
+#endif
+#endif /*IEEE_Arith*/
+
+        /* Get starting approximation = rv * 10**e1 */
+
+        if (e1 > 0) {
+                if (i = e1 & 15)
+                        dval(rv) *= tens[i];
+                if (e1 &= ~15) {
+                        if (e1 > DBL_MAX_10_EXP) {
+ ovfl:
+#ifndef NO_ERRNO
+                                errno = ERANGE;
+#endif
+                                /* Can't trust HUGE_VAL */
+#ifdef IEEE_Arith
+#ifdef Honor_FLT_ROUNDS
+                                switch(Rounding) {
+                                  case 0: /* toward 0 */
+                                  case 3: /* toward -infinity */
+                                        word0(rv) = Big0;
+                                        word1(rv) = Big1;
+                                        break;
+                                  default:
+                                        word0(rv) = Exp_mask;
+                                        word1(rv) = 0;
+                                  }
+#else /*Honor_FLT_ROUNDS*/
+                                word0(rv) = Exp_mask;
+                                word1(rv) = 0;
+#endif /*Honor_FLT_ROUNDS*/
+#ifdef SET_INEXACT
+                                /* set overflow bit */
+                                dval(rv0) = 1e300;
+                                dval(rv0) *= dval(rv0);
+#endif
+#else /*IEEE_Arith*/
+                                word0(rv) = Big0;
+                                word1(rv) = Big1;
+#endif /*IEEE_Arith*/
+                                if (bd0)
+                                        goto retfree;
+                                goto ret;
+                                }
+                        e1 >>= 4;
+                        for(j = 0; e1 > 1; j++, e1 >>= 1)
+                                if (e1 & 1)
+                                        dval(rv) *= bigtens[j];
+                /* The last multiplication could overflow. */
+                        word0(rv) -= P*Exp_msk1;
+                        dval(rv) *= bigtens[j];
+                        if ((z = word0(rv) & Exp_mask)
+                         > Exp_msk1*(DBL_MAX_EXP+Bias-P))
+                                goto ovfl;
+                        if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
+                                /* set to largest number */
+                                /* (Can't trust DBL_MAX) */
+                                word0(rv) = Big0;
+                                word1(rv) = Big1;
+                                }
+                        else
+                                word0(rv) += P*Exp_msk1;
+                        }
+                }
+        else if (e1 < 0) {
+                e1 = -e1;
+                if (i = e1 & 15)
+                        dval(rv) /= tens[i];
+                if (e1 >>= 4) {
+                        if (e1 >= 1 << n_bigtens)
+                                goto undfl;
+#ifdef Avoid_Underflow
+                        if (e1 & Scale_Bit)
+                                scale = 2*P;
+                        for(j = 0; e1 > 0; j++, e1 >>= 1)
+                                if (e1 & 1)
+                                        dval(rv) *= tinytens[j];
+                        if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
+                                                >> Exp_shift)) > 0) {
+                                /* scaled rv is denormal; 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
+                                        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) {
+                                if (word0(rv) == Big0 && word1(rv) == Big1)
+                                        goto ovfl;
+                                dval(rv) += adj;
+                                }
+                        else
+                                dval(rv) -= adj;
+                        goto cont;
+                        }
+#endif /*Honor_FLT_ROUNDS*/
+
+                if (i < 0) {
+                        /* Error is less than half an ulp -- check for
+                         * special case of mantissa a power of two.
+                         */
+                        if (dsign || word1(rv) || word0(rv) & Bndry_mask
+#ifdef IEEE_Arith
+#ifdef Avoid_Underflow
+                         || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
+#else
+                         || (word0(rv) & Exp_mask) <= Exp_msk1
+#endif
+#endif
+                                ) {
+#ifdef SET_INEXACT
+                                if (!delta->x[0] && delta->wds <= 1)
+                                        inexact = 0;
+#endif
+                                break;
+                                }
+                        if (!delta->x[0] && delta->wds <= 1) {
+                                /* exact result */
+#ifdef SET_INEXACT
+                                inexact = 0;
+#endif
+                                break;
+                                }
+                        delta = lshift(delta,Log2P);
+                        if (cmp(delta, bs) > 0)
+                                goto drop_down;
+                        break;
+                        }
+                if (i == 0) {
+                        /* exactly half-way between */
+                        if (dsign) {
+                                if ((word0(rv) & Bndry_mask1) == Bndry_mask1
+                                 &&  word1(rv) == (
+#ifdef Avoid_Underflow
+                        (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
+                ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
+#endif
+                                                   0xffffffff)) {
+                                        /*boundary case -- increment exponent*/
+                                        word0(rv) = (word0(rv) & Exp_mask)
+                                                + Exp_msk1
+#ifdef IBM
+                                                | Exp_msk1 >> 4
+#endif
+                                                ;
+                                        word1(rv) = 0;
+#ifdef Avoid_Underflow
+                                        dsign = 0;
+#endif
+                                        break;
+                                        }
+                                }
+                        else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
+ drop_down:
+                                /* boundary case -- decrement exponent */
+#ifdef Sudden_Underflow /*{{*/
+                                L = word0(rv) & Exp_mask;
+#ifdef IBM
+                                if (L <  Exp_msk1)
+#else
+#ifdef Avoid_Underflow
+                                if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
+#else
+                                if (L <= Exp_msk1)
+#endif /*Avoid_Underflow*/
+#endif /*IBM*/
+                                        goto undfl;
+                                L -= Exp_msk1;
+#else /*Sudden_Underflow}{*/
+#ifdef Avoid_Underflow
+                                if (scale) {
+                                        L = word0(rv) & Exp_mask;
+                                        if (L <= (2*P+1)*Exp_msk1) {
+                                                if (L > (P+2)*Exp_msk1)
+                                                        /* round even ==> */
+                                                        /* accept rv */
+                                                        break;
+                                                /* rv = smallest denormal */
+                                                goto undfl;
+                                                }
+                                        }
+#endif /*Avoid_Underflow*/
+                                L = (word0(rv) & Exp_mask) - Exp_msk1;
+#endif /*Sudden_Underflow}}*/
+                                word0(rv) = L | Bndry_mask1;
+                                word1(rv) = 0xffffffff;
+#ifdef IBM
+                                goto cont;
+#else
+                                break;
+#endif
+                                }
+#ifndef ROUND_BIASED
+                        if (!(word1(rv) & LSB))
+                                break;
+#endif
+                        if (dsign)
+                                dval(rv) += ulp(dval(rv));
+#ifndef ROUND_BIASED
+                        else {
+                                dval(rv) -= ulp(dval(rv));
+#ifndef Sudden_Underflow
+                                if (!dval(rv))
+                                        goto undfl;
+#endif
+                                }
+#ifdef Avoid_Underflow
+                        dsign = 1 - dsign;
+#endif
+#endif
+                        break;
+                        }
+                if ((aadj = ratio(delta, bs)) <= 2.) {
+                        if (dsign)
+                                aadj = aadj1 = 1.;
+                        else if (word1(rv) || word0(rv) & Bndry_mask) {
+#ifndef Sudden_Underflow
+                                if (word1(rv) == Tiny1 && !word0(rv))
+                                        goto undfl;
+#endif
+                                aadj = 1.;
+                                aadj1 = -1.;
+                                }
+                        else {
+                                /* special case -- power of FLT_RADIX to be */
+                                /* rounded down... */
+
+                                if (aadj < 2./FLT_RADIX)
+                                        aadj = 1./FLT_RADIX;
+                                else
+                                        aadj *= 0.5;
+                                aadj1 = -aadj;
+                                }
+                        }
+                else {
+                        aadj *= 0.5;
+                        aadj1 = dsign ? aadj : -aadj;
+#ifdef Check_FLT_ROUNDS
+                        switch(Rounding) {
+                                case 2: /* towards +infinity */
+                                        aadj1 -= 0.5;
+                                        break;
+                                case 0: /* towards 0 */
+                                case 3: /* towards -infinity */
+                                        aadj1 += 0.5;
+                                }
+#else
+                        if (Flt_Rounds == 0)
+                                aadj1 += 0.5;
+#endif /*Check_FLT_ROUNDS*/
+                        }
+                y = word0(rv) & Exp_mask;
+
+                /* Check for overflow */
+
+                if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
+                        dval(rv0) = dval(rv);
+                        word0(rv) -= P*Exp_msk1;
+                        adj = aadj1 * ulp(dval(rv));
+                        dval(rv) += adj;
+                        if ((word0(rv) & Exp_mask) >=
+                                        Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
+                                if (word0(rv0) == Big0 && word1(rv0) == Big1)
+                                        goto ovfl;
+                                word0(rv) = Big0;
+                                word1(rv) = Big1;
+                                goto cont;
+                                }
+                        else
+                                word0(rv) += P*Exp_msk1;
+                        }
+                else {
+#ifdef Avoid_Underflow
+                        if (scale && y <= 2*P*Exp_msk1) {
+                                if (aadj <= 0x7fffffff) {
+                                        if ((z = aadj) <= 0)
+                                                z = 1;
+                                        aadj = z;
+                                        aadj1 = dsign ? aadj : -aadj;
+                                        }
+                                word0(aadj1) += (2*P+1)*Exp_msk1 - y;
+                                }
+                        adj = aadj1 * ulp(dval(rv));
+                        dval(rv) += adj;
+#else
+#ifdef Sudden_Underflow
+                        if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
+                                dval(rv0) = dval(rv);
+                                word0(rv) += P*Exp_msk1;
+                                adj = aadj1 * ulp(dval(rv));
+                                dval(rv) += adj;
+#ifdef IBM
+                                if ((word0(rv) & Exp_mask) <  P*Exp_msk1)
+#else
+                                if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
+#endif
+                                        {
+                                        if (word0(rv0) == Tiny0
+                                         && word1(rv0) == Tiny1)
+                                                goto undfl;
+                                        word0(rv) = Tiny0;
+                                        word1(rv) = Tiny1;
+                                        goto cont;
+                                        }
+                                else
+                                        word0(rv) -= P*Exp_msk1;
+                                }
+                        else {
+                                adj = aadj1 * ulp(dval(rv));
+                                dval(rv) += adj;
+                                }
+#else /*Sudden_Underflow*/
+                        /* Compute adj so that the IEEE rounding rules will
+                         * correctly round rv + adj in some half-way cases.
+                         * If rv * ulp(rv) is denormalized (i.e.,
+                         * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
+                         * trouble from bits lost to denormalization;
+                         * example: 1.2e-307 .
+                         */
+                        if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
+                                aadj1 = (double)(int)(aadj + 0.5);
+                                if (!dsign)
+                                        aadj1 = -aadj1;
+                                }
+                        adj = aadj1 * ulp(dval(rv));
+                        dval(rv) += adj;
+#endif /*Sudden_Underflow*/
+#endif /*Avoid_Underflow*/
+                        }
+                z = word0(rv) & Exp_mask;
+#ifndef SET_INEXACT
+#ifdef Avoid_Underflow
+                if (!scale)
+#endif
+                if (y == z) {
+                        /* Can we stop now? */
+                        L = (Long)aadj;
+                        aadj -= L;
+                        /* The tolerances below are conservative. */
+                        if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
+                                if (aadj < .4999999 || aadj > .5000001)
+                                        break;
+                                }
+                        else if (aadj < .4999999/FLT_RADIX)
+                                break;
+                        }
+#endif
+ cont:
+                Bfree(bb);
+                Bfree(bd);
+                Bfree(bs);
+                Bfree(delta);
+                }
+#ifdef SET_INEXACT
+        if (inexact) {
+                if (!oldinexact) {
+                        word0(rv0) = Exp_1 + (70 << Exp_shift);
+                        word1(rv0) = 0;
+                        dval(rv0) += 1.;
+                        }
+                }
+        else if (!oldinexact)
+                clear_inexact();
+#endif
+#ifdef Avoid_Underflow
+        if (scale) {
+                word0(rv0) = Exp_1 - 2*P*Exp_msk1;
+                word1(rv0) = 0;
+                dval(rv) *= dval(rv0);
+#ifndef NO_ERRNO
+                /* try to avoid the bug of testing an 8087 register value */
+#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 (inexact && !(word0(rv) & Exp_mask)) {
+                /* set underflow bit */
+                dval(rv0) = 1e-300;
+                dval(rv0) *= dval(rv0);
+                }
+#endif
+ retfree:
+        Bfree(bb);
+        Bfree(bd);
+        Bfree(bs);
+        Bfree(bd0);
+        Bfree(delta);
+ ret:
+        if (se)
+                *se = (char *)s;
+        return sign ? -dval(rv) : dval(rv);
+        }
+
+ static int
+quorem
+#ifdef KR_headers
+        (b, S) Bigint *b, *S;
+#else
+        (Bigint *b, Bigint *S)
+#endif
+{
+        int n;
+        ULong *bx, *bxe, q, *sx, *sxe;
+#ifdef ULLong
+        ULLong borrow, carry, y, ys;
+#else
+        ULong borrow, carry, y, ys;
+#ifdef Pack_32
+        ULong si, z, zs;
+#endif
+#endif
+
+        n = S->wds;
+#ifdef DEBUG
+        /*debug*/ if (b->wds > n)
+        /*debug*/       Bug("oversize b in quorem");
+#endif
+        if (b->wds < n)
+                return 0;
+        sx = S->x;
+        sxe = sx + --n;
+        bx = b->x;
+        bxe = bx + n;
+        q = *bxe / (*sxe + 1);  /* ensure q <= true quotient */
+#ifdef DEBUG
+        /*debug*/ if (q > 9)
+        /*debug*/       Bug("oversized quotient in quorem");
+#endif
+        if (q) {
+                borrow = 0;
+                carry = 0;
+                do {
+#ifdef ULLong
+                        ys = *sx++ * (ULLong)q + carry;
+                        carry = ys >> 32;
+                        y = *bx - (ys & FFFFFFFF) - borrow;
+                        borrow = y >> 32 & (ULong)1;
+                        *bx++ = y & FFFFFFFF;
+#else
+#ifdef Pack_32
+                        si = *sx++;
+                        ys = (si & 0xffff) * q + carry;
+                        zs = (si >> 16) * q + (ys >> 16);
+                        carry = zs >> 16;
+                        y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
+                        borrow = (y & 0x10000) >> 16;
+                        z = (*bx >> 16) - (zs & 0xffff) - borrow;
+                        borrow = (z & 0x10000) >> 16;
+                        Storeinc(bx, z, y);
+#else
+                        ys = *sx++ * q + carry;
+                        carry = ys >> 16;
+                        y = *bx - (ys & 0xffff) - borrow;
+                        borrow = (y & 0x10000) >> 16;
+                        *bx++ = y & 0xffff;
+#endif
+#endif
+                        }
+                        while(sx <= sxe);
+                if (!*bxe) {
+                        bx = b->x;
+                        while(--bxe > bx && !*bxe)
+                                --n;
+                        b->wds = n;
+                        }
+                }
+        if (cmp(b, S) >= 0) {
+                q++;
+                borrow = 0;
+                carry = 0;
+                bx = b->x;
+                sx = S->x;
+                do {
+#ifdef ULLong
+                        ys = *sx++ + carry;
+                        carry = ys >> 32;
+                        y = *bx - (ys & FFFFFFFF) - borrow;
+                        borrow = y >> 32 & (ULong)1;
+                        *bx++ = y & FFFFFFFF;
+#else
+#ifdef Pack_32
+                        si = *sx++;
+                        ys = (si & 0xffff) + carry;
+                        zs = (si >> 16) + (ys >> 16);
+                        carry = zs >> 16;
+                        y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
+                        borrow = (y & 0x10000) >> 16;
+                        z = (*bx >> 16) - (zs & 0xffff) - borrow;
+                        borrow = (z & 0x10000) >> 16;
+                        Storeinc(bx, z, y);
+#else
+                        ys = *sx++ + carry;
+                        carry = ys >> 16;
+                        y = *bx - (ys & 0xffff) - borrow;
+                        borrow = (y & 0x10000) >> 16;
+                        *bx++ = y & 0xffff;
+#endif
+#endif
+                        }
+                        while(sx <= sxe);
+                bx = b->x;
+                bxe = bx + n;
+                if (!*bxe) {
+                        while(--bxe > bx && !*bxe)
+                                --n;
+                        b->wds = n;
+                        }
+                }
+        return q;
+        }
+
+#ifndef MULTIPLE_THREADS
+ static char *dtoa_result;
+#endif
+
+ static char *
+#ifdef KR_headers
+rv_alloc(i) int i;
+#else
+rv_alloc(int i)
+#endif
+{
+        int j, k, *r;
+
+        j = sizeof(ULong);
+        for(k = 0;
+                sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= i;
+                j <<= 1)
+                        k++;
+        r = (int*)Balloc(k);
+        *r = k;
+        return
+#ifndef MULTIPLE_THREADS
+        dtoa_result =
+#endif
+                (char *)(r+1);
+        }
+
+ static char *
+#ifdef KR_headers
+nrv_alloc(s, rve, n) char *s, **rve; int n;
+#else
+nrv_alloc(char *s, char **rve, int n)
+#endif
+{
+        char *rv, *t;
+
+        t = rv = rv_alloc(n);
+        while(*t = *s++) t++;
+        if (rve)
+                *rve = t;
+        return rv;
+        }
+
+/* freedtoa(s) must be used to free values s returned by dtoa
+ * when MULTIPLE_THREADS is #defined.  It should be used in all cases,
+ * but for consistency with earlier versions of dtoa, it is optional
+ * when MULTIPLE_THREADS is not defined.
+ */
+
+ void
+#ifdef KR_headers
+freedtoa(s) char *s;
+#else
+freedtoa(char *s)
+#endif
+{
+        Bigint *b = (Bigint *)((int *)s - 1);
+        b->maxwds = 1 << (b->k = *(int*)b);
+        Bfree(b);
+#ifndef MULTIPLE_THREADS
+        if (s == dtoa_result)
+                dtoa_result = 0;
+#endif
+        }
+
+/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
+ *
+ * Inspired by "How to Print Floating-Point Numbers Accurately" by
+ * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
+ *
+ * Modifications:
+ *      1. Rather than iterating, we use a simple numeric overestimate
+ *         to determine k = floor(log10(d)).  We scale relevant
+ *         quantities using O(log2(k)) rather than O(k) multiplications.
+ *      2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
+ *         try to generate digits strictly left to right.  Instead, we
+ *         compute with fewer bits and propagate the carry if necessary
+ *         when rounding the final digit up.  This is often faster.
+ *      3. Under the assumption that input will be rounded nearest,
+ *         mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
+ *         That is, we allow equality in stopping tests when the
+ *         round-nearest rule will give the same floating-point value
+ *         as would satisfaction of the stopping test with strict
+ *         inequality.
+ *      4. We remove common factors of powers of 2 from relevant
+ *         quantities.
+ *      5. When converting floating-point integers less than 1e16,
+ *         we use floating-point arithmetic rather than resorting
+ *         to multiple-precision integers.
+ *      6. When asked to produce fewer than 15 digits, we first try
+ *         to get by with floating-point arithmetic; we resort to
+ *         multiple-precision integer arithmetic only if we cannot
+ *         guarantee that the floating-point calculation has given
+ *         the correctly rounded result.  For k requested digits and
+ *         "uniformly" distributed input, the probability is
+ *         something like 10^(k-15) that we must resort to the Long
+ *         calculation.
+ */
+
+ char *
+dtoa
+#ifdef KR_headers
+        (d, mode, ndigits, decpt, sign, rve)
+        double d; int mode, ndigits, *decpt, *sign; char **rve;
+#else
+        (double d, int mode, int ndigits, int *decpt, int *sign, char **rve)
+#endif
+{
+ /*     Arguments ndigits, decpt, sign are similar to those
+        of ecvt and fcvt; trailing zeros are suppressed from
+        the returned string.  If not null, *rve is set to point
+        to the end of the return value.  If d is +-Infinity or NaN,
+        then *decpt is set to 9999.
+
+        mode:
+                0 ==> shortest string that yields d when read in
+                        and rounded to nearest.
+                1 ==> like 0, but with Steele & White stopping rule;
+                        e.g. with IEEE P754 arithmetic , mode 0 gives
+                        1e23 whereas mode 1 gives 9.999999999999999e22.
+                2 ==> max(1,ndigits) significant digits.  This gives a
+                        return value similar to that of ecvt, except
+                        that trailing zeros are suppressed.
+                3 ==> through ndigits past the decimal point.  This
+                        gives a return value similar to that from fcvt,
+                        except that trailing zeros are suppressed, and
+                        ndigits can be negative.
+                4,5 ==> similar to 2 and 3, respectively, but (in
+                        round-nearest mode) with the tests of mode 0 to
+                        possibly return a shorter string that rounds to d.
+                        With IEEE arithmetic and compilation with
+                        -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
+                        as modes 2 and 3 when FLT_ROUNDS != 1.
+                6-9 ==> Debugging modes similar to mode - 4:  don't try
+                        fast floating-point estimate (if applicable).
+
+                Values of mode other than 0-9 are treated as mode 0.
+
+                Sufficient space is allocated to the return value
+                to hold the suppressed trailing zeros.
+        */
+
+        int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
+                j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
+                spec_case, try_quick;
+        Long L;
+#ifndef Sudden_Underflow
+        int denorm;
+        ULong x;
+#endif
+        Bigint *b, *b1, *delta, *mlo, *mhi, *S;
+        double d2, ds, eps;
+        char *s, *s0;
+#ifdef 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
+
+        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 >= 2) {
+                if (*sign)
+                        Rounding = Rounding == 2 ? 0 : 2;
+                else
+                        if (Rounding != 2)
+                                Rounding = 0;
+                }
+#endif
+
+        b = d2b(dval(d), &be, &bbits);
+#ifdef Sudden_Underflow
+        i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
+#else
+        if (i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1))) {
+#endif
+                dval(d2) = dval(d);
+                word0(d2) &= Frac_mask1;
+                word0(d2) |= Exp_11;
+#ifdef IBM
+                if (j = 11 - hi0bits(word0(d2) & Frac_mask))
+                        dval(d2) /= 1 << j;
+#endif
+
+                /* log(x)       ~=~ log(1.5) + (x-1.5)/1.5
+                 * log10(x)      =  log(x) / log(10)
+                 *              ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
+                 * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
+                 *
+                 * This suggests computing an approximation k to log10(d) by
+                 *
+                 * k = (i - Bias)*0.301029995663981
+                 *      + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
+                 *
+                 * We want k to be too large rather than too small.
+                 * The error in the first-order Taylor series approximation
+                 * is in our favor, so we just round up the constant enough
+                 * to compensate for any error in the multiplication of
+                 * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
+                 * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
+                 * adding 1e-13 to the constant term more than suffices.
+                 * Hence we adjust the constant term to 0.1760912590558.
+                 * (We could get a more accurate k by invoking log10,
+                 *  but this is probably not worthwhile.)
+                 */
+
+                i -= Bias;
+#ifdef IBM
+                i <<= 2;
+                i += j;
+#endif
+#ifndef Sudden_Underflow
+                denorm = 0;
+                }
+        else {
+                /* d is denormalized */
+
+                i = bbits + be + (Bias + (P-1) - 1);
+                x = i > 32  ? word0(d) << 64 - i | word1(d) >> i - 32
+                            : word1(d) << 32 - i;
+                dval(d2) = x;
+                word0(d2) -= 31*Exp_msk1; /* adjust exponent */
+                i -= (Bias + (P-1) - 1) + 1;
+                denorm = 1;
+                }
+#endif
+        ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
+        k = (int)ds;
+        if (ds < 0. && ds != k)
+                k--;    /* want k = floor(ds) */
+        k_check = 1;
+        if (k >= 0 && k <= Ten_pmax) {
+                if (dval(d) < tens[k])
+                        k--;
+                k_check = 0;
+                }
+        j = bbits - i - 1;
+        if (j >= 0) {
+                b2 = 0;
+                s2 = j;
+                }
+        else {
+                b2 = -j;
+                s2 = 0;
+                }
+        if (k >= 0) {
+                b5 = 0;
+                s5 = k;
+                s2 += k;
+                }
+        else {
+                b2 -= k;
+                b5 = -k;
+                s5 = 0;
+                }
+        if (mode < 0 || mode > 9)
+                mode = 0;
+
+#ifndef SET_INEXACT
+#ifdef Check_FLT_ROUNDS
+        try_quick = Rounding == 1;
+#else
+        try_quick = 1;
+#endif
+#endif /*SET_INEXACT*/
+
+        if (mode > 5) {
+                mode -= 4;
+                try_quick = 0;
+                }
+        leftright = 1;
+        switch(mode) {
+                case 0:
+                case 1:
+                        ilim = ilim1 = -1;
+                        i = 18;
+                        ndigits = 0;
+                        break;
+                case 2:
+                        leftright = 0;
+                        /* no break */
+                case 4:
+                        if (ndigits <= 0)
+                                ndigits = 1;
+                        ilim = ilim1 = i = ndigits;
+                        break;
+                case 3:
+                        leftright = 0;
+                        /* no break */
+                case 5:
+                        i = ndigits + k + 1;
+                        ilim = i;
+                        ilim1 = i - 1;
+                        if (i <= 0)
+                                i = 1;
+                }
+        s = s0 = rv_alloc(i);
+
+#ifdef Honor_FLT_ROUNDS
+        if (mode > 1 && Rounding != 1)
+                leftright = 0;
+#endif
+
+        if (ilim >= 0 && ilim <= Quick_max && try_quick) {
+
+                /* Try to get by with floating-point arithmetic. */
+
+                i = 0;
+                dval(d2) = dval(d);
+                k0 = k;
+                ilim0 = ilim;
+                ieps = 2; /* conservative */
+                if (k > 0) {
+                        ds = tens[k&0xf];
+                        j = k >> 4;
+                        if (j & Bletch) {
+                                /* prevent overflows */
+                                j &= Bletch - 1;
+                                dval(d) /= bigtens[n_bigtens-1];
+                                ieps++;
+                                }
+                        for(; j; j >>= 1, i++)
+                                if (j & 1) {
+                                        ieps++;
+                                        ds *= bigtens[i];
+                                        }
+                        dval(d) /= ds;
+                        }
+                else if (j1 = -k) {
+                        dval(d) *= tens[j1 & 0xf];
+                        for(j = j1 >> 4; j; j >>= 1, i++)
+                                if (j & 1) {
+                                        ieps++;
+                                        dval(d) *= bigtens[i];
+                                        }
+                        }
+                if (k_check && dval(d) < 1. && ilim > 0) {
+                        if (ilim1 <= 0)
+                                goto fast_failed;
+                        ilim = ilim1;
+                        k--;
+                        dval(d) *= 10.;
+                        ieps++;
+                        }
+                dval(eps) = ieps*dval(d) + 7.;
+                word0(eps) -= (P-1)*Exp_msk1;
+                if (ilim == 0) {
+                        S = mhi = 0;
+                        dval(d) -= 5.;
+                        if (dval(d) > dval(eps))
+                                goto one_digit;
+                        if (dval(d) < -dval(eps))
+                                goto no_digits;
+                        goto fast_failed;
+                        }
+#ifndef No_leftright
+                if (leftright) {
+                        /* Use Steele & White method of only
+                         * generating digits needed.
+                         */
+                        dval(eps) = 0.5/tens[ilim-1] - dval(eps);
+                        for(i = 0;;) {
+                                L = dval(d);
+                                dval(d) -= L;
+                                *s++ = '0' + (int)L;
+                                if (dval(d) < dval(eps))
+                                        goto ret1;
+                                if (1. - dval(d) < dval(eps))
+                                        goto bump_up;
+                                if (++i >= ilim)
+                                        break;
+                                dval(eps) *= 10.;
+                                dval(d) *= 10.;
+                                }
+                        }
+                else {
+#endif
+                        /* Generate ilim digits, then fix them up. */
+                        dval(eps) *= tens[ilim-1];
+                        for(i = 1;; i++, dval(d) *= 10.) {
+                                L = (Long)(dval(d));
+                                if (!(dval(d) -= L))
+                                        ilim = i;
+                                *s++ = '0' + (int)L;
+                                if (i == ilim) {
+                                        if (dval(d) > 0.5 + dval(eps))
+                                                goto bump_up;
+                                        else if (dval(d) < 0.5 - dval(eps)) {
+                                                while(*--s == '0');
+                                                s++;
+                                                goto ret1;
+                                                }
+                                        break;
+                                        }
+                                }
+#ifndef No_leftright
+                        }
+#endif
+ fast_failed:
+                s = s0;
+                dval(d) = dval(d2);
+                k = k0;
+                ilim = ilim0;
+                }
+
+        /* Do we have a "small" integer? */
+
+        if (be >= 0 && k <= Int_max) {
+                /* Yes. */
+                ds = tens[k];
+                if (ndigits < 0 && ilim <= 0) {
+                        S = mhi = 0;
+                        if (ilim < 0 || dval(d) <= 5*ds)
+                                goto no_digits;
+                        goto one_digit;
+                        }
+                for(i = 1;; i++, dval(d) *= 10.) {
+                        L = (Long)(dval(d) / ds);
+                        dval(d) -= L*ds;
+#ifdef Check_FLT_ROUNDS
+                        /* If FLT_ROUNDS == 2, L will usually be high by 1 */
+                        if (dval(d) < 0) {
+                                L--;
+                                dval(d) += ds;
+                                }
+#endif
+                        *s++ = '0' + (int)L;
+                        if (!dval(d)) {
+#ifdef SET_INEXACT
+                                inexact = 0;
+#endif
+                                break;
+                                }
+                        if (i == ilim) {
+#ifdef Honor_FLT_ROUNDS
+                                if (mode > 1)
+                                switch(Rounding) {
+                                  case 0: goto ret1;
+                                  case 2: goto bump_up;
+                                  }
+#endif
+                                dval(d) += dval(d);
+                                if (dval(d) > ds || dval(d) == ds && L & 1) {
+ bump_up:
+                                        while(*--s == '9')
+                                                if (s == s0) {
+                                                        k++;
+                                                        *s = '0';
+                                                        break;
+                                                        }
+                                        ++*s++;
+                                        }
+                                break;
+                                }
+                        }
+                goto ret1;
+                }
+
+        m2 = b2;
+        m5 = b5;
+        mhi = mlo = 0;
+        if (leftright) {
+                i =
+#ifndef Sudden_Underflow
+                        denorm ? be + (Bias + (P-1) - 1 + 1) :
+#endif
+#ifdef IBM
+                        1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
+#else
+                        1 + P - bbits;
+#endif
+                b2 += i;
+                s2 += i;
+                mhi = i2b(1);
+                }
+        if (m2 > 0 && s2 > 0) {
+                i = m2 < s2 ? m2 : s2;
+                b2 -= i;
+                m2 -= i;
+                s2 -= i;
+                }
+        if (b5 > 0) {
+                if (leftright) {
+                        if (m5 > 0) {
+                                mhi = pow5mult(mhi, m5);
+                                b1 = mult(mhi, b);
+                                Bfree(b);
+                                b = b1;
+                                }
+                        if (j = b5 - m5)
+                                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 {
+ trimzeros:
+                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;
+        }
+
+}  // namespace dmg_fp