/src/moddable/xs/sources/xsdtoa.c

Source (jump to first uncovered line)
/*
 * Copyright (c) 2016-2017  Moddable Tech, Inc.
 *
 *   This file is part of the Moddable SDK Runtime.
 * 
 *   The Moddable SDK Runtime is free software: you can redistribute it and/or modify
 *   it under the terms of the GNU Lesser General Public License as published by
 *   the Free Software Foundation, either version 3 of the License, or
 *   (at your option) any later version.
 * 
 *   The Moddable SDK Runtime is distributed in the hope that it will be useful,
 *   but WITHOUT ANY WARRANTY; without even the implied warranty of
 *   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *   GNU Lesser General Public License for more details.
 * 
 *   You should have received a copy of the GNU Lesser General Public License
 *   along with the Moddable SDK Runtime.  If not, see <http://www.gnu.org/licenses/>.
 *
 * This file incorporates work covered by the following copyright and  
 * permission notice:  
 *
 *       Copyright (C) 2010-2016 Marvell International Ltd.
 *       Copyright (C) 2002-2010 Kinoma, Inc.
 *
 *       Licensed under the Apache License, Version 2.0 (the "License");
 *       you may not use this file except in compliance with the License.
 *       You may obtain a copy of the License at
 *
 *        http://www.apache.org/licenses/LICENSE-2.0
 *
 *       Unless required by applicable law or agreed to in writing, software
 *       distributed under the License is distributed on an "AS IS" BASIS,
 *       WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *       See the License for the specific language governing permissions and
 *       limitations under the License.
 */

#include "xsAll.h"

#if mxNoChunks
#define mxUseChunkHeap 0
#else
#define mxUseChunkHeap 1
#endif

#define __XS__ 1
#define __XS__a , DTOA
#define __XS__d , ThInfo* DTOA

#define FREE fxDTOAFree
#define INFNAN_CHECK
#define MALLOC fxDTOAMalloc
#define NO_BF96
#define NO_HEX_FP
#define Omit_Private_Memory
#define ROUND_BIASED

#if mxLittleEndian
#define IEEE_8087
#endif
#if mxBigEndian
#define IEEE_MC68k
#endif
#if ((defined(__GNUC__) && defined(__LP64__)) || (defined(_MSC_VER) && defined(_M_X64)))
#else
#define NO_LONG_LONG
#endif

static void* fxDTOAMalloc(size_t size, void* it);
static void fxDTOAFree(void* block, void* it);

#undef assert

/****************************************************************
 *
 * 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.
 * (Note that IEEE arithmetic is disabled by gcc's -ffast-math flag.)
 *
 * 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.  This will cause dtoa modes 4 and 5 to be
 *  treated the same as modes 2 and 3 for some inputs.
 * #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_ROUNDS 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 and arithmetic
 *  that rounds toward +Infinity.
 * #define ROUND_BIASED_without_Round_Up for IEEE-format with biased
 *  rounding when the underlying floating-point arithmetic uses
 *  unbiased rounding.  This prevent using ordinary floating-point
 *  arithmetic when the result could be computed with one rounding error.
 * #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 Bad_float_h if your system lacks a float.h or if it does not
 *  define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
 *  FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
 * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
 *  if memory is available and otherwise does something you deem
 *  appropriate.  If MALLOC is undefined, malloc will be invoked
 *  directly -- and assumed always to succeed.  Similarly, if you
 *  want something other than the system's free() to be called to
 *  recycle memory acquired from MALLOC, #define FREE to be the
 *  name of the alternate routine.  (FREE or free is only called in
 *  pathological cases, e.g., in a dtoa call after a dtoa return in
 *  mode 3 with thousands of digits requested.)
 * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
 *  memory allocations from a private pool of memory when possible.
 *  When used, the private pool is PRIVATE_MEM bytes long:  2304 bytes,
 *  unless #defined to be a different length.  This default length
 *  suffices to get rid of MALLOC calls except for unusual cases,
 *  such as decimal-to-binary conversion of a very long string of
 *  digits.  The longest string dtoa can return is about 751 bytes
 *  long.  For conversions by strtod of strings of 800 digits and
 *  all dtoa conversions in single-threaded executions with 8-byte
 *  pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte
 *  pointers, PRIVATE_MEM >= 7112 appears adequate.
 * #define NO_INFNAN_CHECK if you do not wish to have INFNAN_CHECK
 *  #defined automatically on IEEE systems.  On such systems,
 *  when INFNAN_CHECK is #defined, strtod checks
 *  for Infinity and NaN (case insensitively).  On some systems
 *  (e.g., some HP systems), it may be necessary to #define NAN_WORD0
 *  appropriately -- to the most significant word of a quiet NaN.
 *  (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
 *  When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
 *  strtod also accepts (case insensitively) strings of the form
 *  NaN(x), where x is a string of hexadecimal digits and spaces;
 *  if there is only one string of hexadecimal digits, it is taken
 *  for the 52 fraction bits of the resulting NaN; if there are two
 *  or more strings of hex digits, the first is for the high 20 bits,
 *  the second and subsequent for the low 32 bits, with intervening
 *  white space ignored; but if this results in none of the 52
 *  fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0
 *  and NAN_WORD1 are used instead.
 * #define MULTIPLE_THREADS if the system offers preemptively scheduled
 *  multiple threads.  In this case, you must provide (or suitably
 *  #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
 *  by FREE_DTOA_LOCK(n) for n = 0 or 1.  (The second lock, accessed
 *  in pow5mult, ensures lazy evaluation of only one copy of high
 *  powers of 5; omitting this lock would introduce a small
 *  probability of wasting memory, but would otherwise be harmless.)
 *  You must also invoke freedtoa(s) to free the value s returned by
 *  dtoa.  You may do so whether or not MULTIPLE_THREADS is #defined.

 *  When MULTIPLE_THREADS is #defined, this source file provides
 *    void set_max_dtoa_threads(unsigned int n);
 *  and expects
 *    unsigned int dtoa_get_threadno(void);
 *  to be available (possibly provided by
 *    #define dtoa_get_threadno omp_get_thread_num
 *  if OpenMP is in use or by
 *    #define dtoa_get_threadno pthread_self
 *  if Pthreads is in use), to return the current thread number.
 *  If set_max_dtoa_threads(n) was called and the current thread
 *  number is k with k < n, then calls on ACQUIRE_DTOA_LOCK(...) and
 *  FREE_DTOA_LOCK(...) are avoided; instead each thread with thread
 *  number < n has a separate copy of relevant data structures.
 *  After set_max_dtoa_threads(n), a call set_max_dtoa_threads(m)
 *  with m <= n has has no effect, but a call with m > n is honored.
 *  Such a call invokes REALLOC (assumed to be "realloc" if REALLOC
 *  is not #defined) to extend the size of the relevant array.

 * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
 *  avoids underflows on inputs whose result does not underflow.
 *  If you #define NO_IEEE_Scale on a machine that uses IEEE-format
 *  floating-point numbers and flushes underflows to zero rather
 *  than implementing gradual underflow, then you must also #define
 *  Sudden_Underflow.
 * #define USE_LOCALE to use the current locale's decimal_point value.
 * #define SET_INEXACT if IEEE arithmetic is being used and extra
 *  computation should be done to set the inexact flag when the
 *  result is inexact and avoid setting inexact when the result
 *  is exact.  In this case, dtoa.c must be compiled in
 *  an environment, perhaps provided by #include "dtoa.c" in a
 *  suitable wrapper, that defines two functions,
 *    int get_inexact(void);
 *    void clear_inexact(void);
 *  such that get_inexact() returns a nonzero value if the
 *  inexact bit is already set, and clear_inexact() sets the
 *  inexact bit to 0.  When SET_INEXACT is #defined, strtod
 *  also does extra computations to set the underflow and overflow
 *  flags when appropriate (i.e., when the result is tiny and
 *  inexact or when it is a numeric value rounded to +-infinity).
 * #define NO_ERRNO if strtod should not assign errno = ERANGE when
 *  the result overflows to +-Infinity or underflows to 0.
 *  When errno should be assigned, under seemingly rare conditions
 *  it may be necessary to define Set_errno(x) suitably, e.g., in
 *  a local errno.h, such as
 *    #include <errno.h>
 *    #define Set_errno(x) _set_errno(x)
 * #define NO_HEX_FP to omit recognition of hexadecimal floating-point
 *  values by strtod.
 * #define NO_STRTOD_BIGCOMP (on IEEE-arithmetic systems only for now)
 *  to disable logic for "fast" testing of very long input strings
 *  to strtod.  This testing proceeds by initially truncating the
 *  input string, then if necessary comparing the whole string with
 *  a decimal expansion to decide close cases. This logic is only
 *  used for input more than STRTOD_DIGLIM digits long (default 40).
 */

#ifndef Long
#define Long int
#endif
#ifndef ULong
typedef unsigned Long ULong;
#endif

#ifdef DEBUG
#include <assert.h>
#include "stdio.h"
#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
#define Debug(x) x
int dtoa_stats[7]; /* strtod_{64,96,bigcomp},dtoa_{exact,64,96,bigcomp} */
#else
#define assert(x) /*nothing*/
#define Debug(x) /*nothing*/
#endif

#include "stdlib.h"
#include "string.h"

#ifdef USE_LOCALE
#include "locale.h"
#endif

#ifdef Honor_FLT_ROUNDS
#ifndef Trust_FLT_ROUNDS
#include <fenv.h>
#endif
#endif

#ifdef __cplusplus
extern "C" {
#endif
#ifdef MALLOC
extern void *MALLOC(size_t, void*);
#else
#define MALLOC malloc
#endif

#ifdef REALLOC
extern void *REALLOC(void*,size_t);
#else
#define REALLOC realloc
#endif

#ifndef FREE
#define FREE free
#endif

#ifdef __cplusplus
  }
#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
#define NO_STRTOD_BIGCOMP
#endif

#include "errno.h"

#ifdef NO_ERRNO /*{*/
#undef Set_errno
#define Set_errno(x)
#else
#ifndef Set_errno
#define Set_errno(x) errno = x
#endif
#endif /*}*/

#ifdef Bad_float_h

#ifdef IEEE_Arith
#define DBL_DIG 15
#define DBL_MAX_10_EXP 308
#define DBL_MAX_EXP 1024
#define FLT_RADIX 2
#endif /*IEEE_Arith*/

#ifdef IBM
#define DBL_DIG 16
#define DBL_MAX_10_EXP 75
#define DBL_MAX_EXP 63
#define FLT_RADIX 16
#define DBL_MAX 7.2370055773322621e+75
#endif

#ifdef VAX
#define DBL_DIG 16
#define DBL_MAX_10_EXP 38
#define DBL_MAX_EXP 127
#define FLT_RADIX 2
#define DBL_MAX 1.7014118346046923e+38
#endif

#ifndef LONG_MAX
#define LONG_MAX 2147483647
#endif

#else /* ifndef Bad_float_h */
#include "float.h"
#endif /* Bad_float_h */

#ifndef __MATH_H__
#include "math.h"
#endif

#ifdef __cplusplus
extern "C" {
#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

#undef USE_BF96

#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
#ifndef NO_BF96 /*{*/
#define USE_BF96

#ifdef SET_INEXACT
#define dtoa_divmax 27
#else
int dtoa_divmax = 2;  /* Permit experimenting: on some systems, 64-bit integer */
      /* division is slow enough that we may sometimes want to */
      /* avoid using it.   We assume (but do not check) that   */
      /* dtoa_divmax <= 27.*/
#endif

typedef struct BF96 {   /* Normalized 96-bit software floating point numbers */
  unsigned int b0,b1,b2;  /* b0 = most significant, binary point just to its left */
  int e;      /* number represented = b * 2^e, with .5 <= b < 1 */
  } BF96;

 static BF96 pten[667] = {
  { 0xeef453d6, 0x923bd65a, 0x113faa29, -1136 },
  { 0x9558b466, 0x1b6565f8, 0x4ac7ca59, -1132 },
  { 0xbaaee17f, 0xa23ebf76, 0x5d79bcf0, -1129 },
  { 0xe95a99df, 0x8ace6f53, 0xf4d82c2c, -1126 },
  { 0x91d8a02b, 0xb6c10594, 0x79071b9b, -1122 },
  { 0xb64ec836, 0xa47146f9, 0x9748e282, -1119 },
  { 0xe3e27a44, 0x4d8d98b7, 0xfd1b1b23, -1116 },
  { 0x8e6d8c6a, 0xb0787f72, 0xfe30f0f5, -1112 },
  { 0xb208ef85, 0x5c969f4f, 0xbdbd2d33, -1109 },
  { 0xde8b2b66, 0xb3bc4723, 0xad2c7880, -1106 },
  { 0x8b16fb20, 0x3055ac76, 0x4c3bcb50, -1102 },
  { 0xaddcb9e8, 0x3c6b1793, 0xdf4abe24, -1099 },
  { 0xd953e862, 0x4b85dd78, 0xd71d6dad, -1096 },
  { 0x87d4713d, 0x6f33aa6b, 0x8672648c, -1092 },
  { 0xa9c98d8c, 0xcb009506, 0x680efdaf, -1089 },
  { 0xd43bf0ef, 0xfdc0ba48, 0x0212bd1b, -1086 },
  { 0x84a57695, 0xfe98746d, 0x014bb630, -1082 },
  { 0xa5ced43b, 0x7e3e9188, 0x419ea3bd, -1079 },
  { 0xcf42894a, 0x5dce35ea, 0x52064cac, -1076 },
  { 0x818995ce, 0x7aa0e1b2, 0x7343efeb, -1072 },
  { 0xa1ebfb42, 0x19491a1f, 0x1014ebe6, -1069 },
  { 0xca66fa12, 0x9f9b60a6, 0xd41a26e0, -1066 },
  { 0xfd00b897, 0x478238d0, 0x8920b098, -1063 },
  { 0x9e20735e, 0x8cb16382, 0x55b46e5f, -1059 },
  { 0xc5a89036, 0x2fddbc62, 0xeb2189f7, -1056 },
  { 0xf712b443, 0xbbd52b7b, 0xa5e9ec75, -1053 },
  { 0x9a6bb0aa, 0x55653b2d, 0x47b233c9, -1049 },
  { 0xc1069cd4, 0xeabe89f8, 0x999ec0bb, -1046 },
  { 0xf148440a, 0x256e2c76, 0xc00670ea, -1043 },
  { 0x96cd2a86, 0x5764dbca, 0x38040692, -1039 },
  { 0xbc807527, 0xed3e12bc, 0xc6050837, -1036 },
  { 0xeba09271, 0xe88d976b, 0xf7864a44, -1033 },
  { 0x93445b87, 0x31587ea3, 0x7ab3ee6a, -1029 },
  { 0xb8157268, 0xfdae9e4c, 0x5960ea05, -1026 },
  { 0xe61acf03, 0x3d1a45df, 0x6fb92487, -1023 },
  { 0x8fd0c162, 0x06306bab, 0xa5d3b6d4, -1019 },
  { 0xb3c4f1ba, 0x87bc8696, 0x8f48a489, -1016 },
  { 0xe0b62e29, 0x29aba83c, 0x331acdab, -1013 },
  { 0x8c71dcd9, 0xba0b4925, 0x9ff0c08b, -1009 },
  { 0xaf8e5410, 0x288e1b6f, 0x07ecf0ae, -1006 },
  { 0xdb71e914, 0x32b1a24a, 0xc9e82cd9, -1003 },
  { 0x892731ac, 0x9faf056e, 0xbe311c08,  -999 },
  { 0xab70fe17, 0xc79ac6ca, 0x6dbd630a,  -996 },
  { 0xd64d3d9d, 0xb981787d, 0x092cbbcc,  -993 },
  { 0x85f04682, 0x93f0eb4e, 0x25bbf560,  -989 },
  { 0xa76c5823, 0x38ed2621, 0xaf2af2b8,  -986 },
  { 0xd1476e2c, 0x07286faa, 0x1af5af66,  -983 },
  { 0x82cca4db, 0x847945ca, 0x50d98d9f,  -979 },
  { 0xa37fce12, 0x6597973c, 0xe50ff107,  -976 },
  { 0xcc5fc196, 0xfefd7d0c, 0x1e53ed49,  -973 },
  { 0xff77b1fc, 0xbebcdc4f, 0x25e8e89c,  -970 },
  { 0x9faacf3d, 0xf73609b1, 0x77b19161,  -966 },
  { 0xc795830d, 0x75038c1d, 0xd59df5b9,  -963 },
  { 0xf97ae3d0, 0xd2446f25, 0x4b057328,  -960 },
  { 0x9becce62, 0x836ac577, 0x4ee367f9,  -956 },
  { 0xc2e801fb, 0x244576d5, 0x229c41f7,  -953 },
  { 0xf3a20279, 0xed56d48a, 0x6b435275,  -950 },
  { 0x9845418c, 0x345644d6, 0x830a1389,  -946 },
  { 0xbe5691ef, 0x416bd60c, 0x23cc986b,  -943 },
  { 0xedec366b, 0x11c6cb8f, 0x2cbfbe86,  -940 },
  { 0x94b3a202, 0xeb1c3f39, 0x7bf7d714,  -936 },
  { 0xb9e08a83, 0xa5e34f07, 0xdaf5ccd9,  -933 },
  { 0xe858ad24, 0x8f5c22c9, 0xd1b3400f,  -930 },
  { 0x91376c36, 0xd99995be, 0x23100809,  -926 },
  { 0xb5854744, 0x8ffffb2d, 0xabd40a0c,  -923 },
  { 0xe2e69915, 0xb3fff9f9, 0x16c90c8f,  -920 },
  { 0x8dd01fad, 0x907ffc3b, 0xae3da7d9,  -916 },
  { 0xb1442798, 0xf49ffb4a, 0x99cd11cf,  -913 },
  { 0xdd95317f, 0x31c7fa1d, 0x40405643,  -910 },
  { 0x8a7d3eef, 0x7f1cfc52, 0x482835ea,  -906 },
  { 0xad1c8eab, 0x5ee43b66, 0xda324365,  -903 },
  { 0xd863b256, 0x369d4a40, 0x90bed43e,  -900 },
  { 0x873e4f75, 0xe2224e68, 0x5a7744a6,  -896 },
  { 0xa90de353, 0x5aaae202, 0x711515d0,  -893 },
  { 0xd3515c28, 0x31559a83, 0x0d5a5b44,  -890 },
  { 0x8412d999, 0x1ed58091, 0xe858790a,  -886 },
  { 0xa5178fff, 0x668ae0b6, 0x626e974d,  -883 },
  { 0xce5d73ff, 0x402d98e3, 0xfb0a3d21,  -880 },
  { 0x80fa687f, 0x881c7f8e, 0x7ce66634,  -876 },
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  { 0x83126e97, 0x8d4fdf3b, 0x645a1cac,    -9 },
  { 0xa3d70a3d, 0x70a3d70a, 0x3d70a3d7,    -6 },
  { 0xcccccccc, 0xcccccccc, 0xcccccccc,    -3 },
  { 0x80000000, 0x00000000, 0x00000000,    1 },
  { 0xa0000000, 0x00000000, 0x00000000,    4 },
  { 0xc8000000, 0x00000000, 0x00000000,    7 },
  { 0xfa000000, 0x00000000, 0x00000000,   10 },
  { 0x9c400000, 0x00000000, 0x00000000,   14 },
  { 0xc3500000, 0x00000000, 0x00000000,   17 },
  { 0xf4240000, 0x00000000, 0x00000000,   20 },
  { 0x98968000, 0x00000000, 0x00000000,   24 },
  { 0xbebc2000, 0x00000000, 0x00000000,   27 },
  { 0xee6b2800, 0x00000000, 0x00000000,   30 },
  { 0x9502f900, 0x00000000, 0x00000000,   34 },
  { 0xba43b740, 0x00000000, 0x00000000,   37 },
  { 0xe8d4a510, 0x00000000, 0x00000000,   40 },
  { 0x9184e72a, 0x00000000, 0x00000000,   44 },
  { 0xb5e620f4, 0x80000000, 0x00000000,   47 },
  { 0xe35fa931, 0xa0000000, 0x00000000,   50 },
  { 0x8e1bc9bf, 0x04000000, 0x00000000,   54 },
  { 0xb1a2bc2e, 0xc5000000, 0x00000000,   57 },
  { 0xde0b6b3a, 0x76400000, 0x00000000,   60 },
  { 0x8ac72304, 0x89e80000, 0x00000000,   64 },
  { 0xad78ebc5, 0xac620000, 0x00000000,   67 },
  { 0xd8d726b7, 0x177a8000, 0x00000000,   70 },
  { 0x87867832, 0x6eac9000, 0x00000000,   74 },
  { 0xa968163f, 0x0a57b400, 0x00000000,   77 },
  { 0xd3c21bce, 0xcceda100, 0x00000000,   80 },
  { 0x84595161, 0x401484a0, 0x00000000,   84 },
  { 0xa56fa5b9, 0x9019a5c8, 0x00000000,   87 },
  { 0xcecb8f27, 0xf4200f3a, 0x00000000,   90 },
  { 0x813f3978, 0xf8940984, 0x40000000,   94 },
  { 0xa18f07d7, 0x36b90be5, 0x50000000,   97 },
  { 0xc9f2c9cd, 0x04674ede, 0xa4000000,  100 },
  { 0xfc6f7c40, 0x45812296, 0x4d000000,  103 },
  { 0x9dc5ada8, 0x2b70b59d, 0xf0200000,  107 },
  { 0xc5371912, 0x364ce305, 0x6c280000,  110 },
  { 0xf684df56, 0xc3e01bc6, 0xc7320000,  113 },
  { 0x9a130b96, 0x3a6c115c, 0x3c7f4000,  117 },
  { 0xc097ce7b, 0xc90715b3, 0x4b9f1000,  120 },
  { 0xf0bdc21a, 0xbb48db20, 0x1e86d400,  123 },
  { 0x96769950, 0xb50d88f4, 0x13144480,  127 },
  { 0xbc143fa4, 0xe250eb31, 0x17d955a0,  130 },
  { 0xeb194f8e, 0x1ae525fd, 0x5dcfab08,  133 },
  { 0x92efd1b8, 0xd0cf37be, 0x5aa1cae5,  137 },
  { 0xb7abc627, 0x050305ad, 0xf14a3d9e,  140 },
  { 0xe596b7b0, 0xc643c719, 0x6d9ccd05,  143 },
  { 0x8f7e32ce, 0x7bea5c6f, 0xe4820023,  147 },
  { 0xb35dbf82, 0x1ae4f38b, 0xdda2802c,  150 },
  { 0xe0352f62, 0xa19e306e, 0xd50b2037,  153 },
  { 0x8c213d9d, 0xa502de45, 0x4526f422,  157 },
  { 0xaf298d05, 0x0e4395d6, 0x9670b12b,  160 },
  { 0xdaf3f046, 0x51d47b4c, 0x3c0cdd76,  163 },
  { 0x88d8762b, 0xf324cd0f, 0xa5880a69,  167 },
  { 0xab0e93b6, 0xefee0053, 0x8eea0d04,  170 },
  { 0xd5d238a4, 0xabe98068, 0x72a49045,  173 },
  { 0x85a36366, 0xeb71f041, 0x47a6da2b,  177 },
  { 0xa70c3c40, 0xa64e6c51, 0x999090b6,  180 },
  { 0xd0cf4b50, 0xcfe20765, 0xfff4b4e3,  183 },
  { 0x82818f12, 0x81ed449f, 0xbff8f10e,  187 },
  { 0xa321f2d7, 0x226895c7, 0xaff72d52,  190 },
  { 0xcbea6f8c, 0xeb02bb39, 0x9bf4f8a6,  193 },
  { 0xfee50b70, 0x25c36a08, 0x02f236d0,  196 },
  { 0x9f4f2726, 0x179a2245, 0x01d76242,  200 },
  { 0xc722f0ef, 0x9d80aad6, 0x424d3ad2,  203 },
  { 0xf8ebad2b, 0x84e0d58b, 0xd2e08987,  206 },
  { 0x9b934c3b, 0x330c8577, 0x63cc55f4,  210 },
  { 0xc2781f49, 0xffcfa6d5, 0x3cbf6b71,  213 },
  { 0xf316271c, 0x7fc3908a, 0x8bef464e,  216 },
  { 0x97edd871, 0xcfda3a56, 0x97758bf0,  220 },
  { 0xbde94e8e, 0x43d0c8ec, 0x3d52eeed,  223 },
  { 0xed63a231, 0xd4c4fb27, 0x4ca7aaa8,  226 },
  { 0x945e455f, 0x24fb1cf8, 0x8fe8caa9,  230 },
  { 0xb975d6b6, 0xee39e436, 0xb3e2fd53,  233 },
  { 0xe7d34c64, 0xa9c85d44, 0x60dbbca8,  236 },
  { 0x90e40fbe, 0xea1d3a4a, 0xbc8955e9,  240 },
  { 0xb51d13ae, 0xa4a488dd, 0x6babab63,  243 },
  { 0xe264589a, 0x4dcdab14, 0xc696963c,  246 },
  { 0x8d7eb760, 0x70a08aec, 0xfc1e1de5,  250 },
  { 0xb0de6538, 0x8cc8ada8, 0x3b25a55f,  253 },
  { 0xdd15fe86, 0xaffad912, 0x49ef0eb7,  256 },
  { 0x8a2dbf14, 0x2dfcc7ab, 0x6e356932,  260 },
  { 0xacb92ed9, 0x397bf996, 0x49c2c37f,  263 },
  { 0xd7e77a8f, 0x87daf7fb, 0xdc33745e,  266 },
  { 0x86f0ac99, 0xb4e8dafd, 0x69a028bb,  270 },
  { 0xa8acd7c0, 0x222311bc, 0xc40832ea,  273 },
  { 0xd2d80db0, 0x2aabd62b, 0xf50a3fa4,  276 },
  { 0x83c7088e, 0x1aab65db, 0x792667c6,  280 },
  { 0xa4b8cab1, 0xa1563f52, 0x577001b8,  283 },
  { 0xcde6fd5e, 0x09abcf26, 0xed4c0226,  286 },
  { 0x80b05e5a, 0xc60b6178, 0x544f8158,  290 },
  { 0xa0dc75f1, 0x778e39d6, 0x696361ae,  293 },
  { 0xc913936d, 0xd571c84c, 0x03bc3a19,  296 },
  { 0xfb587849, 0x4ace3a5f, 0x04ab48a0,  299 },
  { 0x9d174b2d, 0xcec0e47b, 0x62eb0d64,  303 },
  { 0xc45d1df9, 0x42711d9a, 0x3ba5d0bd,  306 },
  { 0xf5746577, 0x930d6500, 0xca8f44ec,  309 },
  { 0x9968bf6a, 0xbbe85f20, 0x7e998b13,  313 },
  { 0xbfc2ef45, 0x6ae276e8, 0x9e3fedd8,  316 },
  { 0xefb3ab16, 0xc59b14a2, 0xc5cfe94e,  319 },
  { 0x95d04aee, 0x3b80ece5, 0xbba1f1d1,  323 },
  { 0xbb445da9, 0xca61281f, 0x2a8a6e45,  326 },
  { 0xea157514, 0x3cf97226, 0xf52d09d7,  329 },
  { 0x924d692c, 0xa61be758, 0x593c2626,  333 },
  { 0xb6e0c377, 0xcfa2e12e, 0x6f8b2fb0,  336 },
  { 0xe498f455, 0xc38b997a, 0x0b6dfb9c,  339 },
  { 0x8edf98b5, 0x9a373fec, 0x4724bd41,  343 },
  { 0xb2977ee3, 0x00c50fe7, 0x58edec91,  346 },
  { 0xdf3d5e9b, 0xc0f653e1, 0x2f2967b6,  349 },
  { 0x8b865b21, 0x5899f46c, 0xbd79e0d2,  353 },
  { 0xae67f1e9, 0xaec07187, 0xecd85906,  356 },
  { 0xda01ee64, 0x1a708de9, 0xe80e6f48,  359 },
  { 0x884134fe, 0x908658b2, 0x3109058d,  363 },
  { 0xaa51823e, 0x34a7eede, 0xbd4b46f0,  366 },
  { 0xd4e5e2cd, 0xc1d1ea96, 0x6c9e18ac,  369 },
  { 0x850fadc0, 0x9923329e, 0x03e2cf6b,  373 },
  { 0xa6539930, 0xbf6bff45, 0x84db8346,  376 },
  { 0xcfe87f7c, 0xef46ff16, 0xe6126418,  379 },
  { 0x81f14fae, 0x158c5f6e, 0x4fcb7e8f,  383 },
  { 0xa26da399, 0x9aef7749, 0xe3be5e33,  386 },
  { 0xcb090c80, 0x01ab551c, 0x5cadf5bf,  389 },
  { 0xfdcb4fa0, 0x02162a63, 0x73d9732f,  392 },
  { 0x9e9f11c4, 0x014dda7e, 0x2867e7fd,  396 },
  { 0xc646d635, 0x01a1511d, 0xb281e1fd,  399 },
  { 0xf7d88bc2, 0x4209a565, 0x1f225a7c,  402 },
  { 0x9ae75759, 0x6946075f, 0x3375788d,  406 },
  { 0xc1a12d2f, 0xc3978937, 0x0052d6b1,  409 },
  { 0xf209787b, 0xb47d6b84, 0xc0678c5d,  412 },
  { 0x9745eb4d, 0x50ce6332, 0xf840b7ba,  416 },
  { 0xbd176620, 0xa501fbff, 0xb650e5a9,  419 },
  { 0xec5d3fa8, 0xce427aff, 0xa3e51f13,  422 },
  { 0x93ba47c9, 0x80e98cdf, 0xc66f336c,  426 },
  { 0xb8a8d9bb, 0xe123f017, 0xb80b0047,  429 },
  { 0xe6d3102a, 0xd96cec1d, 0xa60dc059,  432 },
  { 0x9043ea1a, 0xc7e41392, 0x87c89837,  436 },
  { 0xb454e4a1, 0x79dd1877, 0x29babe45,  439 },
  { 0xe16a1dc9, 0xd8545e94, 0xf4296dd6,  442 },
  { 0x8ce2529e, 0x2734bb1d, 0x1899e4a6,  446 },
  { 0xb01ae745, 0xb101e9e4, 0x5ec05dcf,  449 },
  { 0xdc21a117, 0x1d42645d, 0x76707543,  452 },
  { 0x899504ae, 0x72497eba, 0x6a06494a,  456 },
  { 0xabfa45da, 0x0edbde69, 0x0487db9d,  459 },
  { 0xd6f8d750, 0x9292d603, 0x45a9d284,  462 },
  { 0x865b8692, 0x5b9bc5c2, 0x0b8a2392,  466 },
  { 0xa7f26836, 0xf282b732, 0x8e6cac77,  469 },
  { 0xd1ef0244, 0xaf2364ff, 0x3207d795,  472 },
  { 0x8335616a, 0xed761f1f, 0x7f44e6bd,  476 },
  { 0xa402b9c5, 0xa8d3a6e7, 0x5f16206c,  479 },
  { 0xcd036837, 0x130890a1, 0x36dba887,  482 },
  { 0x80222122, 0x6be55a64, 0xc2494954,  486 },
  { 0xa02aa96b, 0x06deb0fd, 0xf2db9baa,  489 },
  { 0xc83553c5, 0xc8965d3d, 0x6f928294,  492 },
  { 0xfa42a8b7, 0x3abbf48c, 0xcb772339,  495 },
  { 0x9c69a972, 0x84b578d7, 0xff2a7604,  499 },
  { 0xc38413cf, 0x25e2d70d, 0xfef51385,  502 },
  { 0xf46518c2, 0xef5b8cd1, 0x7eb25866,  505 },
  { 0x98bf2f79, 0xd5993802, 0xef2f773f,  509 },
  { 0xbeeefb58, 0x4aff8603, 0xaafb550f,  512 },
  { 0xeeaaba2e, 0x5dbf6784, 0x95ba2a53,  515 },
  { 0x952ab45c, 0xfa97a0b2, 0xdd945a74,  519 },
  { 0xba756174, 0x393d88df, 0x94f97111,  522 },
  { 0xe912b9d1, 0x478ceb17, 0x7a37cd56,  525 },
  { 0x91abb422, 0xccb812ee, 0xac62e055,  529 },
  { 0xb616a12b, 0x7fe617aa, 0x577b986b,  532 },
  { 0xe39c4976, 0x5fdf9d94, 0xed5a7e85,  535 },
  { 0x8e41ade9, 0xfbebc27d, 0x14588f13,  539 },
  { 0xb1d21964, 0x7ae6b31c, 0x596eb2d8,  542 },
  { 0xde469fbd, 0x99a05fe3, 0x6fca5f8e,  545 },
  { 0x8aec23d6, 0x80043bee, 0x25de7bb9,  549 },
  { 0xada72ccc, 0x20054ae9, 0xaf561aa7,  552 },
  { 0xd910f7ff, 0x28069da4, 0x1b2ba151,  555 },
  { 0x87aa9aff, 0x79042286, 0x90fb44d2,  559 },
  { 0xa99541bf, 0x57452b28, 0x353a1607,  562 },
  { 0xd3fa922f, 0x2d1675f2, 0x42889b89,  565 },
  { 0x847c9b5d, 0x7c2e09b7, 0x69956135,  569 },
  { 0xa59bc234, 0xdb398c25, 0x43fab983,  572 },
  { 0xcf02b2c2, 0x1207ef2e, 0x94f967e4,  575 },
  { 0x8161afb9, 0x4b44f57d, 0x1d1be0ee,  579 },
  { 0xa1ba1ba7, 0x9e1632dc, 0x6462d92a,  582 },
  { 0xca28a291, 0x859bbf93, 0x7d7b8f75,  585 },
  { 0xfcb2cb35, 0xe702af78, 0x5cda7352,  588 },
  { 0x9defbf01, 0xb061adab, 0x3a088813,  592 },
  { 0xc56baec2, 0x1c7a1916, 0x088aaa18,  595 },
  { 0xf6c69a72, 0xa3989f5b, 0x8aad549e,  598 },
  { 0x9a3c2087, 0xa63f6399, 0x36ac54e2,  602 },
  { 0xc0cb28a9, 0x8fcf3c7f, 0x84576a1b,  605 },
  { 0xf0fdf2d3, 0xf3c30b9f, 0x656d44a2,  608 },
  { 0x969eb7c4, 0x7859e743, 0x9f644ae5,  612 },
  { 0xbc4665b5, 0x96706114, 0x873d5d9f,  615 },
  { 0xeb57ff22, 0xfc0c7959, 0xa90cb506,  618 },
  { 0x9316ff75, 0xdd87cbd8, 0x09a7f124,  622 },
  { 0xb7dcbf53, 0x54e9bece, 0x0c11ed6d,  625 },
  { 0xe5d3ef28, 0x2a242e81, 0x8f1668c8,  628 },
  { 0x8fa47579, 0x1a569d10, 0xf96e017d,  632 },
  { 0xb38d92d7, 0x60ec4455, 0x37c981dc,  635 },
  { 0xe070f78d, 0x3927556a, 0x85bbe253,  638 },
  { 0x8c469ab8, 0x43b89562, 0x93956d74,  642 },
  { 0xaf584166, 0x54a6babb, 0x387ac8d1,  645 },
  { 0xdb2e51bf, 0xe9d0696a, 0x06997b05,  648 },
  { 0x88fcf317, 0xf22241e2, 0x441fece3,  652 },
  { 0xab3c2fdd, 0xeeaad25a, 0xd527e81c,  655 },
  { 0xd60b3bd5, 0x6a5586f1, 0x8a71e223,  658 },
  { 0x85c70565, 0x62757456, 0xf6872d56,  662 },
  { 0xa738c6be, 0xbb12d16c, 0xb428f8ac,  665 },
  { 0xd106f86e, 0x69d785c7, 0xe13336d7,  668 },
  { 0x82a45b45, 0x0226b39c, 0xecc00246,  672 },
  { 0xa34d7216, 0x42b06084, 0x27f002d7,  675 },
  { 0xcc20ce9b, 0xd35c78a5, 0x31ec038d,  678 },
  { 0xff290242, 0xc83396ce, 0x7e670471,  681 },
  { 0x9f79a169, 0xbd203e41, 0x0f0062c6,  685 },
  { 0xc75809c4, 0x2c684dd1, 0x52c07b78,  688 },
  { 0xf92e0c35, 0x37826145, 0xa7709a56,  691 },
  { 0x9bbcc7a1, 0x42b17ccb, 0x88a66076,  695 },
  { 0xc2abf989, 0x935ddbfe, 0x6acff893,  698 },
  { 0xf356f7eb, 0xf83552fe, 0x0583f6b8,  701 },
  { 0x98165af3, 0x7b2153de, 0xc3727a33,  705 },
  { 0xbe1bf1b0, 0x59e9a8d6, 0x744f18c0,  708 },
  { 0xeda2ee1c, 0x7064130c, 0x1162def0,  711 },
  { 0x9485d4d1, 0xc63e8be7, 0x8addcb56,  715 },
  { 0xb9a74a06, 0x37ce2ee1, 0x6d953e2b,  718 },
  { 0xe8111c87, 0xc5c1ba99, 0xc8fa8db6,  721 },
  { 0x910ab1d4, 0xdb9914a0, 0x1d9c9892,  725 },
  { 0xb54d5e4a, 0x127f59c8, 0x2503beb6,  728 },
  { 0xe2a0b5dc, 0x971f303a, 0x2e44ae64,  731 },
  { 0x8da471a9, 0xde737e24, 0x5ceaecfe,  735 },
  { 0xb10d8e14, 0x56105dad, 0x7425a83e,  738 },
  { 0xdd50f199, 0x6b947518, 0xd12f124e,  741 },
  { 0x8a5296ff, 0xe33cc92f, 0x82bd6b70,  745 },
  { 0xace73cbf, 0xdc0bfb7b, 0x636cc64d,  748 },
  { 0xd8210bef, 0xd30efa5a, 0x3c47f7e0,  751 },
  { 0x8714a775, 0xe3e95c78, 0x65acfaec,  755 },
  { 0xa8d9d153, 0x5ce3b396, 0x7f1839a7,  758 },
  { 0xd31045a8, 0x341ca07c, 0x1ede4811,  761 },
  { 0x83ea2b89, 0x2091e44d, 0x934aed0a,  765 },
  { 0xa4e4b66b, 0x68b65d60, 0xf81da84d,  768 },
  { 0xce1de406, 0x42e3f4b9, 0x36251260,  771 },
  { 0x80d2ae83, 0xe9ce78f3, 0xc1d72b7c,  775 },
  { 0xa1075a24, 0xe4421730, 0xb24cf65b,  778 },
  { 0xc94930ae, 0x1d529cfc, 0xdee033f2,  781 },
  { 0xfb9b7cd9, 0xa4a7443c, 0x169840ef,  784 },
  { 0x9d412e08, 0x06e88aa5, 0x8e1f2895,  788 },
  { 0xc491798a, 0x08a2ad4e, 0xf1a6f2ba,  791 },
  { 0xf5b5d7ec, 0x8acb58a2, 0xae10af69,  794 },
  { 0x9991a6f3, 0xd6bf1765, 0xacca6da1,  798 },
  { 0xbff610b0, 0xcc6edd3f, 0x17fd090a,  801 },
  { 0xeff394dc, 0xff8a948e, 0xddfc4b4c,  804 },
  { 0x95f83d0a, 0x1fb69cd9, 0x4abdaf10,  808 },
  { 0xbb764c4c, 0xa7a4440f, 0x9d6d1ad4,  811 },
  { 0xea53df5f, 0xd18d5513, 0x84c86189,  814 },
  { 0x92746b9b, 0xe2f8552c, 0x32fd3cf5,  818 },
  { 0xb7118682, 0xdbb66a77, 0x3fbc8c33,  821 },
  { 0xe4d5e823, 0x92a40515, 0x0fabaf3f,  824 },
  { 0x8f05b116, 0x3ba6832d, 0x29cb4d87,  828 },
  { 0xb2c71d5b, 0xca9023f8, 0x743e20e9,  831 },
  { 0xdf78e4b2, 0xbd342cf6, 0x914da924,  834 },
  { 0x8bab8eef, 0xb6409c1a, 0x1ad089b6,  838 },
  { 0xae9672ab, 0xa3d0c320, 0xa184ac24,  841 },
  { 0xda3c0f56, 0x8cc4f3e8, 0xc9e5d72d,  844 },
  { 0x88658996, 0x17fb1871, 0x7e2fa67c,  848 },
  { 0xaa7eebfb, 0x9df9de8d, 0xddbb901b,  851 },
  { 0xd51ea6fa, 0x85785631, 0x552a7422,  854 },
  { 0x8533285c, 0x936b35de, 0xd53a8895,  858 },
  { 0xa67ff273, 0xb8460356, 0x8a892aba,  861 },
  { 0xd01fef10, 0xa657842c, 0x2d2b7569,  864 },
  { 0x8213f56a, 0x67f6b29b, 0x9c3b2962,  868 },
  { 0xa298f2c5, 0x01f45f42, 0x8349f3ba,  871 },
  { 0xcb3f2f76, 0x42717713, 0x241c70a9,  874 },
  { 0xfe0efb53, 0xd30dd4d7, 0xed238cd3,  877 },
  { 0x9ec95d14, 0x63e8a506, 0xf4363804,  881 },
  { 0xc67bb459, 0x7ce2ce48, 0xb143c605,  884 },
  { 0xf81aa16f, 0xdc1b81da, 0xdd94b786,  887 },
  { 0x9b10a4e5, 0xe9913128, 0xca7cf2b4,  891 },
  { 0xc1d4ce1f, 0x63f57d72, 0xfd1c2f61,  894 },
  { 0xf24a01a7, 0x3cf2dccf, 0xbc633b39,  897 },
  { 0x976e4108, 0x8617ca01, 0xd5be0503,  901 },
  { 0xbd49d14a, 0xa79dbc82, 0x4b2d8644,  904 },
  { 0xec9c459d, 0x51852ba2, 0xddf8e7d6,  907 },
  { 0x93e1ab82, 0x52f33b45, 0xcabb90e5,  911 },
  { 0xb8da1662, 0xe7b00a17, 0x3d6a751f,  914 },
  { 0xe7109bfb, 0xa19c0c9d, 0x0cc51267,  917 },
  { 0x906a617d, 0x450187e2, 0x27fb2b80,  921 },
  { 0xb484f9dc, 0x9641e9da, 0xb1f9f660,  924 },
  { 0xe1a63853, 0xbbd26451, 0x5e7873f8,  927 },
  { 0x8d07e334, 0x55637eb2, 0xdb0b487b,  931 },
  { 0xb049dc01, 0x6abc5e5f, 0x91ce1a9a,  934 },
  { 0xdc5c5301, 0xc56b75f7, 0x7641a140,  937 },
  { 0x89b9b3e1, 0x1b6329ba, 0xa9e904c8,  941 },
  { 0xac2820d9, 0x623bf429, 0x546345fa,  944 },
  { 0xd732290f, 0xbacaf133, 0xa97c1779,  947 },
  { 0x867f59a9, 0xd4bed6c0, 0x49ed8eab,  951 },
  { 0xa81f3014, 0x49ee8c70, 0x5c68f256,  954 },
  { 0xd226fc19, 0x5c6a2f8c, 0x73832eec,  957 },
  { 0x83585d8f, 0xd9c25db7, 0xc831fd53,  961 },
  { 0xa42e74f3, 0xd032f525, 0xba3e7ca8,  964 },
  { 0xcd3a1230, 0xc43fb26f, 0x28ce1bd2,  967 },
  { 0x80444b5e, 0x7aa7cf85, 0x7980d163,  971 },
  { 0xa0555e36, 0x1951c366, 0xd7e105bc,  974 },
  { 0xc86ab5c3, 0x9fa63440, 0x8dd9472b,  977 },
  { 0xfa856334, 0x878fc150, 0xb14f98f6,  980 },
  { 0x9c935e00, 0xd4b9d8d2, 0x6ed1bf9a,  984 },
  { 0xc3b83581, 0x09e84f07, 0x0a862f80,  987 },
  { 0xf4a642e1, 0x4c6262c8, 0xcd27bb61,  990 },
  { 0x98e7e9cc, 0xcfbd7dbd, 0x8038d51c,  994 },
  { 0xbf21e440, 0x03acdd2c, 0xe0470a63,  997 },
  { 0xeeea5d50, 0x04981478, 0x1858ccfc, 1000 },
  { 0x95527a52, 0x02df0ccb, 0x0f37801e, 1004 },
  { 0xbaa718e6, 0x8396cffd, 0xd3056025, 1007 },
  { 0xe950df20, 0x247c83fd, 0x47c6b82e, 1010 },
  { 0x91d28b74, 0x16cdd27e, 0x4cdc331d, 1014 },
  { 0xb6472e51, 0x1c81471d, 0xe0133fe4, 1017 },
  { 0xe3d8f9e5, 0x63a198e5, 0x58180fdd, 1020 },
  { 0x8e679c2f, 0x5e44ff8f, 0x570f09ea, 1024 },
  { 0xb201833b, 0x35d63f73, 0x2cd2cc65, 1027 },
  { 0xde81e40a, 0x034bcf4f, 0xf8077f7e, 1030 },
  { 0x8b112e86, 0x420f6191, 0xfb04afaf, 1034 },
  { 0xadd57a27, 0xd29339f6, 0x79c5db9a, 1037 },
  { 0xd94ad8b1, 0xc7380874, 0x18375281, 1040 },
  { 0x87cec76f, 0x1c830548, 0x8f229391, 1044 },
  { 0xa9c2794a, 0xe3a3c69a, 0xb2eb3875, 1047 },
  { 0xd433179d, 0x9c8cb841, 0x5fa60692, 1050 },
  { 0x849feec2, 0x81d7f328, 0xdbc7c41b, 1054 },
  { 0xa5c7ea73, 0x224deff3, 0x12b9b522, 1057 },
  { 0xcf39e50f, 0xeae16bef, 0xd768226b, 1060 },
  { 0x81842f29, 0xf2cce375, 0xe6a11583, 1064 },
  { 0xa1e53af4, 0x6f801c53, 0x60495ae3, 1067 },
  { 0xca5e89b1, 0x8b602368, 0x385bb19c, 1070 },
  { 0xfcf62c1d, 0xee382c42, 0x46729e03, 1073 },
  { 0x9e19db92, 0xb4e31ba9, 0x6c07a2c2, 1077 }
  };
 static short int Lhint[2098] = {
     /*18,*/19,    19,    19,    19,    20,    20,    20,    21,    21,
     21,    22,    22,    22,    23,    23,    23,    23,    24,    24,
     24,    25,    25,    25,    26,    26,    26,    26,    27,    27,
     27,    28,    28,    28,    29,    29,    29,    29,    30,    30,
     30,    31,    31,    31,    32,    32,    32,    32,    33,    33,
     33,    34,    34,    34,    35,    35,    35,    35,    36,    36,
     36,    37,    37,    37,    38,    38,    38,    38,    39,    39,
     39,    40,    40,    40,    41,    41,    41,    41,    42,    42,
     42,    43,    43,    43,    44,    44,    44,    44,    45,    45,
     45,    46,    46,    46,    47,    47,    47,    47,    48,    48,
     48,    49,    49,    49,    50,    50,    50,    51,    51,    51,
     51,    52,    52,    52,    53,    53,    53,    54,    54,    54,
     54,    55,    55,    55,    56,    56,    56,    57,    57,    57,
     57,    58,    58,    58,    59,    59,    59,    60,    60,    60,
     60,    61,    61,    61,    62,    62,    62,    63,    63,    63,
     63,    64,    64,    64,    65,    65,    65,    66,    66,    66,
     66,    67,    67,    67,    68,    68,    68,    69,    69,    69,
     69,    70,    70,    70,    71,    71,    71,    72,    72,    72,
     72,    73,    73,    73,    74,    74,    74,    75,    75,    75,
     75,    76,    76,    76,    77,    77,    77,    78,    78,    78,
     78,    79,    79,    79,    80,    80,    80,    81,    81,    81,
     82,    82,    82,    82,    83,    83,    83,    84,    84,    84,
     85,    85,    85,    85,    86,    86,    86,    87,    87,    87,
     88,    88,    88,    88,    89,    89,    89,    90,    90,    90,
     91,    91,    91,    91,    92,    92,    92,    93,    93,    93,
     94,    94,    94,    94,    95,    95,    95,    96,    96,    96,
     97,    97,    97,    97,    98,    98,    98,    99,    99,    99,
    100,   100,   100,   100,   101,   101,   101,   102,   102,   102,
    103,   103,   103,   103,   104,   104,   104,   105,   105,   105,
    106,   106,   106,   106,   107,   107,   107,   108,   108,   108,
    109,   109,   109,   110,   110,   110,   110,   111,   111,   111,
    112,   112,   112,   113,   113,   113,   113,   114,   114,   114,
    115,   115,   115,   116,   116,   116,   116,   117,   117,   117,
    118,   118,   118,   119,   119,   119,   119,   120,   120,   120,
    121,   121,   121,   122,   122,   122,   122,   123,   123,   123,
    124,   124,   124,   125,   125,   125,   125,   126,   126,   126,
    127,   127,   127,   128,   128,   128,   128,   129,   129,   129,
    130,   130,   130,   131,   131,   131,   131,   132,   132,   132,
    133,   133,   133,   134,   134,   134,   134,   135,   135,   135,
    136,   136,   136,   137,   137,   137,   137,   138,   138,   138,
    139,   139,   139,   140,   140,   140,   141,   141,   141,   141,
    142,   142,   142,   143,   143,   143,   144,   144,   144,   144,
    145,   145,   145,   146,   146,   146,   147,   147,   147,   147,
    148,   148,   148,   149,   149,   149,   150,   150,   150,   150,
    151,   151,   151,   152,   152,   152,   153,   153,   153,   153,
    154,   154,   154,   155,   155,   155,   156,   156,   156,   156,
    157,   157,   157,   158,   158,   158,   159,   159,   159,   159,
    160,   160,   160,   161,   161,   161,   162,   162,   162,   162,
    163,   163,   163,   164,   164,   164,   165,   165,   165,   165,
    166,   166,   166,   167,   167,   167,   168,   168,   168,   169,
    169,   169,   169,   170,   170,   170,   171,   171,   171,   172,
    172,   172,   172,   173,   173,   173,   174,   174,   174,   175,
    175,   175,   175,   176,   176,   176,   177,   177,   177,   178,
    178,   178,   178,   179,   179,   179,   180,   180,   180,   181,
    181,   181,   181,   182,   182,   182,   183,   183,   183,   184,
    184,   184,   184,   185,   185,   185,   186,   186,   186,   187,
    187,   187,   187,   188,   188,   188,   189,   189,   189,   190,
    190,   190,   190,   191,   191,   191,   192,   192,   192,   193,
    193,   193,   193,   194,   194,   194,   195,   195,   195,   196,
    196,   196,   197,   197,   197,   197,   198,   198,   198,   199,
    199,   199,   200,   200,   200,   200,   201,   201,   201,   202,
    202,   202,   203,   203,   203,   203,   204,   204,   204,   205,
    205,   205,   206,   206,   206,   206,   207,   207,   207,   208,
    208,   208,   209,   209,   209,   209,   210,   210,   210,   211,
    211,   211,   212,   212,   212,   212,   213,   213,   213,   214,
    214,   214,   215,   215,   215,   215,   216,   216,   216,   217,
    217,   217,   218,   218,   218,   218,   219,   219,   219,   220,
    220,   220,   221,   221,   221,   221,   222,   222,   222,   223,
    223,   223,   224,   224,   224,   224,   225,   225,   225,   226,
    226,   226,   227,   227,   227,   228,   228,   228,   228,   229,
    229,   229,   230,   230,   230,   231,   231,   231,   231,   232,
    232,   232,   233,   233,   233,   234,   234,   234,   234,   235,
    235,   235,   236,   236,   236,   237,   237,   237,   237,   238,
    238,   238,   239,   239,   239,   240,   240,   240,   240,   241,
    241,   241,   242,   242,   242,   243,   243,   243,   243,   244,
    244,   244,   245,   245,   245,   246,   246,   246,   246,   247,
    247,   247,   248,   248,   248,   249,   249,   249,   249,   250,
    250,   250,   251,   251,   251,   252,   252,   252,   252,   253,
    253,   253,   254,   254,   254,   255,   255,   255,   256,   256,
    256,   256,   257,   257,   257,   258,   258,   258,   259,   259,
    259,   259,   260,   260,   260,   261,   261,   261,   262,   262,
    262,   262,   263,   263,   263,   264,   264,   264,   265,   265,
    265,   265,   266,   266,   266,   267,   267,   267,   268,   268,
    268,   268,   269,   269,   269,   270,   270,   270,   271,   271,
    271,   271,   272,   272,   272,   273,   273,   273,   274,   274,
    274,   274,   275,   275,   275,   276,   276,   276,   277,   277,
    277,   277,   278,   278,   278,   279,   279,   279,   280,   280,
    280,   280,   281,   281,   281,   282,   282,   282,   283,   283,
    283,   283,   284,   284,   284,   285,   285,   285,   286,   286,
    286,   287,   287,   287,   287,   288,   288,   288,   289,   289,
    289,   290,   290,   290,   290,   291,   291,   291,   292,   292,
    292,   293,   293,   293,   293,   294,   294,   294,   295,   295,
    295,   296,   296,   296,   296,   297,   297,   297,   298,   298,
    298,   299,   299,   299,   299,   300,   300,   300,   301,   301,
    301,   302,   302,   302,   302,   303,   303,   303,   304,   304,
    304,   305,   305,   305,   305,   306,   306,   306,   307,   307,
    307,   308,   308,   308,   308,   309,   309,   309,   310,   310,
    310,   311,   311,   311,   311,   312,   312,   312,   313,   313,
    313,   314,   314,   314,   315,   315,   315,   315,   316,   316,
    316,   317,   317,   317,   318,   318,   318,   318,   319,   319,
    319,   320,   320,   320,   321,   321,   321,   321,   322,   322,
    322,   323,   323,   323,   324,   324,   324,   324,   325,   325,
    325,   326,   326,   326,   327,   327,   327,   327,   328,   328,
    328,   329,   329,   329,   330,   330,   330,   330,   331,   331,
    331,   332,   332,   332,   333,   333,   333,   333,   334,   334,
    334,   335,   335,   335,   336,   336,   336,   336,   337,   337,
    337,   338,   338,   338,   339,   339,   339,   339,   340,   340,
    340,   341,   341,   341,   342,   342,   342,   342,   343,   343,
    343,   344,   344,   344,   345,   345,   345,   346,   346,   346,
    346,   347,   347,   347,   348,   348,   348,   349,   349,   349,
    349,   350,   350,   350,   351,   351,   351,   352,   352,   352,
    352,   353,   353,   353,   354,   354,   354,   355,   355,   355,
    355,   356,   356,   356,   357,   357,   357,   358,   358,   358,
    358,   359,   359,   359,   360,   360,   360,   361,   361,   361,
    361,   362,   362,   362,   363,   363,   363,   364,   364,   364,
    364,   365,   365,   365,   366,   366,   366,   367,   367,   367,
    367,   368,   368,   368,   369,   369,   369,   370,   370,   370,
    370,   371,   371,   371,   372,   372,   372,   373,   373,   373,
    374,   374,   374,   374,   375,   375,   375,   376,   376,   376,
    377,   377,   377,   377,   378,   378,   378,   379,   379,   379,
    380,   380,   380,   380,   381,   381,   381,   382,   382,   382,
    383,   383,   383,   383,   384,   384,   384,   385,   385,   385,
    386,   386,   386,   386,   387,   387,   387,   388,   388,   388,
    389,   389,   389,   389,   390,   390,   390,   391,   391,   391,
    392,   392,   392,   392,   393,   393,   393,   394,   394,   394,
    395,   395,   395,   395,   396,   396,   396,   397,   397,   397,
    398,   398,   398,   398,   399,   399,   399,   400,   400,   400,
    401,   401,   401,   402,   402,   402,   402,   403,   403,   403,
    404,   404,   404,   405,   405,   405,   405,   406,   406,   406,
    407,   407,   407,   408,   408,   408,   408,   409,   409,   409,
    410,   410,   410,   411,   411,   411,   411,   412,   412,   412,
    413,   413,   413,   414,   414,   414,   414,   415,   415,   415,
    416,   416,   416,   417,   417,   417,   417,   418,   418,   418,
    419,   419,   419,   420,   420,   420,   420,   421,   421,   421,
    422,   422,   422,   423,   423,   423,   423,   424,   424,   424,
    425,   425,   425,   426,   426,   426,   426,   427,   427,   427,
    428,   428,   428,   429,   429,   429,   429,   430,   430,   430,
    431,   431,   431,   432,   432,   432,   433,   433,   433,   433,
    434,   434,   434,   435,   435,   435,   436,   436,   436,   436,
    437,   437,   437,   438,   438,   438,   439,   439,   439,   439,
    440,   440,   440,   441,   441,   441,   442,   442,   442,   442,
    443,   443,   443,   444,   444,   444,   445,   445,   445,   445,
    446,   446,   446,   447,   447,   447,   448,   448,   448,   448,
    449,   449,   449,   450,   450,   450,   451,   451,   451,   451,
    452,   452,   452,   453,   453,   453,   454,   454,   454,   454,
    455,   455,   455,   456,   456,   456,   457,   457,   457,   457,
    458,   458,   458,   459,   459,   459,   460,   460,   460,   461,
    461,   461,   461,   462,   462,   462,   463,   463,   463,   464,
    464,   464,   464,   465,   465,   465,   466,   466,   466,   467,
    467,   467,   467,   468,   468,   468,   469,   469,   469,   470,
    470,   470,   470,   471,   471,   471,   472,   472,   472,   473,
    473,   473,   473,   474,   474,   474,   475,   475,   475,   476,
    476,   476,   476,   477,   477,   477,   478,   478,   478,   479,
    479,   479,   479,   480,   480,   480,   481,   481,   481,   482,
    482,   482,   482,   483,   483,   483,   484,   484,   484,   485,
    485,   485,   485,   486,   486,   486,   487,   487,   487,   488,
    488,   488,   488,   489,   489,   489,   490,   490,   490,   491,
    491,   491,   492,   492,   492,   492,   493,   493,   493,   494,
    494,   494,   495,   495,   495,   495,   496,   496,   496,   497,
    497,   497,   498,   498,   498,   498,   499,   499,   499,   500,
    500,   500,   501,   501,   501,   501,   502,   502,   502,   503,
    503,   503,   504,   504,   504,   504,   505,   505,   505,   506,
    506,   506,   507,   507,   507,   507,   508,   508,   508,   509,
    509,   509,   510,   510,   510,   510,   511,   511,   511,   512,
    512,   512,   513,   513,   513,   513,   514,   514,   514,   515,
    515,   515,   516,   516,   516,   516,   517,   517,   517,   518,
    518,   518,   519,   519,   519,   520,   520,   520,   520,   521,
    521,   521,   522,   522,   522,   523,   523,   523,   523,   524,
    524,   524,   525,   525,   525,   526,   526,   526,   526,   527,
    527,   527,   528,   528,   528,   529,   529,   529,   529,   530,
    530,   530,   531,   531,   531,   532,   532,   532,   532,   533,
    533,   533,   534,   534,   534,   535,   535,   535,   535,   536,
    536,   536,   537,   537,   537,   538,   538,   538,   538,   539,
    539,   539,   540,   540,   540,   541,   541,   541,   541,   542,
    542,   542,   543,   543,   543,   544,   544,   544,   544,   545,
    545,   545,   546,   546,   546,   547,   547,   547,   548,   548,
    548,   548,   549,   549,   549,   550,   550,   550,   551,   551,
    551,   551,   552,   552,   552,   553,   553,   553,   554,   554,
    554,   554,   555,   555,   555,   556,   556,   556,   557,   557,
    557,   557,   558,   558,   558,   559,   559,   559,   560,   560,
    560,   560,   561,   561,   561,   562,   562,   562,   563,   563,
    563,   563,   564,   564,   564,   565,   565,   565,   566,   566,
    566,   566,   567,   567,   567,   568,   568,   568,   569,   569,
    569,   569,   570,   570,   570,   571,   571,   571,   572,   572,
    572,   572,   573,   573,   573,   574,   574,   574,   575,   575,
    575,   575,   576,   576,   576,   577,   577,   577,   578,   578,
    578,   579,   579,   579,   579,   580,   580,   580,   581,   581,
    581,   582,   582,   582,   582,   583,   583,   583,   584,   584,
    584,   585,   585,   585,   585,   586,   586,   586,   587,   587,
    587,   588,   588,   588,   588,   589,   589,   589,   590,   590,
    590,   591,   591,   591,   591,   592,   592,   592,   593,   593,
    593,   594,   594,   594,   594,   595,   595,   595,   596,   596,
    596,   597,   597,   597,   597,   598,   598,   598,   599,   599,
    599,   600,   600,   600,   600,   601,   601,   601,   602,   602,
    602,   603,   603,   603,   603,   604,   604,   604,   605,   605,
    605,   606,   606,   606,   607,   607,   607,   607,   608,   608,
    608,   609,   609,   609,   610,   610,   610,   610,   611,   611,
    611,   612,   612,   612,   613,   613,   613,   613,   614,   614,
    614,   615,   615,   615,   616,   616,   616,   616,   617,   617,
    617,   618,   618,   618,   619,   619,   619,   619,   620,   620,
    620,   621,   621,   621,   622,   622,   622,   622,   623,   623,
    623,   624,   624,   624,   625,   625,   625,   625,   626,   626,
    626,   627,   627,   627,   628,   628,   628,   628,   629,   629,
    629,   630,   630,   630,   631,   631,   631,   631,   632,   632,
    632,   633,   633,   633,   634,   634,   634,   634,   635,   635,
    635,   636,   636,   636,   637,   637,   637,   638,   638,   638,
    638,   639,   639,   639,   640,   640,   640,   641,   641,   641,
    641,   642,   642,   642,   643,   643,   643,   644,   644,   644,
    644,   645,   645,   645,   646,   646,   646,   647,   647,   647,
    647,   648,   648,   648,   649,   649,   649,   650,   650 };
 static ULLong pfive[27] = {
    5ll,
    25ll,
    125ll,
    625ll,
    3125ll,
    15625ll,
    78125ll,
    390625ll,
    1953125ll,
    9765625ll,
    48828125ll,
    244140625ll,
    1220703125ll,
    6103515625ll,
    30517578125ll,
    152587890625ll,
    762939453125ll,
    3814697265625ll,
    19073486328125ll,
    95367431640625ll,
    476837158203125ll,
    2384185791015625ll,
    11920928955078125ll,
    59604644775390625ll,
    298023223876953125ll,
    1490116119384765625ll,
    7450580596923828125ll
    };

 static int pfivebits[25] = {3, 5, 7, 10, 12, 14, 17, 19, 21, 24, 26, 28, 31,
           33, 35, 38, 40, 42, 45, 47, 49, 52, 54, 56, 59};
#endif /*}*/
#endif /*}} NO_LONG_LONG */

typedef union { double d; ULong L[2];
#ifdef USE_BF96
  ULLong LL;
#endif
  } U;

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

#ifndef STRTOD_DIGLIM
#define STRTOD_DIGLIM 40
#endif

#ifdef DIGLIM_DEBUG
extern int strtod_diglim;
#else
#define strtod_diglim STRTOD_DIGLIM
#endif

/* The following definition of Storeinc is appropriate for MIPS processors.
 * An alternative that might be better on some machines is
 * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
 */
#if defined(IEEE_8087) + defined(VAX)
#define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
((unsigned short *)a)[0] = (unsigned short)c, a++)
#else
#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
((unsigned short *)a)[1] = (unsigned short)c, a++)
#endif

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

#ifdef IEEE_Arith
#define Exp_shift  20
#define Exp_shift1 20
#define Exp_msk1    0x100000
#define Exp_msk11   0x100000
#define Exp_mask  0x7ff00000
#define P 53
#define Nbits 53
#define Bias 1023
#define Emax 1023
#define Emin (-1022)
#define Exp_1  0x3ff00000
#define Exp_11 0x3ff00000
#define Ebits 11
#define Frac_mask  0xfffff
#define Frac_mask1 0xfffff
#define Ten_pmax 22
#define Bletch 0x10
#define Bndry_mask  0xfffff
#define Bndry_mask1 0xfffff
#define LSB 1
#define Sign_bit 0x80000000
#define Log2P 1
#define Tiny0 0
#define Tiny1 1
#define Quick_max 14
#define Int_max 14
#ifndef NO_IEEE_Scale
#define Avoid_Underflow
#ifdef Flush_Denorm /* debugging option */
#undef Sudden_Underflow
#endif
#endif

#ifndef Flt_Rounds
#ifdef FLT_ROUNDS
#define Flt_Rounds FLT_ROUNDS
#else
#define Flt_Rounds 1
#endif
#endif /*Flt_Rounds*/

#ifdef Honor_FLT_ROUNDS
#undef Check_FLT_ROUNDS
#define Check_FLT_ROUNDS
#else
#define Rounding Flt_Rounds
#endif

#else /* ifndef IEEE_Arith */
#undef Check_FLT_ROUNDS
#undef Honor_FLT_ROUNDS
#undef SET_INEXACT
#undef  Sudden_Underflow
#define Sudden_Underflow
#ifdef IBM
#undef Flt_Rounds
#define Flt_Rounds 0
#define Exp_shift  24
#define Exp_shift1 24
#define Exp_msk1   0x1000000
#define Exp_msk11  0x1000000
#define Exp_mask  0x7f000000
#define P 14
#define Nbits 56
#define Bias 65
#define Emax 248
#define Emin (-260)
#define Exp_1  0x41000000
#define Exp_11 0x41000000
#define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
#define Frac_mask  0xffffff
#define Frac_mask1 0xffffff
#define Bletch 4
#define Ten_pmax 22
#define Bndry_mask  0xefffff
#define Bndry_mask1 0xffffff
#define LSB 1
#define Sign_bit 0x80000000
#define Log2P 4
#define Tiny0 0x100000
#define Tiny1 0
#define Quick_max 14
#define Int_max 15
#else /* VAX */
#undef Flt_Rounds
#define Flt_Rounds 1
#define Exp_shift  23
#define Exp_shift1 7
#define Exp_msk1    0x80
#define Exp_msk11   0x800000
#define Exp_mask  0x7f80
#define P 56
#define Nbits 56
#define Bias 129
#define Emax 126
#define Emin (-129)
#define Exp_1  0x40800000
#define Exp_11 0x4080
#define Ebits 8
#define Frac_mask  0x7fffff
#define Frac_mask1 0xffff007f
#define Ten_pmax 24
#define Bletch 2
#define Bndry_mask  0xffff007f
#define Bndry_mask1 0xffff007f
#define LSB 0x10000
#define Sign_bit 0x8000
#define Log2P 1
#define Tiny0 0x80
#define Tiny1 0
#define Quick_max 15
#define Int_max 15
#endif /* IBM, VAX */
#endif /* IEEE_Arith */

#ifndef IEEE_Arith
#define ROUND_BIASED
#else
#ifdef ROUND_BIASED_without_Round_Up
#undef  ROUND_BIASED
#define ROUND_BIASED
#endif
#endif

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

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

#ifndef Pack_32
#define Pack_32
#endif

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

#define FFFFFFFF 0xffffffffUL

#ifdef MULTIPLE_THREADS
#define MTa , PTI
#define MTb , &TI
#define MTd , ThInfo **PTI
static unsigned int maxthreads = 0;
#elif __XS__
#define MTa __XS__a
#define MTb __XS__a
#define MTd __XS__d
#else
#define MTa /*nothing*/
#define MTb /*nothing*/
#define MTd /*nothing*/
#endif

#define Kmax 7

#ifdef __cplusplus
extern "C" double strtod2(const char *s00, char **se __XS__d);
extern "C" char *dtoa(double d, int mode, int ndigits,
      int *decpt, int *sign, char **rve __XS__d);
#endif

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

 typedef struct Bigint Bigint;
 typedef struct
ThInfo {
  Bigint *Freelist[Kmax+1];
  Bigint *P5s;
#ifdef __XS__
  txMachine* the;
  #if mxUseChunkHeap
    txByte* current;
    int dirty;
  #endif
#endif
  } ThInfo;

#ifdef __XS__
#define TI0 (*DTOA)
#else
 static ThInfo TI0;
#endif

#ifdef MULTIPLE_THREADS
 static ThInfo *TI1;
 static int TI0_used;

 void
set_max_dtoa_threads(unsigned int n)
{
  size_t L;

  if (n > maxthreads) {
    L = n*sizeof(ThInfo);
    if (TI1) {
      TI1 = (ThInfo*)REALLOC(TI1, L);
      memset(TI1 + maxthreads, 0, (n-maxthreads)*sizeof(ThInfo));
      }
    else {
      TI1 = (ThInfo*)MALLOC(L);
      if (TI0_used) {
        memcpy(TI1, &TI0, sizeof(ThInfo));
        if (n > 1)
          memset(TI1 + 1, 0, L - sizeof(ThInfo));
        memset(&TI0, 0, sizeof(ThInfo));
        }
      else
        memset(TI1, 0, L);
      }
    maxthreads = n;
    }
  }

 static ThInfo*
get_TI(void)
{
  unsigned int thno = dtoa_get_threadno();
  if (thno < maxthreads)
    return TI1 + thno;
  if (thno == 0)
    TI0_used = 1;
  return &TI0;
  }
#define freelist TI->Freelist
#define p5s TI->P5s
#else
#define freelist TI0.Freelist
#define p5s TI0.P5s
#endif

 static Bigint *
Balloc(int k MTd)
{
  int x;
  Bigint *rv;
#ifndef Omit_Private_Memory
  unsigned int len;
#endif
#ifdef MULTIPLE_THREADS
  ThInfo *TI;

  if (!(TI = *PTI))
    *PTI = TI = get_TI();
  if (TI == &TI0)
    ACQUIRE_DTOA_LOCK(0);
#endif
  /* The k > Kmax case does not need ACQUIRE_DTOA_LOCK(0), */
  /* but this case seems very unlikely. */
  if (k <= Kmax && (rv = freelist[k]))
    freelist[k] = rv->next;
  else {
    x = 1 << k;
#ifdef Omit_Private_Memory
    rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong) __XS__a);
#else
    len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
      /sizeof(double);
    if (k <= Kmax && pmem_next - private_mem + len <= PRIVATE_mem
#ifdef MULTIPLE_THREADS
      && TI == TI1
#endif
      ) {
      rv = (Bigint*)pmem_next;
      pmem_next += len;
      }
    else
      rv = (Bigint*)MALLOC(len*sizeof(double) __XS__a);
#endif
    rv->k = k;
    rv->maxwds = x;
    }
#ifdef MULTIPLE_THREADS
  if (TI == &TI0)
    FREE_DTOA_LOCK(0);
#endif
  rv->sign = rv->wds = 0;
  return rv;
  }

 static void
Bfree(Bigint *v MTd)
{
#ifdef MULTIPLE_THREADS
  ThInfo *TI;
#endif
  if (v) {
    if (v->k > Kmax)
      FREE((void*)v __XS__a);
    else {
#ifdef MULTIPLE_THREADS
      if (!(TI = *PTI))
        *PTI = TI = get_TI();
      if (TI == &TI0)
        ACQUIRE_DTOA_LOCK(0);
#endif
      v->next = freelist[v->k];
      freelist[v->k] = v;
#ifdef MULTIPLE_THREADS
      if (TI == &TI0)
        FREE_DTOA_LOCK(0);
#endif
      }
    }
  }

#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
y->wds*sizeof(Long) + 2*sizeof(int))

 static Bigint *
multadd(Bigint *b, int m, int a MTd)  /* multiply by m and add a */
{
  int i, wds;
#ifdef ULLong
  ULong *x;
  ULLong carry, y;
#else
  ULong carry, *x, y;
#ifdef Pack_32
  ULong xi, z;
#endif
#endif
  Bigint *b1;

  wds = b->wds;
  x = b->x;
  i = 0;
  carry = a;
  do {
#ifdef ULLong
    y = *x * (ULLong)m + carry;
    carry = y >> 32;
    *x++ = y & FFFFFFFF;
#else
#ifdef Pack_32
    xi = *x;
    y = (xi & 0xffff) * m + carry;
    z = (xi >> 16) * m + (y >> 16);
    carry = z >> 16;
    *x++ = (z << 16) + (y & 0xffff);
#else
    y = *x * m + carry;
    carry = y >> 16;
    *x++ = y & 0xffff;
#endif
#endif
    }
    while(++i < wds);
  if (carry) {
    if (wds >= b->maxwds) {
      b1 = Balloc(b->k+1 MTa);
      Bcopy(b1, b);
      Bfree(b MTa);
      b = b1;
      }
    b->x[wds++] = (ULong)carry;
    b->wds = wds;
    }
  return b;
  }

 static Bigint *
s2b(const char *s, int nd0, int nd, ULong y9, int dplen MTd)
{
  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 MTa);
  b->x[0] = y9;
  b->wds = 1;
#else
  b = Balloc(k+1 MTa);
  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' MTa);
      while(++i < nd0);
    s += dplen;
    }
  else
    s += dplen + 9;
  for(; i < nd; i++)
    b = multadd(b, 10, *s++ - '0' MTa);
  return b;
  }

 static int
hi0bits(ULong x)
{
  int k = 0;

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

 static int
lo0bits(ULong *y)
{
  int k;
  ULong x = *y;

  if (x & 7) {
    if (x & 1)
      return 0;
    if (x & 2) {
      *y = x >> 1;
      return 1;
      }
    *y = x >> 2;
    return 2;
    }
  k = 0;
  if (!(x & 0xffff)) {
    k = 16;
    x >>= 16;
    }
  if (!(x & 0xff)) {
    k += 8;
    x >>= 8;
    }
  if (!(x & 0xf)) {
    k += 4;
    x >>= 4;
    }
  if (!(x & 0x3)) {
    k += 2;
    x >>= 2;
    }
  if (!(x & 1)) {
    k++;
    x >>= 1;
    if (!x)
      return 32;
    }
  *y = x;
  return k;
  }

 static Bigint *
i2b(int i MTd)
{
  Bigint *b;

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

 static Bigint *
mult(Bigint *a, Bigint *b MTd)
{
  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 MTa);
  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 = (ULong)carry;
      }
    }
#else
#ifdef Pack_32
  for(; xb < xbe; xb++, xc0++) {
    if ((y = *xb & 0xffff)) {
      x = xa;
      xc = xc0;
      carry = 0;
      do {
        z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
        carry = z >> 16;
        z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
        carry = z2 >> 16;
        Storeinc(xc, z2, z);
        }
        while(x < xae);
      *xc = carry;
      }
    if ((y = *xb >> 16)) {
      x = xa;
      xc = xc0;
      carry = 0;
      z2 = *xc;
      do {
        z = (*x & 0xffff) * y + (*xc >> 16) + carry;
        carry = z >> 16;
        Storeinc(xc, z, z2);
        z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
        carry = z2 >> 16;
        }
        while(x < xae);
      *xc = z2;
      }
    }
#else
  for(; xb < xbe; xc0++) {
    if (y = *xb++) {
      x = xa;
      xc = xc0;
      carry = 0;
      do {
        z = *x++ * y + *xc + carry;
        carry = z >> 16;
        *xc++ = z & 0xffff;
        }
        while(x < xae);
      *xc = carry;
      }
    }
#endif
#endif
  for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
  c->wds = wc;
  return c;
  }

 static Bigint *
pow5mult(Bigint *b, int k MTd)
{
  Bigint *b1, *p5, *p51;
#ifdef MULTIPLE_THREADS
  ThInfo *TI;
#endif
  int i;
  static int p05[3] = { 5, 25, 125 };

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

  if (!(k >>= 2))
    return b;
#ifdef  MULTIPLE_THREADS
  if (!(TI = *PTI))
    *PTI = TI = get_TI();
#endif
  if (!(p5 = p5s)) {
    /* first time */
#ifdef MULTIPLE_THREADS
    if (!(TI = *PTI))
      *PTI = TI = get_TI();
    if (TI == &TI0)
      ACQUIRE_DTOA_LOCK(1);
    if (!(p5 = p5s)) {
      p5 = p5s = i2b(625 MTa);
      p5->next = 0;
      }
    if (TI == &TI0)
      FREE_DTOA_LOCK(1);
#else
    p5 = p5s = i2b(625 MTa);
    p5->next = 0;
#endif
    }
  for(;;) {
    if (k & 1) {
      b1 = mult(b, p5 MTa);
      Bfree(b MTa);
      b = b1;
      }
    if (!(k >>= 1))
      break;
    if (!(p51 = p5->next)) {
#ifdef MULTIPLE_THREADS
      if (!TI && !(TI = *PTI))
        *PTI = TI = get_TI();
      if (TI == &TI0)
        ACQUIRE_DTOA_LOCK(1);
      if (!(p51 = p5->next)) {
        p51 = p5->next = mult(p5,p5 MTa);
        p51->next = 0;
        }
      if (TI == &TI0)
        FREE_DTOA_LOCK(1);
#else
      p51 = p5->next = mult(p5,p5 __XS__a);
      p51->next = 0;
#endif
      }
    p5 = p51;
    }
  return b;
  }

 static Bigint *
lshift(Bigint *b, int k MTd)
{
  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 MTa);
  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 MTa);
  return b1;
  }

 static int
cmp(Bigint *a, Bigint *b)
{
  ULong *xa, *xa0, *xb, *xb0;
  int i, j;

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

 static Bigint *
diff(Bigint *a, Bigint *b MTd)
{
  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 MTa);
    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 MTa);
  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(U *x)
{
  Long L;
  U u;

  L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
#ifndef Avoid_Underflow
#ifndef Sudden_Underflow
  if (L > 0) {
#endif
#endif
#ifdef IBM
    L |= Exp_msk1 >> 4;
#endif
    word0(&u) = L;
    word1(&u) = 0;
#ifndef Avoid_Underflow
#ifndef Sudden_Underflow
    }
  else {
    L = -L >> Exp_shift;
    if (L < Exp_shift) {
      word0(&u) = 0x80000 >> L;
      word1(&u) = 0;
      }
    else {
      word0(&u) = 0;
      L -= Exp_shift;
      word1(&u) = L >= 31 ? 1 : 1 << 31 - L;
      }
    }
#endif
#endif
  return dval(&u);
  }

 static double
b2d(Bigint *a, int *e)
{
  ULong *xa, *xa0, w, y, z;
  int k;
  U d;
#ifdef VAX
  ULong d0, d1;
#else
#define d0 word0(&d)
#define d1 word1(&d)
#endif

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

 static Bigint *
d2b(U *d, int *e, int *bits MTd)
{
  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 MTa);
#else
  b = Balloc(2 MTa);
#endif
  x = b->x;

  z = d0 & Frac_mask;
  d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
#ifdef Sudden_Underflow
  de = (int)(d0 >> Exp_shift);
#ifndef IBM
  z |= Exp_msk11;
#endif
#else
  if ((de = (int)(d0 >> Exp_shift)))
    z |= Exp_msk1;
#endif
#ifdef Pack_32
  if ((y = d1)) {
    if ((k = lo0bits(&y))) {
      x[0] = y | z << (32 - k);
      z >>= k;
      }
    else
      x[0] = y;
#ifndef Sudden_Underflow
    i =
#endif
        b->wds = (x[1] = z) ? 2 : 1;
    }
  else {
    k = lo0bits(&z);
    x[0] = z;
#ifndef Sudden_Underflow
    i =
#endif
        b->wds = 1;
    k += 32;
    }
#else
  if (y = d1) {
    if (k = lo0bits(&y))
      if (k >= 16) {
        x[0] = y | z << 32 - k & 0xffff;
        x[1] = z >> k - 16 & 0xffff;
        x[2] = z >> k;
        i = 2;
        }
      else {
        x[0] = y & 0xffff;
        x[1] = y >> 16 | z << 16 - k & 0xffff;
        x[2] = z >> k & 0xffff;
        x[3] = z >> k+16;
        i = 3;
        }
    else {
      x[0] = y & 0xffff;
      x[1] = y >> 16;
      x[2] = z & 0xffff;
      x[3] = z >> 16;
      i = 3;
      }
    }
  else {
#ifdef DEBUG
    if (!z)
      Bug("Zero passed to d2b");
#endif
    k = lo0bits(&z);
    if (k >= 16) {
      x[0] = z;
      i = 0;
      }
    else {
      x[0] = z & 0xffff;
      x[1] = z >> 16;
      i = 1;
      }
    k += 32;
    }
  while(!x[i])
    --i;
  b->wds = i + 1;
#endif
#ifndef Sudden_Underflow
  if (de) {
#endif
#ifdef IBM
    *e = (de - Bias - (P-1) << 2) + k;
    *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
#else
    *e = de - Bias - (P-1) + k;
    *bits = P - k;
#endif
#ifndef Sudden_Underflow
    }
  else {
    *e = de - Bias - (P-1) + 1 + k;
#ifdef Pack_32
    *bits = 32*i - hi0bits(x[i-1]);
#else
    *bits = (i+2)*16 - hi0bits(x[i]);
#endif
    }
#endif
  return b;
  }
#undef d0
#undef d1

 static double
ratio(Bigint *a, Bigint *b)
{
  U da, db;
  int k, ka, kb;

  dval(&da) = b2d(a, &ka);
  dval(&db) = b2d(b, &kb);
#ifdef Pack_32
  k = ka - kb + 32*(a->wds - b->wds);
#else
  k = ka - kb + 16*(a->wds - b->wds);
#endif
#ifdef IBM
  if (k > 0) {
    word0(&da) += (k >> 2)*Exp_msk1;
    if (k &= 3)
      dval(&da) *= 1 << k;
    }
  else {
    k = -k;
    word0(&db) += (k >> 2)*Exp_msk1;
    if (k &= 3)
      dval(&db) *= 1 << k;
    }
#else
  if (k > 0)
    word0(&da) += k*Exp_msk1;
  else {
    k = -k;
    word0(&db) += k*Exp_msk1;
    }
#endif
  return dval(&da) / dval(&db);
  }

 static const double
tens[] ICACHE_FLASH_ATTR = {
    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[] ICACHE_FLASH_ATTR = { 1e16, 1e32, 1e64, 1e128, 1e256 };
static const double tinytens[] ICACHE_FLASH_ATTR = { 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[] ICACHE_FLASH_ATTR = { 1e16, 1e32 };
static const double tinytens[] ICACHE_FLASH_ATTR = { 1e-16, 1e-32 };
#define n_bigtens 2
#endif
#endif

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

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

#ifdef Need_Hexdig /*{*/
#if 0
static unsigned char hexdig[256];

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

 static void
hexdig_init(void) /* Use of hexdig_init omitted 20121220 to avoid a */
      /* race condition when multiple threads are used. */
{
#define USC (unsigned char *)
  htinit(hexdig, USC "0123456789", 0x10);
  htinit(hexdig, USC "abcdef", 0x10 + 10);
  htinit(hexdig, USC "ABCDEF", 0x10 + 10);
  }
#else
static unsigned char const hexdig[256] ICACHE_RODATA_ATTR = {
  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  16,17,18,19,20,21,22,23,24,25,0,0,0,0,0,0,
  0,26,27,28,29,30,31,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,26,27,28,29,30,31,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
  };
#endif
#endif /* } Need_Hexdig */

#ifdef INFNAN_CHECK

#ifndef NAN_WORD0
#define NAN_WORD0 0x7ff80000
#endif

#ifndef NAN_WORD1
#define NAN_WORD1 0
#endif

 static int
match(const char **sp, const char *t)
{
  int c, d;
  const char *s = *sp;

  while((d = *t++)) {
#ifndef __XS__
    if ((c = *++s) >= 'A' && c <= 'Z')
      c += 'a' - 'A';
#else
        c = *++s;
#endif
    if (c != d)
      return 0;
    }
  *sp = s + 1;
  return 1;
  }

#ifndef No_Hex_NaN
 static void
hexnan(U *rvp, const char **sp)
{
  ULong c, x[2];
  const char *s;
  int c1, havedig, udx0, xshift;

  /**** if (!hexdig['0']) hexdig_init(); ****/
  x[0] = x[1] = 0;
  havedig = xshift = 0;
  udx0 = 1;
  s = *sp;
  /* allow optional initial 0x or 0X */
  while((c = *(const unsigned char*)(s+1)) && c <= ' ')
    ++s;
  if (s[1] == '0' && (s[2] == 'x' || s[2] == 'X'))
    s += 2;
  while((c = *(const unsigned char*)++s)) {
    if ((c1 = hexdig[c]))
      c  = c1 & 0xf;
    else if (c <= ' ') {
      if (udx0 && havedig) {
        udx0 = 0;
        xshift = 1;
        }
      continue;
      }
#ifdef GDTOA_NON_PEDANTIC_NANCHECK
    else if (/*(*/ c == ')' && havedig) {
      *sp = s + 1;
      break;
      }
    else
      return; /* invalid form: don't change *sp */
#else
    else {
      do {
        if (/*(*/ c == ')') {
          *sp = s + 1;
          break;
          }
        } while((c = *++s));
      break;
      }
#endif
    havedig = 1;
    if (xshift) {
      xshift = 0;
      x[0] = x[1];
      x[1] = 0;
      }
    if (udx0)
      x[0] = (x[0] << 4) | (x[1] >> 28);
    x[1] = (x[1] << 4) | c;
    }
  if ((x[0] &= 0xfffff) || x[1]) {
    word0(rvp) = Exp_mask | x[0];
    word1(rvp) = x[1];
    }
  }
#endif /*No_Hex_NaN*/
#endif /* INFNAN_CHECK */

#ifdef Pack_32
#define ULbits 32
#define kshift 5
#define kmask 31
#else
#define ULbits 16
#define kshift 4
#define kmask 15
#endif

#if !defined(NO_HEX_FP) || defined(Honor_FLT_ROUNDS) /*{*/
 static Bigint *
increment(Bigint *b MTd)
{
  ULong *x, *xe;
  Bigint *b1;

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

#endif /*}*/

#ifndef NO_HEX_FP /*{*/

 static void
rshift(Bigint *b, int k)
{
  ULong *x, *x1, *xe, y;
  int n;

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

 static ULong
any_on(Bigint *b, int k)
{
  int n, nwds;
  ULong *x, *x0, x1, x2;

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

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

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

  /**** if (!hexdig['0']) hexdig_init(); ****/
  havedig = 0;
  s0 = *(const unsigned char **)sp + 2;
  while(s0[havedig] == '0')
    havedig++;
  s0 += havedig;
  s = s0;
  decpt = 0;
  zret = 0;
  e = 0;
  if (hexdig[*s])
    havedig++;
  else {
    zret = 1;
#ifdef USE_LOCALE
    for(i = 0; decimalpoint[i]; ++i) {
      if (s[i] != decimalpoint[i])
        goto pcheck;
      }
    decpt = s += i;
#else
    if (*s != '.')
      goto pcheck;
    decpt = ++s;
#endif
    if (!hexdig[*s])
      goto pcheck;
    while(*s == '0')
      s++;
    if (hexdig[*s])
      zret = 0;
    havedig = 1;
    s0 = s;
    }
  while(hexdig[*s])
    s++;
#ifdef USE_LOCALE
  if (*s == *decimalpoint && !decpt) {
    for(i = 1; decimalpoint[i]; ++i) {
      if (s[i] != decimalpoint[i])
        goto pcheck;
      }
    decpt = s += i;
#else
  if (*s == '.' && !decpt) {
    decpt = ++s;
#endif
    while(hexdig[*s])
      s++;
    }/*}*/
  if (decpt)
    e = -(((Long)(s-decpt)) << 2);
 pcheck:
  s1 = s;
  big = esign = 0;
  switch(*s) {
    case 'p':
    case 'P':
    switch(*++s) {
      case '-':
      esign = 1;
      /* no break */
      case '+':
      s++;
      }
    if ((n = hexdig[*s]) == 0 || n > 0x19) {
      s = s1;
      break;
      }
    e1 = n - 0x10;
    while((n = hexdig[*++s]) !=0 && n <= 0x19) {
      if (e1 & 0xf8000000)
        big = 1;
      e1 = 10*e1 + n - 0x10;
      }
    if (esign)
      e1 = -e1;
    e += e1;
    }
  *sp = (char*)s;
  if (!havedig)
    *sp = (char*)s0 - 1;
  if (zret)
    goto retz1;
  if (big) {
    if (esign) {
#ifdef IEEE_Arith
      switch(rounding) {
        case Round_up:
        if (sign)
          break;
        goto ret_tiny;
        case Round_down:
        if (!sign)
          break;
        goto ret_tiny;
        }
#endif
      goto retz;
#ifdef IEEE_Arith
 ret_tinyf:
      Bfree(b MTa);
 ret_tiny:
      Set_errno(ERANGE);
      word0(rvp) = 0;
      word1(rvp) = 1;
      return;
#endif /* IEEE_Arith */
      }
    switch(rounding) {
      case Round_near:
      goto ovfl1;
      case Round_up:
      if (!sign)
        goto ovfl1;
      goto ret_big;
      case Round_down:
      if (sign)
        goto ovfl1;
      goto ret_big;
      }
 ret_big:
    word0(rvp) = Big0;
    word1(rvp) = Big1;
    return;
    }
  n = s1 - s0 - 1;
  for(k = 0; n > (1 << (kshift-2)) - 1; n >>= 1)
    k++;
  b = Balloc(k MTa);
  x = b->x;
  n = 0;
  L = 0;
#ifdef USE_LOCALE
  for(i = 0; decimalpoint[i+1]; ++i);
#endif
  while(s1 > s0) {
#ifdef USE_LOCALE
    if (*--s1 == decimalpoint[i]) {
      s1 -= i;
      continue;
      }
#else
    if (*--s1 == '.')
      continue;
#endif
    if (n == ULbits) {
      *x++ = L;
      L = 0;
      n = 0;
      }
    L |= (hexdig[*s1] & 0x0f) << n;
    n += 4;
    }
  *x++ = L;
  b->wds = n = x - b->x;
  n = ULbits*n - hi0bits(L);
  nbits = Nbits;
  lostbits = 0;
  x = b->x;
  if (n > nbits) {
    n -= nbits;
    if (any_on(b,n)) {
      lostbits = 1;
      k = n - 1;
      if (x[k>>kshift] & 1 << (k & kmask)) {
        lostbits = 2;
        if (k > 0 && any_on(b,k))
          lostbits = 3;
        }
      }
    rshift(b, n);
    e += n;
    }
  else if (n < nbits) {
    n = nbits - n;
    b = lshift(b, n MTa);
    e -= n;
    x = b->x;
    }
  if (e > emax) {
 ovfl:
    Bfree(b MTa);
 ovfl1:
    Set_errno(ERANGE);
#ifdef Honor_FLT_ROUNDS
    switch (rounding) {
      case Round_zero:
      goto ret_big;
      case Round_down:
      if (!sign)
        goto ret_big;
      break;
      case Round_up:
      if (sign)
        goto ret_big;
      }
#endif
    word0(rvp) = Exp_mask;
    word1(rvp) = 0;
    return;
    }
  denorm = 0;
  if (e < emin) {
    denorm = 1;
    n = emin - e;
    if (n >= nbits) {
#ifdef IEEE_Arith /*{*/
      switch (rounding) {
        case Round_near:
        if (n == nbits && (n < 2 || lostbits || any_on(b,n-1)))
          goto ret_tinyf;
        break;
        case Round_up:
        if (!sign)
          goto ret_tinyf;
        break;
        case Round_down:
        if (sign)
          goto ret_tinyf;
        }
#endif /* } IEEE_Arith */
      Bfree(b MTa);
 retz:
      Set_errno(ERANGE);
 retz1:
      rvp->d = 0.;
      return;
      }
    k = n - 1;
    if (lostbits)
      lostbits = 1;
    else if (k > 0)
      lostbits = any_on(b,k);
    if (x[k>>kshift] & 1 << (k & kmask))
      lostbits |= 2;
    nbits -= n;
    rshift(b,n);
    e = emin;
    }
  if (lostbits) {
    up = 0;
    switch(rounding) {
      case Round_zero:
      break;
      case Round_near:
      if (lostbits & 2
       && (lostbits & 1) | (x[0] & 1))
        up = 1;
      break;
      case Round_up:
      up = 1 - sign;
      break;
      case Round_down:
      up = sign;
      }
    if (up) {
      k = b->wds;
      b = increment(b MTa);
      x = b->x;
      if (denorm) {
#if 0
        if (nbits == Nbits - 1
         && x[nbits >> kshift] & 1 << (nbits & kmask))
          denorm = 0; /* not currently used */
#endif
        }
      else if (b->wds > k
       || ((n = nbits & kmask) !=0
           && hi0bits(x[k-1]) < 32-n)) {
        rshift(b,1);
        if (++e > Emax)
          goto ovfl;
        }
      }
    }
#ifdef IEEE_Arith
  if (denorm)
    word0(rvp) = b->wds > 1 ? b->x[1] & ~0x100000 : 0;
  else
    word0(rvp) = (b->x[1] & ~0x100000) | ((e + 0x3ff + 52) << 20);
  word1(rvp) = b->x[0];
#endif
#ifdef IBM
  if ((j = e & 3)) {
    k = b->x[0] & ((1 << j) - 1);
    rshift(b,j);
    if (k) {
      switch(rounding) {
        case Round_up:
        if (!sign)
          increment(b);
        break;
        case Round_down:
        if (sign)
          increment(b);
        break;
        case Round_near:
        j = 1 << (j-1);
        if (k & j && ((k & (j-1)) | lostbits))
          increment(b);
        }
      }
    }
  e >>= 2;
  word0(rvp) = b->x[1] | ((e + 65 + 13) << 24);
  word1(rvp) = b->x[0];
#endif
#ifdef VAX
  /* The next two lines ignore swap of low- and high-order 2 bytes. */
  /* word0(rvp) = (b->x[1] & ~0x800000) | ((e + 129 + 55) << 23); */
  /* word1(rvp) = b->x[0]; */
  word0(rvp) = ((b->x[1] & ~0x800000) >> 16) | ((e + 129 + 55) << 7) | (b->x[1] << 16);
  word1(rvp) = (b->x[0] >> 16) | (b->x[0] << 16);
#endif
  Bfree(b MTa);
  }
#endif /*!NO_HEX_FP}*/

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

 static int
quorem(Bigint *b, Bigint *S)
{
  int n;
  ULong *bx, *bxe, q, *sx, *sxe;
#ifdef ULLong
  ULLong borrow, carry, y, ys;
#else
  ULong borrow, carry, y, ys;
#ifdef Pack_32
  ULong si, z, zs;
#endif
#endif

  n = S->wds;
#ifdef DEBUG
  /*debug*/ if (b->wds > n)
  /*debug*/ Bug("oversize b in quorem");
#endif
  if (b->wds < n)
    return 0;
  sx = S->x;
  sxe = sx + --n;
  bx = b->x;
  bxe = bx + n;
  q = *bxe / (*sxe + 1);  /* ensure q <= true quotient */
#ifdef DEBUG
#ifdef NO_STRTOD_BIGCOMP
  /*debug*/ if (q > 9)
#else
  /* An oversized q is possible when quorem is called from bigcomp and */
  /* the input is near, e.g., twice the smallest denormalized number. */
  /*debug*/ if (q > 15)
#endif
  /*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;
  }

#if defined(Avoid_Underflow) || !defined(NO_STRTOD_BIGCOMP) /*{*/
 static double
sulp(U *x, BCinfo *bc)
{
  U u;
  double rv;
  int i;

  rv = ulp(x);
  if (!bc->scale || (i = 2*P + 1 - ((word0(x) & Exp_mask) >> Exp_shift)) <= 0)
    return rv; /* Is there an example where i <= 0 ? */
  word0(&u) = Exp_1 + (i << Exp_shift);
  word1(&u) = 0;
  return rv * u.d;
  }
#endif /*}*/

#ifndef NO_STRTOD_BIGCOMP
 static void
bigcomp(U *rv, const char *s0, BCinfo *bc MTd)
{
  Bigint *b, *d;
  int b2, bbits, d2, dd, dig, dsign, i, j, nd, nd0, p2, p5, speccase;

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

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

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

  /* Compare b/d with s0 */

  for(i = 0; i < nd0; ) {
    if ((dd = s0[i++] - '0' - dig))
      goto ret;
    if (!b->x[0] && b->wds == 1) {
      if (i < nd)
        dd = 1;
      goto ret;
      }
    b = multadd(b, 10, 0 MTa);
    dig = quorem(b,d);
    }
  for(j = bc->dp1; i++ < nd;) {
    if ((dd = s0[j++] - '0' - dig))
      goto ret;
    if (!b->x[0] && b->wds == 1) {
      if (i < nd)
        dd = 1;
      goto ret;
      }
    b = multadd(b, 10, 0 MTa);
    dig = quorem(b,d);
    }
  if (dig > 0 || b->x[0] || b->wds > 1)
    dd = -1;
 ret:
  Bfree(b MTa);
  Bfree(d MTa);
#ifdef Honor_FLT_ROUNDS
  if (bc->rounding != 1) {
    if (dd < 0) {
      if (bc->rounding == 0) {
        if (!dsign)
          goto retlow1;
        }
      else if (dsign)
        goto rethi1;
      }
    else if (dd > 0) {
      if (bc->rounding == 0) {
        if (dsign)
          goto rethi1;
        goto ret1;
        }
      if (!dsign)
        goto rethi1;
      dval(rv) += 2.*sulp(rv,bc);
      }
    else {
      bc->inexact = 0;
      if (dsign)
        goto rethi1;
      }
    }
  else
#endif
  if (speccase) {
    if (dd <= 0)
      rv->d = 0.;
    }
  else if (dd < 0) {
    if (!dsign)  /* does not happen for round-near */
retlow1:
      dval(rv) -= sulp(rv,bc);
    }
  else if (dd > 0) {
    if (dsign) {
 rethi1:
      dval(rv) += sulp(rv,bc);
      }
    }
  else {
    /* Exact half-way case:  apply round-even rule. */
    if ((j = ((word0(rv) & Exp_mask) >> Exp_shift) - bc->scale) <= 0) {
      i = 1 - j;
      if (i <= 31) {
        if (word1(rv) & (0x1 << i))
          goto odd;
        }
      else if (word0(rv) & (0x1 << (i-32)))
        goto odd;
      }
    else if (word1(rv) & 1) {
 odd:
      if (dsign)
        goto rethi1;
      goto retlow1;
      }
    }

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

 double
strtod2(const char *s00, char **se __XS__d)
{
  int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, e, e1;
  int esign, i, j, k, nd, nd0, nf, nz, nz0, nz1, sign;
  const char *s, *s0, *s1;
  double aadj, aadj1;
  Long L;
  U aadj2, adj, rv, rv0;
  ULong y, z;
  BCinfo bc;
  Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
#ifdef USE_BF96
  ULLong bhi, blo, brv, t00, t01, t02, t10, t11, terv, tg, tlo, yz;
  const BF96 *p10;
  int bexact, erv;
#endif
#ifdef Avoid_Underflow
#ifndef ROUND_BIASED
  ULong Lsb;
  ULong Lsb1;
#endif
#endif
#ifdef SET_INEXACT
  int oldinexact;
#endif
#ifndef NO_STRTOD_BIGCOMP
  int req_bigcomp = 0;
#endif
#ifdef MULTIPLE_THREADS
  ThInfo *TI = 0;
#endif
#ifdef Honor_FLT_ROUNDS /*{*/
#ifdef Trust_FLT_ROUNDS /*{{ only define this if FLT_ROUNDS really works! */
  bc.rounding = Flt_Rounds;
#else /*}{*/
  bc.rounding = 1;
  switch(fegetround()) {
    case FE_TOWARDZERO: bc.rounding = 0; break;
    case FE_UPWARD: bc.rounding = 2; break;
    case FE_DOWNWARD: bc.rounding = 3;
    }
#endif /*}}*/
#endif /*}*/
#ifdef USE_LOCALE
  const char *s2;
#endif

  sign = nz0 = nz1 = nz = bc.dplen = bc.uflchk = 0;
  dval(&rv) = 0.;
  for(s = s00;;s++) switch(c_read8(s)) {
    case '-':
      sign = 1;
      /* no break */
    case '+':
      if (c_read8(++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 (c_read8(s) == '0') {
#ifndef NO_HEX_FP /*{*/
    switch(s[1]) {
      case 'x':
      case 'X':
#ifdef Honor_FLT_ROUNDS
      gethex(&s, &rv, bc.rounding, sign MTb);
#else
      gethex(&s, &rv, 1, sign MTb);
#endif
      goto ret;
      }
#endif /*}*/
    nz0 = 1;
    while(c_read8(++s) == '0') ;
    if (!c_read8(s))
      goto ret;
    }
  s0 = s;
  nd = nf = 0;
#ifdef USE_BF96
  yz = 0;
  for(; (c = c_read8(s)) >= '0' && c <= '9'; nd++, s++)
    if (nd < 19)
      yz = 10*yz + c - '0';
#else
  y = z = 0;
  for(; (c = c_read8(s)) >= '0' && c <= '9'; nd++, s++)
    if (nd < 9)
      y = 10*y + c - '0';
    else if (nd < DBL_DIG + 2)
      z = 10*z + c - '0';
#endif
  nd0 = nd;
  bc.dp0 = bc.dp1 = (int)(s - s0);
  for(s1 = s; s1 > s0 && *--s1 == '0'; )
    ++nz1;
#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 = c_read8(++s);
    bc.dp1 = (int)(s - s0);
    bc.dplen = bc.dp1 - bc.dp0;
    if (!nd) {
      for(; c == '0'; c = c_read8(++s))
        nz++;
      if (c > '0' && c <= '9') {
        bc.dp0 = (int)(s0 - s);
        bc.dp1 = bc.dp0 + bc.dplen;
        s0 = s;
        nf += nz;
        nz = 0;
        goto have_dig;
        }
      goto dig_done;
      }
    for(; c >= '0' && c <= '9'; c = c_read8(++s)) {
 have_dig:
      nz++;
      if (c -= '0') {
        nf += nz;
        i = 1;
#ifdef USE_BF96
        for(; i < nz; ++i) {
          if (++nd <= 19)
            yz *= 10;
          }
        if (++nd <= 19)
          yz = 10*yz + c;
#else
        for(; i < nz; ++i) {
          if (nd++ < 9)
            y *= 10;
          else if (nd <= DBL_DIG + 2)
            z *= 10;
          }
        if (nd++ < 9)
          y = 10*y + c;
        else if (nd <= DBL_DIG + 2)
          z = 10*z + c;
#endif
        nz = nz1 = 0;
        }
      }
    }
 dig_done:
  e = 0;
  if (c == 'e' || c == 'E') {
    if (!nd && !nz && !nz0) {
      goto ret0;
      }
    s00 = s;
    esign = 0;
    switch(c = c_read8(++s)) {
      case '-':
        esign = 1;
      case '+':
        c = c_read8(++s);
      }
    if (c >= '0' && c <= '9') {
      while(c == '0')
        c = c_read8(++s);
      if (c > '0' && c <= '9') {
        L = c - '0';
        s1 = s;
        while((c = *++s) >= '0' && c <= '9') {
          if (L <= 19999)
            L = 10*L + c - '0';
          }
        if (L > 19999)
          /* Avoid confusion from exponents
           * so large that e might overflow.
           */
          e = 19999; /* safe for 16 bit ints */
        else
          e = (int)L;
        if (esign)
          e = -e;
        }
      else
        e = 0;
      }
    else
      s = s00;
    }
  if (!nd) {
    if (!nz && !nz0) {
#ifdef INFNAN_CHECK /*{*/
      /* Check for Nan and Infinity */
      if (!bc.dplen)
       switch(c) {
#ifndef __XS__
        case 'i':
        case 'I':
        if (match(&s,"nf")) {
          --s;
          if (!match(&s,"inity"))
            ++s;
#else
        case 'I':
        if (match(&s,"nfinity")) {
#endif
          word0(&rv) = 0x7ff00000;
          word1(&rv) = 0;
          goto ret;
          }
        break;
#ifndef __XS__
        case 'n':
        case 'N':
        if (match(&s, "an")) {
#else
        case 'N':
        if (match(&s, "aN")) {
#endif
          word0(&rv) = NAN_WORD0;
          word1(&rv) = NAN_WORD1;
#ifndef No_Hex_NaN
          if (c_read8(s) == '(') /*)*/
            hexnan(&rv, &s);
#endif
          goto ret;
          }
        }
#endif /*} INFNAN_CHECK */
 ret0:
      s = s00;
      sign = 0;
      }
    goto ret;
    }
  bc.e0 = e1 = e -= nf;

  /* Now we have nd0 digits, starting at s0, followed by a
   * decimal point, followed by nd-nd0 digits.  The number we're
   * after is the integer represented by those digits times
   * 10**e */

  if (!nd0)
    nd0 = nd;
#ifndef USE_BF96
  k = nd < DBL_DIG + 2 ? nd : DBL_DIG + 2;
  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;
    }
#endif
  bd0 = 0;
  if (nd <= DBL_DIG
#ifndef RND_PRODQUOT
#ifndef Honor_FLT_ROUNDS
    && Flt_Rounds == 1
#endif
#endif
      ) {
#ifdef USE_BF96
    dval(&rv) = yz;
#endif
    if (!e)
      goto ret;
#ifndef ROUND_BIASED_without_Round_Up
    if (e > 0) {
      if (e <= Ten_pmax) {
#ifdef SET_INEXACT
        bc.inexact = 0;
        oldinexact = 1;
#endif
#ifdef VAX
        goto vax_ovfl_check;
#else
#ifdef Honor_FLT_ROUNDS
        /* round correctly FLT_ROUNDS = 2 or 3 */
        if (sign) {
          rv.d = -rv.d;
          sign = 0;
          }
#endif
        /* rv = */ rounded_product(dval(&rv), tens[e]);
        goto ret;
#endif
        }
      i = DBL_DIG - nd;
      if (e <= Ten_pmax + i) {
        /* A fancier test would sometimes let us do
         * this for larger i values.
         */
#ifdef SET_INEXACT
        bc.inexact = 0;
        oldinexact = 1;
#endif
#ifdef Honor_FLT_ROUNDS
        /* round correctly FLT_ROUNDS = 2 or 3 */
        if (sign) {
          rv.d = -rv.d;
          sign = 0;
          }
#endif
        e -= i;
        dval(&rv) *= tens[i];
#ifdef VAX
        /* VAX exponent range is so narrow we must
         * worry about overflow here...
         */
 vax_ovfl_check:
        word0(&rv) -= P*Exp_msk1;
        /* rv = */ rounded_product(dval(&rv), tens[e]);
        if ((word0(&rv) & Exp_mask)
         > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
          goto ovfl;
        word0(&rv) += P*Exp_msk1;
#else
        /* rv = */ rounded_product(dval(&rv), tens[e]);
#endif
        goto ret;
        }
      }
#ifndef Inaccurate_Divide
    else if (e >= -Ten_pmax) {
#ifdef SET_INEXACT
        bc.inexact = 0;
        oldinexact = 1;
#endif
#ifdef Honor_FLT_ROUNDS
      /* round correctly FLT_ROUNDS = 2 or 3 */
      if (sign) {
        rv.d = -rv.d;
        sign = 0;
        }
#endif
      /* rv = */ rounded_quotient(dval(&rv), tens[-e]);
      goto ret;
      }
#endif
#endif /* ROUND_BIASED_without_Round_Up */
    }
#ifdef USE_BF96
  k = nd < 19 ? nd : 19;
#endif
  e1 += nd - k; /* scale factor = 10^e1 */

#ifdef IEEE_Arith
#ifdef SET_INEXACT
  bc.inexact = 1;
#ifndef USE_BF96
  if (k <= DBL_DIG)
#endif
    oldinexact = get_inexact();
#endif
#ifdef Honor_FLT_ROUNDS
  if (bc.rounding >= 2) {
    if (sign)
      bc.rounding = bc.rounding == 2 ? 0 : 2;
    else
      if (bc.rounding != 2)
        bc.rounding = 0;
    }
#endif
#endif /*IEEE_Arith*/

#ifdef USE_BF96 /*{*/
  Debug(++dtoa_stats[0]);
  i = e1 + 342;
  if (i < 0)
    goto undfl;
  if (i > 650)
    goto ovfl;
  p10 = &pten[i];
  brv = yz;
  /* shift brv left, with i =  number of bits shifted */
  i = 0;
  if (!(brv & 0xffffffff00000000ull)) {
    i = 32;
    brv <<= 32;
    }
  if (!(brv & 0xffff000000000000ull)) {
    i += 16;
    brv <<= 16;
    }
  if (!(brv & 0xff00000000000000ull)) {
    i += 8;
    brv <<= 8;
    }
  if (!(brv & 0xf000000000000000ull)) {
    i += 4;
    brv <<= 4;
    }
  if (!(brv & 0xc000000000000000ull)) {
    i += 2;
    brv <<= 2;
    }
  if (!(brv & 0x8000000000000000ull)) {
    i += 1;
    brv <<= 1;
    }
  erv = (64 + 0x3fe) + p10->e - i;
  if (erv <= 0 && nd > 19)
    goto many_digits; /* denormal: may need to look at all digits */
  bhi = brv >> 32;
  blo = brv & 0xffffffffull;
  /* Unsigned 32-bit ints lie in [0,2^32-1] and */
  /* unsigned 64-bit ints lie in [0, 2^64-1].  The product of two unsigned */
  /* 32-bit ints is <= 2^64 - 2*2^32-1 + 1 = 2^64 - 1 - 2*(2^32 - 1), so */
  /* we can add two unsigned 32-bit ints to the product of two such ints, */
  /* and 64 bits suffice to contain the result. */
  t01 = bhi * p10->b1;
  t10 = blo * p10->b0 + (t01 & 0xffffffffull);
  t00 = bhi * p10->b0 + (t01 >> 32) + (t10 >> 32);
  if (t00 & 0x8000000000000000ull) {
    if ((t00 & 0x3ff) && (~t00 & 0x3fe)) { /* unambiguous result? */
      if (nd > 19 && ((t00 + (1<<i) + 2) & 0x400) ^ (t00 & 0x400))
        goto many_digits;
      if (erv <= 0)
        goto denormal;
#ifdef Honor_FLT_ROUNDS
      switch(bc.rounding) {
        case 0: goto noround;
        case 2: goto roundup;
        }
#endif
      if (t00 & 0x400 && t00 & 0xbff)
        goto roundup;
      goto noround;
      }
    }
  else {
    if ((t00 & 0x1ff) && (~t00 & 0x1fe)) { /* unambiguous result? */
      if (nd > 19 && ((t00 + (1<<i) + 2) & 0x200) ^ (t00 & 0x200))
        goto many_digits;
      if (erv <= 1)
        goto denormal1;
#ifdef Honor_FLT_ROUNDS
      switch(bc.rounding) {
        case 0: goto noround1;
        case 2: goto roundup1;
        }
#endif
      if (t00 & 0x200)
        goto roundup1;
      goto noround1;
      }
    }
  /* 3 multiplies did not suffice; try a 96-bit approximation */
  Debug(++dtoa_stats[1]);
  t02 = bhi * p10->b2;
  t11 = blo * p10->b1 + (t02 & 0xffffffffull);
  bexact = 1;
  if (e1 < 0 || e1 > 41 || (t10 | t11) & 0xffffffffull || nd > 19)
    bexact = 0;
  tlo = (t10 & 0xffffffffull) + (t02 >> 32) + (t11 >> 32);
  if (!bexact && (tlo + 0x10) >> 32 > tlo >> 32)
    goto many_digits;
  t00 += tlo >> 32;
  if (t00 & 0x8000000000000000ull) {
    if (erv <= 0) { /* denormal result */
      if (nd >= 20 || !((tlo & 0xfffffff0) | (t00 & 0x3ff)))
        goto many_digits;
 denormal:
      if (erv <= -52) {
#ifdef Honor_FLT_ROUNDS
        switch(bc.rounding) {
          case 0: goto undfl;
          case 2: goto tiniest;
          }
#endif
        if (erv < -52 || !(t00 & 0x7fffffffffffffffull))
          goto undfl;
        goto tiniest;
        }
      tg = 1ull << (11 - erv);
      t00 &= ~(tg - 1); /* clear low bits */
#ifdef Honor_FLT_ROUNDS
      switch(bc.rounding) {
        case 0: goto noround_den;
        case 2: goto roundup_den;
        }
#endif
      if (t00 & tg) {
#ifdef Honor_FLT_ROUNDS
 roundup_den:
#endif
        t00 += tg << 1;
        if (!(t00 & 0x8000000000000000ull)) {
          if (++erv > 0)
            goto smallest_normal;
          t00 = 0x8000000000000000ull;
          }
        }
#ifdef Honor_FLT_ROUNDS
 noround_den:
#endif
      LLval(&rv) = t00 >> (12 - erv);
      Set_errno(ERANGE);
      goto ret;
      }
    if (bexact) {
#ifdef SET_INEXACT
      if (!(t00 & 0x7ff) && !(tlo & 0xffffffffull)) {
        bc.inexact = 0;
        goto noround;
        }
#endif
#ifdef Honor_FLT_ROUNDS
      switch(bc.rounding) {
        case 2:
        if (t00 & 0x7ff)
          goto roundup;
        case 0: goto noround;
        }
#endif
      if (t00 & 0x400 && (tlo & 0xffffffff) | (t00 & 0xbff))
        goto roundup;
      goto noround;
      }
    if ((tlo & 0xfffffff0) | (t00 & 0x3ff)
     && (nd <= 19 ||  ((t00 + (1ull << i)) & 0xfffffffffffffc00ull)
        == (t00 & 0xfffffffffffffc00ull))) {
      /* Unambiguous result. */
      /* If nd > 19, then incrementing the 19th digit */
      /* does not affect rv. */
#ifdef Honor_FLT_ROUNDS
      switch(bc.rounding) {
        case 0: goto noround;
        case 2: goto roundup;
        }
#endif
      if (t00 & 0x400) { /* round up */
 roundup:
        t00 += 0x800;
        if (!(t00 & 0x8000000000000000ull)) {
          /* rounded up to a power of 2 */
          if (erv >= 0x7fe)
            goto ovfl;
          terv = erv + 1;
          LLval(&rv) = terv << 52;
          goto ret;
          }
        }
 noround:
      if (erv >= 0x7ff)
        goto ovfl;
      terv = erv;
      LLval(&rv) = (terv << 52) | ((t00 & 0x7ffffffffffff800ull) >> 11);
      goto ret;
      }
    }
  else {
    if (erv <= 1) { /* denormal result */
      if (nd >= 20 || !((tlo & 0xfffffff0) | (t00 & 0x1ff)))
        goto many_digits;
 denormal1:
      if (erv <= -51) {
#ifdef Honor_FLT_ROUNDS
        switch(bc.rounding) {
          case 0: goto undfl;
          case 2: goto tiniest;
          }
#endif
        if (erv < -51 || !(t00 & 0x3fffffffffffffffull))
          goto undfl;
 tiniest:
        LLval(&rv) = 1;
        Set_errno(ERANGE);
        goto ret;
        }
      tg = 1ull << (11 - erv);
#ifdef Honor_FLT_ROUNDS
      switch(bc.rounding) {
        case 0: goto noround1_den;
        case 2: goto roundup1_den;
        }
#endif
      if (t00 & tg) {
#ifdef Honor_FLT_ROUNDS
 roundup1_den:
#endif
        if (0x8000000000000000ull & (t00 += (tg<<1)) && erv == 1) {

 smallest_normal:
          LLval(&rv) = 0x0010000000000000ull;
          goto ret;
          }
        }
#ifdef Honor_FLT_ROUNDS
 noround1_den:
#endif
      if (erv <= -52)
        goto undfl;
      LLval(&rv) = t00 >> (12 - erv);
      Set_errno(ERANGE);
      goto ret;
      }
    if (bexact) {
#ifdef SET_INEXACT
      if (!(t00 & 0x3ff) && !(tlo & 0xffffffffull)) {
        bc.inexact = 0;
        goto noround1;
        }
#endif
#ifdef Honor_FLT_ROUNDS
      switch(bc.rounding) {
        case 2:
        if (t00 & 0x3ff)
          goto roundup1;
        case 0: goto noround1;
        }
#endif
      if (t00 & 0x200 && (t00 & 0x5ff || tlo))
        goto roundup1;
      goto noround1;
      }
    if ((tlo & 0xfffffff0) | (t00 & 0x1ff)
     && (nd <= 19 ||  ((t00 + (1ull << i)) & 0x7ffffffffffffe00ull)
        == (t00 & 0x7ffffffffffffe00ull))) {
      /* Unambiguous result. */
#ifdef Honor_FLT_ROUNDS
      switch(bc.rounding) {
        case 0: goto noround1;
        case 2: goto roundup1;
        }
#endif
      if (t00 & 0x200) { /* round up */
 roundup1:
        t00 += 0x400;
        if (!(t00 & 0x4000000000000000ull)) {
          /* rounded up to a power of 2 */
          if (erv >= 0x7ff)
            goto ovfl;
          terv = erv;
          LLval(&rv) = terv << 52;
          goto ret;
          }
        }
 noround1:
      if (erv >= 0x800)
        goto ovfl;
      terv = erv - 1;
      LLval(&rv) = (terv << 52) | ((t00 & 0x3ffffffffffffc00ull) >> 10);
      goto ret;
      }
    }
 many_digits:
  Debug(++dtoa_stats[2]);
  if (nd > 17) {
    if (nd > 18) {
      yz /= 100;
      e1 += 2;
      }
    else {
      yz /= 10;
      e1 += 1;
      }
    y = yz / 100000000;
    }
  else if (nd > 9) {
    i = nd - 9;
    y = (yz >> i) / pfive[i-1];
    }
  else
    y = yz;
  dval(&rv) = yz;
#endif /*}*/

#ifdef IEEE_Arith
#ifdef Avoid_Underflow
  bc.scale = 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:
        /* Can't trust HUGE_VAL */
#ifdef IEEE_Arith
#ifdef Honor_FLT_ROUNDS
        switch(bc.rounding) {
          case 0: /* toward 0 */
          case 3: /* toward -infinity */
          word0(&rv) = Big0;
          word1(&rv) = Big1;
          break;
          default:
          word0(&rv) = Exp_mask;
          word1(&rv) = 0;
          }
#else /*Honor_FLT_ROUNDS*/
        word0(&rv) = Exp_mask;
        word1(&rv) = 0;
#endif /*Honor_FLT_ROUNDS*/
#ifdef SET_INEXACT
        /* set overflow bit */
        dval(&rv0) = 1e300;
        dval(&rv0) *= dval(&rv0);
#endif
#else /*IEEE_Arith*/
        word0(&rv) = Big0;
        word1(&rv) = Big1;
#endif /*IEEE_Arith*/
 range_err:
        if (bd0) {
          Bfree(bb MTb);
          Bfree(bd MTb);
          Bfree(bs MTb);
          Bfree(bd0 MTb);
          Bfree(delta MTb);
          }
        Set_errno(ERANGE);
        goto ret;
        }
      e1 >>= 4;
      for(j = 0; e1 > 1; j++, e1 >>= 1)
        if (e1 & 1)
          dval(&rv) *= bigtens[j];
    /* The last multiplication could overflow. */
      word0(&rv) -= P*Exp_msk1;
      dval(&rv) *= bigtens[j];
      if ((z = word0(&rv) & Exp_mask)
       > Exp_msk1*(DBL_MAX_EXP+Bias-P))
        goto ovfl;
      if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
        /* set to largest number */
        /* (Can't trust DBL_MAX) */
        word0(&rv) = Big0;
        word1(&rv) = Big1;
        }
      else
        word0(&rv) += P*Exp_msk1;
      }
    }
  else if (e1 < 0) {
    e1 = -e1;
    if ((i = e1 & 15))
      dval(&rv) /= tens[i];
    if (e1 >>= 4) {
      if (e1 >= 1 << n_bigtens)
        goto undfl;
#ifdef Avoid_Underflow
      if (e1 & Scale_Bit)
        bc.scale = 2*P;
      for(j = 0; e1 > 0; j++, e1 >>= 1)
        if (e1 & 1)
          dval(&rv) *= tinytens[j];
      if (bc.scale && (j = 2*P + 1 - ((word0(&rv) & Exp_mask)
            >> Exp_shift)) > 0) {
        /* scaled rv is denormal; clear j low bits */
        if (j >= 32) {
          if (j > 54)
            goto undfl;
          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.;
#ifdef Honor_FLT_ROUNDS
          if (bc.rounding == 2)
            word1(&rv) = 1;
#endif
          goto range_err;
          }
#ifndef Avoid_Underflow
        word0(&rv) = Tiny0;
        word1(&rv) = Tiny1;
        /* The refinement below will clean
         * this approximation up.
         */
        }
#endif
      }
    }

  /* Now the hard part -- adjusting rv to the correct value.*/

  /* Put digits into bd: true value = bd * 10^e */

  bc.nd = nd - nz1;
#ifndef NO_STRTOD_BIGCOMP
  bc.nd0 = nd0; /* Only needed if nd > strtod_diglim, but done here */
      /* to silence an erroneous warning about bc.nd0 */
      /* possibly not being initialized. */
  if (nd > strtod_diglim) {
    /* ASSERT(strtod_diglim >= 18); 18 == one more than the */
    /* minimum number of decimal digits to distinguish double values */
    /* in IEEE arithmetic. */
    i = j = 18;
    if (i > nd0)
      j += bc.dplen;
    for(;;) {
      if (--j < bc.dp1 && j >= bc.dp0)
        j = bc.dp0 - 1;
      if (s0[j] != '0')
        break;
      --i;
      }
    e += nd - i;
    nd = i;
    if (nd0 > nd)
      nd0 = nd;
    if (nd < 9) { /* must recompute y */
      y = 0;
      for(i = 0; i < nd0; ++i)
        y = 10*y + s0[i] - '0';
      for(j = bc.dp1; i < nd; ++i)
        y = 10*y + s0[j++] - '0';
      }
    }
#endif
  bd0 = s2b(s0, nd0, nd, y, bc.dplen MTb);

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

    if (e >= 0) {
      bb2 = bb5 = 0;
      bd2 = bd5 = e;
      }
    else {
      bb2 = bb5 = -e;
      bd2 = bd5 = 0;
      }
    if (bbe >= 0)
      bb2 += bbe;
    else
      bd2 -= bbe;
    bs2 = bb2;
#ifdef Honor_FLT_ROUNDS
    if (bc.rounding != 1)
      bs2++;
#endif
#ifdef Avoid_Underflow
#ifndef ROUND_BIASED
    Lsb = LSB;
    Lsb1 = 0;
#endif
    j = bbe - bc.scale;
    i = j + bbbits - 1; /* logb(rv) */
    j = P + 1 - bbbits;
    if (i < Emin) { /* denormal */
      i = Emin - i;
      j -= i;
#ifndef ROUND_BIASED
      if (i < 32)
        Lsb <<= i;
      else if (i < 52)
        Lsb1 = Lsb << (i-32);
      else
        Lsb1 = Exp_mask;
#endif
      }
#else /*Avoid_Underflow*/
#ifdef Sudden_Underflow
#ifdef IBM
    j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
#else
    j = P + 1 - bbbits;
#endif
#else /*Sudden_Underflow*/
    j = bbe;
    i = j + bbbits - 1; /* logb(rv) */
    if (i < Emin) /* denormal */
      j += P - Emin;
    else
      j = P + 1 - bbbits;
#endif /*Sudden_Underflow*/
#endif /*Avoid_Underflow*/
    bb2 += j;
    bd2 += j;
#ifdef Avoid_Underflow
    bd2 += bc.scale;
#endif
    i = bb2 < bd2 ? bb2 : bd2;
    if (i > bs2)
      i = bs2;
    if (i > 0) {
      bb2 -= i;
      bd2 -= i;
      bs2 -= i;
      }
    if (bb5 > 0) {
      bs = pow5mult(bs, bb5 MTb);
      bb1 = mult(bs, bb MTb);
      Bfree(bb MTb);
      bb = bb1;
      }
    if (bb2 > 0)
      bb = lshift(bb, bb2 MTb);
    if (bd5 > 0)
      bd = pow5mult(bd, bd5 MTb);
    if (bd2 > 0)
      bd = lshift(bd, bd2 MTb);
    if (bs2 > 0)
      bs = lshift(bs, bs2 MTb);
    delta = diff(bb, bd MTb);
    bc.dsign = delta->sign;
    delta->sign = 0;
    i = cmp(delta, bs);
#ifndef NO_STRTOD_BIGCOMP /*{*/
    if (bc.nd > nd && i <= 0) {
      if (bc.dsign) {
        /* Must use bigcomp(). */
        req_bigcomp = 1;
        break;
        }
#ifdef Honor_FLT_ROUNDS
      if (bc.rounding != 1) {
        if (i < 0) {
          req_bigcomp = 1;
          break;
          }
        }
      else
#endif
        i = -1; /* Discarded digits make delta smaller. */
      }
#endif /*}*/
#ifdef Honor_FLT_ROUNDS /*{*/
    if (bc.rounding != 1) {
      if (i < 0) {
        /* Error is less than an ulp */
        if (!delta->x[0] && delta->wds <= 1) {
          /* exact */
#ifdef SET_INEXACT
          bc.inexact = 0;
#endif
          break;
          }
        if (bc.rounding) {
          if (bc.dsign) {
            adj.d = 1.;
            goto apply_adj;
            }
          }
        else if (!bc.dsign) {
          adj.d = -1.;
          if (!word1(&rv)
           && !(word0(&rv) & Frac_mask)) {
            y = word0(&rv) & Exp_mask;
#ifdef Avoid_Underflow
            if (!bc.scale || y > 2*P*Exp_msk1)
#else
            if (y)
#endif
              {
              delta = lshift(delta,Log2P MTb);
              if (cmp(delta, bs) <= 0)
              adj.d = -0.5;
              }
            }
 apply_adj:
#ifdef Avoid_Underflow /*{*/
          if (bc.scale && (y = word0(&rv) & Exp_mask)
            <= 2*P*Exp_msk1)
            word0(&adj) += (2*P+1)*Exp_msk1 - y;
#else
#ifdef Sudden_Underflow
          if ((word0(&rv) & Exp_mask) <=
              P*Exp_msk1) {
            word0(&rv) += P*Exp_msk1;
            dval(&rv) += adj.d*ulp(dval(&rv));
            word0(&rv) -= P*Exp_msk1;
            }
          else
#endif /*Sudden_Underflow*/
#endif /*Avoid_Underflow}*/
          dval(&rv) += adj.d*ulp(&rv);
          }
        break;
        }
      adj.d = ratio(delta, bs);
      if (adj.d < 1.)
        adj.d = 1.;
      if (adj.d <= 0x7ffffffe) {
        /* adj = rounding ? ceil(adj) : floor(adj); */
        y = adj.d;
        if (y != adj.d) {
          if (!((bc.rounding>>1) ^ bc.dsign))
            y++;
          adj.d = y;
          }
        }
#ifdef Avoid_Underflow /*{*/
      if (bc.scale && (y = word0(&rv) & Exp_mask) <= 2*P*Exp_msk1)
        word0(&adj) += (2*P+1)*Exp_msk1 - y;
#else
#ifdef Sudden_Underflow
      if ((word0(&rv) & Exp_mask) <= P*Exp_msk1) {
        word0(&rv) += P*Exp_msk1;
        adj.d *= ulp(dval(&rv));
        if (bc.dsign)
          dval(&rv) += adj.d;
        else
          dval(&rv) -= adj.d;
        word0(&rv) -= P*Exp_msk1;
        goto cont;
        }
#endif /*Sudden_Underflow*/
#endif /*Avoid_Underflow}*/
      adj.d *= ulp(&rv);
      if (bc.dsign) {
        if (word0(&rv) == Big0 && word1(&rv) == Big1)
          goto ovfl;
        dval(&rv) += adj.d;
        }
      else
        dval(&rv) -= adj.d;
      goto cont;
      }
#endif /*}Honor_FLT_ROUNDS*/

    if (i < 0) {
      /* Error is less than half an ulp -- check for
       * special case of mantissa a power of two.
       */
      if (bc.dsign || word1(&rv) || word0(&rv) & Bndry_mask
#ifdef IEEE_Arith /*{*/
#ifdef Avoid_Underflow
       || (word0(&rv) & Exp_mask) <= (2*P+1)*Exp_msk1
#else
       || (word0(&rv) & Exp_mask) <= Exp_msk1
#endif
#endif /*}*/
        ) {
#ifdef SET_INEXACT
        if (!delta->x[0] && delta->wds <= 1)
          bc.inexact = 0;
#endif
        break;
        }
      if (!delta->x[0] && delta->wds <= 1) {
        /* exact result */
#ifdef SET_INEXACT
        bc.inexact = 0;
#endif
        break;
        }
      delta = lshift(delta,Log2P MTb);
      if (cmp(delta, bs) > 0)
        goto drop_down;
      break;
      }
    if (i == 0) {
      /* exactly half-way between */
      if (bc.dsign) {
        if ((word0(&rv) & Bndry_mask1) == Bndry_mask1
         &&  word1(&rv) == (
#ifdef Avoid_Underflow
      (bc.scale && (y = word0(&rv) & Exp_mask) <= 2*P*Exp_msk1)
    ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
#endif
               0xffffffff)) {
          /*boundary case -- increment exponent*/
          if (word0(&rv) == Big0 && word1(&rv) == Big1)
            goto ovfl;
          word0(&rv) = (word0(&rv) & Exp_mask)
            + Exp_msk1
#ifdef IBM
            | Exp_msk1 >> 4
#endif
            ;
          word1(&rv) = 0;
#ifdef Avoid_Underflow
          bc.dsign = 0;
#endif
          break;
          }
        }
      else if (!(word0(&rv) & Bndry_mask) && !word1(&rv)) {
 drop_down:
        /* boundary case -- decrement exponent */
#ifdef Sudden_Underflow /*{{*/
        L = word0(&rv) & Exp_mask;
#ifdef IBM
        if (L <  Exp_msk1)
#else
#ifdef Avoid_Underflow
        if (L <= (bc.scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
#else
        if (L <= Exp_msk1)
#endif /*Avoid_Underflow*/
#endif /*IBM*/
          {
          if (bc.nd >nd) {
            bc.uflchk = 1;
            break;
            }
          goto undfl;
          }
        L -= Exp_msk1;
#else /*Sudden_Underflow}{*/
#ifdef Avoid_Underflow
        if (bc.scale) {
          L = word0(&rv) & Exp_mask;
          if (L <= (2*P+1)*Exp_msk1) {
            if (L > (P+2)*Exp_msk1)
              /* round even ==> */
              /* accept rv */
              break;
            /* rv = smallest denormal */
            if (bc.nd >nd) {
              bc.uflchk = 1;
              break;
              }
            goto undfl;
            }
          }
#endif /*Avoid_Underflow*/
        L = (word0(&rv) & Exp_mask) - Exp_msk1;
#endif /*Sudden_Underflow}}*/
        word0(&rv) = L | Bndry_mask1;
        word1(&rv) = 0xffffffff;
#ifdef IBM
        goto cont;
#else
#ifndef NO_STRTOD_BIGCOMP
        if (bc.nd > nd)
          goto cont;
#endif
        break;
#endif
        }
#ifndef ROUND_BIASED
#ifdef Avoid_Underflow
      if (Lsb1) {
        if (!(word0(&rv) & Lsb1))
          break;
        }
      else if (!(word1(&rv) & Lsb))
        break;
#else
      if (!(word1(&rv) & LSB))
        break;
#endif
#endif
      if (bc.dsign)
#ifdef Avoid_Underflow
        dval(&rv) += sulp(&rv, &bc);
#else
        dval(&rv) += ulp(&rv);
#endif
#ifndef ROUND_BIASED
      else {
#ifdef Avoid_Underflow
        dval(&rv) -= sulp(&rv, &bc);
#else
        dval(&rv) -= ulp(&rv);
#endif
#ifndef Sudden_Underflow
        if (!dval(&rv)) {
          if (bc.nd >nd) {
            bc.uflchk = 1;
            break;
            }
          goto undfl;
          }
#endif
        }
#ifdef Avoid_Underflow
      bc.dsign = 1 - bc.dsign;
#endif
#endif
      break;
      }
    if ((aadj = ratio(delta, bs)) <= 2.) {
      if (bc.dsign)
        aadj = aadj1 = 1.;
      else if (word1(&rv) || word0(&rv) & Bndry_mask) {
#ifndef Sudden_Underflow
        if (word1(&rv) == Tiny1 && !word0(&rv)) {
          if (bc.nd >nd) {
            bc.uflchk = 1;
            break;
            }
          goto undfl;
          }
#endif
        aadj = 1.;
        aadj1 = -1.;
        }
      else {
        /* special case -- power of FLT_RADIX to be */
        /* rounded down... */

        if (aadj < 2./FLT_RADIX)
          aadj = 1./FLT_RADIX;
        else
          aadj *= 0.5;
        aadj1 = -aadj;
        }
      }
    else {
      aadj *= 0.5;
      aadj1 = bc.dsign ? aadj : -aadj;
#ifdef Check_FLT_ROUNDS
      switch(bc.rounding) {
        case 2: /* towards +infinity */
          aadj1 -= 0.5;
          break;
        case 0: /* towards 0 */
        case 3: /* towards -infinity */
          aadj1 += 0.5;
        }
#else
      if (Flt_Rounds == 0)
        aadj1 += 0.5;
#endif /*Check_FLT_ROUNDS*/
      }
    y = word0(&rv) & Exp_mask;

    /* Check for overflow */

    if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
      dval(&rv0) = dval(&rv);
      word0(&rv) -= P*Exp_msk1;
      adj.d = aadj1 * ulp(&rv);
      dval(&rv) += adj.d;
      if ((word0(&rv) & Exp_mask) >=
          Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
        if (word0(&rv0) == Big0 && word1(&rv0) == Big1)
          goto ovfl;
        word0(&rv) = Big0;
        word1(&rv) = Big1;
        goto cont;
        }
      else
        word0(&rv) += P*Exp_msk1;
      }
    else {
#ifdef Avoid_Underflow
      if (bc.scale && y <= 2*P*Exp_msk1) {
        if (aadj <= 0x7fffffff) {
          if ((z = (ULong)aadj) <= 0)
            z = 1;
          aadj = z;
          aadj1 = bc.dsign ? aadj : -aadj;
          }
        dval(&aadj2) = aadj1;
        word0(&aadj2) += (2*P+1)*Exp_msk1 - y;
        aadj1 = dval(&aadj2);
        adj.d = aadj1 * ulp(&rv);
        dval(&rv) += adj.d;
        if (rv.d == 0.)
#ifdef NO_STRTOD_BIGCOMP
          goto undfl;
#else
          {
          req_bigcomp = 1;
          break;
          }
#endif
        }
      else {
        adj.d = aadj1 * ulp(&rv);
        dval(&rv) += adj.d;
        }
#else
#ifdef Sudden_Underflow
      if ((word0(&rv) & Exp_mask) <= P*Exp_msk1) {
        dval(&rv0) = dval(&rv);
        word0(&rv) += P*Exp_msk1;
        adj.d = aadj1 * ulp(&rv);
        dval(&rv) += adj.d;
#ifdef IBM
        if ((word0(&rv) & Exp_mask) <  P*Exp_msk1)
#else
        if ((word0(&rv) & Exp_mask) <= P*Exp_msk1)
#endif
          {
          if (word0(&rv0) == Tiny0
           && word1(&rv0) == Tiny1) {
            if (bc.nd >nd) {
              bc.uflchk = 1;
              break;
              }
            goto undfl;
            }
          word0(&rv) = Tiny0;
          word1(&rv) = Tiny1;
          goto cont;
          }
        else
          word0(&rv) -= P*Exp_msk1;
        }
      else {
        adj.d = aadj1 * ulp(&rv);
        dval(&rv) += adj.d;
        }
#else /*Sudden_Underflow*/
      /* Compute adj so that the IEEE rounding rules will
       * correctly round rv + adj in some half-way cases.
       * If rv * ulp(rv) is denormalized (i.e.,
       * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
       * trouble from bits lost to denormalization;
       * example: 1.2e-307 .
       */
      if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
        aadj1 = (double)(int)(aadj + 0.5);
        if (!bc.dsign)
          aadj1 = -aadj1;
        }
      adj.d = aadj1 * ulp(&rv);
      dval(&rv) += adj.d;
#endif /*Sudden_Underflow*/
#endif /*Avoid_Underflow*/
      }
    z = word0(&rv) & Exp_mask;
#ifndef SET_INEXACT
    if (bc.nd == nd) {
#ifdef Avoid_Underflow
    if (!bc.scale)
#endif
    if (y == z) {
      /* Can we stop now? */
      L = (Long)aadj;
      aadj -= L;
      /* The tolerances below are conservative. */
      if (bc.dsign || word1(&rv) || word0(&rv) & Bndry_mask) {
        if (aadj < .4999999 || aadj > .5000001)
          break;
        }
      else if (aadj < .4999999/FLT_RADIX)
        break;
      }
    }
#endif
 cont:
    Bfree(bb MTb);
    Bfree(bd MTb);
    Bfree(bs MTb);
    Bfree(delta MTb);
    }
  Bfree(bb MTb);
  Bfree(bd MTb);
  Bfree(bs MTb);
  Bfree(bd0 MTb);
  Bfree(delta MTb);
#ifndef NO_STRTOD_BIGCOMP
  if (req_bigcomp) {
    bd0 = 0;
    bc.e0 += nz1;
    bigcomp(&rv, s0, &bc MTb);
    y = word0(&rv) & Exp_mask;
    if (y == Exp_mask)
      goto ovfl;
    if (y == 0 && rv.d == 0.)
      goto undfl;
    }
#endif
#ifdef Avoid_Underflow
  if (bc.scale) {
    word0(&rv0) = Exp_1 - 2*P*Exp_msk1;
    word1(&rv0) = 0;
    dval(&rv) *= dval(&rv0);
#ifndef NO_ERRNO
    /* try to avoid the bug of testing an 8087 register value */
#ifdef IEEE_Arith
    if (!(word0(&rv) & Exp_mask))
#else
    if (word0(&rv) == 0 && word1(&rv) == 0)
#endif
      Set_errno(ERANGE);
#endif
    }
#endif /* Avoid_Underflow */
 ret:
#ifdef SET_INEXACT
  if (bc.inexact) {
    if (!(word0(&rv) & Exp_mask)) {
      /* set underflow and inexact bits */
      dval(&rv0) = 1e-300;
      dval(&rv0) *= dval(&rv0);
      }
    else if (!oldinexact) {
      word0(&rv0) = Exp_1 + (70 << Exp_shift);
      word1(&rv0) = 0;
      dval(&rv0) += 1.;
      }
    }
  else if (!oldinexact)
    clear_inexact();
#endif
  if (se)
    *se = (char *)s;
  return sign ? -dval(&rv) : dval(&rv);
  }

#ifndef MULTIPLE_THREADS
#ifndef __XS__
  static char *dtoa_result;
#endif
#endif

 static char *
rv_alloc(int i MTd)
{
  int j, k, *r;

  j = sizeof(ULong);
  for(k = 0;
    sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= (size_t)i;
    j <<= 1)
      k++;
  r = (int*)Balloc(k MTa);
  *r = k;
  return
#ifndef MULTIPLE_THREADS
#ifndef __XS__
    dtoa_result =
#endif
#endif
    (char *)(r+1);
  }

 static char *
nrv_alloc(const char *s, char *s0, size_t s0len, char **rve, int n MTd)
{
  char *rv, *t;

  if (!s0)
    s0 = rv_alloc(n MTa);
  else if (s0len <= (size_t)n) {
    rv = 0;
    t = rv + n;
    goto rve_chk;
    }
  t = rv = s0;
  while((*t = *s++))
    ++t;
 rve_chk:
  if (rve)
    *rve = t;
  return rv;
  }

/* freedtoa(s) must be used to free values s returned by dtoa
 * when MULTIPLE_THREADS is #defined.  It should be used in all cases,
 * but for consistency with earlier versions of dtoa, it is optional
 * when MULTIPLE_THREADS is not defined.
 */

 void
freedtoa(char *s __XS__d)
{
#ifdef MULTIPLE_THREADS
  ThInfo *TI = 0;
#endif
  Bigint *b = (Bigint *)((int *)s - 1);
  b->maxwds = 1 << (b->k = *(int*)b);
  Bfree(b MTb);
#ifndef MULTIPLE_THREADS
#ifndef __XS__
  if (s == dtoa_result)
    dtoa_result = 0;
#endif
#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_r(double dd, int mode, int ndigits, int *decpt, int *sign, char **rve, char *buf, size_t blen __XS__d)
{
 /* 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.

  When not NULL, buf is an output buffer of length blen, which must
  be large enough to accommodate suppressed trailing zeros and a trailing
  null byte.  If blen is too small, rv = NULL is returned, in which case
  if rve is not NULL, a subsequent call with blen >= (*rve - rv) + 1
  should succeed in returning buf.

  When buf is NULL, sufficient space is allocated for the return value,
  which, when done using, the caller should pass to freedtoa().

  USE_BF is automatically defined when neither NO_LONG_LONG nor NO_BF96
  is defined.
  */

#ifdef MULTIPLE_THREADS
  ThInfo *TI = 0;
#endif
  int bbits, b2, b5, be, dig, i, ilim, ilim1,
    j, j1, k, leftright, m2, m5, s2, s5, spec_case;
#ifndef Sudden_Underflow
  int denorm;
#endif
  Bigint *b, *b1, *delta, *mlo, *mhi, *S;
  U u;
  char *s;
#ifdef SET_INEXACT
  int inexact, oldinexact;
#endif
#ifdef USE_BF96 /*{{*/
  BF96 *p10;
  ULLong dbhi, dbits, dblo, den, hb, rb, rblo, res, res0, res3, reslo, sres,
    sulp, tv0, tv1, tv2, tv3, ulp, ulplo, ulpmask, ures, ureslo, zb;
  int eulp, k1, n2, ulpadj, ulpshift;
#else /*}{*/
#ifndef Sudden_Underflow
  ULong x;
#endif
  Long L;
  U d2, eps;
  double ds;
  int ieps, ilim0, k0, k_check, try_quick;
#ifndef No_leftright
#ifdef IEEE_Arith
  U eps1;
#endif
#endif
#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 /*}*/

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

#if defined(IEEE_Arith) + defined(VAX)
#ifdef IEEE_Arith
  if ((word0(&u) & Exp_mask) == Exp_mask)
#else
  if (word0(&u)  == 0x8000)
#endif
    {
    /* Infinity or NaN */
    *decpt = 9999;
#ifdef IEEE_Arith
    if (!word1(&u) && !(word0(&u) & 0xfffff))
      return nrv_alloc("Infinity", buf, blen, rve, 8 MTb);
#endif
    *sign = 0; //NaN doesn't have a sign
    return nrv_alloc("NaN", buf, blen, rve, 3 MTb);
    }
#endif
#ifdef IBM
  dval(&u) += 0; /* normalize */
#endif
  if (!dval(&u)) {
    *decpt = 1;
    return nrv_alloc("0", buf, blen, rve, 1 MTb);
    }

#ifdef SET_INEXACT
#ifndef USE_BF96
  try_quick =
#endif
  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
#ifdef USE_BF96 /*{{*/
  dbits = (u.LL & 0xfffffffffffffull) << 11;  /* fraction bits */
  if ((be = u.LL >> 52)) /* biased exponent; nonzero ==> normal */ {
    dbits |= 0x8000000000000000ull;
    denorm = ulpadj = 0;
    }
  else {
    denorm = 1;
    ulpadj = be + 1;
    dbits <<= 1;
    if (!(dbits & 0xffffffff00000000ull)) {
      dbits <<= 32;
      be -= 32;
      }
    if (!(dbits & 0xffff000000000000ull)) {
      dbits <<= 16;
      be -= 16;
      }
    if (!(dbits & 0xff00000000000000ull)) {
      dbits <<= 8;
      be -= 8;
      }
    if (!(dbits & 0xf000000000000000ull)) {
      dbits <<= 4;
      be -= 4;
      }
    if (!(dbits & 0xc000000000000000ull)) {
      dbits <<= 2;
      be -= 2;
      }
    if (!(dbits & 0x8000000000000000ull)) {
      dbits <<= 1;
      be -= 1;
      }
    assert(be >= -51);
    ulpadj -= be;
    }
  j = Lhint[be + 51];
  p10 = &pten[j];
  dbhi = dbits >> 32;
  dblo = dbits & 0xffffffffull;
  i = be - 0x3fe;
  if (i < p10->e
  || (i == p10->e && (dbhi < p10->b0 || (dbhi == p10->b0 && dblo < p10->b1))))
    --j;
  k = j - 342;

  /* now 10^k <= dd < 10^(k+1) */

#else /*}{*/

  b = d2b(&u, &be, &bbits MTb);
#ifdef Sudden_Underflow
  i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
#else
  if ((i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) {
#endif
    dval(&d2) = dval(&u);
    word0(&d2) &= Frac_mask1;
    word0(&d2) |= Exp_11;
#ifdef IBM
    if (j = 11 - hi0bits(word0(&d2) & Frac_mask))
      dval(&d2) /= 1 << j;
#endif

    /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
     * log10(x)  =  log(x) / log(10)
     *    ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
     * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
     *
     * This suggests computing an approximation k to log10(d) by
     *
     * k = (i - Bias)*0.301029995663981
     *  + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
     *
     * We want k to be too large rather than too small.
     * The error in the first-order Taylor series approximation
     * is in our favor, so we just round up the constant enough
     * to compensate for any error in the multiplication of
     * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
     * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
     * adding 1e-13 to the constant term more than suffices.
     * Hence we adjust the constant term to 0.1760912590558.
     * (We could get a more accurate k by invoking log10,
     *  but this is probably not worthwhile.)
     */

    i -= Bias;
#ifdef IBM
    i <<= 2;
    i += j;
#endif
#ifndef Sudden_Underflow
    denorm = 0;
    }
  else {
    /* d is denormalized */

    i = bbits + be + (Bias + (P-1) - 1);
    x = i > 32  ? word0(&u) << (64 - i) | word1(&u) >> (i - 32)
          : word1(&u) << (32 - i);
    dval(&d2) = x;
    word0(&d2) -= 31*Exp_msk1; /* adjust exponent */
    i -= (Bias + (P-1) - 1) + 1;
    denorm = 1;
    }
#endif
  ds = (dval(&d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
  k = (int)ds;
  if (ds < 0. && ds != k)
    k--; /* want k = floor(ds) */
  k_check = 1;
  if (k >= 0 && k <= Ten_pmax) {
    if (dval(&u) < tens[k])
      k--;
    k_check = 0;
    }
  j = bbits - i - 1;
  if (j >= 0) {
    b2 = 0;
    s2 = j;
    }
  else {
    b2 = -j;
    s2 = 0;
    }
  if (k >= 0) {
    b5 = 0;
    s5 = k;
    s2 += k;
    }
  else {
    b2 -= k;
    b5 = -k;
    s5 = 0;
    }
#endif /*}}*/
  if (mode < 0 || mode > 9)
    mode = 0;

#ifndef USE_BF96
#ifndef SET_INEXACT
#ifdef Check_FLT_ROUNDS
  try_quick = Rounding == 1;
#else
  try_quick = 1;
#endif
#endif /*SET_INEXACT*/
#endif

  if (mode > 5) {
    mode -= 4;
#ifndef USE_BF96
    try_quick = 0;
#endif
    }
  leftright = 1;
  ilim = ilim1 = -1;  /* Values for cases 0 and 1; done here to */
        /* silence erroneous "gcc -Wall" warning. */
  switch(mode) {
    case 0:
    case 1:
      i = 18;
      ndigits = 0;
      break;
    case 2:
      leftright = 0;
      /* 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;
    }
  if (!buf) {
    buf = rv_alloc(i MTb);
    blen = sizeof(Bigint) + ((1 << ((int*)buf)[-1]) - 1)*sizeof(ULong) - sizeof(int);
    }
  else if (blen <= (size_t)i) {
    buf = 0;
    if (rve)
      *rve = buf + i;
    return buf;
    }
  s = buf;

  /* Check for special case that d is a normalized power of 2. */

  spec_case = 0;
  if (mode < 2 || (leftright
#ifdef Honor_FLT_ROUNDS
      && Rounding == 1
#endif
        )) {
    if (!word1(&u) && !(word0(&u) & Bndry_mask)
#ifndef Sudden_Underflow
     && word0(&u) & (Exp_mask & ~Exp_msk1)
#endif
        ) {
      /* The special case */
      spec_case = 1;
      }
    }

#ifdef USE_BF96 /*{*/
  b = 0;
  if (ilim < 0 && (mode == 3 || mode == 5)) {
    S = mhi = 0;
    goto no_digits;
    }
  i = 1;
  j = 52 + 0x3ff - be;
  ulpshift = 0;
  ulplo = 0;
  /* Can we do an exact computation with 64-bit integer arithmetic? */
  if (k < 0) {
    if (k < -25)
      goto toobig;
    res = dbits >> 11;
    n2 = pfivebits[k1 = -(k + 1)] + 53;
    j1 = j;
    if (n2 > 61) {
      ulpshift = n2 - 61;
      if (res & (ulpmask = (1ull << ulpshift) - 1))
        goto toobig;
      j -= ulpshift;
      res >>= ulpshift;
      }
    /* Yes. */
    res *= ulp = pfive[k1];
    if (ulpshift) {
      ulplo = ulp;
      ulp >>= ulpshift;
      }
    j += k;
    if (ilim == 0) {
      S = mhi = 0;
      if (res > (5ull << j))
        goto one_digit;
      goto no_digits;
      }
    goto no_div;
    }
  if (ilim == 0 && j + k >= 0) {
    S = mhi = 0;
    if ((dbits >> 11) > (pfive[k-1] << j))
      goto one_digit;
    goto no_digits;
    }
  if (k <= dtoa_divmax && j + k >= 0) {
    /* Another "yes" case -- we will use exact integer arithmetic. */
 use_exact:
    Debug(++dtoa_stats[3]);
    res = dbits >> 11;  /* residual */
    ulp = 1;
    if (k <= 0)
      goto no_div;
    j1 = j + k + 1;
    den = pfive[k-i] << (j1 - i);
    for(;;) {
      dig = res / den;
      *s++ = '0' + dig;
      if (!(res -= dig*den)) {
#ifdef SET_INEXACT
        inexact = 0;
        oldinexact = 1;
#endif
        goto retc;
        }
      if (ilim < 0) {
        ures = den - res;
        if (2*res <= ulp
        && (spec_case ? 4*res <= ulp : (2*res < ulp || dig & 1)))
          goto ulp_reached;
        if (2*ures < ulp)
          goto Roundup;
        }
      else if (i == ilim) {
        switch(Rounding) {
          case 0: goto retc;
          case 2: goto Roundup;
          }
        ures = 2*res;
        if (ures > den
        || (ures == den && dig & 1)
        || (spec_case && res <= ulp && 2*res >= ulp))
          goto Roundup;
        goto retc;
        }
      if (j1 < ++i) {
        res *= 10;
        ulp *= 10;
        }
      else {
        if (i > k)
          break;
        den = pfive[k-i] << (j1 - i);
        }
      }
 no_div:
    for(;;) {
      dig = den = res >> j;
      *s++ = '0' + dig;
      if (!(res -= den << j)) {
#ifdef SET_INEXACT
        inexact = 0;
        oldinexact = 1;
#endif
        goto retc;
        }
      if (ilim < 0) {
        ures = (1ull << j) - res;
        if (2*res <= ulp
        && (spec_case ? 4*res <= ulp : (2*res < ulp || dig & 1))) {
 ulp_reached:
          if (ures < res
          || (ures == res && dig & 1))
            goto Roundup;
          goto retc;
          }
        if (2*ures < ulp)
          goto Roundup;
        }
      --j;
      if (i == ilim) {
#ifdef Honor_FLT_ROUNDS
        switch(Rounding) {
          case 0: goto retc;
          case 2: goto Roundup;
          }
#endif
        hb = 1ull << j;
        if (res & hb && (dig & 1 || res & (hb-1)))
          goto Roundup;
        if (spec_case && res <= ulp && 2*res >= ulp) {
 Roundup:
          while(*--s == '9')
            if (s == buf) {
              ++k;
              *s++ = '1';
              goto ret1;
              }
          ++*s++;
          goto ret1;
          }
        goto retc;
        }
      ++i;
      res *= 5;
      if (ulpshift) {
        ulplo = 5*(ulplo & ulpmask);
        ulp = 5*ulp + (ulplo >> ulpshift);
        }
      else
        ulp *= 5;
      }
    }
 toobig:
  if (ilim > 28)
    goto Fast_failed1;
  /* Scale by 10^-k */
  p10 = &pten[342-k];
  tv0 = p10->b2 * dblo; /* rarely matters, but does, e.g., for 9.862818194192001e18 */
  tv1 = p10->b1 * dblo + (tv0 >> 32);
  tv2 = p10->b2 * dbhi + (tv1 & 0xffffffffull);
  tv3 = p10->b0 * dblo + (tv1>>32) + (tv2>>32);
  res3 = p10->b1 * dbhi + (tv3 & 0xffffffffull);
  res = p10->b0 * dbhi + (tv3>>32) + (res3>>32);
  be += p10->e - 0x3fe;
  eulp = j1 = be - 54 + ulpadj;
  if (!(res & 0x8000000000000000ull)) {
    --be;
    res3 <<= 1;
    res = (res << 1) | ((res3 & 0x100000000ull) >> 32);
    }
  res0 = res; /* save for Fast_failed */
#if !defined(SET_INEXACT) && !defined(NO_DTOA_64) /*{*/
  if (ilim > 19)
    goto Fast_failed;
  Debug(++dtoa_stats[4]);
  assert(be >= 0 && be <= 4); /* be = 0 is rare, but possible, e.g., for 1e20 */
  res >>= 4 - be;
  ulp = p10->b0;  /* ulp */
  ulp = (ulp << 29) | (p10->b1 >> 3);
  /* scaled ulp = ulp * 2^(eulp - 60) */
  /* We maintain 61 bits of the scaled ulp. */
  if (ilim == 0) {
    if (!(res & 0x7fffffffffffffeull)
     || !((~res) & 0x7fffffffffffffeull))
      goto Fast_failed1;
    S = mhi = 0;
    if (res >= 0x5000000000000000ull)
      goto one_digit;
    goto no_digits;
    }
  rb = 1; /* upper bound on rounding error */
  for(;;++i) {
    dig = res >> 60;
    *s++ = '0' + dig;
    res &= 0xfffffffffffffffull;
    if (ilim < 0) {
      ures = 0x1000000000000000ull - res;
      if (eulp > 0) {
        assert(eulp <= 4);
        sulp = ulp << (eulp - 1);
        if (res <= ures) {
          if (res + rb > ures - rb)
            goto Fast_failed;
          if (res < sulp)
            goto retc;
          }
        else {
          if (res - rb <= ures + rb)
            goto Fast_failed;
          if (ures < sulp)
            goto Roundup;
          }
        }
      else {
        zb = -(1ull << (eulp + 63));
        if (!(zb & res)) {
          sres = res << (1 - eulp);
          if (sres < ulp && (!spec_case || 2*sres < ulp)) {
            if ((res+rb) << (1 - eulp) >= ulp)
              goto Fast_failed;
            if (ures < res) {
              if (ures + rb >= res - rb)
                goto Fast_failed;
              goto Roundup;
              }
            if (ures - rb < res + rb)
              goto Fast_failed;
            goto retc;
            }
          }
        if (!(zb & ures) && ures << -eulp < ulp) {
          if (ures << (1 - eulp) < ulp)
            goto  Roundup;
          goto Fast_failed;
          }
        }
      }
    else if (i == ilim) {
      ures = 0x1000000000000000ull - res;
      if (ures < res) {
        if (ures <= rb || res - rb <= ures + rb) {
          if (j + k >= 0 && k >= 0 && k <= 27)
            goto use_exact1;
          goto Fast_failed;
          }
#ifdef Honor_FLT_ROUNDS
        if (Rounding == 0)
          goto retc;
#endif
        goto Roundup;
        }
      if (res <= rb || ures - rb <= res + rb) {
        if (j + k >= 0 && k >= 0 && k <= 27) {
 use_exact1:
          s = buf;
          i = 1;
          goto use_exact;
          }
        goto Fast_failed;
        }
#ifdef Honor_FLT_ROUNDS
      if (Rounding == 2)
        goto Roundup;
#endif
      goto retc;
      }
    rb *= 10;
    if (rb >= 0x1000000000000000ull)
      goto Fast_failed;
    res *= 10;
    ulp *= 5;
    if (ulp & 0x8000000000000000ull) {
      eulp += 4;
      ulp >>= 3;
      }
    else {
      eulp += 3;
      ulp >>= 2;
      }
    }
#endif /*}*/
#ifndef NO_BF96
 Fast_failed:
#endif
  Debug(++dtoa_stats[5]);
  s = buf;
  i = 4 - be;
  res = res0 >> i;
  reslo = 0xffffffffull & res3;
  if (i)
    reslo = (res0 << (64 - i)) >> 32 | (reslo >> i);
  rb = 0;
  rblo = 4; /* roundoff bound */
  ulp = p10->b0;  /* ulp */
  ulp = (ulp << 29) | (p10->b1 >> 3);
  eulp = j1;
  for(i = 1;;++i) {
    dig = res >> 60;
    *s++ = '0' + dig;
    res &= 0xfffffffffffffffull;
#ifdef SET_INEXACT
    if (!res && !reslo) {
      if (!(res3 & 0xffffffffull)) {
        inexact = 0;
        oldinexact = 1;
        }
      goto retc;
      }
#endif
    if (ilim < 0) {
      ures = 0x1000000000000000ull - res;
      ureslo = 0;
      if (reslo) {
        ureslo = 0x100000000ull - reslo;
        --ures;
        }
      if (eulp > 0) {
        assert(eulp <= 4);
        sulp = (ulp << (eulp - 1)) - rb;
        if (res <= ures) {
          if (res < sulp) {
            if (res+rb < ures-rb)
              goto retc;
            }
          }
        else if (ures < sulp) {
          if (res-rb > ures+rb)
            goto Roundup;
          }
        goto Fast_failed1;
        }
      else {
        zb = -(1ull << (eulp + 60));
        if (!(zb & (res + rb))) {
          sres = (res - rb) << (1 - eulp);
          if (sres < ulp && (!spec_case || 2*sres < ulp)) {
            sres = res << (1 - eulp);
            if ((j = eulp + 31) > 0)
              sres += (rblo + reslo) >> j;
            else
              sres += (rblo + reslo) << -j;
            if (sres + (rb << (1 - eulp)) >= ulp)
              goto Fast_failed1;
            if (sres >= ulp)
              goto more96;
            if (ures < res
            || (ures == res && ureslo < reslo)) {
              if (ures + rb >= res - rb)
                goto Fast_failed1;
              goto Roundup;
              }
            if (ures - rb <= res + rb)
              goto Fast_failed1;
            goto retc;
            }
          }
        if (!(zb & ures) && (ures-rb) << (1 - eulp) < ulp) {
          if ((ures + rb) << (1 - eulp) < ulp)
            goto Roundup;
          goto Fast_failed1;
          }
        }
      }
    else if (i == ilim) {
      ures = 0x1000000000000000ull - res;
      sres = ureslo = 0;
      if (reslo) {
        ureslo = 0x100000000ull - reslo;
        --ures;
        sres = (reslo + rblo) >> 31;
        }
      sres += 2*rb;
      if (ures <= res) {
        if (ures <=sres || res - ures <= sres)
          goto Fast_failed1;
#ifdef Honor_FLT_ROUNDS
        if (Rounding == 0)
          goto retc;
#endif
        goto Roundup;
        }
      if (res <= sres || ures - res <= sres)
        goto Fast_failed1;
#ifdef Honor_FLT_ROUNDS
      if (Rounding == 2)
        goto Roundup;
#endif
      goto retc;
      }
 more96:
    rblo *= 10;
    rb = 10*rb + (rblo >> 32);
    rblo &= 0xffffffffull;
    if (rb >= 0x1000000000000000ull)
      goto Fast_failed1;
    reslo *= 10;
    res = 10*res + (reslo >> 32);
    reslo &= 0xffffffffull;
    ulp *= 5;
    if (ulp & 0x8000000000000000ull) {
      eulp += 4;
      ulp >>= 3;
      }
    else {
      eulp += 3;
      ulp >>= 2;
      }
    }
 Fast_failed1:
  Debug(++dtoa_stats[6]);
  S = mhi = mlo = 0;
#ifdef USE_BF96
  b = d2b(&u, &be, &bbits MTb);
#endif
  s = buf;
  i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
  i -= Bias;
  if (ulpadj)
    i -= ulpadj - 1;
  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;
    }
#endif /*}*/

#ifdef Honor_FLT_ROUNDS
  if (mode > 1 && Rounding != 1)
    leftright = 0;
#endif

#ifndef USE_BF96 /*{*/
  if (ilim >= 0 && ilim <= Quick_max && try_quick) {

    /* Try to get by with floating-point arithmetic. */

    i = 0;
    dval(&d2) = dval(&u);
    j1 = -(k0 = k);
    ilim0 = ilim;
    ieps = 2; /* conservative */
    if (k > 0) {
      ds = tens[k&0xf];
      j = k >> 4;
      if (j & Bletch) {
        /* prevent overflows */
        j &= Bletch - 1;
        dval(&u) /= bigtens[n_bigtens-1];
        ieps++;
        }
      for(; j; j >>= 1, i++)
        if (j & 1) {
          ieps++;
          ds *= bigtens[i];
          }
      dval(&u) /= ds;
      }
    else if (j1 > 0) {
      dval(&u) *= tens[j1 & 0xf];
      for(j = j1 >> 4; j; j >>= 1, i++)
        if (j & 1) {
          ieps++;
          dval(&u) *= bigtens[i];
          }
      }
    if (k_check && dval(&u) < 1. && ilim > 0) {
      if (ilim1 <= 0)
        goto fast_failed;
      ilim = ilim1;
      k--;
      dval(&u) *= 10.;
      ieps++;
      }
    dval(&eps) = ieps*dval(&u) + 7.;
    word0(&eps) -= (P-1)*Exp_msk1;
    if (ilim == 0) {
      S = mhi = 0;
      dval(&u) -= 5.;
      if (dval(&u) > dval(&eps))
        goto one_digit;
      if (dval(&u) < -dval(&eps))
        goto no_digits;
      goto fast_failed;
      }
#ifndef No_leftright
    if (leftright) {
      /* Use Steele & White method of only
       * generating digits needed.
       */
      dval(&eps) = 0.5/tens[ilim-1] - dval(&eps);
#ifdef IEEE_Arith
      if (j1 >= 307) {
        eps1.d = 1.01e256; /* 1.01 allows roundoff in the next few lines */
        word0(&eps1) -= Exp_msk1 * (Bias+P-1);
        dval(&eps1) *= tens[j1 & 0xf];
        for(i = 0, j = (j1-256) >> 4; j; j >>= 1, i++)
          if (j & 1)
            dval(&eps1) *= bigtens[i];
        if (eps.d < eps1.d)
          eps.d = eps1.d;
        if (10. - u.d < 10.*eps.d && eps.d < 1.) {
          /* eps.d < 1. excludes trouble with the tiniest denormal */
          *s++ = '1';
          ++k;
          goto ret1;
          }
        }
#endif
      for(i = 0;;) {
        L = (int)dval(&u);
        dval(&u) -= L;
        *s++ = '0' + (int)L;
        if (1. - dval(&u) < dval(&eps))
          goto bump_up;
        if (dval(&u) < dval(&eps))
          goto retc;
        if (++i >= ilim)
          break;
        dval(&eps) *= 10.;
        dval(&u) *= 10.;
        }
      }
    else {
#endif
      /* Generate ilim digits, then fix them up. */
      dval(&eps) *= tens[ilim-1];
      for(i = 1;; i++, dval(&u) *= 10.) {
        L = (Long)(dval(&u));
        if (!(dval(&u) -= L))
          ilim = i;
        *s++ = '0' + (int)L;
        if (i == ilim) {
          if (dval(&u) > 0.5 + dval(&eps))
            goto bump_up;
          else if (dval(&u) < 0.5 - dval(&eps))
            goto retc;
          break;
          }
        }
#ifndef No_leftright
      }
#endif
 fast_failed:
    s = buf;
    dval(&u) = dval(&d2);
    k = k0;
    ilim = ilim0;
    }

  /* Do we have a "small" integer? */

  if (be >= 0 && k <= Int_max) {
    /* Yes. */
    ds = tens[k];
    if (ndigits < 0 && ilim <= 0) {
      S = mhi = 0;
      if (ilim < 0 || dval(&u) <= 5*ds)
        goto no_digits;
      goto one_digit;
      }
    for(i = 1;; i++, dval(&u) *= 10.) {
      L = (Long)(dval(&u) / ds);
      dval(&u) -= L*ds;
#ifdef Check_FLT_ROUNDS
      /* If FLT_ROUNDS == 2, L will usually be high by 1 */
      if (dval(&u) < 0) {
        L--;
        dval(&u) += ds;
        }
#endif
      *s++ = '0' + (int)L;
      if (!dval(&u)) {
#ifdef SET_INEXACT
        inexact = 0;
#endif
        break;
        }
      if (i == ilim) {
#ifdef Honor_FLT_ROUNDS
        if (mode > 1)
        switch(Rounding) {
          case 0: goto retc;
          case 2: goto bump_up;
          }
#endif
        dval(&u) += dval(&u);
#ifdef ROUND_BIASED
        if (dval(&u) >= ds)
#else
        if (dval(&u) > ds || (dval(&u) == ds && L & 1))
#endif
          {
 bump_up:
          while(*--s == '9')
            if (s == buf) {
              k++;
              *s = '0';
              break;
              }
          ++*s++;
          }
        break;
        }
      }
    goto retc;
    }

#endif /*}*/
  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 MTb);
    }
  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 MTb);
        b1 = mult(mhi, b MTb);
        Bfree(b MTb);
        b = b1;
        }
      if ((j = b5 - m5))
        b = pow5mult(b, j MTb);
      }
    else
      b = pow5mult(b, b5 MTb);
    }
  S = i2b(1 MTb);
  if (s5 > 0)
    S = pow5mult(S, s5 MTb);

  if (spec_case) {
    b2 += Log2P;
    s2 += Log2P;
    }

  /* 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.
   */
  i = dshift(S, s2);
  b2 += i;
  m2 += i;
  s2 += i;
  if (b2 > 0)
    b = lshift(b, b2 MTb);
  if (s2 > 0)
    S = lshift(S, s2 MTb);
#ifndef USE_BF96
  if (k_check) {
    if (cmp(b,S) < 0) {
      k--;
      b = multadd(b, 10, 0 MTb);  /* we botched the k estimate */
      if (leftright)
        mhi = multadd(mhi, 10, 0 MTb);
      ilim = ilim1;
      }
    }
#endif
  if (ilim <= 0 && (mode == 3 || mode == 5)) {
    if (ilim < 0 || cmp(b,S = multadd(S,5,0 MTb)) <= 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 MTb);

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

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

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

  /* Round off last digit */

#ifdef Honor_FLT_ROUNDS
  if (mode > 1)
    switch(Rounding) {
      case 0: goto ret;
      case 2: goto roundoff;
      }
#endif
  b = lshift(b, 1 MTb);
  j = cmp(b, S);
#ifdef ROUND_BIASED
  if (j >= 0)
#else
  if (j > 0 || (j == 0 && dig & 1))
#endif
    {
 roundoff:
    while(*--s == '9')
      if (s == buf) {
        k++;
        *s++ = '1';
        goto ret;
        }
    ++*s++;
    }
 ret:
  Bfree(S MTb);
  if (mhi) {
    if (mlo && mlo != mhi)
      Bfree(mlo MTb);
    Bfree(mhi MTb);
    }
 retc:
  while(s > buf && s[-1] == '0')
    --s;
 ret1:
  if (b)
    Bfree(b MTb);
  *s = 0;
  *decpt = k + 1;
  if (rve)
    *rve = s;
#ifdef SET_INEXACT
  if (inexact) {
    if (!oldinexact) {
      word0(&u) = Exp_1 + (70 << Exp_shift);
      word1(&u) = 0;
      dval(&u) += 1.;
      }
    }
  else if (!oldinexact)
    clear_inexact();
#endif
  return buf;
  }

 char *
fx_dtoa(double dd, int mode, int ndigits, int *decpt, int *sign, char **rve __XS__d)
{
  /*  Sufficient space is allocated to the return value
    to hold the suppressed trailing zeros.
    See dtoa_r() above for details on the other arguments.
  */
#ifndef MULTIPLE_THREADS
#ifndef __XS__
  if (dtoa_result)
    freedtoa(dtoa_result __XS__a);
#endif
#endif
  return dtoa_r(dd, mode, ndigits, decpt, sign, rve, 0, 0 __XS__a);
  }

#ifdef __cplusplus
}
#endif

static void fxDTOACleanup(txMachine* the, ThInfo* DTOA);
static void fxDTOASetup(txMachine* the, ThInfo* DTOA);

void fxDTOACleanup(txMachine* the, ThInfo* DTOA)
{
#if mxUseChunkHeap
  if (DTOA->dirty)
#endif
  {
    Bigint* b;
    int i, c = Kmax +1 ;
    for (i = 0; i < c; i++) {
      b = DTOA->Freelist[i];
      while(b) {
        Bigint* next = b->next;
        fxDTOAFree(b, DTOA);
        b = next;
      }
    }

    b = DTOA->P5s;
    while(b) {
      Bigint* next = b->next;
      fxDTOAFree(b, DTOA);
      b = next;
    }
  }
}

static void* fxDTOAMalloc(size_t size, void* it)
{
  ThInfo* DTOA = it;
  txMachine* the = DTOA->the;
  void* block = C_NULL;
#if mxUseChunkHeap
  if (the) {
    if ((DTOA->current + size) <= (txByte*)(the->firstBlock->limit)) {
      block = DTOA->current;
      DTOA->current += size;
      return block;
    }
  }
  DTOA->dirty = 1;
#endif
  block = c_malloc(size);
  if (!block)
    fxAbort(the, XS_NOT_ENOUGH_MEMORY_EXIT);
  //fprintf(stderr, "malloc %zu %p\n", size, block);
  return block;
}

static void fxDTOAFree(void* block, void* it)
{
  //fprintf(stderr, "free %p\n", block);
#if mxUseChunkHeap
  ThInfo* DTOA = it;
  txMachine* the = DTOA->the;
    if (the) {
        if (((txByte*)(the->firstBlock->current) <= (txByte*)block) && ((txByte*)block < DTOA->current))
          return;
    }
#endif
  c_free(block);
}

void fxDTOASetup(txMachine* the, ThInfo* DTOA)
{
  c_memset(DTOA, 0, sizeof(ThInfo));
  if (the) {
    DTOA->the = the;
#if mxUseChunkHeap
  #if 0
    if ((txByte*)(the->firstBlock->limit) - (txByte*)(the->firstBlock->current) > 192)
      DTOA->current = (txByte*)(the->firstBlock->limit) - 192;
    else
  #endif
      DTOA->current = (txByte*)(the->firstBlock->current);
#endif
  }
}

txString fxIntegerToString(void* the, txInteger theValue, txString theBuffer, txSize theSize)
{
  c_snprintf(theBuffer, theSize, "%d", (int)theValue);
  return theBuffer;
}

txInteger fxNumberToInteger(txNumber theValue)
{
  if (c_fpclassify(theValue) == C_FP_NORMAL) {
    #define MODULO 4294967296.0
    txNumber aNumber = c_fmod(c_trunc(theValue), MODULO);
    if (aNumber >= MODULO / 2)
      aNumber -= MODULO;
    else if (aNumber < -MODULO / 2)
      aNumber += MODULO;
    return (txInteger)aNumber;
  }
  return 0; 
}

txString fxNumberToString(void* the, txNumber theValue, txString theBuffer, txSize theSize, txByte theMode, txInteger thePrecision)
{
  ThInfo DTOA;
  char* base = C_NULL;
  int mode, precision, decpt, sign, count, exponent, pad;
  char* start;
  char* stop;
  char* result;

  fxDTOASetup(the, &DTOA);
  switch (theMode) {
  case 'e':
    if (thePrecision > 0) {
      mode = 2;
      precision = thePrecision;
    }
    else {
      mode = 0;
      precision = 0;
    }
    break;
  case 'f':
    mode = 3;
    precision = thePrecision;
    break;
  case 'g':
    mode = 2;
    precision = thePrecision;
    break;
  default:
    mode = 0;
    precision = 0;
    break;
  }
  base = start = fx_dtoa(theValue, mode, precision, &decpt, &sign, &stop, &DTOA);
  count = mxPtrDiff(stop - start);
  result = theBuffer;
  theSize--; // C string
  if (sign && theValue) {
    *result++ = '-';
    theSize--;
  }
    if (decpt != 9999) {
    switch (theMode) {
    case 'e':
      exponent = 1;
      if (thePrecision > 0)
        pad = thePrecision;
      else
        pad = count;
      break;
    case 'f':
      exponent = 0;
      pad = thePrecision;
      break;
    case 'g':
      if ((decpt < -5) || (thePrecision < decpt)) {
        exponent = 1;
        pad = thePrecision; 
      }
      else {
        exponent = 0;
                pad = thePrecision - count - decpt + 1;
      }
      break;
    default:
      if ((decpt < -5) || (21 < decpt)) {
        exponent = 1;
        pad = count;  
      }
      else {
        exponent = 0;
        pad = 0;  
      }
      break;
    }
    if (exponent) {
      theSize -= 5 - pad;
      if (theSize < 0) goto error;
      *result++ = *start++;
      pad--;
      if (pad > 0) {
        *result++ = '.';
        while ((start < stop) && (pad > 0)) {
          *result++ = *start++;
          pad--;
        }
        while  (pad > 0) {
          *result++ = '0';
          pad--;
        }
      }
      *result++ = 'e';
      decpt--;
      if (decpt < 0) {
        *result++ = '-';
        decpt = 0 - decpt;
      }
      else
        *result++ = '+';
      pad = 1000;
      while (pad > 1) {
        if (decpt >= pad) 
          break;
        pad /= 10;
      }
      while (pad) {
        *result++ = '0' + (decpt / pad);
        decpt %= pad;
        pad /= 10;
      }
    }
    else if (decpt <= 0) {
      theSize -= 2 - decpt + (mxPtrDiff(stop - start));
      if (theSize < 0) goto error;
      *result++ = '0';
      if ((decpt < 0) || (start < stop) || (pad > 0))
        *result++ = '.';
      while (decpt < 0) {
        *result++ = '0';
        decpt++;
        pad--;
      }
      while (start < stop) {
        *result++ = *start++;
        pad--;
      }
      if (pad > 0) {
        theSize -= pad;
        if (theSize < 0) goto error;
        while (pad > 0) {
          *result++ = '0';
          pad--;
        }
      }
    }
    else if (decpt < count) {
      theSize -= decpt + 1 + (mxPtrDiff(stop - start));
      if (theSize < 0) goto error;
      while (decpt > 0) {
        *result++ = *start++;
        decpt--;
      }
      *result++ = '.';
      while (start < stop) {
        *result++ = *start++;
        pad--;
      }
      if (pad > 0) {
        theSize -= pad;
        if (theSize < 0) goto error;
        while (pad > 0) {
          *result++ = '0';
          pad--;
        }
      }
    }
    else {
      theSize -= (mxPtrDiff(stop - start));
      if (theSize < 0) goto error;
      while (start < stop) {
        *result++ = *start++;
        decpt--;
      }
            theSize -= decpt;
            if (theSize < 0) goto error;
      while (decpt > 0) {
        *result++ = '0';
        decpt--;
      }
      if (pad > 0) {
        theSize -= 1 + pad;
        if (theSize < 0) goto error;
        *result++ = '.';
        while (pad > 0) {
          *result++ = '0';
          pad--;
        }
      }
    }
  }
  else {
    theSize -= (mxPtrDiff(stop - start));
    if (theSize < 0) goto error;
    while (start < stop)
      *result++ = *start++;
  }
error:
  *result = 0;
  if (base)
    freedtoa(base, &DTOA);
  fxDTOACleanup(the, &DTOA);
  return theBuffer;
}

txNumber fxStringToNumber(void* the, txString theString, txFlag whole)
{
  txNumber result = whole ? 0 : NAN;
  txString p = fxSkipSpaces(theString), q;
  char c = *p;
  if (c) {
    txU4 d = *(p + 1);
    if (whole && (c == '0') && ((d == 'B') || (d == 'b') || (d == 'O') || (d == 'o') || (d == 'X') || (d == 'x'))) {
      p += 2;
            q = p;
      if ((d == 'B') || (d == 'b')) {
        while ((c = *p)) {
          if (('0' <= c) && (c <= '1'))
            result = (result * 2) + (c - '0');
          else
            break;
          p++;
        }
      }
      else if ((d == 'O') || (d == 'o')) {
        while ((c = *p)) {
          if (('0' <= c) && (c <= '7'))
            result = (result * 8) + (c - '0');
          else
            break;
          p++;
        }
      }
      else if ((d == 'X') || (d == 'x')) {
        while ((c = *p)) {
          if (('0' <= c) && (c <= '9'))
            result = (result * 16) + (c - '0');
          else if (('a' <= c) && (c <= 'f'))
            result = (result * 16) + (10 + c - 'a');
          else if (('A' <= c) && (c <= 'F'))
            result = (result * 16) + (10 + c - 'A');
          else
            break;
          p++;
        }
      }
      if (p == q)
        result = NAN;
      else
            q = p;
    }
    else {
      ThInfo DTOA;
      fxDTOASetup(the, &DTOA);
      result = strtod2(p, &q, &DTOA);
      fxDTOACleanup(the, &DTOA);
      if ((p == q) && !whole)
        result = NAN;
    }
    if (whole) {
      p = fxSkipSpaces(q);
      if (*p)
        result = NAN;
    }
  }
  return result;
}

Coverage Report

Created: 2025-06-13 06:17