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/****************************************************************
*
* 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).
*/
#include "dtoa_config.h"
#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);
#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 },
{ 0xa139029f, 0x6a239f72, 0x1c1fffc1, -873 },
{ 0xc9874347, 0x44ac874e, 0xa327ffb2, -870 },
{ 0xfbe91419, 0x15d7a922, 0x4bf1ff9f, -867 },
{ 0x9d71ac8f, 0xada6c9b5, 0x6f773fc3, -863 },
{ 0xc4ce17b3, 0x99107c22, 0xcb550fb4, -860 },
{ 0xf6019da0, 0x7f549b2b, 0x7e2a53a1, -857 },
{ 0x99c10284, 0x4f94e0fb, 0x2eda7444, -853 },
{ 0xc0314325, 0x637a1939, 0xfa911155, -850 },
{ 0xf03d93ee, 0xbc589f88, 0x793555ab, -847 },
{ 0x96267c75, 0x35b763b5, 0x4bc1558b, -843 },
{ 0xbbb01b92, 0x83253ca2, 0x9eb1aaed, -840 },
{ 0xea9c2277, 0x23ee8bcb, 0x465e15a9, -837 },
{ 0x92a1958a, 0x7675175f, 0x0bfacd89, -833 },
{ 0xb749faed, 0x14125d36, 0xcef980ec, -830 },
{ 0xe51c79a8, 0x5916f484, 0x82b7e127, -827 },
{ 0x8f31cc09, 0x37ae58d2, 0xd1b2ecb8, -823 },
{ 0xb2fe3f0b, 0x8599ef07, 0x861fa7e6, -820 },
{ 0xdfbdcece, 0x67006ac9, 0x67a791e0, -817 },
{ 0x8bd6a141, 0x006042bd, 0xe0c8bb2c, -813 },
{ 0xaecc4991, 0x4078536d, 0x58fae9f7, -810 },
{ 0xda7f5bf5, 0x90966848, 0xaf39a475, -807 },
{ 0x888f9979, 0x7a5e012d, 0x6d8406c9, -803 },
{ 0xaab37fd7, 0xd8f58178, 0xc8e5087b, -800 },
{ 0xd5605fcd, 0xcf32e1d6, 0xfb1e4a9a, -797 },
{ 0x855c3be0, 0xa17fcd26, 0x5cf2eea0, -793 },
{ 0xa6b34ad8, 0xc9dfc06f, 0xf42faa48, -790 },
{ 0xd0601d8e, 0xfc57b08b, 0xf13b94da, -787 },
{ 0x823c1279, 0x5db6ce57, 0x76c53d08, -783 },
{ 0xa2cb1717, 0xb52481ed, 0x54768c4b, -780 },
{ 0xcb7ddcdd, 0xa26da268, 0xa9942f5d, -777 },
{ 0xfe5d5415, 0x0b090b02, 0xd3f93b35, -774 },
{ 0x9efa548d, 0x26e5a6e1, 0xc47bc501, -770 },
{ 0xc6b8e9b0, 0x709f109a, 0x359ab641, -767 },
{ 0xf867241c, 0x8cc6d4c0, 0xc30163d2, -764 },
{ 0x9b407691, 0xd7fc44f8, 0x79e0de63, -760 },
{ 0xc2109436, 0x4dfb5636, 0x985915fc, -757 },
{ 0xf294b943, 0xe17a2bc4, 0x3e6f5b7b, -754 },
{ 0x979cf3ca, 0x6cec5b5a, 0xa705992c, -750 },
{ 0xbd8430bd, 0x08277231, 0x50c6ff78, -747 },
{ 0xece53cec, 0x4a314ebd, 0xa4f8bf56, -744 },
{ 0x940f4613, 0xae5ed136, 0x871b7795, -740 },
{ 0xb9131798, 0x99f68584, 0x28e2557b, -737 },
{ 0xe757dd7e, 0xc07426e5, 0x331aeada, -734 },
{ 0x9096ea6f, 0x3848984f, 0x3ff0d2c8, -730 },
{ 0xb4bca50b, 0x065abe63, 0x0fed077a, -727 },
{ 0xe1ebce4d, 0xc7f16dfb, 0xd3e84959, -724 },
{ 0x8d3360f0, 0x9cf6e4bd, 0x64712dd7, -720 },
{ 0xb080392c, 0xc4349dec, 0xbd8d794d, -717 },
{ 0xdca04777, 0xf541c567, 0xecf0d7a0, -714 },
{ 0x89e42caa, 0xf9491b60, 0xf41686c4, -710 },
{ 0xac5d37d5, 0xb79b6239, 0x311c2875, -707 },
{ 0xd77485cb, 0x25823ac7, 0x7d633293, -704 },
{ 0x86a8d39e, 0xf77164bc, 0xae5dff9c, -700 },
{ 0xa8530886, 0xb54dbdeb, 0xd9f57f83, -697 },
{ 0xd267caa8, 0x62a12d66, 0xd072df63, -694 },
{ 0x8380dea9, 0x3da4bc60, 0x4247cb9e, -690 },
{ 0xa4611653, 0x8d0deb78, 0x52d9be85, -687 },
{ 0xcd795be8, 0x70516656, 0x67902e27, -684 },
{ 0x806bd971, 0x4632dff6, 0x00ba1cd8, -680 },
{ 0xa086cfcd, 0x97bf97f3, 0x80e8a40e, -677 },
{ 0xc8a883c0, 0xfdaf7df0, 0x6122cd12, -674 },
{ 0xfad2a4b1, 0x3d1b5d6c, 0x796b8057, -671 },
{ 0x9cc3a6ee, 0xc6311a63, 0xcbe33036, -667 },
{ 0xc3f490aa, 0x77bd60fc, 0xbedbfc44, -664 },
{ 0xf4f1b4d5, 0x15acb93b, 0xee92fb55, -661 },
{ 0x99171105, 0x2d8bf3c5, 0x751bdd15, -657 },
{ 0xbf5cd546, 0x78eef0b6, 0xd262d45a, -654 },
{ 0xef340a98, 0x172aace4, 0x86fb8971, -651 },
{ 0x9580869f, 0x0e7aac0e, 0xd45d35e6, -647 },
{ 0xbae0a846, 0xd2195712, 0x89748360, -644 },
{ 0xe998d258, 0x869facd7, 0x2bd1a438, -641 },
{ 0x91ff8377, 0x5423cc06, 0x7b6306a3, -637 },
{ 0xb67f6455, 0x292cbf08, 0x1a3bc84c, -634 },
{ 0xe41f3d6a, 0x7377eeca, 0x20caba5f, -631 },
{ 0x8e938662, 0x882af53e, 0x547eb47b, -627 },
{ 0xb23867fb, 0x2a35b28d, 0xe99e619a, -624 },
{ 0xdec681f9, 0xf4c31f31, 0x6405fa00, -621 },
{ 0x8b3c113c, 0x38f9f37e, 0xde83bc40, -617 },
{ 0xae0b158b, 0x4738705e, 0x9624ab50, -614 },
{ 0xd98ddaee, 0x19068c76, 0x3badd624, -611 },
{ 0x87f8a8d4, 0xcfa417c9, 0xe54ca5d7, -607 },
{ 0xa9f6d30a, 0x038d1dbc, 0x5e9fcf4c, -604 },
{ 0xd47487cc, 0x8470652b, 0x7647c320, -601 },
{ 0x84c8d4df, 0xd2c63f3b, 0x29ecd9f4, -597 },
{ 0xa5fb0a17, 0xc777cf09, 0xf4681071, -594 },
{ 0xcf79cc9d, 0xb955c2cc, 0x7182148d, -591 },
{ 0x81ac1fe2, 0x93d599bf, 0xc6f14cd8, -587 },
{ 0xa21727db, 0x38cb002f, 0xb8ada00e, -584 },
{ 0xca9cf1d2, 0x06fdc03b, 0xa6d90811, -581 },
{ 0xfd442e46, 0x88bd304a, 0x908f4a16, -578 },
{ 0x9e4a9cec, 0x15763e2e, 0x9a598e4e, -574 },
{ 0xc5dd4427, 0x1ad3cdba, 0x40eff1e1, -571 },
{ 0xf7549530, 0xe188c128, 0xd12bee59, -568 },
{ 0x9a94dd3e, 0x8cf578b9, 0x82bb74f8, -564 },
{ 0xc13a148e, 0x3032d6e7, 0xe36a5236, -561 },
{ 0xf18899b1, 0xbc3f8ca1, 0xdc44e6c3, -558 },
{ 0x96f5600f, 0x15a7b7e5, 0x29ab103a, -554 },
{ 0xbcb2b812, 0xdb11a5de, 0x7415d448, -551 },
{ 0xebdf6617, 0x91d60f56, 0x111b495b, -548 },
{ 0x936b9fce, 0xbb25c995, 0xcab10dd9, -544 },
{ 0xb84687c2, 0x69ef3bfb, 0x3d5d514f, -541 },
{ 0xe65829b3, 0x046b0afa, 0x0cb4a5a3, -538 },
{ 0x8ff71a0f, 0xe2c2e6dc, 0x47f0e785, -534 },
{ 0xb3f4e093, 0xdb73a093, 0x59ed2167, -531 },
{ 0xe0f218b8, 0xd25088b8, 0x306869c1, -528 },
{ 0x8c974f73, 0x83725573, 0x1e414218, -524 },
{ 0xafbd2350, 0x644eeacf, 0xe5d1929e, -521 },
{ 0xdbac6c24, 0x7d62a583, 0xdf45f746, -518 },
{ 0x894bc396, 0xce5da772, 0x6b8bba8c, -514 },
{ 0xab9eb47c, 0x81f5114f, 0x066ea92f, -511 },
{ 0xd686619b, 0xa27255a2, 0xc80a537b, -508 },
{ 0x8613fd01, 0x45877585, 0xbd06742c, -504 },
{ 0xa798fc41, 0x96e952e7, 0x2c481138, -501 },
{ 0xd17f3b51, 0xfca3a7a0, 0xf75a1586, -498 },
{ 0x82ef8513, 0x3de648c4, 0x9a984d73, -494 },
{ 0xa3ab6658, 0x0d5fdaf5, 0xc13e60d0, -491 },
{ 0xcc963fee, 0x10b7d1b3, 0x318df905, -488 },
{ 0xffbbcfe9, 0x94e5c61f, 0xfdf17746, -485 },
{ 0x9fd561f1, 0xfd0f9bd3, 0xfeb6ea8b, -481 },
{ 0xc7caba6e, 0x7c5382c8, 0xfe64a52e, -478 },
{ 0xf9bd690a, 0x1b68637b, 0x3dfdce7a, -475 },
{ 0x9c1661a6, 0x51213e2d, 0x06bea10c, -471 },
{ 0xc31bfa0f, 0xe5698db8, 0x486e494f, -468 },
{ 0xf3e2f893, 0xdec3f126, 0x5a89dba3, -465 },
{ 0x986ddb5c, 0x6b3a76b7, 0xf8962946, -461 },
{ 0xbe895233, 0x86091465, 0xf6bbb397, -458 },
{ 0xee2ba6c0, 0x678b597f, 0x746aa07d, -455 },
{ 0x94db4838, 0x40b717ef, 0xa8c2a44e, -451 },
{ 0xba121a46, 0x50e4ddeb, 0x92f34d62, -448 },
{ 0xe896a0d7, 0xe51e1566, 0x77b020ba, -445 },
{ 0x915e2486, 0xef32cd60, 0x0ace1474, -441 },
{ 0xb5b5ada8, 0xaaff80b8, 0x0d819992, -438 },
{ 0xe3231912, 0xd5bf60e6, 0x10e1fff6, -435 },
{ 0x8df5efab, 0xc5979c8f, 0xca8d3ffa, -431 },
{ 0xb1736b96, 0xb6fd83b3, 0xbd308ff8, -428 },
{ 0xddd0467c, 0x64bce4a0, 0xac7cb3f6, -425 },
{ 0x8aa22c0d, 0xbef60ee4, 0x6bcdf07a, -421 },
{ 0xad4ab711, 0x2eb3929d, 0x86c16c98, -418 },
{ 0xd89d64d5, 0x7a607744, 0xe871c7bf, -415 },
{ 0x87625f05, 0x6c7c4a8b, 0x11471cd7, -411 },
{ 0xa93af6c6, 0xc79b5d2d, 0xd598e40d, -408 },
{ 0xd389b478, 0x79823479, 0x4aff1d10, -405 },
{ 0x843610cb, 0x4bf160cb, 0xcedf722a, -401 },
{ 0xa54394fe, 0x1eedb8fe, 0xc2974eb4, -398 },
{ 0xce947a3d, 0xa6a9273e, 0x733d2262, -395 },
{ 0x811ccc66, 0x8829b887, 0x0806357d, -391 },
{ 0xa163ff80, 0x2a3426a8, 0xca07c2dc, -388 },
{ 0xc9bcff60, 0x34c13052, 0xfc89b393, -385 },
{ 0xfc2c3f38, 0x41f17c67, 0xbbac2078, -382 },
{ 0x9d9ba783, 0x2936edc0, 0xd54b944b, -378 },
{ 0xc5029163, 0xf384a931, 0x0a9e795e, -375 },
{ 0xf64335bc, 0xf065d37d, 0x4d4617b5, -372 },
{ 0x99ea0196, 0x163fa42e, 0x504bced1, -368 },
{ 0xc06481fb, 0x9bcf8d39, 0xe45ec286, -365 },
{ 0xf07da27a, 0x82c37088, 0x5d767327, -362 },
{ 0x964e858c, 0x91ba2655, 0x3a6a07f8, -358 },
{ 0xbbe226ef, 0xb628afea, 0x890489f7, -355 },
{ 0xeadab0ab, 0xa3b2dbe5, 0x2b45ac74, -352 },
{ 0x92c8ae6b, 0x464fc96f, 0x3b0b8bc9, -348 },
{ 0xb77ada06, 0x17e3bbcb, 0x09ce6ebb, -345 },
{ 0xe5599087, 0x9ddcaabd, 0xcc420a6a, -342 },
{ 0x8f57fa54, 0xc2a9eab6, 0x9fa94682, -338 },
{ 0xb32df8e9, 0xf3546564, 0x47939822, -335 },
{ 0xdff97724, 0x70297ebd, 0x59787e2b, -332 },
{ 0x8bfbea76, 0xc619ef36, 0x57eb4edb, -328 },
{ 0xaefae514, 0x77a06b03, 0xede62292, -325 },
{ 0xdab99e59, 0x958885c4, 0xe95fab36, -322 },
{ 0x88b402f7, 0xfd75539b, 0x11dbcb02, -318 },
{ 0xaae103b5, 0xfcd2a881, 0xd652bdc2, -315 },
{ 0xd59944a3, 0x7c0752a2, 0x4be76d33, -312 },
{ 0x857fcae6, 0x2d8493a5, 0x6f70a440, -308 },
{ 0xa6dfbd9f, 0xb8e5b88e, 0xcb4ccd50, -305 },
{ 0xd097ad07, 0xa71f26b2, 0x7e2000a4, -302 },
{ 0x825ecc24, 0xc873782f, 0x8ed40066, -298 },
{ 0xa2f67f2d, 0xfa90563b, 0x72890080, -295 },
{ 0xcbb41ef9, 0x79346bca, 0x4f2b40a0, -292 },
{ 0xfea126b7, 0xd78186bc, 0xe2f610c8, -289 },
{ 0x9f24b832, 0xe6b0f436, 0x0dd9ca7d, -285 },
{ 0xc6ede63f, 0xa05d3143, 0x91503d1c, -282 },
{ 0xf8a95fcf, 0x88747d94, 0x75a44c63, -279 },
{ 0x9b69dbe1, 0xb548ce7c, 0xc986afbe, -275 },
{ 0xc24452da, 0x229b021b, 0xfbe85bad, -272 },
{ 0xf2d56790, 0xab41c2a2, 0xfae27299, -269 },
{ 0x97c560ba, 0x6b0919a5, 0xdccd879f, -265 },
{ 0xbdb6b8e9, 0x05cb600f, 0x5400e987, -262 },
{ 0xed246723, 0x473e3813, 0x290123e9, -259 },
{ 0x9436c076, 0x0c86e30b, 0xf9a0b672, -255 },
{ 0xb9447093, 0x8fa89bce, 0xf808e40e, -252 },
{ 0xe7958cb8, 0x7392c2c2, 0xb60b1d12, -249 },
{ 0x90bd77f3, 0x483bb9b9, 0xb1c6f22b, -245 },
{ 0xb4ecd5f0, 0x1a4aa828, 0x1e38aeb6, -242 },
{ 0xe2280b6c, 0x20dd5232, 0x25c6da63, -239 },
{ 0x8d590723, 0x948a535f, 0x579c487e, -235 },
{ 0xb0af48ec, 0x79ace837, 0x2d835a9d, -232 },
{ 0xdcdb1b27, 0x98182244, 0xf8e43145, -229 },
{ 0x8a08f0f8, 0xbf0f156b, 0x1b8e9ecb, -225 },
{ 0xac8b2d36, 0xeed2dac5, 0xe272467e, -222 },
{ 0xd7adf884, 0xaa879177, 0x5b0ed81d, -219 },
{ 0x86ccbb52, 0xea94baea, 0x98e94712, -215 },
{ 0xa87fea27, 0xa539e9a5, 0x3f2398d7, -212 },
{ 0xd29fe4b1, 0x8e88640e, 0x8eec7f0d, -209 },
{ 0x83a3eeee, 0xf9153e89, 0x1953cf68, -205 },
{ 0xa48ceaaa, 0xb75a8e2b, 0x5fa8c342, -202 },
{ 0xcdb02555, 0x653131b6, 0x3792f412, -199 },
{ 0x808e1755, 0x5f3ebf11, 0xe2bbd88b, -195 },
{ 0xa0b19d2a, 0xb70e6ed6, 0x5b6aceae, -192 },
{ 0xc8de0475, 0x64d20a8b, 0xf245825a, -189 },
{ 0xfb158592, 0xbe068d2e, 0xeed6e2f0, -186 },
{ 0x9ced737b, 0xb6c4183d, 0x55464dd6, -182 },
{ 0xc428d05a, 0xa4751e4c, 0xaa97e14c, -179 },
{ 0xf5330471, 0x4d9265df, 0xd53dd99f, -176 },
{ 0x993fe2c6, 0xd07b7fab, 0xe546a803, -172 },
{ 0xbf8fdb78, 0x849a5f96, 0xde985204, -169 },
{ 0xef73d256, 0xa5c0f77c, 0x963e6685, -166 },
{ 0x95a86376, 0x27989aad, 0xdde70013, -162 },
{ 0xbb127c53, 0xb17ec159, 0x5560c018, -159 },
{ 0xe9d71b68, 0x9dde71af, 0xaab8f01e, -156 },
{ 0x92267121, 0x62ab070d, 0xcab39613, -152 },
{ 0xb6b00d69, 0xbb55c8d1, 0x3d607b97, -149 },
{ 0xe45c10c4, 0x2a2b3b05, 0x8cb89a7d, -146 },
{ 0x8eb98a7a, 0x9a5b04e3, 0x77f3608e, -142 },
{ 0xb267ed19, 0x40f1c61c, 0x55f038b2, -139 },
{ 0xdf01e85f, 0x912e37a3, 0x6b6c46de, -136 },
{ 0x8b61313b, 0xbabce2c6, 0x2323ac4b, -132 },
{ 0xae397d8a, 0xa96c1b77, 0xabec975e, -129 },
{ 0xd9c7dced, 0x53c72255, 0x96e7bd35, -126 },
{ 0x881cea14, 0x545c7575, 0x7e50d641, -122 },
{ 0xaa242499, 0x697392d2, 0xdde50bd1, -119 },
{ 0xd4ad2dbf, 0xc3d07787, 0x955e4ec6, -116 },
{ 0x84ec3c97, 0xda624ab4, 0xbd5af13b, -112 },
{ 0xa6274bbd, 0xd0fadd61, 0xecb1ad8a, -109 },
{ 0xcfb11ead, 0x453994ba, 0x67de18ed, -106 },
{ 0x81ceb32c, 0x4b43fcf4, 0x80eacf94, -102 },
{ 0xa2425ff7, 0x5e14fc31, 0xa1258379, -99 },
{ 0xcad2f7f5, 0x359a3b3e, 0x096ee458, -96 },
{ 0xfd87b5f2, 0x8300ca0d, 0x8bca9d6e, -93 },
{ 0x9e74d1b7, 0x91e07e48, 0x775ea264, -89 },
{ 0xc6120625, 0x76589dda, 0x95364afe, -86 },
{ 0xf79687ae, 0xd3eec551, 0x3a83ddbd, -83 },
{ 0x9abe14cd, 0x44753b52, 0xc4926a96, -79 },
{ 0xc16d9a00, 0x95928a27, 0x75b7053c, -76 },
{ 0xf1c90080, 0xbaf72cb1, 0x5324c68b, -73 },
{ 0x971da050, 0x74da7bee, 0xd3f6fc16, -69 },
{ 0xbce50864, 0x92111aea, 0x88f4bb1c, -66 },
{ 0xec1e4a7d, 0xb69561a5, 0x2b31e9e3, -63 },
{ 0x9392ee8e, 0x921d5d07, 0x3aff322e, -59 },
{ 0xb877aa32, 0x36a4b449, 0x09befeb9, -56 },
{ 0xe69594be, 0xc44de15b, 0x4c2ebe68, -53 },
{ 0x901d7cf7, 0x3ab0acd9, 0x0f9d3701, -49 },
{ 0xb424dc35, 0x095cd80f, 0x538484c1, -46 },
{ 0xe12e1342, 0x4bb40e13, 0x2865a5f2, -43 },
{ 0x8cbccc09, 0x6f5088cb, 0xf93f87b7, -39 },
{ 0xafebff0b, 0xcb24aafe, 0xf78f69a5, -36 },
{ 0xdbe6fece, 0xbdedd5be, 0xb573440e, -33 },
{ 0x89705f41, 0x36b4a597, 0x31680a88, -29 },
{ 0xabcc7711, 0x8461cefc, 0xfdc20d2b, -26 },
{ 0xd6bf94d5, 0xe57a42bc, 0x3d329076, -23 },
{ 0x8637bd05, 0xaf6c69b5, 0xa63f9a49, -19 },
{ 0xa7c5ac47, 0x1b478423, 0x0fcf80dc, -16 },
{ 0xd1b71758, 0xe219652b, 0xd3c36113, -13 },
{ 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;
#else
#define MTa /*nothing*/
#define MTb /*nothing*/
#define MTd /*nothing*/
#endif
#define Kmax 7
#ifdef __cplusplus
extern "C" double fpconv_strtod(const char *s00, char **se);
extern "C" char *dtoa(double d, int mode, int ndigits,
int *decpt, int *sign, char **rve);
#endif
struct
Bigint {
struct Bigint *next;
int k, maxwds, sign, wds;
ULong x[1];
};
typedef struct Bigint Bigint;
typedef struct
ThInfo {
Bigint *Freelist[Kmax+1];
Bigint *P5s;
} ThInfo;
static ThInfo TI0;
#ifdef MULTIPLE_THREADS
static ThInfo *TI1;
static int TI0_used;
void
set_max_dtoa_threads(unsigned int n)
{
size_t L;
ThInfo *newTI1;
if (n > maxthreads) {
L = n*sizeof(ThInfo);
if (TI1) {
newTI1 = (ThInfo*)REALLOC(TI1, L);
if (newTI1) {
TI1 = newTI1;
memset(TI1 + maxthreads, 0, (n-maxthreads)*sizeof(ThInfo));
}
else
return;
}
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));
#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));
#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);
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++] = 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 = 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);
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[] = {
1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1e20, 1e21, 1e22
#ifdef VAX
, 1e23, 1e24
#endif
};
static const double
#ifdef IEEE_Arith
bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
static const double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
#ifdef Avoid_Underflow
9007199254740992.*9007199254740992.e-256
/* = 2^106 * 1e-256 */
#else
1e-256
#endif
};
/* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
/* flag unnecessarily. It leads to a song and dance at the end of strtod. */
#define Scale_Bit 0x10
#define n_bigtens 5
#else
#ifdef IBM
bigtens[] = { 1e16, 1e32, 1e64 };
static const double tinytens[] = { 1e-16, 1e-32, 1e-64 };
#define n_bigtens 3
#else
bigtens[] = { 1e16, 1e32 };
static const double tinytens[] = { 1e-16, 1e-32 };
#define n_bigtens 2
#endif
#endif
#undef Need_Hexdig
#ifdef INFNAN_CHECK
#ifndef No_Hex_NaN
#define Need_Hexdig
#endif
#endif
#ifndef Need_Hexdig
#ifndef NO_HEX_FP
#define Need_Hexdig
#endif
#endif
#ifdef Need_Hexdig /*{*/
#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 hexdig[256] = {
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++)) {
if ((c = *++s) >= 'A' && c <= 'Z')
c += 'a' - 'A';
if (c != d)
return 0;
}
*sp = s + 1;
return 1;
}
#ifndef No_Hex_NaN
static void
hexnan(U *rvp, const char **sp)
{
ULong c, x[2];
const char *s;
int 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;
char d;
const unsigned char *decpt, *s0, *s, *s1;
Long e, e1;
ULong L, lostbits, *x;
int big, denorm, esign, havedig, k, n, nb, nbits, nz, 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 IEEE_Arith
int check_denorm = 0;
#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;
havedig = n = nz = 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 ((d = hexdig[*s1]))
havedig = 1;
else if (!havedig) {
e += 4;
continue;
}
if (n == ULbits) {
*x++ = L;
L = 0;
n = 0;
}
L |= (d & 0x0f) << n;
n += 4;
}
*x++ = L;
b->wds = n = x - b->x;
nb = ULbits*n - hi0bits(L);
nbits = Nbits;
lostbits = 0;
x = b->x;
if (nb > nbits) {
n = nb - 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 (nb < nbits) {
n = nbits - nb;
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;
#ifdef IEEE_Arith
if (!k) {
switch(rounding) {
case Round_near:
if (((b->x[0] & 3) == 3) || (lostbits && (b->x[0] & 1))) {
multadd(b, 1, 1 MTa);
emin_check:
if (b->x[1] == (1 << (Exp_shift + 1))) {
rshift(b,1);
e = emin;
goto normal;
}
}
break;
case Round_up:
if (!sign && (lostbits || (b->x[0] & 1))) {
incr_denorm:
multadd(b, 1, 2 MTa);
check_denorm = 1;
lostbits = 0;
goto emin_check;
}
break;
case Round_down:
if (sign && (lostbits || (b->x[0] & 1)))
goto incr_denorm;
break;
}
}
#endif
if (lostbits)
lostbits = 1;
else if (k > 0)
lostbits = any_on(b,k);
#ifdef IEEE_Arith
else if (check_denorm)
goto no_lostbits;
#endif
if (x[k>>kshift] & 1 << (k & kmask))
lostbits |= 2;
#ifdef IEEE_Arith
no_lostbits:
#endif
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 && (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 {
normal:
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 MTa);
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) {
/* cppcheck-suppress integerOverflowCond */
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
fpconv_strtod(const char *s00, char **se)
{
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
ULong Lsb, Lsb1;
#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(*s) {
case '-':
sign = 1;
/* no break */
case '+':
if (*++s)
goto break2;
/* no break */
case 0:
goto ret0;
case '\t':
case '\n':
case '\v':
case '\f':
case '\r':
case ' ':
continue;
default:
goto break2;
}
break2:
if (*s == '0') {
#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(*++s == '0') ;
if (!*s)
goto ret;
}
s0 = s;
nd = nf = 0;
#ifdef USE_BF96
yz = 0;
for(; (c = *s) >= '0' && c <= '9'; nd++, s++)
if (nd < 19)
yz = 10*yz + c - '0';
#else
y = z = 0;
for(; (c = *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 = 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 = *++s;
bc.dp1 = s - s0;
bc.dplen = bc.dp1 - bc.dp0;
if (!nd) {
for(; c == '0'; c = *++s)
nz++;
if (c > '0' && c <= '9') {
bc.dp0 = 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 = *++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 = *++s) {
case '-':
esign = 1;
case '+':
c = *++s;
}
if (c >= '0' && c <= '9') {
while(c == '0')
c = *++s;
if (c > '0' && c <= '9') {
L = c - '0';
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) {
case 'i':
case 'I':
if (match(&s,"nf")) {
--s;
if (!match(&s,"inity"))
++s;
word0(&rv) = 0x7ff00000;
word1(&rv) = 0;
goto ret;
}
break;
case 'n':
case 'N':
if (match(&s, "an")) {
word0(&rv) = NAN_WORD0;
word1(&rv) = NAN_WORD1;
#ifndef No_Hex_NaN
if (*s == '(') /*)*/
hexnan(&rv, &s);
#endif
goto ret;
}
}
#endif /*} INFNAN_CHECK */
ret0:
s = s00;
sign = 0;
}
goto ret;
}
bc.e0 = e1 = e -= nf;
/* Now we have nd0 digits, starting at s0, followed by a
* decimal point, followed by nd-nd0 digits. The number we're
* after is the integer represented by those digits times
* 10**e */
if (!nd0)
nd0 = nd;
#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
Lsb = LSB;
Lsb1 = 0;
j = bbe - bc.scale;
i = j + bbbits - 1; /* logb(rv) */
j = P + 1 - bbbits;
if (i < Emin) { /* denormal */
i = Emin - i;
j -= i;
if (i < 32)
Lsb <<= i;
else if (i < 52)
Lsb1 = Lsb << (i-32);
else
Lsb1 = Exp_mask;
}
#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 = 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
static char *dtoa_result;
#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 <= i;
j <<= 1)
k++;
r = (int*)Balloc(k MTa);
*r = k;
return
#ifndef MULTIPLE_THREADS
dtoa_result =
#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 <= n) {
rv = 0;
/* cppcheck-suppress nullPointerArithmetic */
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)
{
#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
if (s == dtoa_result)
dtoa_result = 0;
#endif
}
/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
*
* Inspired by "How to Print Floating-Point Numbers Accurately" by
* Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
*
* Modifications:
* 1. Rather than iterating, we use a simple numeric overestimate
* to determine k = floor(log10(d)). We scale relevant
* quantities using O(log2(k)) rather than O(k) multiplications.
* 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
* try to generate digits strictly left to right. Instead, we
* compute with fewer bits and propagate the carry if necessary
* when rounding the final digit up. This is often faster.
* 3. Under the assumption that input will be rounded nearest,
* mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
* That is, we allow equality in stopping tests when the
* round-nearest rule will give the same floating-point value
* as would satisfaction of the stopping test with strict
* inequality.
* 4. We remove common factors of powers of 2 from relevant
* quantities.
* 5. When converting floating-point integers less than 1e16,
* we use floating-point arithmetic rather than resorting
* to multiple-precision integers.
* 6. When asked to produce fewer than 15 digits, we first try
* to get by with floating-point arithmetic; we resort to
* multiple-precision integer arithmetic only if we cannot
* guarantee that the floating-point calculation has given
* the correctly rounded result. For k requested digits and
* "uniformly" distributed input, the probability is
* something like 10^(k-15) that we must resort to the Long
* calculation.
*/
char *
dtoa_r(double dd, int mode, int ndigits, int *decpt, int *sign, char **rve, char *buf, size_t blen)
{
/* 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;
#if !defined(Sudden_Underflow) || defined(USE_BF96)
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
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 /*USE_BF96*/
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 <= i) {
buf = 0;
if (rve)
/* cppcheck-suppress nullPointerArithmetic */
*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;
/* cppcheck-suppress integerOverflowCond */
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 = 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 *
dtoa(double dd, int mode, int ndigits, int *decpt, int *sign, char **rve)
{
/* 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
if (dtoa_result)
freedtoa(dtoa_result);
#endif
return dtoa_r(dd, mode, ndigits, decpt, sign, rve, 0, 0);
}
#ifdef __cplusplus
}
#endif
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