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dtoa.c
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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 },
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{ 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 },