#include "libc/calls/calls.h" #include "libc/limits.h" #include "libc/math.h" #include "libc/runtime/runtime.h" #include "libc/str/str.h" #include "third_party/dtoa/dtoa.h" #define IEEE_8087 1 /* #define SET_INEXACT 1 */ #if __NO_MATH_ERRNO__ + 0 #define NO_ERRNO 1 #endif #if __FINITE_MATH_ONLY__ + 0 #define NO_INFNAN_CHECK 1 #endif asm(".ident\t\"\\n\\n\ dtoa (MIT License)\\n\ The author of this software is David M. Gay.\\n\ Copyright (c) 1991, 2000, 2001 by Lucent Technologies.\""); asm(".include \"libc/disclaimer.inc\""); /**************************************************************** * * 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 dtoa_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 * #define Set_errno(x) _set_errno(x) * #define NO_HEX_FP to omit recognition of hexadecimal floating-point * values by strtod. * #define NO_STRTOD_BIGCOMP (on IEEE-arithmetic systems only for now) * to disable logic for "fast" testing of very long input strings * to strtod. This testing proceeds by initially truncating the * input string, then if necessary comparing the whole string with * a decimal expansion to decide close cases. This logic is only * used for input more than STRTOD_DIGLIM digits long (default 40). */ #ifndef Long #define Long int #endif #ifndef ULong typedef unsigned Long ULong; #endif #ifdef DEBUG #include "libc/assert.h" #define Bug(x) \ { \ dprintf(STDERR_FILENO, "%s\n", x); \ exit(1); \ } #define Debug(x) x int dtoa_stats [7]; /* strtod_{64,96,dtoa_bigcomp},dtoa_{exact,64,96,dtoa_bigcomp} */ #else #define assert(x) /*nothing*/ #define Debug(x) /*nothing*/ #endif #include "libc/mem/mem.h" #include "libc/str/str.h" #include "libc/sysv/errfuns.h" #ifdef Honor_FLT_ROUNDS #ifndef Trust_FLT_ROUNDS #include "libc/math.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; INITIALIZER(300, _init_dtoa_pmem, { 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 "libc/errno.h" #ifdef NO_ERRNO /*{*/ #undef Set_errno #define Set_errno(x) #else #ifndef Set_errno #define Set_errno(x) 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 "libc/math.h" #endif /* Bad_float_h */ #ifndef __MATH_H__ #include "libc/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; /* 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.*/ INITIALIZER(300, _init_dtoa_divmax, { dtoa_divmax = 2; }); #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 const BF96 kDtoaPten[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 const short int kDtoaLhint[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 kDtoaPfive[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 kDtoaPfiveBits[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(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; if (n > maxthreads) { L = n * sizeof(ThInfo); if (TI1) { TI1 = (ThInfo *)REALLOC(TI1, L); memset(TI1 + maxthreads, 0, (n - maxthreads) * sizeof(ThInfo)); } else { TI1 = (ThInfo *)MALLOC(L); if (TI0_used) { memcpy(TI1, &TI0, sizeof(ThInfo)); if (n > 1) memset(TI1 + 1, 0, L - sizeof(ThInfo)); memset(&TI0, 0, sizeof(ThInfo)); } else memset(TI1, 0, L); } maxthreads = n; } } static ThInfo *get_TI(void) { unsigned int thno = dtoa_get_threadno(); if (thno < maxthreads) return TI1 + thno; if (thno == 0) TI0_used = 1; return &TI0; } #define freelist TI->Freelist #define p5s TI->P5s #else #define freelist TI0.Freelist #define p5s TI0.P5s #endif static Bigint *dtoa_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 = 1u << 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 dtoa_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 *dtoa_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 = dtoa_balloc(b->k + 1 MTa); Bcopy(b1, b); dtoa_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 = dtoa_balloc(k MTa); b->x[0] = y9; b->wds = 1; #else b = dtoa_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 = dtoa_multadd(b, 10, *s++ - '0' MTa); while (++i < nd0); s += dplen; } else s += dplen + 9; for (; i < nd; i++) b = dtoa_multadd(b, 10, *s++ - '0' MTa); return b; } static int dtoa_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 dtoa_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 *dtoa_i2b(int i MTd) { Bigint *b; b = dtoa_balloc(1 MTa); b->x[0] = i; b->wds = 1; return b; } static Bigint *dtoa_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 = dtoa_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 *dtoa_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 = dtoa_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 = dtoa_i2b(625 MTa); p5->next = 0; } if (TI == &TI0) FREE_DTOA_LOCK(1); #else p5 = p5s = dtoa_i2b(625 MTa); p5->next = 0; #endif } for (;;) { if (k & 1) { b1 = dtoa_mult(b, p5 MTa); dtoa_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 = dtoa_mult(p5, p5 MTa); p51->next = 0; } if (TI == &TI0) FREE_DTOA_LOCK(1); #else p51 = p5->next = dtoa_mult(p5, p5); p51->next = 0; #endif } p5 = p51; } return b; } static Bigint *dtoa_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 = dtoa_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; dtoa_bfree(b MTa); return b1; } static int dtoa_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("dtoa_cmp called with a->x[a->wds-1] == 0"); if (j > 1 && !b->x[j - 1]) Bug("dtoa_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 *dtoa_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 = dtoa_cmp(a, b); if (!i) { c = dtoa_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 = dtoa_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 dtoa_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 dtoa_b2d"); #endif k = dtoa_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 *dtoa_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 = dtoa_balloc(1 MTa); #else b = dtoa_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 = dtoa_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 = dtoa_lo0bits(&z); x[0] = z; #ifndef Sudden_Underflow i = #endif b->wds = 1; k += 32; } #else if (y = d1) { if (k = dtoa_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 dtoa_d2b"); #endif k = dtoa_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 - dtoa_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 - dtoa_hi0bits(x[i - 1]); #else *bits = (i + 2) * 16 - dtoa_hi0bits(x[i]); #endif } #endif return b; } #undef d0 #undef d1 static double dtoaratio(Bigint *a, Bigint *b) { U da, db; int k, ka, kb; dval(&da) = dtoa_b2d(a, &ka); dval(&db) = dtoa_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) *= 1u << k; } else { k = -k; word0(&db) += (k >> 2) * Exp_msk1; if (k &= 3) dval(&db) *= 1u << 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 kDtoaTens[] = {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 kDtoaBigTens[] = {1e16, 1e32, 1e64, 1e128, 1e256}; static const double kDtoaTinyTens[] = { 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 kDtoaTinyTens[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 kDtoaBigTens[] = {1e16, 1e32, 1e64}; static const double kDtoaTinyTens[] = {1e-16, 1e-32, 1e-64}; #define n_bigtens 3 #else kDtoaBigTens[] = {1e16, 1e32}; static const double kDtoaTinyTens[] = {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 kDtoaHexdig[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 dtoa_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 dtoa_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 = kDtoaHexdig[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 = dtoa_balloc(b->k + 1 MTa); Bcopy(b1, b); dtoa_bfree(b MTa); b = b1; } b->x[b->wds++] = 1; } return b; } #endif /*}*/ #ifndef NO_HEX_FP /*{*/ static void dtoa_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 dtoa_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 }; static void gethex(const char **sp, U *rvp, int rounding, int sign MTd) { Bigint *b; const unsigned char *decpt, *s0, *s, *s1; Long e, e1; ULong L, lostbits, *x; int big, denorm, esign, havedig, k, n, nbits, up, zret; #ifdef IBM int j; #endif enum { #ifdef IEEE_Arith /*{{*/ emax = 0x7fe - Bias - P + 1, emin = Emin - P + 1 #else /*}{*/ emin = Emin - P, #ifdef VAX emax = 0x7ff - Bias - P + 1 #endif #ifdef IBM emax = 0x7f - Bias - P #endif #endif /*}}*/ }; #ifdef USE_LOCALE int i; #ifdef NO_LOCALE_CACHE const unsigned char *decimalpoint = (unsigned char *)localeconv()->decimal_point; #else const unsigned char *decimalpoint; static unsigned char *decimalpoint_cache; if (!(s0 = decimalpoint_cache)) { s0 = (unsigned char *)localeconv()->decimal_point; if ((decimalpoint_cache = (unsigned char *)MALLOC(strlen((const char *)s0) + 1))) { strcpy((char *)decimalpoint_cache, (const char *)s0); s0 = decimalpoint_cache; } } decimalpoint = s0; #endif #endif /**** if (!hexdig['0']) hexdig_init(); ****/ havedig = 0; s0 = *(const unsigned char **)sp + 2; while (s0[havedig] == '0') havedig++; s0 += havedig; s = s0; decpt = 0; zret = 0; e = 0; if (kDtoaHexdig[*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 (!kDtoaHexdig[*s]) goto pcheck; while (*s == '0') s++; if (kDtoaHexdig[*s]) zret = 0; havedig = 1; s0 = s; } while (kDtoaHexdig[*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 (kDtoaHexdig[*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 = kDtoaHexdig[*s]) == 0 || n > 0x19) { s = s1; break; } e1 = n - 0x10; while ((n = kDtoaHexdig[*++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: dtoa_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 = dtoa_balloc(k MTa); x = b->x; n = 0; L = 0; #ifdef USE_LOCALE for (i = 0; decimalpoint[i + 1]; ++i) ; #endif while (s1 > s0) { #ifdef USE_LOCALE if (*--s1 == decimalpoint[i]) { s1 -= i; continue; } #else if (*--s1 == '.') continue; #endif if (n == ULbits) { *x++ = L; L = 0; n = 0; } L |= (kDtoaHexdig[*s1] & 0x0f) << n; n += 4; } *x++ = L; b->wds = n = x - b->x; n = ULbits * n - dtoa_hi0bits(L); nbits = Nbits; lostbits = 0; x = b->x; if (n > nbits) { n -= nbits; if (dtoa_any_on(b, n)) { lostbits = 1; k = n - 1; if (x[k >> kshift] & 1 << (k & kmask)) { lostbits = 2; if (k > 0 && dtoa_any_on(b, k)) lostbits = 3; } } dtoa_rshift(b, n); e += n; } else if (n < nbits) { n = nbits - n; b = dtoa_lshift(b, n MTa); e -= n; x = b->x; } if (e > emax) { ovfl: dtoa_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 || dtoa_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 */ dtoa_bfree(b MTa); retz: Set_errno(erange); retz1: rvp->d = 0.; return; } k = n - 1; if (lostbits) lostbits = 1; else if (k > 0) lostbits = dtoa_any_on(b, k); if (x[k >> kshift] & 1 << (k & kmask)) lostbits |= 2; nbits -= n; dtoa_rshift(b, n); e = emin; } if (lostbits) { up = 0; switch (rounding) { case Round_zero: break; case Round_near: if (lostbits & 2 && (lostbits & 1) | (x[0] & 1)) up = 1; break; case Round_up: up = 1 - sign; break; case Round_down: up = sign; } if (up) { k = b->wds; b = increment(b MTa); x = b->x; if (denorm) { #if 0 if (nbits == Nbits - 1 && x[nbits >> kshift] & 1 << (nbits & kmask)) denorm = 0; /* not currently used */ #endif } else if (b->wds > k || ((n = nbits & kmask) != 0 && dtoa_hi0bits(x[k - 1]) < 32 - n)) { dtoa_rshift(b, 1); if (++e > Emax) goto ovfl; } } } #ifdef IEEE_Arith if (denorm) word0(rvp) = b->wds > 1 ? b->x[1] & ~0x100000 : 0; else word0(rvp) = (b->x[1] & ~0x100000) | ((e + 0x3ff + 52) << 20); word1(rvp) = b->x[0]; #endif #ifdef IBM if ((j = e & 3)) { k = b->x[0] & ((1u << j) - 1); dtoa_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 dtoa_bfree(b MTa); } #endif /*!NO_HEX_FP}*/ static int dtoa_dshift(Bigint *b, int p2) { int rv = dtoa_hi0bits(b->x[b->wds - 1]) - 4; if (p2 > 0) rv -= p2; return rv & kmask; } static int dtoa_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 dtoa_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 dtoa_quorem is called from dtoa_bigcomp and */ /* the input is near, e.g., twice the smallest denormalized number. */ /*debug*/ if (q > 15) #endif /*debug*/ Bug("oversized quotient in dtoa_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 (dtoa_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 dtoa_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 dtoa_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; dd = 0; /* TODO(jart): Why does compiler complain? */ 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 = dtoa_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 = dtoa_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 dtoa_bfree(b MTa); b = dtoa_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 = dtoa_lshift(b, i MTa); if (dsign) b = increment(b MTa); } else #endif { b = dtoa_lshift(b, ++i MTa); b->x[0] |= 1; } #ifndef Sudden_Underflow have_i: #endif p2 -= p5 + i; d = dtoa_i2b(1 MTa); /* Arrange for convenient computation of quotients: * shift left if necessary so divisor has 4 leading 0 bits. */ if (p5 > 0) d = dtoa_pow5mult(d, p5 MTa); else if (p5 < 0) b = dtoa_pow5mult(b, -p5 MTa); if (p2 > 0) { b2 = p2; d2 = 0; } else { b2 = 0; d2 = -p2; } i = dtoa_dshift(d, d2); if ((b2 += i) > 0) b = dtoa_lshift(b, b2 MTa); if ((d2 += i) > 0) d = dtoa_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 = dtoa_quorem(b, d))) { b = dtoa_multadd(b, 10, 0 MTa); /* very unlikely */ dig = dtoa_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 = dtoa_multadd(b, 10, 0 MTa); dig = dtoa_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 = dtoa_multadd(b, 10, 0 MTa); dig = dtoa_quorem(b, d); } if (dig > 0 || b->x[0] || b->wds > 1) dd = -1; ret: dtoa_bfree(b MTa); dtoa_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. * dtoa_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) -= dtoa_sulp(rv, bc); } else if (dd > 0) { if (dsign) { rethi1: dval(rv) += dtoa_sulp(rv, bc); } } else { /* Exact half-way case: apply round-even rule. */ if ((j = ((word0(rv) & Exp_mask) >> Exp_shift) - bc->scale) <= 0) { i = 1 - j; if (i <= 31) { if (word1(rv) & (0x1 << i)) goto odd; } else if (word0(rv) & (0x1 << (i - 32))) goto odd; } else if (word1(rv) & 1) { odd: if (dsign) goto rethi1; goto retlow1; } } #ifdef Honor_FLT_ROUNDS ret1: #endif return; } #endif /* NO_STRTOD_BIGCOMP */ double(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_dtoa_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'; s1 = s; while ((c = *++s) >= '0' && c <= '9') L = 10 * L + c - '0'; if (s - s1 > 8 || L > 19999) /* Avoid confusion from exponents * so large that e might overflow. */ e = 19999; /* safe for 16 bit ints */ else e = (int)L; if (esign) e = -e; } else e = 0; } else s = s00; } if (!nd) { if (!nz && !nz0) { #ifdef INFNAN_CHECK /*{*/ /* Check for Nan and Infinity */ if (!bc.dplen) switch (c) { case 'i': case 'I': if (dtoa_match(&s, "nf")) { --s; if (!dtoa_match(&s, "inity")) ++s; word0(&rv) = 0x7ff00000; word1(&rv) = 0; goto ret; } break; case 'n': case 'N': if (dtoa_match(&s, "an")) { word0(&rv) = NAN_WORD0; word1(&rv) = NAN_WORD1; #ifndef No_Hex_NaN if (*s == '(') /*)*/ dtoa_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) = kDtoaTens[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), kDtoaTens[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) *= kDtoaTens[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), kDtoaTens[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), kDtoaTens[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), kDtoaTens[-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 = &kDtoaPten[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) / kDtoaPfive[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) *= kDtoaTens[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) { dtoa_bfree(bb MTb); dtoa_bfree(bd MTb); dtoa_bfree(bs MTb); dtoa_bfree(bd0 MTb); dtoa_bfree(delta MTb); } Set_errno(erange); goto ret; } e1 >>= 4; for (j = 0; e1 > 1; j++, e1 >>= 1) if (e1 & 1) dval(&rv) *= kDtoaBigTens[j]; /* The last multiplication could overflow. */ word0(&rv) -= P * Exp_msk1; dval(&rv) *= kDtoaBigTens[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) /= kDtoaTens[i]; if (e1 >>= 4) { if (e1 >= 1u << 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) *= kDtoaTinyTens[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) *= kDtoaTinyTens[j]; /* The last multiplication could underflow. */ dval(&rv0) = dval(&rv); dval(&rv) *= kDtoaTinyTens[j]; if (!dval(&rv)) { dval(&rv) = 2. * dval(&rv0); dval(&rv) *= kDtoaTinyTens[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 = dtoa_balloc(bd0->k MTb); Bcopy(bd, bd0); bb = dtoa_d2b(&rv, &bbe, &bbbits MTb); /* rv = bb * 2^bbe */ bs = dtoa_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 = dtoa_pow5mult(bs, bb5 MTb); bb1 = dtoa_mult(bs, bb MTb); dtoa_bfree(bb MTb); bb = bb1; } if (bb2 > 0) bb = dtoa_lshift(bb, bb2 MTb); if (bd5 > 0) bd = dtoa_pow5mult(bd, bd5 MTb); if (bd2 > 0) bd = dtoa_lshift(bd, bd2 MTb); if (bs2 > 0) bs = dtoa_lshift(bs, bs2 MTb); delta = dtoa_diff(bb, bd MTb); bc.dsign = delta->sign; delta->sign = 0; i = dtoa_cmp(delta, bs); #ifndef NO_STRTOD_BIGCOMP /*{*/ if (bc.nd > nd && i <= 0) { if (bc.dsign) { /* Must use dtoa_bigcomp(). */ req_dtoa_bigcomp = 1; break; } #ifdef Honor_FLT_ROUNDS if (bc.rounding != 1) { if (i < 0) { req_dtoa_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 = dtoa_lshift(delta, Log2P MTb); if (dtoa_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 = dtoaratio(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 = dtoa_lshift(delta, Log2P MTb); if (dtoa_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) += dtoa_sulp(&rv, &bc); #else dval(&rv) += ulp(&rv); #endif #ifndef ROUND_BIASED else { #ifdef Avoid_Underflow dval(&rv) -= dtoa_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 = dtoaratio(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_dtoa_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: dtoa_bfree(bb MTb); dtoa_bfree(bd MTb); dtoa_bfree(bs MTb); dtoa_bfree(delta MTb); } dtoa_bfree(bb MTb); dtoa_bfree(bd MTb); dtoa_bfree(bs MTb); dtoa_bfree(bd0 MTb); dtoa_bfree(delta MTb); #ifndef NO_STRTOD_BIGCOMP if (req_dtoa_bigcomp) { bd0 = 0; bc.e0 += nz1; dtoa_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; if (sign) { return -dval(&rv); } else { return dval(&rv); } } #ifndef MULTIPLE_THREADS static char *dtoa_result; #endif static char *dtoa_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 *)dtoa_balloc(k MTa); *r = k; return #ifndef MULTIPLE_THREADS dtoa_result = #endif (char *)(r + 1); } static char *dtoa_nrv_alloc(const char *s, char *s0, size_t s0len, char **rve, int n MTd) { char *rv, *t; if (!s0) s0 = dtoa_rv_alloc(n MTa); else if (s0len <= n) { rv = 0; t = rv + n; goto rve_chk; } t = rv = s0; while ((*t = *s++)) ++t; rve_chk: if (rve) *rve = t; return rv; } /* freedtoa(s) must be used to free values s returned by dtoa * when MULTIPLE_THREADS is #defined. It should be used in all cases, * but for consistency with earlier versions of dtoa, it is optional * when MULTIPLE_THREADS is not defined. */ void freedtoa(char *s) { #ifdef MULTIPLE_THREADS ThInfo *TI = 0; #endif Bigint *b = (Bigint *)((int *)s - 1); b->maxwds = 1 << (b->k = *(int *)b); dtoa_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, dtoa_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 dtoa_nrv_alloc("inf", buf, blen, rve, 8 MTb); #endif return dtoa_nrv_alloc("nan", buf, blen, rve, 3 MTb); } #endif #ifdef IBM dval(&u) += 0; /* normalize */ #endif if (!dval(&u)) { *decpt = 1; return dtoa_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 = kDtoaLhint[be + 51]; p10 = &kDtoaPten[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 = dtoa_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 - dtoa_hi0bits(word0(&d2) & Frac_mask)) dval(&d2) /= 1u << 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) < kDtoaTens[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; #endif #endif /*SET_INEXACT*/ #endif if (mode > 5) { mode -= 4; #ifndef USE_BF96 try_quick = 0; #endif } leftright = 1; ilim = ilim1 = -1; /* Values for cases 0 and 1; done here to */ /* silence erroneous "gcc -Wall" warning. */ switch (mode) { case 0: case 1: i = 18; ndigits = 0; break; case 2: leftright = 0; /* no break */ case 4: if (ndigits <= 0) ndigits = 1; ilim = ilim1 = i = ndigits; break; case 3: leftright = 0; /* no break */ case 5: i = ndigits + k + 1; ilim = i; ilim1 = i - 1; if (i <= 0) i = 1; } if (!buf) { buf = dtoa_rv_alloc(i MTb); blen = sizeof(Bigint) + ((1 << ((int *)buf)[-1]) - 1) * sizeof(ULong) - sizeof(int); } else if (blen <= i) { buf = 0; if (rve) *rve = buf + i; return buf; } s = buf; /* Check for special case that d is a normalized power of 2. */ spec_case = 0; if (mode < 2 || (leftright #ifdef Honor_FLT_ROUNDS && Rounding == 1 #endif )) { if (!word1(&u) && !(word0(&u) & Bndry_mask) #ifndef Sudden_Underflow && word0(&u) & (Exp_mask & ~Exp_msk1) #endif ) { /* The special case */ spec_case = 1; } } #ifdef USE_BF96 /*{*/ b = 0; if (ilim < 0 && (mode == 3 || mode == 5)) { S = mhi = 0; goto no_digits; } i = 1; j = 52 + 0x3ff - be; ulpshift = 0; ulplo = 0; /* Can we do an exact computation with 64-bit integer arithmetic? */ if (k < 0) { if (k < -25) goto toobig; res = dbits >> 11; n2 = kDtoaPfiveBits[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 = kDtoaPfive[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) > (kDtoaPfive[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 = kDtoaPfive[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; default: (void)0; /* added by jart */ } 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 = kDtoaPfive[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 = &kDtoaPten[342 - k]; tv0 = p10->b2 * dblo; /* rarely matters, but does, e.g., for 9.862818194192001e18 */ tv1 = p10->b1 * dblo + (tv0 >> 32); tv2 = p10->b2 * dbhi + (tv1 & 0xffffffffull); tv3 = p10->b0 * dblo + (tv1 >> 32) + (tv2 >> 32); res3 = p10->b1 * dbhi + (tv3 & 0xffffffffull); res = p10->b0 * dbhi + (tv3 >> 32) + (res3 >> 32); be += p10->e - 0x3fe; eulp = j1 = be - 54 + ulpadj; if (!(res & 0x8000000000000000ull)) { --be; res3 <<= 1; res = (res << 1) | ((res3 & 0x100000000ull) >> 32); } res0 = res; /* save for Fast_failed */ #if !defined(SET_INEXACT) && !defined(NO_DTOA_64) /*{*/ if (ilim > 19) goto Fast_failed; Debug(++dtoa_stats[4]); assert(be >= 0 && be <= 4); /* be = 0 is rare, but possible, e.g., for 1e20 */ res >>= 4 - be; ulp = p10->b0; /* ulp */ ulp = (ulp << 29) | (p10->b1 >> 3); /* scaled ulp = ulp * 2^(eulp - 60) */ /* We maintain 61 bits of the scaled ulp. */ if (ilim == 0) { if (!(res & 0x7fffffffffffffeull) || !((~res) & 0x7fffffffffffffeull)) goto Fast_failed1; S = mhi = 0; if (res >= 0x5000000000000000ull) goto one_digit; goto no_digits; } rb = 1; /* upper bound on rounding error */ for (;; ++i) { dig = res >> 60; *s++ = '0' + dig; res &= 0xfffffffffffffffull; if (ilim < 0) { ures = 0x1000000000000000ull - res; if (eulp > 0) { assert(eulp <= 4); dtoa_sulp = ulp << (eulp - 1); if (res <= ures) { if (res + rb > ures - rb) goto Fast_failed; if (res < dtoa_sulp) goto retc; } else { if (res - rb <= ures + rb) goto Fast_failed; if (ures < dtoa_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); dtoa_sulp = (ulp << (eulp - 1)) - rb; if (res <= ures) { if (res < dtoa_sulp) { if (res + rb < ures - rb) goto retc; } } else if (ures < dtoa_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 = dtoa_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 = kDtoaTens[k & 0xf]; j = k >> 4; if (j & Bletch) { /* prevent overflows */ j &= Bletch - 1; dval(&u) /= kDtoaBigTens[n_bigtens - 1]; ieps++; } for (; j; j >>= 1, i++) if (j & 1) { ieps++; ds *= kDtoaBigTens[i]; } dval(&u) /= ds; } else if (j1 > 0) { dval(&u) *= kDtoaTens[j1 & 0xf]; for (j = j1 >> 4; j; j >>= 1, i++) if (j & 1) { ieps++; dval(&u) *= kDtoaBigTens[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 / kDtoaTens[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) *= kDtoaTens[j1 & 0xf]; for (i = 0, j = (j1 - 256) >> 4; j; j >>= 1, i++) if (j & 1) dval(&eps1) *= kDtoaBigTens[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) *= kDtoaTens[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 = kDtoaTens[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 = dtoa_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 = dtoa_pow5mult(mhi, m5 MTb); b1 = dtoa_mult(mhi, b MTb); dtoa_bfree(b MTb); b = b1; } if ((j = b5 - m5)) b = dtoa_pow5mult(b, j MTb); } else b = dtoa_pow5mult(b, b5 MTb); } S = dtoa_i2b(1 MTb); if (s5 > 0) S = dtoa_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 dtoa_quorem, so it * can do shifts and ors to compute the numerator for q. */ i = dtoa_dshift(S, s2); b2 += i; m2 += i; s2 += i; if (b2 > 0) b = dtoa_lshift(b, b2 MTb); if (s2 > 0) S = dtoa_lshift(S, s2 MTb); #ifndef USE_BF96 if (k_check) { if (dtoa_cmp(b, S) < 0) { k--; b = dtoa_multadd(b, 10, 0 MTb); /* we botched the k estimate */ if (leftright) mhi = dtoa_multadd(mhi, 10, 0 MTb); ilim = ilim1; } } #endif if (ilim <= 0 && (mode == 3 || mode == 5)) { if (ilim < 0 || dtoa_cmp(b, S = dtoa_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 = dtoa_lshift(mhi, m2 MTb); /* Compute mlo -- check for special case * that d is a normalized power of 2. */ mlo = mhi; if (spec_case) { mhi = dtoa_balloc(mhi->k MTb); Bcopy(mhi, mlo); mhi = dtoa_lshift(mhi, Log2P MTb); } for (i = 1;; i++) { dig = dtoa_quorem(b, S) + '0'; /* Do we yet have the shortest decimal string * that will round to d? */ j = dtoa_cmp(b, mlo); delta = dtoa_diff(S, mhi MTb); j1 = delta->sign ? 1 : dtoa_cmp(b, delta); dtoa_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 = dtoa_lshift(b, 1 MTb); j1 = dtoa_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 = dtoa_multadd(b, 10, 0 MTb); if (mlo == mhi) mlo = mhi = dtoa_multadd(mhi, 10, 0 MTb); else { mlo = dtoa_multadd(mlo, 10, 0 MTb); mhi = dtoa_multadd(mhi, 10, 0 MTb); } } } else for (i = 1;; i++) { dig = dtoa_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 = dtoa_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 = dtoa_lshift(b, 1 MTb); j = dtoa_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: dtoa_bfree(S MTb); if (mhi) { if (mlo && mlo != mhi) dtoa_bfree(mlo MTb); dtoa_bfree(mhi MTb); } retc: while (s > buf && s[-1] == '0') --s; ret1: if (b) dtoa_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