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Diffstat (limited to 'src/dtoa.c')
| -rw-r--r-- | src/dtoa.c | 6265 |
1 files changed, 6265 insertions, 0 deletions
diff --git a/src/dtoa.c b/src/dtoa.c new file mode 100644 index 0000000..062ac24 --- /dev/null +++ b/src/dtoa.c @@ -0,0 +1,6265 @@ +// clang-format off +/**************************************************************** + * + * 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). + */ + +#include "jansson_private.h" + +#ifdef WORDS_BIGENDIAN +# define IEEE_MC68k 1 +#else +# define IEEE_8087 1 +#endif + +#if defined(JSON_INTEGER_IS_LONG_LONG) && (JSON_INTEGER_IS_LONG_LONG == 0) +# define NO_LONG_LONG 1 +#endif + +#define MALLOC jsonp_malloc +#define FREE jsonp_free + +/* + * #define IEEE_8087 for IEEE-arithmetic machines where the least + * significant byte has the lowest address. + * #define IEEE_MC68k for IEEE-arithmetic machines where the most + * significant byte has the lowest address. + * #define Long int on machines with 32-bit ints and 64-bit longs. + * #define IBM for IBM mainframe-style floating-point arithmetic. + * #define VAX for VAX-style floating-point arithmetic (D_floating). + * #define No_leftright to omit left-right logic in fast floating-point + * computation of dtoa. This will cause dtoa modes 4 and 5 to be + * treated the same as modes 2 and 3 for some inputs. + * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3 + * and strtod and dtoa should round accordingly. Unless Trust_FLT_ROUNDS + * is also #defined, fegetround() will be queried for the rounding mode. + * Note that both FLT_ROUNDS and fegetround() are specified by the C99 + * standard (and are specified to be consistent, with fesetround() + * affecting the value of FLT_ROUNDS), but that some (Linux) systems + * do not work correctly in this regard, so using fegetround() is more + * portable than using FLT_ROUNDS directly. + * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3 + * and Honor_FLT_ROUNDS is not #defined. + * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines + * that use extended-precision instructions to compute rounded + * products and quotients) with IBM. + * #define ROUND_BIASED for IEEE-format with biased rounding and arithmetic + * that rounds toward +Infinity. + * #define ROUND_BIASED_without_Round_Up for IEEE-format with biased + * rounding when the underlying floating-point arithmetic uses + * unbiased rounding. This prevent using ordinary floating-point + * arithmetic when the result could be computed with one rounding error. + * #define Inaccurate_Divide for IEEE-format with correctly rounded + * products but inaccurate quotients, e.g., for Intel i860. + * #define NO_LONG_LONG on machines that do not have a "long long" + * integer type (of >= 64 bits). On such machines, you can + * #define Just_16 to store 16 bits per 32-bit Long when doing + * high-precision integer arithmetic. Whether this speeds things + * up or slows things down depends on the machine and the number + * being converted. If long long is available and the name is + * something other than "long long", #define Llong to be the name, + * and if "unsigned Llong" does not work as an unsigned version of + * Llong, #define #ULLong to be the corresponding unsigned type. + * #define Bad_float_h if your system lacks a float.h or if it does not + * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP, + * FLT_RADIX, FLT_ROUNDS, and DBL_MAX. + * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n) + * if memory is available and otherwise does something you deem + * appropriate. If MALLOC is undefined, malloc will be invoked + * directly -- and assumed always to succeed. Similarly, if you + * want something other than the system's free() to be called to + * recycle memory acquired from MALLOC, #define FREE to be the + * name of the alternate routine. (FREE or free is only called in + * pathological cases, e.g., in a dtoa call after a dtoa return in + * mode 3 with thousands of digits requested.) + * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making + * memory allocations from a private pool of memory when possible. + * When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes, + * unless #defined to be a different length. This default length + * suffices to get rid of MALLOC calls except for unusual cases, + * such as decimal-to-binary conversion of a very long string of + * digits. The longest string dtoa can return is about 751 bytes + * long. For conversions by strtod of strings of 800 digits and + * all dtoa conversions in single-threaded executions with 8-byte + * pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte + * pointers, PRIVATE_MEM >= 7112 appears adequate. + * #define NO_INFNAN_CHECK if you do not wish to have INFNAN_CHECK + * #defined automatically on IEEE systems. On such systems, + * when INFNAN_CHECK is #defined, strtod checks + * for Infinity and NaN (case insensitively). On some systems + * (e.g., some HP systems), it may be necessary to #define NAN_WORD0 + * appropriately -- to the most significant word of a quiet NaN. + * (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.) + * When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined, + * strtod also accepts (case insensitively) strings of the form + * NaN(x), where x is a string of hexadecimal digits and spaces; + * if there is only one string of hexadecimal digits, it is taken + * for the 52 fraction bits of the resulting NaN; if there are two + * or more strings of hex digits, the first is for the high 20 bits, + * the second and subsequent for the low 32 bits, with intervening + * white space ignored; but if this results in none of the 52 + * fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0 + * and NAN_WORD1 are used instead. + * #define MULTIPLE_THREADS if the system offers preemptively scheduled + * multiple threads. In this case, you must provide (or suitably + * #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed + * by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed + * in pow5mult, ensures lazy evaluation of only one copy of high + * powers of 5; omitting this lock would introduce a small + * probability of wasting memory, but would otherwise be harmless.) + * You must also invoke freedtoa(s) to free the value s returned by + * dtoa. You may do so whether or not MULTIPLE_THREADS is #defined. + + * When MULTIPLE_THREADS is #defined, this source file provides + * void set_max_dtoa_threads(unsigned int n); + * and expects + * unsigned int dtoa_get_threadno(void); + * to be available (possibly provided by + * #define dtoa_get_threadno omp_get_thread_num + * if OpenMP is in use or by + * #define dtoa_get_threadno pthread_self + * if Pthreads is in use), to return the current thread number. + * If set_max_dtoa_threads(n) was called and the current thread + * number is k with k < n, then calls on ACQUIRE_DTOA_LOCK(...) and + * FREE_DTOA_LOCK(...) are avoided; instead each thread with thread + * number < n has a separate copy of relevant data structures. + * After set_max_dtoa_threads(n), a call set_max_dtoa_threads(m) + * with m <= n has has no effect, but a call with m > n is honored. + * Such a call invokes REALLOC (assumed to be "realloc" if REALLOC + * is not #defined) to extend the size of the relevant array. + + * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that + * avoids underflows on inputs whose result does not underflow. + * If you #define NO_IEEE_Scale on a machine that uses IEEE-format + * floating-point numbers and flushes underflows to zero rather + * than implementing gradual underflow, then you must also #define + * Sudden_Underflow. + * #define USE_LOCALE to use the current locale's decimal_point value. + * #define SET_INEXACT if IEEE arithmetic is being used and extra + * computation should be done to set the inexact flag when the + * result is inexact and avoid setting inexact when the result + * is exact. In this case, dtoa.c must be compiled in + * an environment, perhaps provided by #include "dtoa.c" in a + * suitable wrapper, that defines two functions, + * int get_inexact(void); + * void clear_inexact(void); + * such that get_inexact() returns a nonzero value if the + * inexact bit is already set, and clear_inexact() sets the + * inexact bit to 0. When SET_INEXACT is #defined, strtod + * also does extra computations to set the underflow and overflow + * flags when appropriate (i.e., when the result is tiny and + * inexact or when it is a numeric value rounded to +-infinity). + * #define NO_ERRNO if strtod should not assign errno = ERANGE when + * the result overflows to +-Infinity or underflows to 0. + * When errno should be assigned, under seemingly rare conditions + * it may be necessary to define Set_errno(x) suitably, e.g., in + * a local errno.h, such as + * #include <errno.h> + * #define Set_errno(x) _set_errno(x) + * #define NO_HEX_FP to omit recognition of hexadecimal floating-point + * values by strtod. + * #define NO_STRTOD_BIGCOMP (on IEEE-arithmetic systems only for now) + * to disable logic for "fast" testing of very long input strings + * to strtod. This testing proceeds by initially truncating the + * input string, then if necessary comparing the whole string with + * a decimal expansion to decide close cases. This logic is only + * used for input more than STRTOD_DIGLIM digits long (default 40). + */ + +#ifndef Long +#define Long int +#endif +#ifndef ULong +typedef unsigned Long ULong; +#endif + +#ifdef DEBUG +#include <assert.h> +#include "stdio.h" +#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);} +#define Debug(x) x +int dtoa_stats[7]; /* strtod_{64,96,bigcomp},dtoa_{exact,64,96,bigcomp} */ +#else +#define assert(x) /*nothing*/ +#define Debug(x) /*nothing*/ +#endif + +#include "stdlib.h" +#include "string.h" + +#ifdef USE_LOCALE +#include "locale.h" +#endif + +#ifdef Honor_FLT_ROUNDS +#ifndef Trust_FLT_ROUNDS +#include <fenv.h> +#endif +#endif + +#ifdef __cplusplus +extern "C" { +#endif +#ifdef MALLOC +extern void *MALLOC(size_t); +#else +#define MALLOC malloc +#endif + +#ifdef REALLOC +extern void *REALLOC(void*,size_t); +#else +#define REALLOC realloc +#endif + +#ifndef FREE +#define FREE free +#endif + +#ifdef __cplusplus + } +#endif + +#ifndef Omit_Private_Memory +#ifndef PRIVATE_MEM +#define PRIVATE_MEM 2304 +#endif +#define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double)) +static double private_mem[PRIVATE_mem], *pmem_next = private_mem; +#endif + +#undef IEEE_Arith +#undef Avoid_Underflow +#ifdef IEEE_MC68k +#define IEEE_Arith +#endif +#ifdef IEEE_8087 +#define IEEE_Arith +#endif + +#ifdef IEEE_Arith +#ifndef NO_INFNAN_CHECK +#undef INFNAN_CHECK +#define INFNAN_CHECK +#endif +#else +#undef INFNAN_CHECK +#define NO_STRTOD_BIGCOMP +#endif + +#include "errno.h" + +#ifdef NO_ERRNO /*{*/ +#undef Set_errno +#define Set_errno(x) +#else +#ifndef Set_errno +#define Set_errno(x) errno = x +#endif +#endif /*}*/ + +#ifdef Bad_float_h + +#ifdef IEEE_Arith +#define DBL_DIG 15 +#define DBL_MAX_10_EXP 308 +#define DBL_MAX_EXP 1024 +#define FLT_RADIX 2 +#endif /*IEEE_Arith*/ + +#ifdef IBM +#define DBL_DIG 16 +#define DBL_MAX_10_EXP 75 +#define DBL_MAX_EXP 63 +#define FLT_RADIX 16 +#define DBL_MAX 7.2370055773322621e+75 +#endif + +#ifdef VAX +#define DBL_DIG 16 +#define DBL_MAX_10_EXP 38 +#define DBL_MAX_EXP 127 +#define FLT_RADIX 2 +#define DBL_MAX 1.7014118346046923e+38 +#endif + +#ifndef LONG_MAX +#define LONG_MAX 2147483647 +#endif + +#else /* ifndef Bad_float_h */ +#include "float.h" +#endif /* Bad_float_h */ + +#ifndef __MATH_H__ +#include "math.h" +#endif + +#ifdef __cplusplus +extern "C" { +#endif + +#if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1 +Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined. +#endif + +#undef USE_BF96 + +#ifdef NO_LONG_LONG /*{{*/ +#undef ULLong +#ifdef Just_16 +#undef Pack_32 +/* When Pack_32 is not defined, we store 16 bits per 32-bit Long. + * This makes some inner loops simpler and sometimes saves work + * during multiplications, but it often seems to make things slightly + * slower. Hence the default is now to store 32 bits per Long. + */ +#endif +#else /*}{ long long available */ +#ifndef Llong +#define Llong long long +#endif +#ifndef ULLong +#define ULLong unsigned Llong +#endif +#ifndef NO_BF96 /*{*/ +#define USE_BF96 + +#ifdef SET_INEXACT +#define dtoa_divmax 27 +#else +int dtoa_divmax = 2; /* Permit experimenting: on some systems, 64-bit integer */ + /* division is slow enough that we may sometimes want to */ + /* avoid using it. We assume (but do not check) that */ + /* dtoa_divmax <= 27.*/ +#endif + +typedef struct BF96 { /* Normalized 96-bit software floating point numbers */ + unsigned int b0,b1,b2; /* b0 = most significant, binary point just to its left */ + int e; /* number represented = b * 2^e, with .5 <= b < 1 */ + } BF96; + + static BF96 pten[667] = { + { 0xeef453d6, 0x923bd65a, 0x113faa29, -1136 }, + { 0x9558b466, 0x1b6565f8, 0x4ac7ca59, -1132 }, + { 0xbaaee17f, 0xa23ebf76, 0x5d79bcf0, -1129 }, + { 0xe95a99df, 0x8ace6f53, 0xf4d82c2c, -1126 }, + { 0x91d8a02b, 0xb6c10594, 0x79071b9b, -1122 }, + { 0xb64ec836, 0xa47146f9, 0x9748e282, -1119 }, + { 0xe3e27a44, 0x4d8d98b7, 0xfd1b1b23, -1116 }, + { 0x8e6d8c6a, 0xb0787f72, 0xfe30f0f5, -1112 }, + { 0xb208ef85, 0x5c969f4f, 0xbdbd2d33, -1109 }, + { 0xde8b2b66, 0xb3bc4723, 0xad2c7880, -1106 }, + { 0x8b16fb20, 0x3055ac76, 0x4c3bcb50, -1102 }, + { 0xaddcb9e8, 0x3c6b1793, 0xdf4abe24, -1099 }, + { 0xd953e862, 0x4b85dd78, 0xd71d6dad, -1096 }, + { 0x87d4713d, 0x6f33aa6b, 0x8672648c, -1092 }, + { 0xa9c98d8c, 0xcb009506, 0x680efdaf, -1089 }, + { 0xd43bf0ef, 0xfdc0ba48, 0x0212bd1b, -1086 }, + { 0x84a57695, 0xfe98746d, 0x014bb630, -1082 }, + { 0xa5ced43b, 0x7e3e9188, 0x419ea3bd, -1079 }, + { 0xcf42894a, 0x5dce35ea, 0x52064cac, -1076 }, + { 0x818995ce, 0x7aa0e1b2, 0x7343efeb, -1072 }, + { 0xa1ebfb42, 0x19491a1f, 0x1014ebe6, -1069 }, + { 0xca66fa12, 0x9f9b60a6, 0xd41a26e0, -1066 }, + { 0xfd00b897, 0x478238d0, 0x8920b098, -1063 }, + { 0x9e20735e, 0x8cb16382, 0x55b46e5f, -1059 }, + { 0xc5a89036, 0x2fddbc62, 0xeb2189f7, -1056 }, + { 0xf712b443, 0xbbd52b7b, 0xa5e9ec75, -1053 }, + { 0x9a6bb0aa, 0x55653b2d, 0x47b233c9, -1049 }, + { 0xc1069cd4, 0xeabe89f8, 0x999ec0bb, -1046 }, + { 0xf148440a, 0x256e2c76, 0xc00670ea, -1043 }, + { 0x96cd2a86, 0x5764dbca, 0x38040692, -1039 }, + { 0xbc807527, 0xed3e12bc, 0xc6050837, -1036 }, + { 0xeba09271, 0xe88d976b, 0xf7864a44, -1033 }, + { 0x93445b87, 0x31587ea3, 0x7ab3ee6a, -1029 }, + { 0xb8157268, 0xfdae9e4c, 0x5960ea05, -1026 }, + { 0xe61acf03, 0x3d1a45df, 0x6fb92487, -1023 }, + { 0x8fd0c162, 0x06306bab, 0xa5d3b6d4, -1019 }, + { 0xb3c4f1ba, 0x87bc8696, 0x8f48a489, -1016 }, + { 0xe0b62e29, 0x29aba83c, 0x331acdab, -1013 }, + { 0x8c71dcd9, 0xba0b4925, 0x9ff0c08b, -1009 }, + { 0xaf8e5410, 0x288e1b6f, 0x07ecf0ae, -1006 }, + { 0xdb71e914, 0x32b1a24a, 0xc9e82cd9, -1003 }, + { 0x892731ac, 0x9faf056e, 0xbe311c08, -999 }, + { 0xab70fe17, 0xc79ac6ca, 0x6dbd630a, -996 }, + { 0xd64d3d9d, 0xb981787d, 0x092cbbcc, -993 }, + { 0x85f04682, 0x93f0eb4e, 0x25bbf560, -989 }, + { 0xa76c5823, 0x38ed2621, 0xaf2af2b8, -986 }, + { 0xd1476e2c, 0x07286faa, 0x1af5af66, -983 }, + { 0x82cca4db, 0x847945ca, 0x50d98d9f, -979 }, + { 0xa37fce12, 0x6597973c, 0xe50ff107, -976 }, + { 0xcc5fc196, 0xfefd7d0c, 0x1e53ed49, -973 }, + { 0xff77b1fc, 0xbebcdc4f, 0x25e8e89c, -970 }, + { 0x9faacf3d, 0xf73609b1, 0x77b19161, -966 }, + { 0xc795830d, 0x75038c1d, 0xd59df5b9, -963 }, + { 0xf97ae3d0, 0xd2446f25, 0x4b057328, -960 }, + { 0x9becce62, 0x836ac577, 0x4ee367f9, -956 }, + { 0xc2e801fb, 0x244576d5, 0x229c41f7, -953 }, + { 0xf3a20279, 0xed56d48a, 0x6b435275, -950 }, + { 0x9845418c, 0x345644d6, 0x830a1389, -946 }, + { 0xbe5691ef, 0x416bd60c, 0x23cc986b, -943 }, + { 0xedec366b, 0x11c6cb8f, 0x2cbfbe86, -940 }, + { 0x94b3a202, 0xeb1c3f39, 0x7bf7d714, -936 }, + { 0xb9e08a83, 0xa5e34f07, 0xdaf5ccd9, -933 }, + { 0xe858ad24, 0x8f5c22c9, 0xd1b3400f, -930 }, + { 0x91376c36, 0xd99995be, 0x23100809, -926 }, + { 0xb5854744, 0x8ffffb2d, 0xabd40a0c, -923 }, + { 0xe2e69915, 0xb3fff9f9, 0x16c90c8f, -920 }, + { 0x8dd01fad, 0x907ffc3b, 0xae3da7d9, -916 }, + { 0xb1442798, 0xf49ffb4a, 0x99cd11cf, -913 }, + { 0xdd95317f, 0x31c7fa1d, 0x40405643, -910 }, + { 0x8a7d3eef, 0x7f1cfc52, 0x482835ea, -906 }, + { 0xad1c8eab, 0x5ee43b66, 0xda324365, -903 }, + { 0xd863b256, 0x369d4a40, 0x90bed43e, -900 }, + { 0x873e4f75, 0xe2224e68, 0x5a7744a6, -896 }, + { 0xa90de353, 0x5aaae202, 0x711515d0, -893 }, + { 0xd3515c28, 0x31559a83, 0x0d5a5b44, -890 }, + { 0x8412d999, 0x1ed58091, 0xe858790a, -886 }, + { 0xa5178fff, 0x668ae0b6, 0x626e974d, -883 }, + { 0xce5d73ff, 0x402d98e3, 0xfb0a3d21, -880 }, + { 0x80fa687f, 0x881c7f8e, 0x7ce66634, -876 }, + { 0xa139029f, 0x6a239f72, 0x1c1fffc1, -873 }, + { 0xc9874347, 0x44ac874e, 0xa327ffb2, -870 }, + { 0xfbe91419, 0x15d7a922, 0x4bf1ff9f, -867 }, + { 0x9d71ac8f, 0xada6c9b5, 0x6f773fc3, -863 }, + { 0xc4ce17b3, 0x99107c22, 0xcb550fb4, -860 }, + { 0xf6019da0, 0x7f549b2b, 0x7e2a53a1, -857 }, + { 0x99c10284, 0x4f94e0fb, 0x2eda7444, -853 }, + { 0xc0314325, 0x637a1939, 0xfa911155, -850 }, + { 0xf03d93ee, 0xbc589f88, 0x793555ab, -847 }, + { 0x96267c75, 0x35b763b5, 0x4bc1558b, -843 }, + { 0xbbb01b92, 0x83253ca2, 0x9eb1aaed, -840 }, + { 0xea9c2277, 0x23ee8bcb, 0x465e15a9, -837 }, + { 0x92a1958a, 0x7675175f, 0x0bfacd89, -833 }, + { 0xb749faed, 0x14125d36, 0xcef980ec, -830 }, + { 0xe51c79a8, 0x5916f484, 0x82b7e127, -827 }, + { 0x8f31cc09, 0x37ae58d2, 0xd1b2ecb8, -823 }, + { 0xb2fe3f0b, 0x8599ef07, 0x861fa7e6, -820 }, + { 0xdfbdcece, 0x67006ac9, 0x67a791e0, -817 }, + { 0x8bd6a141, 0x006042bd, 0xe0c8bb2c, -813 }, + { 0xaecc4991, 0x4078536d, 0x58fae9f7, -810 }, + { 0xda7f5bf5, 0x90966848, 0xaf39a475, -807 }, + { 0x888f9979, 0x7a5e012d, 0x6d8406c9, -803 }, + { 0xaab37fd7, 0xd8f58178, 0xc8e5087b, -800 }, + { 0xd5605fcd, 0xcf32e1d6, 0xfb1e4a9a, -797 }, + { 0x855c3be0, 0xa17fcd26, 0x5cf2eea0, -793 }, + { 0xa6b34ad8, 0xc9dfc06f, 0xf42faa48, -790 }, + { 0xd0601d8e, 0xfc57b08b, 0xf13b94da, -787 }, + { 0x823c1279, 0x5db6ce57, 0x76c53d08, -783 }, + { 0xa2cb1717, 0xb52481ed, 0x54768c4b, -780 }, + { 0xcb7ddcdd, 0xa26da268, 0xa9942f5d, -777 }, + { 0xfe5d5415, 0x0b090b02, 0xd3f93b35, -774 }, + { 0x9efa548d, 0x26e5a6e1, 0xc47bc501, -770 }, + { 0xc6b8e9b0, 0x709f109a, 0x359ab641, -767 }, + { 0xf867241c, 0x8cc6d4c0, 0xc30163d2, -764 }, + { 0x9b407691, 0xd7fc44f8, 0x79e0de63, -760 }, + { 0xc2109436, 0x4dfb5636, 0x985915fc, -757 }, + { 0xf294b943, 0xe17a2bc4, 0x3e6f5b7b, -754 }, + { 0x979cf3ca, 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0x8e1f2895, 788 }, + { 0xc491798a, 0x08a2ad4e, 0xf1a6f2ba, 791 }, + { 0xf5b5d7ec, 0x8acb58a2, 0xae10af69, 794 }, + { 0x9991a6f3, 0xd6bf1765, 0xacca6da1, 798 }, + { 0xbff610b0, 0xcc6edd3f, 0x17fd090a, 801 }, + { 0xeff394dc, 0xff8a948e, 0xddfc4b4c, 804 }, + { 0x95f83d0a, 0x1fb69cd9, 0x4abdaf10, 808 }, + { 0xbb764c4c, 0xa7a4440f, 0x9d6d1ad4, 811 }, + { 0xea53df5f, 0xd18d5513, 0x84c86189, 814 }, + { 0x92746b9b, 0xe2f8552c, 0x32fd3cf5, 818 }, + { 0xb7118682, 0xdbb66a77, 0x3fbc8c33, 821 }, + { 0xe4d5e823, 0x92a40515, 0x0fabaf3f, 824 }, + { 0x8f05b116, 0x3ba6832d, 0x29cb4d87, 828 }, + { 0xb2c71d5b, 0xca9023f8, 0x743e20e9, 831 }, + { 0xdf78e4b2, 0xbd342cf6, 0x914da924, 834 }, + { 0x8bab8eef, 0xb6409c1a, 0x1ad089b6, 838 }, + { 0xae9672ab, 0xa3d0c320, 0xa184ac24, 841 }, + { 0xda3c0f56, 0x8cc4f3e8, 0xc9e5d72d, 844 }, + { 0x88658996, 0x17fb1871, 0x7e2fa67c, 848 }, + { 0xaa7eebfb, 0x9df9de8d, 0xddbb901b, 851 }, + { 0xd51ea6fa, 0x85785631, 0x552a7422, 854 }, + { 0x8533285c, 0x936b35de, 0xd53a8895, 858 }, + { 0xa67ff273, 0xb8460356, 0x8a892aba, 861 }, + { 0xd01fef10, 0xa657842c, 0x2d2b7569, 864 }, + { 0x8213f56a, 0x67f6b29b, 0x9c3b2962, 868 }, + { 0xa298f2c5, 0x01f45f42, 0x8349f3ba, 871 }, + { 0xcb3f2f76, 0x42717713, 0x241c70a9, 874 }, + { 0xfe0efb53, 0xd30dd4d7, 0xed238cd3, 877 }, + { 0x9ec95d14, 0x63e8a506, 0xf4363804, 881 }, + { 0xc67bb459, 0x7ce2ce48, 0xb143c605, 884 }, + { 0xf81aa16f, 0xdc1b81da, 0xdd94b786, 887 }, + { 0x9b10a4e5, 0xe9913128, 0xca7cf2b4, 891 }, + { 0xc1d4ce1f, 0x63f57d72, 0xfd1c2f61, 894 }, + { 0xf24a01a7, 0x3cf2dccf, 0xbc633b39, 897 }, + { 0x976e4108, 0x8617ca01, 0xd5be0503, 901 }, + { 0xbd49d14a, 0xa79dbc82, 0x4b2d8644, 904 }, + { 0xec9c459d, 0x51852ba2, 0xddf8e7d6, 907 }, + { 0x93e1ab82, 0x52f33b45, 0xcabb90e5, 911 }, + { 0xb8da1662, 0xe7b00a17, 0x3d6a751f, 914 }, + { 0xe7109bfb, 0xa19c0c9d, 0x0cc51267, 917 }, + { 0x906a617d, 0x450187e2, 0x27fb2b80, 921 }, + { 0xb484f9dc, 0x9641e9da, 0xb1f9f660, 924 }, + { 0xe1a63853, 0xbbd26451, 0x5e7873f8, 927 }, + { 0x8d07e334, 0x55637eb2, 0xdb0b487b, 931 }, + { 0xb049dc01, 0x6abc5e5f, 0x91ce1a9a, 934 }, + { 0xdc5c5301, 0xc56b75f7, 0x7641a140, 937 }, + { 0x89b9b3e1, 0x1b6329ba, 0xa9e904c8, 941 }, + { 0xac2820d9, 0x623bf429, 0x546345fa, 944 }, + { 0xd732290f, 0xbacaf133, 0xa97c1779, 947 }, + { 0x867f59a9, 0xd4bed6c0, 0x49ed8eab, 951 }, + { 0xa81f3014, 0x49ee8c70, 0x5c68f256, 954 }, + { 0xd226fc19, 0x5c6a2f8c, 0x73832eec, 957 }, + { 0x83585d8f, 0xd9c25db7, 0xc831fd53, 961 }, + { 0xa42e74f3, 0xd032f525, 0xba3e7ca8, 964 }, + { 0xcd3a1230, 0xc43fb26f, 0x28ce1bd2, 967 }, + { 0x80444b5e, 0x7aa7cf85, 0x7980d163, 971 }, + { 0xa0555e36, 0x1951c366, 0xd7e105bc, 974 }, + { 0xc86ab5c3, 0x9fa63440, 0x8dd9472b, 977 }, + { 0xfa856334, 0x878fc150, 0xb14f98f6, 980 }, + { 0x9c935e00, 0xd4b9d8d2, 0x6ed1bf9a, 984 }, + { 0xc3b83581, 0x09e84f07, 0x0a862f80, 987 }, + { 0xf4a642e1, 0x4c6262c8, 0xcd27bb61, 990 }, + { 0x98e7e9cc, 0xcfbd7dbd, 0x8038d51c, 994 }, + { 0xbf21e440, 0x03acdd2c, 0xe0470a63, 997 }, + { 0xeeea5d50, 0x04981478, 0x1858ccfc, 1000 }, + { 0x95527a52, 0x02df0ccb, 0x0f37801e, 1004 }, + { 0xbaa718e6, 0x8396cffd, 0xd3056025, 1007 }, + { 0xe950df20, 0x247c83fd, 0x47c6b82e, 1010 }, + { 0x91d28b74, 0x16cdd27e, 0x4cdc331d, 1014 }, + { 0xb6472e51, 0x1c81471d, 0xe0133fe4, 1017 }, + { 0xe3d8f9e5, 0x63a198e5, 0x58180fdd, 1020 }, + { 0x8e679c2f, 0x5e44ff8f, 0x570f09ea, 1024 }, + { 0xb201833b, 0x35d63f73, 0x2cd2cc65, 1027 }, + { 0xde81e40a, 0x034bcf4f, 0xf8077f7e, 1030 }, + { 0x8b112e86, 0x420f6191, 0xfb04afaf, 1034 }, + { 0xadd57a27, 0xd29339f6, 0x79c5db9a, 1037 }, + { 0xd94ad8b1, 0xc7380874, 0x18375281, 1040 }, + { 0x87cec76f, 0x1c830548, 0x8f229391, 1044 }, + { 0xa9c2794a, 0xe3a3c69a, 0xb2eb3875, 1047 }, + { 0xd433179d, 0x9c8cb841, 0x5fa60692, 1050 }, + { 0x849feec2, 0x81d7f328, 0xdbc7c41b, 1054 }, + { 0xa5c7ea73, 0x224deff3, 0x12b9b522, 1057 }, + { 0xcf39e50f, 0xeae16bef, 0xd768226b, 1060 }, + { 0x81842f29, 0xf2cce375, 0xe6a11583, 1064 }, + { 0xa1e53af4, 0x6f801c53, 0x60495ae3, 1067 }, + { 0xca5e89b1, 0x8b602368, 0x385bb19c, 1070 }, + { 0xfcf62c1d, 0xee382c42, 0x46729e03, 1073 }, + { 0x9e19db92, 0xb4e31ba9, 0x6c07a2c2, 1077 } + }; + static short int Lhint[2098] = { + /*18,*/19, 19, 19, 19, 20, 20, 20, 21, 21, + 21, 22, 22, 22, 23, 23, 23, 23, 24, 24, + 24, 25, 25, 25, 26, 26, 26, 26, 27, 27, + 27, 28, 28, 28, 29, 29, 29, 29, 30, 30, + 30, 31, 31, 31, 32, 32, 32, 32, 33, 33, + 33, 34, 34, 34, 35, 35, 35, 35, 36, 36, + 36, 37, 37, 37, 38, 38, 38, 38, 39, 39, + 39, 40, 40, 40, 41, 41, 41, 41, 42, 42, + 42, 43, 43, 43, 44, 44, 44, 44, 45, 45, + 45, 46, 46, 46, 47, 47, 47, 47, 48, 48, + 48, 49, 49, 49, 50, 50, 50, 51, 51, 51, + 51, 52, 52, 52, 53, 53, 53, 54, 54, 54, + 54, 55, 55, 55, 56, 56, 56, 57, 57, 57, + 57, 58, 58, 58, 59, 59, 59, 60, 60, 60, + 60, 61, 61, 61, 62, 62, 62, 63, 63, 63, + 63, 64, 64, 64, 65, 65, 65, 66, 66, 66, + 66, 67, 67, 67, 68, 68, 68, 69, 69, 69, + 69, 70, 70, 70, 71, 71, 71, 72, 72, 72, + 72, 73, 73, 73, 74, 74, 74, 75, 75, 75, + 75, 76, 76, 76, 77, 77, 77, 78, 78, 78, + 78, 79, 79, 79, 80, 80, 80, 81, 81, 81, + 82, 82, 82, 82, 83, 83, 83, 84, 84, 84, + 85, 85, 85, 85, 86, 86, 86, 87, 87, 87, + 88, 88, 88, 88, 89, 89, 89, 90, 90, 90, + 91, 91, 91, 91, 92, 92, 92, 93, 93, 93, + 94, 94, 94, 94, 95, 95, 95, 96, 96, 96, + 97, 97, 97, 97, 98, 98, 98, 99, 99, 99, + 100, 100, 100, 100, 101, 101, 101, 102, 102, 102, + 103, 103, 103, 103, 104, 104, 104, 105, 105, 105, + 106, 106, 106, 106, 107, 107, 107, 108, 108, 108, + 109, 109, 109, 110, 110, 110, 110, 111, 111, 111, + 112, 112, 112, 113, 113, 113, 113, 114, 114, 114, + 115, 115, 115, 116, 116, 116, 116, 117, 117, 117, + 118, 118, 118, 119, 119, 119, 119, 120, 120, 120, + 121, 121, 121, 122, 122, 122, 122, 123, 123, 123, + 124, 124, 124, 125, 125, 125, 125, 126, 126, 126, + 127, 127, 127, 128, 128, 128, 128, 129, 129, 129, + 130, 130, 130, 131, 131, 131, 131, 132, 132, 132, + 133, 133, 133, 134, 134, 134, 134, 135, 135, 135, + 136, 136, 136, 137, 137, 137, 137, 138, 138, 138, + 139, 139, 139, 140, 140, 140, 141, 141, 141, 141, + 142, 142, 142, 143, 143, 143, 144, 144, 144, 144, + 145, 145, 145, 146, 146, 146, 147, 147, 147, 147, + 148, 148, 148, 149, 149, 149, 150, 150, 150, 150, + 151, 151, 151, 152, 152, 152, 153, 153, 153, 153, + 154, 154, 154, 155, 155, 155, 156, 156, 156, 156, + 157, 157, 157, 158, 158, 158, 159, 159, 159, 159, + 160, 160, 160, 161, 161, 161, 162, 162, 162, 162, + 163, 163, 163, 164, 164, 164, 165, 165, 165, 165, + 166, 166, 166, 167, 167, 167, 168, 168, 168, 169, + 169, 169, 169, 170, 170, 170, 171, 171, 171, 172, + 172, 172, 172, 173, 173, 173, 174, 174, 174, 175, + 175, 175, 175, 176, 176, 176, 177, 177, 177, 178, + 178, 178, 178, 179, 179, 179, 180, 180, 180, 181, + 181, 181, 181, 182, 182, 182, 183, 183, 183, 184, + 184, 184, 184, 185, 185, 185, 186, 186, 186, 187, + 187, 187, 187, 188, 188, 188, 189, 189, 189, 190, + 190, 190, 190, 191, 191, 191, 192, 192, 192, 193, + 193, 193, 193, 194, 194, 194, 195, 195, 195, 196, + 196, 196, 197, 197, 197, 197, 198, 198, 198, 199, + 199, 199, 200, 200, 200, 200, 201, 201, 201, 202, + 202, 202, 203, 203, 203, 203, 204, 204, 204, 205, + 205, 205, 206, 206, 206, 206, 207, 207, 207, 208, + 208, 208, 209, 209, 209, 209, 210, 210, 210, 211, + 211, 211, 212, 212, 212, 212, 213, 213, 213, 214, + 214, 214, 215, 215, 215, 215, 216, 216, 216, 217, + 217, 217, 218, 218, 218, 218, 219, 219, 219, 220, + 220, 220, 221, 221, 221, 221, 222, 222, 222, 223, + 223, 223, 224, 224, 224, 224, 225, 225, 225, 226, + 226, 226, 227, 227, 227, 228, 228, 228, 228, 229, + 229, 229, 230, 230, 230, 231, 231, 231, 231, 232, + 232, 232, 233, 233, 233, 234, 234, 234, 234, 235, + 235, 235, 236, 236, 236, 237, 237, 237, 237, 238, + 238, 238, 239, 239, 239, 240, 240, 240, 240, 241, + 241, 241, 242, 242, 242, 243, 243, 243, 243, 244, + 244, 244, 245, 245, 245, 246, 246, 246, 246, 247, + 247, 247, 248, 248, 248, 249, 249, 249, 249, 250, + 250, 250, 251, 251, 251, 252, 252, 252, 252, 253, + 253, 253, 254, 254, 254, 255, 255, 255, 256, 256, + 256, 256, 257, 257, 257, 258, 258, 258, 259, 259, + 259, 259, 260, 260, 260, 261, 261, 261, 262, 262, + 262, 262, 263, 263, 263, 264, 264, 264, 265, 265, + 265, 265, 266, 266, 266, 267, 267, 267, 268, 268, + 268, 268, 269, 269, 269, 270, 270, 270, 271, 271, + 271, 271, 272, 272, 272, 273, 273, 273, 274, 274, + 274, 274, 275, 275, 275, 276, 276, 276, 277, 277, + 277, 277, 278, 278, 278, 279, 279, 279, 280, 280, + 280, 280, 281, 281, 281, 282, 282, 282, 283, 283, + 283, 283, 284, 284, 284, 285, 285, 285, 286, 286, + 286, 287, 287, 287, 287, 288, 288, 288, 289, 289, + 289, 290, 290, 290, 290, 291, 291, 291, 292, 292, + 292, 293, 293, 293, 293, 294, 294, 294, 295, 295, + 295, 296, 296, 296, 296, 297, 297, 297, 298, 298, + 298, 299, 299, 299, 299, 300, 300, 300, 301, 301, + 301, 302, 302, 302, 302, 303, 303, 303, 304, 304, + 304, 305, 305, 305, 305, 306, 306, 306, 307, 307, + 307, 308, 308, 308, 308, 309, 309, 309, 310, 310, + 310, 311, 311, 311, 311, 312, 312, 312, 313, 313, + 313, 314, 314, 314, 315, 315, 315, 315, 316, 316, + 316, 317, 317, 317, 318, 318, 318, 318, 319, 319, + 319, 320, 320, 320, 321, 321, 321, 321, 322, 322, + 322, 323, 323, 323, 324, 324, 324, 324, 325, 325, + 325, 326, 326, 326, 327, 327, 327, 327, 328, 328, + 328, 329, 329, 329, 330, 330, 330, 330, 331, 331, + 331, 332, 332, 332, 333, 333, 333, 333, 334, 334, + 334, 335, 335, 335, 336, 336, 336, 336, 337, 337, + 337, 338, 338, 338, 339, 339, 339, 339, 340, 340, + 340, 341, 341, 341, 342, 342, 342, 342, 343, 343, + 343, 344, 344, 344, 345, 345, 345, 346, 346, 346, + 346, 347, 347, 347, 348, 348, 348, 349, 349, 349, + 349, 350, 350, 350, 351, 351, 351, 352, 352, 352, + 352, 353, 353, 353, 354, 354, 354, 355, 355, 355, + 355, 356, 356, 356, 357, 357, 357, 358, 358, 358, + 358, 359, 359, 359, 360, 360, 360, 361, 361, 361, + 361, 362, 362, 362, 363, 363, 363, 364, 364, 364, + 364, 365, 365, 365, 366, 366, 366, 367, 367, 367, + 367, 368, 368, 368, 369, 369, 369, 370, 370, 370, + 370, 371, 371, 371, 372, 372, 372, 373, 373, 373, + 374, 374, 374, 374, 375, 375, 375, 376, 376, 376, + 377, 377, 377, 377, 378, 378, 378, 379, 379, 379, + 380, 380, 380, 380, 381, 381, 381, 382, 382, 382, + 383, 383, 383, 383, 384, 384, 384, 385, 385, 385, + 386, 386, 386, 386, 387, 387, 387, 388, 388, 388, + 389, 389, 389, 389, 390, 390, 390, 391, 391, 391, + 392, 392, 392, 392, 393, 393, 393, 394, 394, 394, + 395, 395, 395, 395, 396, 396, 396, 397, 397, 397, + 398, 398, 398, 398, 399, 399, 399, 400, 400, 400, + 401, 401, 401, 402, 402, 402, 402, 403, 403, 403, + 404, 404, 404, 405, 405, 405, 405, 406, 406, 406, + 407, 407, 407, 408, 408, 408, 408, 409, 409, 409, + 410, 410, 410, 411, 411, 411, 411, 412, 412, 412, + 413, 413, 413, 414, 414, 414, 414, 415, 415, 415, + 416, 416, 416, 417, 417, 417, 417, 418, 418, 418, + 419, 419, 419, 420, 420, 420, 420, 421, 421, 421, + 422, 422, 422, 423, 423, 423, 423, 424, 424, 424, + 425, 425, 425, 426, 426, 426, 426, 427, 427, 427, + 428, 428, 428, 429, 429, 429, 429, 430, 430, 430, + 431, 431, 431, 432, 432, 432, 433, 433, 433, 433, + 434, 434, 434, 435, 435, 435, 436, 436, 436, 436, + 437, 437, 437, 438, 438, 438, 439, 439, 439, 439, + 440, 440, 440, 441, 441, 441, 442, 442, 442, 442, + 443, 443, 443, 444, 444, 444, 445, 445, 445, 445, + 446, 446, 446, 447, 447, 447, 448, 448, 448, 448, + 449, 449, 449, 450, 450, 450, 451, 451, 451, 451, + 452, 452, 452, 453, 453, 453, 454, 454, 454, 454, + 455, 455, 455, 456, 456, 456, 457, 457, 457, 457, + 458, 458, 458, 459, 459, 459, 460, 460, 460, 461, + 461, 461, 461, 462, 462, 462, 463, 463, 463, 464, + 464, 464, 464, 465, 465, 465, 466, 466, 466, 467, + 467, 467, 467, 468, 468, 468, 469, 469, 469, 470, + 470, 470, 470, 471, 471, 471, 472, 472, 472, 473, + 473, 473, 473, 474, 474, 474, 475, 475, 475, 476, + 476, 476, 476, 477, 477, 477, 478, 478, 478, 479, + 479, 479, 479, 480, 480, 480, 481, 481, 481, 482, + 482, 482, 482, 483, 483, 483, 484, 484, 484, 485, + 485, 485, 485, 486, 486, 486, 487, 487, 487, 488, + 488, 488, 488, 489, 489, 489, 490, 490, 490, 491, + 491, 491, 492, 492, 492, 492, 493, 493, 493, 494, + 494, 494, 495, 495, 495, 495, 496, 496, 496, 497, + 497, 497, 498, 498, 498, 498, 499, 499, 499, 500, + 500, 500, 501, 501, 501, 501, 502, 502, 502, 503, + 503, 503, 504, 504, 504, 504, 505, 505, 505, 506, + 506, 506, 507, 507, 507, 507, 508, 508, 508, 509, + 509, 509, 510, 510, 510, 510, 511, 511, 511, 512, + 512, 512, 513, 513, 513, 513, 514, 514, 514, 515, + 515, 515, 516, 516, 516, 516, 517, 517, 517, 518, + 518, 518, 519, 519, 519, 520, 520, 520, 520, 521, + 521, 521, 522, 522, 522, 523, 523, 523, 523, 524, + 524, 524, 525, 525, 525, 526, 526, 526, 526, 527, + 527, 527, 528, 528, 528, 529, 529, 529, 529, 530, + 530, 530, 531, 531, 531, 532, 532, 532, 532, 533, + 533, 533, 534, 534, 534, 535, 535, 535, 535, 536, + 536, 536, 537, 537, 537, 538, 538, 538, 538, 539, + 539, 539, 540, 540, 540, 541, 541, 541, 541, 542, + 542, 542, 543, 543, 543, 544, 544, 544, 544, 545, + 545, 545, 546, 546, 546, 547, 547, 547, 548, 548, + 548, 548, 549, 549, 549, 550, 550, 550, 551, 551, + 551, 551, 552, 552, 552, 553, 553, 553, 554, 554, + 554, 554, 555, 555, 555, 556, 556, 556, 557, 557, + 557, 557, 558, 558, 558, 559, 559, 559, 560, 560, + 560, 560, 561, 561, 561, 562, 562, 562, 563, 563, + 563, 563, 564, 564, 564, 565, 565, 565, 566, 566, + 566, 566, 567, 567, 567, 568, 568, 568, 569, 569, + 569, 569, 570, 570, 570, 571, 571, 571, 572, 572, + 572, 572, 573, 573, 573, 574, 574, 574, 575, 575, + 575, 575, 576, 576, 576, 577, 577, 577, 578, 578, + 578, 579, 579, 579, 579, 580, 580, 580, 581, 581, + 581, 582, 582, 582, 582, 583, 583, 583, 584, 584, + 584, 585, 585, 585, 585, 586, 586, 586, 587, 587, + 587, 588, 588, 588, 588, 589, 589, 589, 590, 590, + 590, 591, 591, 591, 591, 592, 592, 592, 593, 593, + 593, 594, 594, 594, 594, 595, 595, 595, 596, 596, + 596, 597, 597, 597, 597, 598, 598, 598, 599, 599, + 599, 600, 600, 600, 600, 601, 601, 601, 602, 602, + 602, 603, 603, 603, 603, 604, 604, 604, 605, 605, + 605, 606, 606, 606, 607, 607, 607, 607, 608, 608, + 608, 609, 609, 609, 610, 610, 610, 610, 611, 611, + 611, 612, 612, 612, 613, 613, 613, 613, 614, 614, + 614, 615, 615, 615, 616, 616, 616, 616, 617, 617, + 617, 618, 618, 618, 619, 619, 619, 619, 620, 620, + 620, 621, 621, 621, 622, 622, 622, 622, 623, 623, + 623, 624, 624, 624, 625, 625, 625, 625, 626, 626, + 626, 627, 627, 627, 628, 628, 628, 628, 629, 629, + 629, 630, 630, 630, 631, 631, 631, 631, 632, 632, + 632, 633, 633, 633, 634, 634, 634, 634, 635, 635, + 635, 636, 636, 636, 637, 637, 637, 638, 638, 638, + 638, 639, 639, 639, 640, 640, 640, 641, 641, 641, + 641, 642, 642, 642, 643, 643, 643, 644, 644, 644, + 644, 645, 645, 645, 646, 646, 646, 647, 647, 647, + 647, 648, 648, 648, 649, 649, 649, 650, 650 }; + static ULLong pfive[27] = { + 5ll, + 25ll, + 125ll, + 625ll, + 3125ll, + 15625ll, + 78125ll, + 390625ll, + 1953125ll, + 9765625ll, + 48828125ll, + 244140625ll, + 1220703125ll, + 6103515625ll, + 30517578125ll, + 152587890625ll, + 762939453125ll, + 3814697265625ll, + 19073486328125ll, + 95367431640625ll, + 476837158203125ll, + 2384185791015625ll, + 11920928955078125ll, + 59604644775390625ll, + 298023223876953125ll, + 1490116119384765625ll, + 7450580596923828125ll + }; + + static int pfivebits[25] = {3, 5, 7, 10, 12, 14, 17, 19, 21, 24, 26, 28, 31, + 33, 35, 38, 40, 42, 45, 47, 49, 52, 54, 56, 59}; +#endif /*}*/ +#endif /*}} NO_LONG_LONG */ + +typedef union { double d; ULong L[2]; +#ifdef USE_BF96 + ULLong LL; +#endif + } U; + +#ifdef IEEE_8087 +#define word0(x) (x)->L[1] +#define word1(x) (x)->L[0] +#else +#define word0(x) (x)->L[0] +#define word1(x) (x)->L[1] +#endif +#define dval(x) (x)->d +#define LLval(x) (x)->LL + +#ifndef STRTOD_DIGLIM +#define STRTOD_DIGLIM 40 +#endif + +#ifdef DIGLIM_DEBUG +extern int strtod_diglim; +#else +#define strtod_diglim STRTOD_DIGLIM +#endif + +/* The following definition of Storeinc is appropriate for MIPS processors. + * An alternative that might be better on some machines is + * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff) + */ +#if defined(IEEE_8087) + defined(VAX) +#define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \ +((unsigned short *)a)[0] = (unsigned short)c, a++) +#else +#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \ +((unsigned short *)a)[1] = (unsigned short)c, a++) +#endif + +/* #define P DBL_MANT_DIG */ +/* Ten_pmax = floor(P*log(2)/log(5)) */ +/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */ +/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */ +/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */ + +#ifdef IEEE_Arith +#define Exp_shift 20 +#define Exp_shift1 20 +#define Exp_msk1 0x100000 +#define Exp_msk11 0x100000 +#define Exp_mask 0x7ff00000 +#define P 53 +#define Nbits 53 +#define Bias 1023 +#define Emax 1023 +#define Emin (-1022) +#define Exp_1 0x3ff00000 +#define Exp_11 0x3ff00000 +#define Ebits 11 +#define Frac_mask 0xfffff +#define Frac_mask1 0xfffff +#define Ten_pmax 22 +#define Bletch 0x10 +#define Bndry_mask 0xfffff +#define Bndry_mask1 0xfffff +#define LSB 1 +#define Sign_bit 0x80000000 +#define Log2P 1 +#define Tiny0 0 +#define Tiny1 1 +#define Quick_max 14 +#define Int_max 14 +#ifndef NO_IEEE_Scale +#define Avoid_Underflow +#ifdef Flush_Denorm /* debugging option */ +#undef Sudden_Underflow +#endif +#endif + +#ifndef Flt_Rounds +#ifdef FLT_ROUNDS +#define Flt_Rounds FLT_ROUNDS +#else +#define Flt_Rounds 1 +#endif +#endif /*Flt_Rounds*/ + +#ifdef Honor_FLT_ROUNDS +#undef Check_FLT_ROUNDS +#define Check_FLT_ROUNDS +#else +#define Rounding Flt_Rounds +#endif + +#else /* ifndef IEEE_Arith */ +#undef Check_FLT_ROUNDS +#undef Honor_FLT_ROUNDS +#undef SET_INEXACT +#undef Sudden_Underflow +#define Sudden_Underflow +#ifdef IBM +#undef Flt_Rounds +#define Flt_Rounds 0 +#define Exp_shift 24 +#define Exp_shift1 24 +#define Exp_msk1 0x1000000 +#define Exp_msk11 0x1000000 +#define Exp_mask 0x7f000000 +#define P 14 +#define Nbits 56 +#define Bias 65 +#define Emax 248 +#define Emin (-260) +#define Exp_1 0x41000000 +#define Exp_11 0x41000000 +#define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */ +#define Frac_mask 0xffffff +#define Frac_mask1 0xffffff +#define Bletch 4 +#define Ten_pmax 22 +#define Bndry_mask 0xefffff +#define Bndry_mask1 0xffffff +#define LSB 1 +#define Sign_bit 0x80000000 +#define Log2P 4 +#define Tiny0 0x100000 +#define Tiny1 0 +#define Quick_max 14 +#define Int_max 15 +#else /* VAX */ +#undef Flt_Rounds +#define Flt_Rounds 1 +#define Exp_shift 23 +#define Exp_shift1 7 +#define Exp_msk1 0x80 +#define Exp_msk11 0x800000 +#define Exp_mask 0x7f80 +#define P 56 +#define Nbits 56 +#define Bias 129 +#define Emax 126 +#define Emin (-129) +#define Exp_1 0x40800000 +#define Exp_11 0x4080 +#define Ebits 8 +#define Frac_mask 0x7fffff +#define Frac_mask1 0xffff007f +#define Ten_pmax 24 +#define Bletch 2 +#define Bndry_mask 0xffff007f +#define Bndry_mask1 0xffff007f +#define LSB 0x10000 +#define Sign_bit 0x8000 +#define Log2P 1 +#define Tiny0 0x80 +#define Tiny1 0 +#define Quick_max 15 +#define Int_max 15 +#endif /* IBM, VAX */ +#endif /* IEEE_Arith */ + +#ifndef IEEE_Arith +#define ROUND_BIASED +#else +#ifdef ROUND_BIASED_without_Round_Up +#undef ROUND_BIASED +#define ROUND_BIASED +#endif +#endif + +#ifdef RND_PRODQUOT +#define rounded_product(a,b) a = rnd_prod(a, b) +#define rounded_quotient(a,b) a = rnd_quot(a, b) +extern double rnd_prod(double, double), rnd_quot(double, double); +#else +#define rounded_product(a,b) a *= b +#define rounded_quotient(a,b) a /= b +#endif + +#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1)) +#define Big1 0xffffffff + +#ifndef Pack_32 +#define Pack_32 +#endif + +typedef struct BCinfo BCinfo; + struct +BCinfo { int dp0, dp1, dplen, dsign, e0, inexact, nd, nd0, rounding, scale, uflchk; }; + +#define FFFFFFFF 0xffffffffUL + +#ifdef MULTIPLE_THREADS +#define MTa , PTI +#define MTb , &TI +#define MTd , ThInfo **PTI +static unsigned int maxthreads = 0; +#else +#define MTa /*nothing*/ +#define MTb /*nothing*/ +#define MTd /*nothing*/ +#endif + +#define Kmax 7 + +#ifdef __cplusplus +extern "C" double 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 * +Balloc(int k MTd) +{ + int x; + Bigint *rv; +#ifndef Omit_Private_Memory + unsigned int len; +#endif +#ifdef MULTIPLE_THREADS + ThInfo *TI; + + if (!(TI = *PTI)) + *PTI = TI = get_TI(); + if (TI == &TI0) + ACQUIRE_DTOA_LOCK(0); +#endif + /* The k > Kmax case does not need ACQUIRE_DTOA_LOCK(0), */ + /* but this case seems very unlikely. */ + if (k <= Kmax && (rv = freelist[k])) + freelist[k] = rv->next; + else { + x = 1 << k; +#ifdef Omit_Private_Memory + rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong)); +#else + len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1) + /sizeof(double); + if (k <= Kmax && (unsigned long)(pmem_next - private_mem + len) <= PRIVATE_mem +#ifdef MULTIPLE_THREADS + && TI == TI1 +#endif + ) { + rv = (Bigint*)pmem_next; + pmem_next += len; + } + else + rv = (Bigint*)MALLOC(len*sizeof(double)); +#endif + rv->k = k; + rv->maxwds = x; + } +#ifdef MULTIPLE_THREADS + if (TI == &TI0) + FREE_DTOA_LOCK(0); +#endif + rv->sign = rv->wds = 0; + return rv; + } + + static void +Bfree(Bigint *v MTd) +{ +#ifdef MULTIPLE_THREADS + ThInfo *TI; +#endif + if (v) { + if (v->k > Kmax) + FREE((void*)v); + else { +#ifdef MULTIPLE_THREADS + if (!(TI = *PTI)) + *PTI = TI = get_TI(); + if (TI == &TI0) + ACQUIRE_DTOA_LOCK(0); +#endif + v->next = freelist[v->k]; + freelist[v->k] = v; +#ifdef MULTIPLE_THREADS + if (TI == &TI0) + FREE_DTOA_LOCK(0); +#endif + } + } + } + +#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \ +y->wds*sizeof(Long) + 2*sizeof(int)) + + static Bigint * +multadd(Bigint *b, int m, int a MTd) /* multiply by m and add a */ +{ + int i, wds; +#ifdef ULLong + ULong *x; + ULLong carry, y; +#else + ULong carry, *x, y; +#ifdef Pack_32 + ULong xi, z; +#endif +#endif + Bigint *b1; + + wds = b->wds; + x = b->x; + i = 0; + carry = a; + do { +#ifdef ULLong + y = *x * (ULLong)m + carry; + carry = y >> 32; + *x++ = y & FFFFFFFF; +#else +#ifdef Pack_32 + xi = *x; + y = (xi & 0xffff) * m + carry; + z = (xi >> 16) * m + (y >> 16); + carry = z >> 16; + *x++ = (z << 16) + (y & 0xffff); +#else + y = *x * m + carry; + carry = y >> 16; + *x++ = y & 0xffff; +#endif +#endif + } + while(++i < wds); + if (carry) { + if (wds >= b->maxwds) { + b1 = Balloc(b->k+1 MTa); + Bcopy(b1, b); + Bfree(b MTa); + b = b1; + } + b->x[wds++] = carry; + b->wds = wds; + } + return b; + } + + static Bigint * +s2b(const char *s, int nd0, int nd, ULong y9, int dplen MTd) +{ + Bigint *b; + int i, k; + Long x, y; + + x = (nd + 8) / 9; + for(k = 0, y = 1; x > y; y <<= 1, k++) ; +#ifdef Pack_32 + b = Balloc(k MTa); + b->x[0] = y9; + b->wds = 1; +#else + b = Balloc(k+1 MTa); + b->x[0] = y9 & 0xffff; + b->wds = (b->x[1] = y9 >> 16) ? 2 : 1; +#endif + + i = 9; + if (9 < nd0) { + s += 9; + do b = multadd(b, 10, *s++ - '0' MTa); + while(++i < nd0); + s += dplen; + } + else + s += dplen + 9; + for(; i < nd; i++) + b = multadd(b, 10, *s++ - '0' MTa); + return b; + } + + static int +hi0bits(ULong x) +{ + int k = 0; + + if (!(x & 0xffff0000)) { + k = 16; + x <<= 16; + } + if (!(x & 0xff000000)) { + k += 8; + x <<= 8; + } + if (!(x & 0xf0000000)) { + k += 4; + x <<= 4; + } + if (!(x & 0xc0000000)) { + k += 2; + x <<= 2; + } + if (!(x & 0x80000000)) { + k++; + if (!(x & 0x40000000)) + return 32; + } + return k; + } + + static int +lo0bits(ULong *y) +{ + int k; + ULong x = *y; + + if (x & 7) { + if (x & 1) + return 0; + if (x & 2) { + *y = x >> 1; + return 1; + } + *y = x >> 2; + return 2; + } + k = 0; + if (!(x & 0xffff)) { + k = 16; + x >>= 16; + } + if (!(x & 0xff)) { + k += 8; + x >>= 8; + } + if (!(x & 0xf)) { + k += 4; + x >>= 4; + } + if (!(x & 0x3)) { + k += 2; + x >>= 2; + } + if (!(x & 1)) { + k++; + x >>= 1; + if (!x) + return 32; + } + *y = x; + return k; + } + + static Bigint * +i2b(int i MTd) +{ + Bigint *b; + + b = Balloc(1 MTa); + b->x[0] = i; + b->wds = 1; + return b; + } + + static Bigint * +mult(Bigint *a, Bigint *b MTd) +{ + Bigint *c; + int k, wa, wb, wc; + ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0; + ULong y; +#ifdef ULLong + ULLong carry, z; +#else + ULong carry, z; +#ifdef Pack_32 + ULong z2; +#endif +#endif + + if (a->wds < b->wds) { + c = a; + a = b; + b = c; + } + k = a->k; + wa = a->wds; + wb = b->wds; + wc = wa + wb; + if (wc > a->maxwds) + k++; + c = Balloc(k MTa); + for(x = c->x, xa = x + wc; x < xa; x++) + *x = 0; + xa = a->x; + xae = xa + wa; + xb = b->x; + xbe = xb + wb; + xc0 = c->x; +#ifdef ULLong + for(; xb < xbe; xc0++) { + if ((y = *xb++)) { + x = xa; + xc = xc0; + carry = 0; + do { + z = *x++ * (ULLong)y + *xc + carry; + carry = z >> 32; + *xc++ = z & FFFFFFFF; + } + while(x < xae); + *xc = carry; + } + } +#else +#ifdef Pack_32 + for(; xb < xbe; xb++, xc0++) { + if ((y = *xb & 0xffff)) { + x = xa; + xc = xc0; + carry = 0; + do { + z = (*x & 0xffff) * y + (*xc & 0xffff) + carry; + carry = z >> 16; + z2 = (*x++ >> 16) * y + (*xc >> 16) + carry; + carry = z2 >> 16; + Storeinc(xc, z2, z); + } + while(x < xae); + *xc = carry; + } + if ((y = *xb >> 16)) { + x = xa; + xc = xc0; + carry = 0; + z2 = *xc; + do { + z = (*x & 0xffff) * y + (*xc >> 16) + carry; + carry = z >> 16; + Storeinc(xc, z, z2); + z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry; + carry = z2 >> 16; + } + while(x < xae); + *xc = z2; + } + } +#else + for(; xb < xbe; xc0++) { + if (y = *xb++) { + x = xa; + xc = xc0; + carry = 0; + do { + z = *x++ * y + *xc + carry; + carry = z >> 16; + *xc++ = z & 0xffff; + } + while(x < xae); + *xc = carry; + } + } +#endif +#endif + for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ; + c->wds = wc; + return c; + } + + static Bigint * +pow5mult(Bigint *b, int k MTd) +{ + Bigint *b1, *p5, *p51; +#ifdef MULTIPLE_THREADS + ThInfo *TI; +#endif + int i; + static int p05[3] = { 5, 25, 125 }; + + if ((i = k & 3)) + b = multadd(b, p05[i-1], 0 MTa); + + if (!(k >>= 2)) + return b; +#ifdef MULTIPLE_THREADS + if (!(TI = *PTI)) + *PTI = TI = get_TI(); +#endif + if (!(p5 = p5s)) { + /* first time */ +#ifdef MULTIPLE_THREADS + if (!(TI = *PTI)) + *PTI = TI = get_TI(); + if (TI == &TI0) + ACQUIRE_DTOA_LOCK(1); + if (!(p5 = p5s)) { + p5 = p5s = i2b(625 MTa); + p5->next = 0; + } + if (TI == &TI0) + FREE_DTOA_LOCK(1); +#else + p5 = p5s = i2b(625 MTa); + p5->next = 0; +#endif + } + for(;;) { + if (k & 1) { + b1 = mult(b, p5 MTa); + Bfree(b MTa); + b = b1; + } + if (!(k >>= 1)) + break; + if (!(p51 = p5->next)) { +#ifdef MULTIPLE_THREADS + if (!TI && !(TI = *PTI)) + *PTI = TI = get_TI(); + if (TI == &TI0) + ACQUIRE_DTOA_LOCK(1); + if (!(p51 = p5->next)) { + p51 = p5->next = mult(p5,p5 MTa); + p51->next = 0; + } + if (TI == &TI0) + FREE_DTOA_LOCK(1); +#else + p51 = p5->next = mult(p5,p5); + p51->next = 0; +#endif + } + p5 = p51; + } + return b; + } + + static Bigint * +lshift(Bigint *b, int k MTd) +{ + int i, k1, n, n1; + Bigint *b1; + ULong *x, *x1, *xe, z; + +#ifdef Pack_32 + n = k >> 5; +#else + n = k >> 4; +#endif + k1 = b->k; + n1 = n + b->wds + 1; + for(i = b->maxwds; n1 > i; i <<= 1) + k1++; + b1 = Balloc(k1 MTa); + x1 = b1->x; + for(i = 0; i < n; i++) + *x1++ = 0; + x = b->x; + xe = x + b->wds; +#ifdef Pack_32 + if (k &= 0x1f) { + k1 = 32 - k; + z = 0; + do { + *x1++ = *x << k | z; + z = *x++ >> k1; + } + while(x < xe); + if ((*x1 = z)) + ++n1; + } +#else + if (k &= 0xf) { + k1 = 16 - k; + z = 0; + do { + *x1++ = *x << k & 0xffff | z; + z = *x++ >> k1; + } + while(x < xe); + if (*x1 = z) + ++n1; + } +#endif + else do + *x1++ = *x++; + while(x < xe); + b1->wds = n1 - 1; + Bfree(b MTa); + return b1; + } + + static int +cmp(Bigint *a, Bigint *b) +{ + ULong *xa, *xa0, *xb, *xb0; + int i, j; + + i = a->wds; + j = b->wds; +#ifdef DEBUG + if (i > 1 && !a->x[i-1]) + Bug("cmp called with a->x[a->wds-1] == 0"); + if (j > 1 && !b->x[j-1]) + Bug("cmp called with b->x[b->wds-1] == 0"); +#endif + if (i -= j) + return i; + xa0 = a->x; + xa = xa0 + j; + xb0 = b->x; + xb = xb0 + j; + for(;;) { + if (*--xa != *--xb) + return *xa < *xb ? -1 : 1; + if (xa <= xa0) + break; + } + return 0; + } + + static Bigint * +diff(Bigint *a, Bigint *b MTd) +{ + Bigint *c; + int i, wa, wb; + ULong *xa, *xae, *xb, *xbe, *xc; +#ifdef ULLong + ULLong borrow, y; +#else + ULong borrow, y; +#ifdef Pack_32 + ULong z; +#endif +#endif + + i = cmp(a,b); + if (!i) { + c = Balloc(0 MTa); + c->wds = 1; + c->x[0] = 0; + return c; + } + if (i < 0) { + c = a; + a = b; + b = c; + i = 1; + } + else + i = 0; + c = Balloc(a->k MTa); + c->sign = i; + wa = a->wds; + xa = a->x; + xae = xa + wa; + wb = b->wds; + xb = b->x; + xbe = xb + wb; + xc = c->x; + borrow = 0; +#ifdef ULLong + do { + y = (ULLong)*xa++ - *xb++ - borrow; + borrow = y >> 32 & (ULong)1; + *xc++ = y & FFFFFFFF; + } + while(xb < xbe); + while(xa < xae) { + y = *xa++ - borrow; + borrow = y >> 32 & (ULong)1; + *xc++ = y & FFFFFFFF; + } +#else +#ifdef Pack_32 + do { + y = (*xa & 0xffff) - (*xb & 0xffff) - borrow; + borrow = (y & 0x10000) >> 16; + z = (*xa++ >> 16) - (*xb++ >> 16) - borrow; + borrow = (z & 0x10000) >> 16; + Storeinc(xc, z, y); + } + while(xb < xbe); + while(xa < xae) { + y = (*xa & 0xffff) - borrow; + borrow = (y & 0x10000) >> 16; + z = (*xa++ >> 16) - borrow; + borrow = (z & 0x10000) >> 16; + Storeinc(xc, z, y); + } +#else + do { + y = *xa++ - *xb++ - borrow; + borrow = (y & 0x10000) >> 16; + *xc++ = y & 0xffff; + } + while(xb < xbe); + while(xa < xae) { + y = *xa++ - borrow; + borrow = (y & 0x10000) >> 16; + *xc++ = y & 0xffff; + } +#endif +#endif + while(!*--xc) + wa--; + c->wds = wa; + return c; + } + + static double +ulp(U *x) +{ + Long L; + U u; + + L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1; +#ifndef Avoid_Underflow +#ifndef Sudden_Underflow + if (L > 0) { +#endif +#endif +#ifdef IBM + L |= Exp_msk1 >> 4; +#endif + word0(&u) = L; + word1(&u) = 0; +#ifndef Avoid_Underflow +#ifndef Sudden_Underflow + } + else { + L = -L >> Exp_shift; + if (L < Exp_shift) { + word0(&u) = 0x80000 >> L; + word1(&u) = 0; + } + else { + word0(&u) = 0; + L -= Exp_shift; + word1(&u) = L >= 31 ? 1 : 1 << 31 - L; + } + } +#endif +#endif + return dval(&u); + } + + static double +b2d(Bigint *a, int *e) +{ + ULong *xa, *xa0, w, y, z; + int k; + U d; +#ifdef VAX + ULong d0, d1; +#else +#define d0 word0(&d) +#define d1 word1(&d) +#endif + + xa0 = a->x; + xa = xa0 + a->wds; + y = *--xa; +#ifdef DEBUG + if (!y) Bug("zero y in b2d"); +#endif + k = hi0bits(y); + *e = 32 - k; +#ifdef Pack_32 + if (k < Ebits) { + d0 = Exp_1 | y >> (Ebits - k); + w = xa > xa0 ? *--xa : 0; + d1 = y << ((32-Ebits) + k) | w >> (Ebits - k); + goto ret_d; + } + z = xa > xa0 ? *--xa : 0; + if (k -= Ebits) { + d0 = Exp_1 | y << k | z >> (32 - k); + y = xa > xa0 ? *--xa : 0; + d1 = z << k | y >> (32 - k); + } + else { + d0 = Exp_1 | y; + d1 = z; + } +#else + if (k < Ebits + 16) { + z = xa > xa0 ? *--xa : 0; + d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k; + w = xa > xa0 ? *--xa : 0; + y = xa > xa0 ? *--xa : 0; + d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k; + goto ret_d; + } + z = xa > xa0 ? *--xa : 0; + w = xa > xa0 ? *--xa : 0; + k -= Ebits + 16; + d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k; + y = xa > xa0 ? *--xa : 0; + d1 = w << k + 16 | y << k; +#endif + ret_d: +#ifdef VAX + word0(&d) = d0 >> 16 | d0 << 16; + word1(&d) = d1 >> 16 | d1 << 16; +#else +#undef d0 +#undef d1 +#endif + return dval(&d); + } + + static Bigint * +d2b(U *d, int *e, int *bits MTd) +{ + Bigint *b; + int de, k; + ULong *x, y, z; +#ifndef Sudden_Underflow + int i; +#endif +#ifdef VAX + ULong d0, d1; + d0 = word0(d) >> 16 | word0(d) << 16; + d1 = word1(d) >> 16 | word1(d) << 16; +#else +#define d0 word0(d) +#define d1 word1(d) +#endif + +#ifdef Pack_32 + b = Balloc(1 MTa); +#else + b = Balloc(2 MTa); +#endif + x = b->x; + + z = d0 & Frac_mask; + d0 &= 0x7fffffff; /* clear sign bit, which we ignore */ +#ifdef Sudden_Underflow + de = (int)(d0 >> Exp_shift); +#ifndef IBM + z |= Exp_msk11; +#endif +#else + if ((de = (int)(d0 >> Exp_shift))) + z |= Exp_msk1; +#endif +#ifdef Pack_32 + if ((y = d1)) { + if ((k = lo0bits(&y))) { + x[0] = y | z << (32 - k); + z >>= k; + } + else + x[0] = y; +#ifndef Sudden_Underflow + i = +#endif + b->wds = (x[1] = z) ? 2 : 1; + } + else { + k = lo0bits(&z); + x[0] = z; +#ifndef Sudden_Underflow + i = +#endif + b->wds = 1; + k += 32; + } +#else + if (y = d1) { + if (k = lo0bits(&y)) + if (k >= 16) { + x[0] = y | z << 32 - k & 0xffff; + x[1] = z >> k - 16 & 0xffff; + x[2] = z >> k; + i = 2; + } + else { + x[0] = y & 0xffff; + x[1] = y >> 16 | z << 16 - k & 0xffff; + x[2] = z >> k & 0xffff; + x[3] = z >> k+16; + i = 3; + } + else { + x[0] = y & 0xffff; + x[1] = y >> 16; + x[2] = z & 0xffff; + x[3] = z >> 16; + i = 3; + } + } + else { +#ifdef DEBUG + if (!z) + Bug("Zero passed to d2b"); +#endif + k = lo0bits(&z); + if (k >= 16) { + x[0] = z; + i = 0; + } + else { + x[0] = z & 0xffff; + x[1] = z >> 16; + i = 1; + } + k += 32; + } + while(!x[i]) + --i; + b->wds = i + 1; +#endif +#ifndef Sudden_Underflow + if (de) { +#endif +#ifdef IBM + *e = (de - Bias - (P-1) << 2) + k; + *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask); +#else + *e = de - Bias - (P-1) + k; + *bits = P - k; +#endif +#ifndef Sudden_Underflow + } + else { + *e = de - Bias - (P-1) + 1 + k; +#ifdef Pack_32 + *bits = 32*i - hi0bits(x[i-1]); +#else + *bits = (i+2)*16 - hi0bits(x[i]); +#endif + } +#endif + return b; + } +#undef d0 +#undef d1 + + static double +ratio(Bigint *a, Bigint *b) +{ + U da, db; + int k, ka, kb; + + dval(&da) = b2d(a, &ka); + dval(&db) = b2d(b, &kb); +#ifdef Pack_32 + k = ka - kb + 32*(a->wds - b->wds); +#else + k = ka - kb + 16*(a->wds - b->wds); +#endif +#ifdef IBM + if (k > 0) { + word0(&da) += (k >> 2)*Exp_msk1; + if (k &= 3) + dval(&da) *= 1 << k; + } + else { + k = -k; + word0(&db) += (k >> 2)*Exp_msk1; + if (k &= 3) + dval(&db) *= 1 << k; + } +#else + if (k > 0) + word0(&da) += k*Exp_msk1; + else { + k = -k; + word0(&db) += k*Exp_msk1; + } +#endif + return dval(&da) / dval(&db); + } + + static const double +tens[] = { + 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, + 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, + 1e20, 1e21, 1e22 +#ifdef VAX + , 1e23, 1e24 +#endif + }; + + static const double +#ifdef IEEE_Arith +bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 }; +static const double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, +#ifdef Avoid_Underflow + 9007199254740992.*9007199254740992.e-256 + /* = 2^106 * 1e-256 */ +#else + 1e-256 +#endif + }; +/* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */ +/* flag unnecessarily. It leads to a song and dance at the end of strtod. */ +#define Scale_Bit 0x10 +#define n_bigtens 5 +#else +#ifdef IBM +bigtens[] = { 1e16, 1e32, 1e64 }; +static const double tinytens[] = { 1e-16, 1e-32, 1e-64 }; +#define n_bigtens 3 +#else +bigtens[] = { 1e16, 1e32 }; +static const double tinytens[] = { 1e-16, 1e-32 }; +#define n_bigtens 2 +#endif +#endif + +#undef Need_Hexdig +#ifdef INFNAN_CHECK +#ifndef No_Hex_NaN +#define Need_Hexdig +#endif +#endif + +#ifndef Need_Hexdig +#ifndef NO_HEX_FP +#define Need_Hexdig +#endif +#endif + +#ifdef Need_Hexdig /*{*/ +#if 0 +static unsigned char hexdig[256]; + + static void +htinit(unsigned char *h, unsigned char *s, int inc) +{ + int i, j; + for(i = 0; (j = s[i]) !=0; i++) + h[j] = i + inc; + } + + static void +hexdig_init(void) /* Use of hexdig_init omitted 20121220 to avoid a */ + /* race condition when multiple threads are used. */ +{ +#define USC (unsigned char *) + htinit(hexdig, USC "0123456789", 0x10); + htinit(hexdig, USC "abcdef", 0x10 + 10); + htinit(hexdig, USC "ABCDEF", 0x10 + 10); + } +#else +static unsigned char hexdig[256] = { + 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, + 16,17,18,19,20,21,22,23,24,25,0,0,0,0,0,0, + 0,26,27,28,29,30,31,0,0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, + 0,26,27,28,29,30,31,0,0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 + }; +#endif +#endif /* } Need_Hexdig */ + +#ifdef INFNAN_CHECK + +#ifndef NAN_WORD0 +#define NAN_WORD0 0x7ff80000 +#endif + +#ifndef NAN_WORD1 +#define NAN_WORD1 0 +#endif + + static int +match(const char **sp, const char *t) +{ + int c, d; + const char *s = *sp; + + while((d = *t++)) { + if ((c = *++s) >= 'A' && c <= 'Z') + c += 'a' - 'A'; + if (c != d) + return 0; + } + *sp = s + 1; + return 1; + } + +#ifndef No_Hex_NaN + static void +hexnan(U *rvp, const char **sp) +{ + ULong c, x[2]; + const char *s; + int c1, havedig, udx0, xshift; + + /**** if (!hexdig['0']) hexdig_init(); ****/ + x[0] = x[1] = 0; + havedig = xshift = 0; + udx0 = 1; + s = *sp; + /* allow optional initial 0x or 0X */ + while((c = *(const unsigned char*)(s+1)) && c <= ' ') + ++s; + if (s[1] == '0' && (s[2] == 'x' || s[2] == 'X')) + s += 2; + while((c = *(const unsigned char*)++s)) { + if ((c1 = hexdig[c])) + c = c1 & 0xf; + else if (c <= ' ') { + if (udx0 && havedig) { + udx0 = 0; + xshift = 1; + } + continue; + } +#ifdef GDTOA_NON_PEDANTIC_NANCHECK + else if (/*(*/ c == ')' && havedig) { + *sp = s + 1; + break; + } + else + return; /* invalid form: don't change *sp */ +#else + else { + do { + if (/*(*/ c == ')') { + *sp = s + 1; + break; + } + } while((c = *++s)); + break; + } +#endif + havedig = 1; + if (xshift) { + xshift = 0; + x[0] = x[1]; + x[1] = 0; + } + if (udx0) + x[0] = (x[0] << 4) | (x[1] >> 28); + x[1] = (x[1] << 4) | c; + } + if ((x[0] &= 0xfffff) || x[1]) { + word0(rvp) = Exp_mask | x[0]; + word1(rvp) = x[1]; + } + } +#endif /*No_Hex_NaN*/ +#endif /* INFNAN_CHECK */ + +#ifdef Pack_32 +#define ULbits 32 +#define kshift 5 +#define kmask 31 +#else +#define ULbits 16 +#define kshift 4 +#define kmask 15 +#endif + +#if !defined(NO_HEX_FP) || defined(Honor_FLT_ROUNDS) /*{*/ + static Bigint * +increment(Bigint *b MTd) +{ + ULong *x, *xe; + Bigint *b1; + + x = b->x; + xe = x + b->wds; + do { + if (*x < (ULong)0xffffffffL) { + ++*x; + return b; + } + *x++ = 0; + } while(x < xe); + { + if (b->wds >= b->maxwds) { + b1 = Balloc(b->k+1 MTa); + Bcopy(b1,b); + Bfree(b MTa); + b = b1; + } + b->x[b->wds++] = 1; + } + return b; + } + +#endif /*}*/ + +#ifndef NO_HEX_FP /*{*/ + + static void +rshift(Bigint *b, int k) +{ + ULong *x, *x1, *xe, y; + int n; + + x = x1 = b->x; + n = k >> kshift; + if (n < b->wds) { + xe = x + b->wds; + x += n; + if (k &= kmask) { + n = 32 - k; + y = *x++ >> k; + while(x < xe) { + *x1++ = (y | (*x << n)) & 0xffffffff; + y = *x++ >> k; + } + if ((*x1 = y) !=0) + x1++; + } + else + while(x < xe) + *x1++ = *x++; + } + if ((b->wds = x1 - b->x) == 0) + b->x[0] = 0; + } + + static ULong +any_on(Bigint *b, int k) +{ + int n, nwds; + ULong *x, *x0, x1, x2; + + x = b->x; + nwds = b->wds; + n = k >> kshift; + if (n > nwds) + n = nwds; + else if (n < nwds && (k &= kmask)) { + x1 = x2 = x[n]; + x1 >>= k; + x1 <<= k; + if (x1 != x2) + return 1; + } + x0 = x; + x += n; + while(x > x0) + if (*--x) + return 1; + return 0; + } + +enum { /* rounding values: same as FLT_ROUNDS */ + Round_zero = 0, + Round_near = 1, + Round_up = 2, + Round_down = 3 + }; + + void +gethex(const char **sp, U *rvp, int rounding, int sign MTd) +{ + Bigint *b; + char d; + const unsigned char *decpt, *s0, *s, *s1; + Long e, e1; + ULong L, lostbits, *x; + int big, denorm, esign, havedig, k, n, nb, nbits, nz, up, zret; +#ifdef IBM + int j; +#endif + enum { +#ifdef IEEE_Arith /*{{*/ + emax = 0x7fe - Bias - P + 1, + emin = Emin - P + 1 +#else /*}{*/ + emin = Emin - P, +#ifdef VAX + emax = 0x7ff - Bias - P + 1 +#endif +#ifdef IBM + emax = 0x7f - Bias - P +#endif +#endif /*}}*/ + }; +#ifdef IEEE_Arith + int check_denorm = 0; +#endif +#ifdef USE_LOCALE + int i; +#ifdef NO_LOCALE_CACHE + const unsigned char *decimalpoint = (unsigned char*) + localeconv()->decimal_point; +#else + const unsigned char *decimalpoint; + static unsigned char *decimalpoint_cache; + if (!(s0 = decimalpoint_cache)) { + s0 = (unsigned char*)localeconv()->decimal_point; + if ((decimalpoint_cache = (unsigned char*) + MALLOC(strlen((const char*)s0) + 1))) { + strcpy((char*)decimalpoint_cache, (const char*)s0); + s0 = decimalpoint_cache; + } + } + decimalpoint = s0; +#endif +#endif + + /**** if (!hexdig['0']) hexdig_init(); ****/ + havedig = 0; + s0 = *(const unsigned char **)sp + 2; + while(s0[havedig] == '0') + havedig++; + s0 += havedig; + s = s0; + decpt = 0; + zret = 0; + e = 0; + if (hexdig[*s]) + havedig++; + else { + zret = 1; +#ifdef USE_LOCALE + for(i = 0; decimalpoint[i]; ++i) { + if (s[i] != decimalpoint[i]) + goto pcheck; + } + decpt = s += i; +#else + if (*s != '.') + goto pcheck; + decpt = ++s; +#endif + if (!hexdig[*s]) + goto pcheck; + while(*s == '0') + s++; + if (hexdig[*s]) + zret = 0; + havedig = 1; + s0 = s; + } + while(hexdig[*s]) + s++; +#ifdef USE_LOCALE + if (*s == *decimalpoint && !decpt) { + for(i = 1; decimalpoint[i]; ++i) { + if (s[i] != decimalpoint[i]) + goto pcheck; + } + decpt = s += i; +#else + if (*s == '.' && !decpt) { + decpt = ++s; +#endif + while(hexdig[*s]) + s++; + }/*}*/ + if (decpt) + e = -(((Long)(s-decpt)) << 2); + pcheck: + s1 = s; + big = esign = 0; + switch(*s) { + case 'p': + case 'P': + switch(*++s) { + case '-': + esign = 1; + /* fall through */ + case '+': + s++; + } + if ((n = hexdig[*s]) == 0 || n > 0x19) { + s = s1; + break; + } + e1 = n - 0x10; + while((n = hexdig[*++s]) !=0 && n <= 0x19) { + if (e1 & 0xf8000000) + big = 1; + e1 = 10*e1 + n - 0x10; + } + if (esign) + e1 = -e1; + e += e1; + } + *sp = (char*)s; + if (!havedig) + *sp = (char*)s0 - 1; + if (zret) + goto retz1; + if (big) { + if (esign) { +#ifdef IEEE_Arith + switch(rounding) { + case Round_up: + if (sign) + break; + goto ret_tiny; + case Round_down: + if (!sign) + break; + goto ret_tiny; + } +#endif + goto retz; +#ifdef IEEE_Arith + ret_tinyf: + Bfree(b MTa); + ret_tiny: + Set_errno(ERANGE); + word0(rvp) = 0; + word1(rvp) = 1; + return; +#endif /* IEEE_Arith */ + } + switch(rounding) { + case Round_near: + goto ovfl1; + case Round_up: + if (!sign) + goto ovfl1; + goto ret_big; + case Round_down: + if (sign) + goto ovfl1; + goto ret_big; + } + ret_big: + word0(rvp) = Big0; + word1(rvp) = Big1; + return; + } + n = s1 - s0 - 1; + for(k = 0; n > (1 << (kshift-2)) - 1; n >>= 1) + k++; + b = Balloc(k MTa); + x = b->x; + havedig = n = nz = 0; + L = 0; +#ifdef USE_LOCALE + for(i = 0; decimalpoint[i+1]; ++i); +#endif + while(s1 > s0) { +#ifdef USE_LOCALE + if (*--s1 == decimalpoint[i]) { + s1 -= i; + continue; + } +#else + if (*--s1 == '.') + continue; +#endif + if ((d = hexdig[*s1])) + havedig = 1; + else if (!havedig) { + e += 4; + continue; + } + if (n == ULbits) { + *x++ = L; + L = 0; + n = 0; + } + L |= (d & 0x0f) << n; + n += 4; + } + *x++ = L; + b->wds = n = x - b->x; + nb = ULbits*n - hi0bits(L); + nbits = Nbits; + lostbits = 0; + x = b->x; + if (nb > nbits) { + n = nb - nbits; + if (any_on(b,n)) { + lostbits = 1; + k = n - 1; + if (x[k>>kshift] & 1 << (k & kmask)) { + lostbits = 2; + if (k > 0 && any_on(b,k)) + lostbits = 3; + } + } + rshift(b, n); + e += n; + } + else if (nb < nbits) { + n = nbits - nb; + b = lshift(b, n MTa); + e -= n; + x = b->x; + } + if (e > emax) { + ovfl: + Bfree(b MTa); + ovfl1: + Set_errno(ERANGE); +#ifdef Honor_FLT_ROUNDS + switch (rounding) { + case Round_zero: + goto ret_big; + case Round_down: + if (!sign) + goto ret_big; + break; + case Round_up: + if (sign) + goto ret_big; + } +#endif + word0(rvp) = Exp_mask; + word1(rvp) = 0; + return; + } + denorm = 0; + if (e < emin) { + denorm = 1; + n = emin - e; + if (n >= nbits) { +#ifdef IEEE_Arith /*{*/ + switch (rounding) { + case Round_near: + if (n == nbits && (n < 2 || lostbits || any_on(b,n-1))) + goto ret_tinyf; + break; + case Round_up: + if (!sign) + goto ret_tinyf; + break; + case Round_down: + if (sign) + goto ret_tinyf; + } +#endif /* } IEEE_Arith */ + Bfree(b MTa); + retz: + Set_errno(ERANGE); + retz1: + rvp->d = 0.; + return; + } + k = n - 1; +#ifdef IEEE_Arith + if (!k) { + switch(rounding) { + case Round_near: + if (((b->x[0] & 3) == 3) || (lostbits && (b->x[0] & 1))) { + multadd(b, 1, 1 MTa); + emin_check: + if (b->x[1] == (1 << (Exp_shift + 1))) { + rshift(b,1); + e = emin; + goto normal; + } + } + break; + case Round_up: + if (!sign && (lostbits || (b->x[0] & 1))) { + incr_denorm: + multadd(b, 1, 2 MTa); + check_denorm = 1; + lostbits = 0; + goto emin_check; + } + break; + case Round_down: + if (sign && (lostbits || (b->x[0] & 1))) + goto incr_denorm; + break; + } + } +#endif + if (lostbits) + lostbits = 1; + else if (k > 0) + lostbits = any_on(b,k); +#ifdef IEEE_Arith + else if (check_denorm) + goto no_lostbits; +#endif + if (x[k>>kshift] & 1 << (k & kmask)) + lostbits |= 2; +#ifdef IEEE_Arith + no_lostbits: +#endif + nbits -= n; + rshift(b,n); + e = emin; + } + if (lostbits) { + up = 0; + switch(rounding) { + case Round_zero: + break; + case Round_near: + if (lostbits & 2 + && (lostbits & 1) | (x[0] & 1)) + up = 1; + break; + case Round_up: + up = 1 - sign; + break; + case Round_down: + up = sign; + } + if (up) { + k = b->wds; + b = increment(b MTa); + x = b->x; + if (!denorm && (b->wds > k + || ((n = nbits & kmask) !=0 + && hi0bits(x[k-1]) < 32-n))) { + rshift(b,1); + if (++e > Emax) + goto ovfl; + } + } + } +#ifdef IEEE_Arith + if (denorm) + word0(rvp) = b->wds > 1 ? b->x[1] & ~0x100000 : 0; + else { + normal: + word0(rvp) = (b->x[1] & ~0x100000) | ((e + 0x3ff + 52) << 20); + } + word1(rvp) = b->x[0]; +#endif +#ifdef IBM + if ((j = e & 3)) { + k = b->x[0] & ((1 << j) - 1); + rshift(b,j); + if (k) { + switch(rounding) { + case Round_up: + if (!sign) + increment(b); + break; + case Round_down: + if (sign) + increment(b); + break; + case Round_near: + j = 1 << (j-1); + if (k & j && ((k & (j-1)) | lostbits)) + increment(b); + } + } + } + e >>= 2; + word0(rvp) = b->x[1] | ((e + 65 + 13) << 24); + word1(rvp) = b->x[0]; +#endif +#ifdef VAX + /* The next two lines ignore swap of low- and high-order 2 bytes. */ + /* word0(rvp) = (b->x[1] & ~0x800000) | ((e + 129 + 55) << 23); */ + /* word1(rvp) = b->x[0]; */ + word0(rvp) = ((b->x[1] & ~0x800000) >> 16) | ((e + 129 + 55) << 7) | (b->x[1] << 16); + word1(rvp) = (b->x[0] >> 16) | (b->x[0] << 16); +#endif + Bfree(b MTa); + } +#endif /*!NO_HEX_FP}*/ + + static int +dshift(Bigint *b, int p2) +{ + int rv = hi0bits(b->x[b->wds-1]) - 4; + if (p2 > 0) + rv -= p2; + return rv & kmask; + } + + static int +quorem(Bigint *b, Bigint *S) +{ + int n; + ULong *bx, *bxe, q, *sx, *sxe; +#ifdef ULLong + ULLong borrow, carry, y, ys; +#else + ULong borrow, carry, y, ys; +#ifdef Pack_32 + ULong si, z, zs; +#endif +#endif + + n = S->wds; +#ifdef DEBUG + /*debug*/ if (b->wds > n) + /*debug*/ Bug("oversize b in quorem"); +#endif + if (b->wds < n) + return 0; + sx = S->x; + sxe = sx + --n; + bx = b->x; + bxe = bx + n; + q = *bxe / (*sxe + 1); /* ensure q <= true quotient */ +#ifdef DEBUG +#ifdef NO_STRTOD_BIGCOMP + /*debug*/ if (q > 9) +#else + /* An oversized q is possible when quorem is called from bigcomp and */ + /* the input is near, e.g., twice the smallest denormalized number. */ + /*debug*/ if (q > 15) +#endif + /*debug*/ Bug("oversized quotient in quorem"); +#endif + if (q) { + borrow = 0; + carry = 0; + do { +#ifdef ULLong + ys = *sx++ * (ULLong)q + carry; + carry = ys >> 32; + y = *bx - (ys & FFFFFFFF) - borrow; + borrow = y >> 32 & (ULong)1; + *bx++ = y & FFFFFFFF; +#else +#ifdef Pack_32 + si = *sx++; + ys = (si & 0xffff) * q + carry; + zs = (si >> 16) * q + (ys >> 16); + carry = zs >> 16; + y = (*bx & 0xffff) - (ys & 0xffff) - borrow; + borrow = (y & 0x10000) >> 16; + z = (*bx >> 16) - (zs & 0xffff) - borrow; + borrow = (z & 0x10000) >> 16; + Storeinc(bx, z, y); +#else + ys = *sx++ * q + carry; + carry = ys >> 16; + y = *bx - (ys & 0xffff) - borrow; + borrow = (y & 0x10000) >> 16; + *bx++ = y & 0xffff; +#endif +#endif + } + while(sx <= sxe); + if (!*bxe) { + bx = b->x; + while(--bxe > bx && !*bxe) + --n; + b->wds = n; + } + } + if (cmp(b, S) >= 0) { + q++; + borrow = 0; + carry = 0; + bx = b->x; + sx = S->x; + do { +#ifdef ULLong + ys = *sx++ + carry; + carry = ys >> 32; + y = *bx - (ys & FFFFFFFF) - borrow; + borrow = y >> 32 & (ULong)1; + *bx++ = y & FFFFFFFF; +#else +#ifdef Pack_32 + si = *sx++; + ys = (si & 0xffff) + carry; + zs = (si >> 16) + (ys >> 16); + carry = zs >> 16; + y = (*bx & 0xffff) - (ys & 0xffff) - borrow; + borrow = (y & 0x10000) >> 16; + z = (*bx >> 16) - (zs & 0xffff) - borrow; + borrow = (z & 0x10000) >> 16; + Storeinc(bx, z, y); +#else + ys = *sx++ + carry; + carry = ys >> 16; + y = *bx - (ys & 0xffff) - borrow; + borrow = (y & 0x10000) >> 16; + *bx++ = y & 0xffff; +#endif +#endif + } + while(sx <= sxe); + bx = b->x; + bxe = bx + n; + if (!*bxe) { + while(--bxe > bx && !*bxe) + --n; + b->wds = n; + } + } + return q; + } + +#if defined(Avoid_Underflow) || !defined(NO_STRTOD_BIGCOMP) /*{*/ + static double +sulp(U *x, BCinfo *bc) +{ + U u; + double rv; + int i; + + rv = ulp(x); + if (!bc->scale || (i = 2*P + 1 - ((word0(x) & Exp_mask) >> Exp_shift)) <= 0) + return rv; /* Is there an example where i <= 0 ? */ + word0(&u) = Exp_1 + (i << Exp_shift); + word1(&u) = 0; + return rv * u.d; + } +#endif /*}*/ + +#ifndef NO_STRTOD_BIGCOMP + static void +bigcomp(U *rv, const char *s0, BCinfo *bc MTd) +{ + Bigint *b, *d; + int b2, bbits, d2, dd, dig, dsign, i, j, nd, nd0, p2, p5, speccase; + + dsign = bc->dsign; + nd = bc->nd; + nd0 = bc->nd0; + p5 = nd + bc->e0 - 1; + speccase = 0; +#ifndef Sudden_Underflow + if (rv->d == 0.) { /* special case: value near underflow-to-zero */ + /* threshold was rounded to zero */ + b = i2b(1 MTa); + p2 = Emin - P + 1; + bbits = 1; +#ifdef Avoid_Underflow + word0(rv) = (P+2) << Exp_shift; +#else + word1(rv) = 1; +#endif + i = 0; +#ifdef Honor_FLT_ROUNDS + if (bc->rounding == 1) +#endif + { + speccase = 1; + --p2; + dsign = 0; + goto have_i; + } + } + else +#endif + b = d2b(rv, &p2, &bbits MTa); +#ifdef Avoid_Underflow + p2 -= bc->scale; +#endif + /* floor(log2(rv)) == bbits - 1 + p2 */ + /* Check for denormal case. */ + i = P - bbits; + if (i > (j = P - Emin - 1 + p2)) { +#ifdef Sudden_Underflow + Bfree(b MTa); + b = i2b(1 MTa); + p2 = Emin; + i = P - 1; +#ifdef Avoid_Underflow + word0(rv) = (1 + bc->scale) << Exp_shift; +#else + word0(rv) = Exp_msk1; +#endif + word1(rv) = 0; +#else + i = j; +#endif + } +#ifdef Honor_FLT_ROUNDS + if (bc->rounding != 1) { + if (i > 0) + b = lshift(b, i MTa); + if (dsign) + b = increment(b MTa); + } + else +#endif + { + b = lshift(b, ++i MTa); + b->x[0] |= 1; + } +#ifndef Sudden_Underflow + have_i: +#endif + p2 -= p5 + i; + d = i2b(1 MTa); + /* Arrange for convenient computation of quotients: + * shift left if necessary so divisor has 4 leading 0 bits. + */ + if (p5 > 0) + d = pow5mult(d, p5 MTa); + else if (p5 < 0) + b = pow5mult(b, -p5 MTa); + if (p2 > 0) { + b2 = p2; + d2 = 0; + } + else { + b2 = 0; + d2 = -p2; + } + i = dshift(d, d2); + if ((b2 += i) > 0) + b = lshift(b, b2 MTa); + if ((d2 += i) > 0) + d = lshift(d, d2 MTa); + + /* Now b/d = exactly half-way between the two floating-point values */ + /* on either side of the input string. Compute first digit of b/d. */ + + if (!(dig = quorem(b,d))) { + b = multadd(b, 10, 0 MTa); /* very unlikely */ + dig = quorem(b,d); + } + + /* Compare b/d with s0 */ + + for(i = 0; i < nd0; ) { + if ((dd = s0[i++] - '0' - dig)) + goto ret; + if (!b->x[0] && b->wds == 1) { + if (i < nd) + dd = 1; + goto ret; + } + b = multadd(b, 10, 0 MTa); + dig = quorem(b,d); + } + for(j = bc->dp1; i++ < nd;) { + if ((dd = s0[j++] - '0' - dig)) + goto ret; + if (!b->x[0] && b->wds == 1) { + if (i < nd) + dd = 1; + goto ret; + } + b = multadd(b, 10, 0 MTa); + dig = quorem(b,d); + } + if (dig > 0 || b->x[0] || b->wds > 1) + dd = -1; + ret: + Bfree(b MTa); + Bfree(d MTa); +#ifdef Honor_FLT_ROUNDS + if (bc->rounding != 1) { + if (dd < 0) { + if (bc->rounding == 0) { + if (!dsign) + goto retlow1; + } + else if (dsign) + goto rethi1; + } + else if (dd > 0) { + if (bc->rounding == 0) { + if (dsign) + goto rethi1; + goto ret1; + } + if (!dsign) + goto rethi1; + dval(rv) += 2.*sulp(rv,bc); + } + else { + bc->inexact = 0; + if (dsign) + goto rethi1; + } + } + else +#endif + if (speccase) { + if (dd <= 0) + rv->d = 0.; + } + else if (dd < 0) { + if (!dsign) /* does not happen for round-near */ +retlow1: + dval(rv) -= sulp(rv,bc); + } + else if (dd > 0) { + if (dsign) { + rethi1: + dval(rv) += sulp(rv,bc); + } + } + else { + /* Exact half-way case: apply round-even rule. */ + if ((j = ((word0(rv) & Exp_mask) >> Exp_shift) - bc->scale) <= 0) { + i = 1 - j; + if (i <= 31) { + 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__unused(const char *s00, char **se) +{ + int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, e, e1; + int esign, i, j, k, nd, nd0, nf, nz, nz0, nz1, sign; + const char *s, *s0, *s1; + double aadj, aadj1; + Long L; + U aadj2, adj, rv, rv0; + ULong y, z; + BCinfo bc; + Bigint *bb, *bb1, *bd, *bd0, *bs, *delta; +#ifdef USE_BF96 + ULLong bhi, blo, brv, t00, t01, t02, t10, t11, terv, tg, tlo, yz; + const BF96 *p10; + int bexact, erv; +#endif +#ifdef Avoid_Underflow + ULong Lsb, Lsb1; +#endif +#ifdef SET_INEXACT + int oldinexact; +#endif +#ifndef NO_STRTOD_BIGCOMP + int req_bigcomp = 0; +#endif +#ifdef MULTIPLE_THREADS + ThInfo *TI = 0; +#endif +#ifdef Honor_FLT_ROUNDS /*{*/ +#ifdef Trust_FLT_ROUNDS /*{{ only define this if FLT_ROUNDS really works! */ + bc.rounding = Flt_Rounds; +#else /*}{*/ + bc.rounding = 1; + switch(fegetround()) { + case FE_TOWARDZERO: bc.rounding = 0; break; + case FE_UPWARD: bc.rounding = 2; break; + case FE_DOWNWARD: bc.rounding = 3; + } +#endif /*}}*/ +#endif /*}*/ +#ifdef USE_LOCALE + const char *s2; +#endif + + sign = nz0 = nz1 = nz = bc.dplen = bc.uflchk = 0; + dval(&rv) = 0.; + for(s = s00;;s++) switch(*s) { + case '-': + sign = 1; + /* fall through */ + 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; + /* fall through */ + case '+': + c = *++s; + } + if (c >= '0' && c <= '9') { + while(c == '0') + c = *++s; + if (c > '0' && c <= '9') { + L = c - '0'; + while((c = *++s) >= '0' && c <= '9') { + if (L <= 19999) + L = 10*L + c - '0'; + } + if (L > 19999) + /* Avoid confusion from exponents + * so large that e might overflow. + */ + e = 19999; /* safe for 16 bit ints */ + else + e = (int)L; + if (esign) + e = -e; + } + else + e = 0; + } + else + s = s00; + } + if (!nd) { + if (!nz && !nz0) { +#ifdef INFNAN_CHECK /*{*/ + /* Check for Nan and Infinity */ + if (!bc.dplen) + switch(c) { + case 'i': + case 'I': + if (match(&s,"nf")) { + --s; + if (!match(&s,"inity")) + ++s; + word0(&rv) = 0x7ff00000; + word1(&rv) = 0; + goto ret; + } + break; + case 'n': + case 'N': + if (match(&s, "an")) { + word0(&rv) = NAN_WORD0; + word1(&rv) = NAN_WORD1; +#ifndef No_Hex_NaN + if (*s == '(') /*)*/ + hexnan(&rv, &s); +#endif + goto ret; + } + } +#endif /*} INFNAN_CHECK */ + ret0: + s = s00; + sign = 0; + } + goto ret; + } + bc.e0 = e1 = e -= nf; + + /* Now we have nd0 digits, starting at s0, followed by a + * decimal point, followed by nd-nd0 digits. The number we're + * after is the integer represented by those digits times + * 10**e */ + + if (!nd0) + nd0 = nd; +#ifndef USE_BF96 + k = nd < DBL_DIG + 2 ? nd : DBL_DIG + 2; + dval(&rv) = y; + if (k > 9) { +#ifdef SET_INEXACT + if (k > DBL_DIG) + oldinexact = get_inexact(); +#endif + dval(&rv) = tens[k - 9] * dval(&rv) + z; + } +#endif + bd0 = 0; + if (nd <= DBL_DIG +#ifndef RND_PRODQUOT +#ifndef Honor_FLT_ROUNDS + && Flt_Rounds == 1 +#endif +#endif + ) { +#ifdef USE_BF96 + dval(&rv) = yz; +#endif + if (!e) + goto ret; +#ifndef ROUND_BIASED_without_Round_Up + if (e > 0) { + if (e <= Ten_pmax) { +#ifdef SET_INEXACT + bc.inexact = 0; + oldinexact = 1; +#endif +#ifdef VAX + goto vax_ovfl_check; +#else +#ifdef Honor_FLT_ROUNDS + /* round correctly FLT_ROUNDS = 2 or 3 */ + if (sign) { + rv.d = -rv.d; + sign = 0; + } +#endif + /* rv = */ rounded_product(dval(&rv), tens[e]); + goto ret; +#endif + } + i = DBL_DIG - nd; + if (e <= Ten_pmax + i) { + /* A fancier test would sometimes let us do + * this for larger i values. + */ +#ifdef SET_INEXACT + bc.inexact = 0; + oldinexact = 1; +#endif +#ifdef Honor_FLT_ROUNDS + /* round correctly FLT_ROUNDS = 2 or 3 */ + if (sign) { + rv.d = -rv.d; + sign = 0; + } +#endif + e -= i; + dval(&rv) *= tens[i]; +#ifdef VAX + /* VAX exponent range is so narrow we must + * worry about overflow here... + */ + vax_ovfl_check: + word0(&rv) -= P*Exp_msk1; + /* rv = */ rounded_product(dval(&rv), tens[e]); + if ((word0(&rv) & Exp_mask) + > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) + goto ovfl; + word0(&rv) += P*Exp_msk1; +#else + /* rv = */ rounded_product(dval(&rv), tens[e]); +#endif + goto ret; + } + } +#ifndef Inaccurate_Divide + else if (e >= -Ten_pmax) { +#ifdef SET_INEXACT + bc.inexact = 0; + oldinexact = 1; +#endif +#ifdef Honor_FLT_ROUNDS + /* round correctly FLT_ROUNDS = 2 or 3 */ + if (sign) { + rv.d = -rv.d; + sign = 0; + } +#endif + /* rv = */ rounded_quotient(dval(&rv), tens[-e]); + goto ret; + } +#endif +#endif /* ROUND_BIASED_without_Round_Up */ + } +#ifdef USE_BF96 + k = nd < 19 ? nd : 19; +#endif + e1 += nd - k; /* scale factor = 10^e1 */ + +#ifdef IEEE_Arith +#ifdef SET_INEXACT + bc.inexact = 1; +#ifndef USE_BF96 + if (k <= DBL_DIG) +#endif + oldinexact = get_inexact(); +#endif +#ifdef Honor_FLT_ROUNDS + if (bc.rounding >= 2) { + if (sign) + bc.rounding = bc.rounding == 2 ? 0 : 2; + else + if (bc.rounding != 2) + bc.rounding = 0; + } +#endif +#endif /*IEEE_Arith*/ + +#ifdef USE_BF96 /*{*/ + Debug(++dtoa_stats[0]); + i = e1 + 342; + if (i < 0) + goto undfl; + if (i > 650) + goto ovfl; + p10 = &pten[i]; + brv = yz; + /* shift brv left, with i = number of bits shifted */ + i = 0; + if (!(brv & 0xffffffff00000000ull)) { + i = 32; + brv <<= 32; + } + if (!(brv & 0xffff000000000000ull)) { + i += 16; + brv <<= 16; + } + if (!(brv & 0xff00000000000000ull)) { + i += 8; + brv <<= 8; + } + if (!(brv & 0xf000000000000000ull)) { + i += 4; + brv <<= 4; + } + if (!(brv & 0xc000000000000000ull)) { + i += 2; + brv <<= 2; + } + if (!(brv & 0x8000000000000000ull)) { + i += 1; + brv <<= 1; + } + erv = (64 + 0x3fe) + p10->e - i; + if (erv <= 0 && nd > 19) + goto many_digits; /* denormal: may need to look at all digits */ + bhi = brv >> 32; + blo = brv & 0xffffffffull; + /* Unsigned 32-bit ints lie in [0,2^32-1] and */ + /* unsigned 64-bit ints lie in [0, 2^64-1]. The product of two unsigned */ + /* 32-bit ints is <= 2^64 - 2*2^32-1 + 1 = 2^64 - 1 - 2*(2^32 - 1), so */ + /* we can add two unsigned 32-bit ints to the product of two such ints, */ + /* and 64 bits suffice to contain the result. */ + t01 = bhi * p10->b1; + t10 = blo * p10->b0 + (t01 & 0xffffffffull); + t00 = bhi * p10->b0 + (t01 >> 32) + (t10 >> 32); + if (t00 & 0x8000000000000000ull) { + if ((t00 & 0x3ff) && (~t00 & 0x3fe)) { /* unambiguous result? */ + if (nd > 19 && ((t00 + (1<<i) + 2) & 0x400) ^ (t00 & 0x400)) + goto many_digits; + if (erv <= 0) + goto denormal; +#ifdef Honor_FLT_ROUNDS + switch(bc.rounding) { + case 0: goto noround; + case 2: goto roundup; + } +#endif + if (t00 & 0x400 && t00 & 0xbff) + goto roundup; + goto noround; + } + } + else { + if ((t00 & 0x1ff) && (~t00 & 0x1fe)) { /* unambiguous result? */ + if (nd > 19 && ((t00 + (1<<i) + 2) & 0x200) ^ (t00 & 0x200)) + goto many_digits; + if (erv <= 1) + goto denormal1; +#ifdef Honor_FLT_ROUNDS + switch(bc.rounding) { + case 0: goto noround1; + case 2: goto roundup1; + } +#endif + if (t00 & 0x200) + goto roundup1; + goto noround1; + } + } + /* 3 multiplies did not suffice; try a 96-bit approximation */ + Debug(++dtoa_stats[1]); + t02 = bhi * p10->b2; + t11 = blo * p10->b1 + (t02 & 0xffffffffull); + bexact = 1; + if (e1 < 0 || e1 > 41 || (t10 | t11) & 0xffffffffull || nd > 19) + bexact = 0; + tlo = (t10 & 0xffffffffull) + (t02 >> 32) + (t11 >> 32); + if (!bexact && (tlo + 0x10) >> 32 > tlo >> 32) + goto many_digits; + t00 += tlo >> 32; + if (t00 & 0x8000000000000000ull) { + if (erv <= 0) { /* denormal result */ + if (nd >= 20 || !((tlo & 0xfffffff0) | (t00 & 0x3ff))) + goto many_digits; + denormal: + if (erv <= -52) { +#ifdef Honor_FLT_ROUNDS + switch(bc.rounding) { + case 0: goto undfl; + case 2: goto tiniest; + } +#endif + if (erv < -52 || !(t00 & 0x7fffffffffffffffull)) + goto undfl; + goto tiniest; + } + tg = 1ull << (11 - erv); + t00 &= ~(tg - 1); /* clear low bits */ +#ifdef Honor_FLT_ROUNDS + switch(bc.rounding) { + case 0: goto noround_den; + case 2: goto roundup_den; + } +#endif + if (t00 & tg) { +#ifdef Honor_FLT_ROUNDS + roundup_den: +#endif + t00 += tg << 1; + if (!(t00 & 0x8000000000000000ull)) { + if (++erv > 0) + goto smallest_normal; + t00 = 0x8000000000000000ull; + } + } +#ifdef Honor_FLT_ROUNDS + noround_den: +#endif + LLval(&rv) = t00 >> (12 - erv); + Set_errno(ERANGE); + goto ret; + } + if (bexact) { +#ifdef SET_INEXACT + if (!(t00 & 0x7ff) && !(tlo & 0xffffffffull)) { + bc.inexact = 0; + goto noround; + } +#endif +#ifdef Honor_FLT_ROUNDS + switch(bc.rounding) { + case 2: + if (t00 & 0x7ff) + goto roundup; + case 0: goto noround; + } +#endif + if (t00 & 0x400 && (tlo & 0xffffffff) | (t00 & 0xbff)) + goto roundup; + goto noround; + } + if ((tlo & 0xfffffff0) | (t00 & 0x3ff) + && (nd <= 19 || ((t00 + (1ull << i)) & 0xfffffffffffffc00ull) + == (t00 & 0xfffffffffffffc00ull))) { + /* Unambiguous result. */ + /* If nd > 19, then incrementing the 19th digit */ + /* does not affect rv. */ +#ifdef Honor_FLT_ROUNDS + switch(bc.rounding) { + case 0: goto noround; + case 2: goto roundup; + } +#endif + if (t00 & 0x400) { /* round up */ + roundup: + t00 += 0x800; + if (!(t00 & 0x8000000000000000ull)) { + /* rounded up to a power of 2 */ + if (erv >= 0x7fe) + goto ovfl; + terv = erv + 1; + LLval(&rv) = terv << 52; + goto ret; + } + } + noround: + if (erv >= 0x7ff) + goto ovfl; + terv = erv; + LLval(&rv) = (terv << 52) | ((t00 & 0x7ffffffffffff800ull) >> 11); + goto ret; + } + } + else { + if (erv <= 1) { /* denormal result */ + if (nd >= 20 || !((tlo & 0xfffffff0) | (t00 & 0x1ff))) + goto many_digits; + denormal1: + if (erv <= -51) { +#ifdef Honor_FLT_ROUNDS + switch(bc.rounding) { + case 0: goto undfl; + case 2: goto tiniest; + } +#endif + if (erv < -51 || !(t00 & 0x3fffffffffffffffull)) + goto undfl; + tiniest: + LLval(&rv) = 1; + Set_errno(ERANGE); + goto ret; + } + tg = 1ull << (11 - erv); +#ifdef Honor_FLT_ROUNDS + switch(bc.rounding) { + case 0: goto noround1_den; + case 2: goto roundup1_den; + } +#endif + if (t00 & tg) { +#ifdef Honor_FLT_ROUNDS + roundup1_den: +#endif + if (0x8000000000000000ull & (t00 += (tg<<1)) && erv == 1) { + + smallest_normal: + LLval(&rv) = 0x0010000000000000ull; + goto ret; + } + } +#ifdef Honor_FLT_ROUNDS + noround1_den: +#endif + if (erv <= -52) + goto undfl; + LLval(&rv) = t00 >> (12 - erv); + Set_errno(ERANGE); + goto ret; + } + if (bexact) { +#ifdef SET_INEXACT + if (!(t00 & 0x3ff) && !(tlo & 0xffffffffull)) { + bc.inexact = 0; + goto noround1; + } +#endif +#ifdef Honor_FLT_ROUNDS + switch(bc.rounding) { + case 2: + if (t00 & 0x3ff) + goto roundup1; + case 0: goto noround1; + } +#endif + if (t00 & 0x200 && (t00 & 0x5ff || tlo)) + goto roundup1; + goto noround1; + } + if ((tlo & 0xfffffff0) | (t00 & 0x1ff) + && (nd <= 19 || ((t00 + (1ull << i)) & 0x7ffffffffffffe00ull) + == (t00 & 0x7ffffffffffffe00ull))) { + /* Unambiguous result. */ +#ifdef Honor_FLT_ROUNDS + switch(bc.rounding) { + case 0: goto noround1; + case 2: goto roundup1; + } +#endif + if (t00 & 0x200) { /* round up */ + roundup1: + t00 += 0x400; + if (!(t00 & 0x4000000000000000ull)) { + /* rounded up to a power of 2 */ + if (erv >= 0x7ff) + goto ovfl; + terv = erv; + LLval(&rv) = terv << 52; + goto ret; + } + } + noround1: + if (erv >= 0x800) + goto ovfl; + terv = erv - 1; + LLval(&rv) = (terv << 52) | ((t00 & 0x3ffffffffffffc00ull) >> 10); + goto ret; + } + } + many_digits: + Debug(++dtoa_stats[2]); + if (nd > 17) { + if (nd > 18) { + yz /= 100; + e1 += 2; + } + else { + yz /= 10; + e1 += 1; + } + y = yz / 100000000; + } + else if (nd > 9) { + i = nd - 9; + y = (yz >> i) / pfive[i-1]; + } + else + y = yz; + dval(&rv) = yz; +#endif /*}*/ + +#ifdef IEEE_Arith +#ifdef Avoid_Underflow + bc.scale = 0; +#endif +#endif /*IEEE_Arith*/ + + /* Get starting approximation = rv * 10**e1 */ + + if (e1 > 0) { + if ((i = e1 & 15)) + dval(&rv) *= tens[i]; + if (e1 &= ~15) { + if (e1 > DBL_MAX_10_EXP) { + ovfl: + /* Can't trust HUGE_VAL */ +#ifdef IEEE_Arith +#ifdef Honor_FLT_ROUNDS + switch(bc.rounding) { + case 0: /* toward 0 */ + case 3: /* toward -infinity */ + word0(&rv) = Big0; + word1(&rv) = Big1; + break; + default: + word0(&rv) = Exp_mask; + word1(&rv) = 0; + } +#else /*Honor_FLT_ROUNDS*/ + word0(&rv) = Exp_mask; + word1(&rv) = 0; +#endif /*Honor_FLT_ROUNDS*/ +#ifdef SET_INEXACT + /* set overflow bit */ + dval(&rv0) = 1e300; + dval(&rv0) *= dval(&rv0); +#endif +#else /*IEEE_Arith*/ + word0(&rv) = Big0; + word1(&rv) = Big1; +#endif /*IEEE_Arith*/ + range_err: + if (bd0) { + Bfree(bb MTb); + Bfree(bd MTb); + Bfree(bs MTb); + Bfree(bd0 MTb); + Bfree(delta MTb); + } + Set_errno(ERANGE); + goto ret; + } + e1 >>= 4; + for(j = 0; e1 > 1; j++, e1 >>= 1) + if (e1 & 1) + dval(&rv) *= bigtens[j]; + /* The last multiplication could overflow. */ + word0(&rv) -= P*Exp_msk1; + dval(&rv) *= bigtens[j]; + if ((z = word0(&rv) & Exp_mask) + > Exp_msk1*(DBL_MAX_EXP+Bias-P)) + goto ovfl; + if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) { + /* set to largest number */ + /* (Can't trust DBL_MAX) */ + word0(&rv) = Big0; + word1(&rv) = Big1; + } + else + word0(&rv) += P*Exp_msk1; + } + } + else if (e1 < 0) { + e1 = -e1; + if ((i = e1 & 15)) + dval(&rv) /= tens[i]; + if (e1 >>= 4) { + if (e1 >= 1 << n_bigtens) + goto undfl; +#ifdef Avoid_Underflow + if (e1 & Scale_Bit) + bc.scale = 2*P; + for(j = 0; e1 > 0; j++, e1 >>= 1) + if (e1 & 1) + dval(&rv) *= tinytens[j]; + if (bc.scale && (j = 2*P + 1 - ((word0(&rv) & Exp_mask) + >> Exp_shift)) > 0) { + /* scaled rv is denormal; clear j low bits */ + if (j >= 32) { + if (j > 54) + goto undfl; + word1(&rv) = 0; + if (j >= 53) + word0(&rv) = (P+2)*Exp_msk1; + else + word0(&rv) &= 0xffffffff << (j-32); + } + else + word1(&rv) &= 0xffffffff << j; + } +#else + for(j = 0; e1 > 1; j++, e1 >>= 1) + if (e1 & 1) + dval(&rv) *= tinytens[j]; + /* The last multiplication could underflow. */ + dval(&rv0) = dval(&rv); + dval(&rv) *= tinytens[j]; + if (!dval(&rv)) { + dval(&rv) = 2.*dval(&rv0); + dval(&rv) *= tinytens[j]; +#endif + if (!dval(&rv)) { + undfl: + dval(&rv) = 0.; +#ifdef Honor_FLT_ROUNDS + if (bc.rounding == 2) + word1(&rv) = 1; +#endif + goto range_err; + } +#ifndef Avoid_Underflow + word0(&rv) = Tiny0; + word1(&rv) = Tiny1; + /* The refinement below will clean + * this approximation up. + */ + } +#endif + } + } + + /* Now the hard part -- adjusting rv to the correct value.*/ + + /* Put digits into bd: true value = bd * 10^e */ + + bc.nd = nd - nz1; +#ifndef NO_STRTOD_BIGCOMP + bc.nd0 = nd0; /* Only needed if nd > strtod_diglim, but done here */ + /* to silence an erroneous warning about bc.nd0 */ + /* possibly not being initialized. */ + if (nd > strtod_diglim) { + /* ASSERT(strtod_diglim >= 18); 18 == one more than the */ + /* minimum number of decimal digits to distinguish double values */ + /* in IEEE arithmetic. */ + i = j = 18; + if (i > nd0) + j += bc.dplen; + for(;;) { + if (--j < bc.dp1 && j >= bc.dp0) + j = bc.dp0 - 1; + if (s0[j] != '0') + break; + --i; + } + e += nd - i; + nd = i; + if (nd0 > nd) + nd0 = nd; + if (nd < 9) { /* must recompute y */ + y = 0; + for(i = 0; i < nd0; ++i) + y = 10*y + s0[i] - '0'; + for(j = bc.dp1; i < nd; ++i) + y = 10*y + s0[j++] - '0'; + } + } +#endif + bd0 = s2b(s0, nd0, nd, y, bc.dplen MTb); + + for(;;) { + bd = Balloc(bd0->k MTb); + Bcopy(bd, bd0); + bb = d2b(&rv, &bbe, &bbbits MTb); /* rv = bb * 2^bbe */ + bs = i2b(1 MTb); + + if (e >= 0) { + bb2 = bb5 = 0; + bd2 = bd5 = e; + } + else { + bb2 = bb5 = -e; + bd2 = bd5 = 0; + } + if (bbe >= 0) + bb2 += bbe; + else + bd2 -= bbe; + bs2 = bb2; +#ifdef Honor_FLT_ROUNDS + if (bc.rounding != 1) + bs2++; +#endif +#ifdef Avoid_Underflow + Lsb = LSB; + Lsb1 = 0; + j = bbe - bc.scale; + i = j + bbbits - 1; /* logb(rv) */ + j = P + 1 - bbbits; + if (i < Emin) { /* denormal */ + i = Emin - i; + j -= i; + if (i < 32) + Lsb <<= i; + else if (i < 52) + Lsb1 = Lsb << (i-32); + else + Lsb1 = Exp_mask; + } +#else /*Avoid_Underflow*/ +#ifdef Sudden_Underflow +#ifdef IBM + j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3); +#else + j = P + 1 - bbbits; +#endif +#else /*Sudden_Underflow*/ + j = bbe; + i = j + bbbits - 1; /* logb(rv) */ + if (i < Emin) /* denormal */ + j += P - Emin; + else + j = P + 1 - bbbits; +#endif /*Sudden_Underflow*/ +#endif /*Avoid_Underflow*/ + bb2 += j; + bd2 += j; +#ifdef Avoid_Underflow + bd2 += bc.scale; +#endif + i = bb2 < bd2 ? bb2 : bd2; + if (i > bs2) + i = bs2; + if (i > 0) { + bb2 -= i; + bd2 -= i; + bs2 -= i; + } + if (bb5 > 0) { + bs = pow5mult(bs, bb5 MTb); + bb1 = mult(bs, bb MTb); + Bfree(bb MTb); + bb = bb1; + } + if (bb2 > 0) + bb = lshift(bb, bb2 MTb); + if (bd5 > 0) + bd = pow5mult(bd, bd5 MTb); + if (bd2 > 0) + bd = lshift(bd, bd2 MTb); + if (bs2 > 0) + bs = lshift(bs, bs2 MTb); + delta = diff(bb, bd MTb); + bc.dsign = delta->sign; + delta->sign = 0; + i = cmp(delta, bs); +#ifndef NO_STRTOD_BIGCOMP /*{*/ + if (bc.nd > nd && i <= 0) { + if (bc.dsign) { + /* Must use bigcomp(). */ + req_bigcomp = 1; + break; + } +#ifdef Honor_FLT_ROUNDS + if (bc.rounding != 1) { + if (i < 0) { + req_bigcomp = 1; + break; + } + } + else +#endif + i = -1; /* Discarded digits make delta smaller. */ + } +#endif /*}*/ +#ifdef Honor_FLT_ROUNDS /*{*/ + if (bc.rounding != 1) { + if (i < 0) { + /* Error is less than an ulp */ + if (!delta->x[0] && delta->wds <= 1) { + /* exact */ +#ifdef SET_INEXACT + bc.inexact = 0; +#endif + break; + } + if (bc.rounding) { + if (bc.dsign) { + adj.d = 1.; + goto apply_adj; + } + } + else if (!bc.dsign) { + adj.d = -1.; + if (!word1(&rv) + && !(word0(&rv) & Frac_mask)) { + y = word0(&rv) & Exp_mask; +#ifdef Avoid_Underflow + if (!bc.scale || y > 2*P*Exp_msk1) +#else + if (y) +#endif + { + delta = lshift(delta,Log2P MTb); + if (cmp(delta, bs) <= 0) + adj.d = -0.5; + } + } + apply_adj: +#ifdef Avoid_Underflow /*{*/ + if (bc.scale && (y = word0(&rv) & Exp_mask) + <= 2*P*Exp_msk1) + word0(&adj) += (2*P+1)*Exp_msk1 - y; +#else +#ifdef Sudden_Underflow + if ((word0(&rv) & Exp_mask) <= + P*Exp_msk1) { + word0(&rv) += P*Exp_msk1; + dval(&rv) += adj.d*ulp(dval(&rv)); + word0(&rv) -= P*Exp_msk1; + } + else +#endif /*Sudden_Underflow*/ +#endif /*Avoid_Underflow}*/ + dval(&rv) += adj.d*ulp(&rv); + } + break; + } + adj.d = ratio(delta, bs); + if (adj.d < 1.) + adj.d = 1.; + if (adj.d <= 0x7ffffffe) { + /* adj = rounding ? ceil(adj) : floor(adj); */ + y = adj.d; + if (y != adj.d) { + if (!((bc.rounding>>1) ^ bc.dsign)) + y++; + adj.d = y; + } + } +#ifdef Avoid_Underflow /*{*/ + if (bc.scale && (y = word0(&rv) & Exp_mask) <= 2*P*Exp_msk1) + word0(&adj) += (2*P+1)*Exp_msk1 - y; +#else +#ifdef Sudden_Underflow + if ((word0(&rv) & Exp_mask) <= P*Exp_msk1) { + word0(&rv) += P*Exp_msk1; + adj.d *= ulp(dval(&rv)); + if (bc.dsign) + dval(&rv) += adj.d; + else + dval(&rv) -= adj.d; + word0(&rv) -= P*Exp_msk1; + goto cont; + } +#endif /*Sudden_Underflow*/ +#endif /*Avoid_Underflow}*/ + adj.d *= ulp(&rv); + if (bc.dsign) { + if (word0(&rv) == Big0 && word1(&rv) == Big1) + goto ovfl; + dval(&rv) += adj.d; + } + else + dval(&rv) -= adj.d; + goto cont; + } +#endif /*}Honor_FLT_ROUNDS*/ + + if (i < 0) { + /* Error is less than half an ulp -- check for + * special case of mantissa a power of two. + */ + if (bc.dsign || word1(&rv) || word0(&rv) & Bndry_mask +#ifdef IEEE_Arith /*{*/ +#ifdef Avoid_Underflow + || (word0(&rv) & Exp_mask) <= (2*P+1)*Exp_msk1 +#else + || (word0(&rv) & Exp_mask) <= Exp_msk1 +#endif +#endif /*}*/ + ) { +#ifdef SET_INEXACT + if (!delta->x[0] && delta->wds <= 1) + bc.inexact = 0; +#endif + break; + } + if (!delta->x[0] && delta->wds <= 1) { + /* exact result */ +#ifdef SET_INEXACT + bc.inexact = 0; +#endif + break; + } + delta = lshift(delta,Log2P MTb); + if (cmp(delta, bs) > 0) + goto drop_down; + break; + } + if (i == 0) { + /* exactly half-way between */ + if (bc.dsign) { + if ((word0(&rv) & Bndry_mask1) == Bndry_mask1 + && word1(&rv) == ( +#ifdef Avoid_Underflow + (bc.scale && (y = word0(&rv) & Exp_mask) <= 2*P*Exp_msk1) + ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) : +#endif + 0xffffffff)) { + /*boundary case -- increment exponent*/ + if (word0(&rv) == Big0 && word1(&rv) == Big1) + goto ovfl; + word0(&rv) = (word0(&rv) & Exp_mask) + + Exp_msk1 +#ifdef IBM + | Exp_msk1 >> 4 +#endif + ; + word1(&rv) = 0; +#ifdef Avoid_Underflow + bc.dsign = 0; +#endif + break; + } + } + else if (!(word0(&rv) & Bndry_mask) && !word1(&rv)) { + drop_down: + /* boundary case -- decrement exponent */ +#ifdef Sudden_Underflow /*{{*/ + L = word0(&rv) & Exp_mask; +#ifdef IBM + if (L < Exp_msk1) +#else +#ifdef Avoid_Underflow + if (L <= (bc.scale ? (2*P+1)*Exp_msk1 : Exp_msk1)) +#else + if (L <= Exp_msk1) +#endif /*Avoid_Underflow*/ +#endif /*IBM*/ + { + if (bc.nd >nd) { + bc.uflchk = 1; + break; + } + goto undfl; + } + L -= Exp_msk1; +#else /*Sudden_Underflow}{*/ +#ifdef Avoid_Underflow + if (bc.scale) { + L = word0(&rv) & Exp_mask; + if (L <= (2*P+1)*Exp_msk1) { + if (L > (P+2)*Exp_msk1) + /* round even ==> */ + /* accept rv */ + break; + /* rv = smallest denormal */ + if (bc.nd >nd) { + bc.uflchk = 1; + break; + } + goto undfl; + } + } +#endif /*Avoid_Underflow*/ + L = (word0(&rv) & Exp_mask) - Exp_msk1; +#endif /*Sudden_Underflow}}*/ + word0(&rv) = L | Bndry_mask1; + word1(&rv) = 0xffffffff; +#ifdef IBM + goto cont; +#else +#ifndef NO_STRTOD_BIGCOMP + if (bc.nd > nd) + goto cont; +#endif + break; +#endif + } +#ifndef ROUND_BIASED +#ifdef Avoid_Underflow + if (Lsb1) { + if (!(word0(&rv) & Lsb1)) + break; + } + else if (!(word1(&rv) & Lsb)) + break; +#else + if (!(word1(&rv) & LSB)) + break; +#endif +#endif + if (bc.dsign) +#ifdef Avoid_Underflow + dval(&rv) += sulp(&rv, &bc); +#else + dval(&rv) += ulp(&rv); +#endif +#ifndef ROUND_BIASED + else { +#ifdef Avoid_Underflow + dval(&rv) -= sulp(&rv, &bc); +#else + dval(&rv) -= ulp(&rv); +#endif +#ifndef Sudden_Underflow + if (!dval(&rv)) { + if (bc.nd >nd) { + bc.uflchk = 1; + break; + } + goto undfl; + } +#endif + } +#ifdef Avoid_Underflow + bc.dsign = 1 - bc.dsign; +#endif +#endif + break; + } + if ((aadj = ratio(delta, bs)) <= 2.) { + if (bc.dsign) + aadj = aadj1 = 1.; + else if (word1(&rv) || word0(&rv) & Bndry_mask) { +#ifndef Sudden_Underflow + if (word1(&rv) == Tiny1 && !word0(&rv)) { + if (bc.nd >nd) { + bc.uflchk = 1; + break; + } + goto undfl; + } +#endif + aadj = 1.; + aadj1 = -1.; + } + else { + /* special case -- power of FLT_RADIX to be */ + /* rounded down... */ + + if (aadj < 2./FLT_RADIX) + aadj = 1./FLT_RADIX; + else + aadj *= 0.5; + aadj1 = -aadj; + } + } + else { + aadj *= 0.5; + aadj1 = bc.dsign ? aadj : -aadj; +#ifdef Check_FLT_ROUNDS + switch(bc.rounding) { + case 2: /* towards +infinity */ + aadj1 -= 0.5; + break; + case 0: /* towards 0 */ + case 3: /* towards -infinity */ + aadj1 += 0.5; + } +#else + if (Flt_Rounds == 0) + aadj1 += 0.5; +#endif /*Check_FLT_ROUNDS*/ + } + y = word0(&rv) & Exp_mask; + + /* Check for overflow */ + + if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) { + dval(&rv0) = dval(&rv); + word0(&rv) -= P*Exp_msk1; + adj.d = aadj1 * ulp(&rv); + dval(&rv) += adj.d; + if ((word0(&rv) & Exp_mask) >= + Exp_msk1*(DBL_MAX_EXP+Bias-P)) { + if (word0(&rv0) == Big0 && word1(&rv0) == Big1) + goto ovfl; + word0(&rv) = Big0; + word1(&rv) = Big1; + goto cont; + } + else + word0(&rv) += P*Exp_msk1; + } + else { +#ifdef Avoid_Underflow + if (bc.scale && y <= 2*P*Exp_msk1) { + if (aadj <= 0x7fffffff) { + if ((z = aadj) <= 0) + z = 1; + aadj = z; + aadj1 = bc.dsign ? aadj : -aadj; + } + dval(&aadj2) = aadj1; + word0(&aadj2) += (2*P+1)*Exp_msk1 - y; + aadj1 = dval(&aadj2); + adj.d = aadj1 * ulp(&rv); + dval(&rv) += adj.d; + if (rv.d == 0.) +#ifdef NO_STRTOD_BIGCOMP + goto undfl; +#else + { + req_bigcomp = 1; + break; + } +#endif + } + else { + adj.d = aadj1 * ulp(&rv); + dval(&rv) += adj.d; + } +#else +#ifdef Sudden_Underflow + if ((word0(&rv) & Exp_mask) <= P*Exp_msk1) { + dval(&rv0) = dval(&rv); + word0(&rv) += P*Exp_msk1; + adj.d = aadj1 * ulp(&rv); + dval(&rv) += adj.d; +#ifdef IBM + if ((word0(&rv) & Exp_mask) < P*Exp_msk1) +#else + if ((word0(&rv) & Exp_mask) <= P*Exp_msk1) +#endif + { + if (word0(&rv0) == Tiny0 + && word1(&rv0) == Tiny1) { + if (bc.nd >nd) { + bc.uflchk = 1; + break; + } + goto undfl; + } + word0(&rv) = Tiny0; + word1(&rv) = Tiny1; + goto cont; + } + else + word0(&rv) -= P*Exp_msk1; + } + else { + adj.d = aadj1 * ulp(&rv); + dval(&rv) += adj.d; + } +#else /*Sudden_Underflow*/ + /* Compute adj so that the IEEE rounding rules will + * correctly round rv + adj in some half-way cases. + * If rv * ulp(rv) is denormalized (i.e., + * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid + * trouble from bits lost to denormalization; + * example: 1.2e-307 . + */ + if (y <= (P-1)*Exp_msk1 && aadj > 1.) { + aadj1 = (double)(int)(aadj + 0.5); + if (!bc.dsign) + aadj1 = -aadj1; + } + adj.d = aadj1 * ulp(&rv); + dval(&rv) += adj.d; +#endif /*Sudden_Underflow*/ +#endif /*Avoid_Underflow*/ + } + z = word0(&rv) & Exp_mask; +#ifndef SET_INEXACT + if (bc.nd == nd) { +#ifdef Avoid_Underflow + if (!bc.scale) +#endif + if (y == z) { + /* Can we stop now? */ + L = (Long)aadj; + aadj -= L; + /* The tolerances below are conservative. */ + if (bc.dsign || word1(&rv) || word0(&rv) & Bndry_mask) { + if (aadj < .4999999 || aadj > .5000001) + break; + } + else if (aadj < .4999999/FLT_RADIX) + break; + } + } +#endif + cont: + Bfree(bb MTb); + Bfree(bd MTb); + Bfree(bs MTb); + Bfree(delta MTb); + } + Bfree(bb MTb); + Bfree(bd MTb); + Bfree(bs MTb); + Bfree(bd0 MTb); + Bfree(delta MTb); +#ifndef NO_STRTOD_BIGCOMP + if (req_bigcomp) { + bd0 = 0; + bc.e0 += nz1; + bigcomp(&rv, s0, &bc MTb); + y = word0(&rv) & Exp_mask; + if (y == Exp_mask) + goto ovfl; + if (y == 0 && rv.d == 0.) + goto undfl; + } +#endif +#ifdef Avoid_Underflow + if (bc.scale) { + word0(&rv0) = Exp_1 - 2*P*Exp_msk1; + word1(&rv0) = 0; + dval(&rv) *= dval(&rv0); +#ifndef NO_ERRNO + /* try to avoid the bug of testing an 8087 register value */ +#ifdef IEEE_Arith + if (!(word0(&rv) & Exp_mask)) +#else + if (word0(&rv) == 0 && word1(&rv) == 0) +#endif + Set_errno(ERANGE); +#endif + } +#endif /* Avoid_Underflow */ + ret: +#ifdef SET_INEXACT + if (bc.inexact) { + if (!(word0(&rv) & Exp_mask)) { + /* set underflow and inexact bits */ + dval(&rv0) = 1e-300; + dval(&rv0) *= dval(&rv0); + } + else if (!oldinexact) { + word0(&rv0) = Exp_1 + (70 << Exp_shift); + word1(&rv0) = 0; + dval(&rv0) += 1.; + } + } + else if (!oldinexact) + clear_inexact(); +#endif + if (se) + *se = (char *)s; + return sign ? -dval(&rv) : dval(&rv); + } + +#ifndef MULTIPLE_THREADS + static char *dtoa_result; +#endif + + static char * +rv_alloc(int i MTd) +{ + int j, k, *r; + + j = sizeof(ULong); + for(k = 0; + sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= (size_t)i; + j <<= 1) + k++; + r = (int*)Balloc(k MTa); + *r = k; + return +#ifndef MULTIPLE_THREADS + dtoa_result = +#endif + (char *)(r+1); + } + + static char * +nrv_alloc(const char *s, char *s0, size_t s0len, char **rve, int n MTd) +{ + char *rv, *t; + + if (!s0) + s0 = rv_alloc(n MTa); + else if (s0len <= (size_t)n) { + rv = 0; + t = rv + n; + goto rve_chk; + } + t = rv = s0; + while((*t = *s++)) + ++t; + rve_chk: + if (rve) + *rve = t; + return rv; + } + +/* freedtoa(s) must be used to free values s returned by dtoa + * when MULTIPLE_THREADS is #defined. It should be used in all cases, + * but for consistency with earlier versions of dtoa, it is optional + * when MULTIPLE_THREADS is not defined. + */ + + void +freedtoa(char *s) +{ +#ifdef MULTIPLE_THREADS + ThInfo *TI = 0; +#endif + Bigint *b = (Bigint *)((int *)s - 1); + b->maxwds = 1 << (b->k = *(int*)b); + Bfree(b MTb); +#ifndef MULTIPLE_THREADS + if (s == dtoa_result) + dtoa_result = 0; +#endif + } + +/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string. + * + * Inspired by "How to Print Floating-Point Numbers Accurately" by + * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126]. + * + * Modifications: + * 1. Rather than iterating, we use a simple numeric overestimate + * to determine k = floor(log10(d)). We scale relevant + * quantities using O(log2(k)) rather than O(k) multiplications. + * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't + * try to generate digits strictly left to right. Instead, we + * compute with fewer bits and propagate the carry if necessary + * when rounding the final digit up. This is often faster. + * 3. Under the assumption that input will be rounded nearest, + * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22. + * That is, we allow equality in stopping tests when the + * round-nearest rule will give the same floating-point value + * as would satisfaction of the stopping test with strict + * inequality. + * 4. We remove common factors of powers of 2 from relevant + * quantities. + * 5. When converting floating-point integers less than 1e16, + * we use floating-point arithmetic rather than resorting + * to multiple-precision integers. + * 6. When asked to produce fewer than 15 digits, we first try + * to get by with floating-point arithmetic; we resort to + * multiple-precision integer arithmetic only if we cannot + * guarantee that the floating-point calculation has given + * the correctly rounded result. For k requested digits and + * "uniformly" distributed input, the probability is + * something like 10^(k-15) that we must resort to the Long + * calculation. + */ + + char * +dtoa_r(double dd, int mode, int ndigits, int *decpt, int *sign, char **rve, char *buf, size_t blen) +{ + /* Arguments ndigits, decpt, sign are similar to those + of ecvt and fcvt; trailing zeros are suppressed from + the returned string. If not null, *rve is set to point + to the end of the return value. If d is +-Infinity or NaN, + then *decpt is set to 9999. + + mode: + 0 ==> shortest string that yields d when read in + and rounded to nearest. + 1 ==> like 0, but with Steele & White stopping rule; + e.g. with IEEE P754 arithmetic , mode 0 gives + 1e23 whereas mode 1 gives 9.999999999999999e22. + 2 ==> max(1,ndigits) significant digits. This gives a + return value similar to that of ecvt, except + that trailing zeros are suppressed. + 3 ==> through ndigits past the decimal point. This + gives a return value similar to that from fcvt, + except that trailing zeros are suppressed, and + ndigits can be negative. + 4,5 ==> similar to 2 and 3, respectively, but (in + round-nearest mode) with the tests of mode 0 to + possibly return a shorter string that rounds to d. + With IEEE arithmetic and compilation with + -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same + as modes 2 and 3 when FLT_ROUNDS != 1. + 6-9 ==> Debugging modes similar to mode - 4: don't try + fast floating-point estimate (if applicable). + + Values of mode other than 0-9 are treated as mode 0. + + When not NULL, buf is an output buffer of length blen, which must + be large enough to accommodate suppressed trailing zeros and a trailing + null byte. If blen is too small, rv = NULL is returned, in which case + if rve is not NULL, a subsequent call with blen >= (*rve - rv) + 1 + should succeed in returning buf. + + When buf is NULL, sufficient space is allocated for the return value, + which, when done using, the caller should pass to freedtoa(). + + USE_BF is automatically defined when neither NO_LONG_LONG nor NO_BF96 + is defined. + */ + +#ifdef MULTIPLE_THREADS + ThInfo *TI = 0; +#endif + int bbits, b2, b5, be, dig, i, ilim, ilim1, + j, j1, k, leftright, m2, m5, s2, s5, spec_case; +#if !defined(Sudden_Underflow) || defined(USE_BF96) + int denorm; +#endif + Bigint *b, *b1, *delta, *mlo, *mhi, *S; + U u; + char *s; +#ifdef SET_INEXACT + int inexact, oldinexact; +#endif +#ifdef USE_BF96 /*{{*/ + BF96 *p10; + ULLong dbhi, dbits, dblo, den, hb, rb, rblo, res, res0, res3, reslo, sres, + sulp, tv0, tv1, tv2, tv3, ulp, ulplo, ulpmask, ures, ureslo, zb; + int eulp, k1, n2, ulpadj, ulpshift; +#else /*}{*/ +#ifndef Sudden_Underflow + ULong x; +#endif + Long L; + U d2, eps; + double ds; + int ieps, ilim0, k0, k_check, try_quick; +#ifndef No_leftright +#ifdef IEEE_Arith + U eps1; +#endif +#endif +#endif /*}}*/ +#ifdef Honor_FLT_ROUNDS /*{*/ + int Rounding; +#ifdef Trust_FLT_ROUNDS /*{{ only define this if FLT_ROUNDS really works! */ + Rounding = Flt_Rounds; +#else /*}{*/ + Rounding = 1; + switch(fegetround()) { + case FE_TOWARDZERO: Rounding = 0; break; + case FE_UPWARD: Rounding = 2; break; + case FE_DOWNWARD: Rounding = 3; + } +#endif /*}}*/ +#endif /*}*/ + + u.d = dd; + if (word0(&u) & Sign_bit) { + /* set sign for everything, including 0's and NaNs */ + *sign = 1; + word0(&u) &= ~Sign_bit; /* clear sign bit */ + } + else + *sign = 0; + +#if defined(IEEE_Arith) + defined(VAX) +#ifdef IEEE_Arith + if ((word0(&u) & Exp_mask) == Exp_mask) +#else + if (word0(&u) == 0x8000) +#endif + { + /* Infinity or NaN */ + *decpt = 9999; +#ifdef IEEE_Arith + if (!word1(&u) && !(word0(&u) & 0xfffff)) + return nrv_alloc("Infinity", buf, blen, rve, 8 MTb); +#endif + return nrv_alloc("NaN", buf, blen, rve, 3 MTb); + } +#endif +#ifdef IBM + dval(&u) += 0; /* normalize */ +#endif + if (!dval(&u)) { + *decpt = 1; + return nrv_alloc("0", buf, blen, rve, 1 MTb); + } + +#ifdef SET_INEXACT +#ifndef USE_BF96 + try_quick = +#endif + oldinexact = get_inexact(); + inexact = 1; +#endif +#ifdef Honor_FLT_ROUNDS + if (Rounding >= 2) { + if (*sign) + Rounding = Rounding == 2 ? 0 : 2; + else + if (Rounding != 2) + Rounding = 0; + } +#endif +#ifdef USE_BF96 /*{{*/ + dbits = (u.LL & 0xfffffffffffffull) << 11; /* fraction bits */ + if ((be = u.LL >> 52)) /* biased exponent; nonzero ==> normal */ { + dbits |= 0x8000000000000000ull; + denorm = ulpadj = 0; + } + else { + denorm = 1; + ulpadj = be + 1; + dbits <<= 1; + if (!(dbits & 0xffffffff00000000ull)) { + dbits <<= 32; + be -= 32; + } + if (!(dbits & 0xffff000000000000ull)) { + dbits <<= 16; + be -= 16; + } + if (!(dbits & 0xff00000000000000ull)) { + dbits <<= 8; + be -= 8; + } + if (!(dbits & 0xf000000000000000ull)) { + dbits <<= 4; + be -= 4; + } + if (!(dbits & 0xc000000000000000ull)) { + dbits <<= 2; + be -= 2; + } + if (!(dbits & 0x8000000000000000ull)) { + dbits <<= 1; + be -= 1; + } + assert(be >= -51); + ulpadj -= be; + } + j = Lhint[be + 51]; + p10 = &pten[j]; + dbhi = dbits >> 32; + dblo = dbits & 0xffffffffull; + i = be - 0x3fe; + if (i < p10->e + || (i == p10->e && (dbhi < p10->b0 || (dbhi == p10->b0 && dblo < p10->b1)))) + --j; + k = j - 342; + + /* now 10^k <= dd < 10^(k+1) */ + +#else /*}{*/ + + b = d2b(&u, &be, &bbits MTb); +#ifdef Sudden_Underflow + i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1)); +#else + if ((i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) { +#endif + dval(&d2) = dval(&u); + word0(&d2) &= Frac_mask1; + word0(&d2) |= Exp_11; +#ifdef IBM + if (j = 11 - hi0bits(word0(&d2) & Frac_mask)) + dval(&d2) /= 1 << j; +#endif + + /* log(x) ~=~ log(1.5) + (x-1.5)/1.5 + * log10(x) = log(x) / log(10) + * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10)) + * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2) + * + * This suggests computing an approximation k to log10(d) by + * + * k = (i - Bias)*0.301029995663981 + * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 ); + * + * We want k to be too large rather than too small. + * The error in the first-order Taylor series approximation + * is in our favor, so we just round up the constant enough + * to compensate for any error in the multiplication of + * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077, + * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14, + * adding 1e-13 to the constant term more than suffices. + * Hence we adjust the constant term to 0.1760912590558. + * (We could get a more accurate k by invoking log10, + * but this is probably not worthwhile.) + */ + + i -= Bias; +#ifdef IBM + i <<= 2; + i += j; +#endif +#ifndef Sudden_Underflow + denorm = 0; + } + else { + /* d is denormalized */ + + i = bbits + be + (Bias + (P-1) - 1); + x = i > 32 ? word0(&u) << (64 - i) | word1(&u) >> (i - 32) + : word1(&u) << (32 - i); + dval(&d2) = x; + word0(&d2) -= 31*Exp_msk1; /* adjust exponent */ + i -= (Bias + (P-1) - 1) + 1; + denorm = 1; + } +#endif + ds = (dval(&d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981; + k = (int)ds; + if (ds < 0. && ds != k) + k--; /* want k = floor(ds) */ + k_check = 1; + if (k >= 0 && k <= Ten_pmax) { + if (dval(&u) < tens[k]) + k--; + k_check = 0; + } + j = bbits - i - 1; + if (j >= 0) { + b2 = 0; + s2 = j; + } + else { + b2 = -j; + s2 = 0; + } + if (k >= 0) { + b5 = 0; + s5 = k; + s2 += k; + } + else { + b2 -= k; + b5 = -k; + s5 = 0; + } +#endif /*}}*/ + if (mode < 0 || mode > 9) + mode = 0; + +#ifndef USE_BF96 +#ifndef SET_INEXACT +#ifdef Check_FLT_ROUNDS + try_quick = Rounding == 1; +#else + try_quick = 1; +#endif +#endif /*SET_INEXACT*/ +#endif /*USE_BF96*/ + + if (mode > 5) { + mode -= 4; +#ifndef USE_BF96 + try_quick = 0; +#endif + } + leftright = 1; + ilim = ilim1 = -1; /* Values for cases 0 and 1; done here to */ + /* silence erroneous "gcc -Wall" warning. */ + switch(mode) { + case 0: + case 1: + i = 18; + ndigits = 0; + break; + case 2: + leftright = 0; + /* fall through */ + case 4: + if (ndigits <= 0) + ndigits = 1; + ilim = ilim1 = i = ndigits; + break; + case 3: + leftright = 0; + /* fall through */ + case 5: + i = ndigits + k + 1; + ilim = i; + ilim1 = i - 1; + if (i <= 0) + i = 1; + } + if (!buf) { + buf = rv_alloc(i MTb); + blen = sizeof(Bigint) + ((1 << ((int*)buf)[-1]) - 1)*sizeof(ULong) - sizeof(int); + } + else if (blen <= (size_t)i) { + buf = 0; + if (rve) + *rve = buf + i; + return buf; + } + s = buf; + + /* Check for special case that d is a normalized power of 2. */ + + spec_case = 0; + if (mode < 2 || (leftright +#ifdef Honor_FLT_ROUNDS + && Rounding == 1 +#endif + )) { + if (!word1(&u) && !(word0(&u) & Bndry_mask) +#ifndef Sudden_Underflow + && word0(&u) & (Exp_mask & ~Exp_msk1) +#endif + ) { + /* The special case */ + spec_case = 1; + } + } + +#ifdef USE_BF96 /*{*/ + b = 0; + if (ilim < 0 && (mode == 3 || mode == 5)) { + S = mhi = 0; + goto no_digits; + } + i = 1; + j = 52 + 0x3ff - be; + ulpshift = 0; + ulplo = 0; + /* Can we do an exact computation with 64-bit integer arithmetic? */ + if (k < 0) { + if (k < -25) + goto toobig; + res = dbits >> 11; + n2 = pfivebits[k1 = -(k + 1)] + 53; + j1 = j; + if (n2 > 61) { + ulpshift = n2 - 61; + if (res & (ulpmask = (1ull << ulpshift) - 1)) + goto toobig; + j -= ulpshift; + res >>= ulpshift; + } + /* Yes. */ + res *= ulp = pfive[k1]; + if (ulpshift) { + ulplo = ulp; + ulp >>= ulpshift; + } + j += k; + if (ilim == 0) { + S = mhi = 0; + if (res > (5ull << j)) + goto one_digit; + goto no_digits; + } + goto no_div; + } + if (ilim == 0 && j + k >= 0) { + S = mhi = 0; + if ((dbits >> 11) > (pfive[k-1] << j)) + goto one_digit; + goto no_digits; + } + if (k <= dtoa_divmax && j + k >= 0) { + /* Another "yes" case -- we will use exact integer arithmetic. */ + use_exact: + Debug(++dtoa_stats[3]); + res = dbits >> 11; /* residual */ + ulp = 1; + if (k <= 0) + goto no_div; + j1 = j + k + 1; + den = pfive[k-i] << (j1 - i); + for(;;) { + dig = res / den; + *s++ = '0' + dig; + if (!(res -= dig*den)) { +#ifdef SET_INEXACT + inexact = 0; + oldinexact = 1; +#endif + goto retc; + } + if (ilim < 0) { + ures = den - res; + if (2*res <= ulp + && (spec_case ? 4*res <= ulp : (2*res < ulp || dig & 1))) + goto ulp_reached; + if (2*ures < ulp) + goto Roundup; + } + else if (i == ilim) { + switch(Rounding) { + case 0: goto retc; + case 2: goto Roundup; + } + ures = 2*res; + if (ures > den + || (ures == den && dig & 1) + || (spec_case && res <= ulp && 2*res >= ulp)) + goto Roundup; + goto retc; + } + if (j1 < ++i) { + res *= 10; + ulp *= 10; + } + else { + if (i > k) + break; + den = pfive[k-i] << (j1 - i); + } + } + no_div: + for(;;) { + dig = den = res >> j; + *s++ = '0' + dig; + if (!(res -= den << j)) { +#ifdef SET_INEXACT + inexact = 0; + oldinexact = 1; +#endif + goto retc; + } + if (ilim < 0) { + ures = (1ull << j) - res; + if (2*res <= ulp + && (spec_case ? 4*res <= ulp : (2*res < ulp || dig & 1))) { + ulp_reached: + if (ures < res + || (ures == res && dig & 1)) + goto Roundup; + goto retc; + } + if (2*ures < ulp) + goto Roundup; + } + --j; + if (i == ilim) { +#ifdef Honor_FLT_ROUNDS + switch(Rounding) { + case 0: goto retc; + case 2: goto Roundup; + } +#endif + hb = 1ull << j; + if (res & hb && (dig & 1 || res & (hb-1))) + goto Roundup; + if (spec_case && res <= ulp && 2*res >= ulp) { + Roundup: + while(*--s == '9') + if (s == buf) { + ++k; + *s++ = '1'; + goto ret1; + } + ++*s++; + goto ret1; + } + goto retc; + } + ++i; + res *= 5; + if (ulpshift) { + ulplo = 5*(ulplo & ulpmask); + ulp = 5*ulp + (ulplo >> ulpshift); + } + else + ulp *= 5; + } + } + toobig: + if (ilim > 28) + goto Fast_failed1; + /* Scale by 10^-k */ + p10 = &pten[342-k]; + tv0 = p10->b2 * dblo; /* rarely matters, but does, e.g., for 9.862818194192001e18 */ + tv1 = p10->b1 * dblo + (tv0 >> 32); + tv2 = p10->b2 * dbhi + (tv1 & 0xffffffffull); + tv3 = p10->b0 * dblo + (tv1>>32) + (tv2>>32); + res3 = p10->b1 * dbhi + (tv3 & 0xffffffffull); + res = p10->b0 * dbhi + (tv3>>32) + (res3>>32); + be += p10->e - 0x3fe; + eulp = j1 = be - 54 + ulpadj; + if (!(res & 0x8000000000000000ull)) { + --be; + res3 <<= 1; + res = (res << 1) | ((res3 & 0x100000000ull) >> 32); + } + res0 = res; /* save for Fast_failed */ +#if !defined(SET_INEXACT) && !defined(NO_DTOA_64) /*{*/ + if (ilim > 19) + goto Fast_failed; + Debug(++dtoa_stats[4]); + assert(be >= 0 && be <= 4); /* be = 0 is rare, but possible, e.g., for 1e20 */ + res >>= 4 - be; + ulp = p10->b0; /* ulp */ + ulp = (ulp << 29) | (p10->b1 >> 3); + /* scaled ulp = ulp * 2^(eulp - 60) */ + /* We maintain 61 bits of the scaled ulp. */ + if (ilim == 0) { + if (!(res & 0x7fffffffffffffeull) + || !((~res) & 0x7fffffffffffffeull)) + goto Fast_failed1; + S = mhi = 0; + if (res >= 0x5000000000000000ull) + goto one_digit; + goto no_digits; + } + rb = 1; /* upper bound on rounding error */ + for(;;++i) { + dig = res >> 60; + *s++ = '0' + dig; + res &= 0xfffffffffffffffull; + if (ilim < 0) { + ures = 0x1000000000000000ull - res; + if (eulp > 0) { + assert(eulp <= 4); + sulp = ulp << (eulp - 1); + if (res <= ures) { + if (res + rb > ures - rb) + goto Fast_failed; + if (res < sulp) + goto retc; + } + else { + if (res - rb <= ures + rb) + goto Fast_failed; + if (ures < sulp) + goto Roundup; + } + } + else { + zb = -(1ull << (eulp + 63)); + if (!(zb & res)) { + sres = res << (1 - eulp); + if (sres < ulp && (!spec_case || 2*sres < ulp)) { + if ((res+rb) << (1 - eulp) >= ulp) + goto Fast_failed; + if (ures < res) { + if (ures + rb >= res - rb) + goto Fast_failed; + goto Roundup; + } + if (ures - rb < res + rb) + goto Fast_failed; + goto retc; + } + } + if (!(zb & ures) && ures << -eulp < ulp) { + if (ures << (1 - eulp) < ulp) + goto Roundup; + goto Fast_failed; + } + } + } + else if (i == ilim) { + ures = 0x1000000000000000ull - res; + if (ures < res) { + if (ures <= rb || res - rb <= ures + rb) { + if (j + k >= 0 && k >= 0 && k <= 27) + goto use_exact1; + goto Fast_failed; + } +#ifdef Honor_FLT_ROUNDS + if (Rounding == 0) + goto retc; +#endif + goto Roundup; + } + if (res <= rb || ures - rb <= res + rb) { + if (j + k >= 0 && k >= 0 && k <= 27) { + use_exact1: + s = buf; + i = 1; + goto use_exact; + } + goto Fast_failed; + } +#ifdef Honor_FLT_ROUNDS + if (Rounding == 2) + goto Roundup; +#endif + goto retc; + } + rb *= 10; + if (rb >= 0x1000000000000000ull) + goto Fast_failed; + res *= 10; + ulp *= 5; + if (ulp & 0x8000000000000000ull) { + eulp += 4; + ulp >>= 3; + } + else { + eulp += 3; + ulp >>= 2; + } + } +#endif /*}*/ +#ifndef NO_BF96 + Fast_failed: +#endif + Debug(++dtoa_stats[5]); + s = buf; + i = 4 - be; + res = res0 >> i; + reslo = 0xffffffffull & res3; + if (i) + reslo = (res0 << (64 - i)) >> 32 | (reslo >> i); + rb = 0; + rblo = 4; /* roundoff bound */ + ulp = p10->b0; /* ulp */ + ulp = (ulp << 29) | (p10->b1 >> 3); + eulp = j1; + for(i = 1;;++i) { + dig = res >> 60; + *s++ = '0' + dig; + res &= 0xfffffffffffffffull; +#ifdef SET_INEXACT + if (!res && !reslo) { + if (!(res3 & 0xffffffffull)) { + inexact = 0; + oldinexact = 1; + } + goto retc; + } +#endif + if (ilim < 0) { + ures = 0x1000000000000000ull - res; + ureslo = 0; + if (reslo) { + ureslo = 0x100000000ull - reslo; + --ures; + } + if (eulp > 0) { + assert(eulp <= 4); + sulp = (ulp << (eulp - 1)) - rb; + if (res <= ures) { + if (res < sulp) { + if (res+rb < ures-rb) + goto retc; + } + } + else if (ures < sulp) { + if (res-rb > ures+rb) + goto Roundup; + } + goto Fast_failed1; + } + else { + zb = -(1ull << (eulp + 60)); + if (!(zb & (res + rb))) { + sres = (res - rb) << (1 - eulp); + if (sres < ulp && (!spec_case || 2*sres < ulp)) { + sres = res << (1 - eulp); + if ((j = eulp + 31) > 0) + sres += (rblo + reslo) >> j; + else + sres += (rblo + reslo) << -j; + if (sres + (rb << (1 - eulp)) >= ulp) + goto Fast_failed1; + if (sres >= ulp) + goto more96; + if (ures < res + || (ures == res && ureslo < reslo)) { + if (ures + rb >= res - rb) + goto Fast_failed1; + goto Roundup; + } + if (ures - rb <= res + rb) + goto Fast_failed1; + goto retc; + } + } + if (!(zb & ures) && (ures-rb) << (1 - eulp) < ulp) { + if ((ures + rb) << (1 - eulp) < ulp) + goto Roundup; + goto Fast_failed1; + } + } + } + else if (i == ilim) { + ures = 0x1000000000000000ull - res; + sres = ureslo = 0; + if (reslo) { + ureslo = 0x100000000ull - reslo; + --ures; + sres = (reslo + rblo) >> 31; + } + sres += 2*rb; + if (ures <= res) { + if (ures <=sres || res - ures <= sres) + goto Fast_failed1; +#ifdef Honor_FLT_ROUNDS + if (Rounding == 0) + goto retc; +#endif + goto Roundup; + } + if (res <= sres || ures - res <= sres) + goto Fast_failed1; +#ifdef Honor_FLT_ROUNDS + if (Rounding == 2) + goto Roundup; +#endif + goto retc; + } + more96: + rblo *= 10; + rb = 10*rb + (rblo >> 32); + rblo &= 0xffffffffull; + if (rb >= 0x1000000000000000ull) + goto Fast_failed1; + reslo *= 10; + res = 10*res + (reslo >> 32); + reslo &= 0xffffffffull; + ulp *= 5; + if (ulp & 0x8000000000000000ull) { + eulp += 4; + ulp >>= 3; + } + else { + eulp += 3; + ulp >>= 2; + } + } + Fast_failed1: + Debug(++dtoa_stats[6]); + S = mhi = mlo = 0; +#ifdef USE_BF96 + b = d2b(&u, &be, &bbits MTb); +#endif + s = buf; + i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1)); + i -= Bias; + if (ulpadj) + i -= ulpadj - 1; + j = bbits - i - 1; + if (j >= 0) { + b2 = 0; + s2 = j; + } + else { + b2 = -j; + s2 = 0; + } + if (k >= 0) { + b5 = 0; + s5 = k; + s2 += k; + } + else { + b2 -= k; + b5 = -k; + s5 = 0; + } +#endif /*}*/ + +#ifdef Honor_FLT_ROUNDS + if (mode > 1 && Rounding != 1) + leftright = 0; +#endif + +#ifndef USE_BF96 /*{*/ + if (ilim >= 0 && ilim <= Quick_max && try_quick) { + + /* Try to get by with floating-point arithmetic. */ + + i = 0; + dval(&d2) = dval(&u); + j1 = -(k0 = k); + ilim0 = ilim; + ieps = 2; /* conservative */ + if (k > 0) { + ds = tens[k&0xf]; + j = k >> 4; + if (j & Bletch) { + /* prevent overflows */ + j &= Bletch - 1; + dval(&u) /= bigtens[n_bigtens-1]; + ieps++; + } + for(; j; j >>= 1, i++) + if (j & 1) { + ieps++; + ds *= bigtens[i]; + } + dval(&u) /= ds; + } + else if (j1 > 0) { + dval(&u) *= tens[j1 & 0xf]; + for(j = j1 >> 4; j; j >>= 1, i++) + if (j & 1) { + ieps++; + dval(&u) *= bigtens[i]; + } + } + if (k_check && dval(&u) < 1. && ilim > 0) { + if (ilim1 <= 0) + goto fast_failed; + ilim = ilim1; + k--; + dval(&u) *= 10.; + ieps++; + } + dval(&eps) = ieps*dval(&u) + 7.; + word0(&eps) -= (P-1)*Exp_msk1; + if (ilim == 0) { + S = mhi = 0; + dval(&u) -= 5.; + if (dval(&u) > dval(&eps)) + goto one_digit; + if (dval(&u) < -dval(&eps)) + goto no_digits; + goto fast_failed; + } +#ifndef No_leftright + if (leftright) { + /* Use Steele & White method of only + * generating digits needed. + */ + dval(&eps) = 0.5/tens[ilim-1] - dval(&eps); +#ifdef IEEE_Arith + if (j1 >= 307) { + eps1.d = 1.01e256; /* 1.01 allows roundoff in the next few lines */ + word0(&eps1) -= Exp_msk1 * (Bias+P-1); + dval(&eps1) *= tens[j1 & 0xf]; + for(i = 0, j = (j1-256) >> 4; j; j >>= 1, i++) + if (j & 1) + dval(&eps1) *= bigtens[i]; + if (eps.d < eps1.d) + eps.d = eps1.d; + if (10. - u.d < 10.*eps.d && eps.d < 1.) { + /* eps.d < 1. excludes trouble with the tiniest denormal */ + *s++ = '1'; + ++k; + goto ret1; + } + } +#endif + for(i = 0;;) { + L = dval(&u); + dval(&u) -= L; + *s++ = '0' + (int)L; + if (1. - dval(&u) < dval(&eps)) + goto bump_up; + if (dval(&u) < dval(&eps)) + goto retc; + if (++i >= ilim) + break; + dval(&eps) *= 10.; + dval(&u) *= 10.; + } + } + else { +#endif + /* Generate ilim digits, then fix them up. */ + dval(&eps) *= tens[ilim-1]; + for(i = 1;; i++, dval(&u) *= 10.) { + L = (Long)(dval(&u)); + if (!(dval(&u) -= L)) + ilim = i; + *s++ = '0' + (int)L; + if (i == ilim) { + if (dval(&u) > 0.5 + dval(&eps)) + goto bump_up; + else if (dval(&u) < 0.5 - dval(&eps)) + goto retc; + break; + } + } +#ifndef No_leftright + } +#endif + fast_failed: + s = buf; + dval(&u) = dval(&d2); + k = k0; + ilim = ilim0; + } + + /* Do we have a "small" integer? */ + + if (be >= 0 && k <= Int_max) { + /* Yes. */ + ds = tens[k]; + if (ndigits < 0 && ilim <= 0) { + S = mhi = 0; + if (ilim < 0 || dval(&u) <= 5*ds) + goto no_digits; + goto one_digit; + } + for(i = 1;; i++, dval(&u) *= 10.) { + L = (Long)(dval(&u) / ds); + dval(&u) -= L*ds; +#ifdef Check_FLT_ROUNDS + /* If FLT_ROUNDS == 2, L will usually be high by 1 */ + if (dval(&u) < 0) { + L--; + dval(&u) += ds; + } +#endif + *s++ = '0' + (int)L; + if (!dval(&u)) { +#ifdef SET_INEXACT + inexact = 0; +#endif + break; + } + if (i == ilim) { +#ifdef Honor_FLT_ROUNDS + if (mode > 1) + switch(Rounding) { + case 0: goto retc; + case 2: goto bump_up; + } +#endif + dval(&u) += dval(&u); +#ifdef ROUND_BIASED + if (dval(&u) >= ds) +#else + if (dval(&u) > ds || (dval(&u) == ds && L & 1)) +#endif + { + bump_up: + while(*--s == '9') + if (s == buf) { + k++; + *s = '0'; + break; + } + ++*s++; + } + break; + } + } + goto retc; + } + +#endif /*}*/ + m2 = b2; + m5 = b5; + mhi = mlo = 0; + if (leftright) { + i = +#ifndef Sudden_Underflow + denorm ? be + (Bias + (P-1) - 1 + 1) : +#endif +#ifdef IBM + 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3); +#else + 1 + P - bbits; +#endif + b2 += i; + s2 += i; + mhi = i2b(1 MTb); + } + if (m2 > 0 && s2 > 0) { + i = m2 < s2 ? m2 : s2; + b2 -= i; + m2 -= i; + s2 -= i; + } + if (b5 > 0) { + if (leftright) { + if (m5 > 0) { + mhi = pow5mult(mhi, m5 MTb); + b1 = mult(mhi, b MTb); + Bfree(b MTb); + b = b1; + } + if ((j = b5 - m5)) + b = pow5mult(b, j MTb); + } + else + b = pow5mult(b, b5 MTb); + } + S = i2b(1 MTb); + if (s5 > 0) + S = pow5mult(S, s5 MTb); + + if (spec_case) { + b2 += Log2P; + s2 += Log2P; + } + + /* Arrange for convenient computation of quotients: + * shift left if necessary so divisor has 4 leading 0 bits. + * + * Perhaps we should just compute leading 28 bits of S once + * and for all and pass them and a shift to quorem, so it + * can do shifts and ors to compute the numerator for q. + */ + i = dshift(S, s2); + b2 += i; + m2 += i; + s2 += i; + if (b2 > 0) + b = lshift(b, b2 MTb); + if (s2 > 0) + S = lshift(S, s2 MTb); +#ifndef USE_BF96 + if (k_check) { + if (cmp(b,S) < 0) { + k--; + b = multadd(b, 10, 0 MTb); /* we botched the k estimate */ + if (leftright) + mhi = multadd(mhi, 10, 0 MTb); + ilim = ilim1; + } + } +#endif + if (ilim <= 0 && (mode == 3 || mode == 5)) { + if (ilim < 0 || cmp(b,S = multadd(S,5,0 MTb)) <= 0) { + /* no digits, fcvt style */ + no_digits: + k = -1 - ndigits; + goto ret; + } + one_digit: + *s++ = '1'; + ++k; + goto ret; + } + if (leftright) { + if (m2 > 0) + mhi = lshift(mhi, m2 MTb); + + /* Compute mlo -- check for special case + * that d is a normalized power of 2. + */ + + mlo = mhi; + if (spec_case) { + mhi = Balloc(mhi->k MTb); + Bcopy(mhi, mlo); + mhi = lshift(mhi, Log2P MTb); + } + + for(i = 1;;i++) { + dig = quorem(b,S) + '0'; + /* Do we yet have the shortest decimal string + * that will round to d? + */ + j = cmp(b, mlo); + delta = diff(S, mhi MTb); + j1 = delta->sign ? 1 : cmp(b, delta); + Bfree(delta MTb); +#ifndef ROUND_BIASED + if (j1 == 0 && mode != 1 && !(word1(&u) & 1) +#ifdef Honor_FLT_ROUNDS + && (mode <= 1 || Rounding >= 1) +#endif + ) { + if (dig == '9') + goto round_9_up; + if (j > 0) + dig++; +#ifdef SET_INEXACT + else if (!b->x[0] && b->wds <= 1) + inexact = 0; +#endif + *s++ = dig; + goto ret; + } +#endif + if (j < 0 || (j == 0 && mode != 1 +#ifndef ROUND_BIASED + && !(word1(&u) & 1) +#endif + )) { + if (!b->x[0] && b->wds <= 1) { +#ifdef SET_INEXACT + inexact = 0; +#endif + goto accept_dig; + } +#ifdef Honor_FLT_ROUNDS + if (mode > 1) + switch(Rounding) { + case 0: goto accept_dig; + case 2: goto keep_dig; + } +#endif /*Honor_FLT_ROUNDS*/ + if (j1 > 0) { + b = lshift(b, 1 MTb); + j1 = cmp(b, S); +#ifdef ROUND_BIASED + if (j1 >= 0 /*)*/ +#else + if ((j1 > 0 || (j1 == 0 && dig & 1)) +#endif + && dig++ == '9') + goto round_9_up; + } + accept_dig: + *s++ = dig; + goto ret; + } + if (j1 > 0) { +#ifdef Honor_FLT_ROUNDS + if (!Rounding && mode > 1) + goto accept_dig; +#endif + if (dig == '9') { /* possible if i == 1 */ + round_9_up: + *s++ = '9'; + goto roundoff; + } + *s++ = dig + 1; + goto ret; + } +#ifdef Honor_FLT_ROUNDS + keep_dig: +#endif + *s++ = dig; + if (i == ilim) + break; + b = multadd(b, 10, 0 MTb); + if (mlo == mhi) + mlo = mhi = multadd(mhi, 10, 0 MTb); + else { + mlo = multadd(mlo, 10, 0 MTb); + mhi = multadd(mhi, 10, 0 MTb); + } + } + } + else + for(i = 1;; i++) { + dig = quorem(b,S) + '0'; + *s++ = dig; + if (!b->x[0] && b->wds <= 1) { +#ifdef SET_INEXACT + inexact = 0; +#endif + goto ret; + } + if (i >= ilim) + break; + b = multadd(b, 10, 0 MTb); + } + + /* Round off last digit */ + +#ifdef Honor_FLT_ROUNDS + if (mode > 1) + switch(Rounding) { + case 0: goto ret; + case 2: goto roundoff; + } +#endif + b = lshift(b, 1 MTb); + j = cmp(b, S); +#ifdef ROUND_BIASED + if (j >= 0) +#else + if (j > 0 || (j == 0 && dig & 1)) +#endif + { + roundoff: + while(*--s == '9') + if (s == buf) { + k++; + *s++ = '1'; + goto ret; + } + ++*s++; + } + ret: + Bfree(S MTb); + if (mhi) { + if (mlo && mlo != mhi) + Bfree(mlo MTb); + Bfree(mhi MTb); + } + retc: + while(s > buf && s[-1] == '0') + --s; + ret1: + if (b) + Bfree(b MTb); + *s = 0; + *decpt = k + 1; + if (rve) + *rve = s; +#ifdef SET_INEXACT + if (inexact) { + if (!oldinexact) { + word0(&u) = Exp_1 + (70 << Exp_shift); + word1(&u) = 0; + dval(&u) += 1.; + } + } + else if (!oldinexact) + clear_inexact(); +#endif + return buf; + } + + char * +dtoa(double dd, int mode, int ndigits, int *decpt, int *sign, char **rve) +{ + /* Sufficient space is allocated to the return value + to hold the suppressed trailing zeros. + See dtoa_r() above for details on the other arguments. + */ +#ifndef MULTIPLE_THREADS + if (dtoa_result) + freedtoa(dtoa_result); +#endif + return dtoa_r(dd, mode, ndigits, decpt, sign, rve, 0, 0); + } + +#ifdef __cplusplus +} +#endif |