mirror of
https://github.com/lemire/fast_double_parser.git
synced 2025-04-03 20:04:57 +00:00
1327 lines
No EOL
64 KiB
C++
1327 lines
No EOL
64 KiB
C++
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#ifndef FAST_DOUBLE_PARSER_H
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#define FAST_DOUBLE_PARSER_H
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#include <cfloat>
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#include <cinttypes>
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#include <cmath>
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#include <cstdint>
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#include <cstdio>
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#include <cstdlib>
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#include <cstring>
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namespace fast_double_parser {
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#define FASTFLOAT_SMALLEST_POWER -325
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#define FASTFLOAT_LARGEST_POWER 308
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#ifdef _MSC_VER
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#ifndef really_inline
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#define really_inline __forceinline
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#endif // really_inline
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#ifndef unlikely
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#define unlikely(x) x
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#endif // unlikely
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#else // _MSC_VER
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#ifndef unlikely
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#define unlikely(x) __builtin_expect(!!(x), 0)
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#endif // unlikely
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#ifndef really_inline
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#define really_inline __attribute__((always_inline))
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#endif // really_inline
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#endif // _MSC_VER
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/* result might be undefined when input_num is zero */
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int leading_zeroes(uint64_t input_num) {
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#ifdef _MSC_VER
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unsigned long leading_zero = 0;
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// Search the mask data from most significant bit (MSB)
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// to least significant bit (LSB) for a set bit (1).
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if (_BitScanReverse64(&leading_zero, input_num))
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return (int)(63 - leading_zero);
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else
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return 64;
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#else
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return __builtin_clzll(input_num);
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#endif // _MSC_VER
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}
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// Precomputed powers of ten from 10^0 to 10^22. These
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// can be represented exactly using the double type.
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static const double power_of_ten[] = {
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1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11,
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1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, 1e20, 1e21, 1e22};
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static inline bool is_integer(char c) {
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return (c >= '0' && c <= '9');
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// this gets compiled to (uint8_t)(c - '0') <= 9 on all decent compilers
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}
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// the mantissas of powers of ten from -308 to 308, extended out to sixty four
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// bits
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// This struct will likely get padded to 16 bytes.
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typedef struct {
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uint64_t mantissa;
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int32_t exp;
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} components;
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// The array power_of_ten_components contain the powers of ten approximated
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// as a 64-bit mantissa, with an exponent part. It goes from 10^
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// FASTFLOAT_SMALLEST_POWER to
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// 10^FASTFLOAT_LARGEST_POWER (inclusively). The mantissa is truncated, and
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// never rounded up.
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// Uses about 10KB.
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static const components power_of_ten_components[] = {
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{0xa5ced43b7e3e9188L, 7}, {0xcf42894a5dce35eaL, 10},
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{0x818995ce7aa0e1b2L, 14}, {0xa1ebfb4219491a1fL, 17},
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{0xca66fa129f9b60a6L, 20}, {0xfd00b897478238d0L, 23},
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{0x9e20735e8cb16382L, 27}, {0xc5a890362fddbc62L, 30},
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{0xf712b443bbd52b7bL, 33}, {0x9a6bb0aa55653b2dL, 37},
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{0xc1069cd4eabe89f8L, 40}, {0xf148440a256e2c76L, 43},
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{0x96cd2a865764dbcaL, 47}, {0xbc807527ed3e12bcL, 50},
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{0xeba09271e88d976bL, 53}, {0x93445b8731587ea3L, 57},
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{0xb8157268fdae9e4cL, 60}, {0xe61acf033d1a45dfL, 63},
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{0x8fd0c16206306babL, 67}, {0xb3c4f1ba87bc8696L, 70},
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{0xe0b62e2929aba83cL, 73}, {0x8c71dcd9ba0b4925L, 77},
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{0xaf8e5410288e1b6fL, 80}, {0xdb71e91432b1a24aL, 83},
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{0x892731ac9faf056eL, 87}, {0xab70fe17c79ac6caL, 90},
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{0xd64d3d9db981787dL, 93}, {0x85f0468293f0eb4eL, 97},
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{0xa76c582338ed2621L, 100}, {0xd1476e2c07286faaL, 103},
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{0x82cca4db847945caL, 107}, {0xa37fce126597973cL, 110},
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{0xcc5fc196fefd7d0cL, 113}, {0xff77b1fcbebcdc4fL, 116},
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{0x9faacf3df73609b1L, 120}, {0xc795830d75038c1dL, 123},
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{0xf97ae3d0d2446f25L, 126}, {0x9becce62836ac577L, 130},
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{0xc2e801fb244576d5L, 133}, {0xf3a20279ed56d48aL, 136},
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{0x9845418c345644d6L, 140}, {0xbe5691ef416bd60cL, 143},
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{0xedec366b11c6cb8fL, 146}, {0x94b3a202eb1c3f39L, 150},
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{0xb9e08a83a5e34f07L, 153}, {0xe858ad248f5c22c9L, 156},
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{0x91376c36d99995beL, 160}, {0xb58547448ffffb2dL, 163},
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{0xe2e69915b3fff9f9L, 166}, {0x8dd01fad907ffc3bL, 170},
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{0xb1442798f49ffb4aL, 173}, {0xdd95317f31c7fa1dL, 176},
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{0x8a7d3eef7f1cfc52L, 180}, {0xad1c8eab5ee43b66L, 183},
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{0xd863b256369d4a40L, 186}, {0x873e4f75e2224e68L, 190},
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{0xa90de3535aaae202L, 193}, {0xd3515c2831559a83L, 196},
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{0x8412d9991ed58091L, 200}, {0xa5178fff668ae0b6L, 203},
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{0xce5d73ff402d98e3L, 206}, {0x80fa687f881c7f8eL, 210},
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{0xa139029f6a239f72L, 213}, {0xc987434744ac874eL, 216},
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{0xfbe9141915d7a922L, 219}, {0x9d71ac8fada6c9b5L, 223},
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{0xc4ce17b399107c22L, 226}, {0xf6019da07f549b2bL, 229},
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{0x99c102844f94e0fbL, 233}, {0xc0314325637a1939L, 236},
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{0xf03d93eebc589f88L, 239}, {0x96267c7535b763b5L, 243},
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{0xbbb01b9283253ca2L, 246}, {0xea9c227723ee8bcbL, 249},
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{0x92a1958a7675175fL, 253}, {0xb749faed14125d36L, 256},
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{0xe51c79a85916f484L, 259}, {0x8f31cc0937ae58d2L, 263},
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{0xb2fe3f0b8599ef07L, 266}, {0xdfbdcece67006ac9L, 269},
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{0x8bd6a141006042bdL, 273}, {0xaecc49914078536dL, 276},
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{0xda7f5bf590966848L, 279}, {0x888f99797a5e012dL, 283},
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{0xaab37fd7d8f58178L, 286}, {0xd5605fcdcf32e1d6L, 289},
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{0x855c3be0a17fcd26L, 293}, {0xa6b34ad8c9dfc06fL, 296},
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{0xd0601d8efc57b08bL, 299}, {0x823c12795db6ce57L, 303},
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{0xa2cb1717b52481edL, 306}, {0xcb7ddcdda26da268L, 309},
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{0xfe5d54150b090b02L, 312}, {0x9efa548d26e5a6e1L, 316},
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{0xc6b8e9b0709f109aL, 319}, {0xf867241c8cc6d4c0L, 322},
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{0x9b407691d7fc44f8L, 326}, {0xc21094364dfb5636L, 329},
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{0xf294b943e17a2bc4L, 332}, {0x979cf3ca6cec5b5aL, 336},
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{0xbd8430bd08277231L, 339}, {0xece53cec4a314ebdL, 342},
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{0x940f4613ae5ed136L, 346}, {0xb913179899f68584L, 349},
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{0xe757dd7ec07426e5L, 352}, {0x9096ea6f3848984fL, 356},
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{0xb4bca50b065abe63L, 359}, {0xe1ebce4dc7f16dfbL, 362},
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{0x8d3360f09cf6e4bdL, 366}, {0xb080392cc4349decL, 369},
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{0xdca04777f541c567L, 372}, {0x89e42caaf9491b60L, 376},
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{0xac5d37d5b79b6239L, 379}, {0xd77485cb25823ac7L, 382},
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{0x86a8d39ef77164bcL, 386}, {0xa8530886b54dbdebL, 389},
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{0xd267caa862a12d66L, 392}, {0x8380dea93da4bc60L, 396},
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{0xa46116538d0deb78L, 399}, {0xcd795be870516656L, 402},
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{0x806bd9714632dff6L, 406}, {0xa086cfcd97bf97f3L, 409},
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{0xc8a883c0fdaf7df0L, 412}, {0xfad2a4b13d1b5d6cL, 415},
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{0x9cc3a6eec6311a63L, 419}, {0xc3f490aa77bd60fcL, 422},
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{0xf4f1b4d515acb93bL, 425}, {0x991711052d8bf3c5L, 429},
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{0xbf5cd54678eef0b6L, 432}, {0xef340a98172aace4L, 435},
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{0x9580869f0e7aac0eL, 439}, {0xbae0a846d2195712L, 442},
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{0xe998d258869facd7L, 445}, {0x91ff83775423cc06L, 449},
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{0xb67f6455292cbf08L, 452}, {0xe41f3d6a7377eecaL, 455},
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{0x8e938662882af53eL, 459}, {0xb23867fb2a35b28dL, 462},
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{0xdec681f9f4c31f31L, 465}, {0x8b3c113c38f9f37eL, 469},
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{0xae0b158b4738705eL, 472}, {0xd98ddaee19068c76L, 475},
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{0x87f8a8d4cfa417c9L, 479}, {0xa9f6d30a038d1dbcL, 482},
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{0xd47487cc8470652bL, 485}, {0x84c8d4dfd2c63f3bL, 489},
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{0xa5fb0a17c777cf09L, 492}, {0xcf79cc9db955c2ccL, 495},
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{0x81ac1fe293d599bfL, 499}, {0xa21727db38cb002fL, 502},
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{0xca9cf1d206fdc03bL, 505}, {0xfd442e4688bd304aL, 508},
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{0x9e4a9cec15763e2eL, 512}, {0xc5dd44271ad3cdbaL, 515},
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{0xf7549530e188c128L, 518}, {0x9a94dd3e8cf578b9L, 522},
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{0xc13a148e3032d6e7L, 525}, {0xf18899b1bc3f8ca1L, 528},
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{0x96f5600f15a7b7e5L, 532}, {0xbcb2b812db11a5deL, 535},
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{0xebdf661791d60f56L, 538}, {0x936b9fcebb25c995L, 542},
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{0xb84687c269ef3bfbL, 545}, {0xe65829b3046b0afaL, 548},
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{0x8ff71a0fe2c2e6dcL, 552}, {0xb3f4e093db73a093L, 555},
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{0xe0f218b8d25088b8L, 558}, {0x8c974f7383725573L, 562},
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{0xafbd2350644eeacfL, 565}, {0xdbac6c247d62a583L, 568},
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{0x894bc396ce5da772L, 572}, {0xab9eb47c81f5114fL, 575},
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{0xd686619ba27255a2L, 578}, {0x8613fd0145877585L, 582},
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{0xa798fc4196e952e7L, 585}, {0xd17f3b51fca3a7a0L, 588},
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{0x82ef85133de648c4L, 592}, {0xa3ab66580d5fdaf5L, 595},
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{0xcc963fee10b7d1b3L, 598}, {0xffbbcfe994e5c61fL, 601},
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{0x9fd561f1fd0f9bd3L, 605}, {0xc7caba6e7c5382c8L, 608},
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{0xf9bd690a1b68637bL, 611}, {0x9c1661a651213e2dL, 615},
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{0xc31bfa0fe5698db8L, 618}, {0xf3e2f893dec3f126L, 621},
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{0x986ddb5c6b3a76b7L, 625}, {0xbe89523386091465L, 628},
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{0xee2ba6c0678b597fL, 631}, {0x94db483840b717efL, 635},
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{0xba121a4650e4ddebL, 638}, {0xe896a0d7e51e1566L, 641},
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{0x915e2486ef32cd60L, 645}, {0xb5b5ada8aaff80b8L, 648},
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{0xe3231912d5bf60e6L, 651}, {0x8df5efabc5979c8fL, 655},
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{0xb1736b96b6fd83b3L, 658}, {0xddd0467c64bce4a0L, 661},
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{0x8aa22c0dbef60ee4L, 665}, {0xad4ab7112eb3929dL, 668},
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{0xd89d64d57a607744L, 671}, {0x87625f056c7c4a8bL, 675},
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{0xa93af6c6c79b5d2dL, 678}, {0xd389b47879823479L, 681},
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{0x843610cb4bf160cbL, 685}, {0xa54394fe1eedb8feL, 688},
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{0xce947a3da6a9273eL, 691}, {0x811ccc668829b887L, 695},
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{0xa163ff802a3426a8L, 698}, {0xc9bcff6034c13052L, 701},
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{0xfc2c3f3841f17c67L, 704}, {0x9d9ba7832936edc0L, 708},
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{0xc5029163f384a931L, 711}, {0xf64335bcf065d37dL, 714},
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{0x99ea0196163fa42eL, 718}, {0xc06481fb9bcf8d39L, 721},
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{0xf07da27a82c37088L, 724}, {0x964e858c91ba2655L, 728},
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{0xbbe226efb628afeaL, 731}, {0xeadab0aba3b2dbe5L, 734},
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{0x92c8ae6b464fc96fL, 738}, {0xb77ada0617e3bbcbL, 741},
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{0xe55990879ddcaabdL, 744}, {0x8f57fa54c2a9eab6L, 748},
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{0xb32df8e9f3546564L, 751}, {0xdff9772470297ebdL, 754},
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{0x8bfbea76c619ef36L, 758}, {0xaefae51477a06b03L, 761},
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{0xdab99e59958885c4L, 764}, {0x88b402f7fd75539bL, 768},
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{0xaae103b5fcd2a881L, 771}, {0xd59944a37c0752a2L, 774},
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{0x857fcae62d8493a5L, 778}, {0xa6dfbd9fb8e5b88eL, 781},
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{0xd097ad07a71f26b2L, 784}, {0x825ecc24c873782fL, 788},
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{0xa2f67f2dfa90563bL, 791}, {0xcbb41ef979346bcaL, 794},
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{0xfea126b7d78186bcL, 797}, {0x9f24b832e6b0f436L, 801},
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{0xc6ede63fa05d3143L, 804}, {0xf8a95fcf88747d94L, 807},
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{0x9b69dbe1b548ce7cL, 811}, {0xc24452da229b021bL, 814},
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{0xf2d56790ab41c2a2L, 817}, {0x97c560ba6b0919a5L, 821},
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{0xbdb6b8e905cb600fL, 824}, {0xed246723473e3813L, 827},
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{0x9436c0760c86e30bL, 831}, {0xb94470938fa89bceL, 834},
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{0xe7958cb87392c2c2L, 837}, {0x90bd77f3483bb9b9L, 841},
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{0xb4ecd5f01a4aa828L, 844}, {0xe2280b6c20dd5232L, 847},
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{0x8d590723948a535fL, 851}, {0xb0af48ec79ace837L, 854},
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{0xdcdb1b2798182244L, 857}, {0x8a08f0f8bf0f156bL, 861},
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{0xac8b2d36eed2dac5L, 864}, {0xd7adf884aa879177L, 867},
|
|
{0x86ccbb52ea94baeaL, 871}, {0xa87fea27a539e9a5L, 874},
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|
{0xd29fe4b18e88640eL, 877}, {0x83a3eeeef9153e89L, 881},
|
|
{0xa48ceaaab75a8e2bL, 884}, {0xcdb02555653131b6L, 887},
|
|
{0x808e17555f3ebf11L, 891}, {0xa0b19d2ab70e6ed6L, 894},
|
|
{0xc8de047564d20a8bL, 897}, {0xfb158592be068d2eL, 900},
|
|
{0x9ced737bb6c4183dL, 904}, {0xc428d05aa4751e4cL, 907},
|
|
{0xf53304714d9265dfL, 910}, {0x993fe2c6d07b7fabL, 914},
|
|
{0xbf8fdb78849a5f96L, 917}, {0xef73d256a5c0f77cL, 920},
|
|
{0x95a8637627989aadL, 924}, {0xbb127c53b17ec159L, 927},
|
|
{0xe9d71b689dde71afL, 930}, {0x9226712162ab070dL, 934},
|
|
{0xb6b00d69bb55c8d1L, 937}, {0xe45c10c42a2b3b05L, 940},
|
|
{0x8eb98a7a9a5b04e3L, 944}, {0xb267ed1940f1c61cL, 947},
|
|
{0xdf01e85f912e37a3L, 950}, {0x8b61313bbabce2c6L, 954},
|
|
{0xae397d8aa96c1b77L, 957}, {0xd9c7dced53c72255L, 960},
|
|
{0x881cea14545c7575L, 964}, {0xaa242499697392d2L, 967},
|
|
{0xd4ad2dbfc3d07787L, 970}, {0x84ec3c97da624ab4L, 974},
|
|
{0xa6274bbdd0fadd61L, 977}, {0xcfb11ead453994baL, 980},
|
|
{0x81ceb32c4b43fcf4L, 984}, {0xa2425ff75e14fc31L, 987},
|
|
{0xcad2f7f5359a3b3eL, 990}, {0xfd87b5f28300ca0dL, 993},
|
|
{0x9e74d1b791e07e48L, 997}, {0xc612062576589ddaL, 1000},
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|
{0xf79687aed3eec551L, 1003}, {0x9abe14cd44753b52L, 1007},
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|
{0xc16d9a0095928a27L, 1010}, {0xf1c90080baf72cb1L, 1013},
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|
{0x971da05074da7beeL, 1017}, {0xbce5086492111aeaL, 1020},
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|
{0xec1e4a7db69561a5L, 1023}, {0x9392ee8e921d5d07L, 1027},
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|
{0xb877aa3236a4b449L, 1030}, {0xe69594bec44de15bL, 1033},
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|
{0x901d7cf73ab0acd9L, 1037}, {0xb424dc35095cd80fL, 1040},
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|
{0xe12e13424bb40e13L, 1043}, {0x8cbccc096f5088cbL, 1047},
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|
{0xafebff0bcb24aafeL, 1050}, {0xdbe6fecebdedd5beL, 1053},
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|
{0x89705f4136b4a597L, 1057}, {0xabcc77118461cefcL, 1060},
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|
{0xd6bf94d5e57a42bcL, 1063}, {0x8637bd05af6c69b5L, 1067},
|
|
{0xa7c5ac471b478423L, 1070}, {0xd1b71758e219652bL, 1073},
|
|
{0x83126e978d4fdf3bL, 1077}, {0xa3d70a3d70a3d70aL, 1080},
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|
{0xccccccccccccccccL, 1083}, {0x8000000000000000L, 1087},
|
|
{0xa000000000000000L, 1090}, {0xc800000000000000L, 1093},
|
|
{0xfa00000000000000L, 1096}, {0x9c40000000000000L, 1100},
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|
{0xc350000000000000L, 1103}, {0xf424000000000000L, 1106},
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|
{0x9896800000000000L, 1110}, {0xbebc200000000000L, 1113},
|
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{0xee6b280000000000L, 1116}, {0x9502f90000000000L, 1120},
|
|
{0xba43b74000000000L, 1123}, {0xe8d4a51000000000L, 1126},
|
|
{0x9184e72a00000000L, 1130}, {0xb5e620f480000000L, 1133},
|
|
{0xe35fa931a0000000L, 1136}, {0x8e1bc9bf04000000L, 1140},
|
|
{0xb1a2bc2ec5000000L, 1143}, {0xde0b6b3a76400000L, 1146},
|
|
{0x8ac7230489e80000L, 1150}, {0xad78ebc5ac620000L, 1153},
|
|
{0xd8d726b7177a8000L, 1156}, {0x878678326eac9000L, 1160},
|
|
{0xa968163f0a57b400L, 1163}, {0xd3c21bcecceda100L, 1166},
|
|
{0x84595161401484a0L, 1170}, {0xa56fa5b99019a5c8L, 1173},
|
|
{0xcecb8f27f4200f3aL, 1176}, {0x813f3978f8940984L, 1180},
|
|
{0xa18f07d736b90be5L, 1183}, {0xc9f2c9cd04674edeL, 1186},
|
|
{0xfc6f7c4045812296L, 1189}, {0x9dc5ada82b70b59dL, 1193},
|
|
{0xc5371912364ce305L, 1196}, {0xf684df56c3e01bc6L, 1199},
|
|
{0x9a130b963a6c115cL, 1203}, {0xc097ce7bc90715b3L, 1206},
|
|
{0xf0bdc21abb48db20L, 1209}, {0x96769950b50d88f4L, 1213},
|
|
{0xbc143fa4e250eb31L, 1216}, {0xeb194f8e1ae525fdL, 1219},
|
|
{0x92efd1b8d0cf37beL, 1223}, {0xb7abc627050305adL, 1226},
|
|
{0xe596b7b0c643c719L, 1229}, {0x8f7e32ce7bea5c6fL, 1233},
|
|
{0xb35dbf821ae4f38bL, 1236}, {0xe0352f62a19e306eL, 1239},
|
|
{0x8c213d9da502de45L, 1243}, {0xaf298d050e4395d6L, 1246},
|
|
{0xdaf3f04651d47b4cL, 1249}, {0x88d8762bf324cd0fL, 1253},
|
|
{0xab0e93b6efee0053L, 1256}, {0xd5d238a4abe98068L, 1259},
|
|
{0x85a36366eb71f041L, 1263}, {0xa70c3c40a64e6c51L, 1266},
|
|
{0xd0cf4b50cfe20765L, 1269}, {0x82818f1281ed449fL, 1273},
|
|
{0xa321f2d7226895c7L, 1276}, {0xcbea6f8ceb02bb39L, 1279},
|
|
{0xfee50b7025c36a08L, 1282}, {0x9f4f2726179a2245L, 1286},
|
|
{0xc722f0ef9d80aad6L, 1289}, {0xf8ebad2b84e0d58bL, 1292},
|
|
{0x9b934c3b330c8577L, 1296}, {0xc2781f49ffcfa6d5L, 1299},
|
|
{0xf316271c7fc3908aL, 1302}, {0x97edd871cfda3a56L, 1306},
|
|
{0xbde94e8e43d0c8ecL, 1309}, {0xed63a231d4c4fb27L, 1312},
|
|
{0x945e455f24fb1cf8L, 1316}, {0xb975d6b6ee39e436L, 1319},
|
|
{0xe7d34c64a9c85d44L, 1322}, {0x90e40fbeea1d3a4aL, 1326},
|
|
{0xb51d13aea4a488ddL, 1329}, {0xe264589a4dcdab14L, 1332},
|
|
{0x8d7eb76070a08aecL, 1336}, {0xb0de65388cc8ada8L, 1339},
|
|
{0xdd15fe86affad912L, 1342}, {0x8a2dbf142dfcc7abL, 1346},
|
|
{0xacb92ed9397bf996L, 1349}, {0xd7e77a8f87daf7fbL, 1352},
|
|
{0x86f0ac99b4e8dafdL, 1356}, {0xa8acd7c0222311bcL, 1359},
|
|
{0xd2d80db02aabd62bL, 1362}, {0x83c7088e1aab65dbL, 1366},
|
|
{0xa4b8cab1a1563f52L, 1369}, {0xcde6fd5e09abcf26L, 1372},
|
|
{0x80b05e5ac60b6178L, 1376}, {0xa0dc75f1778e39d6L, 1379},
|
|
{0xc913936dd571c84cL, 1382}, {0xfb5878494ace3a5fL, 1385},
|
|
{0x9d174b2dcec0e47bL, 1389}, {0xc45d1df942711d9aL, 1392},
|
|
{0xf5746577930d6500L, 1395}, {0x9968bf6abbe85f20L, 1399},
|
|
{0xbfc2ef456ae276e8L, 1402}, {0xefb3ab16c59b14a2L, 1405},
|
|
{0x95d04aee3b80ece5L, 1409}, {0xbb445da9ca61281fL, 1412},
|
|
{0xea1575143cf97226L, 1415}, {0x924d692ca61be758L, 1419},
|
|
{0xb6e0c377cfa2e12eL, 1422}, {0xe498f455c38b997aL, 1425},
|
|
{0x8edf98b59a373fecL, 1429}, {0xb2977ee300c50fe7L, 1432},
|
|
{0xdf3d5e9bc0f653e1L, 1435}, {0x8b865b215899f46cL, 1439},
|
|
{0xae67f1e9aec07187L, 1442}, {0xda01ee641a708de9L, 1445},
|
|
{0x884134fe908658b2L, 1449}, {0xaa51823e34a7eedeL, 1452},
|
|
{0xd4e5e2cdc1d1ea96L, 1455}, {0x850fadc09923329eL, 1459},
|
|
{0xa6539930bf6bff45L, 1462}, {0xcfe87f7cef46ff16L, 1465},
|
|
{0x81f14fae158c5f6eL, 1469}, {0xa26da3999aef7749L, 1472},
|
|
{0xcb090c8001ab551cL, 1475}, {0xfdcb4fa002162a63L, 1478},
|
|
{0x9e9f11c4014dda7eL, 1482}, {0xc646d63501a1511dL, 1485},
|
|
{0xf7d88bc24209a565L, 1488}, {0x9ae757596946075fL, 1492},
|
|
{0xc1a12d2fc3978937L, 1495}, {0xf209787bb47d6b84L, 1498},
|
|
{0x9745eb4d50ce6332L, 1502}, {0xbd176620a501fbffL, 1505},
|
|
{0xec5d3fa8ce427affL, 1508}, {0x93ba47c980e98cdfL, 1512},
|
|
{0xb8a8d9bbe123f017L, 1515}, {0xe6d3102ad96cec1dL, 1518},
|
|
{0x9043ea1ac7e41392L, 1522}, {0xb454e4a179dd1877L, 1525},
|
|
{0xe16a1dc9d8545e94L, 1528}, {0x8ce2529e2734bb1dL, 1532},
|
|
{0xb01ae745b101e9e4L, 1535}, {0xdc21a1171d42645dL, 1538},
|
|
{0x899504ae72497ebaL, 1542}, {0xabfa45da0edbde69L, 1545},
|
|
{0xd6f8d7509292d603L, 1548}, {0x865b86925b9bc5c2L, 1552},
|
|
{0xa7f26836f282b732L, 1555}, {0xd1ef0244af2364ffL, 1558},
|
|
{0x8335616aed761f1fL, 1562}, {0xa402b9c5a8d3a6e7L, 1565},
|
|
{0xcd036837130890a1L, 1568}, {0x802221226be55a64L, 1572},
|
|
{0xa02aa96b06deb0fdL, 1575}, {0xc83553c5c8965d3dL, 1578},
|
|
{0xfa42a8b73abbf48cL, 1581}, {0x9c69a97284b578d7L, 1585},
|
|
{0xc38413cf25e2d70dL, 1588}, {0xf46518c2ef5b8cd1L, 1591},
|
|
{0x98bf2f79d5993802L, 1595}, {0xbeeefb584aff8603L, 1598},
|
|
{0xeeaaba2e5dbf6784L, 1601}, {0x952ab45cfa97a0b2L, 1605},
|
|
{0xba756174393d88dfL, 1608}, {0xe912b9d1478ceb17L, 1611},
|
|
{0x91abb422ccb812eeL, 1615}, {0xb616a12b7fe617aaL, 1618},
|
|
{0xe39c49765fdf9d94L, 1621}, {0x8e41ade9fbebc27dL, 1625},
|
|
{0xb1d219647ae6b31cL, 1628}, {0xde469fbd99a05fe3L, 1631},
|
|
{0x8aec23d680043beeL, 1635}, {0xada72ccc20054ae9L, 1638},
|
|
{0xd910f7ff28069da4L, 1641}, {0x87aa9aff79042286L, 1645},
|
|
{0xa99541bf57452b28L, 1648}, {0xd3fa922f2d1675f2L, 1651},
|
|
{0x847c9b5d7c2e09b7L, 1655}, {0xa59bc234db398c25L, 1658},
|
|
{0xcf02b2c21207ef2eL, 1661}, {0x8161afb94b44f57dL, 1665},
|
|
{0xa1ba1ba79e1632dcL, 1668}, {0xca28a291859bbf93L, 1671},
|
|
{0xfcb2cb35e702af78L, 1674}, {0x9defbf01b061adabL, 1678},
|
|
{0xc56baec21c7a1916L, 1681}, {0xf6c69a72a3989f5bL, 1684},
|
|
{0x9a3c2087a63f6399L, 1688}, {0xc0cb28a98fcf3c7fL, 1691},
|
|
{0xf0fdf2d3f3c30b9fL, 1694}, {0x969eb7c47859e743L, 1698},
|
|
{0xbc4665b596706114L, 1701}, {0xeb57ff22fc0c7959L, 1704},
|
|
{0x9316ff75dd87cbd8L, 1708}, {0xb7dcbf5354e9beceL, 1711},
|
|
{0xe5d3ef282a242e81L, 1714}, {0x8fa475791a569d10L, 1718},
|
|
{0xb38d92d760ec4455L, 1721}, {0xe070f78d3927556aL, 1724},
|
|
{0x8c469ab843b89562L, 1728}, {0xaf58416654a6babbL, 1731},
|
|
{0xdb2e51bfe9d0696aL, 1734}, {0x88fcf317f22241e2L, 1738},
|
|
{0xab3c2fddeeaad25aL, 1741}, {0xd60b3bd56a5586f1L, 1744},
|
|
{0x85c7056562757456L, 1748}, {0xa738c6bebb12d16cL, 1751},
|
|
{0xd106f86e69d785c7L, 1754}, {0x82a45b450226b39cL, 1758},
|
|
{0xa34d721642b06084L, 1761}, {0xcc20ce9bd35c78a5L, 1764},
|
|
{0xff290242c83396ceL, 1767}, {0x9f79a169bd203e41L, 1771},
|
|
{0xc75809c42c684dd1L, 1774}, {0xf92e0c3537826145L, 1777},
|
|
{0x9bbcc7a142b17ccbL, 1781}, {0xc2abf989935ddbfeL, 1784},
|
|
{0xf356f7ebf83552feL, 1787}, {0x98165af37b2153deL, 1791},
|
|
{0xbe1bf1b059e9a8d6L, 1794}, {0xeda2ee1c7064130cL, 1797},
|
|
{0x9485d4d1c63e8be7L, 1801}, {0xb9a74a0637ce2ee1L, 1804},
|
|
{0xe8111c87c5c1ba99L, 1807}, {0x910ab1d4db9914a0L, 1811},
|
|
{0xb54d5e4a127f59c8L, 1814}, {0xe2a0b5dc971f303aL, 1817},
|
|
{0x8da471a9de737e24L, 1821}, {0xb10d8e1456105dadL, 1824},
|
|
{0xdd50f1996b947518L, 1827}, {0x8a5296ffe33cc92fL, 1831},
|
|
{0xace73cbfdc0bfb7bL, 1834}, {0xd8210befd30efa5aL, 1837},
|
|
{0x8714a775e3e95c78L, 1841}, {0xa8d9d1535ce3b396L, 1844},
|
|
{0xd31045a8341ca07cL, 1847}, {0x83ea2b892091e44dL, 1851},
|
|
{0xa4e4b66b68b65d60L, 1854}, {0xce1de40642e3f4b9L, 1857},
|
|
{0x80d2ae83e9ce78f3L, 1861}, {0xa1075a24e4421730L, 1864},
|
|
{0xc94930ae1d529cfcL, 1867}, {0xfb9b7cd9a4a7443cL, 1870},
|
|
{0x9d412e0806e88aa5L, 1874}, {0xc491798a08a2ad4eL, 1877},
|
|
{0xf5b5d7ec8acb58a2L, 1880}, {0x9991a6f3d6bf1765L, 1884},
|
|
{0xbff610b0cc6edd3fL, 1887}, {0xeff394dcff8a948eL, 1890},
|
|
{0x95f83d0a1fb69cd9L, 1894}, {0xbb764c4ca7a4440fL, 1897},
|
|
{0xea53df5fd18d5513L, 1900}, {0x92746b9be2f8552cL, 1904},
|
|
{0xb7118682dbb66a77L, 1907}, {0xe4d5e82392a40515L, 1910},
|
|
{0x8f05b1163ba6832dL, 1914}, {0xb2c71d5bca9023f8L, 1917},
|
|
{0xdf78e4b2bd342cf6L, 1920}, {0x8bab8eefb6409c1aL, 1924},
|
|
{0xae9672aba3d0c320L, 1927}, {0xda3c0f568cc4f3e8L, 1930},
|
|
{0x8865899617fb1871L, 1934}, {0xaa7eebfb9df9de8dL, 1937},
|
|
{0xd51ea6fa85785631L, 1940}, {0x8533285c936b35deL, 1944},
|
|
{0xa67ff273b8460356L, 1947}, {0xd01fef10a657842cL, 1950},
|
|
{0x8213f56a67f6b29bL, 1954}, {0xa298f2c501f45f42L, 1957},
|
|
{0xcb3f2f7642717713L, 1960}, {0xfe0efb53d30dd4d7L, 1963},
|
|
{0x9ec95d1463e8a506L, 1967}, {0xc67bb4597ce2ce48L, 1970},
|
|
{0xf81aa16fdc1b81daL, 1973}, {0x9b10a4e5e9913128L, 1977},
|
|
{0xc1d4ce1f63f57d72L, 1980}, {0xf24a01a73cf2dccfL, 1983},
|
|
{0x976e41088617ca01L, 1987}, {0xbd49d14aa79dbc82L, 1990},
|
|
{0xec9c459d51852ba2L, 1993}, {0x93e1ab8252f33b45L, 1997},
|
|
{0xb8da1662e7b00a17L, 2000}, {0xe7109bfba19c0c9dL, 2003},
|
|
{0x906a617d450187e2L, 2007}, {0xb484f9dc9641e9daL, 2010},
|
|
{0xe1a63853bbd26451L, 2013}, {0x8d07e33455637eb2L, 2017},
|
|
{0xb049dc016abc5e5fL, 2020}, {0xdc5c5301c56b75f7L, 2023},
|
|
{0x89b9b3e11b6329baL, 2027}, {0xac2820d9623bf429L, 2030},
|
|
{0xd732290fbacaf133L, 2033}, {0x867f59a9d4bed6c0L, 2037},
|
|
{0xa81f301449ee8c70L, 2040}, {0xd226fc195c6a2f8cL, 2043},
|
|
{0x83585d8fd9c25db7L, 2047}, {0xa42e74f3d032f525L, 2050},
|
|
{0xcd3a1230c43fb26fL, 2053}, {0x80444b5e7aa7cf85L, 2057},
|
|
{0xa0555e361951c366L, 2060}, {0xc86ab5c39fa63440L, 2063},
|
|
{0xfa856334878fc150L, 2066}, {0x9c935e00d4b9d8d2L, 2070},
|
|
{0xc3b8358109e84f07L, 2073}, {0xf4a642e14c6262c8L, 2076},
|
|
{0x98e7e9cccfbd7dbdL, 2080}, {0xbf21e44003acdd2cL, 2083},
|
|
{0xeeea5d5004981478L, 2086}, {0x95527a5202df0ccbL, 2090},
|
|
{0xbaa718e68396cffdL, 2093}, {0xe950df20247c83fdL, 2096},
|
|
{0x91d28b7416cdd27eL, 2100}, {0xb6472e511c81471dL, 2103},
|
|
{0xe3d8f9e563a198e5L, 2106}, {0x8e679c2f5e44ff8fL, 2110}};
|
|
|
|
// A complement from power_of_ten_components
|
|
// complete to a 128-bit mantissa.
|
|
const uint64_t mantissa_128[] = {0x419ea3bd35385e2d,
|
|
0x52064cac828675b9,
|
|
0x7343efebd1940993,
|
|
0x1014ebe6c5f90bf8,
|
|
0xd41a26e077774ef6,
|
|
0x8920b098955522b4,
|
|
0x55b46e5f5d5535b0,
|
|
0xeb2189f734aa831d,
|
|
0xa5e9ec7501d523e4,
|
|
0x47b233c92125366e,
|
|
0x999ec0bb696e840a,
|
|
0xc00670ea43ca250d,
|
|
0x380406926a5e5728,
|
|
0xc605083704f5ecf2,
|
|
0xf7864a44c633682e,
|
|
0x7ab3ee6afbe0211d,
|
|
0x5960ea05bad82964,
|
|
0x6fb92487298e33bd,
|
|
0xa5d3b6d479f8e056,
|
|
0x8f48a4899877186c,
|
|
0x331acdabfe94de87,
|
|
0x9ff0c08b7f1d0b14,
|
|
0x7ecf0ae5ee44dd9,
|
|
0xc9e82cd9f69d6150,
|
|
0xbe311c083a225cd2,
|
|
0x6dbd630a48aaf406,
|
|
0x92cbbccdad5b108,
|
|
0x25bbf56008c58ea5,
|
|
0xaf2af2b80af6f24e,
|
|
0x1af5af660db4aee1,
|
|
0x50d98d9fc890ed4d,
|
|
0xe50ff107bab528a0,
|
|
0x1e53ed49a96272c8,
|
|
0x25e8e89c13bb0f7a,
|
|
0x77b191618c54e9ac,
|
|
0xd59df5b9ef6a2417,
|
|
0x4b0573286b44ad1d,
|
|
0x4ee367f9430aec32,
|
|
0x229c41f793cda73f,
|
|
0x6b43527578c1110f,
|
|
0x830a13896b78aaa9,
|
|
0x23cc986bc656d553,
|
|
0x2cbfbe86b7ec8aa8,
|
|
0x7bf7d71432f3d6a9,
|
|
0xdaf5ccd93fb0cc53,
|
|
0xd1b3400f8f9cff68,
|
|
0x23100809b9c21fa1,
|
|
0xabd40a0c2832a78a,
|
|
0x16c90c8f323f516c,
|
|
0xae3da7d97f6792e3,
|
|
0x99cd11cfdf41779c,
|
|
0x40405643d711d583,
|
|
0x482835ea666b2572,
|
|
0xda3243650005eecf,
|
|
0x90bed43e40076a82,
|
|
0x5a7744a6e804a291,
|
|
0x711515d0a205cb36,
|
|
0xd5a5b44ca873e03,
|
|
0xe858790afe9486c2,
|
|
0x626e974dbe39a872,
|
|
0xfb0a3d212dc8128f,
|
|
0x7ce66634bc9d0b99,
|
|
0x1c1fffc1ebc44e80,
|
|
0xa327ffb266b56220,
|
|
0x4bf1ff9f0062baa8,
|
|
0x6f773fc3603db4a9,
|
|
0xcb550fb4384d21d3,
|
|
0x7e2a53a146606a48,
|
|
0x2eda7444cbfc426d,
|
|
0xfa911155fefb5308,
|
|
0x793555ab7eba27ca,
|
|
0x4bc1558b2f3458de,
|
|
0x9eb1aaedfb016f16,
|
|
0x465e15a979c1cadc,
|
|
0xbfacd89ec191ec9,
|
|
0xcef980ec671f667b,
|
|
0x82b7e12780e7401a,
|
|
0xd1b2ecb8b0908810,
|
|
0x861fa7e6dcb4aa15,
|
|
0x67a791e093e1d49a,
|
|
0xe0c8bb2c5c6d24e0,
|
|
0x58fae9f773886e18,
|
|
0xaf39a475506a899e,
|
|
0x6d8406c952429603,
|
|
0xc8e5087ba6d33b83,
|
|
0xfb1e4a9a90880a64,
|
|
0x5cf2eea09a55067f,
|
|
0xf42faa48c0ea481e,
|
|
0xf13b94daf124da26,
|
|
0x76c53d08d6b70858,
|
|
0x54768c4b0c64ca6e,
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|
|
0x36ac54e2f678864b,
|
|
0x84576a1bb416a7dd,
|
|
0x656d44a2a11c51d5,
|
|
0x9f644ae5a4b1b325,
|
|
0x873d5d9f0dde1fee,
|
|
0xa90cb506d155a7ea,
|
|
0x9a7f12442d588f2,
|
|
0xc11ed6d538aeb2f,
|
|
0x8f1668c8a86da5fa,
|
|
0xf96e017d694487bc,
|
|
0x37c981dcc395a9ac,
|
|
0x85bbe253f47b1417,
|
|
0x93956d7478ccec8e,
|
|
0x387ac8d1970027b2,
|
|
0x6997b05fcc0319e,
|
|
0x441fece3bdf81f03,
|
|
0xd527e81cad7626c3,
|
|
0x8a71e223d8d3b074,
|
|
0xf6872d5667844e49,
|
|
0xb428f8ac016561db,
|
|
0xe13336d701beba52,
|
|
0xecc0024661173473,
|
|
0x27f002d7f95d0190,
|
|
0x31ec038df7b441f4,
|
|
0x7e67047175a15271,
|
|
0xf0062c6e984d386,
|
|
0x52c07b78a3e60868,
|
|
0xa7709a56ccdf8a82,
|
|
0x88a66076400bb691,
|
|
0x6acff893d00ea435,
|
|
0x583f6b8c4124d43,
|
|
0xc3727a337a8b704a,
|
|
0x744f18c0592e4c5c,
|
|
0x1162def06f79df73,
|
|
0x8addcb5645ac2ba8,
|
|
0x6d953e2bd7173692,
|
|
0xc8fa8db6ccdd0437,
|
|
0x1d9c9892400a22a2,
|
|
0x2503beb6d00cab4b,
|
|
0x2e44ae64840fd61d,
|
|
0x5ceaecfed289e5d2,
|
|
0x7425a83e872c5f47,
|
|
0xd12f124e28f77719,
|
|
0x82bd6b70d99aaa6f,
|
|
0x636cc64d1001550b,
|
|
0x3c47f7e05401aa4e,
|
|
0x65acfaec34810a71,
|
|
0x7f1839a741a14d0d,
|
|
0x1ede48111209a050,
|
|
0x934aed0aab460432,
|
|
0xf81da84d5617853f,
|
|
0x36251260ab9d668e,
|
|
0xc1d72b7c6b426019,
|
|
0xb24cf65b8612f81f,
|
|
0xdee033f26797b627,
|
|
0x169840ef017da3b1,
|
|
0x8e1f289560ee864e,
|
|
0xf1a6f2bab92a27e2,
|
|
0xae10af696774b1db,
|
|
0xacca6da1e0a8ef29,
|
|
0x17fd090a58d32af3,
|
|
0xddfc4b4cef07f5b0,
|
|
0x4abdaf101564f98e,
|
|
0x9d6d1ad41abe37f1,
|
|
0x84c86189216dc5ed,
|
|
0x32fd3cf5b4e49bb4,
|
|
0x3fbc8c33221dc2a1,
|
|
0xfabaf3feaa5334a,
|
|
0x29cb4d87f2a7400e,
|
|
0x743e20e9ef511012,
|
|
0x914da9246b255416,
|
|
0x1ad089b6c2f7548e,
|
|
0xa184ac2473b529b1,
|
|
0xc9e5d72d90a2741e,
|
|
0x7e2fa67c7a658892,
|
|
0xddbb901b98feeab7,
|
|
0x552a74227f3ea565,
|
|
0xd53a88958f87275f,
|
|
0x8a892abaf368f137,
|
|
0x2d2b7569b0432d85,
|
|
0x9c3b29620e29fc73,
|
|
0x8349f3ba91b47b8f,
|
|
0x241c70a936219a73,
|
|
0xed238cd383aa0110,
|
|
0xf4363804324a40aa,
|
|
0xb143c6053edcd0d5,
|
|
0xdd94b7868e94050a,
|
|
0xca7cf2b4191c8326,
|
|
0xfd1c2f611f63a3f0,
|
|
0xbc633b39673c8cec,
|
|
0xd5be0503e085d813,
|
|
0x4b2d8644d8a74e18,
|
|
0xddf8e7d60ed1219e,
|
|
0xcabb90e5c942b503,
|
|
0x3d6a751f3b936243,
|
|
0xcc512670a783ad4,
|
|
0x27fb2b80668b24c5,
|
|
0xb1f9f660802dedf6,
|
|
0x5e7873f8a0396973,
|
|
0xdb0b487b6423e1e8,
|
|
0x91ce1a9a3d2cda62,
|
|
0x7641a140cc7810fb,
|
|
0xa9e904c87fcb0a9d,
|
|
0x546345fa9fbdcd44,
|
|
0xa97c177947ad4095,
|
|
0x49ed8eabcccc485d,
|
|
0x5c68f256bfff5a74,
|
|
0x73832eec6fff3111,
|
|
0xc831fd53c5ff7eab,
|
|
0xba3e7ca8b77f5e55,
|
|
0x28ce1bd2e55f35eb,
|
|
0x7980d163cf5b81b3,
|
|
0xd7e105bcc332621f,
|
|
0x8dd9472bf3fefaa7,
|
|
0xb14f98f6f0feb951,
|
|
0x6ed1bf9a569f33d3,
|
|
0xa862f80ec4700c8,
|
|
0xcd27bb612758c0fa,
|
|
0x8038d51cb897789c,
|
|
0xe0470a63e6bd56c3,
|
|
0x1858ccfce06cac74,
|
|
0xf37801e0c43ebc8,
|
|
0xd30560258f54e6ba,
|
|
0x47c6b82ef32a2069,
|
|
0x4cdc331d57fa5441,
|
|
0xe0133fe4adf8e952,
|
|
0x58180fddd97723a6,
|
|
0x570f09eaa7ea7648};
|
|
|
|
// Attempts to compute i * 10^(power) exactly; and if "negative" is
|
|
// true, negate the result.
|
|
// This function will only work in some cases, when it does not work, success is
|
|
// set to false. This should work *most of the time* (like 99% of the time).
|
|
// We assume that power is in the [FASTFLOAT_SMALLEST_POWER,
|
|
// FASTFLOAT_LARGEST_POWER] interval: the caller is responsible for this check.
|
|
// We assume that i is non-zero: the caller is responsible for this check.
|
|
really_inline double compute_float_64(int64_t power, uint64_t i,
|
|
bool negative, bool *success) {
|
|
// we start with a fast path
|
|
if (-22 <= power && power <= 22 && i <= 9007199254740991) {
|
|
// convert the integer into a double. This is lossless since
|
|
// 0 <= i <= 2^53 - 1.
|
|
double d = i;
|
|
//
|
|
// The general idea is as follows.
|
|
// If 0 <= s < 2^53 and if 10^0 <= p <= 10^22 then
|
|
// 1) Both s and p can be represented exactly as 64-bit floating-point
|
|
// values
|
|
// (binary64).
|
|
// 2) Because s and p can be represented exactly as floating-point values,
|
|
// then s * p
|
|
// and s / p will produce correctly rounded values.
|
|
//
|
|
if (power < 0) {
|
|
d = d / power_of_ten[-power];
|
|
} else {
|
|
d = d * power_of_ten[power];
|
|
}
|
|
if (negative) {
|
|
d = -d;
|
|
}
|
|
*success = true;
|
|
return d;
|
|
}
|
|
|
|
components c =
|
|
power_of_ten_components[power - FASTFLOAT_SMALLEST_POWER]; // safe because
|
|
// power_index
|
|
// <= 2*308
|
|
// we recover the mantissa of the power, it has a leading 1. It is always
|
|
// rounded down.
|
|
uint64_t factor_mantissa = c.mantissa;
|
|
|
|
// We want the most significant bit of i to be 1. Shift if needed.
|
|
int lz = leading_zeroes(i);
|
|
i <<= lz;
|
|
// We want the most significant 64 bits of the product. We know
|
|
// this will be non-zero because the most significant bit of i is
|
|
// 1.
|
|
|
|
uint64_t lower = i * factor_mantissa;
|
|
uint64_t upper = ((__uint128_t)i * factor_mantissa) >> 64;
|
|
|
|
// We know that upper has at most one leading zero because
|
|
// both i and factor_mantissa have a leading one. This means
|
|
// that the result is at least as large as ((1<<63)*(1<<63))/(1<<64).
|
|
|
|
// As long as the first 9 bits of "upper" are not "1", then we
|
|
// know that we have an exact computed value for the leading
|
|
// 55 bits because any imprecision would play out as a +1, in
|
|
// the worst case.
|
|
if (unlikely((upper & 0x1FF) == 0x1FF) && (lower + i < lower)) {
|
|
uint64_t factor_mantissa_low =
|
|
mantissa_128[power - FASTFLOAT_SMALLEST_POWER];
|
|
// next, we compute the 64-bit x 128-bit multiplication, getting a 192-bit
|
|
// result (three 64-bit values)
|
|
uint64_t product_low = i * factor_mantissa_low;
|
|
uint64_t product_middle2 = ((__uint128_t)i * factor_mantissa_low) >> 64;
|
|
uint64_t product_middle1 = lower;
|
|
uint64_t product_high = upper;
|
|
uint64_t product_middle = product_middle1 + product_middle2;
|
|
if (product_middle < product_middle1) {
|
|
product_high++; // overflow carry
|
|
}
|
|
// we want to check whether mantissa *i + i would affect our result
|
|
if (((product_middle + 1 == 0) && ((product_high & 0x1FF) == 0x1FF) &&
|
|
(product_low + i < product_low))) { // let us be prudent and bail out.
|
|
*success = false;
|
|
return 0;
|
|
}
|
|
upper = product_high;
|
|
lower = product_middle;
|
|
}
|
|
// The final mantissa should be 53 bits with a leading 1.
|
|
// We shift it so that it occupies 54 bits with a leading 1.
|
|
///////
|
|
uint64_t upperbit = upper >> 63;
|
|
uint64_t mantissa = upper >> (upperbit + 9);
|
|
lz += 1 ^ upperbit;
|
|
|
|
// Here we have mantissa < (1<<54).
|
|
|
|
// We have to round to even. The "to even" part
|
|
// is only a problem when we are right in between two floats
|
|
// which we guard against.
|
|
// If we have lots of trailing zeros so we may fall right between two
|
|
// floating-point values.
|
|
if (unlikely((lower == 0) && ((upper & 0x1FF) == 0) &&
|
|
((mantissa & 1) == 1))) {
|
|
// It can be triggered with 1e23.
|
|
*success = false;
|
|
return 0;
|
|
}
|
|
mantissa += mantissa & 1;
|
|
mantissa >>= 1;
|
|
// Here we have mantissa < (1<<53), unless there was an overflow
|
|
if (mantissa >= (1ULL << 53)) {
|
|
//////////
|
|
// This will happen when parsing values such as 7.2057594037927933e+16
|
|
////////
|
|
mantissa = (1ULL << 52);
|
|
lz--; // undo previous addition
|
|
}
|
|
mantissa &= ~(1ULL << 52);
|
|
uint64_t real_exponent = c.exp - lz;
|
|
// we have to check that real_exponent is in range, otherwise we bail out
|
|
if (unlikely((real_exponent < 1) || (real_exponent > 2046))) {
|
|
*success = false;
|
|
return 0;
|
|
}
|
|
mantissa |= real_exponent << 52;
|
|
mantissa |= (((uint64_t)negative) << 63);
|
|
double d;
|
|
memcpy(&d, &mantissa, sizeof(d));
|
|
*success = true;
|
|
return d;
|
|
}
|
|
|
|
static bool parse_float_strtod(const char *ptr, double *outDouble) {
|
|
char *endptr;
|
|
*outDouble = strtod(ptr, &endptr);
|
|
// Some libraries will set errno = ERANGE when the value is subnormal,
|
|
// yet we may want to be able to parse subnormal values.
|
|
// However, we do not want to tolerate NAN or infinite values.
|
|
if ((endptr == ptr) || (!std::isfinite(*outDouble))) {
|
|
return false;
|
|
}
|
|
return true;
|
|
}
|
|
|
|
// We need to check that the character following a zero is valid. This is
|
|
// probably frequent and it is hard than it looks. We are building all of this
|
|
// just to differentiate between 0x1 (invalid), 0,1 (valid) 0e1 (valid)...
|
|
const bool structural_or_whitespace_or_exponent_or_decimal_negated[256] = {
|
|
1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
|
|
1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1,
|
|
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1,
|
|
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1,
|
|
1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
|
|
1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
|
|
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
|
|
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
|
|
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
|
|
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
|
|
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1};
|
|
|
|
really_inline bool
|
|
is_not_structural_or_whitespace_or_exponent_or_decimal(unsigned char c) {
|
|
return structural_or_whitespace_or_exponent_or_decimal_negated[c];
|
|
}
|
|
|
|
// parse the number at p
|
|
really_inline bool parse_number(const char *p, double *outDouble) {
|
|
const char *pinit = p;
|
|
bool found_minus = (*p == '-');
|
|
bool negative = false;
|
|
if (found_minus) {
|
|
++p;
|
|
negative = true;
|
|
if (!is_integer(*p)) { // a negative sign must be followed by an integer
|
|
return false;
|
|
}
|
|
}
|
|
const char *const start_digits = p;
|
|
|
|
uint64_t i; // an unsigned int avoids signed overflows (which are bad)
|
|
if (*p == '0') { // 0 cannot be followed by an integer
|
|
++p;
|
|
if (is_not_structural_or_whitespace_or_exponent_or_decimal(*p)) {
|
|
return false;
|
|
}
|
|
i = 0;
|
|
} else {
|
|
if (!(is_integer(*p))) { // must start with an integer
|
|
return false;
|
|
}
|
|
unsigned char digit = *p - '0';
|
|
i = digit;
|
|
p++;
|
|
// the is_made_of_eight_digits_fast routine is unlikely to help here because
|
|
// we rarely see large integer parts like 123456789
|
|
while (is_integer(*p)) {
|
|
digit = *p - '0';
|
|
// a multiplication by 10 is cheaper than an arbitrary integer
|
|
// multiplication
|
|
i = 10 * i + digit; // might overflow, we will handle the overflow later
|
|
++p;
|
|
}
|
|
}
|
|
int64_t exponent = 0;
|
|
const char *first_after_period = NULL;
|
|
if ('.' == *p) {
|
|
++p;
|
|
first_after_period = p;
|
|
if (is_integer(*p)) {
|
|
unsigned char digit = *p - '0';
|
|
++p;
|
|
i = i * 10 + digit; // might overflow + multiplication by 10 is likely
|
|
// cheaper than arbitrary mult.
|
|
// we will handle the overflow later
|
|
} else {
|
|
return false;
|
|
}
|
|
while (is_integer(*p)) {
|
|
unsigned char digit = *p - '0';
|
|
++p;
|
|
i = i * 10 + digit; // in rare cases, this will overflow, but that's ok
|
|
// because we have parse_highprecision_float later.
|
|
}
|
|
exponent = first_after_period - p;
|
|
}
|
|
int digit_count =
|
|
p - start_digits - 1; // used later to guard against overflows
|
|
int64_t exp_number = 0; // exponential part
|
|
if (('e' == *p) || ('E' == *p)) {
|
|
++p;
|
|
bool neg_exp = false;
|
|
if ('-' == *p) {
|
|
neg_exp = true;
|
|
++p;
|
|
} else if ('+' == *p) {
|
|
++p;
|
|
}
|
|
if (!is_integer(*p)) {
|
|
return false;
|
|
}
|
|
unsigned char digit = *p - '0';
|
|
exp_number = digit;
|
|
p++;
|
|
if (is_integer(*p)) {
|
|
digit = *p - '0';
|
|
exp_number = 10 * exp_number + digit;
|
|
++p;
|
|
}
|
|
if (is_integer(*p)) {
|
|
digit = *p - '0';
|
|
exp_number = 10 * exp_number + digit;
|
|
++p;
|
|
}
|
|
while (is_integer(*p)) {
|
|
if (exp_number > 0x100000000) { // we need to check for overflows
|
|
// we refuse to parse this
|
|
return false;
|
|
}
|
|
digit = *p - '0';
|
|
exp_number = 10 * exp_number + digit;
|
|
++p;
|
|
}
|
|
exponent += (neg_exp ? -exp_number : exp_number);
|
|
}
|
|
if (unlikely((digit_count >= 19))) { // this is uncommon
|
|
// It is possible that the integer had an overflow.
|
|
// We have to handle the case where we have 0.0000somenumber.
|
|
const char *start = start_digits;
|
|
while ((*start == '0') || (*start == '.')) {
|
|
start++;
|
|
}
|
|
// we over-decrement by one when there is a '.'
|
|
digit_count -= (start - start_digits);
|
|
if (digit_count >= 19) {
|
|
return parse_float_strtod(pinit, outDouble);
|
|
}
|
|
}
|
|
if (unlikely(exponent < FASTFLOAT_SMALLEST_POWER) ||
|
|
(exponent > FASTFLOAT_LARGEST_POWER)) {
|
|
// this is almost never going to get called!!!
|
|
// exponent could be as low as 325
|
|
return parse_float_strtod(pinit, outDouble);
|
|
}
|
|
// from this point forward, exponent >= FASTFLOAT_SMALLEST_POWER and
|
|
// exponent <= FASTFLOAT_LARGEST_POWER
|
|
double d = 0;
|
|
if (i != 0) {
|
|
bool success = true;
|
|
d = compute_float_64(exponent, i, negative, &success);
|
|
if (!success) {
|
|
// we are almost never going to get here.
|
|
return parse_float_strtod(pinit, outDouble);
|
|
}
|
|
}
|
|
*outDouble = d;
|
|
return true;
|
|
}
|
|
|
|
} // namespace fast_double_parser
|
|
|
|
#endif |