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- // Copyright 2020-2023 Daniel Lemire
- // Copyright 2023 Matt Borland
- // Distributed under the Boost Software License, Version 1.0.
- // https://www.boost.org/LICENSE_1_0.txt
- //
- // Derivative of: https://github.com/fastfloat/fast_float
- #ifndef BOOST_CHARCONV_DETAIL_FASTFLOAT_FAST_TABLE_HPP
- #define BOOST_CHARCONV_DETAIL_FASTFLOAT_FAST_TABLE_HPP
- #include <boost/charconv/detail/fast_float/float_common.hpp>
- #include <cstdint>
- namespace boost { namespace charconv { namespace detail { namespace fast_float {
- /**
- * When mapping numbers from decimal to binary,
- * we go from w * 10^q to m * 2^p but we have
- * 10^q = 5^q * 2^q, so effectively
- * we are trying to match
- * w * 2^q * 5^q to m * 2^p. Thus the powers of two
- * are not a concern since they can be represented
- * exactly using the binary notation, only the powers of five
- * affect the binary significand.
- */
- /**
- * The smallest non-zero float (binary64) is 2^-1074.
- * We take as input numbers of the form w x 10^q where w < 2^64.
- * We have that w * 10^-343 < 2^(64-344) 5^-343 < 2^-1076.
- * However, we have that
- * (2^64-1) * 10^-342 = (2^64-1) * 2^-342 * 5^-342 > 2^-1074.
- * Thus it is possible for a number of the form w * 10^-342 where
- * w is a 64-bit value to be a non-zero floating-point number.
- *********
- * Any number of form w * 10^309 where w>= 1 is going to be
- * infinite in binary64 so we never need to worry about powers
- * of 5 greater than 308.
- */
- template <class unused = void>
- struct powers_template {
- constexpr static int smallest_power_of_five = binary_format<double>::smallest_power_of_ten();
- constexpr static int largest_power_of_five = binary_format<double>::largest_power_of_ten();
- constexpr static int number_of_entries = 2 * (largest_power_of_five - smallest_power_of_five + 1);
- // Powers of five from 5^-342 all the way to 5^308 rounded toward one.
- constexpr static uint64_t power_of_five_128[number_of_entries] = {
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- 0x87d4713d6f33aa6b,0x8672648c40e5ad68,
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- 0xa1ebfb4219491a1f,0x1014ebe6c5f90bf8,
- 0xca66fa129f9b60a6,0xd41a26e077774ef6,
- 0xfd00b897478238d0,0x8920b098955522b4,
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- 0xf712b443bbd52b7b,0xa5e9ec7501d523e4,
- 0x9a6bb0aa55653b2d,0x47b233c92125366e,
- 0xc1069cd4eabe89f8,0x999ec0bb696e840a,
- 0xf148440a256e2c76,0xc00670ea43ca250d,
- 0x96cd2a865764dbca,0x380406926a5e5728,
- 0xbc807527ed3e12bc,0xc605083704f5ecf2,
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- 0xe61acf033d1a45df,0x6fb92487298e33bd,
- 0x8fd0c16206306bab,0xa5d3b6d479f8e056,
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- 0xe0b62e2929aba83c,0x331acdabfe94de87,
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- 0xaf8e5410288e1b6f,0x7ecf0ae5ee44dd9,
- 0xdb71e91432b1a24a,0xc9e82cd9f69d6150,
- 0x892731ac9faf056e,0xbe311c083a225cd2,
- 0xab70fe17c79ac6ca,0x6dbd630a48aaf406,
- 0xd64d3d9db981787d,0x92cbbccdad5b108,
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- 0x82cca4db847945ca,0x50d98d9fc890ed4d,
- 0xa37fce126597973c,0xe50ff107bab528a0,
- 0xcc5fc196fefd7d0c,0x1e53ed49a96272c8,
- 0xff77b1fcbebcdc4f,0x25e8e89c13bb0f7a,
- 0x9faacf3df73609b1,0x77b191618c54e9ac,
- 0xc795830d75038c1d,0xd59df5b9ef6a2417,
- 0xf97ae3d0d2446f25,0x4b0573286b44ad1d,
- 0x9becce62836ac577,0x4ee367f9430aec32,
- 0xc2e801fb244576d5,0x229c41f793cda73f,
- 0xf3a20279ed56d48a,0x6b43527578c1110f,
- 0x9845418c345644d6,0x830a13896b78aaa9,
- 0xbe5691ef416bd60c,0x23cc986bc656d553,
- 0xedec366b11c6cb8f,0x2cbfbe86b7ec8aa8,
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- 0xa2cb1717b52481ed,0x54768c4b0c64ca6e,
- 0xcb7ddcdda26da268,0xa9942f5dcf7dfd09,
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- 0xc75809c42c684dd1,0x52c07b78a3e60868,
- 0xf92e0c3537826145,0xa7709a56ccdf8a82,
- 0x9bbcc7a142b17ccb,0x88a66076400bb691,
- 0xc2abf989935ddbfe,0x6acff893d00ea435,
- 0xf356f7ebf83552fe,0x583f6b8c4124d43,
- 0x98165af37b2153de,0xc3727a337a8b704a,
- 0xbe1bf1b059e9a8d6,0x744f18c0592e4c5c,
- 0xeda2ee1c7064130c,0x1162def06f79df73,
- 0x9485d4d1c63e8be7,0x8addcb5645ac2ba8,
- 0xb9a74a0637ce2ee1,0x6d953e2bd7173692,
- 0xe8111c87c5c1ba99,0xc8fa8db6ccdd0437,
- 0x910ab1d4db9914a0,0x1d9c9892400a22a2,
- 0xb54d5e4a127f59c8,0x2503beb6d00cab4b,
- 0xe2a0b5dc971f303a,0x2e44ae64840fd61d,
- 0x8da471a9de737e24,0x5ceaecfed289e5d2,
- 0xb10d8e1456105dad,0x7425a83e872c5f47,
- 0xdd50f1996b947518,0xd12f124e28f77719,
- 0x8a5296ffe33cc92f,0x82bd6b70d99aaa6f,
- 0xace73cbfdc0bfb7b,0x636cc64d1001550b,
- 0xd8210befd30efa5a,0x3c47f7e05401aa4e,
- 0x8714a775e3e95c78,0x65acfaec34810a71,
- 0xa8d9d1535ce3b396,0x7f1839a741a14d0d,
- 0xd31045a8341ca07c,0x1ede48111209a050,
- 0x83ea2b892091e44d,0x934aed0aab460432,
- 0xa4e4b66b68b65d60,0xf81da84d5617853f,
- 0xce1de40642e3f4b9,0x36251260ab9d668e,
- 0x80d2ae83e9ce78f3,0xc1d72b7c6b426019,
- 0xa1075a24e4421730,0xb24cf65b8612f81f,
- 0xc94930ae1d529cfc,0xdee033f26797b627,
- 0xfb9b7cd9a4a7443c,0x169840ef017da3b1,
- 0x9d412e0806e88aa5,0x8e1f289560ee864e,
- 0xc491798a08a2ad4e,0xf1a6f2bab92a27e2,
- 0xf5b5d7ec8acb58a2,0xae10af696774b1db,
- 0x9991a6f3d6bf1765,0xacca6da1e0a8ef29,
- 0xbff610b0cc6edd3f,0x17fd090a58d32af3,
- 0xeff394dcff8a948e,0xddfc4b4cef07f5b0,
- 0x95f83d0a1fb69cd9,0x4abdaf101564f98e,
- 0xbb764c4ca7a4440f,0x9d6d1ad41abe37f1,
- 0xea53df5fd18d5513,0x84c86189216dc5ed,
- 0x92746b9be2f8552c,0x32fd3cf5b4e49bb4,
- 0xb7118682dbb66a77,0x3fbc8c33221dc2a1,
- 0xe4d5e82392a40515,0xfabaf3feaa5334a,
- 0x8f05b1163ba6832d,0x29cb4d87f2a7400e,
- 0xb2c71d5bca9023f8,0x743e20e9ef511012,
- 0xdf78e4b2bd342cf6,0x914da9246b255416,
- 0x8bab8eefb6409c1a,0x1ad089b6c2f7548e,
- 0xae9672aba3d0c320,0xa184ac2473b529b1,
- 0xda3c0f568cc4f3e8,0xc9e5d72d90a2741e,
- 0x8865899617fb1871,0x7e2fa67c7a658892,
- 0xaa7eebfb9df9de8d,0xddbb901b98feeab7,
- 0xd51ea6fa85785631,0x552a74227f3ea565,
- 0x8533285c936b35de,0xd53a88958f87275f,
- 0xa67ff273b8460356,0x8a892abaf368f137,
- 0xd01fef10a657842c,0x2d2b7569b0432d85,
- 0x8213f56a67f6b29b,0x9c3b29620e29fc73,
- 0xa298f2c501f45f42,0x8349f3ba91b47b8f,
- 0xcb3f2f7642717713,0x241c70a936219a73,
- 0xfe0efb53d30dd4d7,0xed238cd383aa0110,
- 0x9ec95d1463e8a506,0xf4363804324a40aa,
- 0xc67bb4597ce2ce48,0xb143c6053edcd0d5,
- 0xf81aa16fdc1b81da,0xdd94b7868e94050a,
- 0x9b10a4e5e9913128,0xca7cf2b4191c8326,
- 0xc1d4ce1f63f57d72,0xfd1c2f611f63a3f0,
- 0xf24a01a73cf2dccf,0xbc633b39673c8cec,
- 0x976e41088617ca01,0xd5be0503e085d813,
- 0xbd49d14aa79dbc82,0x4b2d8644d8a74e18,
- 0xec9c459d51852ba2,0xddf8e7d60ed1219e,
- 0x93e1ab8252f33b45,0xcabb90e5c942b503,
- 0xb8da1662e7b00a17,0x3d6a751f3b936243,
- 0xe7109bfba19c0c9d,0xcc512670a783ad4,
- 0x906a617d450187e2,0x27fb2b80668b24c5,
- 0xb484f9dc9641e9da,0xb1f9f660802dedf6,
- 0xe1a63853bbd26451,0x5e7873f8a0396973,
- 0x8d07e33455637eb2,0xdb0b487b6423e1e8,
- 0xb049dc016abc5e5f,0x91ce1a9a3d2cda62,
- 0xdc5c5301c56b75f7,0x7641a140cc7810fb,
- 0x89b9b3e11b6329ba,0xa9e904c87fcb0a9d,
- 0xac2820d9623bf429,0x546345fa9fbdcd44,
- 0xd732290fbacaf133,0xa97c177947ad4095,
- 0x867f59a9d4bed6c0,0x49ed8eabcccc485d,
- 0xa81f301449ee8c70,0x5c68f256bfff5a74,
- 0xd226fc195c6a2f8c,0x73832eec6fff3111,
- 0x83585d8fd9c25db7,0xc831fd53c5ff7eab,
- 0xa42e74f3d032f525,0xba3e7ca8b77f5e55,
- 0xcd3a1230c43fb26f,0x28ce1bd2e55f35eb,
- 0x80444b5e7aa7cf85,0x7980d163cf5b81b3,
- 0xa0555e361951c366,0xd7e105bcc332621f,
- 0xc86ab5c39fa63440,0x8dd9472bf3fefaa7,
- 0xfa856334878fc150,0xb14f98f6f0feb951,
- 0x9c935e00d4b9d8d2,0x6ed1bf9a569f33d3,
- 0xc3b8358109e84f07,0xa862f80ec4700c8,
- 0xf4a642e14c6262c8,0xcd27bb612758c0fa,
- 0x98e7e9cccfbd7dbd,0x8038d51cb897789c,
- 0xbf21e44003acdd2c,0xe0470a63e6bd56c3,
- 0xeeea5d5004981478,0x1858ccfce06cac74,
- 0x95527a5202df0ccb,0xf37801e0c43ebc8,
- 0xbaa718e68396cffd,0xd30560258f54e6ba,
- 0xe950df20247c83fd,0x47c6b82ef32a2069,
- 0x91d28b7416cdd27e,0x4cdc331d57fa5441,
- 0xb6472e511c81471d,0xe0133fe4adf8e952,
- 0xe3d8f9e563a198e5,0x58180fddd97723a6,
- 0x8e679c2f5e44ff8f,0x570f09eaa7ea7648,};
- };
- template <class unused>
- constexpr uint64_t powers_template<unused>::power_of_five_128[number_of_entries];
- using powers = powers_template<>;
- }}}} // namespace fast_float
- #endif
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