pxfm 0.1.29

Fast and accurate math
Documentation 
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/*
 * // Copyright (c) Radzivon Bartoshyk 9/2025. All rights reserved.
 * //
 * // Redistribution and use in source and binary forms, with or without modification,
 * // are permitted provided that the following conditions are met:
 * //
 * // 1.  Redistributions of source code must retain the above copyright notice, this
 * // list of conditions and the following disclaimer.
 * //
 * // 2.  Redistributions in binary form must reproduce the above copyright notice,
 * // this list of conditions and the following disclaimer in the documentation
 * // and/or other materials provided with the distribution.
 * //
 * // 3.  Neither the name of the copyright holder nor the names of its
 * // contributors may be used to endorse or promote products derived from
 * // this software without specific prior written permission.
 * //
 * // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 * // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
 * // DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
 * // FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * // DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
 * // SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
 * // CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
 * // OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
 * // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

// Generated by SageMath:
// print("[")
// for k in range(128):
//     k = RealField(150)(k) * RealField(150).pi() / RealField(150)(64)
//     print_double_double("", k.tan())
// print("];")
pub(crate) static TANPI_K_PI_OVER_64: [(u64, u64); 128] = [
    (0x0000000000000000, 0x0000000000000000),
    (0x3bfada13ceebab9d, 0x3fa927278a3b1162),
    (0x3c587d054f689d7a, 0x3fb936bb8c5b2da2),
    (0x3c52cfb5a746f62c, 0x3fc2fcac73a60640),
    (0x3c2ef5d367441946, 0x3fc975f5e0553158),
    (0x3c65a6d6c3c8b6a7, 0x3fd007fa758626ae),
    (0xbc6d704d1bfdb6e8, 0x3fd36a08355c63dc),
    (0x3c678e945dc3913c, 0x3fd6e649f7d78649),
    (0x3c708b2fb1366ea9, 0x3fda827999fcef32),
    (0x3c741522f15e53c5, 0x3fde450e0d273e7a),
    (0xbc8e564bcd1e635d, 0x3fe11ab7190834ec),
    (0xbc810b4421e6a4f8, 0x3fe32e1889047ffd),
    (0x3c87a8c52172b675, 0x3fe561b82ab7f990),
    (0xbc8aa7538e44e996, 0x3fe7bb99ed2990cf),
    (0xbc7a6db80fe796fe, 0x3fea43002ae42850),
    (0x3c78dcad85e60fbe, 0x3fed00cbc7384d2e),
    (0x0000000000000000, 0x3ff0000000000000),
    (0x3c9946cc0b66979f, 0x3ff1a73d55278c4b),
    (0xbc787e5ad9735569, 0x3ff37efd8d87607e),
    (0x3c86a085e3bc3af6, 0x3ff592d11142fa55),
    (0x3c9419fa6954928f, 0x3ff7f218e25a7461),
    (0xbc7b6fb77846d763, 0x3ffab1c35d8a74ea),
    (0x3c80fb3e75c7098e, 0x3ffdef13b73c1406),
    (0x3c97ce6cb463c972, 0x4000ea21d716fbf7),
    (0x3ca21165f626cdd5, 0x4003504f333f9de6),
    (0x3c7aca947bfb1dcc, 0x40065bc6cc825147),
    (0xbc9b7a14d0d691be, 0x400a5f59e90600dd),
    (0xbc889fcd637fbf3b, 0x400ff01305ecd8dc),
    (0x3c810706fed37f0e, 0x40141bfee2424771),
    (0xbcaae397239c5a0d, 0x401af73f4ca3310f),
    (0x3cc351daea79411d, 0x40244e6c595afdcc),
    (0xbc7b6e6b4de0cd24, 0x40345affed201b55),
    (0xc5f4a74167598ceb, 0xc950457bf6be49c7),
    (0x3c7b6e6b4de0cd24, 0xc0345affed201b55),
    (0xbcc351daea79411d, 0xc0244e6c595afdcc),
    (0x3caae397239c5a0d, 0xc01af73f4ca3310f),
    (0xbc810706fed37f0e, 0xc0141bfee2424771),
    (0x3c889fcd637fbf3b, 0xc00ff01305ecd8dc),
    (0x3c9b7a14d0d691be, 0xc00a5f59e90600dd),
    (0xbc7aca947bfb1dcc, 0xc0065bc6cc825147),
    (0xbca21165f626cdd5, 0xc003504f333f9de6),
    (0xbc97ce6cb463c972, 0xc000ea21d716fbf7),
    (0xbc80fb3e75c7098e, 0xbffdef13b73c1406),
    (0x3c7b6fb77846d763, 0xbffab1c35d8a74ea),
    (0xbc9419fa6954928f, 0xbff7f218e25a7461),
    (0xbc86a085e3bc3af6, 0xbff592d11142fa55),
    (0x3c787e5ad9735569, 0xbff37efd8d87607e),
    (0xbc9946cc0b66979f, 0xbff1a73d55278c4b),
    (0x36a8000000000000, 0xbff0000000000000),
    (0xbc78dcad85e60fbe, 0xbfed00cbc7384d2e),
    (0x3c7a6db80fe796fe, 0xbfea43002ae42850),
    (0x3c8aa7538e44e996, 0xbfe7bb99ed2990cf),
    (0xbc87a8c52172b675, 0xbfe561b82ab7f990),
    (0x3c810b4421e6a4f8, 0xbfe32e1889047ffd),
    (0x3c8e564bcd1e635d, 0xbfe11ab7190834ec),
    (0xbc741522f15e53c5, 0xbfde450e0d273e7a),
    (0xbc708b2fb1366ea9, 0xbfda827999fcef32),
    (0xbc678e945dc3913c, 0xbfd6e649f7d78649),
    (0x3c6d704d1bfdb6e8, 0xbfd36a08355c63dc),
    (0xbc65a6d6c3c8b6a7, 0xbfd007fa758626ae),
    (0xbc2ef5d367441946, 0xbfc975f5e0553158),
    (0xbc52cfb5a746f62c, 0xbfc2fcac73a60640),
    (0xbc587d054f689d7a, 0xbfb936bb8c5b2da2),
    (0xbbfada13ceebab9d, 0xbfa927278a3b1162),
    (0x3331056713b19377, 0x369f77598338bfdf),
    (0x3bfada13ceebab9d, 0x3fa927278a3b1162),
    (0x3c587d054f689d7a, 0x3fb936bb8c5b2da2),
    (0x3c52cfb5a746f62c, 0x3fc2fcac73a60640),
    (0x3c2ef5d367441946, 0x3fc975f5e0553158),
    (0x3c65a6d6c3c8b6a7, 0x3fd007fa758626ae),
    (0xbc6d704d1bfdb6e8, 0x3fd36a08355c63dc),
    (0x3c678e945dc3913c, 0x3fd6e649f7d78649),
    (0x3c708b2fb1366ea9, 0x3fda827999fcef32),
    (0x3c741522f15e53c5, 0x3fde450e0d273e7a),
    (0xbc8e564bcd1e635d, 0x3fe11ab7190834ec),
    (0xbc810b4421e6a4f8, 0x3fe32e1889047ffd),
    (0x3c87a8c52172b675, 0x3fe561b82ab7f990),
    (0xbc8aa7538e44e996, 0x3fe7bb99ed2990cf),
    (0xbc7a6db80fe796fe, 0x3fea43002ae42850),
    (0x3c78dcad85e60fbe, 0x3fed00cbc7384d2e),
    (0x36b0000000000000, 0x3ff0000000000000),
    (0x3c9946cc0b66979f, 0x3ff1a73d55278c4b),
    (0xbc787e5ad9735569, 0x3ff37efd8d87607e),
    (0x3c86a085e3bc3af6, 0x3ff592d11142fa55),
    (0x3c9419fa6954928f, 0x3ff7f218e25a7461),
    (0xbc7b6fb77846d763, 0x3ffab1c35d8a74ea),
    (0x3c80fb3e75c7098e, 0x3ffdef13b73c1406),
    (0x3c97ce6cb463c972, 0x4000ea21d716fbf7),
    (0x3ca21165f626cdd5, 0x4003504f333f9de6),
    (0x3c7aca947bfb1dcc, 0x40065bc6cc825147),
    (0xbc9b7a14d0d691be, 0x400a5f59e90600dd),
    (0xbc889fcd637fbf3b, 0x400ff01305ecd8dc),
    (0x3c810706fed37f0e, 0x40141bfee2424771),
    (0xbcaae397239c5a0d, 0x401af73f4ca3310f),
    (0x3cc351daea79411d, 0x40244e6c595afdcc),
    (0xbc7b6e6b4de0cd24, 0x40345affed201b55),
    (0x45ce41fc41bbdd8e, 0xc935b1fa9e530d0a),
    (0x3c7b6e6b4de0cd24, 0xc0345affed201b55),
    (0xbcc351daea79411d, 0xc0244e6c595afdcc),
    (0x3caae397239c5a0d, 0xc01af73f4ca3310f),
    (0xbc810706fed37f0e, 0xc0141bfee2424771),
    (0x3c889fcd637fbf3b, 0xc00ff01305ecd8dc),
    (0x3c9b7a14d0d691be, 0xc00a5f59e90600dd),
    (0xbc7aca947bfb1dcc, 0xc0065bc6cc825147),
    (0xbca21165f626cdd5, 0xc003504f333f9de6),
    (0xbc97ce6cb463c972, 0xc000ea21d716fbf7),
    (0xbc80fb3e75c7098e, 0xbffdef13b73c1406),
    (0x3c7b6fb77846d763, 0xbffab1c35d8a74ea),
    (0xbc9419fa6954928f, 0xbff7f218e25a7461),
    (0xbc86a085e3bc3af6, 0xbff592d11142fa55),
    (0x3c787e5ad9735569, 0xbff37efd8d87607e),
    (0xbc9946cc0b66979f, 0xbff1a73d55278c4b),
    (0x36ce000000000000, 0xbff0000000000000),
    (0xbc78dcad85e60fbe, 0xbfed00cbc7384d2e),
    (0x3c7a6db80fe796fe, 0xbfea43002ae42850),
    (0x3c8aa7538e44e996, 0xbfe7bb99ed2990cf),
    (0xbc87a8c52172b675, 0xbfe561b82ab7f990),
    (0x3c810b4421e6a4f8, 0xbfe32e1889047ffd),
    (0x3c8e564bcd1e635d, 0xbfe11ab7190834ec),
    (0xbc741522f15e53c5, 0xbfde450e0d273e7a),
    (0xbc708b2fb1366ea9, 0xbfda827999fcef32),
    (0xbc678e945dc3913c, 0xbfd6e649f7d78649),
    (0x3c6d704d1bfdb6e8, 0xbfd36a08355c63dc),
    (0xbc65a6d6c3c8b6a7, 0xbfd007fa758626ae),
    (0xbc2ef5d367441946, 0xbfc975f5e0553158),
    (0xbc52cfb5a746f62c, 0xbfc2fcac73a60640),
    (0xbc587d054f689d7a, 0xbfb936bb8c5b2da2),
    (0xbbfada13ceebab9d, 0xbfa927278a3b1162),
];

// Generated by Sollya:
// print("[")
// for k in range(256):
//     k = RealField(150)(k) * RealField(150).pi() / RealField(150)(128)
//     print_double_double("", k.tan())
// print("];")
pub(crate) static TAN_K_PI_OVER_128: [(u64, u64); 256] = [
    (0x0000000000000000, 0x0000000000000000),
    (0xbbf13b5915a8e316, 0x3f992346247a91f0),
    (0x3bfada13ceebab9d, 0x3fa927278a3b1162),
    (0x3c587a2cb08f812c, 0x3fb2e239ccff3831),
    (0x3c587d054f689d7a, 0x3fb936bb8c5b2da2),
    (0xbc412206d2ac3013, 0x3fbf93183a8db9e9),
    (0x3c52cfb5a746f62c, 0x3fc2fcac73a60640),
    (0xbc59debab5988b6b, 0x3fc635c990ce0d36),
    (0x3c2ef5d367441946, 0x3fc975f5e0553158),
    (0x3c64a5be32c624f4, 0x3fccbe4ceb4b4cf2),
    (0x3c65a6d6c3c8b6a7, 0x3fd007fa758626ae),
    (0x3c6cbda4f63658a0, 0x3fd1b6103d3597e9),
    (0xbc6d704d1bfdb6e8, 0x3fd36a08355c63dc),
    (0x3c7be976387851c1, 0x3fd5248ae1701b17),
    (0x3c678e945dc3913c, 0x3fd6e649f7d78649),
    (0xbc67327a64e1229d, 0x3fd8b00196b3d022),
    (0x3c708b2fb1366ea9, 0x3fda827999fcef32),
    (0x3c4ff57fa14eec2f, 0x3fdc5e87185e67b6),
    (0x3c741522f15e53c5, 0x3fde450e0d273e7a),
    (0x3c80bfceebbe8797, 0x3fe01b819b5a7cf7),
    (0xbc8e564bcd1e635d, 0x3fe11ab7190834ec),
    (0x3c5aed6fb930f332, 0x3fe220b5ef047825),
    (0xbc810b4421e6a4f8, 0x3fe32e1889047ffd),
    (0xbc8a7d457cee5076, 0x3fe44386db9ce5db),
    (0x3c87a8c52172b675, 0x3fe561b82ab7f990),
    (0x3c7439bc2d43ebfc, 0x3fe6897514751db6),
    (0xbc8aa7538e44e996, 0x3fe7bb99ed2990cf),
    (0xbc778bf71a952738, 0x3fe8f9197bf85eeb),
    (0xbc7a6db80fe796fe, 0x3fea43002ae42850),
    (0x3c76fc7e578d57ab, 0x3feb9a77c18c1af2),
    (0x3c78dcad85e60fbe, 0x3fed00cbc7384d2e),
    (0x3c8915eabb7f20cb, 0x3fee776eafc91706),
    (0x0000000000000000, 0x3ff0000000000000),
    (0x3c94986267a7063b, 0x3ff0ce29d0883c99),
    (0x3c9946cc0b66979f, 0x3ff1a73d55278c4b),
    (0x3c80322c95986960, 0x3ff28c66fdaf8f09),
    (0xbc787e5ad9735569, 0x3ff37efd8d87607e),
    (0x3c9f86b7ea4ce3dc, 0x3ff48089f8bf42cc),
    (0x3c86a085e3bc3af6, 0x3ff592d11142fa55),
    (0xbc950debdd3e20b2, 0x3ff6b7df86265200),
    (0x3c9419fa6954928f, 0x3ff7f218e25a7461),
    (0x3c9ccbeeba3801a8, 0x3ff9444a7462122a),
    (0xbc7b6fb77846d763, 0x3ffab1c35d8a74ea),
    (0x3c90a392d9ac6a3b, 0x3ffc3e738086bc0f),
    (0x3c80fb3e75c7098e, 0x3ffdef13b73c1406),
    (0x3c8b7127cf34b46c, 0x3fffc95abad6cf4a),
    (0x3c97ce6cb463c972, 0x4000ea21d716fbf7),
    (0xbc9291fd400280bf, 0x40020c36c6a7f38e),
    (0x3ca21165f626cdd5, 0x4003504f333f9de6),
    (0xbca82c5b9ae77a8b, 0x4004bd3d87fe0650),
    (0x3c7aca947bfb1dcc, 0x40065bc6cc825147),
    (0x3c8b35c6e3b49ecd, 0x400837626d70fdb8),
    (0xbc9b7a14d0d691be, 0x400a5f59e90600dd),
    (0x3c777f638a8d7d8a, 0x400ce885653127e7),
    (0xbc889fcd637fbf3b, 0x400ff01305ecd8dc),
    (0xbcaee737686fd43e, 0x4011d0143e71565f),
    (0x3c810706fed37f0e, 0x40141bfee2424771),
    (0xbcb10e285b56fe74, 0x40170d751908c1b1),
    (0xbcaae397239c5a0d, 0x401af73f4ca3310f),
    (0xbcbd4a376685482f, 0x4020372fb36b87e2),
    (0x3cc351daea79411d, 0x40244e6c595afdcc),
    (0x3cb67e518f25e3f8, 0x402b1d03c03d2f7f),
    (0xbc7b6e6b4de0cd24, 0x40345affed201b55),
    (0x3cde2447b82ca2f3, 0x40445e2455e4aaa7),
    (0xc5f4a74167598ceb, 0xc950457bf6be49c7),
    (0xbcde2447b82ca2f3, 0xc0445e2455e4aaa7),
    (0x3c7b6e6b4de0cd24, 0xc0345affed201b55),
    (0xbcb67e518f25e3f8, 0xc02b1d03c03d2f7f),
    (0xbcc351daea79411d, 0xc0244e6c595afdcc),
    (0x3cbd4a376685482f, 0xc020372fb36b87e2),
    (0x3caae397239c5a0d, 0xc01af73f4ca3310f),
    (0x3cb10e285b56fe74, 0xc0170d751908c1b1),
    (0xbc810706fed37f0e, 0xc0141bfee2424771),
    (0x3caee737686fd43e, 0xc011d0143e71565f),
    (0x3c889fcd637fbf3b, 0xc00ff01305ecd8dc),
    (0xbc777f638a8d7d8a, 0xc00ce885653127e7),
    (0x3c9b7a14d0d691be, 0xc00a5f59e90600dd),
    (0xbc8b35c6e3b49ecd, 0xc00837626d70fdb8),
    (0xbc7aca947bfb1dcc, 0xc0065bc6cc825147),
    (0x3ca82c5b9ae77a8b, 0xc004bd3d87fe0650),
    (0xbca21165f626cdd5, 0xc003504f333f9de6),
    (0x3c9291fd400280bf, 0xc0020c36c6a7f38e),
    (0xbc97ce6cb463c972, 0xc000ea21d716fbf7),
    (0xbc8b7127cf34b46c, 0xbfffc95abad6cf4a),
    (0xbc80fb3e75c7098e, 0xbffdef13b73c1406),
    (0xbc90a392d9ac6a3b, 0xbffc3e738086bc0f),
    (0x3c7b6fb77846d763, 0xbffab1c35d8a74ea),
    (0xbc9ccbeeba3801a8, 0xbff9444a7462122a),
    (0xbc9419fa6954928f, 0xbff7f218e25a7461),
    (0x3c950debdd3e20b2, 0xbff6b7df86265200),
    (0xbc86a085e3bc3af6, 0xbff592d11142fa55),
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