pxfm 0.1.29

/*
 * // Copyright (c) Radzivon Bartoshyk 6/2025. 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.
 */

pub(crate) static LOG2P1_EXACT: [u64; 53] = [
    0x3ff0000000000000,
    0x4008000000000000,
    0x401c000000000000,
    0x402e000000000000,
    0x403f000000000000,
    0x404f800000000000,
    0x405fc00000000000,
    0x406fe00000000000,
    0x407ff00000000000,
    0x408ff80000000000,
    0x409ffc0000000000,
    0x40affe0000000000,
    0x40bfff0000000000,
    0x40cfff8000000000,
    0x40dfffc000000000,
    0x40efffe000000000,
    0x40fffff000000000,
    0x410ffff800000000,
    0x411ffffc00000000,
    0x412ffffe00000000,
    0x413fffff00000000,
    0x414fffff80000000,
    0x415fffffc0000000,
    0x416fffffe0000000,
    0x417ffffff0000000,
    0x418ffffff8000000,
    0x419ffffffc000000,
    0x41affffffe000000,
    0x41bfffffff000000,
    0x41cfffffff800000,
    0x41dfffffffc00000,
    0x41efffffffe00000,
    0x41fffffffff00000,
    0x420ffffffff80000,
    0x421ffffffffc0000,
    0x422ffffffffe0000,
    0x423fffffffff0000,
    0x424fffffffff8000,
    0x425fffffffffc000,
    0x426fffffffffe000,
    0x427ffffffffff000,
    0x428ffffffffff800,
    0x429ffffffffffc00,
    0x42affffffffffe00,
    0x42bfffffffffff00,
    0x42cfffffffffff80,
    0x42dfffffffffffc0,
    0x42efffffffffffe0,
    0x42fffffffffffff0,
    0x430ffffffffffff8,
    0x431ffffffffffffc,
    0x432ffffffffffffe,
    0x433fffffffffffff,
];

/* For 362 <= i <= 724, r[i] = LOG2P1_INVERSE[i-362] is a 10-bit approximation of
1/x[i], where i*2^-9 <= x[i] < (i+1)*2^-9.
More precisely r[i] is a 10-bit value such that r[i]*y-1 is representable
exactly on 53 bits for any y, i*2^-9 <= y < (i+1)*2^-9.
Moreover |r[i]*y-1| <= 0.00212097167968735. */

pub(crate) static LOG2P1_INVERSE: [u64; 363] = [
    0x3ff6980000000000,
    0x3ff6880000000000,
    0x3ff6780000000000,
    0x3ff6680000000000,
    0x3ff6580000000000,
    0x3ff6480000000000,
    0x3ff6380000000000,
    0x3ff6300000000000,
    0x3ff6200000000000,
    0x3ff6100000000000,
    0x3ff6000000000000,
    0x3ff5f00000000000,
    0x3ff5e00000000000,
    0x3ff5d00000000000,
    0x3ff5c00000000000,
    0x3ff5b00000000000,
    0x3ff5a80000000000,
    0x3ff5980000000000,
    0x3ff5880000000000,
    0x3ff5780000000000,
    0x3ff5680000000000,
    0x3ff5600000000000,
    0x3ff5500000000000,
    0x3ff5400000000000,
    0x3ff5300000000000,
    0x3ff5200000000000,
    0x3ff5180000000000,
    0x3ff5080000000000,
    0x3ff4f80000000000,
    0x3ff4f00000000000,
    0x3ff4e00000000000,
    0x3ff4d00000000000,
    0x3ff4c00000000000,
    0x3ff4b80000000000,
    0x3ff4a80000000000,
    0x3ff4a00000000000,
    0x3ff4900000000000,
    0x3ff4800000000000,
    0x3ff4780000000000,
    0x3ff4680000000000,
    0x3ff4580000000000,
    0x3ff4500000000000,
    0x3ff4400000000000,
    0x3ff4300000000000,
    0x3ff4280000000000,
    0x3ff4180000000000,
    0x3ff4100000000000,
    0x3ff4000000000000,
    0x3ff3f80000000000,
    0x3ff3e80000000000,
    0x3ff3e00000000000,
    0x3ff3d00000000000,
    0x3ff3c00000000000,
    0x3ff3b80000000000,
    0x3ff3a80000000000,
    0x3ff3a00000000000,
    0x3ff3900000000000,
    0x3ff3880000000000,
    0x3ff3780000000000,
    0x3ff3700000000000,
    0x3ff3600000000000,
    0x3ff3580000000000,
    0x3ff3500000000000,
    0x3ff3400000000000,
    0x3ff3380000000000,
    0x3ff3280000000000,
    0x3ff3200000000000,
    0x3ff3100000000000,
    0x3ff3080000000000,
    0x3ff3000000000000,
    0x3ff2f00000000000,
    0x3ff2e80000000000,
    0x3ff2d80000000000,
    0x3ff2d00000000000,
    0x3ff2c80000000000,
    0x3ff2b80000000000,
    0x3ff2b00000000000,
    0x3ff2a00000000000,
    0x3ff2980000000000,
    0x3ff2900000000000,
    0x3ff2800000000000,
    0x3ff2780000000000,
    0x3ff2700000000000,
    0x3ff2600000000000,
    0x3ff2580000000000,
    0x3ff2500000000000,
    0x3ff2400000000000,
    0x3ff2380000000000,
    0x3ff2300000000000,
    0x3ff2280000000000,
    0x3ff2180000000000,
    0x3ff2100000000000,
    0x3ff2080000000000,
    0x3ff2000000000000,
    0x3ff1f00000000000,
    0x3ff1e80000000000,
    0x3ff1e00000000000,
    0x3ff1d00000000000,
    0x3ff1c80000000000,
    0x3ff1c00000000000,
    0x3ff1b80000000000,
    0x3ff1b00000000000,
    0x3ff1a00000000000,
    0x3ff1980000000000,
    0x3ff1900000000000,
    0x3ff1880000000000,
    0x3ff1800000000000,
    0x3ff1700000000000,
    0x3ff1680000000000,
    0x3ff1600000000000,
    0x3ff1580000000000,
    0x3ff1500000000000,
    0x3ff1400000000000,
    0x3ff1380000000000,
    0x3ff1300000000000,
    0x3ff1280000000000,
    0x3ff1200000000000,
    0x3ff1180000000000,
    0x3ff1100000000000,
    0x3ff1000000000000,
    0x3ff0f80000000000,
    0x3ff0f00000000000,
    0x3ff0e80000000000,
    0x3ff0e00000000000,
    0x3ff0d80000000000,
    0x3ff0d00000000000,
    0x3ff0c80000000000,
    0x3ff0c00000000000,
    0x3ff0b00000000000,
    0x3ff0a80000000000,
    0x3ff0a00000000000,
    0x3ff0980000000000,
    0x3ff0900000000000,
    0x3ff0880000000000,
    0x3ff0800000000000,
    0x3ff0780000000000,
    0x3ff0700000000000,
    0x3ff0680000000000,
    0x3ff0600000000000,
    0x3ff0580000000000,
    0x3ff0500000000000,
    0x3ff0480000000000,
    0x3ff0400000000000,
    0x3ff0380000000000,
    0x3ff0300000000000,
    0x3ff0280000000000,
    0x3ff0200000000000,
    0x3ff0180000000000,
    0x3ff0100000000000,
    0x3ff0080000000000,
    0x3feff80000000000,
    0x3fefe80000000000,
    0x3fefd80000000000,
    0x3fefc80000000000,
    0x3fefb80000000000,
    0x3fefa80000000000,
    0x3fef980000000000,
    0x3fef880000000000,
    0x3fef780000000000,
    0x3fef680000000000,
    0x3fef580000000000,
    0x3fef500000000000,
    0x3fef400000000000,
    0x3fef300000000000,
    0x3fef200000000000,
    0x3fef100000000000,
    0x3fef000000000000,
    0x3feef00000000000,
    0x3feee00000000000,
    0x3feed00000000000,
    0x3feec80000000000,
    0x3feeb80000000000,
    0x3feea80000000000,
    0x3fee980000000000,
    0x3fee880000000000,
    0x3fee780000000000,
    0x3fee700000000000,
    0x3fee600000000000,
    0x3fee500000000000,
    0x3fee400000000000,
    0x3fee300000000000,
    0x3fee280000000000,
    0x3fee180000000000,
    0x3fee080000000000,
    0x3fedf80000000000,
    0x3fedf00000000000,
    0x3fede00000000000,
    0x3fedd00000000000,
    0x3fedc00000000000,
    0x3fedb80000000000,
    0x3feda80000000000,
    0x3fed980000000000,
    0x3fed900000000000,
    0x3fed800000000000,
    0x3fed700000000000,
    0x3fed600000000000,
    0x3fed580000000000,
    0x3fed480000000000,
    0x3fed380000000000,
    0x3fed300000000000,
    0x3fed200000000000,
    0x3fed100000000000,
    0x3fed080000000000,
    0x3fecf80000000000,
    0x3fece80000000000,
    0x3fece00000000000,
    0x3fecd00000000000,
    0x3fecc80000000000,
    0x3fecb80000000000,
    0x3feca80000000000,
    0x3feca00000000000,
    0x3fec900000000000,
    0x3fec880000000000,
    0x3fec780000000000,
    0x3fec680000000000,
    0x3fec600000000000,
    0x3fec500000000000,
    0x3fec480000000000,
    0x3fec380000000000,
    0x3fec300000000000,
    0x3fec200000000000,
    0x3fec180000000000,
    0x3fec080000000000,
    0x3febf80000000000,
    0x3febf00000000000,
    0x3febe00000000000,
    0x3febd80000000000,
    0x3febc80000000000,
    0x3febc00000000000,
    0x3febb00000000000,
    0x3feba80000000000,
    0x3feb980000000000,
    0x3feb900000000000,
    0x3feb800000000000,
    0x3feb780000000000,
    0x3feb680000000000,
    0x3feb600000000000,
    0x3feb580000000000,
    0x3feb480000000000,
    0x3feb400000000000,
    0x3feb300000000000,
    0x3feb280000000000,
    0x3feb180000000000,
    0x3feb100000000000,
    0x3feb000000000000,
    0x3feaf80000000000,
    0x3feaf00000000000,
    0x3feae00000000000,
    0x3fead80000000000,
    0x3feac80000000000,
    0x3feac00000000000,
    0x3feab80000000000,
    0x3feaa80000000000,
    0x3feaa00000000000,
    0x3fea900000000000,
    0x3fea880000000000,
    0x3fea800000000000,
    0x3fea700000000000,
    0x3fea680000000000,
    0x3fea600000000000,
    0x3fea500000000000,
    0x3fea480000000000,
    0x3fea400000000000,
    0x3fea300000000000,
    0x3fea280000000000,
    0x3fea200000000000,
    0x3fea100000000000,
    0x3fea080000000000,
    0x3fea000000000000,
    0x3fe9f00000000000,
    0x3fe9e80000000000,
    0x3fe9e00000000000,
    0x3fe9d00000000000,
    0x3fe9c80000000000,
    0x3fe9c00000000000,
    0x3fe9b00000000000,
    0x3fe9a80000000000,
    0x3fe9a00000000000,
    0x3fe9980000000000,
    0x3fe9880000000000,
    0x3fe9800000000000,
    0x3fe9780000000000,
    0x3fe9680000000000,
    0x3fe9600000000000,
    0x3fe9580000000000,
    0x3fe9500000000000,
    0x3fe9400000000000,
    0x3fe9380000000000,
    0x3fe9300000000000,
    0x3fe9280000000000,
    0x3fe9200000000000,
    0x3fe9100000000000,
    0x3fe9080000000000,
    0x3fe9000000000000,
    0x3fe8f80000000000,
    0x3fe8e80000000000,
    0x3fe8e00000000000,
    0x3fe8d80000000000,
    0x3fe8d00000000000,
    0x3fe8c80000000000,
    0x3fe8b80000000000,
    0x3fe8b00000000000,
    0x3fe8a80000000000,
    0x3fe8a00000000000,
    0x3fe8980000000000,
    0x3fe8880000000000,
    0x3fe8800000000000,
    0x3fe8780000000000,
    0x3fe8700000000000,
    0x3fe8680000000000,
    0x3fe8600000000000,
    0x3fe8500000000000,
    0x3fe8480000000000,
    0x3fe8400000000000,
    0x3fe8380000000000,
    0x3fe8300000000000,
    0x3fe8280000000000,
    0x3fe8200000000000,
    0x3fe8100000000000,
    0x3fe8080000000000,
    0x3fe8000000000000,
    0x3fe7f80000000000,
    0x3fe7f00000000000,
    0x3fe7e80000000000,
    0x3fe7e00000000000,
    0x3fe7d80000000000,
    0x3fe7c80000000000,
    0x3fe7c00000000000,
    0x3fe7b80000000000,
    0x3fe7b00000000000,
    0x3fe7a80000000000,
    0x3fe7a00000000000,
    0x3fe7980000000000,
    0x3fe7900000000000,
    0x3fe7880000000000,
    0x3fe7800000000000,
    0x3fe7780000000000,
    0x3fe7700000000000,
    0x3fe7600000000000,
    0x3fe7580000000000,
    0x3fe7500000000000,
    0x3fe7480000000000,
    0x3fe7400000000000,
    0x3fe7380000000000,
    0x3fe7300000000000,
    0x3fe7280000000000,
    0x3fe7200000000000,
    0x3fe7180000000000,
    0x3fe7100000000000,
    0x3fe7080000000000,
    0x3fe7000000000000,
    0x3fe6f80000000000,
    0x3fe6f00000000000,
    0x3fe6e80000000000,
    0x3fe6e00000000000,
    0x3fe6d80000000000,
    0x3fe6d00000000000,
    0x3fe6c80000000000,
    0x3fe6c00000000000,
    0x3fe6b80000000000,
    0x3fe6b00000000000,
    0x3fe6a80000000000,
    0x3fe6a00000000000,
];

pub(crate) static LOG2P1_LOG_DD_INVERSE: [(u64, u64); 363] = [
    (0xbd13c7ca90bc04b2, 0xbfd615ddb4bec000),
    (0xbd3527d18f7738fa, 0xbfd5e87b20c29000),
    (0x3d339ae8f873fa41, 0xbfd5baf846aa2000),
    (0xbd2791f30a795215, 0xbfd58d54f86e0000),
    (0x3d11e64778df4a62, 0xbfd55f9107a44000),
    (0xbd3df83b7d931501, 0xbfd531ac457ee000),
    (0x3d2a68c8f16f9b5d, 0xbfd503a682cb2000),
    (0xbd234d7aaf04d104, 0xbfd4ec9732600000),
    (0x3d3d7c92cd9ad824, 0xbfd4be5f95778000),
    (0x3d38bccffe1a0f8c, 0xbfd4900680401000),
    (0x3d13d82f484c84cc, 0xbfd4618bc21c6000),
    (0x3d3fb129931715ad, 0xbfd432ef2a04f000),
    (0xbd3f8ef43049f7d3, 0xbfd404308686a000),
    (0xbd3c3e1cd9a395e3, 0xbfd3d54fa5c1f000),
    (0xbd37a71cbcd735d0, 0xbfd3a64c55694000),
    (0x3d3e9436ac53b023, 0xbfd3772662bfe000),
    (0x3d3b07de4ea1a54a, 0xbfd35f865c933000),
    (0xbd36217dc2a3e08b, 0xbfd3302c16586000),
    (0xbd342f568b75fcac, 0xbfd300aead063000),
    (0xbd360c61f7088353, 0xbfd2d10dec508000),
    (0x3d30dbbf51f3aadc, 0xbfd2a1499f763000),
    (0xbd3a8d7ad24c13f0, 0xbfd2895a13de8000),
    (0xbd38e7bc224ea3e3, 0xbfd2596010df7000),
    (0x3d3a6976f5eb0963, 0xbfd22941fbcf8000),
    (0xbd27946c040cbe77, 0xbfd1f8ff9e48a000),
    (0x3d381410e5c62aff, 0xbfd1c898c169a000),
    (0x3d32dd466dc55e2d, 0xbfd1b05791f08000),
    (0x3d3a8a8ba74a2684, 0xbfd17fb98e151000),
    (0x3d3e97a65dfc9794, 0xbfd14ef67f887000),
    (0x3d3d3e8499d67123, 0xbfd136870293b000),
    (0x3d34ab9d817d52cd, 0xbfd1058bf9ae5000),
    (0xbd3d2c81f640e1e6, 0xbfd0d46b579ab000),
    (0xbd0c6bee7ef4030e, 0xbfd0a324e2739000),
    (0xbd3ebc1d40c5a329, 0xbfd08a73667c5000),
    (0x3d30e866bcd236ad, 0xbfd058f3c703f000),
    (0xbcf036b89ef42d7f, 0xbfd0402594b4d000),
    (0xbcdcc68d52e01203, 0xbfd00e6c45ad5000),
    (0x3d0d572aab993c87, 0xbfcfb9186d5e4000),
    (0x3d3f75fd6a526efe, 0xbfcf871b28956000),
    (0x3d3f454f1417e41f, 0xbfcf22e5e72f2000),
    (0x3d23d45330fdca4d, 0xbfcebe61f4dd8000),
    (0x3d26805b80e8e6ff, 0xbfce8c0252aa6000),
    (0x3d3a342c2af0003c, 0xbfce27076e2b0000),
    (0xbd38fac1a628ccc6, 0xbfcdc1bca0abe000),
    (0x3d15105fc364c784, 0xbfcd8ef91af32000),
    (0x3d383270128aaa5f, 0xbfcd293581b6c000),
    (0xbd2771239a07d55b, 0xbfccf6354e09c000),
    (0x3d27794f689f8434, 0xbfcc8ff7c79aa000),
    (0xbd20929decb454fc, 0xbfcc5cba543ae000),
    (0xbd2386a947c378b5, 0xbfcbf601bb0e4000),
    (0xbd39ac53f39d121c, 0xbfcbc286742d8000),
    (0x3d34b722ec011f31, 0xbfcb5b519e8fc000),
    (0x3cba4e633fcd9066, 0xbfcaf3c94e80c000),
    (0x3d3b68f5395f139d, 0xbfcabfe5ae462000),
    (0xbd3b99c8ca1d9abb, 0xbfca57df28244000),
    (0x3d3539cd91dc9f0b, 0xbfca23bc1fe2c000),
    (0x3d21f2a8a1ce0ffc, 0xbfc9bb362e7e0000),
    (0xbcf93b564dd44000, 0xbfc986d322818000),
    (0xbd37bc6abddeff46, 0xbfc91dcc8c340000),
    (0xbd3a8154b13d72d5, 0xbfc8e928de886000),
    (0xbd322120401202fc, 0xbfc87fa06520c000),
    (0x3d3d8daadf4e2bd2, 0xbfc84abb75866000),
    (0x3d302a52f9201ce8, 0xbfc815c0a1436000),
    (0x3d2bdb9072534a58, 0xbfc7ab890210e000),
    (0xbd0274903479e3d1, 0xbfc7764c128f2000),
    (0xbd34ea64f6a95bef, 0xbfc70b8f97a1a000),
    (0x3d3bc6e557134767, 0xbfc6d60fe719e000),
    (0xbd3aa1bdbfc6c785, 0xbfc66acd4272a000),
    (0xbd2d5ec0ab8163af, 0xbfc6350a28aaa000),
    (0x3d38586f183bebf2, 0xbfc5ff3070a7a000),
    (0xbcf0ba68b7555d4a, 0xbfc59338d9982000),
    (0xbd3add94dda647e8, 0xbfc55d1ad4232000),
    (0x3d3e9bf2fafeaf27, 0xbfc4f099f4a24000),
    (0x3d34354bb3f219e5, 0xbfc4ba36f39a6000),
    (0xbd1eea52723f6369, 0xbfc483bccce6e000),
    (0x3d210047081f849d, 0xbfc41682bf728000),
    (0xbd28a72a62b8c13f, 0xbfc3dfc2b0ecc000),
    (0xbd3ee8779b2d8abc, 0xbfc371fc201e8000),
    (0xbd3c9ecca2fe72a5, 0xbfc33af575770000),
    (0x3cd680b5ce3ecb05, 0xbfc303d718e48000),
    (0x3d35b967f4471dfc, 0xbfc29552f8200000),
    (0xbd35a3854f176449, 0xbfc25ded0abc6000),
    (0x3d24d20ab840e7f6, 0xbfc2266f190a6000),
    (0xbd2e80a41811a396, 0xbfc1b72ad52f6000),
    (0xbd2843fad093c8dc, 0xbfc17f6458fca000),
    (0xbd1563451027c750, 0xbfc1478584674000),
    (0xbd3cb2cd2ee2f482, 0xbfc0d77e7cd08000),
    (0x3d28f3057157d1a8, 0xbfc09f561ee72000),
    (0x3d2a47579cdc0a3d, 0xbfc0671512ca6000),
    (0x3d15a8fa5ce00e5d, 0xbfc02ebb42bf4000),
    (0x3d010987e897ed01, 0xbfbf7b79fec38000),
    (0x3d3d599e83368e91, 0xbfbf0a30c0118000),
    (0xbd34677489c50e97, 0xbfbe98b549670000),
    (0x3d2a342c2af0003c, 0xbfbe27076e2b0000),
    (0x3d29454379135713, 0xbfbd4313d66cc000),
    (0xbd33e14db50dd743, 0xbfbcd0cdbf8c0000),
    (0xbd1d0c57585fbe06, 0xbfbc5e548f5bc000),
    (0x3d325ef7bc3987e7, 0xbfbb78c82bb10000),
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