pub const SMALLEST_POWER_OF_FIVE: i32 = -342;
pub const LARGEST_POWER_OF_FIVE: i32 = 308;
pub const N_POWERS_OF_FIVE: usize = (LARGEST_POWER_OF_FIVE - SMALLEST_POWER_OF_FIVE + 1) as usize;
#[cfg(test)]
mod tests {
use super::*;
use num_bigint::BigUint;
fn compute_pow5_128(q: i32) -> (u64, u64) {
let mut c = if q < 0 {
let pow5 = BigUint::from(5_u8).pow((-q) as u32);
let mut z = 0_u16;
while (BigUint::from(1_u8) << z) < pow5 {
z += 1;
}
let b = if q < -27 { 2 * z + 128 } else { z + 127 };
(BigUint::from(1_u8) << b) / pow5 + BigUint::from(1_u8)
} else {
BigUint::from(5_u8).pow(q as u32)
};
while c < (BigUint::from(1_u8) << 127) {
c <<= 1;
}
while c >= (BigUint::from(1_u8) << 128) {
c >>= 1;
}
let mut digits = c.to_u32_digits();
while digits.len() < 4 {
digits.push(0);
}
assert_eq!(digits.len(), 4);
let lo = (digits[0] as u64) + (digits[1] as u64 * (1_u64 << 32));
let hi = (digits[2] as u64) + (digits[3] as u64 * (1_u64 << 32));
(hi, lo)
}
#[test]
fn test_pow5_table() {
for q in SMALLEST_POWER_OF_FIVE..=LARGEST_POWER_OF_FIVE {
let (hi, lo) = compute_pow5_128(q);
let expected = POWER_OF_FIVE_128[(q - SMALLEST_POWER_OF_FIVE) as usize];
assert_eq!(hi, expected.0);
assert_eq!(lo, expected.1);
}
}
}
#[allow(clippy::unreadable_literal)]
pub const POWER_OF_FIVE_128: [(u64, u64); N_POWERS_OF_FIVE] = [
(0xeef453d6923bd65a, 0x113faa2906a13b3f),
(0x9558b4661b6565f8, 0x4ac7ca59a424c507),
(0xbaaee17fa23ebf76, 0x5d79bcf00d2df649),
(0xe95a99df8ace6f53, 0xf4d82c2c107973dc),
(0x91d8a02bb6c10594, 0x79071b9b8a4be869),
(0xb64ec836a47146f9, 0x9748e2826cdee284),
(0xe3e27a444d8d98b7, 0xfd1b1b2308169b25),
(0x8e6d8c6ab0787f72, 0xfe30f0f5e50e20f7),
(0xb208ef855c969f4f, 0xbdbd2d335e51a935),
(0xde8b2b66b3bc4723, 0xad2c788035e61382),
(0x8b16fb203055ac76, 0x4c3bcb5021afcc31),
(0xaddcb9e83c6b1793, 0xdf4abe242a1bbf3d),
(0xd953e8624b85dd78, 0xd71d6dad34a2af0d),
(0x87d4713d6f33aa6b, 0x8672648c40e5ad68),
(0xa9c98d8ccb009506, 0x680efdaf511f18c2),
(0xd43bf0effdc0ba48, 0x212bd1b2566def2),
(0x84a57695fe98746d, 0x14bb630f7604b57),
(0xa5ced43b7e3e9188, 0x419ea3bd35385e2d),
(0xcf42894a5dce35ea, 0x52064cac828675b9),
(0x818995ce7aa0e1b2, 0x7343efebd1940993),
(0xa1ebfb4219491a1f, 0x1014ebe6c5f90bf8),
(0xca66fa129f9b60a6, 0xd41a26e077774ef6),
(0xfd00b897478238d0, 0x8920b098955522b4),
(0x9e20735e8cb16382, 0x55b46e5f5d5535b0),
(0xc5a890362fddbc62, 0xeb2189f734aa831d),
(0xf712b443bbd52b7b, 0xa5e9ec7501d523e4),
(0x9a6bb0aa55653b2d, 0x47b233c92125366e),
(0xc1069cd4eabe89f8, 0x999ec0bb696e840a),
(0xf148440a256e2c76, 0xc00670ea43ca250d),
(0x96cd2a865764dbca, 0x380406926a5e5728),
(0xbc807527ed3e12bc, 0xc605083704f5ecf2),
(0xeba09271e88d976b, 0xf7864a44c633682e),
(0x93445b8731587ea3, 0x7ab3ee6afbe0211d),
(0xb8157268fdae9e4c, 0x5960ea05bad82964),
(0xe61acf033d1a45df, 0x6fb92487298e33bd),
(0x8fd0c16206306bab, 0xa5d3b6d479f8e056),
(0xb3c4f1ba87bc8696, 0x8f48a4899877186c),
(0xe0b62e2929aba83c, 0x331acdabfe94de87),
(0x8c71dcd9ba0b4925, 0x9ff0c08b7f1d0b14),
(0xaf8e5410288e1b6f, 0x7ecf0ae5ee44dd9),
(0xdb71e91432b1a24a, 0xc9e82cd9f69d6150),
(0x892731ac9faf056e, 0xbe311c083a225cd2),
(0xab70fe17c79ac6ca, 0x6dbd630a48aaf406),
(0xd64d3d9db981787d, 0x92cbbccdad5b108),
(0x85f0468293f0eb4e, 0x25bbf56008c58ea5),
(0xa76c582338ed2621, 0xaf2af2b80af6f24e),
(0xd1476e2c07286faa, 0x1af5af660db4aee1),
(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),
(0x94b3a202eb1c3f39, 0x7bf7d71432f3d6a9),
(0xb9e08a83a5e34f07, 0xdaf5ccd93fb0cc53),
(0xe858ad248f5c22c9, 0xd1b3400f8f9cff68),
(0x91376c36d99995be, 0x23100809b9c21fa1),
(0xb58547448ffffb2d, 0xabd40a0c2832a78a),
(0xe2e69915b3fff9f9, 0x16c90c8f323f516c),
(0x8dd01fad907ffc3b, 0xae3da7d97f6792e3),
(0xb1442798f49ffb4a, 0x99cd11cfdf41779c),
(0xdd95317f31c7fa1d, 0x40405643d711d583),
(0x8a7d3eef7f1cfc52, 0x482835ea666b2572),
(0xad1c8eab5ee43b66, 0xda3243650005eecf),
(0xd863b256369d4a40, 0x90bed43e40076a82),
(0x873e4f75e2224e68, 0x5a7744a6e804a291),
(0xa90de3535aaae202, 0x711515d0a205cb36),
(0xd3515c2831559a83, 0xd5a5b44ca873e03),
(0x8412d9991ed58091, 0xe858790afe9486c2),
(0xa5178fff668ae0b6, 0x626e974dbe39a872),
(0xce5d73ff402d98e3, 0xfb0a3d212dc8128f),
(0x80fa687f881c7f8e, 0x7ce66634bc9d0b99),
(0xa139029f6a239f72, 0x1c1fffc1ebc44e80),
(0xc987434744ac874e, 0xa327ffb266b56220),
(0xfbe9141915d7a922, 0x4bf1ff9f0062baa8),
(0x9d71ac8fada6c9b5, 0x6f773fc3603db4a9),
(0xc4ce17b399107c22, 0xcb550fb4384d21d3),
(0xf6019da07f549b2b, 0x7e2a53a146606a48),
(0x99c102844f94e0fb, 0x2eda7444cbfc426d),
(0xc0314325637a1939, 0xfa911155fefb5308),
(0xf03d93eebc589f88, 0x793555ab7eba27ca),
(0x96267c7535b763b5, 0x4bc1558b2f3458de),
(0xbbb01b9283253ca2, 0x9eb1aaedfb016f16),
(0xea9c227723ee8bcb, 0x465e15a979c1cadc),
(0x92a1958a7675175f, 0xbfacd89ec191ec9),
(0xb749faed14125d36, 0xcef980ec671f667b),
(0xe51c79a85916f484, 0x82b7e12780e7401a),
(0x8f31cc0937ae58d2, 0xd1b2ecb8b0908810),
(0xb2fe3f0b8599ef07, 0x861fa7e6dcb4aa15),
(0xdfbdcece67006ac9, 0x67a791e093e1d49a),
(0x8bd6a141006042bd, 0xe0c8bb2c5c6d24e0),
(0xaecc49914078536d, 0x58fae9f773886e18),
(0xda7f5bf590966848, 0xaf39a475506a899e),
(0x888f99797a5e012d, 0x6d8406c952429603),
(0xaab37fd7d8f58178, 0xc8e5087ba6d33b83),
(0xd5605fcdcf32e1d6, 0xfb1e4a9a90880a64),
(0x855c3be0a17fcd26, 0x5cf2eea09a55067f),
(0xa6b34ad8c9dfc06f, 0xf42faa48c0ea481e),
(0xd0601d8efc57b08b, 0xf13b94daf124da26),
(0x823c12795db6ce57, 0x76c53d08d6b70858),
(0xa2cb1717b52481ed, 0x54768c4b0c64ca6e),
(0xcb7ddcdda26da268, 0xa9942f5dcf7dfd09),
(0xfe5d54150b090b02, 0xd3f93b35435d7c4c),
(0x9efa548d26e5a6e1, 0xc47bc5014a1a6daf),
(0xc6b8e9b0709f109a, 0x359ab6419ca1091b),
(0xf867241c8cc6d4c0, 0xc30163d203c94b62),
(0x9b407691d7fc44f8, 0x79e0de63425dcf1d),
(0xc21094364dfb5636, 0x985915fc12f542e4),
(0xf294b943e17a2bc4, 0x3e6f5b7b17b2939d),
(0x979cf3ca6cec5b5a, 0xa705992ceecf9c42),
(0xbd8430bd08277231, 0x50c6ff782a838353),
(0xece53cec4a314ebd, 0xa4f8bf5635246428),
(0x940f4613ae5ed136, 0x871b7795e136be99),
(0xb913179899f68584, 0x28e2557b59846e3f),
(0xe757dd7ec07426e5, 0x331aeada2fe589cf),
(0x9096ea6f3848984f, 0x3ff0d2c85def7621),
(0xb4bca50b065abe63, 0xfed077a756b53a9),
(0xe1ebce4dc7f16dfb, 0xd3e8495912c62894),
(0x8d3360f09cf6e4bd, 0x64712dd7abbbd95c),
(0xb080392cc4349dec, 0xbd8d794d96aacfb3),
(0xdca04777f541c567, 0xecf0d7a0fc5583a0),
(0x89e42caaf9491b60, 0xf41686c49db57244),
(0xac5d37d5b79b6239, 0x311c2875c522ced5),
(0xd77485cb25823ac7, 0x7d633293366b828b),
(0x86a8d39ef77164bc, 0xae5dff9c02033197),
(0xa8530886b54dbdeb, 0xd9f57f830283fdfc),
(0xd267caa862a12d66, 0xd072df63c324fd7b),
(0x8380dea93da4bc60, 0x4247cb9e59f71e6d),
(0xa46116538d0deb78, 0x52d9be85f074e608),
(0xcd795be870516656, 0x67902e276c921f8b),
(0x806bd9714632dff6, 0xba1cd8a3db53b6),
(0xa086cfcd97bf97f3, 0x80e8a40eccd228a4),
(0xc8a883c0fdaf7df0, 0x6122cd128006b2cd),
(0xfad2a4b13d1b5d6c, 0x796b805720085f81),
(0x9cc3a6eec6311a63, 0xcbe3303674053bb0),
(0xc3f490aa77bd60fc, 0xbedbfc4411068a9c),
(0xf4f1b4d515acb93b, 0xee92fb5515482d44),
(0x991711052d8bf3c5, 0x751bdd152d4d1c4a),
(0xbf5cd54678eef0b6, 0xd262d45a78a0635d),
(0xef340a98172aace4, 0x86fb897116c87c34),
(0x9580869f0e7aac0e, 0xd45d35e6ae3d4da0),
(0xbae0a846d2195712, 0x8974836059cca109),
(0xe998d258869facd7, 0x2bd1a438703fc94b),
(0x91ff83775423cc06, 0x7b6306a34627ddcf),
(0xb67f6455292cbf08, 0x1a3bc84c17b1d542),
(0xe41f3d6a7377eeca, 0x20caba5f1d9e4a93),
(0x8e938662882af53e, 0x547eb47b7282ee9c),
(0xb23867fb2a35b28d, 0xe99e619a4f23aa43),
(0xdec681f9f4c31f31, 0x6405fa00e2ec94d4),
(0x8b3c113c38f9f37e, 0xde83bc408dd3dd04),
(0xae0b158b4738705e, 0x9624ab50b148d445),
(0xd98ddaee19068c76, 0x3badd624dd9b0957),
(0x87f8a8d4cfa417c9, 0xe54ca5d70a80e5d6),
(0xa9f6d30a038d1dbc, 0x5e9fcf4ccd211f4c),
(0xd47487cc8470652b, 0x7647c3200069671f),
(0x84c8d4dfd2c63f3b, 0x29ecd9f40041e073),
(0xa5fb0a17c777cf09, 0xf468107100525890),
(0xcf79cc9db955c2cc, 0x7182148d4066eeb4),
(0x81ac1fe293d599bf, 0xc6f14cd848405530),
(0xa21727db38cb002f, 0xb8ada00e5a506a7c),
(0xca9cf1d206fdc03b, 0xa6d90811f0e4851c),
(0xfd442e4688bd304a, 0x908f4a166d1da663),
(0x9e4a9cec15763e2e, 0x9a598e4e043287fe),
(0xc5dd44271ad3cdba, 0x40eff1e1853f29fd),
(0xf7549530e188c128, 0xd12bee59e68ef47c),
(0x9a94dd3e8cf578b9, 0x82bb74f8301958ce),
(0xc13a148e3032d6e7, 0xe36a52363c1faf01),
(0xf18899b1bc3f8ca1, 0xdc44e6c3cb279ac1),
(0x96f5600f15a7b7e5, 0x29ab103a5ef8c0b9),
(0xbcb2b812db11a5de, 0x7415d448f6b6f0e7),
(0xebdf661791d60f56, 0x111b495b3464ad21),
(0x936b9fcebb25c995, 0xcab10dd900beec34),
(0xb84687c269ef3bfb, 0x3d5d514f40eea742),
(0xe65829b3046b0afa, 0xcb4a5a3112a5112),
(0x8ff71a0fe2c2e6dc, 0x47f0e785eaba72ab),
(0xb3f4e093db73a093, 0x59ed216765690f56),
(0xe0f218b8d25088b8, 0x306869c13ec3532c),
(0x8c974f7383725573, 0x1e414218c73a13fb),
(0xafbd2350644eeacf, 0xe5d1929ef90898fa),
(0xdbac6c247d62a583, 0xdf45f746b74abf39),
(0x894bc396ce5da772, 0x6b8bba8c328eb783),
(0xab9eb47c81f5114f, 0x66ea92f3f326564),
(0xd686619ba27255a2, 0xc80a537b0efefebd),
(0x8613fd0145877585, 0xbd06742ce95f5f36),
(0xa798fc4196e952e7, 0x2c48113823b73704),
(0xd17f3b51fca3a7a0, 0xf75a15862ca504c5),
(0x82ef85133de648c4, 0x9a984d73dbe722fb),
(0xa3ab66580d5fdaf5, 0xc13e60d0d2e0ebba),
(0xcc963fee10b7d1b3, 0x318df905079926a8),
(0xffbbcfe994e5c61f, 0xfdf17746497f7052),
(0x9fd561f1fd0f9bd3, 0xfeb6ea8bedefa633),
(0xc7caba6e7c5382c8, 0xfe64a52ee96b8fc0),
(0xf9bd690a1b68637b, 0x3dfdce7aa3c673b0),
(0x9c1661a651213e2d, 0x6bea10ca65c084e),
(0xc31bfa0fe5698db8, 0x486e494fcff30a62),
(0xf3e2f893dec3f126, 0x5a89dba3c3efccfa),
(0x986ddb5c6b3a76b7, 0xf89629465a75e01c),
(0xbe89523386091465, 0xf6bbb397f1135823),
(0xee2ba6c0678b597f, 0x746aa07ded582e2c),
(0x94db483840b717ef, 0xa8c2a44eb4571cdc),
(0xba121a4650e4ddeb, 0x92f34d62616ce413),
(0xe896a0d7e51e1566, 0x77b020baf9c81d17),
(0x915e2486ef32cd60, 0xace1474dc1d122e),
(0xb5b5ada8aaff80b8, 0xd819992132456ba),
(0xe3231912d5bf60e6, 0x10e1fff697ed6c69),
(0x8df5efabc5979c8f, 0xca8d3ffa1ef463c1),
(0xb1736b96b6fd83b3, 0xbd308ff8a6b17cb2),
(0xddd0467c64bce4a0, 0xac7cb3f6d05ddbde),
(0x8aa22c0dbef60ee4, 0x6bcdf07a423aa96b),
(0xad4ab7112eb3929d, 0x86c16c98d2c953c6),
(0xd89d64d57a607744, 0xe871c7bf077ba8b7),
(0x87625f056c7c4a8b, 0x11471cd764ad4972),
(0xa93af6c6c79b5d2d, 0xd598e40d3dd89bcf),
(0xd389b47879823479, 0x4aff1d108d4ec2c3),
(0x843610cb4bf160cb, 0xcedf722a585139ba),
(0xa54394fe1eedb8fe, 0xc2974eb4ee658828),
(0xce947a3da6a9273e, 0x733d226229feea32),
(0x811ccc668829b887, 0x806357d5a3f525f),
(0xa163ff802a3426a8, 0xca07c2dcb0cf26f7),
(0xc9bcff6034c13052, 0xfc89b393dd02f0b5),
(0xfc2c3f3841f17c67, 0xbbac2078d443ace2),
(0x9d9ba7832936edc0, 0xd54b944b84aa4c0d),
(0xc5029163f384a931, 0xa9e795e65d4df11),
(0xf64335bcf065d37d, 0x4d4617b5ff4a16d5),
(0x99ea0196163fa42e, 0x504bced1bf8e4e45),
(0xc06481fb9bcf8d39, 0xe45ec2862f71e1d6),
(0xf07da27a82c37088, 0x5d767327bb4e5a4c),
(0x964e858c91ba2655, 0x3a6a07f8d510f86f),
(0xbbe226efb628afea, 0x890489f70a55368b),
(0xeadab0aba3b2dbe5, 0x2b45ac74ccea842e),
(0x92c8ae6b464fc96f, 0x3b0b8bc90012929d),
(0xb77ada0617e3bbcb, 0x9ce6ebb40173744),
(0xe55990879ddcaabd, 0xcc420a6a101d0515),
(0x8f57fa54c2a9eab6, 0x9fa946824a12232d),
(0xb32df8e9f3546564, 0x47939822dc96abf9),
(0xdff9772470297ebd, 0x59787e2b93bc56f7),
(0x8bfbea76c619ef36, 0x57eb4edb3c55b65a),
(0xaefae51477a06b03, 0xede622920b6b23f1),
(0xdab99e59958885c4, 0xe95fab368e45eced),
(0x88b402f7fd75539b, 0x11dbcb0218ebb414),
(0xaae103b5fcd2a881, 0xd652bdc29f26a119),
(0xd59944a37c0752a2, 0x4be76d3346f0495f),
(0x857fcae62d8493a5, 0x6f70a4400c562ddb),
(0xa6dfbd9fb8e5b88e, 0xcb4ccd500f6bb952),
(0xd097ad07a71f26b2, 0x7e2000a41346a7a7),
(0x825ecc24c873782f, 0x8ed400668c0c28c8),
(0xa2f67f2dfa90563b, 0x728900802f0f32fa),
(0xcbb41ef979346bca, 0x4f2b40a03ad2ffb9),
(0xfea126b7d78186bc, 0xe2f610c84987bfa8),
(0x9f24b832e6b0f436, 0xdd9ca7d2df4d7c9),
(0xc6ede63fa05d3143, 0x91503d1c79720dbb),
(0xf8a95fcf88747d94, 0x75a44c6397ce912a),
(0x9b69dbe1b548ce7c, 0xc986afbe3ee11aba),
(0xc24452da229b021b, 0xfbe85badce996168),
(0xf2d56790ab41c2a2, 0xfae27299423fb9c3),
(0x97c560ba6b0919a5, 0xdccd879fc967d41a),
(0xbdb6b8e905cb600f, 0x5400e987bbc1c920),
(0xed246723473e3813, 0x290123e9aab23b68),
(0x9436c0760c86e30b, 0xf9a0b6720aaf6521),
(0xb94470938fa89bce, 0xf808e40e8d5b3e69),
(0xe7958cb87392c2c2, 0xb60b1d1230b20e04),
(0x90bd77f3483bb9b9, 0xb1c6f22b5e6f48c2),
(0xb4ecd5f01a4aa828, 0x1e38aeb6360b1af3),
(0xe2280b6c20dd5232, 0x25c6da63c38de1b0),
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];