From 0752505755f2d6a5e27f0cbf8b6ffa3b6d184144 Mon Sep 17 00:00:00 2001 From: Jacob Zhong Date: Sun, 18 Sep 2022 12:21:17 -0400 Subject: [PATCH] Change the prime table (fix #5) --- src/integer.rs | 6 +- src/mint.rs | 138 +-- src/nt_funcs.rs | 112 +- src/tables.rs | 2917 ++++++++++++++++++++++++++++++----------------- 4 files changed, 1971 insertions(+), 1202 deletions(-) diff --git a/src/integer.rs b/src/integer.rs index 8d256ef..15b61e1 100644 --- a/src/integer.rs +++ b/src/integer.rs @@ -229,7 +229,11 @@ mod tests { let x = rng.gen_biguint(150); assert!(matches!(ExactRoots::sqrt_exact(&(&x * &x)), Some(v) if v == x)); let x = rng.gen_biguint(150); - assert!(matches!(ExactRoots::cbrt_exact(&(&x * &x * &x)), Some(v) if v == x), "failed at {}", x); + assert!( + matches!(ExactRoots::cbrt_exact(&(&x * &x * &x)), Some(v) if v == x), + "failed at {}", + x + ); } // test non-perfect powers for _ in 0..10 { diff --git a/src/mint.rs b/src/mint.rs index a3364d5..1a093ed 100644 --- a/src/mint.rs +++ b/src/mint.rs @@ -5,8 +5,8 @@ use core::ops::*; use either::*; use num_integer::{Integer, Roots}; use num_modular::{ - ModularCoreOps, ModularInteger, ModularPow, ModularSymbols, ModularUnaryOps, Reducer, - ReducedInt, Montgomery, + ModularCoreOps, ModularInteger, ModularPow, ModularSymbols, ModularUnaryOps, Montgomery, + ReducedInt, Reducer, }; use num_traits::{FromPrimitive, Num, One, Pow, ToPrimitive, Zero}; @@ -20,27 +20,6 @@ use crate::{BitTest, ExactRoots}; #[derive(Debug, Clone, Copy)] pub struct Mint>(Either>); -// // it seems that auto derivation struggles to provide an implementation for Copy, Clone and Debug with proper trait bounds -// impl Clone for Mint -// where -// T::Inv: Clone, -// { -// #[inline(always)] -// fn clone(&self) -> Self { -// Self(self.0.clone()) -// } -// } -// impl Copy for Mint where T::Inv: Copy {} -// impl core::fmt::Debug for Mint -// where -// T::Inv: core::fmt::Debug, -// { -// #[inline(always)] -// fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result { -// self.0.fmt(f) -// } -// } - impl> From for Mint { #[inline(always)] fn from(v: T) -> Self { @@ -102,8 +81,7 @@ macro_rules! forward_uops_ref { }; } -impl> PartialEq for Mint -{ +impl> PartialEq for Mint { fn eq(&self, other: &Self) -> bool { match (&self.0, &other.0) { (Left(v1), Left(v2)) => v1 == v2, @@ -112,12 +90,9 @@ impl> PartialEq for Mint } } } -impl> Eq for Mint -{ -} +impl> Eq for Mint {} -impl + Clone> PartialOrd for Mint -{ +impl + Clone> PartialOrd for Mint { fn partial_cmp(&self, other: &Self) -> Option { match (&self.0, &other.0) { (Left(v1), Left(v2)) => v1.partial_cmp(v2), @@ -130,8 +105,7 @@ impl + Clone> PartialOrd for Mint } } } -impl + Clone> Ord for Mint -{ +impl + Clone> Ord for Mint { fn cmp(&self, other: &Self) -> std::cmp::Ordering { match (&self.0, &other.0) { (Left(v1), Left(v2)) => v1.cmp(v2), @@ -142,8 +116,7 @@ impl + Clone> Ord for Mint } } -impl + Clone> Mint -{ +impl + Clone> Mint { #[inline(always)] pub fn value(&self) -> T { match &self.0 { @@ -156,8 +129,7 @@ impl + Clone> Mint // forward binary operators by converting result to MontgomeryInt whenever possible macro_rules! forward_binops_right { (impl $imp:ident, $method:ident) => { - impl + Clone> $imp for Mint - { + impl + Clone> $imp for Mint { type Output = Self; #[inline] fn $method(self, rhs: Self) -> Self::Output { @@ -173,8 +145,8 @@ macro_rules! forward_binops_right { } } - impl $imp<&'r T, Output = T>, R: Reducer + Clone> $imp<&Self> - for Mint + impl $imp<&'r T, Output = T>, R: Reducer + Clone> + $imp<&Self> for Mint { type Output = Mint; #[inline] @@ -191,8 +163,7 @@ macro_rules! forward_binops_right { } } - impl + Clone> $imp> for &Mint - { + impl + Clone> $imp> for &Mint { type Output = Mint; // FIXME: additional clone here due to https://github.com/rust-lang/rust/issues/39959 // (same for ref & ref operation below, and those for Div and Rem) @@ -209,8 +180,12 @@ macro_rules! forward_binops_right { }) } } - impl<'a, 'b, T: Integer + Clone + for<'r> $imp<&'r T, Output = T>, R: Reducer + Clone> - $imp<&'b Mint> for &'a Mint + impl< + 'a, + 'b, + T: Integer + Clone + for<'r> $imp<&'r T, Output = T>, + R: Reducer + Clone, + > $imp<&'b Mint> for &'a Mint { type Output = Mint; #[inline] @@ -233,8 +208,7 @@ forward_binops_right!(impl Add, add); forward_binops_right!(impl Sub, sub); forward_binops_right!(impl Mul, mul); -impl> Div for Mint -{ +impl> Div for Mint { type Output = Self; #[inline] @@ -243,8 +217,7 @@ impl> Div for Mint Self(Left(v1.div(v2))) } } -impl Div<&'r T, Output = T>, R: Reducer> Div<&Self> for Mint -{ +impl Div<&'r T, Output = T>, R: Reducer> Div<&Self> for Mint { type Output = Self; #[inline] @@ -255,8 +228,7 @@ impl Div<&'r T, Output = T>, R: Reducer> Div<&Se } } } -impl> Div> for &Mint -{ +impl> Div> for &Mint { type Output = Mint; #[inline] @@ -280,8 +252,7 @@ impl<'a, 'b, T: Integer + Clone + for<'r> Div<&'r T, Output = T>, R: Reducer> } } -impl + Clone> Rem for Mint -{ +impl + Clone> Rem for Mint { type Output = Self; #[inline] @@ -296,8 +267,7 @@ impl + Clone> Rem for Mint } } } -impl + Clone> Rem<&Self> for Mint -{ +impl + Clone> Rem<&Self> for Mint { type Output = Self; #[inline] @@ -312,9 +282,7 @@ impl + Clone> Rem<&Self> for Mint } } } -impl + Clone> Rem> for &Mint -where -{ +impl + Clone> Rem> for &Mint { type Output = Mint; #[inline] @@ -329,9 +297,7 @@ where } } } -impl<'a, 'b, T: Integer + Clone, R: Reducer + Clone> Rem<&'b Mint> - for &'a Mint -{ +impl<'a, 'b, T: Integer + Clone, R: Reducer + Clone> Rem<&'b Mint> for &'a Mint { type Output = Mint; #[inline] @@ -347,8 +313,7 @@ impl<'a, 'b, T: Integer + Clone, R: Reducer + Clone> Rem<&'b Mint> } } -impl + Clone> Zero for Mint -{ +impl + Clone> Zero for Mint { #[inline(always)] fn zero() -> Self { Self(Left(T::zero())) @@ -362,8 +327,7 @@ impl + Clone> Zero for Mint } } -impl + Clone> One for Mint -{ +impl + Clone> One for Mint { #[inline(always)] fn one() -> Self { Self(Left(T::one())) @@ -371,8 +335,7 @@ impl + Clone> One for Mint forward_uops_ref!(is_one => bool); } -impl + Clone> Num for Mint -{ +impl + Clone> Num for Mint { type FromStrRadixErr = ::FromStrRadixErr; #[inline(always)] @@ -381,8 +344,7 @@ impl + Clone> Num for Mint } } -impl + Clone> Integer for Mint -{ +impl + Clone> Integer for Mint { forward_binops_left_ref_only!(div_floor); forward_binops_left_ref_only!(mod_floor); forward_binops_left_ref_only!(lcm); @@ -408,8 +370,7 @@ impl + Clone> Integer for Mint } } -impl + Clone> Roots for Mint -{ +impl + Clone> Roots for Mint { #[inline] fn nth_root(&self, n: u32) -> Self { match &self.0 { @@ -419,8 +380,7 @@ impl + Clone> Roots for Mint } } -impl> FromPrimitive for Mint -{ +impl> FromPrimitive for Mint { #[inline] fn from_f64(n: f64) -> Option { T::from_f64(n).map(|v| Self(Left(v))) @@ -435,8 +395,7 @@ impl> FromPrimitive for Mint + Clone> ToPrimitive for Mint -{ +impl + Clone> ToPrimitive for Mint { #[inline] fn to_f64(&self) -> Option { match &self.0 { @@ -460,8 +419,7 @@ impl + Clone> ToPrimitive for Mi } } -impl, R: Reducer> Pow for Mint -{ +impl, R: Reducer> Pow for Mint { type Output = Self; #[inline] fn pow(self, rhs: u32) -> Self::Output { @@ -472,8 +430,7 @@ impl, R: Reducer> Pow for Mint } } -impl + Clone> ExactRoots for Mint -{ +impl + Clone> ExactRoots for Mint { #[inline] fn nth_root_exact(&self, n: u32) -> Option { match &self.0 { @@ -483,8 +440,7 @@ impl + Clone> ExactRoots for Mint } } -impl> BitTest for Mint -{ +impl> BitTest for Mint { #[inline] fn bit(&self, position: usize) -> bool { match &self.0 { @@ -508,8 +464,7 @@ impl> BitTest for Mint } } -impl, R: Reducer> Shr for Mint -{ +impl, R: Reducer> Shr for Mint { type Output = Self; #[inline] fn shr(self, rhs: usize) -> Self::Output { @@ -519,8 +474,7 @@ impl, R: Reducer> Shr for } } } -impl, R: Reducer> Shr for &Mint -{ +impl, R: Reducer> Shr for &Mint { type Output = Mint; #[inline] fn shr(self, rhs: usize) -> Self::Output { @@ -531,8 +485,7 @@ impl, R: Reducer> Shr for } } -impl + Clone> ModularCoreOps<&Self, &Self> for Mint -{ +impl + Clone> ModularCoreOps<&Self, &Self> for Mint { type Output = Self; #[inline] fn addm(self, rhs: &Self, m: &Self) -> Self::Output { @@ -565,8 +518,8 @@ impl + Clone> ModularCoreOps<&Self, &Self> for } } } -impl<'a, 'b, T: Integer + Clone, R: Reducer + Clone> ModularCoreOps<&'b Mint, &'b Mint> - for &'a Mint +impl<'a, 'b, T: Integer + Clone, R: Reducer + Clone> + ModularCoreOps<&'b Mint, &'b Mint> for &'a Mint { type Output = Mint; #[inline] @@ -601,8 +554,7 @@ impl<'a, 'b, T: Integer + Clone, R: Reducer + Clone> ModularCoreOps<&'b Mint< } } -impl + Clone> ModularUnaryOps<&Self> for Mint -{ +impl + Clone> ModularUnaryOps<&Self> for Mint { type Output = Self; #[inline] fn negm(self, m: &Self) -> Self::Output { @@ -641,7 +593,8 @@ impl + Clone> ModularUnaryOps<&Self> for Mint< })) } } -impl<'a, 'b, T: Integer + Clone, R: Reducer + Clone> ModularUnaryOps<&'b Mint> for &'a Mint +impl<'a, 'b, T: Integer + Clone, R: Reducer + Clone> ModularUnaryOps<&'b Mint> + for &'a Mint { type Output = Mint; #[inline] @@ -682,8 +635,8 @@ impl<'a, 'b, T: Integer + Clone, R: Reducer + Clone> ModularUnaryOps<&'b Mint } } -impl ModularSymbols<&'r T>, R: Reducer + Clone> ModularSymbols<&Self> - for Mint +impl ModularSymbols<&'r T>, R: Reducer + Clone> + ModularSymbols<&Self> for Mint { #[inline] fn checked_jacobi(&self, n: &Self) -> Option { @@ -711,8 +664,7 @@ impl ModularSymbols<&'r T>, R: Reducer + Clone> } } -impl + Clone> ModularPow<&Self, &Self> for Mint -{ +impl + Clone> ModularPow<&Self, &Self> for Mint { type Output = Self; #[inline] fn powm(self, exp: &Self, m: &Self) -> Self::Output { diff --git a/src/nt_funcs.rs b/src/nt_funcs.rs index 59d7f6a..f9ba995 100644 --- a/src/nt_funcs.rs +++ b/src/nt_funcs.rs @@ -16,7 +16,8 @@ use crate::factor::{one_line, pollard_rho, squfof, SQUFOF_MULTIPLIERS}; use crate::mint::SmallMint; use crate::primality::{PrimalityBase, PrimalityRefBase}; use crate::tables::{ - MOEBIUS_ODD, SMALL_PRIMES, SMALL_PRIMES_NEXT, WHEEL_NEXT, WHEEL_PREV, WHEEL_SIZE, + MILLER_RABIN_BASE32, MOEBIUS_ODD, SMALL_PRIMES, SMALL_PRIMES_NEXT, WHEEL_NEXT, WHEEL_PREV, + WHEEL_SIZE, }; #[cfg(feature = "big-table")] use crate::tables::{SMALL_PRIMES_INV, ZETA_LOG_TABLE}; @@ -32,10 +33,10 @@ use std::collections::BTreeMap; use std::convert::TryFrom; #[cfg(feature = "big-table")] -use crate::tables::{MILLER_RABIN_BASE32, MILLER_RABIN_BASE64}; +use crate::tables::MILLER_RABIN_BASE64; /// Fast primality test on a u64 integer. It's based on -/// deterministic Miller-rabin tests. if target is larger than 2^64 or more +/// deterministic Miller-rabin tests. If target is larger than 2^64 or more /// controlled primality tests are desired, please use [is_prime()] #[cfg(not(feature = "big-table"))] pub fn is_prime64(target: u64) -> bool { @@ -62,28 +63,6 @@ pub fn is_prime64(target: u64) -> bool { is_prime64_miller(target) } -// Primality test for u64 with only miller-rabin tests, used during factorization. -// It assumes the target is odd, not too small and cannot be divided small primes -#[cfg(not(feature = "big-table"))] -fn is_prime64_miller(target: u64) -> bool { - // The collection of witnesses are from http://miller-rabin.appspot.com/ - if let Ok(u) = u16::try_from(target) { - // 2, 3 for u16 range - let u = Mint::from(u); - return u.is_sprp(Mint::from(2)) && u.is_sprp(Mint::from(3)); - } - if let Ok(u) = u32::try_from(target) { - // 2, 7, 61 for u32 range - let u = Mint::from(u); - return u.is_sprp(Mint::from(2)) && u.is_sprp(Mint::from(7)) && u.is_sprp(Mint::from(61)); - } - - // 2, 325, 9375, 28178, 450775, 9780504, 1795265022 for u64 range - const WITNESS64: [u64; 7] = [2, 325, 9375, 28178, 450775, 9780504, 1795265022]; - let u = Mint::from(target); - WITNESS64.iter().all(|&x| u.is_sprp(Mint::from(x))) -} - /// Very fast primality test on a u64 integer is a prime number. It's based on /// deterministic Miller-rabin tests with hashing. if target is larger than 2^64 or more controlled /// primality tests are desired, please use [is_prime()] @@ -97,7 +76,7 @@ pub fn is_prime64(target: u64) -> bool { return target == 2; } - // trial division + // remove small factors if target < SMALL_PRIMES_NEXT { // find in the prime list if the target is small enough return SMALL_PRIMES.binary_search(&(target as u16)).is_ok(); @@ -110,40 +89,52 @@ pub fn is_prime64(target: u64) -> bool { } } + // Then do a deterministic Miller-rabin test is_prime64_miller(target) } +fn is_prime32_miller(target: u32) -> bool { + let h = target; + let h = ((h >> 16) ^ h).wrapping_mul(0x45d9f3b); + let h = ((h >> 16) ^ h).wrapping_mul(0x45d9f3b); + let h = ((h >> 16) ^ h) & 255; + let u = SmallMint::from(target); + return u.is_sprp(SmallMint::from(MILLER_RABIN_BASE32[h as usize] as u32)); +} + +// Primality test for u64 with only miller-rabin tests, used during factorization. +// It assumes the target is odd, not too small and cannot be divided small primes +#[cfg(not(feature = "big-table"))] +fn is_prime64_miller(target: u64) -> bool { + if let Ok(u) = u32::try_from(target) { + return is_prime32_miller(u); + } + + // The collection of witnesses are from http://miller-rabin.appspot.com/ + const WITNESS64: [u64; 7] = [2, 325, 9375, 28178, 450775, 9780504, 1795265022]; + let u = SmallMint::from(target); + WITNESS64.iter().all(|&x| u.is_sprp(SmallMint::from(x))) +} + // Primality test for u64 with only miller-rabin tests, used during factorization. // It assumes the target is odd, not too small and cannot be divided small primes #[cfg(feature = "big-table")] fn is_prime64_miller(target: u64) -> bool { - // 32bit test - const MAGIC: u32 = 0xAD625B89; if let Ok(u) = u32::try_from(target) { - let base = u.wrapping_mul(MAGIC) >> 24; - let u = SmallMint::from(u); - return u.is_sprp(SmallMint::from(MILLER_RABIN_BASE32[base as usize] as u32)); + return is_prime32_miller(u); } - // 49bit test - let mt = SmallMint::from(target); - if !mt.is_sprp(2.into()) { + let u = SmallMint::from(target); + if !u.is_sprp(2.into()) { return false; } - let u = target as u32; // truncate - let base = u.wrapping_mul(MAGIC) >> 18; - if !mt.is_sprp(SmallMint::from(MILLER_RABIN_BASE64[base as usize] as u64)) { - return false; - } - if target < (1u64 << 49) { - return true; - } - - // 64bit test - const SECOND_BASES: [u64; 8] = [15, 135, 13, 60, 15, 117, 65, 29]; - let base = base >> 13; - mt.is_sprp(SmallMint::from(SECOND_BASES[base as usize])) + let h = target; + let h = ((h >> 32) ^ h).wrapping_mul(0x45d9f3b3335b369); + let h = ((h >> 32) ^ h).wrapping_mul(0x3335b36945d9f3b); + let h = ((h >> 32) ^ h) & 16383; + let b = MILLER_RABIN_BASE64[h as usize]; + return u.is_sprp((b as u64 & 4095).into()) && u.is_sprp((b as u64 >> 12).into()); } /// Fast integer factorization on a u64 target. It's based on a selection of factorization methods. @@ -276,9 +267,12 @@ pub(crate) fn factorize64_advanced(cofactors: &[(u64, usize)]) -> Vec<(u64, usiz let start = MontgomeryInt::new(random::(), &target); let offset = start.convert(random::()); let max_iter = max_iter_ratio << (target.bits() / 6); // unoptimized heuristic - if let (Some(p), _) = - pollard_rho(&SmallMint::from(target), start.into(), offset.into(), max_iter) - { + if let (Some(p), _) = pollard_rho( + &SmallMint::from(target), + start.into(), + offset.into(), + max_iter, + ) { break p.value(); } } @@ -434,9 +428,12 @@ pub(crate) fn factorize128_advanced(cofactors: &[(u128, usize)]) -> Vec<(u128, u let start = MontgomeryInt::new(random::(), &target); let offset = start.convert(random::()); let max_iter = max_iter_ratio << (target.bits() / 6); // unoptimized heuristic - if let (Some(p), _) = - pollard_rho(&SmallMint::from(target), start.into(), offset.into(), max_iter) - { + if let (Some(p), _) = pollard_rho( + &SmallMint::from(target), + start.into(), + offset.into(), + max_iter, + ) { break p.value(); } } @@ -1000,7 +997,8 @@ pub fn prime_pi_est(target: &T) -> T { T::from_f64(total + 1f64).unwrap() } -/// Estimate the value of nth prime by bisecting on [prime_pi_est] +/// Estimate the value of nth prime by bisecting on [prime_pi_est]. +/// If the result is larger than maximum of `T`, [None] will be returned. pub fn nth_prime_est(target: &T) -> Option where for<'r> &'r T: RefNum, @@ -1044,6 +1042,7 @@ mod tests { for x in 2..100 { assert_eq!(SMALL_PRIMES.contains(&x), is_prime64(x as u64)); } + assert!(is_prime64(677)); // some large primes assert!(is_prime64(6469693333)); @@ -1060,6 +1059,11 @@ mod tests { assert!(!is_prime64(8651776913431)); assert!(!is_prime64(1152965996591997761)); + // false positives reported by JASory (#4) + assert!(!is_prime64(600437059821397)); + assert!(!is_prime64(3866032210719337)); + assert!(!is_prime64(4100599722623587)); + // ensure no factor for 100 random primes let mut rng = rand::thread_rng(); for _ in 0..100 { diff --git a/src/tables.rs b/src/tables.rs index bc9bdd4..8dd41d0 100644 --- a/src/tables.rs +++ b/src/tables.rs @@ -1124,1064 +1124,1861 @@ pub const SMALL_PRIMES_INV: [P64; 1024] = [ P64::new(0xb1037b5f84886421, 0x000807c7894d029a), ]; -//////////////////// Tables for Miller-rabin bases of 32/64-bit integers using Bradley's hashing //////////////////// +//////////////////// Tables for deterministic Miller-rabin bases of 32/64-bit integers based on hashing //////////////////// /* - * Copyright 2019 Bradley Berg < (My last name) @ techneon.com > - * - * Permission to use, copy, modify, and distribute this software for any - * purpose with or without fee is hereby granted, provided that the above - * copyright notice and this permission notice appear in all copies. + * ForiĊĦek, Michal, and Jakub Jancina. "Fast Primality Testing for Integers That Fit into a Machine Word." (2015). + * http://ceur-ws.org/Vol-1326/020-Forisek.pdf + * https://people.ksp.sk/~misof/primes/ */ -#[cfg(feature = "big-table")] + pub const MILLER_RABIN_BASE32: [u16; 256] = [ - 1216, 1836, 8885, 4564, 10978, 5228, 15613, 13941, 1553, 173, 3615, 3144, 10065, 9259, 233, - 2362, 6244, 6431, 10863, 5920, 6408, 6841, 22124, 2290, 45597, 6935, 4835, 7652, 1051, 445, - 5807, 842, 1534, 22140, 1282, 1733, 347, 6311, 14081, 11157, 186, 703, 9862, 15490, 1720, - 17816, 10433, 49185, 2535, 9158, 2143, 2840, 664, 29074, 24924, 1035, 41482, 1065, 10189, 8417, - 130, 4551, 5159, 48886, 786, 1938, 1013, 2139, 7171, 2143, 16873, 188, 5555, 42007, 1045, 3891, - 2853, 23642, 148, 3585, 3027, 280, 3101, 9918, 6452, 2716, 855, 990, 1925, 13557, 1063, 6916, - 4965, 4380, 587, 3214, 1808, 1036, 6356, 8191, 6783, 14424, 6929, 1002, 840, 422, 44215, 7753, - 5799, 3415, 231, 2013, 8895, 2081, 883, 3855, 5577, 876, 3574, 1925, 1192, 865, 7376, 12254, - 5952, 2516, 20463, 186, 5411, 35353, 50898, 1084, 2127, 4305, 115, 7821, 1265, 16169, 1705, - 1857, 24938, 220, 3650, 1057, 482, 1690, 2718, 4309, 7496, 1515, 7972, 3763, 10954, 2817, 3430, - 1423, 714, 6734, 328, 2581, 2580, 10047, 2797, 155, 5951, 3817, 54850, 2173, 1318, 246, 1807, - 2958, 2697, 337, 4871, 2439, 736, 37112, 1226, 527, 7531, 5418, 7242, 2421, 16135, 7015, 8432, - 2605, 5638, 5161, 11515, 14949, 748, 5003, 9048, 4679, 1915, 7652, 9657, 660, 3054, 15469, - 2910, 775, 14106, 1749, 136, 2673, 61814, 5633, 1244, 2567, 4989, 1637, 1273, 11423, 7974, - 7509, 6061, 531, 6608, 1088, 1627, 160, 6416, 11350, 921, 306, 18117, 1238, 463, 1722, 996, - 3866, 6576, 6055, 130, 24080, 7331, 3922, 8632, 2706, 24108, 32374, 4237, 15302, 287, 2296, - 1220, 20922, 3350, 2089, 562, 11745, 163, 11951, + 0x3ce7, 0x07e2, 0x00a6, 0x1d05, 0x1f80, 0x3ead, 0x2907, 0x112f, 0x079d, 0x050f, 0x0ad8, 0x0e24, + 0x0230, 0x0c38, 0x145c, 0x0a61, 0x08fc, 0x07e5, 0x122c, 0x05bf, 0x2478, 0x0fb2, 0x095e, 0x4fee, + 0x2825, 0x1f5c, 0x08a5, 0x184b, 0x026c, 0x0eb3, 0x12f4, 0x1394, 0x0c71, 0x0535, 0x1853, 0x14b2, + 0x0432, 0x0957, 0x13f9, 0x1b95, 0x0323, 0x04f5, 0x0f23, 0x01a6, 0x02ef, 0x0244, 0x1279, 0x27ff, + 0x02ea, 0x0b87, 0x022c, 0x089e, 0x0ec2, 0x01e1, 0x05f2, 0x0d94, 0x01e1, 0x09b7, 0x0cc2, 0x1601, + 0x01e8, 0x0d2d, 0x1929, 0x0d10, 0x0011, 0x3b01, 0x05d2, 0x103a, 0x07f4, 0x075a, 0x0715, 0x01d3, + 0x0ceb, 0x36da, 0x18e3, 0x0292, 0x03ed, 0x0387, 0x02e1, 0x075f, 0x1d17, 0x0760, 0x0b20, 0x06f8, + 0x1d87, 0x0d48, 0x03b7, 0x3691, 0x10d0, 0x00b1, 0x0029, 0x4da3, 0x0c26, 0x33a5, 0x2216, 0x023b, + 0x1b83, 0x1b1f, 0x04af, 0x0160, 0x1923, 0x00a5, 0x0491, 0x0cf3, 0x03d2, 0x00e9, 0x0bbb, 0x0a02, + 0x0bb2, 0x295b, 0x272e, 0x0949, 0x076e, 0x14ea, 0x115f, 0x0613, 0x0107, 0x6993, 0x08eb, 0x0131, + 0x029d, 0x0778, 0x0259, 0x182a, 0x01ad, 0x078a, 0x3a19, 0x06f8, 0x067d, 0x020c, 0x0df9, 0x00ec, + 0x0938, 0x1802, 0x0b22, 0xd955, 0x06d9, 0x1052, 0x2112, 0x00de, 0x0a13, 0x0ab7, 0x07ef, 0x08b2, + 0x08e4, 0x0176, 0x0854, 0x032d, 0x5cec, 0x064a, 0x1146, 0x1427, 0x06bd, 0x0e0d, 0x0d26, 0x3800, + 0x0243, 0x00a5, 0x055f, 0x2722, 0x3148, 0x2658, 0x055b, 0x0218, 0x074b, 0x2a70, 0x0359, 0x089e, + 0x169c, 0x01b2, 0x1f95, 0x44d2, 0x02d7, 0x0e37, 0x063b, 0x1350, 0x0851, 0x07ed, 0x2003, 0x2098, + 0x1858, 0x23df, 0x1fbe, 0x074e, 0x0ce0, 0x1d1f, 0x22f3, 0x61b9, 0x021d, 0x4aab, 0x0170, 0x0236, + 0x162a, 0x019b, 0x020a, 0x0403, 0x2017, 0x0802, 0x1990, 0x2741, 0x0266, 0x0306, 0x091d, 0x0bbf, + 0x8981, 0x1262, 0x0480, 0x06f9, 0x0404, 0x0604, 0x0e9f, 0x01ed, 0x117a, 0x09d9, 0x68dd, 0x20a2, + 0x0360, 0x49e3, 0x1559, 0x098f, 0x002a, 0x119f, 0x067c, 0x00a6, 0x04e1, 0x1873, 0x09f9, 0x0130, + 0x0110, 0x1c76, 0x0049, 0x199a, 0x0383, 0x0b00, 0x144d, 0x3412, 0x1b8e, 0x0b02, 0x0c7f, 0x032b, + 0x039a, 0x015e, 0x1d5a, 0x1164, 0x0d79, 0x0a67, 0x1264, 0x01a2, 0x0655, 0x0493, 0x0d8f, 0x0058, + 0x2c51, 0x019c, 0x0617, 0x00c2, ]; #[cfg(feature = "big-table")] -pub const MILLER_RABIN_BASE64: [u16; 16384] = [ - 1814, 1307, 1714, 6838, 1801, 179, 219, 1317, 6834, 3281, 8345, 4034, 1899, 5746, 4977, 117, - 12578, 18141, 4434, 4236, 543, 9046, 4005, 385, 4231, 3425, 859, 1450, 2199, 4262, 7025, 1562, - 717, 5611, 5298, 871, 1959, 258, 4543, 8969, 1075, 15030, 21041, 7917, 913, 15929, 3450, 9218, - 518, 11775, 7993, 175, 107, 407, 4738, 14388, 86, 6360, 3535, 3818, 8083, 11, 4337, 19601, - 32654, 2566, 974, 1549, 5047, 1542, 1941, 3887, 933, 295, 106, 823, 1529, 7999, 8424, 2958, - 17995, 1430, 8541, 5213, 341, 13034, 4437, 4058, 21281, 715, 1898, 434, 1298, 8930, 33, 3466, - 397, 14181, 2685, 2179, 15160, 271, 175, 5403, 1303, 2091, 4133, 466, 2143, 3908, 2819, 159, - 358, 302, 7778, 2001, 1029, 182, 7405, 13580, 26511, 11758, 743, 4841, 12448, 3585, 3123, 1959, - 3999, 1906, 597, 8293, 2508, 8231, 8676, 485, 4925, 12605, 22286, 1099, 1385, 382, 10310, 746, - 293, 415, 2947, 61, 295, 4797, 11775, 2902, 4254, 12326, 1335, 1541, 17775, 8067, 13739, 4254, - 685, 3963, 2258, 3827, 1151, 2962, 1981, 1043, 2910, 8555, 2478, 3181, 1399, 12907, 5843, 2056, - 7, 598, 17287, 609, 1823, 9968, 12866, 9614, 1177, 1799, 8135, 8861, 6242, 3655, 8700, 11136, - 3693, 229, 6637, 8587, 4915, 820, 6594, 8899, 3012, 833, 5439, 402, 387, 9998, 10074, 401, - 9281, 2246, 12470, 7919, 1533, 2725, 947, 6314, 6681, 2733, 10132, 1535, 7066, 17066, 1529, - 507, 29293, 5893, 6323, 551, 506, 1686, 394, 2355, 2394, 199, 8744, 3451, 1759, 12630, 8251, - 21127, 603, 1349, 16013, 1916, 657, 3143, 10920, 344, 1522, 3123, 10732, 635, 4927, 2641, 2786, - 554, 77, 8759, 2047, 8638, 233, 19015, 237, 29990, 4033, 110, 3949, 351, 293, 12792, 2370, - 3878, 9235, 1477, 14719, 4439, 4571, 3606, 6895, 1256, 8271, 2189, 73, 1006, 28711, 1970, 8162, - 1034, 1258, 3018, 5062, 2381, 1326, 19172, 17936, 17446, 4714, 7939, 975, 11261, 17179, 1138, - 9907, 7654, 8844, 213, 3378, 7937, 118, 3421, 1217, 7742, 52, 18125, 381, 1131, 545, 9748, - 8528, 1219, 2206, 415, 6235, 50334, 74, 397, 1773, 1150, 16385, 1419, 8899, 811, 3813, 2511, - 10359, 17270, 22652, 9646, 34497, 3474, 141, 1554, 1287, 4642, 1571, 934, 2834, 101, 749, 258, - 302, 26159, 1291, 5105, 1783, 7310, 415, 1558, 2393, 13393, 263, 1362, 7985, 9569, 8240, 2279, - 5018, 8430, 1961, 6005, 17635, 3622, 4213, 36293, 9985, 11, 1254, 2251, 27396, 239, 17364, - 3863, 4615, 7899, 3674, 5531, 199, 8996, 1293, 6098, 514, 8538, 17311, 2015, 6226, 4459, 5731, - 887, 5449, 8085, 1851, 206, 2925, 8337, 2363, 9490, 1085, 590, 9094, 78, 7190, 2843, 86, 497, - 1658, 113, 24990, 5302, 3141, 18856, 16074, 5754, 9497, 1757, 1353, 4013, 3739, 6930, 6179, - 813, 6894, 2527, 2218, 14648, 397, 2979, 3074, 2314, 6521, 18390, 2157, 10642, 1177, 5007, 391, - 1982, 4373, 26, 1917, 1567, 3091, 22352, 9374, 935, 3263, 8242, 3239, 3558, 18600, 9839, 2440, - 5325, 6414, 1303, 2995, 109, 5731, 9966, 1478, 8867, 9094, 284, 433, 1750, 277, 9773, 22660, - 181, 127, 279, 641, 851, 199, 539, 1190, 446, 10526, 2566, 677, 127, 2404, 9715, 8319, 15005, - 3086, 2779, 3951, 7, 6929, 461, 27337, 8909, 9543, 5150, 6703, 3327, 769, 901, 851, 2227, 819, - 1879, 3130, 4927, 2302, 802, 7599, 1163, 71, 33, 925, 5550, 2971, 8201, 23865, 114, 5886, 1145, - 19851, 6219, 1877, 613, 827, 11302, 5726, 1237, 769, 590, 9156, 9048, 6049, 7379, 5462, 12522, - 5706, 823, 8431, 3349, 1623, 2245, 5198, 1329, 14794, 6193, 2266, 9722, 3716, 10294, 2009, - 1193, 233, 3979, 1077, 418, 941, 4613, 8635, 26786, 1507, 8508, 258, 1419, 5225, 7485, 1051, - 13020, 31711, 22593, 3331, 3338, 12526, 161, 5338, 7302, 78, 23889, 571, 26734, 8013, 8305, - 9053, 1566, 2482, 191, 12703, 1703, 3385, 654, 26390, 3647, 2639, 8498, 3813, 1161, 7777, 117, - 2265, 813, 8069, 2053, 2091, 5033, 6637, 8588, 15954, 325, 1713, 9719, 1983, 619, 107, 419, - 9104, 9019, 8688, 577, 1773, 237, 3379, 2946, 1151, 13815, 1119, 1393, 11565, 2177, 530, 265, - 1663, 4058, 11031, 12256, 2443, 173, 1405, 1258, 8592, 4364, 4883, 1201, 2470, 119, 2775, - 37084, 6690, 1067, 10479, 337, 4147, 19565, 853, 4005, 1790, 855, 2329, 481, 585, 2616, 1741, - 10908, 17057, 9267, 4403, 10597, 4963, 7154, 3079, 8245, 3271, 10807, 1513, 691, 2821, 5285, - 681, 9822, 690, 566, 46, 639, 141, 6706, 9308, 1009, 7433, 24590, 29, 25809, 710, 4839, 2857, - 17910, 383, 4630, 2993, 1059, 39, 13218, 10597, 6607, 3466, 3029, 8639, 1646, 8895, 231, 4885, - 3305, 5734, 10310, 5954, 7773, 3329, 587, 14302, 9806, 2130, 189, 1267, 7397, 12364, 953, 299, - 5297, 3354, 1921, 2486, 6827, 2202, 2369, 15279, 871, 713, 8273, 1227, 9691, 3475, 469, 865, - 2230, 353, 6249, 9310, 1546, 38417, 2199, 1789, 9051, 6555, 3766, 1701, 10210, 1270, 3279, - 8620, 3039, 929, 2029, 618, 6641, 7122, 4215, 34, 89, 5251, 1293, 6401, 409, 537, 935, 26421, - 2882, 4129, 55, 7427, 369, 12218, 9918, 1870, 4888, 1449, 1430, 4430, 5291, 1699, 2074, 67, - 12096, 6687, 8414, 573, 2803, 887, 2435, 1138, 2413, 4129, 205, 2190, 1654, 3697, 3170, 3538, - 1574, 555, 1338, 2822, 1077, 610, 8391, 1539, 11, 6637, 1053, 179, 698, 1495, 1217, 1436, 9935, - 778, 310, 801, 718, 1066, 3066, 261, 839, 651, 3293, 20997, 8527, 8721, 2146, 37272, 3607, - 9206, 698, 9983, 28805, 221, 3686, 11549, 348, 181, 1293, 3846, 2717, 6926, 5133, 137, 1785, - 9727, 2325, 2723, 8678, 607, 3010, 8749, 8855, 10668, 2675, 301, 7899, 8191, 9141, 6622, 9435, - 1579, 1539, 3261, 5773, 218, 1654, 4466, 739, 3366, 2047, 557, 3189, 7558, 2867, 2810, 3842, - 1663, 4635, 34027, 269, 9256, 3533, 4074, 1022, 3365, 1633, 15096, 8323, 9249, 1767, 1326, 39, - 9211, 165, 8797, 9519, 1006, 5738, 18521, 323, 1746, 10996, 1517, 8204, 6547, 4359, 1834, 2966, - 716, 715, 2470, 1443, 8518, 2938, 1962, 2387, 10961, 851, 5533, 553, 5150, 934, 554, 157, 4429, - 15949, 2194, 1657, 1449, 7391, 377, 2065, 3307, 6695, 2731, 1141, 813, 3238, 8318, 2255, 9003, - 618, 3697, 24981, 4401, 1523, 219, 721, 6284, 6220, 7747, 333, 12835, 5619, 949, 4346, 1206, - 846, 8063, 6167, 1383, 6843, 10299, 3085, 9018, 277, 221, 12774, 1173, 1926, 21591, 4182, 2194, - 8223, 3983, 550, 2254, 8371, 606, 1202, 29, 1273, 6557, 8808, 7918, 3797, 2941, 1566, 15003, - 1955, 2796, 2583, 233, 10105, 1418, 2889, 24939, 9590, 3573, 613, 70, 247, 934, 1822, 895, - 4197, 30570, 8511, 9367, 11295, 4715, 3145, 3103, 57, 5810, 11354, 6406, 1111, 30851, 2838, - 2639, 8673, 18562, 2999, 9448, 11625, 1773, 9272, 13946, 1498, 4613, 21674, 30566, 5053, 11644, - 3701, 2654, 4693, 19, 1986, 14647, 1615, 1711, 1259, 4569, 2798, 1070, 25016, 1461, 358, 1457, - 807, 1018, 9256, 1249, 9589, 8615, 2290, 2073, 21, 1363, 321, 3059, 6965, 865, 12695, 287, - 4322, 6173, 8206, 1967, 457, 59, 1417, 15449, 5635, 2734, 5122, 1630, 1115, 4194, 3458, 10494, - 5373, 2266, 7884, 8637, 6114, 8655, 4279, 6438, 1383, 3838, 2078, 1721, 2485, 2447, 541, 8289, - 2291, 221, 138, 567, 7194, 1141, 1941, 1311, 1522, 1687, 3510, 2446, 8578, 10349, 25626, 32066, - 1654, 413, 129, 11851, 4902, 547, 2014, 4427, 11738, 1661, 2081, 10933, 3226, 438, 4433, 4679, - 339, 617, 9451, 6134, 6822, 8957, 5171, 14095, 11767, 2697, 3351, 9461, 2207, 1501, 930, 617, - 435, 8966, 3185, 6603, 10993, 908, 881, 1033, 254, 1538, 1383, 7890, 1489, 18615, 1070, 20332, - 3867, 5666, 1513, 2661, 7297, 3263, 37879, 5883, 11163, 1081, 2589, 5033, 10067, 56007, 8629, - 53493, 5443, 5749, 3982, 791, 5573, 3967, 549, 3371, 727, 6788, 4382, 607, 4111, 2837, 4565, - 2273, 2567, 286, 39, 1441, 4254, 27375, 5061, 442, 3597, 8308, 8035, 3041, 967, 27275, 1939, - 1034, 1038, 913, 4649, 426, 87, 36883, 4918, 2381, 478, 3965, 883, 3855, 4366, 7214, 3562, 681, - 763, 8538, 1229, 3223, 5371, 773, 1825, 2061, 446, 629, 8832, 2269, 3393, 6712, 9365, 11001, - 1459, 9795, 1247, 1966, 1117, 717, 1547, 19975, 3428, 253, 421, 10245, 933, 926, 3789, 3351, - 5138, 262, 2193, 1910, 1183, 193, 1497, 151, 1343, 7343, 2817, 351, 1767, 6540, 6179, 1983, - 2985, 14, 2811, 17706, 1271, 737, 10887, 305, 2794, 4717, 12567, 1507, 17602, 1523, 5209, 463, - 8866, 11923, 4955, 5265, 5288, 6043, 5641, 595, 282, 446, 6497, 911, 1661, 6946, 609, 8322, - 457, 3393, 7889, 649, 5663, 2237, 8149, 5867, 1249, 7135, 1079, 17165, 32290, 26529, 26547, - 483, 4357, 4110, 1893, 4482, 1930, 3294, 9811, 35577, 2541, 11035, 1091, 129, 513, 445, 12330, - 3553, 2689, 9003, 29917, 23793, 8814, 8380, 738, 6846, 1693, 127, 2667, 5245, 787, 2058, 217, - 1073, 462, 311, 5087, 10108, 291, 2431, 951, 41, 16869, 9010, 10398, 1531, 4053, 2456, 727, - 4636, 2689, 1526, 2126, 3736, 279, 4038, 1005, 2186, 9358, 5537, 3729, 693, 530, 749, 4379, - 1583, 34038, 2590, 457, 311, 3077, 12423, 1006, 1923, 3071, 811, 10642, 8501, 4835, 1735, 9606, - 35324, 85, 8232, 2425, 177, 8384, 933, 341, 2481, 2017, 3694, 1381, 131, 713, 4213, 13802, 959, - 1343, 3674, 325, 4090, 265, 1147, 4209, 785, 1970, 110, 4262, 297, 6074, 4769, 5299, 2309, - 4433, 3833, 17427, 6914, 9188, 2246, 7726, 8747, 7501, 10637, 278, 655, 10539, 349, 414, 2871, - 31558, 3958, 10727, 3338, 1703, 11716, 22687, 8919, 17340, 2461, 231, 1994, 797, 12341, 307, - 5114, 691, 20111, 532, 2286, 12881, 4121, 2453, 874, 2947, 5494, 1866, 2543, 665, 3864, 1581, - 11513, 35676, 4961, 2715, 447, 73, 5211, 818, 4286, 5691, 6021, 466, 5606, 1077, 5970, 1293, - 4499, 11210, 2006, 9794, 1141, 4861, 21132, 1068, 2033, 251, 6987, 5718, 3218, 629, 755, 453, - 3259, 457, 5181, 6482, 25951, 8372, 233, 1397, 511, 7157, 10090, 8219, 10289, 9257, 29842, 670, - 4025, 2471, 35572, 1035, 354, 831, 1713, 2215, 3393, 16440, 16076, 32137, 2806, 723, 1223, - 2007, 137, 463, 38, 1195, 3566, 1462, 33400, 101, 785, 89, 6471, 3595, 187, 7006, 3323, 322, - 20079, 413, 3115, 12292, 575, 2635, 5479, 9336, 5319, 10302, 1801, 2925, 1530, 1139, 6043, - 5654, 565, 6333, 842, 67, 16995, 3923, 9546, 1697, 4877, 239, 55, 5989, 9439, 366, 3723, 839, - 3097, 10983, 395, 4135, 40693, 619, 1310, 19017, 7057, 9101, 7513, 2173, 1314, 9023, 13279, - 281, 82, 1007, 8011, 706, 3061, 6470, 7503, 1547, 33138, 183, 345, 2533, 118, 10472, 563, 505, - 11464, 5123, 8943, 4149, 2203, 489, 2511, 682, 8525, 4387, 1127, 4066, 14636, 2982, 5560, 2310, - 7825, 497, 2938, 3787, 1306, 3791, 10147, 215, 9734, 12660, 1397, 1079, 1907, 10889, 97, 11659, - 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1027, 127, 8512, 471, 925, 1195, 8284, 9319, 3113, 5006, 214, - 2995, 4037, 32185, 3587, 23182, 2573, 309, 1143, 2539, 15576, 2361, 7807, 106, 3473, 8238, - 5814, 3143, 2221, 998, 2225, 409, 8539, 9340, 838, 8932, 957, 22832, 59, 14862, 2527, 25938, - 2069, 5218, 1075, 4961, 3159, 2595, 2425, 2265, 6093, 2010, 10451, 5862, 133, 1650, 1917, 620, - 5831, 247, 2119, 10366, 3827, 1251, 11192, 9668, 1737, 199, 1543, 3205, 13474, 9411, 1991, 442, - 6378, 3319, 15449, 335, 2165, 1494, 3889, 4789, 1410, 2938, 8686, 6401, 51, 7782, 2321, 1611, - 2465, 10338, 8655, 17946, 1217, 1529, 2930, 4239, 142, 1342, 13711, 1226, 11451, 1574, 6231, - 1601, 8305, 4519, 7247, 886, 4317, 38430, 17965, 2937, 3, 9592, 1921, 1661, 3788, 1146, 4169, - 2929, 547, 2402, 1647, 1107, 2935, 6247, 1631, 355, 2373, 2141, 1169, 2455, 14720, 369, 5355, - 1053, 10699, 2123, 4021, 7361, 922, 39, 4459, 3505, 2243, 2267, 3195, 2334, 3129, 5379, 790, - 12504, 5089, 7682, 9985, 29227, 5651, 902, 9647, 32794, 2109, 19794, 233, 253, 2337, 1585, 601, - 1255, 2018, 4254, 4009, 1725, 857, 65, 1165, 4693, 9262, 25157, 6225, 2665, 11374, 1349, 19697, - 1965, 3491, 7526, 2842, 30969, 1422, 967, 34364, 637, 3819, 3210, 4919, 21444, 33354, 167, - 1450, 2542, 1530, 14684, 4005, 214, 3215, 7421, 2455, 191, 1057, 8631, 1377, 575, 2981, 3027, - 5942, 1485, 11218, 5998, 7644, 1318, 2803, 9428, 9625, 1267, 1915, 1702, 1201, 19335, 1172, - 2861, 1011, 16163, 524, 747, 5639, 6195, 1971, 223, 6469, 11985, 8510, 259, 1791, 18567, 9267, - 4843, 1252, 3994, 1767, 10614, 8416, 263, 23459, 10837, 4173, 1669, 2379, 4033, 11705, 6749, - 67, 506, 1989, 5225, 5074, 74, 2618, 35, 419, 34, 467, 2305, 5589, 5777, 2599, 4957, 29, 37712, - 2462, 5563, 1535, 2290, 7386, 1642, 5821, 990, 6947, 749, 1087, 110, 635, 16080, 3003, 4758, - 3542, 651, 663, 1997, 1981, 2855, 4413, 15183, 435, 591, 285, 2099, 15978, 9906, 10479, 2595, - 9196, 11464, 25723, 4218, 29515, 10660, 24195, 6843, 11805, 733, 255, 838, 2815, 6717, 9791, - 14339, 4709, 4702, 4967, 5075, 9512, 1346, 7126, 16150, 5277, 1327, 4135, 161, 563, 11, 1259, - 2435, 275, 1686, 186, 3023, 8819, 10050, 1863, 4578, 218, 12108, 4869, 1031, 7467, 6337, 861, - 2834, 4775, 5371, 782, 11457, 1543, 12694, 705, 9143, 1871, 1704, 251, 217, 117, 809, 293, - 9077, 3211, 6837, 2982, 6199, 4126, 907, 8033, 15097, 1894, 5826, 12785, 241, 3715, 1583, 2857, - 16459, 657, 1653, 9582, 1795, 695, 10461, 1314, 4062, 511, 12379, 3022, 795, 365, 5719, 1039, - 4497, 4926, 7013, 5401, 14153, 2289, 667, 3268, 9070, 8906, 5425, 71, 1820, 8474, 1102, 2994, - 4849, 7430, 629, 16702, 1559, 5387, 790, 6742, 8634, 1255, 5279, 1926, 13868, 1347, 11504, - 2354, 1219, 1041, 3447, 1821, 894, 1238, 697, 3706, 1135, 9157, 1038, 5001, 950, 927, 1122, - 2461, 959, 287, 9209, 11219, 790, 7709, 266, 183, 10857, 7306, 34, 185, 303, 6413, 3153, 285, - 2059, 2707, 10863, 673, 3187, 6791, 8766, 9605, 7506, 1879, 16066, 371, 15962, 885, 8528, 359, - 8965, 2153, 178, 695, 7233, 29898, 11600, 5910, 20985, 7341, 9215, 10928, 3297, 1341, 19247, - 3037, 11758, 610, 1313, 969, 743, 660, 8441, 12867, 788, 9012, 175, 883, 577, 522, 3902, 3357, - 7222, 6279, 18376, 11043, 453, 266, 3290, 1335, 1651, 381, 5449, 2301, 24103, 2163, 5767, 2177, - 2847, 1798, 7978, 182, 1267, 6582, 1241, 14002, 3839, 381, 1465, 53, 6285, 2867, 4011, 2375, - 175, 13959, 2995, 9991, 707, 10411, 1546, 3614, 851, 4836, 807, 2417, 154, 1870, 322, 9944, - 1102, 247, 7363, 1006, 24838, 974, 10099, 10034, 634, 12851, 9298, 2101, 690, 2065, 8935, 5377, - 4922, 15273, 2149, 2595, 16671, 1854, 1963, 1193, 4290, 1599, 11067, 28, 8114, 1569, 341, 263, - 2698, 10930, 2149, 3339, 1911, 143, 8337, 29431, 29, 3945, 1675, 434, 555, 3413, 8437, 4997, - 233, 833, 539, 8998, 9057, 995, 163, 4237, 11454, 663, 1795, 1722, 3495, 16491, 8726, 7727, - 1147, 2503, 2573, 2930, 5627, 4105, 7385, 4634, 402, 8517, 1578, 10040, 3003, 725, 111, 8519, - 477, 271, 1235, 4111, 9612, 1480, 546, 699, 3842, 1927, 3321, 201, 9133, 1033, 1286, 9715, - 13596, 11580, 2717, 11271, 533, 8167, 5306, 8220, 1338, 4115, 3517, 6905, 28417, 2175, 3757, - 3207, 5791, 5826, 1023, 797, 2323, 7595, 2071, 761, 7636, 7447, 4799, 1057, 470, 2329, 2006, - 201, 635, 538, 1679, 371, 5579, 1140, 1097, 1299, 6481, 11547, 12056, 14638, 25754, 1529, 1146, - 11408, 715, 428, 983, 3053, 2886, 2527, 6702, 542, 11825, 7373, 3133, 638, 1337, 977, 1053, - 9042, 22742, 1873, 8707, 309, 1937, 4137, 253, 2991, 919, 1203, 1955, 4754, 6829, 9052, 351, - 801, 2405, 17945, 3081, 5098, 8528, 342, 5995, 17229, 10371, 1117, 15692, 5642, 3405, 6477, - 4893, 7035, 873, 8316, 3314, 1077, 1037, 1081, 1591, 9941, 4978, 1191, 635, 11027, 3955, 2959, - 2466, 16160, 433, 861, 5982, 1477, 142, 1407, 14880, 241, 455, 1410, 3749, 3005, 366, 847, - 10527, 777, 7715, 9691, 3541, 46, 2007, 1793, 1115, 222, 8421, 4325, 2227, 133, 569, 4701, - 3349, 1122, 9930, 8196, 191, 2314, 2461, 655, 2049, 319, 9320, 634, 1199, 22, 2049, 8747, - 10096, 1489, 10390, 3142, 1593, 1341, 10033, 1230, 1791, 1738, 1522, 10984, 3194, 14522, 2927, - 1733, 1093, 13680, 1469, 907, 990, 4822, 403, 1743, 620, 9855, 1953, 5030, 1327, 8635, 3065, - 2989, 5157, 2797, 8637, 4377, 759, 1174, 517, 5307, 1626, 7422, 4195, 14469, 2086, 6205, 20548, - 5369, 478, 8792, 63, 2387, 11896, 689, 1743, 4897, 15664, 593, 5794, 70, 1046, 3277, 998, 6585, - 6402, 7550, 3377, 13446, 6297, 3813, 3063, 4607, 42559, 701, 1914, 9970, 3631, 287, 573, 1597, - 1491, 3873, 1794, 1271, 5611, 2150, 153, 5691, 5039, 325, 1142, 2253, 62, 2050, 1142, 18879, - 95, 4515, 523, 4967, 3725, 9098, 18274, 2290, 2871, 633, 14582, 269, 7923, 8149, 3053, 1982, - 2039, 15796, 2983, 12818, 498, 2834, 2665, 2158, 426, 1938, 6567, 466, 82, 18667, 909, 15857, - 2035, 291, 241, 654, 31194, 167, 349, 819, 4809, 12879, 9479, 386, 1750, 3283, 141, 2427, 2873, - 1449, 9942, 154, 987, 4365, 3967, 11048, 659, 2827, 6573, 2121, 22450, 8014, 5939, 1107, 1491, - 1069, 1147, 22, 3334, 5273, 13168, 5217, 78, 2889, 8742, 166, 677, 249, 246, 1240, 3954, 7174, - 12082, 4307, 12917, 823, 821, 3686, 593, 28979, 5650, 9321, 12380, 997, 950, 3043, 1813, 4593, - 7292, 1737, 309, 3399, 3955, 11160, 8434, 6302, 2918, 31003, 5181, 5146, 459, 1633, 1787, 2339, - 3047, 14577, 36985, 1983, 4757, 1699, 24406, 3819, 2654, 433, 1015, 12878, 1302, 10336, 1741, - 3373, 7170, 5785, 1053, 13374, 11913, 533, 941, 599, 5086, 9586, 2747, 4458, 1666, 11487, 5645, - 40577, 7163, 9925, 279, 2009, 407, 2693, 9102, 5273, 10107, 1422, 115, 12049, 119, 11801, 341, - 9129, 8514, 1614, 1043, 2349, 366, 903, 3702, 3609, 2705, 2328, 1414, 2293, 2727, 2113, 3127, - 19308, 2329, 1023, 10175, 925, 8544, 4115, 2194, 1359, 9252, 138, 817, 7897, 918, 323, 8530, - 2829, 1751, 5581, 25658, 1517, 445, 2397, 163, 241, 14777, 171, 2782, 3930, 39974, 1277, 318, - 12735, 12044, 4934, 2323, 6697, 698, 6036, 4694, 5269, 587, 8445, 2218, 4630, 1954, 3981, 8067, - 8187, 4522, 1041, 10402, 37117, 1182, 1543, 11430, 9242, 834, 3537, 11522, 33957, 4995, 491, - 2279, 4122, 637, 8722, 3317, 6163, 1349, 455, 843, 995, 681, 42, 1783, 959, 3095, 1469, 28598, - 9902, 5909, 1163, 8572, 1722, 566, 9001, 2725, 3226, 7830, 2051, 1354, 1151, 8228, 1735, 19522, - 6446, 178, 1223, 5197, 51, 1074, 893, 381, 5286, 8925, 27691, 681, 1239, 9390, 1159, 7178, 598, - 10187, 10721, 12067, 891, 9191, 783, 2377, 2889, 137, 5050, 2581, 394, 5383, 1110, 6173, 9401, - 9059, 1275, 10477, 2108, 2211, 510, 8195, 4039, 13323, 4398, 4829, 1828, 5146, 5553, 9105, 209, - 9466, 201, 941, 8550, 3713, 2761, 12454, 3582, 3270, 15090, 3446, 8658, 7411, 2694, 419, 9631, - 8598, 5405, 911, 2447, 2630, 5381, 2755, 4395, 3385, 8224, 3201, 10432, 2437, 4091, 8499, 2335, - 777, 20517, 643, 2641, 5426, 2302, 1266, 386, 1115, 2494, 165, 2802, 4617, 695, 1625, 922, 701, - 1757, 8954, 510, 2072, 4207, 1966, 7815, 914, 26081, 2099, 917, 4625, 6695, 7186, 6210, 117, - 5026, 1271, 5254, 1715, 4462, 5370, 8965, 1593, 1116, 2115, 673, 1307, 62, 3722, 4870, 1913, - 253, 8632, 550, 876, 205, 943, 20717, 1486, 1779, 3334, 3878, 1266, 499, 7989, 15711, 7187, - 4325, 8247, 658, 5398, 2698, 3269, 1706, 5141, 30431, 1649, 1094, 13996, 3847, 4390, 3694, - 15908, 17573, 20205, 2870, 14429, 2837, 383, 2124, 2607, 5042, 5186, 1502, 2006, 8628, 2963, - 2653, 442, 1579, 1353, 3183, 893, 3977, 8346, 11853, 714, 417, 466, 762, 967, 495, 275, 10096, - 3197, 3982, 1911, 2821, 21737, 2510, 9330, 1671, 6513, 8563, 6061, 2022, 2153, 4302, 8330, - 1195, 5967, 10342, 543, 766, 519, 2371, 511, 417, 1446, 14731, 389, 2687, 431, 319, 117, 561, - 638, 2563, 4293, 1303, 1289, 5850, 467, 2709, 1828, 154, 24097, 419, 178, 2094, 587, 653, 9920, - 6697, 3799, 3747, 323, 1437, 2619, 1630, 1379, 924, 3523, 8811, 1134, 1299, 991, 1659, 11179, - 3105, 34590, 8896, 362, 2595, 1254, 1393, 379, 6677, 571, 155, 379, 4726, 501, 1186, 1025, 447, - 10505, 975, 754, 1386, 2117, 20220, 5143, 7843, 2795, 3011, 713, 389, 1101, 767, 1116, 447, - 1307, 2059, 4058, 3598, 610, 2921, 2353, 166, 4433, 199, 1477, 4025, 9850, 301, 5006, 14630, - 693, 10889, 12815, 151, 2526, 4595, 1159, 4087, 1795, 7707, 30981, 10557, 10197, 5281, 6233, - 7310, 1823, 2131, 4621, 2283, 3510, 1310, 1449, 4606, 2231, 326, 2062, 9019, 10527, 3577, 6812, - 4229, 323, 669, 2413, 3601, 4041, 2151, 8904, 10171, 5683, 1349, 2763, 7486, 1189, 771, 1139, - 3803, 12249, 431, 13170, 1091, 37694, 3891, 9607, 2221, 5779, 7870, 11678, 998, 969, 2133, - 8933, 14255, 11624, 2465, 15753, 2838, 4187, 3367, 1286, 5679, 2186, 715, 2143, 998, 342, 751, - 12177, 6259, 1302, 571, 8110, 7923, 12334, 8286, 1113, 1222, 8769, 371, 876, 7991, 2706, 4717, - 2705, 541, 394, 1883, 7507, 643, 835, 357, 929, 8694, 8122, 1973, 2503, 357, 130, 937, 8681, - 975, 91, 123, 13290, 4583, 2078, 3270, 2682, 8936, 8249, 1775, 8519, 1439, 6295, 4151, 10817, - 8942, 3263, 18933, 1293, 183, 4601, 9155, 5481, 481, 39192, 358, 16721, 419, 2142, 4135, 16945, - 10998, 6490, 1175, 8490, 846, 6409, 12493, 23326, 2899, 415, 36491, 13051, 866, 161, 22, 2150, - 849, 4670, 3849, 489, 833, 549, 5675, 14716, 8764, 1685, 161, 4785, 30101, 1067, 635, 126, - 1387, 5495, 985, 1942, 166, 453, 2101, 8602, 1389, 6802, 193, 4307, 1302, 6233, 3138, 1199, - 3111, 10278, 2852, 8693, 13152, 10313, 10246, 66, 554, 1941, 8070, 5726, 9988, 1997, 693, 2405, - 549, 350, 11750, 5111, 6237, 5873, 4531, 1289, 1709, 2238, 831, 202, 2893, 1726, 47, 23812, - 1553, 1053, 2927, 635, 5906, 4088, 1084, 7304, 7714, 1363, 3417, 2427, 3119, 7934, 4549, 2271, - 1330, 1483, 650, 223, 649, 7917, 3966, 7318, 411, 8992, 2455, 1135, 4953, 919, 2130, 610, 1844, - 137, 403, 3757, 9114, 1366, 646, 8467, 7277, 7171, 2442, 93, 857, 895, 2134, 38617, 11100, - 12622, 67, 3883, 5807, 743, 5005, 731, 10084, 69, 46255, 865, 6671, 1071, 3798, 1855, 1426, - 3361, 571, 2697, 161, 286, 497, 2207, 2038, 2015, 12745, 10440, 313, 1443, 8753, 11702, 267, - 7226, 27666, 398, 1309, 170, 10128, 1398, 1839, 8276, 3414, 55, 3107, 3154, 2405, 1814, 8903, - 4845, 1417, 1667, 2427, 549, 818, 475, 1499, 1169, 767, 537, 1697, 2386, 2075, 3673, 1871, - 9379, 1938, 3229, 1237, 222, 209, 5473, 5589, 4397, 9112, 5233, 12487, 1835, 149, 7860, 5289, - 10055, 4185, 53, 1394, 2265, 2610, 6079, 8316, 13263, 3475, 9011, 22, 159, 6061, 82, 2361, 349, - 25061, 10631, 2375, 10013, 9529, 10695, 17510, 231, 9334, 1798, 1263, 4233, 1565, 23669, 930, - 1958, 4258, 1674, 6817, 33844, 2653, 5899, 749, 1627, 639, 4551, 2575, 11826, 2063, 8731, 1695, - 514, 339, 233, 3975, 1795, 7759, 1851, 1463, 3431, 1310, 4105, 4382, 3243, 9196, 4133, 14732, - 1146, 4154, 3782, 1494, 1370, 2986, 5165, 12898, 2091, 143, 11820, 22253, 874, 3347, 14570, - 13432, 29171, 581, 12929, 770, 9338, 3913, 2067, 466, 1442, 1065, 10328, 3273, 197, 4811, 8897, - 5417, 1769, 206, 119, 3406, 6754, 309, 3909, 646, 3677, 3514, 8797, 1435, 301, 9215, 3730, - 7282, 165, 3381, 303, 6369, 2627, 115, 761, 3695, 1233, 1297, 1803, 1130, 122, 511, 58, 6426, - 1389, 1433, 9102, 943, 2795, 13162, 9905, 899, 9740, 8719, 517, 5115, 4977, 1486, 8259, 7163, - 13549, 7561, 305, 119, 973, 7698, 5619, 5326, 5772, 32611, 8846, 1709, 4641, 782, 2503, 3905, - 4051, 4923, 165, 16132, 16827, 1913, 6590, 322, 741, 522, 7666, 1655, 5087, 468, 8541, 1169, - 4455, 22993, 2801, 6623, 446, 1979, 10923, 3503, 32053, 523, 5721, 9608, 955, 11766, 49919, - 1982, 66, 3347, 9508, 439, 145, 5697, 1026, 1569, +pub const MILLER_RABIN_BASE64: [u32; 16384] = [ + 0x24b047, 0x2e32a1, 0x38b06b, 0x31d047, 0x1850d3, 0x595115, 0x17b04f, 0x1cf1b1, 0x2c502b, + 0x55732b, 0x14b137, 0x1f315b, 0x047005, 0x119005, 0x1910df, 0x2ef125, 0x0a3029, 0x28708b, + 0x1250c7, 0x1a5005, 0x3f11eb, 0x449347, 0x11901d, 0x28d02f, 0x24b1a5, 0x0a3053, 0x03d029, + 0x2c5017, 0x13304f, 0x13d10f, 0x0c703d, 0x03b005, 0x0f10c5, 0x1c11b7, 0x10d0ad, 0x02501d, + 0x21d101, 0x32917b, 0x33b0e5, 0x16f151, 0x17f0fb, 0x28d0a3, 0x2511fd, 0x2ab2a1, 0x151005, + 0x067043, 0x239017, 0x1a3115, 0x10d095, 0x2a1257, 0x125047, 0x33d03b, 0x0f1011, 0x13302f, + 0x2cf23b, 0x1e7049, 0x19117f, 0x1a317f, 0x167049, 0x043029, 0x4cd259, 0x2951bb, 0x0b5065, + 0x2bd25f, 0x04f03b, 0x101005, 0x16f119, 0x10f0c5, 0x3370e5, 0x0d3059, 0x4eb36d, 0x2b303d, + 0x48118d, 0x1cf049, 0x35b0a7, 0x0df04f, 0x28d025, 0x1370e9, 0x161005, 0x061005, 0x28715d, + 0x071059, 0x26b02f, 0x0c7043, 0x119011, 0x04901d, 0x199011, 0x1eb095, 0x137005, 0x22d10f, + 0x047005, 0x41b35b, 0x17b095, 0x2cf0b5, 0x139089, 0x281025, 0x05301f, 0x0fb0b3, 0x15d125, + 0x035005, 0x3f12d7, 0x10f011, 0x3012e7, 0x1d3115, 0x04300d, 0x32b0ad, 0x1e70fb, 0x175095, + 0x0e90e3, 0x0ef07f, 0x06d01f, 0x1cf03d, 0x0f10bf, 0x191005, 0x3732ef, 0x0b308b, 0x0ef09d, + 0x32920b, 0x13d047, 0x26b1b1, 0x19103b, 0x10102b, 0x33714b, 0x3e5125, 0x161035, 0x0bf059, + 0x0ef067, 0x1250b3, 0x17502b, 0x1cd1c9, 0x1fd005, 0x097071, 0x17b0a7, 0x07f007, 0x1010c1, + 0x0f1005, 0x17507f, 0x101007, 0x185017, 0x0fb0e3, 0x0c700d, 0x0df00d, 0x11b047, 0x161029, + 0x27715d, 0x125107, 0x0e3067, 0x1c104f, 0x191059, 0x1cd007, 0x0ef07f, 0x059049, 0x07f06d, + 0x3f1295, 0x47f16f, 0x359065, 0x35f259, 0x22d1cf, 0x0c1065, 0x1a517f, 0x3351cf, 0x3011cf, + 0x14b035, 0x1f3035, 0x3df01d, 0x08b083, 0x1cd15b, 0x097083, 0x043035, 0x0fb089, 0x0a302f, + 0x04301f, 0x18d0fb, 0x2f50e5, 0x25723b, 0x035029, 0x061017, 0x13d035, 0x0c5003, 0x10f047, + 0x11906d, 0x191049, 0x3fd1fd, 0x065025, 0x1fd16f, 0x0fb0c1, 0x0f1095, 0x125089, 0x08b035, + 0x06b03b, 0x1cf08b, 0x2ab175, 0x09700b, 0x0df0bf, 0x22d003, 0x1390ad, 0x35b0c5, 0x2dd101, + 0x1cf005, 0x1cf0fb, 0x10d0a3, 0x3df07f, 0x1d30e3, 0x373185, 0x2571f7, 0x1250d3, 0x04903d, + 0x28121d, 0x115013, 0x13703d, 0x17f101, 0x31d283, 0x35f33b, 0x119053, 0x355083, 0x3551c9, + 0x0ef02b, 0x04900b, 0x2511e7, 0x0d30c5, 0x1b7067, 0x23b0f1, 0x04f017, 0x1f71b7, 0x685047, + 0x1b1065, 0x0a3049, 0x1c11bb, 0x0ef005, 0x0a300d, 0x10d06d, 0x125029, 0x3b335f, 0x2231fd, + 0x21d0f1, 0x29315b, 0x161125, 0x185035, 0x337071, 0x0a706b, 0x0a7029, 0x0c5025, 0x22d175, + 0x0b3059, 0x161071, 0x097017, 0x1c107f, 0x28306d, 0x4071bb, 0x4191c1, 0x06b02b, 0x223137, + 0x25103d, 0x071035, 0x09703b, 0x38b02f, 0x06b01f, 0x10703b, 0x0e5083, 0x0f1067, 0x0bf00d, + 0x4bd283, 0x185071, 0x2331f3, 0x24b005, 0x19902f, 0x10d071, 0x3e5161, 0x0ad035, 0x2390bf, + 0x12503b, 0x13300d, 0x0ef0b5, 0x043035, 0x1a5133, 0x2dd1a5, 0x13710f, 0x1f311b, 0x19900d, + 0x25911b, 0x10d01f, 0x41b03d, 0x1af0bf, 0x2810f1, 0x1eb007, 0x1850d3, 0x0c100d, 0x0fb065, + 0x0b5035, 0x07106d, 0x24b0df, 0x1fd071, 0x55135b, 0x0c109d, 0x10f0d3, 0x1250c7, 0x3b9071, + 0x0c5043, 0x3552b3, 0x13d0ad, 0x22301d, 0x0c106b, 0x0b503b, 0x17507f, 0x44f0b3, 0x45542d, + 0x209043, 0x1a500d, 0x19918d, 0x38f25f, 0x2b3119, 0x26503d, 0x1150b5, 0x1df1cd, 0x13d04f, + 0x2e302f, 0x43f2dd, 0x26b1bb, 0x3fb1e7, 0x3f124b, 0x0fb0c5, 0x167137, 0x329133, 0x257013, + 0x095053, 0x1cd061, 0x08907f, 0x26b259, 0x115017, 0x21d053, 0x0c1011, 0x13d011, 0x3d715b, + 0x0bf06d, 0x1670fb, 0x23b0d3, 0x08b083, 0x0ad00b, 0x1eb167, 0x0a306d, 0x33d0f1, 0x1df0fb, + 0x0c101f, 0x17f025, 0x0c70b5, 0x269067, 0x2dd1b7, 0x20b097, 0x18d0ad, 0x0f1029, 0x295071, + 0x0c1005, 0x26b095, 0x071035, 0x17f0b5, 0x25f06b, 0x0b5083, 0x49d17b, 0x0e301d, 0x13311b, + 0x2a1287, 0x089071, 0x125061, 0x065017, 0x17b01f, 0x25f067, 0x55d0c7, 0x1b71af, 0x33d191, + 0x0e302b, 0x14b0e5, 0x0a7053, 0x04703b, 0x445185, 0x0a3043, 0x05901f, 0x44f0fb, 0x0d30c7, + 0x0fb0c7, 0x1af025, 0x3591fd, 0x0fb013, 0x49314b, 0x15103b, 0x15b14b, 0x2cf185, 0x10f01d, + 0x101011, 0x1a5191, 0x2330b5, 0x3a900b, 0x0f1025, 0x29317b, 0x025007, 0x1bb067, 0x2bd295, + 0x0ad047, 0x0c70a7, 0x0ef065, 0x125065, 0x293119, 0x2e7071, 0x21d101, 0x3471eb, 0x3010c7, + 0x33704f, 0x03d02b, 0x3fb3e5, 0x50315d, 0x3d721d, 0x1750c1, 0x09d02b, 0x11904f, 0x28126b, + 0x47f1f7, 0x359167, 0x10f0b3, 0x2c5049, 0x02900d, 0x1750f1, 0x017011, 0x8412cf, 0x0df03b, + 0x025017, 0x18d0b3, 0x1bb0f1, 0x28100d, 0x05300d, 0x03b02b, 0x28109d, 0x21d0e5, 0x26b0a7, + 0x01f00d, 0x277071, 0x0fb09d, 0x5171b1, 0x15b07f, 0x089035, 0x2091e7, 0x1510e5, 0x101025, + 0x5e7125, 0x3df26b, 0x26b1cf, 0x0d306d, 0x0a3049, 0x23b089, 0x3b3119, 0x233095, 0x1a3053, + 0x25710d, 0x0c70b3, 0x10f0a3, 0x35532b, 0x295101, 0x2ef1f7, 0x09703d, 0x17b067, 0x26504f, + 0x1bb191, 0x64d61f, 0x10d09d, 0x277259, 0x4ff33b, 0x16f0df, 0x03502f, 0x125095, 0x0a3003, + 0x04703d, 0x25907f, 0x56500d, 0x0e307f, 0x2091df, 0x06d017, 0x2dd2c5, 0x15101f, 0x25f02b, + 0x1910ad, 0x053029, 0x2bd137, 0x24b1b7, 0x18510d, 0x20b161, 0x1e71c1, 0x443329, 0x1cd0e9, + 0x3fb337, 0x1eb0d3, 0x1eb067, 0x0df095, 0x1af07f, 0x34702b, 0x0fb0a3, 0x10d043, 0x4cd481, + 0x1fd1df, 0x1bb0b5, 0x287283, 0x16f0b5, 0x35f0c1, 0x0c709d, 0x0c706b, 0x33d2f5, 0x03d00d, + 0x04f011, 0x2090e3, 0x0a3005, 0x13d029, 0x08b003, 0x2a52a1, 0x0e90ad, 0x281139, 0x22d191, + 0x37735f, 0x0b3047, 0x2f9151, 0x10f101, 0x035017, 0x0df0d3, 0x5273b9, 0x0d3029, 0x14b115, + 0x26b1fd, 0x281239, 0x22d06d, 0x1af0a3, 0x24b10d, 0x1bb107, 0x3472d7, 0x10100b, 0x2770ef, + 0x1150f1, 0x06704f, 0x0e30df, 0x115013, 0x283151, 0x043025, 0x02b00d, 0x2bd259, 0x24b0ad, + 0x05304f, 0x14b047, 0x17b0df, 0x1850b5, 0x0d3043, 0x0c1043, 0x239107, 0x125035, 0x0bf0a7, + 0x1250bf, 0x0a701d, 0x1eb0b3, 0x1370d3, 0x10f0bf, 0x061005, 0x139125, 0x15b029, 0x13906b, + 0x0a3089, 0x13d00d, 0x19906b, 0x4cf065, 0x11900d, 0x0bf043, 0x1a501d, 0x07101d, 0x2cf25f, + 0x10100d, 0x28d0e3, 0x0ef03b, 0x0a703b, 0x241089, 0x1b1025, 0x46335b, 0x3c72a1, 0x371089, + 0x623397, 0x58f125, 0x2590ef, 0x191043, 0x0e906d, 0x0c70b5, 0x16f065, 0x08b089, 0x2931f3, + 0x01300d, 0x11b0c7, 0x40708b, 0x1c10d3, 0x42d1df, 0x137017, 0x0d301d, 0x2a510d, 0x3d102f, + 0x0e902b, 0x101089, 0x1af00b, 0x115005, 0x283101, 0x2dd02b, 0x29307f, 0x06b00d, 0x14b115, + 0x16706d, 0x1c1175, 0x2770d3, 0x1d301f, 0x18d06d, 0x1a5191, 0x2f5043, 0x35f295, 0x0e30b3, + 0x11b067, 0x067005, 0x26b0a7, 0x1e70ad, 0x2230df, 0x15b10d, 0x09d071, 0x067043, 0x1cf06d, + 0x09d053, 0x16f03b, 0x2230c1, 0x25f0fb, 0x14b053, 0x17f15b, 0x16f097, 0x1cf083, 0x13906d, + 0x1a30b5, 0x2ef1cf, 0x23b17f, 0x0fb00d, 0x1f30fb, 0x19117f, 0x09706d, 0x1cf151, 0x277185, + 0x10108b, 0x17b03d, 0x09d061, 0x1e70ad, 0x07f005, 0x209139, 0x1b717f, 0x23308b, 0x1df18d, + 0x17f095, 0x1bb011, 0x515301, 0x1510ef, 0x48131d, 0x16f09d, 0x33d259, 0x1990df, 0x5114c1, + 0x0e506d, 0x0d3053, 0x265061, 0x1a30f1, 0x139049, 0x287097, 0x137101, 0x2a100b, 0x1a5005, + 0x0c7083, 0x1af125, 0x1b1025, 0x35f167, 0x24b095, 0x3732a5, 0x1cf071, 0x11b065, 0x3470fb, + 0x20b04f, 0x335265, 0x17b0b5, 0x51501f, 0x3a9161, 0x0df0c7, 0x3b331d, 0x10f0c1, 0x16106b, + 0x3df281, 0x1e70fb, 0x19908b, 0x0a309d, 0x23901d, 0x2a1101, 0x0c70b5, 0x0bf029, 0x16101d, + 0x10d061, 0x06500d, 0x161115, 0x39721d, 0x409305, 0x0df0a3, 0x21d06b, 0x28100d, 0x2771df, + 0x1bb0b3, 0x1a314b, 0x233185, 0x137011, 0x241137, 0x3a12d7, 0x1010fb, 0x40f20b, 0x22d15d, + 0x061011, 0x0d306d, 0x283139, 0x167119, 0x23b18d, 0x17b01d, 0x2bd295, 0x12500d, 0x43f233, + 0x0df09d, 0x0c1067, 0x1f303d, 0x0fb053, 0x10d083, 0x33d06b, 0x3292cf, 0x4a940f, 0x199083, + 0x0b5049, 0x15d09d, 0x13d01f, 0x08303d, 0x1c1017, 0x17f095, 0x06700d, 0x1cd15b, 0x2ab1a5, + 0x0bf0b3, 0x09503d, 0x427017, 0x1d30ef, 0x25702b, 0x0fb04f, 0x0e507f, 0x1150e5, 0x061005, + 0x19902f, 0x18d10d, 0x2230e9, 0x09501d, 0x1cd03b, 0x41936d, 0x199013, 0x17f125, 0x1a50e9, + 0x15b0c5, 0x1b702f, 0x04703b, 0x061059, 0x061059, 0x2830fb, 0x1bb107, 0x31309d, 0x0c50a3, + 0x2e3277, 0x1b10fb, 0x305029, 0x46340f, 0x0e9043, 0x2f900d, 0x1250e3, 0x2931f7, 0x10d025, + 0x13d0ef, 0x06b01f, 0x32b24b, 0x185119, 0x0df049, 0x19907f, 0x3d7151, 0x1e714b, 0x0c1017, + 0x19918d, 0x1af139, 0x125059, 0x20911b, 0x0b5067, 0x1fd0a3, 0x167125, 0x06b049, 0x1eb107, + 0x241101, 0x0c7049, 0x2091c1, 0x2dd1cf, 0x1c101f, 0x18514b, 0x0df0b5, 0x11b013, 0x2411bb, + 0x0b5005, 0x0fb095, 0x0b3029, 0x4fd22d, 0x0a3029, 0x0d300d, 0x03501d, 0x33b06d, 0x2930e9, + 0x08b065, 0x06d065, 0x10102f, 0x083029, 0x08b089, 0x3ad337, 0x06b035, 0x1a3053, 0x01d013, + 0x1990c7, 0x33d1df, 0x15d083, 0x4a93fb, 0x397005, 0x11900b, 0x0f106b, 0x33d06d, 0x0e9067, + 0x04902b, 0x13d0a7, 0x15d151, 0x295259, 0x35917f, 0x2d7241, 0x04300b, 0x18d167, 0x22300d, + 0x0b3005, 0x18d0a3, 0x2c525f, 0x51b3c7, 0x18500d, 0x101025, 0x3370c7, 0x065025, 0x23b09d, + 0x0fb09d, 0x185107, 0x08b065, 0x0ef0e5, 0x10d01f, 0x4c1469, 0x133119, 0x02b00d, 0x3b31f3, + 0x2651c1, 0x1150a7, 0x0c70a7, 0x0e501f, 0x2931b1, 0x1a5017, 0x1010c1, 0x15d139, 0x0d307f, + 0x2ef2c5, 0x1330c1, 0x1d30d3, 0x1150c1, 0x0e506b, 0x0b3005, 0x1c115b, 0x00d003, 0x08307f, + 0x23b1af, 0x4cf133, 0x4691fd, 0x313025, 0x1fd1cd, 0x07f065, 0x0c500d, 0x3050e9, 0x4630a7, + 0x33b029, 0x0e90bf, 0x39735b, 0x11b115, 0x0fb01f, 0x09d013, 0x161005, 0x2e317b, 0x15b115, + 0x3f10c1, 0x3730e9, 0x1f3125, 0x269061, 0x2f92b3, 0x3d7373, 0x4930e9, 0x1c10ad, 0x373295, + 0x3c72a1, 0x101059, 0x335185, 0x01100b, 0x0ad067, 0x1e70fb, 0x1a314b, 0x2690ef, 0x4270b3, + 0x0bf007, 0x089053, 0x13d0a3, 0x2bd049, 0x2871f3, 0x0df02f, 0x167035, 0x1010e5, 0x0c100d, + 0x2c502b, 0x287035, 0x09d00d, 0x0c1003, 0x16f0e9, 0x15b13d, 0x1af089, 0x22d067, 0x2e308b, + 0x04f02b, 0x67949d, 0x397059, 0x1f3119, 0x25114b, 0x19910f, 0x137115, 0x22d007, 0x241049, + 0x19100d, 0x1190ef, 0x21d0c7, 0x2cf095, 0x16106d, 0x10107f, 0x26915d, 0x1c91c1, 0x18503d, + 0x06704f, 0x1b7029, 0x0fb0e9, 0x035011, 0x0f10e5, 0x1eb139, 0x1990c5, 0x2391d3, 0x0e903d, + 0x08902b, 0x0c7035, 0x0a306d, 0x097095, 0x0a3065, 0x185005, 0x265259, 0x23b1df, 0x1610c5, + 0x095065, 0x18513d, 0x01d011, 0x2dd233, 0x259083, 0x0ef061, 0x515043, 0x1e70bf, 0x1af0e5, + 0x2bd21d, 0x14b029, 0x2570df, 0x1cf1bb, 0x119097, 0x25f209, 0x17b0df, 0x097059, 0x36d04f, + 0x02f005, 0x1250df, 0x599125, 0x26b0fb, 0x1510e5, 0x2dd1a5, 0x1b714b, 0x04300d, 0x265107, + 0x071061, 0x199013, 0x409161, 0x2590c1, 0x0df083, 0x4b136d, 0x11b053, 0x4fd0df, 0x03d02f, + 0x2e702f, 0x2e702f, 0x3292f9, 0x1c9059, 0x04703b, 0x2dd1f7, 0x101071, 0x2cf1bb, 0x1cf01f, + 0x241025, 0x0e500d, 0x17f10d, 0x08b03d, 0x2dd1fd, 0x287107, 0x3e5043, 0x2e70ad, 0x16f161, + 0x09d08b, 0x0fb067, 0x10f029, 0x251125, 0x0ef0c7, 0x2591bb, 0x22d047, 0x1af167, 0x2a50ef, + 0x607493, 0x11510f, 0x3c7005, 0x305199, 0x08b005, 0x3710c1, 0x2f903b, 0x329287, 0x28d061, + 0x2bd107, 0x17f04f, 0x1c9095, 0x19102b, 0x0df02b, 0x1f302b, 0x15b11b, 0x0a3067, 0x1cd095, + 0x14b10d, 0x1d300d, 0x1c110f, 0x06b01d, 0x3f5265, 0x16f0c5, 0x17b119, 0x1750b5, 0x5030bf, + 0x0d300d, 0x283241, 0x4d50c7, 0x3590c7, 0x22d1f7, 0x32b2e3, 0x28d005, 0x2691a5, 0x25f01f, + 0x083067, 0x28d1bb, 0x26911b, 0x10f053, 0x223137, 0x0bf00d, 0x3352cf, 0x397035, 0x1a3101, + 0x329175, 0x15d0ad, 0x33b0ad, 0x1390a7, 0x09d025, 0x2870c1, 0x2f5133, 0x48b06b, 0x0b3005, + 0x0f1089, 0x2a5277, 0x191097, 0x1f70a3, 0x2d726b, 0x01f017, 0x185175, 0x09d02b, 0x31d1a3, + 0x2570fb, 0x2770e3, 0x3131fd, 0x2a50e5, 0x1cf0ef, 0x40902f, 0x2390b3, 0x097095, 0x18d0ef, + 0x26b067, 0x265241, 0x33d2e3, 0x22d167, 0x71f2b3, 0x19104f, 0x287003, 0x06504f, 0x175005, + 0x1f30a7, 0x0c7089, 0x0bf065, 0x38f00d, 0x3fb2f5, 0x02f00d, 0x33b101, 0x097049, 0x0f102b, + 0x4a333d, 0x11503b, 0x20b1eb, 0x16f0e3, 0x20b11b, 0x22d01f, 0x60d5b3, 0x377313, 0x0c7097, + 0x29315d, 0x0ef065, 0x2a1293, 0x0c1043, 0x10f0e5, 0x2951c9, 0x0ef0df, 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0x20b02b, 0x28107f, 0x1750e9, 0x1f717f, 0x1c10c7, 0x3f50bf, 0x23b03b, 0x33d17b, + 0x21d1f7, 0x277097, 0x21d1b7, 0x2390df, 0x083029, 0x10700d, 0x17f03d, 0x10d0c1, 0x2cf043, + 0x09701f, 0x053029, 0x1010e3, 0x5512dd, 0x18d013, 0x29509d, 0x13d083, 0x25f0c7, 0x3cb3b3, + 0x0a703d, 0x17b13d, 0x347257, 0x1fd0c5, 0x0ad025, 0x25f089, 0x6ad425, 0x35b0c5, 0x12500b, + 0x07100b, 0x2ef259, 0x32b28d, 0x04903d, 0x1a50e9, 0x1750a7, 0x44f335, 0x38b33d, 0x02b00d, + 0x06500d, 0x3fb065, 0x30504f, 0x1330d3, 0x24b1af, 0x03d03b, 0x06d029, 0x2dd16f, 0x00b005, + 0x1cd06b, 0x08b043, 0x287233, 0x25915d, 0x19106b, 0x5150ad, 0x20b095, 0x1d317f, 0x17f11b, + 0x1bb0e5, 0x07100b, 0x09d03b, 0x133029, 0x1cd0b5, 0x1e70e9, 0x10709d, 0x26b0f1, 0x1cd115, + 0x035005, 0x03500d, 0x16708b, 0x0a7061, 0x0b3053, 0x0e5071, 0x1eb14b, 0x07101f, 0x1f3003, + 0x17b047, 0x28723b, 0x0f109d, 0x17b03b, 0x3b90f1, 0x0a3029, 0x0e302b, 0x0ad09d, 0x1d31b1, + 0x1cf08b, 0x083049, 0x0c700b, 0x4811eb, 0x3d10e3, 0x0ad04f, 0x0c506d, 0x0e50bf, 0x38f061, + 0x18517b, 0x137097, 0x035007, 0x0bf025, 0x1f71a5, 0x08903b, 0x0ef0c5, 0x329175, 0x16f10d, + 0x25f043, 0x277017, 0x23b017, 0x28304f, 0x3372a5, 0x24b035, 0x1a3101, 0x19114b, 0x15d04f, + 0x09d01d, 0x313097, 0x517011, 0x32b125, 0x107065, 0x10f08b, 0x295005, 0x2b324b, 0x1cd043, + 0x1eb16f, 0x683577, 0x0bf005, 0x095005, 0x1bb025, 0x17b017, 0x26521d, 0x0f1053, 0x22301d, + 0x23b011, 0x13d007, 0x3cb02f, 0x1af101, 0x24b191, 0x1bb06d, 0x16107f, 0x137029, 0x281035, + 0x28d007, 0x1f31bb, 0x0e500b, 0x3ad01d, 0x1eb0b3, 0x161013, 0x175125, 0x25f241, 0x0c500d, + 0x3370a3, 0x11b119, 0x239061, 0x5fb2ef, 0x3b3251, 0x2c5035, 0x10703d, 0x00d005, 0x33723b, + 0x1df15d, 0x11901d, 0x241137, 0x095013, 0x281083, 0x1df137, 0x1370b5, 0x31d0b3, 0x10d00d, + 0x1e70c5, 0x1c9191, 0x2a1191, 0x1e70fb, 0x23900b, 0x15b035, 0x0e906d, 0x1f714b, 0x0ad04f, + 0x4250f1, 0x2f51e7, 0x25f1a5, 0x2e3281, 0x1c913d, 0x20b025, 0x21d017, 0x3ad1bb, 0x5512bd, + 0x0c503d, 0x2411cd, 0x1c90bf, 0x7c922d, 0x1c107f, 0x3050b5, 0x2e7043, 0x07f03d, 0x1a51a3, + 0x19111b, 0x0ad0a7, 0x2d7185, 0x02901d, 0x0c500b, 0x26900d, 0x18503d, 0x5b3287, 0x5bf359, + 0x0c5097, 0x50923b, 0x2b323b, 0x04901f, 0x371233, 0x1c10fb, 0x02501f, 0x0ad08b, 0x3df301, + 0x1eb007, 0x2811f3, 0x3ad059, 0x107011, 0x407251, 0x239097, 0x167151, 0x21d0b5, 0x22d1df, + 0x167083, 0x08901f, 0x0c7013, 0x18d17b, 0x03b029, 0x1fd0e5, 0x35f0e5, 0x493125, 0x28d277, + 0x33d199, 0x1df1bb, 0x06b047, 0x15d0e5, 0x0c504f, 0x2a117f, 0x0d308b, 0x41b1a5, 0x1eb06d, + 0x17514b, 0x1250a7, 0x02f025, 0x1c116f, 0x65b4eb, 0x1cf151, 0x1d317b, 0x17b0e5, 0x1f714b, + 0x24b1f7, 0x0e30b3, 0x26b185, 0x10700b, 0x283241, 0x17f10d, 0x38f06d, 0x0c502f, 0x29525f, + 0x241047, 0x3a90c1, 0x28d0c1, 0x053047, 0x125083, 0x09d047, 0x259167, 0x137049, 0x07f04f, + 0x0ef0a3, 0x1d30bf, 0x3131c1, 0x0e30c7, 0x133107, 0x293223, 0x29524b, 0x31d0c7, 0x17b139, + 0x1190e5, 0x059025, 0x2950f1, 0x50b0b3, 0x1b1185, 0x139013, 0x09d01d, 0x07100d, 0x17b035, + 0x49344f, 0x3b3139, 0x06b011, 0x2dd00d, 0x24b089, 0x1b7095, 0x137047, 0x2830fb, 0x029013, + 0x11903d, 0x0d3025, 0x161151, 0x23301f, 0x27725f, 0x1c1151, 0x089053, 0x01100d, 0x2771b1, + 0x1850c1, 0x2f91c1, 0x2f51fd, 0x0c5011, 0x10103b, 0x2c5283, 0x265067, 0x0bf03d, 0x2d700b, + 0x15d125, 0x43f419, 0x3b3269, 0x1510b5, 0x13700d, 0x17f01d, 0x1cf185, 0x0a7059, 0x277191, + 0x04303d, 0x2a1293, 0x1cd0d3, 0x1bb115, 0x125061, 0x23b22d, 0x151137, 0x101083, 0x1f30f1, + 0x175053, 0x097025, 0x22d0b3, 0x23b13d, 0x02f011, 0x1a515d, 0x11b115, 0x11906b, 0x0e5005, + 0x0e90b3, 0x4cd0fb, 0x2d7089, 0x1f71a3, 0x06b02f, 0x25901d, 0x24b0c7, 0x0e900b, 0x1b1139, + 0x1f3107, 0x2ab083, 0x1f31df, 0x20906d, 0x251061, 0x31d137, 0x2590fb, 0x31d1bb, 0x1eb133, + 0x199161, 0x1f71eb, 0x1e7007, 0x1eb089, 0x10f005, 0x0bf083, 0x101095, 0x36d335, 0x2e3223, + 0x1e70ad, 0x1f303b, 0x2ef1a3, 0x06b01f, 0x2ab1cd, 0x0e9005, 0x4ff455, 0x0f10b3, 0x0b506b, + 0x14b013, 0x137029, 0x33b119, 0x1a3025, 0x3ad061, 0x2810e9, 0x02b025, 0x1af125, 0x06b025, + 0x0a306d, 0x0e3067, 0x1c11b7, 0x0b5059, 0x06b005, 0x257035, 0x23b059, 0x2090ad, 0x07f02f, + 0x5e747f, 0x167035, 0x12506d, 0x2d715b, 0x1c9125, 0x2230b5, 0x09501f, 0x1990c5, 0x2f9049, + 0x191175, 0x1c900b, 0x0ef013, 0x2090c1, 0x1b101d, 0x377251, 0x4d5301, 0x0c5047, 0x1a3025, + 0x0ef061, 0x2ab23b, 0x15103b, 0x10f097, 0x0d3043, 0x0a702b, 0x5171bb, 0x33d32b, 0x10f0e9, + 0x1070b5, 0x22309d, 0x2831b1, 0x03b035, 0x16f089, 0x2831c1, 0x00d005, 0x329005, 0x277083, + 0x167005, 0x095007, 0x251199, 0x185101, 0x0c106d, 0x1390b5, 0x1750e3, 0x10f083, 0x1cf03d, + 0x1f70df, 0x36d04f, 0x67f185, 0x25f047, 0x1bb065, 0x1d300d, 0x25f101, 0x0ad03d, 0x0b3095, + 0x04f005, 0x1c90a3, 0x38f1fd, 0x34710d, 0x067017, 0x15d00d, 0x1330e5, 0x20b133, 0x2b31b7, + 0x22d223, 0x2590d3, 0x50b035, 0x23b125, 0x125059, 0x0c703b, 0x0ad00b, 0x175005, 0x36d10d, + 0x0ef095, 0x11b10d, 0x13300d, 0x11b043, 0x1df067, 0x13302b, 0x1fd029, 0x1a5013, 0x1cd04f, + 0x05904f, 0x0bf061, 0x08b005, 0x0a306b, 0x1f7097, 0x1a317b, 0x2bd13d, 0x1df049, 0x00d005, + 0x0ad00d, 0x2b3277, 0x1c100b, 0x3012f5, 0x0ad00d, 0x0a3059, 0x26520b, 0x29503d, 0x02500b, + 0x0e501f, 0x2a50b5, 0x18504f, 0x1af08b, 0x199175, 0x4cd427, 0x16106d, 0x32b265, 0x1eb059, + 0x133101, 0x09701d, 0x251119, 0x10d01d, 0x15d14b, 0x01300d, 0x2a1287, 0x161025, 0x3fd371, + 0x19917f, 0x1af0f1, 0x24b00d, 0x199029, 0x35b007, 0x13d02b, 0x06d03d, 0x20b097, 0x64d01d, + 0x241191, 0x1df18d, 0x2ef185, 0x0bf0b5, 0x25f07f, 0x16f0c7, 0x1f702b, 0x3f5139, 0x1cf0c1, + 0x13908b, 0x0e500d, 0x0c7005, 0x67f31d, 0x36d2f5, 0x2331df, 0x097035, 0x25713d, 0x0c1083, + 0x1330bf, 0x4c72ab, 0x0c100b, 0x251043, 0x2e3259, 0x37102b, 0x38b35f, 0x449277, 0x4491f7, + 0x0b3053, 0x45d00b, 0x427359, 0x17515d, 0x26b0a3, 0x2d70e9, 0x1150e5, 0x1750c1, 0x3df09d, + 0x17f03d, 0x0ef053, 0x0fb049, 0x209005, 0x2bd049, 0x45d005, 0x11b013, 0x02500d, 0x557529, + 0x0c701d, 0x0b3017, 0x15d013, 0x24b061, 0x2a51cd, 0x241199, 0x0a7065, 0x38b33d, 0x0d3005, + 0x1f70bf, 0x3fd2dd, 0x0c7071, 0x1670f1, 0x065013, 0x043017, 0x35f047, 0x1510ef, 0x23301d, + 0x2590e3, 0x06d005, 0x6a1509, 0x04701f, 0x065035, 0x089067, 0x35f1e7, 0x3fb09d, 0x12509d, + 0x2ef251, 0x2590bf, 0x313043, 0x09502b, 0x7b5445, 0x251191, 0x01300d, 0x61f295, 0x2871c9, + 0x0c50bf, 0x10f03b, 0x0a3025, 0x21d025, 0x12500b, 0x0b506b, 0x1b7061, 0x065013, 0x2c5097, + 0x3ad0fb, 0x3772f9, 0x1f71e7, 0x1e7003, 0x24b1b1, 0x07f029, 0x1af0df, 0x1a5095, 0x16f00d, + 0x1cd09d, 0x265013, 0x3c7151, 0x17b101, 0x0ad047, 0x0b301f, 0x16f101, 0x15b061, 0x14b11b, + 0x4a3115, 0x065005, 0x02500d, 0x047005, 0x1510b5, 0x0fb0c1, 0x38b2c5, 0x26909d, 0x025003, + 0x0bf011, 0x0bf095, 0x0e9071, 0x16f161, 0x283013, 0x26b15b, 0x38f301, 0x15d0e9, 0x3b9035, + 0x15b043, 0x4ff36d, 0x12511b, 0x07f029, 0x16702b, 0x257071, 0x25703d, 0x50b427, 0x2e315d, + 0x1cd0a7, 0x2091af, 0x02501d, 0x257125, 0x09700d, 0x1b1067, 0x2591cf, 0x23b01d, 0x0c506b, + 0x24b065, 0x2ef185, 0x1e7013, 0x049007, 0x239119, 0x2dd059, 0x4cd40f, 0x0f1029, 0x4cd287, + 0x31d26b, 0x2f92a5, 0x2ef28d, 0x1670ef, 0x3e5329, 0x23b161, 0x3372dd, 0x17515d, 0x1df1a3, + 0x16f047, 0x1250b3, 0x3a11d3, 0x1a306b, 0x02b00d, 0x1cf065, 0x1330b3, 0x1eb17b, 0x29526b, + 0x257199, 0x13d005, 0x0bf00b, 0x223151, 0x233097, 0x1eb15b, 0x33d2ef, 0x10d0ef, 0x335095, + 0x257095, 0x3e5053, 0x03d02b, 0x0e908b, 0x1d3047, 0x15b053, 0x2231f7, 0x119043, 0x3c7059, + 0x5f31fd, 0x23b01d, 0x10f02f, 0x33b06d, 0x097005, 0x07f03b, 0x083035, 0x43f277, 0x10f017, + 0x0a7083, 0x09d061, 0x33d035, 0x0c7061, 0x1750b5, 0x377305, 0x107061, 0x2330c7, 0x18510f, + 0x26b0e5, 0x137089, 0x17507f, 0x33b049, 0x10f0df, 0x52706d, 0x241025, 0x0a7067, 0x23b119, + 0x1c1125, 0x11502f, 0x3771a5, 0x313287, 0x419007, 0x09703d, 0x409397, 0x0d3049, 0x329097, + 0x083005, 0x1a306d, 0x2e720b, 0x08b083, 0x15d0e3, 0x0e5071, 0x065059, 0x2f5151, 0x191101, + 0x0a7095, 0x3470a3, 0x125107, 0x095011, 0x5db061, 0x1c1119, 0x33700d, 0x167125, 0x15d02b, + 0x1c9043, 0x2f50e3, 0x1df0b5, 0x0fb011, 0x33d1c1, 0x29325f, 0x1fd00d, 0x0c50ad, 0x25900d, + 0x12500b, 0x11504f, 0x05300d, 0x313241, 0x175003, 0x1f30e9, 0x15b025, 0x1cf007, 0x1fd18d, + 0x2cf17b, 0x305043, 0x4073f1, 0x3b3241, 0x1670e3, 0x4ff089, 0x233043, 0x23b035, 0x2ef15b, + 0x185101, 0x65b611, 0x2e326b, 0x2770fb, 0x17f005, 0x065025, 0x265137, 0x1150bf, 0x0f100d, + 0x1b1061, 0x11b03d, 0x095049, 0x283059, 0x0a301d, 0x03d01f, 0x17f16f, 0x13710f, 0x01700d, + 0x2870ad, 0x1a302b, 0x5031cf, 0x1610b3, 0x209089, 0x02501d, 0x059053, 0x11b0e3, 0x3372a1, + 0x0c5005, 0x18d185, 0x1e70bf, 0x10103d, 0x0e50ad, 0x47f0bf, 0x15d14b, 0x2f9025, 0x11b0ef, + 0x3771bb, 0x23315d, 0x11b0a3, 0x1f3005, 0x223071, 0x04f01d, 0x1fd005, 0x151043, 0x095007, + 0x14b083, 0x36d06d, 0x11b0bf, 0x21d01f, 0x03d00b, 0x15b0b3, 0x02b01f, 0x07106b, 0x407397, + 0x097035, 0x071049, 0x511269, 0x283161, 0x1df191, 0x3ad125, 0x5510c1, 0x161115, 0x2410fb, + 0x2e7101, 0x14b01d, 0x31d209, 0x09d003, 0x0f1053, 0x08907f, 0x239095, 0x029005, 0x3a918d, + 0x28d0c1, 0x02b01d, 0x36d071, 0x09503d, ]; //////////////////// Lookup tables for number theoretic functions @@ -2502,15 +3299,26 @@ for s in selections: #[cfg(not(feature = "big-table"))] pub const QUAD_MODULI: [u8; 4] = [63, 65, 61, 59]; // note that 0 and 64 are both square mod 65 #[cfg(not(feature = "big-table"))] -pub const QUAD_RESIDUAL: [u64; 4] = [0x0402483012450293, 0x218a019866014613, 0x1713e6940a59f23b, 0x022b62183e7b92bb]; +pub const QUAD_RESIDUAL: [u64; 4] = [ + 0x0402483012450293, + 0x218a019866014613, + 0x1713e6940a59f23b, + 0x022b62183e7b92bb, +]; #[cfg(not(feature = "big-table"))] pub const CUBIC_MODULI: [u8; 4] = [63, 61, 43, 37]; #[cfg(not(feature = "big-table"))] -pub const CUBIC_RESIDUAL: [u64; 4] = [0x4080001818000103, 0x1434026619900b0b, 0x0000068908610917, 0x00000010ac804d43]; +pub const CUBIC_RESIDUAL: [u64; 4] = [ + 0x4080001818000103, + 0x1434026619900b0b, + 0x0000068908610917, + 0x00000010ac804d43, +]; #[cfg(feature = "big-table")] pub const QUAD_MODULI: [u16; 8] = [819, 935, 989, 899, 1007, 1021, 1019, 1013]; +#[rustfmt::skip] #[cfg(feature = "big-table")] pub const QUAD_RESIDUAL: [[u64; 16]; 8] = [ [0x0002081002410213, 0xc200001009028001, 0x0000120000014024, 0x008048020208a050, 0x1800048200244029, 0x0420120180020014, 0x2600000080490408, 0x9100041060200800, 0x0904004800120100, 0x2402000400082201, 0x402100920c000040, 0x0820804002004880, 0x0000002403012000, 0, 0, 0], @@ -2525,6 +3333,7 @@ pub const QUAD_RESIDUAL: [[u64; 16]; 8] = [ #[cfg(feature = "big-table")] pub const CUBIC_MODULI: [u16; 8] = [819, 817, 925, 961, 1021, 1009, 997, 991]; +#[rustfmt::skip] #[cfg(feature = "big-table")] pub const CUBIC_RESIDUAL: [[u64; 16]; 8] = [ [0x0000000008000103, 0x204000080c000001, 0x4020000200000000, 0x1000000001000000, 0x0008000080000010, 0x06000000c0800000, 0x0600000000000000, 0x0000000010300000, 0x0080800000100001, 0x4020000008000000, 0x2040000000040000, 0x0008000003010000, 0x0004080001000000, 0, 0, 0 ],