結果
問題 | No.8030 ミラー・ラビン素数判定法のテスト |
ユーザー | 👑 Mizar |
提出日時 | 2022-11-18 04:43:47 |
言語 | Rust (1.77.0 + proconio) |
結果 |
AC
|
実行時間 | 13 ms / 9,973 ms |
コード長 | 45,776 bytes |
コンパイル時間 | 15,675 ms |
コンパイル使用メモリ | 379,016 KB |
実行使用メモリ | 5,376 KB |
最終ジャッジ日時 | 2024-09-19 14:32:56 |
合計ジャッジ時間 | 13,520 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge3 |
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テストケース
テストケース表示入力 | 結果 | 実行時間 実行使用メモリ |
---|---|---|
testcase_00 | AC | 1 ms
5,248 KB |
testcase_01 | AC | 1 ms
5,248 KB |
testcase_02 | AC | 1 ms
5,248 KB |
testcase_03 | AC | 1 ms
5,376 KB |
testcase_04 | AC | 8 ms
5,376 KB |
testcase_05 | AC | 10 ms
5,376 KB |
testcase_06 | AC | 8 ms
5,376 KB |
testcase_07 | AC | 8 ms
5,376 KB |
testcase_08 | AC | 7 ms
5,376 KB |
testcase_09 | AC | 13 ms
5,376 KB |
ソースコード
// -*- coding:utf-8-unix -*- extern crate core; // 除算/剰余算インラインセンブリコード切替: inline assembly divrem code switch macro_rules! cond_div { ($normal_div:expr, $asm_div:expr) => { //$normal_div // normal $asm_div // 1.59.0 or later (feature = "asm") } } // モンゴメリ剰余乗算: Montgomery modular multiplication pub trait MontVal<T, BitCountType=u32> { fn n(&self) -> T; fn ni(&self) -> T; fn nh(&self) -> T; fn r(&self) -> T; fn rn(&self) -> T; fn r2(&self) -> T; fn d(&self) -> T; fn k(&self) -> BitCountType; } pub trait MontOps<T, BitCountType=u32> { fn add(&self, a: T, b: T) -> T; fn sub(&self, a: T, b: T) -> T; fn div2(&self, ar: T) -> T; fn mrmul(&self, ar: T, br: T) -> T; fn mr(&self, ar: T) -> T; fn ar(&self, a: T) -> T; fn pow(&self, ar: T, b: T) -> T; fn powodd(&self, ar: T, b: T) -> T; } pub trait MontModN<T, BitCountType=u32> { fn modn(&self, x: T) -> T; } pub trait MontNew<T, U=T, BitCountType=u32> { fn new(n: T) -> Self; } struct Mont<T, BitCountType=u32> { n: T, // n is odd, and n > 2 ni: T, // n * ni == 1 (mod 2**64) nh: T, // == (n + 1) / 2 r: T, // == 2**64 (mod n) rn: T, // == -(2**64) (mod n) r2: T, // == 2**128 (mod n) d: T, // == (n - 1) >> (n - 1).trailing_zeros() k: BitCountType, // == (n - 1).trailing_zeros() } macro_rules! impl_mont_val_pr { ($x:ty) => { impl MontVal<$x> for Mont<$x> { fn n(&self) -> $x { self.n } fn ni(&self) -> $x { self.ni } fn nh(&self) -> $x { self.nh } fn r(&self) -> $x { self.r } fn rn(&self) -> $x { self.rn } fn r2(&self) -> $x { self.r2 } fn d(&self) -> $x { self.d } fn k(&self) -> u32 { self.k } }}} impl_mont_val_pr!(u64); impl_mont_val_pr!(u32); macro_rules! impl_mont_ops { ($x:ty, $y:ty, $y2:ty, $w:literal) => { impl MontOps<$y> for $x { fn add(&self, a: $y, b: $y) -> $y { // == a + b (mod n) debug_assert!(a < self.n()); debug_assert!(b < self.n()); match a.overflowing_add(b) { (t, false) => match t.overflowing_sub(self.n()) { (u, false) => u, (_, true) => t, }, (t, true) => t.wrapping_sub(self.n()), } } fn sub(&self, a: $y, b: $y) -> $y { // == a - b (mod n) debug_assert!(a < self.n()); debug_assert!(b < self.n()); match a.overflowing_sub(b) { (t, false) => t, (t, true) => t.wrapping_add(self.n()), } } fn div2(&self, ar: $y) -> $y { // == ar / 2 (mod n) debug_assert!(ar < self.n()); let t = ar >> 1; match ar & 1 { 0 => t, _ => t + self.nh(), } } fn mrmul(&self, ar: $y, br: $y) -> $y { // == (ar * br) / r (mod n) debug_assert!(ar < self.n()); debug_assert!(br < self.n()); let (n, ni) = (self.n(), self.ni()); let t: $y2 = (ar as $y2) * (br as $y2); match ((t >> $w) as $y).overflowing_sub((((((t as $y).wrapping_mul(ni)) as $y2) * (n as $y2)) >> $w) as $y) { (t, false) => t, (t, true) => t.wrapping_add(n), } } fn mr(&self, ar: $y) -> $y { // == ar / r (mod n) debug_assert!(ar < self.n()); let (n, ni) = (self.n(), self.ni()); match (((((ar.wrapping_mul(ni)) as $y2) * (n as $y2)) >> $w) as $y).overflowing_neg() { (t, false) => t, (t, true) => t.wrapping_add(n), } } fn ar(&self, a: $y) -> $y { // == a * r (mod n) debug_assert!(a < self.n()); self.mrmul(a, self.r2()) } fn pow(&self, mut ar: $y, mut b: $y) -> $y { // == ((ar / r) ** b) * r (mod n) debug_assert!(ar < self.n()); let mut t = if (b & 1) == 0 { self.r() } else { ar }; loop { b >>= 1; if b == 0 { return t; } ar = self.mrmul(ar, ar); if (b & 1) != 0 { t = self.mrmul(t, ar); } } } fn powodd(&self, mut ar: $y, mut b: $y) -> $y { // == ((ar / r) ** b) * r (mod n) debug_assert!(ar < self.n()); debug_assert_eq!(b & 1, 1); // b is odd let mut t = ar; loop { b >>= 1; if b == 0 { return t; } ar = self.mrmul(ar, ar); if (b & 1) != 0 { t = self.mrmul(t, ar); } } } }}} impl_mont_ops!(Mont<u64>, u64, u128, 64); impl_mont_ops!(Mont<u32>, u32, u64, 32); #[allow(unused)] fn asm_div32(a: u32, b: u32) -> u32 { // a / b (32bit) debug_assert_ne!(b, 0); cond_div!( a / b, if cfg!(target_arch = "x86_64") { let mut quot: u32; unsafe{core::arch::asm!( "div {0:e}", in(reg) b, inout("eax") a => quot, inout("edx") 0u32 => _, options(pure, nomem, nostack) )} debug_assert_eq!(a / b, quot); quot } else { a / b } ) } #[allow(unused)] fn asm_rem32(a: u32, b: u32) -> u32 { // a mod b (32bit) debug_assert_ne!(b, 0); cond_div!( a % b, if cfg!(target_arch = "x86_64") { let mut rem: u32; unsafe{core::arch::asm!( "div {0:e}", in(reg) b, inout("eax") a => _, inout("edx") 0u32 => rem, options(pure, nomem, nostack) )} debug_assert_eq!(a % b, rem); rem } else { a % b } ) } #[allow(unused)] fn asm_div64(a: u64, b: u64) -> u64 { // a / b (64bit) debug_assert_ne!(b, 0); cond_div!( a / b, if cfg!(target_arch = "x86_64") { let mut quot: u64; unsafe{core::arch::asm!( "div {0}", in(reg) b, inout("rax") a => quot, inout("rdx") 0u64 => _, options(pure, nomem, nostack) )} debug_assert_eq!(a / b, quot); quot } else { a / b } ) } #[allow(unused)] fn asm_rem64(a: u64, b: u64) -> u64 { // a mod b (64bit) debug_assert_ne!(b, 0); cond_div!( a % b, if cfg!(target_arch = "x86_64") { let mut rem: u64; unsafe{core::arch::asm!( "div {0}", in(reg) b, inout("rax") a => _, inout("rdx") 0u64 => rem, options(pure, nomem, nostack) )} debug_assert_eq!(a % b, rem); rem } else { a % b } ) } #[allow(unused)] fn asm_r2_32(n: u32) -> (u32, u32) { // 2**32 mod n, 2**64 mod n (32bit) debug_assert!(n > 1 && (n & 1) == 1); // cause throw when n <= 1 (zero divide or quot overflow) cond_div!( ((1u32.wrapping_neg() % n).wrapping_add(1), ((1u64.wrapping_neg() % (n as u64)) as u32).wrapping_add(1)), if cfg!(target_arch = "x86_64") { let (mut r1, mut r2): (u32, u32); unsafe{core::arch::asm!( "xor eax, eax", "mov edx, 1", "div {0:e}", "mov {1:e}, edx", "xor eax, eax", "div {0:e}", in(reg) n, out(reg) r1, out("eax") _, out("edx") r2, options(pure, nomem, nostack) )} debug_assert_eq!((1u32.wrapping_neg() % n).wrapping_add(1), r1); debug_assert_eq!(((1u64.wrapping_neg() % (n as u64)) as u32).wrapping_add(1), r2); (r1, r2) } else { ((1u32.wrapping_neg() % n).wrapping_add(1), ((1u64.wrapping_neg() % (n as u64)) as u32).wrapping_add(1)) } ) } #[allow(unused)] fn asm_r2_64(n: u64) -> (u64, u64) { // 2**64 mod n, 2**128 mod n (64bit) debug_assert!(n > 1 && (n & 1) == 1); // cause throw when n <= 1 (zero divide or quot overflow) cond_div!( ((1u64.wrapping_neg() % n).wrapping_add(1), ((1u128.wrapping_neg() % (n as u128)) as u64).wrapping_add(1)), if cfg!(target_arch = "x86_64") { let (mut r1, mut r2): (u64, u64); unsafe{core::arch::asm!( "xor rax, rax", "mov rdx, 1", "div {0}", "mov {1}, rdx", "xor rax, rax", "div {0}", in(reg) n, out(reg) r1, out("rax") _, out("rdx") r2, options(pure, nomem, nostack) )} debug_assert_eq!((1u64.wrapping_neg() % n).wrapping_add(1), r1); debug_assert_eq!(((1u128.wrapping_neg() % (n as u128)) as u64).wrapping_add(1), r2); (r1, r2) } else { ((1u64.wrapping_neg() % n).wrapping_add(1), ((1u128.wrapping_neg() % (n as u128)) as u64).wrapping_add(1)) } ) } macro_rules! impl_mont_modn { ($x:ty) => { impl MontModN<$x> for Mont<$x> { fn modn(&self, x: $x) -> $x { if x < self.n() { x } else { cond_div!( x % self.n(), match stringify!($x) { "u64" => asm_rem64(x as u64, self.n() as u64) as $x, "u32" => asm_rem32(x as u32, self.n() as u32) as $x, _ => unimplemented!(), } ) }} }}} impl_mont_modn!(u64); impl_mont_modn!(u32); macro_rules! impl_mont_new { ($x:ty, $x2:ty) => { impl MontNew<$x> for Mont<$x> { fn new(n: $x) -> Self { debug_assert!(n > 1 && (n & 1) == 1); // // n is odd number, n = 2*k+1, n >= 1, n < 2**BITS, k is non-negative integer, k >= 0, k < 2**(BITS-1) // // As (k*(k+1)) is even, (k*(k+1)/2) is an integer. // ni0 := n; // = 2*k+1 = (1+(2**3)*((k*(k+1)/2)**1))/n let mut ni = n; /* // ni1 := ni0 * (2 - (n * ni0)); // = (1+(2**6)*((k*(k+1)/2)**2))/(2*k+1) // ni2 := ni0 * (2 - (n * ni1)); // = (1+(2**12)*((k*(k+1)/2)**4))/(2*k+1) // ni3 := ni0 * (2 - (n * ni2)); // = (1+(2**24)*((k*(k+1)/2)**8))/(2*k+1) // ni4 := ni0 * (2 - (n * ni3)); // = (1+(2**48)*((k*(k+1)/2)**16))/(2*k+1) // ni5 := ni0 * (2 - (n * ni4)); // = (1+(2**96)*((k*(k+1)/2)**32))/(2*k+1) // // (n * ni5) mod 2**64 = ((2*k+1) * ni5) mod 2**64 = 1 mod 2**64 for _ in 0..5 { ni = ni.wrapping_mul((2 as $x).wrapping_sub(n.wrapping_mul(ni))); } // */ //* // ni1 := ni0 * ((n * ni0 - 3) * (n * ni0) + 3); // = (1+(2**9)*((k*(k+1)/2)**3))/(2*k+1) // ni2 := ni1 * ((n * ni1 - 3) * (n * ni1) + 3); // = (1+(2**27)*((k*(k+1)/2)**9))/(2*k+1) // ni3 := ni2 * ((n * ni2 - 3) * (n * ni2) + 3); // = (1+(2**81)*((k*(k+1)/2)**27))/(2*k+1) // // (n * ni3) mod 2**64 = ((2*k+1) * ni3) mod 2**64 = 1 mod 2**64 for _ in 0..3 { let t = n.wrapping_mul(ni); ni = t.wrapping_sub(3).wrapping_mul(t).wrapping_add(3).wrapping_mul(ni); } // */ debug_assert_eq!(n.wrapping_mul(ni), 1); // n * ni == 1 (mod 2**BITS) let nh = (n >> 1) + 1; // == (n + 1) / 2 == floor(n / 2) + 1 { n is odd } let (r, r2) = cond_div!( // == ( 2**BITS, (2**BITS)**2 ) (mod n) ( (((1 as $x).wrapping_neg() % n).wrapping_add(1)), ((((1 as $x2).wrapping_neg() % (n as $x2)) as $x).wrapping_add(1)), ), match stringify!($x) { "u64" => { let (r1, r2) = asm_r2_64(n as u64); (r1 as $x, r2 as $x) }, "u32" => { let (r1, r2) = asm_r2_32(n as u32); (r1 as $x, r2 as $x) }, _ => unimplemented!(), } ); let rn = n - r; let mut d = n - 1; let k = d.trailing_zeros(); d >>= k; debug_assert_eq!(Self { n, ni, nh, r, rn, r2, d, k }.mr(r), 1); // r / r == 1 (mod n) debug_assert_eq!(Self { n, ni, nh, r, rn, r2, d, k }.mrmul(1, r2), r); // r2 / r == r (mod n) Self { n, ni, nh, r, rn, r2, d, k } } }}} impl_mont_new!(u64, u128); impl_mont_new!(u32, u64); macro_rules! fn_isqrt_n { ($sqrt_newton:ident, $issq_newton:ident, $issq_mod32:ident, $issq_mod3960:ident, $issq_mod4095:ident, $issq:ident, $x:ty, $w:literal) => { // 擬平方数判定: pseudo-square-number determination (mod32 7/32 0.2188) (true: Could be a square number, false: Not a square number) fn $issq_mod32(x: $x) -> bool { // The detection rate for odd square number is similar to mod8 (only x mod 8 == 1) (0x02030213u32 >> ((x as u32) & 31)) & 1 == 1 } #[allow(unused)] // 擬平方数判定: pseudo-square-number determination (mod3960: 216/3960 0.0545) (true: Could be a square number, false: Not a square number) fn $issq_mod3960(x: $x) -> bool { const SQTABLE_MOD3960: [u64; 62] = [0x2001002010213,0x1200001000020001,0x10020000010100,0x210000010,0x201000201,0x120000000010,0x200000000011002,0x101001000001000,0x110020100,0x2010000000001,0x1001000200,0x100000002110000,0x210010000,0x201000001000200,0x110000100010,0x2,0x200001000000001,0x100000110020002,0x10000010000010,0x1000000000000300,0x100120000010000,0x10002000002,0x1001200001000,0x2100000020000,0x3010000000010,0x100201,0x100020000120002,0x10001000000000,0x201000001021000,0x2000100,0x1002000002010000,0x1000020100001001,0x100000100000000,0x3000000001010,0x1000000201000001,0x20000100000,0x10000000001,0x200000200021100,0x10100100000100,0x1002000011000010,0x21000000000,0x20100120000,0x10000000011002,0x200000001001200,0x100000100000,0x2011002010001,0x1200000000000000,0x100020000,0x10000211000000,0x1000201000001,0x102000000000010,0x10010002001002,0x1000000000,0x100100000100,0x10002000200,0x1000101000000201,0x2030000,0x10000000010000,0x1000300000200,0x100000100100,0x2000010,0x1000]; let p = (x % 3960) as usize; (SQTABLE_MOD3960[p >> 6] >> (p & 63)) & 1 == 1 } // 擬平方数判定: pseudo-square-number determination (mod4095 336/4095 0.0821) (true: Could be a square number, false: Not a square number) fn $issq_mod4095(x: $x) -> bool { const SQTABLE_MOD4095: [u64; 64] = [0x2001002010213,0x4200001008028001,0x20000010004,0x80200082010,0x1800008200044029,0x120080000010,0x2200000080410400,0x8100041000200800,0x800004000020100,0x402000400082201,0x9004000040,0x800002000880,0x18002000012000,0x801208,0x26100000804010,0x80000080000002,0x108040040101045,0x20c00004000102,0x400000100c0010,0x1300000040208,0x804000020010000,0x1008402002400080,0x201001000200040,0x4402000000806000,0x10402000000,0x1040008001200801,0x4080000000020400,0x10083080000002,0x8220140000040000,0x800084020100000,0x80010400010000,0x1200020108008060,0x180000000,0x400002400000018,0x4241000200,0x100800000000,0x10201008400483,0xc008000208201000,0x800420000100,0x2010002000410,0x28041000000,0x4010080000024,0x400480010010080,0x200040028000008,0x100810084020,0x20c0401000080000,0x1000240000220000,0x4000020800,0x410000000480000,0x8004008000804201,0x806020000104000,0x2080002000211000,0x1001008001000,0x20000010024000,0x480200002040000,0x48200044008000,0x100000000010080,0x80090400042,0x41040200800200,0x4000020100110,0x2000400082200010,0x1008200000000040,0x2004800002,0x2002010000080]; let p = (x % 4095) as usize; (SQTABLE_MOD4095[p >> 6] >> (p & 63)) & 1 == 1 } // ニュートン法による整数平方根: integer square-root by Newton's method fn $sqrt_newton(x: $x) -> $x { // == floor(sqrt(x)) if x <= 1 { return x; } let k = $w - ((x - 1).leading_zeros() >> 1); let mut s = (1 as $x) << k; // s = 2**k let mut t = (s + (x >> k)) >> 1; // t = (s + x/s)/2 // while loop count (= divide count) may be { u64: max 6 times, u32: max 5 times } // s > floor(sqrt(x)) -> floor(sqrt(x)) <= t < s // s == floor(sqrt(x)) -> s == floor(sqrt(x)) <= t <= floor(sqrt(x)) + 1 while t < s { s = t; t = (s + match stringify!($x) { "u64" => asm_div64(x as u64, s as u64) as $x, "u32" => asm_div32(x as u32, s as u32) as $x, _ => unimplemented!(), }) >> 1; } s } // 平方数判定(ニュートン法): square-number determination (Newton's method) (true: Its a square number, false: Not a square number) fn $issq_newton(x: $x) -> bool { let sqrt = $sqrt_newton(x); // == floor(sqrt(x)) sqrt * sqrt == x } // 平方数判定(複合): square-number determination (combined) (true: Its a square number, false: Not a square number) fn $issq(x: $x) -> bool { $issq_mod32(x) && // 擬平方数判定: pseudo-square-number determination (mod32 7/32 0.2188) //$issq_mod3960(x) && // 擬平方数判定: pseudo-square-number determination (mod3960: 216/3960 0.0545) $issq_mod4095(x) && // 擬平方数判定: pseudo-square-number determination (mod4095 336/4095 0.0821) $issq_newton(x) // 平方数判定(ニュートン法): square-number determination (Newton's method) } }} fn_isqrt_n!(isqrt_64_newton, issq_u64_newton, issq_u64_mod32, issq_u64_mod3960, issq_u64_mod4095, issq_u64, u64, 32); fn_isqrt_n!(isqrt_32_newton, issq_u32_newton, issq_u32_mod32, issq_u32_mod3960, issq_u32_mod4095, issq_u32, u32, 16); macro_rules! fn_jacobi { ($jacobi:ident, $u:ty, $i:ty, $($x:literal),*) => { // ヤコビ記号: Jacobi symbol fn $jacobi(ai: $i, mut n: $u) -> i32 { debug_assert!((n & 1) == 1 && ai > <$i>::MIN); let (mut a, mut j) = (ai.abs() as $u, if ai < 0 && (n & 3) == 3 { -1 } else { 1 }); while a != 0 { let ba = a.trailing_zeros(); if (ba & 1) != 0 && (n.wrapping_sub(2) & 5) == 1 { j = -j; } a >>= ba; if (a & n & 3) == 3 { j = -j; } std::mem::swap(&mut n, &mut a); a = match n { $($x => a % $x,)* _ => match stringify!($u) { "u64" => asm_rem64(a as u64, n as u64) as $u, "u32" => asm_rem32(a as u32, n as u32) as $u, _ => a % n, }, }; /* if a > (n >> 1) { a = n - a; if (n & 3) == 3 { j = -j; } } // */ } if n == 1 { j } else { 0 } }}} fn_jacobi!(jacobi_64, u64, i64, 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31); fn_jacobi!(jacobi_32, u32, i32, 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31); macro_rules! trait_primetest { ($tr:ident, $jacobi:ident, $issq:ident, $u:ty, $i:ty, $w:literal) => { pub trait $tr<T> : MontOps<$u> + MontVal<$u> + MontModN<$u> { fn primetest_base2(&self) -> bool { // Mirrer-Rabin primality test (base 2) // strong pseudoprimes to base 2 ( https://oeis.org/A001262 ): 2047,3277,4033,4681,8321,15841,29341,42799,49141,52633,... let (r, rn, d, k) = (self.r(), self.rn(), self.d(), self.k()); let mut br = self.powodd(self.add(self.r(), self.r()), d); if br == r || br == rn { return true; } for _ in 1..k { br = self.mrmul(br, br); if br == rn { return true; } } false } fn primetest_miller(&self, mut base: $u) -> bool { // Miller-Rabin primality test let (n, r, rn, d, k) = (self.n(), self.r(), self.rn(), self.d(), self.k()); if base >= n { base = self.modn(base); if base == 0 { return true; } } let mut tr = self.pow(self.ar(base), d); if tr == r || tr == rn { return true; } for _ in 1..k { tr = self.mrmul(tr, tr); if tr == rn { return true; } } false } fn primetest_lucas_dprobe(&self) -> Option<$i> { let n = self.n(); let mut d = 5 as $i; for i in 0u32.. { debug_assert!(i < 64); match $jacobi(d, n) { -1 => { return Some(d); }, 0 => if ((d.abs()) as $u) < n { return None; }, _ => {}, } if i == 32 && $issq(n) { return None; } if (i & 1) == 1 { d = 2 - d; } else { d = -(d + 2); } } None } fn primetest_lucas(&self) -> bool { // Lucas primality test // strong Lucas pseudoprimes ( https://oeis.org/A217255 ): 5459,5777,10877,16109,18971,22499,24569,25199,40309,58519,... let n = self.n(); let d = match self.primetest_lucas_dprobe() { Some(d) => d, None => { return false; }, }; let qm = self.ar(self.modn(if d < 0 {((1 - d) as $u) / 4} else {n - ((d - 1) as $u) / 4})); let mut k = (n + 1) << (n + 1).leading_zeros(); let mut um = self.r(); let mut vm = self.r(); let mut qn = qm; let dm = self.ar(if d < 0 { n - self.modn((-d) as $u) } else { self.modn(d as $u) }); k <<= 1; while k != 0 { um = self.mrmul(um, vm); vm = self.sub(self.mrmul(vm, vm), self.add(qn, qn)); qn = self.mrmul(qn, qn); if (k >> ($w - 1)) != 0 { let uu = self.div2(self.add(um, vm)); vm = self.div2(self.add(self.mrmul(dm, um), vm)); um = uu; qn = self.mrmul(qn, qm); } k <<= 1; } if um == 0 || vm == 0 { return true; } let mut x = (n + 1) & (!n); x >>= 1; while x != 0 { um = self.mrmul(um, vm); vm = self.sub(self.mrmul(vm, vm), self.add(qn, qn)); if vm == 0 { return true; } qn = self.mrmul(qn, qn); x >>= 1; } false } fn primetest_bpsw(&self) -> bool { // Mirrer-Rabin primality test (base 2) // strong pseudoprimes to base 2 ( https://oeis.org/A001262 ): 2047,3277,4033,4681,8321,15841,29341,42799,49141,52633,... self.primetest_base2() && // Lucas primality test // strong Lucas pseudoprimes ( https://oeis.org/A217255 ): 5459,5777,10877,16109,18971,22499,24569,25199,40309,58519,... self.primetest_lucas() } }}} trait_primetest!(PrimeTestU64Trait, jacobi_64, issq_u64, u64, i64, 64); trait_primetest!(PrimeTestU32Trait, jacobi_32, issq_u32, u32, i32, 32); impl PrimeTestU64Trait<u64> for Mont<u64> {} impl PrimeTestU32Trait<u32> for Mont<u32> {} // Deterministic variants of the Miller-Rabin primality test http://miller-rabin.appspot.com/ pub trait MillerU64<T> : PrimeTestU64Trait<T> { const MILLER_U64_1BASES: [u64; 1] = [ 9345883071009581737, ]; const MILLER_U64_2BASES: [u64; 2] = [ 336781006125, 9639812373923155, ]; const MILLER_U64_3BASES: [u64; 3] = [ 4230279247111683200, 14694767155120705706, 16641139526367750375, ]; const MILLER_U64_4BASES: [u64; 4] = [ 2, 141889084524735, 1199124725622454117, 11096072698276303650, ]; const MILLER_U64_5BASES: [u64; 5] = [ 2, 4130806001517, 149795463772692060, 186635894390467037, 3967304179347715805, ]; const MILLER_U64_6BASES: [u64; 6] = [ 2, 123635709730000, 9233062284813009, 43835965440333360, 761179012939631437, 1263739024124850375, ]; const MILLER_U64_7BASES: [u64; 7] = [ 2, 325, 9375, 28178, 450775, 9780504, 1795265022, ]; fn primetest_miller_1bases(&self) -> bool { debug_assert!(self.n() < 341531); Self::MILLER_U64_1BASES.iter().all(|&base| self.primetest_miller(base)) } fn primetest_miller_2bases(&self) -> bool { debug_assert!(self.n() < 1050535501); Self::MILLER_U64_2BASES.iter().all(|&base| self.primetest_miller(base)) } fn primetest_miller_3bases(&self) -> bool { debug_assert!(self.n() < 350269456337); Self::MILLER_U64_3BASES.iter().all(|&base| self.primetest_miller(base)) } fn primetest_miller_4bases(&self) -> bool { debug_assert!(self.n() < 55245642489451); Self::MILLER_U64_4BASES.iter().all(|&base| self.primetest_miller(base)) } fn primetest_miller_5bases(&self) -> bool { debug_assert!(self.n() < 7999252175582851); Self::MILLER_U64_5BASES.iter().all(|&base| self.primetest_miller(base)) } fn primetest_miller_6bases(&self) -> bool { debug_assert!(self.n() < 585226005592931977); Self::MILLER_U64_6BASES.iter().all(|&base| self.primetest_miller(base)) } fn primetest_miller_7bases(&self) -> bool { Self::MILLER_U64_7BASES.iter().all(|&base| self.primetest_miller(base)) } fn primetest_miller_mbases(&self) -> bool { // Deterministic variants of the Miller-Rabin primality test http://miller-rabin.appspot.com/ match self.n() { 0..=341530 => Self::MILLER_U64_1BASES.iter(), 0..=1050535500 => Self::MILLER_U64_2BASES.iter(), 0..=350269456336 => Self::MILLER_U64_3BASES.iter(), 0..=55245642489450 => Self::MILLER_U64_4BASES.iter(), 0..=7999252175582850 => Self::MILLER_U64_5BASES.iter(), 0..=585226005592931976 => Self::MILLER_U64_6BASES.iter(), _ => Self::MILLER_U64_7BASES.iter(), }.all(|&base| self.primetest_miller(base)) } } impl MillerU64<u64> for Mont<u64> {} // Deterministic variants of the Miller-Rabin primality test http://miller-rabin.appspot.com/ pub trait MillerU32<T> : PrimeTestU32Trait<T> { const MILLER_U32_1BASES: [u32; 1] = [921211727]; const MILLER_U32_2BASES: [u32; 2] = [1143370,2350307676]; const MILLER_U32_3BASES: [u32; 3] = [2,7,61]; fn primetest_miller_1bases(&self) -> bool { debug_assert!(self.n() < 49141); Self::MILLER_U32_1BASES.iter().all(|&base| self.primetest_miller(base)) } fn primetest_miller_2bases(&self) -> bool { debug_assert!(self.n() < 360018361); Self::MILLER_U32_2BASES.iter().all(|&base| self.primetest_miller(base)) } fn primetest_miller_3bases(&self) -> bool { Self::MILLER_U32_3BASES.iter().all(|&base| self.primetest_miller(base)) } fn primetest_miller_mbases(&self) -> bool { // Deterministic variants of the Miller-Rabin primality test http://miller-rabin.appspot.com/ match self.n() { 0..=49140 => Self::MILLER_U32_1BASES.iter(), 0..=360018360 => Self::MILLER_U32_2BASES.iter(), _ => Self::MILLER_U32_3BASES.iter(), }.all(|&base| self.primetest_miller(base)) } } impl MillerU32<u32> for Mont<u32> {} // Baillie–PSW primarity test (u64) pub fn primetest_u64_bpsw(n: u64) -> bool { if n == 2 { return true; } if n == 1 || (n & 1) == 0 { return false; } let mont = Mont::<u64>::new(n); mont.primetest_bpsw() } // Baillie–PSW primarity test (u32) pub fn primetest_u32_bpsw(n: u32) -> bool { if n == 2 { return true; } if n == 1 || (n & 1) == 0 { return false; } let mont = Mont::<u32>::new(n); mont.primetest_bpsw() } // Miller-Rabin primarity test (u64) pub fn primetest_u64_miller_mbases(n: u64) -> bool { if n == 2 { return true; } if n == 1 || (n & 1) == 0 { return false; } let mont = Mont::<u64>::new(n); mont.primetest_miller_mbases() } // Miller-Rabin primarity test (u32) pub fn primetest_u32_miller_mbases(n: u32) -> bool { if n == 2 { return true; } if n == 1 || (n & 1) == 0 { return false; } let mont = Mont::<u32>::new(n); mont.primetest_miller_mbases() } #[cfg(test)] mod tests { use crate::*; enum MontTestType { U32, U64, } // ten least k's for which (2**n)-k is prime // https://primes.utm.edu/lists/2small/0bit.html const PRIMES_LAST10: [(u32,[u64;10]);57] = [ (8,[5,15,17,23,27,29,33,45,57,59]), (9,[3,9,13,21,25,33,45,49,51,55]), (10,[3,5,11,15,27,33,41,47,53,57]), (11,[9,19,21,31,37,45,49,51,55,61]), (12,[3,5,17,23,39,45,47,69,75,77]), (13,[1,13,21,25,31,45,69,75,81,91]), (14,[3,15,21,23,35,45,51,65,83,111]), (15,[19,49,51,55,61,75,81,115,121,135]), (16,[15,17,39,57,87,89,99,113,117,123]), (17,[1,9,13,31,49,61,63,85,91,99]), (18,[5,11,17,23,33,35,41,65,75,93]), (19,[1,19,27,31,45,57,67,69,85,87]), (20,[3,5,17,27,59,69,129,143,153,185]), (21,[9,19,21,55,61,69,105,111,121,129]), (22,[3,17,27,33,57,87,105,113,117,123]), (23,[15,21,27,37,61,69,135,147,157,159]), (24,[3,17,33,63,75,77,89,95,117,167]), (25,[39,49,61,85,91,115,141,159,165,183]), (26,[5,27,45,87,101,107,111,117,125,135]), (27,[39,79,111,115,135,187,199,219,231,235]), (28,[57,89,95,119,125,143,165,183,213,273]), (29,[3,33,43,63,73,75,93,99,121,133]), (30,[35,41,83,101,105,107,135,153,161,173]), (31,[1,19,61,69,85,99,105,151,159,171]), (32,[5,17,65,99,107,135,153,185,209,267]), (33,[9,25,49,79,105,285,301,303,321,355]), (34,[41,77,113,131,143,165,185,207,227,281]), (35,[31,49,61,69,79,121,141,247,309,325]), (36,[5,17,23,65,117,137,159,173,189,233]), (37,[25,31,45,69,123,141,199,201,351,375]), (38,[45,87,107,131,153,185,191,227,231,257]), (39,[7,19,67,91,135,165,219,231,241,301]), (40,[87,167,195,203,213,285,293,299,389,437]), (41,[21,31,55,63,73,75,91,111,133,139]), (42,[11,17,33,53,65,143,161,165,215,227]), (43,[57,67,117,175,255,267,291,309,319,369]), (44,[17,117,119,129,143,149,287,327,359,377]), (45,[55,69,81,93,121,133,139,159,193,229]), (46,[21,57,63,77,167,197,237,287,305,311]), (47,[115,127,147,279,297,339,435,541,619,649]), (48,[59,65,89,93,147,165,189,233,243,257]), (49,[81,111,123,139,181,201,213,265,283,339]), (50,[27,35,51,71,113,117,131,161,195,233]), (51,[129,139,165,231,237,247,355,391,397,439]), (52,[47,143,173,183,197,209,269,285,335,395]), (53,[111,145,231,265,315,339,343,369,379,421]), (54,[33,53,131,165,195,245,255,257,315,327]), (55,[55,67,99,127,147,169,171,199,207,267]), (56,[5,27,47,57,89,93,147,177,189,195]), (57,[13,25,49,61,69,111,195,273,363,423]), (58,[27,57,63,137,141,147,161,203,213,251]), (59,[55,99,225,427,517,607,649,687,861,871]), (60,[93,107,173,179,257,279,369,395,399,453]), (61,[1,31,45,229,259,283,339,391,403,465]), (62,[57,87,117,143,153,167,171,195,203,273]), (63,[25,165,259,301,375,387,391,409,457,471]), (64,[59,83,95,179,189,257,279,323,353,363]), ]; // #SPSP-2 Miller-Rabin base 2 (up to 1e7) // strong pseudoprimes to base 2 ( https://oeis.org/A001262 ): 2047,3277,4033,4681,8321,15841,29341,42799,49141,52633,... // composite 2-SPRP list up to 2**64 ( http://miller-rabin.appspot.com/#links ) // Pseudoprime Statistics, Tables, and Data ( http://ntheory.org/pseudoprimes.html ) // Miller-Rabin base 2 data (up to 1e15) ( http://ntheory.org/data/spsps.txt ) const SPRP_2: [u64; 162] = [ 2047,3277,4033,4681,8321,15841,29341,42799,49141,52633,65281,74665,80581,85489,88357,90751,104653, 130561,196093,220729,233017,252601,253241,256999,271951,280601,314821,357761,390937,458989,476971, 486737,489997,514447,580337,635401,647089,741751,800605,818201,838861,873181,877099,916327,976873, 983401,1004653,1016801,1023121,1082401,1145257,1194649,1207361,1251949,1252697,1302451,1325843,1357441, 1373653,1397419,1441091,1493857,1507963,1509709,1530787,1678541,1730977,1811573,1876393,1907851,1909001, 1969417,1987021,2004403,2081713,2181961,2205967,2264369,2269093,2284453,2304167,2387797,2419385,2510569, 2746477,2748023,2757241,2811271,2909197,2953711,2976487,3090091,3116107,3125281,3375041,3400013,3429037, 3539101,3567481,3581761,3605429,3898129,4181921,4188889,4335241,4360621,4469471,4502485,4513841,4682833, 4835209,4863127,5016191,5044033,5049001,5173169,5173601,5256091,5310721,5444489,5489641,5590621,5599765, 5672041,5681809,5919187,6140161,6226193,6233977,6334351,6368689,6386993,6787327,6836233,6952037,7177105, 7306261,7306561,7462001,7674967,7759937,7820201,7883731,8036033,8095447,8384513,8388607,8534233,8725753, 8727391,9006401,9056501,9069229,9073513,9371251,9564169,9567673,9588151,9729301,9774181,9863461,9995671 ]; // #SLPSP Strong Lucas-Selfridge (up to 1e7) // strong Lucas pseudoprimes ( https://oeis.org/A217255 ): 5459,5777,10877,16109,18971,22499,24569,25199,40309,58519,... // Pseudoprime Statistics, Tables, and Data ( http://ntheory.org/pseudoprimes.html ) // Strong Lucas-Selfridge data (up to 1e15) ( http://ntheory.org/data/slpsps-baillie.txt ) const SLPRP: [u64; 178] = [ 5459,5777,10877,16109,18971,22499,24569,25199,40309,58519,75077,97439,100127,113573,115639,130139,155819, 158399,161027,162133,176399,176471,189419,192509,197801,224369,230691,231703,243629,253259,268349,288919, 313499,324899,353219,366799,391169,430127,436409,455519,487199,510479,572669,611399,622169,635627,636199, 701999,794611,835999,839159,851927,871859,875879,887879,895439,950821,960859,1033997,1106327,1241099, 1256293,1308119,1311389,1388903,1422319,1501439,1697183,1711469,1777159,1981559,2003579,2263127,2435423, 2461211,2518889,2566409,2624399,2662277,2666711,2690759,2738969,2782079,2828699,2942081,2952071,3109049, 3165119,3175883,3179609,3204599,3373649,3399527,3410531,3441239,3452147,3479111,3498879,3579599,3684251, 3694079,3700559,3706169,3735521,3774377,3776219,3785699,3802499,3813011,3865319,3892529,3900797,3903791, 4067279,4109363,4226777,4309631,4322399,4368869,4403027,4563719,4828277,4870847,5133281,5208377,5299139, 5396999,5450201,5479109,5514479,5720219,5762629,5807759,5879411,5942627,6001379,6003923,6296291,6562891, 6641189,6668099,6784721,6784861,6863291,6893531,6965639,7017949,7163441,7199399,7241639,7353917,7453619, 7621499,8112899,8159759,8221121,8234159,8361989,8372849,8518127,8530559,8555009,8574551,8581219,8711699, 8817899,8990279,9049319,9335969,9401893,9485951,9587411,9713027,9793313,9800981,9827711,9922337,9965069 ]; fn exec_eq(n: u64, f: bool, ty: &MontTestType) { if n < 3 || (n & 1) == 0 { return; } match ty { MontTestType::U64 => { let mont = Mont::<u64>::new(n); // Deterministic variants of the Miller-Rabin primality test // http://miller-rabin.appspot.com/ if n < 341531 { assert_eq!(mont.primetest_miller_1bases(), f); } if n < 1050535501 { assert_eq!(mont.primetest_miller_2bases(), f); } if n < 350269456337 { assert_eq!(mont.primetest_miller_3bases(), f); } if n < 55245642489451 { assert_eq!(mont.primetest_miller_4bases(), f); } if n < 7999252175582851 { assert_eq!(mont.primetest_miller_5bases(), f); } if n < 585226005592931977 { assert_eq!(mont.primetest_miller_6bases(), f); } assert_eq!(mont.primetest_miller_7bases(), f); assert_eq!(mont.primetest_miller_mbases(), f); // Baillie–PSW primality test assert_eq!(mont.primetest_bpsw(), f); }, MontTestType::U32 => { if n > 0xffff_ffff { return; } let mont = Mont::<u32>::new(n as u32); // Deterministic variants of the Miller-Rabin primality test if n < 49140 { assert_eq!(mont.primetest_miller_1bases(), f); } if n < 360018360 { assert_eq!(mont.primetest_miller_2bases(), f); } assert_eq!(mont.primetest_miller_3bases(), f); assert_eq!(mont.primetest_miller_mbases(), f); // Baillie–PSW primality test assert_eq!(mont.primetest_bpsw(), f); }, } } fn gen_nbits(ty: &MontTestType) { // ten least k's for which (2**n)-k is prime // https://primes.utm.edu/lists/2small/0bit.html for (bit_ref, kvec) in PRIMES_LAST10.iter() { let bit = *bit_ref; if bit > 32 { match ty { MontTestType::U32 => continue, _ => {}, } } let &lastk = kvec.iter().last().unwrap(); for k in 1..=lastk { if (k & 1) == 0 { continue; } let n = (if bit < 64 { 1u64 << bit } else { 0u64 }).wrapping_sub(k); let f = kvec.binary_search(&k).is_ok(); exec_eq(n, f, ty); } } } #[test] fn nbits_u64() { let start_time = std::time::Instant::now(); gen_nbits(&MontTestType::U64); eprint!("nbits_u64 {}us\n", start_time.elapsed().as_micros()); } #[test] fn nbits_u32() { let start_time = std::time::Instant::now(); gen_nbits(&MontTestType::U32); eprint!("nbits_u32 {}us\n", start_time.elapsed().as_micros()); } fn exec_base2(n: u64, ty: &MontTestType) -> (bool, bool) { match ty { MontTestType::U64 => { let mont = Mont::<u64>::new(n); let res_base2 = mont.primetest_base2(); let res_mbases = mont.primetest_miller_mbases(); (res_base2, res_mbases) }, MontTestType::U32 => { let mont = Mont::<u32>::new(n as u32); let res_base2 = mont.primetest_base2(); let res_mbases = mont.primetest_miller_mbases(); (res_base2, res_mbases) }, } } fn gen_base2_1e7(ty: &MontTestType) { // Miller-Rabin primality test (base 2) // strong pseudoprimes to base 2 ( https://oeis.org/A001262 ): 2047,3277,4033,4681,8321,15841,29341,42799,49141,52633,... // composite 2-SPRP list up to 2**64 ( http://miller-rabin.appspot.com/#links ) // Pseudoprime Statistics, Tables, and Data ( http://ntheory.org/pseudoprimes.html ) // Miller-Rabin base 2 data (up to 1e15) ( http://ntheory.org/data/spsps.txt ) let result: Vec<u64> = (3..10_000_000).filter(|&n| { if (n & 1) == 0 { return false; } let (res_base2, res_mbases) = exec_base2(n, ty); assert!(!res_mbases || res_base2); res_mbases != res_base2 }).collect(); assert_eq!(Vec::from(SPRP_2), result); } #[test] fn base2_u64_1e7() { let start_time = std::time::Instant::now(); gen_base2_1e7(&MontTestType::U64); eprint!("base2_u64_1e7 {}us\n", start_time.elapsed().as_micros()); } #[test] fn base2_u32_1e7() { let start_time = std::time::Instant::now(); gen_base2_1e7(&MontTestType::U32); eprint!("base2_u32_1e7 {}us\n", start_time.elapsed().as_micros()); } fn exec_lucas(n: u64, ty: &MontTestType) -> (bool, bool) { match ty { MontTestType::U64 => { let mont = Mont::<u64>::new(n); let res_lucas = mont.primetest_lucas(); let res_mbases = mont.primetest_miller_mbases(); (res_lucas, res_mbases) }, MontTestType::U32 => { let mont = Mont::<u32>::new(n as u32); let res_lucas = mont.primetest_lucas(); let res_mbases = mont.primetest_miller_mbases(); (res_lucas, res_mbases) }, } } fn gen_lucas_1e7(ty: &MontTestType) { // Lucas primality test // strong Lucas pseudoprimes ( https://oeis.org/A217255 ): 5459,5777,10877,16109,18971,22499,24569,25199,40309,58519,... // Pseudoprime Statistics, Tables, and Data ( http://ntheory.org/pseudoprimes.html ) // Strong Lucas-Selfridge data (up to 1e15) ( http://ntheory.org/data/slpsps-baillie.txt ) let result: Vec<u64> = (3..10_000_000).filter(|&n| { if (n & 1) == 0 { return false; } let (res_base2, res_mbases) = exec_lucas(n, ty); assert!(!res_mbases || res_base2); res_mbases != res_base2 }).collect(); assert_eq!(Vec::from(SLPRP), result); } #[test] fn lucas_u64_1e7() { let start_time = std::time::Instant::now(); gen_lucas_1e7(&MontTestType::U64); eprint!("lucas_u64_1e7 {}us\n", start_time.elapsed().as_micros()); } #[test] fn lucas_u32_1e7() { let start_time = std::time::Instant::now(); gen_lucas_1e7(&MontTestType::U32); eprint!("lucas_u32_1e7 {}us\n", start_time.elapsed().as_micros()); } fn exec_bpsw(n: u64, ty: &MontTestType) { match ty { MontTestType::U64 => { let mont = Mont::<u64>::new(n); let res_bpsw = mont.primetest_bpsw(); let res_mbases = mont.primetest_miller_mbases(); assert_eq!(res_mbases, res_bpsw); }, MontTestType::U32 => { let mont = Mont::<u32>::new(n as u32); let res_bpsw = mont.primetest_bpsw(); let res_mbases = mont.primetest_miller_mbases(); assert_eq!(res_mbases, res_bpsw); }, } } fn gen_bpsw(minn: u64, maxn: u64, ty: &MontTestType) { // Baillie–PSW primarity test for n in minn..maxn { if n < 3 || (n & 1) == 0 { continue; } exec_bpsw(n, ty); } } #[test] fn bpsw_u64_1e7() { // 24bit let start_time = std::time::Instant::now(); gen_bpsw(3, 10_000_000, &MontTestType::U64); eprint!("bpsw_u64_1e7 {}us\n", start_time.elapsed().as_micros()); } #[test] fn bpsw_u32_1e7() { // 24bit let start_time = std::time::Instant::now(); gen_bpsw(3, 10_000_000, &MontTestType::U32); eprint!("bpsw_u32_1e7 {}us\n", start_time.elapsed().as_micros()); } #[test] fn bpsw_u64_4e9() { // 32bit let start_time = std::time::Instant::now(); gen_bpsw(4_000_000_000, 4_010_000_000, &MontTestType::U64); eprint!("bpsw_u64_4e9 {}us\n", start_time.elapsed().as_micros()); } #[test] fn bpsw_u32_4e9() { // 32bit let start_time = std::time::Instant::now(); gen_bpsw(4_000_000_000, 4_010_000_000, &MontTestType::U32); eprint!("bpsw_u32_4e9 {}us\n", start_time.elapsed().as_micros()); } #[test] fn bpsw_u64_1e16() { // 54bit let start_time = std::time::Instant::now(); gen_bpsw(10_000_000_000_000_000, 10_000_000_010_000_000, &MontTestType::U64); eprint!("bpsw_u64_1e16 {}us\n", start_time.elapsed().as_micros()); } #[test] fn bpsw_u64_9e18() { // 63bit let start_time = std::time::Instant::now(); gen_bpsw(9_000_000_000_000_000_000, 9_000_000_000_010_000_000, &MontTestType::U64); eprint!("bpsw_u64_9e18 {}us\n", start_time.elapsed().as_micros()); } #[test] fn bpsw_u64_10e18() { // 64bit let start_time = std::time::Instant::now(); gen_bpsw(10_000_000_000_000_000_000, 10_000_000_000_010_000_000, &MontTestType::U64); eprint!("bpsw_u64_10e18 {}us\n", start_time.elapsed().as_micros()); } #[test] fn bpsw_u64_18e18() { // 64bit let start_time = std::time::Instant::now(); gen_bpsw(18_000_000_000_000_000_000, 18_000_000_000_010_000_000, &MontTestType::U64); eprint!("bpsw_u64_18e18 {}us\n", start_time.elapsed().as_micros()); } #[test] fn sq_u64() { let start_time = std::time::Instant::now(); for i in 0xff00_0000u64..=0xffff_ffff { let n = i * i; assert!(issq_u64(n)); } eprint!("sq_u64 {}us\n", start_time.elapsed().as_micros()); } #[test] fn sq_u64_p1() { let start_time = std::time::Instant::now(); for i in 0xff00_0000u64..=0xffff_ffff { let n = i * i + 1; assert!(!issq_u64(n)); } eprint!("sq_u64_p1 {}us\n", start_time.elapsed().as_micros()); } #[test] fn sq_u64_m1() { let start_time = std::time::Instant::now(); for i in 0xff00_0000u64..=0xffff_ffff { let n = i * i - 1; assert!(!issq_u64(n)); } eprint!("sq_u64_m1 {}us\n", start_time.elapsed().as_micros()); } } pub fn main() { use std::io::{stdin, stdout, BufWriter, Read, Write}; let start_time = std::time::Instant::now(); let out = stdout(); let mut writer = BufWriter::new(out.lock()); let inp = stdin(); let mut reader = inp.lock(); let mut ibuf = Vec::<u8>::new(); let _len = reader.read_to_end(&mut ibuf).unwrap(); let mut it = ibuf.iter().cloned().enumerate(); let n = { let mut a = (it.next().unwrap().1 & 0x0f) as usize; while let Some((_, c)) = it.next() { if c < b'!' { break; } a = a * 10 + (c & 0x0f) as usize; } a }; for _ in 0..n { let (x, tr) = { let (i, c) = it.next().unwrap(); let mut a = (c & 0x0f) as u64; let mut j = i; while let Some((k, c)) = it.next() { if c < b'!' { j = k; break; } a = a * 10 + (c & 0x0f) as u64; } (a, &ibuf[i..j]) }; let res = primetest_u64_bpsw(x); writer.write(tr).unwrap(); writer.write(if res { b" 1\n" } else { b" 0\n" }).unwrap(); } writer.flush().unwrap(); eprint!("{}us\n", start_time.elapsed().as_micros()); }