Acid
73 lines
1.2 KiB
Go
73 lines
1.2 KiB
Go
package algo
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// Deterministic Miller Rabin primality test
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import (
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"math/bits"
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)
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// mulMod() :: using bits to prevent 2^x overflow
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func mulMod(a, b, m uint64) uint64 {
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hi, lo := bits.Mul64(a, b)
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_, rem := bits.Div64(hi, lo, m)
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return rem
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}
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// (base ^ exp) % m square and multiply
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func powMod(base, exp, m uint64) uint64 {
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result := uint64(1)
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base %= m
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for exp > 0 {
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// exp is odd
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if exp&1 == 1 {
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result = mulMod(result, base, m)
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}
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base = mulMod(base, base, m)
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// exp = exp / 2
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exp >>= 1
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}
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return result
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}
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// IsPrime() -> uses Miller Rabin primality test
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func IsPrime(n uint64) bool {
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if n < 2 {
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return false
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}
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// quick trial small primes bases
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smallPrimes := []uint64{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
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for _, p := range smallPrimes {
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if n%p == 0 {
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return n == p
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}
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}
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// n-1 = 2^r * d
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d := n - 1
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r := 0
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for d%2 == 0 {
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d /= 2
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r++
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}
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// bases test
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for _, a := range smallPrimes {
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x := powMod(a, d, n)
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if x == 1 || x == n-1 {
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continue
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}
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composite := true
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for i := 0; i < r-1; i++ {
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x = mulMod(x, x, n)
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if x == n-1 {
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composite = false
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break
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}
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}
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if composite {
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return false
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}
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}
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return true
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}
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