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Diffstat (limited to 'vendor/modernc.org/mathutil/primes.go')
-rw-r--r--vendor/modernc.org/mathutil/primes.go331
1 files changed, 0 insertions, 331 deletions
diff --git a/vendor/modernc.org/mathutil/primes.go b/vendor/modernc.org/mathutil/primes.go
deleted file mode 100644
index ec1e5f5a5..000000000
--- a/vendor/modernc.org/mathutil/primes.go
+++ /dev/null
@@ -1,331 +0,0 @@
-// Copyright (c) 2014 The mathutil Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-package mathutil // import "modernc.org/mathutil"
-
-import (
- "math"
-)
-
-// IsPrimeUint16 returns true if n is prime. Typical run time is few ns.
-func IsPrimeUint16(n uint16) bool {
- return n > 0 && primes16[n-1] == 1
-}
-
-// NextPrimeUint16 returns first prime > n and true if successful or an
-// undefined value and false if there is no next prime in the uint16 limits.
-// Typical run time is few ns.
-func NextPrimeUint16(n uint16) (p uint16, ok bool) {
- return n + uint16(primes16[n]), n < 65521
-}
-
-// IsPrime returns true if n is prime. Typical run time is about 100 ns.
-func IsPrime(n uint32) bool {
- switch {
- case n&1 == 0:
- return n == 2
- case n%3 == 0:
- return n == 3
- case n%5 == 0:
- return n == 5
- case n%7 == 0:
- return n == 7
- case n%11 == 0:
- return n == 11
- case n%13 == 0:
- return n == 13
- case n%17 == 0:
- return n == 17
- case n%19 == 0:
- return n == 19
- case n%23 == 0:
- return n == 23
- case n%29 == 0:
- return n == 29
- case n%31 == 0:
- return n == 31
- case n%37 == 0:
- return n == 37
- case n%41 == 0:
- return n == 41
- case n%43 == 0:
- return n == 43
- case n%47 == 0:
- return n == 47
- case n%53 == 0:
- return n == 53 // Benchmarked optimum
- case n < 65536:
- // use table data
- return IsPrimeUint16(uint16(n))
- default:
- mod := ModPowUint32(2, (n+1)/2, n)
- if mod != 2 && mod != n-2 {
- return false
- }
- blk := &lohi[n>>24]
- lo, hi := blk.lo, blk.hi
- for lo <= hi {
- index := (lo + hi) >> 1
- liar := liars[index]
- switch {
- case n > liar:
- lo = index + 1
- case n < liar:
- hi = index - 1
- default:
- return false
- }
- }
- return true
- }
-}
-
-// IsPrimeUint64 returns true if n is prime. Typical run time is few tens of µs.
-//
-// SPRP bases: http://miller-rabin.appspot.com
-func IsPrimeUint64(n uint64) bool {
- switch {
- case n%2 == 0:
- return n == 2
- case n%3 == 0:
- return n == 3
- case n%5 == 0:
- return n == 5
- case n%7 == 0:
- return n == 7
- case n%11 == 0:
- return n == 11
- case n%13 == 0:
- return n == 13
- case n%17 == 0:
- return n == 17
- case n%19 == 0:
- return n == 19
- case n%23 == 0:
- return n == 23
- case n%29 == 0:
- return n == 29
- case n%31 == 0:
- return n == 31
- case n%37 == 0:
- return n == 37
- case n%41 == 0:
- return n == 41
- case n%43 == 0:
- return n == 43
- case n%47 == 0:
- return n == 47
- case n%53 == 0:
- return n == 53
- case n%59 == 0:
- return n == 59
- case n%61 == 0:
- return n == 61
- case n%67 == 0:
- return n == 67
- case n%71 == 0:
- return n == 71
- case n%73 == 0:
- return n == 73
- case n%79 == 0:
- return n == 79
- case n%83 == 0:
- return n == 83
- case n%89 == 0:
- return n == 89 // Benchmarked optimum
- case n <= math.MaxUint16:
- return IsPrimeUint16(uint16(n))
- case n <= math.MaxUint32:
- return ProbablyPrimeUint32(uint32(n), 11000544) &&
- ProbablyPrimeUint32(uint32(n), 31481107)
- case n < 105936894253:
- return ProbablyPrimeUint64_32(n, 2) &&
- ProbablyPrimeUint64_32(n, 1005905886) &&
- ProbablyPrimeUint64_32(n, 1340600841)
- case n < 31858317218647:
- return ProbablyPrimeUint64_32(n, 2) &&
- ProbablyPrimeUint64_32(n, 642735) &&
- ProbablyPrimeUint64_32(n, 553174392) &&
- ProbablyPrimeUint64_32(n, 3046413974)
- case n < 3071837692357849:
- return ProbablyPrimeUint64_32(n, 2) &&
- ProbablyPrimeUint64_32(n, 75088) &&
- ProbablyPrimeUint64_32(n, 642735) &&
- ProbablyPrimeUint64_32(n, 203659041) &&
- ProbablyPrimeUint64_32(n, 3613982119)
- default:
- return ProbablyPrimeUint64_32(n, 2) &&
- ProbablyPrimeUint64_32(n, 325) &&
- ProbablyPrimeUint64_32(n, 9375) &&
- ProbablyPrimeUint64_32(n, 28178) &&
- ProbablyPrimeUint64_32(n, 450775) &&
- ProbablyPrimeUint64_32(n, 9780504) &&
- ProbablyPrimeUint64_32(n, 1795265022)
- }
-}
-
-// NextPrime returns first prime > n and true if successful or an undefined value and false if there
-// is no next prime in the uint32 limits. Typical run time is about 2 µs.
-func NextPrime(n uint32) (p uint32, ok bool) {
- switch {
- case n < 65521:
- p16, _ := NextPrimeUint16(uint16(n))
- return uint32(p16), true
- case n >= math.MaxUint32-4:
- return
- }
-
- n++
- var d0, d uint32
- switch mod := n % 6; mod {
- case 0:
- d0, d = 1, 4
- case 1:
- d = 4
- case 2, 3, 4:
- d0, d = 5-mod, 2
- case 5:
- d = 2
- }
-
- p = n + d0
- if p < n { // overflow
- return
- }
-
- for {
- if IsPrime(p) {
- return p, true
- }
-
- p0 := p
- p += d
- if p < p0 { // overflow
- break
- }
-
- d ^= 6
- }
- return
-}
-
-// NextPrimeUint64 returns first prime > n and true if successful or an undefined value and false if there
-// is no next prime in the uint64 limits. Typical run time is in hundreds of µs.
-func NextPrimeUint64(n uint64) (p uint64, ok bool) {
- switch {
- case n < 65521:
- p16, _ := NextPrimeUint16(uint16(n))
- return uint64(p16), true
- case n >= 18446744073709551557: // last uint64 prime
- return
- }
-
- n++
- var d0, d uint64
- switch mod := n % 6; mod {
- case 0:
- d0, d = 1, 4
- case 1:
- d = 4
- case 2, 3, 4:
- d0, d = 5-mod, 2
- case 5:
- d = 2
- }
-
- p = n + d0
- if p < n { // overflow
- return
- }
-
- for {
- if ok = IsPrimeUint64(p); ok {
- break
- }
-
- p0 := p
- p += d
- if p < p0 { // overflow
- break
- }
-
- d ^= 6
- }
- return
-}
-
-// FactorTerm is one term of an integer factorization.
-type FactorTerm struct {
- Prime uint32 // The divisor
- Power uint32 // Term == Prime^Power
-}
-
-// FactorTerms represent a factorization of an integer
-type FactorTerms []FactorTerm
-
-// FactorInt returns prime factorization of n > 1 or nil otherwise.
-// Resulting factors are ordered by Prime. Typical run time is few µs.
-func FactorInt(n uint32) (f FactorTerms) {
- switch {
- case n < 2:
- return
- case IsPrime(n):
- return []FactorTerm{{n, 1}}
- }
-
- f, w := make([]FactorTerm, 9), 0
- for p := 2; p < len(primes16); p += int(primes16[p]) {
- if uint(p*p) > uint(n) {
- break
- }
-
- power := uint32(0)
- for n%uint32(p) == 0 {
- n /= uint32(p)
- power++
- }
- if power != 0 {
- f[w] = FactorTerm{uint32(p), power}
- w++
- }
- if n == 1 {
- break
- }
- }
- if n != 1 {
- f[w] = FactorTerm{n, 1}
- w++
- }
- return f[:w]
-}
-
-// PrimorialProductsUint32 returns a slice of numbers in [lo, hi] which are a
-// product of max 'max' primorials. The slice is not sorted.
-//
-// See also: http://en.wikipedia.org/wiki/Primorial
-func PrimorialProductsUint32(lo, hi, max uint32) (r []uint32) {
- lo64, hi64 := int64(lo), int64(hi)
- if max > 31 { // N/A
- max = 31
- }
-
- var f func(int64, int64, uint32)
- f = func(n, p int64, emax uint32) {
- e := uint32(1)
- for n <= hi64 && e <= emax {
- n *= p
- if n >= lo64 && n <= hi64 {
- r = append(r, uint32(n))
- }
- if n < hi64 {
- p, _ := NextPrime(uint32(p))
- f(n, int64(p), e)
- }
- e++
- }
- }
-
- f(1, 2, max)
- return
-}