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vendor: Add dependencies for discosrv

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This commit is contained in:
Jakob Borg
2016-05-31 22:35:35 +02:00
parent eacae83886
commit f9e2623fdc
126 changed files with 60401 additions and 0 deletions
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27
vendor/github.com/cznic/mathutil/LICENSE generated vendored Normal file
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Copyright (c) 2014 The mathutil Authors. All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:
* Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following disclaimer
in the documentation and/or other materials provided with the
distribution.
* Neither the names of the authors nor the names of the
contributors may be used to endorse or promote products derived from
this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

207
vendor/github.com/cznic/mathutil/bits.go generated vendored Normal file
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// 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 (
"math/big"
)
// BitLenByte returns the bit width of the non zero part of n.
func BitLenByte(n byte) int {
return log2[n] + 1
}
// BitLenUint16 returns the bit width of the non zero part of n.
func BitLenUint16(n uint16) int {
if b := n >> 8; b != 0 {
return log2[b] + 8 + 1
}
return log2[n] + 1
}
// BitLenUint32 returns the bit width of the non zero part of n.
func BitLenUint32(n uint32) int {
if b := n >> 24; b != 0 {
return log2[b] + 24 + 1
}
if b := n >> 16; b != 0 {
return log2[b] + 16 + 1
}
if b := n >> 8; b != 0 {
return log2[b] + 8 + 1
}
return log2[n] + 1
}
// BitLen returns the bit width of the non zero part of n.
func BitLen(n int) int { // Should handle correctly [future] 64 bit Go ints
if IntBits == 64 {
return BitLenUint64(uint64(n))
}
if b := byte(n >> 24); b != 0 {
return log2[b] + 24 + 1
}
if b := byte(n >> 16); b != 0 {
return log2[b] + 16 + 1
}
if b := byte(n >> 8); b != 0 {
return log2[b] + 8 + 1
}
return log2[byte(n)] + 1
}
// BitLenUint returns the bit width of the non zero part of n.
func BitLenUint(n uint) int { // Should handle correctly [future] 64 bit Go uints
if IntBits == 64 {
return BitLenUint64(uint64(n))
}
if b := n >> 24; b != 0 {
return log2[b] + 24 + 1
}
if b := n >> 16; b != 0 {
return log2[b] + 16 + 1
}
if b := n >> 8; b != 0 {
return log2[b] + 8 + 1
}
return log2[n] + 1
}
// BitLenUint64 returns the bit width of the non zero part of n.
func BitLenUint64(n uint64) int {
if b := n >> 56; b != 0 {
return log2[b] + 56 + 1
}
if b := n >> 48; b != 0 {
return log2[b] + 48 + 1
}
if b := n >> 40; b != 0 {
return log2[b] + 40 + 1
}
if b := n >> 32; b != 0 {
return log2[b] + 32 + 1
}
if b := n >> 24; b != 0 {
return log2[b] + 24 + 1
}
if b := n >> 16; b != 0 {
return log2[b] + 16 + 1
}
if b := n >> 8; b != 0 {
return log2[b] + 8 + 1
}
return log2[n] + 1
}
// BitLenUintptr returns the bit width of the non zero part of n.
func BitLenUintptr(n uintptr) int {
if b := n >> 56; b != 0 {
return log2[b] + 56 + 1
}
if b := n >> 48; b != 0 {
return log2[b] + 48 + 1
}
if b := n >> 40; b != 0 {
return log2[b] + 40 + 1
}
if b := n >> 32; b != 0 {
return log2[b] + 32 + 1
}
if b := n >> 24; b != 0 {
return log2[b] + 24 + 1
}
if b := n >> 16; b != 0 {
return log2[b] + 16 + 1
}
if b := n >> 8; b != 0 {
return log2[b] + 8 + 1
}
return log2[n] + 1
}
// PopCountByte returns population count of n (number of bits set in n).
func PopCountByte(n byte) int {
return int(popcnt[byte(n)])
}
// PopCountUint16 returns population count of n (number of bits set in n).
func PopCountUint16(n uint16) int {
return int(popcnt[byte(n>>8)]) + int(popcnt[byte(n)])
}
// PopCountUint32 returns population count of n (number of bits set in n).
func PopCountUint32(n uint32) int {
return int(popcnt[byte(n>>24)]) + int(popcnt[byte(n>>16)]) +
int(popcnt[byte(n>>8)]) + int(popcnt[byte(n)])
}
// PopCount returns population count of n (number of bits set in n).
func PopCount(n int) int { // Should handle correctly [future] 64 bit Go ints
if IntBits == 64 {
return PopCountUint64(uint64(n))
}
return PopCountUint32(uint32(n))
}
// PopCountUint returns population count of n (number of bits set in n).
func PopCountUint(n uint) int { // Should handle correctly [future] 64 bit Go uints
if IntBits == 64 {
return PopCountUint64(uint64(n))
}
return PopCountUint32(uint32(n))
}
// PopCountUintptr returns population count of n (number of bits set in n).
func PopCountUintptr(n uintptr) int {
if UintPtrBits == 64 {
return PopCountUint64(uint64(n))
}
return PopCountUint32(uint32(n))
}
// PopCountUint64 returns population count of n (number of bits set in n).
func PopCountUint64(n uint64) int {
return int(popcnt[byte(n>>56)]) + int(popcnt[byte(n>>48)]) +
int(popcnt[byte(n>>40)]) + int(popcnt[byte(n>>32)]) +
int(popcnt[byte(n>>24)]) + int(popcnt[byte(n>>16)]) +
int(popcnt[byte(n>>8)]) + int(popcnt[byte(n)])
}
// PopCountBigInt returns population count of |n| (number of bits set in |n|).
func PopCountBigInt(n *big.Int) (r int) {
for _, v := range n.Bits() {
r += PopCountUintptr(uintptr(v))
}
return
}

46
vendor/github.com/cznic/mathutil/envelope.go generated vendored Normal file
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// 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 (
"math"
)
// Approximation type determines approximation methods used by e.g. Envelope.
type Approximation int
// Specific approximation method tags
const (
_ Approximation = iota
Linear // As named
Sinusoidal // Smooth for all derivations
)
// Envelope is an utility for defining simple curves using a small (usually)
// set of data points. Envelope returns a value defined by x, points and
// approximation. The value of x must be in [0,1) otherwise the result is
// undefined or the function may panic. Points are interpreted as dividing the
// [0,1) interval in len(points)-1 sections, so len(points) must be > 1 or the
// function may panic. According to the left and right points closing/adjacent
// to the section the resulting value is interpolated using the chosen
// approximation method. Unsupported values of approximation are silently
// interpreted as 'Linear'.
func Envelope(x float64, points []float64, approximation Approximation) float64 {
step := 1 / float64(len(points)-1)
fslot := math.Floor(x / step)
mod := x - fslot*step
slot := int(fslot)
l, r := points[slot], points[slot+1]
rmod := mod / step
switch approximation {
case Sinusoidal:
k := (math.Sin(math.Pi*(rmod-0.5)) + 1) / 2
return l + (r-l)*k
case Linear:
fallthrough
default:
return l + (r-l)*rmod
}
}

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vendor/github.com/cznic/mathutil/example/example.go generated vendored Normal file
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// Copyright (c) 2011 CZ.NIC z.s.p.o. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// blame: jnml, labs.nic.cz
// +build ignore
package main
import (
"bufio"
"flag"
"github.com/cznic/mathutil"
"log"
"math"
"os"
)
/*
$ # Usage e.g.:
$ go run example.go -max 1024 > mathutil.dat # generate 1kB of "random" data
*/
func main() {
r, err := mathutil.NewFC32(math.MinInt32, math.MaxInt32, true)
if err != nil {
log.Fatal(err)
}
var mflag uint64
flag.Uint64Var(&mflag, "max", 0, "limit output to max bytes")
flag.Parse()
stdout := bufio.NewWriter(os.Stdout)
if mflag != 0 {
for i := uint64(0); i < mflag; i++ {
if err := stdout.WriteByte(byte(r.Next())); err != nil {
log.Fatal(err)
}
}
stdout.Flush()
return
}
for stdout.WriteByte(byte(r.Next())) == nil {
}
}

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vendor/github.com/cznic/mathutil/example2/example2.go generated vendored Normal file
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// Copyright (c) 2011 CZ.NIC z.s.p.o. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// blame: jnml, labs.nic.cz
// +build ignore
package main
import (
"bytes"
"github.com/cznic/mathutil"
"image"
"image/png"
"io/ioutil"
"log"
"math"
"math/rand"
)
// $ go run example2.go # view rand.png and rnd.png by your favorite pic viewer
//
// see http://www.boallen.com/random-numbers.html
func main() {
sqr := image.Rect(0, 0, 511, 511)
r, err := mathutil.NewFC32(math.MinInt32, math.MaxInt32, true)
if err != nil {
log.Fatal("NewFC32", err)
}
img := image.NewGray(sqr)
for y := 0; y < 512; y++ {
for x := 0; x < 512; x++ {
if r.Next()&1 != 0 {
img.Set(x, y, image.White)
}
}
}
buf := bytes.NewBuffer(nil)
if err := png.Encode(buf, img); err != nil {
log.Fatal("Encode rnd.png ", err)
}
if err := ioutil.WriteFile("rnd.png", buf.Bytes(), 0666); err != nil {
log.Fatal("ioutil.WriteFile/rnd.png ", err)
}
r2 := rand.New(rand.NewSource(0))
img = image.NewGray(sqr)
for y := 0; y < 512; y++ {
for x := 0; x < 512; x++ {
if r2.Int()&1 != 0 {
img.Set(x, y, image.White)
}
}
}
buf = bytes.NewBuffer(nil)
if err := png.Encode(buf, img); err != nil {
log.Fatal("Encode rand.png ", err)
}
if err := ioutil.WriteFile("rand.png", buf.Bytes(), 0666); err != nil {
log.Fatal("ioutil.WriteFile/rand.png ", err)
}
}

43
vendor/github.com/cznic/mathutil/example3/example3.go generated vendored Normal file
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// Copyright (c) 2011 CZ.NIC z.s.p.o. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// blame: jnml, labs.nic.cz
// +build ignore
package main
import (
"bufio"
"flag"
"log"
"math/rand"
"os"
)
/*
$ # Usage e.g.:
$ go run example3.go -max 1024 > rand.dat # generate 1kB of "random" data
*/
func main() {
r := rand.New(rand.NewSource(1))
var mflag uint64
flag.Uint64Var(&mflag, "max", 0, "limit output to max bytes")
flag.Parse()
stdout := bufio.NewWriter(os.Stdout)
if mflag != 0 {
for i := uint64(0); i < mflag; i++ {
if err := stdout.WriteByte(byte(r.Int())); err != nil {
log.Fatal(err)
}
}
stdout.Flush()
return
}
for stdout.WriteByte(byte(r.Int())) == nil {
}
}

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vendor/github.com/cznic/mathutil/example4/main.go generated vendored Normal file
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// Copyright (c) 2011 jnml. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// +build ignore
// Let QRN be the number of quadratic residues of N. Let Q be QRN/N. From a
// sorted list of primorial products < 2^32 find "record breakers". "Record
// breaker" is N with new lowest Q.
//
// There are only 49 "record breakers" < 2^32.
//
// To run the example $ go run main.go
package main
import (
"fmt"
"math"
"sort"
"time"
"github.com/cznic/mathutil"
"github.com/cznic/sortutil"
)
func main() {
pp := mathutil.PrimorialProductsUint32(0, math.MaxUint32, 32)
sort.Sort(sortutil.Uint32Slice(pp))
var bestN, bestD uint32 = 1, 1
order, checks := 0, 0
var ixDirty uint32
m := make([]byte, math.MaxUint32>>3)
for _, n := range pp {
for i := range m[:ixDirty+1] {
m[i] = 0
}
ixDirty = 0
checks++
limit0 := mathutil.QScaleUint32(n, bestN, bestD)
if limit0 > math.MaxUint32 {
panic(0)
}
limit := uint32(limit0)
n64 := uint64(n)
hi := n64 >> 1
hits := uint32(0)
check := true
fmt.Printf("\r%10d %d/%d", n, checks, len(pp))
t0 := time.Now()
for i := uint64(0); i < hi; i++ {
sq := uint32(i * i % n64)
ix := sq >> 3
msk := byte(1 << (sq & 7))
if m[ix]&msk == 0 {
hits++
if hits >= limit {
check = false
break
}
}
m[ix] |= msk
if ix > ixDirty {
ixDirty = ix
}
}
adjPrime := ".." // Composite before
if mathutil.IsPrime(n - 1) {
adjPrime = "P." // Prime before
}
switch mathutil.IsPrime(n + 1) {
case true:
adjPrime += "P" // Prime after
case false:
adjPrime += "." // Composite after
}
if check && mathutil.QCmpUint32(hits, n, bestN, bestD) < 0 {
order++
d := time.Since(t0)
bestN, bestD = hits, n
q := float64(hits) / float64(n)
fmt.Printf(
"\r%2s #%03d %d %d %.2f %.2E %s %s %v\n",
adjPrime, order, n, hits,
1/q, q, d, time.Now().Format("15:04:05"), mathutil.FactorInt(n),
)
}
}
}

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vendor/github.com/cznic/mathutil/ff/main.go generated vendored Normal file
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// Copyright (c) jnml. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// +build ignore
// Factor Finder - searches for Mersenne number factors of one specific special
// form.
package main
import (
"flag"
"fmt"
"math/big"
"runtime"
"time"
"github.com/cznic/mathutil"
)
const (
pp = 1
pp2 = 10
)
var (
_1 = big.NewInt(1)
_2 = big.NewInt(2)
)
func main() {
runtime.GOMAXPROCS(2)
oClass := flag.Uint64("c", 2, `factor "class" number`)
oDuration := flag.Duration("d", time.Second, "duration to spend on one class")
flag.Parse()
class := *oClass
for class&1 != 0 {
class >>= 1
}
class = mathutil.MaxUint64(class, 2)
for {
c := time.After(*oDuration)
factor := big.NewInt(0)
factor.SetUint64(class)
exp := big.NewInt(0)
oneClass:
for {
select {
case <-c:
break oneClass
default:
}
exp.Set(factor)
factor.Lsh(factor, 1)
factor.Add(factor, _1)
if !factor.ProbablyPrime(pp) {
continue
}
if !exp.ProbablyPrime(pp) {
continue
}
if mathutil.ModPowBigInt(_2, exp, factor).Cmp(_1) != 0 {
continue
}
if !factor.ProbablyPrime(pp2) {
continue
}
if !exp.ProbablyPrime(pp2) {
continue
}
fmt.Printf("%d: %s | M%s (%d bits)\n", class, factor, exp, factor.BitLen())
}
class += 2
}
}

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vendor/github.com/cznic/mathutil/mathutil.go generated vendored Normal file
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// 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 provides utilities supplementing the standard 'math' and
// 'math/rand' packages.
//
// Compatibility issues
//
// 2013-12-13: The following functions have been REMOVED
//
// func Uint64ToBigInt(n uint64) *big.Int
// func Uint64FromBigInt(n *big.Int) (uint64, bool)
//
// 2013-05-13: The following functions are now DEPRECATED
//
// func Uint64ToBigInt(n uint64) *big.Int
// func Uint64FromBigInt(n *big.Int) (uint64, bool)
//
// These functions will be REMOVED with Go release 1.1+1.
//
// 2013-01-21: The following functions have been REMOVED
//
// func MaxInt() int
// func MinInt() int
// func MaxUint() uint
// func UintPtrBits() int
//
// They are now replaced by untyped constants
//
// MaxInt
// MinInt
// MaxUint
// UintPtrBits
//
// Additionally one more untyped constant was added
//
// IntBits
//
// This change breaks any existing code depending on the above removed
// functions. They should have not been published in the first place, that was
// unfortunate. Instead, defining such architecture and/or implementation
// specific integer limits and bit widths as untyped constants improves
// performance and allows for static dead code elimination if it depends on
// these values. Thanks to minux for pointing it out in the mail list
// (https://groups.google.com/d/msg/golang-nuts/tlPpLW6aJw8/NT3mpToH-a4J).
//
// 2012-12-12: The following functions will be DEPRECATED with Go release
// 1.0.3+1 and REMOVED with Go release 1.0.3+2, b/c of
// http://code.google.com/p/go/source/detail?r=954a79ee3ea8
//
// func Uint64ToBigInt(n uint64) *big.Int
// func Uint64FromBigInt(n *big.Int) (uint64, bool)
package mathutil
import (
"math"
"math/big"
)
// Architecture and/or implementation specific integer limits and bit widths.
const (
MaxInt = 1<<(IntBits-1) - 1
MinInt = -MaxInt - 1
MaxUint = 1<<IntBits - 1
IntBits = 1 << (^uint(0)>>32&1 + ^uint(0)>>16&1 + ^uint(0)>>8&1 + 3)
UintPtrBits = 1 << (^uintptr(0)>>32&1 + ^uintptr(0)>>16&1 + ^uintptr(0)>>8&1 + 3)
)
var (
_1 = big.NewInt(1)
_2 = big.NewInt(2)
)
// GCDByte returns the greatest common divisor of a and b. Based on:
// http://en.wikipedia.org/wiki/Euclidean_algorithm#Implementations
func GCDByte(a, b byte) byte {
for b != 0 {
a, b = b, a%b
}
return a
}
// GCDUint16 returns the greatest common divisor of a and b.
func GCDUint16(a, b uint16) uint16 {
for b != 0 {
a, b = b, a%b
}
return a
}
// GCD returns the greatest common divisor of a and b.
func GCDUint32(a, b uint32) uint32 {
for b != 0 {
a, b = b, a%b
}
return a
}
// GCD64 returns the greatest common divisor of a and b.
func GCDUint64(a, b uint64) uint64 {
for b != 0 {
a, b = b, a%b
}
return a
}
// ISqrt returns floor(sqrt(n)). Typical run time is few hundreds of ns.
func ISqrt(n uint32) (x uint32) {
if n == 0 {
return
}
if n >= math.MaxUint16*math.MaxUint16 {
return math.MaxUint16
}
var px, nx uint32
for x = n; ; px, x = x, nx {
nx = (x + n/x) / 2
if nx == x || nx == px {
break
}
}
return
}
// SqrtUint64 returns floor(sqrt(n)). Typical run time is about 0.5 µs.
func SqrtUint64(n uint64) (x uint64) {
if n == 0 {
return
}
if n >= math.MaxUint32*math.MaxUint32 {
return math.MaxUint32
}
var px, nx uint64
for x = n; ; px, x = x, nx {
nx = (x + n/x) / 2
if nx == x || nx == px {
break
}
}
return
}
// SqrtBig returns floor(sqrt(n)). It panics on n < 0.
func SqrtBig(n *big.Int) (x *big.Int) {
switch n.Sign() {
case -1:
panic(-1)
case 0:
return big.NewInt(0)
}
var px, nx big.Int
x = big.NewInt(0)
x.SetBit(x, n.BitLen()/2+1, 1)
for {
nx.Rsh(nx.Add(x, nx.Div(n, x)), 1)
if nx.Cmp(x) == 0 || nx.Cmp(&px) == 0 {
break
}
px.Set(x)
x.Set(&nx)
}
return
}
// Log2Byte returns log base 2 of n. It's the same as index of the highest
// bit set in n. For n == 0 -1 is returned.
func Log2Byte(n byte) int {
return log2[n]
}
// Log2Uint16 returns log base 2 of n. It's the same as index of the highest
// bit set in n. For n == 0 -1 is returned.
func Log2Uint16(n uint16) int {
if b := n >> 8; b != 0 {
return log2[b] + 8
}
return log2[n]
}
// Log2Uint32 returns log base 2 of n. It's the same as index of the highest
// bit set in n. For n == 0 -1 is returned.
func Log2Uint32(n uint32) int {
if b := n >> 24; b != 0 {
return log2[b] + 24
}
if b := n >> 16; b != 0 {
return log2[b] + 16
}
if b := n >> 8; b != 0 {
return log2[b] + 8
}
return log2[n]
}
// Log2Uint64 returns log base 2 of n. It's the same as index of the highest
// bit set in n. For n == 0 -1 is returned.
func Log2Uint64(n uint64) int {
if b := n >> 56; b != 0 {
return log2[b] + 56
}
if b := n >> 48; b != 0 {
return log2[b] + 48
}
if b := n >> 40; b != 0 {
return log2[b] + 40
}
if b := n >> 32; b != 0 {
return log2[b] + 32
}
if b := n >> 24; b != 0 {
return log2[b] + 24
}
if b := n >> 16; b != 0 {
return log2[b] + 16
}
if b := n >> 8; b != 0 {
return log2[b] + 8
}
return log2[n]
}
// ModPowByte computes (b^e)%m. It panics for m == 0 || b == e == 0.
//
// See also: http://en.wikipedia.org/wiki/Modular_exponentiation#Right-to-left_binary_method
func ModPowByte(b, e, m byte) byte {
if b == 0 && e == 0 {
panic(0)
}
if m == 1 {
return 0
}
r := uint16(1)
for b, m := uint16(b), uint16(m); e > 0; b, e = b*b%m, e>>1 {
if e&1 == 1 {
r = r * b % m
}
}
return byte(r)
}
// ModPowByte computes (b^e)%m. It panics for m == 0 || b == e == 0.
func ModPowUint16(b, e, m uint16) uint16 {
if b == 0 && e == 0 {
panic(0)
}
if m == 1 {
return 0
}
r := uint32(1)
for b, m := uint32(b), uint32(m); e > 0; b, e = b*b%m, e>>1 {
if e&1 == 1 {
r = r * b % m
}
}
return uint16(r)
}
// ModPowUint32 computes (b^e)%m. It panics for m == 0 || b == e == 0.
func ModPowUint32(b, e, m uint32) uint32 {
if b == 0 && e == 0 {
panic(0)
}
if m == 1 {
return 0
}
r := uint64(1)
for b, m := uint64(b), uint64(m); e > 0; b, e = b*b%m, e>>1 {
if e&1 == 1 {
r = r * b % m
}
}
return uint32(r)
}
// ModPowUint64 computes (b^e)%m. It panics for m == 0 || b == e == 0.
func ModPowUint64(b, e, m uint64) (r uint64) {
if b == 0 && e == 0 {
panic(0)
}
if m == 1 {
return 0
}
return modPowBigInt(big.NewInt(0).SetUint64(b), big.NewInt(0).SetUint64(e), big.NewInt(0).SetUint64(m)).Uint64()
}
func modPowBigInt(b, e, m *big.Int) (r *big.Int) {
r = big.NewInt(1)
for i, n := 0, e.BitLen(); i < n; i++ {
if e.Bit(i) != 0 {
r.Mod(r.Mul(r, b), m)
}
b.Mod(b.Mul(b, b), m)
}
return
}
// ModPowBigInt computes (b^e)%m. Returns nil for e < 0. It panics for m == 0 || b == e == 0.
func ModPowBigInt(b, e, m *big.Int) (r *big.Int) {
if b.Sign() == 0 && e.Sign() == 0 {
panic(0)
}
if m.Cmp(_1) == 0 {
return big.NewInt(0)
}
if e.Sign() < 0 {
return
}
return modPowBigInt(big.NewInt(0).Set(b), big.NewInt(0).Set(e), m)
}
var uint64ToBigIntDelta big.Int
func init() {
uint64ToBigIntDelta.SetBit(&uint64ToBigIntDelta, 63, 1)
}
var uintptrBits int
func init() {
x := uint64(math.MaxUint64)
uintptrBits = BitLenUintptr(uintptr(x))
}
// UintptrBits returns the bit width of an uintptr at the executing machine.
func UintptrBits() int {
return uintptrBits
}
// AddUint128_64 returns the uint128 sum of uint64 a and b.
func AddUint128_64(a, b uint64) (hi uint64, lo uint64) {
lo = a + b
if lo < a {
hi = 1
}
return
}
// MulUint128_64 returns the uint128 bit product of uint64 a and b.
func MulUint128_64(a, b uint64) (hi, lo uint64) {
/*
2^(2 W) ahi bhi + 2^W alo bhi + 2^W ahi blo + alo blo
FEDCBA98 76543210 FEDCBA98 76543210
---- alo*blo ----
---- alo*bhi ----
---- ahi*blo ----
---- ahi*bhi ----
*/
const w = 32
const m = 1<<w - 1
ahi, bhi, alo, blo := a>>w, b>>w, a&m, b&m
lo = alo * blo
mid1 := alo * bhi
mid2 := ahi * blo
c1, lo := AddUint128_64(lo, mid1<<w)
c2, lo := AddUint128_64(lo, mid2<<w)
_, hi = AddUint128_64(ahi*bhi, mid1>>w+mid2>>w+uint64(c1+c2))
return
}
// PowerizeBigInt returns (e, p) such that e is the smallest number for which p
// == b^e is greater or equal n. For n < 0 or b < 2 (0, nil) is returned.
//
// NOTE: Run time for large values of n (above about 2^1e6 ~= 1e300000) can be
// significant and/or unacceptabe. For any smaller values of n the function
// typically performs in sub second time. For "small" values of n (cca bellow
// 2^1e3 ~= 1e300) the same can be easily below 10 µs.
//
// A special (and trivial) case of b == 2 is handled separately and performs
// much faster.
func PowerizeBigInt(b, n *big.Int) (e uint32, p *big.Int) {
switch {
case b.Cmp(_2) < 0 || n.Sign() < 0:
return
case n.Sign() == 0 || n.Cmp(_1) == 0:
return 0, big.NewInt(1)
case b.Cmp(_2) == 0:
p = big.NewInt(0)
e = uint32(n.BitLen() - 1)
p.SetBit(p, int(e), 1)
if p.Cmp(n) < 0 {
p.Mul(p, _2)
e++
}
return
}
bw := b.BitLen()
nw := n.BitLen()
p = big.NewInt(1)
var bb, r big.Int
for {
switch p.Cmp(n) {
case -1:
x := uint32((nw - p.BitLen()) / bw)
if x == 0 {
x = 1
}
e += x
switch x {
case 1:
p.Mul(p, b)
default:
r.Set(_1)
bb.Set(b)
e := x
for {
if e&1 != 0 {
r.Mul(&r, &bb)
}
if e >>= 1; e == 0 {
break
}
bb.Mul(&bb, &bb)
}
p.Mul(p, &r)
}
case 0, 1:
return
}
}
}
// PowerizeUint32BigInt returns (e, p) such that e is the smallest number for
// which p == b^e is greater or equal n. For n < 0 or b < 2 (0, nil) is
// returned.
//
// More info: see PowerizeBigInt.
func PowerizeUint32BigInt(b uint32, n *big.Int) (e uint32, p *big.Int) {
switch {
case b < 2 || n.Sign() < 0:
return
case n.Sign() == 0 || n.Cmp(_1) == 0:
return 0, big.NewInt(1)
case b == 2:
p = big.NewInt(0)
e = uint32(n.BitLen() - 1)
p.SetBit(p, int(e), 1)
if p.Cmp(n) < 0 {
p.Mul(p, _2)
e++
}
return
}
var bb big.Int
bb.SetInt64(int64(b))
return PowerizeBigInt(&bb, n)
}
/*
ProbablyPrimeUint32 returns true if n is prime or n is a pseudoprime to base a.
It implements the Miller-Rabin primality test for one specific value of 'a' and
k == 1.
Wrt pseudocode shown at
http://en.wikipedia.org/wiki/Miller-Rabin_primality_test#Algorithm_and_running_time
Input: n > 3, an odd integer to be tested for primality;
Input: k, a parameter that determines the accuracy of the test
Output: composite if n is composite, otherwise probably prime
write n − 1 as 2^s·d with d odd by factoring powers of 2 from n − 1
LOOP: repeat k times:
pick a random integer a in the range [2, n − 2]
x ← a^d mod n
if x = 1 or x = n − 1 then do next LOOP
for r = 1 .. s − 1
x ← x^2 mod n
if x = 1 then return composite
if x = n − 1 then do next LOOP
return composite
return probably prime
... this function behaves like passing 1 for 'k' and additionaly a
fixed/non-random 'a'. Otherwise it's the same algorithm.
See also: http://mathworld.wolfram.com/Rabin-MillerStrongPseudoprimeTest.html
*/
func ProbablyPrimeUint32(n, a uint32) bool {
d, s := n-1, 0
for ; d&1 == 0; d, s = d>>1, s+1 {
}
x := uint64(ModPowUint32(a, d, n))
if x == 1 || uint32(x) == n-1 {
return true
}
for ; s > 1; s-- {
if x = x * x % uint64(n); x == 1 {
return false
}
if uint32(x) == n-1 {
return true
}
}
return false
}
// ProbablyPrimeUint64_32 returns true if n is prime or n is a pseudoprime to
// base a. It implements the Miller-Rabin primality test for one specific value
// of 'a' and k == 1. See also ProbablyPrimeUint32.
func ProbablyPrimeUint64_32(n uint64, a uint32) bool {
d, s := n-1, 0
for ; d&1 == 0; d, s = d>>1, s+1 {
}
x := ModPowUint64(uint64(a), d, n)
if x == 1 || x == n-1 {
return true
}
bx, bn := big.NewInt(0).SetUint64(x), big.NewInt(0).SetUint64(n)
for ; s > 1; s-- {
if x = bx.Mod(bx.Mul(bx, bx), bn).Uint64(); x == 1 {
return false
}
if x == n-1 {
return true
}
}
return false
}
// ProbablyPrimeBigInt_32 returns true if n is prime or n is a pseudoprime to
// base a. It implements the Miller-Rabin primality test for one specific value
// of 'a' and k == 1. See also ProbablyPrimeUint32.
func ProbablyPrimeBigInt_32(n *big.Int, a uint32) bool {
var d big.Int
d.Set(n)
d.Sub(&d, _1) // d <- n-1
s := 0
for ; d.Bit(s) == 0; s++ {
}
nMinus1 := big.NewInt(0).Set(&d)
d.Rsh(&d, uint(s))
x := ModPowBigInt(big.NewInt(int64(a)), &d, n)
if x.Cmp(_1) == 0 || x.Cmp(nMinus1) == 0 {
return true
}
for ; s > 1; s-- {
if x = x.Mod(x.Mul(x, x), n); x.Cmp(_1) == 0 {
return false
}
if x.Cmp(nMinus1) == 0 {
return true
}
}
return false
}
// ProbablyPrimeBigInt returns true if n is prime or n is a pseudoprime to base
// a. It implements the Miller-Rabin primality test for one specific value of
// 'a' and k == 1. See also ProbablyPrimeUint32.
func ProbablyPrimeBigInt(n, a *big.Int) bool {
var d big.Int
d.Set(n)
d.Sub(&d, _1) // d <- n-1
s := 0
for ; d.Bit(s) == 0; s++ {
}
nMinus1 := big.NewInt(0).Set(&d)
d.Rsh(&d, uint(s))
x := ModPowBigInt(a, &d, n)
if x.Cmp(_1) == 0 || x.Cmp(nMinus1) == 0 {
return true
}
for ; s > 1; s-- {
if x = x.Mod(x.Mul(x, x), n); x.Cmp(_1) == 0 {
return false
}
if x.Cmp(nMinus1) == 0 {
return true
}
}
return false
}
// Max returns the larger of a and b.
func Max(a, b int) int {
if a > b {
return a
}
return b
}
// Min returns the smaller of a and b.
func Min(a, b int) int {
if a < b {
return a
}
return b
}
// UMax returns the larger of a and b.
func UMax(a, b uint) uint {
if a > b {
return a
}
return b
}
// UMin returns the smaller of a and b.
func UMin(a, b uint) uint {
if a < b {
return a
}
return b
}
// MaxByte returns the larger of a and b.
func MaxByte(a, b byte) byte {
if a > b {
return a
}
return b
}
// MinByte returns the smaller of a and b.
func MinByte(a, b byte) byte {
if a < b {
return a
}
return b
}
// MaxInt8 returns the larger of a and b.
func MaxInt8(a, b int8) int8 {
if a > b {
return a
}
return b
}
// MinInt8 returns the smaller of a and b.
func MinInt8(a, b int8) int8 {
if a < b {
return a
}
return b
}
// MaxUint16 returns the larger of a and b.
func MaxUint16(a, b uint16) uint16 {
if a > b {
return a
}
return b
}
// MinUint16 returns the smaller of a and b.
func MinUint16(a, b uint16) uint16 {
if a < b {
return a
}
return b
}
// MaxInt16 returns the larger of a and b.
func MaxInt16(a, b int16) int16 {
if a > b {
return a
}
return b
}
// MinInt16 returns the smaller of a and b.
func MinInt16(a, b int16) int16 {
if a < b {
return a
}
return b
}
// MaxUint32 returns the larger of a and b.
func MaxUint32(a, b uint32) uint32 {
if a > b {
return a
}
return b
}
// MinUint32 returns the smaller of a and b.
func MinUint32(a, b uint32) uint32 {
if a < b {
return a
}
return b
}
// MaxInt32 returns the larger of a and b.
func MaxInt32(a, b int32) int32 {
if a > b {
return a
}
return b
}
// MinInt32 returns the smaller of a and b.
func MinInt32(a, b int32) int32 {
if a < b {
return a
}
return b
}
// MaxUint64 returns the larger of a and b.
func MaxUint64(a, b uint64) uint64 {
if a > b {
return a
}
return b
}
// MinUint64 returns the smaller of a and b.
func MinUint64(a, b uint64) uint64 {
if a < b {
return a
}
return b
}
// MaxInt64 returns the larger of a and b.
func MaxInt64(a, b int64) int64 {
if a > b {
return a
}
return b
}
// MinInt64 returns the smaller of a and b.
func MinInt64(a, b int64) int64 {
if a < b {
return a
}
return b
}
// ToBase produces n in base b. For example
//
// ToBase(2047, 22) -> [1, 5, 4]
//
// 1 * 22^0 1
// 5 * 22^1 110
// 4 * 22^2 1936
// ----
// 2047
//
// ToBase panics for bases < 2.
func ToBase(n *big.Int, b int) []int {
var nn big.Int
nn.Set(n)
if b < 2 {
panic("invalid base")
}
k := 1
switch nn.Sign() {
case -1:
nn.Neg(&nn)
k = -1
case 0:
return []int{0}
}
bb := big.NewInt(int64(b))
var r []int
rem := big.NewInt(0)
for nn.Sign() != 0 {
nn.QuoRem(&nn, bb, rem)
r = append(r, k*int(rem.Int64()))
}
return r
}

297
vendor/github.com/cznic/mathutil/mersenne/mersenne.go generated vendored Normal file
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// Copyright (c) 2014 The mersenne 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 mersenne collects utilities related to Mersenne numbers[1] and/or some
of their properties.
Exponent
In this documentation the term 'exponent' refers to 'n' of a Mersenne number Mn
equal to 2^n-1. This package supports only uint32 sized exponents. New()
currently supports exponents only up to math.MaxInt32 (31 bits, up to 256 MB
required to represent such Mn in memory as a big.Int).
Links
Referenced from above:
[1] http://en.wikipedia.org/wiki/Mersenne_number
*/
package mersenne
import (
"math"
"math/big"
"github.com/cznic/mathutil"
"github.com/remyoudompheng/bigfft"
)
var (
_0 = big.NewInt(0)
_1 = big.NewInt(1)
_2 = big.NewInt(2)
)
// Knowns list the exponent of currently (March 2012) known Mersenne primes
// exponents in order. See also: http://oeis.org/A000043 for a partial list.
var Knowns = []uint32{
2, // #1
3, // #2
5, // #3
7, // #4
13, // #5
17, // #6
19, // #7
31, // #8
61, // #9
89, // #10
107, // #11
127, // #12
521, // #13
607, // #14
1279, // #15
2203, // #16
2281, // #17
3217, // #18
4253, // #19
4423, // #20
9689, // #21
9941, // #22
11213, // #23
19937, // #24
21701, // #25
23209, // #26
44497, // #27
86243, // #28
110503, // #29
132049, // #30
216091, // #31
756839, // #32
859433, // #33
1257787, // #34
1398269, // #35
2976221, // #36
3021377, // #37
6972593, // #38
13466917, // #39
20996011, // #40
24036583, // #41
25964951, // #42
30402457, // #43
32582657, // #44
37156667, // #45
42643801, // #46
43112609, // #47
57885161, // #48
74207281, // #49
}
// Known maps the exponent of known Mersenne primes its ordinal number/rank.
// Ranks > 41 are currently provisional.
var Known map[uint32]int
func init() {
Known = map[uint32]int{}
for i, v := range Knowns {
Known[v] = i + 1
}
}
// New returns Mn == 2^n-1 for n <= math.MaxInt32 or nil otherwise.
func New(n uint32) (m *big.Int) {
if n > math.MaxInt32 {
return
}
m = big.NewInt(0)
return m.Sub(m.SetBit(m, int(n), 1), _1)
}
// HasFactorUint32 returns true if d | Mn. Typical run time for a 32 bit factor
// and a 32 bit exponent is < 1 µs.
func HasFactorUint32(d, n uint32) bool {
return d == 1 || d&1 != 0 && mathutil.ModPowUint32(2, n, d) == 1
}
// HasFactorUint64 returns true if d | Mn. Typical run time for a 64 bit factor
// and a 32 bit exponent is < 30 µs.
func HasFactorUint64(d uint64, n uint32) bool {
return d == 1 || d&1 != 0 && mathutil.ModPowUint64(2, uint64(n), d) == 1
}
// HasFactorBigInt returns true if d | Mn, d > 0. Typical run time for a 128
// bit factor and a 32 bit exponent is < 75 µs.
func HasFactorBigInt(d *big.Int, n uint32) bool {
return d.Cmp(_1) == 0 || d.Sign() > 0 && d.Bit(0) == 1 &&
mathutil.ModPowBigInt(_2, big.NewInt(int64(n)), d).Cmp(_1) == 0
}
// HasFactorBigInt2 returns true if d | Mn, d > 0
func HasFactorBigInt2(d, n *big.Int) bool {
return d.Cmp(_1) == 0 || d.Sign() > 0 && d.Bit(0) == 1 &&
mathutil.ModPowBigInt(_2, n, d).Cmp(_1) == 0
}
/*
FromFactorBigInt returns n such that d | Mn if n <= max and d is odd. In other
cases zero is returned.
It is conjectured that every odd d ∊ N divides infinitely many Mersenne numbers.
The returned n should be the exponent of smallest such Mn.
NOTE: The computation of n from a given d performs roughly in O(n). It is
thus highly recomended to use the 'max' argument to limit the "searched"
exponent upper bound as appropriate. Otherwise the computation can take a long
time as a large factor can be a divisor of a Mn with exponent above the uint32
limits.
The FromFactorBigInt function is a modification of the original Will
Edgington's "reverse method", discussed here:
http://tech.groups.yahoo.com/group/primenumbers/message/15061
*/
func FromFactorBigInt(d *big.Int, max uint32) (n uint32) {
if d.Bit(0) == 0 {
return
}
var m big.Int
for n < max {
m.Add(&m, d)
i := 0
for ; m.Bit(i) == 1; i++ {
if n == math.MaxUint32 {
return 0
}
n++
}
m.Rsh(&m, uint(i))
if m.Sign() == 0 {
if n > max {
n = 0
}
return
}
}
return 0
}
// Mod sets mod to n % Mexp and returns mod. It panics for exp == 0 || exp >=
// math.MaxInt32 || n < 0.
func Mod(mod, n *big.Int, exp uint32) *big.Int {
if exp == 0 || exp >= math.MaxInt32 || n.Sign() < 0 {
panic(0)
}
m := New(exp)
mod.Set(n)
var x big.Int
for mod.BitLen() > int(exp) {
x.Set(mod)
x.Rsh(&x, uint(exp))
mod.And(mod, m)
mod.Add(mod, &x)
}
if mod.BitLen() == int(exp) && mod.Cmp(m) == 0 {
mod.SetInt64(0)
}
return mod
}
// ModPow2 returns x such that 2^Me % Mm == 2^x. It panics for m < 2. Typical
// run time is < 1 µs. Use instead of ModPow(2, e, m) wherever possible.
func ModPow2(e, m uint32) (x uint32) {
/*
m < 2 -> panic
e == 0 -> x == 0
e == 1 -> x == 1
2^M1 % M2 == 2^1 % 3 == 2^1 10 // 2^1, 3, 5, 7 ... +2k
2^M1 % M3 == 2^1 % 7 == 2^1 010 // 2^1, 4, 7, ... +3k
2^M1 % M4 == 2^1 % 15 == 2^1 0010 // 2^1, 5, 9, 13... +4k
2^M1 % M5 == 2^1 % 31 == 2^1 00010 // 2^1, 6, 11, 16... +5k
2^M2 % M2 == 2^3 % 3 == 2^1 10.. // 2^3, 5, 7, 9, 11, ... +2k
2^M2 % M3 == 2^3 % 7 == 2^0 001... // 2^3, 6, 9, 12, 15, ... +3k
2^M2 % M4 == 2^3 % 15 == 2^3 1000 // 2^3, 7, 11, 15, 19, ... +4k
2^M2 % M5 == 2^3 % 31 == 2^3 01000 // 2^3, 8, 13, 18, 23, ... +5k
2^M3 % M2 == 2^7 % 3 == 2^1 10..--.. // 2^3, 5, 7... +2k
2^M3 % M3 == 2^7 % 7 == 2^1 010...--- // 2^1, 4, 7... +3k
2^M3 % M4 == 2^7 % 15 == 2^3 1000.... // +4k
2^M3 % M5 == 2^7 % 31 == 2^2 00100..... // +5k
2^M3 % M6 == 2^7 % 63 == 2^1 000010...... // +6k
2^M3 % M7 == 2^7 % 127 == 2^0 0000001.......
2^M3 % M8 == 2^7 % 255 == 2^7 10000000
2^M3 % M9 == 2^7 % 511 == 2^7 010000000
2^M4 % M2 == 2^15 % 3 == 2^1 10..--..--..--..
2^M4 % M3 == 2^15 % 7 == 2^0 1...---...---...
2^M4 % M4 == 2^15 % 15 == 2^3 1000....----....
2^M4 % M5 == 2^15 % 31 == 2^0 1.....-----.....
2^M4 % M6 == 2^15 % 63 == 2^3 1000......------
2^M4 % M7 == 2^15 % 127 == 2^1 10.......-------
2^M4 % M8 == 2^15 % 255 == 2^7 10000000........
2^M4 % M9 == 2^15 % 511 == 2^6 1000000.........
*/
switch {
case m < 2:
panic(0)
case e < 2:
return e
}
if x = mathutil.ModPowUint32(2, e, m); x == 0 {
return m - 1
}
return x - 1
}
// ModPow returns b^Me % Mm. Run time grows quickly with 'e' and/or 'm' when b
// != 2 (then ModPow2 is used).
func ModPow(b, e, m uint32) (r *big.Int) {
if m == 1 {
return big.NewInt(0)
}
if b == 2 {
x := ModPow2(e, m)
r = big.NewInt(0)
r.SetBit(r, int(x), 1)
return
}
bb := big.NewInt(int64(b))
r = big.NewInt(1)
for ; e != 0; e-- {
r = bigfft.Mul(r, bb)
Mod(r, r, m)
bb = bigfft.Mul(bb, bb)
Mod(bb, bb, m)
}
return
}
// ProbablyPrime returns true if Mn is prime or is a pseudoprime to base a.
// Note: Every Mp, prime p, is a prime or is a pseudoprime to base 2, actually
// to every base 2^i, i ∊ [1, p). In contrast - it is conjectured (w/o any
// known counterexamples) that no composite Mp, prime p, is a pseudoprime to
// base 3.
func ProbablyPrime(n, a uint32) bool {
//TODO +test, +bench
if a == 2 {
return ModPow2(n-1, n) == 0
}
nMinus1 := New(n)
nMinus1.Sub(nMinus1, _1)
x := ModPow(a, n-1, n)
return x.Cmp(_1) == 0 || x.Cmp(nMinus1) == 0
}

39
vendor/github.com/cznic/mathutil/permute.go generated vendored Normal file
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// 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 (
"sort"
)
// Generate the first permutation of data.
func PermutationFirst(data sort.Interface) {
sort.Sort(data)
}
// Generate the next permutation of data if possible and return true.
// Return false if there is no more permutation left.
// Based on the algorithm described here:
// http://en.wikipedia.org/wiki/Permutation#Generation_in_lexicographic_order
func PermutationNext(data sort.Interface) bool {
var k, l int
for k = data.Len() - 2; ; k-- { // 1.
if k < 0 {
return false
}
if data.Less(k, k+1) {
break
}
}
for l = data.Len() - 1; !data.Less(k, l); l-- { // 2.
}
data.Swap(k, l) // 3.
for i, j := k+1, data.Len()-1; i < j; i++ { // 4.
data.Swap(i, j)
j--
}
return true
}

335
vendor/github.com/cznic/mathutil/primes.go generated vendored Normal file
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// 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 (
"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.
//
//TODO rename to IsPrimeUint32
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.
//
//TODO rename to NextPrimeUint32
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
}

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vendor/github.com/cznic/mathutil/rat.go generated vendored Normal file
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// 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
// QCmpUint32 compares a/b and c/d and returns:
//
// -1 if a/b < c/d
// 0 if a/b == c/d
// +1 if a/b > c/d
//
func QCmpUint32(a, b, c, d uint32) int {
switch x, y := uint64(a)*uint64(d), uint64(b)*uint64(c); {
case x < y:
return -1
case x == y:
return 0
default: // x > y
return 1
}
}
// QScaleUint32 returns a such that a/b >= c/d.
func QScaleUint32(b, c, d uint32) (a uint64) {
return 1 + (uint64(b)*uint64(c))/uint64(d)
}

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vendor/github.com/cznic/mathutil/rnd.go generated vendored Normal file
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// 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 (
"fmt"
"math"
"math/big"
)
// FC32 is a full cycle PRNG covering the 32 bit signed integer range.
// In contrast to full cycle generators shown at e.g. http://en.wikipedia.org/wiki/Full_cycle,
// this code doesn't produce values at constant delta (mod cycle length).
// The 32 bit limit is per this implementation, the algorithm used has no intrinsic limit on the cycle size.
// Properties include:
// - Adjustable limits on creation (hi, lo).
// - Positionable/randomly accessible (Pos, Seek).
// - Repeatable (deterministic).
// - Can run forward or backward (Next, Prev).
// - For a billion numbers cycle the Next/Prev PRN can be produced in cca 100-150ns.
// That's like 5-10 times slower compared to PRNs generated using the (non FC) rand package.
type FC32 struct {
cycle int64 // On average: 3 * delta / 2, (HQ: 2 * delta)
delta int64 // hi - lo
factors [][]int64 // This trades some space for hopefully a bit of speed (multiple adding vs multiplying).
lo int
mods []int // pos % set
pos int64 // Within cycle.
primes []int64 // Ordered. ∏ primes == cycle.
set []int64 // Reordered primes (magnitude order bases) according to seed.
}
// NewFC32 returns a newly created FC32 adjusted for the closed interval [lo, hi] or an Error if any.
// If hq == true then trade some generation time for improved (pseudo)randomness.
func NewFC32(lo, hi int, hq bool) (r *FC32, err error) {
if lo > hi {
return nil, fmt.Errorf("invalid range %d > %d", lo, hi)
}
if uint64(hi)-uint64(lo) > math.MaxUint32 {
return nil, fmt.Errorf("range out of int32 limits %d, %d", lo, hi)
}
delta := int64(hi) - int64(lo)
// Find the primorial covering whole delta
n, set, p := int64(1), []int64{}, uint32(2)
if hq {
p++
}
for {
set = append(set, int64(p))
n *= int64(p)
if n > delta {
break
}
p, _ = NextPrime(p)
}
// Adjust the set so n ∊ [delta, 2 * delta] (HQ: [delta, 3 * delta])
// while keeping the cardinality of the set (correlates with the statistic "randomness quality")
// at max, i.e. discard atmost one member.
i := -1 // no candidate prime
if n > 2*(delta+1) {
for j, p := range set {
q := n / p
if q < delta+1 {
break
}
i = j // mark the highest candidate prime set index
}
}
if i >= 0 { // shrink the inner cycle
n = n / set[i]
set = delete(set, i)
}
r = &FC32{
cycle: n,
delta: delta,
factors: make([][]int64, len(set)),
lo: lo,
mods: make([]int, len(set)),
primes: set,
}
r.Seed(1) // the default seed should be always non zero
return
}
// Cycle reports the length of the inner FCPRNG cycle.
// Cycle is atmost the double (HQ: triple) of the generator period (hi - lo + 1).
func (r *FC32) Cycle() int64 {
return r.cycle
}
// Next returns the first PRN after Pos.
func (r *FC32) Next() int {
return r.step(1)
}
// Pos reports the current position within the inner cycle.
func (r *FC32) Pos() int64 {
return r.pos
}
// Prev return the first PRN before Pos.
func (r *FC32) Prev() int {
return r.step(-1)
}
// Seed uses the provided seed value to initialize the generator to a deterministic state.
// A zero seed produces a "canonical" generator with worse randomness than for most non zero seeds.
// Still, the FC property holds for any seed value.
func (r *FC32) Seed(seed int64) {
u := uint64(seed)
r.set = mix(r.primes, &u)
n := int64(1)
for i, p := range r.set {
k := make([]int64, p)
v := int64(0)
for j := range k {
k[j] = v
v += n
}
n *= p
r.factors[i] = mix(k, &u)
}
}
// Seek sets Pos to |pos| % Cycle.
func (r *FC32) Seek(pos int64) { //vet:ignore
if pos < 0 {
pos = -pos
}
pos %= r.cycle
r.pos = pos
for i, p := range r.set {
r.mods[i] = int(pos % p)
}
}
func (r *FC32) step(dir int) int {
for { // avg loops per step: 3/2 (HQ: 2)
y := int64(0)
pos := r.pos
pos += int64(dir)
switch {
case pos < 0:
pos = r.cycle - 1
case pos >= r.cycle:
pos = 0
}
r.pos = pos
for i, mod := range r.mods {
mod += dir
p := int(r.set[i])
switch {
case mod < 0:
mod = p - 1
case mod >= p:
mod = 0
}
r.mods[i] = mod
y += r.factors[i][mod]
}
if y <= r.delta {
return int(y) + r.lo
}
}
}
func delete(set []int64, i int) (y []int64) {
for j, v := range set {
if j != i {
y = append(y, v)
}
}
return
}
func mix(set []int64, seed *uint64) (y []int64) {
for len(set) != 0 {
*seed = rol(*seed)
i := int(*seed % uint64(len(set)))
y = append(y, set[i])
set = delete(set, i)
}
return
}
func rol(u uint64) (y uint64) {
y = u << 1
if int64(u) < 0 {
y |= 1
}
return
}
// FCBig is a full cycle PRNG covering ranges outside of the int32 limits.
// For more info see the FC32 docs.
// Next/Prev PRN on a 1e15 cycle can be produced in about 2 µsec.
type FCBig struct {
cycle *big.Int // On average: 3 * delta / 2, (HQ: 2 * delta)
delta *big.Int // hi - lo
factors [][]*big.Int // This trades some space for hopefully a bit of speed (multiple adding vs multiplying).
lo *big.Int
mods []int // pos % set
pos *big.Int // Within cycle.
primes []int64 // Ordered. ∏ primes == cycle.
set []int64 // Reordered primes (magnitude order bases) according to seed.
}
// NewFCBig returns a newly created FCBig adjusted for the closed interval [lo, hi] or an Error if any.
// If hq == true then trade some generation time for improved (pseudo)randomness.
func NewFCBig(lo, hi *big.Int, hq bool) (r *FCBig, err error) {
if lo.Cmp(hi) > 0 {
return nil, fmt.Errorf("invalid range %d > %d", lo, hi)
}
delta := big.NewInt(0)
delta.Add(delta, hi).Sub(delta, lo)
// Find the primorial covering whole delta
n, set, pp, p := big.NewInt(1), []int64{}, big.NewInt(0), uint32(2)
if hq {
p++
}
for {
set = append(set, int64(p))
pp.SetInt64(int64(p))
n.Mul(n, pp)
if n.Cmp(delta) > 0 {
break
}
p, _ = NextPrime(p)
}
// Adjust the set so n ∊ [delta, 2 * delta] (HQ: [delta, 3 * delta])
// while keeping the cardinality of the set (correlates with the statistic "randomness quality")
// at max, i.e. discard atmost one member.
dd1 := big.NewInt(1)
dd1.Add(dd1, delta)
dd2 := big.NewInt(0)
dd2.Lsh(dd1, 1)
i := -1 // no candidate prime
if n.Cmp(dd2) > 0 {
q := big.NewInt(0)
for j, p := range set {
pp.SetInt64(p)
q.Set(n)
q.Div(q, pp)
if q.Cmp(dd1) < 0 {
break
}
i = j // mark the highest candidate prime set index
}
}
if i >= 0 { // shrink the inner cycle
pp.SetInt64(set[i])
n.Div(n, pp)
set = delete(set, i)
}
r = &FCBig{
cycle: n,
delta: delta,
factors: make([][]*big.Int, len(set)),
lo: lo,
mods: make([]int, len(set)),
pos: big.NewInt(0),
primes: set,
}
r.Seed(1) // the default seed should be always non zero
return
}
// Cycle reports the length of the inner FCPRNG cycle.
// Cycle is atmost the double (HQ: triple) of the generator period (hi - lo + 1).
func (r *FCBig) Cycle() *big.Int {
return r.cycle
}
// Next returns the first PRN after Pos.
func (r *FCBig) Next() *big.Int {
return r.step(1)
}
// Pos reports the current position within the inner cycle.
func (r *FCBig) Pos() *big.Int {
return r.pos
}
// Prev return the first PRN before Pos.
func (r *FCBig) Prev() *big.Int {
return r.step(-1)
}
// Seed uses the provided seed value to initialize the generator to a deterministic state.
// A zero seed produces a "canonical" generator with worse randomness than for most non zero seeds.
// Still, the FC property holds for any seed value.
func (r *FCBig) Seed(seed int64) {
u := uint64(seed)
r.set = mix(r.primes, &u)
n := big.NewInt(1)
v := big.NewInt(0)
pp := big.NewInt(0)
for i, p := range r.set {
k := make([]*big.Int, p)
v.SetInt64(0)
for j := range k {
k[j] = big.NewInt(0)
k[j].Set(v)
v.Add(v, n)
}
pp.SetInt64(p)
n.Mul(n, pp)
r.factors[i] = mixBig(k, &u)
}
}
// Seek sets Pos to |pos| % Cycle.
func (r *FCBig) Seek(pos *big.Int) {
r.pos.Set(pos)
r.pos.Abs(r.pos)
r.pos.Mod(r.pos, r.cycle)
mod := big.NewInt(0)
pp := big.NewInt(0)
for i, p := range r.set {
pp.SetInt64(p)
r.mods[i] = int(mod.Mod(r.pos, pp).Int64())
}
}
func (r *FCBig) step(dir int) (y *big.Int) {
y = big.NewInt(0)
d := big.NewInt(int64(dir))
for { // avg loops per step: 3/2 (HQ: 2)
r.pos.Add(r.pos, d)
switch {
case r.pos.Sign() < 0:
r.pos.Add(r.pos, r.cycle)
case r.pos.Cmp(r.cycle) >= 0:
r.pos.SetInt64(0)
}
for i, mod := range r.mods {
mod += dir
p := int(r.set[i])
switch {
case mod < 0:
mod = p - 1
case mod >= p:
mod = 0
}
r.mods[i] = mod
y.Add(y, r.factors[i][mod])
}
if y.Cmp(r.delta) <= 0 {
y.Add(y, r.lo)
return
}
y.SetInt64(0)
}
}
func deleteBig(set []*big.Int, i int) (y []*big.Int) {
for j, v := range set {
if j != i {
y = append(y, v)
}
}
return
}
func mixBig(set []*big.Int, seed *uint64) (y []*big.Int) {
for len(set) != 0 {
*seed = rol(*seed)
i := int(*seed % uint64(len(set)))
y = append(y, set[i])
set = deleteBig(set, i)
}
return
}

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vendor/github.com/cznic/mathutil/test_deps.go generated vendored Normal file
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// 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
// Pull test dependencies too.
// Enables easy 'go test X' after 'go get X'
import (
// nothing yet
)