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mt19937.go
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mt19937.go
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// This code is available on the terms of the project LICENSE.md file,
// also available online at https://blueoakcouncil.org/license/1.0.0.
// Package mt19937 implements the 64-bit version of the Mersenne Twister (MT)
// pseudo-random number generator (PRNG) with a period of 2^19937-1, also known
// as mt19937_64, according to the reference implementation by Matsumoto and
// Nishimura at http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt64.html
//
// MT is not cryptographically secure. Given a sufficiently long sequence of the
// generated values, one may predict additional values without knowing the seed.
// A secure hashing algorithm should be used with MT if a CSPRNG is required.
//
// When possible, the MT generator should be seeded with a slice of bytes or
// uint64 values to address known "zero-excess" seed initialization issues where
// "shifted" sequences may be generated for seeds with only a few non-zero bits.
// For more information, see
// http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/emt19937ar.html
package mt19937
import (
"encoding/binary"
)
const (
defaultSeed int64 = 5489
sliceSeed int64 = 19650218
n = 312 // state size
m = 156 // shift size
msbm uint64 = 0xffffffff80000000 // 33 most sig. bits
lsbm uint64 = 0x000000007fffffff // 31 least sig. bits
a uint64 = 0xb5026f5aa96619e9 // xor mask
// tempering shift sizes and xor masks
uShift uint64 = 29
uMask uint64 = 0x5555555555555555
sShift uint64 = 17
sMask uint64 = 0x71d67fffeda60000
tShift uint64 = 37
tMask uint64 = 0xfff7eee000000000
lShift uint64 = 43
// initialization values for seeding the state sequence
ivInt uint64 = 6364136223846793005
ivSlice0 uint64 = 3935559000370003845
ivSlice1 uint64 = 2862933555777941757
)
// Source is a pseudo-random number generator that satisfies both
// math/rand.Source and math/rand.Source64.
type Source struct {
state [n]uint64
index int
}
// NewSource creates a new unseeded Source.
func NewSource() *Source {
return &Source{
index: n + 1, // not seeded
}
}
// Seed initializes the source with the provided value. Note that SeedBytes or
// SeedValues should be preferred since Mersenne Twister suffers from a
// "zero-excess" initial state defect where seeds with many zero bits can result
// in similar/"shifted" sequences. The authors describe the issues:
// http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/emt19937ar.html
func (s *Source) Seed(seed int64) {
s.state[0] = uint64(seed)
prev := s.state[0]
for i := 1; i < n; i++ {
s.state[i] = ivInt*(prev^prev>>62) + uint64(i)
prev = s.state[i]
}
s.index = n
}
// SeedBytes seeds the mt19937 engine with up to 2496 bytes from a slice. Only
// the first 2496 bytes of the slice are used. Additional elements are unused.
func (s *Source) SeedBytes(b []byte) {
// Pad the slice to a multiple of 8 elements if not already.
numVals := len(b) / 8
if len(b)%8 != 0 {
numVals++
bx := make([]byte, numVals*8)
copy(bx, b)
b = bx
}
// Convert the byte slice to a uint64 slice.
vals := make([]uint64, numVals)
for i := range vals {
ib := i * 8
vals[i] = binary.BigEndian.Uint64(b[ib : ib+8])
}
s.SeedVals(vals)
}
// SeedVals seeds the mt19937 engine with up to 312 uint64 values. Only the
// first 312 values of the slice are used. Additional elements are unused.
func (s *Source) SeedVals(v []uint64) {
s.Seed(sliceSeed)
is := 1 // state index
next := func() {
is++
if is >= n {
is = 1
s.state[0] = s.state[n-1]
}
}
i := n // iterator
if len(v) > n {
i = len(v) // TODO: test this case
}
for iv := 0; i > 0; i-- {
s.state[is] = v[iv] + uint64(iv) + (s.state[is] ^ ((s.state[is-1] ^ (s.state[is-1] >> 62)) * ivSlice0))
next()
iv++
if iv >= len(v) {
iv = 0
}
}
for i = n - 1; i > 0; i-- {
s.state[is] = (s.state[is] ^ ((s.state[is-1] ^ (s.state[is-1] >> 62)) * ivSlice1)) - uint64(is)
next()
}
s.state[0] = 1 << 63
}
func (s *Source) newState() {
var i int
for ; i < n-m; i++ {
x := s.state[i]&msbm | s.state[i+1]&lsbm
x = x>>1 ^ a*(x&1)
s.state[i] = s.state[i+m] ^ x
}
for ; i < n-1; i++ {
x := s.state[i]&msbm | s.state[i+1]&lsbm
x = x>>1 ^ a*(x&1)
s.state[i] = s.state[i+m-n] ^ x
}
x := s.state[n-1]&msbm | s.state[0]&lsbm
x = x>>1 ^ a*(x&1)
s.state[n-1] = s.state[m-1] ^ x
s.index = 0
}
// Uint64 returns the next pseudo-random integer on [0, 2^64-1) in the sequence.
// Uint64 satisfies math/rand.Source.
func (s *Source) Uint64() uint64 {
if s.index >= n {
if s.index == n+1 {
s.Seed(defaultSeed)
}
s.newState()
}
x := s.state[s.index]
x ^= x >> uShift & uMask
x ^= x << sShift & sMask
x ^= x << tShift & tMask
x ^= x >> lShift
s.index++
return x
}
// Int63 returns the next pseudo-random integer on [0, 2^63-1) in the sequence.
// Both Uint64 and Int63 advance the sequence. Int63 satisfies
// math/rand.Source64.
func (s *Source) Int63() int64 {
// TODO: shift or mask?
//return int64(s.Uint64() & 0x7fffffffffffffff)
return int64(s.Uint64() >> 1)
}
// TODO: implement io.Reader