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prng: Mersenne Twister PRNG implementations

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Dan Kortschak
2019-11-26 15:16:37 +10:30
parent d566097651
commit 049d3cc4d0
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52
THIRD_PARTY_LICENSES/MT19937-64-LICENSE Normal file
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A C-program for MT19937-64 (2004/9/29 version).
Coded by Takuji Nishimura and Makoto Matsumoto.
This is a 64-bit version of Mersenne Twister pseudorandom number
generator.
Before using, initialize the state by using init_genrand64(seed)
or init_by_array64(init_key, key_length).
Copyright (C) 2004, Makoto Matsumoto and Takuji Nishimura,
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
1. Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
2. 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.
3. The names of its contributors may not 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.
References:
T. Nishimura, ``Tables of 64-bit Mersenne Twisters''
ACM Transactions on Modeling and
Computer Simulation 10. (2000) 348--357.
M. Matsumoto and T. Nishimura,
``Mersenne Twister: a 623-dimensionally equidistributed
uniform pseudorandom number generator''
ACM Transactions on Modeling and
Computer Simulation 8. (Jan. 1998) 3--30.
Any feedback is very welcome.
http://www.math.hiroshima-u.ac.jp/~m-mat/MT/emt.html
email: m-mat @ math.sci.hiroshima-u.ac.jp (remove spaces)

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THIRD_PARTY_LICENSES/MT19937-LICENSE Normal file
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A C-program for MT19937, with initialization improved 2002/1/26.
Coded by Takuji Nishimura and Makoto Matsumoto.
Before using, initialize the state by using init_genrand(seed)
or init_by_array(init_key, key_length).
Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
1. Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
2. 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.
3. The names of its contributors may not 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.
Any feedback is very welcome.
http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html
email: m-mat @ math.sci.hiroshima-u.ac.jp (remove space)

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mathext/prng/mt19937.go Normal file
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// Copyright ©2019 The Gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// Original C program copyright Takuji Nishimura and Makoto Matsumoto 2002.
// http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/CODES/mt19937ar.c
package prng
import (
"encoding/binary"
"io"
)
const (
mt19937N = 624
mt19937M = 397
mt19937matrixA = 0x9908b0df
mt19937UpperMask = 0x80000000
mt19937LowerMask = 0x7fffffff
)
// MT19937 implements the 32 bit Mersenne Twister PRNG. MT19937
// is the default PRNG for a wide variety of programming systems.
// See https://en.wikipedia.org/wiki/Mersenne_Twister.
type MT19937 struct {
mt [mt19937N]uint32
mti uint32
}
// NewMT19937 returns a new MT19937 PRNG. The returned PRNG will
// use the default seed 5489 unless the Seed method is called with
// another value.
func NewMT19937() *MT19937 {
return &MT19937{mti: mt19937N + 1}
}
// Seed uses the provided seed value to initialize the generator to a
// deterministic state. Only the lower 32 bits of seed are used to seed
// the PRNG.
func (src *MT19937) Seed(seed uint64) {
src.mt[0] = uint32(seed)
for src.mti = 1; src.mti < mt19937N; src.mti++ {
src.mt[src.mti] = (1812433253*(src.mt[src.mti-1]^(src.mt[src.mti-1]>>30)) + src.mti)
}
}
// SeedFromKeys uses the provided seed key value to initialize the
// generator to a deterministic state. It is provided for compatibility
// with C implementations.
func (src *MT19937) SeedFromKeys(keys []uint32) {
src.Seed(19650218)
i := uint32(1)
j := uint32(0)
k := uint32(mt19937N)
if k <= uint32(len(keys)) {
k = uint32(len(keys))
}
for ; k != 0; k-- {
src.mt[i] = (src.mt[i] ^ ((src.mt[i-1] ^ (src.mt[i-1] >> 30)) * 1664525)) + keys[j] + j // Non linear.
i++
j++
if i >= mt19937N {
src.mt[0] = src.mt[mt19937N-1]
i = 1
}
if j >= uint32(len(keys)) {
j = 0
}
}
for k = mt19937N - 1; k != 0; k-- {
src.mt[i] = (src.mt[i] ^ ((src.mt[i-1] ^ (src.mt[i-1] >> 30)) * 1566083941)) - i // Non linear.
i++
if i >= mt19937N {
src.mt[0] = src.mt[mt19937N-1]
i = 1
}
}
src.mt[0] = 0x80000000 // MSB is 1; assuring non-zero initial array.
}
// Uint32 returns a pseudo-random 32-bit unsigned integer as a uint32.
func (src *MT19937) Uint32() uint32 {
mag01 := [2]uint32{0x0, mt19937matrixA}
var y uint32
if src.mti >= mt19937N { // Generate mt19937N words at one time.
if src.mti == mt19937N+1 {
// If Seed() has not been called
// a default initial seed is used.
src.Seed(5489)
}
var kk int
for ; kk < mt19937N-mt19937M; kk++ {
y = (src.mt[kk] & mt19937UpperMask) | (src.mt[kk+1] & mt19937LowerMask)
src.mt[kk] = src.mt[kk+mt19937M] ^ (y >> 1) ^ mag01[y&0x1]
}
for ; kk < mt19937N-1; kk++ {
y = (src.mt[kk] & mt19937UpperMask) | (src.mt[kk+1] & mt19937LowerMask)
src.mt[kk] = src.mt[kk+(mt19937M-mt19937N)] ^ (y >> 1) ^ mag01[y&0x1]
}
y = (src.mt[mt19937N-1] & mt19937UpperMask) | (src.mt[0] & mt19937LowerMask)
src.mt[mt19937N-1] = src.mt[mt19937M-1] ^ (y >> 1) ^ mag01[y&0x1]
src.mti = 0
}
y = src.mt[src.mti]
src.mti++
// Tempering.
y ^= (y >> 11)
y ^= (y << 7) & 0x9d2c5680
y ^= (y << 15) & 0xefc60000
y ^= (y >> 18)
return y
}
// Uint64 returns a pseudo-random 64-bit unsigned integer as a uint64.
// It makes use of two calls to Uint32 placing the first result in the
// upper bits and the second result in the lower bits of the returned
// value.
func (src *MT19937) Uint64() uint64 {
h := uint64(src.Uint32())
l := uint64(src.Uint32())
return h<<32 | l
}
// MarshalBinary returns the binary representation of the current state of the generator.
func (src *MT19937) MarshalBinary() ([]byte, error) {
var buf [(mt19937N + 1) * 4]byte
for i := 0; i < mt19937N; i++ {
binary.BigEndian.PutUint32(buf[i*4:(i+1)*4], src.mt[i])
}
binary.BigEndian.PutUint32(buf[mt19937N*4:], src.mti)
return buf[:], nil
}
// UnmarshalBinary sets the state of the generator to the state represented in data.
func (src *MT19937) UnmarshalBinary(data []byte) error {
if len(data) < (mt19937N+1)*4 {
return io.ErrUnexpectedEOF
}
for i := 0; i < mt19937N; i++ {
src.mt[i] = binary.BigEndian.Uint32(data[i*4 : (i+1)*4])
}
src.mti = binary.BigEndian.Uint32(data[mt19937N*4:])
return nil
}

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mathext/prng/mt19937_64.go Normal file
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// Copyright ©2019 The Gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// Original C program copyright Takuji Nishimura and Makoto Matsumoto 2004.
// http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/VERSIONS/C-LANG/mt19937-64.c
package prng
import (
"encoding/binary"
"io"
)
const (
mt19937_64NN = 312
mt19937_64MM = 156
mt19937_64MatrixA = 0xB5026F5AA96619E9
mt19937_64UpperMask = 0xFFFFFFFF80000000
mt19937_64LowerMask = 0x7FFFFFFF
)
// MT19937_64 implements the 64 bit Mersenne Twister PRNG. MT19937_64
// is the 64 bit version of MT19937, it has the same sized state, but
// generates a different sequence.
// See https://en.wikipedia.org/wiki/Mersenne_Twister.
type MT19937_64 struct {
mt [mt19937_64NN]uint64
mti uint64
}
// NewMT19937_64 returns a new MT19937_64 PRNG. The returned PRNG will
// use the default seed 5489 unless the Seed method is called with
// another value.
func NewMT19937_64() *MT19937_64 {
return &MT19937_64{mti: mt19937_64NN + 1}
}
// Seed uses the provided seed value to initialize the generator to a
// deterministic state.
func (src *MT19937_64) Seed(seed uint64) {
src.mt[0] = seed
for src.mti = 1; src.mti < mt19937_64NN; src.mti++ {
src.mt[src.mti] = (6364136223846793005*(src.mt[src.mti-1]^(src.mt[src.mti-1]>>62)) + src.mti)
}
}
// SeedFromKeys uses the provided seed key value to initialize the
// generator to a deterministic state. It is provided for compatibility
// with C implementations.
func (src *MT19937_64) SeedFromKeys(keys []uint64) {
src.Seed(19650218)
i := uint64(1)
j := uint64(0)
k := uint64(mt19937_64NN)
if k <= uint64(len(keys)) {
k = uint64(len(keys))
}
for ; k != 0; k-- {
src.mt[i] = (src.mt[i] ^ ((src.mt[i-1] ^ (src.mt[i-1] >> 62)) * 3935559000370003845)) + keys[j] + j // Non linear.
i++
j++
if i >= mt19937_64NN {
src.mt[0] = src.mt[mt19937_64NN-1]
i = 1
}
if j >= uint64(len(keys)) {
j = 0
}
}
for k = mt19937_64NN - 1; k != 0; k-- {
src.mt[i] = (src.mt[i] ^ ((src.mt[i-1] ^ (src.mt[i-1] >> 62)) * 2862933555777941757)) - i // Non linear.
i++
if i >= mt19937_64NN {
src.mt[0] = src.mt[mt19937_64NN-1]
i = 1
}
}
src.mt[0] = 1 << 63 /* MSB is 1; assuring non-zero initial array */
}
// Uint64 returns a pseudo-random 64-bit unsigned integer as a uint64.
func (src *MT19937_64) Uint64() uint64 {
mag01 := [2]uint64{0, mt19937_64MatrixA}
var x uint64
if src.mti >= mt19937_64NN { // Generate mt19937_64NN words at one time.
if src.mti == mt19937_64NN+1 {
// If Seed() has not been called
// a default initial seed is used.
src.Seed(5489)
}
var i int
for ; i < mt19937_64NN-mt19937_64MM; i++ {
x = (src.mt[i] & mt19937_64UpperMask) | (src.mt[i+1] & mt19937_64LowerMask)
src.mt[i] = src.mt[i+mt19937_64MM] ^ (x >> 1) ^ mag01[(int)(x&0x1)]
}
for ; i < mt19937_64NN-1; i++ {
x = (src.mt[i] & mt19937_64UpperMask) | (src.mt[i+1] & mt19937_64LowerMask)
src.mt[i] = src.mt[i+(mt19937_64MM-mt19937_64NN)] ^ (x >> 1) ^ mag01[(int)(x&0x1)]
}
x = (src.mt[mt19937_64NN-1] & mt19937_64UpperMask) | (src.mt[0] & mt19937_64LowerMask)
src.mt[mt19937_64NN-1] = src.mt[mt19937_64MM-1] ^ (x >> 1) ^ mag01[(int)(x&0x1)]
src.mti = 0
}
x = src.mt[src.mti]
src.mti++
// Tempering.
x ^= (x >> 29) & 0x5555555555555555
x ^= (x << 17) & 0x71D67FFFEDA60000
x ^= (x << 37) & 0xFFF7EEE000000000
x ^= (x >> 43)
return x
}
// MarshalBinary returns the binary representation of the current state of the generator.
func (src *MT19937_64) MarshalBinary() ([]byte, error) {
var buf [(mt19937_64NN + 1) * 8]byte
for i := 0; i < mt19937_64NN; i++ {
binary.BigEndian.PutUint64(buf[i*8:(i+1)*8], src.mt[i])
}
binary.BigEndian.PutUint64(buf[mt19937_64NN*8:], src.mti)
return buf[:], nil
}
// UnmarshalBinary sets the state of the generator to the state represented in data.
func (src *MT19937_64) UnmarshalBinary(data []byte) error {
if len(data) < (mt19937_64NN+1)*8 {
return io.ErrUnexpectedEOF
}
for i := 0; i < mt19937_64NN; i++ {
src.mt[i] = binary.BigEndian.Uint64(data[i*8 : (i+1)*8])
}
src.mti = binary.BigEndian.Uint64(data[mt19937_64NN*8:])
return nil
}

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// Copyright ©2019 The Gonum 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 prng
import (
"testing"
"time"
"golang.org/x/exp/rand"
)
var _ rand.Source = (*MT19937_64)(nil)
// Random values in tests are produced by 40 iterations of the C code
// with or without an initial seed array.
func TestMT19937_64(t *testing.T) {
want := []uint64{
14514284786278117030, 4620546740167642908, 13109570281517897720, 17462938647148434322, 355488278567739596,
7469126240319926998, 4635995468481642529, 418970542659199878, 9604170989252516556, 6358044926049913402,
5058016125798318033, 10349215569089701407, 2583272014892537200, 10032373690199166667, 9627645531742285868,
15810285301089087632, 9219209713614924562, 7736011505917826031, 13729552270962724157, 4596340717661012313,
4413874586873285858, 5904155143473820934, 16795776195466785825, 3040631852046752166, 4529279813148173111,
3658352497551999605, 13205889818278417278, 17853215078830450730, 14193508720503142180, 1488787817663097441,
8484116316263611556, 4745643133208116498, 14333959900198994173, 10770733876927207790, 17529942701849009476,
8081518017574486547, 5945178879512507902, 9821139136195250096, 4728986788662773602, 840062144447779464,
}
mt := NewMT19937_64()
for i := range want {
got := mt.Uint64()
if got != want[i] {
t.Errorf("unexpected random value at iteration %d: got:%d want:%d", i, got, want[i])
}
}
}
func TestMT19937_64SeedFromKeys(t *testing.T) {
want := []uint64{
7266447313870364031, 4946485549665804864, 16945909448695747420, 16394063075524226720, 4873882236456199058,
14877448043947020171, 6740343660852211943, 13857871200353263164, 5249110015610582907, 10205081126064480383,
1235879089597390050, 17320312680810499042, 16489141110565194782, 8942268601720066061, 13520575722002588570,
14226945236717732373, 9383926873555417063, 15690281668532552105, 11510704754157191257, 15864264574919463609,
6489677788245343319, 5112602299894754389, 10828930062652518694, 15942305434158995996, 15445717675088218264,
4764500002345775851, 14673753115101942098, 236502320419669032, 13670483975188204088, 14931360615268175698,
8904234204977263924, 12836915408046564963, 12120302420213647524, 15755110976537356441, 5405758943702519480,
10951858968426898805, 17251681303478610375, 4144140664012008120, 18286145806977825275, 13075804672185204371,
}
mt := NewMT19937_64()
mt.SeedFromKeys([]uint64{0x12345, 0x23456, 0x34567, 0x45678})
for i := range want {
got := mt.Uint64()
if got != want[i] {
t.Errorf("unexpected random value at iteration %d: got:%d want:%d", i, got, want[i])
}
}
}
func TestMT19937_64RoundTrip(t *testing.T) {
var src MT19937_64
src.Seed(uint64(time.Now().Unix()))
src.Uint64() // Step PRNG once to makes sure states are mixed.
buf, err := src.MarshalBinary()
if err != nil {
t.Errorf("unexpected error marshaling state: %v", err)
}
var dst MT19937_64
// Get dst into a non-zero state.
dst.Seed(1)
for i := 0; i < 10; i++ {
dst.Uint64()
}
err = dst.UnmarshalBinary(buf)
if err != nil {
t.Errorf("unexpected error unmarshaling state: %v", err)
}
if dst != src {
t.Errorf("mismatch between generator states: got:%+v want:%+v", dst, src)
}
}

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// Copyright ©2019 The Gonum 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 prng
import (
"testing"
"time"
"golang.org/x/exp/rand"
)
var _ rand.Source = (*MT19937)(nil)
// Random values in tests are produced by 40 iterations of the C code
// with or without an initial seed array.
func TestMT19937(t *testing.T) {
want := []uint32{
3499211612, 581869302, 3890346734, 3586334585, 545404204,
4161255391, 3922919429, 949333985, 2715962298, 1323567403,
418932835, 2350294565, 1196140740, 809094426, 2348838239,
4264392720, 4112460519, 4279768804, 4144164697, 4156218106,
676943009, 3117454609, 4168664243, 4213834039, 4111000746,
471852626, 2084672536, 3427838553, 3437178460, 1275731771,
609397212, 20544909, 1811450929, 483031418, 3933054126,
2747762695, 3402504553, 3772830893, 4120988587, 2163214728,
}
mt := NewMT19937()
for i := range want {
got := mt.Uint32()
if got != want[i] {
t.Errorf("unexpected random value at iteration %d: got:%d want:%d", i, got, want[i])
}
}
}
func TestMT19937SeedFromKeys(t *testing.T) {
want := []uint32{
1067595299, 955945823, 477289528, 4107218783, 4228976476,
3344332714, 3355579695, 227628506, 810200273, 2591290167,
2560260675, 3242736208, 646746669, 1479517882, 4245472273,
1143372638, 3863670494, 3221021970, 1773610557, 1138697238,
1421897700, 1269916527, 2859934041, 1764463362, 3874892047,
3965319921, 72549643, 2383988930, 2600218693, 3237492380,
2792901476, 725331109, 605841842, 271258942, 715137098,
3297999536, 1322965544, 4229579109, 1395091102, 3735697720,
}
mt := NewMT19937()
mt.SeedFromKeys([]uint32{0x123, 0x234, 0x345, 0x456})
for i := range want {
got := mt.Uint32()
if got != want[i] {
t.Errorf("unexpected random value at iteration %d: got:%d want:%d", i, got, want[i])
}
}
}
func TestMT19937RoundTrip(t *testing.T) {
var src MT19937
src.Seed(uint64(time.Now().Unix()))
src.Uint64() // Step PRNG once to makes sure states are mixed.
buf, err := src.MarshalBinary()
if err != nil {
t.Errorf("unexpected error marshaling state: %v", err)
}
var dst MT19937
// Get dst into a non-zero state.
dst.Seed(1)
for i := 0; i < 10; i++ {
dst.Uint64()
}
err = dst.UnmarshalBinary(buf)
if err != nil {
t.Errorf("unexpected error unmarshaling state: %v", err)
}
if dst != src {
t.Errorf("mismatch between generator states: got:%+v want:%+v", dst, src)
}
}