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matterbridge/vendor/modernc.org/mathutil/rnd.go

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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 "modernc.org/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
}