src/math/rand/v2/pcg.go

// Copyright 2023 The Go 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 rand

import (
	"errors"
	"math/bits"
)

// https://numpy.org/devdocs/reference/random/upgrading-pcg64.html
// https://github.com/imneme/pcg-cpp/commit/871d0494ee9c9a7b7c43f753e3d8ca47c26f8005

// A PCG is a PCG generator with 128 bits of internal state.
// A zero PCG is equivalent to NewPCG(0, 0).
type PCG struct {
	hi uint64
	lo uint64
}

// NewPCG returns a new PCG seeded with the given values.
func NewPCG(seed1, seed2 uint64) *PCG {
	return &PCG{seed1, seed2}
}

// Seed resets the PCG to behave the same way as NewPCG(seed1, seed2).
func (p *PCG) Seed(seed1, seed2 uint64) {
	p.hi = seed1
	p.lo = seed2
}

// binary.bigEndian.Uint64, copied to avoid dependency
func beUint64(b []byte) uint64 {
	_ = b[7] // bounds check hint to compiler; see golang.org/issue/14808
	return uint64(b[7]) | uint64(b[6])<<8 | uint64(b[5])<<16 | uint64(b[4])<<24 |
		uint64(b[3])<<32 | uint64(b[2])<<40 | uint64(b[1])<<48 | uint64(b[0])<<56
}

// binary.bigEndian.PutUint64, copied to avoid dependency
func bePutUint64(b []byte, v uint64) {
	_ = b[7] // early bounds check to guarantee safety of writes below
	b[0] = byte(v >> 56)
	b[1] = byte(v >> 48)
	b[2] = byte(v >> 40)
	b[3] = byte(v >> 32)
	b[4] = byte(v >> 24)
	b[5] = byte(v >> 16)
	b[6] = byte(v >> 8)
	b[7] = byte(v)
}

// MarshalBinary implements the encoding.BinaryMarshaler interface.
func (p *PCG) MarshalBinary() ([]byte, error) {
	b := make([]byte, 20)
	copy(b, "pcg:")
	bePutUint64(b[4:], p.hi)
	bePutUint64(b[4+8:], p.lo)
	return b, nil
}

var errUnmarshalPCG = errors.New("invalid PCG encoding")

// UnmarshalBinary implements the encoding.BinaryUnmarshaler interface.
func (p *PCG) UnmarshalBinary(data []byte) error {
	if len(data) != 20 || string(data[:4]) != "pcg:" {
		return errUnmarshalPCG
	}
	p.hi = beUint64(data[4:])
	p.lo = beUint64(data[4+8:])
	return nil
}

func (p *PCG) next() (hi, lo uint64) {
	// https://github.com/imneme/pcg-cpp/blob/428802d1a5/include/pcg_random.hpp#L161
	//
	// Numpy's PCG multiplies by the 64-bit value cheapMul
	// instead of the 128-bit value used here and in the official PCG code.
	// This does not seem worthwhile, at least for Go: not having any high
	// bits in the multiplier reduces the effect of low bits on the highest bits,
	// and it only saves 1 multiply out of 3.
	// (On 32-bit systems, it saves 1 out of 6, since Mul64 is doing 4.)
	const (
		mulHi = 2549297995355413924
		mulLo = 4865540595714422341
		incHi = 6364136223846793005
		incLo = 1442695040888963407
	)

	// state = state * mul + inc
	hi, lo = bits.Mul64(p.lo, mulLo)
	hi += p.hi*mulLo + p.lo*mulHi
	lo, c := bits.Add64(lo, incLo, 0)
	hi, _ = bits.Add64(hi, incHi, c)
	p.lo = lo
	p.hi = hi
	return hi, lo
}

// Uint64 return a uniformly-distributed random uint64 value.
func (p *PCG) Uint64() uint64 {
	hi, lo := p.next()

	// XSL-RR would be
	//	hi, lo := p.next()
	//	return bits.RotateLeft64(lo^hi, -int(hi>>58))
	// but Numpy uses DXSM and O'Neill suggests doing the same.
	// See https://github.com/golang/go/issues/21835#issuecomment-739065688
	// and following comments.

	// DXSM "double xorshift multiply"
	// https://github.com/imneme/pcg-cpp/blob/428802d1a5/include/pcg_random.hpp#L1015

	// https://github.com/imneme/pcg-cpp/blob/428802d1a5/include/pcg_random.hpp#L176
	const cheapMul = 0xda942042e4dd58b5
	hi ^= hi >> 32
	hi *= cheapMul
	hi ^= hi >> 48
	hi *= (lo | 1)
	return hi
}