pcg.go

     1  // Copyright 2023 The Go Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package rand
     6  
     7  import (
     8  	"errors"
     9  	"internal/byteorder"
    10  	"math/bits"
    11  )
    12  
    13  // https://numpy.org/devdocs/reference/random/upgrading-pcg64.html
    14  // https://github.com/imneme/pcg-cpp/commit/871d0494ee9c9a7b7c43f753e3d8ca47c26f8005
    15  
    16  // A PCG is a PCG generator with 128 bits of internal state.
    17  // A zero PCG is equivalent to NewPCG(0, 0).
    18  type PCG struct {
    19  	hi uint64
    20  	lo uint64
    21  }
    22  
    23  // NewPCG returns a new PCG seeded with the given values.
    24  func NewPCG(seed1, seed2 uint64) *PCG {
    25  	return &PCG{seed1, seed2}
    26  }
    27  
    28  // Seed resets the PCG to behave the same way as NewPCG(seed1, seed2).
    29  func (p *PCG) Seed(seed1, seed2 uint64) {
    30  	p.hi = seed1
    31  	p.lo = seed2
    32  }
    33  
    34  // MarshalBinary implements the encoding.BinaryMarshaler interface.
    35  func (p *PCG) MarshalBinary() ([]byte, error) {
    36  	b := make([]byte, 20)
    37  	copy(b, "pcg:")
    38  	byteorder.BePutUint64(b[4:], p.hi)
    39  	byteorder.BePutUint64(b[4+8:], p.lo)
    40  	return b, nil
    41  }
    42  
    43  var errUnmarshalPCG = errors.New("invalid PCG encoding")
    44  
    45  // UnmarshalBinary implements the encoding.BinaryUnmarshaler interface.
    46  func (p *PCG) UnmarshalBinary(data []byte) error {
    47  	if len(data) != 20 || string(data[:4]) != "pcg:" {
    48  		return errUnmarshalPCG
    49  	}
    50  	p.hi = byteorder.BeUint64(data[4:])
    51  	p.lo = byteorder.BeUint64(data[4+8:])
    52  	return nil
    53  }
    54  
    55  func (p *PCG) next() (hi, lo uint64) {
    56  	// https://github.com/imneme/pcg-cpp/blob/428802d1a5/include/pcg_random.hpp#L161
    57  	//
    58  	// Numpy's PCG multiplies by the 64-bit value cheapMul
    59  	// instead of the 128-bit value used here and in the official PCG code.
    60  	// This does not seem worthwhile, at least for Go: not having any high
    61  	// bits in the multiplier reduces the effect of low bits on the highest bits,
    62  	// and it only saves 1 multiply out of 3.
    63  	// (On 32-bit systems, it saves 1 out of 6, since Mul64 is doing 4.)
    64  	const (
    65  		mulHi = 2549297995355413924
    66  		mulLo = 4865540595714422341
    67  		incHi = 6364136223846793005
    68  		incLo = 1442695040888963407
    69  	)
    70  
    71  	// state = state * mul + inc
    72  	hi, lo = bits.Mul64(p.lo, mulLo)
    73  	hi += p.hi*mulLo + p.lo*mulHi
    74  	lo, c := bits.Add64(lo, incLo, 0)
    75  	hi, _ = bits.Add64(hi, incHi, c)
    76  	p.lo = lo
    77  	p.hi = hi
    78  	return hi, lo
    79  }
    80  
    81  // Uint64 return a uniformly-distributed random uint64 value.
    82  func (p *PCG) Uint64() uint64 {
    83  	hi, lo := p.next()
    84  
    85  	// XSL-RR would be
    86  	//	hi, lo := p.next()
    87  	//	return bits.RotateLeft64(lo^hi, -int(hi>>58))
    88  	// but Numpy uses DXSM and O'Neill suggests doing the same.
    89  	// See https://github.com/golang/go/issues/21835#issuecomment-739065688
    90  	// and following comments.
    91  
    92  	// DXSM "double xorshift multiply"
    93  	// https://github.com/imneme/pcg-cpp/blob/428802d1a5/include/pcg_random.hpp#L1015
    94  
    95  	// https://github.com/imneme/pcg-cpp/blob/428802d1a5/include/pcg_random.hpp#L176
    96  	const cheapMul = 0xda942042e4dd58b5
    97  	hi ^= hi >> 32
    98  	hi *= cheapMul
    99  	hi ^= hi >> 48
   100  	hi *= (lo | 1)
   101  	return hi
   102  }
   103
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