go/src/math/rand/v2/rand.go

// Copyright 2009 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 implements pseudo-random number generators suitable for tasks
// such as simulation, but it should not be used for security-sensitive work.
//
// Random numbers are generated by a [Source], usually wrapped in a [Rand].
// Both types should be used by a single goroutine at a time: sharing among
// multiple goroutines requires some kind of synchronization.
//
// Top-level functions, such as [Float64] and [Int],
// are safe for concurrent use by multiple goroutines.
//
// This package's outputs might be easily predictable regardless of how it's
// seeded. For random numbers suitable for security-sensitive work, see the
// crypto/rand package.
package rand

import (
	"math/bits"
	_ "unsafe" // for go:linkname
)

// A Source is a source of uniformly-distributed
// pseudo-random uint64 values in the range [0, 1<<64).
//
// A Source is not safe for concurrent use by multiple goroutines.
type Source interface {
	Uint64() uint64
}

// NewSource returns a new pseudo-random Source seeded with the given value.
// Unlike the default Source used by top-level functions, this source is not
// safe for concurrent use by multiple goroutines.
// The returned Source implements Source64.
func NewSource(seed int64) Source {
	return newSource(seed)
}

func newSource(seed int64) *rngSource {
	var rng rngSource
	rng.Seed(seed)
	return &rng
}

// A Rand is a source of random numbers.
type Rand struct {
	src Source
}

// New returns a new Rand that uses random values from src
// to generate other random values.
func New(src Source) *Rand {
	return &Rand{src: src}
}

// Int64 returns a non-negative pseudo-random 63-bit integer as an int64.
func (r *Rand) Int64() int64 { return int64(r.src.Uint64() &^ (1 << 63)) }

// Uint32 returns a pseudo-random 32-bit value as a uint32.
func (r *Rand) Uint32() uint32 { return uint32(r.src.Uint64() >> 32) }

// Uint64 returns a pseudo-random 64-bit value as a uint64.
func (r *Rand) Uint64() uint64 { return r.src.Uint64() }

// Int32 returns a non-negative pseudo-random 31-bit integer as an int32.
func (r *Rand) Int32() int32 { return int32(r.src.Uint64() >> 33) }

// Int returns a non-negative pseudo-random int.
func (r *Rand) Int() int { return int(uint(r.src.Uint64()) << 1 >> 1) }

// Int64N returns, as an int64, a non-negative pseudo-random number in the half-open interval [0,n).
// It panics if n <= 0.
func (r *Rand) Int64N(n int64) int64 {
	if n <= 0 {
		panic("invalid argument to Int64N")
	}
	return int64(r.uint64n(uint64(n)))
}

// Uint64N returns, as a uint64, a non-negative pseudo-random number in the half-open interval [0,n).
// It panics if n == 0.
func (r *Rand) Uint64N(n uint64) uint64 {
	if n == 0 {
		panic("invalid argument to Uint64N")
	}
	return r.uint64n(n)
}

// uint64n is the no-bounds-checks version of Uint64N.
func (r *Rand) uint64n(n uint64) uint64 {
	if is32bit && uint64(uint32(n)) == n {
		return uint64(r.uint32n(uint32(n)))
	}
	if n&(n-1) == 0 { // n is power of two, can mask
		return r.Uint64() & (n - 1)
	}

	// Suppose we have a uint64 x uniform in the range [0,2⁶⁴)
	// and want to reduce it to the range [0,n) preserving exact uniformity.
	// We can simulate a scaling arbitrary precision x * (n/2⁶⁴) by
	// the high bits of a double-width multiply of x*n, meaning (x*n)/2⁶⁴.
	// Since there are 2⁶⁴ possible inputs x and only n possible outputs,
	// the output is necessarily biased if n does not divide 2⁶⁴.
	// In general (x*n)/2⁶⁴ = k for x*n in [k*2⁶⁴,(k+1)*2⁶⁴).
	// There are either floor(2⁶⁴/n) or ceil(2⁶⁴/n) possible products
	// in that range, depending on k.
	// But suppose we reject the sample and try again when
	// x*n is in [k*2⁶⁴, k*2⁶⁴+(2⁶⁴%n)), meaning rejecting fewer than n possible
	// outcomes out of the 2⁶⁴.
	// Now there are exactly floor(2⁶⁴/n) possible ways to produce
	// each output value k, so we've restored uniformity.
	// To get valid uint64 math, 2⁶⁴ % n = (2⁶⁴ - n) % n = -n % n,
	// so the direct implementation of this algorithm would be:
	//
	//	hi, lo := bits.Mul64(r.Uint64(), n)
	//	thresh := -n % n
	//	for lo < thresh {
	//		hi, lo = bits.Mul64(r.Uint64(), n)
	//	}
	//
	// That still leaves an expensive 64-bit division that we would rather avoid.
	// We know that thresh < n, and n is usually much less than 2⁶⁴, so we can
	// avoid the last four lines unless lo < n.
	//
	// See also:
	// https://lemire.me/blog/2016/06/27/a-fast-alternative-to-the-modulo-reduction
	// https://lemire.me/blog/2016/06/30/fast-random-shuffling
	hi, lo := bits.Mul64(r.Uint64(), n)
	if lo < n {
		thresh := -n % n
		for lo < thresh {
			hi, lo = bits.Mul64(r.Uint64(), n)
		}
	}
	return hi
}

// uint32n is an identical computation to uint64n
// but optimized for 32-bit systems.
func (r *Rand) uint32n(n uint32) uint32 {
	if n&(n-1) == 0 { // n is power of two, can mask
		return uint32(r.Uint64()) & (n - 1)
	}
	// On 64-bit systems we still use the uint64 code below because
	// the probability of a random uint64 lo being < a uint32 n is near zero,
	// meaning the unbiasing loop almost never runs.
	// On 32-bit systems, here we need to implement that same logic in 32-bit math,
	// both to preserve the exact output sequence observed on 64-bit machines
	// and to preserve the optimization that the unbiasing loop almost never runs.
	//
	// We want to compute
	// 	hi, lo := bits.Mul64(r.Uint64(), n)
	// In terms of 32-bit halves, this is:
	// 	x1:x0 := r.Uint64()
	// 	0:hi, lo1:lo0 := bits.Mul64(x1:x0, 0:n)
	// Writing out the multiplication in terms of bits.Mul32 allows
	// using direct hardware instructions and avoiding
	// the computations involving these zeros.
	x := r.Uint64()
	lo1a, lo0 := bits.Mul32(uint32(x), n)
	hi, lo1b := bits.Mul32(uint32(x>>32), n)
	lo1, c := bits.Add32(lo1a, lo1b, 0)
	hi += c
	if lo1 == 0 && lo0 < uint32(n) {
		n64 := uint64(n)
		thresh := uint32(-n64 % n64)
		for lo1 == 0 && lo0 < thresh {
			x := r.Uint64()
			lo1a, lo0 = bits.Mul32(uint32(x), n)
			hi, lo1b = bits.Mul32(uint32(x>>32), n)
			lo1, c = bits.Add32(lo1a, lo1b, 0)
			hi += c
		}
	}
	return hi
}

// Int32N returns, as an int32, a non-negative pseudo-random number in the half-open interval [0,n).
// It panics if n <= 0.
func (r *Rand) Int32N(n int32) int32 {
	if n <= 0 {
		panic("invalid argument to Int32N")
	}
	return int32(r.uint64n(uint64(n)))
}

// Uint32N returns, as a uint32, a non-negative pseudo-random number in the half-open interval [0,n).
// It panics if n == 0.
func (r *Rand) Uint32N(n uint32) uint32 {
	if n == 0 {
		panic("invalid argument to Uint32N")
	}
	return uint32(r.uint64n(uint64(n)))
}

const is32bit = ^uint(0)>>32 == 0

// IntN returns, as an int, a non-negative pseudo-random number in the half-open interval [0,n).
// It panics if n <= 0.
func (r *Rand) IntN(n int) int {
	if n <= 0 {
		panic("invalid argument to IntN")
	}
	return int(r.uint64n(uint64(n)))
}

// UintN returns, as a uint, a non-negative pseudo-random number in the half-open interval [0,n).
// It panics if n == 0.
func (r *Rand) UintN(n uint) uint {
	if n == 0 {
		panic("invalid argument to UintN")
	}
	return uint(r.uint64n(uint64(n)))
}

// Float64 returns, as a float64, a pseudo-random number in the half-open interval [0.0,1.0).
func (r *Rand) Float64() float64 {
	// A clearer, simpler implementation would be:
	//	return float64(r.Int64N(1<<53)) / (1<<53)
	// However, Go 1 shipped with
	//	return float64(r.Int64()) / (1 << 63)
	// and we want to preserve that value stream.
	//
	// There is one bug in the value stream: r.Int64() may be so close
	// to 1<<63 that the division rounds up to 1.0, and we've guaranteed
	// that the result is always less than 1.0.
	//
	// We tried to fix this by mapping 1.0 back to 0.0, but since float64
	// values near 0 are much denser than near 1, mapping 1 to 0 caused
	// a theoretically significant overshoot in the probability of returning 0.
	// Instead of that, if we round up to 1, just try again.
	// Getting 1 only happens 1/2⁵³ of the time, so most clients
	// will not observe it anyway.
again:
	f := float64(r.Int64()) / (1 << 63)
	if f == 1 {
		goto again // resample; this branch is taken O(never)
	}
	return f
}

// Float32 returns, as a float32, a pseudo-random number in the half-open interval [0.0,1.0).
func (r *Rand) Float32() float32 {
	// Same rationale as in Float64: we want to preserve the Go 1 value
	// stream except we want to fix it not to return 1.0
	// This only happens 1/2²⁴ of the time (plus the 1/2⁵³ of the time in Float64).
again:
	f := float32(r.Float64())
	if f == 1 {
		goto again // resample; this branch is taken O(very rarely)
	}
	return f
}

// Perm returns, as a slice of n ints, a pseudo-random permutation of the integers
// in the half-open interval [0,n).
func (r *Rand) Perm(n int) []int {
	m := make([]int, n)
	// In the following loop, the iteration when i=0 always swaps m[0] with m[0].
	// A change to remove this useless iteration is to assign 1 to i in the init
	// statement. But Perm also effects r. Making this change will affect
	// the final state of r. So this change can't be made for compatibility
	// reasons for Go 1.
	for i := 0; i < n; i++ {
		j := r.IntN(i + 1)
		m[i] = m[j]
		m[j] = i
	}
	return m
}

// Shuffle pseudo-randomizes the order of elements.
// n is the number of elements. Shuffle panics if n < 0.
// swap swaps the elements with indexes i and j.
func (r *Rand) Shuffle(n int, swap func(i, j int)) {
	if n < 0 {
		panic("invalid argument to Shuffle")
	}

	// Fisher-Yates shuffle: https://en.wikipedia.org/wiki/Fisher%E2%80%93Yates_shuffle
	// Shuffle really ought not be called with n that doesn't fit in 32 bits.
	// Not only will it take a very long time, but with 2³¹! possible permutations,
	// there's no way that any PRNG can have a big enough internal state to
	// generate even a minuscule percentage of the possible permutations.
	// Nevertheless, the right API signature accepts an int n, so handle it as best we can.
	for i := n - 1; i > 0; i-- {
		j := int(r.uint64n(uint64(i + 1)))
		swap(i, j)
	}
}

/*
 * Top-level convenience functions
 */

// globalRand is the source of random numbers for the top-level
// convenience functions.
var globalRand = &Rand{src: &fastSource{}}

//go:linkname fastrand64
func fastrand64() uint64

// fastSource is a Source that uses the runtime fastrand functions.
type fastSource struct{}

func (*fastSource) Int64() int64 {
	return int64(fastrand64() & rngMask)
}

func (*fastSource) Uint64() uint64 {
	return fastrand64()
}

// Int64 returns a non-negative pseudo-random 63-bit integer as an int64
// from the default Source.
func Int64() int64 { return globalRand.Int64() }

// Uint32 returns a pseudo-random 32-bit value as a uint32
// from the default Source.
func Uint32() uint32 { return globalRand.Uint32() }

// Uint64N returns, as a uint64, a pseudo-random number in the half-open interval [0,n)
// from the default Source.
// It panics if n <= 0.
func Uint64N(n uint64) uint64 { return globalRand.Uint64N(n) }

// Uint32N returns, as a uint32, a pseudo-random number in the half-open interval [0,n)
// from the default Source.
// It panics if n <= 0.
func Uint32N(n uint32) uint32 { return globalRand.Uint32N(n) }

// Uint64 returns a pseudo-random 64-bit value as a uint64
// from the default Source.
func Uint64() uint64 { return globalRand.Uint64() }

// Int32 returns a non-negative pseudo-random 31-bit integer as an int32
// from the default Source.
func Int32() int32 { return globalRand.Int32() }

// Int returns a non-negative pseudo-random int from the default Source.
func Int() int { return globalRand.Int() }

// Int64N returns, as an int64, a pseudo-random number in the half-open interval [0,n)
// from the default Source.
// It panics if n <= 0.
func Int64N(n int64) int64 { return globalRand.Int64N(n) }

// Int32N returns, as an int32, a pseudo-random number in the half-open interval [0,n)
// from the default Source.
// It panics if n <= 0.
func Int32N(n int32) int32 { return globalRand.Int32N(n) }

// IntN returns, as an int, a pseudo-random number in the half-open interval [0,n)
// from the default Source.
// It panics if n <= 0.
func IntN(n int) int { return globalRand.IntN(n) }

// UintN returns, as a uint, a pseudo-random number in the half-open interval [0,n)
// from the default Source.
// It panics if n <= 0.
func UintN(n uint) uint { return globalRand.UintN(n) }

// N returns a pseudo-random number in the half-open interval [0,n) from the default Source.
// The type parameter Int can be any integer type.
// It panics if n <= 0.
func N[Int intType](n Int) Int {
	if n <= 0 {
		panic("invalid argument to N")
	}
	return Int(globalRand.uint64n(uint64(n)))
}

type intType interface {
	~int | ~int8 | ~int16 | ~int32 | ~int64 |
		~uint | ~uint8 | ~uint16 | ~uint32 | ~uint64 | ~uintptr
}

// Float64 returns, as a float64, a pseudo-random number in the half-open interval [0.0,1.0)
// from the default Source.
func Float64() float64 { return globalRand.Float64() }

// Float32 returns, as a float32, a pseudo-random number in the half-open interval [0.0,1.0)
// from the default Source.
func Float32() float32 { return globalRand.Float32() }

// Perm returns, as a slice of n ints, a pseudo-random permutation of the integers
// in the half-open interval [0,n) from the default Source.
func Perm(n int) []int { return globalRand.Perm(n) }

// Shuffle pseudo-randomizes the order of elements using the default Source.
// n is the number of elements. Shuffle panics if n < 0.
// swap swaps the elements with indexes i and j.
func Shuffle(n int, swap func(i, j int)) { globalRand.Shuffle(n, swap) }

// NormFloat64 returns a normally distributed float64 in the range
// [-math.MaxFloat64, +math.MaxFloat64] with
// standard normal distribution (mean = 0, stddev = 1)
// from the default Source.
// To produce a different normal distribution, callers can
// adjust the output using:
//
//	sample = NormFloat64() * desiredStdDev + desiredMean
func NormFloat64() float64 { return globalRand.NormFloat64() }

// ExpFloat64 returns an exponentially distributed float64 in the range
// (0, +math.MaxFloat64] with an exponential distribution whose rate parameter
// (lambda) is 1 and whose mean is 1/lambda (1) from the default Source.
// To produce a distribution with a different rate parameter,
// callers can adjust the output using:
//
//	sample = ExpFloat64() / desiredRateParameter
func ExpFloat64() float64 { return globalRand.ExpFloat64() }