src/math/rand/rand.go - go - Git at Google

 // 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 (
 	"internal/godebug"
 	"sync"
 	"sync/atomic"
 	_ "unsafe" // for go:linkname
 )

 // A Source represents a source of uniformly-distributed
 // pseudo-random int64 values in the range [0, 1<<63).
 //
 // A Source is not safe for concurrent use by multiple goroutines.
 type Source interface {
 	Int63() int64
 	Seed(seed int64)
 }

 // A Source64 is a Source that can also generate
 // uniformly-distributed pseudo-random uint64 values in
 // the range [0, 1<<64) directly.
 // If a Rand r's underlying Source s implements Source64,
 // then r.Uint64 returns the result of one call to s.Uint64
 // instead of making two calls to s.Int63.
 type Source64 interface {
 	Source
 	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
 	s64 Source64 // non-nil if src is source64

 	// readVal contains remainder of 63-bit integer used for bytes
 	// generation during most recent Read call.
 	// It is saved so next Read call can start where the previous
 	// one finished.
 	readVal int64
 	// readPos indicates the number of low-order bytes of readVal
 	// that are still valid.
 	readPos int8
 }

 // New returns a new Rand that uses random values from src
 // to generate other random values.
 func New(src Source) *Rand {
 	s64, _ := src.(Source64)
 	return &Rand{src: src, s64: s64}
 }

 // Seed uses the provided seed value to initialize the generator to a deterministic state.
 // Seed should not be called concurrently with any other Rand method.
 func (r *Rand) Seed(seed int64) {
 	if lk, ok := r.src.(*lockedSource); ok {
 		lk.seedPos(seed, &r.readPos)
 		return
 	}

 	r.src.Seed(seed)
 	r.readPos = 0
 }

 // Int63 returns a non-negative pseudo-random 63-bit integer as an int64.
 func (r *Rand) Int63() int64 { return r.src.Int63() }

 // Uint32 returns a pseudo-random 32-bit value as a uint32.
 func (r *Rand) Uint32() uint32 { return uint32(r.Int63() >> 31) }

 // Uint64 returns a pseudo-random 64-bit value as a uint64.
 func (r *Rand) Uint64() uint64 {
 	if r.s64 != nil {
 		return r.s64.Uint64()
 	}
 	return uint64(r.Int63())>>31 | uint64(r.Int63())<<32
 }

 // Int31 returns a non-negative pseudo-random 31-bit integer as an int32.
 func (r *Rand) Int31() int32 { return int32(r.Int63() >> 32) }

 // Int returns a non-negative pseudo-random int.
 func (r *Rand) Int() int {
 	u := uint(r.Int63())
 	return int(u << 1 >> 1) // clear sign bit if int == int32
 }

 // Int63n 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) Int63n(n int64) int64 {
 	if n <= 0 {
 		panic("invalid argument to Int63n")
 	}
 	if n&(n-1) == 0 { // n is power of two, can mask
 		return r.Int63() & (n - 1)
 	}
 	max := int64((1 << 63) - 1 - (1<<63)%uint64(n))
 	v := r.Int63()
 	for v > max {
 		v = r.Int63()
 	}
 	return v % n
 }

 // Int31n 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) Int31n(n int32) int32 {
 	if n <= 0 {
 		panic("invalid argument to Int31n")
 	}
 	if n&(n-1) == 0 { // n is power of two, can mask
 		return r.Int31() & (n - 1)
 	}
 	max := int32((1 << 31) - 1 - (1<<31)%uint32(n))
 	v := r.Int31()
 	for v > max {
 		v = r.Int31()
 	}
 	return v % n
 }

 // int31n returns, as an int32, a non-negative pseudo-random number in the half-open interval [0,n).
 // n must be > 0, but int31n does not check this; the caller must ensure it.
 // int31n exists because Int31n is inefficient, but Go 1 compatibility
 // requires that the stream of values produced by math/rand remain unchanged.
 // int31n can thus only be used internally, by newly introduced APIs.
 //
 // For implementation details, see:
 // https://lemire.me/blog/2016/06/27/a-fast-alternative-to-the-modulo-reduction
 // https://lemire.me/blog/2016/06/30/fast-random-shuffling
 func (r *Rand) int31n(n int32) int32 {
 	v := r.Uint32()
 	prod := uint64(v) * uint64(n)
 	low := uint32(prod)
 	if low < uint32(n) {
 		thresh := uint32(-n) % uint32(n)
 		for low < thresh {
 			v = r.Uint32()
 			prod = uint64(v) * uint64(n)
 			low = uint32(prod)
 		}
 	}
 	return int32(prod >> 32)
 }

 // 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")
 	}
 	if n <= 1<<31-1 {
 		return int(r.Int31n(int32(n)))
 	}
 	return int(r.Int63n(int64(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.Int63n(1<<53)) / (1<<53)
 	// However, Go 1 shipped with
 	//	return float64(r.Int63()) / (1 << 63)
 	// and we want to preserve that value stream.
 	//
 	// There is one bug in the value stream: r.Int63() 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.Int63()) / (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.
 	i := n - 1
 	for ; i > 1<<31-1-1; i-- {
 		j := int(r.Int63n(int64(i + 1)))
 		swap(i, j)
 	}
 	for ; i > 0; i-- {
 		j := int(r.int31n(int32(i + 1)))
 		swap(i, j)
 	}
 }

 // Read generates len(p) random bytes and writes them into p. It
 // always returns len(p) and a nil error.
 // Read should not be called concurrently with any other Rand method.
 func (r *Rand) Read(p []byte) (n int, err error) {
 	switch src := r.src.(type) {
 	case *lockedSource:
 		return src.read(p, &r.readVal, &r.readPos)
 	case *fastSource:
 		return src.read(p, &r.readVal, &r.readPos)
 	}
 	return read(p, r.src, &r.readVal, &r.readPos)
 }

 func read(p []byte, src Source, readVal *int64, readPos *int8) (n int, err error) {
 	pos := *readPos
 	val := *readVal
 	rng, _ := src.(*rngSource)
 	for n = 0; n < len(p); n++ {
 		if pos == 0 {
 			if rng != nil {
 				val = rng.Int63()
 			} else {
 				val = src.Int63()
 			}
 			pos = 7
 		}
 		p[n] = byte(val)
 		val >>= 8
 		pos--
 	}
 	*readPos = pos
 	*readVal = val
 	return
 }

 /*
  * Top-level convenience functions
  */

 // globalRandGenerator is the source of random numbers for the top-level
 // convenience functions. When possible it uses the runtime fastrand64
 // function to avoid locking. This is not possible if the user called Seed,
 // either explicitly or implicitly via GODEBUG=randautoseed=0.
 var globalRandGenerator atomic.Pointer[Rand]

 var randautoseed = godebug.New("randautoseed")

 // globalRand returns the generator to use for the top-level convenience
 // functions.
 func globalRand() *Rand {
 	if r := globalRandGenerator.Load(); r != nil {
 		return r
 	}

 	// This is the first call. Initialize based on GODEBUG.
 	var r *Rand
 	if randautoseed.Value() == "0" {
 		randautoseed.IncNonDefault()
 		r = New(new(lockedSource))
 		r.Seed(1)
 	} else {
 		r = &Rand{
 			src: &fastSource{},
 			s64: &fastSource{},
 		}
 	}

 	if !globalRandGenerator.CompareAndSwap(nil, r) {
 		// Two different goroutines called some top-level
 		// function at the same time. While the results in
 		// that case are unpredictable, if we just use r here,
 		// and we are using a seed, we will most likely return
 		// the same value for both calls. That doesn't seem ideal.
 		// Just use the first one to get in.
 		return globalRandGenerator.Load()
 	}

 	return r
 }

 //go:linkname fastrand64
 func fastrand64() uint64

 // fastSource is an implementation of Source64 that uses the runtime
 // fastrand functions.
 type fastSource struct {
 	// The mutex is used to avoid race conditions in Read.
 	mu sync.Mutex
 }

 func (*fastSource) Int63() int64 {
 	return int64(fastrand64() & rngMask)
 }

 func (*fastSource) Seed(int64) {
 	panic("internal error: call to fastSource.Seed")
 }

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

 func (fs *fastSource) read(p []byte, readVal *int64, readPos *int8) (n int, err error) {
 	fs.mu.Lock()
 	n, err = read(p, fs, readVal, readPos)
 	fs.mu.Unlock()
 	return
 }

 // Seed uses the provided seed value to initialize the default Source to a
 // deterministic state. Seed values that have the same remainder when
 // divided by 2³¹-1 generate the same pseudo-random sequence.
 // Seed, unlike the Rand.Seed method, is safe for concurrent use.
 //
 // If Seed is not called, the generator is seeded randomly at program startup.
 //
 // Prior to Go 1.20, the generator was seeded like Seed(1) at program startup.
 // To force the old behavior, call Seed(1) at program startup.
 // Alternately, set GODEBUG=randautoseed=0 in the environment
 // before making any calls to functions in this package.
 //
 // Deprecated: As of Go 1.20 there is no reason to call Seed with
 // a random value. Programs that call Seed with a known value to get
 // a specific sequence of results should use New(NewSource(seed)) to
 // obtain a local random generator.
 func Seed(seed int64) {
 	orig := globalRandGenerator.Load()

 	// If we are already using a lockedSource, we can just re-seed it.
 	if orig != nil {
 		if _, ok := orig.src.(*lockedSource); ok {
 			orig.Seed(seed)
 			return
 		}
 	}

 	// Otherwise either
 	// 1) orig == nil, which is the normal case when Seed is the first
 	// top-level function to be called, or
 	// 2) orig is already a fastSource, in which case we need to change
 	// to a lockedSource.
 	// Either way we do the same thing.

 	r := New(new(lockedSource))
 	r.Seed(seed)

 	if !globalRandGenerator.CompareAndSwap(orig, r) {
 		// Something changed underfoot. Retry to be safe.
 		Seed(seed)
 	}
 }

 // Int63 returns a non-negative pseudo-random 63-bit integer as an int64
 // from the default Source.
 func Int63() int64 { return globalRand().Int63() }

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

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

 // Int31 returns a non-negative pseudo-random 31-bit integer as an int32
 // from the default Source.
 func Int31() int32 { return globalRand().Int31() }

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

 // Int63n returns, as an int64, a non-negative pseudo-random number in the half-open interval [0,n)
 // from the default Source.
 // It panics if n <= 0.
 func Int63n(n int64) int64 { return globalRand().Int63n(n) }

 // Int31n returns, as an int32, a non-negative pseudo-random number in the half-open interval [0,n)
 // from the default Source.
 // It panics if n <= 0.
 func Int31n(n int32) int32 { return globalRand().Int31n(n) }

 // Intn returns, as an int, a non-negative 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) }

 // 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) }

 // Read generates len(p) random bytes from the default Source and
 // writes them into p. It always returns len(p) and a nil error.
 // Read, unlike the Rand.Read method, is safe for concurrent use.
 //
 // Deprecated: For almost all use cases, crypto/rand.Read is more appropriate.
 func Read(p []byte) (n int, err error) { return globalRand().Read(p) }

 // 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() }

 type lockedSource struct {
 	lk sync.Mutex
 	s  *rngSource
 }

 func (r *lockedSource) Int63() (n int64) {
 	r.lk.Lock()
 	n = r.s.Int63()
 	r.lk.Unlock()
 	return
 }

 func (r *lockedSource) Uint64() (n uint64) {
 	r.lk.Lock()
 	n = r.s.Uint64()
 	r.lk.Unlock()
 	return
 }

 func (r *lockedSource) Seed(seed int64) {
 	r.lk.Lock()
 	r.seed(seed)
 	r.lk.Unlock()
 }

 // seedPos implements Seed for a lockedSource without a race condition.
 func (r *lockedSource) seedPos(seed int64, readPos *int8) {
 	r.lk.Lock()
 	r.seed(seed)
 	*readPos = 0
 	r.lk.Unlock()
 }

 // seed seeds the underlying source.
 // The caller must have locked r.lk.
 func (r *lockedSource) seed(seed int64) {
 	if r.s == nil {
 		r.s = newSource(seed)
 	} else {
 		r.s.Seed(seed)
 	}
 }

 // read implements Read for a lockedSource without a race condition.
 func (r *lockedSource) read(p []byte, readVal *int64, readPos *int8) (n int, err error) {
 	r.lk.Lock()
 	n, err = read(p, r.s, readVal, readPos)
 	r.lk.Unlock()
 	return
 }
	// 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 (
	"internal/godebug"
	"sync"
	"sync/atomic"
	_ "unsafe" // for go:linkname
	)

	// A Source represents a source of uniformly-distributed
	// pseudo-random int64 values in the range [0, 1<<63).
	//
	// A Source is not safe for concurrent use by multiple goroutines.
	type Source interface {
	Int63() int64
	Seed(seed int64)
	}

	// A Source64 is a Source that can also generate
	// uniformly-distributed pseudo-random uint64 values in
	// the range [0, 1<<64) directly.
	// If a Rand r's underlying Source s implements Source64,
	// then r.Uint64 returns the result of one call to s.Uint64
	// instead of making two calls to s.Int63.
	type Source64 interface {
	Source
	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
	s64 Source64 // non-nil if src is source64

	// readVal contains remainder of 63-bit integer used for bytes
	// generation during most recent Read call.
	// It is saved so next Read call can start where the previous
	// one finished.
	readVal int64
	// readPos indicates the number of low-order bytes of readVal
	// that are still valid.
	readPos int8
	}

	// New returns a new Rand that uses random values from src
	// to generate other random values.
	func New(src Source) *Rand {
	s64, _ := src.(Source64)
	return &Rand{src: src, s64: s64}
	}

	// Seed uses the provided seed value to initialize the generator to a deterministic state.
	// Seed should not be called concurrently with any other Rand method.
	func (r *Rand) Seed(seed int64) {
	if lk, ok := r.src.(*lockedSource); ok {
	lk.seedPos(seed, &r.readPos)
	return
	}

	r.src.Seed(seed)
	r.readPos = 0
	}

	// Int63 returns a non-negative pseudo-random 63-bit integer as an int64.
	func (r *Rand) Int63() int64 { return r.src.Int63() }

	// Uint32 returns a pseudo-random 32-bit value as a uint32.
	func (r *Rand) Uint32() uint32 { return uint32(r.Int63() >> 31) }

	// Uint64 returns a pseudo-random 64-bit value as a uint64.
	func (r *Rand) Uint64() uint64 {
	if r.s64 != nil {
	return r.s64.Uint64()
	}
	return uint64(r.Int63())>>31 \| uint64(r.Int63())<<32
	}

	// Int31 returns a non-negative pseudo-random 31-bit integer as an int32.
	func (r *Rand) Int31() int32 { return int32(r.Int63() >> 32) }

	// Int returns a non-negative pseudo-random int.
	func (r *Rand) Int() int {
	u := uint(r.Int63())
	return int(u << 1 >> 1) // clear sign bit if int == int32
	}

	// Int63n 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) Int63n(n int64) int64 {
	if n <= 0 {
	panic("invalid argument to Int63n")
	}
	if n&(n-1) == 0 { // n is power of two, can mask
	return r.Int63() & (n - 1)
	}
	max := int64((1 << 63) - 1 - (1<<63)%uint64(n))
	v := r.Int63()
	for v > max {
	v = r.Int63()
	}
	return v % n
	}

	// Int31n 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) Int31n(n int32) int32 {
	if n <= 0 {
	panic("invalid argument to Int31n")
	}
	if n&(n-1) == 0 { // n is power of two, can mask
	return r.Int31() & (n - 1)
	}
	max := int32((1 << 31) - 1 - (1<<31)%uint32(n))
	v := r.Int31()
	for v > max {
	v = r.Int31()
	}
	return v % n
	}

	// int31n returns, as an int32, a non-negative pseudo-random number in the half-open interval [0,n).
	// n must be > 0, but int31n does not check this; the caller must ensure it.
	// int31n exists because Int31n is inefficient, but Go 1 compatibility
	// requires that the stream of values produced by math/rand remain unchanged.
	// int31n can thus only be used internally, by newly introduced APIs.
	//
	// For implementation details, see:
	// https://lemire.me/blog/2016/06/27/a-fast-alternative-to-the-modulo-reduction
	// https://lemire.me/blog/2016/06/30/fast-random-shuffling
	func (r *Rand) int31n(n int32) int32 {
	v := r.Uint32()
	prod := uint64(v) * uint64(n)
	low := uint32(prod)
	if low < uint32(n) {
	thresh := uint32(-n) % uint32(n)
	for low < thresh {
	v = r.Uint32()
	prod = uint64(v) * uint64(n)
	low = uint32(prod)
	}
	}
	return int32(prod >> 32)
	}

	// 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")
	}
	if n <= 1<<31-1 {
	return int(r.Int31n(int32(n)))
	}
	return int(r.Int63n(int64(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.Int63n(1<<53)) / (1<<53)
	// However, Go 1 shipped with
	// return float64(r.Int63()) / (1 << 63)
	// and we want to preserve that value stream.
	//
	// There is one bug in the value stream: r.Int63() 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.Int63()) / (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.
	i := n - 1
	for ; i > 1<<31-1-1; i-- {
	j := int(r.Int63n(int64(i + 1)))
	swap(i, j)
	}
	for ; i > 0; i-- {
	j := int(r.int31n(int32(i + 1)))
	swap(i, j)
	}
	}

	// Read generates len(p) random bytes and writes them into p. It
	// always returns len(p) and a nil error.
	// Read should not be called concurrently with any other Rand method.
	func (r *Rand) Read(p []byte) (n int, err error) {
	switch src := r.src.(type) {
	case *lockedSource:
	return src.read(p, &r.readVal, &r.readPos)
	case *fastSource:
	return src.read(p, &r.readVal, &r.readPos)
	}
	return read(p, r.src, &r.readVal, &r.readPos)
	}

	func read(p []byte, src Source, readVal int64, readPos int8) (n int, err error) {
	pos := *readPos
	val := *readVal
	rng, _ := src.(*rngSource)
	for n = 0; n < len(p); n++ {
	if pos == 0 {
	if rng != nil {
	val = rng.Int63()
	} else {
	val = src.Int63()
	}
	pos = 7
	}
	p[n] = byte(val)
	val >>= 8
	pos--
	}
	*readPos = pos
	*readVal = val
	return
	}

	/*
	* Top-level convenience functions
	*/

	// globalRandGenerator is the source of random numbers for the top-level
	// convenience functions. When possible it uses the runtime fastrand64
	// function to avoid locking. This is not possible if the user called Seed,
	// either explicitly or implicitly via GODEBUG=randautoseed=0.
	var globalRandGenerator atomic.Pointer[Rand]

	var randautoseed = godebug.New("randautoseed")

	// globalRand returns the generator to use for the top-level convenience
	// functions.
	func globalRand() *Rand {
	if r := globalRandGenerator.Load(); r != nil {
	return r
	}

	// This is the first call. Initialize based on GODEBUG.
	var r *Rand
	if randautoseed.Value() == "0" {
	randautoseed.IncNonDefault()
	r = New(new(lockedSource))
	r.Seed(1)
	} else {
	r = &Rand{
	src: &fastSource{},
	s64: &fastSource{},
	}
	}

	if !globalRandGenerator.CompareAndSwap(nil, r) {
	// Two different goroutines called some top-level
	// function at the same time. While the results in
	// that case are unpredictable, if we just use r here,
	// and we are using a seed, we will most likely return
	// the same value for both calls. That doesn't seem ideal.
	// Just use the first one to get in.
	return globalRandGenerator.Load()
	}

	return r
	}

	//go:linkname fastrand64
	func fastrand64() uint64

	// fastSource is an implementation of Source64 that uses the runtime
	// fastrand functions.
	type fastSource struct {
	// The mutex is used to avoid race conditions in Read.
	mu sync.Mutex
	}

	func (*fastSource) Int63() int64 {
	return int64(fastrand64() & rngMask)
	}

	func (*fastSource) Seed(int64) {
	panic("internal error: call to fastSource.Seed")
	}

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

	func (fs fastSource) read(p []byte, readVal int64, readPos *int8) (n int, err error) {
	fs.mu.Lock()
	n, err = read(p, fs, readVal, readPos)
	fs.mu.Unlock()
	return
	}

	// Seed uses the provided seed value to initialize the default Source to a
	// deterministic state. Seed values that have the same remainder when
	// divided by 2³¹-1 generate the same pseudo-random sequence.
	// Seed, unlike the Rand.Seed method, is safe for concurrent use.
	//
	// If Seed is not called, the generator is seeded randomly at program startup.
	//
	// Prior to Go 1.20, the generator was seeded like Seed(1) at program startup.
	// To force the old behavior, call Seed(1) at program startup.
	// Alternately, set GODEBUG=randautoseed=0 in the environment
	// before making any calls to functions in this package.
	//
	// Deprecated: As of Go 1.20 there is no reason to call Seed with
	// a random value. Programs that call Seed with a known value to get
	// a specific sequence of results should use New(NewSource(seed)) to
	// obtain a local random generator.
	func Seed(seed int64) {
	orig := globalRandGenerator.Load()

	// If we are already using a lockedSource, we can just re-seed it.
	if orig != nil {
	if _, ok := orig.src.(*lockedSource); ok {
	orig.Seed(seed)
	return
	}
	}

	// Otherwise either
	// 1) orig == nil, which is the normal case when Seed is the first
	// top-level function to be called, or
	// 2) orig is already a fastSource, in which case we need to change
	// to a lockedSource.
	// Either way we do the same thing.

	r := New(new(lockedSource))
	r.Seed(seed)

	if !globalRandGenerator.CompareAndSwap(orig, r) {
	// Something changed underfoot. Retry to be safe.
	Seed(seed)
	}
	}

	// Int63 returns a non-negative pseudo-random 63-bit integer as an int64
	// from the default Source.
	func Int63() int64 { return globalRand().Int63() }

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

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

	// Int31 returns a non-negative pseudo-random 31-bit integer as an int32
	// from the default Source.
	func Int31() int32 { return globalRand().Int31() }

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

	// Int63n returns, as an int64, a non-negative pseudo-random number in the half-open interval [0,n)
	// from the default Source.
	// It panics if n <= 0.
	func Int63n(n int64) int64 { return globalRand().Int63n(n) }

	// Int31n returns, as an int32, a non-negative pseudo-random number in the half-open interval [0,n)
	// from the default Source.
	// It panics if n <= 0.
	func Int31n(n int32) int32 { return globalRand().Int31n(n) }

	// Intn returns, as an int, a non-negative 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) }

	// 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) }

	// Read generates len(p) random bytes from the default Source and
	// writes them into p. It always returns len(p) and a nil error.
	// Read, unlike the Rand.Read method, is safe for concurrent use.
	//
	// Deprecated: For almost all use cases, crypto/rand.Read is more appropriate.
	func Read(p []byte) (n int, err error) { return globalRand().Read(p) }

	// 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() }

	type lockedSource struct {
	lk sync.Mutex
	s *rngSource
	}

	func (r *lockedSource) Int63() (n int64) {
	r.lk.Lock()
	n = r.s.Int63()
	r.lk.Unlock()
	return
	}

	func (r *lockedSource) Uint64() (n uint64) {
	r.lk.Lock()
	n = r.s.Uint64()
	r.lk.Unlock()
	return
	}

	func (r *lockedSource) Seed(seed int64) {
	r.lk.Lock()
	r.seed(seed)
	r.lk.Unlock()
	}

	// seedPos implements Seed for a lockedSource without a race condition.
	func (r lockedSource) seedPos(seed int64, readPos int8) {
	r.lk.Lock()
	r.seed(seed)
	*readPos = 0
	r.lk.Unlock()
	}

	// seed seeds the underlying source.
	// The caller must have locked r.lk.
	func (r *lockedSource) seed(seed int64) {
	if r.s == nil {
	r.s = newSource(seed)
	} else {
	r.s.Seed(seed)
	}
	}

	// read implements Read for a lockedSource without a race condition.
	func (r lockedSource) read(p []byte, readVal int64, readPos *int8) (n int, err error) {
	r.lk.Lock()
	n, err = read(p, r.s, readVal, readPos)
	r.lk.Unlock()
	return
	}