math/rand/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.
//
// Random numbers are generated by a Source. Top-level functions, such as
// Float64 and Int, use a default shared Source that produces a deterministic
// sequence of values each time a program is run. Use the Seed function to
// initialize the default Source if different behavior is required for each run.
// The default Source is safe for concurrent use by multiple goroutines.
//
// For random numbers suitable for security-sensitive work, see the crypto/rand
// package.
package rand

import "sync"

// A Source represents a source of uniformly-distributed
// pseudo-random int64 values in the range [0, 1<<63).
type Source interface {
	Int63() int64
	Seed(seed int64)
}

// NewSource returns a new pseudo-random Source seeded with the given value.
func NewSource(seed int64) Source {
	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} }

// Seed uses the provided seed value to initialize the generator to a deterministic state.
func (r *Rand) Seed(seed int64) { r.src.Seed(seed) }

// 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) }

// 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 [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 [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
}

// Intn returns, as an int, a non-negative pseudo-random number in [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 [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. To fix that, we treat the
	// range as cyclic and map 1 back to 0. This is justified by observing
	// that while some of the values rounded down to 0, nothing was
	// rounding up to 0, so 0 was underrepresented in the results.
	// Mapping 1 back to zero restores some balance.
	// (The balance is not perfect because the implementation
	// returns denormalized numbers for very small r.Int63(),
	// and those steal from what would normally be 0 results.)
	// The remapping only happens 1/2 of the time, so most clients
	// will not observe it anyway.
	f := float64(r.Int63()) / (1 << 63)
	if f == 1 {
		f = 0
	}
	return f
}

// Float32 returns, as a float32, a pseudo-random number in [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
	// There is a double rounding going on here, but the argument for
	// mapping 1 to 0 still applies: 0 was underrepresented before,
	// so mapping 1 to 0 doesn't cause too many 0s.
	// This only happens 1/2 of the time (plus the 1/2 of the time in Float64).
	f := float32(r.Float64())
	if f == 1 {
		f = 0
	}
	return f
}

// Perm returns, as a slice of n ints, a pseudo-random permutation of the integers [0,n).
func (r *Rand) Perm(n int) []int {
	m := make([]int, n)
	for i := 0; i < n; i++ {
		j := r.Intn(i + 1)
		m[i] = m[j]
		m[j] = i
	}
	return m
}

/*
 * Top-level convenience functions
 */

var globalRand = New(&lockedSource{src: NewSource(1)})

// Seed uses the provided seed value to initialize the default Source to a
// deterministic state. If Seed is not called, the generator behaves as
// if seeded by Seed(1).
func Seed(seed int64) { globalRand.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() }

// 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 [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 [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 [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 [0.0,1.0)
// from the default Source.
func Float64() float64 { return globalRand.Float64() }

// Float32 returns, as a float32, a pseudo-random number in [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 [0,n)
// from the default Source.
func Perm(n int) []int { return globalRand.Perm(n) }

// 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
	src Source
}

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

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