package rand

Import Path
	math/rand (on golang.org and go.dev)

Dependency Relation
	imports 2 packages, and imported by 2 packages

Involved Source Files

	      exp.go
	      normal.go
	   d➜ rand.go
		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, but
		Sources created by NewSource are not.

		Mathematical interval notation such as [0, n) is used throughout the
		documentation for this package.

		For random numbers suitable for security-sensitive work, see the crypto/rand
		package.

	      rng.go
	      zipf.go
Code Examples

	
		package main
		
		import (
			"fmt"
			"math/rand"
		)
		
		func main() {
			// Seeding with the same value results in the same random sequence each run.
			// For different numbers, seed with a different value, such as
			// time.Now().UnixNano(), which yields a constantly-changing number.
			rand.Seed(42)
			answers := []string{
				"It is certain",
				"It is decidedly so",
				"Without a doubt",
				"Yes definitely",
				"You may rely on it",
				"As I see it yes",
				"Most likely",
				"Outlook good",
				"Yes",
				"Signs point to yes",
				"Reply hazy try again",
				"Ask again later",
				"Better not tell you now",
				"Cannot predict now",
				"Concentrate and ask again",
				"Don't count on it",
				"My reply is no",
				"My sources say no",
				"Outlook not so good",
				"Very doubtful",
			}
			fmt.Println("Magic 8-Ball says:", answers[rand.Intn(len(answers))])
		}


	Intn
		package main
		
		import (
			"fmt"
			"math/rand"
		)
		
		func main() {
			// Seeding with the same value results in the same random sequence each run.
			// For different numbers, seed with a different value, such as
			// time.Now().UnixNano(), which yields a constantly-changing number.
			rand.Seed(86)
			fmt.Println(rand.Intn(100))
			fmt.Println(rand.Intn(100))
			fmt.Println(rand.Intn(100))
		
		}


	Perm
		package main
		
		import (
			"fmt"
			"math/rand"
		)
		
		func main() {
			for _, value := range rand.Perm(3) {
				fmt.Println(value)
			}
		
		}


	Shuffle
		package main
		
		import (
			"fmt"
			"math/rand"
			"strings"
		)
		
		func main() {
			words := strings.Fields("ink runs from the corners of my mouth")
			rand.Shuffle(len(words), func(i, j int) {
				words[i], words[j] = words[j], words[i]
			})
			fmt.Println(words)
		
		}


	Shuffle_slicesInUnison
		package main
		
		import (
			"fmt"
			"math/rand"
		)
		
		func main() {
			numbers := []byte("12345")
			letters := []byte("ABCDE")
			// Shuffle numbers, swapping corresponding entries in letters at the same time.
			rand.Shuffle(len(numbers), func(i, j int) {
				numbers[i], numbers[j] = numbers[j], numbers[i]
				letters[i], letters[j] = letters[j], letters[i]
			})
			for i := range numbers {
				fmt.Printf("%c: %c\n", letters[i], numbers[i])
			}
		
		}


	_rand
		package main
		
		import (
			"fmt"
			"math/rand"
			"os"
			"text/tabwriter"
		)
		
		func main() {
			// Create and seed the generator.
			// Typically a non-fixed seed should be used, such as time.Now().UnixNano().
			// Using a fixed seed will produce the same output on every run.
			r := rand.New(rand.NewSource(99))
		
			// The tabwriter here helps us generate aligned output.
			w := tabwriter.NewWriter(os.Stdout, 1, 1, 1, ' ', 0)
			defer w.Flush()
			show := func(name string, v1, v2, v3 interface{}) {
				fmt.Fprintf(w, "%s\t%v\t%v\t%v\n", name, v1, v2, v3)
			}
		
			// Float32 and Float64 values are in [0, 1).
			show("Float32", r.Float32(), r.Float32(), r.Float32())
			show("Float64", r.Float64(), r.Float64(), r.Float64())
		
			// ExpFloat64 values have an average of 1 but decay exponentially.
			show("ExpFloat64", r.ExpFloat64(), r.ExpFloat64(), r.ExpFloat64())
		
			// NormFloat64 values have an average of 0 and a standard deviation of 1.
			show("NormFloat64", r.NormFloat64(), r.NormFloat64(), r.NormFloat64())
		
			// Int31, Int63, and Uint32 generate values of the given width.
			// The Int method (not shown) is like either Int31 or Int63
			// depending on the size of 'int'.
			show("Int31", r.Int31(), r.Int31(), r.Int31())
			show("Int63", r.Int63(), r.Int63(), r.Int63())
			show("Uint32", r.Uint32(), r.Uint32(), r.Uint32())
		
			// Intn, Int31n, and Int63n limit their output to be < n.
			// They do so more carefully than using r.Int()%n.
			show("Intn(10)", r.Intn(10), r.Intn(10), r.Intn(10))
			show("Int31n(10)", r.Int31n(10), r.Int31n(10), r.Int31n(10))
			show("Int63n(10)", r.Int63n(10), r.Int63n(10), r.Int63n(10))
		
			// Perm generates a random permutation of the numbers [0, n).
			show("Perm", r.Perm(5), r.Perm(5), r.Perm(5))
		}


Package-Level Type Names (total 6, in which 4 are exported)

	/* sort exporteds by: alphabet | popularity */
	 type Rand (struct)
		A Rand is a source of random numbers.

		Fields (total 4, none are exported)
			/* 4 unexporteds ... *//* 4 unexporteds: */
			readPos int8
				readPos indicates the number of low-order bytes of readVal
				that are still valid.

			readVal int64
				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.

			s64 Source64
				// non-nil if src is source64

			src Source
		Methods (total 17, in which 16 are exported)
			(*T) ExpFloat64() float64
				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).
				To produce a distribution with a different rate parameter,
				callers can adjust the output using:

				 sample = ExpFloat64() / desiredRateParameter

			(*T) Float32() float32
				Float32 returns, as a float32, a pseudo-random number in [0.0,1.0).

			(*T) Float64() float64
				Float64 returns, as a float64, a pseudo-random number in [0.0,1.0).

			(*T) Int() int
				Int returns a non-negative pseudo-random int.

			(*T) Int31() int32
				Int31 returns a non-negative pseudo-random 31-bit integer as an int32.

			(*T) Int31n(n int32) int32
				Int31n returns, as an int32, a non-negative pseudo-random number in [0,n).
				It panics if n <= 0.

			(*T) Int63() int64
				Int63 returns a non-negative pseudo-random 63-bit integer as an int64.

			(*T) Int63n(n int64) int64
				Int63n returns, as an int64, a non-negative pseudo-random number in [0,n).
				It panics if n <= 0.

			(*T) Intn(n int) int
				Intn returns, as an int, a non-negative pseudo-random number in [0,n).
				It panics if n <= 0.

			(*T) NormFloat64() float64
				NormFloat64 returns a normally distributed float64 in
				the range -math.MaxFloat64 through +math.MaxFloat64 inclusive,
				with standard normal distribution (mean = 0, stddev = 1).
				To produce a different normal distribution, callers can
				adjust the output using:

				 sample = NormFloat64() * desiredStdDev + desiredMean

			(*T) Perm(n int) []int
				Perm returns, as a slice of n ints, a pseudo-random permutation of the integers [0,n).

			(*T) Read(p []byte) (n int, err error)
				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.

			(*T) Seed(seed int64)
				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.

			(*T) Shuffle(n int, swap func(i, j int))
				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.

			(*T) Uint32() uint32
				Uint32 returns a pseudo-random 32-bit value as a uint32.

			(*T) Uint64() uint64
				Uint64 returns a pseudo-random 64-bit value as a uint64.

			/* one unexported ... *//* one unexported: */
			(*T) int31n(n int32) int32
				int31n returns, as an int32, a non-negative pseudo-random number in [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

		Implements (at least 3, all are exported)
			*T : Source
			*T : Source64
			*T : io.Reader
		As Outputs Of (at least one exported)
			func New(src Source) *Rand
		As Inputs Of (at least 2, both are exported)
			func NewZipf(r *Rand, s float64, v float64, imax uint64) *Zipf
			func math/big.(*Int).Rand(rnd *Rand, n *big.Int) *big.Int
		As Types Of (only one, which is unexported)
			/* one unexported ... *//* one unexported: */
			  var globalRand *Rand

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

		Methods (total 2, both are exported)
			( T) Int63() int64
			( T) Seed(seed int64)
		Implemented By (at least 4, in which 2 are exported)
			*Rand
			 Source64 (interface)
			/* 2+ unexporteds ... *//* 2+ unexporteds: */
			*lockedSource
			*rngSource
		As Outputs Of (at least one exported)
			func NewSource(seed int64) Source
		As Inputs Of (at least 2, in which 1 are exported)
			func New(src Source) *Rand
			/* at least one unexported ... *//* at least one unexported: */
			func read(p []byte, src Source, readVal *int64, readPos *int8) (n int, err error)

	 type Source64 (interface)
		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.

		Methods (total 3, all are exported)
			( T) Int63() int64
			( T) Seed(seed int64)
			( T) Uint64() uint64
		Implemented By (at least 3, in which 1 are exported)
			*Rand
			/* 2+ unexporteds ... *//* 2+ unexporteds: */
			*lockedSource
			*rngSource
		Implements (at least one exported)
			 T : Source

	 type Zipf (struct)
		A Zipf generates Zipf distributed variates.

		Fields (total 9, none are exported)
			/* 9 unexporteds ... *//* 9 unexporteds: */
			hx0minusHxm float64
			hxm float64
			imax float64
			oneminusQ float64
			oneminusQinv float64
			q float64
			r *Rand
			s float64
			v float64
		Methods (total 3, in which 1 are exported)
			(*T) Uint64() uint64
				Uint64 returns a value drawn from the Zipf distribution described
				by the Zipf object.

			/* 2 unexporteds ... *//* 2 unexporteds: */
			(*T) h(x float64) float64
			(*T) hinv(x float64) float64
		As Outputs Of (at least one exported)
			func NewZipf(r *Rand, s float64, v float64, imax uint64) *Zipf

	/* 2 unexporteds ... *//* 2 unexporteds: */
	 type lockedSource (struct)

		Fields (total 2, neither is exported)
			/* 2 unexporteds ... *//* 2 unexporteds: */
			lk sync.Mutex
			src *rngSource
		Methods (total 5, in which 3 are exported)
			(*T) Int63() (n int64)
			(*T) Seed(seed int64)
			(*T) Uint64() (n uint64)
			/* 2 unexporteds ... *//* 2 unexporteds: */
			(*T) read(p []byte, readVal *int64, readPos *int8) (n int, err error)
				read implements Read for a lockedSource without a race condition.

			(*T) seedPos(seed int64, readPos *int8)
				seedPos implements Seed for a lockedSource without a race condition.

		Implements (at least 2, both are exported)
			*T : Source
			*T : Source64

	 type rngSource (struct)

		Fields (total 3, none are exported)
			/* 3 unexporteds ... *//* 3 unexporteds: */
			feed int
				// index into vec

			tap int
				// index into vec

			vec [607]int64
				// current feedback register

		Methods (total 3, all are exported)
			(*T) Int63() int64
				Int63 returns a non-negative pseudo-random 63-bit integer as an int64.

			(*T) Seed(seed int64)
				Seed uses the provided seed value to initialize the generator to a deterministic state.

			(*T) Uint64() uint64
				Uint64 returns a non-negative pseudo-random 64-bit integer as an uint64.

		Implements (at least 2, both are exported)
			*T : Source
			*T : Source64


Package-Level Functions (total 22, in which 19 are exported)

	 func ExpFloat64() float64
		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 Float32() float32
		Float32 returns, as a float32, a pseudo-random number in [0.0,1.0)
		from the default Source.

	 func Float64() float64
		Float64 returns, as a float64, a pseudo-random number in [0.0,1.0)
		from the default Source.

	 func Int() int
		Int returns a non-negative pseudo-random int from the default Source.

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

	 func Int31n(n int32) int32
		Int31n returns, as an int32, a non-negative pseudo-random number in [0,n)
		from the default Source.
		It panics if n <= 0.

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

	 func Int63n(n int64) int64
		Int63n returns, as an int64, a non-negative pseudo-random number in [0,n)
		from the default Source.
		It panics if n <= 0.

	 func Intn(n int) int
		Intn returns, as an int, a non-negative pseudo-random number in [0,n)
		from the default Source.
		It panics if n <= 0.

	 func New(src Source) *Rand
		New returns a new Rand that uses random values from src
		to generate other random values.

	 func NewSource(seed int64) Source
		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.

	 func NewZipf(r *Rand, s float64, v float64, imax uint64) *Zipf
		NewZipf returns a Zipf variate generator.
		The generator generates values k ∈ [0, imax]
		such that P(k) is proportional to (v + k) ** (-s).
		Requirements: s > 1 and v >= 1.

	 func NormFloat64() float64
		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 Perm(n int) []int
		Perm returns, as a slice of n ints, a pseudo-random permutation of the integers [0,n)
		from the default Source.

	 func Read(p []byte) (n int, err error)
		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.

	 func Seed(seed int64)
		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). 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.

	 func Shuffle(n int, swap func(i, j int))
		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 Uint32() uint32
		Uint32 returns a pseudo-random 32-bit value as a uint32
		from the default Source.

	 func Uint64() uint64
		Uint64 returns a pseudo-random 64-bit value as a uint64
		from the default Source.

	/* 3 unexporteds ... *//* 3 unexporteds: */
	 func absInt32(i int32) uint32
	 func read(p []byte, src Source, readVal *int64, readPos *int8) (n int, err error)
	 func seedrand(x int32) int32
		seed rng x[n+1] = 48271 * x[n] mod (2**31 - 1)


Package-Level Variables (total 8, none are exported)

	/* 8 unexporteds ... *//* 8 unexporteds: */
	  var fe [256]float32
	  var fn [128]float32
	  var globalRand *Rand
	  var ke [256]uint32
	  var kn [128]uint32
	  var rngCooked [607]int64
		rngCooked used for seeding. See gen_cooked.go for details.

	  var we [256]float32
	  var wn [128]float32
Package-Level Constants (total 7, none are exported)

	/* 7 unexporteds ... *//* 7 unexporteds: */
	const int32max = 2147483647
	const re = 7.69712
	const rn = 3.44262
	const rngLen = 607
	const rngMask = 9223372036854775807
	const rngMax = 9223372036854775808
	const rngTap = 273

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