Source file src/math/rand/rand.go

     1  // Copyright 2009 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 implements pseudo-random number generators unsuitable for
     6  // security-sensitive work.
     7  //
     8  // Random numbers are generated by a Source. Top-level functions, such as
     9  // Float64 and Int, use a default shared Source that produces a deterministic
    10  // sequence of values each time a program is run. Use the Seed function to
    11  // initialize the default Source if different behavior is required for each run.
    12  // The default Source is safe for concurrent use by multiple goroutines, but
    13  // Sources created by NewSource are not.
    14  //
    15  // This package's outputs might be easily predictable regardless of how it's
    16  // seeded. For random numbers suitable for security-sensitive work, see the
    17  // crypto/rand package.
    18  package rand
    19  
    20  import "sync"
    21  
    22  // A Source represents a source of uniformly-distributed
    23  // pseudo-random int64 values in the range [0, 1<<63).
    24  type Source interface {
    25  	Int63() int64
    26  	Seed(seed int64)
    27  }
    28  
    29  // A Source64 is a Source that can also generate
    30  // uniformly-distributed pseudo-random uint64 values in
    31  // the range [0, 1<<64) directly.
    32  // If a Rand r's underlying Source s implements Source64,
    33  // then r.Uint64 returns the result of one call to s.Uint64
    34  // instead of making two calls to s.Int63.
    35  type Source64 interface {
    36  	Source
    37  	Uint64() uint64
    38  }
    39  
    40  // NewSource returns a new pseudo-random Source seeded with the given value.
    41  // Unlike the default Source used by top-level functions, this source is not
    42  // safe for concurrent use by multiple goroutines.
    43  func NewSource(seed int64) Source {
    44  	var rng rngSource
    45  	rng.Seed(seed)
    46  	return &rng
    47  }
    48  
    49  // A Rand is a source of random numbers.
    50  type Rand struct {
    51  	src Source
    52  	s64 Source64 // non-nil if src is source64
    53  
    54  	// readVal contains remainder of 63-bit integer used for bytes
    55  	// generation during most recent Read call.
    56  	// It is saved so next Read call can start where the previous
    57  	// one finished.
    58  	readVal int64
    59  	// readPos indicates the number of low-order bytes of readVal
    60  	// that are still valid.
    61  	readPos int8
    62  }
    63  
    64  // New returns a new Rand that uses random values from src
    65  // to generate other random values.
    66  func New(src Source) *Rand {
    67  	s64, _ := src.(Source64)
    68  	return &Rand{src: src, s64: s64}
    69  }
    70  
    71  // Seed uses the provided seed value to initialize the generator to a deterministic state.
    72  // Seed should not be called concurrently with any other Rand method.
    73  func (r *Rand) Seed(seed int64) {
    74  	if lk, ok := r.src.(*lockedSource); ok {
    75  		lk.seedPos(seed, &r.readPos)
    76  		return
    77  	}
    78  
    79  	r.src.Seed(seed)
    80  	r.readPos = 0
    81  }
    82  
    83  // Int63 returns a non-negative pseudo-random 63-bit integer as an int64.
    84  func (r *Rand) Int63() int64 { return r.src.Int63() }
    85  
    86  // Uint32 returns a pseudo-random 32-bit value as a uint32.
    87  func (r *Rand) Uint32() uint32 { return uint32(r.Int63() >> 31) }
    88  
    89  // Uint64 returns a pseudo-random 64-bit value as a uint64.
    90  func (r *Rand) Uint64() uint64 {
    91  	if r.s64 != nil {
    92  		return r.s64.Uint64()
    93  	}
    94  	return uint64(r.Int63())>>31 | uint64(r.Int63())<<32
    95  }
    96  
    97  // Int31 returns a non-negative pseudo-random 31-bit integer as an int32.
    98  func (r *Rand) Int31() int32 { return int32(r.Int63() >> 32) }
    99  
   100  // Int returns a non-negative pseudo-random int.
   101  func (r *Rand) Int() int {
   102  	u := uint(r.Int63())
   103  	return int(u << 1 >> 1) // clear sign bit if int == int32
   104  }
   105  
   106  // Int63n returns, as an int64, a non-negative pseudo-random number in the half-open interval [0,n).
   107  // It panics if n <= 0.
   108  func (r *Rand) Int63n(n int64) int64 {
   109  	if n <= 0 {
   110  		panic("invalid argument to Int63n")
   111  	}
   112  	if n&(n-1) == 0 { // n is power of two, can mask
   113  		return r.Int63() & (n - 1)
   114  	}
   115  	max := int64((1 << 63) - 1 - (1<<63)%uint64(n))
   116  	v := r.Int63()
   117  	for v > max {
   118  		v = r.Int63()
   119  	}
   120  	return v % n
   121  }
   122  
   123  // Int31n returns, as an int32, a non-negative pseudo-random number in the half-open interval [0,n).
   124  // It panics if n <= 0.
   125  func (r *Rand) Int31n(n int32) int32 {
   126  	if n <= 0 {
   127  		panic("invalid argument to Int31n")
   128  	}
   129  	if n&(n-1) == 0 { // n is power of two, can mask
   130  		return r.Int31() & (n - 1)
   131  	}
   132  	max := int32((1 << 31) - 1 - (1<<31)%uint32(n))
   133  	v := r.Int31()
   134  	for v > max {
   135  		v = r.Int31()
   136  	}
   137  	return v % n
   138  }
   139  
   140  // int31n returns, as an int32, a non-negative pseudo-random number in the half-open interval [0,n).
   141  // n must be > 0, but int31n does not check this; the caller must ensure it.
   142  // int31n exists because Int31n is inefficient, but Go 1 compatibility
   143  // requires that the stream of values produced by math/rand remain unchanged.
   144  // int31n can thus only be used internally, by newly introduced APIs.
   145  //
   146  // For implementation details, see:
   147  // https://lemire.me/blog/2016/06/27/a-fast-alternative-to-the-modulo-reduction
   148  // https://lemire.me/blog/2016/06/30/fast-random-shuffling
   149  func (r *Rand) int31n(n int32) int32 {
   150  	v := r.Uint32()
   151  	prod := uint64(v) * uint64(n)
   152  	low := uint32(prod)
   153  	if low < uint32(n) {
   154  		thresh := uint32(-n) % uint32(n)
   155  		for low < thresh {
   156  			v = r.Uint32()
   157  			prod = uint64(v) * uint64(n)
   158  			low = uint32(prod)
   159  		}
   160  	}
   161  	return int32(prod >> 32)
   162  }
   163  
   164  // Intn returns, as an int, a non-negative pseudo-random number in the half-open interval [0,n).
   165  // It panics if n <= 0.
   166  func (r *Rand) Intn(n int) int {
   167  	if n <= 0 {
   168  		panic("invalid argument to Intn")
   169  	}
   170  	if n <= 1<<31-1 {
   171  		return int(r.Int31n(int32(n)))
   172  	}
   173  	return int(r.Int63n(int64(n)))
   174  }
   175  
   176  // Float64 returns, as a float64, a pseudo-random number in the half-open interval [0.0,1.0).
   177  func (r *Rand) Float64() float64 {
   178  	// A clearer, simpler implementation would be:
   179  	//	return float64(r.Int63n(1<<53)) / (1<<53)
   180  	// However, Go 1 shipped with
   181  	//	return float64(r.Int63()) / (1 << 63)
   182  	// and we want to preserve that value stream.
   183  	//
   184  	// There is one bug in the value stream: r.Int63() may be so close
   185  	// to 1<<63 that the division rounds up to 1.0, and we've guaranteed
   186  	// that the result is always less than 1.0.
   187  	//
   188  	// We tried to fix this by mapping 1.0 back to 0.0, but since float64
   189  	// values near 0 are much denser than near 1, mapping 1 to 0 caused
   190  	// a theoretically significant overshoot in the probability of returning 0.
   191  	// Instead of that, if we round up to 1, just try again.
   192  	// Getting 1 only happens 1/2⁵³ of the time, so most clients
   193  	// will not observe it anyway.
   194  again:
   195  	f := float64(r.Int63()) / (1 << 63)
   196  	if f == 1 {
   197  		goto again // resample; this branch is taken O(never)
   198  	}
   199  	return f
   200  }
   201  
   202  // Float32 returns, as a float32, a pseudo-random number in the half-open interval [0.0,1.0).
   203  func (r *Rand) Float32() float32 {
   204  	// Same rationale as in Float64: we want to preserve the Go 1 value
   205  	// stream except we want to fix it not to return 1.0
   206  	// This only happens 1/2²⁴ of the time (plus the 1/2⁵³ of the time in Float64).
   207  again:
   208  	f := float32(r.Float64())
   209  	if f == 1 {
   210  		goto again // resample; this branch is taken O(very rarely)
   211  	}
   212  	return f
   213  }
   214  
   215  // Perm returns, as a slice of n ints, a pseudo-random permutation of the integers
   216  // in the half-open interval [0,n).
   217  func (r *Rand) Perm(n int) []int {
   218  	m := make([]int, n)
   219  	// In the following loop, the iteration when i=0 always swaps m[0] with m[0].
   220  	// A change to remove this useless iteration is to assign 1 to i in the init
   221  	// statement. But Perm also effects r. Making this change will affect
   222  	// the final state of r. So this change can't be made for compatibility
   223  	// reasons for Go 1.
   224  	for i := 0; i < n; i++ {
   225  		j := r.Intn(i + 1)
   226  		m[i] = m[j]
   227  		m[j] = i
   228  	}
   229  	return m
   230  }
   231  
   232  // Shuffle pseudo-randomizes the order of elements.
   233  // n is the number of elements. Shuffle panics if n < 0.
   234  // swap swaps the elements with indexes i and j.
   235  func (r *Rand) Shuffle(n int, swap func(i, j int)) {
   236  	if n < 0 {
   237  		panic("invalid argument to Shuffle")
   238  	}
   239  
   240  	// Fisher-Yates shuffle: https://en.wikipedia.org/wiki/Fisher%E2%80%93Yates_shuffle
   241  	// Shuffle really ought not be called with n that doesn't fit in 32 bits.
   242  	// Not only will it take a very long time, but with 2³¹! possible permutations,
   243  	// there's no way that any PRNG can have a big enough internal state to
   244  	// generate even a minuscule percentage of the possible permutations.
   245  	// Nevertheless, the right API signature accepts an int n, so handle it as best we can.
   246  	i := n - 1
   247  	for ; i > 1<<31-1-1; i-- {
   248  		j := int(r.Int63n(int64(i + 1)))
   249  		swap(i, j)
   250  	}
   251  	for ; i > 0; i-- {
   252  		j := int(r.int31n(int32(i + 1)))
   253  		swap(i, j)
   254  	}
   255  }
   256  
   257  // Read generates len(p) random bytes and writes them into p. It
   258  // always returns len(p) and a nil error.
   259  // Read should not be called concurrently with any other Rand method.
   260  func (r *Rand) Read(p []byte) (n int, err error) {
   261  	if lk, ok := r.src.(*lockedSource); ok {
   262  		return lk.read(p, &r.readVal, &r.readPos)
   263  	}
   264  	return read(p, r.src, &r.readVal, &r.readPos)
   265  }
   266  
   267  func read(p []byte, src Source, readVal *int64, readPos *int8) (n int, err error) {
   268  	pos := *readPos
   269  	val := *readVal
   270  	rng, _ := src.(*rngSource)
   271  	for n = 0; n < len(p); n++ {
   272  		if pos == 0 {
   273  			if rng != nil {
   274  				val = rng.Int63()
   275  			} else {
   276  				val = src.Int63()
   277  			}
   278  			pos = 7
   279  		}
   280  		p[n] = byte(val)
   281  		val >>= 8
   282  		pos--
   283  	}
   284  	*readPos = pos
   285  	*readVal = val
   286  	return
   287  }
   288  
   289  /*
   290   * Top-level convenience functions
   291   */
   292  
   293  var globalRand = New(&lockedSource{src: NewSource(1).(*rngSource)})
   294  
   295  // Type assert that globalRand's source is a lockedSource whose src is a *rngSource.
   296  var _ *rngSource = globalRand.src.(*lockedSource).src
   297  
   298  // Seed uses the provided seed value to initialize the default Source to a
   299  // deterministic state. If Seed is not called, the generator behaves as
   300  // if seeded by Seed(1). Seed values that have the same remainder when
   301  // divided by 2³¹-1 generate the same pseudo-random sequence.
   302  // Seed, unlike the Rand.Seed method, is safe for concurrent use.
   303  func Seed(seed int64) { globalRand.Seed(seed) }
   304  
   305  // Int63 returns a non-negative pseudo-random 63-bit integer as an int64
   306  // from the default Source.
   307  func Int63() int64 { return globalRand.Int63() }
   308  
   309  // Uint32 returns a pseudo-random 32-bit value as a uint32
   310  // from the default Source.
   311  func Uint32() uint32 { return globalRand.Uint32() }
   312  
   313  // Uint64 returns a pseudo-random 64-bit value as a uint64
   314  // from the default Source.
   315  func Uint64() uint64 { return globalRand.Uint64() }
   316  
   317  // Int31 returns a non-negative pseudo-random 31-bit integer as an int32
   318  // from the default Source.
   319  func Int31() int32 { return globalRand.Int31() }
   320  
   321  // Int returns a non-negative pseudo-random int from the default Source.
   322  func Int() int { return globalRand.Int() }
   323  
   324  // Int63n returns, as an int64, a non-negative pseudo-random number in the half-open interval [0,n)
   325  // from the default Source.
   326  // It panics if n <= 0.
   327  func Int63n(n int64) int64 { return globalRand.Int63n(n) }
   328  
   329  // Int31n returns, as an int32, a non-negative pseudo-random number in the half-open interval [0,n)
   330  // from the default Source.
   331  // It panics if n <= 0.
   332  func Int31n(n int32) int32 { return globalRand.Int31n(n) }
   333  
   334  // Intn returns, as an int, a non-negative pseudo-random number in the half-open interval [0,n)
   335  // from the default Source.
   336  // It panics if n <= 0.
   337  func Intn(n int) int { return globalRand.Intn(n) }
   338  
   339  // Float64 returns, as a float64, a pseudo-random number in the half-open interval [0.0,1.0)
   340  // from the default Source.
   341  func Float64() float64 { return globalRand.Float64() }
   342  
   343  // Float32 returns, as a float32, a pseudo-random number in the half-open interval [0.0,1.0)
   344  // from the default Source.
   345  func Float32() float32 { return globalRand.Float32() }
   346  
   347  // Perm returns, as a slice of n ints, a pseudo-random permutation of the integers
   348  // in the half-open interval [0,n) from the default Source.
   349  func Perm(n int) []int { return globalRand.Perm(n) }
   350  
   351  // Shuffle pseudo-randomizes the order of elements using the default Source.
   352  // n is the number of elements. Shuffle panics if n < 0.
   353  // swap swaps the elements with indexes i and j.
   354  func Shuffle(n int, swap func(i, j int)) { globalRand.Shuffle(n, swap) }
   355  
   356  // Read generates len(p) random bytes from the default Source and
   357  // writes them into p. It always returns len(p) and a nil error.
   358  // Read, unlike the Rand.Read method, is safe for concurrent use.
   359  func Read(p []byte) (n int, err error) { return globalRand.Read(p) }
   360  
   361  // NormFloat64 returns a normally distributed float64 in the range
   362  // [-math.MaxFloat64, +math.MaxFloat64] with
   363  // standard normal distribution (mean = 0, stddev = 1)
   364  // from the default Source.
   365  // To produce a different normal distribution, callers can
   366  // adjust the output using:
   367  //
   368  //	sample = NormFloat64() * desiredStdDev + desiredMean
   369  func NormFloat64() float64 { return globalRand.NormFloat64() }
   370  
   371  // ExpFloat64 returns an exponentially distributed float64 in the range
   372  // (0, +math.MaxFloat64] with an exponential distribution whose rate parameter
   373  // (lambda) is 1 and whose mean is 1/lambda (1) from the default Source.
   374  // To produce a distribution with a different rate parameter,
   375  // callers can adjust the output using:
   376  //
   377  //	sample = ExpFloat64() / desiredRateParameter
   378  func ExpFloat64() float64 { return globalRand.ExpFloat64() }
   379  
   380  type lockedSource struct {
   381  	lk  sync.Mutex
   382  	src *rngSource
   383  }
   384  
   385  func (r *lockedSource) Int63() (n int64) {
   386  	r.lk.Lock()
   387  	n = r.src.Int63()
   388  	r.lk.Unlock()
   389  	return
   390  }
   391  
   392  func (r *lockedSource) Uint64() (n uint64) {
   393  	r.lk.Lock()
   394  	n = r.src.Uint64()
   395  	r.lk.Unlock()
   396  	return
   397  }
   398  
   399  func (r *lockedSource) Seed(seed int64) {
   400  	r.lk.Lock()
   401  	r.src.Seed(seed)
   402  	r.lk.Unlock()
   403  }
   404  
   405  // seedPos implements Seed for a lockedSource without a race condition.
   406  func (r *lockedSource) seedPos(seed int64, readPos *int8) {
   407  	r.lk.Lock()
   408  	r.src.Seed(seed)
   409  	*readPos = 0
   410  	r.lk.Unlock()
   411  }
   412  
   413  // read implements Read for a lockedSource without a race condition.
   414  func (r *lockedSource) read(p []byte, readVal *int64, readPos *int8) (n int, err error) {
   415  	r.lk.Lock()
   416  	n, err = read(p, r.src, readVal, readPos)
   417  	r.lk.Unlock()
   418  	return
   419  }
   420  

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