x/exp/rand: new rand package
This is an approximately compatible new implementation of math/rand.
The differences are:
Source emits uint64s rather than positive int64s.
The method is now
Uint64() uint64; not
Int63() int64
There are corresponding new methods on Rand:
func (r *Rand) Uint64() uint64
func (r *Rand) Uint64n(n uint64) uint64
The default Source is now an exported type, PCGSource.
The default Source holds 128 bits of state for a 64-bit
result. This has good statistical properties but is slower,
largely because the multiplication step is inefficient.
That can be improved with assembler.
Thus the default Source has a two 64-bit words of state (in
math/rand it has 607 words). It is thus practical to have
millions of Sources in the address space, making it well
suited to lock-free simulations using random numbers.
Benchmarks:
benchmark old ns/op new ns/op delta
BenchmarkInt63Threadsafe-4 20.0 24.4 +22.00%
BenchmarkInt63Unthreadsafe-4 6.32 13.0 +105.70%
BenchmarkIntn1000-4 16.4 23.8 +45.12%
BenchmarkInt63n1000-4 25.5 23.8 -6.67%
BenchmarkInt31n1000-4 14.2 23.8 +67.61%
BenchmarkFloat32-4 11.8 21.0 +77.97%
BenchmarkFloat64-4 8.76 18.3 +108.90%
BenchmarkPerm3-4 80.3 94.3 +17.43%
BenchmarkPerm30-4 627 814 +29.82%
The new generator is PCG XSL RR 128/64 (LCG) from
http://www.pcg-random.org/pdf/toms-oneill-pcg-family-v1.02.pdf
It has been tested against the C version and generates the same
output if initialized to the same value.
See also http://www.pcg-random.org/.
TODO: Improve performance, make initialization better.
Independently, this fixes a bug in the bias-prevention code that
appears, in this package, in Uint64n.
This also exports LockedSource:
Update golang/go#21393.
Change-Id: I48a410fade5d78b8ec993cc1210b96b7a9ab462f
Reviewed-on: https://go-review.googlesource.com/10161
Reviewed-by: Rob Pike <r@golang.org>
diff --git a/rand/arith128_test.go b/rand/arith128_test.go
new file mode 100644
index 0000000..eed655b
--- /dev/null
+++ b/rand/arith128_test.go
@@ -0,0 +1,126 @@
+// Copyright 2017 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
+
+import (
+ "math/big"
+ "math/rand"
+ "testing"
+)
+
+var bigMaxUint64 = big.NewInt(0).SetUint64(maxUint64)
+
+func bigInt(xHi, xLo uint64) *big.Int {
+ b := big.NewInt(0).SetUint64(xHi)
+ b.Lsh(b, 64)
+ b.Or(b, big.NewInt(0).SetUint64(xLo))
+ return b
+}
+
+func splitBigInt(b *big.Int) (outHi, outLo uint64) {
+ outHi = big.NewInt(0).Rsh(b, 64).Uint64()
+ outLo = big.NewInt(0).And(b, bigMaxUint64).Uint64()
+ return
+}
+
+func bigMulMod128bits(xHi, xLo, yHi, yLo uint64) (outHi, outLo uint64) {
+ bigX := bigInt(xHi, xLo)
+ bigY := bigInt(yHi, yLo)
+ return splitBigInt(bigX.Mul(bigX, bigY))
+}
+
+func bigAddMod128bits(xHi, xLo, yHi, yLo uint64) (outHi, outLo uint64) {
+ bigX := bigInt(xHi, xLo)
+ bigY := bigInt(yHi, yLo)
+ return splitBigInt(bigX.Add(bigX, bigY))
+}
+
+type arithTest struct {
+ xHi, xLo uint64
+}
+
+const (
+ iLo = increment & maxUint64
+ iHi = (increment >> 64) & maxUint64
+)
+
+var arithTests = []arithTest{
+ {0, 0},
+ {0, 1},
+ {1, 0},
+ {0, maxUint64},
+ {maxUint64, 0},
+ {maxUint64, maxUint64},
+ // Randomly generated 64-bit integers.
+ {3757956613005209672, 17983933746665545631},
+ {511324141977587414, 5626651684620191081},
+ {1534313104606153588, 2415006486399353367},
+ {6873586429837825902, 13854394671140464137},
+ {6617134480561088940, 18421520694158684312},
+}
+
+func TestPCGAdd(t *testing.T) {
+ for i, test := range arithTests {
+ p := &PCGSource{
+ low: test.xLo,
+ high: test.xHi,
+ }
+ p.add()
+ expectHi, expectLo := bigAddMod128bits(test.xHi, test.xLo, iHi, iLo)
+ if p.low != expectLo || p.high != expectHi {
+ t.Errorf("%d: got hi=%d lo=%d; expect hi=%d lo=%d", i, p.high, p.low, expectHi, expectLo)
+ }
+ }
+}
+
+const (
+ mLo = multiplier & maxUint64
+ mHi = (multiplier >> 64) & maxUint64
+)
+
+func TestPCGMultiply(t *testing.T) {
+ for i, test := range arithTests {
+ p := &PCGSource{
+ low: test.xLo,
+ high: test.xHi,
+ }
+ p.multiply()
+ expectHi, expectLo := bigMulMod128bits(test.xHi, test.xLo, mHi, mLo)
+ if p.low != expectLo || p.high != expectHi {
+ t.Errorf("%d: got hi=%d lo=%d; expect hi=%d lo=%d", i, p.high, p.low, expectHi, expectLo)
+ }
+ }
+}
+
+func TestPCGMultiplyLong(t *testing.T) {
+ if testing.Short() {
+ return
+ }
+ for i := 0; i < 1e6; i++ {
+ low := rand.Uint64()
+ high := rand.Uint64()
+ p := &PCGSource{
+ low: low,
+ high: high,
+ }
+ p.multiply()
+ expectHi, expectLo := bigMulMod128bits(high, low, mHi, mLo)
+ if p.low != expectLo || p.high != expectHi {
+ t.Fatalf("%d: (%d,%d): got hi=%d lo=%d; expect hi=%d lo=%d", i, high, low, p.high, p.low, expectHi, expectLo)
+ }
+ }
+}
+
+func BenchmarkPCGMultiply(b *testing.B) {
+ low := rand.Uint64()
+ high := rand.Uint64()
+ p := &PCGSource{
+ low: low,
+ high: high,
+ }
+ for i := 0; i < b.N; i++ {
+ p.multiply()
+ }
+}
diff --git a/rand/example_test.go b/rand/example_test.go
new file mode 100644
index 0000000..3b119fc
--- /dev/null
+++ b/rand/example_test.go
@@ -0,0 +1,102 @@
+// Copyright 2012 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_test
+
+import (
+ "fmt"
+ "os"
+ "text/tabwriter"
+
+ "golang.org/x/exp/rand"
+)
+
+// These tests serve as an example but also make sure we don't change
+// the output of the random number generator when given a fixed seed.
+
+func Example() {
+ rand.Seed(42) // Try changing this number!
+ 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))])
+ // Output: Magic 8-Ball says: Most likely
+}
+
+// This example shows the use of each of the methods on a *Rand.
+// The use of the global functions is the same, without the receiver.
+func Example_rand() {
+ // 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(1234))
+
+ // 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())
+ show("Uint64", r.Uint64(), r.Uint64(), r.Uint64())
+
+ // Intn, Int31n, Int63n and Uint64n 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))
+ show("Uint64n(10)", r.Uint64n(10), r.Uint64n(10), r.Uint64n(10))
+
+ // Perm generates a random permutation of the numbers [0, n).
+ show("Perm", r.Perm(5), r.Perm(5), r.Perm(5))
+ // Output:
+ // Float32 0.030719291 0.47512934 0.031019364
+ // Float64 0.6906635660087743 0.9898818576905045 0.2683634639782333
+ // ExpFloat64 1.24979080914592 0.3451975160045876 0.5456817760595064
+ // NormFloat64 0.879221333732727 -0.01508980368383761 -1.962250558270421
+ // Int31 2043816560 1870670250 1334960143
+ // Int63 7860766611810691572 1466711535823962239 3836585920276818709
+ // Uint32 2051241581 751073909 1353986074
+ // Uint64 10802154207635843641 14398820303406316826 11052107950969057042
+ // Intn(10) 3 0 1
+ // Int31n(10) 3 8 1
+ // Int63n(10) 4 6 0
+ // Uint64n(10) 2 9 4
+ // Perm [1 3 4 0 2] [2 4 0 3 1] [3 2 0 4 1]
+}
diff --git a/rand/exp.go b/rand/exp.go
new file mode 100644
index 0000000..4bc110f
--- /dev/null
+++ b/rand/exp.go
@@ -0,0 +1,222 @@
+// 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
+
+import (
+ "math"
+)
+
+/*
+ * Exponential distribution
+ *
+ * See "The Ziggurat Method for Generating Random Variables"
+ * (Marsaglia & Tsang, 2000)
+ * http://www.jstatsoft.org/v05/i08/paper [pdf]
+ */
+
+const (
+ re = 7.69711747013104972
+)
+
+// 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
+//
+func (r *Rand) ExpFloat64() float64 {
+ for {
+ j := r.Uint32()
+ i := j & 0xFF
+ x := float64(j) * float64(we[i])
+ if j < ke[i] {
+ return x
+ }
+ if i == 0 {
+ return re - math.Log(r.Float64())
+ }
+ if fe[i]+float32(r.Float64())*(fe[i-1]-fe[i]) < float32(math.Exp(-x)) {
+ return x
+ }
+ }
+}
+
+var ke = [256]uint32{
+ 0xe290a139, 0x0, 0x9beadebc, 0xc377ac71, 0xd4ddb990,
+ 0xde893fb8, 0xe4a8e87c, 0xe8dff16a, 0xebf2deab, 0xee49a6e8,
+ 0xf0204efd, 0xf19bdb8e, 0xf2d458bb, 0xf3da104b, 0xf4b86d78,
+ 0xf577ad8a, 0xf61de83d, 0xf6afb784, 0xf730a573, 0xf7a37651,
+ 0xf80a5bb6, 0xf867189d, 0xf8bb1b4f, 0xf9079062, 0xf94d70ca,
+ 0xf98d8c7d, 0xf9c8928a, 0xf9ff175b, 0xfa319996, 0xfa6085f8,
+ 0xfa8c3a62, 0xfab5084e, 0xfadb36c8, 0xfaff0410, 0xfb20a6ea,
+ 0xfb404fb4, 0xfb5e2951, 0xfb7a59e9, 0xfb95038c, 0xfbae44ba,
+ 0xfbc638d8, 0xfbdcf892, 0xfbf29a30, 0xfc0731df, 0xfc1ad1ed,
+ 0xfc2d8b02, 0xfc3f6c4d, 0xfc5083ac, 0xfc60ddd1, 0xfc708662,
+ 0xfc7f8810, 0xfc8decb4, 0xfc9bbd62, 0xfca9027c, 0xfcb5c3c3,
+ 0xfcc20864, 0xfccdd70a, 0xfcd935e3, 0xfce42ab0, 0xfceebace,
+ 0xfcf8eb3b, 0xfd02c0a0, 0xfd0c3f59, 0xfd156b7b, 0xfd1e48d6,
+ 0xfd26daff, 0xfd2f2552, 0xfd372af7, 0xfd3eeee5, 0xfd4673e7,
+ 0xfd4dbc9e, 0xfd54cb85, 0xfd5ba2f2, 0xfd62451b, 0xfd68b415,
+ 0xfd6ef1da, 0xfd750047, 0xfd7ae120, 0xfd809612, 0xfd8620b4,
+ 0xfd8b8285, 0xfd90bcf5, 0xfd95d15e, 0xfd9ac10b, 0xfd9f8d36,
+ 0xfda43708, 0xfda8bf9e, 0xfdad2806, 0xfdb17141, 0xfdb59c46,
+ 0xfdb9a9fd, 0xfdbd9b46, 0xfdc170f6, 0xfdc52bd8, 0xfdc8ccac,
+ 0xfdcc542d, 0xfdcfc30b, 0xfdd319ef, 0xfdd6597a, 0xfdd98245,
+ 0xfddc94e5, 0xfddf91e6, 0xfde279ce, 0xfde54d1f, 0xfde80c52,
+ 0xfdeab7de, 0xfded5034, 0xfdefd5be, 0xfdf248e3, 0xfdf4aa06,
+ 0xfdf6f984, 0xfdf937b6, 0xfdfb64f4, 0xfdfd818d, 0xfdff8dd0,
+ 0xfe018a08, 0xfe03767a, 0xfe05536c, 0xfe07211c, 0xfe08dfc9,
+ 0xfe0a8fab, 0xfe0c30fb, 0xfe0dc3ec, 0xfe0f48b1, 0xfe10bf76,
+ 0xfe122869, 0xfe1383b4, 0xfe14d17c, 0xfe1611e7, 0xfe174516,
+ 0xfe186b2a, 0xfe19843e, 0xfe1a9070, 0xfe1b8fd6, 0xfe1c8289,
+ 0xfe1d689b, 0xfe1e4220, 0xfe1f0f26, 0xfe1fcfbc, 0xfe2083ed,
+ 0xfe212bc3, 0xfe21c745, 0xfe225678, 0xfe22d95f, 0xfe234ffb,
+ 0xfe23ba4a, 0xfe241849, 0xfe2469f2, 0xfe24af3c, 0xfe24e81e,
+ 0xfe25148b, 0xfe253474, 0xfe2547c7, 0xfe254e70, 0xfe25485a,
+ 0xfe25356a, 0xfe251586, 0xfe24e88f, 0xfe24ae64, 0xfe2466e1,
+ 0xfe2411df, 0xfe23af34, 0xfe233eb4, 0xfe22c02c, 0xfe22336b,
+ 0xfe219838, 0xfe20ee58, 0xfe20358c, 0xfe1f6d92, 0xfe1e9621,
+ 0xfe1daef0, 0xfe1cb7ac, 0xfe1bb002, 0xfe1a9798, 0xfe196e0d,
+ 0xfe1832fd, 0xfe16e5fe, 0xfe15869d, 0xfe141464, 0xfe128ed3,
+ 0xfe10f565, 0xfe0f478c, 0xfe0d84b1, 0xfe0bac36, 0xfe09bd73,
+ 0xfe07b7b5, 0xfe059a40, 0xfe03644c, 0xfe011504, 0xfdfeab88,
+ 0xfdfc26e9, 0xfdf98629, 0xfdf6c83b, 0xfdf3ec01, 0xfdf0f04a,
+ 0xfdedd3d1, 0xfdea953d, 0xfde7331e, 0xfde3abe9, 0xfddffdfb,
+ 0xfddc2791, 0xfdd826cd, 0xfdd3f9a8, 0xfdcf9dfc, 0xfdcb1176,
+ 0xfdc65198, 0xfdc15bb3, 0xfdbc2ce2, 0xfdb6c206, 0xfdb117be,
+ 0xfdab2a63, 0xfda4f5fd, 0xfd9e7640, 0xfd97a67a, 0xfd908192,
+ 0xfd8901f2, 0xfd812182, 0xfd78d98e, 0xfd7022bb, 0xfd66f4ed,
+ 0xfd5d4732, 0xfd530f9c, 0xfd48432b, 0xfd3cd59a, 0xfd30b936,
+ 0xfd23dea4, 0xfd16349e, 0xfd07a7a3, 0xfcf8219b, 0xfce7895b,
+ 0xfcd5c220, 0xfcc2aadb, 0xfcae1d5e, 0xfc97ed4e, 0xfc7fe6d4,
+ 0xfc65ccf3, 0xfc495762, 0xfc2a2fc8, 0xfc07ee19, 0xfbe213c1,
+ 0xfbb8051a, 0xfb890078, 0xfb5411a5, 0xfb180005, 0xfad33482,
+ 0xfa839276, 0xfa263b32, 0xf9b72d1c, 0xf930a1a2, 0xf889f023,
+ 0xf7b577d2, 0xf69c650c, 0xf51530f0, 0xf2cb0e3c, 0xeeefb15d,
+ 0xe6da6ecf,
+}
+var we = [256]float32{
+ 2.0249555e-09, 1.486674e-11, 2.4409617e-11, 3.1968806e-11,
+ 3.844677e-11, 4.4228204e-11, 4.9516443e-11, 5.443359e-11,
+ 5.905944e-11, 6.344942e-11, 6.7643814e-11, 7.1672945e-11,
+ 7.556032e-11, 7.932458e-11, 8.298079e-11, 8.654132e-11,
+ 9.0016515e-11, 9.3415074e-11, 9.674443e-11, 1.0001099e-10,
+ 1.03220314e-10, 1.06377254e-10, 1.09486115e-10, 1.1255068e-10,
+ 1.1557435e-10, 1.1856015e-10, 1.2151083e-10, 1.2442886e-10,
+ 1.2731648e-10, 1.3017575e-10, 1.3300853e-10, 1.3581657e-10,
+ 1.3860142e-10, 1.4136457e-10, 1.4410738e-10, 1.4683108e-10,
+ 1.4953687e-10, 1.5222583e-10, 1.54899e-10, 1.5755733e-10,
+ 1.6020171e-10, 1.6283301e-10, 1.6545203e-10, 1.6805951e-10,
+ 1.7065617e-10, 1.732427e-10, 1.7581973e-10, 1.7838787e-10,
+ 1.8094774e-10, 1.8349985e-10, 1.8604476e-10, 1.8858298e-10,
+ 1.9111498e-10, 1.9364126e-10, 1.9616223e-10, 1.9867835e-10,
+ 2.0119004e-10, 2.0369768e-10, 2.0620168e-10, 2.087024e-10,
+ 2.1120022e-10, 2.136955e-10, 2.1618855e-10, 2.1867974e-10,
+ 2.2116936e-10, 2.2365775e-10, 2.261452e-10, 2.2863202e-10,
+ 2.311185e-10, 2.3360494e-10, 2.360916e-10, 2.3857874e-10,
+ 2.4106667e-10, 2.4355562e-10, 2.4604588e-10, 2.485377e-10,
+ 2.5103128e-10, 2.5352695e-10, 2.560249e-10, 2.585254e-10,
+ 2.6102867e-10, 2.6353494e-10, 2.6604446e-10, 2.6855745e-10,
+ 2.7107416e-10, 2.7359479e-10, 2.761196e-10, 2.7864877e-10,
+ 2.8118255e-10, 2.8372119e-10, 2.8626485e-10, 2.888138e-10,
+ 2.9136826e-10, 2.939284e-10, 2.9649452e-10, 2.9906677e-10,
+ 3.016454e-10, 3.0423064e-10, 3.0682268e-10, 3.0942177e-10,
+ 3.1202813e-10, 3.1464195e-10, 3.1726352e-10, 3.19893e-10,
+ 3.2253064e-10, 3.251767e-10, 3.2783135e-10, 3.3049485e-10,
+ 3.3316744e-10, 3.3584938e-10, 3.3854083e-10, 3.4124212e-10,
+ 3.4395342e-10, 3.46675e-10, 3.4940711e-10, 3.5215003e-10,
+ 3.5490397e-10, 3.5766917e-10, 3.6044595e-10, 3.6323455e-10,
+ 3.660352e-10, 3.6884823e-10, 3.7167386e-10, 3.745124e-10,
+ 3.773641e-10, 3.802293e-10, 3.8310827e-10, 3.860013e-10,
+ 3.8890866e-10, 3.918307e-10, 3.9476775e-10, 3.9772008e-10,
+ 4.0068804e-10, 4.0367196e-10, 4.0667217e-10, 4.09689e-10,
+ 4.1272286e-10, 4.1577405e-10, 4.1884296e-10, 4.2192994e-10,
+ 4.250354e-10, 4.281597e-10, 4.313033e-10, 4.3446652e-10,
+ 4.3764986e-10, 4.408537e-10, 4.4407847e-10, 4.4732465e-10,
+ 4.5059267e-10, 4.5388301e-10, 4.571962e-10, 4.6053267e-10,
+ 4.6389292e-10, 4.6727755e-10, 4.70687e-10, 4.741219e-10,
+ 4.7758275e-10, 4.810702e-10, 4.845848e-10, 4.8812715e-10,
+ 4.9169796e-10, 4.9529775e-10, 4.989273e-10, 5.0258725e-10,
+ 5.0627835e-10, 5.100013e-10, 5.1375687e-10, 5.1754584e-10,
+ 5.21369e-10, 5.2522725e-10, 5.2912136e-10, 5.330522e-10,
+ 5.370208e-10, 5.4102806e-10, 5.45075e-10, 5.491625e-10,
+ 5.532918e-10, 5.5746385e-10, 5.616799e-10, 5.6594107e-10,
+ 5.7024857e-10, 5.746037e-10, 5.7900773e-10, 5.834621e-10,
+ 5.8796823e-10, 5.925276e-10, 5.971417e-10, 6.018122e-10,
+ 6.065408e-10, 6.113292e-10, 6.1617933e-10, 6.2109295e-10,
+ 6.260722e-10, 6.3111916e-10, 6.3623595e-10, 6.4142497e-10,
+ 6.4668854e-10, 6.5202926e-10, 6.5744976e-10, 6.6295286e-10,
+ 6.6854156e-10, 6.742188e-10, 6.79988e-10, 6.858526e-10,
+ 6.9181616e-10, 6.978826e-10, 7.04056e-10, 7.103407e-10,
+ 7.167412e-10, 7.2326256e-10, 7.2990985e-10, 7.366886e-10,
+ 7.4360473e-10, 7.5066453e-10, 7.5787476e-10, 7.6524265e-10,
+ 7.7277595e-10, 7.80483e-10, 7.883728e-10, 7.9645507e-10,
+ 8.047402e-10, 8.1323964e-10, 8.219657e-10, 8.309319e-10,
+ 8.401528e-10, 8.496445e-10, 8.594247e-10, 8.6951274e-10,
+ 8.799301e-10, 8.9070046e-10, 9.018503e-10, 9.134092e-10,
+ 9.254101e-10, 9.378904e-10, 9.508923e-10, 9.644638e-10,
+ 9.786603e-10, 9.935448e-10, 1.0091913e-09, 1.025686e-09,
+ 1.0431306e-09, 1.0616465e-09, 1.08138e-09, 1.1025096e-09,
+ 1.1252564e-09, 1.1498986e-09, 1.1767932e-09, 1.206409e-09,
+ 1.2393786e-09, 1.276585e-09, 1.3193139e-09, 1.3695435e-09,
+ 1.4305498e-09, 1.508365e-09, 1.6160854e-09, 1.7921248e-09,
+}
+var fe = [256]float32{
+ 1, 0.9381437, 0.90046996, 0.87170434, 0.8477855, 0.8269933,
+ 0.8084217, 0.7915276, 0.77595687, 0.7614634, 0.7478686,
+ 0.7350381, 0.72286767, 0.71127474, 0.70019263, 0.6895665,
+ 0.67935055, 0.6695063, 0.66000086, 0.65080583, 0.6418967,
+ 0.63325197, 0.6248527, 0.6166822, 0.60872537, 0.60096896,
+ 0.5934009, 0.58601034, 0.5787874, 0.57172304, 0.5648092,
+ 0.5580383, 0.5514034, 0.5448982, 0.5385169, 0.53225386,
+ 0.5261042, 0.52006316, 0.5141264, 0.50828975, 0.5025495,
+ 0.496902, 0.49134386, 0.485872, 0.48048335, 0.4751752,
+ 0.46994483, 0.46478975, 0.45970762, 0.45469615, 0.44975325,
+ 0.44487688, 0.44006512, 0.43531612, 0.43062815, 0.42599955,
+ 0.42142874, 0.4169142, 0.41245446, 0.40804818, 0.403694,
+ 0.3993907, 0.39513698, 0.39093173, 0.38677382, 0.38266218,
+ 0.37859577, 0.37457356, 0.37059465, 0.3666581, 0.362763,
+ 0.35890847, 0.35509375, 0.351318, 0.3475805, 0.34388044,
+ 0.34021714, 0.3365899, 0.33299807, 0.32944095, 0.32591796,
+ 0.3224285, 0.3189719, 0.31554767, 0.31215525, 0.30879408,
+ 0.3054636, 0.3021634, 0.29889292, 0.2956517, 0.29243928,
+ 0.28925523, 0.28609908, 0.28297043, 0.27986884, 0.27679393,
+ 0.2737453, 0.2707226, 0.2677254, 0.26475343, 0.26180625,
+ 0.25888354, 0.25598502, 0.2531103, 0.25025907, 0.24743107,
+ 0.24462597, 0.24184346, 0.23908329, 0.23634516, 0.23362878,
+ 0.23093392, 0.2282603, 0.22560766, 0.22297576, 0.22036438,
+ 0.21777324, 0.21520215, 0.21265087, 0.21011916, 0.20760682,
+ 0.20511365, 0.20263945, 0.20018397, 0.19774707, 0.19532852,
+ 0.19292815, 0.19054577, 0.1881812, 0.18583426, 0.18350479,
+ 0.1811926, 0.17889754, 0.17661946, 0.17435817, 0.17211354,
+ 0.1698854, 0.16767362, 0.16547804, 0.16329853, 0.16113494,
+ 0.15898713, 0.15685499, 0.15473837, 0.15263714, 0.15055119,
+ 0.14848037, 0.14642459, 0.14438373, 0.14235765, 0.14034624,
+ 0.13834943, 0.13636707, 0.13439907, 0.13244532, 0.13050574,
+ 0.1285802, 0.12666863, 0.12477092, 0.12288698, 0.12101672,
+ 0.119160056, 0.1173169, 0.115487166, 0.11367077, 0.11186763,
+ 0.11007768, 0.10830083, 0.10653701, 0.10478614, 0.10304816,
+ 0.101323, 0.09961058, 0.09791085, 0.09622374, 0.09454919,
+ 0.09288713, 0.091237515, 0.08960028, 0.087975375, 0.08636274,
+ 0.08476233, 0.083174095, 0.081597984, 0.08003395, 0.07848195,
+ 0.076941945, 0.07541389, 0.07389775, 0.072393484, 0.07090106,
+ 0.069420435, 0.06795159, 0.066494495, 0.06504912, 0.063615434,
+ 0.062193416, 0.060783047, 0.059384305, 0.057997175,
+ 0.05662164, 0.05525769, 0.053905312, 0.052564494, 0.051235236,
+ 0.049917534, 0.048611384, 0.047316793, 0.046033762, 0.0447623,
+ 0.043502413, 0.042254124, 0.041017443, 0.039792392,
+ 0.038578995, 0.037377283, 0.036187284, 0.035009038,
+ 0.033842582, 0.032687962, 0.031545233, 0.030414443, 0.02929566,
+ 0.02818895, 0.027094385, 0.026012046, 0.024942026, 0.023884421,
+ 0.022839336, 0.021806888, 0.020787204, 0.019780423, 0.0187867,
+ 0.0178062, 0.016839107, 0.015885621, 0.014945968, 0.014020392,
+ 0.013109165, 0.012212592, 0.011331013, 0.01046481, 0.009614414,
+ 0.008780315, 0.007963077, 0.0071633533, 0.006381906,
+ 0.0056196423, 0.0048776558, 0.004157295, 0.0034602648,
+ 0.0027887989, 0.0021459677, 0.0015362998, 0.0009672693,
+ 0.00045413437,
+}
diff --git a/rand/modulo_test.go b/rand/modulo_test.go
new file mode 100644
index 0000000..da963c7
--- /dev/null
+++ b/rand/modulo_test.go
@@ -0,0 +1,50 @@
+// Copyright 2017 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.
+
+// This file validates that the calculation in Uint64n corrects for
+// possible bias.
+
+package rand
+
+import (
+ "testing"
+)
+
+// modSource is used to probe the upper region of uint64 space. It
+// generates values sequentially in [maxUint64-15,maxUint64]. With
+// modEdge == 15 and maxUint64 == 1<<64-1 == 18446744073709551615,
+// this means that Uint64n(10) will repeatedly probe the top range.
+// We thus expect a bias to result unless the calculation in Uint64n
+// gets the edge condition right. We test this by calling Uint64n 100
+// times; the results should be perfectly evenly distributed across
+// [0,10).
+type modSource uint64
+
+const modEdge = 15
+
+func (m *modSource) Seed(uint64) {}
+
+// Uint64 returns a non-pseudo-random 64-bit unsigned integer as a uint64.
+func (m *modSource) Uint64() uint64 {
+ if *m > modEdge {
+ *m = 0
+ }
+ r := maxUint64 - *m
+ *m++
+ return uint64(r)
+}
+
+func TestUint64Modulo(t *testing.T) {
+ var src modSource
+ rng := New(&src)
+ var result [10]uint64
+ for i := 0; i < 100; i++ {
+ result[rng.Uint64n(10)]++
+ }
+ for _, r := range result {
+ if r != 10 {
+ t.Fatal(result)
+ }
+ }
+}
diff --git a/rand/normal.go b/rand/normal.go
new file mode 100644
index 0000000..ba4ea54
--- /dev/null
+++ b/rand/normal.go
@@ -0,0 +1,157 @@
+// 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
+
+import (
+ "math"
+)
+
+/*
+ * Normal distribution
+ *
+ * See "The Ziggurat Method for Generating Random Variables"
+ * (Marsaglia & Tsang, 2000)
+ * http://www.jstatsoft.org/v05/i08/paper [pdf]
+ */
+
+const (
+ rn = 3.442619855899
+)
+
+func absInt32(i int32) uint32 {
+ if i < 0 {
+ return uint32(-i)
+ }
+ return uint32(i)
+}
+
+// NormFloat64 returns a normally distributed float64 in the range
+// [-math.MaxFloat64, +math.MaxFloat64] with
+// standard normal distribution (mean = 0, stddev = 1).
+// To produce a different normal distribution, callers can
+// adjust the output using:
+//
+// sample = NormFloat64() * desiredStdDev + desiredMean
+//
+func (r *Rand) NormFloat64() float64 {
+ for {
+ j := int32(r.Uint32()) // Possibly negative
+ i := j & 0x7F
+ x := float64(j) * float64(wn[i])
+ if absInt32(j) < kn[i] {
+ // This case should be hit better than 99% of the time.
+ return x
+ }
+
+ if i == 0 {
+ // This extra work is only required for the base strip.
+ for {
+ x = -math.Log(r.Float64()) * (1.0 / rn)
+ y := -math.Log(r.Float64())
+ if y+y >= x*x {
+ break
+ }
+ }
+ if j > 0 {
+ return rn + x
+ }
+ return -rn - x
+ }
+ if fn[i]+float32(r.Float64())*(fn[i-1]-fn[i]) < float32(math.Exp(-.5*x*x)) {
+ return x
+ }
+ }
+}
+
+var kn = [128]uint32{
+ 0x76ad2212, 0x0, 0x600f1b53, 0x6ce447a6, 0x725b46a2,
+ 0x7560051d, 0x774921eb, 0x789a25bd, 0x799045c3, 0x7a4bce5d,
+ 0x7adf629f, 0x7b5682a6, 0x7bb8a8c6, 0x7c0ae722, 0x7c50cce7,
+ 0x7c8cec5b, 0x7cc12cd6, 0x7ceefed2, 0x7d177e0b, 0x7d3b8883,
+ 0x7d5bce6c, 0x7d78dd64, 0x7d932886, 0x7dab0e57, 0x7dc0dd30,
+ 0x7dd4d688, 0x7de73185, 0x7df81cea, 0x7e07c0a3, 0x7e163efa,
+ 0x7e23b587, 0x7e303dfd, 0x7e3beec2, 0x7e46db77, 0x7e51155d,
+ 0x7e5aabb3, 0x7e63abf7, 0x7e6c222c, 0x7e741906, 0x7e7b9a18,
+ 0x7e82adfa, 0x7e895c63, 0x7e8fac4b, 0x7e95a3fb, 0x7e9b4924,
+ 0x7ea0a0ef, 0x7ea5b00d, 0x7eaa7ac3, 0x7eaf04f3, 0x7eb3522a,
+ 0x7eb765a5, 0x7ebb4259, 0x7ebeeafd, 0x7ec2620a, 0x7ec5a9c4,
+ 0x7ec8c441, 0x7ecbb365, 0x7ece78ed, 0x7ed11671, 0x7ed38d62,
+ 0x7ed5df12, 0x7ed80cb4, 0x7eda175c, 0x7edc0005, 0x7eddc78e,
+ 0x7edf6ebf, 0x7ee0f647, 0x7ee25ebe, 0x7ee3a8a9, 0x7ee4d473,
+ 0x7ee5e276, 0x7ee6d2f5, 0x7ee7a620, 0x7ee85c10, 0x7ee8f4cd,
+ 0x7ee97047, 0x7ee9ce59, 0x7eea0eca, 0x7eea3147, 0x7eea3568,
+ 0x7eea1aab, 0x7ee9e071, 0x7ee98602, 0x7ee90a88, 0x7ee86d08,
+ 0x7ee7ac6a, 0x7ee6c769, 0x7ee5bc9c, 0x7ee48a67, 0x7ee32efc,
+ 0x7ee1a857, 0x7edff42f, 0x7ede0ffa, 0x7edbf8d9, 0x7ed9ab94,
+ 0x7ed7248d, 0x7ed45fae, 0x7ed1585c, 0x7ece095f, 0x7eca6ccb,
+ 0x7ec67be2, 0x7ec22eee, 0x7ebd7d1a, 0x7eb85c35, 0x7eb2c075,
+ 0x7eac9c20, 0x7ea5df27, 0x7e9e769f, 0x7e964c16, 0x7e8d44ba,
+ 0x7e834033, 0x7e781728, 0x7e6b9933, 0x7e5d8a1a, 0x7e4d9ded,
+ 0x7e3b737a, 0x7e268c2f, 0x7e0e3ff5, 0x7df1aa5d, 0x7dcf8c72,
+ 0x7da61a1e, 0x7d72a0fb, 0x7d30e097, 0x7cd9b4ab, 0x7c600f1a,
+ 0x7ba90bdc, 0x7a722176, 0x77d664e5,
+}
+var wn = [128]float32{
+ 1.7290405e-09, 1.2680929e-10, 1.6897518e-10, 1.9862688e-10,
+ 2.2232431e-10, 2.4244937e-10, 2.601613e-10, 2.7611988e-10,
+ 2.9073963e-10, 3.042997e-10, 3.1699796e-10, 3.289802e-10,
+ 3.4035738e-10, 3.5121603e-10, 3.616251e-10, 3.7164058e-10,
+ 3.8130857e-10, 3.9066758e-10, 3.9975012e-10, 4.08584e-10,
+ 4.1719309e-10, 4.2559822e-10, 4.338176e-10, 4.418672e-10,
+ 4.497613e-10, 4.5751258e-10, 4.651324e-10, 4.7263105e-10,
+ 4.8001775e-10, 4.87301e-10, 4.944885e-10, 5.015873e-10,
+ 5.0860405e-10, 5.155446e-10, 5.2241467e-10, 5.2921934e-10,
+ 5.359635e-10, 5.426517e-10, 5.4928817e-10, 5.5587696e-10,
+ 5.624219e-10, 5.6892646e-10, 5.753941e-10, 5.818282e-10,
+ 5.882317e-10, 5.946077e-10, 6.00959e-10, 6.072884e-10,
+ 6.135985e-10, 6.19892e-10, 6.2617134e-10, 6.3243905e-10,
+ 6.386974e-10, 6.449488e-10, 6.511956e-10, 6.5744005e-10,
+ 6.6368433e-10, 6.699307e-10, 6.7618144e-10, 6.824387e-10,
+ 6.8870465e-10, 6.949815e-10, 7.012715e-10, 7.075768e-10,
+ 7.1389966e-10, 7.202424e-10, 7.266073e-10, 7.329966e-10,
+ 7.394128e-10, 7.4585826e-10, 7.5233547e-10, 7.58847e-10,
+ 7.653954e-10, 7.719835e-10, 7.7861395e-10, 7.852897e-10,
+ 7.920138e-10, 7.987892e-10, 8.0561924e-10, 8.125073e-10,
+ 8.194569e-10, 8.2647167e-10, 8.3355556e-10, 8.407127e-10,
+ 8.479473e-10, 8.55264e-10, 8.6266755e-10, 8.7016316e-10,
+ 8.777562e-10, 8.8545243e-10, 8.932582e-10, 9.0117996e-10,
+ 9.09225e-10, 9.174008e-10, 9.2571584e-10, 9.341788e-10,
+ 9.427997e-10, 9.515889e-10, 9.605579e-10, 9.697193e-10,
+ 9.790869e-10, 9.88676e-10, 9.985036e-10, 1.0085882e-09,
+ 1.0189509e-09, 1.0296151e-09, 1.0406069e-09, 1.0519566e-09,
+ 1.063698e-09, 1.0758702e-09, 1.0885183e-09, 1.1016947e-09,
+ 1.1154611e-09, 1.1298902e-09, 1.1450696e-09, 1.1611052e-09,
+ 1.1781276e-09, 1.1962995e-09, 1.2158287e-09, 1.2369856e-09,
+ 1.2601323e-09, 1.2857697e-09, 1.3146202e-09, 1.347784e-09,
+ 1.3870636e-09, 1.4357403e-09, 1.5008659e-09, 1.6030948e-09,
+}
+var fn = [128]float32{
+ 1, 0.9635997, 0.9362827, 0.9130436, 0.89228165, 0.87324303,
+ 0.8555006, 0.8387836, 0.8229072, 0.8077383, 0.793177,
+ 0.7791461, 0.7655842, 0.7524416, 0.73967725, 0.7272569,
+ 0.7151515, 0.7033361, 0.69178915, 0.68049186, 0.6694277,
+ 0.658582, 0.6479418, 0.63749546, 0.6272325, 0.6171434,
+ 0.6072195, 0.5974532, 0.58783704, 0.5783647, 0.56903,
+ 0.5598274, 0.5507518, 0.54179835, 0.5329627, 0.52424055,
+ 0.5156282, 0.50712204, 0.49871865, 0.49041483, 0.48220766,
+ 0.4740943, 0.46607214, 0.4581387, 0.45029163, 0.44252872,
+ 0.43484783, 0.427247, 0.41972435, 0.41227803, 0.40490642,
+ 0.39760786, 0.3903808, 0.3832238, 0.37613547, 0.36911446,
+ 0.3621595, 0.35526937, 0.34844297, 0.34167916, 0.33497685,
+ 0.3283351, 0.3217529, 0.3152294, 0.30876362, 0.30235484,
+ 0.29600215, 0.28970486, 0.2834622, 0.2772735, 0.27113807,
+ 0.2650553, 0.25902456, 0.2530453, 0.24711695, 0.241239,
+ 0.23541094, 0.22963232, 0.2239027, 0.21822165, 0.21258877,
+ 0.20700371, 0.20146611, 0.19597565, 0.19053204, 0.18513499,
+ 0.17978427, 0.17447963, 0.1692209, 0.16400786, 0.15884037,
+ 0.15371831, 0.14864157, 0.14361008, 0.13862377, 0.13368265,
+ 0.12878671, 0.12393598, 0.119130544, 0.11437051, 0.10965602,
+ 0.104987256, 0.10036444, 0.095787846, 0.0912578, 0.08677467,
+ 0.0823389, 0.077950984, 0.073611505, 0.06932112, 0.06508058,
+ 0.06089077, 0.056752663, 0.0526674, 0.048636295, 0.044660863,
+ 0.040742867, 0.03688439, 0.033087887, 0.029356318,
+ 0.025693292, 0.022103304, 0.018592102, 0.015167298,
+ 0.011839478, 0.008624485, 0.005548995, 0.0026696292,
+}
diff --git a/rand/race_test.go b/rand/race_test.go
new file mode 100644
index 0000000..376224f
--- /dev/null
+++ b/rand/race_test.go
@@ -0,0 +1,48 @@
+// Copyright 2016 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
+
+import (
+ "sync"
+ "testing"
+)
+
+// TestConcurrent exercises the rand API concurrently, triggering situations
+// where the race detector is likely to detect issues.
+func TestConcurrent(t *testing.T) {
+ const (
+ numRoutines = 10
+ numCycles = 10
+ )
+ var wg sync.WaitGroup
+ defer wg.Wait()
+ wg.Add(numRoutines)
+ for i := 0; i < numRoutines; i++ {
+ go func(i int) {
+ defer wg.Done()
+ buf := make([]byte, 997)
+ for j := 0; j < numCycles; j++ {
+ var seed uint64
+ seed += uint64(ExpFloat64())
+ seed += uint64(Float32())
+ seed += uint64(Float64())
+ seed += uint64(Intn(Int()))
+ seed += uint64(Int31n(Int31()))
+ seed += uint64(Int63n(Int63()))
+ seed += uint64(NormFloat64())
+ seed += uint64(Uint32())
+ seed += uint64(Uint64())
+ for _, p := range Perm(10) {
+ seed += uint64(p)
+ }
+ Read(buf)
+ for _, b := range buf {
+ seed += uint64(b)
+ }
+ Seed(uint64(i*j) * seed)
+ }
+ }(i)
+ }
+}
diff --git a/rand/rand.go b/rand/rand.go
new file mode 100644
index 0000000..47ccd1f
--- /dev/null
+++ b/rand/rand.go
@@ -0,0 +1,334 @@
+// 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, a LockedSource, is safe for concurrent use by multiple
+// goroutines, but Sources created by NewSource are not. However, Sources are small
+// and it is reasonable to have a separate Source for each goroutine, seeded
+// differently, to avoid locking.
+//
+// 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<<64).
+type Source interface {
+ Uint64() uint64
+ Seed(seed uint64)
+}
+
+// NewSource returns a new pseudo-random Source seeded with the given value.
+func NewSource(seed uint64) Source {
+ var rng PCGSource
+ rng.Seed(seed)
+ return &rng
+}
+
+// A Rand is a source of random numbers.
+type Rand struct {
+ src Source
+
+ // readVal contains remainder of 64-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 uint64
+ // 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 {
+ return &Rand{src: src}
+}
+
+// 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 uint64) {
+ if lk, ok := r.src.(*LockedSource); ok {
+ lk.seedPos(seed, &r.readPos)
+ return
+ }
+
+ r.src.Seed(seed)
+ r.readPos = 0
+}
+
+// Uint64 returns a pseudo-random 64-bit integer as a uint64.
+func (r *Rand) Uint64() uint64 { return r.src.Uint64() }
+
+// Int63 returns a non-negative pseudo-random 63-bit integer as an int64.
+func (r *Rand) Int63() 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.Uint64() >> 32) }
+
+// Int31 returns a non-negative pseudo-random 31-bit integer as an int32.
+func (r *Rand) Int31() int32 { return int32(r.Uint64() >> 33) }
+
+// Int returns a non-negative pseudo-random int.
+func (r *Rand) Int() int {
+ u := uint(r.Uint64())
+ return int(u << 1 >> 1) // clear sign bit.
+}
+
+const maxUint64 = (1 << 64) - 1
+
+// Uint64n returns, as a uint64, a pseudo-random number in [0,n).
+// It is guaranteed more uniform than taking a Source value mod n
+// for any n that is not a power of 2.
+func (r *Rand) Uint64n(n uint64) uint64 {
+ if n&(n-1) == 0 { // n is power of two, can mask
+ if n == 0 {
+ panic("invalid argument to Uint64n")
+ }
+ return r.Uint64() & (n - 1)
+ }
+ // If n does not divide v, to avoid bias we must not use
+ // a v that is within maxUint64%n of the top of the range.
+ v := r.Uint64()
+ if v > maxUint64-n { // Fast check.
+ ceiling := maxUint64 - maxUint64%n
+ for v >= ceiling {
+ v = r.Uint64()
+ }
+ }
+
+ return v % n
+}
+
+// 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")
+ }
+ return int64(r.Uint64n(uint64(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")
+ }
+ // TODO: Avoid some 64-bit ops to make it more efficient on 32-bit machines.
+ return int32(r.Uint64n(uint64(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")
+ }
+ // TODO: Avoid some 64-bit ops to make it more efficient on 32-bit machines.
+ return int(r.Uint64n(uint64(n)))
+}
+
+// Float64 returns, as a float64, a pseudo-random number in [0.0,1.0).
+func (r *Rand) Float64() float64 {
+ return float64(r.Uint64n(1<<53)) / (1 << 53)
+ // 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.Uint64n(1<<53)) / (1 << 53)
+ if f == 1.0 {
+ goto again // resample; this branch is taken O(never)
+ }
+ return f
+}
+
+// Float32 returns, as a float32, a pseudo-random number in [0.0,1.0).
+func (r *Rand) Float32() float32 {
+ // We do not want 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 [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
+}
+
+// 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) {
+ if lk, ok := r.src.(*LockedSource); ok {
+ return lk.Read(p, &r.readVal, &r.readPos)
+ }
+ return read(p, r.Uint64, &r.readVal, &r.readPos)
+}
+
+func read(p []byte, uint64 func() uint64, readVal *uint64, readPos *int8) (n int, err error) {
+ pos := *readPos
+ val := *readVal
+ for n = 0; n < len(p); n++ {
+ if pos == 0 {
+ val = uint64()
+ pos = 8
+ }
+ p[n] = byte(val)
+ val >>= 8
+ pos--
+ }
+ *readPos = pos
+ *readVal = val
+ return
+}
+
+/*
+ * 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).
+// Seed, unlike the Rand.Seed method, is safe for concurrent use.
+func Seed(seed uint64) { 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() }
+
+// 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 [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) }
+
+// 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 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() }
+
+// LockedSource is an implementation of Source that is concurrency-safe.
+// It is just a standard Source with its operations protected by a sync.Mutex.
+type LockedSource struct {
+ lk sync.Mutex
+ src Source
+}
+
+func (s *LockedSource) Uint64() (n uint64) {
+ s.lk.Lock()
+ n = s.src.Uint64()
+ s.lk.Unlock()
+ return
+}
+
+func (s *LockedSource) Seed(seed uint64) {
+ s.lk.Lock()
+ s.src.Seed(seed)
+ s.lk.Unlock()
+}
+
+// seedPos implements Seed for a LockedSource without a race condiiton.
+func (s *LockedSource) seedPos(seed uint64, readPos *int8) {
+ s.lk.Lock()
+ s.src.Seed(seed)
+ *readPos = 0
+ s.lk.Unlock()
+}
+
+// Read implements Read for a LockedSource.
+func (s *LockedSource) Read(p []byte, readVal *uint64, readPos *int8) (n int, err error) {
+ s.lk.Lock()
+ n, err = read(p, s.src.Uint64, readVal, readPos)
+ s.lk.Unlock()
+ return
+}
diff --git a/rand/rand_test.go b/rand/rand_test.go
new file mode 100644
index 0000000..c81293f
--- /dev/null
+++ b/rand/rand_test.go
@@ -0,0 +1,548 @@
+// 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
+
+import (
+ "bytes"
+ "errors"
+ "fmt"
+ "io"
+ "math"
+ "os"
+ "runtime"
+ "testing"
+ "testing/iotest"
+)
+
+const (
+ numTestSamples = 10000
+)
+
+type statsResults struct {
+ mean float64
+ stddev float64
+ closeEnough float64
+ maxError float64
+}
+
+func max(a, b float64) float64 {
+ if a > b {
+ return a
+ }
+ return b
+}
+
+func nearEqual(a, b, closeEnough, maxError float64) bool {
+ absDiff := math.Abs(a - b)
+ if absDiff < closeEnough { // Necessary when one value is zero and one value is close to zero.
+ return true
+ }
+ return absDiff/max(math.Abs(a), math.Abs(b)) < maxError
+}
+
+var testSeeds = []uint64{1, 1754801282, 1698661970, 1550503961}
+
+// checkSimilarDistribution returns success if the mean and stddev of the
+// two statsResults are similar.
+func (this *statsResults) checkSimilarDistribution(expected *statsResults) error {
+ if !nearEqual(this.mean, expected.mean, expected.closeEnough, expected.maxError) {
+ s := fmt.Sprintf("mean %v != %v (allowed error %v, %v)", this.mean, expected.mean, expected.closeEnough, expected.maxError)
+ fmt.Println(s)
+ return errors.New(s)
+ }
+ if !nearEqual(this.stddev, expected.stddev, 0, expected.maxError) {
+ s := fmt.Sprintf("stddev %v != %v (allowed error %v, %v)", this.stddev, expected.stddev, expected.closeEnough, expected.maxError)
+ fmt.Println(s)
+ return errors.New(s)
+ }
+ return nil
+}
+
+func getStatsResults(samples []float64) *statsResults {
+ res := new(statsResults)
+ var sum, squaresum float64
+ for _, s := range samples {
+ sum += s
+ squaresum += s * s
+ }
+ res.mean = sum / float64(len(samples))
+ res.stddev = math.Sqrt(squaresum/float64(len(samples)) - res.mean*res.mean)
+ return res
+}
+
+func checkSampleDistribution(t *testing.T, samples []float64, expected *statsResults) {
+ t.Helper()
+ actual := getStatsResults(samples)
+ err := actual.checkSimilarDistribution(expected)
+ if err != nil {
+ t.Errorf(err.Error())
+ }
+}
+
+func checkSampleSliceDistributions(t *testing.T, samples []float64, nslices int, expected *statsResults) {
+ t.Helper()
+ chunk := len(samples) / nslices
+ for i := 0; i < nslices; i++ {
+ low := i * chunk
+ var high int
+ if i == nslices-1 {
+ high = len(samples) - 1
+ } else {
+ high = (i + 1) * chunk
+ }
+ checkSampleDistribution(t, samples[low:high], expected)
+ }
+}
+
+//
+// Normal distribution tests
+//
+
+func generateNormalSamples(nsamples int, mean, stddev float64, seed uint64) []float64 {
+ r := New(NewSource(seed))
+ samples := make([]float64, nsamples)
+ for i := range samples {
+ samples[i] = r.NormFloat64()*stddev + mean
+ }
+ return samples
+}
+
+func testNormalDistribution(t *testing.T, nsamples int, mean, stddev float64, seed uint64) {
+ //fmt.Printf("testing nsamples=%v mean=%v stddev=%v seed=%v\n", nsamples, mean, stddev, seed);
+
+ samples := generateNormalSamples(nsamples, mean, stddev, seed)
+ errorScale := max(1.0, stddev) // Error scales with stddev
+ expected := &statsResults{mean, stddev, 0.10 * errorScale, 0.08 * errorScale}
+
+ // Make sure that the entire set matches the expected distribution.
+ checkSampleDistribution(t, samples, expected)
+
+ // Make sure that each half of the set matches the expected distribution.
+ checkSampleSliceDistributions(t, samples, 2, expected)
+
+ // Make sure that each 7th of the set matches the expected distribution.
+ checkSampleSliceDistributions(t, samples, 7, expected)
+}
+
+// Actual tests
+
+func TestStandardNormalValues(t *testing.T) {
+ for _, seed := range testSeeds {
+ testNormalDistribution(t, numTestSamples, 0, 1, seed)
+ }
+}
+
+func TestNonStandardNormalValues(t *testing.T) {
+ sdmax := 1000.0
+ mmax := 1000.0
+ if testing.Short() {
+ sdmax = 5
+ mmax = 5
+ }
+ for sd := 0.5; sd < sdmax; sd *= 2 {
+ for m := 0.5; m < mmax; m *= 2 {
+ for _, seed := range testSeeds {
+ testNormalDistribution(t, numTestSamples, m, sd, seed)
+ if testing.Short() {
+ break
+ }
+ }
+ }
+ }
+}
+
+//
+// Exponential distribution tests
+//
+
+func generateExponentialSamples(nsamples int, rate float64, seed uint64) []float64 {
+ r := New(NewSource(seed))
+ samples := make([]float64, nsamples)
+ for i := range samples {
+ samples[i] = r.ExpFloat64() / rate
+ }
+ return samples
+}
+
+func testExponentialDistribution(t *testing.T, nsamples int, rate float64, seed uint64) {
+ //fmt.Printf("testing nsamples=%v rate=%v seed=%v\n", nsamples, rate, seed)
+
+ mean := 1 / rate
+ stddev := mean
+
+ samples := generateExponentialSamples(nsamples, rate, seed)
+ errorScale := max(1.0, 1/rate) // Error scales with the inverse of the rate
+ expected := &statsResults{mean, stddev, 0.10 * errorScale, 0.20 * errorScale}
+
+ // Make sure that the entire set matches the expected distribution.
+ checkSampleDistribution(t, samples, expected)
+
+ // Make sure that each half of the set matches the expected distribution.
+ checkSampleSliceDistributions(t, samples, 2, expected)
+
+ // Make sure that each 7th of the set matches the expected distribution.
+ checkSampleSliceDistributions(t, samples, 7, expected)
+}
+
+// Actual tests
+
+func TestStandardExponentialValues(t *testing.T) {
+ for _, seed := range testSeeds {
+ testExponentialDistribution(t, numTestSamples, 1, seed)
+ }
+}
+
+func TestNonStandardExponentialValues(t *testing.T) {
+ for rate := 0.05; rate < 10; rate *= 2 {
+ for _, seed := range testSeeds {
+ testExponentialDistribution(t, numTestSamples, rate, seed)
+ if testing.Short() {
+ break
+ }
+ }
+ }
+}
+
+//
+// Table generation tests
+//
+
+func initNorm() (testKn []uint32, testWn, testFn []float32) {
+ const m1 = 1 << 31
+ var (
+ dn float64 = rn
+ tn = dn
+ vn float64 = 9.91256303526217e-3
+ )
+
+ testKn = make([]uint32, 128)
+ testWn = make([]float32, 128)
+ testFn = make([]float32, 128)
+
+ q := vn / math.Exp(-0.5*dn*dn)
+ testKn[0] = uint32((dn / q) * m1)
+ testKn[1] = 0
+ testWn[0] = float32(q / m1)
+ testWn[127] = float32(dn / m1)
+ testFn[0] = 1.0
+ testFn[127] = float32(math.Exp(-0.5 * dn * dn))
+ for i := 126; i >= 1; i-- {
+ dn = math.Sqrt(-2.0 * math.Log(vn/dn+math.Exp(-0.5*dn*dn)))
+ testKn[i+1] = uint32((dn / tn) * m1)
+ tn = dn
+ testFn[i] = float32(math.Exp(-0.5 * dn * dn))
+ testWn[i] = float32(dn / m1)
+ }
+ return
+}
+
+func initExp() (testKe []uint32, testWe, testFe []float32) {
+ const m2 = 1 << 32
+ var (
+ de float64 = re
+ te = de
+ ve float64 = 3.9496598225815571993e-3
+ )
+
+ testKe = make([]uint32, 256)
+ testWe = make([]float32, 256)
+ testFe = make([]float32, 256)
+
+ q := ve / math.Exp(-de)
+ testKe[0] = uint32((de / q) * m2)
+ testKe[1] = 0
+ testWe[0] = float32(q / m2)
+ testWe[255] = float32(de / m2)
+ testFe[0] = 1.0
+ testFe[255] = float32(math.Exp(-de))
+ for i := 254; i >= 1; i-- {
+ de = -math.Log(ve/de + math.Exp(-de))
+ testKe[i+1] = uint32((de / te) * m2)
+ te = de
+ testFe[i] = float32(math.Exp(-de))
+ testWe[i] = float32(de / m2)
+ }
+ return
+}
+
+// compareUint32Slices returns the first index where the two slices
+// disagree, or <0 if the lengths are the same and all elements
+// are identical.
+func compareUint32Slices(s1, s2 []uint32) int {
+ if len(s1) != len(s2) {
+ if len(s1) > len(s2) {
+ return len(s2) + 1
+ }
+ return len(s1) + 1
+ }
+ for i := range s1 {
+ if s1[i] != s2[i] {
+ return i
+ }
+ }
+ return -1
+}
+
+// compareFloat32Slices returns the first index where the two slices
+// disagree, or <0 if the lengths are the same and all elements
+// are identical.
+func compareFloat32Slices(s1, s2 []float32) int {
+ if len(s1) != len(s2) {
+ if len(s1) > len(s2) {
+ return len(s2) + 1
+ }
+ return len(s1) + 1
+ }
+ for i := range s1 {
+ if !nearEqual(float64(s1[i]), float64(s2[i]), 0, 1e-7) {
+ return i
+ }
+ }
+ return -1
+}
+
+func TestNormTables(t *testing.T) {
+ testKn, testWn, testFn := initNorm()
+ if i := compareUint32Slices(kn[0:], testKn); i >= 0 {
+ t.Errorf("kn disagrees at index %v; %v != %v", i, kn[i], testKn[i])
+ }
+ if i := compareFloat32Slices(wn[0:], testWn); i >= 0 {
+ t.Errorf("wn disagrees at index %v; %v != %v", i, wn[i], testWn[i])
+ }
+ if i := compareFloat32Slices(fn[0:], testFn); i >= 0 {
+ t.Errorf("fn disagrees at index %v; %v != %v", i, fn[i], testFn[i])
+ }
+}
+
+func TestExpTables(t *testing.T) {
+ testKe, testWe, testFe := initExp()
+ if i := compareUint32Slices(ke[0:], testKe); i >= 0 {
+ t.Errorf("ke disagrees at index %v; %v != %v", i, ke[i], testKe[i])
+ }
+ if i := compareFloat32Slices(we[0:], testWe); i >= 0 {
+ t.Errorf("we disagrees at index %v; %v != %v", i, we[i], testWe[i])
+ }
+ if i := compareFloat32Slices(fe[0:], testFe); i >= 0 {
+ t.Errorf("fe disagrees at index %v; %v != %v", i, fe[i], testFe[i])
+ }
+}
+
+func hasSlowFloatingPoint() bool {
+ switch runtime.GOARCH {
+ case "arm":
+ return os.Getenv("GOARM") == "5"
+ case "mips", "mipsle", "mips64", "mips64le":
+ // Be conservative and assume that all mips boards
+ // have emulated floating point.
+ // TODO: detect what it actually has.
+ return true
+ }
+ return false
+}
+
+func TestFloat32(t *testing.T) {
+ // For issue 6721, the problem came after 7533753 calls, so check 10e6.
+ num := int(10e6)
+ // But do the full amount only on builders (not locally).
+ // But ARM5 floating point emulation is slow (Issue 10749), so
+ // do less for that builder:
+ if testing.Short() && hasSlowFloatingPoint() { // TODO: (testenv.Builder() == "" || hasSlowFloatingPoint())
+ num /= 100 // 1.72 seconds instead of 172 seconds
+ }
+
+ r := New(NewSource(1))
+ for ct := 0; ct < num; ct++ {
+ f := r.Float32()
+ if f >= 1 {
+ t.Fatal("Float32() should be in range [0,1). ct:", ct, "f:", f)
+ }
+ }
+}
+
+func testReadUniformity(t *testing.T, n int, seed uint64) {
+ r := New(NewSource(seed))
+ buf := make([]byte, n)
+ nRead, err := r.Read(buf)
+ if err != nil {
+ t.Errorf("Read err %v", err)
+ }
+ if nRead != n {
+ t.Errorf("Read returned unexpected n; %d != %d", nRead, n)
+ }
+
+ // Expect a uniform distribution of byte values, which lie in [0, 255].
+ var (
+ mean = 255.0 / 2
+ stddev = 256.0 / math.Sqrt(12.0)
+ errorScale = stddev / math.Sqrt(float64(n))
+ )
+
+ expected := &statsResults{mean, stddev, 0.10 * errorScale, 0.08 * errorScale}
+
+ // Cast bytes as floats to use the common distribution-validity checks.
+ samples := make([]float64, n)
+ for i, val := range buf {
+ samples[i] = float64(val)
+ }
+ // Make sure that the entire set matches the expected distribution.
+ checkSampleDistribution(t, samples, expected)
+}
+
+func TestReadUniformity(t *testing.T) {
+ testBufferSizes := []int{
+ 2, 4, 7, 64, 1024, 1 << 16, 1 << 20,
+ }
+ for _, seed := range testSeeds {
+ for _, n := range testBufferSizes {
+ testReadUniformity(t, n, seed)
+ }
+ }
+}
+
+func TestReadEmpty(t *testing.T) {
+ r := New(NewSource(1))
+ buf := make([]byte, 0)
+ n, err := r.Read(buf)
+ if err != nil {
+ t.Errorf("Read err into empty buffer; %v", err)
+ }
+ if n != 0 {
+ t.Errorf("Read into empty buffer returned unexpected n of %d", n)
+ }
+}
+
+func TestReadByOneByte(t *testing.T) {
+ r := New(NewSource(1))
+ b1 := make([]byte, 100)
+ _, err := io.ReadFull(iotest.OneByteReader(r), b1)
+ if err != nil {
+ t.Errorf("read by one byte: %v", err)
+ }
+ r = New(NewSource(1))
+ b2 := make([]byte, 100)
+ _, err = r.Read(b2)
+ if err != nil {
+ t.Errorf("read: %v", err)
+ }
+ if !bytes.Equal(b1, b2) {
+ t.Errorf("read by one byte vs single read:\n%x\n%x", b1, b2)
+ }
+}
+
+func TestReadSeedReset(t *testing.T) {
+ r := New(NewSource(42))
+ b1 := make([]byte, 128)
+ _, err := r.Read(b1)
+ if err != nil {
+ t.Errorf("read: %v", err)
+ }
+ r.Seed(42)
+ b2 := make([]byte, 128)
+ _, err = r.Read(b2)
+ if err != nil {
+ t.Errorf("read: %v", err)
+ }
+ if !bytes.Equal(b1, b2) {
+ t.Errorf("mismatch after re-seed:\n%x\n%x", b1, b2)
+ }
+}
+
+// Benchmarks
+
+func BenchmarkSource(b *testing.B) {
+ rng := NewSource(0)
+ for n := b.N; n > 0; n-- {
+ rng.Uint64()
+ }
+}
+
+func BenchmarkInt63Threadsafe(b *testing.B) {
+ for n := b.N; n > 0; n-- {
+ Int63()
+ }
+}
+
+func BenchmarkInt63Unthreadsafe(b *testing.B) {
+ r := New(NewSource(1))
+ for n := b.N; n > 0; n-- {
+ r.Int63()
+ }
+}
+
+func BenchmarkIntn1000(b *testing.B) {
+ r := New(NewSource(1))
+ for n := b.N; n > 0; n-- {
+ r.Intn(1000)
+ }
+}
+
+func BenchmarkInt63n1000(b *testing.B) {
+ r := New(NewSource(1))
+ for n := b.N; n > 0; n-- {
+ r.Int63n(1000)
+ }
+}
+
+func BenchmarkInt31n1000(b *testing.B) {
+ r := New(NewSource(1))
+ for n := b.N; n > 0; n-- {
+ r.Int31n(1000)
+ }
+}
+
+func BenchmarkFloat32(b *testing.B) {
+ r := New(NewSource(1))
+ for n := b.N; n > 0; n-- {
+ r.Float32()
+ }
+}
+
+func BenchmarkFloat64(b *testing.B) {
+ r := New(NewSource(1))
+ for n := b.N; n > 0; n-- {
+ r.Float64()
+ }
+}
+
+func BenchmarkPerm3(b *testing.B) {
+ r := New(NewSource(1))
+ for n := b.N; n > 0; n-- {
+ r.Perm(3)
+ }
+}
+
+func BenchmarkPerm30(b *testing.B) {
+ r := New(NewSource(1))
+ for n := b.N; n > 0; n-- {
+ r.Perm(30)
+ }
+}
+
+func BenchmarkRead3(b *testing.B) {
+ r := New(NewSource(1))
+ buf := make([]byte, 3)
+ b.ResetTimer()
+ for n := b.N; n > 0; n-- {
+ r.Read(buf)
+ }
+}
+
+func BenchmarkRead64(b *testing.B) {
+ r := New(NewSource(1))
+ buf := make([]byte, 64)
+ b.ResetTimer()
+ for n := b.N; n > 0; n-- {
+ r.Read(buf)
+ }
+}
+
+func BenchmarkRead1000(b *testing.B) {
+ r := New(NewSource(1))
+ buf := make([]byte, 1000)
+ b.ResetTimer()
+ for n := b.N; n > 0; n-- {
+ r.Read(buf)
+ }
+}
diff --git a/rand/regress_test.go b/rand/regress_test.go
new file mode 100644
index 0000000..ace8107
--- /dev/null
+++ b/rand/regress_test.go
@@ -0,0 +1,490 @@
+// Copyright 2014 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.
+
+// Test that random number sequences generated by a specific seed
+// do not change from version to version.
+//
+// If the generator changes, the golden outputs need updating, and
+// client programs may break. Although the desire for compatibility
+// is not as stringent as in the original math/rand package,
+// when possible avoid changing the generator.
+
+package rand_test
+
+import (
+ "flag"
+ "fmt"
+ "reflect"
+ "testing"
+
+ . "golang.org/x/exp/rand"
+)
+
+var printgolden = flag.Bool("printgolden", false, "print golden results for regression test")
+
+// TestSource verifies that the output of the default Source is locked down.
+func TestSourceRegress(t *testing.T) {
+ src := NewSource(1)
+ var got [20]uint64
+ for i := range got {
+ got[i] = src.Uint64()
+ }
+ want := [20]uint64{
+ 0x34e936394905d167,
+ 0x817c0ef62fe4c731,
+ 0x937987e6e24f5a40,
+ 0x0c0a8307fe226199,
+ 0xf96363568d8bab56,
+ 0xbaef3af36bd02620,
+ 0x8f18e416eb6b936b,
+ 0x05a43fc149f3a67a,
+ 0xdab012eb3ce01697,
+ 0xf76c495a133c6aa9,
+ 0x304b24c5040ce457,
+ 0x47d77e0abb413159,
+ 0x52a810fa9e452f04,
+ 0x2d24b66380cf4780,
+ 0x5ec7691b92018ef5,
+ 0x5076dfa749261ea0,
+ 0xac8f11ad3941d213,
+ 0x13fa8d67de91db25,
+ 0xb50883a9893274eb,
+ 0xeb8f59263f9109ac,
+ }
+ if got != want {
+ t.Errorf("got:\n\t%#016x\nwant:\n\t%#016x", got, want)
+ if *printgolden {
+ for _, x := range got {
+ fmt.Printf("\t\t%#016x,\n", x)
+ }
+ }
+ }
+}
+
+// TestRegress validates that the output stream is locked down, for instance so
+// optimizations do not change the output. It iterates over methods of the
+// Rand type to find functions to evaluate and checks the first 20 results
+// against the golden results.
+func TestRegress(t *testing.T) {
+ var int32s = []int32{1, 10, 32, 1 << 20, 1<<20 + 1, 1000000000, 1 << 30, 1<<31 - 2, 1<<31 - 1}
+ var int64s = []int64{1, 10, 32, 1 << 20, 1<<20 + 1, 1000000000, 1 << 30, 1<<31 - 2, 1<<31 - 1, 1000000000000000000, 1 << 60, 1<<63 - 2, 1<<63 - 1}
+ var uint64s = []uint64{1, 10, 32, 1 << 20, 1<<20 + 1, 1000000000, 1 << 30, 1<<31 - 2, 1<<31 - 1, 1000000000000000000, 1 << 60, 1<<64 - 2, 1<<64 - 1}
+ var permSizes = []int{0, 1, 5, 8, 9, 10, 16}
+ var readBufferSizes = []int{1, 7, 8, 9, 10}
+ r := New(NewSource(0))
+
+ rv := reflect.ValueOf(r)
+ n := rv.NumMethod()
+ p := 0
+ if *printgolden {
+ fmt.Printf("var regressGolden = []interface{}{\n")
+ }
+ for i := 0; i < n; i++ {
+ m := rv.Type().Method(i)
+ mv := rv.Method(i)
+ mt := mv.Type()
+ if mt.NumOut() == 0 {
+ continue
+ }
+ r.Seed(0)
+ if *printgolden && i > 0 {
+ fmt.Println()
+ }
+ for repeat := 0; repeat < 20; repeat++ {
+ var args []reflect.Value
+ var argstr string
+ if mt.NumIn() == 1 {
+ var x interface{}
+ switch mt.In(0).Kind() {
+ default:
+ t.Fatalf("unexpected argument type for r.%s", m.Name)
+
+ case reflect.Int:
+ if m.Name == "Perm" {
+ x = permSizes[repeat%len(permSizes)]
+ break
+ }
+ big := int64s[repeat%len(int64s)]
+ if int64(int(big)) != big {
+ r.Int63n(big) // what would happen on 64-bit machine, to keep stream in sync
+ if *printgolden {
+ fmt.Printf("\tskipped, // must run printgolden on 64-bit machine\n")
+ }
+ p++
+ continue
+ }
+ x = int(big)
+
+ case reflect.Int32:
+ x = int32s[repeat%len(int32s)]
+
+ case reflect.Int64:
+ x = int64s[repeat%len(int64s)]
+
+ case reflect.Uint64:
+ x = uint64s[repeat%len(uint64s)]
+
+ case reflect.Slice:
+ if m.Name == "Read" {
+ n := readBufferSizes[repeat%len(readBufferSizes)]
+ x = make([]byte, n)
+ }
+ }
+ argstr = fmt.Sprint(x)
+ args = append(args, reflect.ValueOf(x))
+ }
+
+ var out interface{}
+ out = mv.Call(args)[0].Interface()
+ if m.Name == "Int" || m.Name == "Intn" {
+ out = int64(out.(int))
+ }
+ if m.Name == "Read" {
+ out = args[0].Interface().([]byte)
+ }
+ if *printgolden {
+ var val string
+ big := int64(1 << 60)
+ if int64(int(big)) != big && (m.Name == "Int" || m.Name == "Intn") {
+ // 32-bit machine cannot print 64-bit results
+ val = "truncated"
+ } else if reflect.TypeOf(out).Kind() == reflect.Slice {
+ val = fmt.Sprintf("%#v", out)
+ } else {
+ val = fmt.Sprintf("%T(%v)", out, out)
+ }
+ fmt.Printf("\t%s, // %s(%s)\n", val, m.Name, argstr)
+ } else {
+ want := regressGolden[p]
+ if m.Name == "Int" {
+ want = int64(int(uint(want.(int64)) << 1 >> 1))
+ }
+ if !reflect.DeepEqual(out, want) {
+ t.Errorf("r.%s(%s) = %v, want %v", m.Name, argstr, out, want)
+ }
+ }
+ p++
+ }
+ }
+ if *printgolden {
+ fmt.Printf("}\n")
+ }
+}
+
+var regressGolden = []interface{}{
+ float64(0.6279600685109523), // ExpFloat64()
+ float64(0.16198826513357806), // ExpFloat64()
+ float64(0.007880404652650552), // ExpFloat64()
+ float64(0.41649788761745654), // ExpFloat64()
+ float64(1.6958707787276301), // ExpFloat64()
+ float64(2.7227327706138036), // ExpFloat64()
+ float64(2.4235600263079657), // ExpFloat64()
+ float64(1.277967771105418), // ExpFloat64()
+ float64(0.7111660437031769), // ExpFloat64()
+ float64(0.23090401427981888), // ExpFloat64()
+ float64(1.4746763588379928), // ExpFloat64()
+ float64(1.4868726779832278), // ExpFloat64()
+ float64(0.1686257242078103), // ExpFloat64()
+ float64(0.2732721816228957), // ExpFloat64()
+ float64(0.4644536065869748), // ExpFloat64()
+ float64(0.01319850986379164), // ExpFloat64()
+ float64(0.7184492551742854), // ExpFloat64()
+ float64(0.1913536422195827), // ExpFloat64()
+ float64(0.16034475958495667), // ExpFloat64()
+ float64(0.40599859014785644), // ExpFloat64()
+
+ float32(0.7979972), // Float32()
+ float32(0.7725961), // Float32()
+ float32(0.21894403), // Float32()
+ float32(0.96194494), // Float32()
+ float32(0.2915732), // Float32()
+ float32(0.59569645), // Float32()
+ float32(0.99596655), // Float32()
+ float32(0.4979039), // Float32()
+ float32(0.98148686), // Float32()
+ float32(0.01380035), // Float32()
+ float32(0.086487144), // Float32()
+ float32(0.6114401), // Float32()
+ float32(0.71081316), // Float32()
+ float32(0.6342346), // Float32()
+ float32(0.008082573), // Float32()
+ float32(0.33020085), // Float32()
+ float32(0.032625034), // Float32()
+ float32(0.9278005), // Float32()
+ float32(0.34497985), // Float32()
+ float32(0.66506875), // Float32()
+
+ float64(0.797997151016231), // Float64()
+ float64(0.7725961454373316), // Float64()
+ float64(0.21894402538580782), // Float64()
+ float64(0.9619449481780457), // Float64()
+ float64(0.2915731877602916), // Float64()
+ float64(0.5956964580775652), // Float64()
+ float64(0.9959665347028619), // Float64()
+ float64(0.49790390966591147), // Float64()
+ float64(0.9814868602566785), // Float64()
+ float64(0.013800350332924483), // Float64()
+ float64(0.08648714463652596), // Float64()
+ float64(0.6114401479210267), // Float64()
+ float64(0.7108131531183706), // Float64()
+ float64(0.6342346133706837), // Float64()
+ float64(0.008082572853887138), // Float64()
+ float64(0.3302008651926287), // Float64()
+ float64(0.03262503454637655), // Float64()
+ float64(0.9278004634858956), // Float64()
+ float64(0.3449798628384906), // Float64()
+ float64(0.665068719316529), // Float64()
+
+ int64(5474557666971700975), // Int()
+ int64(5591422465364813936), // Int()
+ int64(74029666500212977), // Int()
+ int64(8088122161323000979), // Int()
+ int64(7298457654139700474), // Int()
+ int64(1590632625527662686), // Int()
+ int64(9052198920789078554), // Int()
+ int64(7381380909356947872), // Int()
+ int64(1738222704626512495), // Int()
+ int64(3278744831230954970), // Int()
+ int64(7062423222661652521), // Int()
+ int64(6715870808026712034), // Int()
+ int64(528819992478005418), // Int()
+ int64(2284534088986354339), // Int()
+ int64(945828723091990082), // Int()
+ int64(3813019469742317492), // Int()
+ int64(1369388146907482806), // Int()
+ int64(7367238674766648970), // Int()
+ int64(8217673022687244206), // Int()
+ int64(3185531743396549562), // Int()
+
+ int32(1711064216), // Int31()
+ int32(650927245), // Int31()
+ int32(8618187), // Int31()
+ int32(941581344), // Int31()
+ int32(1923394120), // Int31()
+ int32(1258915833), // Int31()
+ int32(1053814650), // Int31()
+ int32(859305834), // Int31()
+ int32(1276097579), // Int31()
+ int32(1455437958), // Int31()
+ int32(1895916096), // Int31()
+ int32(781830261), // Int31()
+ int32(61562749), // Int31()
+ int32(265954771), // Int31()
+ int32(1183850779), // Int31()
+ int32(443893888), // Int31()
+ int32(1233159585), // Int31()
+ int32(857659461), // Int31()
+ int32(956663049), // Int31()
+ int32(370844703), // Int31()
+
+ int32(0), // Int31n(1)
+ int32(6), // Int31n(10)
+ int32(17), // Int31n(32)
+ int32(1000595), // Int31n(1048576)
+ int32(424333), // Int31n(1048577)
+ int32(382438494), // Int31n(1000000000)
+ int32(902738458), // Int31n(1073741824)
+ int32(1204933878), // Int31n(2147483646)
+ int32(1376191263), // Int31n(2147483647)
+ int32(0), // Int31n(1)
+ int32(9), // Int31n(10)
+ int32(2), // Int31n(32)
+ int32(440490), // Int31n(1048576)
+ int32(176312), // Int31n(1048577)
+ int32(946765890), // Int31n(1000000000)
+ int32(665034676), // Int31n(1073741824)
+ int32(1947285452), // Int31n(2147483646)
+ int32(1702344608), // Int31n(2147483647)
+ int32(0), // Int31n(1)
+ int32(2), // Int31n(10)
+
+ int64(5474557666971700975), // Int63()
+ int64(5591422465364813936), // Int63()
+ int64(74029666500212977), // Int63()
+ int64(8088122161323000979), // Int63()
+ int64(7298457654139700474), // Int63()
+ int64(1590632625527662686), // Int63()
+ int64(9052198920789078554), // Int63()
+ int64(7381380909356947872), // Int63()
+ int64(1738222704626512495), // Int63()
+ int64(3278744831230954970), // Int63()
+ int64(7062423222661652521), // Int63()
+ int64(6715870808026712034), // Int63()
+ int64(528819992478005418), // Int63()
+ int64(2284534088986354339), // Int63()
+ int64(945828723091990082), // Int63()
+ int64(3813019469742317492), // Int63()
+ int64(1369388146907482806), // Int63()
+ int64(7367238674766648970), // Int63()
+ int64(8217673022687244206), // Int63()
+ int64(3185531743396549562), // Int63()
+
+ int64(0), // Int63n(1)
+ int64(6), // Int63n(10)
+ int64(17), // Int63n(32)
+ int64(1000595), // Int63n(1048576)
+ int64(424333), // Int63n(1048577)
+ int64(382438494), // Int63n(1000000000)
+ int64(902738458), // Int63n(1073741824)
+ int64(1204933878), // Int63n(2147483646)
+ int64(1376191263), // Int63n(2147483647)
+ int64(502116868085730778), // Int63n(1000000000000000000)
+ int64(144894195020570665), // Int63n(1152921504606846976)
+ int64(6715870808026712034), // Int63n(9223372036854775806)
+ int64(528819992478005418), // Int63n(9223372036854775807)
+ int64(0), // Int63n(1)
+ int64(0), // Int63n(10)
+ int64(20), // Int63n(32)
+ int64(854710), // Int63n(1048576)
+ int64(649893), // Int63n(1048577)
+ int64(687244206), // Int63n(1000000000)
+ int64(836883386), // Int63n(1073741824)
+
+ int64(0), // Intn(1)
+ int64(6), // Intn(10)
+ int64(17), // Intn(32)
+ int64(1000595), // Intn(1048576)
+ int64(424333), // Intn(1048577)
+ int64(382438494), // Intn(1000000000)
+ int64(902738458), // Intn(1073741824)
+ int64(1204933878), // Intn(2147483646)
+ int64(1376191263), // Intn(2147483647)
+ int64(502116868085730778), // Intn(1000000000000000000)
+ int64(144894195020570665), // Intn(1152921504606846976)
+ int64(6715870808026712034), // Intn(9223372036854775806)
+ int64(528819992478005418), // Intn(9223372036854775807)
+ int64(0), // Intn(1)
+ int64(0), // Intn(10)
+ int64(20), // Intn(32)
+ int64(854710), // Intn(1048576)
+ int64(649893), // Intn(1048577)
+ int64(687244206), // Intn(1000000000)
+ int64(836883386), // Intn(1073741824)
+
+ float64(-0.5410658516792047), // NormFloat64()
+ float64(0.615296849055287), // NormFloat64()
+ float64(0.007477442280032887), // NormFloat64()
+ float64(1.3443892057169684), // NormFloat64()
+ float64(-0.17508902754863512), // NormFloat64()
+ float64(-2.03494397556937), // NormFloat64()
+ float64(2.5213558871972306), // NormFloat64()
+ float64(1.4572921639613627), // NormFloat64()
+ float64(-1.5164961164210644), // NormFloat64()
+ float64(-0.4861150771891445), // NormFloat64()
+ float64(-0.8699409548614199), // NormFloat64()
+ float64(1.6271559815452794), // NormFloat64()
+ float64(0.1659465769926195), // NormFloat64()
+ float64(0.2921716191987018), // NormFloat64()
+ float64(-1.2550269636927838), // NormFloat64()
+ float64(0.11257973349467548), // NormFloat64()
+ float64(0.5437525915836436), // NormFloat64()
+ float64(0.781754430770282), // NormFloat64()
+ float64(0.5201256313962235), // NormFloat64()
+ float64(1.3826174159276245), // NormFloat64()
+
+ []int{}, // Perm(0)
+ []int{0}, // Perm(1)
+ []int{0, 2, 3, 1, 4}, // Perm(5)
+ []int{5, 6, 3, 7, 4, 2, 0, 1}, // Perm(8)
+ []int{8, 4, 5, 2, 7, 3, 0, 6, 1}, // Perm(9)
+ []int{6, 1, 5, 3, 2, 9, 7, 0, 8, 4}, // Perm(10)
+ []int{12, 5, 1, 9, 15, 7, 13, 6, 10, 11, 8, 0, 4, 2, 14, 3}, // Perm(16)
+ []int{}, // Perm(0)
+ []int{0}, // Perm(1)
+ []int{0, 2, 3, 4, 1}, // Perm(5)
+ []int{3, 2, 7, 4, 0, 6, 5, 1}, // Perm(8)
+ []int{0, 6, 2, 1, 3, 7, 5, 8, 4}, // Perm(9)
+ []int{2, 5, 6, 4, 7, 3, 0, 8, 1, 9}, // Perm(10)
+ []int{3, 6, 5, 4, 9, 15, 13, 7, 1, 11, 10, 8, 12, 0, 2, 14}, // Perm(16)
+ []int{}, // Perm(0)
+ []int{0}, // Perm(1)
+ []int{2, 4, 3, 1, 0}, // Perm(5)
+ []int{1, 6, 7, 5, 4, 3, 2, 0}, // Perm(8)
+ []int{7, 6, 8, 2, 0, 1, 3, 4, 5}, // Perm(9)
+ []int{2, 9, 7, 1, 5, 4, 0, 6, 8, 3}, // Perm(10)
+
+ []byte{0xef}, // Read([0])
+ []byte{0x4e, 0x3d, 0x52, 0x31, 0x89, 0xf9, 0xcb}, // Read([0 0 0 0 0 0 0])
+ []byte{0x70, 0x68, 0x35, 0x8d, 0x1b, 0xb9, 0x98, 0x4d}, // Read([0 0 0 0 0 0 0 0])
+ []byte{0xf1, 0xf8, 0x95, 0xe6, 0x96, 0x1, 0x7, 0x1, 0x93}, // Read([0 0 0 0 0 0 0 0 0])
+ []byte{0x44, 0x9f, 0xc5, 0x40, 0xc8, 0x3e, 0x70, 0xfa, 0x44, 0x3a}, // Read([0 0 0 0 0 0 0 0 0 0])
+ []byte{0x4b}, // Read([0])
+ []byte{0x91, 0x54, 0x49, 0xe5, 0x5e, 0x28, 0xb9}, // Read([0 0 0 0 0 0 0])
+ []byte{0x4, 0xf2, 0xf, 0x13, 0x96, 0x1a, 0xb2, 0xce}, // Read([0 0 0 0 0 0 0 0])
+ []byte{0x35, 0xf5, 0xde, 0x9f, 0x7d, 0xa0, 0x19, 0x12, 0x2e}, // Read([0 0 0 0 0 0 0 0 0])
+ []byte{0xd4, 0xee, 0x6f, 0x66, 0x6f, 0x32, 0xc8, 0x21, 0x57, 0x68}, // Read([0 0 0 0 0 0 0 0 0 0])
+ []byte{0x1f}, // Read([0])
+ []byte{0x98, 0xda, 0x4d, 0xab, 0x6e, 0xd, 0x71}, // Read([0 0 0 0 0 0 0])
+ []byte{0x80, 0xad, 0x29, 0xa0, 0x37, 0xb0, 0x80, 0xc4}, // Read([0 0 0 0 0 0 0 0])
+ []byte{0x2, 0xe2, 0xe2, 0x7, 0xd9, 0xed, 0xea, 0x90, 0x33}, // Read([0 0 0 0 0 0 0 0 0])
+ []byte{0x5d, 0xaa, 0xb8, 0xc6, 0x39, 0xfb, 0xbe, 0x56, 0x7, 0xa3}, // Read([0 0 0 0 0 0 0 0 0 0])
+ []byte{0x62}, // Read([0])
+ []byte{0x4d, 0x63, 0xa6, 0x4b, 0xb4, 0x1f, 0x42}, // Read([0 0 0 0 0 0 0])
+ []byte{0x66, 0x42, 0x62, 0x36, 0x42, 0x20, 0x8d, 0xb4}, // Read([0 0 0 0 0 0 0 0])
+ []byte{0x9f, 0xa3, 0x67, 0x1, 0x91, 0xea, 0x34, 0xb6, 0xa}, // Read([0 0 0 0 0 0 0 0 0])
+ []byte{0xd, 0xa8, 0x43, 0xb, 0x1, 0x93, 0x8a, 0x56, 0xfc, 0x98}, // Read([0 0 0 0 0 0 0 0 0 0])
+
+ uint32(3422128433), // Uint32()
+ uint32(1301854491), // Uint32()
+ uint32(17236374), // Uint32()
+ uint32(1883162688), // Uint32()
+ uint32(3846788241), // Uint32()
+ uint32(2517831666), // Uint32()
+ uint32(2107629301), // Uint32()
+ uint32(1718611668), // Uint32()
+ uint32(2552195159), // Uint32()
+ uint32(2910875917), // Uint32()
+ uint32(3791832192), // Uint32()
+ uint32(1563660522), // Uint32()
+ uint32(123125499), // Uint32()
+ uint32(531909542), // Uint32()
+ uint32(2367701558), // Uint32()
+ uint32(887787777), // Uint32()
+ uint32(2466319171), // Uint32()
+ uint32(1715318922), // Uint32()
+ uint32(1913326099), // Uint32()
+ uint32(741689406), // Uint32()
+
+ uint64(14697929703826476783), // Uint64()
+ uint64(5591422465364813936), // Uint64()
+ uint64(74029666500212977), // Uint64()
+ uint64(8088122161323000979), // Uint64()
+ uint64(16521829690994476282), // Uint64()
+ uint64(10814004662382438494), // Uint64()
+ uint64(9052198920789078554), // Uint64()
+ uint64(7381380909356947872), // Uint64()
+ uint64(10961594741481288303), // Uint64()
+ uint64(12502116868085730778), // Uint64()
+ uint64(16285795259516428329), // Uint64()
+ uint64(6715870808026712034), // Uint64()
+ uint64(528819992478005418), // Uint64()
+ uint64(2284534088986354339), // Uint64()
+ uint64(10169200759946765890), // Uint64()
+ uint64(3813019469742317492), // Uint64()
+ uint64(10592760183762258614), // Uint64()
+ uint64(7367238674766648970), // Uint64()
+ uint64(8217673022687244206), // Uint64()
+ uint64(3185531743396549562), // Uint64()
+
+ uint64(0), // Uint64n(1)
+ uint64(6), // Uint64n(10)
+ uint64(17), // Uint64n(32)
+ uint64(1000595), // Uint64n(1048576)
+ uint64(424333), // Uint64n(1048577)
+ uint64(382438494), // Uint64n(1000000000)
+ uint64(902738458), // Uint64n(1073741824)
+ uint64(1204933878), // Uint64n(2147483646)
+ uint64(1376191263), // Uint64n(2147483647)
+ uint64(502116868085730778), // Uint64n(1000000000000000000)
+ uint64(144894195020570665), // Uint64n(1152921504606846976)
+ uint64(6715870808026712034), // Uint64n(18446744073709551614)
+ uint64(528819992478005418), // Uint64n(18446744073709551615)
+ uint64(0), // Uint64n(1)
+ uint64(0), // Uint64n(10)
+ uint64(20), // Uint64n(32)
+ uint64(854710), // Uint64n(1048576)
+ uint64(649893), // Uint64n(1048577)
+ uint64(687244206), // Uint64n(1000000000)
+ uint64(836883386), // Uint64n(1073741824)
+}
diff --git a/rand/rng.go b/rand/rng.go
new file mode 100644
index 0000000..d442985
--- /dev/null
+++ b/rand/rng.go
@@ -0,0 +1,91 @@
+// Copyright 2017 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
+
+import "math/bits"
+
+// PCGSource is an implementation of a 64-bit permuted congruential
+// generator as defined in
+//
+// PCG: A Family of Simple Fast Space-Efficient Statistically Good
+// Algorithms for Random Number Generation
+// Melissa E. O’Neill, Harvey Mudd College
+// http://www.pcg-random.org/pdf/toms-oneill-pcg-family-v1.02.pdf
+//
+// The generator here is the congruential generator PCG XSL RR 128/64 (LCG)
+// as found in the software available at http://www.pcg-random.org/.
+// It has period 2^128 with 128 bits of state, producing 64-bit values.
+// Is state is represented by two uint64 words.
+
+type PCGSource struct {
+ low uint64
+ high uint64
+}
+
+const (
+ maxUint32 = (1 << 32) - 1
+
+ multiplier = 47026247687942121848144207491837523525
+
+ increment = 117397592171526113268558934119004209487
+ incHigh = increment >> 64
+ incLow = increment & maxUint64
+
+ // TODO: Use these?
+ initializer = 245720598905631564143578724636268694099
+ initHigh = initializer >> 64
+ initLow = initializer & maxUint64
+)
+
+// Seed uses the provided seed value to initialize the generator to a deterministic state.
+func (pcg *PCGSource) Seed(seed uint64) {
+ pcg.low = seed
+ pcg.high = seed // TODO: What is right?
+}
+
+// Uint64 returns a pseudo-random 64-bit unsigned integer as a uint64.
+func (pcg *PCGSource) Uint64() uint64 {
+ pcg.multiply()
+ pcg.add()
+ // XOR high and low 64 bits together and rotate right by high 6 bits of state.
+ return bits.RotateLeft64(pcg.high^pcg.low, -int(pcg.high>>58))
+}
+
+func (pcg *PCGSource) add() {
+ old := pcg.low
+ pcg.low += incLow
+ if pcg.low < old {
+ // Carry occurred.
+ pcg.high++
+ }
+ pcg.high += incHigh
+}
+
+func (pcg *PCGSource) multiply() {
+ // Break each lower word into two separate 32-bit 'digits' each stored
+ // in a 64-bit word with 32 high zero bits. This allows the overflow
+ // into the high word to be computed.
+ s0 := (pcg.low >> 00) & maxUint32
+ s1 := (pcg.low >> 32) & maxUint32
+
+ const (
+ m0 = (multiplier >> 00) & maxUint32
+ m1 = (multiplier >> 32) & maxUint32
+ mLow = multiplier & (1<<64 - 1)
+ mHigh = multiplier >> 64 & (1<<64 - 1)
+ )
+
+ high := pcg.low*mHigh + pcg.high*mLow
+ s0m0 := s0 * m0
+ s0m1 := s0 * m1
+ s1m0 := s1 * m0
+ s1m1 := s1 * m1
+ high += (s0m1 >> 32) + (s1m0 >> 32)
+ carry := (s0m1 & maxUint32) + (s1m0 & maxUint32) + s0m0>>32
+ high += (carry >> 32)
+
+ pcg.low *= mLow
+ pcg.high = high + s1m1
+}
diff --git a/rand/zipf.go b/rand/zipf.go
new file mode 100644
index 0000000..f04c814
--- /dev/null
+++ b/rand/zipf.go
@@ -0,0 +1,77 @@
+// 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.
+
+// W.Hormann, G.Derflinger:
+// "Rejection-Inversion to Generate Variates
+// from Monotone Discrete Distributions"
+// http://eeyore.wu-wien.ac.at/papers/96-04-04.wh-der.ps.gz
+
+package rand
+
+import "math"
+
+// A Zipf generates Zipf distributed variates.
+type Zipf struct {
+ r *Rand
+ imax float64
+ v float64
+ q float64
+ s float64
+ oneminusQ float64
+ oneminusQinv float64
+ hxm float64
+ hx0minusHxm float64
+}
+
+func (z *Zipf) h(x float64) float64 {
+ return math.Exp(z.oneminusQ*math.Log(z.v+x)) * z.oneminusQinv
+}
+
+func (z *Zipf) hinv(x float64) float64 {
+ return math.Exp(z.oneminusQinv*math.Log(z.oneminusQ*x)) - z.v
+}
+
+// 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 NewZipf(r *Rand, s float64, v float64, imax uint64) *Zipf {
+ z := new(Zipf)
+ if s <= 1.0 || v < 1 {
+ return nil
+ }
+ z.r = r
+ z.imax = float64(imax)
+ z.v = v
+ z.q = s
+ z.oneminusQ = 1.0 - z.q
+ z.oneminusQinv = 1.0 / z.oneminusQ
+ z.hxm = z.h(z.imax + 0.5)
+ z.hx0minusHxm = z.h(0.5) - math.Exp(math.Log(z.v)*(-z.q)) - z.hxm
+ z.s = 1 - z.hinv(z.h(1.5)-math.Exp(-z.q*math.Log(z.v+1.0)))
+ return z
+}
+
+// Uint64 returns a value drawn from the Zipf distribution described
+// by the Zipf object.
+func (z *Zipf) Uint64() uint64 {
+ if z == nil {
+ panic("rand: nil Zipf")
+ }
+ k := 0.0
+
+ for {
+ r := z.r.Float64() // r on [0,1]
+ ur := z.hxm + r*z.hx0minusHxm
+ x := z.hinv(ur)
+ k = math.Floor(x + 0.5)
+ if k-x <= z.s {
+ break
+ }
+ if ur >= z.h(k+0.5)-math.Exp(-math.Log(k+z.v)*z.q) {
+ break
+ }
+ }
+ return uint64(k)
+}
