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-rw-r--r--src/math/rand/example_test.go97
-rw-r--r--src/math/rand/exp.go222
-rw-r--r--src/math/rand/normal.go157
-rw-r--r--src/math/rand/rand.go246
-rw-r--r--src/math/rand/rand_test.go398
-rw-r--r--src/math/rand/regress_test.go355
-rw-r--r--src/math/rand/rng.go246
-rw-r--r--src/math/rand/zipf.go75
8 files changed, 1796 insertions, 0 deletions
diff --git a/src/math/rand/example_test.go b/src/math/rand/example_test.go
new file mode 100644
index 000000000..f42991453
--- /dev/null
+++ b/src/math/rand/example_test.go
@@ -0,0 +1,97 @@
+// 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"
+ "math/rand"
+ "os"
+ "text/tabwriter"
+)
+
+// 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: As I see it yes
+}
+
+// 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(99))
+
+ // The tabwriter here helps us generate aligned output.
+ w := tabwriter.NewWriter(os.Stdout, 1, 1, 1, ' ', 0)
+ defer w.Flush()
+ show := func(name string, v1, v2, v3 interface{}) {
+ fmt.Fprintf(w, "%s\t%v\t%v\t%v\n", name, v1, v2, v3)
+ }
+
+ // Float32 and Float64 values are in [0, 1).
+ show("Float32", r.Float32(), r.Float32(), r.Float32())
+ show("Float64", r.Float64(), r.Float64(), r.Float64())
+
+ // ExpFloat64 values have an average of 1 but decay exponentially.
+ show("ExpFloat64", r.ExpFloat64(), r.ExpFloat64(), r.ExpFloat64())
+
+ // NormFloat64 values have an average of 0 and a standard deviation of 1.
+ show("NormFloat64", r.NormFloat64(), r.NormFloat64(), r.NormFloat64())
+
+ // Int31, Int63, and Uint32 generate values of the given width.
+ // The Int method (not shown) is like either Int31 or Int63
+ // depending on the size of 'int'.
+ show("Int31", r.Int31(), r.Int31(), r.Int31())
+ show("Int63", r.Int63(), r.Int63(), r.Int63())
+ show("Uint32", r.Int63(), r.Int63(), r.Int63())
+
+ // Intn, Int31n, and Int63n limit their output to be < n.
+ // They do so more carefully than using r.Int()%n.
+ show("Intn(10)", r.Intn(10), r.Intn(10), r.Intn(10))
+ show("Int31n(10)", r.Int31n(10), r.Int31n(10), r.Int31n(10))
+ show("Int63n(10)", r.Int63n(10), r.Int63n(10), r.Int63n(10))
+
+ // Perm generates a random permutation of the numbers [0, n).
+ show("Perm", r.Perm(5), r.Perm(5), r.Perm(5))
+ // Output:
+ // Float32 0.2635776 0.6358173 0.6718283
+ // Float64 0.628605430454327 0.4504798828572669 0.9562755949377957
+ // ExpFloat64 0.3362240648200941 1.4256072328483647 0.24354758816173044
+ // NormFloat64 0.17233959114940064 1.577014951434847 0.04259129641113857
+ // Int31 1501292890 1486668269 182840835
+ // Int63 3546343826724305832 5724354148158589552 5239846799706671610
+ // Uint32 5927547564735367388 637072299495207830 4128311955958246186
+ // Intn(10) 1 2 5
+ // Int31n(10) 4 7 8
+ // Int63n(10) 7 6 3
+ // Perm [1 4 2 3 0] [4 2 1 3 0] [1 2 4 0 3]
+}
diff --git a/src/math/rand/exp.go b/src/math/rand/exp.go
new file mode 100644
index 000000000..4bc110f91
--- /dev/null
+++ b/src/math/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/src/math/rand/normal.go b/src/math/rand/normal.go
new file mode 100644
index 000000000..ba4ea54ca
--- /dev/null
+++ b/src/math/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/src/math/rand/rand.go b/src/math/rand/rand.go
new file mode 100644
index 000000000..3ffb5c4e5
--- /dev/null
+++ b/src/math/rand/rand.go
@@ -0,0 +1,246 @@
+// Copyright 2009 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package rand implements pseudo-random number generators.
+//
+// Random numbers are generated by a Source. Top-level functions, such as
+// Float64 and Int, use a default shared Source that produces a deterministic
+// sequence of values each time a program is run. Use the Seed function to
+// initialize the default Source if different behavior is required for each run.
+// The default Source is safe for concurrent use by multiple goroutines.
+package rand
+
+import "sync"
+
+// A Source represents a source of uniformly-distributed
+// pseudo-random int64 values in the range [0, 1<<63).
+type Source interface {
+ Int63() int64
+ Seed(seed int64)
+}
+
+// NewSource returns a new pseudo-random Source seeded with the given value.
+func NewSource(seed int64) Source {
+ var rng rngSource
+ rng.Seed(seed)
+ return &rng
+}
+
+// A Rand is a source of random numbers.
+type Rand struct {
+ src Source
+}
+
+// New returns a new Rand that uses random values from src
+// to generate other random values.
+func New(src Source) *Rand { return &Rand{src} }
+
+// Seed uses the provided seed value to initialize the generator to a deterministic state.
+func (r *Rand) Seed(seed int64) { r.src.Seed(seed) }
+
+// Int63 returns a non-negative pseudo-random 63-bit integer as an int64.
+func (r *Rand) Int63() int64 { return r.src.Int63() }
+
+// Uint32 returns a pseudo-random 32-bit value as a uint32.
+func (r *Rand) Uint32() uint32 { return uint32(r.Int63() >> 31) }
+
+// Int31 returns a non-negative pseudo-random 31-bit integer as an int32.
+func (r *Rand) Int31() int32 { return int32(r.Int63() >> 32) }
+
+// Int returns a non-negative pseudo-random int.
+func (r *Rand) Int() int {
+ u := uint(r.Int63())
+ return int(u << 1 >> 1) // clear sign bit if int == int32
+}
+
+// Int63n returns, as an int64, a non-negative pseudo-random number in [0,n).
+// It panics if n <= 0.
+func (r *Rand) Int63n(n int64) int64 {
+ if n <= 0 {
+ panic("invalid argument to Int63n")
+ }
+ if n&(n-1) == 0 { // n is power of two, can mask
+ return r.Int63() & (n - 1)
+ }
+ max := int64((1 << 63) - 1 - (1<<63)%uint64(n))
+ v := r.Int63()
+ for v > max {
+ v = r.Int63()
+ }
+ return v % n
+}
+
+// Int31n returns, as an int32, a non-negative pseudo-random number in [0,n).
+// It panics if n <= 0.
+func (r *Rand) Int31n(n int32) int32 {
+ if n <= 0 {
+ panic("invalid argument to Int31n")
+ }
+ if n&(n-1) == 0 { // n is power of two, can mask
+ return r.Int31() & (n - 1)
+ }
+ max := int32((1 << 31) - 1 - (1<<31)%uint32(n))
+ v := r.Int31()
+ for v > max {
+ v = r.Int31()
+ }
+ return v % n
+}
+
+// Intn returns, as an int, a non-negative pseudo-random number in [0,n).
+// It panics if n <= 0.
+func (r *Rand) Intn(n int) int {
+ if n <= 0 {
+ panic("invalid argument to Intn")
+ }
+ if n <= 1<<31-1 {
+ return int(r.Int31n(int32(n)))
+ }
+ return int(r.Int63n(int64(n)))
+}
+
+// Float64 returns, as a float64, a pseudo-random number in [0.0,1.0).
+func (r *Rand) Float64() float64 {
+ // A clearer, simpler implementation would be:
+ // return float64(r.Int63n(1<<53)) / (1<<53)
+ // However, Go 1 shipped with
+ // return float64(r.Int63()) / (1 << 63)
+ // and we want to preserve that value stream.
+ //
+ // There is one bug in the value stream: r.Int63() may be so close
+ // to 1<<63 that the division rounds up to 1.0, and we've guaranteed
+ // that the result is always less than 1.0. To fix that, we treat the
+ // range as cyclic and map 1 back to 0. This is justified by observing
+ // that while some of the values rounded down to 0, nothing was
+ // rounding up to 0, so 0 was underrepresented in the results.
+ // Mapping 1 back to zero restores some balance.
+ // (The balance is not perfect because the implementation
+ // returns denormalized numbers for very small r.Int63(),
+ // and those steal from what would normally be 0 results.)
+ // The remapping only happens 1/2⁵³ of the time, so most clients
+ // will not observe it anyway.
+ f := float64(r.Int63()) / (1 << 63)
+ if f == 1 {
+ f = 0
+ }
+ return f
+}
+
+// Float32 returns, as a float32, a pseudo-random number in [0.0,1.0).
+func (r *Rand) Float32() float32 {
+ // Same rationale as in Float64: we want to preserve the Go 1 value
+ // stream except we want to fix it not to return 1.0
+ // There is a double rounding going on here, but the argument for
+ // mapping 1 to 0 still applies: 0 was underrepresented before,
+ // so mapping 1 to 0 doesn't cause too many 0s.
+ // This only happens 1/2²⁴ of the time (plus the 1/2⁵³ of the time in Float64).
+ f := float32(r.Float64())
+ if f == 1 {
+ f = 0
+ }
+ return f
+}
+
+// Perm returns, as a slice of n ints, a pseudo-random permutation of the integers [0,n).
+func (r *Rand) Perm(n int) []int {
+ m := make([]int, n)
+ for i := 0; i < n; i++ {
+ j := r.Intn(i + 1)
+ m[i] = m[j]
+ m[j] = i
+ }
+ return m
+}
+
+/*
+ * Top-level convenience functions
+ */
+
+var globalRand = New(&lockedSource{src: NewSource(1)})
+
+// Seed uses the provided seed value to initialize the default Source to a
+// deterministic state. If Seed is not called, the generator behaves as
+// if seeded by Seed(1).
+func Seed(seed int64) { globalRand.Seed(seed) }
+
+// Int63 returns a non-negative pseudo-random 63-bit integer as an int64
+// from the default Source.
+func Int63() int64 { return globalRand.Int63() }
+
+// Uint32 returns a pseudo-random 32-bit value as a uint32
+// from the default Source.
+func Uint32() uint32 { return globalRand.Uint32() }
+
+// Int31 returns a non-negative pseudo-random 31-bit integer as an int32
+// from the default Source.
+func Int31() int32 { return globalRand.Int31() }
+
+// Int returns a non-negative pseudo-random int from the default Source.
+func Int() int { return globalRand.Int() }
+
+// Int63n returns, as an int64, a non-negative pseudo-random number in [0,n)
+// from the default Source.
+// It panics if n <= 0.
+func Int63n(n int64) int64 { return globalRand.Int63n(n) }
+
+// Int31n returns, as an int32, a non-negative pseudo-random number in [0,n)
+// from the default Source.
+// It panics if n <= 0.
+func Int31n(n int32) int32 { return globalRand.Int31n(n) }
+
+// Intn returns, as an int, a non-negative pseudo-random number in [0,n)
+// from the default Source.
+// It panics if n <= 0.
+func Intn(n int) int { return globalRand.Intn(n) }
+
+// Float64 returns, as a float64, a pseudo-random number in [0.0,1.0)
+// from the default Source.
+func Float64() float64 { return globalRand.Float64() }
+
+// Float32 returns, as a float32, a pseudo-random number in [0.0,1.0)
+// from the default Source.
+func Float32() float32 { return globalRand.Float32() }
+
+// Perm returns, as a slice of n ints, a pseudo-random permutation of the integers [0,n)
+// from the default Source.
+func Perm(n int) []int { return globalRand.Perm(n) }
+
+// NormFloat64 returns a normally distributed float64 in the range
+// [-math.MaxFloat64, +math.MaxFloat64] with
+// standard normal distribution (mean = 0, stddev = 1)
+// from the default Source.
+// To produce a different normal distribution, callers can
+// adjust the output using:
+//
+// sample = NormFloat64() * desiredStdDev + desiredMean
+//
+func NormFloat64() float64 { return globalRand.NormFloat64() }
+
+// ExpFloat64 returns an exponentially distributed float64 in the range
+// (0, +math.MaxFloat64] with an exponential distribution whose rate parameter
+// (lambda) is 1 and whose mean is 1/lambda (1) from the default Source.
+// To produce a distribution with a different rate parameter,
+// callers can adjust the output using:
+//
+// sample = ExpFloat64() / desiredRateParameter
+//
+func ExpFloat64() float64 { return globalRand.ExpFloat64() }
+
+type lockedSource struct {
+ lk sync.Mutex
+ src Source
+}
+
+func (r *lockedSource) Int63() (n int64) {
+ r.lk.Lock()
+ n = r.src.Int63()
+ r.lk.Unlock()
+ return
+}
+
+func (r *lockedSource) Seed(seed int64) {
+ r.lk.Lock()
+ r.src.Seed(seed)
+ r.lk.Unlock()
+}
diff --git a/src/math/rand/rand_test.go b/src/math/rand/rand_test.go
new file mode 100644
index 000000000..ab0dc49b4
--- /dev/null
+++ b/src/math/rand/rand_test.go
@@ -0,0 +1,398 @@
+// 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 (
+ "errors"
+ "fmt"
+ "math"
+ "testing"
+)
+
+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 = []int64{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) {
+ 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) {
+ 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 int64) []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 int64) {
+ //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 int64) []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 int64) {
+ //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])
+ }
+}
+
+// For issue 6721, the problem came after 7533753 calls, so check 10e6.
+func TestFloat32(t *testing.T) {
+ r := New(NewSource(1))
+ for ct := 0; ct < 10e6; ct++ {
+ f := r.Float32()
+ if f >= 1 {
+ t.Fatal("Float32() should be in range [0,1). ct:", ct, "f:", f)
+ }
+ }
+}
+
+// Benchmarks
+
+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)
+ }
+}
diff --git a/src/math/rand/regress_test.go b/src/math/rand/regress_test.go
new file mode 100644
index 000000000..2b012af89
--- /dev/null
+++ b/src/math/rand/regress_test.go
@@ -0,0 +1,355 @@
+// 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.
+//
+// Do NOT make changes to the golden outputs. If bugs need to be fixed
+// in the underlying code, find ways to fix them that do not affect the
+// outputs.
+
+package rand_test
+
+import (
+ "flag"
+ "fmt"
+ . "math/rand"
+ "reflect"
+ "testing"
+)
+
+var printgolden = flag.Bool("printgolden", false, "print golden results for regression test")
+
+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 permSizes = []int{0, 1, 5, 8, 9, 10, 16}
+ 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
+ }
+ if mt.NumOut() != 1 {
+ t.Fatalf("unexpected result count for r.%s", m.Name)
+ }
+ r.Seed(0)
+ 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)]
+ }
+ argstr = fmt.Sprint(x)
+ args = append(args, reflect.ValueOf(x))
+ }
+ out := mv.Call(args)[0].Interface()
+ if m.Name == "Int" || m.Name == "Intn" {
+ out = int64(out.(int))
+ }
+ 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(4.668112973579268), // ExpFloat64()
+ float64(0.1601593871172866), // ExpFloat64()
+ float64(3.0465834105636), // ExpFloat64()
+ float64(0.06385839451671879), // ExpFloat64()
+ float64(1.8578917487258961), // ExpFloat64()
+ float64(0.784676123472182), // ExpFloat64()
+ float64(0.11225477361256932), // ExpFloat64()
+ float64(0.20173283329802255), // ExpFloat64()
+ float64(0.3468619496201105), // ExpFloat64()
+ float64(0.35601103454384536), // ExpFloat64()
+ float64(0.888376329507869), // ExpFloat64()
+ float64(1.4081362450365698), // ExpFloat64()
+ float64(1.0077753823151994), // ExpFloat64()
+ float64(0.23594100766227588), // ExpFloat64()
+ float64(2.777245612300007), // ExpFloat64()
+ float64(0.5202997830662377), // ExpFloat64()
+ float64(1.2842705247770294), // ExpFloat64()
+ float64(0.030307408362776206), // ExpFloat64()
+ float64(2.204156824853721), // ExpFloat64()
+ float64(2.09891923895058), // ExpFloat64()
+ float32(0.94519615), // Float32()
+ float32(0.24496509), // Float32()
+ float32(0.65595627), // Float32()
+ float32(0.05434384), // Float32()
+ float32(0.3675872), // Float32()
+ float32(0.28948045), // Float32()
+ float32(0.1924386), // Float32()
+ float32(0.65533215), // Float32()
+ float32(0.8971697), // Float32()
+ float32(0.16735445), // Float32()
+ float32(0.28858566), // Float32()
+ float32(0.9026048), // Float32()
+ float32(0.84978026), // Float32()
+ float32(0.2730468), // Float32()
+ float32(0.6090802), // Float32()
+ float32(0.253656), // Float32()
+ float32(0.7746542), // Float32()
+ float32(0.017480763), // Float32()
+ float32(0.78707397), // Float32()
+ float32(0.7993937), // Float32()
+ float64(0.9451961492941164), // Float64()
+ float64(0.24496508529377975), // Float64()
+ float64(0.6559562651954052), // Float64()
+ float64(0.05434383959970039), // Float64()
+ float64(0.36758720663245853), // Float64()
+ float64(0.2894804331565928), // Float64()
+ float64(0.19243860967493215), // Float64()
+ float64(0.6553321508148324), // Float64()
+ float64(0.897169713149801), // Float64()
+ float64(0.16735444255905835), // Float64()
+ float64(0.2885856518054551), // Float64()
+ float64(0.9026048462705047), // Float64()
+ float64(0.8497802817628735), // Float64()
+ float64(0.2730468047134829), // Float64()
+ float64(0.6090801919903561), // Float64()
+ float64(0.25365600644283687), // Float64()
+ float64(0.7746542391859803), // Float64()
+ float64(0.017480762156647272), // Float64()
+ float64(0.7870739563039942), // Float64()
+ float64(0.7993936979594545), // Float64()
+ int64(8717895732742165505), // Int()
+ int64(2259404117704393152), // Int()
+ int64(6050128673802995827), // Int()
+ int64(501233450539197794), // Int()
+ int64(3390393562759376202), // Int()
+ int64(2669985732393126063), // Int()
+ int64(1774932891286980153), // Int()
+ int64(6044372234677422456), // Int()
+ int64(8274930044578894929), // Int()
+ int64(1543572285742637646), // Int()
+ int64(2661732831099943416), // Int()
+ int64(8325060299420976708), // Int()
+ int64(7837839688282259259), // Int()
+ int64(2518412263346885298), // Int()
+ int64(5617773211005988520), // Int()
+ int64(2339563716805116249), // Int()
+ int64(7144924247938981575), // Int()
+ int64(161231572858529631), // Int()
+ int64(7259475919510918339), // Int()
+ int64(7373105480197164748), // Int()
+ int32(2029793274), // Int31()
+ int32(526058514), // Int31()
+ int32(1408655353), // Int31()
+ int32(116702506), // Int31()
+ int32(789387515), // Int31()
+ int32(621654496), // Int31()
+ int32(413258767), // Int31()
+ int32(1407315077), // Int31()
+ int32(1926657288), // Int31()
+ int32(359390928), // Int31()
+ int32(619732968), // Int31()
+ int32(1938329147), // Int31()
+ int32(1824889259), // Int31()
+ int32(586363548), // Int31()
+ int32(1307989752), // Int31()
+ int32(544722126), // Int31()
+ int32(1663557311), // Int31()
+ int32(37539650), // Int31()
+ int32(1690228450), // Int31()
+ int32(1716684894), // Int31()
+ int32(0), // Int31n(1)
+ int32(4), // Int31n(10)
+ int32(25), // Int31n(32)
+ int32(310570), // Int31n(1048576)
+ int32(857611), // Int31n(1048577)
+ int32(621654496), // Int31n(1000000000)
+ int32(413258767), // Int31n(1073741824)
+ int32(1407315077), // Int31n(2147483646)
+ int32(1926657288), // Int31n(2147483647)
+ int32(0), // Int31n(1)
+ int32(8), // Int31n(10)
+ int32(27), // Int31n(32)
+ int32(367019), // Int31n(1048576)
+ int32(209005), // Int31n(1048577)
+ int32(307989752), // Int31n(1000000000)
+ int32(544722126), // Int31n(1073741824)
+ int32(1663557311), // Int31n(2147483646)
+ int32(37539650), // Int31n(2147483647)
+ int32(0), // Int31n(1)
+ int32(4), // Int31n(10)
+ int64(8717895732742165505), // Int63()
+ int64(2259404117704393152), // Int63()
+ int64(6050128673802995827), // Int63()
+ int64(501233450539197794), // Int63()
+ int64(3390393562759376202), // Int63()
+ int64(2669985732393126063), // Int63()
+ int64(1774932891286980153), // Int63()
+ int64(6044372234677422456), // Int63()
+ int64(8274930044578894929), // Int63()
+ int64(1543572285742637646), // Int63()
+ int64(2661732831099943416), // Int63()
+ int64(8325060299420976708), // Int63()
+ int64(7837839688282259259), // Int63()
+ int64(2518412263346885298), // Int63()
+ int64(5617773211005988520), // Int63()
+ int64(2339563716805116249), // Int63()
+ int64(7144924247938981575), // Int63()
+ int64(161231572858529631), // Int63()
+ int64(7259475919510918339), // Int63()
+ int64(7373105480197164748), // Int63()
+ int64(0), // Int63n(1)
+ int64(2), // Int63n(10)
+ int64(19), // Int63n(32)
+ int64(959842), // Int63n(1048576)
+ int64(688912), // Int63n(1048577)
+ int64(393126063), // Int63n(1000000000)
+ int64(89212473), // Int63n(1073741824)
+ int64(834026388), // Int63n(2147483646)
+ int64(1577188963), // Int63n(2147483647)
+ int64(543572285742637646), // Int63n(1000000000000000000)
+ int64(355889821886249464), // Int63n(1152921504606846976)
+ int64(8325060299420976708), // Int63n(9223372036854775806)
+ int64(7837839688282259259), // Int63n(9223372036854775807)
+ int64(0), // Int63n(1)
+ int64(0), // Int63n(10)
+ int64(25), // Int63n(32)
+ int64(679623), // Int63n(1048576)
+ int64(882178), // Int63n(1048577)
+ int64(510918339), // Int63n(1000000000)
+ int64(782454476), // Int63n(1073741824)
+ int64(0), // Intn(1)
+ int64(4), // Intn(10)
+ int64(25), // Intn(32)
+ int64(310570), // Intn(1048576)
+ int64(857611), // Intn(1048577)
+ int64(621654496), // Intn(1000000000)
+ int64(413258767), // Intn(1073741824)
+ int64(1407315077), // Intn(2147483646)
+ int64(1926657288), // Intn(2147483647)
+ int64(543572285742637646), // Intn(1000000000000000000)
+ int64(355889821886249464), // Intn(1152921504606846976)
+ int64(8325060299420976708), // Intn(9223372036854775806)
+ int64(7837839688282259259), // Intn(9223372036854775807)
+ int64(0), // Intn(1)
+ int64(2), // Intn(10)
+ int64(14), // Intn(32)
+ int64(515775), // Intn(1048576)
+ int64(839455), // Intn(1048577)
+ int64(690228450), // Intn(1000000000)
+ int64(642943070), // Intn(1073741824)
+ float64(-0.28158587086436215), // NormFloat64()
+ float64(0.570933095808067), // NormFloat64()
+ float64(-1.6920196326157044), // NormFloat64()
+ float64(0.1996229111693099), // NormFloat64()
+ float64(1.9195199291234621), // NormFloat64()
+ float64(0.8954838794918353), // NormFloat64()
+ float64(0.41457072128813166), // NormFloat64()
+ float64(-0.48700161491544713), // NormFloat64()
+ float64(-0.1684059662402393), // NormFloat64()
+ float64(0.37056410998929545), // NormFloat64()
+ float64(1.0156889027029008), // NormFloat64()
+ float64(-0.5174422210625114), // NormFloat64()
+ float64(-0.5565834214413804), // NormFloat64()
+ float64(0.778320596648391), // NormFloat64()
+ float64(-1.8970718197702225), // NormFloat64()
+ float64(0.5229525761688676), // NormFloat64()
+ float64(-1.5515595563231523), // NormFloat64()
+ float64(0.0182029289376123), // NormFloat64()
+ float64(-0.6820951356608795), // NormFloat64()
+ float64(-0.5987943422687668), // NormFloat64()
+ []int{}, // Perm(0)
+ []int{0}, // Perm(1)
+ []int{0, 4, 1, 3, 2}, // Perm(5)
+ []int{3, 1, 0, 4, 7, 5, 2, 6}, // Perm(8)
+ []int{5, 0, 3, 6, 7, 4, 2, 1, 8}, // Perm(9)
+ []int{4, 5, 0, 2, 6, 9, 3, 1, 8, 7}, // Perm(10)
+ []int{14, 2, 0, 8, 3, 5, 13, 12, 1, 4, 6, 7, 11, 9, 15, 10}, // Perm(16)
+ []int{}, // Perm(0)
+ []int{0}, // Perm(1)
+ []int{3, 0, 1, 2, 4}, // Perm(5)
+ []int{5, 1, 2, 0, 4, 7, 3, 6}, // Perm(8)
+ []int{4, 0, 6, 8, 1, 5, 2, 7, 3}, // Perm(9)
+ []int{8, 6, 1, 7, 5, 4, 3, 2, 9, 0}, // Perm(10)
+ []int{0, 3, 13, 2, 15, 4, 10, 1, 8, 14, 7, 6, 12, 9, 5, 11}, // Perm(16)
+ []int{}, // Perm(0)
+ []int{0}, // Perm(1)
+ []int{0, 4, 2, 1, 3}, // Perm(5)
+ []int{2, 1, 7, 0, 6, 3, 4, 5}, // Perm(8)
+ []int{8, 7, 5, 3, 4, 6, 0, 1, 2}, // Perm(9)
+ []int{1, 0, 2, 5, 7, 6, 9, 8, 3, 4}, // Perm(10)
+ uint32(4059586549), // Uint32()
+ uint32(1052117029), // Uint32()
+ uint32(2817310706), // Uint32()
+ uint32(233405013), // Uint32()
+ uint32(1578775030), // Uint32()
+ uint32(1243308993), // Uint32()
+ uint32(826517535), // Uint32()
+ uint32(2814630155), // Uint32()
+ uint32(3853314576), // Uint32()
+ uint32(718781857), // Uint32()
+ uint32(1239465936), // Uint32()
+ uint32(3876658295), // Uint32()
+ uint32(3649778518), // Uint32()
+ uint32(1172727096), // Uint32()
+ uint32(2615979505), // Uint32()
+ uint32(1089444252), // Uint32()
+ uint32(3327114623), // Uint32()
+ uint32(75079301), // Uint32()
+ uint32(3380456901), // Uint32()
+ uint32(3433369789), // Uint32()
+}
diff --git a/src/math/rand/rng.go b/src/math/rand/rng.go
new file mode 100644
index 000000000..947c49f0f
--- /dev/null
+++ b/src/math/rand/rng.go
@@ -0,0 +1,246 @@
+// 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
+
+/*
+ * Uniform distribution
+ *
+ * algorithm by
+ * DP Mitchell and JA Reeds
+ */
+
+const (
+ _LEN = 607
+ _TAP = 273
+ _MAX = 1 << 63
+ _MASK = _MAX - 1
+ _A = 48271
+ _M = (1 << 31) - 1
+ _Q = 44488
+ _R = 3399
+)
+
+var (
+ // cooked random numbers
+ // the state of the rng
+ // after 780e10 iterations
+ rng_cooked [_LEN]int64 = [...]int64{
+ 5041579894721019882, 4646389086726545243, 1395769623340756751, 5333664234075297259,
+ 2875692520355975054, 9033628115061424579, 7143218595135194537, 4812947590706362721,
+ 7937252194349799378, 5307299880338848416, 8209348851763925077, 2115741599318814044,
+ 4593015457530856296, 8140875735541888011, 3319429241265089026, 8619815648190321034,
+ 1727074043483619500, 113108499721038619, 4569519971459345583, 5062833859075314731,
+ 2387618771259064424, 2716131344356686112, 6559392774825876886, 7650093201692370310,
+ 7684323884043752161, 257867835996031390, 6593456519409015164, 271327514973697897,
+ 2789386447340118284, 1065192797246149621, 3344507881999356393, 4459797941780066633,
+ 7465081662728599889, 1014950805555097187, 4449440729345990775, 3481109366438502643,
+ 2418672789110888383, 5796562887576294778, 4484266064449540171, 3738982361971787048,
+ 4523597184512354423, 10530508058128498, 8633833783282346118, 2625309929628791628,
+ 8660405965245884302, 10162832508971942, 6540714680961817391, 7031802312784620857,
+ 6240911277345944669, 831864355460801054, 8004434137542152891, 2116287251661052151,
+ 2202309800992166967, 9161020366945053561, 4069299552407763864, 4936383537992622449,
+ 457351505131524928, 342195045928179354, 2847771682816600509, 2068020115986376518,
+ 4368649989588021065, 887231587095185257, 5563591506886576496, 6816225200251950296,
+ 5616972787034086048, 8471809303394836566, 1686575021641186857, 4045484338074262002,
+ 4244156215201778923, 7848217333783577387, 5632136521049761902, 833283142057835272,
+ 9029726508369077193, 3243583134664087292, 4316371101804477087, 8937849979965997980,
+ 6446940406810434101, 1679342092332374735, 6050638460742422078, 6993520719509581582,
+ 7640877852514293609, 5881353426285907985, 812786550756860885, 4541845584483343330,
+ 2725470216277009086, 4980675660146853729, 5210769080603236061, 8894283318990530821,
+ 6326442804750084282, 1495812843684243920, 7069751578799128019, 7370257291860230865,
+ 6756929275356942261, 4706794511633873654, 7824520467827898663, 8549875090542453214,
+ 33650829478596156, 1328918435751322643, 7297902601803624459, 1011190183918857495,
+ 2238025036817854944, 5147159997473910359, 896512091560522982, 2659470849286379941,
+ 6097729358393448602, 1731725986304753684, 4106255841983812711, 8327155210721535508,
+ 8477511620686074402, 5803876044675762232, 8435417780860221662, 5988852856651071244,
+ 4715837297103951910, 7566171971264485114, 505808562678895611, 5070098180695063370,
+ 842110666775871513, 572156825025677802, 1791881013492340891, 3393267094866038768,
+ 3778721850472236509, 2352769483186201278, 1292459583847367458, 8897907043675088419,
+ 5781809037144163536, 2733958794029492513, 5092019688680754699, 8996124554772526841,
+ 4234737173186232084, 5027558287275472836, 4635198586344772304, 8687338893267139351,
+ 5907508150730407386, 784756255473944452, 972392927514829904, 5422057694808175112,
+ 5158420642969283891, 9048531678558643225, 2407211146698877100, 7583282216521099569,
+ 3940796514530962282, 3341174631045206375, 3095313889586102949, 7405321895688238710,
+ 5832080132947175283, 7890064875145919662, 8184139210799583195, 1149859861409226130,
+ 1464597243840211302, 4641648007187991873, 3516491885471466898, 956288521791657692,
+ 6657089965014657519, 5220884358887979358, 1796677326474620641, 5340761970648932916,
+ 1147977171614181568, 5066037465548252321, 2574765911837859848, 1085848279845204775,
+ 3350107529868390359, 6116438694366558490, 2107701075971293812, 1803294065921269267,
+ 2469478054175558874, 7368243281019965984, 3791908367843677526, 185046971116456637,
+ 2257095756513439648, 7217693971077460129, 909049953079504259, 7196649268545224266,
+ 5637660345400869599, 3955544945427965183, 8057528650917418961, 4139268440301127643,
+ 6621926588513568059, 1373361136802681441, 6527366231383600011, 3507654575162700890,
+ 9202058512774729859, 1954818376891585542, 6640380907130175705, 8299563319178235687,
+ 3901867355218954373, 7046310742295574065, 6847195391333990232, 1572638100518868053,
+ 8850422670118399721, 3631909142291992901, 5158881091950831288, 2882958317343121593,
+ 4763258931815816403, 6280052734341785344, 4243789408204964850, 2043464728020827976,
+ 6545300466022085465, 4562580375758598164, 5495451168795427352, 1738312861590151095,
+ 553004618757816492, 6895160632757959823, 8233623922264685171, 7139506338801360852,
+ 8550891222387991669, 5535668688139305547, 2430933853350256242, 5401941257863201076,
+ 8159640039107728799, 6157493831600770366, 7632066283658143750, 6308328381617103346,
+ 3681878764086140361, 3289686137190109749, 6587997200611086848, 244714774258135476,
+ 4079788377417136100, 8090302575944624335, 2945117363431356361, 864324395848741045,
+ 3009039260312620700, 8430027460082534031, 401084700045993341, 7254622446438694921,
+ 4707864159563588614, 5640248530963493951, 5982507712689997893, 3315098242282210105,
+ 5503847578771918426, 3941971367175193882, 8118566580304798074, 3839261274019871296,
+ 7062410411742090847, 741381002980207668, 6027994129690250817, 2497829994150063930,
+ 6251390334426228834, 1368930247903518833, 8809096399316380241, 6492004350391900708,
+ 2462145737463489636, 404828418920299174, 4153026434231690595, 261785715255475940,
+ 5464715384600071357, 592710404378763017, 6764129236657751224, 8513655718539357449,
+ 5820343663801914208, 385298524683789911, 5224135003438199467, 6303131641338802145,
+ 7150122561309371392, 368107899140673753, 3115186834558311558, 2915636353584281051,
+ 4782583894627718279, 6718292300699989587, 8387085186914375220, 3387513132024756289,
+ 4654329375432538231, 8930667561363381602, 5374373436876319273, 7623042350483453954,
+ 7725442901813263321, 9186225467561587250, 4091027289597503355, 2357631606492579800,
+ 2530936820058611833, 1636551876240043639, 5564664674334965799, 1452244145334316253,
+ 2061642381019690829, 1279580266495294036, 9108481583171221009, 6023278686734049809,
+ 5007630032676973346, 2153168792952589781, 6720334534964750538, 6041546491134794105,
+ 3433922409283786309, 2285479922797300912, 3110614940896576130, 6366559590722842893,
+ 5418791419666136509, 7163298419643543757, 4891138053923696990, 580618510277907015,
+ 1684034065251686769, 4429514767357295841, 330346578555450005, 1119637995812174675,
+ 7177515271653460134, 4589042248470800257, 7693288629059004563, 143607045258444228,
+ 246994305896273627, 866417324803099287, 6473547110565816071, 3092379936208876896,
+ 2058427839513754051, 5133784708526867938, 8785882556301281247, 6149332666841167611,
+ 8585842181454472135, 6137678347805511274, 2070447184436970006, 5708223427705576541,
+ 5999657892458244504, 4358391411789012426, 325123008708389849, 6837621693887290924,
+ 4843721905315627004, 6010651222149276415, 5398352198963874652, 4602025990114250980,
+ 1044646352569048800, 9106614159853161675, 829256115228593269, 4919284369102997000,
+ 2681532557646850893, 3681559472488511871, 5307999518958214035, 6334130388442829274,
+ 2658708232916537604, 1163313865052186287, 581945337509520675, 3648778920718647903,
+ 4423673246306544414, 1620799783996955743, 220828013409515943, 8150384699999389761,
+ 4287360518296753003, 4590000184845883843, 5513660857261085186, 6964829100392774275,
+ 478991688350776035, 8746140185685648781, 228500091334420247, 1356187007457302238,
+ 3019253992034194581, 3152601605678500003, 430152752706002213, 5559581553696971176,
+ 4916432985369275664, 663574931734554391, 3420773838927732076, 2868348622579915573,
+ 1999319134044418520, 3328689518636282723, 2587672709781371173, 1517255313529399333,
+ 3092343956317362483, 3662252519007064108, 972445599196498113, 7664865435875959367,
+ 1708913533482282562, 6917817162668868494, 3217629022545312900, 2570043027221707107,
+ 8739788839543624613, 2488075924621352812, 4694002395387436668, 4559628481798514356,
+ 2997203966153298104, 1282559373026354493, 240113143146674385, 8665713329246516443,
+ 628141331766346752, 4571950817186770476, 1472811188152235408, 7596648026010355826,
+ 6091219417754424743, 7834161864828164065, 7103445518877254909, 4390861237357459201,
+ 4442653864240571734, 8903482404847331368, 622261699494173647, 6037261250297213248,
+ 504404948065709118, 7275215526217113061, 1011176780856001400, 2194750105623461063,
+ 2623071828615234808, 5157313728073836108, 3738405111966602044, 2539767524076729570,
+ 2467284396349269342, 5256026990536851868, 7841086888628396109, 6640857538655893162,
+ 1202087339038317498, 2113514992440715978, 7534350895342931403, 4925284734898484745,
+ 5145623771477493805, 8225140880134972332, 2719520354384050532, 9132346697815513771,
+ 4332154495710163773, 7137789594094346916, 6994721091344268833, 6667228574869048934,
+ 655440045726677499, 59934747298466858, 6124974028078036405, 8957774780655365418,
+ 2332206071942466437, 1701056712286369627, 3154897383618636503, 1637766181387607527,
+ 2460521277767576533, 197309393502684135, 643677854385267315, 2543179307861934850,
+ 4350769010207485119, 4754652089410667672, 2015595502641514512, 7999059458976458608,
+ 4287946071480840813, 8362686366770308971, 6486469209321732151, 3617727845841796026,
+ 7554353525834302244, 4450022655153542367, 1605195740213535749, 5327014565305508387,
+ 4626575813550328320, 2692222020597705149, 241045573717249868, 5098046974627094010,
+ 7916882295460730264, 884817090297530579, 5329160409530630596, 7790979528857726136,
+ 4955070238059373407, 4918537275422674302, 3008076183950404629, 3007769226071157901,
+ 2470346235617803020, 8928702772696731736, 7856187920214445904, 4474874585391974885,
+ 7900176660600710914, 2140571127916226672, 2425445057265199971, 2486055153341847830,
+ 4186670094382025798, 1883939007446035042, 8808666044074867985, 3734134241178479257,
+ 4065968871360089196, 6953124200385847784, 1305686814738899057, 1637739099014457647,
+ 3656125660947993209, 3966759634633167020, 3106378204088556331, 6328899822778449810,
+ 4565385105440252958, 1979884289539493806, 2331793186920865425, 3783206694208922581,
+ 8464961209802336085, 2843963751609577687, 3030678195484896323, 4793717574095772604,
+ 4459239494808162889, 402587895800087237, 8057891408711167515, 4541888170938985079,
+ 1042662272908816815, 5557303057122568958, 2647678726283249984, 2144477441549833761,
+ 5806352215355387087, 7117771003473903623, 5916597177708541638, 462597715452321361,
+ 8833658097025758785, 5970273481425315300, 563813119381731307, 2768349550652697015,
+ 1598828206250873866, 5206393647403558110, 6235043485709261823, 3152217402014639496,
+ 8469693267274066490, 125672920241807416, 5311079624024060938, 6663754932310491587,
+ 8736848295048751716, 4488039774992061878, 5923302823487327109, 140891791083103236,
+ 7414942793393574290, 7990420780896957397, 4317817392807076702, 3625184369705367340,
+ 2740722765288122703, 5743100009702758344, 5997898640509039159, 8854493341352484163,
+ 5242208035432907801, 701338899890987198, 7609280429197514109, 3020985755112334161,
+ 6651322707055512866, 2635195723621160615, 5144520864246028816, 1035086515727829828,
+ 1567242097116389047, 8172389260191636581, 6337820351429292273, 2163012566996458925,
+ 2743190902890262681, 1906367633221323427, 6011544915663598137, 5932255307352610768,
+ 2241128460406315459, 895504896216695588, 3094483003111372717, 4583857460292963101,
+ 9079887171656594975, 8839289181930711403, 5762740387243057873, 4225072055348026230,
+ 1838220598389033063, 3801620336801580414, 8823526620080073856, 1776617605585100335,
+ 7899055018877642622, 5421679761463003041, 5521102963086275121, 4248279443559365898,
+ 8735487530905098534, 1760527091573692978, 7142485049657745894, 8222656872927218123,
+ 4969531564923704323, 3394475942196872480, 6424174453260338141, 359248545074932887,
+ 3273651282831730598, 6797106199797138596, 3030918217665093212, 145600834617314036,
+ 6036575856065626233, 740416251634527158, 7080427635449935582, 6951781370868335478,
+ 399922722363687927, 294902314447253185, 7844950936339178523, 880320858634709042,
+ 6192655680808675579, 411604686384710388, 9026808440365124461, 6440783557497587732,
+ 4615674634722404292, 539897290441580544, 2096238225866883852, 8751955639408182687,
+ 1907224908052289603, 7381039757301768559, 6157238513393239656, 7749994231914157575,
+ 8629571604380892756, 5280433031239081479, 7101611890139813254, 2479018537985767835,
+ 7169176924412769570, 7942066497793203302, 1357759729055557688, 2278447439451174845,
+ 3625338785743880657, 6477479539006708521, 8976185375579272206, 5511371554711836120,
+ 1326024180520890843, 7537449876596048829, 5464680203499696154, 3189671183162196045,
+ 6346751753565857109, 241159987320630307, 3095793449658682053, 8978332846736310159,
+ 2902794662273147216, 7208698530190629697, 7276901792339343736, 1732385229314443140,
+ 4133292154170828382, 2918308698224194548, 1519461397937144458, 5293934712616591764,
+ 4922828954023452664, 2879211533496425641, 5896236396443472108, 8465043815351752425,
+ 7329020396871624740, 8915471717014488588, 2944902635677463047, 7052079073493465134,
+ 8382142935188824023, 9103922860780351547, 4152330101494654406,
+ }
+)
+
+type rngSource struct {
+ tap int // index into vec
+ feed int // index into vec
+ vec [_LEN]int64 // current feedback register
+}
+
+// seed rng x[n+1] = 48271 * x[n] mod (2**31 - 1)
+func seedrand(x int32) int32 {
+ hi := x / _Q
+ lo := x % _Q
+ x = _A*lo - _R*hi
+ if x < 0 {
+ x += _M
+ }
+ return x
+}
+
+// Seed uses the provided seed value to initialize the generator to a deterministic state.
+func (rng *rngSource) Seed(seed int64) {
+ rng.tap = 0
+ rng.feed = _LEN - _TAP
+
+ seed = seed % _M
+ if seed < 0 {
+ seed += _M
+ }
+ if seed == 0 {
+ seed = 89482311
+ }
+
+ x := int32(seed)
+ for i := -20; i < _LEN; i++ {
+ x = seedrand(x)
+ if i >= 0 {
+ var u int64
+ u = int64(x) << 40
+ x = seedrand(x)
+ u ^= int64(x) << 20
+ x = seedrand(x)
+ u ^= int64(x)
+ u ^= rng_cooked[i]
+ rng.vec[i] = u & _MASK
+ }
+ }
+}
+
+// Int63 returns a non-negative pseudo-random 63-bit integer as an int64.
+func (rng *rngSource) Int63() int64 {
+ rng.tap--
+ if rng.tap < 0 {
+ rng.tap += _LEN
+ }
+
+ rng.feed--
+ if rng.feed < 0 {
+ rng.feed += _LEN
+ }
+
+ x := (rng.vec[rng.feed] + rng.vec[rng.tap]) & _MASK
+ rng.vec[rng.feed] = x
+ return x
+}
diff --git a/src/math/rand/zipf.go b/src/math/rand/zipf.go
new file mode 100644
index 000000000..8db2c6f5b
--- /dev/null
+++ b/src/math/rand/zipf.go
@@ -0,0 +1,75 @@
+// 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 generating variates p(k) on [0, imax]
+// proportional to (v+k)**(-s) where s>1 and k>=0, 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)
+}
generated by cgit v1.2.3 (git 2.39.1) at 2024-06-08 00:02:13 +0000