library: math/rand

README.md

@@ -270,6 +270,7 @@ Here are the Go packages that can be imported correctly:
 * [math](https://pkg.go.dev/math)
 * [math/bits](https://pkg.go.dev/math/bits)
 * [math/cmplx](https://pkg.go.dev/math/cmplx)
+* [math/rand](https://pkg.go.dev/math/rand)
 * [errors](https://pkg.go.dev/errors)
 * [context](https://pkg.go.dev/context)
 * [io](https://pkg.go.dev/io)

_cmptest/_bigsqrt2/sqrt2.go

@@ -0,0 +1,47 @@
+package main
+
+import (
+	"fmt"
+	"math"
+	"math/big"
+)
+
+func main() {
+	// We'll do computations with 200 bits of precision in the mantissa.
+	const prec = 200
+
+	// Compute the square root of 2 using Newton's Method. We start with
+	// an initial estimate for sqrt(2), and then iterate:
+	//     x_{n+1} = 1/2 * ( x_n + (2.0 / x_n) )
+
+	// Since Newton's Method doubles the number of correct digits at each
+	// iteration, we need at least log_2(prec) steps.
+	steps := int(math.Log2(prec))
+
+	// Initialize values we need for the computation.
+	two := new(big.Float).SetPrec(prec).SetInt64(2)
+	half := new(big.Float).SetPrec(prec).SetFloat64(0.5)
+
+	// Use 1 as the initial estimate.
+	x := new(big.Float).SetPrec(prec).SetInt64(1)
+
+	// We use t as a temporary variable. There's no need to set its precision
+	// since big.Float values with unset (== 0) precision automatically assume
+	// the largest precision of the arguments when used as the result (receiver)
+	// of a big.Float operation.
+	t := new(big.Float)
+
+	// Iterate.
+	for i := 0; i <= steps; i++ {
+		t.Quo(two, x)  // t = 2.0 / x_n
+		t.Add(x, t)    // t = x_n + (2.0 / x_n)
+		x.Mul(half, t) // x_{n+1} = 0.5 * t
+	}
+
+	// We can use the usual fmt.Printf verbs since big.Float implements fmt.Formatter
+	fmt.Printf("sqrt(2) = %.50f\n", x)
+
+	// Print the error between 2 and x*x.
+	t.Mul(x, x) // t = x*x
+	fmt.Printf("error = %e\n", t.Sub(two, t))
+}

_demo/crand/rand.go

@@ -0,0 +1,26 @@
+package main
+
+import (
+	"fmt"
+
+	"github.com/goplus/llgo/c"
+	"github.com/goplus/llgo/c/math/rand"
+	"github.com/goplus/llgo/c/time"
+)
+
+func fastrand64() uint64 {
+	v1 := uint64(rand.Random())
+	v2 := uint64(rand.Random())
+	return v1 ^ (v2 << 32)
+}
+
+func main() {
+	rand.Srand(c.Uint(time.Time(nil)))
+	fmt.Printf("%x\n", rand.Rand())
+	fmt.Printf("%x\n", rand.Rand())
+
+	rand.Srandom(c.Uint(time.Time(nil)))
+	fmt.Printf("%x\n", rand.Random())
+	fmt.Printf("%x\n", rand.Random())
+	fmt.Printf("%x\n", fastrand64())
+}

_demo/llama2-c/run.go

@@ -3,6 +3,7 @@ package main
 import (
 	"github.com/goplus/llgo/c"
 	"github.com/goplus/llgo/c/llama2"
+	"github.com/goplus/llgo/c/time"
 )
 
 func main() {
@@ -11,7 +12,7 @@ func main() {
 	var tokenizerPath *c.Char = c.Str("tokenizer.bin")
 	var temperature, topp c.Float = 1.0, 0.9
 	var steps c.Int = 256
-	var rngSeed uint64 = uint64(c.Time(nil))
+	var rngSeed uint64 = uint64(time.Time(nil))
 
 loop: // parse command line arguments
 	for {

_demo/rand/rand.go

@@ -1,15 +0,0 @@
-package main
-
-import (
-	"github.com/goplus/llgo/c"
-	"github.com/goplus/llgo/c/math/rand"
-)
-
-func main() {
-	var s c.Uint = 6
-	rand.Srand(s)
-	rr := rand.RandR(&s)
-	r := rand.Rand()
-	println("r:", r)
-	println("rr:", rr)
-}

_demo/randdemo/rand.go

@@ -0,0 +1,12 @@
+package main
+
+import (
+	"fmt"
+	"math/rand"
+)
+
+func main() {
+	fmt.Println(rand.Intn(100))
+	fmt.Println(rand.Intn(100))
+	fmt.Println(rand.Intn(100))
+}

c/c.go

@@ -227,9 +227,6 @@ func Perror(s *Char)
 
 // -----------------------------------------------------------------------------
 
-//go:linkname Time C.time
-func Time(*int32) int32
-
 //go:linkname Usleep C.usleep
 func Usleep(useconds Uint) Int
 

internal/build/build.go

@@ -769,6 +769,7 @@ var hasAltPkg = map[string]none{
 	"internal/syscall/unix":    {},
 	"math":                     {},
 	"math/cmplx":               {},
+	"math/rand":                {},
 	"reflect":                  {},
 	"sync":                     {},
 	"sync/atomic":              {},

internal/lib/math/rand/exp.go

@@ -0,0 +1,221 @@
+// 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)
+ * https://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,
+}

internal/lib/math/rand/normal.go

@@ -0,0 +1,156 @@
+// 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 through +math.MaxFloat64 inclusive,
+// with standard normal distribution (mean = 0, stddev = 1).
+// To produce a different normal distribution, callers can
+// adjust the output using:
+//
+//	sample = NormFloat64() * desiredStdDev + desiredMean
+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,
+}

internal/lib/math/rand/rand.go

@@ -0,0 +1,547 @@
+// 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 suitable for tasks
+// such as simulation, but it should not be used for security-sensitive work.
+//
+// Random numbers are generated by a [Source], usually wrapped in a [Rand].
+// Both types should be used by a single goroutine at a time: sharing among
+// multiple goroutines requires some kind of synchronization.
+//
+// Top-level functions, such as [Float64] and [Int],
+// are safe for concurrent use by multiple goroutines.
+//
+// This package's outputs might be easily predictable regardless of how it's
+// seeded. For random numbers suitable for security-sensitive work, see the
+// crypto/rand package.
+package rand
+
+// llgo:skipall
+import (
+	"sync"
+	"sync/atomic"
+	_ "unsafe" // for go:linkname
+
+	"github.com/goplus/llgo/c"
+	"github.com/goplus/llgo/c/math/rand"
+	"github.com/goplus/llgo/c/time"
+)
+
+// A Source represents a source of uniformly-distributed
+// pseudo-random int64 values in the range [0, 1<<63).
+//
+// A Source is not safe for concurrent use by multiple goroutines.
+type Source interface {
+	Int63() int64
+	Seed(seed int64)
+}
+
+// A Source64 is a Source that can also generate
+// uniformly-distributed pseudo-random uint64 values in
+// the range [0, 1<<64) directly.
+// If a Rand r's underlying Source s implements Source64,
+// then r.Uint64 returns the result of one call to s.Uint64
+// instead of making two calls to s.Int63.
+type Source64 interface {
+	Source
+	Uint64() uint64
+}
+
+// NewSource returns a new pseudo-random Source seeded with the given value.
+// Unlike the default Source used by top-level functions, this source is not
+// safe for concurrent use by multiple goroutines.
+// The returned Source implements Source64.
+func NewSource(seed int64) Source {
+	return newSource(seed)
+}
+
+func newSource(seed int64) *rngSource {
+	var rng rngSource
+	rng.Seed(seed)
+	return &rng
+}
+
+// A Rand is a source of random numbers.
+type Rand struct {
+	src Source
+	s64 Source64 // non-nil if src is source64
+
+	// readVal contains remainder of 63-bit integer used for bytes
+	// generation during most recent Read call.
+	// It is saved so next Read call can start where the previous
+	// one finished.
+	readVal int64
+	// 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 {
+	s64, _ := src.(Source64)
+	return &Rand{src: src, s64: s64}
+}
+
+// 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 int64) {
+	if lk, ok := r.src.(*lockedSource); ok {
+		lk.seedPos(seed, &r.readPos)
+		return
+	}
+
+	r.src.Seed(seed)
+	r.readPos = 0
+}
+
+// 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) }
+
+// Uint64 returns a pseudo-random 64-bit value as a uint64.
+func (r *Rand) Uint64() uint64 {
+	if r.s64 != nil {
+		return r.s64.Uint64()
+	}
+	return uint64(r.Int63())>>31 | uint64(r.Int63())<<32
+}
+
+// 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 the half-open interval [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 the half-open interval [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
+}
+
+// int31n returns, as an int32, a non-negative pseudo-random number in the half-open interval [0,n).
+// n must be > 0, but int31n does not check this; the caller must ensure it.
+// int31n exists because Int31n is inefficient, but Go 1 compatibility
+// requires that the stream of values produced by math/rand remain unchanged.
+// int31n can thus only be used internally, by newly introduced APIs.
+//
+// For implementation details, see:
+// https://lemire.me/blog/2016/06/27/a-fast-alternative-to-the-modulo-reduction
+// https://lemire.me/blog/2016/06/30/fast-random-shuffling
+func (r *Rand) int31n(n int32) int32 {
+	v := r.Uint32()
+	prod := uint64(v) * uint64(n)
+	low := uint32(prod)
+	if low < uint32(n) {
+		thresh := uint32(-n) % uint32(n)
+		for low < thresh {
+			v = r.Uint32()
+			prod = uint64(v) * uint64(n)
+			low = uint32(prod)
+		}
+	}
+	return int32(prod >> 32)
+}
+
+// Intn returns, as an int, a non-negative pseudo-random number in the half-open interval [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 the half-open interval [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.
+	//
+	// 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.Int63()) / (1 << 63)
+	if f == 1 {
+		goto again // resample; this branch is taken O(never)
+	}
+	return f
+}
+
+// Float32 returns, as a float32, a pseudo-random number in the half-open interval [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
+	// 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
+// in the half-open interval [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
+}
+
+// Shuffle pseudo-randomizes the order of elements.
+// n is the number of elements. Shuffle panics if n < 0.
+// swap swaps the elements with indexes i and j.
+func (r *Rand) Shuffle(n int, swap func(i, j int)) {
+	if n < 0 {
+		panic("invalid argument to Shuffle")
+	}
+
+	// Fisher-Yates shuffle: https://en.wikipedia.org/wiki/Fisher%E2%80%93Yates_shuffle
+	// Shuffle really ought not be called with n that doesn't fit in 32 bits.
+	// Not only will it take a very long time, but with 2³¹! possible permutations,
+	// there's no way that any PRNG can have a big enough internal state to
+	// generate even a minuscule percentage of the possible permutations.
+	// Nevertheless, the right API signature accepts an int n, so handle it as best we can.
+	i := n - 1
+	for ; i > 1<<31-1-1; i-- {
+		j := int(r.Int63n(int64(i + 1)))
+		swap(i, j)
+	}
+	for ; i > 0; i-- {
+		j := int(r.int31n(int32(i + 1)))
+		swap(i, j)
+	}
+}
+
+// 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) {
+	switch src := r.src.(type) {
+	case *lockedSource:
+		return src.read(p, &r.readVal, &r.readPos)
+	case *fastSource:
+		return src.read(p, &r.readVal, &r.readPos)
+	}
+	return read(p, r.src, &r.readVal, &r.readPos)
+}
+
+func read(p []byte, src Source, readVal *int64, readPos *int8) (n int, err error) {
+	pos := *readPos
+	val := *readVal
+	rng, _ := src.(*rngSource)
+	for n = 0; n < len(p); n++ {
+		if pos == 0 {
+			if rng != nil {
+				val = rng.Int63()
+			} else {
+				val = src.Int63()
+			}
+			pos = 7
+		}
+		p[n] = byte(val)
+		val >>= 8
+		pos--
+	}
+	*readPos = pos
+	*readVal = val
+	return
+}
+
+/*
+ * Top-level convenience functions
+ */
+
+// globalRandGenerator is the source of random numbers for the top-level
+// convenience functions. When possible it uses the runtime fastrand64
+// function to avoid locking. This is not possible if the user called Seed,
+// either explicitly or implicitly via GODEBUG=randautoseed=0.
+var globalRandGenerator atomic.Pointer[Rand]
+
+// globalRand returns the generator to use for the top-level convenience
+// functions.
+func globalRand() *Rand {
+	if r := globalRandGenerator.Load(); r != nil {
+		return r
+	}
+
+	// This is the first call. Initialize based on GODEBUG.
+	var r = &Rand{
+		src: &fastSource{},
+		s64: &fastSource{},
+	}
+	if !globalRandGenerator.CompareAndSwap(nil, r) {
+		// Two different goroutines called some top-level
+		// function at the same time. While the results in
+		// that case are unpredictable, if we just use r here,
+		// and we are using a seed, we will most likely return
+		// the same value for both calls. That doesn't seem ideal.
+		// Just use the first one to get in.
+		return globalRandGenerator.Load()
+	}
+	return r
+}
+
+func fastrand64() uint64 {
+	v1 := uint64(rand.Random())
+	v2 := uint64(rand.Random())
+	return v1 ^ (v2 << 32)
+}
+
+func init() {
+	rand.Srandom(c.Uint(time.Time(nil)))
+}
+
+// fastSource is an implementation of Source64 that uses the runtime
+// fastrand functions.
+type fastSource struct {
+	// The mutex is used to avoid race conditions in Read.
+	mu sync.Mutex
+}
+
+func (*fastSource) Int63() int64 {
+	return int64(fastrand64() & rngMask)
+}
+
+func (*fastSource) Seed(int64) {
+	panic("internal error: call to fastSource.Seed")
+}
+
+func (*fastSource) Uint64() uint64 {
+	return fastrand64()
+}
+
+func (fs *fastSource) read(p []byte, readVal *int64, readPos *int8) (n int, err error) {
+	fs.mu.Lock()
+	n, err = read(p, fs, readVal, readPos)
+	fs.mu.Unlock()
+	return
+}
+
+// Seed uses the provided seed value to initialize the default Source to a
+// deterministic state. Seed values that have the same remainder when
+// divided by 2³¹-1 generate the same pseudo-random sequence.
+// Seed, unlike the Rand.Seed method, is safe for concurrent use.
+//
+// If Seed is not called, the generator is seeded randomly at program startup.
+//
+// Prior to Go 1.20, the generator was seeded like Seed(1) at program startup.
+// To force the old behavior, call Seed(1) at program startup.
+// Alternately, set GODEBUG=randautoseed=0 in the environment
+// before making any calls to functions in this package.
+//
+// Deprecated: As of Go 1.20 there is no reason to call Seed with
+// a random value. Programs that call Seed with a known value to get
+// a specific sequence of results should use New(NewSource(seed)) to
+// obtain a local random generator.
+func Seed(seed int64) {
+	orig := globalRandGenerator.Load()
+
+	// If we are already using a lockedSource, we can just re-seed it.
+	if orig != nil {
+		if _, ok := orig.src.(*lockedSource); ok {
+			orig.Seed(seed)
+			return
+		}
+	}
+
+	// Otherwise either
+	// 1) orig == nil, which is the normal case when Seed is the first
+	// top-level function to be called, or
+	// 2) orig is already a fastSource, in which case we need to change
+	// to a lockedSource.
+	// Either way we do the same thing.
+
+	r := New(new(lockedSource))
+	r.Seed(seed)
+
+	if !globalRandGenerator.CompareAndSwap(orig, r) {
+		// Something changed underfoot. Retry to be safe.
+		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 the half-open interval [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 the half-open interval [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 the half-open interval [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 the half-open interval [0.0,1.0)
+// from the default Source.
+func Float64() float64 { return globalRand().Float64() }
+
+// Float32 returns, as a float32, a pseudo-random number in the half-open interval [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
+// in the half-open interval [0,n) from the default Source.
+func Perm(n int) []int { return globalRand().Perm(n) }
+
+// Shuffle pseudo-randomizes the order of elements using the default Source.
+// n is the number of elements. Shuffle panics if n < 0.
+// swap swaps the elements with indexes i and j.
+func Shuffle(n int, swap func(i, j int)) { globalRand().Shuffle(n, swap) }
+
+// 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.
+//
+// Deprecated: For almost all use cases, crypto/rand.Read is more appropriate.
+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() }
+
+type lockedSource struct {
+	lk sync.Mutex
+	s  *rngSource
+}
+
+func (r *lockedSource) Int63() (n int64) {
+	r.lk.Lock()
+	n = r.s.Int63()
+	r.lk.Unlock()
+	return
+}
+
+func (r *lockedSource) Uint64() (n uint64) {
+	r.lk.Lock()
+	n = r.s.Uint64()
+	r.lk.Unlock()
+	return
+}
+
+func (r *lockedSource) Seed(seed int64) {
+	r.lk.Lock()
+	r.seed(seed)
+	r.lk.Unlock()
+}
+
+// seedPos implements Seed for a lockedSource without a race condition.
+func (r *lockedSource) seedPos(seed int64, readPos *int8) {
+	r.lk.Lock()
+	r.seed(seed)
+	*readPos = 0
+	r.lk.Unlock()
+}
+
+// seed seeds the underlying source.
+// The caller must have locked r.lk.
+func (r *lockedSource) seed(seed int64) {
+	if r.s == nil {
+		r.s = newSource(seed)
+	} else {
+		r.s.Seed(seed)
+	}
+}
+
+// read implements Read for a lockedSource without a race condition.
+func (r *lockedSource) read(p []byte, readVal *int64, readPos *int8) (n int, err error) {
+	r.lk.Lock()
+	n, err = read(p, r.s, readVal, readPos)
+	r.lk.Unlock()
+	return
+}

internal/lib/math/rand/rng.go

@@ -0,0 +1,252 @@
+// 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 (
+	rngLen   = 607
+	rngTap   = 273
+	rngMax   = 1 << 63
+	rngMask  = rngMax - 1
+	int32max = (1 << 31) - 1
+)
+
+var (
+	// rngCooked used for seeding. See gen_cooked.go for details.
+	rngCooked [rngLen]int64 = [...]int64{
+		-4181792142133755926, -4576982950128230565, 1395769623340756751, 5333664234075297259,
+		-6347679516498800754, 9033628115061424579, 7143218595135194537, 4812947590706362721,
+		7937252194349799378, 5307299880338848416, 8209348851763925077, -7107630437535961764,
+		4593015457530856296, 8140875735541888011, -5903942795589686782, -603556388664454774,
+		-7496297993371156308, 113108499721038619, 4569519971459345583, -4160538177779461077,
+		-6835753265595711384, -6507240692498089696, 6559392774825876886, 7650093201692370310,
+		7684323884043752161, -8965504200858744418, -2629915517445760644, 271327514973697897,
+		-6433985589514657524, 1065192797246149621, 3344507881999356393, -4763574095074709175,
+		7465081662728599889, 1014950805555097187, -4773931307508785033, -5742262670416273165,
+		2418672789110888383, 5796562887576294778, 4484266064449540171, 3738982361971787048,
+		-4699774852342421385, 10530508058128498, -589538253572429690, -6598062107225984180,
+		8660405965245884302, 10162832508971942, -2682657355892958417, 7031802312784620857,
+		6240911277345944669, 831864355460801054, -1218937899312622917, 2116287251661052151,
+		2202309800992166967, 9161020366945053561, 4069299552407763864, 4936383537992622449,
+		457351505131524928, -8881176990926596454, -6375600354038175299, -7155351920868399290,
+		4368649989588021065, 887231587095185257, -3659780529968199312, -2407146836602825512,
+		5616972787034086048, -751562733459939242, 1686575021641186857, -5177887698780513806,
+		-4979215821652996885, -1375154703071198421, 5632136521049761902, -8390088894796940536,
+		-193645528485698615, -5979788902190688516, -4907000935050298721, -285522056888777828,
+		-2776431630044341707, 1679342092332374735, 6050638460742422078, -2229851317345194226,
+		-1582494184340482199, 5881353426285907985, 812786550756860885, 4541845584483343330,
+		-6497901820577766722, 4980675660146853729, -4012602956251539747, -329088717864244987,
+		-2896929232104691526, 1495812843684243920, -2153620458055647789, 7370257291860230865,
+		-2466442761497833547, 4706794511633873654, -1398851569026877145, 8549875090542453214,
+		-9189721207376179652, -7894453601103453165, 7297902601803624459, 1011190183918857495,
+		-6985347000036920864, 5147159997473910359, -8326859945294252826, 2659470849286379941,
+		6097729358393448602, -7491646050550022124, -5117116194870963097, -896216826133240300,
+		-745860416168701406, 5803876044675762232, -787954255994554146, -3234519180203704564,
+		-4507534739750823898, -1657200065590290694, 505808562678895611, -4153273856159712438,
+		-8381261370078904295, 572156825025677802, 1791881013492340891, 3393267094866038768,
+		-5444650186382539299, 2352769483186201278, -7930912453007408350, -325464993179687389,
+		-3441562999710612272, -6489413242825283295, 5092019688680754699, -227247482082248967,
+		4234737173186232084, 5027558287275472836, 4635198586344772304, -536033143587636457,
+		5907508150730407386, -8438615781380831356, 972392927514829904, -3801314342046600696,
+		-4064951393885491917, -174840358296132583, 2407211146698877100, -1640089820333676239,
+		3940796514530962282, -5882197405809569433, 3095313889586102949, -1818050141166537098,
+		5832080132947175283, 7890064875145919662, 8184139210799583195, -8073512175445549678,
+		-7758774793014564506, -4581724029666783935, 3516491885471466898, -8267083515063118116,
+		6657089965014657519, 5220884358887979358, 1796677326474620641, 5340761970648932916,
+		1147977171614181568, 5066037465548252321, 2574765911837859848, 1085848279845204775,
+		-5873264506986385449, 6116438694366558490, 2107701075971293812, -7420077970933506541,
+		2469478054175558874, -1855128755834809824, -5431463669011098282, -9038325065738319171,
+		-6966276280341336160, 7217693971077460129, -8314322083775271549, 7196649268545224266,
+		-3585711691453906209, -5267827091426810625, 8057528650917418961, -5084103596553648165,
+		-2601445448341207749, -7850010900052094367, 6527366231383600011, 3507654575162700890,
+		9202058512774729859, 1954818376891585542, -2582991129724600103, 8299563319178235687,
+		-5321504681635821435, 7046310742295574065, -2376176645520785576, -7650733936335907755,
+		8850422670118399721, 3631909142291992901, 5158881091950831288, -6340413719511654215,
+		4763258931815816403, 6280052734341785344, -4979582628649810958, 2043464728020827976,
+		-2678071570832690343, 4562580375758598164, 5495451168795427352, -7485059175264624713,
+		553004618757816492, 6895160632757959823, -989748114590090637, 7139506338801360852,
+		-672480814466784139, 5535668688139305547, 2430933853350256242, -3821430778991574732,
+		-1063731997747047009, -3065878205254005442, 7632066283658143750, 6308328381617103346,
+		3681878764086140361, 3289686137190109749, 6587997200611086848, 244714774258135476,
+		-5143583659437639708, 8090302575944624335, 2945117363431356361, -8359047641006034763,
+		3009039260312620700, -793344576772241777, 401084700045993341, -1968749590416080887,
+		4707864159563588614, -3583123505891281857, -3240864324164777915, -5908273794572565703,
+		-3719524458082857382, -5281400669679581926, 8118566580304798074, 3839261274019871296,
+		7062410411742090847, -8481991033874568140, 6027994129690250817, -6725542042704711878,
+		-2971981702428546974, -7854441788951256975, 8809096399316380241, 6492004350391900708,
+		2462145737463489636, -8818543617934476634, -5070345602623085213, -8961586321599299868,
+		-3758656652254704451, -8630661632476012791, 6764129236657751224, -709716318315418359,
+		-3403028373052861600, -8838073512170985897, -3999237033416576341, -2920240395515973663,
+		-2073249475545404416, 368107899140673753, -6108185202296464250, -6307735683270494757,
+		4782583894627718279, 6718292300699989587, 8387085186914375220, 3387513132024756289,
+		4654329375432538231, -292704475491394206, -3848998599978456535, 7623042350483453954,
+		7725442901813263321, 9186225467561587250, -5132344747257272453, -6865740430362196008,
+		2530936820058611833, 1636551876240043639, -3658707362519810009, 1452244145334316253,
+		-7161729655835084979, -7943791770359481772, 9108481583171221009, -3200093350120725999,
+		5007630032676973346, 2153168792952589781, 6720334534964750538, -3181825545719981703,
+		3433922409283786309, 2285479922797300912, 3110614940896576130, -2856812446131932915,
+		-3804580617188639299, 7163298419643543757, 4891138053923696990, 580618510277907015,
+		1684034065251686769, 4429514767357295841, -8893025458299325803, -8103734041042601133,
+		7177515271653460134, 4589042248470800257, -1530083407795771245, 143607045258444228,
+		246994305896273627, -8356954712051676521, 6473547110565816071, 3092379936208876896,
+		2058427839513754051, -4089587328327907870, 8785882556301281247, -3074039370013608197,
+		-637529855400303673, 6137678347805511274, -7152924852417805802, 5708223427705576541,
+		-3223714144396531304, 4358391411789012426, 325123008708389849, 6837621693887290924,
+		4843721905315627004, -3212720814705499393, -3825019837890901156, 4602025990114250980,
+		1044646352569048800, 9106614159853161675, -8394115921626182539, -4304087667751778808,
+		2681532557646850893, 3681559472488511871, -3915372517896561773, -2889241648411946534,
+		-6564663803938238204, -8060058171802589521, 581945337509520675, 3648778920718647903,
+		-4799698790548231394, -7602572252857820065, 220828013409515943, -1072987336855386047,
+		4287360518296753003, -4633371852008891965, 5513660857261085186, -2258542936462001533,
+		-8744380348503999773, 8746140185685648781, 228500091334420247, 1356187007457302238,
+		3019253992034194581, 3152601605678500003, -8793219284148773595, 5559581553696971176,
+		4916432985369275664, -8559797105120221417, -5802598197927043732, 2868348622579915573,
+		-7224052902810357288, -5894682518218493085, 2587672709781371173, -7706116723325376475,
+		3092343956317362483, -5561119517847711700, 972445599196498113, -1558506600978816441,
+		1708913533482282562, -2305554874185907314, -6005743014309462908, -6653329009633068701,
+		-483583197311151195, 2488075924621352812, -4529369641467339140, -4663743555056261452,
+		2997203966153298104, 1282559373026354493, 240113143146674385, 8665713329246516443,
+		628141331766346752, -4651421219668005332, -7750560848702540400, 7596648026010355826,
+		-3132152619100351065, 7834161864828164065, 7103445518877254909, 4390861237357459201,
+		-4780718172614204074, -319889632007444440, 622261699494173647, -3186110786557562560,
+		-8718967088789066690, -1948156510637662747, -8212195255998774408, -7028621931231314745,
+		2623071828615234808, -4066058308780939700, -5484966924888173764, -6683604512778046238,
+		-6756087640505506466, 5256026990536851868, 7841086888628396109, 6640857538655893162,
+		-8021284697816458310, -7109857044414059830, -1689021141511844405, -4298087301956291063,
+		-4077748265377282003, -998231156719803476, 2719520354384050532, 9132346697815513771,
+		4332154495710163773, -2085582442760428892, 6994721091344268833, -2556143461985726874,
+		-8567931991128098309, 59934747298466858, -3098398008776739403, -265597256199410390,
+		2332206071942466437, -7522315324568406181, 3154897383618636503, -7585605855467168281,
+		-6762850759087199275, 197309393502684135, -8579694182469508493, 2543179307861934850,
+		4350769010207485119, -4468719947444108136, -7207776534213261296, -1224312577878317200,
+		4287946071480840813, 8362686366770308971, 6486469209321732151, -5605644191012979782,
+		-1669018511020473564, 4450022655153542367, -7618176296641240059, -3896357471549267421,
+		-4596796223304447488, -6531150016257070659, -8982326463137525940, -4125325062227681798,
+		-1306489741394045544, -8338554946557245229, 5329160409530630596, 7790979528857726136,
+		4955070238059373407, -4304834761432101506, -6215295852904371179, 3007769226071157901,
+		-6753025801236972788, 8928702772696731736, 7856187920214445904, -4748497451462800923,
+		7900176660600710914, -7082800908938549136, -6797926979589575837, -6737316883512927978,
+		4186670094382025798, 1883939007446035042, -414705992779907823, 3734134241178479257,
+		4065968871360089196, 6953124200385847784, -7917685222115876751, -7585632937840318161,
+		-5567246375906782599, -5256612402221608788, 3106378204088556331, -2894472214076325998,
+		4565385105440252958, 1979884289539493806, -6891578849933910383, 3783206694208922581,
+		8464961209802336085, 2843963751609577687, 3030678195484896323, -4429654462759003204,
+		4459239494808162889, 402587895800087237, 8057891408711167515, 4541888170938985079,
+		1042662272908816815, -3666068979732206850, 2647678726283249984, 2144477441549833761,
+		-3417019821499388721, -2105601033380872185, 5916597177708541638, -8760774321402454447,
+		8833658097025758785, 5970273481425315300, 563813119381731307, -6455022486202078793,
+		1598828206250873866, -4016978389451217698, -2988328551145513985, -6071154634840136312,
+		8469693267274066490, 125672920241807416, -3912292412830714870, -2559617104544284221,
+		-486523741806024092, -4735332261862713930, 5923302823487327109, -9082480245771672572,
+		-1808429243461201518, 7990420780896957397, 4317817392807076702, 3625184369705367340,
+		-6482649271566653105, -3480272027152017464, -3225473396345736649, -368878695502291645,
+		-3981164001421868007, -8522033136963788610, 7609280429197514109, 3020985755112334161,
+		-2572049329799262942, 2635195723621160615, 5144520864246028816, -8188285521126945980,
+		1567242097116389047, 8172389260191636581, -2885551685425483535, -7060359469858316883,
+		-6480181133964513127, -7317004403633452381, 6011544915663598137, 5932255307352610768,
+		2241128460406315459, -8327867140638080220, 3094483003111372717, 4583857460292963101,
+		9079887171656594975, -384082854924064405, -3460631649611717935, 4225072055348026230,
+		-7385151438465742745, 3801620336801580414, -399845416774701952, -7446754431269675473,
+		7899055018877642622, 5421679761463003041, 5521102963086275121, -4975092593295409910,
+		8735487530905098534, -7462844945281082830, -2080886987197029914, -1000715163927557685,
+		-4253840471931071485, -5828896094657903328, 6424174453260338141, 359248545074932887,
+		-5949720754023045210, -2426265837057637212, 3030918217665093212, -9077771202237461772,
+		-3186796180789149575, 740416251634527158, -2142944401404840226, 6951781370868335478,
+		399922722363687927, -8928469722407522623, -1378421100515597285, -8343051178220066766,
+		-3030716356046100229, -8811767350470065420, 9026808440365124461, 6440783557497587732,
+		4615674634722404292, 539897290441580544, 2096238225866883852, 8751955639408182687,
+		-7316147128802486205, 7381039757301768559, 6157238513393239656, -1473377804940618233,
+		8629571604380892756, 5280433031239081479, 7101611890139813254, 2479018537985767835,
+		7169176924412769570, -1281305539061572506, -7865612307799218120, 2278447439451174845,
+		3625338785743880657, 6477479539006708521, 8976185375579272206, -3712000482142939688,
+		1326024180520890843, 7537449876596048829, 5464680203499696154, 3189671183162196045,
+		6346751753565857109, -8982212049534145501, -6127578587196093755, -245039190118465649,
+		-6320577374581628592, 7208698530190629697, 7276901792339343736, -7490986807540332668,
+		4133292154170828382, 2918308698224194548, -7703910638917631350, -3929437324238184044,
+		-4300543082831323144, -6344160503358350167, 5896236396443472108, -758328221503023383,
+		-1894351639983151068, -307900319840287220, -6278469401177312761, -2171292963361310674,
+		8382142935188824023, 9103922860780351547, 4152330101494654406,
+	}
+)
+
+type rngSource struct {
+	tap  int           // index into vec
+	feed int           // index into vec
+	vec  [rngLen]int64 // current feedback register
+}
+
+// seed rng x[n+1] = 48271 * x[n] mod (2**31 - 1)
+func seedrand(x int32) int32 {
+	const (
+		A = 48271
+		Q = 44488
+		R = 3399
+	)
+
+	hi := x / Q
+	lo := x % Q
+	x = A*lo - R*hi
+	if x < 0 {
+		x += int32max
+	}
+	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 = rngLen - rngTap
+
+	seed = seed % int32max
+	if seed < 0 {
+		seed += int32max
+	}
+	if seed == 0 {
+		seed = 89482311
+	}
+
+	x := int32(seed)
+	for i := -20; i < rngLen; 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 ^= rngCooked[i]
+			rng.vec[i] = u
+		}
+	}
+}
+
+// Int63 returns a non-negative pseudo-random 63-bit integer as an int64.
+func (rng *rngSource) Int63() int64 {
+	return int64(rng.Uint64() & rngMask)
+}
+
+// Uint64 returns a non-negative pseudo-random 64-bit integer as a uint64.
+func (rng *rngSource) Uint64() uint64 {
+	rng.tap--
+	if rng.tap < 0 {
+		rng.tap += rngLen
+	}
+
+	rng.feed--
+	if rng.feed < 0 {
+		rng.feed += rngLen
+	}
+
+	x := rng.vec[rng.feed] + rng.vec[rng.tap]
+	rng.vec[rng.feed] = x
+	return uint64(x)
+}

internal/lib/math/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)
+}