util/rands: add Shuffle and Perm functions with on-stack RNG state

The new math/rand/v2 package includes an m-local global random number
generator that can not be reseeded by the user, which is suitable for
most uses without the RNG pools we have in a number of areas of the code
base.

The new API still does not have an allocation-free way of performing a
seeded operations, due to the long term compiler bug around interface
parameter escapes, and the Source interface.

This change introduces the two APIs that math/rand/v2 can not yet
replace efficiently: seeded Perm() and Shuffle() operations. This
implementation chooses to use the PCG random source from math/rand/v2,
as with sufficient compiler optimization, this source should boil down
to only two on-stack registers for random state under ideal conditions.

Updates #17243

Signed-off-by: James Tucker <james@tailscale.com>
This commit is contained in:
James Tucker 2024-02-06 14:31:31 -08:00 committed by James Tucker
parent 2bb837a9cf
commit 24bac27632
3 changed files with 179 additions and 0 deletions

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@ -519,6 +519,7 @@ tailscale.com/cmd/tailscaled dependencies: (generated by github.com/tailscale/de
math/big from crypto/dsa+ math/big from crypto/dsa+
math/bits from compress/flate+ math/bits from compress/flate+
math/rand from github.com/mdlayher/netlink+ math/rand from github.com/mdlayher/netlink+
math/rand/v2 from tailscale.com/util/rands
mime from github.com/tailscale/xnet/webdav+ mime from github.com/tailscale/xnet/webdav+
mime/multipart from net/http mime/multipart from net/http
mime/quotedprintable from mime/multipart mime/quotedprintable from mime/multipart

82
util/rands/cheap.go Normal file
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@ -0,0 +1,82 @@
// Copyright (c) Tailscale Inc & AUTHORS
// SPDX-License-Identifier: BSD-3-Clause
// 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 rands
import (
"math/bits"
randv2 "math/rand/v2"
)
// Shuffle is like rand.Shuffle, but it does not allocate or lock any RNG state.
func Shuffle[T any](seed uint64, data []T) {
var pcg randv2.PCG
pcg.Seed(seed, seed)
for i := len(data) - 1; i > 0; i-- {
j := int(uint64n(&pcg, uint64(i+1)))
data[i], data[j] = data[j], data[i]
}
}
// Perm is like rand.Perm, but it is seeded on the stack and does not allocate
// or lock any RNG state.
func Perm(seed uint64, n int) []int {
p := make([]int, n)
for i := range p {
p[i] = i
}
Shuffle(seed, p)
return p
}
// uint64n is the no-bounds-checks version of rand.Uint64N from the standard
// library. 32-bit optimizations have been elided.
func uint64n(pcg *randv2.PCG, n uint64) uint64 {
if n&(n-1) == 0 { // n is power of two, can mask
return pcg.Uint64() & (n - 1)
}
// Suppose we have a uint64 x uniform in the range [0,2⁶⁴)
// and want to reduce it to the range [0,n) preserving exact uniformity.
// We can simulate a scaling arbitrary precision x * (n/2⁶⁴) by
// the high bits of a double-width multiply of x*n, meaning (x*n)/2⁶⁴.
// Since there are 2⁶⁴ possible inputs x and only n possible outputs,
// the output is necessarily biased if n does not divide 2⁶⁴.
// In general (x*n)/2⁶⁴ = k for x*n in [k*2⁶⁴,(k+1)*2⁶⁴).
// There are either floor(2⁶⁴/n) or ceil(2⁶⁴/n) possible products
// in that range, depending on k.
// But suppose we reject the sample and try again when
// x*n is in [k*2⁶⁴, k*2⁶⁴+(2⁶⁴%n)), meaning rejecting fewer than n possible
// outcomes out of the 2⁶⁴.
// Now there are exactly floor(2⁶⁴/n) possible ways to produce
// each output value k, so we've restored uniformity.
// To get valid uint64 math, 2⁶⁴ % n = (2⁶⁴ - n) % n = -n % n,
// so the direct implementation of this algorithm would be:
//
// hi, lo := bits.Mul64(r.Uint64(), n)
// thresh := -n % n
// for lo < thresh {
// hi, lo = bits.Mul64(r.Uint64(), n)
// }
//
// That still leaves an expensive 64-bit division that we would rather avoid.
// We know that thresh < n, and n is usually much less than 2⁶⁴, so we can
// avoid the last four lines unless lo < n.
//
// See also:
// https://lemire.me/blog/2016/06/27/a-fast-alternative-to-the-modulo-reduction
// https://lemire.me/blog/2016/06/30/fast-random-shuffling
hi, lo := bits.Mul64(pcg.Uint64(), n)
if lo < n {
thresh := -n % n
for lo < thresh {
hi, lo = bits.Mul64(pcg.Uint64(), n)
}
}
return hi
}

96
util/rands/cheap_test.go Normal file
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@ -0,0 +1,96 @@
// Copyright (c) Tailscale Inc & AUTHORS
// SPDX-License-Identifier: BSD-3-Clause
package rands
import (
"slices"
"testing"
randv2 "math/rand/v2"
)
func TestShuffleNoAllocs(t *testing.T) {
seed := randv2.Uint64()
data := make([]int, 100)
for i := range data {
data[i] = i
}
if n := testing.AllocsPerRun(1000, func() {
Shuffle(seed, data)
}); n > 0 {
t.Errorf("Rand got %v allocs per run", n)
}
}
func BenchmarkStdRandV2Shuffle(b *testing.B) {
seed := randv2.Uint64()
data := make([]int, 100)
for i := range data {
data[i] = i
}
b.ReportAllocs()
for range b.N {
// PCG is the lightest source, taking just two uint64s, the chacha8
// source has much larger state.
rng := randv2.New(randv2.NewPCG(seed, seed))
rng.Shuffle(len(data), func(i, j int) { data[i], data[j] = data[j], data[i] })
}
}
func BenchmarkLocalShuffle(b *testing.B) {
seed := randv2.Uint64()
data := make([]int, 100)
for i := range data {
data[i] = i
}
b.ReportAllocs()
for range b.N {
Shuffle(seed, data)
}
}
func TestPerm(t *testing.T) {
seed := uint64(12345)
p := Perm(seed, 100)
if len(p) != 100 {
t.Errorf("got %v; want 100", len(p))
}
expect := [][]int{
{5, 7, 1, 4, 0, 9, 2, 3, 6, 8},
{0, 5, 9, 8, 1, 6, 2, 4, 3, 7},
{5, 2, 3, 1, 9, 7, 6, 8, 4, 0},
{4, 5, 7, 1, 6, 3, 8, 2, 0, 9},
{5, 7, 0, 9, 2, 1, 8, 4, 6, 3},
}
for i := range 5 {
got := Perm(seed+uint64(i), 10)
want := expect[i]
if !slices.Equal(got, want) {
t.Errorf("got %v; want %v", got, want)
}
}
}
func TestShuffle(t *testing.T) {
seed := uint64(12345)
p := Perm(seed, 10)
if len(p) != 10 {
t.Errorf("got %v; want 10", len(p))
}
expect := [][]int{
{9, 3, 7, 0, 5, 8, 1, 4, 2, 6},
{9, 8, 6, 2, 3, 1, 7, 5, 0, 4},
{1, 6, 2, 8, 4, 5, 7, 0, 3, 9},
{4, 5, 0, 6, 7, 8, 3, 2, 1, 9},
{8, 2, 4, 9, 0, 5, 1, 7, 3, 6},
}
for i := range 5 {
Shuffle(seed+uint64(i), p)
want := expect[i]
if !slices.Equal(p, want) {
t.Errorf("got %v; want %v", p, want)
}
}
}