zig/lib/std/rand.zig
Andrew Kelley d29871977f remove redundant license headers from zig standard library
We already have a LICENSE file that covers the Zig Standard Library. We
no longer need to remind everyone that the license is MIT in every single
file.

Previously this was introduced to clarify the situation for a fork of
Zig that made Zig's LICENSE file harder to find, and replaced it with
their own license that required annual payments to their company.
However that fork now appears to be dead. So there is no need to
reinforce the copyright notice in every single file.
2021-08-24 12:25:09 -07:00

632 lines
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Zig

//! The engines provided here should be initialized from an external source.
//! For a thread-local cryptographically secure pseudo random number generator,
//! use `std.crypto.random`.
//! Be sure to use a CSPRNG when required, otherwise using a normal PRNG will
//! be faster and use substantially less stack space.
//!
//! TODO(tiehuis): Benchmark these against other reference implementations.
const std = @import("std.zig");
const builtin = std.builtin;
const assert = std.debug.assert;
const expect = std.testing.expect;
const expectEqual = std.testing.expectEqual;
const mem = std.mem;
const math = std.math;
const ziggurat = @import("rand/ziggurat.zig");
const maxInt = std.math.maxInt;
/// Fast unbiased random numbers.
pub const DefaultPrng = Xoshiro256;
/// Cryptographically secure random numbers.
pub const DefaultCsprng = Gimli;
pub const Isaac64 = @import("rand/Isaac64.zig");
pub const Gimli = @import("rand/Gimli.zig");
pub const Pcg = @import("rand/Pcg.zig");
pub const Xoroshiro128 = @import("rand/Xoroshiro128.zig");
pub const Xoshiro256 = @import("rand/Xoshiro256.zig");
pub const Sfc64 = @import("rand/Sfc64.zig");
pub const Random = struct {
fillFn: fn (r: *Random, buf: []u8) void,
/// Read random bytes into the specified buffer until full.
pub fn bytes(r: *Random, buf: []u8) void {
r.fillFn(r, buf);
}
pub fn boolean(r: *Random) bool {
return r.int(u1) != 0;
}
/// Returns a random value from an enum, evenly distributed.
pub fn enumValue(r: *Random, comptime EnumType: type) EnumType {
if (comptime !std.meta.trait.is(.Enum)(EnumType)) {
@compileError("Random.enumValue requires an enum type, not a " ++ @typeName(EnumType));
}
// We won't use int -> enum casting because enum elements can have
// arbitrary values. Instead we'll randomly pick one of the type's values.
const values = std.enums.values(EnumType);
const index = r.uintLessThan(usize, values.len);
return values[index];
}
/// Returns a random int `i` such that `0 <= i <= maxInt(T)`.
/// `i` is evenly distributed.
pub fn int(r: *Random, comptime T: type) T {
const bits = @typeInfo(T).Int.bits;
const UnsignedT = std.meta.Int(.unsigned, bits);
const ByteAlignedT = std.meta.Int(.unsigned, @divTrunc(bits + 7, 8) * 8);
var rand_bytes: [@sizeOf(ByteAlignedT)]u8 = undefined;
r.bytes(rand_bytes[0..]);
// use LE instead of native endian for better portability maybe?
// TODO: endian portability is pointless if the underlying prng isn't endian portable.
// TODO: document the endian portability of this library.
const byte_aligned_result = mem.readIntSliceLittle(ByteAlignedT, &rand_bytes);
const unsigned_result = @truncate(UnsignedT, byte_aligned_result);
return @bitCast(T, unsigned_result);
}
/// Constant-time implementation off `uintLessThan`.
/// The results of this function may be biased.
pub fn uintLessThanBiased(r: *Random, comptime T: type, less_than: T) T {
comptime assert(@typeInfo(T).Int.signedness == .unsigned);
const bits = @typeInfo(T).Int.bits;
comptime assert(bits <= 64); // TODO: workaround: LLVM ERROR: Unsupported library call operation!
assert(0 < less_than);
if (bits <= 32) {
return @intCast(T, limitRangeBiased(u32, r.int(u32), less_than));
} else {
return @intCast(T, limitRangeBiased(u64, r.int(u64), less_than));
}
}
/// Returns an evenly distributed random unsigned integer `0 <= i < less_than`.
/// This function assumes that the underlying `fillFn` produces evenly distributed values.
/// Within this assumption, the runtime of this function is exponentially distributed.
/// If `fillFn` were backed by a true random generator,
/// the runtime of this function would technically be unbounded.
/// However, if `fillFn` is backed by any evenly distributed pseudo random number generator,
/// this function is guaranteed to return.
/// If you need deterministic runtime bounds, use `uintLessThanBiased`.
pub fn uintLessThan(r: *Random, comptime T: type, less_than: T) T {
comptime assert(@typeInfo(T).Int.signedness == .unsigned);
const bits = @typeInfo(T).Int.bits;
comptime assert(bits <= 64); // TODO: workaround: LLVM ERROR: Unsupported library call operation!
assert(0 < less_than);
// Small is typically u32
const small_bits = @divTrunc(bits + 31, 32) * 32;
const Small = std.meta.Int(.unsigned, small_bits);
// Large is typically u64
const Large = std.meta.Int(.unsigned, small_bits * 2);
// adapted from:
// http://www.pcg-random.org/posts/bounded-rands.html
// "Lemire's (with an extra tweak from me)"
var x: Small = r.int(Small);
var m: Large = @as(Large, x) * @as(Large, less_than);
var l: Small = @truncate(Small, m);
if (l < less_than) {
// TODO: workaround for https://github.com/ziglang/zig/issues/1770
// should be:
// var t: Small = -%less_than;
var t: Small = @bitCast(Small, -%@bitCast(std.meta.Int(.signed, small_bits), @as(Small, less_than)));
if (t >= less_than) {
t -= less_than;
if (t >= less_than) {
t %= less_than;
}
}
while (l < t) {
x = r.int(Small);
m = @as(Large, x) * @as(Large, less_than);
l = @truncate(Small, m);
}
}
return @intCast(T, m >> small_bits);
}
/// Constant-time implementation off `uintAtMost`.
/// The results of this function may be biased.
pub fn uintAtMostBiased(r: *Random, comptime T: type, at_most: T) T {
assert(@typeInfo(T).Int.signedness == .unsigned);
if (at_most == maxInt(T)) {
// have the full range
return r.int(T);
}
return r.uintLessThanBiased(T, at_most + 1);
}
/// Returns an evenly distributed random unsigned integer `0 <= i <= at_most`.
/// See `uintLessThan`, which this function uses in most cases,
/// for commentary on the runtime of this function.
pub fn uintAtMost(r: *Random, comptime T: type, at_most: T) T {
assert(@typeInfo(T).Int.signedness == .unsigned);
if (at_most == maxInt(T)) {
// have the full range
return r.int(T);
}
return r.uintLessThan(T, at_most + 1);
}
/// Constant-time implementation off `intRangeLessThan`.
/// The results of this function may be biased.
pub fn intRangeLessThanBiased(r: *Random, comptime T: type, at_least: T, less_than: T) T {
assert(at_least < less_than);
const info = @typeInfo(T).Int;
if (info.signedness == .signed) {
// Two's complement makes this math pretty easy.
const UnsignedT = std.meta.Int(.unsigned, info.bits);
const lo = @bitCast(UnsignedT, at_least);
const hi = @bitCast(UnsignedT, less_than);
const result = lo +% r.uintLessThanBiased(UnsignedT, hi -% lo);
return @bitCast(T, result);
} else {
// The signed implementation would work fine, but we can use stricter arithmetic operators here.
return at_least + r.uintLessThanBiased(T, less_than - at_least);
}
}
/// Returns an evenly distributed random integer `at_least <= i < less_than`.
/// See `uintLessThan`, which this function uses in most cases,
/// for commentary on the runtime of this function.
pub fn intRangeLessThan(r: *Random, comptime T: type, at_least: T, less_than: T) T {
assert(at_least < less_than);
const info = @typeInfo(T).Int;
if (info.signedness == .signed) {
// Two's complement makes this math pretty easy.
const UnsignedT = std.meta.Int(.unsigned, info.bits);
const lo = @bitCast(UnsignedT, at_least);
const hi = @bitCast(UnsignedT, less_than);
const result = lo +% r.uintLessThan(UnsignedT, hi -% lo);
return @bitCast(T, result);
} else {
// The signed implementation would work fine, but we can use stricter arithmetic operators here.
return at_least + r.uintLessThan(T, less_than - at_least);
}
}
/// Constant-time implementation off `intRangeAtMostBiased`.
/// The results of this function may be biased.
pub fn intRangeAtMostBiased(r: *Random, comptime T: type, at_least: T, at_most: T) T {
assert(at_least <= at_most);
const info = @typeInfo(T).Int;
if (info.signedness == .signed) {
// Two's complement makes this math pretty easy.
const UnsignedT = std.meta.Int(.unsigned, info.bits);
const lo = @bitCast(UnsignedT, at_least);
const hi = @bitCast(UnsignedT, at_most);
const result = lo +% r.uintAtMostBiased(UnsignedT, hi -% lo);
return @bitCast(T, result);
} else {
// The signed implementation would work fine, but we can use stricter arithmetic operators here.
return at_least + r.uintAtMostBiased(T, at_most - at_least);
}
}
/// Returns an evenly distributed random integer `at_least <= i <= at_most`.
/// See `uintLessThan`, which this function uses in most cases,
/// for commentary on the runtime of this function.
pub fn intRangeAtMost(r: *Random, comptime T: type, at_least: T, at_most: T) T {
assert(at_least <= at_most);
const info = @typeInfo(T).Int;
if (info.signedness == .signed) {
// Two's complement makes this math pretty easy.
const UnsignedT = std.meta.Int(.unsigned, info.bits);
const lo = @bitCast(UnsignedT, at_least);
const hi = @bitCast(UnsignedT, at_most);
const result = lo +% r.uintAtMost(UnsignedT, hi -% lo);
return @bitCast(T, result);
} else {
// The signed implementation would work fine, but we can use stricter arithmetic operators here.
return at_least + r.uintAtMost(T, at_most - at_least);
}
}
pub const scalar = @compileError("deprecated; use boolean() or int() instead");
pub const range = @compileError("deprecated; use intRangeLessThan()");
/// Return a floating point value evenly distributed in the range [0, 1).
pub fn float(r: *Random, comptime T: type) T {
// Generate a uniform value between [1, 2) and scale down to [0, 1).
// Note: The lowest mantissa bit is always set to 0 so we only use half the available range.
switch (T) {
f32 => {
const s = r.int(u32);
const repr = (0x7f << 23) | (s >> 9);
return @bitCast(f32, repr) - 1.0;
},
f64 => {
const s = r.int(u64);
const repr = (0x3ff << 52) | (s >> 12);
return @bitCast(f64, repr) - 1.0;
},
else => @compileError("unknown floating point type"),
}
}
/// Return a floating point value normally distributed with mean = 0, stddev = 1.
///
/// To use different parameters, use: floatNorm(...) * desiredStddev + desiredMean.
pub fn floatNorm(r: *Random, comptime T: type) T {
const value = ziggurat.next_f64(r, ziggurat.NormDist);
switch (T) {
f32 => return @floatCast(f32, value),
f64 => return value,
else => @compileError("unknown floating point type"),
}
}
/// Return an exponentially distributed float with a rate parameter of 1.
///
/// To use a different rate parameter, use: floatExp(...) / desiredRate.
pub fn floatExp(r: *Random, comptime T: type) T {
const value = ziggurat.next_f64(r, ziggurat.ExpDist);
switch (T) {
f32 => return @floatCast(f32, value),
f64 => return value,
else => @compileError("unknown floating point type"),
}
}
/// Shuffle a slice into a random order.
pub fn shuffle(r: *Random, comptime T: type, buf: []T) void {
if (buf.len < 2) {
return;
}
var i: usize = 0;
while (i < buf.len - 1) : (i += 1) {
const j = r.intRangeLessThan(usize, i, buf.len);
mem.swap(T, &buf[i], &buf[j]);
}
}
};
/// Convert a random integer 0 <= random_int <= maxValue(T),
/// into an integer 0 <= result < less_than.
/// This function introduces a minor bias.
pub fn limitRangeBiased(comptime T: type, random_int: T, less_than: T) T {
comptime assert(@typeInfo(T).Int.signedness == .unsigned);
const bits = @typeInfo(T).Int.bits;
const T2 = std.meta.Int(.unsigned, bits * 2);
// adapted from:
// http://www.pcg-random.org/posts/bounded-rands.html
// "Integer Multiplication (Biased)"
var m: T2 = @as(T2, random_int) * @as(T2, less_than);
return @intCast(T, m >> bits);
}
const SequentialPrng = struct {
const Self = @This();
random: Random,
next_value: u8,
pub fn init() Self {
return Self{
.random = Random{ .fillFn = fill },
.next_value = 0,
};
}
fn fill(r: *Random, buf: []u8) void {
const self = @fieldParentPtr(Self, "random", r);
for (buf) |*b| {
b.* = self.next_value;
}
self.next_value +%= 1;
}
};
test "Random int" {
try testRandomInt();
comptime try testRandomInt();
}
fn testRandomInt() !void {
var r = SequentialPrng.init();
try expect(r.random.int(u0) == 0);
r.next_value = 0;
try expect(r.random.int(u1) == 0);
try expect(r.random.int(u1) == 1);
try expect(r.random.int(u2) == 2);
try expect(r.random.int(u2) == 3);
try expect(r.random.int(u2) == 0);
r.next_value = 0xff;
try expect(r.random.int(u8) == 0xff);
r.next_value = 0x11;
try expect(r.random.int(u8) == 0x11);
r.next_value = 0xff;
try expect(r.random.int(u32) == 0xffffffff);
r.next_value = 0x11;
try expect(r.random.int(u32) == 0x11111111);
r.next_value = 0xff;
try expect(r.random.int(i32) == -1);
r.next_value = 0x11;
try expect(r.random.int(i32) == 0x11111111);
r.next_value = 0xff;
try expect(r.random.int(i8) == -1);
r.next_value = 0x11;
try expect(r.random.int(i8) == 0x11);
r.next_value = 0xff;
try expect(r.random.int(u33) == 0x1ffffffff);
r.next_value = 0xff;
try expect(r.random.int(i1) == -1);
r.next_value = 0xff;
try expect(r.random.int(i2) == -1);
r.next_value = 0xff;
try expect(r.random.int(i33) == -1);
}
test "Random boolean" {
try testRandomBoolean();
comptime try testRandomBoolean();
}
fn testRandomBoolean() !void {
var r = SequentialPrng.init();
try expect(r.random.boolean() == false);
try expect(r.random.boolean() == true);
try expect(r.random.boolean() == false);
try expect(r.random.boolean() == true);
}
test "Random enum" {
try testRandomEnumValue();
comptime try testRandomEnumValue();
}
fn testRandomEnumValue() !void {
const TestEnum = enum {
First,
Second,
Third,
};
var r = SequentialPrng.init();
r.next_value = 0;
try expect(r.random.enumValue(TestEnum) == TestEnum.First);
try expect(r.random.enumValue(TestEnum) == TestEnum.First);
try expect(r.random.enumValue(TestEnum) == TestEnum.First);
}
test "Random intLessThan" {
@setEvalBranchQuota(10000);
try testRandomIntLessThan();
comptime try testRandomIntLessThan();
}
fn testRandomIntLessThan() !void {
var r = SequentialPrng.init();
r.next_value = 0xff;
try expect(r.random.uintLessThan(u8, 4) == 3);
try expect(r.next_value == 0);
try expect(r.random.uintLessThan(u8, 4) == 0);
try expect(r.next_value == 1);
r.next_value = 0;
try expect(r.random.uintLessThan(u64, 32) == 0);
// trigger the bias rejection code path
r.next_value = 0;
try expect(r.random.uintLessThan(u8, 3) == 0);
// verify we incremented twice
try expect(r.next_value == 2);
r.next_value = 0xff;
try expect(r.random.intRangeLessThan(u8, 0, 0x80) == 0x7f);
r.next_value = 0xff;
try expect(r.random.intRangeLessThan(u8, 0x7f, 0xff) == 0xfe);
r.next_value = 0xff;
try expect(r.random.intRangeLessThan(i8, 0, 0x40) == 0x3f);
r.next_value = 0xff;
try expect(r.random.intRangeLessThan(i8, -0x40, 0x40) == 0x3f);
r.next_value = 0xff;
try expect(r.random.intRangeLessThan(i8, -0x80, 0) == -1);
r.next_value = 0xff;
try expect(r.random.intRangeLessThan(i3, -4, 0) == -1);
r.next_value = 0xff;
try expect(r.random.intRangeLessThan(i3, -2, 2) == 1);
}
test "Random intAtMost" {
@setEvalBranchQuota(10000);
try testRandomIntAtMost();
comptime try testRandomIntAtMost();
}
fn testRandomIntAtMost() !void {
var r = SequentialPrng.init();
r.next_value = 0xff;
try expect(r.random.uintAtMost(u8, 3) == 3);
try expect(r.next_value == 0);
try expect(r.random.uintAtMost(u8, 3) == 0);
// trigger the bias rejection code path
r.next_value = 0;
try expect(r.random.uintAtMost(u8, 2) == 0);
// verify we incremented twice
try expect(r.next_value == 2);
r.next_value = 0xff;
try expect(r.random.intRangeAtMost(u8, 0, 0x7f) == 0x7f);
r.next_value = 0xff;
try expect(r.random.intRangeAtMost(u8, 0x7f, 0xfe) == 0xfe);
r.next_value = 0xff;
try expect(r.random.intRangeAtMost(i8, 0, 0x3f) == 0x3f);
r.next_value = 0xff;
try expect(r.random.intRangeAtMost(i8, -0x40, 0x3f) == 0x3f);
r.next_value = 0xff;
try expect(r.random.intRangeAtMost(i8, -0x80, -1) == -1);
r.next_value = 0xff;
try expect(r.random.intRangeAtMost(i3, -4, -1) == -1);
r.next_value = 0xff;
try expect(r.random.intRangeAtMost(i3, -2, 1) == 1);
try expect(r.random.uintAtMost(u0, 0) == 0);
}
test "Random Biased" {
var r = DefaultPrng.init(0);
// Not thoroughly checking the logic here.
// Just want to execute all the paths with different types.
try expect(r.random.uintLessThanBiased(u1, 1) == 0);
try expect(r.random.uintLessThanBiased(u32, 10) < 10);
try expect(r.random.uintLessThanBiased(u64, 20) < 20);
try expect(r.random.uintAtMostBiased(u0, 0) == 0);
try expect(r.random.uintAtMostBiased(u1, 0) <= 0);
try expect(r.random.uintAtMostBiased(u32, 10) <= 10);
try expect(r.random.uintAtMostBiased(u64, 20) <= 20);
try expect(r.random.intRangeLessThanBiased(u1, 0, 1) == 0);
try expect(r.random.intRangeLessThanBiased(i1, -1, 0) == -1);
try expect(r.random.intRangeLessThanBiased(u32, 10, 20) >= 10);
try expect(r.random.intRangeLessThanBiased(i32, 10, 20) >= 10);
try expect(r.random.intRangeLessThanBiased(u64, 20, 40) >= 20);
try expect(r.random.intRangeLessThanBiased(i64, 20, 40) >= 20);
// uncomment for broken module error:
//expect(r.random.intRangeAtMostBiased(u0, 0, 0) == 0);
try expect(r.random.intRangeAtMostBiased(u1, 0, 1) >= 0);
try expect(r.random.intRangeAtMostBiased(i1, -1, 0) >= -1);
try expect(r.random.intRangeAtMostBiased(u32, 10, 20) >= 10);
try expect(r.random.intRangeAtMostBiased(i32, 10, 20) >= 10);
try expect(r.random.intRangeAtMostBiased(u64, 20, 40) >= 20);
try expect(r.random.intRangeAtMostBiased(i64, 20, 40) >= 20);
}
// Generator to extend 64-bit seed values into longer sequences.
//
// The number of cycles is thus limited to 64-bits regardless of the engine, but this
// is still plenty for practical purposes.
pub const SplitMix64 = struct {
s: u64,
pub fn init(seed: u64) SplitMix64 {
return SplitMix64{ .s = seed };
}
pub fn next(self: *SplitMix64) u64 {
self.s +%= 0x9e3779b97f4a7c15;
var z = self.s;
z = (z ^ (z >> 30)) *% 0xbf58476d1ce4e5b9;
z = (z ^ (z >> 27)) *% 0x94d049bb133111eb;
return z ^ (z >> 31);
}
};
test "splitmix64 sequence" {
var r = SplitMix64.init(0xaeecf86f7878dd75);
const seq = [_]u64{
0x5dbd39db0178eb44,
0xa9900fb66b397da3,
0x5c1a28b1aeebcf5c,
0x64a963238f776912,
0xc6d4177b21d1c0ab,
0xb2cbdbdb5ea35394,
};
for (seq) |s| {
try expect(s == r.next());
}
}
// Actual Random helper function tests, pcg engine is assumed correct.
test "Random float" {
var prng = DefaultPrng.init(0);
var i: usize = 0;
while (i < 1000) : (i += 1) {
const val1 = prng.random.float(f32);
try expect(val1 >= 0.0);
try expect(val1 < 1.0);
const val2 = prng.random.float(f64);
try expect(val2 >= 0.0);
try expect(val2 < 1.0);
}
}
test "Random shuffle" {
var prng = DefaultPrng.init(0);
var seq = [_]u8{ 0, 1, 2, 3, 4 };
var seen = [_]bool{false} ** 5;
var i: usize = 0;
while (i < 1000) : (i += 1) {
prng.random.shuffle(u8, seq[0..]);
seen[seq[0]] = true;
try expect(sumArray(seq[0..]) == 10);
}
// we should see every entry at the head at least once
for (seen) |e| {
try expect(e == true);
}
}
fn sumArray(s: []const u8) u32 {
var r: u32 = 0;
for (s) |e|
r += e;
return r;
}
test "Random range" {
var prng = DefaultPrng.init(0);
try testRange(&prng.random, -4, 3);
try testRange(&prng.random, -4, -1);
try testRange(&prng.random, 10, 14);
try testRange(&prng.random, -0x80, 0x7f);
}
fn testRange(r: *Random, start: i8, end: i8) !void {
try testRangeBias(r, start, end, true);
try testRangeBias(r, start, end, false);
}
fn testRangeBias(r: *Random, start: i8, end: i8, biased: bool) !void {
const count = @intCast(usize, @as(i32, end) - @as(i32, start));
var values_buffer = [_]bool{false} ** 0x100;
const values = values_buffer[0..count];
var i: usize = 0;
while (i < count) {
const value: i32 = if (biased) r.intRangeLessThanBiased(i8, start, end) else r.intRangeLessThan(i8, start, end);
const index = @intCast(usize, value - start);
if (!values[index]) {
i += 1;
values[index] = true;
}
}
}
test "CSPRNG" {
var secret_seed: [DefaultCsprng.secret_seed_length]u8 = undefined;
std.crypto.random.bytes(&secret_seed);
var csprng = DefaultCsprng.init(secret_seed);
const a = csprng.random.int(u64);
const b = csprng.random.int(u64);
const c = csprng.random.int(u64);
try expect(a ^ b ^ c != 0);
}
test {
std.testing.refAllDecls(@This());
}