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std.rand: Move to std.Random

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e4m2 2024-02-08 14:43:20 +01:00
parent 919a3bae1c
commit 9af077d71e
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438
lib/std/Random.zig Normal file
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//! 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.
const std = @import("std.zig");
const math = std.math;
const mem = std.mem;
const assert = std.debug.assert;
const maxInt = std.math.maxInt;
pub const Random = @This(); // Remove pub when `std.rand` namespace is removed.
/// Fast unbiased random numbers.
pub const DefaultPrng = Xoshiro256;
/// Cryptographically secure random numbers.
pub const DefaultCsprng = ChaCha;
pub const Ascon = @import("Random/Ascon.zig");
pub const ChaCha = @import("Random/ChaCha.zig");
pub const Isaac64 = @import("Random/Isaac64.zig");
pub const Pcg = @import("Random/Pcg.zig");
pub const Xoroshiro128 = @import("Random/Xoroshiro128.zig");
pub const Xoshiro256 = @import("Random/Xoshiro256.zig");
pub const Sfc64 = @import("Random/Sfc64.zig");
pub const RomuTrio = @import("Random/RomuTrio.zig");
pub const SplitMix64 = @import("Random/Splitmix64.zig");
pub const ziggurat = @import("Random/ziggurat.zig");
ptr: *anyopaque,
fillFn: *const fn (ptr: *anyopaque, buf: []u8) void,
pub fn init(pointer: anytype, comptime fillFn: fn (ptr: @TypeOf(pointer), buf: []u8) void) Random {
const Ptr = @TypeOf(pointer);
assert(@typeInfo(Ptr) == .Pointer); // Must be a pointer
assert(@typeInfo(Ptr).Pointer.size == .One); // Must be a single-item pointer
assert(@typeInfo(@typeInfo(Ptr).Pointer.child) == .Struct); // Must point to a struct
const gen = struct {
fn fill(ptr: *anyopaque, buf: []u8) void {
const self: Ptr = @ptrCast(@alignCast(ptr));
fillFn(self, buf);
}
};
return .{
.ptr = pointer,
.fillFn = gen.fill,
};
}
/// Read random bytes into the specified buffer until full.
pub fn bytes(r: Random, buf: []u8) void {
r.fillFn(r.ptr, buf);
}
pub fn boolean(r: Random) bool {
return r.int(u1) != 0;
}
/// Returns a random value from an enum, evenly distributed.
///
/// Note that this will not yield consistent results across all targets
/// due to dependence on the representation of `usize` as an index.
/// See `enumValueWithIndex` for further commentary.
pub inline fn enumValue(r: Random, comptime EnumType: type) EnumType {
return r.enumValueWithIndex(EnumType, usize);
}
/// Returns a random value from an enum, evenly distributed.
///
/// An index into an array of all named values is generated using the
/// specified `Index` type to determine the return value.
/// This allows for results to be independent of `usize` representation.
///
/// Prefer `enumValue` if this isn't important.
///
/// See `uintLessThan`, which this function uses in most cases,
/// for commentary on the runtime of this function.
pub fn enumValueWithIndex(r: Random, comptime EnumType: type, comptime Index: type) EnumType {
comptime assert(@typeInfo(EnumType) == .Enum);
// 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 = comptime std.enums.values(EnumType);
comptime assert(values.len > 0); // can't return anything
comptime assert(maxInt(Index) >= values.len - 1); // can't access all values
comptime if (values.len == 1) return values[0];
const index = if (comptime values.len - 1 == maxInt(Index))
r.int(Index)
else
r.uintLessThan(Index, values.len);
const MinInt = MinArrayIndex(Index);
return values[@as(MinInt, @intCast(index))];
}
/// Returns a random int `i` such that `minInt(T) <= 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 ceil_bytes = comptime std.math.divCeil(u16, bits, 8) catch unreachable;
const ByteAlignedT = std.meta.Int(.unsigned, ceil_bytes * 8);
var rand_bytes: [ceil_bytes]u8 = undefined;
r.bytes(&rand_bytes);
// 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.readInt(ByteAlignedT, &rand_bytes, .little);
const unsigned_result: UnsignedT = @truncate(byte_aligned_result);
return @bitCast(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);
assert(0 < less_than);
return limitRangeBiased(T, r.int(T), 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;
assert(0 < less_than);
// adapted from:
// http://www.pcg-random.org/posts/bounded-rands.html
// "Lemire's (with an extra tweak from me)"
var x = r.int(T);
var m = math.mulWide(T, x, less_than);
var l: T = @truncate(m);
if (l < less_than) {
var t = -%less_than;
if (t >= less_than) {
t -= less_than;
if (t >= less_than) {
t %= less_than;
}
}
while (l < t) {
x = r.int(T);
m = math.mulWide(T, x, less_than);
l = @truncate(m);
}
}
return @intCast(m >> 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: UnsignedT = @bitCast(at_least);
const hi: UnsignedT = @bitCast(less_than);
const result = lo +% r.uintLessThanBiased(UnsignedT, hi -% lo);
return @bitCast(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: UnsignedT = @bitCast(at_least);
const hi: UnsignedT = @bitCast(less_than);
const result = lo +% r.uintLessThan(UnsignedT, hi -% lo);
return @bitCast(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: UnsignedT = @bitCast(at_least);
const hi: UnsignedT = @bitCast(at_most);
const result = lo +% r.uintAtMostBiased(UnsignedT, hi -% lo);
return @bitCast(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: UnsignedT = @bitCast(at_least);
const hi: UnsignedT = @bitCast(at_most);
const result = lo +% r.uintAtMost(UnsignedT, hi -% lo);
return @bitCast(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);
}
}
/// Return a floating point value evenly distributed in the range [0, 1).
pub fn float(r: Random, comptime T: type) T {
// Generate a uniformly random value for the mantissa.
// Then generate an exponentially biased random value for the exponent.
// This covers every possible value in the range.
switch (T) {
f32 => {
// Use 23 random bits for the mantissa, and the rest for the exponent.
// If all 41 bits are zero, generate additional random bits, until a
// set bit is found, or 126 bits have been generated.
const rand = r.int(u64);
var rand_lz = @clz(rand);
if (rand_lz >= 41) {
// TODO: when #5177 or #489 is implemented,
// tell the compiler it is unlikely (1/2^41) to reach this point.
// (Same for the if branch and the f64 calculations below.)
rand_lz = 41 + @clz(r.int(u64));
if (rand_lz == 41 + 64) {
// It is astronomically unlikely to reach this point.
rand_lz += @clz(r.int(u32) | 0x7FF);
}
}
const mantissa: u23 = @truncate(rand);
const exponent = @as(u32, 126 - rand_lz) << 23;
return @bitCast(exponent | mantissa);
},
f64 => {
// Use 52 random bits for the mantissa, and the rest for the exponent.
// If all 12 bits are zero, generate additional random bits, until a
// set bit is found, or 1022 bits have been generated.
const rand = r.int(u64);
var rand_lz: u64 = @clz(rand);
if (rand_lz >= 12) {
rand_lz = 12;
while (true) {
// It is astronomically unlikely for this loop to execute more than once.
const addl_rand_lz = @clz(r.int(u64));
rand_lz += addl_rand_lz;
if (addl_rand_lz != 64) {
break;
}
if (rand_lz >= 1022) {
rand_lz = 1022;
break;
}
}
}
const mantissa = rand & 0xFFFFFFFFFFFFF;
const exponent = (1022 - rand_lz) << 52;
return @bitCast(exponent | mantissa);
},
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(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(value),
f64 => return value,
else => @compileError("unknown floating point type"),
}
}
/// Shuffle a slice into a random order.
///
/// Note that this will not yield consistent results across all targets
/// due to dependence on the representation of `usize` as an index.
/// See `shuffleWithIndex` for further commentary.
pub inline fn shuffle(r: Random, comptime T: type, buf: []T) void {
r.shuffleWithIndex(T, buf, usize);
}
/// Shuffle a slice into a random order, using an index of a
/// specified type to maintain distribution across targets.
/// Asserts the index type can represent `buf.len`.
///
/// Indexes into the slice are generated using the specified `Index`
/// type, which determines distribution properties. This allows for
/// results to be independent of `usize` representation.
///
/// Prefer `shuffle` if this isn't important.
///
/// See `intRangeLessThan`, which this function uses,
/// for commentary on the runtime of this function.
pub fn shuffleWithIndex(r: Random, comptime T: type, buf: []T, comptime Index: type) void {
const MinInt = MinArrayIndex(Index);
if (buf.len < 2) {
return;
}
// `i <= j < max <= maxInt(MinInt)`
const max: MinInt = @intCast(buf.len);
var i: MinInt = 0;
while (i < max - 1) : (i += 1) {
const j: MinInt = @intCast(r.intRangeLessThan(Index, i, max));
mem.swap(T, &buf[i], &buf[j]);
}
}
/// Randomly selects an index into `proportions`, where the likelihood of each
/// index is weighted by that proportion.
/// It is more likely for the index of the last proportion to be returned
/// than the index of the first proportion in the slice, and vice versa.
///
/// This is useful for selecting an item from a slice where weights are not equal.
/// `T` must be a numeric type capable of holding the sum of `proportions`.
pub fn weightedIndex(r: std.rand.Random, comptime T: type, proportions: []const T) usize {
// This implementation works by summing the proportions and picking a
// random point in [0, sum). We then loop over the proportions,
// accumulating until our accumulator is greater than the random point.
const sum = s: {
var sum: T = 0;
for (proportions) |v| sum += v;
break :s sum;
};
const point = switch (@typeInfo(T)) {
.Int => |int_info| switch (int_info.signedness) {
.signed => r.intRangeLessThan(T, 0, sum),
.unsigned => r.uintLessThan(T, sum),
},
// take care that imprecision doesn't lead to a value slightly greater than sum
.Float => @min(r.float(T) * sum, sum - std.math.floatEps(T)),
else => @compileError("weightedIndex does not support proportions of type " ++
@typeName(T)),
};
assert(point < sum);
var accumulator: T = 0;
for (proportions, 0..) |p, index| {
accumulator += p;
if (point < accumulator) return index;
} else unreachable;
}
/// 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;
// adapted from:
// http://www.pcg-random.org/posts/bounded-rands.html
// "Integer Multiplication (Biased)"
const m = math.mulWide(T, random_int, less_than);
return @intCast(m >> bits);
}
/// Returns the smallest of `Index` and `usize`.
fn MinArrayIndex(comptime Index: type) type {
const index_info = @typeInfo(Index).Int;
assert(index_info.signedness == .unsigned);
return if (index_info.bits >= @typeInfo(usize).Int.bits) usize else Index;
}
test {
std.testing.refAllDecls(@This());
_ = @import("Random/test.zig");
}

0
lib/std/rand/Ascon.zig → lib/std/Random/Ascon.zig
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0
lib/std/rand/ChaCha.zig → lib/std/Random/ChaCha.zig
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0
lib/std/rand/Isaac64.zig → lib/std/Random/Isaac64.zig
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lib/std/rand/Pcg.zig → lib/std/Random/Pcg.zig
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lib/std/rand/RomuTrio.zig → lib/std/Random/RomuTrio.zig
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0
lib/std/rand/Sfc64.zig → lib/std/Random/Sfc64.zig
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lib/std/Random/SplitMix64.zig Normal file
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//! 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.
const SplitMix64 = @This();
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);
}

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lib/std/rand/Xoroshiro128.zig → lib/std/Random/Xoroshiro128.zig
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lib/std/rand/Xoshiro256.zig → lib/std/Random/Xoshiro256.zig
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0
lib/std/rand/benchmark.zig → lib/std/Random/benchmark.zig
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lib/std/rand/test.zig → lib/std/Random/test.zig
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@ -1,9 +1,9 @@
const std = @import("../std.zig");
const math = std.math;
const DefaultPrng = std.rand.DefaultPrng;
const Random = std.rand.Random;
const SplitMix64 = std.rand.SplitMix64;
const DefaultCsprng = std.rand.DefaultCsprng;
const Random = std.Random;
const DefaultPrng = Random.DefaultPrng;
const SplitMix64 = Random.SplitMix64;
const DefaultCsprng = Random.DefaultCsprng;
const expect = std.testing.expect;
const expectEqual = std.testing.expectEqual;

0
lib/std/rand/ziggurat.zig → lib/std/Random/ziggurat.zig
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lib/std/rand.zig
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@ -1,460 +0,0 @@
//! 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.
const std = @import("std.zig");
const builtin = @import("builtin");
const assert = std.debug.assert;
const mem = std.mem;
const math = std.math;
const maxInt = std.math.maxInt;
/// Fast unbiased random numbers.
pub const DefaultPrng = Xoshiro256;
/// Cryptographically secure random numbers.
pub const DefaultCsprng = ChaCha;
pub const Ascon = @import("rand/Ascon.zig");
pub const ChaCha = @import("rand/ChaCha.zig");
pub const Isaac64 = @import("rand/Isaac64.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 RomuTrio = @import("rand/RomuTrio.zig");
pub const ziggurat = @import("rand/ziggurat.zig");
pub const Random = struct {
ptr: *anyopaque,
fillFn: *const fn (ptr: *anyopaque, buf: []u8) void,
pub fn init(pointer: anytype, comptime fillFn: fn (ptr: @TypeOf(pointer), buf: []u8) void) Random {
const Ptr = @TypeOf(pointer);
assert(@typeInfo(Ptr) == .Pointer); // Must be a pointer
assert(@typeInfo(Ptr).Pointer.size == .One); // Must be a single-item pointer
assert(@typeInfo(@typeInfo(Ptr).Pointer.child) == .Struct); // Must point to a struct
const gen = struct {
fn fill(ptr: *anyopaque, buf: []u8) void {
const self: Ptr = @ptrCast(@alignCast(ptr));
fillFn(self, buf);
}
};
return .{
.ptr = pointer,
.fillFn = gen.fill,
};
}
/// Read random bytes into the specified buffer until full.
pub fn bytes(r: Random, buf: []u8) void {
r.fillFn(r.ptr, buf);
}
pub fn boolean(r: Random) bool {
return r.int(u1) != 0;
}
/// Returns a random value from an enum, evenly distributed.
///
/// Note that this will not yield consistent results across all targets
/// due to dependence on the representation of `usize` as an index.
/// See `enumValueWithIndex` for further commentary.
pub inline fn enumValue(r: Random, comptime EnumType: type) EnumType {
return r.enumValueWithIndex(EnumType, usize);
}
/// Returns a random value from an enum, evenly distributed.
///
/// An index into an array of all named values is generated using the
/// specified `Index` type to determine the return value.
/// This allows for results to be independent of `usize` representation.
///
/// Prefer `enumValue` if this isn't important.
///
/// See `uintLessThan`, which this function uses in most cases,
/// for commentary on the runtime of this function.
pub fn enumValueWithIndex(r: Random, comptime EnumType: type, comptime Index: type) EnumType {
comptime assert(@typeInfo(EnumType) == .Enum);
// 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 = comptime std.enums.values(EnumType);
comptime assert(values.len > 0); // can't return anything
comptime assert(maxInt(Index) >= values.len - 1); // can't access all values
comptime if (values.len == 1) return values[0];
const index = if (comptime values.len - 1 == maxInt(Index))
r.int(Index)
else
r.uintLessThan(Index, values.len);
const MinInt = MinArrayIndex(Index);
return values[@as(MinInt, @intCast(index))];
}
/// Returns a random int `i` such that `minInt(T) <= 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 ceil_bytes = comptime std.math.divCeil(u16, bits, 8) catch unreachable;
const ByteAlignedT = std.meta.Int(.unsigned, ceil_bytes * 8);
var rand_bytes: [ceil_bytes]u8 = undefined;
r.bytes(&rand_bytes);
// 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.readInt(ByteAlignedT, &rand_bytes, .little);
const unsigned_result: UnsignedT = @truncate(byte_aligned_result);
return @bitCast(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);
assert(0 < less_than);
return limitRangeBiased(T, r.int(T), 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;
assert(0 < less_than);
// adapted from:
// http://www.pcg-random.org/posts/bounded-rands.html
// "Lemire's (with an extra tweak from me)"
var x = r.int(T);
var m = math.mulWide(T, x, less_than);
var l: T = @truncate(m);
if (l < less_than) {
var t = -%less_than;
if (t >= less_than) {
t -= less_than;
if (t >= less_than) {
t %= less_than;
}
}
while (l < t) {
x = r.int(T);
m = math.mulWide(T, x, less_than);
l = @truncate(m);
}
}
return @intCast(m >> 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: UnsignedT = @bitCast(at_least);
const hi: UnsignedT = @bitCast(less_than);
const result = lo +% r.uintLessThanBiased(UnsignedT, hi -% lo);
return @bitCast(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: UnsignedT = @bitCast(at_least);
const hi: UnsignedT = @bitCast(less_than);
const result = lo +% r.uintLessThan(UnsignedT, hi -% lo);
return @bitCast(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: UnsignedT = @bitCast(at_least);
const hi: UnsignedT = @bitCast(at_most);
const result = lo +% r.uintAtMostBiased(UnsignedT, hi -% lo);
return @bitCast(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: UnsignedT = @bitCast(at_least);
const hi: UnsignedT = @bitCast(at_most);
const result = lo +% r.uintAtMost(UnsignedT, hi -% lo);
return @bitCast(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);
}
}
/// Return a floating point value evenly distributed in the range [0, 1).
pub fn float(r: Random, comptime T: type) T {
// Generate a uniformly random value for the mantissa.
// Then generate an exponentially biased random value for the exponent.
// This covers every possible value in the range.
switch (T) {
f32 => {
// Use 23 random bits for the mantissa, and the rest for the exponent.
// If all 41 bits are zero, generate additional random bits, until a
// set bit is found, or 126 bits have been generated.
const rand = r.int(u64);
var rand_lz = @clz(rand);
if (rand_lz >= 41) {
// TODO: when #5177 or #489 is implemented,
// tell the compiler it is unlikely (1/2^41) to reach this point.
// (Same for the if branch and the f64 calculations below.)
rand_lz = 41 + @clz(r.int(u64));
if (rand_lz == 41 + 64) {
// It is astronomically unlikely to reach this point.
rand_lz += @clz(r.int(u32) | 0x7FF);
}
}
const mantissa: u23 = @truncate(rand);
const exponent = @as(u32, 126 - rand_lz) << 23;
return @bitCast(exponent | mantissa);
},
f64 => {
// Use 52 random bits for the mantissa, and the rest for the exponent.
// If all 12 bits are zero, generate additional random bits, until a
// set bit is found, or 1022 bits have been generated.
const rand = r.int(u64);
var rand_lz: u64 = @clz(rand);
if (rand_lz >= 12) {
rand_lz = 12;
while (true) {
// It is astronomically unlikely for this loop to execute more than once.
const addl_rand_lz = @clz(r.int(u64));
rand_lz += addl_rand_lz;
if (addl_rand_lz != 64) {
break;
}
if (rand_lz >= 1022) {
rand_lz = 1022;
break;
}
}
}
const mantissa = rand & 0xFFFFFFFFFFFFF;
const exponent = (1022 - rand_lz) << 52;
return @bitCast(exponent | mantissa);
},
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(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(value),
f64 => return value,
else => @compileError("unknown floating point type"),
}
}
/// Shuffle a slice into a random order.
///
/// Note that this will not yield consistent results across all targets
/// due to dependence on the representation of `usize` as an index.
/// See `shuffleWithIndex` for further commentary.
pub inline fn shuffle(r: Random, comptime T: type, buf: []T) void {
r.shuffleWithIndex(T, buf, usize);
}
/// Shuffle a slice into a random order, using an index of a
/// specified type to maintain distribution across targets.
/// Asserts the index type can represent `buf.len`.
///
/// Indexes into the slice are generated using the specified `Index`
/// type, which determines distribution properties. This allows for
/// results to be independent of `usize` representation.
///
/// Prefer `shuffle` if this isn't important.
///
/// See `intRangeLessThan`, which this function uses,
/// for commentary on the runtime of this function.
pub fn shuffleWithIndex(r: Random, comptime T: type, buf: []T, comptime Index: type) void {
const MinInt = MinArrayIndex(Index);
if (buf.len < 2) {
return;
}
// `i <= j < max <= maxInt(MinInt)`
const max: MinInt = @intCast(buf.len);
var i: MinInt = 0;
while (i < max - 1) : (i += 1) {
const j: MinInt = @intCast(r.intRangeLessThan(Index, i, max));
mem.swap(T, &buf[i], &buf[j]);
}
}
/// Randomly selects an index into `proportions`, where the likelihood of each
/// index is weighted by that proportion.
/// It is more likely for the index of the last proportion to be returned
/// than the index of the first proportion in the slice, and vice versa.
///
/// This is useful for selecting an item from a slice where weights are not equal.
/// `T` must be a numeric type capable of holding the sum of `proportions`.
pub fn weightedIndex(r: std.rand.Random, comptime T: type, proportions: []const T) usize {
// This implementation works by summing the proportions and picking a
// random point in [0, sum). We then loop over the proportions,
// accumulating until our accumulator is greater than the random point.
const sum = s: {
var sum: T = 0;
for (proportions) |v| sum += v;
break :s sum;
};
const point = switch (@typeInfo(T)) {
.Int => |int_info| switch (int_info.signedness) {
.signed => r.intRangeLessThan(T, 0, sum),
.unsigned => r.uintLessThan(T, sum),
},
// take care that imprecision doesn't lead to a value slightly greater than sum
.Float => @min(r.float(T) * sum, sum - std.math.floatEps(T)),
else => @compileError("weightedIndex does not support proportions of type " ++
@typeName(T)),
};
assert(point < sum);
var accumulator: T = 0;
for (proportions, 0..) |p, index| {
accumulator += p;
if (point < accumulator) return index;
} else unreachable;
}
/// Returns the smallest of `Index` and `usize`.
fn MinArrayIndex(comptime Index: type) type {
const index_info = @typeInfo(Index).Int;
assert(index_info.signedness == .unsigned);
return if (index_info.bits >= @typeInfo(usize).Int.bits) usize else Index;
}
};
/// 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;
// adapted from:
// http://www.pcg-random.org/posts/bounded-rands.html
// "Integer Multiplication (Biased)"
const m = math.mulWide(T, random_int, less_than);
return @intCast(m >> bits);
}
// 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 {
std.testing.refAllDecls(@This());
_ = @import("rand/test.zig");
}

5
lib/std/std.zig
View File

@ -36,6 +36,7 @@ pub const PackedIntSliceEndian = @import("packed_int_array.zig").PackedIntSliceE
pub const PriorityQueue = @import("priority_queue.zig").PriorityQueue;
pub const PriorityDequeue = @import("priority_dequeue.zig").PriorityDequeue;
pub const Progress = @import("Progress.zig");
pub const Random = @import("Random.zig");
pub const RingBuffer = @import("RingBuffer.zig");
pub const SegmentedList = @import("segmented_list.zig").SegmentedList;
pub const SemanticVersion = @import("SemanticVersion.zig");
@ -159,8 +160,8 @@ pub const pdb = @import("pdb.zig");
/// and spawning of child processes.
pub const process = @import("process.zig");
/// Fast pseudo-random number generators (i.e. not cryptographically secure).
pub const rand = @import("rand.zig");
/// Deprecated: use `Random` instead.
pub const rand = Random;
/// Sorting.
pub const sort = @import("sort.zig");