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Rewrite Rand functions

Browse Source 
We now use a generic Rand structure which abstracts the core functions
from the backing engine.

The old Mersenne Twister engine is removed and replaced instead with
three alternatives:

 - Pcg32
 - Xoroshiro128+
 - Isaac64

These should provide sufficient coverage for most purposes, including a
CSPRNG using Isaac64. Consumers of the library that do not care about
the actual engine implementation should use DefaultPrng and DefaultCsprng.
This commit is contained in:
Marc Tiehuis 2018-03-30 01:36:04 +13:00
parent 032fccf615
commit 0fd0f6fd1f
7 changed files with 735 additions and 830 deletions
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2
CMakeLists.txt
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@ -509,7 +509,7 @@ set(ZIG_STD_FILES
"os/windows/index.zig"
"os/windows/util.zig"
"os/zen.zig"
"rand.zig"
"rand/index.zig"
"sort.zig"
"special/bootstrap.zig"
"special/bootstrap_lib.zig"

4
std/index.zig
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@ -26,7 +26,7 @@ pub const math = @import("math/index.zig");
pub const mem = @import("mem.zig");
pub const net = @import("net.zig");
pub const os = @import("os/index.zig");
pub const rand = @import("rand.zig");
pub const rand = @import("rand/index.zig");
pub const sort = @import("sort.zig");
pub const unicode = @import("unicode.zig");
pub const zig = @import("zig/index.zig");
@ -58,7 +58,7 @@ test "std" {
_ = @import("heap.zig");
_ = @import("net.zig");
_ = @import("os/index.zig");
_ = @import("rand.zig");
_ = @import("rand/index.zig");
_ = @import("sort.zig");
_ = @import("unicode.zig");
_ = @import("zig/index.zig");

6
std/io_test.zig
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@ -1,7 +1,7 @@
const std = @import("index.zig");
const io = std.io;
const allocator = std.debug.global_allocator;
const Rand = std.rand.Rand;
const DefaultPrng = std.rand.DefaultPrng;
const assert = std.debug.assert;
const mem = std.mem;
const os = std.os;
@ -9,8 +9,8 @@ const builtin = @import("builtin");
test "write a file, read it, then delete it" {
var data: [1024]u8 = undefined;
var rng = Rand.init(1234);
rng.fillBytes(data[0..]);
var prng = DefaultPrng.init(1234);
prng.random.bytes(data[0..]);
const tmp_file_name = "temp_test_file.txt";
{
var file = try os.File.openWrite(allocator, tmp_file_name);

240
std/rand.zig
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@ -1,240 +0,0 @@
const std = @import("index.zig");
const builtin = @import("builtin");
const assert = std.debug.assert;
const rand_test = @import("rand_test.zig");
const mem = std.mem;
const math = std.math;
pub const MT19937_32 = MersenneTwister(
u32, 624, 397, 31,
0x9908B0DF,
11, 0xFFFFFFFF,
7, 0x9D2C5680,
15, 0xEFC60000,
18, 1812433253);
pub const MT19937_64 = MersenneTwister(
u64, 312, 156, 31,
0xB5026F5AA96619E9,
29, 0x5555555555555555,
17, 0x71D67FFFEDA60000,
37, 0xFFF7EEE000000000,
43, 6364136223846793005);
/// Use `init` to initialize this state.
pub const Rand = struct {
const Rng = if (@sizeOf(usize) >= 8) MT19937_64 else MT19937_32;
rng: Rng,
/// Initialize random state with the given seed.
pub fn init(seed: usize) Rand {
return Rand {
.rng = Rng.init(seed),
};
}
/// Get an integer or boolean with random bits.
pub fn scalar(r: &Rand, comptime T: type) T {
if (T == usize) {
return r.rng.get();
} else if (T == bool) {
return (r.rng.get() & 0b1) == 0;
} else {
var result: [@sizeOf(T)]u8 = undefined;
r.fillBytes(result[0..]);
return mem.readInt(result, T, builtin.Endian.Little);
}
}
/// Fill `buf` with randomness.
pub fn fillBytes(r: &Rand, buf: []u8) void {
var bytes_left = buf.len;
while (bytes_left >= @sizeOf(usize)) {
mem.writeInt(buf[buf.len - bytes_left..], r.rng.get(), builtin.Endian.Little);
bytes_left -= @sizeOf(usize);
}
if (bytes_left > 0) {
var rand_val_array: [@sizeOf(usize)]u8 = undefined;
mem.writeInt(rand_val_array[0..], r.rng.get(), builtin.Endian.Little);
while (bytes_left > 0) {
buf[buf.len - bytes_left] = rand_val_array[@sizeOf(usize) - bytes_left];
bytes_left -= 1;
}
}
}
/// Get a random unsigned integer with even distribution between `start`
/// inclusive and `end` exclusive.
pub fn range(r: &Rand, comptime T: type, start: T, end: T) T {
assert(start <= end);
if (T.is_signed) {
const uint = @IntType(false, T.bit_count);
if (start >= 0 and end >= 0) {
return T(r.range(uint, uint(start), uint(end)));
} else if (start < 0 and end < 0) {
// Can't overflow because the range is over signed ints
return math.negateCast(r.range(uint, math.absCast(end), math.absCast(start)) + 1) catch unreachable;
} else if (start < 0 and end >= 0) {
const end_uint = uint(end);
const total_range = math.absCast(start) + end_uint;
const value = r.range(uint, 0, total_range);
const result = if (value < end_uint) x: {
break :x T(value);
} else if (value == end_uint) x: {
break :x start;
} else x: {
// Can't overflow because the range is over signed ints
break :x math.negateCast(value - end_uint) catch unreachable;
};
return result;
} else {
unreachable;
}
} else {
const total_range = end - start;
const leftover = @maxValue(T) % total_range;
const upper_bound = @maxValue(T) - leftover;
var rand_val_array: [@sizeOf(T)]u8 = undefined;
while (true) {
r.fillBytes(rand_val_array[0..]);
const rand_val = mem.readInt(rand_val_array, T, builtin.Endian.Little);
if (rand_val < upper_bound) {
return start + (rand_val % total_range);
}
}
}
}
/// Get a floating point value in the range 0.0..1.0.
pub fn float(r: &Rand, comptime T: type) T {
// TODO Implement this way instead:
// const int = @int_type(false, @sizeOf(T) * 8);
// const mask = ((1 << @float_mantissa_bit_count(T)) - 1);
// const rand_bits = r.rng.scalar(int) & mask;
// return @float_compose(T, false, 0, rand_bits) - 1.0
const int_type = @IntType(false, @sizeOf(T) * 8);
const precision = if (T == f32)
16777216
else if (T == f64)
9007199254740992
else
@compileError("unknown floating point type")
;
return T(r.range(int_type, 0, precision)) / T(precision);
}
};
fn MersenneTwister(
comptime int: type, comptime n: usize, comptime m: usize, comptime r: int,
comptime a: int,
comptime u: math.Log2Int(int), comptime d: int,
comptime s: math.Log2Int(int), comptime b: int,
comptime t: math.Log2Int(int), comptime c: int,
comptime l: math.Log2Int(int), comptime f: int) type
{
return struct {
const Self = this;
array: [n]int,
index: usize,
pub fn init(seed: int) Self {
var mt = Self {
.array = undefined,
.index = n,
};
var prev_value = seed;
mt.array[0] = prev_value;
var i: usize = 1;
while (i < n) : (i += 1) {
prev_value = int(i) +% f *% (prev_value ^ (prev_value >> (int.bit_count - 2)));
mt.array[i] = prev_value;
}
return mt;
}
pub fn get(mt: &Self) int {
const mag01 = []int{0, a};
const LM: int = (1 << r) - 1;
const UM = ~LM;
if (mt.index >= n) {
var i: usize = 0;
while (i < n - m) : (i += 1) {
const x = (mt.array[i] & UM) | (mt.array[i + 1] & LM);
mt.array[i] = mt.array[i + m] ^ (x >> 1) ^ mag01[usize(x & 0x1)];
}
while (i < n - 1) : (i += 1) {
const x = (mt.array[i] & UM) | (mt.array[i + 1] & LM);
mt.array[i] = mt.array[i + m - n] ^ (x >> 1) ^ mag01[usize(x & 0x1)];
}
const x = (mt.array[i] & UM) | (mt.array[0] & LM);
mt.array[i] = mt.array[m - 1] ^ (x >> 1) ^ mag01[usize(x & 0x1)];
mt.index = 0;
}
var x = mt.array[mt.index];
mt.index += 1;
x ^= ((x >> u) & d);
x ^= ((x << s) & b);
x ^= ((x << t) & c);
x ^= (x >> l);
return x;
}
};
}
test "rand float 32" {
var r = Rand.init(42);
var i: usize = 0;
while (i < 1000) : (i += 1) {
const val = r.float(f32);
assert(val >= 0.0);
assert(val < 1.0);
}
}
test "rand.MT19937_64" {
var rng = MT19937_64.init(rand_test.mt64_seed);
for (rand_test.mt64_data) |value| {
assert(value == rng.get());
}
}
test "rand.MT19937_32" {
var rng = MT19937_32.init(rand_test.mt32_seed);
for (rand_test.mt32_data) |value| {
assert(value == rng.get());
}
}
test "rand.Rand.range" {
var r = Rand.init(42);
testRange(&r, -4, 3);
testRange(&r, -4, -1);
testRange(&r, 10, 14);
}
fn testRange(r: &Rand, start: i32, end: i32) void {
const count = usize(end - start);
var values_buffer = []bool{false} ** 20;
const values = values_buffer[0..count];
var i: usize = 0;
while (i < count) {
const value = r.range(i32, start, end);
const index = usize(value - start);
if (!values[index]) {
i += 1;
values[index] = true;
}
}
}

652
std/rand/index.zig Normal file
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@ -0,0 +1,652 @@
// The engines provided here should be initialized from an external source. For now, getRandomBytes
// from the os package is the most suitable. Be sure to use a CSPRNG when required, otherwise using
// a normal PRNG will be faster and use substantially less stack space.
//
// ```
// var buf: [8]u8 = undefined;
// try std.os.getRandomBytes(buf[0..]);
// const seed = mem.readInt(buf[0..8], u64, builtin.Endian.Little);
//
// var r = DefaultPrng.init(seed);
//
// const s = r.random.scalar(u64);
// ```
//
// TODO(tiehuis): Benchmark these against other reference implementations.
const std = @import("../index.zig");
const builtin = @import("builtin");
const assert = std.debug.assert;
const mem = std.mem;
const math = std.math;
// When you need fast unbiased random numbers
pub const DefaultPrng = Xoroshiro128;
// When you need cryptographically secure random numbers
pub const DefaultCsprng = Isaac64;
pub const Rand = struct {
fillFn: fn(r: &Rand, buf: []u8) void,
/// Read random bytes into the specified buffer until fill.
pub fn bytes(r: &Rand, buf: []u8) void {
r.fillFn(r, buf);
}
/// Return a random integer/boolean type.
pub fn scalar(r: &Rand, comptime T: type) T {
var rand_bytes: [@sizeOf(T)]u8 = undefined;
r.bytes(rand_bytes[0..]);
if (T == bool) {
return rand_bytes[0] & 0b1 == 0;
} else {
// NOTE: Cannot @bitCast array to integer type.
return mem.readInt(rand_bytes, T, builtin.Endian.Little);
}
}
/// Get a random unsigned integer with even distribution between `start`
/// inclusive and `end` exclusive.
pub fn range(r: &Rand, comptime T: type, start: T, end: T) T {
assert(start <= end);
if (T.is_signed) {
const uint = @IntType(false, T.bit_count);
if (start >= 0 and end >= 0) {
return T(r.range(uint, uint(start), uint(end)));
} else if (start < 0 and end < 0) {
// Can't overflow because the range is over signed ints
return math.negateCast(r.range(uint, math.absCast(end), math.absCast(start)) + 1) catch unreachable;
} else if (start < 0 and end >= 0) {
const end_uint = uint(end);
const total_range = math.absCast(start) + end_uint;
const value = r.range(uint, 0, total_range);
const result = if (value < end_uint) x: {
break :x T(value);
} else if (value == end_uint) x: {
break :x start;
} else x: {
// Can't overflow because the range is over signed ints
break :x math.negateCast(value - end_uint) catch unreachable;
};
return result;
} else {
unreachable;
}
} else {
const total_range = end - start;
const leftover = @maxValue(T) % total_range;
const upper_bound = @maxValue(T) - leftover;
var rand_val_array: [@sizeOf(T)]u8 = undefined;
while (true) {
r.bytes(rand_val_array[0..]);
const rand_val = mem.readInt(rand_val_array, T, builtin.Endian.Little);
if (rand_val < upper_bound) {
return start + (rand_val % total_range);
}
}
}
}
/// Return a floating point value evenly distributed in the range [0, 1).
pub fn float(r: &Rand, 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.scalar(u32);
const repr = (0x7f << 23) | (s >> 9);
return @bitCast(f32, repr) - 1.0;
},
f64 => {
const s = r.scalar(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 in the range [0, 1].
pub fn floatNorm(r: &Rand, comptime T: type) T {
// TODO(tiehuis): See https://www.doornik.com/research/ziggurat.pdf
@compileError("floatNorm is unimplemented");
}
/// Return a exponentially distributed float between (0, @maxValue(f64))
pub fn floatExp(r: &Rand, comptime T: type) T {
@compileError("floatExp is unimplemented");
}
/// Shuffle a slice into a random order.
pub fn shuffle(r: &Rand, 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.range(usize, i, buf.len);
mem.swap(T, &buf[i], &buf[j]);
}
}
};
// 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 = 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 = []const u64 {
0x5dbd39db0178eb44,
0xa9900fb66b397da3,
0x5c1a28b1aeebcf5c,
0x64a963238f776912,
0xc6d4177b21d1c0ab,
0xb2cbdbdb5ea35394,
};
for (seq) |s| {
std.debug.assert(s == r.next());
}
}
// PCG32 - http://www.pcg-random.org/
//
// PRNG
pub const Pcg = struct {
const default_multiplier = 6364136223846793005;
random: Rand,
s: u64,
i: u64,
pub fn init(init_s: u64) Pcg {
var pcg = Pcg {
.random = Rand { .fillFn = fill },
.s = undefined,
.i = undefined,
};
pcg.seed(init_s);
return pcg;
}
fn next(self: &Pcg) u32 {
const l = self.s;
self.s = l *% default_multiplier +% (self.i | 1);
const xor_s = @truncate(u32, ((l >> 18) ^ l) >> 27);
const rot = u32(l >> 59);
return (xor_s >> u5(rot)) | (xor_s << u5((0 -% rot) & 31));
}
fn seed(self: &Pcg, init_s: u64) void {
// Pcg requires 128-bits of seed.
var gen = SplitMix64.init(init_s);
self.seedTwo(gen.next(), gen.next());
}
fn seedTwo(self: &Pcg, init_s: u64, init_i: u64) void {
self.s = 0;
self.i = (init_s << 1) | 1;
self.s = self.s *% default_multiplier +% self.i;
self.s +%= init_i;
self.s = self.s *% default_multiplier +% self.i;
}
fn fill(r: &Rand, buf: []u8) void {
const self = @fieldParentPtr(Pcg, "random", r);
var i: usize = 0;
const aligned_len = buf.len - (buf.len & 7);
// Complete 4 byte segments.
while (i < aligned_len) : (i += 4) {
var n = self.next();
comptime var j: usize = 0;
inline while (j < 4) : (j += 1) {
buf[i + j] = @truncate(u8, n);
n >>= 8;
}
}
// Remaining. (cuts the stream)
if (i != buf.len) {
var n = self.next();
while (i < buf.len) : (i += 1) {
buf[i] = @truncate(u8, n);
n >>= 4;
}
}
}
};
test "pcg sequence" {
var r = Pcg.init(0);
const s0: u64 = 0x9394bf54ce5d79de;
const s1: u64 = 0x84e9c579ef59bbf7;
r.seedTwo(s0, s1);
const seq = []const u32 {
2881561918,
3063928540,
1199791034,
2487695858,
1479648952,
3247963454,
};
for (seq) |s| {
std.debug.assert(s == r.next());
}
}
// Xoroshiro128+ - http://xoroshiro.di.unimi.it/
//
// PRNG
pub const Xoroshiro128 = struct {
random: Rand,
s: [2]u64,
pub fn init(init_s: u64) Xoroshiro128 {
var x = Xoroshiro128 {
.random = Rand { .fillFn = fill },
.s = undefined,
};
x.seed(init_s);
return x;
}
fn next(self: &Xoroshiro128) u64 {
const s0 = self.s[0];
var s1 = self.s[1];
const r = s0 +% s1;
s1 ^= s0;
self.s[0] = math.rotl(u64, s0, u8(55)) ^ s1 ^ (s1 << 14);
self.s[1] = math.rotl(u64, s1, u8(36));
return r;
}
// Skip 2^64 places ahead in the sequence
fn jump(self: &Xoroshiro128) void {
var s0: u64 = 0;
var s1: u64 = 0;
const table = []const u64 {
0xbeac0467eba5facb,
0xd86b048b86aa9922
};
inline for (table) |entry| {
var b: usize = 0;
while (b < 64) : (b += 1) {
if ((entry & (u64(1) << u6(b))) != 0) {
s0 ^= self.s[0];
s1 ^= self.s[1];
}
_ = self.next();
}
}
self.s[0] = s0;
self.s[1] = s1;
}
fn seed(self: &Xoroshiro128, init_s: u64) void {
// Xoroshiro requires 128-bits of seed.
var gen = SplitMix64.init(init_s);
self.s[0] = gen.next();
self.s[1] = gen.next();
}
fn fill(r: &Rand, buf: []u8) void {
const self = @fieldParentPtr(Xoroshiro128, "random", r);
var i: usize = 0;
const aligned_len = buf.len - (buf.len & 7);
// Complete 8 byte segments.
while (i < aligned_len) : (i += 8) {
var n = self.next();
comptime var j: usize = 0;
inline while (j < 8) : (j += 1) {
buf[i + j] = @truncate(u8, n);
n >>= 8;
}
}
// Remaining. (cuts the stream)
if (i != buf.len) {
var n = self.next();
while (i < buf.len) : (i += 1) {
buf[i] = @truncate(u8, n);
n >>= 8;
}
}
}
};
test "xoroshiro sequence" {
var r = Xoroshiro128.init(0);
r.s[0] = 0xaeecf86f7878dd75;
r.s[1] = 0x01cd153642e72622;
const seq1 = []const u64 {
0xb0ba0da5bb600397,
0x18a08afde614dccc,
0xa2635b956a31b929,
0xabe633c971efa045,
0x9ac19f9706ca3cac,
0xf62b426578c1e3fb,
};
for (seq1) |s| {
std.debug.assert(s == r.next());
}
r.jump();
const seq2 = []const u64 {
0x95344a13556d3e22,
0xb4fb32dafa4d00df,
0xb2011d9ccdcfe2dd,
0x05679a9b2119b908,
0xa860a1da7c9cd8a0,
0x658a96efe3f86550,
};
for (seq2) |s| {
std.debug.assert(s == r.next());
}
}
// ISAAC64 - http://www.burtleburtle.net/bob/rand/isaacafa.html
//
// CSPRNG
//
// Follows the general idea of the implementation from here with a few shortcuts.
// https://doc.rust-lang.org/rand/src/rand/prng/isaac64.rs.html
pub const Isaac64 = struct {
random: Rand,
r: [256]u64,
m: [256]u64,
a: u64,
b: u64,
c: u64,
i: usize,
pub fn init(init_s: u64) Isaac64 {
var isaac = Isaac64 {
.random = Rand { .fillFn = fill },
.r = undefined,
.m = undefined,
.a = undefined,
.b = undefined,
.c = undefined,
.i = undefined,
};
// seed == 0 => same result as the unseeded reference implementation
isaac.seed(init_s, 1);
return isaac;
}
fn step(self: &Isaac64, mix: u64, base: usize, comptime m1: usize, comptime m2: usize) void {
const x = self.m[base + m1];
self.a = mix +% self.m[base + m2];
const y = self.a +% self.b +% self.m[(x >> 3) % self.m.len];
self.m[base + m1] = y;
self.b = x +% self.m[(y >> 11) % self.m.len];
self.r[self.r.len - 1 - base - m1] = self.b;
}
fn refill(self: &Isaac64) void {
const midpoint = self.r.len / 2;
self.c +%= 1;
self.b +%= self.c;
{
var i: usize = 0;
while (i < midpoint) : (i += 4) {
self.step( ~(self.a ^ (self.a << 21)), i + 0, 0, midpoint);
self.step( self.a ^ (self.a >> 5) , i + 1, 0, midpoint);
self.step( self.a ^ (self.a << 12) , i + 2, 0, midpoint);
self.step( self.a ^ (self.a >> 33) , i + 3, 0, midpoint);
}
}
{
var i: usize = 0;
while (i < midpoint) : (i += 4) {
self.step( ~(self.a ^ (self.a << 21)), i + 0, midpoint, 0);
self.step( self.a ^ (self.a >> 5) , i + 1, midpoint, 0);
self.step( self.a ^ (self.a << 12) , i + 2, midpoint, 0);
self.step( self.a ^ (self.a >> 33) , i + 3, midpoint, 0);
}
}
self.i = 0;
}
fn next(self: &Isaac64) u64 {
if (self.i >= self.r.len) {
self.refill();
}
const value = self.r[self.i];
self.i += 1;
return value;
}
fn seed(self: &Isaac64, init_s: u64, comptime rounds: usize) void {
// We ignore the multi-pass requirement since we don't currently expose full access to
// seeding the self.m array completely.
mem.set(u64, self.m[0..], 0);
self.m[0] = init_s;
// prescrambled golden ratio constants
var a = []const u64 {
0x647c4677a2884b7c,
0xb9f8b322c73ac862,
0x8c0ea5053d4712a0,
0xb29b2e824a595524,
0x82f053db8355e0ce,
0x48fe4a0fa5a09315,
0xae985bf2cbfc89ed,
0x98f5704f6c44c0ab,
};
comptime var i: usize = 0;
inline while (i < rounds) : (i += 1) {
var j: usize = 0;
while (j < self.m.len) : (j += 8) {
comptime var x1: usize = 0;
inline while (x1 < 8) : (x1 += 1) {
a[x1] +%= self.m[j + x1];
}
a[0] -%= a[4]; a[5] ^= a[7] >> 9; a[7] +%= a[0];
a[1] -%= a[5]; a[6] ^= a[0] << 9; a[0] +%= a[1];
a[2] -%= a[6]; a[7] ^= a[1] >> 23; a[1] +%= a[2];
a[3] -%= a[7]; a[0] ^= a[2] << 15; a[2] +%= a[3];
a[4] -%= a[0]; a[1] ^= a[3] >> 14; a[3] +%= a[4];
a[5] -%= a[1]; a[2] ^= a[4] << 20; a[4] +%= a[5];
a[6] -%= a[2]; a[3] ^= a[5] >> 17; a[5] +%= a[6];
a[7] -%= a[3]; a[4] ^= a[6] << 14; a[6] +%= a[7];
comptime var x2: usize = 0;
inline while (x2 < 8) : (x2 += 1) {
self.m[j + x2] = a[x2];
}
}
}
mem.set(u64, self.r[0..], 0);
self.a = 0;
self.b = 0;
self.c = 0;
self.i = self.r.len; // trigger refill on first value
}
fn fill(r: &Rand, buf: []u8) void {
const self = @fieldParentPtr(Isaac64, "random", r);
var i: usize = 0;
const aligned_len = buf.len - (buf.len & 7);
// Fill complete 64-byte segments
while (i < aligned_len) : (i += 8) {
var n = self.next();
comptime var j: usize = 0;
inline while (j < 8) : (j += 1) {
buf[i + j] = @truncate(u8, n);
n >>= 8;
}
}
// Fill trailing, ignoring excess (cut the stream).
if (i != buf.len) {
var n = self.next();
while (i < buf.len) : (i += 1) {
buf[i] = @truncate(u8, n);
n >>= 8;
}
}
}
};
test "isaac64 sequence" {
var r = Isaac64.init(0);
// from reference implementation
const seq = []const u64 {
0xf67dfba498e4937c,
0x84a5066a9204f380,
0xfee34bd5f5514dbb,
0x4d1664739b8f80d6,
0x8607459ab52a14aa,
0x0e78bc5a98529e49,
0xfe5332822ad13777,
0x556c27525e33d01a,
0x08643ca615f3149f,
0xd0771faf3cb04714,
0x30e86f68a37b008d,
0x3074ebc0488a3adf,
0x270645ea7a2790bc,
0x5601a0a8d3763c6a,
0x2f83071f53f325dd,
0xb9090f3d42d2d2ea,
};
for (seq) |s| {
std.debug.assert(s == r.next());
}
}
// Actual Rand helper function tests, pcg engine is assumed correct.
test "Rand float" {
var prng = DefaultPrng.init(0);
var i: usize = 0;
while (i < 1000) : (i += 1) {
const val1 = prng.random.float(f32);
std.debug.assert(val1 >= 0.0);
std.debug.assert(val1 < 1.0);
const val2 = prng.random.float(f64);
std.debug.assert(val2 >= 0.0);
std.debug.assert(val2 < 1.0);
}
}
test "Rand scalar" {
var prng = DefaultPrng.init(0);
const s = prng .random.scalar(u64);
}
test "Rand bytes" {
var prng = DefaultPrng.init(0);
var buf: [2048]u8 = undefined;
prng.random.bytes(buf[0..]);
}
test "Rand shuffle" {
var prng = DefaultPrng.init(0);
var seq = []const 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;
std.debug.assert(sumArray(seq[0..]) == 10);
}
// we should see every entry at the head at least once
for (seen) |e| {
std.debug.assert(e == true);
}
}
fn sumArray(s: []const u8) u32 {
var r: u32 = 0;
for (s) |e| r += e;
return r;
}
test "Rand range" {
var prng = DefaultPrng.init(0);
testRange(&prng.random, -4, 3);
testRange(&prng.random, -4, -1);
testRange(&prng.random, 10, 14);
}
fn testRange(r: &Rand, start: i32, end: i32) void {
const count = usize(end - start);
var values_buffer = []bool{false} ** 20;
const values = values_buffer[0..count];
var i: usize = 0;
while (i < count) {
const value = r.range(i32, start, end);
const index = usize(value - start);
if (!values[index]) {
i += 1;
values[index] = true;
}
}
}

507
std/rand_test.zig
View File

@ -1,507 +0,0 @@
pub const mt64_seed = 0xb334e49d0977c37e;
pub const mt64_data = []u64 {
0x2ad1a63fab6d25a9, 0xb7143aba12569814, 0xc1b60d8d49e53e8, 0x5652adfc8da656dc,
0x43e3beb6d9e484a9, 0x17b09b71e9418ff7, 0x541646292686cfa4, 0x260457071268ecfc,
0x1627af31774e1dc1, 0x362a49b34ed75bb3, 0x7acf72002fe0f733, 0x3aaaf2e7b9409452,
0x9cfc2d9908115c2, 0x6e81a7f16ae613e9, 0xfc4da89c04acf3c7, 0x6984b6adb4feb9ae,
0x6a128b334e27b03d, 0xcc45a2b02937871a, 0xe585b229e00b2283, 0x7a92c0664a6f678a,
0x972735011bdc0744, 0xb494e743d658a084, 0x1eda3c4e7b1b2d0c, 0x4c7adb3831d87332,
0x12f8c7355f5ec631, 0xfc2bcb6be7d60eba, 0x74b95b47895f8687, 0x171de6fe92b97f5a,
0x86383730f52719ac, 0xe4e43ce0f61274f6, 0x514f7e072d96f19c, 0xabef324fbc6cb7fe,
0x7534b945b742f14f, 0x47f9efe33265adbe, 0x7bcab027a0abf16b, 0x3312a2b34225bff7,
0xb61455ce8c2e3e0b, 0x2b81008deeee4d94, 0x743b0b2b4974c7b6, 0xfc219101fd665f7d,
0x863d78891cbfe5e5, 0x7531bb1839181778, 0xf614359a65356e72, 0xfcdd1f6e3f250bdd,
0x528e10bd536eed5b, 0x9f69386ac60cd618, 0xbf5f242706817f01, 0x8e7da8070072cf64,
0xaa318b622da0667f, 0xc9580540fb7efd66, 0xb5d996deccd02e0e, 0x81c6a799ea3f5a41,
0xe6b896f4e21a8550, 0xde5206f177a24ceb, 0x53343e81639ec0b6, 0x5a6edb63d08be9f6,
0x3602c2892f7da1b9, 0xda84f4259841bdea, 0x5880e169a7746e45, 0x57cddb5ffd3c2423,
0x28fe1166fe7b8595, 0x92136c9decb42243, 0xa8c4199818ca7d62, 0x5042cd96f62854dd,
0x22b2d38c3f21f8d0, 0x73a2bfccf1b5f7bb, 0xaba3718f40b6984e, 0x9c1f5dc3e399f5f0,
0x9cf463f95369c149, 0xa7546d69e4232e18, 0x9ea57317d19ab7fc, 0xfb13c83d830731fb,
0x635a123eaa099259, 0x9a2fe7d0ba6e3c5c, 0x40b903cd0d0d3b4e, 0xc8210eb2d2e941cb,
0xd2582d4b1e016484, 0x1d048030875af39c, 0xb51c31a6c193d76f, 0x5ce9b801b8d61626,
0x2bae30455cbb0022, 0xba54df5998b2443f, 0x927abb9342c9a90a, 0xc431eb7df3e06727,
0x726f885d3da88d5, 0x7d85ff1ca4260280, 0xaf3fecf8f019817, 0x31d39105d6fc4fe8,
0x262d9842dbafd4bd, 0x54c28a2876e62e39, 0x95a986e24e214dde, 0xbf677a1abd2e553,
0x48ac890ff787b2b6, 0x2890ec1c67c539f4, 0x7ce88bf3975882c3, 0x88ef340414a29c88,
0xe30de9c88a00805b, 0xe772225e3ee6c68a, 0xa3a7d0921c5d5816, 0x8354957227b1663f,
0xb5b65ded7c747cbc, 0x93b4a12ff2e8fcea, 0x6359579c3c438b3c, 0x45b2c12e9722f2bd,
0x659a604414f19e1, 0x4ec9a149d4219ca5, 0xd830290dd6aebe2b, 0xabc7874a6b4827f8,
0xc91be5dd875847e7, 0x5b761d39f3f96aee, 0x5749dffad692b6c8, 0x86c94840cbd249d2,
0x411a466e886ad7, 0x27dca1f51aebb9a0, 0x1cceb093fbab7a42, 0x7140c2d6706e927c,
0x6881fdb87299a92f, 0xa81a28de171f3c47, 0x8fa9a1b3bb5dfb2a, 0xae076853e3e0abde,
0xe76572308ecd6b54, 0x6cd926c2e2760d8a, 0xdf080266cfbe3dc3, 0xb99b961999765d7b,
0xadb5d4e2b896ddf1, 0x8d3aaf4c83c83c56, 0x9b66e4f6eb65bef7, 0x7a81c3bf785eb1df,
0xc53f02b3e8c38647, 0xcdfeb25ee787759d, 0xead5e734d64ab5f6, 0x7930d87af1072499,
0xf30690a71d88ad6e, 0x73c347923c84728a, 0x3f2b588221003fe4, 0xe747052d0b453af2,
0xabe6fa70539b5edf, 0x4db6d1530d628c2, 0x4ec929af434eb1b0, 0x15afbe39886181ff,
0xa9141b9c89a07b80, 0x7d33f966c6232057, 0x8ddcb412f34a491d, 0xa74472b8ecc1e2f2,
0x34d745de1cb7de2e, 0x6cf67091309e5e93, 0xfb25004efa59450a, 0x3355947066522286,
0x5a8cffdf079dac21, 0x419445d6e6825887, 0x6e9c064f84381dcf, 0xbbcaf462a3a8ad76,
0x75836c68d6c1a13e, 0xf38141565d5c3759, 0x8c65989142ffa802, 0x106067ec26e6463,
0xadfac5e3a80de9c2, 0xc48b16e2df25b9f2, 0xa3257889c33669e6, 0x5bc760d4d65a1745,
0x303cd31fead81139, 0xfb97f78cade31e1d, 0xb888b8e05820a469, 0x7ebb8e44d47f54d9,
0xce76cdbb5ecdc529, 0xb1eb29949a099d52, 0xb6affc1b240a7eb3, 0x22977eac542906f1,
0x9b105b391ff729df, 0x83371186b2834968, 0xd5b893f382ea9e90, 0x5d17aa80a1fd4854,
0xe8ed8525eb29210c, 0xc789f3cd36c4dae3, 0x556e50a5f46b73fb, 0xef1d129b523dff77,
0x851de0f53f6707f9, 0x8deeeadfb1fa8bfc, 0x3d8c89c0e08c4f2e, 0xecfaaea537123333,
0x5bc9053d2dfd7669, 0x408c5bb2e880a9a2, 0x495726b3f3248219, 0x2b23cca4a6ea1ccc,
0x1df3663045092d61, 0xaf977a46e965e45b, 0x43a2facfff7f97e, 0x9b7714344c7b51e,
0x35643b24efb0559a, 0x502820785dc1af13, 0xbf82d2775b46433d, 0x1db626f2e16ca66,
0x744b031447c1e27d, 0x99e79898612f4606, 0xda02a728d234821f, 0xcf00c6fbb637a6e9,
0x242f2963196fd8b, 0x7aed8efc2dd562bb, 0x6204fb5d3dc6208a, 0x3e84861182fc7f6,
0xd14c4ee5aeef5c7a, 0x3749fbef94378dc1, 0x8fe710ec5cfc8566, 0xf43d7e495d5384d7,
0x8ff6396f1f1ce7c4, 0xf1252a6b6f86b42c, 0xddbbd098d6dca83f, 0x4e228724a227232a,
0x92a5a52ba2b24fa8, 0xdfc172b03fde669c, 0x34ee55adf7f0711c, 0x21d181e79b8000bc,
0xc788b1f48b37b693, 0x544fc4cfed0e0f92, 0xafca0c6de41789cc, 0xbb37bb5107ef97f8,
0xb9d62bf1dc0f6c95, 0xc78b5a36110dfb1, 0x1d615b658f39657e, 0x2bb2cd04cabcc360,
0xe563488ece6362f0, 0x213b56ce006fecc6, 0xc38207089fed0270, 0xa33199ff4a51d095,
0x1802ad28fb1896b1, 0xbead8f18c164a332, 0xceb5149101aa450f, 0x39ad89851ee8b62a,
0x317229aafabf37c4, 0xee68b8b9bf3520b3, 0xe4db499288350f04, 0xf8ea27feddb0ae7a,
0xa17235067b489c42, 0xbf4a570245f95d78, 0x8065c67e1d1537ab, 0xbd9357fb1b30aee5,
0xc224166ebeb24c42, 0xf9baf8ccd01b53bf, 0x5c13775c3fea8038, 0x4ea66f6d650ce62d,
0x470592ed81c140f2, 0xc2d0eb6f7999321f, 0x85d762f20290dc0c, 0x9f7d0d13936f6e78,
0x41f1fd2d20f2d62d, 0x891cb19ce1af2c2f, 0xe7ff34c3b29c3719, 0x246743f43126c69c,
0xea4b2da3195ebab9, 0x4831e4de995187dc, 0x7fb8969bbee45ce5, 0xe35b483da73c44ed,
0xf89158ca9af36227, 0x9fc7f34a35469a7a, 0xd02483ebca6564e7, 0xca00da156aaeda03,
0x303d1514646822f1, 0x226832ae582b8eac, 0xf772d719e413504e, 0x87603b928c068ab1,
0x4dc1552230e9b883, 0xef8c5e9db946fc87, 0x935581290bf7a4ee, 0xca632d2c7674bf2,
0xd8a3933b80d39efd, 0xf026574d0ffee6fb, 0xe4412d0dcd2fe94f, 0x668916490a2983ec,
0x73b1fe84a995718, 0x729bedefe21cc0e7, 0xd3a770f1c683b98f, 0x5d597a96323a10c2,
0xfbb7834bbf5fed23, 0xf3546c805a42ccdd, 0x9ef3e2164bb31a0c, 0x388363ce6c6c2253,
0x8120f4a949f017cb, 0x925a61942bbd3d10, 0xa03182d8599c0521, 0x2412e23004b40ebb,
0x35010a126bf2aecc, 0x21147869a1a84ca7, 0x53cba503b6127b98, 0x10c89dd62ab3591c,
0xf4c7f84faaf9f5f1, 0x8b4a37a2e844b97b, 0x23ddeb236a0bd9af, 0x4fd51d7207f49e62,
0x6cdab447c27706b2, 0x9e8f54b9a2d1a790, 0x191aed85d4d77087, 0xf74ecf5015265af6,
0x45925e25404922a1, 0xcf5467a0f5b42b98, 0x73590809c85c728c, 0xc16beeda74a1a1b8,
0xc3bbe7999803dd6a, 0x1a368bb32eec184, 0xafad2d86b7bb574f, 0xdc7c7b8960dc921a,
0xd9b68d854f5e0ae1, 0xe9e1a6a16efe0bea, 0x304a15bd6ca1cb14, 0x713ce3144e0af4b9,
0xc50eb410981be1d2, 0xb0fba6119bf7a300, 0x7a107296731fd314, 0xdd764898a90042b3,
0x8a69973262da3bc8, 0x29c6b9d048596c44, 0x62581bd20da76f1b, 0x4d1a3941d6d3e4bb,
0x19c447306245055, 0xb2978afcd04ba357, 0x7c01cdefcfe24432, 0xc4b268314411deae,
0x5ba56d49da714765, 0x33299186ac6dfd09, 0xede087aec096ef0d, 0xf758da2c7bcf9ddb,
0x5ea6c40d56824cdd, 0x121ff879d6ba905b, 0xb5fed0c42b616f5c, 0x21029cdc347de152,
0xb251d93f4cd7bf4a, 0xaedcb2dc6402cf13, 0x840e5e0d96e89407, 0x6a92fd328efcc6ef,
0xc63f5d8f6fcadcbd, 0x405bd64d1621128e, 0xe1318888172f58ed, 0x1009c9764d49da2b,
0x4bc0592cbfdf9f91, 0x972f0e080dfecd02, 0xa1cb961958eeb6aa, 0x6ee6467ad8c20aca,
0xb3f1c738390d6a83, 0x6504eb7ac498650d, 0xdf7dda67f198f59f, 0x72615652e56a82c3,
0x85e0fa2dfb51755a, 0x98b1f92a3d2ad940, 0xce81d51d875c0045, 0x437004d0be0a4d69,
0x64065895526f896c, 0xe1e1fea920785d49, 0x7d507ffd56fda19a, 0x17309b625cecb42,
0x67b6d83f0fd0f572, 0x5178665a5bcd38f4, 0x3c49fda2d35a8606, 0x7f058d2cb0ad351c,
0xfb95691559245416, 0xc991b857662b1b9f, 0x9e6d0f4e19774f96, 0x26cc7502212ca578,
0x3466110f03225e49, 0x2ae4958375eab9f3, 0x939a8d94c8871191, 0xa27356548ac6b28d,
0xacf86d43ec3aa030, 0xe0d16c7fa0b13a8c, 0x408ec2b2f8da531b, 0xde72494115ee4e83,
0xd26d7f79a02c5b1e, 0x2b6f835520c97f6a, 0x1f30f008b109ae7d, 0x698dbf9acaa222f1,
0xbd55de40838376d5, 0xebe53822cec7eb80, 0x7ce900793008d2bc, 0x494fc7d10e8331bb,
0x53509b90bdb7d588, 0x62aa920e9554b2f2, 0xe103098542011b6f, 0xeb722b9523d68af8,
0xb71b1a6ea2c6591b, 0x97cd7da55c940270, 0x8ab70184427e45dc, 0x6cb6907427808465,
0xf69232a42dbe7475, 0xbc9816d429fa8909, 0xef1e74244539d41b, 0x5569b6d10440d5c,
0x7dda6817985c8ef5, 0xb270ed19cc8161b3, 0x87d80b66c8a15db0, 0x96966684c3ba47fb,
0x996669bc87aff3bf, 0x17c015383c793f2, 0xa4b5de41fc69f61a, 0x14a0eb4e3055742f,
0x5f0da5a7a2b8bc79, 0x5fe0353728aac023, 0x1554daf4abe92eed, 0x545722dac774b6a4,
0x733fc54174f2e0d1, 0x3478ef85dd994316, 0x58ba2ac090ef7575, 0xa66b9b0cbc77b6e2,
0xdc78cab5c708a3ee, 0x97a30c27be510f61, 0xb95d0b06fc0910b6, 0xdc80bdc42f79a25f,
0x5cadc438e65b3070, 0x6263df49ce691b9c, 0xa7ce160daa64416b, 0xa4f8bfedb57288c1,
0xa51714e187bbcfe9, 0xe25df4e9fc44644c, 0xeaf1854b3116ce11, 0xde1b8f810991a604,
0xd4fc2e365e99be4b, 0x8d1b0d2799527e06, 0x7cac59eaf46baba, 0x4fa63c74d2dabaf1,
0x4f6c5d5e676733a6, 0x7ab7ddb9c1b789b7, 0x5d9beb4877a37034, 0x5e96bc9de3985bcb,
0x72bab4dcb75b3228, 0xfa40f33c4d799e1f, 0x73e6f61a69984a6b, 0x7499c9af466cf22f,
0x42fab9136bfa64dd, 0xd5e8e39513b6fffd, 0x8eda1fd5ad8cd51d, 0x95338744859dff44,
0x4f0c5e5ae768c729, 0x5bc92c60495ae348, 0xcbb48c170ac21168, 0x8374aa2440eeb138,
0x70b663d6f6d70ca9, 0x11264ca6dd79e5a0, 0xf058a2c156974514, 0x36820eefc435ba63,
0xd7b69f3d0c0c27a1, 0xe1a2eddf3b41d205, 0x80508ec93b038bc8, 0xd7e0429bd511ff37,
0x7bf55a4e87e183b8, 0x4cb370ce7edb4bea, 0x26fbd0b31dcef45b, 0xf7acbd6781419fa6,
0xf7849659f05c90c, 0xb686271ea57a47c6, 0x16f3f839dbfb4e1b, 0x906872b08b2c61a,
0xc30c86d0a0203c15, 0xdaf238a6aa4fc9f7, 0x2399aa09ad2c069a, 0xf133c3aca703f545,
0x868a10304a1c98ba, 0x60ef0607f46f7e90, 0xe4e69f26931e11a5, 0x487b8f6bd6d92941,
0xd10cb2971798c0c7, 0x7126d81aa4bd0106, 0xcb620311dc84ab82, 0x26f8734a7a356bb2,
0xcf9b9eeb02ee978c, 0x8a9ff0285d4d6b30, 0xe30e3b957e2cc7f8, 0x7c15a09e4d275809,
0xdf723ae1dda5d167, 0xac212e4f6264bba2, 0xe3d60920ed983308, 0x91b403cbc91e290c,
0xcdb905b012aff7c7, 0xb5ee73d45f900897, 0xafacc7cd7f5d52e7, 0xa8653272621165d6,
0x90e2efc485ddd0d1, 0x56ef1ca9097b1a96, 0xc7a20f85777eb0a, 0xf4cec0271a50eae9,
0x21acd76442024973, 0x19a46be82a4abdbe, 0x1bc12e0b8bf41fbb, 0x3766fe3d8e5119f2,
0x7fea355c4c18e8ad, 0xd08b496a24fb8017, 0xe1a7cfaa0877aa2, 0xd37ad9e2a2a3fa96,
0xaa362ba0e696f679, 0x7e7de89142c3aca5, 0x2dedb0842a3575b8, 0xb74c1e1d9082fe5b,
0xb1ae74323699140f, 0x73623f80c727a6ea, 0x132ed204b0f10441, 0xc3e6ebe8ffc252bf,
0x5f15cffb8286dce0, 0x66dab32df780fa8f, 0xeb00da7b25ea99e4, 0x113ad2448fafb671,
0xee065c10a8f1924f, 0x2fcb7367cc01fe5, 0x484338f5c2d0aacd, 0xecfacd785e42d7a6,
0x11513f845de8af3a, 0xd11be6b29054de0d, 0x2536e5d2856af9b7, 0x60ab519760acd4c4,
0x6bfe010250a831ac, 0xb28a93e44b53b21b, 0x281cf9b233858583, 0x4ca6139abc79a710,
0x5717d33616d77a95, 0x9ba52d2b7dfe71b5, 0x32e1c543476aa17d, 0xae242cc75806b7fa,
0xa1415cb8fde770da, 0x3956c67542dc004d, 0x3a6f51518fdd20ce, 0x448c848f6c936d93,
0x8fec38ff51bb5fab, 0x7463816cfc0754ac, 0x83b38e531ba39e73, 0xf9fc84dcf4f8c93e,
0xdf20dbe8b91c3d6f, 0xec65939ac9516f9a, 0x888346f6c1aaa94a, 0xe42cabb108f60d95,
0x39bb2e46b0599fa9, 0x529335ed75acba9e, 0x6a8767c5d00776c4, 0x8243346104fe61a5,
0x7a2bd0339b3e9bac, 0xb68ccdf14473f4ba, 0xa06f389531ab553a, 0xc7c6f074fc2882d3,
0x50a5fd6e6d0df962, 0xd7c0000d194139b7, 0x5ae27ef4033f873d, 0x4e7abe8a6d3570f8,
0x27011ccd3885e709, 0x3dae53f7b7a8924a, 0xa9086c9b2b86fb71, 0xa3f9e534a399e62c,
0x9f2f0379f9a33ec6, 0xceb51af95d4472bd, 0x15aa534182f8465, 0x96373b9cd28a627b,
0x9fdce0ad99d41907, 0x2755bb0f52b8c239, 0x2f2e241b6aa7d243, 0xf040afbacb2f6001,
0x552267c5f8b4c1b0, 0x22bfb3f0b58f9e48, 0x6bff8de368dbee3a, 0x652025c63d4069ce,
0x743eb697b25f9c90, 0x8a3742c9dbf67b1c, 0xaf3bcfc260d7e69, 0x491facaa59b7e1d,
0xd07d0761e6535fcd, 0x79ef09d9d3859232, 0xe0e0a013317d9207, 0x4b94baecf6fe4b4e,
0x574576ed054cfc38, 0x90e90edd1a26f0aa, 0x616d32a371af78c6, 0x392cea9c34ffb0a8,
0x692a6e730c33ac6f, 0x9e4b92ef425b78a6, 0x291d4c962d2f3e7c, 0x5f0f8ebb67f308fc,
0xc1a0faf70ec747a3, 0x641da9550cd89392, 0x6adbe38115f09648, 0x3a51980fb324da0d,
0xee894f2b5c17a380, 0x58788fa693f767c9, 0xc9f490ff5d88c4c0, 0x2ca6e8b204aa3070,
0x7693837d7910c40c, 0x9240e04f16051720, 0xab773072d922faa2, 0xacb6892db8362872,
0x5ac8b4d130613c0e, 0x65cd5ac259c653cb, 0x9647e0276864f3f8, 0xe207c57ee9237a53,
0xe41f2663482a8fdb, 0xf605931fce8b95bd, 0x5b0247a9009255d2, 0xae949df3ab5a4ab5,
0xc0e912dacbb72c42, 0x4226971e6351f33a, 0xd98d41f9f0fdb6c3, 0x64bf6a0af66782d5,
0xb4ca689b3959bf46, 0xb4cbf621b4970922, 0xe9f27469c2412fe6, 0xb529d406d27c785e,
0xf33be21f2672ec78, 0x34b3c4c4603656cd, 0x4a7efe099a0ae9d1, 0xa6ad5b909667945b,
0xe20850e47ab440f7, 0x68739e1b4fa069e5, 0x4c191300a9207cf4, 0x9b613a1a38160c98,
0x2cc631eb015081c9, 0x52af80aad7b676f4, 0x904b38943300ca8f, 0x50a515c0d302620f,
0x52ae95b8a0c1f36c, 0x6a62ab87786774e2, 0x17ea45367ad58985, 0x92959c57166aa21b,
0x2a9d91bd1a9716b4, 0x552c2f8528220174, 0xd665856c96b47d17, 0x14c6cba13b6dca3b,
0x865f1c93ec9000d0, 0x23dda8b5e161910e, 0xc191ac4342717953, 0x6783fdb95e098f1d,
0x1a4c26a5cad1e8ee, 0xde96e2a1e33e3046, 0xa57e65bedcf9047e, 0xa1cdef163fe7f80c,
0xeb0abcc13feeb7b2, 0xaa158c61b0e44470, 0x98dc901679caf85b, 0x954046758f8d2e96,
0x56db5e99c5d8c68, 0x7bb8d36962a4ac81, 0x2e301b4ecb03821, 0x121c1b2df70f0e1c,
0x3fbdad1e8faa0543, 0x6efb222398a2f88b, 0x65760de4d96338e0, 0x15b2c58a67fb43fa,
0x22f1532c89367d77, 0x1f726ffdad411d9e, 0x42572b54dcedf3ba, 0x3f8e0f6e9f0bbb7b,
0x4b0e705c86571a1c, 0xf8c9b04f8bd75117, 0x67ed2e9e4545557, 0x57e8853f681bbf8c,
0x6f99d1fd5fdbf582, 0xd2aa9bd48ad692e2, 0x2efc88bddecfe616, 0x8e9779a1e119abf4,
0x52dfee4722a20b75, 0x79465be3aea146d6, 0x588997dbcbd5f005, 0x79bda8bcc5d4c650,
0x2384e131ed3b5330, 0x229cb1d89738aa26, 0x1526d1a020a96507, 0xc7b6ac961a740cb9,
0xe78cec14478c4f71, 0xaba61cfd8f1e2a71, 0x24123c8a37ae66f3, 0xbad8b07709aa215d,
0x7896fa53fd2418e7, 0x72265842e8c4f955, 0x9f6331fd80527661, 0x7c649eeddb382c9d,
0xd3b0708dd6b5ae84, 0xeda51f244551e15, 0xb7822c860b93dd44, 0xdf9afcc3c9cac88f,
0x9244b9816573be70, 0xf3d103887cc4ce2d, 0xb3295c2e5bcb0218, 0x85243b7a2e0af441,
0xbffd3df508d06098, 0x4908b967f6765c12, 0x8886ac94c0dabb, 0x9c7865af133eb6c0,
0x5946fee66e64d7b2, 0x7737bc5af713087f, 0xbec815a80782dd5d, 0xe7672cfe0f7945fb,
0xe1f80b6df5beece1, 0x5b749d3a22450fd6, 0xaf34a567bf838668, 0xa72a177d20943ceb,
0x257c45c1601c4922, 0x3d7c68f6fe36ce59, 0x1b8ef47186e06c96, 0x8040426656154c17,
0xc15f74f980647bda, 0x36389393336a78be, 0x15d174ed5536afe2, 0x51e702e8adb61f63,
0xc9c95ca3f1c08f30, 0x6653094c8531c93a, 0xf7be5dfc2eb3b5b, 0xb5e21ec5c63850b0,
0x9ab5f082e01021a5, 0x75c4ca38d7678fb1, 0xb20bd13e05e5bd67, 0x3378133e631fbaee,
0x17cb3686511aeb6e, 0x4c0dea4c80ec7bc, 0x21fe874bf5509300, 0xece4f84e34d52e54,
0x3f2649803ca9918b, 0xdb493adeac5c60f5, 0x7c02a1d153afedd, 0x2d08ceda0fef7967,
0x6a32e018e432b0ea, 0x86479f3ea38ad57e, 0x84e3e04f1e5877be, 0x41b898cb02772049,
0xd6dded3714d71084, 0x9df5b2f3a0ab275d, 0xd5ab652dfa73ee0a, 0x4633e03fa37d6edb,
0x226314b8c4b937ff, 0x45d66a00ab031188, 0xb93ce1cfbcd1eaa0, 0xf88e0756f7e7c1c1,
0xf3611966fed51e03, 0x81235048c662d9f7, 0xcc8275f866147b4f, 0xd3b3ca0f5033a863,
0x970212eb8c2b3429, 0xec848dd58f3449d6, 0xa1d527af824d09f2, 0x60bd5e91448b9cf4,
0x1210ddfac603aa88, 0xcbf4270f3407e25a, 0x212955fec55466a0, 0x3afeaef4c9ccc793,
0xdd114286ec304817, 0x849e6ae3c2cf794f, 0x71c08228d6a05310, 0x177e77779d155b11,
0xdc59148f219a9c04, 0xb0702a7802d5276d, 0x56085d6761aee015, 0x3f79ce06bcfb4f3,
0x459a1f917f8f3e0, 0xe4ea5635e8bcd512, 0xa88e99b63f135a39, 0x95bd628d77d39446,
0xe6432158ef4c7d98, 0xb349cd3d1c74369e, 0x25b1a32db58efb0a, 0xc2add3a44cecc0b5,
0x5d676629f23010b5, 0x9890b3a62599408e, 0xef68ea8144d97805, 0x429e0fda34046a85,
0x7723d9043053bf52, 0xbb78842d9b67ae91, 0x9155ef932192e6a3, 0xdb523ea403d39f6b,
0xdb8fa1eee23ea58, 0x7c735492524a3448, 0xc580cb82e81505, 0xb0be6a006414841c,
0xdec2e763b5cedaa5, 0x8da58bb23638af5f, 0xb0e6b33f6736e7d0, 0x8146bbcd3dd4df61,
0x978080148a8989bb, 0x7f8119caa3308095, 0x4e88c318ea0604f3, 0x6ee5262f16b3cf83,
0xc44395c7a578ace9, 0x92016ee635de27e1, 0xb8dc5ceb36e67fd2, 0x95c851d65bd35f8c,
0xbe393620503c49fa, 0x42af183b92eac923, 0xfef0e660435135ce, 0x262d67d480451ed1,
0x590f92e1ee0502b3, 0x18825c97d49e3700, 0x2cd8c30a848c9acf, 0x1025c7747fda0115,
0x54109f23e82590aa, 0x93917bf1f8325981, 0xda674b183fa0e3cf, 0x2a0b2467eb8aefc5,
0xb0085eb83468793c, 0x607cabb2c9d3a81b, 0xe7a6b6013804d665, 0x67629a769c1efede,
0x2830ab6ef6d10166, 0xffd02b0655332bd4, 0x19bd056c3117568f, 0x385a834785662c6f,
0x938b5d56bd5f7248, 0x969afe82dd4829c8, 0xf455d4ace41c797d, 0x23d9cd67eff27512,
0x2b0c7037ecb322e2, 0x73df193328258bda, 0x5d7ee05cf2054f93, 0xdabfbd5b46b61cea,
0xcea02d82546b96de, 0x2245d5e74d5f60ae, 0x842ca45f8ef2a44, 0x7505cc4e1c3060d8,
0x869146ac8e68565e, 0x22ea711fb30e73e3, 0x53cd64736898a0c0, 0xfa88458b920684df,
0xc3ae23f451e0616f, 0xe2dd69393141ff32, 0x98863ab129bcd866, 0x8c9756a40dd5b834,
0x2eeeef78c36fede5, 0xe84d2eb23e22153b, 0xb0ccc2f7ac541d78, 0x151faba0f513acfa,
0x4300e3cea0260717, 0xaba308c6d857d2d0, 0x5eb25dd325256c6a, 0x3342627b68038da4,
0x70d7d75526da35, 0x80ff3f5ea2ac3cf1, 0xe7434f2f026394b0, 0xa7c5ff17f7d2cb07,
0xdfed0bb33a06ff78, 0x485cc64d38ce2596, 0x88db8580147aa8fc, 0xf52a5111d693b973,
0xeeaa031c02b370a8, 0xbb3b1678222d0e81, 0x27b569f2a6630939, 0x2b301fa3e50efeb8,
0x4dbc1f85bf3f8972, 0xb37e4f2cb75a825b, 0x3c8848e0f1777cc7, 0x8fae2e6938ba00aa,
0xfb4674b50884992c, 0x2b765005b85b7388, 0xaaf0007fb9662ce5, 0x684bd59009a4ad65,
0x221ffead3d73ab35, 0xccfe6d02d46856b5, 0x54d3323359e1b114, 0xcb412202ed42f097,
0x15d63df422771b9b, 0x71852bca1581d14f, 0xf30dcbb6cf891e63, 0x478fb1eed3cc5a10,
0x849a3b52bc5bb196, 0x4c1a98dbc546dd81, 0x846dc8c2258ec4f8, 0xbd4da447c7340bd0,
0x8f1ee1d6a85b9db0, 0x123ebfa8aaec07f2, 0xae34948e375d4477, 0xd466a4177842d8e4,
0xd5108efeb19cac6, 0x3266f7db8f133bdb, 0xe69af4e5d8d767e4, 0xea0efc0331df64a2,
0xb879052746ed72ed, 0x2c8233cc84de4144, 0xdcd5dda825186731, 0xb9e3b679d268f34c,
0x7ce12e2fa95bda8b, 0xa34afd12e611a4c1, 0x6043d06ee7619f90, 0xca3a3d4813c0addf,
0x6e97a61d1e4b3c4f, 0x8cdeae467a4bb292, 0xf08a6c69e70076b5, 0x97aa5c3180d3edbe,
0xc39813e1573904d5, 0x42577549d026e8c8, 0xaf5827ffe259b62a, 0x9e1d48596c4f0b24,
0xab9dd230ba8efb64, 0x81769493b85868d4, 0x715b45c5e3952245, 0x84735e138d228f35,
0xf4f987da7d19c74d, 0x1bdc77979baf29b, 0x785b3640158e0278, 0x77fc9d00681bcdd,
0xb5980cc490dcab93, 0x9062c158196b8244, 0xc16af5418cc97c4a, 0xdd4a4e9e8e00e524,
0x870b554b629277f1, 0xf90ff72bb54322c0, 0xd4c273bc2199823, 0xeebc75970d438466,
0xe4cad67413074a53, 0x6eccde71bd09dc0c, 0x14278b0ca6b910b4, 0x6e8895f17cdb933c,
0xa0b3987821416e11, 0x71b7d24b81fa769f, 0x1d3b1a805b885a58, 0x1bc737b1719736a,
0xea4d1dbb8823037, 0xe50ce48c8469adbd, 0x34c2d5e6c41a888e, 0x446a756eb06dc3a4,
0xbac5ed8a8f90262, 0x7f1b76e0c707ab9d, 0xb31323309b94a12e, 0xf58269b9852f986e,
0x3b74c2b338c244fc, 0x879b46f23a4deae4, 0x3f2591e34cdce1c9, 0x73c6f81eb560ed5c,
0xd2aa923c7a5c18a9, 0x7170c1f7621cace9, 0xa18b327b11b951a, 0x2b36315510f56370,
0x5cfed2f703dfc0bb, 0x1e43b99175054c07, 0x392dfa3210e8013b, 0x65e0c5c0454ee693,
0x2a795f6f493349db, 0x17995ebdfe848db0, 0xf23174b823a52cf7, 0xaac6ef104bfd396e,
0xfa0f5b29156eeccd, 0x9ccb3590a6e88c1a, 0x2edae0b1b80aafab, 0x1e1e92baae39aa30,
0x24475af89cec7f33, 0xacdbeceaadb9936c, 0x7725948da8586e93, 0xcc05595e17947215,
0x1f3cbde17a508faa, 0x2795f58ff5c8919b, 0x309658d1748f30d3, 0xe90c11962e5ed4bb,
0xc22b876286d32e27, 0x495c8b667c6ea3dd, 0x84263045f7d6eab5, 0xf8d3a9ab1494a315,
0xabc42cf769a21d9d, 0x3fef7fb40bdf3a81, 0xfd35336e188925a3, 0xd472bdaf277ab26d,
0x4949e8ff51da2307, 0xbec86dce960ff3b, 0x1aa1ce4f70256b10, 0xd52986ff8cd700ea,
0x364d8efc0f5afad6, 0xca3d1958f57a9050, 0x17a0a2ec122dc677, 0x7992695be3363fd6,
0x5c66a265e0607da8, 0x7250114e050bb917, 0x30cd3a70bc7b723d, 0x7b77433392b3fbf8,
0x295bb7bf46318b38, 0xdb15025af2a71c65, 0x26a82b21ef67f50c, 0x14a5573d4fc798c1,
0xd8cad4642ec68e5e, 0x9276d7f60142822c, 0xf7b8efc27522e52f, 0xd0a3f36f6d340bed,
0x341260fb11765c02, 0xcd1d394d796702cc, 0x7d483ef031eb3346, 0x74eaab49374576c1,
0xa073bea32a71a273, 0xd65ce2552993b5cf, 0x8670afe77caaeb16, 0xb607f1455d072a47,
0x30ed96be92809559, 0xa58380a503c23c9c, 0x916aa68fb957a30d, 0x30c5a675bf19738c,
0xd4cbad34e4e4b886, 0xd6cb83061f2b0ebf, 0xceddb4040f535fa9, 0x778c586927b1e247,
0xe4bb5c4b6e0f3c3d, 0x3e857d671db80667, 0x2b909dd8725f1fa2, 0x558ffd0772db7841,
0x710f9638d3edb2c4, 0x21a4ccee53d46556, 0xf76e8e4737b9628b, 0x71cd157f23581c71,
0x68d8fded9b66efd6, 0x7d9f5e182c0b9457, 0x2140757748a217ff, 0xdd1e5365520b77a4,
0x644d8e4b2f30dcfa, 0xa1de42f4e9791564, 0x70e148ababfe9f86, 0xb97f463e0ac7daec,
0x82844f729d9fa554, 0x5c8475e84470c924, 0x3a83de748eac32fd, 0x68725fbc9c202c5b,
};
pub const mt32_seed = 0x7dc0d160;
pub const mt32_data = []u32 {
0x59327332, 0x200858fa, 0xab53c028, 0x5c442427,
0xd8be0287, 0x3b69d304, 0x15fdf62f, 0x59b8ecd,
0x6d7ab30c, 0x3a3dd6f1, 0xc1b9773e, 0xa12fb017,
0xa805b5c1, 0x4a313ba5, 0xd82c790c, 0x8de311f2,
0xe7cb23dd, 0x784b2efb, 0x9743487c, 0x73e2f2fb,
0x1a7ac286, 0xaef90d, 0x6c0a4514, 0xae1d83aa,
0x412fcca1, 0x3acd2d28, 0xde78292f, 0x13237756,
0xdd6cdeba, 0x44ae4df9, 0x3e9902eb, 0x39e1cf20,
0x62f561b9, 0x6cbdf531, 0x4a000673, 0xb1c82daa,
0x896156ca, 0x75e410f2, 0x9c69e72c, 0x396b42bb,
0x25c97ec0, 0xe12173f1, 0x8dcd42e5, 0x82aac3e3,
0xcdc1c84d, 0x13509c0c, 0x46a696d2, 0xb89ad987,
0x92da5e7f, 0xaa87d8a9, 0xe433ff57, 0x80a7ee49,
0xd387cfcc, 0x7dc47d92, 0x21516140, 0x989ca465,
0xf2a8e002, 0x73b99ddb, 0x2204108f, 0x27e84890,
0x371c81c0, 0x9f581854, 0xc0841c35, 0x770f6804,
0x87c55f4e, 0xd29516bb, 0x2b6d6bde, 0x5541f6ee,
0x1ec9b182, 0x7d599729, 0x4f4b9a14, 0x6f8c8562,
0x2d5151aa, 0xb54f5bc, 0xa252452b, 0x2a4266da,
0x25a6b75d, 0x2d11106e, 0xc5d77943, 0xb10b6e0b,
0xeb5cae4a, 0x43a0dd53, 0xa40bea1f, 0x63e632c2,
0xf420b6ce, 0x8b080233, 0x7f70ae87, 0xf460f0d6,
0x147c7e74, 0x710692ea, 0xa0a7d8fb, 0xe7f05808,
0xa6173aaf, 0xae608de0, 0x8702036, 0xbf1bfc7b,
0xf14cd548, 0xbbc7553d, 0x5358dd1d, 0xcc0c1fe5,
0xfab6f78d, 0x9365c118, 0xf64216a3, 0xb4bdcf1b,
0xc90b8a7a, 0x8b7b78a, 0x4c7b6854, 0xba7b5628,
0xdd728c15, 0xcb1f8905, 0xa63e2342, 0xa78822,
0xbda61b18, 0x160a59fa, 0xeccf473b, 0xc5a445b5,
0x7aa86430, 0x362e0d7c, 0x8006a0cb, 0x8b11586f,
0x6677bba9, 0x6208cf27, 0xeec9b5, 0x3dfedfc9,
0x886cc0e8, 0x32ed77ca, 0x43525faf, 0x9786354a,
0x1a2eb378, 0xf0e6b168, 0x49064b09, 0x8ab39681,
0x7b6655fc, 0x35adb168, 0xc417d430, 0x2784288a,
0xea17836, 0xc85006e7, 0x673dfdc3, 0x42765688,
0xc2b9251, 0x840a45b, 0xcac98e2f, 0x1a6f9777,
0x34959b23, 0xf0dcec81, 0xcaa2c6c8, 0x1cf93061,
0x787e598d, 0xd5d9e31e, 0x14e08791, 0xd9d9d782,
0xef162f23, 0x238f4113, 0x23f42107, 0x6ed5cc3f,
0xa55e5a7c, 0x4650595, 0x5217da8b, 0x6eeaacdc,
0xb453d7b1, 0xfa1ff004, 0xb9d17f74, 0x2bd6a53e,
0xe4c2d9dd, 0xed66375e, 0xf8215568, 0x9bcadbb3,
0x9c4f9d51, 0xff68312, 0x82308422, 0x83e990b0,
0x38b6135b, 0x70e2aa13, 0xa30065d2, 0x6396a00,
0x77d423bc, 0xa93abf0a, 0xc7bb8c31, 0x5d7bd3d3,
0x6a374f2e, 0xe4b5bc88, 0x39f6e512, 0xd6aea995,
0x878c1bfa, 0x4636014d, 0x9caa2c09, 0x7ac4758b,
0xbd3b957e, 0x518c2fd6, 0xea009a2e, 0x542bf419,
0x59090006, 0xb1d94703, 0xe0d9eefc, 0xe7fccb17,
0x40111951, 0xf2560485, 0xb50ce9e1, 0xd7a1ee51,
0x28dffa99, 0x41d12275, 0xdd89a365, 0xf22eda29,
0x104f94ee, 0xe669983b, 0x6346a250, 0x86326fc5,
0xb7f347df, 0x3849a39f, 0xf433929a, 0xeea5155,
0x4cf9b778, 0x6bd7926a, 0xcda9496, 0xf430d7a2,
0x41637670, 0xaf3bbad6, 0xeb66e44e, 0x2499605d,
0x9988920d, 0xf9d652ef, 0x67aa80c0, 0x505073c9,
0x85cd418f, 0x9f83fb65, 0xf50b3eac, 0x812ba6bd,
0x74d61788, 0x86d64f3b, 0xb1f8fc1c, 0x3e2af667,
0x4d118a2, 0xd028ffa9, 0x32e88a44, 0x4ed9ba35,
0xea3c7030, 0xffe44aaf, 0x5e39c467, 0xeabcfebb,
0x53e656ec, 0xced701d0, 0x31020b02, 0x4b4c1dc5,
0x8744885c, 0xa8e93656, 0x3ef457e5, 0x272bde23,
0xe541477c, 0x3ad3ac04, 0x63eaa692, 0x81055cf9,
0x3ff5f782, 0xa8efe6bc, 0x15f37656, 0xaaaebf1d,
0xf73d461a, 0xe8b2c0b5, 0x5035ff48, 0x3a95e34b,
0x6f21d94f, 0x6f6d1f96, 0xdaf79f37, 0x826f69f3,
0x209a00b8, 0x2ad1b2f2, 0x2c64fb45, 0xcf8bf26e,
0x9befcff2, 0xc08f6951, 0x96d98205, 0xa267dcb5,
0xbc43ec5, 0xee6a7e1c, 0x49224eae, 0x14e820e,
0xbb340212, 0x68ed572c, 0x45e9e623, 0x1297f3af,
0x49a98ed2, 0xddd34ae8, 0x211838ab, 0x47e7652d,
0xb40430c6, 0xc8d3bd7, 0x4352356e, 0xf0e5cac9,
0x21880df4, 0xc16b343a, 0xd9ed7350, 0x17fe1f65,
0x6637192e, 0xd81c93aa, 0x7d6e17d2, 0xd407b13f,
0x425da072, 0x380d423d, 0x6ce57b22, 0x7b17ed17,
0x95fbf626, 0x768303d6, 0x76ab6b3e, 0x591491e3,
0x259f79ab, 0xd4babeaf, 0x9c7de2f8, 0x4fe6cb58,
0xf43680a9, 0x651a1266, 0x730ea3c8, 0x9188d4c5,
0x12d01e34, 0x47afb2e9, 0xb4b76d35, 0x5e5164bc,
0xc864fc46, 0x5d018aa7, 0x17fac975, 0x5a775fbd,
0x40e6fa14, 0x7a00b683, 0x99e4e102, 0x2f933b90,
0x474e14ba, 0xde1b0754, 0xe84aba2b, 0xb386cd43,
0x17ca77c9, 0x7b4f38ef, 0x803ea1a8, 0x93553947,
0x806c8224, 0x2608451e, 0x63157fe3, 0xaf53930e,
0x5dfe8c16, 0x65592bda, 0x7086eb3f, 0x838e6a50,
0xa27836d9, 0xf2f16d92, 0xdc0a981, 0xfbf8f915,
0x2caea00d, 0x86bb3e18, 0x6d94c209, 0x3bbbeb6c,
0x114d68f4, 0xc271e48f, 0xa3350dc1, 0xb8d55eb4,
0x68be5ee1, 0xbf22ef29, 0xd6e0aa54, 0x48f7219,
0x21aca253, 0xfbf07910, 0xfcdd61a8, 0x118a09b,
0x3f2bbde6, 0x46eea63f, 0xdb51ed16, 0xf8a9fc36,
0x31614dc0, 0xdd84f54d, 0xd2b66065, 0xdae0af99,
0x6d071a51, 0xbdbac46c, 0x15deee25, 0xf792e64c,
0x910194e8, 0xfc989a8f, 0x919727fd, 0x6f93a56c,
0x2df36e9a, 0xd395b948, 0xb026b54a, 0xf0938a5,
0xe9c64399, 0xb5cda15b, 0xb7b8dd41, 0x7146f944,
0x8d41ce2f, 0x47c74099, 0x2e5a8e5f, 0x28f7a19c,
0xef7a8ef9, 0x6a763eb9, 0xf13a3ec4, 0x9f352360,
0x42317561, 0x6c6a0ca5, 0x5e40b472, 0x3ddaadd4,
0x2f5d14eb, 0x5dd49aeb, 0xc89edb24, 0xa2da269b,
0x5cf0a38b, 0x8e2f435c, 0x40970e54, 0xa2cb730e,
0xf9d8c301, 0x8ef29fb1, 0xf08b1840, 0x7d45e4a2,
0xa0fe4ce1, 0x939a21c4, 0xfdeebfea, 0x4c661550,
0xdd304d1c, 0x3cdb078d, 0x94ae8db2, 0x4f6b4287,
0xffe64fa8, 0x50384bb0, 0x16cf5ed3, 0xa91a8fec,
0xdb8ebb1, 0x59c2898b, 0xd587edc9, 0xdec2e75a,
0x496ccdd2, 0x897db91d, 0xf8ea5149, 0x6bed4bad,
0xce76e472, 0x43c7f976, 0xb055dc01, 0x7ffd5671,
0xe193b86a, 0xe288ce11, 0x514d531e, 0xa42fa47e,
0xe7c0e194, 0xffc059ba, 0x26548e36, 0xe1f10d92,
0x3ef5d95e, 0xa6e69282, 0xffacb09e, 0xf4a16ff5,
0x9b7f03bd, 0x588c54b4, 0xc2b6eaa1, 0x2d83acdc,
0x7fdbb606, 0x2b160650, 0x9923e57e, 0x32bd23bd,
0x50cd6d4c, 0x205d901f, 0x810a9935, 0x27ce6e7a,
0xe0c6c66, 0xac06c99c, 0x4326aa9b, 0xe1af1e90,
0xe358c8b1, 0x2f601c2a, 0xefca77e7, 0x1a7ed2f8,
0x8ad2e191, 0xe5520809, 0x27084438, 0xe4d8e782,
0x5e8a4038, 0x87bba694, 0x65f07eba, 0x616f8f07,
0xc5565d9, 0x555955e4, 0xf41c2caa, 0xb085fbf5,
0xa5f9d9ff, 0x418fa0df, 0xec5a576d, 0x7fc332ab,
0x7683ed33, 0x968ef54b, 0x834d598d, 0x6833f356,
0x59dc7e7f, 0x779661dc, 0x58942dd4, 0x80387aab,
0xf6dac9e5, 0xe043be04, 0x2ae4f872, 0x881f8d01,
0x82cfd69d, 0x931f4648, 0x2a76ab31, 0xa3f1dd7c,
0xd7f4826a, 0xe74918da, 0xe4c98636, 0x441164f,
0x15a0e9aa, 0xce7480ad, 0xba39076b, 0x233aa8d,
0x6c32f0e6, 0x169c62bf, 0xa2cd17f6, 0xb5590084,
0xb2036f00, 0x18315935, 0x11e9c9c7, 0x25c77861,
0x41596cda, 0x635e5e02, 0x8f396cc, 0x4cd00d8d,
0xd665597e, 0x90f891ef, 0x547b93ee, 0x376959c1,
0xdc5fa80, 0x9b4797a6, 0x53673041, 0x25ab117a,
0x7b8b8292, 0xf4e99584, 0x5139da98, 0x30e2afeb,
0xff2664b9, 0x591eb6f0, 0x9e87e602, 0xf5e26193,
0x61831f07, 0xabc139f9, 0x984eda0a, 0xaea1b8da,
0x65c7410d, 0x2b84800d, 0x1d3cfec3, 0xd05cb8a1,
0x4529641b, 0x7d6712e6, 0xc38cbde7, 0xacad7787,
0xd8482f3a, 0xa5662eaa, 0x24836ee9, 0xf3b5cc97,
0x50a581ae, 0xff6004b6, 0x650fc547, 0x161898b1,
0xa7593447, 0x325827dd, 0xf1844a1a, 0x7eb56de2,
0x89882452, 0xfebb49a, 0xfe86ae9c, 0x7dba98b1,
0x1d65adb5, 0xb71acffa, 0x861215af, 0xc0f1496,
0x70967c72, 0x3803d127, 0x6c8fdd84, 0xe40991f1,
0x1343e3a, 0xf57b4e73, 0x25f34f76, 0xaebcdee8,
0x8752d71f, 0xfc710e54, 0x34f3af44, 0xfa7dea4e,
0x477d4d83, 0x42640ff1, 0x2c5c31ce, 0xa82de5e4,
0xcc813271, 0x4d40bf86, 0x4e416095, 0xb5ac332c,
0xd2d44703, 0xe4c5ef57, 0xde193a29, 0xbf3e7974,
0xbb313d75, 0x8dc973d5, 0x301b2657, 0x44dc5064,
0x8c58c633, 0x83424c74, 0xb7cbf7ac, 0xa04238c2,
0x6ceabd59, 0xd25e6fd0, 0x3409167, 0x42d6ef80,
0x1f47c437, 0xdb21e45f, 0x2fd48e29, 0x9498cfb7,
0xc9e4cb12, 0xc6dcf0df, 0xa1633c39, 0x1b349670,
0xf76d4a64, 0x15ecd8dd, 0x777bb76d, 0xc46008e7,
0x23d94e44, 0x78aa07de, 0x2eeac782, 0x3757b114,
0x2b22de2a, 0x37726519, 0xf107546d, 0xe9847f74,
0x449a4ea6, 0x2e31fa5a, 0xd719ea88, 0xb2115c87,
0xfa6b7231, 0xf72fc9ff, 0xcd22bc37, 0x9080778a,
0x93430a21, 0x97c24360, 0x6e5b1a76, 0x5e8baa7c,
0x300c94f8, 0x2843d9da, 0xdceac0ae, 0xeeed885,
0x1898ffd0, 0xa3bbee3c, 0xc16f8fd7, 0x82992b68,
0x39c153b6, 0x1b3ba4c8, 0x41e7c3ac, 0xcdf8f06a,
0xd40b8ae6, 0x4982b6c2, 0xb32f7437, 0x22ed3691,
0x16579a2a, 0xff9de457, 0xc421e8e4, 0x17c8f6cb,
0xa5c4a8da, 0x49bd8afa, 0xe2be081c, 0x95170f28,
0xd679fbdf, 0xcf39d563, 0x4e2d2ee9, 0x39471096,
0x3918bef0, 0x279b7679, 0xa5281a0f, 0x49481d6f,
0x11f95ee1, 0xd9df649f, 0x2993eb27, 0x48ad815f,
0x99cf306d, 0xca9457e4, 0xc27c51d2, 0xc2a838ec,
0x537faf4c, 0x55dccddf, 0x8df5aeb8, 0xabb317ca,
0xfc1bcf6b, 0x669c2b1b, 0x719b62d5, 0x6b9325cf,
0xc123d0d3, 0x2ddc6ace, 0x27fdc30a, 0xd3f93cd8,
0x704f5486, 0xd3f448ec, 0xbbd1e32c, 0x3bcd4c0b,
0x86f8166, 0x957db888, 0x899b6a5e, 0x270dc8b7,
0xff16222e, 0x51e139a8, 0x3d8b4b9f, 0x68d20818,
0xa639ad00, 0x4c2e0fd2, 0xb4949cdc, 0x2ab6eb32,
0xdd0c67ad, 0xd2208cbe, 0xcd17a0bc, 0xacc541f7,
0xfa9e714f, 0x316d31a7, 0xed79fa91, 0xb5c0e980,
0x412ecc9b, 0x9815753, 0xd0df1f43, 0x8e37dbb9,
0xe640df75, 0x379c2fb6, 0xc7ed26a4, 0xc5190400,
0x1cc81b53, 0xcb0b0cd5, 0x360f061b, 0x6d90284e,
0x83c05bd0, 0xbd80bae9, 0xd584ef12, 0x228a46ec,
0x657c4fbe, 0x5ca1043c, 0x852aca0f, 0x31ce950,
0x33ee2cd8, 0x3cdecbf7, 0x787ef08c, 0xea610ee,
0x47c1db89, 0x90eeda11, 0x74f8d429, 0x51d3a4c5,
0x3135b401, 0x2e14783c, 0xb9af855c, 0xb66348d9,
0xa3a47387, 0x6eb72af1, 0x7bb56088, 0xc664542d,
0x7ed96b8, 0x995870a8, 0x385b1fd6, 0xa430680d,
0x98a883ec, 0x2497a389, 0x7a880627, 0x8350ba9d,
0x4cb35c33, 0x30bf6b14, 0x8695a469, 0x9a81e44b,
0x8bb27c9a, 0xbfb6a4dd, 0xbae7cf6e, 0x4ebccc87,
0xb712ed3d, 0x31e90365, 0xcc1fa63f, 0x32b93df6,
0xbad4c7bc, 0xb2570e17, 0x73fa21be, 0x5c02a8d2,
0x94446d75, 0x7265f3ad, 0xd58487a2, 0x919b7a07,
0xbe2d0e05, 0xd36ccf4f, 0x6d5c66d7, 0x8448522f,
0x8409c294, 0x6f1c7af7, 0x173a13bc, 0x1b3e4a0b,
0x705b941b, 0x77eb584f, 0x85b68458, 0x8e3ad1ac,
0x4aa99702, 0x7ae1b24c, 0x899ba29c, 0x860a3711,
0xabe53a4f, 0x37870133, 0x1ed7cb89, 0xea539762,
0x4ba64130, 0x48517a2d, 0xce0a869d, 0x937ba48,
0xd0f234c4, 0xf9b2cf26, 0xc3c311f0, 0x153d09a9,
0x404d3af9, 0x9f7edbc1, 0xbdcecded, 0x97969ba8,
0x3379437, 0xadd3c893, 0x7c024639, 0x459390b,
0xcb7c7320, 0xa5c63725, 0x65907e3e, 0xbf70583b,
0xcebb601b, 0x4edfb286, 0x9350336f, 0xdfb4be76,
0x88b56f39, 0x9937d7f9, 0xa12a286d, 0x34f141c,
0xa2e75c15, 0xd69a7060, 0x931340c3, 0x22447f25,
0xe8aed82c, 0xd76a9ae7, 0xc967288, 0xe572facd,
0xbe82b0ee, 0x10f5dce1, 0x4f03ee35, 0x2340b923,
0xf4fb6bd0, 0x64adbf01, 0x3d277a0a, 0x39e76f2c,
0xe3c024d9, 0x57869c82, 0x743b7826, 0xf66f1574,
0xc93965c, 0xf86a552, 0x13557069, 0x9e0845de,
0xaee084f9, 0x5eafaedb, 0xc06f5f3, 0x9051f6ea,
0x98fceda2, 0x2af2f8cc, 0x6c41b5a8, 0xc1af74de,
0x57302276, 0x253923c9, 0xd79996b3, 0x8ecb3141,
0x641387cc, 0xf87a4101, 0x96a50c76, 0xbcf24a11,
0x87b6bb6, 0x58ee501b, 0xaa859695, 0xb2eed107,
0x554173f0, 0xb12ec0e6, 0x57785c1b, 0x53685c9a,
0x114c3163, 0x9383cf19, 0x31fd7cdf, 0xaeb8225c,
0x58774fe7, 0x54700ad4, 0xad418726, 0xf055b71c,
0x7d31237f, 0xdd97cad5, 0xcdd5325e, 0x42f2acf4,
0x4bed262b, 0x7a8faaf2, 0x2b1eafdd, 0xa1b806ac,
0x26965c6e, 0xb41b7168, 0x15e2e70b, 0x7daa8e13,
0x6198aa5a, 0xc9b8b94c, 0x339b5754, 0xcd3b285c,
0xffd1486c, 0xf224979a, 0xafb89ec5, 0x222058c,
0xcb4814d0, 0x2b0e7c7d, 0x9eb25b84, 0x271564b0,
0xbb72e076, 0x48251020, 0x18008023, 0x48d10005,
0x4a452eaa, 0xb2365308, 0x19cdb632, 0x1fd56d04,
0xffa5ff2a, 0xaba89e42, 0x388fc17d, 0xea61c00f,
0x5156273d, 0x776f1a56, 0x8d539d28, 0x289c01cb,
0x857aa71f, 0x348e411f, 0xc9eb3c91, 0x67a61079,
0xe4276a0f, 0x45bdc15f, 0x8e0a698e, 0xbdefc310,
0x82377ba6, 0x3bfbf404, 0xcbf22c79, 0x35f501bc,
0xb16044a7, 0xeffdb8, 0xdbac383d, 0x7816663f,
0x18f5a318, 0x3d04f1cb, 0x735da9b4, 0x75e339a1,
0x5b6c55f, 0x1c18887e, 0xf698e14f, 0x338a6da1,
0xdac85699, 0x1aca7768, 0x8eb0fa7a, 0xc98fa71d,
0x3b794408, 0x92913041, 0xf8dc8827, 0x1cf706e9,
0x3aeee292, 0x321dbaa8, 0xee1eb8d1, 0x23554be9,
0x811c7804, 0xf0f4de6b, 0xd457e382, 0xeda56795,
0xeffdfc71, 0xf2a52829, 0xa7460732, 0x2c1321c0,
0x2f734db0, 0xf04ecb0b, 0xec7d777e, 0x43c54317,
0xccaa74cd, 0xfe49dd9d, 0x4c509829, 0x278f9bd7,
0x581dc500, 0x4ad38c2e, 0xcbee1047, 0x13302c1c,
0xbc0cb734, 0xc1c8f234, 0x1df52b35, 0xd8815548,
0x319edefb, 0x437cebe5, 0x3dcb6026, 0xe9d4f93f,
0xb2661154, 0xeb8c15a0, 0xb008505, 0x5f869981,
0xf5588ca4, 0xd6929c5b, 0xa3dd13d1, 0xdc863314,
0x891a454f, 0x91737e49, 0x5064d4d8, 0x2fd32675,
0xadefe9b1, 0xdde32b11, 0x741bbd6, 0x3b4363a9,
0xb121d9e8, 0x916ca61d, 0x38c0af15, 0x5e3dfd72,
};

154
std/sort.zig
View File

@ -67,7 +67,7 @@ const Iterator = struct {
self.numerator -= self.denominator;
self.decimal += 1;
}
return Range {.start = start, .end = self.decimal};
}
@ -82,7 +82,7 @@ const Iterator = struct {
self.numerator_step -= self.denominator;
self.decimal_step += 1;
}
return (self.decimal_step < self.size);
}
@ -219,7 +219,7 @@ pub fn sort(comptime T: type, items: []T, lessThan: fn(lhs: &const T, rhs: &cons
var B1 = iterator.nextRange();
var A2 = iterator.nextRange();
var B2 = iterator.nextRange();
if (lessThan(items[B1.end - 1], items[A1.start])) {
// the two ranges are in reverse order, so copy them in reverse order into the cache
mem.copy(T, cache[B1.length()..], items[A1.start..A1.end]);
@ -230,13 +230,13 @@ pub fn sort(comptime T: type, items: []T, lessThan: fn(lhs: &const T, rhs: &cons
} else {
// if A1, B1, A2, and B2 are all in order, skip doing anything else
if (!lessThan(items[B2.start], items[A2.end - 1]) and !lessThan(items[A2.start], items[B1.end - 1])) continue;
// copy A1 and B1 into the cache in the same order
mem.copy(T, cache[0..], items[A1.start..A1.end]);
mem.copy(T, cache[A1.length()..], items[B1.start..B1.end]);
}
A1 = Range.init(A1.start, B1.end);
// merge A2 and B2 into the cache
if (lessThan(items[B2.end - 1], items[A2.start])) {
// the two ranges are in reverse order, so copy them in reverse order into the cache
@ -251,11 +251,11 @@ pub fn sort(comptime T: type, items: []T, lessThan: fn(lhs: &const T, rhs: &cons
mem.copy(T, cache[A1.length() + A2.length()..], items[B2.start..B2.end]);
}
A2 = Range.init(A2.start, B2.end);
// merge A1 and A2 from the cache into the items
const A3 = Range.init(0, A1.length());
const B3 = Range.init(A1.length(), A1.length() + A2.length());
if (lessThan(cache[B3.end - 1], cache[A3.start])) {
// the two ranges are in reverse order, so copy them in reverse order into the items
mem.copy(T, items[A1.start + A2.length()..], cache[A3.start..A3.end]);
@ -269,17 +269,17 @@ pub fn sort(comptime T: type, items: []T, lessThan: fn(lhs: &const T, rhs: &cons
mem.copy(T, items[A1.start + A1.length()..], cache[B3.start..B3.end]);
}
}
// we merged two levels at the same time, so we're done with this level already
// (iterator.nextLevel() is called again at the bottom of this outer merge loop)
_ = iterator.nextLevel();
} else {
iterator.begin();
while (!iterator.finished()) {
var A = iterator.nextRange();
var B = iterator.nextRange();
if (lessThan(items[B.end - 1], items[A.start])) {
// the two ranges are in reverse order, so a simple rotation should fix it
mem.rotate(T, items[A.start..B.end], A.length());
@ -301,10 +301,10 @@ pub fn sort(comptime T: type, items: []T, lessThan: fn(lhs: &const T, rhs: &cons
// 6. merge each A block with any B values that follow, using the cache or the second internal buffer
// 7. sort the second internal buffer if it exists
// 8. redistribute the two internal buffers back into the items
var block_size: usize = math.sqrt(iterator.length());
var buffer_size = iterator.length()/block_size + 1;
// as an optimization, we really only need to pull out the internal buffers once for each level of merges
// after that we can reuse the same buffers over and over, then redistribute it when we're finished with this level
var A: Range = undefined;
@ -322,11 +322,11 @@ pub fn sort(comptime T: type, items: []T, lessThan: fn(lhs: &const T, rhs: &cons
var buffer1 = Range.init(0, 0);
var buffer2 = Range.init(0, 0);
// find two internal buffers of size 'buffer_size' each
find = buffer_size + buffer_size;
var find_separately = false;
if (block_size <= cache.len) {
// if every A block fits into the cache then we won't need the second internal buffer,
// so we really only need to find 'buffer_size' unique values
@ -336,21 +336,21 @@ pub fn sort(comptime T: type, items: []T, lessThan: fn(lhs: &const T, rhs: &cons
find = buffer_size;
find_separately = true;
}
// we need to find either a single contiguous space containing 2√A unique values (which will be split up into two buffers of size √A each),
// or we need to find one buffer of < 2√A unique values, and a second buffer of √A unique values,
// OR if we couldn't find that many unique values, we need the largest possible buffer we can get
// in the case where it couldn't find a single buffer of at least √A unique values,
// all of the Merge steps must be replaced by a different merge algorithm (MergeInPlace)
iterator.begin();
while (!iterator.finished()) {
A = iterator.nextRange();
B = iterator.nextRange();
// just store information about where the values will be pulled from and to,
// as well as how many values there are, to create the two internal buffers
// check A for the number of unique values we need to fill an internal buffer
// these values will be pulled out to the start of A
last = A.start;
@ -360,7 +360,7 @@ pub fn sort(comptime T: type, items: []T, lessThan: fn(lhs: &const T, rhs: &cons
if (index == A.end) break;
}
index = last;
if (count >= buffer_size) {
// keep track of the range within the items where we'll need to "pull out" these values to create the internal buffer
pull[pull_index] = Pull {
@ -370,7 +370,7 @@ pub fn sort(comptime T: type, items: []T, lessThan: fn(lhs: &const T, rhs: &cons
.to = A.start,
};
pull_index = 1;
if (count == buffer_size + buffer_size) {
// we were able to find a single contiguous section containing 2√A unique values,
// so this section can be used to contain both of the internal buffers we'll need
@ -405,7 +405,7 @@ pub fn sort(comptime T: type, items: []T, lessThan: fn(lhs: &const T, rhs: &cons
.to = A.start,
};
}
// check B for the number of unique values we need to fill an internal buffer
// these values will be pulled out to the end of B
last = B.end - 1;
@ -415,7 +415,7 @@ pub fn sort(comptime T: type, items: []T, lessThan: fn(lhs: &const T, rhs: &cons
if (index == B.start) break;
}
index = last;
if (count >= buffer_size) {
// keep track of the range within the items where we'll need to "pull out" these values to create the internal buffe
pull[pull_index] = Pull {
@ -425,7 +425,7 @@ pub fn sort(comptime T: type, items: []T, lessThan: fn(lhs: &const T, rhs: &cons
.to = B.end,
};
pull_index = 1;
if (count == buffer_size + buffer_size) {
// we were able to find a single contiguous section containing 2√A unique values,
// so this section can be used to contain both of the internal buffers we'll need
@ -449,7 +449,7 @@ pub fn sort(comptime T: type, items: []T, lessThan: fn(lhs: &const T, rhs: &cons
// buffer2 will be pulled out from a 'B' subarray, so if the first buffer was pulled out from the corresponding 'A' subarray,
// we need to adjust the end point for that A subarray so it knows to stop redistributing its values before reaching buffer2
if (pull[0].range.start == A.start) pull[0].range.end -= pull[1].count;
// we found a second buffer in an 'B' subarray containing √A unique values, so we're done!
buffer2 = Range.init(B.end - count, B.end);
break;
@ -465,12 +465,12 @@ pub fn sort(comptime T: type, items: []T, lessThan: fn(lhs: &const T, rhs: &cons
};
}
}
// pull out the two ranges so we can use them as internal buffers
pull_index = 0;
while (pull_index < 2) : (pull_index += 1) {
const length = pull[pull_index].count;
if (pull[pull_index].to < pull[pull_index].from) {
// we're pulling the values out to the left, which means the start of an A subarray
index = pull[pull_index].from;
@ -493,27 +493,27 @@ pub fn sort(comptime T: type, items: []T, lessThan: fn(lhs: &const T, rhs: &cons
}
}
}
// adjust block_size and buffer_size based on the values we were able to pull out
buffer_size = buffer1.length();
block_size = iterator.length()/buffer_size + 1;
// the first buffer NEEDS to be large enough to tag each of the evenly sized A blocks,
// so this was originally here to test the math for adjusting block_size above
// assert((iterator.length() + 1)/block_size <= buffer_size);
// now that the two internal buffers have been created, it's time to merge each A+B combination at this level of the merge sort!
iterator.begin();
while (!iterator.finished()) {
A = iterator.nextRange();
B = iterator.nextRange();
// remove any parts of A or B that are being used by the internal buffers
start = A.start;
if (start == pull[0].range.start) {
if (pull[0].from > pull[0].to) {
A.start += pull[0].count;
// if the internal buffer takes up the entire A or B subarray, then there's nothing to merge
// this only happens for very small subarrays, like √4 = 2, 2 * (2 internal buffers) = 4,
// which also only happens when cache.len is small or 0 since it'd otherwise use MergeExternal
@ -532,25 +532,25 @@ pub fn sort(comptime T: type, items: []T, lessThan: fn(lhs: &const T, rhs: &cons
if (B.length() == 0) continue;
}
}
if (lessThan(items[B.end - 1], items[A.start])) {
// the two ranges are in reverse order, so a simple rotation should fix it
mem.rotate(T, items[A.start..B.end], A.length());
} else if (lessThan(items[A.end], items[A.end - 1])) {
// these two ranges weren't already in order, so we'll need to merge them!
var findA: usize = undefined;
// break the remainder of A into blocks. firstA is the uneven-sized first A block
var blockA = Range.init(A.start, A.end);
var firstA = Range.init(A.start, A.start + blockA.length() % block_size);
// swap the first value of each A block with the value in buffer1
var indexA = buffer1.start;
index = firstA.end;
while (index < blockA.end) : ({indexA += 1; index += block_size;}) {
mem.swap(T, &items[indexA], &items[index]);
}
// start rolling the A blocks through the B blocks!
// whenever we leave an A block behind, we'll need to merge the previous A block with any B blocks that follow it, so track that information as well
var lastA = firstA;
@ -558,7 +558,7 @@ pub fn sort(comptime T: type, items: []T, lessThan: fn(lhs: &const T, rhs: &cons
var blockB = Range.init(B.start, B.start + math.min(block_size, B.length()));
blockA.start += firstA.length();
indexA = buffer1.start;
// if the first unevenly sized A block fits into the cache, copy it there for when we go to Merge it
// otherwise, if the second buffer is available, block swap the contents into that
if (lastA.length() <= cache.len) {
@ -566,7 +566,7 @@ pub fn sort(comptime T: type, items: []T, lessThan: fn(lhs: &const T, rhs: &cons
} else if (buffer2.length() > 0) {
blockSwap(T, items, lastA.start, buffer2.start, lastA.length());
}
if (blockA.length() > 0) {
while (true) {
// if there's a previous B block and the first value of the minimum A block is <= the last value of the previous B block,
@ -575,7 +575,7 @@ pub fn sort(comptime T: type, items: []T, lessThan: fn(lhs: &const T, rhs: &cons
// figure out where to split the previous B block, and rotate it at the split
const B_split = binaryFirst(T, items, items[indexA], lastB, lessThan);
const B_remaining = lastB.end - B_split;
// swap the minimum A block to the beginning of the rolling A blocks
var minA = blockA.start;
findA = minA + block_size;
@ -585,16 +585,16 @@ pub fn sort(comptime T: type, items: []T, lessThan: fn(lhs: &const T, rhs: &cons
}
}
blockSwap(T, items, blockA.start, minA, block_size);
// swap the first item of the previous A block back with its original value, which is stored in buffer1
mem.swap(T, &items[blockA.start], &items[indexA]);
indexA += 1;
// locally merge the previous A block with the B values that follow it
// if lastA fits into the external cache we'll use that (with MergeExternal),
// or if the second internal buffer exists we'll use that (with MergeInternal),
// or failing that we'll use a strictly in-place merge algorithm (MergeInPlace)
if (lastA.length() <= cache.len) {
mergeExternal(T, items, lastA, Range.init(lastA.end, B_split), lessThan, cache[0..]);
} else if (buffer2.length() > 0) {
@ -602,7 +602,7 @@ pub fn sort(comptime T: type, items: []T, lessThan: fn(lhs: &const T, rhs: &cons
} else {
mergeInPlace(T, items, lastA, Range.init(lastA.end, B_split), lessThan);
}
if (buffer2.length() > 0 or block_size <= cache.len) {
// copy the previous A block into the cache or buffer2, since that's where we need it to be when we go to merge it anyway
if (block_size <= cache.len) {
@ -610,7 +610,7 @@ pub fn sort(comptime T: type, items: []T, lessThan: fn(lhs: &const T, rhs: &cons
} else {
blockSwap(T, items, blockA.start, buffer2.start, block_size);
}
// this is equivalent to rotating, but faster
// the area normally taken up by the A block is either the contents of buffer2, or data we don't need anymore since we memcopied it
// either way, we don't need to retain the order of those items, so instead of rotating we can just block swap B to where it belongs
@ -619,21 +619,21 @@ pub fn sort(comptime T: type, items: []T, lessThan: fn(lhs: &const T, rhs: &cons
// we are unable to use the 'buffer2' trick to speed up the rotation operation since buffer2 doesn't exist, so perform a normal rotation
mem.rotate(T, items[B_split..blockA.start + block_size], blockA.start - B_split);
}
// update the range for the remaining A blocks, and the range remaining from the B block after it was split
lastA = Range.init(blockA.start - B_remaining, blockA.start - B_remaining + block_size);
lastB = Range.init(lastA.end, lastA.end + B_remaining);
// if there are no more A blocks remaining, this step is finished!
blockA.start += block_size;
if (blockA.length() == 0)
break;
} else if (blockB.length() < block_size) {
// move the last B block, which is unevenly sized, to before the remaining A blocks, by using a rotation
// the cache is disabled here since it might contain the contents of the previous A block
mem.rotate(T, items[blockA.start..blockB.end], blockB.start - blockA.start);
lastB = Range.init(blockA.start, blockA.start + blockB.length());
blockA.start += blockB.length();
blockA.end += blockB.length();
@ -642,11 +642,11 @@ pub fn sort(comptime T: type, items: []T, lessThan: fn(lhs: &const T, rhs: &cons
// roll the leftmost A block to the end by swapping it with the next B block
blockSwap(T, items, blockA.start, blockB.start, block_size);
lastB = Range.init(blockA.start, blockA.start + block_size);
blockA.start += block_size;
blockA.end += block_size;
blockB.start += block_size;
if (blockB.end > B.end - block_size) {
blockB.end = B.end;
} else {
@ -655,7 +655,7 @@ pub fn sort(comptime T: type, items: []T, lessThan: fn(lhs: &const T, rhs: &cons
}
}
}
// merge the last A block with the remaining B values
if (lastA.length() <= cache.len) {
mergeExternal(T, items, lastA, Range.init(lastA.end, B.end), lessThan, cache[0..]);
@ -666,14 +666,14 @@ pub fn sort(comptime T: type, items: []T, lessThan: fn(lhs: &const T, rhs: &cons
}
}
}
// when we're finished with this merge step we should have the one or two internal buffers left over, where the second buffer is all jumbled up
// insertion sort the second buffer, then redistribute the buffers back into the items using the opposite process used for creating the buffer
// while an unstable sort like quicksort could be applied here, in benchmarks it was consistently slightly slower than a simple insertion sort,
// even for tens of millions of items. this may be because insertion sort is quite fast when the data is already somewhat sorted, like it is here
insertionSort(T, items[buffer2.start..buffer2.end], lessThan);
pull_index = 0;
while (pull_index < 2) : (pull_index += 1) {
var unique = pull[pull_index].count * 2;
@ -702,7 +702,7 @@ pub fn sort(comptime T: type, items: []T, lessThan: fn(lhs: &const T, rhs: &cons
}
}
}
// double the size of each A and B subarray that will be merged in the next level
if (!iterator.nextLevel()) break;
}
@ -711,37 +711,37 @@ pub fn sort(comptime T: type, items: []T, lessThan: fn(lhs: &const T, rhs: &cons
// merge operation without a buffer
fn mergeInPlace(comptime T: type, items: []T, A_arg: &const Range, B_arg: &const Range, lessThan: fn(&const T,&const T)bool) void {
if (A_arg.length() == 0 or B_arg.length() == 0) return;
// this just repeatedly binary searches into B and rotates A into position.
// the paper suggests using the 'rotation-based Hwang and Lin algorithm' here,
// but I decided to stick with this because it had better situational performance
//
//
// (Hwang and Lin is designed for merging subarrays of very different sizes,
// but WikiSort almost always uses subarrays that are roughly the same size)
//
//
// normally this is incredibly suboptimal, but this function is only called
// when none of the A or B blocks in any subarray contained 2√A unique values,
// which places a hard limit on the number of times this will ACTUALLY need
// to binary search and rotate.
//
//
// according to my analysis the worst case is √A rotations performed on √A items
// once the constant factors are removed, which ends up being O(n)
//
//
// again, this is NOT a general-purpose solution – it only works well in this case!
// kind of like how the O(n^2) insertion sort is used in some places
var A = *A_arg;
var B = *B_arg;
while (true) {
// find the first place in B where the first item in A needs to be inserted
const mid = binaryFirst(T, items, items[A.start], B, lessThan);
// rotate A into place
const amount = mid - A.end;
mem.rotate(T, items[A.start..mid], A.length());
if (B.end == mid) break;
// calculate the new A and B ranges
B.start = mid;
A = Range.init(A.start + amount, B.start);
@ -757,7 +757,7 @@ fn mergeInternal(comptime T: type, items: []T, A: &const Range, B: &const Range,
var A_count: usize = 0;
var B_count: usize = 0;
var insert: usize = 0;
if (B.length() > 0 and A.length() > 0) {
while (true) {
if (!lessThan(items[B.start + B_count], items[buffer.start + A_count])) {
@ -773,7 +773,7 @@ fn mergeInternal(comptime T: type, items: []T, A: &const Range, B: &const Range,
}
}
}
// swap the remainder of A into the final array
blockSwap(T, items, buffer.start + A_count, A.start + insert, A.length() - A_count);
}
@ -790,56 +790,56 @@ fn blockSwap(comptime T: type, items: []T, start1: usize, start2: usize, block_s
fn findFirstForward(comptime T: type, items: []T, value: &const T, range: &const Range, lessThan: fn(&const T,&const T)bool, unique: usize) usize {
if (range.length() == 0) return range.start;
const skip = math.max(range.length()/unique, usize(1));
var index = range.start + skip;
while (lessThan(items[index - 1], value)) : (index += skip) {
if (index >= range.end - skip) {
return binaryFirst(T, items, value, Range.init(index, range.end), lessThan);
}
}
return binaryFirst(T, items, value, Range.init(index - skip, index), lessThan);
}
fn findFirstBackward(comptime T: type, items: []T, value: &const T, range: &const Range, lessThan: fn(&const T,&const T)bool, unique: usize) usize {
if (range.length() == 0) return range.start;
const skip = math.max(range.length()/unique, usize(1));
var index = range.end - skip;
while (index > range.start and !lessThan(items[index - 1], value)) : (index -= skip) {
if (index < range.start + skip) {
return binaryFirst(T, items, value, Range.init(range.start, index), lessThan);
}
}
return binaryFirst(T, items, value, Range.init(index, index + skip), lessThan);
}
fn findLastForward(comptime T: type, items: []T, value: &const T, range: &const Range, lessThan: fn(&const T,&const T)bool, unique: usize) usize {
if (range.length() == 0) return range.start;
const skip = math.max(range.length()/unique, usize(1));
var index = range.start + skip;
while (!lessThan(value, items[index - 1])) : (index += skip) {
if (index >= range.end - skip) {
return binaryLast(T, items, value, Range.init(index, range.end), lessThan);
}
}
return binaryLast(T, items, value, Range.init(index - skip, index), lessThan);
}
fn findLastBackward(comptime T: type, items: []T, value: &const T, range: &const Range, lessThan: fn(&const T,&const T)bool, unique: usize) usize {
if (range.length() == 0) return range.start;
const skip = math.max(range.length()/unique, usize(1));
var index = range.end - skip;
while (index > range.start and lessThan(value, items[index - 1])) : (index -= skip) {
if (index < range.start + skip) {
return binaryLast(T, items, value, Range.init(range.start, index), lessThan);
}
}
return binaryLast(T, items, value, Range.init(index, index + skip), lessThan);
}
@ -885,7 +885,7 @@ fn mergeInto(comptime T: type, from: []T, A: &const Range, B: &const Range, less
const A_last = A.end;
const B_last = B.end;
var insert_index: usize = 0;
while (true) {
if (!lessThan(from[B_index], from[A_index])) {
into[insert_index] = from[A_index];
@ -916,7 +916,7 @@ fn mergeExternal(comptime T: type, items: []T, A: &const Range, B: &const Range,
var insert_index: usize = A.start;
const A_last = A.length();
const B_last = B.end;
if (B.length() > 0 and A.length() > 0) {
while (true) {
if (!lessThan(items[B_index], cache[A_index])) {
@ -932,7 +932,7 @@ fn mergeExternal(comptime T: type, items: []T, A: &const Range, B: &const Range,
}
}
}
// copy the remainder of A into the final array
mem.copy(T, items[insert_index..], cache[A_index..A_last]);
}
@ -1081,11 +1081,11 @@ test "another sort case" {
}
test "sort fuzz testing" {
var rng = std.rand.Rand.init(0x12345678);
var prng = std.rand.DefaultPrng.init(0x12345678);
const test_case_count = 10;
var i: usize = 0;
while (i < test_case_count) : (i += 1) {
fuzzTest(&rng);
fuzzTest(&prng.random);
}
}