diff --git a/CMakeLists.txt b/CMakeLists.txt index 979d771cda..fbaf929e85 100644 --- a/CMakeLists.txt +++ b/CMakeLists.txt @@ -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" diff --git a/example/guess_number/main.zig b/example/guess_number/main.zig index d6a7b94b6c..d26518a1ed 100644 --- a/example/guess_number/main.zig +++ b/example/guess_number/main.zig @@ -2,7 +2,6 @@ const builtin = @import("builtin"); const std = @import("std"); const io = std.io; const fmt = std.fmt; -const Rand = std.rand.Rand; const os = std.os; pub fn main() !void { @@ -14,15 +13,15 @@ pub fn main() !void { try stdout.print("Welcome to the Guess Number Game in Zig.\n"); - var seed_bytes: [@sizeOf(usize)]u8 = undefined; + var seed_bytes: [@sizeOf(u64)]u8 = undefined; os.getRandomBytes(seed_bytes[0..]) catch |err| { std.debug.warn("unable to seed random number generator: {}", err); return err; }; - const seed = std.mem.readInt(seed_bytes, usize, builtin.Endian.Big); - var rand = Rand.init(seed); + const seed = std.mem.readInt(seed_bytes, u64, builtin.Endian.Big); + var prng = std.rand.DefaultPrng.init(seed); - const answer = rand.range(u8, 0, 100) + 1; + const answer = prng.random.range(u8, 0, 100) + 1; while (true) { try stdout.print("\nGuess a number between 1 and 100: "); diff --git a/src/parser.hpp b/src/parser.hpp index 21922db4ed..224e289bf5 100644 --- a/src/parser.hpp +++ b/src/parser.hpp @@ -16,7 +16,6 @@ ATTRIBUTE_PRINTF(2, 3) void ast_token_error(Token *token, const char *format, ...); -// This function is provided by generated code, generated by parsergen.cpp AstNode * ast_parse(Buf *buf, ZigList *tokens, ImportTableEntry *owner, ErrColor err_color); void ast_print(AstNode *node, int indent); diff --git a/std/index.zig b/std/index.zig index 179eae159e..4bc1444ac9 100644 --- a/std/index.zig +++ b/std/index.zig @@ -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"); diff --git a/std/io_test.zig b/std/io_test.zig index 993ec84d20..89959b7b54 100644 --- a/std/io_test.zig +++ b/std/io_test.zig @@ -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); diff --git a/std/rand.zig b/std/rand.zig deleted file mode 100644 index 96f0a385a4..0000000000 --- a/std/rand.zig +++ /dev/null @@ -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; - } - } -} diff --git a/std/rand/index.zig b/std/rand/index.zig new file mode 100644 index 0000000000..6a746fce92 --- /dev/null +++ b/std/rand/index.zig @@ -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 Random = struct { + fillFn: fn(r: &Random, buf: []u8) void, + + /// Read random bytes into the specified buffer until fill. + pub fn bytes(r: &Random, buf: []u8) void { + r.fillFn(r, buf); + } + + /// Return a random integer/boolean type. + pub fn scalar(r: &Random, 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: &Random, 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: &Random, comptime T: type) T { + // Generate a uniform value between [1, 2) and scale down to [0, 1). + // Note: The lowest mantissa bit is always set to 0 so we only use half the available range. + switch (T) { + f32 => { + const s = r.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: &Random, 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: &Random, comptime T: type) T { + @compileError("floatExp is unimplemented"); + } + + /// Shuffle a slice into a random order. + pub fn shuffle(r: &Random, comptime T: type, buf: []T) void { + if (buf.len < 2) { + return; + } + + var i: usize = 0; + while (i < buf.len - 1) : (i += 1) { + const j = r.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: Random, + + s: u64, + i: u64, + + pub fn init(init_s: u64) Pcg { + var pcg = Pcg { + .random = Random { .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: &Random, 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: Random, + + s: [2]u64, + + pub fn init(init_s: u64) Xoroshiro128 { + var x = Xoroshiro128 { + .random = Random { .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: &Random, 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: Random, + + 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 = Random { .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: &Random, 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 Random helper function tests, pcg engine is assumed correct. +test "Random float" { + var prng = DefaultPrng.init(0); + + var i: usize = 0; + while (i < 1000) : (i += 1) { + const val1 = prng.random.float(f32); + 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 "Random scalar" { + var prng = DefaultPrng.init(0); + const s = prng .random.scalar(u64); +} + +test "Random bytes" { + var prng = DefaultPrng.init(0); + var buf: [2048]u8 = undefined; + prng.random.bytes(buf[0..]); +} + +test "Random 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 "Random range" { + var prng = DefaultPrng.init(0); + testRange(&prng.random, -4, 3); + testRange(&prng.random, -4, -1); + testRange(&prng.random, 10, 14); +} + +fn testRange(r: &Random, 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; + } + } +} diff --git a/std/rand_test.zig b/std/rand_test.zig deleted file mode 100644 index 200b50a5b6..0000000000 --- a/std/rand_test.zig +++ /dev/null @@ -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, - 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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, - 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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, - 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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, -}; diff --git a/std/sort.zig b/std/sort.zig index c13e99feda..0f83df7bb4 100644 --- a/std/sort.zig +++ b/std/sort.zig @@ -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]); } @@ -1081,17 +1081,17 @@ 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); } } var fixed_buffer_mem: [100 * 1024]u8 = undefined; -fn fuzzTest(rng: &std.rand.Rand) void { +fn fuzzTest(rng: &std.rand.Random) void { const array_size = rng.range(usize, 0, 1000); var fixed_allocator = std.heap.FixedBufferAllocator.init(fixed_buffer_mem[0..]); var array = fixed_allocator.allocator.alloc(IdAndValue, array_size) catch unreachable;