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#include <metal_stdlib>
#include <metal_integer>
#include <metal_atomic>
using namespace metal;
// Constants
// 2^32 and 1/2^32. Useful for converting between float and uint.
static constexpr constant ulong UNIF01_NORM32 = 4294967296;
static constexpr constant float UNIF01_INV32 = 2.328306436538696289e-10;
// 2 * pi
static constexpr constant float TWO_PI = 2.0 * M_PI_F;
static constexpr constant int3 S1 = {13, 19, 12};
static constexpr constant int3 S2 = {2, 25, 4};
static constexpr constant int3 S3 = {3, 11, 17};
// Used to prevent bad seeds.
static constexpr constant uint64_t PHI[16] = {
0x9E3779B97F4A7C15,
0xF39CC0605CEDC834,
0x1082276BF3A27251,
0xF86C6A11D0C18E95,
0x2767F0B153D27B7F,
0x0347045B5BF1827F,
0x01886F0928403002,
0xC1D64BA40F335E36,
0xF06AD7AE9717877E,
0x85839D6EFFBD7DC6,
0x64D325D1C5371682,
0xCADD0CCCFDFFBBE1,
0x626E33B8D04B4331,
0xBBF73C790D94F79D,
0x471C4AB3ED3D82A5,
0xFEC507705E4AE6E5,
};
// Combined Tausworthe and LCG Random Number Generator.
// https://developer.nvidia.com/gpugems/gpugems3/part-vi-gpu-computing/chapter-37-efficient-random-number-generation-and-application
// https://indico.cern.ch/event/93877/contributions/2118070/attachments/1104200/1575343/acat3_revised_final.pdf
struct HybridTaus {
float state;
HybridTaus() thread = default;
HybridTaus() threadgroup = default;
HybridTaus() device = default;
HybridTaus() constant = default;
// Generate seeds for each thread.
METAL_FUNC static uint4 seed_per_thread(const ulong4 seeds) {
return uint4(ulong4(seeds) * ulong4(PHI[0], PHI[1], PHI[2], PHI[3]) * ulong4(1099087573UL));
}
// Tausworthe generator.
METAL_FUNC static uint taus(const uint z, const int3 s, const uint M) {
uint b = (((z << s.x) ^ z) >> s.y);
return (((z & M) << s.z) ^ b);
}
// LCG generator.
METAL_FUNC static uint lcg(const uint z) {
return (1664525 * z + 1013904223UL);
}
// Initialize the RNG state.
METAL_FUNC static HybridTaus init(const ulong4 seeds) {
uint4 seed = seed_per_thread(seeds);
// Seed #1
uint z1 = taus(seed.x, S1, 4294967294UL);
uint z2 = taus(seed.y, S2, 4294967288UL);
uint z3 = taus(seed.z, S3, 4294967280UL);
uint z4 = lcg(seed.x);
// Seed #2
uint r1 = (z1^z2^z3^z4^seed.y);
z1 = taus(r1, S1, 429496729UL);
z2 = taus(r1, S2, 4294967288UL);
z3 = taus(r1, S3, 429496280UL);
z4 = lcg(r1);
// Seed #3
r1 = (z1^z2^z3^z4^seed.z);
z1 = taus(r1, S1, 429496729UL);
z2 = taus(r1, S2, 4294967288UL);
z3 = taus(r1, S3, 429496280UL);
z4 = lcg(r1);
// Seed #4
r1 = (z1^z2^z3^z4^seed.w);
z1 = taus(r1, S1, 429496729UL);
z2 = taus(r1, S2, 4294967288UL);
z3 = taus(r1, S3, 429496280UL);
z4 = lcg(r1);
HybridTaus rng;
rng.state = (z1^z2^z3^z4) * UNIF01_INV32;
return rng;
}
METAL_FUNC float rand() {
uint seed = this->state * UNIF01_NORM32;
uint z1 = taus(seed, S1, 429496729UL);
uint z2 = taus(seed, S2, 4294967288UL);
uint z3 = taus(seed, S3, 429496280UL);
uint z4 = lcg(seed);
thread float result = this->state;
this->state = (z1^z2^z3^z4) * UNIF01_INV32;
return result;
}
};
template<typename T> METAL_FUNC void rand_uniform(
constant size_t &size,
constant float &min,
constant float &max,
device atomic_uint *seed,
device T *out,
uint tid [[thread_position_in_grid]]
) {
if (tid >= size) {
return;
}
// Evenly sized vectors need an offset when writing the mirror element.
uint off = 1 - size % 2;
float diff = abs(min - max);
uint s = atomic_load_explicit(seed, memory_order_relaxed);
HybridTaus rng = HybridTaus::init({ulong(s), tid, 1, 1});
out[tid] = static_cast<T>(rng.rand() * diff + min);
if (tid == 0) {
atomic_store_explicit(seed, uint(rng.rand() * UNIF01_NORM32), memory_order_relaxed);
// Return early if tid == 0 && off == 0, otherwise we will write to out[size].
if (off == 0)
return;
}
// Use symmetry to fill the other half of the array.
out[size - off - tid] = static_cast<T>(rng.rand() * diff + min);
}
// Create Gaussian normal distribution using Box-Muller transform:
// https://en.wikipedia.org/wiki/Box–Muller_transform
template<typename T> METAL_FUNC void normal(
constant size_t &size,
constant float &mean,
constant float &stddev,
device atomic_uint *seed,
device T *out,
uint tid [[thread_position_in_grid]]
) {
if (tid >= size) {
return;
}
// Evenly sized vectors need an offset when writing the mirror element.
uint off = 1 - size % 2;
uint s = atomic_load_explicit(seed, memory_order_relaxed);
HybridTaus rng = HybridTaus::init({ulong(s), tid, 1, 1});
float u1 = rng.rand();
float u2 = rng.rand();
float cosval;
float sinval = sincos(TWO_PI * u2, cosval);
float mag = stddev * sqrt(-2.0 * log(u1));
float z0 = mag * cosval + mean;
float z1 = mag * sinval + mean;
out[tid] = static_cast<T>(z0);
if (tid == 0) {
atomic_store_explicit(seed, uint(rng.rand() * UNIF01_NORM32), memory_order_relaxed);
// Return early if tid == 0 && off == 0, otherwise we will write to out[size].
if (off == 0)
return;
}
// Use symmetry to fill the other half of the array.
out[size - off - tid] = static_cast<T>(z1);
}
#define UNIFORM_OP(NAME, T) \
kernel void rand_uniform_##NAME( \
constant size_t &size, \
constant float &min, \
constant float &max, \
device atomic_uint *seed, \
device T *out, \
uint tid [[thread_position_in_grid]] \
) { \
rand_uniform<T>(size, min, max, seed, out, tid); \
} \
#define NORMAL_OP(NAME, T) \
kernel void rand_normal_##NAME( \
constant size_t &size, \
constant float &mean, \
constant float &stddev, \
device atomic_uint *seed, \
device T *out, \
uint tid [[thread_position_in_grid]] \
) { \
normal<T>(size, mean, stddev, seed, out, tid); \
} \
#define RANDOM_OPS(NAME, T) \
UNIFORM_OP(NAME, T) \
NORMAL_OP(NAME, T) \
RANDOM_OPS(f32, float)
RANDOM_OPS(f16, half)
#if __METAL_VERSION__ >= 310
RANDOM_OPS(bf16, bfloat)
#endif
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