// Utilities for use in __device__ code #ifndef CUDA_UTILS_CUH #define CUDA_UTILS_CUH #include "cuda_common.h" // ---------------------------------------------------------------------------- // Packed128 data structure that forces the compiler to use 128-bit loads/stores // in GPUs that support (the LDG.128 and STS.128 instructions) // This is a bit similar to the use of float4 in the case of 32-bit floats, but // supports arbitrary precision. template struct alignas(16) Packed128 { Packed128() = default; __device__ explicit Packed128(int4 bits) { static_assert(sizeof(bits) == sizeof(payload), "Size mismatch."); memcpy(&payload, &bits, sizeof(bits)); } __device__ static Packed128 constant(ElementType value) { Packed128 result; for(int k = 0; k < size; ++k) { result.payload[k] = value; } return result; } __device__ static Packed128 zeros() { return constant(0.f); } __device__ static Packed128 ones() { return constant(1.f); } __device__ ElementType& operator[](int index) { return payload[index]; } __device__ const ElementType& operator[](int index) const { return payload[index]; } __device__ int4 get_bits() const { int4 bits; static_assert(sizeof(bits) == sizeof(payload), "Size mismatch."); memcpy(&bits, &payload, sizeof(bits)); return bits; } static constexpr const size_t size = sizeof(int4) / sizeof(ElementType); ElementType payload[size]; }; // load a Packed128 from an aligned memory address template __device__ Packed128 load128(const ElementType* address) { return Packed128{*reinterpret_cast(address)}; } // load a Packed128 from an aligned memory address with streaming cache hint template __device__ Packed128 load128cs(const ElementType* address) { return Packed128{__ldcs(reinterpret_cast(address))}; } // store a Packed128 to an aligned memory address template __device__ void store128(ElementType* target, Packed128 value) { *reinterpret_cast(target) = value.get_bits(); } // store a Packed128 to an aligned memory address with streaming cache hint template __device__ void store128cs(ElementType* target, Packed128 value) { __stcs(reinterpret_cast(target), value.get_bits()); } // store a Packed128 to an aligned memory address while caching in L2 but bypassing L1 template __device__ void store128cg(ElementType* target, Packed128 value) { __stcg(reinterpret_cast(target), value.get_bits()); } // short-form typedefs typedef Packed128 f128; typedef Packed128 x128; // ---------------------------------------------------------------------------- // Warp/Block communication primitives // warp-level reduction for summing values __device__ inline float warpReduceSum(float val) { for (int offset = 16; offset > 0; offset /= 2) { val += __shfl_xor_sync(0xFFFFFFFF, val, offset); } return val; } // warp-level reduction for finding the maximum value __device__ inline float warpReduceMax(float val) { for (int offset = 16; offset > 0; offset /= 2) { val = fmaxf(val, __shfl_xor_sync(0xFFFFFFFF, val, offset)); } return val; } // requires all 32 threads in the warp to be active, but should work for any block size // uses non-dynamic shared memory so every call increases shared memory requirements by 128 bytes // the fact it's unique shared memory allows us to avoid an extra __syncthreads() call at the end // but if called inside a loop, the shared memory will be implicitly reused, so set final_sync to 1 using reduction_func_t = float (*) (float); template __device__ inline float blockReduce(float val, bool final_sync=false, float out_of_bounds=0.0f) { // two reductions of up to 1024 threads: // 1) inside warp (shuffle), 2) cross-warp (shared memory), 3) inside warp (shuffle) __shared__ float shared_val[WARP_SIZE]; const int lane_id = threadIdx.x % WARP_SIZE; const int warp_id = threadIdx.x / WARP_SIZE; const int num_warps = blockDim.x / WARP_SIZE; float warp_val = warp_reduction(val); if (lane_id == 0) { shared_val[warp_id] = warp_val; } __syncthreads(); warp_val = (lane_id < num_warps) ? shared_val[lane_id] : out_of_bounds; float block_val = warp_reduction(warp_val); if (final_sync) { __syncthreads(); // only needed in loops when effectively reusing shared memory etc. } return block_val; } // ---------------------------------------------------------------------------- // Random Number Generation used in Stochastic Rounding // SquirrelNoise5 - Squirrel's Raw Noise utilities (version 5) // This gives us a random number from threadIdx/blockIdx + a single seed for the entire GPU // todo - possibly overkill and we don't need such high quality random numbers? (tbd) // http://eiserloh.net/noise/SquirrelNoise5.hpp __device__ __host__ constexpr unsigned int SquirrelNoise5(int positionX, unsigned int seed) { constexpr unsigned int SQ5_BIT_NOISE1 = 0xd2a80a3f; // 11010010101010000000101000111111 constexpr unsigned int SQ5_BIT_NOISE2 = 0xa884f197; // 10101000100001001111000110010111 constexpr unsigned int SQ5_BIT_NOISE3 = 0x6C736F4B; // 01101100011100110110111101001011 constexpr unsigned int SQ5_BIT_NOISE4 = 0xB79F3ABB; // 10110111100111110011101010111011 constexpr unsigned int SQ5_BIT_NOISE5 = 0x1b56c4f5; // 00011011010101101100010011110101 unsigned int mangledBits = (unsigned int) positionX; mangledBits *= SQ5_BIT_NOISE1; mangledBits += seed; mangledBits ^= (mangledBits >> 9); mangledBits += SQ5_BIT_NOISE2; mangledBits ^= (mangledBits >> 11); mangledBits *= SQ5_BIT_NOISE3; mangledBits ^= (mangledBits >> 13); mangledBits += SQ5_BIT_NOISE4; mangledBits ^= (mangledBits >> 15); mangledBits *= SQ5_BIT_NOISE5; mangledBits ^= (mangledBits >> 17); return mangledBits; } __device__ __host__ constexpr unsigned int Get2dNoiseUint(int indexX, int indexY, unsigned int seed) { constexpr int PRIME_NUMBER = 198491317; // Large prime number with non-boring bits return SquirrelNoise5(indexX + (PRIME_NUMBER * indexY), seed); } // stochastic rounding built on top of Squirel Noise above (with seed updated per step via xorshift) __device__ __forceinline__ void stochastic_rounding(float in, __nv_bfloat16 *out, unsigned int seed) { // todo - is this stochastic rounding *too good*? can we cut any corners? unsigned int random = Get2dNoiseUint(threadIdx.x, blockIdx.x, seed); unsigned int threshold = random & 0xFFFF; unsigned int float_bits = __float_as_uint(in); unsigned int rounded_bits = float_bits & 0x0000FFFF; float_bits = (rounded_bits > threshold) ? (float_bits | 0xFFFF) : (float_bits & ~0xFFFF); *out = __float2bfloat16_rn(__uint_as_float(float_bits)); } __device__ __forceinline__ void stochastic_rounding(float in, half *out, unsigned int random) { *out = (float)in; // todo - implement this... } __device__ __forceinline__ void stochastic_rounding(float in, float *out, unsigned int random) { *out = in; // dummy function for when floatX is float (FP32 mode) } #endif