From 16beb68283f11b990617ca912e8b40992a503f0f Mon Sep 17 00:00:00 2001 From: xzgao Date: Mon, 3 Jul 2023 04:18:02 +0000 Subject: [PATCH 1/3] added wrapped c code and runable examples --- src/SGEMM/CuTropicalSGEMM_example.jl | 46 ++ src/SGEMM/JuliaLib_build.sh | 1 + src/SGEMM/TropicalSGemm.cu | 622 ++++++++++++++++++++ src/SGEMM/TropicalSGemm.so | Bin 0 -> 909440 bytes src/SGEMM/benchmark_CuTropicalSGEMM.sh | 6 + src/SGEMM/benchmark_GemmKerenls_Tropical.jl | 87 +++ 6 files changed, 762 insertions(+) create mode 100644 src/SGEMM/CuTropicalSGEMM_example.jl create mode 100644 src/SGEMM/JuliaLib_build.sh create mode 100644 src/SGEMM/TropicalSGemm.cu create mode 100755 src/SGEMM/TropicalSGemm.so create mode 100644 src/SGEMM/benchmark_CuTropicalSGEMM.sh create mode 100644 src/SGEMM/benchmark_GemmKerenls_Tropical.jl diff --git a/src/SGEMM/CuTropicalSGEMM_example.jl b/src/SGEMM/CuTropicalSGEMM_example.jl new file mode 100644 index 0000000..135a1cc --- /dev/null +++ b/src/SGEMM/CuTropicalSGEMM_example.jl @@ -0,0 +1,46 @@ +using CUDA, Test, BenchmarkTools, Dates + +function CuTropicalGemmMatmul!(m::Integer, n::Integer, k::Integer, A::CuArray{Float32}, B::CuArray{Float32}, C::CuArray{Float32}) + A_ptr = pointer(A); + B_ptr = pointer(B); + C_ptr = pointer(C); + + @ccall "./TropicalSGemm.so".TropicalMatmul(m::Cint, n::Cint, k::Cint, A_ptr::CuPtr{Cfloat}, B_ptr::CuPtr{Cfloat}, C_ptr::CuPtr{Cfloat})::Cvoid + return nothing +end + +# this function will return the (i, j) element of the Tropical result of C + A * B +function TropicalDirectMatmul_ij(i::Integer, j::Integer, m::Integer, n::Integer, k::Integer, A::Array{Float32}, B::Array{Float32}, C::Array{Float32}) + sum = zero(Float32) + for l in 1:k + sum = max(A[(i - 1) * k + l] + B[(l - 1) * n + j], sum) + end + return sum +end + +#init the system +m, n, k = 1024, 1024, 1024 + +A = rand(Float32, (m * k)); +B = rand(Float32, (k * n)); +C = rand(Float32, (m * n)); + +CuA = CuArray(A); +CuB = CuArray(B); +CuC = CuArray(C); + +CuTropicalGemmMatmul!(m, n, k, CuA, CuB, CuC) + +C_result = Array(CuC); + + +# test +@testset begin + for _ in 1:40 + for _ in 1:40 + a = rand(1:m) + b = rand(1:n) + @test TropicalDirectMatmul_ij(a, b, m, n, k, A, B, C) ≈ C_result[(a - 1) * n + b] + end + end +end \ No newline at end of file diff --git a/src/SGEMM/JuliaLib_build.sh b/src/SGEMM/JuliaLib_build.sh new file mode 100644 index 0000000..cccfab5 --- /dev/null +++ b/src/SGEMM/JuliaLib_build.sh @@ -0,0 +1 @@ +nvcc -Xcompiler -fPIC --shared TropicalSGemm.cu -o TropicalSGemm.so \ No newline at end of file diff --git a/src/SGEMM/TropicalSGemm.cu b/src/SGEMM/TropicalSGemm.cu new file mode 100644 index 0000000..fae7b15 --- /dev/null +++ b/src/SGEMM/TropicalSGemm.cu @@ -0,0 +1,622 @@ +#include +#include +#include +#include +#include + +void random_init(float *data, size_t size) { + for (size_t i = 0; i < size; ++i) { + data[i] = float(rand()) / RAND_MAX; + } +} + + +bool check(const float *A, + const float *B, + const float *C, + int m, int n, int k) { + for (int i = 0; i < 20; ++i) { + int a = rand() % m; + for (int j = 0; j < 20; ++j) { + int b = rand() % n; + float sum = 0.f; + for (int p = 0; p < k; ++p) { + sum = max(sum, A[a * k + p] + B[b + p * n]); + } + + if (std::fabs(sum - C[a * n + b]) / std::fabs(sum) > 1e-5f) { + printf("C[%d][%d] not match, %f vs %f\n", i, j, sum, C[a * n + b]); + return false; + } + } + } + + return true; +} + +__device__ __forceinline__ +uint32_t smem_u32addr(const void *smem_ptr) { + uint32_t addr; + asm ("{.reg .u64 u64addr;\n" + " cvta.to.shared.u64 u64addr, %1;\n" + " cvt.u32.u64 %0, u64addr;}\n" + : "=r"(addr) + : "l"(smem_ptr) + ); + + return addr; +} + +__device__ __forceinline__ +void ldg32_nc(float ®, const void *ptr, bool guard) { + asm volatile ( + "{.reg .pred p;\n" + " setp.ne.b32 p, %2, 0;\n" +#if __CUDACC_VER_MAJOR__ >= 11 && __CUDACC_VER_MINOR__ >= 4 && \ + __CUDA_ARCH__ >= 750 + " @p ld.global.nc.L2::128B.f32 %0, [%1];}\n" +#else + " @p ld.global.nc.f32 %0, [%1];}\n" +#endif + : "=f"(reg) + : "l"(ptr), "r"((int)guard) + ); +} + +__device__ __forceinline__ +void ldg32_nc_0(float ®, const void *ptr, bool guard) { + asm volatile ( + "{.reg .pred p;\n" + " setp.ne.b32 p, %2, 0;\n" + " @!p mov.b32 %0, 0;\n" +#if __CUDACC_VER_MAJOR__ >= 11 && __CUDACC_VER_MINOR__ >= 4 && \ + __CUDA_ARCH__ >= 750 + " @p ld.global.nc.L2::128B.f32 %0, [%1];}\n" +#else + " @p ld.global.nc.f32 %0, [%1];}\n" +#endif + : "=f"(reg) + : "l"(ptr), "r"((int)guard) + ); +} + +__device__ __forceinline__ +void stg32(const float ®, void *ptr, bool guard) { + asm volatile ( + "{.reg .pred p;\n" + " setp.ne.b32 p, %2, 0;\n" + " @p st.global.f32 [%0], %1;}\n" + : : "l"(ptr), "f"(reg), "r"((int)guard) + ); +} + +__device__ __forceinline__ +void lds128(float ®0, float ®1, + float ®2, float ®3, + const uint32_t &addr) { + asm volatile ( + "ld.shared.v4.f32 {%0, %1, %2, %3}, [%4];\n" + : "=f"(reg0), "=f"(reg1), "=f"(reg2), "=f"(reg3) + : "r"(addr) + ); +} + +__device__ __forceinline__ +void sts32(const float ®, const uint32_t &addr) { + asm volatile ( + "st.shared.f32 [%0], %1;\n" + : : "r"(addr), "f"(reg) + ); +} + +__device__ __forceinline__ +void sts128(const float ®0, const float ®1, + const float ®2, const float ®3, + const uint32_t &addr) { + asm volatile ( + "st.shared.v4.f32 [%0], {%1, %2, %3, %4};\n" + : : "r"(addr), "f"(reg0), "f"(reg1), "f"(reg2), "f"(reg3) + ); +} + +struct StgFrag { + float data[4][4]; + + __device__ __forceinline__ + StgFrag(const float (&C_frag)[8][8], int tile_x, int tile_y) { + #pragma unroll + for (int i = 0; i < 4; ++i) { + #pragma unroll + for (int j = 0; j < 4; ++j) { + data[i][j] = C_frag[tile_y * 4 + i][tile_x * 4 + j]; + } + } + } +}; + +__device__ __noinline__ +void C_tile_wb(StgFrag C_frag, + float *C_stg_ptr, + const float *C_lds_ptr, + uint32_t C_sts_addr, + uint32_t m, + uint32_t n, + uint32_t m_idx, + uint32_t n_idx) { + __syncthreads(); + + #pragma unroll + for (int i = 0; i < 4; ++i) { + sts128(C_frag.data[i][0], + C_frag.data[i][1], + C_frag.data[i][2], + C_frag.data[i][3], + C_sts_addr + i * 8 * sizeof(float4)); + } + + __syncthreads(); + + uint32_t m_guard = m < m_idx ? 0 : m - m_idx; + + #pragma unroll + for (int i = 0; i < 16; ++i) { + stg32(C_lds_ptr[i * 32], + C_stg_ptr + i * n, + i < m_guard && n_idx < n); + } +} + +/* + * matrix A, B and C: row-major + * + * mma block: + * thread block tile: m128n128k8 + * warp tile: m32n64k8 + * thread tile: m8n8k8 + * thread fragment: + * matrixA: 8x1 FP32 + * matrixB: 1x8 FP32 + * + * ---------------------------------------------------------------- + * thread block tile map: + * + * 128 + * --|---------------------| + * B_tile 8| | + * --|---------------------| + * + * A_tile | 8 | | 64 | + * --|---| --|----------|----------| + * | | 32| warp_0 | warp_1 | + * | | --|----------|----------| + * | | | warp_2 | warp_3 | + * 128| | |----------|----------| + * | | | warp_4 | warp_5 | + * | | |----------|----------| + * | | | warp_6 | warp_7 | + * --|---| |----------|----------| + * + * ---------------------------------------------------------------- + * warp tile map: + * + * 'z' thread map to avoid LDS.128 shared memory broadcast limitation. + * + * | 32 || + * B_frag --|---|---|---|---|---|---|---|---||---|---|---|---|---|---|---|---| + * 1|///| | | | | | | ||///| | | | | | | | + * --|---|---|---|---|---|---|---|---||---|---|---|---|---|---|---|---| + * A_frag | 4 | || + * | 1 | || + * --|---|-- |---|---|---|---|---|---|---|---||---|---------------------------| + * |///|4 |t0 |t2 |t4 |t6 |t8 |t10|t12|t14||t0 | | + * |---|-- |---|---|---|---|---|---|---|---||---| | + * | | |t1 |t3 |t5 |t7 |t9 |t11|t13|t15|| | + * 16|---| |---|---|---|---|---|---|---|---|| | + * | | |t16|t18|t20|t22|t24|t26|t28|t30|| | + * |---| |---|---|---|---|---|---|---|---|| | + * | | |t17|t19|t21|t23|t25|t27|t29|t31|| | + * ==|===|=====|===|===|===|===|===|===|===|===||===|============================ + * |///| |t0 | ||t0 | | + * |---| |---| ||---| | + * | | | || | + * |---| | || | + * | | | || | + * |---| | || | + * | | | || | + * |---| |-------------------------------||-------------------------------| + * + */ +__global__ __launch_bounds__(256, 2) +void sgemm_128x128x8_kernel(const float *A, + const float *B, + float *C, + uint32_t m, + uint32_t n, + uint32_t k, + uint32_t A_ldg_step, // k * sizeof(float) + uint32_t B_ldg_step) { // n * sizeof(float) * 8 + /* + * matrix A & B thread block tile shared memory (double buffer) + * matrix A: 132 * 8 * 4Byte/item * double buffer = 4.125KB * 2 + * matrix B: 128 * 8 * 4Byte/item * double buffer = 8KB + * + * for double buffer faster switch, A_smem requires 8KB * 2 shared memory + * and 16KB aligned, B_smem should be 8KB aligned, then the double buffer + * can be switched by only 1 xor instruction: + * (uint32_t &)A_smem ^= 0x2000; + * (uint32_t &)B_smem ^= 0x1000; + */ + __shared__ __align__(16 * 1024) char smem[24 * 1024]; + float *A_smem = reinterpret_cast(smem); + float *B_smem = reinterpret_cast(smem + 16 * 1024); + + // A, B and C register fragment + float A_frag[2][8]; + float B_frag[2][8]; + float C_frag[8][8]; + #pragma unroll + for (int i = 0; i < 8; ++i) { + #pragma unroll + for (int j = 0; j < 8; ++j) { + C_frag[i][j] = 0; + } + } + + const uint32_t lane_id = threadIdx.x % 32; + const uint32_t warp_id = threadIdx.x / 32; + + // 4x8 threads each warp for FFMA + const uint32_t mma_tid_x = (lane_id / 2) % 8; + const uint32_t mma_tid_y = (lane_id / 16) * 2 + (lane_id % 2); + + // A_tile & B_tile ldg pointer + const char *A_ldg_ptr = (const char *)( + A + (blockIdx.y * 128 + threadIdx.x / 8 * 4) * k + threadIdx.x % 8); + const char *B_ldg_ptr = (const char *)( + B + (threadIdx.x / 32) * n + blockIdx.x * 128 + threadIdx.x % 32); + + // A_tile & B_tile sts/lds pointer + // using uint32_t pointer for faster double buffer switch + uint32_t A_sts_addr = smem_u32addr( + A_smem + (threadIdx.x % 8) * 132 + (threadIdx.x / 8) * 4); + uint32_t B_sts_addr = smem_u32addr( + B_smem + (threadIdx.x / 32) * 128 + (threadIdx.x % 32)); + + uint32_t A_lds_addr = smem_u32addr( + A_smem + (warp_id / 2) * 32 + mma_tid_y * 4); + uint32_t B_lds_addr = smem_u32addr( + B_smem + (warp_id % 2) * 64 + mma_tid_x * 4); + + // ldg_guard to avoid LDG out of bound + uint32_t A_ldg_guard = 0; + #pragma unroll + for (int i = 0; i < 4; ++i) { + int m_idx = blockIdx.y * 128 + threadIdx.x / 8 * 4 + i; + if (m_idx < m) { + A_ldg_guard |= (1u << i); + } + } + + uint32_t B_ldg_guard = 0; + #pragma unroll + for (int i = 0; i < 4; ++i) { + int n_idx = blockIdx.x * 128 + threadIdx.x % 32 + i * 32; + if (n_idx < n) { + B_ldg_guard |= (1u << i); + } + } + + float A_ldg_reg[4]; + float B_ldg_reg[4]; + + // 1'st A&B tile loaded before the k_tile loop + uint32_t k_tiles = (k + 7) / 8 - 1; + + // load 1'st tile to shared memory + { + uint32_t first_k_tile = k - k_tiles * 8; + + #pragma unroll + for (int i = 0; i < 4; ++i) { + bool guard = (A_ldg_guard & (1u << i)) != 0 && + threadIdx.x % 8 < first_k_tile; + ldg32_nc_0(A_ldg_reg[i], + A_ldg_ptr + i * A_ldg_step, + guard); + } + + sts128(A_ldg_reg[0], A_ldg_reg[1], A_ldg_reg[2], A_ldg_reg[3], + A_sts_addr); + + #pragma unroll + for (int i = 0; i < 4; ++i) { + bool guard = (B_ldg_guard & (1u << i)) != 0 && + threadIdx.x / 32 < first_k_tile; + ldg32_nc_0(B_ldg_reg[i], + B_ldg_ptr + i * 32 * sizeof(float), + guard); + } + + #pragma unroll + for (int i = 0; i < 4; ++i) { + sts32(B_ldg_reg[i], B_sts_addr + i * 32 * sizeof(float)); + } + + __syncthreads(); + + // switch double buffer + A_sts_addr ^= 0x2000; + B_sts_addr ^= 0x1000; + + // ldg pointer for next tile + A_ldg_ptr += first_k_tile * sizeof(float); + B_ldg_ptr += n * first_k_tile * sizeof(float); + } + + // load 1'st fragment + lds128(A_frag[0][0], A_frag[0][1], A_frag[0][2], A_frag[0][3], + A_lds_addr); + lds128(A_frag[0][4], A_frag[0][5], A_frag[0][6], A_frag[0][7], + A_lds_addr + 16 * sizeof(float)); + lds128(B_frag[0][0], B_frag[0][1], B_frag[0][2], B_frag[0][3], + B_lds_addr); + lds128(B_frag[0][4], B_frag[0][5], B_frag[0][6], B_frag[0][7], + B_lds_addr + 32 * sizeof(float)); + + // k_tiles loop + for (; k_tiles > 0; --k_tiles) { + #pragma unroll + for (int k_frag = 0; k_frag < 8; ++k_frag) { + // store next A&B tile to shared memory + if (k_frag == 7) { + sts128(A_ldg_reg[0], A_ldg_reg[1], A_ldg_reg[2], A_ldg_reg[3], + A_sts_addr); + #pragma unroll + for (int i = 0; i < 4; ++i) { + sts32(B_ldg_reg[i], B_sts_addr + i * 32 * sizeof(float)); + } + + __syncthreads(); + + // switch double buffer + A_lds_addr ^= 0x2000; + B_lds_addr ^= 0x1000; + A_sts_addr ^= 0x2000; + B_sts_addr ^= 0x1000; + + // ldg pointer for next tile + A_ldg_ptr += 8 * sizeof(float); + B_ldg_ptr += B_ldg_step; + } + + // load next A&B fragment from shared memory to register + lds128(A_frag[(k_frag + 1) % 2][0], + A_frag[(k_frag + 1) % 2][1], + A_frag[(k_frag + 1) % 2][2], + A_frag[(k_frag + 1) % 2][3], + A_lds_addr + (k_frag + 1) % 8 * 132 * sizeof(float)); + lds128(A_frag[(k_frag + 1) % 2][4], + A_frag[(k_frag + 1) % 2][5], + A_frag[(k_frag + 1) % 2][6], + A_frag[(k_frag + 1) % 2][7], + A_lds_addr + ((k_frag + 1) % 8 * 132 + 16) * sizeof(float)); + lds128(B_frag[(k_frag + 1) % 2][0], + B_frag[(k_frag + 1) % 2][1], + B_frag[(k_frag + 1) % 2][2], + B_frag[(k_frag + 1) % 2][3], + B_lds_addr + (k_frag + 1) % 8 * 128 * sizeof(float)); + lds128(B_frag[(k_frag + 1) % 2][4], + B_frag[(k_frag + 1) % 2][5], + B_frag[(k_frag + 1) % 2][6], + B_frag[(k_frag + 1) % 2][7], + B_lds_addr + ((k_frag + 1) % 8 * 128 + 32) * sizeof(float)); + + // load next A&B tile + if (k_frag == 0) { + #pragma unroll + for (int i = 0; i < 4; ++i) { + ldg32_nc(A_ldg_reg[i], + A_ldg_ptr + i * A_ldg_step, + (A_ldg_guard & (1u << i)) != 0); + } + + #pragma unroll + for (int i = 0; i < 4; ++i) { + ldg32_nc(B_ldg_reg[i], + B_ldg_ptr + i * 32 * sizeof(float), + (B_ldg_guard & (1u << i)) != 0); + } + } + + // FFMA loop + #pragma unroll + for (int i = 0; i < 8; ++i) { + #pragma unroll + for (int j = 0; j < 8; ++j) { + C_frag[i][j] = max(C_frag[i][j], A_frag[k_frag % 2][i] + B_frag[k_frag % 2][j]); + } + } + } + } + + // FFMA for the last tile + #pragma unroll + for (int k_frag = 0; k_frag < 8; ++k_frag) { + if (k_frag < 7) { + // load next A&B fragment from shared memory to register + lds128(A_frag[(k_frag + 1) % 2][0], + A_frag[(k_frag + 1) % 2][1], + A_frag[(k_frag + 1) % 2][2], + A_frag[(k_frag + 1) % 2][3], + A_lds_addr + (k_frag + 1) % 8 * 132 * sizeof(float)); + lds128(A_frag[(k_frag + 1) % 2][4], + A_frag[(k_frag + 1) % 2][5], + A_frag[(k_frag + 1) % 2][6], + A_frag[(k_frag + 1) % 2][7], + A_lds_addr + ((k_frag + 1) % 8 * 132 + 16) * sizeof(float)); + lds128(B_frag[(k_frag + 1) % 2][0], + B_frag[(k_frag + 1) % 2][1], + B_frag[(k_frag + 1) % 2][2], + B_frag[(k_frag + 1) % 2][3], + B_lds_addr + (k_frag + 1) % 8 * 128 * sizeof(float)); + lds128(B_frag[(k_frag + 1) % 2][4], + B_frag[(k_frag + 1) % 2][5], + B_frag[(k_frag + 1) % 2][6], + B_frag[(k_frag + 1) % 2][7], + B_lds_addr + ((k_frag + 1) % 8 * 128 + 32) * sizeof(float)); + } + + // FFMA loop + #pragma unroll + for (int i = 0; i < 8; ++i) { + #pragma unroll + for (int j = 0; j < 8; ++j) { + C_frag[i][j] = max(C_frag[i][j], A_frag[k_frag % 2][i] + B_frag[k_frag % 2][j]); + } + } + } + + // C_tile write back, reuse A&B tile shared memory buffer + uint32_t C_sts_addr = smem_u32addr((float4 *)(smem + warp_id * 2048) + + mma_tid_y * 4 * 8 + mma_tid_x); + const float *C_lds_ptr = (float *)(smem + warp_id * 2048) + lane_id; + + uint32_t m_idx = blockIdx.y * 128 + warp_id / 2 * 32; + uint32_t n_idx = blockIdx.x * 128 + warp_id % 2 * 64 + lane_id; + + float *C_stg_ptr = C + m_idx * n + n_idx; + + if (m_idx >= m) { + return; + } else if (m_idx + 32 <= m) { + uint32_t n_guard = n < n_idx ? 0 : n - n_idx; + + #pragma unroll + for (int i = 0; i < 2; ++i) { + #pragma unroll + for (int j = 0; j < 2; ++j) { + __syncthreads(); + + #pragma unroll + for (int p = 0; p < 4; ++p) { + sts128(C_frag[i * 4 + p][j * 4], + C_frag[i * 4 + p][j * 4 + 1], + C_frag[i * 4 + p][j * 4 + 2], + C_frag[i * 4 + p][j * 4 + 3], + C_sts_addr + p * 8 * sizeof(float4)); + } + + __syncthreads(); + + #pragma unroll + for (int p = 0; p < 16; ++p) { + stg32(C_lds_ptr[p * 32], + C_stg_ptr + (i * 16 + p) * n + j * 32, + j * 32 < n_guard); + } + } + } + } else { + #pragma unroll + for (int i = 0; i < 2; ++i) { + #pragma unroll + for (int j = 0; j < 2; ++j) { + StgFrag stg_frag(C_frag, j, i); + + C_tile_wb(stg_frag, + C_stg_ptr + i * 16 * n + j * 32, + C_lds_ptr, + C_sts_addr, + m, + n, + m_idx + i * 16, + n_idx + j * 32); + } + } + } +} + +extern "C" +void TropicalMatmul(int m, int n, int k, float *d_A, float *d_B, float *d_C){ + + dim3 grid((n + 127) / 128, (m + 127) / 128); + sgemm_128x128x8_kernel<<>>(d_A, d_B, d_C, m, n, k, k * sizeof(float), n * sizeof(float) * 8); + +} + +extern "C" +void MatrixPrint(int m, int k, float *A){ + // float *cpu_A; + // cudaMallocHost(&cpu_A, m * k * sizeof(float)); + // cudaMemcpy(A, cpu_A, m * k * sizeof(float), cudaMemcpyDefault); + + for(int i = 0; i < m; ++i){ + for(int j = 0; j < k; ++j){ + // printf("%f\n", cpu_A[i * k + j]); + printf("%f\n", A[i * k + j]); + } + } + + // cudaFreeHost(cpu_A); +} + +int main() { + int m = 4 * 2560; + int n = 4 * 2000; + int k = 4 * 2048; + int n_iter = 10; + + float *h_A, *h_B, *h_C; + cudaMallocHost(&h_A, m * k * sizeof(float)); + cudaMallocHost(&h_B, k * n * sizeof(float)); + cudaMallocHost(&h_C, m * n * sizeof(float)); + random_init(h_A, m * k); + random_init(h_B, k * n); + + float *d_A, *d_B, *d_C; + cudaMalloc(&d_A, m * k * sizeof(float)); + cudaMalloc(&d_B, k * n * sizeof(float)); + cudaMalloc(&d_C, m * n * sizeof(float)); + + cudaMemcpy(d_A, h_A, m * k * sizeof(float), cudaMemcpyDefault); + cudaMemcpy(d_B, h_B, k * n * sizeof(float), cudaMemcpyDefault); + + cudaEvent_t start, end; + cudaEventCreate(&start); + cudaEventCreate(&end); + + // dim3 grid((n + 127) / 128, (m + 127) / 128); + + // warmup + // sgemm_128x128x8_kernel<<>>( + // d_A, d_B, d_C, m, n, k, k * sizeof(float), n * sizeof(float) * 8); + + cudaEventRecord(start); + for (int i = 0; i < n_iter; ++i) { + // sgemm_128x128x8_kernel<<>>(d_A, d_B, d_C, m, n, k, k * sizeof(float), n * sizeof(float) * 8); + TropicalMatmul(m, n, k, d_A, d_B, d_C); + } + cudaEventRecord(end); + cudaEventSynchronize(end); + + float ms; + cudaEventElapsedTime(&ms, start, end); + cudaEventDestroy(start); + cudaEventDestroy(end); + + long workload = n_iter * long(m) * n * k * 2; + double gflops = (double(workload) / 1e9) / (double(ms) / 1e3); + printf("TropicalSGemm: %f GFLOPS\n", gflops); + printf("time: %f ms\n", ms); + cudaMemcpy(h_C, d_C, m * n * sizeof(float), cudaMemcpyDefault); + + bool chk = check(h_A, h_B, h_C, m, n, k); + printf("Matrix_C check: %s\n", chk ? 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ze?nh!zK;vd|J7e|c}YJZ1$~;<|A!u4^q1Z9^n7~vUlu{n-ex~a;P3vFYbNRLSG)mw zIH|Xw`EdgOhj-cFCH3l;;z9qC@rwlhZysLKm-nP3r)m9voxtxt#R`}7{8@b5e?kev4HZT4T>Q`-~x-mkdcy`ORVZ!bO(kI)q{ya8BEf9E$0xASvO z5Aj_81YXjI0IcD&`wW-e&q+y6d-gVa+S5h!_c@%d)orbor%3l7Rm*dyDVFJiENZJs;2A&iV8O@Q?nL;lC`5dZ6Ss`#*!7o6i6M literal 0 HcmV?d00001 diff --git a/src/SGEMM/benchmark_CuTropicalSGEMM.sh b/src/SGEMM/benchmark_CuTropicalSGEMM.sh new file mode 100644 index 0000000..32e9a72 --- /dev/null +++ b/src/SGEMM/benchmark_CuTropicalSGEMM.sh @@ -0,0 +1,6 @@ +#! /bin/bash + +nvcc -arch=sm_80 TropicalSGemm.cu +./a.out + +rm a.out \ No newline at end of file diff --git a/src/SGEMM/benchmark_GemmKerenls_Tropical.jl b/src/SGEMM/benchmark_GemmKerenls_Tropical.jl new file mode 100644 index 0000000..b31fdbd --- /dev/null +++ b/src/SGEMM/benchmark_GemmKerenls_Tropical.jl @@ -0,0 +1,87 @@ +using GemmKernels + +import CUDA +import InteractiveUtils + +using CUDA +using ForwardDiff +using GemmKernels +using LinearAlgebra +using Dates +using Test + +CUDA.allowscalar(false) + +function try_tropical(M, N, K) + for (A_type, B_type, CD_type, min_dimension) in [(Float32, Float32, Float32, 128)], + transpose_a = [true, false], + transpose_b = [true, false], + (OP_M, OP_N, OP_K) in [(8, 16, 2)] + + a_h = rand(A_type, (M, K)) / sqrt(A_type(K)) + b_h = rand(B_type, (K, N)) / sqrt(B_type(K)) + c_h = rand(CD_type, (M, N)) + d_h = similar(c_h) + + + # Transpose input if necessary + a_h = transpose_a ? transpose(a_h) : a_h + b_h = transpose_b ? transpose(b_h) : b_h + + a = CuArray(a_h) + b = CuArray(b_h) + c = CuArray(c_h) + d = similar(c) + + conf = GemmKernels.get_config( + gemm_shape = (M = M, N = N, K = K), + block_shape = (M = 64, N = 64, K = 32), + operator = Operator.TropicalFPUOp{OP_M, OP_N, OP_K, CD_type, A_type}, + global_a_layout = transpose_a ? Layout.AlignedRowMajor{A_type} : Layout.AlignedColMajor{A_type}, + global_b_layout = transpose_b ? Layout.AlignedRowMajor{B_type} : Layout.AlignedColMajor{B_type}, + + global_c_layout = Layout.AlignedColMajor{CD_type}, + global_d_layout = Layout.AlignedColMajor{CD_type}, + + is_a_col_major = !transpose_a, + is_b_col_major = !transpose_b, + ) + + # this line is used to skip the compiling time + GemmKernels.matmul(a, b, c, d, conf; kernel = Kernel.matmul_pipelined) + n_iter = 10 + elapsed_time = @elapsed @time CUDA.@sync begin + for _ = 1:n_iter + GemmKernels.matmul(a, b, c, d, conf; kernel = Kernel.matmul_pipelined) + end + end + TFlops = (n_iter * M * N * K * 2 / elapsed_time) / 1e9 + @show TFlops, elapsed_time, transpose_a, transpose_b, M, N, K + + + d_c = Array(d) + + # random 1600 points took to test + if transpose_a == transpose_b == false + @testset begin + for _ in 1 : 40 + for _ in 1 : 40 + i = rand(1:M) + j = rand(1:N) + d_h[i, j] = c_h[i, j] + for k in 1 : K + d_h[i, j] = max(a_h[i, k] + b_h[k, j], d_h[i, j]) + end + @test isapprox(d_h[i, j], d_c[i, j]; rtol = sqrt(eps(A_type))) + end + end + end + end + end + return nothing +end + + +try_tropical(2560, 2048, 2048) +try_tropical(2 * 2560, 2 * 2048, 2 * 2048) +try_tropical(4 * 2560, 4 * 2048, 4 * 2048) \ No newline at end of file From b9cb5bd16bf111a569ae8606bdaba4c52916fedf Mon Sep 17 00:00:00 2001 From: xzgao Date: Wed, 5 Jul 2023 08:29:57 +0000 Subject: [PATCH 2/3] relocated all the files --- .gitignore | 1 + .vscode/settings.json | 1 + Artifacts.toml | 6 +++ Project.toml | 6 +++ benchmark/benchmark_CUDA_mapreduce.jl | 20 ++++++++ benchmark/benchmark_CuTropicalGemm.jl | 29 +++++++++++ benchmark/benchmark_CuTropicalGemm_C.sh | 6 +++ .../benchmark_GemmKerenls_Tropical.jl | 16 +++--- src/CuTropicalGEMM.jl | 7 ++- src/SGEMM/CuTropicalSGEMM_example.jl | 46 ------------------ src/SGEMM/JuliaLib_build.sh | 1 - src/SGEMM/TropicalSGemm.so | Bin 909440 -> 0 bytes src/SGEMM/benchmark_CuTropicalSGEMM.sh | 6 --- .../TropicalSGemm.cu => TropicalGemmFP32.cu} | 5 ++ src/TropicalGemm_Cuda_wrapper.jl | 15 ++++++ test/runtests.jl | 3 +- test/test_FP32_matmul.jl | 32 ++++++++++++ 17 files changed, 135 insertions(+), 65 deletions(-) create mode 100644 .vscode/settings.json create mode 100644 Artifacts.toml create mode 100644 benchmark/benchmark_CUDA_mapreduce.jl create mode 100644 benchmark/benchmark_CuTropicalGemm.jl create mode 100644 benchmark/benchmark_CuTropicalGemm_C.sh rename {src/SGEMM => benchmark}/benchmark_GemmKerenls_Tropical.jl (85%) delete mode 100644 src/SGEMM/CuTropicalSGEMM_example.jl delete mode 100644 src/SGEMM/JuliaLib_build.sh delete mode 100755 src/SGEMM/TropicalSGemm.so delete mode 100644 src/SGEMM/benchmark_CuTropicalSGEMM.sh rename src/{SGEMM/TropicalSGemm.cu => TropicalGemmFP32.cu} (98%) create mode 100644 src/TropicalGemm_Cuda_wrapper.jl create mode 100644 test/test_FP32_matmul.jl diff --git a/.gitignore b/.gitignore index 0f84bed..e8f3c1c 100644 --- a/.gitignore +++ b/.gitignore @@ -2,3 +2,4 @@ *.jl.cov *.jl.mem /Manifest.toml +lib \ No newline at end of file diff --git a/.vscode/settings.json b/.vscode/settings.json new file mode 100644 index 0000000..9e26dfe --- /dev/null +++ b/.vscode/settings.json @@ -0,0 +1 @@ +{} \ No newline at end of file diff --git a/Artifacts.toml b/Artifacts.toml new file mode 100644 index 0000000..473b517 --- /dev/null +++ b/Artifacts.toml @@ -0,0 +1,6 @@ +[CUDA_lib] +git-tree-sha1 = "2918fba865582556e219191a7f393c47c2e822e0" + + [[CUDA_lib.download]] + sha256 = "751bf9d1f2921d4176ffb8ed1ddbd59bb60d6a517e6784bb71d61b62357c0007" + url = "https://gist.github.com/ArrogantGao/c38791f143d36d4b2481ac7e4aa4ecce/raw/2918fba865582556e219191a7f393c47c2e822e0.tar.gz" diff --git a/Project.toml b/Project.toml index 0f40dd3..f65924a 100644 --- a/Project.toml +++ b/Project.toml @@ -3,6 +3,12 @@ uuid = "c2b282c3-c9c2-431d-80f7-a1a0561ebe55" authors = ["Xuanzhao Gao and contributors"] version = "1.0.0-DEV" +[deps] +ArtifactUtils = "8b73e784-e7d8-4ea5-973d-377fed4e3bce" +Artifacts = "56f22d72-fd6d-98f1-02f0-08ddc0907c33" +CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba" +Libdl = "8f399da3-3557-5675-b5ff-fb832c97cbdb" + [compat] julia = "1" diff --git a/benchmark/benchmark_CUDA_mapreduce.jl b/benchmark/benchmark_CUDA_mapreduce.jl new file mode 100644 index 0000000..50ff682 --- /dev/null +++ b/benchmark/benchmark_CUDA_mapreduce.jl @@ -0,0 +1,20 @@ +using TropicalNumbers, CUDA, BenchmarkTools + +function map_reduce_benchmark(m::T, n::T, k::T) where{T} + A = Tropical.(CUDA.randn(Float32, (m, k))) + B = Tropical.(CUDA.randn(Float32, (k, n))) + C = Tropical.(CUDA.randn(Float32, (k, n))) + + elapsed_time = @belapsed CUDA.@sync begin + $C = $A * $B + end + + work_load = 2 * m * n * k + flops = work_load / elapsed_time / 1e9 + @show m, n, k, elapsed_time, flops + return nothing +end + +map_reduce_benchmark(2560, 2048, 2048) +map_reduce_benchmark(2 * 2560, 2 * 2048, 2 * 2048) +map_reduce_benchmark(4 * 2560, 4 * 2048, 4 * 2048) \ No newline at end of file diff --git a/benchmark/benchmark_CuTropicalGemm.jl b/benchmark/benchmark_CuTropicalGemm.jl new file mode 100644 index 0000000..2e8082a --- /dev/null +++ b/benchmark/benchmark_CuTropicalGemm.jl @@ -0,0 +1,29 @@ +using CUDA +using BenchmarkTools +using CuTropicalGEMM + +function benchmakr_CuTropicalGemmFP32(m::T, n::T, k::T) where{T} + A = rand(Float32, (m * k)) + B = rand(Float32, (k * n)) + C = rand(Float32, (m * n)) + + CuA = CuArray(A) + CuB = CuArray(B) + CuC = CuArray(C) + + # I found hat @belapsed and CUDA.@sync can not properly benchmark the function from .so lib + elapsed_time = @belapsed CUDA.@sync begin + 1 + 1 + CuTropicalGemmMatmulFP32!($m, $n, $k, $CuA, $CuB, $CuC) + 1 + 1 + end + + work_load = 2 * m * n * k + flops = work_load / elapsed_time / 1e9 + @show m, n, k, elapsed_time, flops + return nothing +end + +benchmakr_CuTropicalGemmFP32(2560, 2048, 2048) +benchmakr_CuTropicalGemmFP32(2 * 2560, 2 * 2048, 2 * 2048) +benchmakr_CuTropicalGemmFP32(4 * 2560, 4 * 2048, 4 * 2048) \ No newline at end of file diff --git a/benchmark/benchmark_CuTropicalGemm_C.sh b/benchmark/benchmark_CuTropicalGemm_C.sh new file mode 100644 index 0000000..a6dd5e6 --- /dev/null +++ b/benchmark/benchmark_CuTropicalGemm_C.sh @@ -0,0 +1,6 @@ +#! /bin/bash + +nvcc -arch=sm_80 ../src/TropicalSGemmFP32.cu +./a.out + +rm a.out \ No newline at end of file diff --git a/src/SGEMM/benchmark_GemmKerenls_Tropical.jl b/benchmark/benchmark_GemmKerenls_Tropical.jl similarity index 85% rename from src/SGEMM/benchmark_GemmKerenls_Tropical.jl rename to benchmark/benchmark_GemmKerenls_Tropical.jl index b31fdbd..6b71d6a 100644 --- a/src/SGEMM/benchmark_GemmKerenls_Tropical.jl +++ b/benchmark/benchmark_GemmKerenls_Tropical.jl @@ -1,13 +1,13 @@ -using GemmKernels +# notice: this code is used to benchmark the Tropical matmul in GemmKernels.jl, which is not yet released in the latest version and only supported in julia@v1.7 +# to run the code, you need to manually download the latest version repo of GemmKernels.jl and activate the enviroment import CUDA import InteractiveUtils using CUDA -using ForwardDiff using GemmKernels using LinearAlgebra -using Dates +using BenchmarkTools using Test CUDA.allowscalar(false) @@ -47,13 +47,9 @@ function try_tropical(M, N, K) is_b_col_major = !transpose_b, ) - # this line is used to skip the compiling time - GemmKernels.matmul(a, b, c, d, conf; kernel = Kernel.matmul_pipelined) - n_iter = 10 - elapsed_time = @elapsed @time CUDA.@sync begin - for _ = 1:n_iter - GemmKernels.matmul(a, b, c, d, conf; kernel = Kernel.matmul_pipelined) - end + n_iter = 1 + elapsed_time = @belapsed CUDA.@sync begin + GemmKernels.matmul($a, $b, $c, $d, $conf; kernel = Kernel.matmul_pipelined) end TFlops = (n_iter * M * N * K * 2 / elapsed_time) / 1e9 @show TFlops, elapsed_time, transpose_a, transpose_b, M, N, K diff --git a/src/CuTropicalGEMM.jl b/src/CuTropicalGEMM.jl index 0caf629..168c111 100644 --- a/src/CuTropicalGEMM.jl +++ b/src/CuTropicalGEMM.jl @@ -1,5 +1,10 @@ module CuTropicalGEMM -# Write your package code here. +export CuTropicalGemmMatmulFP32! + +using CUDA +using Artifacts + +include("TropicalGemm_Cuda_wrapper.jl") end diff --git a/src/SGEMM/CuTropicalSGEMM_example.jl b/src/SGEMM/CuTropicalSGEMM_example.jl deleted file mode 100644 index 135a1cc..0000000 --- a/src/SGEMM/CuTropicalSGEMM_example.jl +++ /dev/null @@ -1,46 +0,0 @@ -using CUDA, Test, BenchmarkTools, Dates - -function CuTropicalGemmMatmul!(m::Integer, n::Integer, k::Integer, A::CuArray{Float32}, B::CuArray{Float32}, C::CuArray{Float32}) - A_ptr = pointer(A); - B_ptr = pointer(B); - C_ptr = pointer(C); - - @ccall "./TropicalSGemm.so".TropicalMatmul(m::Cint, n::Cint, k::Cint, A_ptr::CuPtr{Cfloat}, B_ptr::CuPtr{Cfloat}, C_ptr::CuPtr{Cfloat})::Cvoid - return nothing -end - -# this function will return the (i, j) element of the Tropical result of C + A * B -function TropicalDirectMatmul_ij(i::Integer, j::Integer, m::Integer, n::Integer, k::Integer, A::Array{Float32}, B::Array{Float32}, C::Array{Float32}) - sum = zero(Float32) - for l in 1:k - sum = max(A[(i - 1) * k + l] + B[(l - 1) * n + j], sum) - end - return sum -end - -#init the system -m, n, k = 1024, 1024, 1024 - -A = rand(Float32, (m * k)); -B = rand(Float32, (k * n)); -C = rand(Float32, (m * n)); - -CuA = CuArray(A); -CuB = CuArray(B); -CuC = CuArray(C); - -CuTropicalGemmMatmul!(m, n, k, CuA, CuB, CuC) - -C_result = Array(CuC); - - -# test -@testset begin - for _ in 1:40 - for _ in 1:40 - a = rand(1:m) - b = rand(1:n) - @test TropicalDirectMatmul_ij(a, b, m, n, k, A, B, C) ≈ C_result[(a - 1) * n + b] - end - end -end \ No newline at end of file diff --git a/src/SGEMM/JuliaLib_build.sh b/src/SGEMM/JuliaLib_build.sh deleted file mode 100644 index cccfab5..0000000 --- a/src/SGEMM/JuliaLib_build.sh +++ /dev/null @@ -1 +0,0 @@ -nvcc -Xcompiler -fPIC --shared TropicalSGemm.cu -o TropicalSGemm.so \ No newline at end of file diff --git a/src/SGEMM/TropicalSGemm.so b/src/SGEMM/TropicalSGemm.so deleted file mode 100755 index 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ze?nh!zK;vd|J7e|c}YJZ1$~;<|A!u4^q1Z9^n7~vUlu{n-ex~a;P3vFYbNRLSG)mw zIH|Xw`EdgOhj-cFCH3l;;z9qC@rwlhZysLKm-nP3r)m9voxtxt#R`}7{8@b5e?kev4HZT4T>Q`-~x-mkdcy`ORVZ!bO(kI)q{ya8BEf9E$0xASvO z5Aj_81YXjI0IcD&`wW-e&q+y6d-gVa+S5h!_c@%d)orbor%3l7Rm*dyDVFJiENZJs;2A&iV8O@Q?nL;lC`5dZ6Ss`#*!7o6i6M diff --git a/src/SGEMM/benchmark_CuTropicalSGEMM.sh b/src/SGEMM/benchmark_CuTropicalSGEMM.sh deleted file mode 100644 index 32e9a72..0000000 --- a/src/SGEMM/benchmark_CuTropicalSGEMM.sh +++ /dev/null @@ -1,6 +0,0 @@ -#! /bin/bash - -nvcc -arch=sm_80 TropicalSGemm.cu -./a.out - -rm a.out \ No newline at end of file diff --git a/src/SGEMM/TropicalSGemm.cu b/src/TropicalGemmFP32.cu similarity index 98% rename from src/SGEMM/TropicalSGemm.cu rename to src/TropicalGemmFP32.cu index fae7b15..c015ad6 100644 --- a/src/SGEMM/TropicalSGemm.cu +++ b/src/TropicalGemmFP32.cu @@ -1,3 +1,7 @@ +// This CUDA code is modified based on github repo https://github.com/Yinghan-Li/YHs_Sample, which is under GPL 3.0 License +// To build this code as .so lib, use command +// nvcc -Xcompiler -fPIC --shared TropicalGemmFP32.cu -o TropicalGemmFP32.so + #include #include #include @@ -606,6 +610,7 @@ int main() { long workload = n_iter * long(m) * n * k * 2; double gflops = (double(workload) / 1e9) / (double(ms) / 1e3); + printf("M: %d, N: %d, K: %d\n", M, N, K); printf("TropicalSGemm: %f GFLOPS\n", gflops); printf("time: %f ms\n", ms); cudaMemcpy(h_C, d_C, m * n * sizeof(float), cudaMemcpyDefault); diff --git a/src/TropicalGemm_Cuda_wrapper.jl b/src/TropicalGemm_Cuda_wrapper.jl new file mode 100644 index 0000000..b476de6 --- /dev/null +++ b/src/TropicalGemm_Cuda_wrapper.jl @@ -0,0 +1,15 @@ +export CuTropicalGemmMatmulFP32! + +const FP32_lib = joinpath(artifact"CUDA_lib", "TropicalGemmFP32.so") + + +# A wrapper for FP32 Tropical GEMM +function CuTropicalGemmMatmulFP32!(m::Integer, n::Integer, k::Integer, A::CuArray{Float32}, B::CuArray{Float32}, C::CuArray{Float32}) + A_ptr = pointer(A); + B_ptr = pointer(B); + C_ptr = pointer(C); + + @ccall FP32_lib.TropicalMatmul(m::Cint, n::Cint, k::Cint, A_ptr::CuPtr{Cfloat}, B_ptr::CuPtr{Cfloat}, C_ptr::CuPtr{Cfloat})::Cvoid + + return nothing +end \ No newline at end of file diff --git a/test/runtests.jl b/test/runtests.jl index 5684d84..2089f76 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -1,6 +1,7 @@ using CuTropicalGEMM using Test +using CUDA @testset "CuTropicalGEMM.jl" begin - # Write your tests here. + include("test_FP32_matmul.jl") end diff --git a/test/test_FP32_matmul.jl b/test/test_FP32_matmul.jl new file mode 100644 index 0000000..3742321 --- /dev/null +++ b/test/test_FP32_matmul.jl @@ -0,0 +1,32 @@ +# this function will return the (i, j) element of the Tropical result of C + A * B +function TropicalDirectMatmul_ij(i::Integer, j::Integer, m::Integer, n::Integer, k::Integer, A::Array{Float32}, B::Array{Float32}, C::Array{Float32}) + sum = zero(Float32) + for l in 1:k + sum = max(A[(i - 1) * k + l] + B[(l - 1) * n + j], sum) + end + return sum +end + +@testset "FP32 matmul 1024 * 1024 * 1024, random 1600 terms" begin + m, n, k = 1024, 1024, 1024 + + A = rand(Float32, (m * k)) + B = rand(Float32, (k * n)) + C = rand(Float32, (m * n)) + + CuA = CuArray(A) + CuB = CuArray(B) + CuC = CuArray(C) + + CuTropicalGemmMatmulFP32!(m, n, k, CuA, CuB, CuC) + + C_result = Array(CuC) + + for _ in 1:40 + for _ in 1:40 + a = rand(1:m) + b = rand(1:n) + @test TropicalDirectMatmul_ij(a, b, m, n, k, A, B, C) ≈ C_result[(a - 1) * n + b] + end + end +end \ No newline at end of file From d77cddc5a9875f80d99238d407e26762ae75c3cd Mon Sep 17 00:00:00 2001 From: xzgao Date: Wed, 5 Jul 2023 10:49:15 +0000 Subject: [PATCH 3/3] changed license to GPL 3.0 --- .gitignore | 3 +- .vscode/settings.json | 1 - LICENSE | 695 ++++++++++++++++++++++++++++++++++++++++-- 3 files changed, 676 insertions(+), 23 deletions(-) delete mode 100644 .vscode/settings.json diff --git a/.gitignore b/.gitignore index e8f3c1c..cc4cf6e 100644 --- a/.gitignore +++ b/.gitignore 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Interpretation of Sections 15 and 16. + + If the disclaimer of warranty and limitation of liability provided +above cannot be given local legal effect according to their terms, +reviewing courts shall apply local law that most closely approximates +an absolute waiver of all civil liability in connection with the +Program, unless a warranty or assumption of liability accompanies a +copy of the Program in return for a fee. + + END OF TERMS AND CONDITIONS + + How to Apply These Terms to Your New Programs + + If you develop a new program, and you want it to be of the greatest +possible use to the public, the best way to achieve this is to make it +free software which everyone can redistribute and change under these terms. + + To do so, attach the following notices to the program. It is safest +to attach them to the start of each source file to most effectively +state the exclusion of warranty; and each file should have at least +the "copyright" line and a pointer to where the full notice is found. + + + Copyright (C) + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU General Public License for more details. + + You should have received a copy of the GNU General Public License + along with this program. If not, see . + +Also add information on how to contact you by electronic and paper mail. + + If the program does terminal interaction, make it output a short +notice like this when it starts in an interactive mode: + + Copyright (C) + This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. + This is free software, and you are welcome to redistribute it + under certain conditions; type `show c' for details. + +The hypothetical commands `show w' and `show c' should show the appropriate +parts of the General Public License. Of course, your program's commands +might be different; for a GUI interface, you would use an "about box". + + You should also get your employer (if you work as a programmer) or school, +if any, to sign a "copyright disclaimer" for the program, if necessary. +For more information on this, and how to apply and follow the GNU GPL, see +. + + The GNU General Public License does not permit incorporating your program +into proprietary programs. If your program is a subroutine library, you +may consider it more useful to permit linking proprietary applications with +the library. If this is what you want to do, use the GNU Lesser General +Public License instead of this License. But first, please read +. \ No newline at end of file

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