Commit 1bcc08ff authored by Andriy Roshchenko's avatar Andriy Roshchenko
Browse files

Refactor `load_A_col_major` to follow scale mapping

parent 938256dd
...@@ -80,195 +80,105 @@ static constexpr int32_t vectorSize(const VecT&) ...@@ -80,195 +80,105 @@ static constexpr int32_t vectorSize(const VecT&)
// Define a load function for input A blocks: // Define a load function for input A blocks:
// Size: (BLOCK_M x BLOCK_K) // Size: (BLOCK_M x BLOCK_K)
// ASSUMPTION: // - Data is in column major format
// - We want contiguous BLOCK_M sized column neighbors in register. // - Rows are loaded in contiguous chunks that map to corresponding microscales
// - Data is in col_major format // - Each row is loaded in chunks of size 16 and each thread loads 32 elements
// This means:
// - From A we will load K columns of size BLOCK_M to satisfy our input data
template <typename AType, typename AFragT, int32_t BLOCK_M, int32_t BLOCK_K> template <typename AType, typename AFragT, int32_t BLOCK_M, int32_t BLOCK_K>
__device__ AFragT load_A_col_major(AType const* input_ptr) struct load_A_col_major
{ {
__device__ AFragT operator()(AType const* input_ptr)
{
// clang-format off // clang-format off
// Register Mapping for 16x128: || Register Mapping for 32x64: // Register Mapping for 16x128: || Register Mapping for 32x64:
// Size | BLOCK_M | BLOCK_M | BLOCK_M | BLOCK_M | || Size | BLOCK_M | BLOCK_M | // Size | BLOCK_M | BLOCK_M | BLOCK_M | BLOCK_M | || Size | BLOCK_M | BLOCK_M | |
// M | 0 ... 15 | 0 ... 15 | 0 ... 15 | 0 ... 15 | || M | 0 ... 31 | 0 ... 31 | // M | 0 ... 15 | 0 ... 15 | 0 ... 15 | 0 ... 15 | Vector || M | 0 ... 31 | 0 ... 31 | Vector |
// Thread Id | 0 ... 15 | 16 ... 31 | 32 ... 47 | 48 ... 63 | Vector || Thread Id | 0 ... 31 | 32 ... 63 | Vector // Thread Id | 0 ... 15 | 16 ... 31 | 32 ... 47 | 48 ... 63 | Element || Thread Id | 0 ... 31 | 32 ... 63 | Element|
// Register Element ------------ ------------- ------------ ------------- Element || Register Element ------------ ------------- Element // Register Element |------------|-------------|------------|-------------|-----------|| Register Element |------------|-------------|--------|
// Reg 0 [0:7] | K0 | K32 | K64 | K96 | v[0] || Reg 0 [0:7] | K0 | K32 | v[0] // Reg 0 [0:7] | K0 | K16 | K32 | K48 | v[0] || Reg 0 [0:7] | K0 | K16 | v[0] |
// Reg 0 [8:15] | K1 | K33 | K65 | K97 | v[1] || Reg 0 [8:15] | K1 | K33 | v[1] // Reg 0 [8:15] | K1 | K17 | K33 | K49 | v[1] || Reg 0 [8:15] | K1 | K17 | v[1] |
// Reg 0 [16:23] | K2 | K34 | K66 | K98 | v[2] || Reg 0 [16:23] | K2 | K34 | v[2] // Reg 0 [16:23] | K2 | K18 | K34 | K50 | v[2] || Reg 0 [16:23] | K2 | K18 | v[2] |
// Reg 0 [24:31] | K3 | K35 | K67 | K99 | v[3] || Reg 0 [24:31] | K3 | K35 | v[3] // Reg 0 [24:31] | K3 | K19 | K35 | K51 | v[3] || Reg 0 [24:31] | K3 | K19 | v[3] |
// Reg 1 [0:7] | K4 | K36 | K68 | K100 | v[4] || Reg 1 [0:7] | K4 | K36 | v[4] // Reg 1 [0:7] | K4 | K20 | K36 | K52 | v[4] || Reg 1 [0:7] | K4 | K20 | v[4] |
// Reg 1 [8:15] | K5 | K37 | K69 | K101 | v[5] || Reg 1 [8:15] | K5 | K37 | v[5] // Reg 1 [8:15] | K5 | K21 | K37 | K53 | v[5] || Reg 1 [8:15] | K5 | K21 | v[5] |
// Reg 1 [16:23] | K6 | K38 | K70 | K102 | v[6] || Reg 1 [16:23] | K6 | K38 | v[6] // Reg 1 [16:23] | K6 | K22 | K38 | K54 | v[6] || Reg 1 [16:23] | K6 | K22 | v[6] |
// Reg 1 [24:31] | K7 | K39 | K71 | K103 | v[7] || Reg 1 [24:31] | K7 | K39 | v[7] // Reg 1 [24:31] | K7 | K23 | K39 | K55 | v[7] || Reg 1 [24:31] | K7 | K23 | v[7] |
// Reg 2 [0:7] | K8 | K40 | K72 | K104 | v[8] || Reg 2 [0:7] | K8 | K40 | v[8] // Reg 2 [0:7] | K8 | K24 | K40 | K56 | v[8] || Reg 2 [0:7] | K8 | K24 | v[8] |
// Reg 2 [8:15] | K9 | K41 | K73 | K105 | v[9] || Reg 2 [8:15] | K9 | K41 | v[9] // Reg 2 [8:15] | K9 | K25 | K41 | K57 | v[9] || Reg 2 [8:15] | K9 | K25 | v[9] |
// Reg 2 [16:23] | K10 | K42 | K74 | K106 | v[10] || Reg 2 [16:23] | K10 | K42 | v[10] // Reg 2 [16:23] | K10 | K26 | K42 | K58 | v[10] || Reg 2 [16:23] | K10 | K26 | v[10] |
// Reg 2 [24:31] | K11 | K43 | K75 | K107 | v[11] || Reg 2 [24:31] | K11 | K43 | v[11] // Reg 2 [24:31] | K11 | K27 | K43 | K59 | v[11] || Reg 2 [24:31] | K11 | K27 | v[11] |
// Reg 3 [0:7] | K12 | K44 | K76 | K108 | v[12] || Reg 3 [0:7] | K12 | K44 | v[12] // Reg 3 [0:7] | K12 | K28 | K44 | K60 | v[12] || Reg 3 [0:7] | K12 | K28 | v[12] |
// Reg 3 [8:15] | K13 | K45 | K77 | K109 | v[13] || Reg 3 [8:15] | K13 | K45 | v[13] // Reg 3 [8:15] | K13 | K29 | K45 | K61 | v[13] || Reg 3 [8:15] | K13 | K29 | v[13] |
// Reg 3 [16:23] | K14 | K46 | K78 | K110 | v[14] || Reg 3 [16:23] | K14 | K46 | v[14] // Reg 3 [16:23] | K14 | K30 | K46 | K62 | v[14] || Reg 3 [16:23] | K14 | K30 | v[14] |
// Reg 3 [24:31] | K15 | K47 | K79 | K111 | v[15] || Reg 3 [24:31] | K15 | K47 | v[15] // Reg 3 [24:31] | K15 | K31 | K47 | K63 | v[15] || Reg 3 [24:31] | K15 | K31 | v[15] |
// Reg 4 [0:7] | K16 | K48 | K80 | K112 | v[16] || Reg 4 [0:7] | K16 | K48 | v[16] // Reg 4 [0:7] | K64 | K80 | K96 | K112 | v[16] || Reg 4 [0:7] | K32 | K48 | v[16] |
// Reg 4 [8:15] | K17 | K49 | K81 | K113 | v[17] || Reg 4 [8:15] | K17 | K49 | v[17] // Reg 4 [8:15] | K65 | K81 | K97 | K113 | v[17] || Reg 4 [8:15] | K33 | K49 | v[17] |
// Reg 4 [16:23] | K18 | K50 | K82 | K114 | v[18] || Reg 4 [16:23] | K18 | K50 | v[18] // Reg 4 [16:23] | K66 | K82 | K98 | K114 | v[18] || Reg 4 [16:23] | K34 | K50 | v[18] |
// Reg 4 [24:31] | K19 | K51 | K83 | K115 | v[19] || Reg 4 [24:31] | K19 | K51 | v[19] // Reg 4 [24:31] | K67 | K83 | K99 | K115 | v[19] || Reg 4 [24:31] | K35 | K51 | v[19] |
// Reg 5 [0:7] | K20 | K52 | K84 | K116 | v[20] || Reg 5 [0:7] | K20 | K52 | v[20] // Reg 5 [0:7] | K68 | K84 | K100 | K116 | v[20] || Reg 5 [0:7] | K36 | K52 | v[20] |
// Reg 5 [8:15] | K21 | K53 | K85 | K117 | v[21] || Reg 5 [8:15] | K21 | K53 | v[21] // Reg 5 [8:15] | K69 | K85 | K101 | K117 | v[21] || Reg 5 [8:15] | K37 | K53 | v[21] |
// Reg 5 [16:23] | K22 | K54 | K86 | K118 | v[22] || Reg 5 [16:23] | K22 | K54 | v[22] // Reg 5 [16:23] | K70 | K86 | K102 | K118 | v[22] || Reg 5 [16:23] | K38 | K54 | v[22] |
// Reg 5 [24:31] | K23 | K55 | K87 | K119 | v[23] || Reg 5 [24:31] | K23 | K55 | v[23] // Reg 5 [24:31] | K71 | K87 | K103 | K119 | v[23] || Reg 5 [24:31] | K39 | K55 | v[23] |
// Reg 6 [0:7] | K24 | K56 | K88 | K120 | v[24] || Reg 6 [0:7] | K24 | K56 | v[24] // Reg 6 [0:7] | K72 | K88 | K104 | K120 | v[24] || Reg 6 [0:7] | K40 | K56 | v[24] |
// Reg 6 [8:15] | K25 | K57 | K89 | K121 | v[25] || Reg 6 [8:15] | K25 | K57 | v[25] // Reg 6 [8:15] | K73 | K89 | K105 | K121 | v[25] || Reg 6 [8:15] | K41 | K57 | v[25] |
// Reg 6 [16:23] | K26 | K58 | K90 | K122 | v[26] || Reg 6 [16:23] | K26 | K58 | v[26] // Reg 6 [16:23] | K74 | K90 | K106 | K122 | v[26] || Reg 6 [16:23] | K42 | K58 | v[26] |
// Reg 6 [24:31] | K27 | K59 | K91 | K123 | v[27] || Reg 6 [24:31] | K27 | K59 | v[27] // Reg 6 [24:31] | K75 | K91 | K107 | K123 | v[27] || Reg 6 [24:31] | K43 | K59 | v[27] |
// Reg 7 [0:7] | K28 | K60 | K92 | K124 | v[28] || Reg 7 [0:7] | K28 | K60 | v[28] // Reg 7 [0:7] | K76 | K92 | K108 | K124 | v[28] || Reg 7 [0:7] | K44 | K60 | v[28] |
// Reg 7 [8:15] | K29 | K61 | K93 | K125 | v[29] || Reg 7 [8:15] | K29 | K61 | v[29] // Reg 7 [8:15] | K77 | K93 | K109 | K125 | v[29] || Reg 7 [8:15] | K45 | K61 | v[29] |
// Reg 7 [16:23] | K30 | K62 | K94 | K126 | v[30] || Reg 7 [16:23] | K30 | K62 | v[30] // Reg 7 [16:23] | K78 | K94 | K110 | K126 | v[30] || Reg 7 [16:23] | K46 | K62 | v[30] |
// Reg 7 [24:31] | K31 | K63 | K95 | K127 | v[31] || Reg 7 [24:31] | K31 | K63 | v[31] // Reg 7 [24:31] | K79 | K95 | K111 | K127 | v[31] || Reg 7 [24:31] | K47 | K63 | v[31] |
// clang-format on // clang-format on
// Here we want to load a BLOCK_M x BLOCK_K block of data. static constexpr int32_t WAVE_SIZE = 64;
static constexpr uint32_t VW = vectorSize(AFragT{});
using ARawT = typename scalar_type<AFragT>::type; // Here we want to load from rows of A in chunks of 16 elements each.
using AScalarFragT = vector_type<ARawT, VW>::type; static constexpr uint32_t chunk_size = 16;
// each chunk is separated by offset
static constexpr uint32_t chunk_offset = chunk_size * WAVE_SIZE / BLOCK_M;
// To start the loading process, let's visualize in 2D coords. // To start the loading process, let's visualize in 2D coords.
// Each thread will load 32 elements. // Each thread will load 32 elements.
// We need to know where they start, and where the next elements are. // We need to know where they start, and where the next elements are.
auto startCoord2D = std::make_pair(threadIdx.x % BLOCK_M, // Row auto startCoord2D =
(threadIdx.x / BLOCK_M) * VW); // Col std::make_pair(threadIdx.x % BLOCK_M, // Row {0-31} | {0-15}
auto stepCoord2D = std::make_pair(0u, 1u); (threadIdx.x / BLOCK_M) * chunk_size); // Col {0, 16} | {0, 16, 32, 48}
auto minorStepCoord2D = std::make_pair(0u, 1u); // read rows
auto majorStepCoord2D = std::make_pair(0, chunk_offset); // read a chunk from a row
// Flatten to 1D col_major offsets. // Flatten to 1D col_major offsets.
auto col_major = [](auto const& coord, auto ld) { return coord.first + coord.second * ld; }; auto col_major = [](auto const& coord, auto ld) { return coord.first + coord.second * ld; };
// BLOCK_M is a stride in A matrix // BLOCK_M is a stride in A matrix
auto startOffset = col_major(startCoord2D, BLOCK_M); auto startOffset = col_major(startCoord2D, BLOCK_M);
auto kOffset = col_major(stepCoord2D, BLOCK_M); auto kMinorOffset = col_major(minorStepCoord2D, BLOCK_M);
auto kMajorOffset = col_major(majorStepCoord2D, BLOCK_M);
using ARawT = typename scalar_type<AFragT>::type;
using AScalarFragT = vector_type<ARawT, vectorSize(AFragT{})>::type;
// kOffset == BLOCK_M AScalarFragT fragA{};
// This means every BLOCK_M element is loaded into output vector
auto fragA = AScalarFragT{}; #pragma unroll
#pragma unroll VW for(int chunk = 0; chunk < 2; chunk++)
for(uint32_t i = 0; i < VW; i++) {
#pragma unroll
for(uint32_t i = 0; i < chunk_size; i++)
{ {
fragA[i] = bit_cast<ARawT>(input_ptr[startOffset + i * kOffset]); fragA[chunk * chunk_size + i] = bit_cast<ARawT>(
input_ptr[startOffset + chunk * kMajorOffset + i * kMinorOffset]);
}
} }
return fragA; return fragA;
} }
};
// Define a load function for input A blocks: // Define a load function for input A blocks:
// Size: (BLOCK_M x BLOCK_K) // Size: (BLOCK_M x BLOCK_K)
// ASSUMPTION:
// - We want contiguous BLOCK_M sized column neighbors in register.
// - Data is in row major format // - Data is in row major format
// This means: // - Rows are loaded in contiguous chunks that map to corresponding microscales
// - From A we will load BLOCK_M rows of size K to satisfy our input data // - Each row is loaded in chunks of size 16 and each thread loads 32 elements
// template <typename AType, typename AFragT, int32_t BLOCK_M, int32_t BLOCK_K>
// struct load_A_row_major
// {
// __device__ AFragT operator()(AType const* input_ptr)
// {
// // clang-format off
// // Register Mapping for 16x128: ||
// Register Mapping for 32x64:
// // Size | BLOCK_M | BLOCK_M | BLOCK_M | BLOCK_M | ||
// Size | BLOCK_M | BLOCK_M |
// // M | 0 ... 15 | 0 ... 15 | 0 ... 15 | 0 ... 15 | || M
// | 0 ... 31 | 0 ... 31 |
// // Thread Id | 0 ... 15 | 16 ... 31 | 32 ... 47 | 48 ... 63 | Vector ||
// Thread Id | 0 ... 31 | 32 ... 63 | Vector
// // Register Element ------------ ------------- ------------ ------------- Element ||
// Register Element ------------ ------------- Element
// // Reg 0 [0:7] | K0 | K32 | K64 | K96 | v[0] || Reg
// 0 [0:7] | K0 | K32 | v[0]
// // Reg 0 [8:15] | K1 | K33 | K65 | K97 | v[1] || Reg
// 0 [8:15] | K1 | K33 | v[1]
// // Reg 0 [16:23] | K2 | K34 | K66 | K98 | v[2] || Reg
// 0 [16:23] | K2 | K34 | v[2]
// // Reg 0 [24:31] | K3 | K35 | K67 | K99 | v[3] || Reg
// 0 [24:31] | K3 | K35 | v[3]
// // Reg 1 [0:7] | K4 | K36 | K68 | K100 | v[4] || Reg
// 1 [0:7] | K4 | K36 | v[4]
// // Reg 1 [8:15] | K5 | K37 | K69 | K101 | v[5] || Reg
// 1 [8:15] | K5 | K37 | v[5]
// // Reg 1 [16:23] | K6 | K38 | K70 | K102 | v[6] || Reg
// 1 [16:23] | K6 | K38 | v[6]
// // Reg 1 [24:31] | K7 | K39 | K71 | K103 | v[7] || Reg
// 1 [24:31] | K7 | K39 | v[7]
// // Reg 2 [0:7] | K8 | K40 | K72 | K104 | v[8] || Reg
// 2 [0:7] | K8 | K40 | v[8]
// // Reg 2 [8:15] | K9 | K41 | K73 | K105 | v[9] || Reg
// 2 [8:15] | K9 | K41 | v[9]
// // Reg 2 [16:23] | K10 | K42 | K74 | K106 | v[10] || Reg
// 2 [16:23] | K10 | K42 | v[10]
// // Reg 2 [24:31] | K11 | K43 | K75 | K107 | v[11] || Reg
// 2 [24:31] | K11 | K43 | v[11]
// // Reg 3 [0:7] | K12 | K44 | K76 | K108 | v[12] || Reg
// 3 [0:7] | K12 | K44 | v[12]
// // Reg 3 [8:15] | K13 | K45 | K77 | K109 | v[13] || Reg
// 3 [8:15] | K13 | K45 | v[13]
// // Reg 3 [16:23] | K14 | K46 | K78 | K110 | v[14] || Reg
// 3 [16:23] | K14 | K46 | v[14]
// // Reg 3 [24:31] | K15 | K47 | K79 | K111 | v[15] || Reg
// 3 [24:31] | K15 | K47 | v[15]
// // Reg 4 [0:7] | K16 | K48 | K80 | K112 | v[16] || Reg
// 4 [0:7] | K16 | K48 | v[16]
// // Reg 4 [8:15] | K17 | K49 | K81 | K113 | v[17] || Reg
// 4 [8:15] | K17 | K49 | v[17]
// // Reg 4 [16:23] | K18 | K50 | K82 | K114 | v[18] || Reg
// 4 [16:23] | K18 | K50 | v[18]
// // Reg 4 [24:31] | K19 | K51 | K83 | K115 | v[19] || Reg
// 4 [24:31] | K19 | K51 | v[19]
// // Reg 5 [0:7] | K20 | K52 | K84 | K116 | v[20] || Reg
// 5 [0:7] | K20 | K52 | v[20]
// // Reg 5 [8:15] | K21 | K53 | K85 | K117 | v[21] || Reg
// 5 [8:15] | K21 | K53 | v[21]
// // Reg 5 [16:23] | K22 | K54 | K86 | K118 | v[22] || Reg
// 5 [16:23] | K22 | K54 | v[22]
// // Reg 5 [24:31] | K23 | K55 | K87 | K119 | v[23] || Reg
// 5 [24:31] | K23 | K55 | v[23]
// // Reg 6 [0:7] | K24 | K56 | K88 | K120 | v[24] || Reg
// 6 [0:7] | K24 | K56 | v[24]
// // Reg 6 [8:15] | K25 | K57 | K89 | K121 | v[25] || Reg
// 6 [8:15] | K25 | K57 | v[25]
// // Reg 6 [16:23] | K26 | K58 | K90 | K122 | v[26] || Reg
// 6 [16:23] | K26 | K58 | v[26]
// // Reg 6 [24:31] | K27 | K59 | K91 | K123 | v[27] || Reg
// 6 [24:31] | K27 | K59 | v[27]
// // Reg 7 [0:7] | K28 | K60 | K92 | K124 | v[28] || Reg
// 7 [0:7] | K28 | K60 | v[28]
// // Reg 7 [8:15] | K29 | K61 | K93 | K125 | v[29] || Reg
// 7 [8:15] | K29 | K61 | v[29]
// // Reg 7 [16:23] | K30 | K62 | K94 | K126 | v[30] || Reg
// 7 [16:23] | K30 | K62 | v[30]
// // Reg 7 [24:31] | K31 | K63 | K95 | K127 | v[31] || Reg
// 7 [24:31] | K31 | K63 | v[31]
// // clang-format on
// // Here we want to load a BLOCK_M x BLOCK_K block of data.
// static constexpr uint32_t VW = vectorSize(AFragT{});
// // To start the loading process, let's visualize in 2D coords.
// // Each thread will load 32 elements.
// // We need to know where they start, and where the next elements are.
// auto startCoord2D = std::make_pair(threadIdx.x % BLOCK_M, // Row
// (threadIdx.x / BLOCK_M) * VW); // Col
// // Flatten to 1D row_major offsets.
// auto row_major = [](auto const& coord, auto ld) { return coord.first * ld + coord.second;
// };
// // BLOCK_K is a stride in A matrix
// auto startOffset = row_major(startCoord2D, BLOCK_K);
// auto const* fragPtr = reinterpret_cast<AFragT const*>(input_ptr + startOffset);
// return *fragPtr;
// }
// }
template <typename AType, typename AFragT, int32_t BLOCK_M, int32_t BLOCK_K> template <typename AType, typename AFragT, int32_t BLOCK_M, int32_t BLOCK_K>
struct load_A_row_major struct load_A_row_major
{ {
...@@ -805,7 +715,7 @@ __global__ void matmul(const AType* a, const BType* b, CType* c) ...@@ -805,7 +715,7 @@ __global__ void matmul(const AType* a, const BType* b, CType* c)
// Load the inputs. // Load the inputs.
// A = col major, BLOCK_M x BLOCK_K // A = col major, BLOCK_M x BLOCK_K
fragA = load_A_col_major<AType, AFragT, BLOCK_M, BLOCK_K>(a); fragA = load_A_col_major<AType, AFragT, BLOCK_M, BLOCK_K>{}(a);
// B = col major, BLOCK_K x BLOCK_N // B = col major, BLOCK_K x BLOCK_N
fragB = load_B_col_major<BType, BFragT, BLOCK_K, BLOCK_N>(b); fragB = load_B_col_major<BType, BFragT, BLOCK_K, BLOCK_N>(b);
......
a(0,0) is scaled from thread 0.000000
a(0,1) is scaled from thread 0.000000
a(0,2) is scaled from thread 0.000000
a(0,3) is scaled from thread 0.000000
a(0,4) is scaled from thread 0.000000
a(0,5) is scaled from thread 0.000000
a(0,6) is scaled from thread 0.000000
a(0,7) is scaled from thread 0.000000
a(0,8) is scaled from thread 0.000000
a(0,9) is scaled from thread 0.000000
a(0,10) is scaled from thread 0.000000
a(0,11) is scaled from thread 0.000000
a(0,12) is scaled from thread 0.000000
a(0,13) is scaled from thread 0.000000
a(0,14) is scaled from thread 0.000000
a(0,15) is scaled from thread 0.000000
a(0,16) is scaled from thread 32.000000
a(0,17) is scaled from thread 32.000000
a(0,18) is scaled from thread 32.000000
a(0,19) is scaled from thread 32.000000
a(0,20) is scaled from thread 32.000000
a(0,21) is scaled from thread 32.000000
a(0,22) is scaled from thread 32.000000
a(0,23) is scaled from thread 32.000000
a(0,24) is scaled from thread 32.000000
a(0,25) is scaled from thread 32.000000
a(0,26) is scaled from thread 32.000000
a(0,27) is scaled from thread 32.000000
a(0,28) is scaled from thread 32.000000
a(0,29) is scaled from thread 32.000000
a(0,30) is scaled from thread 32.000000
a(0,31) is scaled from thread 32.000000
a(0,32) is scaled from thread 0.000000
a(0,33) is scaled from thread 0.000000
a(0,34) is scaled from thread 0.000000
a(0,35) is scaled from thread 0.000000
a(0,36) is scaled from thread 0.000000
a(0,37) is scaled from thread 0.000000
a(0,38) is scaled from thread 0.000000
a(0,39) is scaled from thread 0.000000
a(0,40) is scaled from thread 0.000000
a(0,41) is scaled from thread 0.000000
a(0,42) is scaled from thread 0.000000
a(0,43) is scaled from thread 0.000000
a(0,44) is scaled from thread 0.000000
a(0,45) is scaled from thread 0.000000
a(0,46) is scaled from thread 0.000000
a(0,47) is scaled from thread 0.000000
a(0,48) is scaled from thread 32.000000
a(0,49) is scaled from thread 32.000000
a(0,50) is scaled from thread 32.000000
a(0,51) is scaled from thread 32.000000
a(0,52) is scaled from thread 32.000000
a(0,53) is scaled from thread 32.000000
a(0,54) is scaled from thread 32.000000
a(0,55) is scaled from thread 32.000000
a(0,56) is scaled from thread 32.000000
a(0,57) is scaled from thread 32.000000
a(0,58) is scaled from thread 32.000000
a(0,59) is scaled from thread 32.000000
a(0,60) is scaled from thread 32.000000
a(0,61) is scaled from thread 32.000000
a(0,62) is scaled from thread 32.000000
a(0,63) is scaled from thread 32.000000
a(0,64) is scaled from thread 16.000000
a(0,65) is scaled from thread 16.000000
a(0,66) is scaled from thread 16.000000
a(0,67) is scaled from thread 16.000000
a(0,68) is scaled from thread 16.000000
a(0,69) is scaled from thread 16.000000
a(0,70) is scaled from thread 16.000000
a(0,71) is scaled from thread 16.000000
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