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multi_reduction.mlir
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// Tested on Intel(R) Xeon(R) CPU @ 2.00GHz w/ AVX512
func @compute(%input : memref<${M}xf32>, %filter : memref<${K}xf32>, %output : memref<${N}xf32>)
attributes { passthrough = ["inline" ${TARGET_CPU} ${PREFER_VECTOR_WIDTH}]} {
call @compute_v${FN}(%input, %filter, %output) : (memref<${M}xf32>, memref<${K}xf32>, memref<${N}xf32>) -> ()
return
}
// Size 18 * 3 -> 16
// ~18 GFlops/s when inlined
// Iterations: 100
// Instructions: 1200
// Total Cycles: 527
// Total uOps: 2500
// Dispatch Width: 6
// uOps Per Cycle: 4.74
// IPC: 2.28
// Block RThroughput: 5.0
func @compute_v1(%input : memref<${M}xf32>, %filter : memref<${K}xf32>, %output : memref<${N}xf32>)
attributes { passthrough = ["inline" ${TARGET_CPU} ${PREFER_VECTOR_WIDTH}]} {
%c0 = constant 0 : index
%c1 = constant 1 : index
%c2 = constant 2 : index
%c0i32 = constant 0 : i32
%c1i32 = constant 1 : i32
%c2i32 = constant 2 : i32
%cf0 = constant 0.0 : f32
// %acc = constant dense<0.0> : vector<${N}xf32>
%acc = vector.transfer_read %output[%c0], %cf0 : memref<${N}xf32>, vector<${N}xf32>
%f0 = memref.load %filter[%c0] : memref<${K}xf32>
%f1 = memref.load %filter[%c1] : memref<${K}xf32>
%f2 = memref.load %filter[%c2] : memref<${K}xf32>
%i0 = vector.transfer_read %input[%c0], %cf0 : memref<${M}xf32>, vector<${N}xf32>
%i1 = vector.transfer_read %input[%c1], %cf0 : memref<${M}xf32>, vector<${N}xf32>
%i2 = vector.transfer_read %input[%c2], %cf0 : memref<${M}xf32>, vector<${N}xf32>
%b0 = vector.broadcast %f0 : f32 to vector<${N}xf32>
%b1 = vector.broadcast %f1 : f32 to vector<${N}xf32>
%b2 = vector.broadcast %f2 : f32 to vector<${N}xf32>
%acc0 = vector.fma %i0, %b0, %acc : vector<${N}xf32>
%acc1 = vector.fma %i1, %b1, %acc0 : vector<${N}xf32>
%acc2 = vector.fma %i2, %b2, %acc1 : vector<${N}xf32>
vector.store %acc2, %output[%c0] : memref<${N}xf32>, vector<${N}xf32>
return
}
// Size 18 * 3 -> 16
// ~18 GFlops/s when inlined
// Iterations: 100
// Instructions: 1400
// Total Cycles: 530
// Total uOps: 2600
// Dispatch Width: 6
// uOps Per Cycle: 4.91
// IPC: 2.64
// Block RThroughput: 5.0
func @compute_v2(%input : memref<${M}xf32>, %filter : memref<${K}xf32>, %output : memref<${N}xf32>)
attributes { passthrough = ["inline" ${TARGET_CPU} ${PREFER_VECTOR_WIDTH}]} {
%c0 = constant 0 : index
%c1 = constant 1 : index
%c2 = constant 2 : index
%c0i32 = constant 0 : i32
%c1i32 = constant 1 : i32
%c2i32 = constant 2 : i32
%cf0 = constant 0.0 : f32
// %acc = constant dense<0.0> : vector<${N}xf32>
%acc = vector.transfer_read %output[%c0], %cf0 : memref<${N}xf32>, vector<${N}xf32>
%f = vector.transfer_read %filter[%c0], %cf0 : memref<${K}xf32>, vector<${K}xf32>
%f0 = vector.extractelement %f[%c0i32 : i32] : vector<${K}xf32>
%f1 = vector.extractelement %f[%c1i32 : i32] : vector<${K}xf32>
%f2 = vector.extractelement %f[%c2i32 : i32] : vector<${K}xf32>
%i0 = vector.transfer_read %input[%c0], %cf0 : memref<${M}xf32>, vector<${N}xf32>
%i1 = vector.transfer_read %input[%c1], %cf0 : memref<${M}xf32>, vector<${N}xf32>
%i2 = vector.transfer_read %input[%c2], %cf0 : memref<${M}xf32>, vector<${N}xf32>
%b0 = vector.broadcast %f0 : f32 to vector<${N}xf32>
%b1 = vector.broadcast %f1 : f32 to vector<${N}xf32>
%b2 = vector.broadcast %f2 : f32 to vector<${N}xf32>
%acc0 = vector.fma %i0, %b0, %acc : vector<${N}xf32>
%acc1 = vector.fma %i1, %b1, %acc0 : vector<${N}xf32>
%acc2 = vector.fma %i2, %b2, %acc1 : vector<${N}xf32>
vector.store %acc2, %output[%c0] : memref<${N}xf32>, vector<${N}xf32>
return
}
// Size 18 * 3 -> 16
// ~22 GFlops/s when inlined
// Iterations: 100
// Instructions: 2100
// Total Cycles: 632
// Total uOps: 3300
// Dispatch Width: 6
// uOps Per Cycle: 5.22
// IPC: 3.32
// Block RThroughput: 5.5
func @compute_v3(%input : memref<${M}xf32>, %filter : memref<${K}xf32>, %output : memref<${N}xf32>)
attributes { passthrough = ["inline" ${TARGET_CPU} ${PREFER_VECTOR_WIDTH}]} {
%c0 = constant 0 : index
%c1 = constant 1 : index
%c2 = constant 2 : index
%cf0 = constant 0.0 : f32
// %acc = constant dense<0.0> : vector<${N}xf32>
%acc = vector.transfer_read %output[%c0], %cf0 : memref<${N}xf32>, vector<${N}xf32>
%in0 = vector.transfer_read %input[%c0], %cf0 : memref<${M}xf32>, vector<${M}xf32>
%f = vector.transfer_read %filter[%c0], %cf0 : memref<${K}xf32>, vector<${K}xf32>
%in1 = vector.shuffle %in0, %in0
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15,
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17] : vector<${M}xf32>, vector<${M}xf32>
%in = vector.shape_cast %in1 : vector<48xf32> to vector<${K}x${N}xf32>
%6 = vector.broadcast %f : vector<${K}xf32> to vector<${N}x${K}xf32>
%7 = vector.transpose %6, [1, 0] : vector<${N}x${K}xf32> to vector<${K}x${N}xf32>
// vector.print %7 : vector<${K}x${N}xf32>
// %v5 = vector.multi_reduction #vector.kind<mul>, %v4 [0] : vector<${2x${K}x${N}xf32> to vector<${K}x${N}xf32>
%v5 = mulf %in, %7 : vector<${K}x${N}xf32>
// %v6 = vector.multi_reduction #vector.kind<add>, %v5 [0] : vector<${K}x${N}xf32> to vector<${N}xf32>
%ve0 = vector.extract %v5[0] : vector<${K}x${N}xf32>
%ve1 = vector.extract %v5[1] : vector<${K}x${N}xf32>
%ve2 = vector.extract %v5[2] : vector<${K}x${N}xf32>
%res0 = addf %acc, %ve0 : vector<${N}xf32>
%res1 = addf %ve1, %ve2 : vector<${N}xf32>
%res = addf %res0, %res1 : vector<${N}xf32>
vector.transfer_write %res, %output[%c0] : vector<${N}xf32> , memref<${N}xf32>
return
}
// Size 18 * 3 -> 16
// ~21 GFlops/s when inlined
// Iterations: 100
// Instructions: 1700
// Total Cycles: 630
// Total uOps: 3000
// Dispatch Width: 6
// uOps Per Cycle: 4.76
// IPC: 2.70
// Block RThroughput: 5.5
func @compute_v4(%input : memref<${M}xf32>, %filter : memref<${K}xf32>, %output : memref<${N}xf32>)
attributes { passthrough = ["inline" ${TARGET_CPU} ${PREFER_VECTOR_WIDTH}]} {
%c0 = constant 0 : index
%c1 = constant 1 : index
%c2 = constant 2 : index
%cf0 = constant 0.0 : f32
// %acc = constant dense<0.0> : vector<${N}xf32>
%acc = vector.transfer_read %output[%c0], %cf0 : memref<${N}xf32>, vector<${N}xf32>
%in0 = vector.transfer_read %input[%c0], %cf0 : memref<${M}xf32>, vector<${M}xf32>
%f0 = memref.load %filter[%c0] : memref<${K}xf32>
%f1 = memref.load %filter[%c1] : memref<${K}xf32>
%f2 = memref.load %filter[%c2] : memref<${K}xf32>
%b = vector.broadcast %cf0 : f32 to vector<${K}xf32>
%b0 = vector.insert %f0, %b[0] : f32 into vector<${K}xf32>
%b1 = vector.insert %f1, %b0[1] : f32 into vector<${K}xf32>
%f = vector.insert %f2, %b1[2] : f32 into vector<${K}xf32>
%in1 = vector.shuffle %in0, %in0
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15,
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17] : vector<${M}xf32>, vector<${M}xf32>
%in = vector.shape_cast %in1 : vector<48xf32> to vector<${K}x${N}xf32>
%6 = vector.broadcast %f : vector<${K}xf32> to vector<${N}x${K}xf32>
%7 = vector.transpose %6, [1, 0] : vector<${N}x${K}xf32> to vector<${K}x${N}xf32>
// %v5 = vector.multi_reduction #vector.kind<mul>, %v4 [0] : vector<2x${K}x${N}xf32> to vector<${K}x${N}xf32>
%v5 = mulf %in, %7 : vector<${K}x${N}xf32>
// %v6 = vector.multi_reduction #vector.kind<add>, %v5 [0] : vector<${K}x${N}xf32> to vector<${N}xf32>
%ve0 = vector.extract %v5[0] : vector<${K}x${N}xf32>
%ve1 = vector.extract %v5[1] : vector<${K}x${N}xf32>
%ve2 = vector.extract %v5[2] : vector<${K}x${N}xf32>
%res0 = addf %acc, %ve0 : vector<${N}xf32>
%res1 = addf %ve1, %ve2 : vector<${N}xf32>
%res = addf %res0, %res1 : vector<${N}xf32>
vector.transfer_write %res, %output[%c0] : vector<${N}xf32> , memref<${N}xf32>
return
}
// Size 18 * 3 -> 16
// ~20-23 GFlops/s when inlined
// Iterations: 100
// Instructions: 2100
// Total Cycles: 632
// Total uOps: 3300
// Dispatch Width: 6
// uOps Per Cycle: 5.22
// IPC: 3.32
// Block RThroughput: 5.5
func @compute_v5(%input : memref<${M}xf32>, %filter : memref<${K}xf32>, %output : memref<${N}xf32>)
attributes { passthrough = ["inline" ${TARGET_CPU} ${PREFER_VECTOR_WIDTH}]} {
%c0 = constant 0 : index
%c1 = constant 1 : index
%c2 = constant 2 : index
%cf0 = constant 0.0 : f32
// %acc = constant dense<0.0> : vector<${N}xf32>
%acc = vector.transfer_read %output[%c0], %cf0 : memref<${N}xf32>, vector<${N}xf32>
%f = vector.transfer_read %filter[%c0], %cf0 : memref<${K}xf32>, vector<${K}xf32>
%in0 = vector.transfer_read %input[%c0], %cf0 : memref<${M}xf32>, vector<${M}xf32>
%in1 = vector.shuffle %in0, %in0
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15,
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17] : vector<${M}xf32>, vector<${M}xf32>
%in = vector.shape_cast %in1 : vector<48xf32> to vector<${K}x${N}xf32>
%6 = vector.broadcast %f : vector<${K}xf32> to vector<${N}x${K}xf32>
%7 = vector.transpose %6, [1, 0] : vector<${N}x${K}xf32> to vector<${K}x${N}xf32>
// %v5 = vector.multi_reduction #vector.kind<mul>, %v4 [0] : vector<2x${K}x${N}xf32> to vector<${K}x${N}xf32>
%v5 = mulf %in, %7 : vector<${K}x${N}xf32>
// %v6 = vector.multi_reduction #vector.kind<add>, %v5 [0] : vector<${K}x${N}xf32> to vector<${N}xf32>
%ve0 = vector.extract %v5[0] : vector<${K}x${N}xf32>
%ve1 = vector.extract %v5[1] : vector<${K}x${N}xf32>
%ve2 = vector.extract %v5[2] : vector<${K}x${N}xf32>
%res0 = addf %acc, %ve0 : vector<${N}xf32>
%res1 = addf %ve1, %ve2 : vector<${N}xf32>
%res = addf %res0, %res1 : vector<${N}xf32>
vector.transfer_write %res, %output[%c0] : vector<${N}xf32> , memref<${N}xf32>
return
}
// Size 18 * 3 -> 16
// ~3.5 GFlops/s when inlined
// Iterations: 100
// Instructions: 12800
// Total Cycles: 6734
// Total uOps: 14000
// Dispatch Width: 6
// uOps Per Cycle: 2.08
// IPC: 1.90
// Block RThroughput: 64.0
func @compute_v6(%input : memref<${M}xf32>, %filter : memref<${K}xf32>, %output : memref<${N}xf32>)
attributes { passthrough = ["inline" ${TARGET_CPU} ${PREFER_VECTOR_WIDTH}]} {
%c0 = constant 0 : index
%c1 = constant 1 : index
%c2 = constant 2 : index
%cf0 = constant 0.0 : f32
// %acc = constant dense<0.0> : vector<${N}xf32>
%acc = vector.transfer_read %output[%c0], %cf0 : memref<${N}xf32>, vector<${N}xf32>
%f = vector.transfer_read %filter[%c0], %cf0 : memref<${K}xf32>, vector<${K}xf32>
%in0 = vector.transfer_read %input[%c0], %cf0 : memref<${M}xf32>, vector<${M}xf32>
%in1 = vector.shuffle %in0, %in0
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15,
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17] : vector<${M}xf32>, vector<${M}xf32>
%in = vector.shape_cast %in1 : vector<48xf32> to vector<${K}x${N}xf32>
%6 = vector.broadcast %f : vector<${K}xf32> to vector<${N}x${K}xf32>
%7 = vector.transpose %6, [1, 0] : vector<${N}x${K}xf32> to vector<${K}x${N}xf32>
// %v5 = vector.multi_reduction #vector.kind<mul>, %v4 [0] : vector<2x${K}x${N}xf32> to vector<${K}x${N}xf32>
%v5 = mulf %in, %7 : vector<${K}x${N}xf32>
%res0 = vector.multi_reduction #vector.kind<add>, %v5 [0] : vector<${K}x${N}xf32> to vector<${N}xf32>
%res = addf %res0, %acc : vector<${N}xf32>
vector.transfer_write %res, %output[%c0] : vector<${N}xf32> , memref<${N}xf32>
return
}
// This one is so bad it does not want to inline even when told so.
// Size 18 * 3 -> 16
// ~1.9 GFlops/s
func @compute_v7(%input : memref<${M}xf32>, %filter : memref<${K}xf32>, %output : memref<${N}xf32>)
attributes { passthrough = ["inline" ${TARGET_CPU} ${PREFER_VECTOR_WIDTH}]} {
%c0 = constant 0 : index
%c1 = constant 1 : index
%c2 = constant 2 : index
%cf0 = constant 0.0 : f32
// %acc = constant dense<0.0> : vector<${N}xf32>
%acc = vector.transfer_read %output[%c0], %cf0 : memref<${N}xf32>, vector<${N}xf32>
%z0 = vector.broadcast %cf0 : f32 to vector<${M}xf32>
%v0 = vector.broadcast %cf0 : f32 to vector<2x${K}x${M}xf32>
%1 = vector.transfer_read %filter[%c0], %cf0 : memref<${K}xf32>, vector<${K}xf32>
%2 = vector.constant_mask [${N}] : vector<${M}xi1>
%3 = vector.expandload %input[%c0], %2, %z0 : memref<${M}xf32>, vector<${M}xi1>, vector<${M}xf32> into vector<${M}xf32>
%v1 = vector.insert %3, %v0[0, 0] : vector<${M}xf32> into vector<2x${K}x${M}xf32>
%4 = vector.expandload %input[%c1], %2, %z0 : memref<${M}xf32>, vector<${M}xi1>, vector<${M}xf32> into vector<${M}xf32>
%v2 = vector.insert %4, %v1[0, 1] : vector<${M}xf32> into vector<2x${K}x${M}xf32>
%5 = vector.expandload %input[%c2], %2, %z0 : memref<${M}xf32>, vector<${M}xi1>, vector<${M}xf32> into vector<${M}xf32>
%v3 = vector.insert %5, %v2[0, 2] : vector<${M}xf32> into vector<2x${K}x${M}xf32>
%6 = vector.broadcast %1 : vector<${K}xf32> to vector<${M}x${K}xf32>
%7 = vector.transpose %6, [1, 0] : vector<${M}x${K}xf32> to vector<${K}x${M}xf32>
%v4 = vector.insert %7, %v3[1] : vector<${K}x${M}xf32> into vector<2x${K}x${M}xf32>
%v5 = vector.multi_reduction #vector.kind<mul>, %v4 [0] : vector<2x${K}x${M}xf32> to vector<${K}x${M}xf32>
%v6 = vector.multi_reduction #vector.kind<add>, %v5 [0] : vector<${K}x${M}xf32> to vector<${M}xf32>
%v7 = vector.extract_strided_slice %v6 {offsets = [0], sizes=[${N}], strides=[1]} : vector<${M}xf32> to vector<${N}xf32>
%res = addf %v7, %acc : vector<${N}xf32>
vector.transfer_write %res, %output[%c0] : vector<${N}xf32> , memref<${N}xf32>
return
}
func @print_perf(%iters: index, %total_time: f64) {
%c1 = constant 1: index
%cF = constant ${K} : index
%cO = constant ${N} : index
// For each output point we have ${K} muls and ${K-1} adds.
%cFm1 = subi %cF, %c1 : index
%flops_filter = addi %cF, %cFm1 : index
%flops_per_iter = muli %cO, %flops_filter : index
%flops = muli %iters, %flops_per_iter : index
%flops_i64 = index_cast %flops : index to i64
%flops_f = sitofp %flops_i64 : i64 to f64
%flops_per_s = divf %flops_f, %total_time : f64
// vector.print %total_time : f64
vector.print %flops_per_s : f64
return
}
func @main() {
%c0 = constant 0 : index
%c1 = constant 1 : index
%iters = constant ${ITERS} : index
%mvinput = memref.alloc() : memref<vector<${M}xf32>>
%vInput = constant dense<[0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0, 13.0, 14.0, 15.0, 16.0, 17.0]> :
vector<${M}xf32>
memref.store %vInput, %mvinput[] : memref<vector<${M}xf32>>
%mvfilter = memref.alloc() : memref<vector<${K}xf32>>
%vFilter = constant dense<[1.0, 2.0, 3.0]> : vector<${K}xf32>
memref.store %vFilter, %mvfilter[] : memref<vector<${K}xf32>>
%mvoutput = memref.alloc() : memref<vector<${N}xf32>>
%vOutput = constant dense<1.0> : vector<${N}xf32>
memref.store %vOutput, %mvoutput[] : memref<vector<${N}xf32>>
%input = vector.type_cast %mvinput: memref<vector<${M}xf32>> to memref<${M}xf32>
%filter = vector.type_cast %mvfilter: memref<vector<${K}xf32>> to memref<${K}xf32>
%output = vector.type_cast %mvoutput: memref<vector<${N}xf32>> to memref<${N}xf32>
call @compute(%input, %filter, %output) : (memref<${M}xf32>, memref<${K}xf32>, memref<${N}xf32>) -> ()
// CHECK: Unranked Memref base@ = {{.*}} rank = 1 offset = 0 sizes = [16] strides = [1] data =
// CHECK: [9, 15, 21, 27, 33, 39, 45, 51, 57, 63, 69, 75, 81, 87, 93, 99]
%p = memref.cast %output : memref<${N}xf32> to memref<*xf32>
call @print_memref_f32(%p) : (memref<*xf32>) -> ()
%t_start = call @rtclock() : () -> f64
scf.for %arg0 = %c0 to %iters step %c1 {
call @compute(%input, %filter, %output) : (memref<${M}xf32>, memref<${K}xf32>, memref<${N}xf32>) -> ()
}
%t_end = call @rtclock() : () -> f64
%t_conv = subf %t_end, %t_start: f64
call @print_perf(%iters, %t_conv) : (index, f64) -> ()
return
}
func private @rtclock() -> f64
func private @print_memref_f32(%ptr : memref<*xf32>)