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prefix_sum_recursive.metal
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prefix_sum_recursive.metal
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#include <metal_stdlib>
using namespace metal;
struct prefix_sum_constants
{
uint num_elements;
};
kernel void scan_threadgroupwise_intermediate_32_X_int(
device const int* in [[ buffer(0) ]],
device int* out [[ buffer(1) ]],
device int* grid_prefix_sums [[ buffer(2) ]],
device const prefix_sum_constants& c [[ buffer(3) ]],
const uint thread_position_in_grid [[ thread_position_in_grid ]],
const uint thread_position_in_threadgroup [[ thread_position_in_threadgroup ]],
const uint thread_index_in_simdgroup [[ thread_index_in_simdgroup ]],
const uint threadgroup_position_in_grid [[ threadgroup_position_in_grid ]],
const uint simdgroup_index_in_threadgroup [[ simdgroup_index_in_threadgroup ]],
const uint threadgroups_per_grid [[ threadgroups_per_grid ]],
const uint threads_per_threadgroup [[ threads_per_threadgroup ]],
const uint simdgroups_per_threadgroup [[ simdgroups_per_threadgroup ]],
const uint thread_execution_width [[ thread_execution_width ]]
) {
threadgroup int threadgroup_partial_sums[32];
// The SIMD group size must be 32.
if ( thread_execution_width != 32 ) {
return;
}
// Reset all the 32 elements in case threads_per_threadgroup < 1024.
if ( simdgroup_index_in_threadgroup == 0 ) {
threadgroup_partial_sums[thread_index_in_simdgroup] = 0;
}
threadgroup_barrier( mem_flags::mem_threadgroup );
// Warp-wise prefix sum
thread int local_sum = ( thread_position_in_grid < c.num_elements )? in[ thread_position_in_grid ] : 0 ;
if ( thread_index_in_simdgroup >= 1 ) local_sum += simd_shuffle_up( local_sum, 1 );
if ( thread_index_in_simdgroup >= 2 ) local_sum += simd_shuffle_up( local_sum, 2 );
if ( thread_index_in_simdgroup >= 4 ) local_sum += simd_shuffle_up( local_sum, 4 );
if ( thread_index_in_simdgroup >= 8 ) local_sum += simd_shuffle_up( local_sum, 8 );
if ( thread_index_in_simdgroup >= 16 ) local_sum += simd_shuffle_up( local_sum, 16 );
if ( thread_index_in_simdgroup == 31 ) {
if ( simdgroup_index_in_threadgroup == 0 ) {
threadgroup_partial_sums[ simdgroup_index_in_threadgroup ] = 0;
}
if ( simdgroup_index_in_threadgroup < ( simdgroups_per_threadgroup - 1 ) ) {
threadgroup_partial_sums[ simdgroup_index_in_threadgroup + 1 ] = local_sum;
}
}
threadgroup_barrier( mem_flags::mem_threadgroup );
// Threadgroup-wise coarse prefix sum
if ( simdgroup_index_in_threadgroup == 0 ) {
thread int local_sum_rep = threadgroup_partial_sums[ thread_index_in_simdgroup ];
if ( thread_index_in_simdgroup >= 1 ) local_sum_rep += simd_shuffle_up( local_sum_rep, 1 );
if ( thread_index_in_simdgroup >= 2 ) local_sum_rep += simd_shuffle_up( local_sum_rep, 2 );
if ( thread_index_in_simdgroup >= 4 ) local_sum_rep += simd_shuffle_up( local_sum_rep, 4 );
if ( thread_index_in_simdgroup >= 8 ) local_sum_rep += simd_shuffle_up( local_sum_rep, 8 );
if ( thread_index_in_simdgroup >= 16 ) local_sum_rep += simd_shuffle_up( local_sum_rep, 16 );
threadgroup_partial_sums[ thread_position_in_threadgroup ] = local_sum_rep;
}
threadgroup_barrier( mem_flags::mem_threadgroup );
// Propagate coarse prefix sum to warp-wise prefix sum
if ( thread_position_in_grid < c.num_elements ) {
out[ thread_position_in_grid ] = ( simdgroup_index_in_threadgroup > 0 )
?( local_sum + threadgroup_partial_sums[ simdgroup_index_in_threadgroup ] )
:( local_sum );
}
if ( threadgroups_per_grid > 1 ) {
if ( thread_position_in_threadgroup == threads_per_threadgroup - 1 ) {
if ( threadgroup_position_in_grid == 0 ) {
grid_prefix_sums[ 0 ] = 0;
}
if ( threadgroup_position_in_grid < threadgroups_per_grid - 1 ) {
grid_prefix_sums[ threadgroup_position_in_grid + 1 ]
= local_sum + threadgroup_partial_sums[ simdgroup_index_in_threadgroup ];
}
}
}
}
kernel void add_base_32_X_int(
device int* out [[ buffer(0) ]],
device const int* grid_prefix_sums [[ buffer(1) ]],
device const prefix_sum_constants& c [[ buffer(2) ]],
const uint thread_position_in_grid [[ thread_position_in_grid ]],
const uint threadgroup_position_in_grid [[ threadgroup_position_in_grid ]]
) {
if ( threadgroup_position_in_grid > 0 && thread_position_in_grid < c.num_elements ) {
out[ thread_position_in_grid ] += grid_prefix_sums[ threadgroup_position_in_grid ];
}
}
kernel void sum_threadgroup_32_X_int(
device const int* in [[ buffer(0) ]],
device int* grid_prefix_sums [[ buffer(1) ]],
device const prefix_sum_constants& c [[ buffer(2) ]],
const uint thread_position_in_grid [[ thread_position_in_grid ]],
const uint thread_position_in_threadgroup [[ thread_position_in_threadgroup ]],
const uint thread_index_in_simdgroup [[ thread_index_in_simdgroup ]],
const uint threadgroup_position_in_grid [[ threadgroup_position_in_grid ]],
const uint simdgroup_index_in_threadgroup [[ simdgroup_index_in_threadgroup ]],
const uint threadgroups_per_grid [[ threadgroups_per_grid ]],
const uint thread_execution_width [[ thread_execution_width ]]
) {
threadgroup int threadgroup_partial_sums[32];
// The SIMD group size must be 32.
if ( thread_execution_width != 32 ) {
return;
}
// Reset all the 32 elements in case threads_per_threadgroup < 1024.
if ( simdgroup_index_in_threadgroup == 0 ) {
threadgroup_partial_sums[thread_index_in_simdgroup] = 0;
}
threadgroup_barrier( mem_flags::mem_threadgroup );
thread const int local_sum = ( thread_position_in_grid < c.num_elements ) ? (in [ thread_position_in_grid ]) : 0;
thread const int warp_sum = simd_sum(local_sum);
if ( thread_index_in_simdgroup == 0 ){
threadgroup_partial_sums[simdgroup_index_in_threadgroup] = warp_sum;
}
threadgroup_barrier( mem_flags::mem_threadgroup );
if ( simdgroup_index_in_threadgroup == 0 ) {
thread const int local_sum2 = threadgroup_partial_sums[ thread_index_in_simdgroup ];
thread const int warp_sum2 = simd_sum(local_sum2);
if ( thread_position_in_threadgroup == 0 ) {
grid_prefix_sums[ threadgroup_position_in_grid ] = warp_sum2;
}
}
}
kernel void scan_with_base_threadgroupwise_32_X_int(
device const int* in [[ buffer(0) ]],
device int* out [[ buffer(1) ]],
device const int* grid_prefix_sums [[ buffer(2) ]],
device const prefix_sum_constants& c [[ buffer(3) ]],
const uint thread_position_in_grid [[ thread_position_in_grid ]],
const uint thread_position_in_threadgroup [[ thread_position_in_threadgroup ]],
const uint thread_index_in_simdgroup [[ thread_index_in_simdgroup ]],
const uint threadgroup_position_in_grid [[ threadgroup_position_in_grid ]],
const uint simdgroup_index_in_threadgroup [[ simdgroup_index_in_threadgroup ]],
const uint threads_per_threadgroup [[ threads_per_threadgroup ]],
const uint simdgroups_per_threadgroup [[ simdgroups_per_threadgroup ]],
const uint thread_execution_width [[ thread_execution_width ]]
) {
threadgroup int threadgroup_partial_sums[32];
// The SIMD group size must be 32.
if ( thread_execution_width != 32 ) {
return;
}
// Reset all the 32 elements in case threads_per_threadgroup < 1024.
if ( simdgroup_index_in_threadgroup == 0 ) {
threadgroup_partial_sums[thread_index_in_simdgroup] = 0;
}
threadgroup_barrier( mem_flags::mem_threadgroup );
// Warp-wise prefix sum
thread int local_sum = ( thread_position_in_grid < c.num_elements ) ? (
in[ thread_position_in_grid ]
+ ( ( ( thread_position_in_threadgroup == 0 ) && ( threadgroup_position_in_grid > 0 ) )
? ( grid_prefix_sums[ threadgroup_position_in_grid - 1 ] )
: 0 )
) : 0;
if ( thread_index_in_simdgroup >= 1 ) local_sum += simd_shuffle_up( local_sum, 1 );
if ( thread_index_in_simdgroup >= 2 ) local_sum += simd_shuffle_up( local_sum, 2 );
if ( thread_index_in_simdgroup >= 4 ) local_sum += simd_shuffle_up( local_sum, 4 );
if ( thread_index_in_simdgroup >= 8 ) local_sum += simd_shuffle_up( local_sum, 8 );
if ( thread_index_in_simdgroup >= 16 ) local_sum += simd_shuffle_up( local_sum, 16 );
if ( thread_index_in_simdgroup == 31 ) {
if ( simdgroup_index_in_threadgroup == 0 ) {
threadgroup_partial_sums[ simdgroup_index_in_threadgroup ] = 0;
}
if ( simdgroup_index_in_threadgroup < (simdgroups_per_threadgroup - 1) ) {
threadgroup_partial_sums[ simdgroup_index_in_threadgroup + 1 ] = local_sum;
}
}
threadgroup_barrier( mem_flags::mem_threadgroup );
// Threadgroup-wise coarse prefix sum
if ( simdgroup_index_in_threadgroup == 0 ) {
thread int local_sum_rep = threadgroup_partial_sums[ thread_position_in_threadgroup ];
if ( thread_index_in_simdgroup >= 1 ) local_sum_rep += simd_shuffle_up( local_sum_rep, 1 );
if ( thread_index_in_simdgroup >= 2 ) local_sum_rep += simd_shuffle_up( local_sum_rep, 2 );
if ( thread_index_in_simdgroup >= 4 ) local_sum_rep += simd_shuffle_up( local_sum_rep, 4 );
if ( thread_index_in_simdgroup >= 8 ) local_sum_rep += simd_shuffle_up( local_sum_rep, 8 );
if ( thread_index_in_simdgroup >= 16 ) local_sum_rep += simd_shuffle_up( local_sum_rep, 16 );
threadgroup_partial_sums[ thread_position_in_threadgroup ] = local_sum_rep;
}
threadgroup_barrier( mem_flags::mem_threadgroup );
// Propagate coarse prefix sum to warp-wise prefix sum
if ( thread_position_in_grid < c.num_elements ) {
out[ thread_position_in_grid ] = ( simdgroup_index_in_threadgroup > 0 )
?( local_sum + threadgroup_partial_sums[ simdgroup_index_in_threadgroup ] )
:( local_sum );
}
}