1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
|
// https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2023/p2642r2.html
// C99:
#include <stdio.h>
#include <time.h>
#include <stc/cspan.h>
using_cspan3(Mat, double);
typedef Mat2 OutMat;
typedef struct { Mat2 m00, m01, m10, m11; } Partition;
Partition partition(Mat2 A)
{
int32_t M = A.shape[0];
int32_t N = A.shape[1];
return (Partition){
.m00 = cspan_slice(Mat2, &A, {0, M/2}, {0, N/2}),
.m01 = cspan_slice(Mat2, &A, {0, M/2}, {N/2, N}),
.m10 = cspan_slice(Mat2, &A, {M/2, M}, {0, N/2}),
.m11 = cspan_slice(Mat2, &A, {M/2, M}, {N/2, N}),
};
}
// Slow generic implementation
void base_case_matrix_product(Mat2 A, Mat2 B, OutMat C)
{
for (int j = 0; j < C.shape[1]; ++j) {
for (int i = 0; i < C.shape[0]; ++i) {
Mat2_value C_ij = 0;
for (int k = 0; k < A.shape[1]; ++k) {
C_ij += *cspan_at(&A, i,k) * *cspan_at(&B, k,j);
}
*cspan_at(&C, i,j) += C_ij;
}
}
}
void recursive_matrix_product(Mat2 A, Mat2 B, OutMat C)
{
// Some hardware-dependent constant
enum {recursion_threshold = 16};
if (C.shape[0] <= recursion_threshold || C.shape[1] <= recursion_threshold) {
base_case_matrix_product(A, B, C);
} else {
Partition c = partition(C),
a = partition(A),
b = partition(B);
recursive_matrix_product(a.m00, b.m00, c.m00);
recursive_matrix_product(a.m01, b.m10, c.m00);
recursive_matrix_product(a.m10, b.m00, c.m10);
recursive_matrix_product(a.m11, b.m10, c.m10);
recursive_matrix_product(a.m00, b.m01, c.m01);
recursive_matrix_product(a.m01, b.m11, c.m01);
recursive_matrix_product(a.m10, b.m01, c.m11);
recursive_matrix_product(a.m11, b.m11, c.m11);
}
}
#define i_type Values
#define i_val double
#include <stc/cstack.h>
#include <stc/crand.h>
int main(void)
{
enum {N = 10, D1 = 256, D2 = D1};
Values values = {0};
for (int i=0; i < N*D1*D2; ++i)
Values_push(&values, (crandf() - 0.5)*4.0);
double out[D1*D2];
Mat3 data = cspan_md_layout(c_ROWMAJOR, values.data, N, D1, D2);
OutMat c = cspan_md_layout(c_ROWMAJOR, out, D1, D2);
Mat2 a = cspan_submd3(&data, 0);
double sum = 0.0;
clock_t t = clock();
for (int i=1; i<N; ++i) {
Mat2 b = cspan_submd3(&data, i);
memset(out, 0, sizeof out);
recursive_matrix_product(a, b, c);
//base_case_matrix_product(a, b, c);
sum += *cspan_at(&c, 0, 1);
}
t = clock() - t;
printf("%.16g: %f\n", sum, (double)t*1000.0/CLOCKS_PER_SEC);
Values_drop(&values);
}
|
