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! Compile and run in Release mode with:
! gfortran -O3 -march=native -ffast-math -funroll-loops matmul_01.f90 && ./a.out
! To develop, compile and run with:
! gfortran -Wall -Wextra -Wimplicit-interface -g -fcheck=all -fbacktrace matmul_01.f90 && ./a.out
module matmul_01_cpu
implicit none
contains
subroutine matmul1(A, B, C)
real, intent(in) :: A(:,:), B(:,:)
real, intent(out) :: C(:,:)
integer :: n
integer :: i, j, k
n = size(A, 1)
C = 0
do j = 1, n
do k = 1, n
do i = 1, n
C(i,j) = C(i,j) + A(i,k)*B(k,j)
end do
end do
end do
end subroutine
! The arguments A, B are swapped,
! and all accesses to A, B, C are tranposed
subroutine kernel2(B, A, C, x, y, i1, s1)
real, intent(in) :: A(:,:), B(:,:)
real, intent(out) :: C(:,:)
integer, intent(in) :: x, y, i1, s1
integer :: k
!LF$ attributes simd :: A0, A1, A2, A3, A4, A5
real, dimension(8) :: A0, A1, A2, A3, A4, A5
!LF$ attributes simd :: u00, u01, u10, u11, u20, u21
!LF$ attributes simd :: u30, u31, u40, u41, u50, u51
real, dimension(8) :: u00, u01, u10, u11, u20, u21, u30, u31, &
u40, u41, u50, u51
! This function computes:
!C(x:x+6-1, y:y+16-1) = C(x:x+6-1, y:y+16-1) + matmul( &
! A(x:x+6-1, i1:i1+s1-1), &
! B(i1:i1+s1-1, y:y+16-1) )
u00 = C(y :y+ 7,x+0)
u01 = C(y+8:y+15,x+0)
u10 = C(y :y+ 7,x+1)
u11 = C(y+8:y+15,x+1)
u20 = C(y :y+ 7,x+2)
u21 = C(y+8:y+15,x+2)
u30 = C(y :y+ 7,x+3)
u31 = C(y+8:y+15,x+3)
u40 = C(y :y+ 7,x+4)
u41 = C(y+8:y+15,x+4)
u50 = C(y :y+ 7,x+5)
u51 = C(y+8:y+15,x+5)
do k = i1, i1+s1-1
A0 = A(k,x+0)
u00 = u00 + A0 * B(y :y+ 7,k)
u01 = u01 + A0 * B(y+8:y+15,k)
A1 = A(k,x+1)
u10 = u10 + A1 * B(y :y+ 7,k)
u11 = u11 + A1 * B(y+8:y+15,k)
A2 = A(k,x+2)
u20 = u20 + A2 * B(y :y+ 7,k)
u21 = u21 + A2 * B(y+8:y+15,k)
A3 = A(k,x+3)
u30 = u30 + A3 * B(y :y+ 7,k)
u31 = u31 + A3 * B(y+8:y+15,k)
A4 = A(k,x+4)
u40 = u40 + A4 * B(y :y+ 7,k)
u41 = u41 + A4 * B(y+8:y+15,k)
A5 = A(k,x+5)
u50 = u50 + A5 * B(y :y+ 7,k)
u51 = u51 + A5 * B(y+8:y+15,k)
end do
C(y :y+ 7,x+0) = u00
C(y+8:y+15,x+0) = u01
C(y :y+ 7,x+1) = u10
C(y+8:y+15,x+1) = u11
C(y :y+ 7,x+2) = u20
C(y+8:y+15,x+2) = u21
C(y :y+ 7,x+3) = u30
C(y+8:y+15,x+3) = u31
C(y :y+ 7,x+4) = u40
C(y+8:y+15,x+4) = u41
C(y :y+ 7,x+5) = u50
C(y+8:y+15,x+5) = u51
end subroutine
subroutine matmul2(A, B, C)
real, intent(in) :: A(:,:), B(:,:)
real, intent(out) :: C(:,:)
integer :: s1, s2, s3, n
integer :: i1, i2, i3, x, y
n = size(A, 1)
! Use the commented out numbers for a good benchmark
s3 = 48 ! 64
s2 = 12 ! 120
s1 = 24 ! 240
C = 0
do i3 = 1, n, s3
do i2 = 1, n, s2
do i1 = 1, n, s1
do x = i2, i2+s2-1, 6
do y = i3, i3+s3-1, 16
call kernel2(A, B, C, x, y, i1, s1)
end do
end do
end do
end do
end do
end subroutine
end module
program matmul_01
use matmul_01_cpu, only: matmul1, matmul2
implicit none
integer, parameter :: dp = kind(0.d0)
integer :: n, iter, i
real(dp) :: t1, t2, t, GHz, fma_clock, freq, measured, percent_peak
real, allocatable :: A(:,:), B(:,:), C(:,:), C2(:,:)
real :: err
! Use n = 960 for a good benchmark
n = 96
! Increase `iter` so that the total time for a given benchmark is about 1s
! in order to get accurate timings
iter = 1
print *, "Size (n x n): n =", n
print *, "Iter =", iter
print *, "Size MB:", 4._dp*n*n/1024**2
allocate(A(n,n), B(n,n), C(n,n), C2(n,n))
call random_number(A)
call random_number(B)
print *, "Fortran intrinsic matmul:"
call cpu_time(t1)
do i = 1, iter
C = matmul(A, B)
end do
call cpu_time(t2)
t = (t2-t1)/iter
GHz = 1e9_dp
fma_clock = 0.0625_dp ! This is CPU specific (Apple M1 number here)
freq = 3.2_dp*GHz
measured = t * freq / n**3
percent_peak = fma_clock / measured * 100
print *, "Time: ", t
print *, "Clock cycles per element:"
print *, "Theoretical performance peak:", fma_clock, "cycles"
print *, "Measured: ", measured, "cycles"
print *, "Percent peak: ", percent_peak, "%"
print *
print *, "matmul2:"
call cpu_time(t1)
do i = 1, iter
call matmul2(A, B, C2)
end do
call cpu_time(t2)
err = maxval(abs(C-C2))
print *, "Error:", err
t = (t2-t1)/iter
GHz = 1e9_dp
fma_clock = 0.0625_dp
freq = 3.2_dp*GHz
measured = t * freq / n**3
percent_peak = fma_clock / measured * 100
print *, "Time: ", t
print *, "Clock cycles per element:"
print *, "Theoretical performance peak:", fma_clock, "cycles"
print *, "Measured: ", measured, "cycles"
print *, "Percent peak: ", percent_peak, "%"
if (err > 1e-3) error stop
print *
print *, "matmul1:"
call cpu_time(t1)
do i = 1, iter
call matmul1(A, B, C2)
end do
call cpu_time(t2)
err = maxval(abs(C-C2))
print *, "Error:", err
t = (t2-t1)/iter
GHz = 1e9_dp
fma_clock = 0.0625_dp
freq = 3.2_dp*GHz
measured = t * freq / n**3
percent_peak = fma_clock / measured * 100
print *, "Time: ", t
print *, "Clock cycles per element:"
print *, "Theoretical performance peak:", fma_clock, "cycles"
print *, "Measured: ", measured, "cycles"
print *, "Percent peak: ", percent_peak, "%"
if (err > 1e-3) error stop
end program
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