FADDS_GEMM and FMULS_GEMM in flops.h do same operation

[luiceur]

Hi,

I am trying to understand how magma is measuring the number of flops in a matrix multiplication. it defines a

FLOPS(m,n,k) (FMULS_GEMM(m,n,k) + FADDS_GEMM(m,n,k))

FMULS_GEMM and FADDS_GEMM do the same operation -> m*n*k. I think the number of operations is right for single precision, but why 2 macros doing the same with different names?

[Stan Tomov]

Hi,
This is just for convenience in maintaining the codes in different precisions. We keep one version in double complex and generate all the rest with a python script. Besides this there is no other reason to have two macros.
Stan

[mgates3]

As the macro names state, one is the number of multiplies, the other is the number of adds. For gemm, these are the same, but for other functions, these are different formulas. E.g.,

#define FMULS_SYR2K( k, n ) ((k) * (n) * (n) )
#define FADDS_SYR2K( k, n ) ((k) * (n) * (n) + (n))

Then, as Stan stated, we need multiplies and adds separately to deal with complex arithmetic. Note the difference between flops for a complex cgemm and real sgemm:

#define FLOPS_CGEMM(m, n, k) (6.0 * FMULS_GEMM(m, n, k) + 2.0 * FADDS_GEMM(m, n, k) )
#define FLOPS_SGEMM(m, n, k) ( FMULS_GEMM(m, n, k) + FADDS_GEMM(m, n, k) )

-mark