Algorithms for matrix matrix multiplication, dgemm

The algorithms are taken form the books:

1. David A. Patterson, John L. Hennessy "Computer Organization and Design. The hardware software interface. RISK-V Edition",
2. David A. Patterson, John L. Hennessy "Computer Organization and Design. The hardware software interface. MIPS Edition"

There are the following algorithms implemented:

1. Basic, unoptimized, dgemm_basic.cpp
2. Using AVX 256-bit intrinsics, dgemm_avx256.cpp
3. Using AVX 512-bit intinsics, dgemm_avx512.cpp
4. Using AVX 512-bit intinsics with loop unrolling, dgemm_unrolled.cpp
5. Blocked version, unoptimized, dgemm_basic_blocked.cpp
6. Blocked version with AVX 512-bit intinsics with loop unrolling dgemm_blocked.cpp

How to build?

To build the system, execute the following commands:

1. git clone https://github.com/romz-pl/matrix-matrix-multiply
2. cd matrix-matrix-multiply
3. mkdir build
4. cd build
5. cmake ..
6. make
7. ./src/dgemm

The command ./src/dgemm executes the programm.

Results

1. For Core i7 CPU, with matrix size equal to 128, I obtained the following results averaged over 1000 randomly generated matrices:

         dgemm_basic:  elapsed-time=      1661
 dgemm_basic_blocked:  elapsed-time=      1260     speed-up=    1.31
        dgemm_avx256:  elapsed-time=       443     speed-up=    3.74
        dgemm_avx512:  elapsed-time=       233     speed-up=    7.12
      dgemm_unrolled:  elapsed-time=       106     speed-up=   15.66
       dgemm_blocked:  elapsed-time=       100     speed-up=   16.61

2. For Core i7 CPU, with matrix size equal to 640, I obtained the following results averaged over 10 randomly generated matrices:

         dgemm_basic:  elapsed-time=    241958
 dgemm_basic_blocked:  elapsed-time=    162224     speed-up=   1.49
        dgemm_avx256:  elapsed-time=     66246     speed-up=   3.65
        dgemm_avx512:  elapsed-time=     35604     speed-up=   6.79
      dgemm_unrolled:  elapsed-time=     16634     speed-up=  14.54
       dgemm_blocked:  elapsed-time=     12981     speed-up=  18.63

3. For Core i7 CPU, with matrix size equal to 1280, I obtained the following results averaged over 5 randomly generated matrices:

         dgemm_basic:  elapsed-time=   4592295
 dgemm_basic_blocked:  elapsed-time=   1626700     speed-up=   2.82
        dgemm_avx256:  elapsed-time=   1227037     speed-up=   3.74
        dgemm_avx512:  elapsed-time=    637091     speed-up=   7.20
      dgemm_unrolled:  elapsed-time=    558080     speed-up=   8.22
       dgemm_blocked:  elapsed-time=    181634     speed-up=  25.28

4. For Core i7 CPU, with matrix size equal to 2560, I obtained the following results for one randomly generated matrices:

         dgemm_basic:  elapsed-time=  62731813
 dgemm_basic_blocked:  elapsed-time=  16474759     speed-up=   3.80
        dgemm_avx256:  elapsed-time=  17050012     speed-up=   3.67
        dgemm_avx512:  elapsed-time=   9012450     speed-up=   6.96
      dgemm_unrolled:  elapsed-time=   5958033     speed-up=  10.52
       dgemm_blocked:  elapsed-time=   1837494     speed-up=  34.13

5. For Core i7 CPU, with matrix size equal to 5120, I obtained the following results for one randomly generated matrices:

        dgemm_basic:   elapsed-time= 1154120417
 dgemm_basic_blocked:  elapsed-time=  137582063    speed-up=   8.38
        dgemm_avx256:  elapsed-time=  297156247    speed-up=   3.88
        dgemm_avx512:  elapsed-time=  144941094    speed-up=   7.96
      dgemm_unrolled:  elapsed-time=   97428303    speed-up=  11.84
       dgemm_blocked:  elapsed-time=   18558107    speed-up=  62.18