hw1: added sources
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# On Euler, we will benchmark your DGEMM's performance against the performance
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# of the default vendor-tuned DGEMM. This is done in benchmark-blas.
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#
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CC = gcc
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OPT = -O2
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CFLAGS = -Wall -std=gnu99 $(OPT)
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LDFLAGS = -Wall
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# librt is needed for clock_gettime
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LDLIBS = -lrt -Wl,--no-as-needed -L${MKLROOT}/lib/intel64 -lmkl_intel_lp64 -lmkl_core -lmkl_sequential -lpthread -lm -ldl -m64 -I${MKLROOT}/include
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targets = benchmark-naive benchmark-blocked benchmark-blas
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objects = benchmark.o dgemm-naive.o dgemm-blocked.o dgemm-blas.o
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.PHONY : default
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default : all
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.PHONY : all
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all : clean $(targets)
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benchmark-naive : benchmark.o dgemm-naive.o
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$(CC) -o $@ $^ $(LDLIBS)
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benchmark-blocked : benchmark.o dgemm-blocked.o
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$(CC) -o $@ $^ $(LDLIBS)
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benchmark-blas : benchmark.o dgemm-blas.o
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$(CC) -o $@ $^ $(LDLIBS)
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%.o : %.c
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$(CC) -c $(CFLAGS) $<
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.PHONY : clean
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clean:
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rm -f $(targets) $(objects)
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#include <stdlib.h> // For: exit, drand48, malloc, free, NULL, EXIT_FAILURE
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#include <stdio.h> // For: perror
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#include <string.h> // For: memset
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#include <float.h> // For: DBL_EPSILON
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#include <math.h> // For: fabs
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#ifdef GETTIMEOFDAY
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#include <sys/time.h> // For struct timeval, gettimeofday
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#else
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#include <time.h> // For struct timespec, clock_gettime, CLOCK_MONOTONIC
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#endif
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// On icsmaster
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// 2.3 GHz * 8 vector width * 2 flops for FMA = 36.8 GF/s
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#define MAX_SPEED 36.8
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/* reference_dgemm wraps a call to the BLAS-3 routine DGEMM, via the standard FORTRAN interface - hence the reference semantics. */
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#define DGEMM dgemm_
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extern void DGEMM (char*, char*, int*, int*, int*, double*, double*, int*, double*, int*, double*, double*, int*);
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void reference_dgemm (int N, double ALPHA, double* A, double* B, double* C)
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{
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char TRANSA = 'N';
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char TRANSB = 'N';
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int M = N;
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int K = N;
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double BETA = 1.;
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int LDA = N;
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int LDB = N;
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int LDC = N;
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DGEMM(&TRANSA, &TRANSB, &M, &N, &K, &ALPHA, A, &LDA, B, &LDB, &BETA, C, &LDC);
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}
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/* Your function must have the following signature: */
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extern const char* dgemm_desc;
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extern void square_dgemm (int, double*, double*, double*);
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double wall_time ()
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{
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#ifdef GETTIMEOFDAY
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struct timeval t;
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gettimeofday (&t, NULL);
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return 1.*t.tv_sec + 1.e-6*t.tv_usec;
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#else
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struct timespec t;
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clock_gettime (CLOCK_MONOTONIC, &t);
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return 1.*t.tv_sec + 1.e-9*t.tv_nsec;
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#endif
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}
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void die (const char* message)
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{
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perror (message);
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exit (EXIT_FAILURE);
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}
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void fill (double* p, int n)
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{
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for (int i = 0; i < n; ++i)
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p[i] = 2 * drand48() - 1; // Uniformly distributed over [-1, 1]
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}
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void absolute_value (double *p, int n)
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{
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for (int i = 0; i < n; ++i)
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p[i] = fabs (p[i]);
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}
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/* The benchmarking program */
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int main (int argc, char **argv)
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{
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printf ("#Description:\t%s\n\n", dgemm_desc);
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/* Test sizes should highlight performance dips at multiples of certain powers-of-two */
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int test_sizes[] =
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/* Multiples-of-32, +/- 1. Currently commented. */
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/* {31,32,33,63,64,65,95,96,97,127,128,129,159,160,161,191,192,193,223,224,225,255,256,257,287,288,289,319,320,321,351,352,353,383,384,385,415,416,417,447,448,449,479,480,481,511,512,513,543,544,545,575,576,577,607,608,609,639,640,641,671,672,673,703,704,705,735,736,737,767,768,769,799,800,801,831,832,833,863,864,865,895,896,897,927,928,929,959,960,961,991,992,993,1023,1024,1025}; */
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/* A representative subset of the first list. Currently uncommented. */
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{ 31, 32, 96, 97, 127, 128, 129, 191, 192, 229, 255, 256, 257,
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319, 320, 321, 417, 479, 480, 511, 512, 639, 640, 767, 768, 769 };
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int nsizes = sizeof(test_sizes)/sizeof(test_sizes[0]);
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/* assume last size is also the largest size */
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int nmax = test_sizes[nsizes-1];
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/* allocate memory for all problems */
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double* buf = NULL;
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buf = (double*) malloc (3 * nmax * nmax * sizeof(double));
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if (buf == NULL) die ("failed to allocate largest problem size");
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double Mflops_s[nsizes],per[nsizes],aveper;
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/* For each test size */
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for (int isize = 0; isize < sizeof(test_sizes)/sizeof(test_sizes[0]); ++isize)
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{
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/* Create and fill 3 random matrices A,B,C*/
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int n = test_sizes[isize];
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double* A = buf + 0;
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double* B = A + nmax*nmax;
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double* C = B + nmax*nmax;
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fill (A, n*n);
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fill (B, n*n);
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fill (C, n*n);
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/* Measure performance (in Gflops/s). */
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/* Time a "sufficiently long" sequence of calls to reduce noise */
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double Gflops_s, seconds = -1.0;
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double timeout = 0.1; // "sufficiently long" := at least 1/10 second.
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for (int n_iterations = 1; seconds < timeout; n_iterations *= 2)
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{
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/* Warm-up */
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square_dgemm (n, A, B, C);
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/* Benchmark n_iterations runs of square_dgemm */
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seconds = -wall_time();
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for (int it = 0; it < n_iterations; ++it)
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square_dgemm (n, A, B, C);
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seconds += wall_time();
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/* compute Gflop/s rate */
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Gflops_s = 2.e-9 * n_iterations * n * n * n / seconds;
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}
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/* Storing Mflop rate and calculating percentage of peak */
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Mflops_s[isize] = Gflops_s*1000;
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per[isize] = Gflops_s*100/MAX_SPEED;
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printf ("Size: %d\tMflop/s: %8g\tPercentage:%6.2lf\n", n, Mflops_s[isize],per[isize]);
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/* Ensure that error does not exceed the theoretical error bound. */
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/* C := A * B, computed with square_dgemm */
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memset (C, 0, n * n * sizeof(double));
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square_dgemm (n, A, B, C);
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/* Do not explicitly check that A and B were unmodified on square_dgemm exit
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* - if they were, the following will most likely detect it:
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* C := C - A * B, computed with reference_dgemm */
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reference_dgemm(n, -1., A, B, C);
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/* A := |A|, B := |B|, C := |C| */
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absolute_value (A, n * n);
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absolute_value (B, n * n);
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absolute_value (C, n * n);
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/* C := |C| - 3 * e_mach * n * |A| * |B|, computed with reference_dgemm */
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reference_dgemm (n, -3.*DBL_EPSILON*n, A, B, C);
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/* If any element in C is positive, then something went wrong in square_dgemm */
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for (int i = 0; i < n * n; ++i)
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if (C[i] > 0)
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die("*** FAILURE *** Error in matrix multiply exceeds componentwise error bounds.\n" );
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}
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/* Calculating average percentage of peak reached by algorithm */
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aveper=0;
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for (int i=0; i<nsizes;i++)
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aveper+= per[i];
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aveper/=nsizes*1.0;
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/* Printing average percentage to screen */
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printf("#Average percentage of Peak = %g\n",aveper);
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free (buf);
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return 0;
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}
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/*
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Please include compiler name below (you may also include any other modules you would like to be loaded)
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COMPILER= gnu
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Please include All compiler flags and libraries as you want them run. You can simply copy this over from the Makefile's first few lines
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CC = cc
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OPT = -O3
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CFLAGS = -Wall -std=gnu99 $(OPT)
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MKLROOT = /opt/intel/composer_xe_2013.1.117/mkl
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LDLIBS = -lrt -Wl,--start-group $(MKLROOT)/lib/intel64/libmkl_intel_lp64.a $(MKLROOT)/lib/intel64/libmkl_sequential.a $(MKLROOT)/lib/intel64/libmkl_core.a -Wl,--end-group -lpthread -lm
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*/
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#define DGEMM dgemm_
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extern void DGEMM (char*, char*, int*, int*, int*, double*, double*, int*, double*, int*, double*, double*, int*);
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const char* dgemm_desc = "Reference dgemm.";
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/* This routine performs a dgemm operation
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* C := C + A * B
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* where A, B, and C are lda-by-lda matrices stored in column-major format.
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* On exit, A and B maintain their input values.
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* This function wraps a call to the BLAS-3 routine DGEMM, via the standard FORTRAN interface - hence the reference semantics. */
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void square_dgemm (int N, double* A, double* B, double* C)
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{
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char TRANSA = 'N';
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char TRANSB = 'N';
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int M = N;
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int K = N;
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double ALPHA = 1.;
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double BETA = 1.;
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int LDA = N;
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int LDB = N;
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int LDC = N;
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DGEMM(&TRANSA, &TRANSB, &M, &N, &K, &ALPHA, A, &LDA, B, &LDB, &BETA, C, &LDC);
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}
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/*
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Please include compiler name below (you may also include any other modules you would like to be loaded)
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COMPILER= gnu
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Please include All compiler flags and libraries as you want them run. You can simply copy this over from the Makefile's first few lines
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CC = cc
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OPT = -O3
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CFLAGS = -Wall -std=gnu99 $(OPT)
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MKLROOT = /opt/intel/composer_xe_2013.1.117/mkl
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LDLIBS = -lrt -Wl,--start-group $(MKLROOT)/lib/intel64/libmkl_intel_lp64.a $(MKLROOT)/lib/intel64/libmkl_sequential.a $(MKLROOT)/lib/intel64/libmkl_core.a -Wl,--end-group -lpthread -lm
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*/
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const char* dgemm_desc = "Naive, three-loop dgemm.";
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/* This routine performs a dgemm operation
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* C := C + A * B
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* where A, B, and C are lda-by-lda matrices stored in column-major format.
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* On exit, A and B maintain their input values. */
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void square_dgemm (int n, double* A, double* B, double* C)
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{
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// TODO: Implement the blocking optimization
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/* For each row i of A */
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for (int i = 0; i < n; ++i)
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/* For each column j of B */
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for (int j = 0; j < n; ++j)
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{
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/* Compute C(i,j) */
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double cij = C[i+j*n];
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for( int k = 0; k < n; k++ )
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cij += A[i+k*n] * B[k+j*n];
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C[i+j*n] = cij;
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}
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}
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/*
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Please include compiler name below (you may also include any other modules you would like to be loaded)
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COMPILER= gnu
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Please include All compiler flags and libraries as you want them run. You can simply copy this over from the Makefile's first few lines
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CC = cc
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OPT = -O3
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CFLAGS = -Wall -std=gnu99 $(OPT)
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MKLROOT = /opt/intel/composer_xe_2013.1.117/mkl
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LDLIBS = -lrt -Wl,--start-group $(MKLROOT)/lib/intel64/libmkl_intel_lp64.a $(MKLROOT)/lib/intel64/libmkl_sequential.a $(MKLROOT)/lib/intel64/libmkl_core.a -Wl,--end-group -lpthread -lm
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*/
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const char* dgemm_desc = "Naive, three-loop dgemm.";
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/* This routine performs a dgemm operation
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* C := C + A * B
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* where A, B, and C are lda-by-lda matrices stored in column-major format.
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* On exit, A and B maintain their input values. */
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void square_dgemm (int n, double* A, double* B, double* C)
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{
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/* For each row i of A */
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for (int i = 0; i < n; ++i)
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/* For each column j of B */
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for (int j = 0; j < n; ++j)
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{
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/* Compute C(i,j) */
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double cij = C[i+j*n];
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for( int k = 0; k < n; k++ )
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cij += A[i+k*n] * B[k+j*n];
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C[i+j*n] = cij;
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}
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}
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#!/bin/bash -l
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#SBATCH --job-name=matrixmult
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#SBATCH --time=00:30:00
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#SBATCH --nodes=1
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#SBATCH --output=matrixmult-%j.out
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#SBATCH --error=matrixmult-%j.err
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# load modules
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if command -v module 1>/dev/null 2>&1; then
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module load gcc/10.1.0 intel-mkl/2020.1.217-gcc-10.1.0-qsctnr6 gnuplot
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fi
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export OMP_NUM_THREADS=1
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export MKL_NUM_THREADS=1
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echo "==== benchmark-naive ======================"
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./benchmark-naive | tee timing_basic_dgemm.data
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echo
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echo "==== benchmark-blas ======================="
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./benchmark-blas | tee timing_blas_dgemm.data
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echo
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echo "==== benchmark-blocked ===================="
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./benchmark-blocked | tee timing_blocked_dgemm.data
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echo
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echo "==== plot results ========================="
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gnuplot timing.gp
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set title "NxN matrix-matrix-multiplication on 4-Core Intel(R) Xeon(R) CPU E3-1585L v5 @ 3.00GHz"
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set xlabel "Matrix size (N)"
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set ylabel "Performance (GFlop/s)"
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set grid
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set logscale y 10
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set terminal postscript color "Helvetica" 14
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set output "timing.ps"
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# set terminal png color "Helvetica" 14
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# set output "timing.png"
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# plot "timing.data" using 2:4 title "square_dgemm" with linespoints
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# For performance comparisons
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plot "timing_basic_dgemm.data" using 2:4 title "Naive dgemm" with linespoints, \
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"timing_blocked_dgemm.data" using 2:4 title "Blocked dgemm" with linespoints, \
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"timing_blas_dgemm.data" using 2:4 title "MKL blas dgemm" with linespoints
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