Starting to collect thing in ulmBLAS (and better Testing)
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We will now start to collect our BLAS implementation in an extra compile unit so that we can reuse them for further exercises. Here an overview of the source and header files needed:
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ulmblas.h
This file is given and contains declarations of BLAS functions.
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ulmblas.c
This file is supposed to contain function definitions (i.e. implementations) of BLAS functions. You have to fill this file with you implementation. For this exercise it should contain (at least) the following implementations:
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dswap for interchanging elements of two vectors.
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dgetrf for computing the LU factorization with pivoting. Implicitly this will require that you also provide functions dscal, idamax and dger (as they are required for dgetrf).
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ulmaux.h, ulmaux.c, test_dgetrf.c
These files are given:
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ulmaux.c contains for example functions for initializing and printing matrices, the timer walltime, etc. In ulmaux.h are declarations for these functions.
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test_dgetrf.c is the actual program for checking and benchmarking the LU factorization.
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Header File for ulmBLAS
#ifndef ULMBLAS_H #define ULMBLAS_H #include <stdbool.h> // for typedef bool #include <stddef.h> // for size_t, ptrdiff_t //-- BLAS Level 1 functions ---------------------------------------------------- void dcopy(size_t n, const double *x, ptrdiff_t incX, double *y, ptrdiff_t incY); void daxpy(size_t n, double alpha, const double *x, ptrdiff_t incX, double *y, ptrdiff_t incY); double ddot(size_t n, const double *x, ptrdiff_t incX, const double *y, ptrdiff_t incY); void dscal(size_t n, double alpha, double *x, ptrdiff_t incX); size_t idamax(size_t n, const double *x, ptrdiff_t incX); void dswap(size_t n, double *x, ptrdiff_t incX, double *y, ptrdiff_t incY); //-- BLAS Level 2 functions ---------------------------------------------------- void dgemv(size_t m, size_t n, double alpha, const double *A, ptrdiff_t incRowA, ptrdiff_t incColA, const double *x, ptrdiff_t incX, double beta, double *y, ptrdiff_t incY); void dger(size_t m, size_t n, double alpha, const double *x, ptrdiff_t incX, const double *y, ptrdiff_t incY, double *A, ptrdiff_t incRowA, ptrdiff_t incColA); void dtrsv(size_t n, bool lower, bool unit, const double *A, ptrdiff_t incRowA, ptrdiff_t incColA, double *x, ptrdiff_t incX); //-- LAPACK functions ---------------------------------------------------------- ptrdiff_t dgetrf(size_t m, size_t n, double *A, ptrdiff_t incRowA, ptrdiff_t incColA, size_t *p, ptrdiff_t incP); #endif // ULMBLAS_H
Exercise: Source File for ulmBLAS
Write the source file ulmblas.c:
Start with an empty file. Then include ulmblas.h and add your implementation for dswap, dgetrf, dger, dscal and idamax. Also include further header files required by your code.
So you get a structure like this:
#include <ulmblas.h> /* include other header files required by your code */ /* Implementation for your BLAS functions */
Exercise: Test your LU factorization (with pivoting)
Download the following files:
#ifndef ULMAUX_H #define ULMAUX_H #include <stddef.h> // for size_t, ptrdiff_t #include <stdbool.h> // for typedef bool //-- Functions for benchmarking and testing ------------------------------------ // timer double walltime(); // random fill matrix void randDGeMatrix(size_t m, size_t n, bool withNan, double *A, ptrdiff_t incRowA, ptrdiff_t incColA); // print matrix of doubles using format string fmt void printfDGeMatrix(const char * fmt, size_t m, size_t n, const double *A, ptrdiff_t incRowA, ptrdiff_t incColA); // print matrix of doubles (using a default format) void printDGeMatrix(size_t m, size_t n, const double *A, ptrdiff_t incRowA, ptrdiff_t incColA); // print matrix of size_ts void printIGeMatrix(size_t m, size_t n, const size_t *A, ptrdiff_t incRowA, ptrdiff_t incColA); // absolute value of a ptrdiff_t value inline size_t ptrdiff_abs(ptrdiff_t x) { return x>0 ? x : -x; } // random fill an array of doubles void dfill_nan(size_t bufsize, double *buf); // random fill an array of size_t values void ifill_rand(size_t bufsize, size_t *buf); //-- BLAS extensions ----------------------------------------------------------- // copy matrices void dgecopy(size_t m, size_t n, const double *A, ptrdiff_t incRowA, ptrdiff_t incColA, double *B, ptrdiff_t incRowB, ptrdiff_t incColB); // axpy for matrices void dgeaxpy(size_t m, size_t n, double alpha, const double *X, ptrdiff_t incRowX, ptrdiff_t incColX, double *Y, ptrdiff_t incRowY, ptrdiff_t incColY); // compute and return matrix (infinity) norm double dgenrm_inf(size_t m, size_t n, const double *A, ptrdiff_t incRowA, ptrdiff_t incColA); #endif // ULMAUX_H
#include <ulmaux.h> #include <stdio.h> // for printf() #include <stdlib.h> // for malloc(), free(), rand(), srand() #include <math.h> // for nan(), fabs() #include <stdbool.h> // for typedef bool #include <sys/times.h> // needed for walltime() #include <unistd.h> // needed for walltime() //-- Functions for benchmarking and testing ------------------------------------ double walltime() { struct tms ts; static double ClockTick=0.0; if (ClockTick==0.0) { ClockTick = 1.0 / ((double) sysconf(_SC_CLK_TCK)); } return ((double) times(&ts)) * ClockTick; } void randDGeMatrix(size_t m, size_t n, bool withNan, double *A, ptrdiff_t incRowA, ptrdiff_t incColA) { for (size_t i=0; i<m; ++i) { for (size_t j=0; j<n; ++j) { A[i*incRowA + j*incColA] = withNan ? nan("") : 2.*(rand()-RAND_MAX/2)/RAND_MAX; } } } void printfDGeMatrix(const char * fmt, size_t m, size_t n, const double *A, ptrdiff_t incRowA, ptrdiff_t incColA) { for (size_t i=0; i<m; ++i) { for (size_t j=0; j<n; ++j) { printf(fmt, A[i*incRowA + j*incColA]); } printf("\n"); } printf("\n"); } void printDGeMatrix(size_t m, size_t n, const double *A, ptrdiff_t incRowA, ptrdiff_t incColA) { printfDGeMatrix("%9.2lf ", m, n, A, incRowA, incColA); } void printIGeMatrix(size_t m, size_t n, const size_t *A, ptrdiff_t incRowA, ptrdiff_t incColA) { for (size_t i=0; i<m; ++i) { for (size_t j=0; j<n; ++j) { printf("%6zu ", A[i*incRowA + j*incColA]); } printf("\n"); } printf("\n"); } extern inline size_t ptrdiff_abs(ptrdiff_t x); void dfill_nan(size_t bufsize, double *buf) { for (size_t i=0; i<bufsize; ++i) { buf[i] = nan(""); } } void ifill_rand(size_t bufsize, size_t *buf) { for (size_t i=0; i<bufsize; ++i) { buf[i] = rand(); } } //-- BLAS extensions ----------------------------------------------------------- void dgecopy(size_t m, size_t n, const double *A, ptrdiff_t incRowA, ptrdiff_t incColA, double *B, ptrdiff_t incRowB, ptrdiff_t incColB) { if (incRowB>incColB && incRowA>incColA) { dgecopy(n, m, A, incColA, incRowA, B, incColB, incRowB); return; } for (size_t j=0; j<n; ++j) { for (size_t i=0; i<m; ++i) { B[i*incRowB + j*incColB] = A[i*incRowA + j*incColA]; } } } void dgeaxpy(size_t m, size_t n, double alpha, const double *X, ptrdiff_t incRowX, ptrdiff_t incColX, double *Y, ptrdiff_t incRowY, ptrdiff_t incColY) { if (incRowY>incColY && incRowX>incColX) { dgeaxpy(n, m, alpha, X, incColX, incRowX, Y, incColY, incRowY); return; } for (size_t j=0; j<n; ++j) { for (size_t i=0; i<m; ++i) { Y[i*incRowY + j*incColY] += alpha * X[i*incRowX + j*incColX]; } } } double dgenrm_inf(size_t m, size_t n, const double *A, ptrdiff_t incRowA, ptrdiff_t incColA) { double result = 0; for (size_t i=0; i<m; ++i) { double sum = 0; for (size_t j=0; j<n; ++j) { sum += fabs(A[i*incRowA+j*incColA]); } if (sum>result) { result = sum; } } return result; }
#include <ulmaux.h> #include <ulmblas.h> #include <assert.h> // for assert() #include <stdlib.h> // for malloc(), free(), rand(), srand(), abort() #include <stdbool.h> // for typedef bool #include <stdio.h> // for printf() #include <math.h> // for nan(), fabs() #include <float.h> // for DBL_EPSILON #include <string.h> // for strcmp #ifndef DGETRF #define DGETRF dgetrf #endif #ifndef SEED_RAND #define SEED_RAND 0 #endif #ifndef TOL_ERR #define TOL_ERR 1 #endif //-- reference implementation and numerical test ------------------------------- double dgetrf_err(size_t m, size_t n, const double *A, ptrdiff_t incRowA, ptrdiff_t incColA, double *LU, ptrdiff_t incRowLU, ptrdiff_t incColLU, const size_t *p, ptrdiff_t incP) { if (m==0 || n==0) { return 0; } size_t k = m<n ? m : n; double *L = malloc(m*k*sizeof(double)); double *U = malloc(k*n*sizeof(double)); if (!L || !U) { abort(); } // L, U, A are all stored col major ptrdiff_t ldL = m; ptrdiff_t ldU = k; // copy L for (size_t i=0; i<m; ++i) { for (size_t j=0; j<k; ++j) { L[i+j*ldL] = j<i ? LU[i*incRowLU+j*incColLU] : j==i ? 1 : 0; } } // copy U for (size_t i=0; i<k; ++i) { for (size_t j=0; j<n; ++j) { U[i+j*ldU] = j>=i ? LU[i*incRowLU+j*incColLU] : 0; } } for (size_t i=0; i<m; ++i) { for (size_t j=0; j<n; ++j) { LU[i*incRowLU + j*incColLU] = 0; for (size_t l=0; l<k; ++l) { LU[i*incRowLU+j*incColLU] += L[i+l*ldL] * U[l+j*ldU]; } } } for (size_t i=k; i-- >0; ) { if (p[i*incP]!=i) { dswap(n, &LU[i*incRowLU], incColLU, &LU[p[i*incP]*incRowLU], incColLU); } } double nrmA = dgenrm_inf(m, n, A, incRowA, incColA); dgeaxpy(m, n, -1, A, incRowA, incColA, LU, incRowLU, incColLU); double err = dgenrm_inf(m, n, LU, incRowLU, incColLU) / (k*nrmA*DBL_EPSILON); free(L); free(U); return err; } //-- tests for dgetrf ---------------------------------------------------------- // Get parameters for testing. Returns true if more test parameters are // available, and otherwise false. bool get_next_param(bool reset, size_t *m, size_t *n, ptrdiff_t *incRowA, ptrdiff_t *incColA, ptrdiff_t *incP) { // static variables defined in a function are technically global variables // that are only visible to the function. So by default these static // variables are initialized with zero when the program starts execution. static size_t dim[] = {5, 0, 1, 32, 31}; static ptrdiff_t inc[] = {1, 2, -1, -2}; static bool colMajor; static size_t idx_m; static size_t idx_n; static size_t idx_incRowA; static size_t idx_incColA; static size_t idx_incP; if (reset) { colMajor = false; idx_m = 0; idx_n = 0; idx_incRowA = 0; idx_incColA = 0; idx_incP = 0; } *m = dim[idx_m]; *n = dim[idx_n]; *incP = inc[idx_incP]; if (colMajor) { *incRowA = inc[idx_incRowA]; *incColA = dim[idx_m]*ptrdiff_abs(inc[idx_incRowA]*inc[idx_incColA]); } else { *incRowA = dim[idx_n]*ptrdiff_abs(inc[idx_incRowA]*inc[idx_incColA]); *incColA = inc[idx_incColA]; } if (!colMajor) { colMajor = true; return true; } colMajor = false; if (++idx_incRowA < sizeof(inc)/sizeof(ptrdiff_t)) { return true; } idx_incRowA = 0; if (++idx_incColA < sizeof(inc)/sizeof(ptrdiff_t)) { return true; } idx_incColA = 0; if (++idx_m < sizeof(dim)/sizeof(size_t)) { return true; } idx_m = 0; if (++idx_n < sizeof(dim)/sizeof(size_t)) { return true; } idx_n = 0; if (++idx_incP < sizeof(inc)/sizeof(ptrdiff_t)) { return true; } idx_incP = 0; return false; } int check_dgetrf(int argc, char **argv) { size_t m, n; ptrdiff_t incRowA, incColA, incP; bool more, reset = true; unsigned seed_rand = SEED_RAND; for (int i=0; i<argc; ++i) { if (!strcmp(argv[i], "seed")) { assert(i+1<argc); assert(sscanf(argv[i+1], "%u", &seed_rand)==1); } } srand(seed_rand); printf("%8s %8s %8s %8s %8s %8s %8s\n", "m", "n", "incRowA", "incColA", "incP", "err", "res"); do { more = get_next_param(reset, &m, &n, &incRowA, &incColA, &incP); reset = false; size_t mn = m<n ? m : n; size_t bufsize_A = 1+m*ptrdiff_abs(incRowA) * n*ptrdiff_abs(incColA); size_t bufsize_p = 1+mn*ptrdiff_abs(incP); double *buf_A = malloc(bufsize_A*sizeof(double)); double *buf_LU = malloc(bufsize_A*sizeof(double)); size_t *buf_p = malloc(bufsize_p*sizeof(size_t)); if (!buf_A || !buf_LU || !buf_p) { abort(); } dfill_nan(bufsize_A, buf_A); dfill_nan(bufsize_A, buf_LU); ifill_rand(bufsize_p, buf_p); double *A = buf_A; double *LU = buf_LU; size_t *p = buf_p; if (incRowA<0) { A -= m*incRowA; LU -= m*incRowA; } if (incColA<0) { A -= n*incColA; LU -= n*incColA; } if (incP<0) { p -= mn*incP; } randDGeMatrix(m, n, false, A, incRowA, incColA); // call implementation to be tested dgecopy(m, n, A, incRowA, incColA, LU, incRowA, incColA); DGETRF(m, n, LU, incRowA, incColA, p, incP); // compare results double err = dgetrf_err(m, n, A, incRowA, incColA, LU, incRowA, incColA, p, incP); bool pass = err<TOL_ERR; if (!pass) { printf("A =\n"); printDGeMatrix(m, n, A, incRowA, incColA); printf("p=\n"); printIGeMatrix(1, mn, p, 0, incP); printf("L*U - A = \n"); printfDGeMatrix("%10.1e ", m, n, LU, incRowA, incColA); } printf("%8zu %8zu %8td %8td %8td %7.1e %8s\n", m, n, incRowA, incColA, incP, err, pass ? "PASS" : "FAILED"); free(buf_A); free(buf_LU); free(buf_p); if (!pass) { return 1; } } while (more); return 0; } //-- benchmark for dgemv ------------------------------------------------------- #ifndef COLMAJOR #define COLMAJOR 1 #endif #ifndef MAX_M #define MAX_M 3000 #endif #ifndef MAX_N #define MAX_N 3000 #endif #ifndef ALPHA #define ALPHA 1 #endif #ifndef BETA #define BETA 1 #endif void bench_dgetrf(int argc, char **argv) { bool colmajor = COLMAJOR; ptrdiff_t incP = 1; ptrdiff_t incRowA_ = 1; ptrdiff_t incColA_ = 1; size_t min_m = 100; size_t min_n = 100; size_t inc_m = 100; size_t inc_n = 100; size_t max_m = MAX_M; size_t max_n = MAX_N; for (int i=0; i<argc; ++i) { if (!strcmp(argv[i], "colmajor")) { colmajor = true; } if (!strcmp(argv[i], "rowmajor")) { colmajor = false; } if (!strcmp(argv[i], "incP")) { assert(i+1<argc); assert(sscanf(argv[i+1], "%td", &incP)==1); } if (!strcmp(argv[i], "incRowA")) { assert(i+1<argc); assert(sscanf(argv[i+1], "%td", &incRowA_)==1); } if (!strcmp(argv[i], "incColA")) { assert(i+1<argc); assert(sscanf(argv[i+1], "%td", &incColA_)==1); } if (!strcmp(argv[i], "min_m")) { assert(i+1<argc); assert(sscanf(argv[i+1], "%td", &min_m)==1); } if (!strcmp(argv[i], "min_n")) { assert(i+1<argc); assert(sscanf(argv[i+1], "%td", &min_n)==1); } if (!strcmp(argv[i], "max_m")) { assert(i+1<argc); assert(sscanf(argv[i+1], "%td", &max_m)==1); } if (!strcmp(argv[i], "max_n")) { assert(i+1<argc); assert(sscanf(argv[i+1], "%td", &max_n)==1); } if (!strcmp(argv[i], "inc_m")) { assert(i+1<argc); assert(sscanf(argv[i+1], "%td", &inc_m)==1); } if (!strcmp(argv[i], "inc_n")) { assert(i+1<argc); assert(sscanf(argv[i+1], "%td", &inc_n)==1); } } srand(SEED_RAND); printf("#colmajor = %d\n", colmajor); printf("#incP = %td\n", incP); size_t min_mn = max_m<max_n ? max_m : max_n; size_t bufsize_A = max_m*ptrdiff_abs(incRowA_) * max_n*ptrdiff_abs(incColA_) + 1; size_t bufsize_p = min_mn*ptrdiff_abs(incP) + 1; double *buf_A = malloc(bufsize_A*sizeof(double)); double *buf_LU = malloc(bufsize_A*sizeof(double)); size_t *buf_p = malloc(bufsize_p*sizeof(size_t)); if (!buf_A || !buf_LU || !buf_p) { abort(); } // print header printf("#%7s %7s %7s %7s ", "m", "n", "incRowA", "incColA"); printf("%10s %10s %7s", "time", "mflops", "err"); printf("\n"); for (size_t m=min_m, n=min_n; m<=max_m && n<=max_n; m+=inc_m, n+=inc_n) { size_t max_mn = m<n ? n : m; size_t min_mn = m<n ? m : n; double mflop = max_mn * min_mn * min_mn -(min_mn * min_mn * min_mn) / 3.0 -(min_mn * min_mn) / 2.0; mflop /= 1000000.0; ptrdiff_t incRowA = incRowA_ * (colmajor ? 1 : n); ptrdiff_t incColA = incColA_ * (colmajor ? m : 1); double *A = buf_A; double *LU = buf_LU; size_t *p = buf_p; if (incRowA<0) { A -= m*incRowA; LU -= m*incRowA; } if (incColA<0) { A -= n*incColA; LU -= n*incColA; } if (incP<0) { p -= min_mn*incP; } randDGeMatrix(m, n, false, A, incRowA, incColA); ifill_rand(bufsize_p, buf_p); double t = 0; size_t runs = 0; while (t<0.1 || runs<3) { dgecopy(m, n, A, incRowA, incColA, LU, incRowA, incColA); double t0 = walltime(); DGETRF(m, n, LU, incRowA, incColA, p, incP); t += walltime() - t0; ++runs; } t /= runs; printf(" %7zu %7zu %7td %7td %10.2lf %10.2lf", m, n, incRowA, incColA, t, mflop/t); #ifndef BENCH_NOCHECK double err = dgetrf_err(m, n, A, incRowA, incColA, LU, incRowA, incColA, p, incP); printf(" %7.1e", err); #else printf(" %7s", "---"); #endif printf("\n"); fflush(stdout); } free(buf_A); free(buf_LU); free(buf_p); } //------------------------------------------------------------------------------ int main(int argc, char **argv) { if (argc<2 || (strcmp(argv[1], "check") && strcmp(argv[1], "bench"))) { fprintf(stderr, "usage:\n"); fprintf(stderr, " %s check [seed]\n", argv[0]); fprintf(stderr, " %s bench [colmajor | rowmajor]" " [incP <value>]" "\n", argv[0]); return 1; } if (!strcmp(argv[1], "check")) { return check_dgetrf(argc-2, argv+2); } if (!strcmp(argv[1], "bench")) { bench_dgetrf(argc-2, argv+2); } }
You can compile the test and link it with your ulmBLAS by
heim$ gcc -Wall -O3 -I. -std=c99 -o test_dgetrf ulmblas.c ulmaux.c test_dgetrf.c heim$
Run the tests with ./test_dgetrf check and the benchmark with ./test_dgetrf bench.
Example: Running the test
heim$ ./test_dgetrf check m n incRowA incColA incP err res 5 5 5 1 1 4.8e-02 PASS 5 5 1 5 1 9.7e-02 PASS 5 5 10 1 1 5.7e-02 PASS 5 5 2 10 1 4.7e-02 PASS 5 5 5 1 1 7.1e-02 PASS 5 5 -1 5 1 1.2e-01 PASS 5 5 10 1 1 1.3e-01 PASS 5 5 -2 10 1 1.1e-01 PASS 5 5 10 2 1 7.7e-02 PASS 5 5 1 10 1 8.0e-02 PASS 5 5 20 2 1 9.1e-02 PASS 5 5 2 20 1 4.8e-02 PASS 5 5 10 2 1 9.1e-02 PASS 5 5 -1 10 1 5.4e-02 PASS 5 5 20 2 1 1.1e-01 PASS 5 5 -2 20 1 3.6e-02 PASS 5 5 5 -1 1 1.8e-01 PASS 5 5 1 5 1 4.1e-02 PASS 5 5 10 -1 1 3.5e-02 PASS 5 5 2 10 1 7.7e-02 PASS 5 5 5 -1 1 7.6e-02 PASS 5 5 -1 5 1 8.9e-02 PASS 5 5 10 -1 1 8.6e-02 PASS 5 5 -2 10 1 4.8e-02 PASS 5 5 10 -2 1 1.5e-01 PASS 5 5 1 10 1 3.1e-02 PASS 5 5 20 -2 1 3.8e-02 PASS 5 5 2 20 1 7.4e-02 PASS 5 5 10 -2 1 3.4e-02 PASS 5 5 -1 10 1 7.7e-02 PASS 5 5 20 -2 1 6.0e-02 PASS 5 5 -2 20 1 7.3e-02 PASS 0 5 5 1 1 0.0e+00 PASS 0 5 1 0 1 0.0e+00 PASS 0 5 10 1 1 0.0e+00 PASS 0 5 2 0 1 0.0e+00 PASS 0 5 5 1 1 0.0e+00 PASS 0 5 -1 0 1 0.0e+00 PASS 0 5 10 1 1 0.0e+00 PASS 0 5 -2 0 1 0.0e+00 PASS 0 5 10 2 1 0.0e+00 PASS 0 5 1 0 1 0.0e+00 PASS 0 5 20 2 1 0.0e+00 PASS 0 5 2 0 1 0.0e+00 PASS 0 5 10 2 1 0.0e+00 PASS 0 5 -1 0 1 0.0e+00 PASS 0 5 20 2 1 0.0e+00 PASS 0 5 -2 0 1 0.0e+00 PASS 0 5 5 -1 1 0.0e+00 PASS 0 5 1 0 1 0.0e+00 PASS 0 5 10 -1 1 0.0e+00 PASS 0 5 2 0 1 0.0e+00 PASS 0 5 5 -1 1 0.0e+00 PASS 0 5 -1 0 1 0.0e+00 PASS 0 5 10 -1 1 0.0e+00 PASS 0 5 -2 0 1 0.0e+00 PASS 0 5 10 -2 1 0.0e+00 PASS 0 5 1 0 1 0.0e+00 PASS 0 5 20 -2 1 0.0e+00 PASS 0 5 2 0 1 0.0e+00 PASS 0 5 10 -2 1 0.0e+00 PASS 0 5 -1 0 1 0.0e+00 PASS 0 5 20 -2 1 0.0e+00 PASS 0 5 -2 0 1 0.0e+00 PASS 1 5 5 1 1 0.0e+00 PASS 1 5 1 1 1 0.0e+00 PASS 1 5 10 1 1 0.0e+00 PASS 1 5 2 2 1 0.0e+00 PASS 1 5 5 1 1 0.0e+00 PASS 1 5 -1 1 1 0.0e+00 PASS 1 5 10 1 1 0.0e+00 PASS 1 5 -2 2 1 0.0e+00 PASS 1 5 10 2 1 0.0e+00 PASS 1 5 1 2 1 0.0e+00 PASS 1 5 20 2 1 0.0e+00 PASS 1 5 2 4 1 0.0e+00 PASS 1 5 10 2 1 0.0e+00 PASS 1 5 -1 2 1 0.0e+00 PASS 1 5 20 2 1 0.0e+00 PASS 1 5 -2 4 1 0.0e+00 PASS 1 5 5 -1 1 0.0e+00 PASS 1 5 1 1 1 0.0e+00 PASS 1 5 10 -1 1 0.0e+00 PASS 1 5 2 2 1 0.0e+00 PASS 1 5 5 -1 1 0.0e+00 PASS 1 5 -1 1 1 0.0e+00 PASS 1 5 10 -1 1 0.0e+00 PASS 1 5 -2 2 1 0.0e+00 PASS 1 5 10 -2 1 0.0e+00 PASS 1 5 1 2 1 0.0e+00 PASS 1 5 20 -2 1 0.0e+00 PASS 1 5 2 4 1 0.0e+00 PASS 1 5 10 -2 1 0.0e+00 PASS 1 5 -1 2 1 0.0e+00 PASS 1 5 20 -2 1 0.0e+00 PASS 1 5 -2 4 1 0.0e+00 PASS 32 5 5 1 1 9.3e-02 PASS 32 5 1 32 1 1.5e-01 PASS 32 5 10 1 1 1.5e-01 PASS 32 5 2 64 1 8.3e-02 PASS 32 5 5 1 1 1.5e-01 PASS 32 5 -1 32 1 1.1e-01 PASS 32 5 10 1 1 1.4e-01 PASS 32 5 -2 64 1 1.1e-01 PASS 32 5 10 2 1 1.3e-01 PASS 32 5 1 64 1 1.2e-01 PASS 32 5 20 2 1 1.1e-01 PASS 32 5 2 128 1 1.7e-01 PASS 32 5 10 2 1 1.4e-01 PASS 32 5 -1 64 1 1.3e-01 PASS 32 5 20 2 1 1.3e-01 PASS 32 5 -2 128 1 1.0e-01 PASS 32 5 5 -1 1 1.5e-01 PASS 32 5 1 32 1 1.1e-01 PASS 32 5 10 -1 1 1.2e-01 PASS 32 5 2 64 1 1.2e-01 PASS 32 5 5 -1 1 1.3e-01 PASS 32 5 -1 32 1 1.4e-01 PASS 32 5 10 -1 1 1.9e-01 PASS 32 5 -2 64 1 9.3e-02 PASS 32 5 10 -2 1 2.1e-01 PASS 32 5 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4.0e-02 PASS 32 32 2 64 -2 5.2e-02 PASS 32 32 32 -1 -2 4.9e-02 PASS 32 32 -1 32 -2 4.9e-02 PASS 32 32 64 -1 -2 4.6e-02 PASS 32 32 -2 64 -2 5.0e-02 PASS 32 32 64 -2 -2 4.7e-02 PASS 32 32 1 64 -2 6.1e-02 PASS 32 32 128 -2 -2 4.7e-02 PASS 32 32 2 128 -2 5.0e-02 PASS 32 32 64 -2 -2 5.3e-02 PASS 32 32 -1 64 -2 4.7e-02 PASS 32 32 128 -2 -2 5.1e-02 PASS 32 32 -2 128 -2 4.4e-02 PASS 31 32 32 1 -2 4.5e-02 PASS 31 32 1 31 -2 5.0e-02 PASS 31 32 64 1 -2 5.2e-02 PASS 31 32 2 62 -2 6.0e-02 PASS 31 32 32 1 -2 4.6e-02 PASS 31 32 -1 31 -2 6.3e-02 PASS 31 32 64 1 -2 6.4e-02 PASS 31 32 -2 62 -2 4.8e-02 PASS 31 32 64 2 -2 6.0e-02 PASS 31 32 1 62 -2 4.2e-02 PASS 31 32 128 2 -2 5.1e-02 PASS 31 32 2 124 -2 5.7e-02 PASS 31 32 64 2 -2 4.5e-02 PASS 31 32 -1 62 -2 4.2e-02 PASS 31 32 128 2 -2 6.0e-02 PASS 31 32 -2 124 -2 4.8e-02 PASS 31 32 32 -1 -2 4.6e-02 PASS 31 32 1 31 -2 4.5e-02 PASS 31 32 64 -1 -2 5.1e-02 PASS 31 32 2 62 -2 4.2e-02 PASS 31 32 32 -1 -2 4.5e-02 PASS 31 32 -1 31 -2 3.9e-02 PASS 31 32 64 -1 -2 4.6e-02 PASS 31 32 -2 62 -2 4.8e-02 PASS 31 32 64 -2 -2 4.6e-02 PASS 31 32 1 62 -2 5.9e-02 PASS 31 32 128 -2 -2 5.1e-02 PASS 31 32 2 124 -2 5.1e-02 PASS 31 32 64 -2 -2 5.2e-02 PASS 31 32 -1 62 -2 4.3e-02 PASS 31 32 128 -2 -2 5.6e-02 PASS 31 32 -2 124 -2 4.7e-02 PASS 5 31 31 1 -2 7.8e-02 PASS 5 31 1 5 -2 8.8e-02 PASS 5 31 62 1 -2 1.4e-01 PASS 5 31 2 10 -2 6.8e-02 PASS 5 31 31 1 -2 1.5e-01 PASS 5 31 -1 5 -2 1.0e-01 PASS 5 31 62 1 -2 9.4e-02 PASS 5 31 -2 10 -2 1.1e-01 PASS 5 31 62 2 -2 9.2e-02 PASS 5 31 1 10 -2 1.0e-01 PASS 5 31 124 2 -2 9.2e-02 PASS 5 31 2 20 -2 8.2e-02 PASS 5 31 62 2 -2 6.9e-02 PASS 5 31 -1 10 -2 1.2e-01 PASS 5 31 124 2 -2 7.0e-02 PASS 5 31 -2 20 -2 1.2e-01 PASS 5 31 31 -1 -2 8.4e-02 PASS 5 31 1 5 -2 6.1e-02 PASS 5 31 62 -1 -2 1.2e-01 PASS 5 31 2 10 -2 9.0e-02 PASS 5 31 31 -1 -2 1.1e-01 PASS 5 31 -1 5 -2 1.1e-01 PASS 5 31 62 -1 -2 1.4e-01 PASS 5 31 -2 10 -2 7.3e-02 PASS 5 31 62 -2 -2 1.1e-01 PASS 5 31 1 10 -2 8.4e-02 PASS 5 31 124 -2 -2 1.1e-01 PASS 5 31 2 20 -2 1.2e-01 PASS 5 31 62 -2 -2 9.2e-02 PASS 5 31 -1 10 -2 7.5e-02 PASS 5 31 124 -2 -2 9.0e-02 PASS 5 31 -2 20 -2 8.9e-02 PASS 0 31 31 1 -2 0.0e+00 PASS 0 31 1 0 -2 0.0e+00 PASS 0 31 62 1 -2 0.0e+00 PASS 0 31 2 0 -2 0.0e+00 PASS 0 31 31 1 -2 0.0e+00 PASS 0 31 -1 0 -2 0.0e+00 PASS 0 31 62 1 -2 0.0e+00 PASS 0 31 -2 0 -2 0.0e+00 PASS 0 31 62 2 -2 0.0e+00 PASS 0 31 1 0 -2 0.0e+00 PASS 0 31 124 2 -2 0.0e+00 PASS 0 31 2 0 -2 0.0e+00 PASS 0 31 62 2 -2 0.0e+00 PASS 0 31 -1 0 -2 0.0e+00 PASS 0 31 124 2 -2 0.0e+00 PASS 0 31 -2 0 -2 0.0e+00 PASS 0 31 31 -1 -2 0.0e+00 PASS 0 31 1 0 -2 0.0e+00 PASS 0 31 62 -1 -2 0.0e+00 PASS 0 31 2 0 -2 0.0e+00 PASS 0 31 31 -1 -2 0.0e+00 PASS 0 31 -1 0 -2 0.0e+00 PASS 0 31 62 -1 -2 0.0e+00 PASS 0 31 -2 0 -2 0.0e+00 PASS 0 31 62 -2 -2 0.0e+00 PASS 0 31 1 0 -2 0.0e+00 PASS 0 31 124 -2 -2 0.0e+00 PASS 0 31 2 0 -2 0.0e+00 PASS 0 31 62 -2 -2 0.0e+00 PASS 0 31 -1 0 -2 0.0e+00 PASS 0 31 124 -2 -2 0.0e+00 PASS 0 31 -2 0 -2 0.0e+00 PASS 1 31 31 1 -2 0.0e+00 PASS 1 31 1 1 -2 0.0e+00 PASS 1 31 62 1 -2 0.0e+00 PASS 1 31 2 2 -2 0.0e+00 PASS 1 31 31 1 -2 0.0e+00 PASS 1 31 -1 1 -2 0.0e+00 PASS 1 31 62 1 -2 0.0e+00 PASS 1 31 -2 2 -2 0.0e+00 PASS 1 31 62 2 -2 0.0e+00 PASS 1 31 1 2 -2 0.0e+00 PASS 1 31 124 2 -2 0.0e+00 PASS 1 31 2 4 -2 0.0e+00 PASS 1 31 62 2 -2 0.0e+00 PASS 1 31 -1 2 -2 0.0e+00 PASS 1 31 124 2 -2 0.0e+00 PASS 1 31 -2 4 -2 0.0e+00 PASS 1 31 31 -1 -2 0.0e+00 PASS 1 31 1 1 -2 0.0e+00 PASS 1 31 62 -1 -2 0.0e+00 PASS 1 31 2 2 -2 0.0e+00 PASS 1 31 31 -1 -2 0.0e+00 PASS 1 31 -1 1 -2 0.0e+00 PASS 1 31 62 -1 -2 0.0e+00 PASS 1 31 -2 2 -2 0.0e+00 PASS 1 31 62 -2 -2 0.0e+00 PASS 1 31 1 2 -2 0.0e+00 PASS 1 31 124 -2 -2 0.0e+00 PASS 1 31 2 4 -2 0.0e+00 PASS 1 31 62 -2 -2 0.0e+00 PASS 1 31 -1 2 -2 0.0e+00 PASS 1 31 124 -2 -2 0.0e+00 PASS 1 31 -2 4 -2 0.0e+00 PASS 32 31 31 1 -2 4.8e-02 PASS 32 31 1 32 -2 5.6e-02 PASS 32 31 62 1 -2 5.1e-02 PASS 32 31 2 64 -2 5.5e-02 PASS 32 31 31 1 -2 4.2e-02 PASS 32 31 -1 32 -2 5.5e-02 PASS 32 31 62 1 -2 6.6e-02 PASS 32 31 -2 64 -2 4.8e-02 PASS 32 31 62 2 -2 4.7e-02 PASS 32 31 1 64 -2 5.4e-02 PASS 32 31 124 2 -2 6.3e-02 PASS 32 31 2 128 -2 5.2e-02 PASS 32 31 62 2 -2 5.0e-02 PASS 32 31 -1 64 -2 5.5e-02 PASS 32 31 124 2 -2 5.2e-02 PASS 32 31 -2 128 -2 5.1e-02 PASS 32 31 31 -1 -2 5.1e-02 PASS 32 31 1 32 -2 4.4e-02 PASS 32 31 62 -1 -2 5.2e-02 PASS 32 31 2 64 -2 4.6e-02 PASS 32 31 31 -1 -2 5.2e-02 PASS 32 31 -1 32 -2 5.4e-02 PASS 32 31 62 -1 -2 4.9e-02 PASS 32 31 -2 64 -2 5.9e-02 PASS 32 31 62 -2 -2 4.7e-02 PASS 32 31 1 64 -2 4.6e-02 PASS 32 31 124 -2 -2 5.7e-02 PASS 32 31 2 128 -2 4.5e-02 PASS 32 31 62 -2 -2 6.7e-02 PASS 32 31 -1 64 -2 5.3e-02 PASS 32 31 124 -2 -2 5.9e-02 PASS 32 31 -2 128 -2 5.8e-02 PASS 31 31 31 1 -2 5.0e-02 PASS 31 31 1 31 -2 4.7e-02 PASS 31 31 62 1 -2 4.3e-02 PASS 31 31 2 62 -2 4.8e-02 PASS 31 31 31 1 -2 6.0e-02 PASS 31 31 -1 31 -2 4.6e-02 PASS 31 31 62 1 -2 5.1e-02 PASS 31 31 -2 62 -2 5.8e-02 PASS 31 31 62 2 -2 5.2e-02 PASS 31 31 1 62 -2 5.9e-02 PASS 31 31 124 2 -2 5.0e-02 PASS 31 31 2 124 -2 4.7e-02 PASS 31 31 62 2 -2 4.2e-02 PASS 31 31 -1 62 -2 4.8e-02 PASS 31 31 124 2 -2 5.9e-02 PASS 31 31 -2 124 -2 5.2e-02 PASS 31 31 31 -1 -2 5.4e-02 PASS 31 31 1 31 -2 4.7e-02 PASS 31 31 62 -1 -2 5.4e-02 PASS 31 31 2 62 -2 5.8e-02 PASS 31 31 31 -1 -2 5.9e-02 PASS 31 31 -1 31 -2 5.4e-02 PASS 31 31 62 -1 -2 4.5e-02 PASS 31 31 -2 62 -2 4.7e-02 PASS 31 31 62 -2 -2 4.9e-02 PASS 31 31 1 62 -2 5.8e-02 PASS 31 31 124 -2 -2 4.6e-02 PASS 31 31 2 124 -2 5.4e-02 PASS 31 31 62 -2 -2 5.7e-02 PASS 31 31 -1 62 -2 5.6e-02 PASS 31 31 124 -2 -2 4.6e-02 PASS 31 31 -2 124 -2 4.6e-02 PASS heim$
Example: Running the benchmark
heim$ ./test_dgetrf bench #colmajor = 1 #incP = 1 # m n incRowA incColA time mflops err 100 100 1 100 0.00 1515.22 3.5e-02 200 200 1 200 0.00 2125.33 3.1e-02 300 300 1 300 0.01 2154.60 2.7e-02 400 400 1 400 0.02 2129.33 2.7e-02 500 500 1 500 0.04 2269.32 2.5e-02 600 600 1 600 0.06 2270.84 2.4e-02 700 700 1 700 0.10 2210.53 2.2e-02 800 800 1 800 0.15 2224.00 2.2e-02 900 900 1 900 0.22 2174.31 2.1e-02 1000 1000 1 1000 0.31 2148.92 2.1e-02 1100 1100 1 1100 0.42 2111.26 2.0e-02 1200 1200 1 1200 0.55 2093.24 2.0e-02 1300 1300 1 1300 0.71 2061.72 2.0e-02 1400 1400 1 1400 0.89 2054.33 1.9e-02 1500 1500 1 1500 1.10 2038.26 2.0e-02 1600 1600 1 1600 1.34 2031.80 2.0e-02 1700 1700 1 1700 1.63 2008.52 1.9e-02 1800 1800 1 1800 1.96 1979.48 1.8e-02 1900 1900 1 1900 2.33 1964.55 1.8e-02 2000 2000 1 2000 2.72 1960.05 1.8e-02 2100 2100 1 2100 3.15 1961.38 1.8e-02 2200 2200 1 2200 3.62 1958.49 1.8e-02 2300 2300 1 2300 4.14 1960.20 1.7e-02 2400 2400 1 2400 4.68 1968.62 1.7e-02 2500 2500 1 2500 5.29 1969.77 1.7e-02 2600 2600 1 2600 5.95 1969.84 1.7e-02 2700 2700 1 2700 6.63 1978.64 1.7e-02 2800 2800 1 2800 7.38 1982.49 1.7e-02 2900 2900 1 2900 8.21 1979.11 1.7e-02 3000 3000 1 3000 9.07 1984.80 1.7e-02 heim$