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Linpack Floating Point benchmark that runs as an Arduino sketch. (Yes, I know...) I wanted to generically measure Arduino Floating Point performance, this seemed like a reasonable(ish) way to do it. Runs with N=10, single precision, but produces sane looking results & residual. (89 Linpack kFLOPS on a Freetronics Eleven, ie Arduino Uno compatibl…
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# include <stdlib.h> | |
# include <stdio.h> | |
# include <math.h> | |
int do_benchmark ( void ); | |
double cpu_time ( void ); | |
void daxpy ( int n, double da, double dx[], int incx, double dy[], int incy ); | |
double ddot ( int n, double dx[], int incx, double dy[], int incy ); | |
int dgefa ( double a[], int lda, int n, int ipvt[] ); | |
void dgesl ( double a[], int lda, int n, int ipvt[], double b[], int job ); | |
void dscal ( int n, double sa, double x[], int incx ); | |
int idamax ( int n, double dx[], int incx ); | |
double r8_abs ( double x ); | |
double r8_epsilon ( void ); | |
double r8_max ( double x, double y ); | |
double r8_random ( int iseed[4] ); | |
double *r8mat_gen ( int lda, int n ); | |
static FILE uartout = {0} ; | |
static int uart_putchar (char c, FILE *stream) | |
{ | |
Serial.write(c) ; | |
return 0 ; | |
} | |
void setup() { | |
Serial.begin(9600); | |
fdev_setup_stream (&uartout, uart_putchar, NULL, _FDEV_SETUP_WRITE); | |
stdout = &uartout ; | |
} | |
void loop() { | |
printf("Starting benchmark...\n"); | |
do_benchmark(); | |
} | |
/******************************************************************************/ | |
int do_benchmark ( void ) | |
/******************************************************************************/ | |
/* | |
Purpose: | |
MAIN is the main program for LINPACK_BENCH. | |
Discussion: | |
LINPACK_BENCH drives the double precision LINPACK benchmark program. | |
Modified: | |
25 July 2008 | |
Parameters: | |
N is the problem size. | |
*/ | |
{ | |
# define N 8 | |
# define LDA ( N + 1 ) | |
static double a[N * LDA]; | |
static double a_max; | |
static double b[N]; | |
static double b_max; | |
const double cray = 0.056; | |
static double eps; | |
int i; | |
int info; | |
static int ipvt[N]; | |
int j; | |
int job; | |
double ops; | |
static double resid[N]; | |
double resid_max; | |
double residn; | |
static double rhs[N]; | |
double t1; | |
double t2; | |
static double time[6]; | |
double total; | |
double x[N]; | |
printf ( "\n" ); | |
printf ( "LINPACK_BENCH\n" ); | |
printf ( " C version\n" ); | |
printf ( "\n" ); | |
printf ( " The LINPACK benchmark.\n" ); | |
printf ( " Language: C\n" ); | |
printf ( " Datatype: Double precision real\n" ); | |
printf ( " Matrix order N = %d\n", N ); | |
printf ( " Leading matrix dimension LDA = %d\n", LDA ); | |
ops = ( double ) ( 2L * N * N * N ) / 3.0 + 2.0 * ( double ) ( (long)N * N ); | |
/* | |
Allocate space for arrays. | |
*/ | |
r8mat_gen ( LDA, N, a); | |
a_max = 0.0; | |
for ( j = 0; j < N; j++ ) | |
{ | |
for ( i = 0; i < N; i++ ) | |
{ | |
a_max = r8_max ( a_max, a[i+j*LDA] ); | |
} | |
} | |
for ( i = 0; i < N; i++ ) | |
{ | |
x[i] = 1.0; | |
} | |
for ( i = 0; i < N; i++ ) | |
{ | |
b[i] = 0.0; | |
for ( j = 0; j < N; j++ ) | |
{ | |
b[i] = b[i] + a[i+j*LDA] * x[j]; | |
} | |
} | |
t1 = cpu_time ( ); | |
info = dgefa ( a, LDA, N, ipvt ); | |
if ( info != 0 ) | |
{ | |
printf ( "\n" ); | |
printf ( "LINPACK_BENCH - Fatal error!\n" ); | |
printf ( " The matrix A is apparently singular.\n" ); | |
printf ( " Abnormal end of execution.\n" ); | |
return 1; | |
} | |
t2 = cpu_time ( ); | |
time[0] = t2 - t1; | |
t1 = cpu_time ( ); | |
job = 0; | |
dgesl ( a, LDA, N, ipvt, b, job ); | |
t2 = cpu_time ( ); | |
time[1] = t2 - t1; | |
total = time[0] + time[1]; | |
/* | |
Compute a residual to verify results. | |
*/ | |
r8mat_gen ( LDA, N, a ); | |
for ( i = 0; i < N; i++ ) | |
{ | |
x[i] = 1.0; | |
} | |
for ( i = 0; i < N; i++ ) | |
{ | |
rhs[i] = 0.0; | |
for ( j = 0; j < N; j++ ) | |
{ | |
rhs[i] = rhs[i] + a[i+j*LDA] * x[j]; | |
} | |
} | |
for ( i = 0; i < N; i++ ) | |
{ | |
resid[i] = -rhs[i]; | |
for ( j = 0; j < N; j++ ) | |
{ | |
resid[i] = resid[i] + a[i+j*LDA] * b[j]; | |
} | |
} | |
resid_max = 0.0; | |
for ( i = 0; i < N; i++ ) | |
{ | |
resid_max = r8_max ( resid_max, r8_abs ( resid[i] ) ); | |
} | |
b_max = 0.0; | |
for ( i = 0; i < N; i++ ) | |
{ | |
b_max = r8_max ( b_max, r8_abs ( b[i] ) ); | |
} | |
eps = r8_epsilon ( ); | |
residn = resid_max / ( double ) N / a_max / b_max / eps; | |
time[2] = total; | |
if ( 0.0 < total ) | |
{ | |
time[3] = ops / ( 1.0E+06 * total ); | |
} | |
else | |
{ | |
time[3] = -1.0; | |
} | |
time[4] = 2.0 / time[3]; | |
time[5] = total / cray; | |
printf ( "\n" ); | |
printf ( " Norm. Resid Resid MACHEP X[1] X[N]\n" ); | |
printf ( "\n" ); | |
Serial.print(" "); | |
Serial.print(residn, 14); | |
Serial.print(" "); | |
Serial.print(resid_max, 14); | |
Serial.print(" "); | |
Serial.print(eps, 14); | |
Serial.print(" "); | |
Serial.print(b[0], 14); | |
Serial.print(" "); | |
Serial.print(b[N-1], 14); | |
Serial.print(" "); | |
//printf ( " %14f %14f %14e %14f %14f\n", residn, resid_max, eps, b[0], b[N-1] ); | |
printf ( "\n" ); | |
printf ( " Factor Solve Total MFLOPS Unit Cray-Ratio\n" ); | |
printf ( "\n" ); | |
for(int i =0; i<6;i++) { | |
Serial.print(" "); | |
Serial.print(time[i], 9); | |
} | |
//printf ( " %9f %9f %9f %9f %9f %9f\n", | |
// time[0], time[1], time[2], time[3], time[4], time[5] ); | |
/* | |
Terminate. | |
*/ | |
printf ( "\n" ); | |
printf ( "LINPACK_BENCH\n" ); | |
printf ( " Normal end of execution.\n" ); | |
printf ( "\n" ); | |
return 0; | |
# undef LDA | |
# undef N | |
} | |
/******************************************************************************/ | |
double cpu_time ( void ) | |
/******************************************************************************/ | |
/* | |
Purpose: | |
CPU_TIME returns the current reading on the CPU clock. | |
Discussion: | |
The CPU time measurements available through this routine are often | |
not very accurate. In some cases, the accuracy is no better than | |
a hundredth of a second. | |
Licensing: | |
This code is distributed under the GNU LGPL license. | |
Modified: | |
06 June 2005 | |
Author: | |
John Burkardt | |
Parameters: | |
Output, double CPU_TIME, the current reading of the CPU clock, in seconds. | |
*/ | |
{ | |
double value; | |
value = ( double ) micros ( ) | |
/ ( double ) 1000000; | |
return value; | |
} | |
/******************************************************************************/ | |
void daxpy ( int n, double da, double dx[], int incx, double dy[], int incy ) | |
/******************************************************************************/ | |
/* | |
Purpose: | |
DAXPY computes constant times a vector plus a vector. | |
Discussion: | |
This routine uses unrolled loops for increments equal to one. | |
Modified: | |
30 March 2007 | |
Author: | |
FORTRAN77 original by Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart. | |
C version by John Burkardt | |
Reference: | |
Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart, | |
LINPACK User's Guide, | |
SIAM, 1979. | |
Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh, | |
Basic Linear Algebra Subprograms for Fortran Usage, | |
Algorithm 539, | |
ACM Transactions on Mathematical Software, | |
Volume 5, Number 3, September 1979, pages 308-323. | |
Parameters: | |
Input, int N, the number of elements in DX and DY. | |
Input, double DA, the multiplier of DX. | |
Input, double DX[*], the first vector. | |
Input, int INCX, the increment between successive entries of DX. | |
Input/output, double DY[*], the second vector. | |
On output, DY[*] has been replaced by DY[*] + DA * DX[*]. | |
Input, int INCY, the increment between successive entries of DY. | |
*/ | |
{ | |
int i; | |
int ix; | |
int iy; | |
int m; | |
if ( n <= 0 ) | |
{ | |
return; | |
} | |
if ( da == 0.0 ) | |
{ | |
return; | |
} | |
/* | |
Code for unequal increments or equal increments | |
not equal to 1. | |
*/ | |
if ( incx != 1 || incy != 1 ) | |
{ | |
if ( 0 <= incx ) | |
{ | |
ix = 0; | |
} | |
else | |
{ | |
ix = ( - n + 1 ) * incx; | |
} | |
if ( 0 <= incy ) | |
{ | |
iy = 0; | |
} | |
else | |
{ | |
iy = ( - n + 1 ) * incy; | |
} | |
for ( i = 0; i < n; i++ ) | |
{ | |
dy[iy] = dy[iy] + da * dx[ix]; | |
ix = ix + incx; | |
iy = iy + incy; | |
} | |
} | |
/* | |
Code for both increments equal to 1. | |
*/ | |
else | |
{ | |
m = n % 4; | |
for ( i = 0; i < m; i++ ) | |
{ | |
dy[i] = dy[i] + da * dx[i]; | |
} | |
for ( i = m; i < n; i = i + 4 ) | |
{ | |
dy[i ] = dy[i ] + da * dx[i ]; | |
dy[i+1] = dy[i+1] + da * dx[i+1]; | |
dy[i+2] = dy[i+2] + da * dx[i+2]; | |
dy[i+3] = dy[i+3] + da * dx[i+3]; | |
} | |
} | |
return; | |
} | |
/******************************************************************************/ | |
double ddot ( int n, double dx[], int incx, double dy[], int incy ) | |
/******************************************************************************/ | |
/* | |
Purpose: | |
DDOT forms the dot product of two vectors. | |
Discussion: | |
This routine uses unrolled loops for increments equal to one. | |
Modified: | |
30 March 2007 | |
Author: | |
FORTRAN77 original by Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart. | |
C version by John Burkardt | |
Reference: | |
Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart, | |
LINPACK User's Guide, | |
SIAM, 1979. | |
Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh, | |
Basic Linear Algebra Subprograms for Fortran Usage, | |
Algorithm 539, | |
ACM Transactions on Mathematical Software, | |
Volume 5, Number 3, September 1979, pages 308-323. | |
Parameters: | |
Input, int N, the number of entries in the vectors. | |
Input, double DX[*], the first vector. | |
Input, int INCX, the increment between successive entries in DX. | |
Input, double DY[*], the second vector. | |
Input, int INCY, the increment between successive entries in DY. | |
Output, double DDOT, the sum of the product of the corresponding | |
entries of DX and DY. | |
*/ | |
{ | |
double dtemp; | |
int i; | |
int ix; | |
int iy; | |
int m; | |
dtemp = 0.0; | |
if ( n <= 0 ) | |
{ | |
return dtemp; | |
} | |
/* | |
Code for unequal increments or equal increments | |
not equal to 1. | |
*/ | |
if ( incx != 1 || incy != 1 ) | |
{ | |
if ( 0 <= incx ) | |
{ | |
ix = 0; | |
} | |
else | |
{ | |
ix = ( - n + 1 ) * incx; | |
} | |
if ( 0 <= incy ) | |
{ | |
iy = 0; | |
} | |
else | |
{ | |
iy = ( - n + 1 ) * incy; | |
} | |
for ( i = 0; i < n; i++ ) | |
{ | |
dtemp = dtemp + dx[ix] * dy[iy]; | |
ix = ix + incx; | |
iy = iy + incy; | |
} | |
} | |
/* | |
Code for both increments equal to 1. | |
*/ | |
else | |
{ | |
m = n % 5; | |
for ( i = 0; i < m; i++ ) | |
{ | |
dtemp = dtemp + dx[i] * dy[i]; | |
} | |
for ( i = m; i < n; i = i + 5 ) | |
{ | |
dtemp = dtemp + dx[i ] * dy[i ] | |
+ dx[i+1] * dy[i+1] | |
+ dx[i+2] * dy[i+2] | |
+ dx[i+3] * dy[i+3] | |
+ dx[i+4] * dy[i+4]; | |
} | |
} | |
return dtemp; | |
} | |
/******************************************************************************/ | |
int dgefa ( double a[], int lda, int n, int ipvt[] ) | |
/******************************************************************************/ | |
/* | |
Purpose: | |
DGEFA factors a real general matrix. | |
Modified: | |
16 May 2005 | |
Author: | |
C version by John Burkardt. | |
Reference: | |
Jack Dongarra, Cleve Moler, Jim Bunch and Pete Stewart, | |
LINPACK User's Guide, | |
SIAM, (Society for Industrial and Applied Mathematics), | |
3600 University City Science Center, | |
Philadelphia, PA, 19104-2688. | |
ISBN 0-89871-172-X | |
Parameters: | |
Input/output, double A[LDA*N]. | |
On intput, the matrix to be factored. | |
On output, an upper triangular matrix and the multipliers used to obtain | |
it. The factorization can be written A=L*U, where L is a product of | |
permutation and unit lower triangular matrices, and U is upper triangular. | |
Input, int LDA, the leading dimension of A. | |
Input, int N, the order of the matrix A. | |
Output, int IPVT[N], the pivot indices. | |
Output, int DGEFA, singularity indicator. | |
0, normal value. | |
K, if U(K,K) == 0. This is not an error condition for this subroutine, | |
but it does indicate that DGESL or DGEDI will divide by zero if called. | |
Use RCOND in DGECO for a reliable indication of singularity. | |
*/ | |
{ | |
int info; | |
int j; | |
int k; | |
int l; | |
double t; | |
/* | |
Gaussian elimination with partial pivoting. | |
*/ | |
info = 0; | |
for ( k = 1; k <= n-1; k++ ) | |
{ | |
/* | |
Find L = pivot index. | |
*/ | |
l = idamax ( n-k+1, a+(k-1)+(k-1)*lda, 1 ) + k - 1; | |
ipvt[k-1] = l; | |
/* | |
Zero pivot implies this column already triangularized. | |
*/ | |
if ( a[l-1+(k-1)*lda] == 0.0 ) | |
{ | |
info = k; | |
continue; | |
} | |
/* | |
Interchange if necessary. | |
*/ | |
if ( l != k ) | |
{ | |
t = a[l-1+(k-1)*lda]; | |
a[l-1+(k-1)*lda] = a[k-1+(k-1)*lda]; | |
a[k-1+(k-1)*lda] = t; | |
} | |
/* | |
Compute multipliers. | |
*/ | |
t = -1.0 / a[k-1+(k-1)*lda]; | |
dscal ( n-k, t, a+k+(k-1)*lda, 1 ); | |
/* | |
Row elimination with column indexing. | |
*/ | |
for ( j = k+1; j <= n; j++ ) | |
{ | |
t = a[l-1+(j-1)*lda]; | |
if ( l != k ) | |
{ | |
a[l-1+(j-1)*lda] = a[k-1+(j-1)*lda]; | |
a[k-1+(j-1)*lda] = t; | |
} | |
daxpy ( n-k, t, a+k+(k-1)*lda, 1, a+k+(j-1)*lda, 1 ); | |
} | |
} | |
ipvt[n-1] = n; | |
if ( a[n-1+(n-1)*lda] == 0.0 ) | |
{ | |
info = n; | |
} | |
return info; | |
} | |
/******************************************************************************/ | |
void dgesl ( double a[], int lda, int n, int ipvt[], double b[], int job ) | |
/******************************************************************************/ | |
/* | |
Purpose: | |
DGESL solves a real general linear system A * X = B. | |
Discussion: | |
DGESL can solve either of the systems A * X = B or A' * X = B. | |
The system matrix must have been factored by DGECO or DGEFA. | |
A division by zero will occur if the input factor contains a | |
zero on the diagonal. Technically this indicates singularity | |
but it is often caused by improper arguments or improper | |
setting of LDA. It will not occur if the subroutines are | |
called correctly and if DGECO has set 0.0 < RCOND | |
or DGEFA has set INFO == 0. | |
Modified: | |
16 May 2005 | |
Author: | |
C version by John Burkardt. | |
Reference: | |
Jack Dongarra, Cleve Moler, Jim Bunch and Pete Stewart, | |
LINPACK User's Guide, | |
SIAM, (Society for Industrial and Applied Mathematics), | |
3600 University City Science Center, | |
Philadelphia, PA, 19104-2688. | |
ISBN 0-89871-172-X | |
Parameters: | |
Input, double A[LDA*N], the output from DGECO or DGEFA. | |
Input, int LDA, the leading dimension of A. | |
Input, int N, the order of the matrix A. | |
Input, int IPVT[N], the pivot vector from DGECO or DGEFA. | |
Input/output, double B[N]. | |
On input, the right hand side vector. | |
On output, the solution vector. | |
Input, int JOB. | |
0, solve A * X = B; | |
nonzero, solve A' * X = B. | |
*/ | |
{ | |
int k; | |
int l; | |
double t; | |
/* | |
Solve A * X = B. | |
*/ | |
if ( job == 0 ) | |
{ | |
for ( k = 1; k <= n-1; k++ ) | |
{ | |
l = ipvt[k-1]; | |
t = b[l-1]; | |
if ( l != k ) | |
{ | |
b[l-1] = b[k-1]; | |
b[k-1] = t; | |
} | |
daxpy ( n-k, t, a+k+(k-1)*lda, 1, b+k, 1 ); | |
} | |
for ( k = n; 1 <= k; k-- ) | |
{ | |
b[k-1] = b[k-1] / a[k-1+(k-1)*lda]; | |
t = -b[k-1]; | |
daxpy ( k-1, t, a+0+(k-1)*lda, 1, b, 1 ); | |
} | |
} | |
/* | |
Solve A' * X = B. | |
*/ | |
else | |
{ | |
for ( k = 1; k <= n; k++ ) | |
{ | |
t = ddot ( k-1, a+0+(k-1)*lda, 1, b, 1 ); | |
b[k-1] = ( b[k-1] - t ) / a[k-1+(k-1)*lda]; | |
} | |
for ( k = n-1; 1 <= k; k-- ) | |
{ | |
b[k-1] = b[k-1] + ddot ( n-k, a+k+(k-1)*lda, 1, b+k, 1 ); | |
l = ipvt[k-1]; | |
if ( l != k ) | |
{ | |
t = b[l-1]; | |
b[l-1] = b[k-1]; | |
b[k-1] = t; | |
} | |
} | |
} | |
return; | |
} | |
/******************************************************************************/ | |
void dscal ( int n, double sa, double x[], int incx ) | |
/******************************************************************************/ | |
/* | |
Purpose: | |
DSCAL scales a vector by a constant. | |
Modified: | |
30 March 2007 | |
Author: | |
FORTRAN77 original by Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart. | |
C version by John Burkardt | |
Reference: | |
Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart, | |
LINPACK User's Guide, | |
SIAM, 1979. | |
Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh, | |
Basic Linear Algebra Subprograms for Fortran Usage, | |
Algorithm 539, | |
ACM Transactions on Mathematical Software, | |
Volume 5, Number 3, September 1979, pages 308-323. | |
Parameters: | |
Input, int N, the number of entries in the vector. | |
Input, double SA, the multiplier. | |
Input/output, double X[*], the vector to be scaled. | |
Input, int INCX, the increment between successive entries of X. | |
*/ | |
{ | |
int i; | |
int ix; | |
int m; | |
if ( n <= 0 ) | |
{ | |
} | |
else if ( incx == 1 ) | |
{ | |
m = n % 5; | |
for ( i = 0; i < m; i++ ) | |
{ | |
x[i] = sa * x[i]; | |
} | |
for ( i = m; i < n; i = i + 5 ) | |
{ | |
x[i] = sa * x[i]; | |
x[i+1] = sa * x[i+1]; | |
x[i+2] = sa * x[i+2]; | |
x[i+3] = sa * x[i+3]; | |
x[i+4] = sa * x[i+4]; | |
} | |
} | |
else | |
{ | |
if ( 0 <= incx ) | |
{ | |
ix = 0; | |
} | |
else | |
{ | |
ix = ( - n + 1 ) * incx; | |
} | |
for ( i = 0; i < n; i++ ) | |
{ | |
x[ix] = sa * x[ix]; | |
ix = ix + incx; | |
} | |
} | |
return; | |
} | |
/******************************************************************************/ | |
int idamax ( int n, double dx[], int incx ) | |
/******************************************************************************/ | |
/* | |
Purpose: | |
IDAMAX finds the index of the vector element of maximum absolute value. | |
Discussion: | |
WARNING: This index is a 1-based index, not a 0-based index! | |
Modified: | |
30 March 2007 | |
Author: | |
FORTRAN77 original by Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart. | |
C version by John Burkardt | |
Reference: | |
Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart, | |
LINPACK User's Guide, | |
SIAM, 1979. | |
Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh, | |
Basic Linear Algebra Subprograms for Fortran Usage, | |
Algorithm 539, | |
ACM Transactions on Mathematical Software, | |
Volume 5, Number 3, September 1979, pages 308-323. | |
Parameters: | |
Input, int N, the number of entries in the vector. | |
Input, double X[*], the vector to be examined. | |
Input, int INCX, the increment between successive entries of SX. | |
Output, int IDAMAX, the index of the element of maximum | |
absolute value. | |
*/ | |
{ | |
double dmax; | |
int i; | |
int ix; | |
int value; | |
value = 0; | |
if ( n < 1 || incx <= 0 ) | |
{ | |
return value; | |
} | |
value = 1; | |
if ( n == 1 ) | |
{ | |
return value; | |
} | |
if ( incx == 1 ) | |
{ | |
dmax = r8_abs ( dx[0] ); | |
for ( i = 1; i < n; i++ ) | |
{ | |
if ( dmax < r8_abs ( dx[i] ) ) | |
{ | |
value = i + 1; | |
dmax = r8_abs ( dx[i] ); | |
} | |
} | |
} | |
else | |
{ | |
ix = 0; | |
dmax = r8_abs ( dx[0] ); | |
ix = ix + incx; | |
for ( i = 1; i < n; i++ ) | |
{ | |
if ( dmax < r8_abs ( dx[ix] ) ) | |
{ | |
value = i + 1; | |
dmax = r8_abs ( dx[ix] ); | |
} | |
ix = ix + incx; | |
} | |
} | |
return value; | |
} | |
/******************************************************************************/ | |
double r8_abs ( double x ) | |
/******************************************************************************/ | |
/* | |
Purpose: | |
R8_ABS returns the absolute value of a R8. | |
Modified: | |
02 April 2005 | |
Author: | |
John Burkardt | |
Parameters: | |
Input, double X, the quantity whose absolute value is desired. | |
Output, double R8_ABS, the absolute value of X. | |
*/ | |
{ | |
double value; | |
if ( 0.0 <= x ) | |
{ | |
value = x; | |
} | |
else | |
{ | |
value = -x; | |
} | |
return value; | |
} | |
/******************************************************************************/ | |
double r8_epsilon ( void ) | |
/******************************************************************************/ | |
/* | |
Purpose: | |
R8_EPSILON returns the R8 round off unit. | |
Discussion: | |
R8_EPSILON is a number R which is a power of 2 with the property that, | |
to the precision of the computer's arithmetic, | |
1 < 1 + R | |
but | |
1 = ( 1 + R / 2 ) | |
Licensing: | |
This code is distributed under the GNU LGPL license. | |
Modified: | |
08 May 2006 | |
Author: | |
John Burkardt | |
Parameters: | |
Output, double R8_EPSILON, the double precision round-off unit. | |
*/ | |
{ | |
double r; | |
r = 1.0; | |
while ( 1.0 < ( double ) ( 1.0 + r ) ) | |
{ | |
r = r / 2.0; | |
} | |
r = 2.0 * r; | |
return r; | |
} | |
/******************************************************************************/ | |
double r8_max ( double x, double y ) | |
/******************************************************************************/ | |
/* | |
Purpose: | |
R8_MAX returns the maximum of two R8's. | |
Modified: | |
18 August 2004 | |
Author: | |
John Burkardt | |
Parameters: | |
Input, double X, Y, the quantities to compare. | |
Output, double R8_MAX, the maximum of X and Y. | |
*/ | |
{ | |
double value; | |
if ( y < x ) | |
{ | |
value = x; | |
} | |
else | |
{ | |
value = y; | |
} | |
return value; | |
} | |
/******************************************************************************/ | |
double r8_random ( int iseed[4] ) | |
/******************************************************************************/ | |
/* | |
Purpose: | |
R8_RANDOM returns a uniformly distributed random number between 0 and 1. | |
Discussion: | |
This routine uses a multiplicative congruential method with modulus | |
2**48 and multiplier 33952834046453 (see G.S.Fishman, | |
'Multiplicative congruential random number generators with modulus | |
2**b: an exhaustive analysis for b = 32 and a partial analysis for | |
b = 48', Math. Comp. 189, pp 331-344, 1990). | |
48-bit integers are stored in 4 integer array elements with 12 bits | |
per element. Hence the routine is portable across machines with | |
integers of 32 bits or more. | |
Parameters: | |
Input/output, integer ISEED(4). | |
On entry, the seed of the random number generator; the array | |
elements must be between 0 and 4095, and ISEED(4) must be odd. | |
On exit, the seed is updated. | |
Output, double R8_RANDOM, the next pseudorandom number. | |
*/ | |
{ | |
int ipw2 = 4096; | |
int it1; | |
int it2; | |
int it3; | |
int it4; | |
int m1 = 494; | |
int m2 = 322; | |
int m3 = 2508; | |
int m4 = 2549; | |
double r = 1.0 / 4096.0; | |
double value; | |
/* | |
Multiply the seed by the multiplier modulo 2**48. | |
*/ | |
it4 = iseed[3] * m4; | |
it3 = it4 / ipw2; | |
it4 = it4 - ipw2 * it3; | |
it3 = it3 + iseed[2] * m4 + iseed[3] * m3; | |
it2 = it3 / ipw2; | |
it3 = it3 - ipw2 * it2; | |
it2 = it2 + iseed[1] * m4 + iseed[2] * m3 + iseed[3] * m2; | |
it1 = it2 / ipw2; | |
it2 = it2 - ipw2 * it1; | |
it1 = it1 + iseed[0] * m4 + iseed[1] * m3 + iseed[2] * m2 + iseed[3] * m1; | |
it1 = ( it1 % ipw2 ); | |
/* | |
Return updated seed | |
*/ | |
iseed[0] = it1; | |
iseed[1] = it2; | |
iseed[2] = it3; | |
iseed[3] = it4; | |
/* | |
Convert 48-bit integer to a real number in the interval (0,1) | |
*/ | |
value = | |
r * ( ( double ) ( it1 ) | |
+ r * ( ( double ) ( it2 ) | |
+ r * ( ( double ) ( it3 ) | |
+ r * ( ( double ) ( it4 ) ) ) ) ); | |
return value; | |
} | |
/******************************************************************************/ | |
void r8mat_gen ( int lda, int n, double*a ) | |
/******************************************************************************/ | |
/* | |
Purpose: | |
R8MAT_GEN generates a random R8MAT. | |
Modified: | |
06 June 2005 | |
Parameters: | |
Input, integer LDA, the leading dimension of the matrix. | |
Input, integer N, the order of the matrix. | |
Output, double R8MAT_GEN[LDA*N], the N by N matrix. | |
*/ | |
{ | |
int i; | |
int init[4] = { 1, 2, 3, 1325 }; | |
int j; | |
for ( j = 1; j <= n; j++ ) | |
{ | |
for ( i = 1; i <= n; i++ ) | |
{ | |
a[i-1+(j-1)*lda] = r8_random ( init ) - 0.5; | |
} | |
} | |
} | |
/******************************************************************************/ | |
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I've forked this sketch to fix compilation for Arduino Due and Espressif ESP32, and also made a few minor changes to my liking: https://gist.github.com/VioletGiraffe/c95f7382298c97d6215f56ee31c56ff7