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<pre class="sourcecodebox">//
// File: twoDimFFT.c
//
// Contains: A sample program to illustrate the usage of 2-d FFT functions of real
// and complex number. This program also times the functions using the
// microsecond timer.
//
// Copyright: Copyright (c) 2007 Apple Inc., All Rights Reserved
//
// Disclaimer: IMPORTANT: This Apple software is supplied to you by
// Apple Inc. ("Apple") in consideration of your agreement to the
// following terms, and your use, installation, modification or
// redistribution of this Apple software constitutes acceptance of these
// terms. If you do not agree with these terms, please do not use,
// install, modify or redistribute this Apple software.
//
// In consideration of your agreement to abide by the following terms, and
// subject to these terms, Apple grants you a personal, non-exclusive
// license, under Apple's copyrights in this original Apple software (the
// "Apple Software"), to use, reproduce, modify and redistribute the Apple
// Software, with or without modifications, in source and/or binary forms;
// provided that if you redistribute the Apple Software in its entirety and
// without modifications, you must retain this notice and the following
// text and disclaimers in all such redistributions of the Apple Software.
// Neither the name, trademarks, service marks or logos of Apple Inc.
// may be used to endorse or promote products derived from the Apple
// Software without specific prior written permission from Apple. Except
// as expressly stated in this notice, no other rights or licenses, express
// or implied, are granted by Apple herein, including but not limited to
// any patent rights that may be infringed by your derivative works or by
// other works in which the Apple Software may be incorporated.
//
// The Apple Software is provided by Apple on an "AS IS" basis. APPLE
// MAKES NO WARRANTIES, EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION
// THE IMPLIED WARRANTIES OF NON-INFRINGEMENT, MERCHANTABILITY AND FITNESS
// FOR A PARTICULAR PURPOSE, REGARDING THE APPLE SOFTWARE OR ITS USE AND
// OPERATION ALONE OR IN COMBINATION WITH YOUR PRODUCTS.
//
// IN NO EVENT SHALL APPLE BE LIABLE FOR ANY SPECIAL, INDIRECT, INCIDENTAL
// OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
// INTERRUPTION) ARISING IN ANY WAY OUT OF THE USE, REPRODUCTION,
// MODIFICATION AND/OR DISTRIBUTION OF THE APPLE SOFTWARE, HOWEVER CAUSED
// AND WHETHER UNDER THEORY OF CONTRACT, TORT (INCLUDING NEGLIGENCE),
// STRICT LIABILITY OR OTHERWISE, EVEN IF APPLE HAS BEEN ADVISED OF THE
// POSSIBILITY OF SUCH DAMAGE.
//
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <CoreServices/CoreServices.h>
#include <Accelerate/Accelerate.h>
#include "javamode.h"
#include "main.h"
#define MAX_LOOP_NUM 10000 // Number of iterations used in the timing loop
#define kHasAltiVecMask ( 1 << gestaltPowerPCHasVectorInstructions ) // used in looking for a g4
#define MAX(a,b) ( (a>b)?a:b )
#define N 10 // This is a power of 2 defining the length of the FFTs
// function prototypes
static void Dummy_fft2d_zip ( FFTSetup setup, COMPLEX_SPLIT *A, long rowStride, long columnStride, unsigned log2nc, unsigned log2nr, long flag );
static void Dummy_fft2d_zrip ( FFTSetup setup, COMPLEX_SPLIT *A, long rowStride, long columnStride, unsigned log2nc, unsigned log2nr, long flag );
static void Dummy_fft2d_zop ( FFTSetup setup, COMPLEX_SPLIT *A, long rowStride, long columnStride, COMPLEX_SPLIT *B, long resultRowStride, long resultColumnStride, unsigned log2nc, unsigned log2nr, long flag );
static void Dummy_fft2d_zrop ( FFTSetup setup, COMPLEX_SPLIT *A, long rowStride, long columnStride, COMPLEX_SPLIT *B, long resultRowStride, long resultColumnStride, unsigned log2nc, unsigned log2nr, long flag );
static void Complex2dFFTUsageAndTiming( void );
static void Complex2dFFTUsageAndTimingOutOfPlace( void );
static void Real2dFFTUsageAndTiming( void );
static void Real2dFFTUsageAndTimingOutOfPlace ( void );
// called by main.c and that call eventually runs all functions in this file.
void RunTwoDimFFT(void)
{
Complex2dFFTUsageAndTiming( );
Complex2dFFTUsageAndTimingOutOfPlace( );
Real2dFFTUsageAndTiming( );
Real2dFFTUsageAndTimingOutOfPlace( );
}
// For the difference between in-place and out-place way, please refer to oneDimFFT.c
/*******************************************************************************
* Complex Two Dimensional FFT. ( In-Place way ) *
*******************************************************************************/
static void Complex2dFFTUsageAndTiming()
{
COMPLEX_SPLIT originalValue, A;
FFTSetup setup;
UInt32 log2nr, log2nc;
UInt32 n;
SInt32 rowStride, columnStride;
UInt32 i;
float scale;
// Set the size of 2d FFT.
log2nr = N / 2; // (2^(N/2)) * (2^(N/2)) = 2^n To allocate n nodes, you specify row and column as a half of it.
log2nc = N / 2;
n = 1 << ( log2nr + log2nc ); // n = 2^N
rowStride = 1;
columnStride = 0; // choose 0 for the default value, which is nc * stridInRow or ( 1 << log2nc )
printf ( "\n2D complex FFT of length log2 ( %d x %d ) = ( %d x %d )\n", 1 << log2nr, 1 << log2nc, (unsigned int)log2nr, (unsigned int)log2nc );
// Allocate memory for the input operands and check its availability.
originalValue.realp = ( float* ) malloc ( n * sizeof ( float) );
originalValue.imagp = ( float* ) malloc ( n * sizeof ( float ) );
A.realp = ( float* ) malloc ( n * sizeof ( float ) );
A.imagp = ( float* ) malloc ( n * sizeof ( float ) );
if ( originalValue.realp == NULL || originalValue.imagp == NULL || A.realp == NULL || A.imagp == NULL )
{
printf ( "\nmalloc failed to allocate memory for the 2D FFT section of the test.\n");
exit ( 0 );
}
// Set the input vector of length n: [(1+j1),...,(1+j1)], where j^2 = -1.
for ( i = 0; i < n; i++ )
{
originalValue.realp[i] = ( float ) (i+1);
originalValue.imagp[i] = 0.0;
}
memcpy ( A.realp, originalValue.realp, ( n * sizeof ( float ) ) );
memcpy ( A.imagp, originalValue.imagp, ( n * sizeof ( float ) ) );
// Set up the required memory for the FFT routines and check its availability.
setup = create_fftsetup ( MAX ( log2nr, log2nc ), FFT_RADIX2 );
if( setup == NULL )
{
printf ( "\nFFT_Setup failed to allocate enough memory.\n" );
exit(0);
}
// Carry out a Forward and Inverse 2d FFT transform, check for errors.
fft2d_zip ( setup, &A, rowStride, columnStride, log2nc, log2nr, FFT_FORWARD );
fft2d_zip ( setup, &A, rowStride, columnStride, log2nc, log2nr, FFT_INVERSE );
// Verify correctness of the results.
scale = 1.0 / (float) n; // make constants to scale the result.
// scale the result.
vsmul( A.realp, 1, &scale, A.realp, 1, n );
vsmul( A.imagp, 1, &scale, A.imagp, 1, n );
// compare for accuracy report
Compare ( originalValue.realp, A.realp, n );
Compare ( originalValue.imagp, A.imagp, n );
// Timing section for the 2d FFT.
{
float time, overheadTime;
#if defined(__VEC__)
// Turn Java mode off. Otherwise, there is an extra cycle added to the vfpu.
// WARNING: Java mode has to be treated with care. Some algorithms may be
// sensitive to flush to zero and may need proper IEEE-754 denormal handling.
TurnJavaModeOffOnG4();
#endif
StartClock();
for ( i = 0; i < MAX_LOOP_NUM; i++ )
fft2d_zip ( setup, &A, rowStride, columnStride, log2nc, log2nr, FFT_FORWARD );
StopClock ( &time );
#if defined(__VEC__)
// Restore Java mode.
RestoreJavaModeOnG4();
#endif
// Measure and take off the calling overhead of the 2d FFT (very minimal impact).
StartClock();
for ( i = 0; i < MAX_LOOP_NUM; i++ )
Dummy_fft2d_zip ( setup, &A, rowStride, columnStride, log2nc, log2nr, FFT_FORWARD );
StopClock ( &overheadTime );
time -= overheadTime;
time /= MAX_LOOP_NUM;
printf("\n2D complex FFT of length log2 ( %d x %d ) = ( %d x %d ) is %4.4f µsecs\n", 1 << log2nr, 1 << log2nc, (unsigned int)log2nr, (unsigned int)log2nc, time );
}
// Free allocated memory.
destroy_fftsetup ( setup );
free ( originalValue.realp );
free ( originalValue.imagp );
free ( A.realp );
free ( A.imagp );
}
/**************************************************************
* Complex Two Dimensional FFT. ( Out-Of-Place way ) *
**************************************************************/
static void Complex2dFFTUsageAndTimingOutOfPlace()
{
COMPLEX_SPLIT originalValue, A, result;
FFTSetup setup;
UInt32 log2nr, log2nc;
UInt32 n;
SInt32 rowStride, columnStride;
SInt32 resultRowStride, resultColumnStride;
UInt32 i;
float scale;
// Set the size of 2d FFT.
log2nr = N / 2;
log2nc = N / 2;
n = 1 << ( log2nr + log2nc );
rowStride = 1;
columnStride = 0; // choose 0 for the default value, which is nc * stridInRow or ( 1 << log2nc )
resultRowStride = 1;
resultColumnStride = 0;
printf ( "\n2D complex FFT out-of-place of length log2 ( %d x %d ) = ( %d x %d )\n", 1 << log2nr, 1 << log2nc, (unsigned int)log2nr, (unsigned int)log2nc );
// Allocate memory for the input operands and check its availability.
originalValue.realp = ( float* ) malloc ( n * sizeof ( float) );
originalValue.imagp = ( float* ) malloc ( n * sizeof ( float ) );
A.realp = ( float* ) malloc ( n * sizeof ( float ) );
A.imagp = ( float* ) malloc ( n * sizeof ( float ) );
result.realp = ( float* ) malloc ( n * sizeof ( float ) );
result.imagp = ( float* ) malloc ( n * sizeof ( float ) );
if ( originalValue.realp == NULL || originalValue.imagp == NULL || A.realp == NULL || A.imagp == NULL || result.realp == NULL || result.imagp == NULL )
{
printf ( "\nmalloc failed to allocate memory for the 2D FFT section of the test.\n");
exit ( 0 );
}
// Set the input vector of length n: [(1+j1),...,(1+j1)], where j^2 = -1.
for ( i = 0; i < n; i++ )
{
originalValue.realp[i] = ( float ) (i+1);
originalValue.imagp[i] = 0.0;
}
memcpy ( A.realp, originalValue.realp, ( n * sizeof ( float ) ) );
memcpy ( A.imagp, originalValue.imagp, ( n * sizeof ( float ) ) );
// Set up the required memory for the FFT routines and check its availability.
setup = create_fftsetup ( MAX ( log2nr, log2nc ), FFT_RADIX2 );
if( setup == NULL )
{
printf ( "\nFFT_Setup failed to allocate enough memory.\n" );
exit(0);
}
// Carry out a Forward and Inverse 2d FFT transform, check for errors.
fft2d_zop ( setup, &A, rowStride, columnStride, &result, resultRowStride, resultColumnStride, log2nc, log2nr, FFT_FORWARD );
fft2d_zop ( setup, &result, resultRowStride, resultColumnStride, &result, resultRowStride, resultColumnStride, log2nc, log2nr, FFT_INVERSE );
// Verify correctness of the results.
scale = 1.0 / (float) n;
vsmul( result.realp, 1, &scale, result.realp, 1, n );
vsmul( result.imagp, 1, &scale, result.imagp, 1, n );
Compare ( originalValue.realp, result.realp, n );
Compare ( originalValue.imagp, result.imagp, n );
// Timing section for the 2d FFT.
{
float time, overheadTime;
#if defined(__VEC__)
// Turn Java mode off. Otherwise, there is an extra cycle added to the vfpu.
// WARNING: Java mode has to be treated with care. Some algorithms may be
// sensitive to flush to zero and may need proper IEEE-754 denormal handling.
TurnJavaModeOffOnG4();
#endif
StartClock();
for ( i = 0; i < MAX_LOOP_NUM; i++ )
fft2d_zop ( setup, &A, rowStride, columnStride, &result, resultRowStride, resultColumnStride, log2nc, log2nr, FFT_FORWARD );
StopClock ( &time );
#if defined(__VEC__)
// Restore Java mode.
RestoreJavaModeOnG4();
#endif
// Measure and take off the calling overhead of the 2d FFT (very minimal impact).
StartClock();
for ( i = 0; i < MAX_LOOP_NUM; i++ )
Dummy_fft2d_zop ( setup, &A, rowStride, columnStride, &result, resultRowStride, resultColumnStride, log2nc, log2nr, FFT_FORWARD );
StopClock ( &overheadTime );
time -= overheadTime;
time /= MAX_LOOP_NUM;
printf("\n2D complex FFT out-of-place of length log2 ( %d x %d ) = ( %d x %d ) is %4.4f µsecs\n", 1 << log2nr, 1 << log2nc, (unsigned int)log2nr, (unsigned int)log2nc, time );
}
// Free allocated memory.
destroy_fftsetup ( setup );
free ( originalValue.realp );
free ( originalValue.imagp );
free ( A.realp );
free ( A.imagp );
free ( result.realp );
free ( result.imagp );
}
/*******************************************************************************
* Real Two Dimensional FFT. ( In-Place way ) *
*******************************************************************************/
static void Real2dFFTUsageAndTiming()
{
COMPLEX_SPLIT A;
FFTSetup setup;
UInt32 log2nr, log2nc;
UInt32 n, nOver2;
SInt32 rowStride, columnStride;
UInt32 i;
float scale;
float *originalReal, *obtainedReal;
// Set the size of 2d FFT.
log2nr = N / 2;
log2nc = N / 2;
n = 1 << ( log2nr + log2nc );
nOver2 = n/2; // Since one pair of real numbers are considered as one complex number,
// if you have n real numbers, then it equivalent to n/2 complex number.
rowStride = 1;
columnStride = 0; // choose 0 for the default value, which is nc * stridInRow or ( 1 << log2nc )
printf ( "\n2D real FFT of length log2 ( %d x %d ) = ( %d x %d )\n", 1 << log2nr, 1 << log2nc, (unsigned int)log2nr, (unsigned int)log2nc );
// Allocate memory for the input operands and check its availability.
originalReal = ( float* ) malloc ( n * sizeof ( float ) );
obtainedReal = ( float* ) malloc ( n * sizeof ( float ) );
A.realp = ( float* ) malloc ( nOver2 * sizeof ( float ) );
A.imagp = ( float* ) malloc ( nOver2 * sizeof ( float ) );
if ( originalReal == NULL || obtainedReal == NULL || A.realp == NULL || A.imagp == NULL )
{
printf ( "\nmalloc failed to allocate memory for the 2D FFT section of the test.\n");
exit ( 0 );
}
// Set the input vector of length n: [(1+j1),...,(1+j1)], where j^2 = -1.
for ( i = 0; i < n; i++ )
{
originalReal[i] = ( float )i;
}
//treat originalRealInput as interleaved complex number. change the format to split
//so that we can pass it to fft functions
ctoz( (COMPLEX*) originalReal, 2, &A, 1, nOver2 );
// Set up the required memory for the FFT routines and check its availability.
setup = create_fftsetup ( MAX ( log2nr, log2nc ), FFT_RADIX2 );
if( setup == NULL )
{
printf ( "\nFFT_Setup failed to allocate enough memory.\n" );
exit(0);
}
// Carry out a Forward and Inverse 2d FFT transform, check for errors.
fft2d_zrip ( setup, &A, rowStride, columnStride, log2nc, log2nr, FFT_FORWARD );
fft2d_zrip ( setup, &A, rowStride, columnStride, log2nc, log2nr, FFT_INVERSE );
// Verify correctness of the results.
scale = 1.0 / (float) (2*n); // get scale factor
// scale the result
vsmul( A.realp, 1, &scale, A.realp, 1, nOver2 );
vsmul( A.imagp, 1, &scale, A.imagp, 1, nOver2 );
// The output signal is now in a split real form. Use the function
// ztoc to get a split real vector.
ztoc ( &A, 1, ( COMPLEX * ) obtainedReal, 2, nOver2 );
// Check for accuracy by looking at the inverse transform results.
Compare ( originalReal, obtainedReal, n );
// Timing section for the 2d FFT.
{
float time, overheadTime;
#if defined(__VEC__)
// Turn Java mode off. Otherwise, there is an extra cycle added to the vfpu.
// WARNING: Java mode has to be treated with care. Some algorithms may be
// sensitive to flush to zero and may need proper IEEE-754 denormal handling.
TurnJavaModeOffOnG4();
#endif
StartClock();
for ( i = 0; i < MAX_LOOP_NUM; i++ )
fft2d_zrip ( setup, &A, rowStride, columnStride, log2nc, log2nr, FFT_FORWARD );
StopClock ( &time );
#if defined(__VEC__)
// Restore Java mode.
RestoreJavaModeOnG4();
#endif
// Measure and take off the calling overhead of the 2d FFT (very minimal impact).
StartClock();
for ( i = 0; i < MAX_LOOP_NUM; i++ )
Dummy_fft2d_zrip ( setup, &A, rowStride, columnStride, log2nc, log2nr, FFT_FORWARD );
StopClock ( &overheadTime );
time -= overheadTime;
time /= MAX_LOOP_NUM;
printf("\n2D real FFT of length log2 ( %d x %d ) = ( %d x %d ) is %4.4f µsecs\n", 1 << log2nr, 1 << log2nc, (unsigned int)log2nr, (unsigned int)log2nc, time );
}
// Free allocated memory.
destroy_fftsetup ( setup );
free ( originalReal );
free ( obtainedReal );
free ( A.realp );
free ( A.imagp );
}
/*******************************************************************************
* Real Two Dimensional FFT. ( Out-Of-Place ) *
*******************************************************************************/
static void Real2dFFTUsageAndTimingOutOfPlace()
{
COMPLEX_SPLIT A, result1, result2;
FFTSetup setup;
UInt32 log2nr, log2nc;
UInt32 n, nOver2;
SInt32 rowStride, columnStride, result1RowStride, result1ColumnStride, result2RowStride, result2ColumnStride;
UInt32 i;
float scale;
float *originalReal, *obtainedReal;
// Set the size of 2d FFT.
log2nr = N / 2;
log2nc = N / 2;
n = 1 << ( log2nr + log2nc );
nOver2 = n/2;
rowStride = 1;
columnStride = 0; // choose 0 for the default value, which is nc * stridInRow or ( 1 << log2nc )
result1RowStride = 1;
result1ColumnStride = 0;
result2RowStride = 1;
result2ColumnStride = 0;
printf ( "\n2D real FFT out-of-place of length log2 ( %d x %d ) = ( %d x %d )\n", 1 << log2nr, 1 << log2nc, (unsigned int)log2nr, (unsigned int)log2nc );
// Allocate memory for the input operands and check its availability.
originalReal = ( float* ) malloc ( n * sizeof ( float ) );
obtainedReal = ( float* ) malloc ( n * sizeof ( float ) );
A.realp = ( float* ) malloc ( nOver2 * sizeof ( float ) );
A.imagp = ( float* ) malloc ( nOver2 * sizeof ( float ) );
result1.realp = ( float* ) malloc ( nOver2 * sizeof ( float ) );
result1.imagp = ( float* ) malloc ( nOver2 * sizeof ( float ) );
result2.realp = ( float* ) malloc ( nOver2 * sizeof ( float ) );
result2.imagp = ( float* ) malloc ( nOver2 * sizeof ( float ) );
if ( originalReal == NULL || obtainedReal == NULL || A.realp == NULL || A.imagp == NULL )
{
printf ( "\nmalloc failed to allocate memory for the 2D FFT section of the test.\n");
exit ( 0 );
}
// Set the input vector of length n: [(1+j1),...,(1+j1)], where j^2 = -1.
for ( i = 0; i < n; i++ )
{
originalReal[i] = ( float )i;
}
//treat originalRealInput as interleaved complex number. change the format to split
//so that we can pass it to fft functions
ctoz( (COMPLEX*) originalReal, 2, &A, 1, nOver2 );
// Set up the required memory for the FFT routines and check its availability.
setup = create_fftsetup ( MAX ( log2nr, log2nc ), FFT_RADIX2 );
if( setup == NULL )
{
printf ( "\nFFT_Setup failed to allocate enough memory.\n" );
exit(0);
}
// Carry out a Forward and Inverse 2d FFT transform, check for errors.
fft2d_zrop ( setup, &A, rowStride, columnStride, &result1, result1RowStride, result1ColumnStride, log2nc, log2nr, FFT_FORWARD );
fft2d_zrop ( setup, &result1, result1RowStride, result1ColumnStride, &result2, result2RowStride, result2ColumnStride, log2nc, log2nr,
FFT_INVERSE );
// Verify correctness of the results.
scale = 1.0 / (float) (2*n);
vsmul( result2.realp, 1, &scale, result2.realp, 1, nOver2 );
vsmul( result2.imagp, 1, &scale, result2.imagp, 1, nOver2 );
// The output signal is now in a split real form. Use the function
// ztoc to get a split real vector.
ztoc ( &result2, 1, ( COMPLEX * ) obtainedReal, 2, nOver2 );
// Check for accuracy by looking at the inverse transform results.
Compare ( originalReal, obtainedReal, n );
// Timing section for the 2d FFT.
{
float time, overheadTime;
#if defined(__VEC__)
// Turn Java mode off. Otherwise, there is an extra cycle added to the vfpu.
// WARNING: Java mode has to be treated with care. Some algorithms may be
// sensitive to flush to zero and may need proper IEEE-754 denormal handling.
TurnJavaModeOffOnG4();
#endif
StartClock();
for ( i = 0; i < MAX_LOOP_NUM; i++ )
fft2d_zrop ( setup, &A, rowStride, columnStride, &result1, result1RowStride, result1ColumnStride, log2nc, log2nr, FFT_FORWARD );
StopClock ( &time );
#if defined(__VEC__)
// Restore Java mode.
RestoreJavaModeOnG4();
#endif
// Measure and take off the calling overhead of the 2d FFT (very minimal impact).
StartClock();
for ( i = 0; i < MAX_LOOP_NUM; i++ )
Dummy_fft2d_zrop ( setup, &A, rowStride, columnStride, &result1, result1RowStride, result1ColumnStride, log2nc, log2nr, FFT_FORWARD );
StopClock ( &overheadTime );
time -= overheadTime;
time /= MAX_LOOP_NUM;
printf("\n2D real FFT out-of-place of length log2 ( %d x %d ) = ( %d x %d ) is %4.4f µsecs\n", 1 << log2nr, 1 << log2nc, (unsigned int)log2nr, (unsigned int)log2nc, time );
}
// Free allocated memory.
destroy_fftsetup ( setup );
free ( originalReal );
free ( obtainedReal );
free ( A.realp );
free ( A.imagp );
free ( result1.realp );
free ( result1.imagp );
free ( result2.realp );
free ( result2.imagp );
}
void Compare ( float *original, float *computed, long length )
{
long i, absErrorIndex, relErrorIndex, maxIndex;
float absoluteError, relativeError, absTmp, relTmp, maximum, average, noise, signal;
relativeError = 0.0f;
absoluteError = 0.0f;
relErrorIndex = 0;
absErrorIndex = 0;
maxIndex = 0;
maximum = 0.0f;
average = 0.0f;
signal = 0.0f;
noise = 0.0f;
for ( i = 0; i < length; i++ )
{
absTmp = fabs ( ( original[i] - computed[i] ) ); // |original[i] - computed[i]|
relTmp = absTmp / fabs ( original[i] ); // |(original[i] - computed[i])/original[i]|
if ( absTmp > absoluteError )
{
absoluteError = absTmp;
absErrorIndex = i;
}
if ( relTmp > relativeError )
{
relativeError = relTmp;
relErrorIndex = i;
}
if ( computed[i] > maximum )
{
maximum = original[i];
maxIndex = i;
}
average += computed[i];
signal += computed[i] * computed[i];
noise += absTmp * absTmp;
}
average /= length;
printf ( " Acuracy Report:\n");
printf ( " The absolute error %13.6e is at node %3d;\n", absoluteError, (unsigned int)absErrorIndex );
if ( relativeError != HUGE_VAL )
printf ( " The relative error %13.6e is at node %3d;\n", relativeError, (unsigned int)relErrorIndex );
else
printf ( " The relative error is meaningless;\n" );
printf ( " The maximum value %13.6e is at node %3d;\n", maximum, (unsigned int)maxIndex );
printf ( " The average value is %13.6e;\n", average );
printf ( " The signal/noise is %13.6e.\n", signal/noise );
}
// Dummy functions to measure the overhead time for the function call
static void Dummy_fft2d_zip ( FFTSetup setup, COMPLEX_SPLIT *A, long rowStride, long columnStride, unsigned log2nc, unsigned log2nr, long flag )
{
#pragma unused( setup )
#pragma unused( A )
#pragma unused( flag )
#pragma unused( log2nr )
#pragma unused( log2nc )
#pragma unused( columnStride )
rowStride = 1;
}
static void Dummy_fft2d_zrip ( FFTSetup setup, COMPLEX_SPLIT *A, long rowStride, long columnStride, unsigned log2nc, unsigned log2nr, long flag )
{
#pragma unused( setup )
#pragma unused( A )
#pragma unused( flag )
#pragma unused( log2nr )
#pragma unused( log2nc )
#pragma unused( columnStride )
rowStride = 1;
}
static void Dummy_fft2d_zop ( FFTSetup setup, COMPLEX_SPLIT *A, long rowStride, long columnStride, COMPLEX_SPLIT *B, long resultRowStride, long resultColumnStride, unsigned log2nc, unsigned log2nr, long flag )
{
#pragma unused( setup )
#pragma unused( A )
#pragma unused( flag )
#pragma unused( log2nr )
#pragma unused( log2nc )
#pragma unused( columnStride )
#pragma unused( B )
#pragma unused( resultColumnStride )
rowStride = 1;
resultRowStride = 1;
}
static void Dummy_fft2d_zrop ( FFTSetup setup, COMPLEX_SPLIT *A, long rowStride, long columnStride, COMPLEX_SPLIT *B, long resultRowStride, long resultColumnStride, unsigned log2nc, unsigned log2nr, long flag )
{
#pragma unused( setup )
#pragma unused( A )
#pragma unused( flag )
#pragma unused( log2nr )
#pragma unused( log2nc )
#pragma unused( columnStride )
#pragma unused( B )
#pragma unused( resultColumnStride )
rowStride = 1;
resultRowStride = 1;
}
void Dummy_ctoz ( COMPLEX *C, SInt32 strideC, COMPLEX_SPLIT *Z, SInt32 strideZ, SInt32 size )
{
#pragma unused( C )
#pragma unused( strideC )
#pragma unused( Z )
#pragma unused( strideZ )
size = 1;
}
void Dummy_ztoc ( COMPLEX_SPLIT *A, SInt32 strideZ, COMPLEX *C, SInt32 strideC, SInt32 size )
{
#pragma unused ( A )
#pragma unused ( strideZ )
#pragma unused ( C )
#pragma unused ( strideC )
size = 1;
}
</pre>
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