/*****************************************************************************
TestAccuracy.hpp
Copyright (c) 2005 Laurent de Soras
--- Legal stuff ---
This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
This library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*Tab=3***********************************************************************/
#if defined (TestAccuracy_CURRENT_CODEHEADER)
#error Recursive inclusion of TestAccuracy code header.
#endif
#define TestAccuracy_CURRENT_CODEHEADER
#if ! defined (TestAccuracy_CODEHEADER_INCLUDED)
#define TestAccuracy_CODEHEADER_INCLUDED
/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
#include "def.h"
#include "test_fnc.h"
#include "TestWhiteNoiseGen.h"
#include <typeinfo>
#include <vector>
#include <cmath>
#include <cstdio>
static const double TestAccuracy_LN10 = 2.3025850929940456840179914546844;
/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
template <class FO>
int TestAccuracy <FO>::perform_test_single_object (FO &fft)
{
assert (&fft != 0);
using namespace std;
int ret_val = 0;
const std::type_info & ti = typeid (fft);
const char * class_name_0 = ti.name ();
if (ret_val == 0)
{
ret_val = perform_test_d (fft, class_name_0);
}
if (ret_val == 0)
{
ret_val = perform_test_i (fft, class_name_0);
}
if (ret_val == 0)
{
ret_val = perform_test_di (fft, class_name_0);
}
if (ret_val == 0)
{
printf ("\n");
}
return (ret_val);
}
template <class FO>
int TestAccuracy <FO>::perform_test_d (FO &fft, const char *class_name_0)
{
assert (&fft != 0);
assert (class_name_0 != 0);
using namespace std;
int ret_val = 0;
const long len = fft.get_length ();
const long nbr_tests = limit (
NBR_ACC_TESTS / len / len,
1L,
static_cast <long> (MAX_NBR_TESTS)
);
printf ("Testing %s::do_fft () [%ld samples]... ", class_name_0, len);
fflush (stdout);
TestWhiteNoiseGen <DataType> noise;
std::vector <DataType> x (len);
std::vector <DataType> s1 (len);
std::vector <DataType> s2 (len);
BigFloat err_avg = 0;
for (long test = 0; test < nbr_tests && ret_val == 0; ++ test)
{
noise.generate (&x [0], len);
fft.do_fft (&s1 [0], &x [0]);
compute_tf (&s2 [0], &x [0], len);
BigFloat max_err;
compare_vect_display (&s1 [0], &s2 [0], len, max_err);
err_avg += max_err;
}
err_avg /= NBR_ACC_TESTS;
printf ("done.\n");
printf (
"Average maximum error: %.6f %% (%f dB)\n",
static_cast <double> (err_avg * 100),
static_cast <double> ((20 / TestAccuracy_LN10) * log (err_avg))
);
return (ret_val);
}
template <class FO>
int TestAccuracy <FO>::perform_test_i (FO &fft, const char *class_name_0)
{
assert (&fft != 0);
assert (class_name_0 != 0);
using namespace std;
int ret_val = 0;
const long len = fft.get_length ();
const long nbr_tests = limit (
NBR_ACC_TESTS / len / len,
10L,
static_cast <long> (MAX_NBR_TESTS)
);
printf ("Testing %s::do_ifft () [%ld samples]... ", class_name_0, len);
fflush (stdout);
TestWhiteNoiseGen <DataType> noise;
std::vector <DataType> s (len);
std::vector <DataType> x1 (len);
std::vector <DataType> x2 (len);
BigFloat err_avg = 0;
for (long test = 0; test < nbr_tests && ret_val == 0; ++ test)
{
noise.generate (&s [0], len);
fft.do_ifft (&s [0], &x1 [0]);
compute_itf (&x2 [0], &s [0], len);
BigFloat max_err;
compare_vect_display (&x1 [0], &x2 [0], len, max_err);
err_avg += max_err;
}
err_avg /= NBR_ACC_TESTS;
printf ("done.\n");
printf (
"Average maximum error: %.6f %% (%f dB)\n",
static_cast <double> (err_avg * 100),
static_cast <double> ((20 / TestAccuracy_LN10) * log (err_avg))
);
return (ret_val);
}
template <class FO>
int TestAccuracy <FO>::perform_test_di (FO &fft, const char *class_name_0)
{
assert (&fft != 0);
assert (class_name_0 != 0);
using namespace std;
int ret_val = 0;
const long len = fft.get_length ();
const long nbr_tests = limit (
NBR_ACC_TESTS / len / len,
1L,
static_cast <long> (MAX_NBR_TESTS)
);
printf (
"Testing %s::do_fft () / do_ifft () / rescale () [%ld samples]... ",
class_name_0,
len
);
fflush (stdout);
TestWhiteNoiseGen <DataType> noise;
std::vector <DataType> x (len);
std::vector <DataType> s (len);
std::vector <DataType> y (len);
BigFloat err_avg = 0;
for (long test = 0; test < nbr_tests && ret_val == 0; ++ test)
{
noise.generate (&x [0], len);
fft.do_fft (&s [0], &x [0]);
fft.do_ifft (&s [0], &y [0]);
fft.rescale (&y [0]);
BigFloat max_err;
compare_vect_display (&x [0], &y [0], len, max_err);
err_avg += max_err;
}
err_avg /= NBR_ACC_TESTS;
printf ("done.\n");
printf (
"Average maximum error: %.6f %% (%f dB)\n",
static_cast <double> (err_avg * 100),
static_cast <double> ((20 / TestAccuracy_LN10) * log (err_avg))
);
return (ret_val);
}
/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
// Positive transform
template <class FO>
void TestAccuracy <FO>::compute_tf (DataType s [], const DataType x [], long length)
{
assert (s != 0);
assert (x != 0);
assert (length >= 2);
assert ((length & 1) == 0);
const long nbr_bins = length >> 1;
// DC and Nyquist
BigFloat dc = 0;
BigFloat ny = 0;
for (long pos = 0; pos < length; pos += 2)
{
const BigFloat even = x [pos ];
const BigFloat odd = x [pos + 1];
dc += even + odd;
ny += even - odd;
}
s [0 ] = static_cast <DataType> (dc);
s [nbr_bins] = static_cast <DataType> (ny);
// Regular bins
for (long bin = 1; bin < nbr_bins; ++ bin)
{
BigFloat sum_r = 0;
BigFloat sum_i = 0;
const BigFloat m = bin * static_cast <BigFloat> (2 * PI) / length;
for (long pos = 0; pos < length; ++pos)
{
using namespace std;
const BigFloat phase = pos * m;
const BigFloat e_r = cos (phase);
const BigFloat e_i = sin (phase);
sum_r += x [pos] * e_r;
sum_i += x [pos] * e_i;
}
s [ bin] = static_cast <DataType> (sum_r);
s [nbr_bins + bin] = static_cast <DataType> (sum_i);
}
}
// Negative transform
template <class FO>
void TestAccuracy <FO>::compute_itf (DataType x [], const DataType s [], long length)
{
assert (s != 0);
assert (x != 0);
assert (length >= 2);
assert ((length & 1) == 0);
const long nbr_bins = length >> 1;
// DC and Nyquist
BigFloat dc = s [0 ];
BigFloat ny = s [nbr_bins];
// Regular bins
for (long pos = 0; pos < length; ++pos)
{
BigFloat sum = dc + ny * (1 - 2 * (pos & 1));
const BigFloat m = pos * static_cast <BigFloat> (-2 * PI) / length;
for (long bin = 1; bin < nbr_bins; ++ bin)
{
using namespace std;
const BigFloat phase = bin * m;
const BigFloat e_r = cos (phase);
const BigFloat e_i = sin (phase);
sum += 2 * ( e_r * s [bin ]
- e_i * s [bin + nbr_bins]);
}
x [pos] = static_cast <DataType> (sum);
}
}
template <class FO>
int TestAccuracy <FO>::compare_vect_display (const DataType x_ptr [], const DataType y_ptr [], long len, BigFloat &max_err_rel)
{
assert (x_ptr != 0);
assert (y_ptr != 0);
assert (len > 0);
assert (&max_err_rel != 0);
using namespace std;
int ret_val = 0;
BigFloat power = compute_power (&x_ptr [0], &y_ptr [0], len);
BigFloat power_dif;
long max_err_pos;
compare_vect (&x_ptr [0], &y_ptr [0], power_dif, max_err_pos, len);
if (power == 0)
{
power = power_dif;
}
const BigFloat power_err_rel = power_dif / power;
BigFloat max_err = 0;
max_err_rel = 0;
if (max_err_pos >= 0)
{
max_err = y_ptr [max_err_pos] - x_ptr [max_err_pos];
max_err_rel = 2 * fabs (max_err) / ( fabs (y_ptr [max_err_pos])
+ fabs (x_ptr [max_err_pos]));
}
if (power_err_rel > 0.001)
{
printf ("Power error : %f (%.6f %%)\n",
static_cast <double> (power_err_rel),
static_cast <double> (power_err_rel * 100)
);
if (max_err_pos >= 0)
{
printf (
"Maximum error: %f - %f = %f (%f)\n",
static_cast <double> (y_ptr [max_err_pos]),
static_cast <double> (x_ptr [max_err_pos]),
static_cast <double> (max_err),
static_cast <double> (max_err_pos)
);
}
}
return (ret_val);
}
template <class FO>
typename TestAccuracy <FO>::BigFloat TestAccuracy <FO>::compute_power (const DataType x_ptr [], long len)
{
assert (x_ptr != 0);
assert (len > 0);
BigFloat power = 0;
for (long pos = 0; pos < len; ++pos)
{
const BigFloat val = x_ptr [pos];
power += val * val;
}
using namespace std;
power = sqrt (power) / len;
return (power);
}
template <class FO>
typename TestAccuracy <FO>::BigFloat TestAccuracy <FO>::compute_power (const DataType x_ptr [], const DataType y_ptr [], long len)
{
assert (x_ptr != 0);
assert (y_ptr != 0);
assert (len > 0);
return ((compute_power (x_ptr, len) + compute_power (y_ptr, len)) * 0.5);
}
template <class FO>
void TestAccuracy <FO>::compare_vect (const DataType x_ptr [], const DataType y_ptr [], BigFloat &power, long &max_err_pos, long len)
{
assert (x_ptr != 0);
assert (y_ptr != 0);
assert (len > 0);
assert (&power != 0);
assert (&max_err_pos != 0);
power = 0;
BigFloat max_dif2 = 0;
max_err_pos = -1;
for (long pos = 0; pos < len; ++pos)
{
const BigFloat x = x_ptr [pos];
const BigFloat y = y_ptr [pos];
const BigFloat dif = y - x;
const BigFloat dif2 = dif * dif;
power += dif2;
if (dif2 > max_dif2)
{
max_err_pos = pos;
max_dif2 = dif2;
}
}
using namespace std;
power = sqrt (power) / len;
}
#endif // TestAccuracy_CODEHEADER_INCLUDED
#undef TestAccuracy_CURRENT_CODEHEADER
/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/