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+/*****************************************************************************
+
+ 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 \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
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