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+#!/bin/sh
+# GSL-GENFFT - Power2 FFT C Code Generator
+# Copyright (C) 2001 Tim Janik
+#
+# This program is free software; you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation; either version 2 of the License, or
+# (at your option) any later version.
+#
+# This program 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 General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program; if not, write to the Free Software
+# Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
+
+# include files
+echo "#include $2"
+echo "#include <math.h>"
+
+MKFFT="$1"
+IEEE_TYPE="double"
+OPTIONS="--double"
+
+# provide macros and inline stubs
+$MKFFT $OPTIONS 0
+
+#
+# generate small fft sizes, seperating stage 2
+#
+for dir in --analysis --synthesis ; do
+ DOPT="$OPTIONS --skip-macros $dir"
+ echo "Generating FFT functions: $dir" >&2
+ $MKFFT $DOPT 2 F # standalone fft2
+ $MKFFT $DOPT 4 S F # reusable fft4
+ $MKFFT $DOPT 4 F X # standalone fft4
+ $MKFFT $DOPT 8 s F F # reusable fft8 w/o input fft2
+ $MKFFT $DOPT 8 F s X # standalone fft8
+ $MKFFT $DOPT 16 s F F F # reusable fft16
+ $MKFFT $DOPT 16 F s s X # standalone fft16
+ $MKFFT $DOPT 32 s F F F F
+ $MKFFT $DOPT 32 F s s s X
+ $MKFFT $DOPT 64 s R R R R F # reusable fft64
+ $MKFFT $DOPT 64 F s s s s X # standalone fft64
+ $MKFFT $DOPT 128 s R R R R R F # reusable fft128
+ $MKFFT $DOPT 128 L s s s s s X #
+ $MKFFT $DOPT 256 s s s s s s X T # reuse fft128
+ $MKFFT $DOPT 256 L s s s s s s X #
+ $MKFFT $DOPT 512 s s s s s s X T T # reuse fft128
+ $MKFFT $DOPT 512 L s s s s s s s X # fft512
+ $MKFFT $DOPT 1024 s s s s s s s s X L #
+ $MKFFT $DOPT 1024 L s s s s s s s s X #
+ $MKFFT $DOPT 2048 s s s s s s s s X L L # reusable fft2048
+ $MKFFT $DOPT 2048 L s s s s s s s s s X #
+ $MKFFT $DOPT 4096 s s s s s s s s s s X L # reuses fft2048
+ $MKFFT $DOPT 4096 L s s s s s s s s s s X # fft4096
+ $MKFFT $DOPT 8192 s s s s s s s s s s s X L # reusable impl. for 8192, reuses 2048
+ $MKFFT $DOPT 8192 L s s s s s s s s s s s X # real impl. for 8192
+done
+
+#
+# generic variable length implementation
+#
+echo "Generating generic FFT function for sizes >8192" >&2
+cat <<__EOF
+
+
+/* public FFT frontends and generic handling of huge fft sizes */
+
+
+static void
+gsl_power2_fftc_big (const unsigned int n_values,
+ const $IEEE_TYPE *rivalues_in,
+ $IEEE_TYPE *rivalues,
+ const int esign)
+{
+ const unsigned int n_values2 = n_values << 1;
+ double theta = esign < 0 ? -3.1415926535897932384626433832795029 : 3.1415926535897932384626433832795029;
+ unsigned int i, block_size = 8192 << 1;
+ double last_sin;
+
+ if (esign > 0)
+ {
+ if (rivalues_in)
+ bitreverse_fft2analysis (n_values, rivalues_in, rivalues);
+ for (i = 0; i < n_values; i += 8192)
+ gsl_power2_fft8192analysis_skip2 (rivalues + (i << 1), rivalues + (i << 1));
+ }
+ else
+ {
+ if (rivalues_in)
+ bitreverse_fft2synthesis (n_values, rivalues_in, rivalues);
+ for (i = 0; i < n_values; i += 8192)
+ gsl_power2_fft8192synthesis_skip2 (rivalues + (i << 1), rivalues + (i << 1));
+ }
+ theta *= (double) 1.0 / 8192.;
+ last_sin = sin (theta);
+
+ /* we're not combining the first and second halves coefficients
+ * in the below loop, since for fft sizes beyond 8192, it'd actually
+ * harm performance due to paging
+ */
+ do
+ {
+ double Dre, Dim, Wre, Wim;
+ unsigned int k, i, half_block = block_size >> 1;
+ unsigned int block_size2 = block_size << 1;
+
+ theta *= 0.5;
+ Dim = last_sin;
+ last_sin = sin (theta);
+ Dre = last_sin * last_sin * -2.;
+
+ /* loop over first coefficient in each block ==> w == {1,0} */
+ for (i = 0; i < n_values2; i += block_size2)
+ {
+ unsigned int v1 = i, v2 = i + block_size;
+
+ BUTTERFLY_10 (rivalues[v1], rivalues[v1 + 1],
+ rivalues[v2], rivalues[v2 + 1],
+ rivalues[v1], rivalues[v1 + 1],
+ rivalues[v2], rivalues[v2 + 1],
+ __1, __0);
+ }
+ Wre = Dre + 1.0; /* update Wk */
+ Wim = Dim; /* update Wk */
+ /* loop for every Wk in the first half of each subblock */
+ for (k = 2; k < half_block; k += 2)
+ {
+ /* loop over kth coefficient in each block */
+ for (i = k; i < n_values2; i += block_size2)
+ {
+ unsigned int v1 = i, v2 = i + block_size;
+
+ BUTTERFLY_XY (rivalues[v1], rivalues[v1 + 1],
+ rivalues[v2], rivalues[v2 + 1],
+ rivalues[v1], rivalues[v1 + 1],
+ rivalues[v2], rivalues[v2 + 1],
+ Wre, Wim);
+ }
+ WMULTIPLY (Wre, Wim, Dre, Dim); /* update Wk */
+ }
+ /* handle middle coefficient ==> w == {0,+-1} */
+ if (k < block_size)
+ {
+ /* loop over kth coefficient in each block */
+ if (esign > 0)
+ for (i = k; i < n_values2; i += block_size2)
+ {
+ unsigned int v1 = i, v2 = i + block_size;
+
+ BUTTERFLY_01 (rivalues[v1], rivalues[v1 + 1],
+ rivalues[v2], rivalues[v2 + 1],
+ rivalues[v1], rivalues[v1 + 1],
+ rivalues[v2], rivalues[v2 + 1],
+ __0, __1);
+ }
+ else
+ for (i = k; i < n_values2; i += block_size2)
+ {
+ unsigned int v1 = i, v2 = i + block_size;
+
+ BUTTERFLY_0m (rivalues[v1], rivalues[v1 + 1],
+ rivalues[v2], rivalues[v2 + 1],
+ rivalues[v1], rivalues[v1 + 1],
+ rivalues[v2], rivalues[v2 + 1],
+ __0, __1);
+ }
+ /* update Wk */
+ if (esign > 0)
+ {
+ Wre = -Dim;
+ Wim = Dre + 1.0;
+ }
+ else
+ {
+ Wre = Dim;
+ Wim = -Dre - 1.0;
+ }
+ k += 2;
+ }
+ /* loop for every Wk in the second half of each subblock */
+ for (; k < block_size; k += 2)
+ {
+ /* loop over kth coefficient in each block */
+ for (i = k; i < n_values2; i += block_size2)
+ {
+ unsigned int v1 = i, v2 = i + block_size;
+
+ BUTTERFLY_XY (rivalues[v1], rivalues[v1 + 1],
+ rivalues[v2], rivalues[v2 + 1],
+ rivalues[v1], rivalues[v1 + 1],
+ rivalues[v2], rivalues[v2 + 1],
+ Wre, Wim);
+ }
+ WMULTIPLY (Wre, Wim, Dre, Dim); /* update Wk */
+ }
+ block_size = block_size2;
+ }
+ while (block_size <= n_values);
+}
+__EOF
+
+
+#
+# public complex fft frontends
+#
+echo "Generating public complex FFT frontends" >&2
+cat <<__EOF
+void
+gsl_power2_fftac (const unsigned int n_values,
+ const $IEEE_TYPE *rivalues_in,
+ $IEEE_TYPE *rivalues_out)
+{
+ g_return_if_fail ((n_values & (n_values - 1)) == 0 && n_values >= 1);
+
+ switch (n_values)
+ {
+ case 1: rivalues_out[0] = rivalues_in[0], rivalues_out[1] = rivalues_in[1]; break;
+ case 2: gsl_power2_fft2analysis (rivalues_in, rivalues_out); break;
+ case 4: gsl_power2_fft4analysis (rivalues_in, rivalues_out); break;
+ case 8: gsl_power2_fft8analysis (rivalues_in, rivalues_out); break;
+ case 16: gsl_power2_fft16analysis (rivalues_in, rivalues_out); break;
+ case 32: gsl_power2_fft32analysis (rivalues_in, rivalues_out); break;
+ case 64: gsl_power2_fft64analysis (rivalues_in, rivalues_out); break;
+ case 128: gsl_power2_fft128analysis (rivalues_in, rivalues_out); break;
+ case 256: gsl_power2_fft256analysis (rivalues_in, rivalues_out); break;
+ case 512: gsl_power2_fft512analysis (rivalues_in, rivalues_out); break;
+ case 1024: gsl_power2_fft1024analysis (rivalues_in, rivalues_out); break;
+ case 2048: gsl_power2_fft2048analysis (rivalues_in, rivalues_out); break;
+ case 4096: gsl_power2_fft4096analysis (rivalues_in, rivalues_out); break;
+ case 8192: gsl_power2_fft8192analysis (rivalues_in, rivalues_out); break;
+ default: gsl_power2_fftc_big (n_values, rivalues_in, rivalues_out, +1);
+ }
+}
+void
+gsl_power2_fftsc (const unsigned int n_values,
+ const $IEEE_TYPE *rivalues_in,
+ $IEEE_TYPE *rivalues_out)
+{
+ g_return_if_fail ((n_values & (n_values - 1)) == 0 && n_values >= 1);
+
+ switch (n_values)
+ {
+ case 1: rivalues_out[0] = rivalues_in[0], rivalues_out[1] = rivalues_in[1]; break;
+ case 2: gsl_power2_fft2synthesis (rivalues_in, rivalues_out); break;
+ case 4: gsl_power2_fft4synthesis (rivalues_in, rivalues_out); break;
+ case 8: gsl_power2_fft8synthesis (rivalues_in, rivalues_out); break;
+ case 16: gsl_power2_fft16synthesis (rivalues_in, rivalues_out); break;
+ case 32: gsl_power2_fft32synthesis (rivalues_in, rivalues_out); break;
+ case 64: gsl_power2_fft64synthesis (rivalues_in, rivalues_out); break;
+ case 128: gsl_power2_fft128synthesis (rivalues_in, rivalues_out); break;
+ case 256: gsl_power2_fft256synthesis (rivalues_in, rivalues_out); break;
+ case 512: gsl_power2_fft512synthesis (rivalues_in, rivalues_out); break;
+ case 1024: gsl_power2_fft1024synthesis (rivalues_in, rivalues_out); break;
+ case 2048: gsl_power2_fft2048synthesis (rivalues_in, rivalues_out); break;
+ case 4096: gsl_power2_fft4096synthesis (rivalues_in, rivalues_out); break;
+ case 8192: gsl_power2_fft8192synthesis (rivalues_in, rivalues_out); break;
+ default: gsl_power2_fftc_big (n_values, rivalues_in, rivalues_out, -1);
+ }
+ /* { unsigned int i; for (i = 0; i < n_values << 1; i++) rivalues_out[i] *= (double) n_values; } */
+}
+__EOF
+
+
+#
+# public real fft frontends
+#
+echo "Generating public real FFT frontends" >&2
+cat <<__EOF
+void
+gsl_power2_fftar (const unsigned int n_values,
+ const $IEEE_TYPE *r_values_in,
+ $IEEE_TYPE *rivalues_out)
+{
+ unsigned int n_cvalues = n_values >> 1;
+ double Dre, Dim, Wre, Wim, theta;
+ unsigned int i;
+
+ g_return_if_fail ((n_values & (n_values - 1)) == 0 && n_values >= 2);
+
+ gsl_power2_fftac (n_cvalues, r_values_in, rivalues_out);
+ theta = 3.1415926535897932384626433832795029;
+ theta /= (double) n_cvalues;
+
+ Dre = sin (0.5 * theta);
+ Dim = sin (theta);
+ Dre = Dre * Dre;
+ Wre = 0.5 - Dre;
+ Dre *= -2.;
+ Wim = Dim * 0.5;
+ for (i = 2; i < n_values >> 1; i += 2)
+ {
+ double F1re, F1im, F2re, F2im, H1re, H1im, H2re, H2im;
+ unsigned int r = n_values - i;
+ double FEre = rivalues_out[i] + rivalues_out[r];
+ double FEim = rivalues_out[i + 1] - rivalues_out[r + 1];
+ double FOre = rivalues_out[r] - rivalues_out[i];
+ double FOim = rivalues_out[r + 1] + rivalues_out[i + 1];
+
+ FEre *= 0.5;
+ FEim *= 0.5;
+ F2re = FOre * Wim;
+ F2im = FOim * Wim;
+ F1re = FOre * Wre;
+ F1im = FOim * Wre;
+
+ H1im = F2im + F1re;
+ H1re = F1im - F2re;
+ H2re = F2re - F1im;
+ H2im = H1im - FEim;
+ H1re += FEre;
+ H2re += FEre;
+ H1im += FEim;
+ rivalues_out[i] = H1re;
+ rivalues_out[i + 1] = H1im;
+ rivalues_out[r] = H2re;
+ rivalues_out[r + 1] = H2im;
+ WMULTIPLY (Wre, Wim, Dre, Dim);
+ }
+ Dre = rivalues_out[0];
+ rivalues_out[0] = Dre + rivalues_out[1];
+ rivalues_out[1] = Dre - rivalues_out[1];
+}
+void
+gsl_power2_fftsr (const unsigned int n_values,
+ const double *rivalues_in,
+ double *r_values_out)
+{
+ unsigned int n_cvalues = n_values >> 1;
+ double Dre, Dim, Wre, Wim, theta, scale;
+ unsigned int i, ri;
+
+ g_return_if_fail ((n_values & (n_values - 1)) == 0 && n_values >= 2);
+
+ theta = -3.1415926535897932384626433832795029;
+ theta /= (double) n_cvalues;
+
+ Dre = sin (0.5 * theta);
+ Dim = sin (theta);
+ Dre = Dre * Dre;
+ Wre = 0.5 - Dre;
+ Dre *= -2.;
+ Wim = Dim * 0.5;
+ for (i = 2, ri = 0; i < n_values >> 1; i += 2)
+ {
+ double F1re, F1im, F2re, F2im, H1re, H1im, H2re, H2im;
+ unsigned int g = n_values - i, j = n_values >> 2, rg = n_values - (ri << 1) - 2;
+ double FEre = rivalues_in[i] + rivalues_in[g];
+ double FEim = rivalues_in[i + 1] - rivalues_in[g + 1];
+ double FOre = rivalues_in[g] - rivalues_in[i];
+ double FOim = rivalues_in[g + 1] + rivalues_in[i + 1];
+
+ while (ri >= j)
+ {
+ ri -= j;
+ j >>= 1;
+ }
+ ri |= j;
+
+ FOre = -FOre;
+ FOim = -FOim;
+ FEre *= 0.5;
+ FEim *= 0.5;
+ F2re = FOre * Wim;
+ F2im = FOim * Wim;
+ F1re = FOre * Wre;
+ F1im = FOim * Wre;
+
+ H1im = F2im + F1re;
+ H1re = F1im - F2re;
+ H2re = F2re - F1im;
+ H2im = H1im - FEim;
+ H1re += FEre;
+ H2re += FEre;
+ H1im += FEim;
+
+ j = ri << 1;
+ r_values_out[j] = H1re;
+ r_values_out[j + 1] = H1im;
+ r_values_out[rg] = H2re;
+ r_values_out[rg + 1] = H2im;
+ WMULTIPLY (Wre, Wim, Dre, Dim);
+ }
+ Dre = rivalues_in[0];
+ r_values_out[0] = Dre + rivalues_in[1];
+ r_values_out[1] = Dre - rivalues_in[1];
+ r_values_out[0] *= 0.5;
+ r_values_out[1] *= 0.5;
+ if (n_values < 4)
+ return;
+ r_values_out[2] = rivalues_in[i];
+ r_values_out[2 + 1] = rivalues_in[i + 1];
+ scale = n_cvalues;
+ scale = 1.0 / scale;
+ for (i = 0; i < n_values; i += 4)
+ BUTTERFLY_10scale (r_values_out[i], r_values_out[i + 1],
+ r_values_out[i + 2], r_values_out[i + 3],
+ r_values_out[i], r_values_out[i + 1],
+ r_values_out[i + 2], r_values_out[i + 3],
+ scale);
+ switch (n_cvalues)
+ {
+ case 2: break;
+ case 4: gsl_power2_fft4synthesis_skip2 (NULL, r_values_out); break;
+ case 8: gsl_power2_fft8synthesis_skip2 (NULL, r_values_out); break;
+ case 16: gsl_power2_fft16synthesis_skip2 (NULL, r_values_out); break;
+ case 32: gsl_power2_fft32synthesis_skip2 (NULL, r_values_out); break;
+ case 64: gsl_power2_fft64synthesis_skip2 (NULL, r_values_out); break;
+ case 128: gsl_power2_fft128synthesis_skip2 (NULL, r_values_out); break;
+ case 256: gsl_power2_fft256synthesis_skip2 (NULL, r_values_out); break;
+ case 512: gsl_power2_fft512synthesis_skip2 (NULL, r_values_out); break;
+ case 1024: gsl_power2_fft1024synthesis_skip2 (NULL, r_values_out); break;
+ case 2048: gsl_power2_fft2048synthesis_skip2 (NULL, r_values_out); break;
+ case 4096: gsl_power2_fft4096synthesis_skip2 (NULL, r_values_out); break;
+ case 8192: gsl_power2_fft8192synthesis_skip2 (NULL, r_values_out); break;
+ default: gsl_power2_fftc_big (n_cvalues, NULL, r_values_out, -1);
+ }
+}
+void
+gsl_power2_fftar_simple (const unsigned int n_values,
+ const float *real_values,
+ float *complex_values)
+{
+ double *rv, *cv;
+ guint i;
+
+ g_return_if_fail ((n_values & (n_values - 1)) == 0 && n_values >= 2);
+
+ rv = g_new (double, n_values * 2);
+ cv = rv + n_values;
+ i = n_values;
+ while (i--)
+ rv[i] = real_values[i];
+ gsl_power2_fftar (n_values, rv, cv);
+ i = n_values;
+ while (i--)
+ complex_values[i] = cv[i];
+ complex_values[n_values] = complex_values[1];
+ complex_values[1] = 0.0;
+ complex_values[n_values + 1] = 0.0;
+ g_free (rv);
+}
+void
+gsl_power2_fftsr_simple (const unsigned int n_values,
+ const float *complex_values,
+ float *real_values)
+{
+ double *cv, *rv;
+ guint i;
+
+ g_return_if_fail ((n_values & (n_values - 1)) == 0 && n_values >= 2);
+
+ cv = g_new (double, n_values * 2);
+ rv = cv + n_values;
+ i = n_values;
+ while (i--)
+ cv[i] = complex_values[i];
+ cv[1] = complex_values[n_values];
+ gsl_power2_fftsr (n_values, cv, rv);
+ i = n_values;
+ while (i--)
+ real_values[i] = rv[i];
+ g_free (cv);
+}
+__EOF
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