#include "gslfft.h" #include #define BUTTERFLY_XY(X1re,X1im,X2re,X2im,Y1re,Y1im,Y2re,Y2im,Wre,Wim) { \ double T1re, T1im, T2re, T2im; \ T1re = X2re * Wre; \ T1im = X2im * Wre; \ T2re = X2im * Wim; \ T2im = X2re * Wim; \ T1re -= T2re; \ T1im += T2im; \ T2re = X1re - T1re; \ T2im = X1im - T1im; \ Y1re = X1re + T1re; \ Y1im = X1im + T1im; \ Y2re = T2re; \ Y2im = T2im; \ } #define BUTTERFLY_Yx(X1re,X1im,X2re,X2im,Y1re,Y1im,Y2re,Y2im,Wre,Wim) { \ double T1re, T1im, T2re, T2im; \ T1re = X2re * Wim; \ T1im = X2im * Wim; \ T2re = X2im * Wre; \ T2im = X2re * Wre; \ T1re += T2re; \ T1im -= T2im; \ T2re = X1re + T1re; \ T2im = X1im + T1im; \ Y1re = X1re - T1re; \ Y1im = X1im - T1im; \ Y2re = T2re; \ Y2im = T2im; \ } #define BUTTERFLY_yX(X1re,X1im,X2re,X2im,Y1re,Y1im,Y2re,Y2im,Wre,Wim) { \ double T1re, T1im, T2re, T2im; \ T1re = X2re * Wim; \ T1im = X2im * Wim; \ T2re = X2im * Wre; \ T2im = X2re * Wre; \ T1re += T2re; \ T1im -= T2im; \ T2re = X1re - T1re; \ T2im = X1im - T1im; \ Y1re = X1re + T1re; \ Y1im = X1im + T1im; \ Y2re = T2re; \ Y2im = T2im; \ } #define BUTTERFLY_10(X1re,X1im,X2re,X2im,Y1re,Y1im,Y2re,Y2im,_1,_2) { \ double T2re, T2im; \ T2re = X1re - X2re; \ T2im = X1im - X2im; \ Y1re = X1re + X2re; \ Y1im = X1im + X2im; \ Y2re = T2re; \ Y2im = T2im; \ } #define BUTTERFLY_01(X1re,X1im,X2re,X2im,Y1re,Y1im,Y2re,Y2im,_1,_2) { \ double T2re, T2im; \ T2re = X1re + X2im; \ T2im = X1im - X2re; \ Y1re = X1re - X2im; \ Y1im = X1im + X2re; \ Y2re = T2re; \ Y2im = T2im; \ } #define BUTTERFLY_0m(X1re,X1im,X2re,X2im,Y1re,Y1im,Y2re,Y2im,_1,_2) { \ double T2re, T2im; \ T2re = X1re - X2im; \ T2im = X1im + X2re; \ Y1re = X1re + X2im; \ Y1im = X1im - X2re; \ Y2re = T2re; \ Y2im = T2im; \ } #define BUTTERFLY_XX(X1re,X1im,X2re,X2im,Y1re,Y1im,Y2re,Y2im,Wre,_2) { \ double T1re, T1im, T2re, T2im; \ T1re = X2re * Wre; \ T1im = X2im * Wre; \ T2re = T1im; \ T2im = T1re; \ T1re -= T2re; \ T1im += T2im; \ T2re = X1re - T1re; \ T2im = X1im - T1im; \ Y1re = X1re + T1re; \ Y1im = X1im + T1im; \ Y2re = T2re; \ Y2im = T2im; \ } #define BUTTERFLY_yY(X1re,X1im,X2re,X2im,Y1re,Y1im,Y2re,Y2im,Wre,_2) { \ double T1re, T1im, T2re, T2im; \ T1re = X2re * Wre; \ T1im = X2im * Wre; \ T2re = T1im; \ T2im = T1re; \ T1re += T2re; \ T1im -= T2im; \ T2re = X1re - T1re; \ T2im = X1im - T1im; \ Y1re = X1re + T1re; \ Y1im = X1im + T1im; \ Y2re = T2re; \ Y2im = T2im; \ } #define BUTTERFLY_10scale(X1re,X1im,X2re,X2im,Y1re,Y1im,Y2re,Y2im,S) { \ double T2re, T2im; \ T2re = X1re - X2re; \ T2im = X1im - X2im; \ Y1re = X1re + X2re; \ Y1im = X1im + X2im; \ Y2re = T2re * S; \ Y2im = T2im * S; \ Y1re *= S; \ Y1im *= S; \ } #define WMULTIPLY(Wre,Wim,Dre,Dim) { \ double T1re, T1im, T2re, T2im; \ T1re = Wre * Dre; \ T1im = Wim * Dre; \ T2re = Wim * Dim; \ T2im = Wre * Dim; \ T1re -= T2re; \ T1im += T2im; \ Wre += T1re; \ Wim += T1im; \ } static inline void bitreverse_fft2analysis (const unsigned int n, const double *X, double *Y) { const unsigned int n2 = n >> 1, n1 = n + n2, max = n >> 2; unsigned int i, r; BUTTERFLY_10 (X[0], X[1], X[n], X[n + 1], Y[0], Y[1], Y[2], Y[3], __1, __0); BUTTERFLY_10 (X[n2], X[n2 + 1], X[n1], X[n1 + 1], Y[4], Y[5], Y[6], Y[7], __1, __0); for (i = 1, r = 0; i < max; i++) { unsigned int k, j = n >> 1; while (r >= j) { r -= j; j >>= 1; } r |= j; k = r >> 1; j = i << 3; BUTTERFLY_10 (X[k], X[k + 1], X[k + n], X[k + n + 1], Y[j], Y[j + 1], Y[j + 2], Y[j + 3], __1, __0); k += n2; j += 4; BUTTERFLY_10 (X[k], X[k + 1], X[k + n], X[k + n + 1], Y[j], Y[j + 1], Y[j + 2], Y[j + 3], __1, __0); } } static inline void bitreverse_fft2synthesis (const unsigned int n, const double *X, double *Y) { const unsigned int n2 = n >> 1, n1 = n + n2, max = n >> 2; unsigned int i, r; double scale = n; scale = 1.0 / scale; BUTTERFLY_10scale (X[0], X[1], X[n], X[n + 1], Y[0], Y[1], Y[2], Y[3], scale); BUTTERFLY_10scale (X[n2], X[n2 + 1], X[n1], X[n1 + 1], Y[4], Y[5], Y[6], Y[7], scale); for (i = 1, r = 0; i < max; i++) { unsigned int k, j = n >> 1; while (r >= j) { r -= j; j >>= 1; } r |= j; k = r >> 1; j = i << 3; BUTTERFLY_10scale (X[k], X[k + 1], X[k + n], X[k + n + 1], Y[j], Y[j + 1], Y[j + 2], Y[j + 3], scale); k += n2; j += 4; BUTTERFLY_10scale (X[k], X[k + 1], X[k + n], X[k + n + 1], Y[j], Y[j + 1], Y[j + 2], Y[j + 3], scale); } } /** ** Generated data (by gsl-genfft 2 F) **/ static void gsl_power2_fft2analysis (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* perform 1 times fft2 */ BUTTERFLY_10 (X[0], X[0 + 1], X[2], X[2 + 1], Y[0], Y[0 + 1], Y[2], Y[2 + 1], __1, __0); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 4 S F) **/ static void gsl_power2_fft4analysis_skip2 (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* skipping 2 times fft2 */ /* perform 1 times fft4 */ BUTTERFLY_10 (Y[0], /* W0 */ Y[0 + 1], Y[4], Y[4 + 1], Y[0], Y[0 + 1], Y[4], Y[4 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_01 (Y[2], /* W1 */ Y[2 + 1], Y[6], Y[6 + 1], Y[2], Y[2 + 1], Y[6], Y[6 + 1], (double) +0.000000000000000, (double) +1.000000000000000); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 4 F X) **/ static void gsl_power2_fft4analysis (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* perform 2 times fft2 */ BUTTERFLY_10 (X[0], X[0 + 1], X[4], X[4 + 1], Y[0], Y[0 + 1], Y[2], Y[2 + 1], __1, __0); BUTTERFLY_10 (X[2], X[2 + 1], X[6], X[6 + 1], Y[4], Y[4 + 1], Y[6], Y[6 + 1], __1, __0); /* perform 1 times fft4 */ gsl_power2_fft4analysis_skip2 (X, Y); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 8 S F F) **/ static void gsl_power2_fft8analysis_skip2 (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* skipping 4 times fft2 */ /* perform 2 times fft4 */ BUTTERFLY_10 (Y[0], /* W0 */ Y[0 + 1], Y[4], Y[4 + 1], Y[0], Y[0 + 1], Y[4], Y[4 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[8], /* W0 */ Y[8 + 1], Y[12], Y[12 + 1], Y[8], Y[8 + 1], Y[12], Y[12 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_01 (Y[2], /* W2 */ Y[2 + 1], Y[6], Y[6 + 1], Y[2], Y[2 + 1], Y[6], Y[6 + 1], (double) +0.000000000000000, (double) +1.000000000000000); BUTTERFLY_01 (Y[10], /* W2 */ Y[10 + 1], Y[14], Y[14 + 1], Y[10], Y[10 + 1], Y[14], Y[14 + 1], (double) +0.000000000000000, (double) +1.000000000000000); /* perform 1 times fft8 */ BUTTERFLY_10 (Y[0], /* W0 */ Y[0 + 1], Y[8], Y[8 + 1], Y[0], Y[0 + 1], Y[8], Y[8 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_XX (Y[2], /* W1 */ Y[2 + 1], Y[10], Y[10 + 1], Y[2], Y[2 + 1], Y[10], Y[10 + 1], (double) +0.707106781186548, (double) +0.707106781186547); BUTTERFLY_01 (Y[4], /* W2 */ Y[4 + 1], Y[12], Y[12 + 1], Y[4], Y[4 + 1], Y[12], Y[12 + 1], (double) +0.000000000000000, (double) +1.000000000000000); BUTTERFLY_yY (Y[6], /* W3 */ Y[6 + 1], Y[14], Y[14 + 1], Y[6], Y[6 + 1], Y[14], Y[14 + 1], (double) -0.707106781186547, (double) +0.707106781186548); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 8 F S X) **/ static void gsl_power2_fft8analysis (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* perform 4 times fft2 */ BUTTERFLY_10 (X[0], X[0 + 1], X[8], X[8 + 1], Y[0], Y[0 + 1], Y[2], Y[2 + 1], __1, __0); BUTTERFLY_10 (X[4], X[4 + 1], X[12], X[12 + 1], Y[4], Y[4 + 1], Y[6], Y[6 + 1], __1, __0); BUTTERFLY_10 (X[2], X[2 + 1], X[10], X[10 + 1], Y[8], Y[8 + 1], Y[10], Y[10 + 1], __1, __0); BUTTERFLY_10 (X[6], X[6 + 1], X[14], X[14 + 1], Y[12], Y[12 + 1], Y[14], Y[14 + 1], __1, __0); /* skipping 2 times fft4 */ /* perform 1 times fft8 */ gsl_power2_fft8analysis_skip2 (X, Y); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 16 S F F F) **/ static void gsl_power2_fft16analysis_skip2 (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* skipping 8 times fft2 */ /* perform 4 times fft4 */ BUTTERFLY_10 (Y[0], /* W0 */ Y[0 + 1], Y[4], Y[4 + 1], Y[0], Y[0 + 1], Y[4], Y[4 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[8], /* W0 */ Y[8 + 1], Y[12], Y[12 + 1], Y[8], Y[8 + 1], Y[12], Y[12 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[16], /* W0 */ Y[16 + 1], Y[20], Y[20 + 1], Y[16], Y[16 + 1], Y[20], Y[20 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[24], /* W0 */ Y[24 + 1], Y[28], Y[28 + 1], Y[24], Y[24 + 1], Y[28], Y[28 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_01 (Y[2], /* W4 */ Y[2 + 1], Y[6], Y[6 + 1], Y[2], Y[2 + 1], Y[6], Y[6 + 1], (double) +0.000000000000000, (double) +1.000000000000000); BUTTERFLY_01 (Y[10], /* W4 */ Y[10 + 1], Y[14], Y[14 + 1], Y[10], Y[10 + 1], Y[14], Y[14 + 1], (double) +0.000000000000000, (double) +1.000000000000000); BUTTERFLY_01 (Y[18], /* W4 */ Y[18 + 1], Y[22], Y[22 + 1], Y[18], Y[18 + 1], Y[22], Y[22 + 1], (double) +0.000000000000000, (double) +1.000000000000000); BUTTERFLY_01 (Y[26], /* W4 */ Y[26 + 1], Y[30], Y[30 + 1], Y[26], Y[26 + 1], Y[30], Y[30 + 1], (double) +0.000000000000000, (double) +1.000000000000000); /* perform 2 times fft8 */ BUTTERFLY_10 (Y[0], /* W0 */ Y[0 + 1], Y[8], Y[8 + 1], Y[0], Y[0 + 1], Y[8], Y[8 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[16], /* W0 */ Y[16 + 1], Y[24], Y[24 + 1], Y[16], Y[16 + 1], Y[24], Y[24 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_XX (Y[2], /* W2 */ Y[2 + 1], Y[10], Y[10 + 1], Y[2], Y[2 + 1], Y[10], Y[10 + 1], (double) +0.707106781186548, (double) +0.707106781186547); BUTTERFLY_XX (Y[18], /* W2 */ Y[18 + 1], Y[26], Y[26 + 1], Y[18], Y[18 + 1], Y[26], Y[26 + 1], (double) +0.707106781186548, (double) +0.707106781186547); BUTTERFLY_01 (Y[4], /* W4 */ Y[4 + 1], Y[12], Y[12 + 1], Y[4], Y[4 + 1], Y[12], Y[12 + 1], (double) +0.000000000000000, (double) +1.000000000000000); BUTTERFLY_01 (Y[20], /* W4 */ Y[20 + 1], Y[28], Y[28 + 1], Y[20], Y[20 + 1], Y[28], Y[28 + 1], (double) +0.000000000000000, (double) +1.000000000000000); BUTTERFLY_yY (Y[6], /* W6 */ Y[6 + 1], Y[14], Y[14 + 1], Y[6], Y[6 + 1], Y[14], Y[14 + 1], (double) -0.707106781186547, (double) +0.707106781186548); BUTTERFLY_yY (Y[22], /* W6 */ Y[22 + 1], Y[30], Y[30 + 1], Y[22], Y[22 + 1], Y[30], Y[30 + 1], (double) -0.707106781186547, (double) +0.707106781186548); /* perform 1 times fft16 */ BUTTERFLY_10 (Y[0], /* W0 */ Y[0 + 1], Y[16], Y[16 + 1], Y[0], Y[0 + 1], Y[16], Y[16 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_XY (Y[2], /* W1 */ Y[2 + 1], Y[18], Y[18 + 1], Y[2], Y[2 + 1], Y[18], Y[18 + 1], (double) +0.923879532511287, (double) +0.382683432365090); BUTTERFLY_XX (Y[4], /* W2 */ Y[4 + 1], Y[20], Y[20 + 1], Y[4], Y[4 + 1], Y[20], Y[20 + 1], (double) +0.707106781186548, (double) +0.707106781186547); BUTTERFLY_XY (Y[6], /* W3 */ Y[6 + 1], Y[22], Y[22 + 1], Y[6], Y[6 + 1], Y[22], Y[22 + 1], (double) +0.382683432365090, (double) +0.923879532511287); BUTTERFLY_01 (Y[8], /* W4 */ Y[8 + 1], Y[24], Y[24 + 1], Y[8], Y[8 + 1], Y[24], Y[24 + 1], (double) +0.000000000000000, (double) +1.000000000000000); BUTTERFLY_XY (Y[10], /* W5 */ Y[10 + 1], Y[26], Y[26 + 1], Y[10], Y[10 + 1], Y[26], Y[26 + 1], (double) -0.382683432365090, (double) +0.923879532511287); BUTTERFLY_yY (Y[12], /* W6 */ Y[12 + 1], Y[28], Y[28 + 1], Y[12], Y[12 + 1], Y[28], Y[28 + 1], (double) -0.707106781186547, (double) +0.707106781186548); BUTTERFLY_XY (Y[14], /* W7 */ Y[14 + 1], Y[30], Y[30 + 1], Y[14], Y[14 + 1], Y[30], Y[30 + 1], (double) -0.923879532511287, (double) +0.382683432365090); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 16 F S S X) **/ static void gsl_power2_fft16analysis (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* perform 8 times fft2 */ BUTTERFLY_10 (X[0], X[0 + 1], X[16], X[16 + 1], Y[0], Y[0 + 1], Y[2], Y[2 + 1], __1, __0); BUTTERFLY_10 (X[8], X[8 + 1], X[24], X[24 + 1], Y[4], Y[4 + 1], Y[6], Y[6 + 1], __1, __0); BUTTERFLY_10 (X[4], X[4 + 1], X[20], X[20 + 1], Y[8], Y[8 + 1], Y[10], Y[10 + 1], __1, __0); BUTTERFLY_10 (X[12], X[12 + 1], X[28], X[28 + 1], Y[12], Y[12 + 1], Y[14], Y[14 + 1], __1, __0); BUTTERFLY_10 (X[2], X[2 + 1], X[18], X[18 + 1], Y[16], Y[16 + 1], Y[18], Y[18 + 1], __1, __0); BUTTERFLY_10 (X[10], X[10 + 1], X[26], X[26 + 1], Y[20], Y[20 + 1], Y[22], Y[22 + 1], __1, __0); BUTTERFLY_10 (X[6], X[6 + 1], X[22], X[22 + 1], Y[24], Y[24 + 1], Y[26], Y[26 + 1], __1, __0); BUTTERFLY_10 (X[14], X[14 + 1], X[30], X[30 + 1], Y[28], Y[28 + 1], Y[30], Y[30 + 1], __1, __0); /* skipping 4 times fft4 */ /* skipping 2 times fft8 */ /* perform 1 times fft16 */ gsl_power2_fft16analysis_skip2 (X, Y); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 32 S F F F F) **/ static void gsl_power2_fft32analysis_skip2 (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* skipping 16 times fft2 */ /* perform 8 times fft4 */ BUTTERFLY_10 (Y[0], /* W0 */ Y[0 + 1], Y[4], Y[4 + 1], Y[0], Y[0 + 1], Y[4], Y[4 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[8], /* W0 */ Y[8 + 1], Y[12], Y[12 + 1], Y[8], Y[8 + 1], Y[12], Y[12 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[16], /* W0 */ Y[16 + 1], Y[20], Y[20 + 1], Y[16], Y[16 + 1], Y[20], Y[20 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[24], /* W0 */ Y[24 + 1], Y[28], Y[28 + 1], Y[24], Y[24 + 1], Y[28], Y[28 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[32], /* W0 */ Y[32 + 1], Y[36], Y[36 + 1], Y[32], Y[32 + 1], Y[36], Y[36 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[40], /* W0 */ Y[40 + 1], Y[44], Y[44 + 1], Y[40], Y[40 + 1], Y[44], Y[44 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[48], /* W0 */ Y[48 + 1], Y[52], Y[52 + 1], Y[48], Y[48 + 1], Y[52], Y[52 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[56], /* W0 */ Y[56 + 1], Y[60], Y[60 + 1], Y[56], Y[56 + 1], Y[60], Y[60 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_01 (Y[2], /* W8 */ Y[2 + 1], Y[6], Y[6 + 1], Y[2], Y[2 + 1], Y[6], Y[6 + 1], (double) +0.000000000000000, (double) +1.000000000000000); BUTTERFLY_01 (Y[10], /* W8 */ Y[10 + 1], Y[14], Y[14 + 1], Y[10], Y[10 + 1], Y[14], Y[14 + 1], (double) +0.000000000000000, (double) +1.000000000000000); BUTTERFLY_01 (Y[18], /* W8 */ Y[18 + 1], Y[22], Y[22 + 1], Y[18], Y[18 + 1], Y[22], Y[22 + 1], (double) +0.000000000000000, (double) +1.000000000000000); BUTTERFLY_01 (Y[26], /* W8 */ Y[26 + 1], Y[30], Y[30 + 1], Y[26], Y[26 + 1], Y[30], Y[30 + 1], (double) +0.000000000000000, (double) +1.000000000000000); BUTTERFLY_01 (Y[34], /* W8 */ Y[34 + 1], Y[38], Y[38 + 1], Y[34], Y[34 + 1], Y[38], Y[38 + 1], (double) +0.000000000000000, (double) +1.000000000000000); BUTTERFLY_01 (Y[42], /* W8 */ Y[42 + 1], Y[46], Y[46 + 1], Y[42], Y[42 + 1], Y[46], Y[46 + 1], (double) +0.000000000000000, (double) +1.000000000000000); BUTTERFLY_01 (Y[50], /* W8 */ Y[50 + 1], Y[54], Y[54 + 1], Y[50], Y[50 + 1], Y[54], Y[54 + 1], (double) +0.000000000000000, (double) +1.000000000000000); BUTTERFLY_01 (Y[58], /* W8 */ Y[58 + 1], Y[62], Y[62 + 1], Y[58], Y[58 + 1], Y[62], Y[62 + 1], (double) +0.000000000000000, (double) +1.000000000000000); /* perform 4 times fft8 */ BUTTERFLY_10 (Y[0], /* W0 */ Y[0 + 1], Y[8], Y[8 + 1], Y[0], Y[0 + 1], Y[8], Y[8 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[16], /* W0 */ Y[16 + 1], Y[24], Y[24 + 1], Y[16], Y[16 + 1], Y[24], Y[24 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[32], /* W0 */ Y[32 + 1], Y[40], Y[40 + 1], Y[32], Y[32 + 1], Y[40], Y[40 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[48], /* W0 */ Y[48 + 1], Y[56], Y[56 + 1], Y[48], Y[48 + 1], Y[56], Y[56 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_XX (Y[2], /* W4 */ Y[2 + 1], Y[10], Y[10 + 1], Y[2], Y[2 + 1], Y[10], Y[10 + 1], (double) +0.707106781186548, (double) +0.707106781186547); BUTTERFLY_XX (Y[18], /* W4 */ Y[18 + 1], Y[26], Y[26 + 1], Y[18], Y[18 + 1], Y[26], Y[26 + 1], (double) +0.707106781186548, (double) +0.707106781186547); BUTTERFLY_XX (Y[34], /* W4 */ Y[34 + 1], Y[42], Y[42 + 1], Y[34], Y[34 + 1], Y[42], Y[42 + 1], (double) +0.707106781186548, (double) +0.707106781186547); BUTTERFLY_XX (Y[50], /* W4 */ Y[50 + 1], Y[58], Y[58 + 1], Y[50], Y[50 + 1], Y[58], Y[58 + 1], (double) +0.707106781186548, (double) +0.707106781186547); BUTTERFLY_01 (Y[4], /* W8 */ Y[4 + 1], Y[12], Y[12 + 1], Y[4], Y[4 + 1], Y[12], Y[12 + 1], (double) +0.000000000000000, (double) +1.000000000000000); BUTTERFLY_01 (Y[20], /* W8 */ Y[20 + 1], Y[28], Y[28 + 1], Y[20], Y[20 + 1], Y[28], Y[28 + 1], (double) +0.000000000000000, (double) +1.000000000000000); BUTTERFLY_01 (Y[36], /* W8 */ Y[36 + 1], Y[44], Y[44 + 1], Y[36], Y[36 + 1], Y[44], Y[44 + 1], (double) +0.000000000000000, (double) +1.000000000000000); BUTTERFLY_01 (Y[52], /* W8 */ Y[52 + 1], Y[60], Y[60 + 1], Y[52], Y[52 + 1], Y[60], Y[60 + 1], (double) +0.000000000000000, (double) +1.000000000000000); BUTTERFLY_yY (Y[6], /* W12 */ Y[6 + 1], Y[14], Y[14 + 1], Y[6], Y[6 + 1], Y[14], Y[14 + 1], (double) -0.707106781186547, (double) +0.707106781186548); BUTTERFLY_yY (Y[22], /* W12 */ Y[22 + 1], Y[30], Y[30 + 1], Y[22], Y[22 + 1], Y[30], Y[30 + 1], (double) -0.707106781186547, (double) +0.707106781186548); BUTTERFLY_yY (Y[38], /* W12 */ Y[38 + 1], Y[46], Y[46 + 1], Y[38], Y[38 + 1], Y[46], Y[46 + 1], (double) -0.707106781186547, (double) +0.707106781186548); BUTTERFLY_yY (Y[54], /* W12 */ Y[54 + 1], Y[62], Y[62 + 1], Y[54], Y[54 + 1], Y[62], Y[62 + 1], (double) -0.707106781186547, (double) +0.707106781186548); /* perform 2 times fft16 */ BUTTERFLY_10 (Y[0], /* W0 */ Y[0 + 1], Y[16], Y[16 + 1], Y[0], Y[0 + 1], Y[16], Y[16 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[32], /* W0 */ Y[32 + 1], Y[48], Y[48 + 1], Y[32], Y[32 + 1], Y[48], Y[48 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_XY (Y[2], /* W2 */ Y[2 + 1], Y[18], Y[18 + 1], Y[2], Y[2 + 1], Y[18], Y[18 + 1], (double) +0.923879532511287, (double) +0.382683432365090); BUTTERFLY_XY (Y[34], /* W2 */ Y[34 + 1], Y[50], Y[50 + 1], Y[34], Y[34 + 1], Y[50], Y[50 + 1], (double) +0.923879532511287, (double) +0.382683432365090); BUTTERFLY_XX (Y[4], /* W4 */ Y[4 + 1], Y[20], Y[20 + 1], Y[4], Y[4 + 1], Y[20], Y[20 + 1], (double) +0.707106781186548, (double) +0.707106781186547); BUTTERFLY_XX (Y[36], /* W4 */ Y[36 + 1], Y[52], Y[52 + 1], Y[36], Y[36 + 1], Y[52], Y[52 + 1], (double) +0.707106781186548, (double) +0.707106781186547); BUTTERFLY_XY (Y[6], /* W6 */ Y[6 + 1], Y[22], Y[22 + 1], Y[6], Y[6 + 1], Y[22], Y[22 + 1], (double) +0.382683432365090, (double) +0.923879532511287); BUTTERFLY_XY (Y[38], /* W6 */ Y[38 + 1], Y[54], Y[54 + 1], Y[38], Y[38 + 1], Y[54], Y[54 + 1], (double) +0.382683432365090, (double) +0.923879532511287); BUTTERFLY_01 (Y[8], /* W8 */ Y[8 + 1], Y[24], Y[24 + 1], Y[8], Y[8 + 1], Y[24], Y[24 + 1], (double) +0.000000000000000, (double) +1.000000000000000); BUTTERFLY_01 (Y[40], /* W8 */ Y[40 + 1], Y[56], Y[56 + 1], Y[40], Y[40 + 1], Y[56], Y[56 + 1], (double) +0.000000000000000, (double) +1.000000000000000); BUTTERFLY_XY (Y[10], /* W10 */ Y[10 + 1], Y[26], Y[26 + 1], Y[10], Y[10 + 1], Y[26], Y[26 + 1], (double) -0.382683432365090, (double) +0.923879532511287); BUTTERFLY_XY (Y[42], /* W10 */ Y[42 + 1], Y[58], Y[58 + 1], Y[42], Y[42 + 1], Y[58], Y[58 + 1], (double) -0.382683432365090, (double) +0.923879532511287); BUTTERFLY_yY (Y[12], /* W12 */ Y[12 + 1], Y[28], Y[28 + 1], Y[12], Y[12 + 1], Y[28], Y[28 + 1], (double) -0.707106781186547, (double) +0.707106781186548); BUTTERFLY_yY (Y[44], /* W12 */ Y[44 + 1], Y[60], Y[60 + 1], Y[44], Y[44 + 1], Y[60], Y[60 + 1], (double) -0.707106781186547, (double) +0.707106781186548); BUTTERFLY_XY (Y[14], /* W14 */ Y[14 + 1], Y[30], Y[30 + 1], Y[14], Y[14 + 1], Y[30], Y[30 + 1], (double) -0.923879532511287, (double) +0.382683432365090); BUTTERFLY_XY (Y[46], /* W14 */ Y[46 + 1], Y[62], Y[62 + 1], Y[46], Y[46 + 1], Y[62], Y[62 + 1], (double) -0.923879532511287, (double) +0.382683432365090); /* perform 1 times fft32 */ BUTTERFLY_10 (Y[0], /* W0 */ Y[0 + 1], Y[32], Y[32 + 1], Y[0], Y[0 + 1], Y[32], Y[32 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_XY (Y[2], /* W1 */ Y[2 + 1], Y[34], Y[34 + 1], Y[2], Y[2 + 1], Y[34], Y[34 + 1], (double) +0.980785280403230, (double) +0.195090322016128); BUTTERFLY_XY (Y[4], /* W2 */ Y[4 + 1], Y[36], Y[36 + 1], Y[4], Y[4 + 1], Y[36], Y[36 + 1], (double) +0.923879532511287, (double) +0.382683432365090); BUTTERFLY_XY (Y[6], /* W3 */ Y[6 + 1], Y[38], Y[38 + 1], Y[6], Y[6 + 1], Y[38], Y[38 + 1], (double) +0.831469612302545, (double) +0.555570233019602); BUTTERFLY_XX (Y[8], /* W4 */ Y[8 + 1], Y[40], Y[40 + 1], Y[8], Y[8 + 1], Y[40], Y[40 + 1], (double) +0.707106781186548, (double) +0.707106781186547); BUTTERFLY_XY (Y[10], /* W5 */ Y[10 + 1], Y[42], Y[42 + 1], Y[10], Y[10 + 1], Y[42], Y[42 + 1], (double) +0.555570233019602, (double) +0.831469612302545); BUTTERFLY_XY (Y[12], /* W6 */ Y[12 + 1], Y[44], Y[44 + 1], Y[12], Y[12 + 1], Y[44], Y[44 + 1], (double) +0.382683432365090, (double) +0.923879532511287); BUTTERFLY_XY (Y[14], /* W7 */ Y[14 + 1], Y[46], Y[46 + 1], Y[14], Y[14 + 1], Y[46], Y[46 + 1], (double) +0.195090322016128, (double) +0.980785280403230); BUTTERFLY_01 (Y[16], /* W8 */ Y[16 + 1], Y[48], Y[48 + 1], Y[16], Y[16 + 1], Y[48], Y[48 + 1], (double) +0.000000000000000, (double) +1.000000000000000); BUTTERFLY_XY (Y[18], /* W9 */ Y[18 + 1], Y[50], Y[50 + 1], Y[18], Y[18 + 1], Y[50], Y[50 + 1], (double) -0.195090322016128, (double) +0.980785280403230); BUTTERFLY_XY (Y[20], /* W10 */ Y[20 + 1], Y[52], Y[52 + 1], Y[20], Y[20 + 1], Y[52], Y[52 + 1], (double) -0.382683432365090, (double) +0.923879532511287); BUTTERFLY_XY (Y[22], /* W11 */ Y[22 + 1], Y[54], Y[54 + 1], Y[22], Y[22 + 1], Y[54], Y[54 + 1], (double) -0.555570233019602, (double) +0.831469612302545); BUTTERFLY_yY (Y[24], /* W12 */ Y[24 + 1], Y[56], Y[56 + 1], Y[24], Y[24 + 1], Y[56], Y[56 + 1], (double) -0.707106781186547, (double) +0.707106781186548); BUTTERFLY_XY (Y[26], /* W13 */ Y[26 + 1], Y[58], Y[58 + 1], Y[26], Y[26 + 1], Y[58], Y[58 + 1], (double) -0.831469612302545, (double) +0.555570233019602); BUTTERFLY_XY (Y[28], /* W14 */ Y[28 + 1], Y[60], Y[60 + 1], Y[28], Y[28 + 1], Y[60], Y[60 + 1], (double) -0.923879532511287, (double) +0.382683432365090); BUTTERFLY_XY (Y[30], /* W15 */ Y[30 + 1], Y[62], Y[62 + 1], Y[30], Y[30 + 1], Y[62], Y[62 + 1], (double) -0.980785280403230, (double) +0.195090322016129); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 32 F S S S X) **/ static void gsl_power2_fft32analysis (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* perform 16 times fft2 */ BUTTERFLY_10 (X[0], X[0 + 1], X[32], X[32 + 1], Y[0], Y[0 + 1], Y[2], Y[2 + 1], __1, __0); BUTTERFLY_10 (X[16], X[16 + 1], X[48], X[48 + 1], Y[4], Y[4 + 1], Y[6], Y[6 + 1], __1, __0); BUTTERFLY_10 (X[8], X[8 + 1], X[40], X[40 + 1], Y[8], Y[8 + 1], Y[10], Y[10 + 1], __1, __0); BUTTERFLY_10 (X[24], X[24 + 1], X[56], X[56 + 1], Y[12], Y[12 + 1], Y[14], Y[14 + 1], __1, __0); BUTTERFLY_10 (X[4], X[4 + 1], X[36], X[36 + 1], Y[16], Y[16 + 1], Y[18], Y[18 + 1], __1, __0); BUTTERFLY_10 (X[20], X[20 + 1], X[52], X[52 + 1], Y[20], Y[20 + 1], Y[22], Y[22 + 1], __1, __0); BUTTERFLY_10 (X[12], X[12 + 1], X[44], X[44 + 1], Y[24], Y[24 + 1], Y[26], Y[26 + 1], __1, __0); BUTTERFLY_10 (X[28], X[28 + 1], X[60], X[60 + 1], Y[28], Y[28 + 1], Y[30], Y[30 + 1], __1, __0); BUTTERFLY_10 (X[2], X[2 + 1], X[34], X[34 + 1], Y[32], Y[32 + 1], Y[34], Y[34 + 1], __1, __0); BUTTERFLY_10 (X[18], X[18 + 1], X[50], X[50 + 1], Y[36], Y[36 + 1], Y[38], Y[38 + 1], __1, __0); BUTTERFLY_10 (X[10], X[10 + 1], X[42], X[42 + 1], Y[40], Y[40 + 1], Y[42], Y[42 + 1], __1, __0); BUTTERFLY_10 (X[26], X[26 + 1], X[58], X[58 + 1], Y[44], Y[44 + 1], Y[46], Y[46 + 1], __1, __0); BUTTERFLY_10 (X[6], X[6 + 1], X[38], X[38 + 1], Y[48], Y[48 + 1], Y[50], Y[50 + 1], __1, __0); BUTTERFLY_10 (X[22], X[22 + 1], X[54], X[54 + 1], Y[52], Y[52 + 1], Y[54], Y[54 + 1], __1, __0); BUTTERFLY_10 (X[14], X[14 + 1], X[46], X[46 + 1], Y[56], Y[56 + 1], Y[58], Y[58 + 1], __1, __0); BUTTERFLY_10 (X[30], X[30 + 1], X[62], X[62 + 1], Y[60], Y[60 + 1], Y[62], Y[62 + 1], __1, __0); /* skipping 8 times fft4 */ /* skipping 4 times fft8 */ /* skipping 2 times fft16 */ /* perform 1 times fft32 */ gsl_power2_fft32analysis_skip2 (X, Y); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 64 S R R R R F) **/ static void gsl_power2_fft64analysis_skip2 (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* skipping 32 times fft2 */ /* perform 16 times fft4 */ for (block = 0; block < 128; block += 8) { BUTTERFLY_10 (Y[block + 0], /* W0 */ Y[block + 0 + 1], Y[block + 4], Y[block + 4 + 1], Y[block + 0], Y[block + 0 + 1], Y[block + 4], Y[block + 4 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_01 (Y[block + 2], /* W16 */ Y[block + 2 + 1], Y[block + 6], Y[block + 6 + 1], Y[block + 2], Y[block + 2 + 1], Y[block + 6], Y[block + 6 + 1], (double) +0.000000000000000, (double) +1.000000000000000); } /* perform 8 times fft8 */ for (block = 0; block < 128; block += 16) { BUTTERFLY_10 (Y[block + 0], /* W0 */ Y[block + 0 + 1], Y[block + 8], Y[block + 8 + 1], Y[block + 0], Y[block + 0 + 1], Y[block + 8], Y[block + 8 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_XX (Y[block + 2], /* W8 */ Y[block + 2 + 1], Y[block + 10], Y[block + 10 + 1], Y[block + 2], Y[block + 2 + 1], Y[block + 10], Y[block + 10 + 1], (double) +0.707106781186548, (double) +0.707106781186547); BUTTERFLY_01 (Y[block + 4], /* W16 */ Y[block + 4 + 1], Y[block + 12], Y[block + 12 + 1], Y[block + 4], Y[block + 4 + 1], Y[block + 12], Y[block + 12 + 1], (double) +0.000000000000000, (double) +1.000000000000000); BUTTERFLY_yY (Y[block + 6], /* W24 */ Y[block + 6 + 1], Y[block + 14], Y[block + 14 + 1], Y[block + 6], Y[block + 6 + 1], Y[block + 14], Y[block + 14 + 1], (double) -0.707106781186547, (double) +0.707106781186548); } /* perform 4 times fft16 */ for (block = 0; block < 128; block += 32) { BUTTERFLY_10 (Y[block + 0], /* W0 */ Y[block + 0 + 1], Y[block + 16], Y[block + 16 + 1], Y[block + 0], Y[block + 0 + 1], Y[block + 16], Y[block + 16 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_XY (Y[block + 2], /* W4 */ Y[block + 2 + 1], Y[block + 18], Y[block + 18 + 1], Y[block + 2], Y[block + 2 + 1], Y[block + 18], Y[block + 18 + 1], (double) +0.923879532511287, (double) +0.382683432365090); BUTTERFLY_XX (Y[block + 4], /* W8 */ Y[block + 4 + 1], Y[block + 20], Y[block + 20 + 1], Y[block + 4], Y[block + 4 + 1], Y[block + 20], Y[block + 20 + 1], (double) +0.707106781186548, (double) +0.707106781186547); BUTTERFLY_XY (Y[block + 6], /* W12 */ Y[block + 6 + 1], Y[block + 22], Y[block + 22 + 1], Y[block + 6], Y[block + 6 + 1], Y[block + 22], Y[block + 22 + 1], (double) +0.382683432365090, (double) +0.923879532511287); BUTTERFLY_01 (Y[block + 8], /* W16 */ Y[block + 8 + 1], Y[block + 24], Y[block + 24 + 1], Y[block + 8], Y[block + 8 + 1], Y[block + 24], Y[block + 24 + 1], (double) +0.000000000000000, (double) +1.000000000000000); BUTTERFLY_XY (Y[block + 10], /* W20 */ Y[block + 10 + 1], Y[block + 26], Y[block + 26 + 1], Y[block + 10], Y[block + 10 + 1], Y[block + 26], Y[block + 26 + 1], (double) -0.382683432365090, (double) +0.923879532511287); BUTTERFLY_yY (Y[block + 12], /* W24 */ Y[block + 12 + 1], Y[block + 28], Y[block + 28 + 1], Y[block + 12], Y[block + 12 + 1], Y[block + 28], Y[block + 28 + 1], (double) -0.707106781186547, (double) +0.707106781186548); BUTTERFLY_XY (Y[block + 14], /* W28 */ Y[block + 14 + 1], Y[block + 30], Y[block + 30 + 1], Y[block + 14], Y[block + 14 + 1], Y[block + 30], Y[block + 30 + 1], (double) -0.923879532511287, (double) +0.382683432365090); } /* perform 2 times fft32 */ for (block = 0; block < 128; block += 64) { BUTTERFLY_10 (Y[block + 0], /* W0 */ Y[block + 0 + 1], Y[block + 32], Y[block + 32 + 1], Y[block + 0], Y[block + 0 + 1], Y[block + 32], Y[block + 32 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_XY (Y[block + 2], /* W2 */ Y[block + 2 + 1], Y[block + 34], Y[block + 34 + 1], Y[block + 2], Y[block + 2 + 1], Y[block + 34], Y[block + 34 + 1], (double) +0.980785280403230, (double) +0.195090322016128); BUTTERFLY_XY (Y[block + 4], /* W4 */ Y[block + 4 + 1], Y[block + 36], Y[block + 36 + 1], Y[block + 4], Y[block + 4 + 1], Y[block + 36], Y[block + 36 + 1], (double) +0.923879532511287, (double) +0.382683432365090); BUTTERFLY_XY (Y[block + 6], /* W6 */ Y[block + 6 + 1], Y[block + 38], Y[block + 38 + 1], Y[block + 6], Y[block + 6 + 1], Y[block + 38], Y[block + 38 + 1], (double) +0.831469612302545, (double) +0.555570233019602); BUTTERFLY_XX (Y[block + 8], /* W8 */ Y[block + 8 + 1], Y[block + 40], Y[block + 40 + 1], Y[block + 8], Y[block + 8 + 1], Y[block + 40], Y[block + 40 + 1], (double) +0.707106781186548, (double) +0.707106781186547); BUTTERFLY_XY (Y[block + 10], /* W10 */ Y[block + 10 + 1], Y[block + 42], Y[block + 42 + 1], Y[block + 10], Y[block + 10 + 1], Y[block + 42], Y[block + 42 + 1], (double) +0.555570233019602, (double) +0.831469612302545); BUTTERFLY_XY (Y[block + 12], /* W12 */ Y[block + 12 + 1], Y[block + 44], Y[block + 44 + 1], Y[block + 12], Y[block + 12 + 1], Y[block + 44], Y[block + 44 + 1], (double) +0.382683432365090, (double) +0.923879532511287); BUTTERFLY_XY (Y[block + 14], /* W14 */ Y[block + 14 + 1], Y[block + 46], Y[block + 46 + 1], Y[block + 14], Y[block + 14 + 1], Y[block + 46], Y[block + 46 + 1], (double) +0.195090322016128, (double) +0.980785280403230); BUTTERFLY_01 (Y[block + 16], /* W16 */ Y[block + 16 + 1], Y[block + 48], Y[block + 48 + 1], Y[block + 16], Y[block + 16 + 1], Y[block + 48], Y[block + 48 + 1], (double) +0.000000000000000, (double) +1.000000000000000); BUTTERFLY_XY (Y[block + 18], /* W18 */ Y[block + 18 + 1], Y[block + 50], Y[block + 50 + 1], Y[block + 18], Y[block + 18 + 1], Y[block + 50], Y[block + 50 + 1], (double) -0.195090322016128, (double) +0.980785280403230); BUTTERFLY_XY (Y[block + 20], /* W20 */ Y[block + 20 + 1], Y[block + 52], Y[block + 52 + 1], Y[block + 20], Y[block + 20 + 1], Y[block + 52], Y[block + 52 + 1], (double) -0.382683432365090, (double) +0.923879532511287); BUTTERFLY_XY (Y[block + 22], /* W22 */ Y[block + 22 + 1], Y[block + 54], Y[block + 54 + 1], Y[block + 22], Y[block + 22 + 1], Y[block + 54], Y[block + 54 + 1], (double) -0.555570233019602, (double) +0.831469612302545); BUTTERFLY_yY (Y[block + 24], /* W24 */ Y[block + 24 + 1], Y[block + 56], Y[block + 56 + 1], Y[block + 24], Y[block + 24 + 1], Y[block + 56], Y[block + 56 + 1], (double) -0.707106781186547, (double) +0.707106781186548); BUTTERFLY_XY (Y[block + 26], /* W26 */ Y[block + 26 + 1], Y[block + 58], Y[block + 58 + 1], Y[block + 26], Y[block + 26 + 1], Y[block + 58], Y[block + 58 + 1], (double) -0.831469612302545, (double) +0.555570233019602); BUTTERFLY_XY (Y[block + 28], /* W28 */ Y[block + 28 + 1], Y[block + 60], Y[block + 60 + 1], Y[block + 28], Y[block + 28 + 1], Y[block + 60], Y[block + 60 + 1], (double) -0.923879532511287, (double) +0.382683432365090); BUTTERFLY_XY (Y[block + 30], /* W30 */ Y[block + 30 + 1], Y[block + 62], Y[block + 62 + 1], Y[block + 30], Y[block + 30 + 1], Y[block + 62], Y[block + 62 + 1], (double) -0.980785280403230, (double) +0.195090322016129); } /* perform 1 times fft64 */ BUTTERFLY_10 (Y[0], /* W0 */ Y[0 + 1], Y[64], Y[64 + 1], Y[0], Y[0 + 1], Y[64], Y[64 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_XY (Y[2], /* W1 */ Y[2 + 1], Y[66], Y[66 + 1], Y[2], Y[2 + 1], Y[66], Y[66 + 1], (double) +0.995184726672197, (double) +0.098017140329561); BUTTERFLY_XY (Y[4], /* W2 */ Y[4 + 1], Y[68], Y[68 + 1], Y[4], Y[4 + 1], Y[68], Y[68 + 1], (double) +0.980785280403230, (double) +0.195090322016128); BUTTERFLY_XY (Y[6], /* W3 */ Y[6 + 1], Y[70], Y[70 + 1], Y[6], Y[6 + 1], Y[70], Y[70 + 1], (double) +0.956940335732209, (double) +0.290284677254462); BUTTERFLY_XY (Y[8], /* W4 */ Y[8 + 1], Y[72], Y[72 + 1], Y[8], Y[8 + 1], Y[72], Y[72 + 1], (double) +0.923879532511287, (double) +0.382683432365090); BUTTERFLY_XY (Y[10], /* W5 */ Y[10 + 1], Y[74], Y[74 + 1], Y[10], Y[10 + 1], Y[74], Y[74 + 1], (double) +0.881921264348355, (double) +0.471396736825998); BUTTERFLY_XY (Y[12], /* W6 */ Y[12 + 1], Y[76], Y[76 + 1], Y[12], Y[12 + 1], Y[76], Y[76 + 1], (double) +0.831469612302545, (double) +0.555570233019602); BUTTERFLY_XY (Y[14], /* W7 */ Y[14 + 1], Y[78], Y[78 + 1], Y[14], Y[14 + 1], Y[78], Y[78 + 1], (double) +0.773010453362737, (double) +0.634393284163645); BUTTERFLY_XX (Y[16], /* W8 */ Y[16 + 1], Y[80], Y[80 + 1], Y[16], Y[16 + 1], Y[80], Y[80 + 1], (double) +0.707106781186548, (double) +0.707106781186547); BUTTERFLY_XY (Y[18], /* W9 */ Y[18 + 1], Y[82], Y[82 + 1], Y[18], Y[18 + 1], Y[82], Y[82 + 1], (double) +0.634393284163645, (double) +0.773010453362737); BUTTERFLY_XY (Y[20], /* W10 */ Y[20 + 1], Y[84], Y[84 + 1], Y[20], Y[20 + 1], Y[84], Y[84 + 1], (double) +0.555570233019602, (double) +0.831469612302545); BUTTERFLY_XY (Y[22], /* W11 */ Y[22 + 1], Y[86], Y[86 + 1], Y[22], Y[22 + 1], Y[86], Y[86 + 1], (double) +0.471396736825998, (double) +0.881921264348355); BUTTERFLY_XY (Y[24], /* W12 */ Y[24 + 1], Y[88], Y[88 + 1], Y[24], Y[24 + 1], Y[88], Y[88 + 1], (double) +0.382683432365090, (double) +0.923879532511287); BUTTERFLY_XY (Y[26], /* W13 */ Y[26 + 1], Y[90], Y[90 + 1], Y[26], Y[26 + 1], Y[90], Y[90 + 1], (double) +0.290284677254462, (double) +0.956940335732209); BUTTERFLY_XY (Y[28], /* W14 */ Y[28 + 1], Y[92], Y[92 + 1], Y[28], Y[28 + 1], Y[92], Y[92 + 1], (double) +0.195090322016128, (double) +0.980785280403230); BUTTERFLY_XY (Y[30], /* W15 */ Y[30 + 1], Y[94], Y[94 + 1], Y[30], Y[30 + 1], Y[94], Y[94 + 1], (double) +0.098017140329561, (double) +0.995184726672197); BUTTERFLY_01 (Y[32], /* W16 */ Y[32 + 1], Y[96], Y[96 + 1], Y[32], Y[32 + 1], Y[96], Y[96 + 1], (double) +0.000000000000000, (double) +1.000000000000000); BUTTERFLY_XY (Y[34], /* W17 */ Y[34 + 1], Y[98], Y[98 + 1], Y[34], Y[34 + 1], Y[98], Y[98 + 1], (double) -0.098017140329561, (double) +0.995184726672197); BUTTERFLY_XY (Y[36], /* W18 */ Y[36 + 1], Y[100], Y[100 + 1], Y[36], Y[36 + 1], Y[100], Y[100 + 1], (double) -0.195090322016128, (double) +0.980785280403230); BUTTERFLY_XY (Y[38], /* W19 */ Y[38 + 1], Y[102], Y[102 + 1], Y[38], Y[38 + 1], Y[102], Y[102 + 1], (double) -0.290284677254462, (double) +0.956940335732209); BUTTERFLY_XY (Y[40], /* W20 */ Y[40 + 1], Y[104], Y[104 + 1], Y[40], Y[40 + 1], Y[104], Y[104 + 1], (double) -0.382683432365090, (double) +0.923879532511287); BUTTERFLY_XY (Y[42], /* W21 */ Y[42 + 1], Y[106], Y[106 + 1], Y[42], Y[42 + 1], Y[106], Y[106 + 1], (double) -0.471396736825998, (double) +0.881921264348355); BUTTERFLY_XY (Y[44], /* W22 */ Y[44 + 1], Y[108], Y[108 + 1], Y[44], Y[44 + 1], Y[108], Y[108 + 1], (double) -0.555570233019602, (double) +0.831469612302545); BUTTERFLY_XY (Y[46], /* W23 */ Y[46 + 1], Y[110], Y[110 + 1], Y[46], Y[46 + 1], Y[110], Y[110 + 1], (double) -0.634393284163645, (double) +0.773010453362737); BUTTERFLY_yY (Y[48], /* W24 */ Y[48 + 1], Y[112], Y[112 + 1], Y[48], Y[48 + 1], Y[112], Y[112 + 1], (double) -0.707106781186547, (double) +0.707106781186548); BUTTERFLY_XY (Y[50], /* W25 */ Y[50 + 1], Y[114], Y[114 + 1], Y[50], Y[50 + 1], Y[114], Y[114 + 1], (double) -0.773010453362737, (double) +0.634393284163645); BUTTERFLY_XY (Y[52], /* W26 */ Y[52 + 1], Y[116], Y[116 + 1], Y[52], Y[52 + 1], Y[116], Y[116 + 1], (double) -0.831469612302545, (double) +0.555570233019602); BUTTERFLY_XY (Y[54], /* W27 */ Y[54 + 1], Y[118], Y[118 + 1], Y[54], Y[54 + 1], Y[118], Y[118 + 1], (double) -0.881921264348355, (double) +0.471396736825998); BUTTERFLY_XY (Y[56], /* W28 */ Y[56 + 1], Y[120], Y[120 + 1], Y[56], Y[56 + 1], Y[120], Y[120 + 1], (double) -0.923879532511287, (double) +0.382683432365090); BUTTERFLY_XY (Y[58], /* W29 */ Y[58 + 1], Y[122], Y[122 + 1], Y[58], Y[58 + 1], Y[122], Y[122 + 1], (double) -0.956940335732209, (double) +0.290284677254462); BUTTERFLY_XY (Y[60], /* W30 */ Y[60 + 1], Y[124], Y[124 + 1], Y[60], Y[60 + 1], Y[124], Y[124 + 1], (double) -0.980785280403230, (double) +0.195090322016129); BUTTERFLY_XY (Y[62], /* W31 */ Y[62 + 1], Y[126], Y[126 + 1], Y[62], Y[62 + 1], Y[126], Y[126 + 1], (double) -0.995184726672197, (double) +0.098017140329561); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 64 F S S S S X) **/ static void gsl_power2_fft64analysis (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* perform 32 times fft2 */ BUTTERFLY_10 (X[0], X[0 + 1], X[64], X[64 + 1], Y[0], Y[0 + 1], Y[2], Y[2 + 1], __1, __0); BUTTERFLY_10 (X[32], X[32 + 1], X[96], X[96 + 1], Y[4], Y[4 + 1], Y[6], Y[6 + 1], __1, __0); BUTTERFLY_10 (X[16], X[16 + 1], X[80], X[80 + 1], Y[8], Y[8 + 1], Y[10], Y[10 + 1], __1, __0); BUTTERFLY_10 (X[48], X[48 + 1], X[112], X[112 + 1], Y[12], Y[12 + 1], Y[14], Y[14 + 1], __1, __0); BUTTERFLY_10 (X[8], X[8 + 1], X[72], X[72 + 1], Y[16], Y[16 + 1], Y[18], Y[18 + 1], __1, __0); BUTTERFLY_10 (X[40], X[40 + 1], X[104], X[104 + 1], Y[20], Y[20 + 1], Y[22], Y[22 + 1], __1, __0); BUTTERFLY_10 (X[24], X[24 + 1], X[88], X[88 + 1], Y[24], Y[24 + 1], Y[26], Y[26 + 1], __1, __0); BUTTERFLY_10 (X[56], X[56 + 1], X[120], X[120 + 1], Y[28], Y[28 + 1], Y[30], Y[30 + 1], __1, __0); BUTTERFLY_10 (X[4], X[4 + 1], X[68], X[68 + 1], Y[32], Y[32 + 1], Y[34], Y[34 + 1], __1, __0); BUTTERFLY_10 (X[36], X[36 + 1], X[100], X[100 + 1], Y[36], Y[36 + 1], Y[38], Y[38 + 1], __1, __0); BUTTERFLY_10 (X[20], X[20 + 1], X[84], X[84 + 1], Y[40], Y[40 + 1], Y[42], Y[42 + 1], __1, __0); BUTTERFLY_10 (X[52], X[52 + 1], X[116], X[116 + 1], Y[44], Y[44 + 1], Y[46], Y[46 + 1], __1, __0); BUTTERFLY_10 (X[12], X[12 + 1], X[76], X[76 + 1], Y[48], Y[48 + 1], Y[50], Y[50 + 1], __1, __0); BUTTERFLY_10 (X[44], X[44 + 1], X[108], X[108 + 1], Y[52], Y[52 + 1], Y[54], Y[54 + 1], __1, __0); BUTTERFLY_10 (X[28], X[28 + 1], X[92], X[92 + 1], Y[56], Y[56 + 1], Y[58], Y[58 + 1], __1, __0); BUTTERFLY_10 (X[60], X[60 + 1], X[124], X[124 + 1], Y[60], Y[60 + 1], Y[62], Y[62 + 1], __1, __0); BUTTERFLY_10 (X[2], X[2 + 1], X[66], X[66 + 1], Y[64], Y[64 + 1], Y[66], Y[66 + 1], __1, __0); BUTTERFLY_10 (X[34], X[34 + 1], X[98], X[98 + 1], Y[68], Y[68 + 1], Y[70], Y[70 + 1], __1, __0); BUTTERFLY_10 (X[18], X[18 + 1], X[82], X[82 + 1], Y[72], Y[72 + 1], Y[74], Y[74 + 1], __1, __0); BUTTERFLY_10 (X[50], X[50 + 1], X[114], X[114 + 1], Y[76], Y[76 + 1], Y[78], Y[78 + 1], __1, __0); BUTTERFLY_10 (X[10], X[10 + 1], X[74], X[74 + 1], Y[80], Y[80 + 1], Y[82], Y[82 + 1], __1, __0); BUTTERFLY_10 (X[42], X[42 + 1], X[106], X[106 + 1], Y[84], Y[84 + 1], Y[86], Y[86 + 1], __1, __0); BUTTERFLY_10 (X[26], X[26 + 1], X[90], X[90 + 1], Y[88], Y[88 + 1], Y[90], Y[90 + 1], __1, __0); BUTTERFLY_10 (X[58], X[58 + 1], X[122], X[122 + 1], Y[92], Y[92 + 1], Y[94], Y[94 + 1], __1, __0); BUTTERFLY_10 (X[6], X[6 + 1], X[70], X[70 + 1], Y[96], Y[96 + 1], Y[98], Y[98 + 1], __1, __0); BUTTERFLY_10 (X[38], X[38 + 1], X[102], X[102 + 1], Y[100], Y[100 + 1], Y[102], Y[102 + 1], __1, __0); BUTTERFLY_10 (X[22], X[22 + 1], X[86], X[86 + 1], Y[104], Y[104 + 1], Y[106], Y[106 + 1], __1, __0); BUTTERFLY_10 (X[54], X[54 + 1], X[118], X[118 + 1], Y[108], Y[108 + 1], Y[110], Y[110 + 1], __1, __0); BUTTERFLY_10 (X[14], X[14 + 1], X[78], X[78 + 1], Y[112], Y[112 + 1], Y[114], Y[114 + 1], __1, __0); BUTTERFLY_10 (X[46], X[46 + 1], X[110], X[110 + 1], Y[116], Y[116 + 1], Y[118], Y[118 + 1], __1, __0); BUTTERFLY_10 (X[30], X[30 + 1], X[94], X[94 + 1], Y[120], Y[120 + 1], Y[122], Y[122 + 1], __1, __0); BUTTERFLY_10 (X[62], X[62 + 1], X[126], X[126 + 1], Y[124], Y[124 + 1], Y[126], Y[126 + 1], __1, __0); /* skipping 16 times fft4 */ /* skipping 8 times fft8 */ /* skipping 4 times fft16 */ /* skipping 2 times fft32 */ /* perform 1 times fft64 */ gsl_power2_fft64analysis_skip2 (X, Y); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 128 S R R R R R F) **/ static void gsl_power2_fft128analysis_skip2 (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* skipping 64 times fft2 */ /* perform 32 times fft4 */ for (block = 0; block < 256; block += 8) { BUTTERFLY_10 (Y[block + 0], /* W0 */ Y[block + 0 + 1], Y[block + 4], Y[block + 4 + 1], Y[block + 0], Y[block + 0 + 1], Y[block + 4], Y[block + 4 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_01 (Y[block + 2], /* W32 */ Y[block + 2 + 1], Y[block + 6], Y[block + 6 + 1], Y[block + 2], Y[block + 2 + 1], Y[block + 6], Y[block + 6 + 1], (double) +0.000000000000000, (double) +1.000000000000000); } /* perform 16 times fft8 */ for (block = 0; block < 256; block += 16) { BUTTERFLY_10 (Y[block + 0], /* W0 */ Y[block + 0 + 1], Y[block + 8], Y[block + 8 + 1], Y[block + 0], Y[block + 0 + 1], Y[block + 8], Y[block + 8 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_XX (Y[block + 2], /* W16 */ Y[block + 2 + 1], Y[block + 10], Y[block + 10 + 1], Y[block + 2], Y[block + 2 + 1], Y[block + 10], Y[block + 10 + 1], (double) +0.707106781186548, (double) +0.707106781186547); BUTTERFLY_01 (Y[block + 4], /* W32 */ Y[block + 4 + 1], Y[block + 12], Y[block + 12 + 1], Y[block + 4], Y[block + 4 + 1], Y[block + 12], Y[block + 12 + 1], (double) +0.000000000000000, (double) +1.000000000000000); BUTTERFLY_yY (Y[block + 6], /* W48 */ Y[block + 6 + 1], Y[block + 14], Y[block + 14 + 1], Y[block + 6], Y[block + 6 + 1], Y[block + 14], Y[block + 14 + 1], (double) -0.707106781186547, (double) +0.707106781186548); } /* perform 8 times fft16 */ for (block = 0; block < 256; block += 32) { BUTTERFLY_10 (Y[block + 0], /* W0 */ Y[block + 0 + 1], Y[block + 16], Y[block + 16 + 1], Y[block + 0], Y[block + 0 + 1], Y[block + 16], Y[block + 16 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_XY (Y[block + 2], /* W8 */ Y[block + 2 + 1], Y[block + 18], Y[block + 18 + 1], Y[block + 2], Y[block + 2 + 1], Y[block + 18], Y[block + 18 + 1], (double) +0.923879532511287, (double) +0.382683432365090); BUTTERFLY_XX (Y[block + 4], /* W16 */ Y[block + 4 + 1], Y[block + 20], Y[block + 20 + 1], Y[block + 4], Y[block + 4 + 1], Y[block + 20], Y[block + 20 + 1], (double) +0.707106781186548, (double) +0.707106781186547); BUTTERFLY_XY (Y[block + 6], /* W24 */ Y[block + 6 + 1], Y[block + 22], Y[block + 22 + 1], Y[block + 6], Y[block + 6 + 1], Y[block + 22], Y[block + 22 + 1], (double) +0.382683432365090, (double) +0.923879532511287); BUTTERFLY_01 (Y[block + 8], /* W32 */ Y[block + 8 + 1], Y[block + 24], Y[block + 24 + 1], Y[block + 8], Y[block + 8 + 1], Y[block + 24], Y[block + 24 + 1], (double) +0.000000000000000, (double) +1.000000000000000); BUTTERFLY_XY (Y[block + 10], /* W40 */ Y[block + 10 + 1], Y[block + 26], Y[block + 26 + 1], Y[block + 10], Y[block + 10 + 1], Y[block + 26], Y[block + 26 + 1], (double) -0.382683432365090, (double) +0.923879532511287); BUTTERFLY_yY (Y[block + 12], /* W48 */ Y[block + 12 + 1], Y[block + 28], Y[block + 28 + 1], Y[block + 12], Y[block + 12 + 1], Y[block + 28], Y[block + 28 + 1], (double) -0.707106781186547, (double) +0.707106781186548); BUTTERFLY_XY (Y[block + 14], /* W56 */ Y[block + 14 + 1], Y[block + 30], Y[block + 30 + 1], Y[block + 14], Y[block + 14 + 1], Y[block + 30], Y[block + 30 + 1], (double) -0.923879532511287, (double) +0.382683432365090); } /* perform 4 times fft32 */ for (block = 0; block < 256; block += 64) { BUTTERFLY_10 (Y[block + 0], /* W0 */ Y[block + 0 + 1], Y[block + 32], Y[block + 32 + 1], Y[block + 0], Y[block + 0 + 1], Y[block + 32], Y[block + 32 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_XY (Y[block + 2], /* W4 */ Y[block + 2 + 1], Y[block + 34], Y[block + 34 + 1], Y[block + 2], Y[block + 2 + 1], Y[block + 34], Y[block + 34 + 1], (double) +0.980785280403230, (double) +0.195090322016128); BUTTERFLY_XY (Y[block + 4], /* W8 */ Y[block + 4 + 1], Y[block + 36], Y[block + 36 + 1], Y[block + 4], Y[block + 4 + 1], Y[block + 36], Y[block + 36 + 1], (double) +0.923879532511287, (double) +0.382683432365090); BUTTERFLY_XY (Y[block + 6], /* W12 */ Y[block + 6 + 1], Y[block + 38], Y[block + 38 + 1], Y[block + 6], Y[block + 6 + 1], Y[block + 38], Y[block + 38 + 1], (double) +0.831469612302545, (double) +0.555570233019602); BUTTERFLY_XX (Y[block + 8], /* W16 */ Y[block + 8 + 1], Y[block + 40], Y[block + 40 + 1], Y[block + 8], Y[block + 8 + 1], Y[block + 40], Y[block + 40 + 1], (double) +0.707106781186548, (double) +0.707106781186547); BUTTERFLY_XY (Y[block + 10], /* W20 */ Y[block + 10 + 1], Y[block + 42], Y[block + 42 + 1], Y[block + 10], Y[block + 10 + 1], Y[block + 42], Y[block + 42 + 1], (double) +0.555570233019602, (double) +0.831469612302545); BUTTERFLY_XY (Y[block + 12], /* W24 */ Y[block + 12 + 1], Y[block + 44], Y[block + 44 + 1], Y[block + 12], Y[block + 12 + 1], Y[block + 44], Y[block + 44 + 1], (double) +0.382683432365090, (double) +0.923879532511287); BUTTERFLY_XY (Y[block + 14], /* W28 */ Y[block + 14 + 1], Y[block + 46], Y[block + 46 + 1], Y[block + 14], Y[block + 14 + 1], Y[block + 46], Y[block + 46 + 1], (double) +0.195090322016128, (double) +0.980785280403230); BUTTERFLY_01 (Y[block + 16], /* W32 */ Y[block + 16 + 1], Y[block + 48], Y[block + 48 + 1], Y[block + 16], Y[block + 16 + 1], Y[block + 48], Y[block + 48 + 1], (double) +0.000000000000000, (double) +1.000000000000000); BUTTERFLY_XY (Y[block + 18], /* W36 */ Y[block + 18 + 1], Y[block + 50], Y[block + 50 + 1], Y[block + 18], Y[block + 18 + 1], Y[block + 50], Y[block + 50 + 1], (double) -0.195090322016128, (double) +0.980785280403230); BUTTERFLY_XY (Y[block + 20], /* W40 */ Y[block + 20 + 1], Y[block + 52], Y[block + 52 + 1], Y[block + 20], Y[block + 20 + 1], Y[block + 52], Y[block + 52 + 1], (double) -0.382683432365090, (double) +0.923879532511287); BUTTERFLY_XY (Y[block + 22], /* W44 */ Y[block + 22 + 1], Y[block + 54], Y[block + 54 + 1], Y[block + 22], Y[block + 22 + 1], Y[block + 54], Y[block + 54 + 1], (double) -0.555570233019602, (double) +0.831469612302545); BUTTERFLY_yY (Y[block + 24], /* W48 */ Y[block + 24 + 1], Y[block + 56], Y[block + 56 + 1], Y[block + 24], Y[block + 24 + 1], Y[block + 56], Y[block + 56 + 1], (double) -0.707106781186547, (double) +0.707106781186548); BUTTERFLY_XY (Y[block + 26], /* W52 */ Y[block + 26 + 1], Y[block + 58], Y[block + 58 + 1], Y[block + 26], Y[block + 26 + 1], Y[block + 58], Y[block + 58 + 1], (double) -0.831469612302545, (double) +0.555570233019602); BUTTERFLY_XY (Y[block + 28], /* W56 */ Y[block + 28 + 1], Y[block + 60], Y[block + 60 + 1], Y[block + 28], Y[block + 28 + 1], Y[block + 60], Y[block + 60 + 1], (double) -0.923879532511287, (double) +0.382683432365090); BUTTERFLY_XY (Y[block + 30], /* W60 */ Y[block + 30 + 1], Y[block + 62], Y[block + 62 + 1], Y[block + 30], Y[block + 30 + 1], Y[block + 62], Y[block + 62 + 1], (double) -0.980785280403230, (double) +0.195090322016129); } /* perform 2 times fft64 */ for (block = 0; block < 256; block += 128) { BUTTERFLY_10 (Y[block + 0], /* W0 */ Y[block + 0 + 1], Y[block + 64], Y[block + 64 + 1], Y[block + 0], Y[block + 0 + 1], Y[block + 64], Y[block + 64 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_XY (Y[block + 2], /* W2 */ Y[block + 2 + 1], Y[block + 66], Y[block + 66 + 1], Y[block + 2], Y[block + 2 + 1], Y[block + 66], Y[block + 66 + 1], (double) +0.995184726672197, (double) +0.098017140329561); BUTTERFLY_XY (Y[block + 4], /* W4 */ Y[block + 4 + 1], Y[block + 68], Y[block + 68 + 1], Y[block + 4], Y[block + 4 + 1], Y[block + 68], Y[block + 68 + 1], (double) +0.980785280403230, (double) +0.195090322016128); BUTTERFLY_XY (Y[block + 6], /* W6 */ Y[block + 6 + 1], Y[block + 70], Y[block + 70 + 1], Y[block + 6], Y[block + 6 + 1], Y[block + 70], Y[block + 70 + 1], (double) +0.956940335732209, (double) +0.290284677254462); BUTTERFLY_XY (Y[block + 8], /* W8 */ Y[block + 8 + 1], Y[block + 72], Y[block + 72 + 1], Y[block + 8], Y[block + 8 + 1], Y[block + 72], Y[block + 72 + 1], (double) +0.923879532511287, (double) +0.382683432365090); BUTTERFLY_XY (Y[block + 10], /* W10 */ Y[block + 10 + 1], Y[block + 74], Y[block + 74 + 1], Y[block + 10], Y[block + 10 + 1], Y[block + 74], Y[block + 74 + 1], (double) +0.881921264348355, (double) +0.471396736825998); BUTTERFLY_XY (Y[block + 12], /* W12 */ Y[block + 12 + 1], Y[block + 76], Y[block + 76 + 1], Y[block + 12], Y[block + 12 + 1], Y[block + 76], Y[block + 76 + 1], (double) +0.831469612302545, (double) +0.555570233019602); BUTTERFLY_XY (Y[block + 14], /* W14 */ Y[block + 14 + 1], Y[block + 78], Y[block + 78 + 1], Y[block + 14], Y[block + 14 + 1], Y[block + 78], Y[block + 78 + 1], (double) +0.773010453362737, (double) +0.634393284163645); BUTTERFLY_XX (Y[block + 16], /* W16 */ Y[block + 16 + 1], Y[block + 80], Y[block + 80 + 1], Y[block + 16], Y[block + 16 + 1], Y[block + 80], Y[block + 80 + 1], (double) +0.707106781186548, (double) +0.707106781186547); BUTTERFLY_XY (Y[block + 18], /* W18 */ Y[block + 18 + 1], Y[block + 82], Y[block + 82 + 1], Y[block + 18], Y[block + 18 + 1], Y[block + 82], Y[block + 82 + 1], (double) +0.634393284163645, (double) +0.773010453362737); BUTTERFLY_XY (Y[block + 20], /* W20 */ Y[block + 20 + 1], Y[block + 84], Y[block + 84 + 1], Y[block + 20], Y[block + 20 + 1], Y[block + 84], Y[block + 84 + 1], (double) +0.555570233019602, (double) +0.831469612302545); BUTTERFLY_XY (Y[block + 22], /* W22 */ Y[block + 22 + 1], Y[block + 86], Y[block + 86 + 1], Y[block + 22], Y[block + 22 + 1], Y[block + 86], Y[block + 86 + 1], (double) +0.471396736825998, (double) +0.881921264348355); BUTTERFLY_XY (Y[block + 24], /* W24 */ Y[block + 24 + 1], Y[block + 88], Y[block + 88 + 1], Y[block + 24], Y[block + 24 + 1], Y[block + 88], Y[block + 88 + 1], (double) +0.382683432365090, (double) +0.923879532511287); BUTTERFLY_XY (Y[block + 26], /* W26 */ Y[block + 26 + 1], Y[block + 90], Y[block + 90 + 1], Y[block + 26], Y[block + 26 + 1], Y[block + 90], Y[block + 90 + 1], (double) +0.290284677254462, (double) +0.956940335732209); BUTTERFLY_XY (Y[block + 28], /* W28 */ Y[block + 28 + 1], Y[block + 92], Y[block + 92 + 1], Y[block + 28], Y[block + 28 + 1], Y[block + 92], Y[block + 92 + 1], (double) +0.195090322016128, (double) +0.980785280403230); BUTTERFLY_XY (Y[block + 30], /* W30 */ Y[block + 30 + 1], Y[block + 94], Y[block + 94 + 1], Y[block + 30], Y[block + 30 + 1], Y[block + 94], Y[block + 94 + 1], (double) +0.098017140329561, (double) +0.995184726672197); BUTTERFLY_01 (Y[block + 32], /* W32 */ Y[block + 32 + 1], Y[block + 96], Y[block + 96 + 1], Y[block + 32], Y[block + 32 + 1], Y[block + 96], Y[block + 96 + 1], (double) +0.000000000000000, (double) +1.000000000000000); BUTTERFLY_XY (Y[block + 34], /* W34 */ Y[block + 34 + 1], Y[block + 98], Y[block + 98 + 1], Y[block + 34], Y[block + 34 + 1], Y[block + 98], Y[block + 98 + 1], (double) -0.098017140329561, (double) +0.995184726672197); BUTTERFLY_XY (Y[block + 36], /* W36 */ Y[block + 36 + 1], Y[block + 100], Y[block + 100 + 1], Y[block + 36], Y[block + 36 + 1], Y[block + 100], Y[block + 100 + 1], (double) -0.195090322016128, (double) +0.980785280403230); BUTTERFLY_XY (Y[block + 38], /* W38 */ Y[block + 38 + 1], Y[block + 102], Y[block + 102 + 1], Y[block + 38], Y[block + 38 + 1], Y[block + 102], Y[block + 102 + 1], (double) -0.290284677254462, (double) +0.956940335732209); BUTTERFLY_XY (Y[block + 40], /* W40 */ Y[block + 40 + 1], Y[block + 104], Y[block + 104 + 1], Y[block + 40], Y[block + 40 + 1], Y[block + 104], Y[block + 104 + 1], (double) -0.382683432365090, (double) +0.923879532511287); BUTTERFLY_XY (Y[block + 42], /* W42 */ Y[block + 42 + 1], Y[block + 106], Y[block + 106 + 1], Y[block + 42], Y[block + 42 + 1], Y[block + 106], Y[block + 106 + 1], (double) -0.471396736825998, (double) +0.881921264348355); BUTTERFLY_XY (Y[block + 44], /* W44 */ Y[block + 44 + 1], Y[block + 108], Y[block + 108 + 1], Y[block + 44], Y[block + 44 + 1], Y[block + 108], Y[block + 108 + 1], (double) -0.555570233019602, (double) +0.831469612302545); BUTTERFLY_XY (Y[block + 46], /* W46 */ Y[block + 46 + 1], Y[block + 110], Y[block + 110 + 1], Y[block + 46], Y[block + 46 + 1], Y[block + 110], Y[block + 110 + 1], (double) -0.634393284163645, (double) +0.773010453362737); BUTTERFLY_yY (Y[block + 48], /* W48 */ Y[block + 48 + 1], Y[block + 112], Y[block + 112 + 1], Y[block + 48], Y[block + 48 + 1], Y[block + 112], Y[block + 112 + 1], (double) -0.707106781186547, (double) +0.707106781186548); BUTTERFLY_XY (Y[block + 50], /* W50 */ Y[block + 50 + 1], Y[block + 114], Y[block + 114 + 1], Y[block + 50], Y[block + 50 + 1], Y[block + 114], Y[block + 114 + 1], (double) -0.773010453362737, (double) +0.634393284163645); BUTTERFLY_XY (Y[block + 52], /* W52 */ Y[block + 52 + 1], Y[block + 116], Y[block + 116 + 1], Y[block + 52], Y[block + 52 + 1], Y[block + 116], Y[block + 116 + 1], (double) -0.831469612302545, (double) +0.555570233019602); BUTTERFLY_XY (Y[block + 54], /* W54 */ Y[block + 54 + 1], Y[block + 118], Y[block + 118 + 1], Y[block + 54], Y[block + 54 + 1], Y[block + 118], Y[block + 118 + 1], (double) -0.881921264348355, (double) +0.471396736825998); BUTTERFLY_XY (Y[block + 56], /* W56 */ Y[block + 56 + 1], Y[block + 120], Y[block + 120 + 1], Y[block + 56], Y[block + 56 + 1], Y[block + 120], Y[block + 120 + 1], (double) -0.923879532511287, (double) +0.382683432365090); BUTTERFLY_XY (Y[block + 58], /* W58 */ Y[block + 58 + 1], Y[block + 122], Y[block + 122 + 1], Y[block + 58], Y[block + 58 + 1], Y[block + 122], Y[block + 122 + 1], (double) -0.956940335732209, (double) +0.290284677254462); BUTTERFLY_XY (Y[block + 60], /* W60 */ Y[block + 60 + 1], Y[block + 124], Y[block + 124 + 1], Y[block + 60], Y[block + 60 + 1], Y[block + 124], Y[block + 124 + 1], (double) -0.980785280403230, (double) +0.195090322016129); BUTTERFLY_XY (Y[block + 62], /* W62 */ Y[block + 62 + 1], Y[block + 126], Y[block + 126 + 1], Y[block + 62], Y[block + 62 + 1], Y[block + 126], Y[block + 126 + 1], (double) -0.995184726672197, (double) +0.098017140329561); } /* perform 1 times fft128 */ BUTTERFLY_10 (Y[0], /* W0 */ Y[0 + 1], Y[128], Y[128 + 1], Y[0], Y[0 + 1], Y[128], Y[128 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_XY (Y[2], /* W1 */ Y[2 + 1], Y[130], Y[130 + 1], Y[2], Y[2 + 1], Y[130], Y[130 + 1], (double) +0.998795456205172, (double) +0.049067674327418); BUTTERFLY_XY (Y[4], /* W2 */ Y[4 + 1], Y[132], Y[132 + 1], Y[4], Y[4 + 1], Y[132], Y[132 + 1], (double) +0.995184726672197, (double) +0.098017140329561); BUTTERFLY_XY (Y[6], /* W3 */ Y[6 + 1], Y[134], Y[134 + 1], Y[6], Y[6 + 1], Y[134], Y[134 + 1], (double) +0.989176509964781, (double) +0.146730474455362); BUTTERFLY_XY (Y[8], /* W4 */ Y[8 + 1], Y[136], Y[136 + 1], Y[8], Y[8 + 1], Y[136], Y[136 + 1], (double) +0.980785280403230, (double) +0.195090322016128); BUTTERFLY_XY (Y[10], /* W5 */ Y[10 + 1], Y[138], Y[138 + 1], Y[10], Y[10 + 1], Y[138], Y[138 + 1], (double) +0.970031253194544, (double) +0.242980179903264); BUTTERFLY_XY (Y[12], /* W6 */ Y[12 + 1], Y[140], Y[140 + 1], Y[12], Y[12 + 1], Y[140], Y[140 + 1], (double) +0.956940335732209, (double) +0.290284677254462); BUTTERFLY_XY (Y[14], /* W7 */ Y[14 + 1], Y[142], Y[142 + 1], Y[14], Y[14 + 1], Y[142], Y[142 + 1], (double) +0.941544065183021, (double) +0.336889853392220); BUTTERFLY_XY (Y[16], /* W8 */ Y[16 + 1], Y[144], Y[144 + 1], Y[16], Y[16 + 1], Y[144], Y[144 + 1], (double) +0.923879532511287, (double) +0.382683432365090); BUTTERFLY_XY (Y[18], /* W9 */ Y[18 + 1], Y[146], Y[146 + 1], Y[18], Y[18 + 1], Y[146], Y[146 + 1], (double) +0.903989293123443, (double) +0.427555093430282); BUTTERFLY_XY (Y[20], /* W10 */ Y[20 + 1], Y[148], Y[148 + 1], Y[20], Y[20 + 1], Y[148], Y[148 + 1], (double) +0.881921264348355, (double) +0.471396736825998); BUTTERFLY_XY (Y[22], /* W11 */ Y[22 + 1], Y[150], Y[150 + 1], Y[22], Y[22 + 1], Y[150], Y[150 + 1], (double) +0.857728610000272, (double) +0.514102744193222); BUTTERFLY_XY (Y[24], /* W12 */ Y[24 + 1], Y[152], Y[152 + 1], Y[24], Y[24 + 1], Y[152], Y[152 + 1], (double) +0.831469612302545, (double) +0.555570233019602); BUTTERFLY_XY (Y[26], /* W13 */ Y[26 + 1], Y[154], Y[154 + 1], Y[26], Y[26 + 1], Y[154], Y[154 + 1], (double) +0.803207531480645, (double) +0.595699304492433); BUTTERFLY_XY (Y[28], /* W14 */ Y[28 + 1], Y[156], Y[156 + 1], Y[28], Y[28 + 1], Y[156], Y[156 + 1], (double) +0.773010453362737, (double) +0.634393284163645); BUTTERFLY_XY (Y[30], /* W15 */ Y[30 + 1], Y[158], Y[158 + 1], Y[30], Y[30 + 1], Y[158], Y[158 + 1], (double) +0.740951125354959, (double) +0.671558954847018); BUTTERFLY_XX (Y[32], /* W16 */ Y[32 + 1], Y[160], Y[160 + 1], Y[32], Y[32 + 1], Y[160], Y[160 + 1], (double) +0.707106781186548, (double) +0.707106781186547); BUTTERFLY_XY (Y[34], /* W17 */ Y[34 + 1], Y[162], Y[162 + 1], Y[34], Y[34 + 1], Y[162], Y[162 + 1], (double) +0.671558954847018, (double) +0.740951125354959); BUTTERFLY_XY (Y[36], /* W18 */ Y[36 + 1], Y[164], Y[164 + 1], Y[36], Y[36 + 1], Y[164], Y[164 + 1], (double) +0.634393284163645, (double) +0.773010453362737); BUTTERFLY_XY (Y[38], /* W19 */ Y[38 + 1], Y[166], Y[166 + 1], Y[38], Y[38 + 1], Y[166], Y[166 + 1], (double) +0.595699304492433, (double) +0.803207531480645); BUTTERFLY_XY (Y[40], /* W20 */ Y[40 + 1], Y[168], Y[168 + 1], Y[40], Y[40 + 1], Y[168], Y[168 + 1], (double) +0.555570233019602, (double) +0.831469612302545); BUTTERFLY_XY (Y[42], /* W21 */ Y[42 + 1], Y[170], Y[170 + 1], Y[42], Y[42 + 1], Y[170], Y[170 + 1], (double) +0.514102744193222, (double) +0.857728610000272); BUTTERFLY_XY (Y[44], /* W22 */ Y[44 + 1], Y[172], Y[172 + 1], Y[44], Y[44 + 1], Y[172], Y[172 + 1], (double) +0.471396736825998, (double) +0.881921264348355); BUTTERFLY_XY (Y[46], /* W23 */ Y[46 + 1], Y[174], Y[174 + 1], Y[46], Y[46 + 1], Y[174], Y[174 + 1], (double) +0.427555093430282, (double) +0.903989293123443); BUTTERFLY_XY (Y[48], /* W24 */ Y[48 + 1], Y[176], Y[176 + 1], Y[48], Y[48 + 1], Y[176], Y[176 + 1], (double) +0.382683432365090, (double) +0.923879532511287); BUTTERFLY_XY (Y[50], /* W25 */ Y[50 + 1], Y[178], Y[178 + 1], Y[50], Y[50 + 1], Y[178], Y[178 + 1], (double) +0.336889853392220, (double) +0.941544065183021); BUTTERFLY_XY (Y[52], /* W26 */ Y[52 + 1], Y[180], Y[180 + 1], Y[52], Y[52 + 1], Y[180], Y[180 + 1], (double) +0.290284677254462, (double) +0.956940335732209); BUTTERFLY_XY (Y[54], /* W27 */ Y[54 + 1], Y[182], Y[182 + 1], Y[54], Y[54 + 1], Y[182], Y[182 + 1], (double) +0.242980179903264, (double) +0.970031253194544); BUTTERFLY_XY (Y[56], /* W28 */ Y[56 + 1], Y[184], Y[184 + 1], Y[56], Y[56 + 1], Y[184], Y[184 + 1], (double) +0.195090322016128, (double) +0.980785280403230); BUTTERFLY_XY (Y[58], /* W29 */ Y[58 + 1], Y[186], Y[186 + 1], Y[58], Y[58 + 1], Y[186], Y[186 + 1], (double) +0.146730474455362, (double) +0.989176509964781); BUTTERFLY_XY (Y[60], /* W30 */ Y[60 + 1], Y[188], Y[188 + 1], Y[60], Y[60 + 1], Y[188], Y[188 + 1], (double) +0.098017140329561, (double) +0.995184726672197); BUTTERFLY_XY (Y[62], /* W31 */ Y[62 + 1], Y[190], Y[190 + 1], Y[62], Y[62 + 1], Y[190], Y[190 + 1], (double) +0.049067674327418, (double) +0.998795456205172); BUTTERFLY_01 (Y[64], /* W32 */ Y[64 + 1], Y[192], Y[192 + 1], Y[64], Y[64 + 1], Y[192], Y[192 + 1], (double) +0.000000000000000, (double) +1.000000000000000); BUTTERFLY_XY (Y[66], /* W33 */ Y[66 + 1], Y[194], Y[194 + 1], Y[66], Y[66 + 1], Y[194], Y[194 + 1], (double) -0.049067674327418, (double) +0.998795456205172); BUTTERFLY_XY (Y[68], /* W34 */ Y[68 + 1], Y[196], Y[196 + 1], Y[68], Y[68 + 1], Y[196], Y[196 + 1], (double) -0.098017140329561, (double) +0.995184726672197); BUTTERFLY_XY (Y[70], /* W35 */ Y[70 + 1], Y[198], Y[198 + 1], Y[70], Y[70 + 1], Y[198], Y[198 + 1], (double) -0.146730474455362, (double) +0.989176509964781); BUTTERFLY_XY (Y[72], /* W36 */ Y[72 + 1], Y[200], Y[200 + 1], Y[72], Y[72 + 1], Y[200], Y[200 + 1], (double) -0.195090322016128, (double) +0.980785280403230); BUTTERFLY_XY (Y[74], /* W37 */ Y[74 + 1], Y[202], Y[202 + 1], Y[74], Y[74 + 1], Y[202], Y[202 + 1], (double) -0.242980179903264, (double) +0.970031253194544); BUTTERFLY_XY (Y[76], /* W38 */ Y[76 + 1], Y[204], Y[204 + 1], Y[76], Y[76 + 1], Y[204], Y[204 + 1], (double) -0.290284677254462, (double) +0.956940335732209); BUTTERFLY_XY (Y[78], /* W39 */ Y[78 + 1], Y[206], Y[206 + 1], Y[78], Y[78 + 1], Y[206], Y[206 + 1], (double) -0.336889853392220, (double) +0.941544065183021); BUTTERFLY_XY (Y[80], /* W40 */ Y[80 + 1], Y[208], Y[208 + 1], Y[80], Y[80 + 1], Y[208], Y[208 + 1], (double) -0.382683432365090, (double) +0.923879532511287); BUTTERFLY_XY (Y[82], /* W41 */ Y[82 + 1], Y[210], Y[210 + 1], Y[82], Y[82 + 1], Y[210], Y[210 + 1], (double) -0.427555093430282, (double) +0.903989293123443); BUTTERFLY_XY (Y[84], /* W42 */ Y[84 + 1], Y[212], Y[212 + 1], Y[84], Y[84 + 1], Y[212], Y[212 + 1], (double) -0.471396736825998, (double) +0.881921264348355); BUTTERFLY_XY (Y[86], /* W43 */ Y[86 + 1], Y[214], Y[214 + 1], Y[86], Y[86 + 1], Y[214], Y[214 + 1], (double) -0.514102744193222, (double) +0.857728610000272); BUTTERFLY_XY (Y[88], /* W44 */ Y[88 + 1], Y[216], Y[216 + 1], Y[88], Y[88 + 1], Y[216], Y[216 + 1], (double) -0.555570233019602, (double) +0.831469612302545); BUTTERFLY_XY (Y[90], /* W45 */ Y[90 + 1], Y[218], Y[218 + 1], Y[90], Y[90 + 1], Y[218], Y[218 + 1], (double) -0.595699304492433, (double) +0.803207531480645); BUTTERFLY_XY (Y[92], /* W46 */ Y[92 + 1], Y[220], Y[220 + 1], Y[92], Y[92 + 1], Y[220], Y[220 + 1], (double) -0.634393284163645, (double) +0.773010453362737); BUTTERFLY_XY (Y[94], /* W47 */ Y[94 + 1], Y[222], Y[222 + 1], Y[94], Y[94 + 1], Y[222], Y[222 + 1], (double) -0.671558954847018, (double) +0.740951125354959); BUTTERFLY_yY (Y[96], /* W48 */ Y[96 + 1], Y[224], Y[224 + 1], Y[96], Y[96 + 1], Y[224], Y[224 + 1], (double) -0.707106781186547, (double) +0.707106781186548); BUTTERFLY_XY (Y[98], /* W49 */ Y[98 + 1], Y[226], Y[226 + 1], Y[98], Y[98 + 1], Y[226], Y[226 + 1], (double) -0.740951125354959, (double) +0.671558954847019); BUTTERFLY_XY (Y[100], /* W50 */ Y[100 + 1], Y[228], Y[228 + 1], Y[100], Y[100 + 1], Y[228], Y[228 + 1], (double) -0.773010453362737, (double) +0.634393284163645); BUTTERFLY_XY (Y[102], /* W51 */ Y[102 + 1], Y[230], Y[230 + 1], Y[102], Y[102 + 1], Y[230], Y[230 + 1], (double) -0.803207531480645, (double) +0.595699304492433); BUTTERFLY_XY (Y[104], /* W52 */ Y[104 + 1], Y[232], Y[232 + 1], Y[104], Y[104 + 1], Y[232], Y[232 + 1], (double) -0.831469612302545, (double) +0.555570233019602); BUTTERFLY_XY (Y[106], /* W53 */ Y[106 + 1], Y[234], Y[234 + 1], Y[106], Y[106 + 1], Y[234], Y[234 + 1], (double) -0.857728610000272, (double) +0.514102744193222); BUTTERFLY_XY (Y[108], /* W54 */ Y[108 + 1], Y[236], Y[236 + 1], Y[108], Y[108 + 1], Y[236], Y[236 + 1], (double) -0.881921264348355, (double) +0.471396736825998); BUTTERFLY_XY (Y[110], /* W55 */ Y[110 + 1], Y[238], Y[238 + 1], Y[110], Y[110 + 1], Y[238], Y[238 + 1], (double) -0.903989293123443, (double) +0.427555093430282); BUTTERFLY_XY (Y[112], /* W56 */ Y[112 + 1], Y[240], Y[240 + 1], Y[112], Y[112 + 1], Y[240], Y[240 + 1], (double) -0.923879532511287, (double) +0.382683432365090); BUTTERFLY_XY (Y[114], /* W57 */ Y[114 + 1], Y[242], Y[242 + 1], Y[114], Y[114 + 1], Y[242], Y[242 + 1], (double) -0.941544065183021, (double) +0.336889853392220); BUTTERFLY_XY (Y[116], /* W58 */ Y[116 + 1], Y[244], Y[244 + 1], Y[116], Y[116 + 1], Y[244], Y[244 + 1], (double) -0.956940335732209, (double) +0.290284677254462); BUTTERFLY_XY (Y[118], /* W59 */ Y[118 + 1], Y[246], Y[246 + 1], Y[118], Y[118 + 1], Y[246], Y[246 + 1], (double) -0.970031253194544, (double) +0.242980179903264); BUTTERFLY_XY (Y[120], /* W60 */ Y[120 + 1], Y[248], Y[248 + 1], Y[120], Y[120 + 1], Y[248], Y[248 + 1], (double) -0.980785280403230, (double) +0.195090322016129); BUTTERFLY_XY (Y[122], /* W61 */ Y[122 + 1], Y[250], Y[250 + 1], Y[122], Y[122 + 1], Y[250], Y[250 + 1], (double) -0.989176509964781, (double) +0.146730474455362); BUTTERFLY_XY (Y[124], /* W62 */ Y[124 + 1], Y[252], Y[252 + 1], Y[124], Y[124 + 1], Y[252], Y[252 + 1], (double) -0.995184726672197, (double) +0.098017140329561); BUTTERFLY_XY (Y[126], /* W63 */ Y[126 + 1], Y[254], Y[254 + 1], Y[126], Y[126 + 1], Y[254], Y[254 + 1], (double) -0.998795456205172, (double) +0.049067674327418); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 128 L S S S S S X) **/ static void gsl_power2_fft128analysis (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* perform fft2 and bitreverse input */ bitreverse_fft2analysis (128, X, Y); /* skipping 32 times fft4 */ /* skipping 16 times fft8 */ /* skipping 8 times fft16 */ /* skipping 4 times fft32 */ /* skipping 2 times fft64 */ /* perform 1 times fft128 */ gsl_power2_fft128analysis_skip2 (X, Y); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 256 S S S S S S X T) **/ static void gsl_power2_fft256analysis_skip2 (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* skipping 128 times fft2 */ /* skipping 64 times fft4 */ /* skipping 32 times fft8 */ /* skipping 16 times fft16 */ /* skipping 8 times fft32 */ /* skipping 4 times fft64 */ /* perform 2 times fft128 */ gsl_power2_fft128analysis_skip2 (X, Y); gsl_power2_fft128analysis_skip2 (X + 256, Y + 256); /* perform 1 times fft256 */ { static const double Wconst256[] = { +0.999698818696204, +0.024541228522912, +0.998795456205172, +0.049067674327418, +0.997290456678690, +0.073564563599667, +0.995184726672197, +0.098017140329561, +0.992479534598710, +0.122410675199216, +0.989176509964781, +0.146730474455362, +0.985277642388941, +0.170961888760301, +0.980785280403230, +0.195090322016128, +0.975702130038529, +0.219101240156870, +0.970031253194544, +0.242980179903264, +0.963776065795440, +0.266712757474898, +0.956940335732209, +0.290284677254462, +0.949528180593037, +0.313681740398892, +0.941544065183021, +0.336889853392220, +0.932992798834739, +0.359895036534988, +0.923879532511287, +0.382683432365090, +0.914209755703531, +0.405241314004990, +0.903989293123443, +0.427555093430282, +0.893224301195515, +0.449611329654607, +0.881921264348355, +0.471396736825998, +0.870086991108711, +0.492898192229784, +0.857728610000272, +0.514102744193222, +0.844853565249707, +0.534997619887097, +0.831469612302545, +0.555570233019602, +0.817584813151584, +0.575808191417845, +0.803207531480645, +0.595699304492433, +0.788346427626606, +0.615231590580627, +0.773010453362737, +0.634393284163645, +0.757208846506485, +0.653172842953777, +0.740951125354959, +0.671558954847018, +0.724247082951467, +0.689540544737067, +0.707106781186548, +0.707106781186547, +0.689540544737067, +0.724247082951467, +0.671558954847018, +0.740951125354959, +0.653172842953777, +0.757208846506484, +0.634393284163645, +0.773010453362737, +0.615231590580627, +0.788346427626606, +0.595699304492433, +0.803207531480645, +0.575808191417845, +0.817584813151584, +0.555570233019602, +0.831469612302545, +0.534997619887097, +0.844853565249707, +0.514102744193222, +0.857728610000272, +0.492898192229784, +0.870086991108711, +0.471396736825998, +0.881921264348355, +0.449611329654607, +0.893224301195515, +0.427555093430282, +0.903989293123443, +0.405241314004990, +0.914209755703531, +0.382683432365090, +0.923879532511287, +0.359895036534988, +0.932992798834739, +0.336889853392220, +0.941544065183021, +0.313681740398892, +0.949528180593037, +0.290284677254462, +0.956940335732209, +0.266712757474898, +0.963776065795440, +0.242980179903264, +0.970031253194544, +0.219101240156870, +0.975702130038529, +0.195090322016128, +0.980785280403230, +0.170961888760301, +0.985277642388941, +0.146730474455362, +0.989176509964781, +0.122410675199216, +0.992479534598710, +0.098017140329561, +0.995184726672197, +0.073564563599667, +0.997290456678690, +0.049067674327418, +0.998795456205172, +0.024541228522912, +0.999698818696204, }; const double *W = Wconst256 - 2; double *Z = Y + 128; for (offset = 0; offset < 512; offset += 512) { BUTTERFLY_10 (Y[offset], Y[offset + 1], Y[offset + 256], Y[offset + 256 + 1], Y[offset], Y[offset + 1], Y[offset + 256], Y[offset + 256 + 1], __1, __0); BUTTERFLY_01 (Z[offset], Z[offset + 1], Z[offset + 256], Z[offset + 256 + 1], Z[offset], Z[offset + 1], Z[offset + 256], Z[offset + 256 + 1], __0, __1); } for (butterfly = 2; butterfly < 128; butterfly += 2) { Wre = W[butterfly]; Wim = W[butterfly + 1]; for (block = 0; block < 512; block += 512) { offset = butterfly + block; BUTTERFLY_XY (Y[offset], Y[offset + 1], Y[offset + 256], Y[offset + 256 + 1], Y[offset], Y[offset + 1], Y[offset + 256], Y[offset + 256 + 1], Wre, Wim); BUTTERFLY_Yx (Z[offset], Z[offset + 1], Z[offset + 256], Z[offset + 256 + 1], Z[offset], Z[offset + 1], Z[offset + 256], Z[offset + 256 + 1], Wre, Wim); } } } } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 256 L S S S S S S X) **/ static void gsl_power2_fft256analysis (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* perform fft2 and bitreverse input */ bitreverse_fft2analysis (256, X, Y); /* skipping 64 times fft4 */ /* skipping 32 times fft8 */ /* skipping 16 times fft16 */ /* skipping 8 times fft32 */ /* skipping 4 times fft64 */ /* skipping 2 times fft128 */ /* perform 1 times fft256 */ gsl_power2_fft256analysis_skip2 (X, Y); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 512 S S S S S S X T T) **/ static void gsl_power2_fft512analysis_skip2 (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* skipping 256 times fft2 */ /* skipping 128 times fft4 */ /* skipping 64 times fft8 */ /* skipping 32 times fft16 */ /* skipping 16 times fft32 */ /* skipping 8 times fft64 */ /* perform 4 times fft128 */ gsl_power2_fft128analysis_skip2 (X, Y); gsl_power2_fft128analysis_skip2 (X + 256, Y + 256); gsl_power2_fft128analysis_skip2 (X + 512, Y + 512); gsl_power2_fft128analysis_skip2 (X + 768, Y + 768); /* perform 2 times fft256 */ { static const double Wconst256[] = { +0.999698818696204, +0.024541228522912, +0.998795456205172, +0.049067674327418, +0.997290456678690, +0.073564563599667, +0.995184726672197, +0.098017140329561, +0.992479534598710, +0.122410675199216, +0.989176509964781, +0.146730474455362, +0.985277642388941, +0.170961888760301, +0.980785280403230, +0.195090322016128, +0.975702130038529, +0.219101240156870, +0.970031253194544, +0.242980179903264, +0.963776065795440, +0.266712757474898, +0.956940335732209, +0.290284677254462, +0.949528180593037, +0.313681740398892, +0.941544065183021, +0.336889853392220, +0.932992798834739, +0.359895036534988, +0.923879532511287, +0.382683432365090, +0.914209755703531, +0.405241314004990, +0.903989293123443, +0.427555093430282, +0.893224301195515, +0.449611329654607, +0.881921264348355, +0.471396736825998, +0.870086991108711, +0.492898192229784, +0.857728610000272, +0.514102744193222, +0.844853565249707, +0.534997619887097, +0.831469612302545, +0.555570233019602, +0.817584813151584, +0.575808191417845, +0.803207531480645, +0.595699304492433, +0.788346427626606, +0.615231590580627, +0.773010453362737, +0.634393284163645, +0.757208846506485, +0.653172842953777, +0.740951125354959, +0.671558954847018, +0.724247082951467, +0.689540544737067, +0.707106781186548, +0.707106781186547, +0.689540544737067, +0.724247082951467, +0.671558954847018, +0.740951125354959, +0.653172842953777, +0.757208846506484, +0.634393284163645, +0.773010453362737, +0.615231590580627, +0.788346427626606, +0.595699304492433, +0.803207531480645, +0.575808191417845, +0.817584813151584, +0.555570233019602, +0.831469612302545, +0.534997619887097, +0.844853565249707, +0.514102744193222, +0.857728610000272, +0.492898192229784, +0.870086991108711, +0.471396736825998, +0.881921264348355, +0.449611329654607, +0.893224301195515, +0.427555093430282, +0.903989293123443, +0.405241314004990, +0.914209755703531, +0.382683432365090, +0.923879532511287, +0.359895036534988, +0.932992798834739, +0.336889853392220, +0.941544065183021, +0.313681740398892, +0.949528180593037, +0.290284677254462, +0.956940335732209, +0.266712757474898, +0.963776065795440, +0.242980179903264, +0.970031253194544, +0.219101240156870, +0.975702130038529, +0.195090322016128, +0.980785280403230, +0.170961888760301, +0.985277642388941, +0.146730474455362, +0.989176509964781, +0.122410675199216, +0.992479534598710, +0.098017140329561, +0.995184726672197, +0.073564563599667, +0.997290456678690, +0.049067674327418, +0.998795456205172, +0.024541228522912, +0.999698818696204, }; const double *W = Wconst256 - 2; double *Z = Y + 128; for (offset = 0; offset < 1024; offset += 512) { BUTTERFLY_10 (Y[offset], Y[offset + 1], Y[offset + 256], Y[offset + 256 + 1], Y[offset], Y[offset + 1], Y[offset + 256], Y[offset + 256 + 1], __1, __0); BUTTERFLY_01 (Z[offset], Z[offset + 1], Z[offset + 256], Z[offset + 256 + 1], Z[offset], Z[offset + 1], Z[offset + 256], Z[offset + 256 + 1], __0, __1); } for (butterfly = 2; butterfly < 128; butterfly += 2) { Wre = W[butterfly]; Wim = W[butterfly + 1]; for (block = 0; block < 1024; block += 512) { offset = butterfly + block; BUTTERFLY_XY (Y[offset], Y[offset + 1], Y[offset + 256], Y[offset + 256 + 1], Y[offset], Y[offset + 1], Y[offset + 256], Y[offset + 256 + 1], Wre, Wim); BUTTERFLY_Yx (Z[offset], Z[offset + 1], Z[offset + 256], Z[offset + 256 + 1], Z[offset], Z[offset + 1], Z[offset + 256], Z[offset + 256 + 1], Wre, Wim); } } } /* perform 1 times fft512 */ { static const double Wconst512[] = { +0.999924701839145, +0.012271538285720, +0.999698818696204, +0.024541228522912, +0.999322384588350, +0.036807222941359, +0.998795456205172, +0.049067674327418, +0.998118112900149, +0.061320736302209, +0.997290456678690, +0.073564563599667, +0.996312612182778, +0.085797312344440, +0.995184726672197, +0.098017140329561, +0.993906970002356, +0.110222207293883, +0.992479534598710, +0.122410675199216, +0.990902635427780, +0.134580708507126, +0.989176509964781, +0.146730474455362, +0.987301418157858, +0.158858143333861, +0.985277642388941, +0.170961888760301, +0.983105487431216, +0.183039887955141, +0.980785280403230, +0.195090322016128, +0.978317370719628, +0.207111376192219, +0.975702130038529, +0.219101240156870, +0.972939952205560, +0.231058108280671, +0.970031253194544, +0.242980179903264, +0.966976471044852, +0.254865659604515, +0.963776065795440, +0.266712757474898, +0.960430519415566, +0.278519689385053, +0.956940335732209, +0.290284677254462, +0.953306040354194, +0.302005949319228, +0.949528180593037, +0.313681740398892, +0.945607325380521, +0.325310292162263, +0.941544065183021, +0.336889853392220, +0.937339011912575, +0.348418680249435, +0.932992798834739, +0.359895036534988, +0.928506080473216, +0.371317193951838, +0.923879532511287, +0.382683432365090, +0.919113851690058, +0.393992040061048, +0.914209755703531, +0.405241314004990, +0.909167983090522, +0.416429560097637, +0.903989293123443, +0.427555093430282, +0.898674465693954, +0.438616238538528, +0.893224301195515, +0.449611329654607, +0.887639620402854, +0.460538710958240, +0.881921264348355, +0.471396736825998, +0.876070094195407, +0.482183772079123, +0.870086991108711, +0.492898192229784, +0.863972856121587, +0.503538383725718, +0.857728610000272, +0.514102744193222, +0.851355193105265, +0.524589682678469, +0.844853565249707, +0.534997619887097, +0.838224705554838, +0.545324988422046, +0.831469612302545, +0.555570233019602, +0.824589302785025, +0.565731810783613, +0.817584813151584, +0.575808191417845, +0.810457198252595, +0.585797857456439, +0.803207531480645, +0.595699304492433, +0.795836904608884, +0.605511041404326, +0.788346427626606, +0.615231590580627, +0.780737228572094, +0.624859488142386, +0.773010453362737, +0.634393284163645, +0.765167265622459, +0.643831542889791, +0.757208846506485, +0.653172842953777, +0.749136394523459, +0.662415777590172, +0.740951125354959, +0.671558954847018, +0.732654271672413, +0.680600997795453, 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+0.482183772079123, +0.876070094195407, +0.471396736825998, +0.881921264348355, +0.460538710958240, +0.887639620402854, +0.449611329654607, +0.893224301195515, +0.438616238538528, +0.898674465693954, +0.427555093430282, +0.903989293123443, +0.416429560097637, +0.909167983090522, +0.405241314004990, +0.914209755703531, +0.393992040061048, +0.919113851690058, +0.382683432365090, +0.923879532511287, +0.371317193951838, +0.928506080473215, +0.359895036534988, +0.932992798834739, +0.348418680249435, +0.937339011912575, +0.336889853392220, +0.941544065183021, +0.325310292162263, +0.945607325380521, +0.313681740398892, +0.949528180593037, +0.302005949319228, +0.953306040354194, +0.290284677254462, +0.956940335732209, +0.278519689385053, +0.960430519415566, +0.266712757474898, +0.963776065795440, +0.254865659604515, +0.966976471044852, +0.242980179903264, +0.970031253194544, +0.231058108280671, +0.972939952205560, +0.219101240156870, +0.975702130038529, +0.207111376192219, +0.978317370719628, +0.195090322016128, +0.980785280403230, +0.183039887955141, +0.983105487431216, +0.170961888760301, +0.985277642388941, +0.158858143333861, +0.987301418157858, +0.146730474455362, +0.989176509964781, +0.134580708507126, +0.990902635427780, +0.122410675199216, +0.992479534598710, +0.110222207293883, +0.993906970002356, +0.098017140329561, +0.995184726672197, +0.085797312344440, +0.996312612182778, +0.073564563599667, +0.997290456678690, +0.061320736302209, +0.998118112900149, +0.049067674327418, +0.998795456205172, +0.036807222941359, +0.999322384588350, +0.024541228522912, +0.999698818696204, +0.012271538285720, +0.999924701839145, }; const double *W = Wconst512 - 2; double *Z = Y + 256; for (offset = 0; offset < 1024; offset += 1024) { BUTTERFLY_10 (Y[offset], Y[offset + 1], Y[offset + 512], Y[offset + 512 + 1], Y[offset], Y[offset + 1], Y[offset + 512], Y[offset + 512 + 1], __1, __0); BUTTERFLY_01 (Z[offset], Z[offset + 1], Z[offset + 512], Z[offset + 512 + 1], Z[offset], Z[offset + 1], Z[offset + 512], Z[offset + 512 + 1], __0, __1); } for (butterfly = 2; butterfly < 256; butterfly += 2) { Wre = W[butterfly]; Wim = W[butterfly + 1]; for (block = 0; block < 1024; block += 1024) { offset = butterfly + block; BUTTERFLY_XY (Y[offset], Y[offset + 1], Y[offset + 512], Y[offset + 512 + 1], Y[offset], Y[offset + 1], Y[offset + 512], Y[offset + 512 + 1], Wre, Wim); BUTTERFLY_Yx (Z[offset], Z[offset + 1], Z[offset + 512], Z[offset + 512 + 1], Z[offset], Z[offset + 1], Z[offset + 512], Z[offset + 512 + 1], Wre, Wim); } } } } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 512 L S S S S S S S X) **/ static void gsl_power2_fft512analysis (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* perform fft2 and bitreverse input */ bitreverse_fft2analysis (512, X, Y); /* skipping 128 times fft4 */ /* skipping 64 times fft8 */ /* skipping 32 times fft16 */ /* skipping 16 times fft32 */ /* skipping 8 times fft64 */ /* skipping 4 times fft128 */ /* skipping 2 times fft256 */ /* perform 1 times fft512 */ gsl_power2_fft512analysis_skip2 (X, Y); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 1024 S S S S S S S S X L) **/ static void gsl_power2_fft1024analysis_skip2 (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* skipping 512 times fft2 */ /* skipping 256 times fft4 */ /* skipping 128 times fft8 */ /* skipping 64 times fft16 */ /* skipping 32 times fft32 */ /* skipping 16 times fft64 */ /* skipping 8 times fft128 */ /* skipping 4 times fft256 */ /* perform 2 times fft512 */ gsl_power2_fft512analysis_skip2 (X, Y); gsl_power2_fft512analysis_skip2 (X + 1024, Y + 1024); /* perform 1 times fft1024 */ for (offset = 0; offset < 2048; offset += 2048) { BUTTERFLY_10 (Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], __1, __0); } Wre = +0.999981175282601; Wim = +0.006135884649154; for (butterfly = 2; butterfly < 512; butterfly += 2) { for (block = 0; block < 2048; block += 2048) { offset = butterfly + block; BUTTERFLY_XY (Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], Wre, Wim); } WMULTIPLY (Wre, Wim, -0.000018824717399, +0.006135884649154); } for (offset = 512; offset < 2048; offset += 2048) { BUTTERFLY_01 (Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], __0, __1); } Wre = -0.006135884649154; Wim = +0.999981175282601; for (butterfly = 514; butterfly < 1024; butterfly += 2) { for (block = 0; block < 2048; block += 2048) { offset = butterfly + block; BUTTERFLY_XY (Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], Wre, Wim); } WMULTIPLY (Wre, Wim, -0.000018824717399, +0.006135884649154); } } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 1024 L S S S S S S S S X) **/ static void gsl_power2_fft1024analysis (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* perform fft2 and bitreverse input */ bitreverse_fft2analysis (1024, X, Y); /* skipping 256 times fft4 */ /* skipping 128 times fft8 */ /* skipping 64 times fft16 */ /* skipping 32 times fft32 */ /* skipping 16 times fft64 */ /* skipping 8 times fft128 */ /* skipping 4 times fft256 */ /* skipping 2 times fft512 */ /* perform 1 times fft1024 */ gsl_power2_fft1024analysis_skip2 (X, Y); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 2048 S S S S S S S S X L L) **/ static void gsl_power2_fft2048analysis_skip2 (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* skipping 1024 times fft2 */ /* skipping 512 times fft4 */ /* skipping 256 times fft8 */ /* skipping 128 times fft16 */ /* skipping 64 times fft32 */ /* skipping 32 times fft64 */ /* skipping 16 times fft128 */ /* skipping 8 times fft256 */ /* perform 4 times fft512 */ gsl_power2_fft512analysis_skip2 (X, Y); gsl_power2_fft512analysis_skip2 (X + 1024, Y + 1024); gsl_power2_fft512analysis_skip2 (X + 2048, Y + 2048); gsl_power2_fft512analysis_skip2 (X + 3072, Y + 3072); /* perform 2 times fft1024 */ for (offset = 0; offset < 4096; offset += 2048) { BUTTERFLY_10 (Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], __1, __0); } Wre = +0.999981175282601; Wim = +0.006135884649154; for (butterfly = 2; butterfly < 512; butterfly += 2) { for (block = 0; block < 4096; block += 2048) { offset = butterfly + block; BUTTERFLY_XY (Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], Wre, Wim); } WMULTIPLY (Wre, Wim, -0.000018824717399, +0.006135884649154); } for (offset = 512; offset < 4096; offset += 2048) { BUTTERFLY_01 (Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], __0, __1); } Wre = -0.006135884649154; Wim = +0.999981175282601; for (butterfly = 514; butterfly < 1024; butterfly += 2) { for (block = 0; block < 4096; block += 2048) { offset = butterfly + block; BUTTERFLY_XY (Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], Wre, Wim); } WMULTIPLY (Wre, Wim, -0.000018824717399, +0.006135884649154); } /* perform 1 times fft2048 */ for (offset = 0; offset < 4096; offset += 4096) { BUTTERFLY_10 (Y[offset], Y[offset + 1], Y[offset + 2048], Y[offset + 2048 + 1], Y[offset], Y[offset + 1], Y[offset + 2048], Y[offset + 2048 + 1], __1, __0); } Wre = +0.999995293809576; Wim = +0.003067956762966; for (butterfly = 2; butterfly < 1024; butterfly += 2) { for (block = 0; block < 4096; block += 4096) { offset = butterfly + block; BUTTERFLY_XY (Y[offset], Y[offset + 1], Y[offset + 2048], Y[offset + 2048 + 1], Y[offset], Y[offset + 1], Y[offset + 2048], Y[offset + 2048 + 1], Wre, Wim); } WMULTIPLY (Wre, Wim, -0.000004706190424, +0.003067956762966); } for (offset = 1024; offset < 4096; offset += 4096) { BUTTERFLY_01 (Y[offset], Y[offset + 1], Y[offset + 2048], Y[offset + 2048 + 1], Y[offset], Y[offset + 1], Y[offset + 2048], Y[offset + 2048 + 1], __0, __1); } Wre = -0.003067956762966; Wim = +0.999995293809576; for (butterfly = 1026; butterfly < 2048; butterfly += 2) { for (block = 0; block < 4096; block += 4096) { offset = butterfly + block; BUTTERFLY_XY (Y[offset], Y[offset + 1], Y[offset + 2048], Y[offset + 2048 + 1], Y[offset], Y[offset + 1], Y[offset + 2048], Y[offset + 2048 + 1], Wre, Wim); } WMULTIPLY (Wre, Wim, -0.000004706190424, +0.003067956762966); } } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 2048 L S S S S S S S S S X) **/ static void gsl_power2_fft2048analysis (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* perform fft2 and bitreverse input */ bitreverse_fft2analysis (2048, X, Y); /* skipping 512 times fft4 */ /* skipping 256 times fft8 */ /* skipping 128 times fft16 */ /* skipping 64 times fft32 */ /* skipping 32 times fft64 */ /* skipping 16 times fft128 */ /* skipping 8 times fft256 */ /* skipping 4 times fft512 */ /* skipping 2 times fft1024 */ /* perform 1 times fft2048 */ gsl_power2_fft2048analysis_skip2 (X, Y); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 4096 S S S S S S S S S S X L) **/ static void gsl_power2_fft4096analysis_skip2 (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* skipping 2048 times fft2 */ /* skipping 1024 times fft4 */ /* skipping 512 times fft8 */ /* skipping 256 times fft16 */ /* skipping 128 times fft32 */ /* skipping 64 times fft64 */ /* skipping 32 times fft128 */ /* skipping 16 times fft256 */ /* skipping 8 times fft512 */ /* skipping 4 times fft1024 */ /* perform 2 times fft2048 */ gsl_power2_fft2048analysis_skip2 (X, Y); gsl_power2_fft2048analysis_skip2 (X + 4096, Y + 4096); /* perform 1 times fft4096 */ for (offset = 0; offset < 8192; offset += 8192) { BUTTERFLY_10 (Y[offset], Y[offset + 1], Y[offset + 4096], Y[offset + 4096 + 1], Y[offset], Y[offset + 1], Y[offset + 4096], Y[offset + 4096 + 1], __1, __0); } Wre = +0.999998823451702; Wim = +0.001533980186285; for (butterfly = 2; butterfly < 2048; butterfly += 2) { for (block = 0; block < 8192; block += 8192) { offset = butterfly + block; BUTTERFLY_XY (Y[offset], Y[offset + 1], Y[offset + 4096], Y[offset + 4096 + 1], Y[offset], Y[offset + 1], Y[offset + 4096], Y[offset + 4096 + 1], Wre, Wim); } WMULTIPLY (Wre, Wim, -0.000001176548298, +0.001533980186285); } for (offset = 2048; offset < 8192; offset += 8192) { BUTTERFLY_01 (Y[offset], Y[offset + 1], Y[offset + 4096], Y[offset + 4096 + 1], Y[offset], Y[offset + 1], Y[offset + 4096], Y[offset + 4096 + 1], __0, __1); } Wre = -0.001533980186285; Wim = +0.999998823451702; for (butterfly = 2050; butterfly < 4096; butterfly += 2) { for (block = 0; block < 8192; block += 8192) { offset = butterfly + block; BUTTERFLY_XY (Y[offset], Y[offset + 1], Y[offset + 4096], Y[offset + 4096 + 1], Y[offset], Y[offset + 1], Y[offset + 4096], Y[offset + 4096 + 1], Wre, Wim); } WMULTIPLY (Wre, Wim, -0.000001176548298, +0.001533980186285); } } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 4096 L S S S S S S S S S S X) **/ static void gsl_power2_fft4096analysis (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* perform fft2 and bitreverse input */ bitreverse_fft2analysis (4096, X, Y); /* skipping 1024 times fft4 */ /* skipping 512 times fft8 */ /* skipping 256 times fft16 */ /* skipping 128 times fft32 */ /* skipping 64 times fft64 */ /* skipping 32 times fft128 */ /* skipping 16 times fft256 */ /* skipping 8 times fft512 */ /* skipping 4 times fft1024 */ /* skipping 2 times fft2048 */ /* perform 1 times fft4096 */ gsl_power2_fft4096analysis_skip2 (X, Y); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 8192 S S S S S S S S S S S X L) **/ static void gsl_power2_fft8192analysis_skip2 (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* skipping 4096 times fft2 */ /* skipping 2048 times fft4 */ /* skipping 1024 times fft8 */ /* skipping 512 times fft16 */ /* skipping 256 times fft32 */ /* skipping 128 times fft64 */ /* skipping 64 times fft128 */ /* skipping 32 times fft256 */ /* skipping 16 times fft512 */ /* skipping 8 times fft1024 */ /* skipping 4 times fft2048 */ /* perform 2 times fft4096 */ gsl_power2_fft4096analysis_skip2 (X, Y); gsl_power2_fft4096analysis_skip2 (X + 8192, Y + 8192); /* perform 1 times fft8192 */ for (offset = 0; offset < 16384; offset += 16384) { BUTTERFLY_10 (Y[offset], Y[offset + 1], Y[offset + 8192], Y[offset + 8192 + 1], Y[offset], Y[offset + 1], Y[offset + 8192], Y[offset + 8192 + 1], __1, __0); } Wre = +0.999999705862882; Wim = +0.000766990318743; for (butterfly = 2; butterfly < 4096; butterfly += 2) { for (block = 0; block < 16384; block += 16384) { offset = butterfly + block; BUTTERFLY_XY (Y[offset], Y[offset + 1], Y[offset + 8192], Y[offset + 8192 + 1], Y[offset], Y[offset + 1], Y[offset + 8192], Y[offset + 8192 + 1], Wre, Wim); } WMULTIPLY (Wre, Wim, -0.000000294137118, +0.000766990318743); } for (offset = 4096; offset < 16384; offset += 16384) { BUTTERFLY_01 (Y[offset], Y[offset + 1], Y[offset + 8192], Y[offset + 8192 + 1], Y[offset], Y[offset + 1], Y[offset + 8192], Y[offset + 8192 + 1], __0, __1); } Wre = -0.000766990318743; Wim = +0.999999705862882; for (butterfly = 4098; butterfly < 8192; butterfly += 2) { for (block = 0; block < 16384; block += 16384) { offset = butterfly + block; BUTTERFLY_XY (Y[offset], Y[offset + 1], Y[offset + 8192], Y[offset + 8192 + 1], Y[offset], Y[offset + 1], Y[offset + 8192], Y[offset + 8192 + 1], Wre, Wim); } WMULTIPLY (Wre, Wim, -0.000000294137118, +0.000766990318743); } } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 8192 L S S S S S S S S S S S X) **/ static void gsl_power2_fft8192analysis (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* perform fft2 and bitreverse input */ bitreverse_fft2analysis (8192, X, Y); /* skipping 2048 times fft4 */ /* skipping 1024 times fft8 */ /* skipping 512 times fft16 */ /* skipping 256 times fft32 */ /* skipping 128 times fft64 */ /* skipping 64 times fft128 */ /* skipping 32 times fft256 */ /* skipping 16 times fft512 */ /* skipping 8 times fft1024 */ /* skipping 4 times fft2048 */ /* skipping 2 times fft4096 */ /* perform 1 times fft8192 */ gsl_power2_fft8192analysis_skip2 (X, Y); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 2 F) **/ static void gsl_power2_fft2synthesis (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* perform 1 times fft2 */ BUTTERFLY_10scale (X[0], X[0 + 1], X[2], X[2 + 1], Y[0], Y[0 + 1], Y[2], Y[2 + 1], 1.0 / (double) 2); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 4 S F) **/ static void gsl_power2_fft4synthesis_skip2 (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* skipping 2 times fft2 */ /* perform 1 times fft4 */ BUTTERFLY_10 (Y[0], /* W0 */ Y[0 + 1], Y[4], Y[4 + 1], Y[0], Y[0 + 1], Y[4], Y[4 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_0m (Y[2], /* W1 */ Y[2 + 1], Y[6], Y[6 + 1], Y[2], Y[2 + 1], Y[6], Y[6 + 1], (double) +0.000000000000000, (double) -1.000000000000000); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 4 F X) **/ static void gsl_power2_fft4synthesis (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* perform 2 times fft2 */ BUTTERFLY_10scale (X[0], X[0 + 1], X[4], X[4 + 1], Y[0], Y[0 + 1], Y[2], Y[2 + 1], 1.0 / (double) 4); BUTTERFLY_10scale (X[2], X[2 + 1], X[6], X[6 + 1], Y[4], Y[4 + 1], Y[6], Y[6 + 1], 1.0 / (double) 4); /* perform 1 times fft4 */ gsl_power2_fft4synthesis_skip2 (X, Y); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 8 S F F) **/ static void gsl_power2_fft8synthesis_skip2 (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* skipping 4 times fft2 */ /* perform 2 times fft4 */ BUTTERFLY_10 (Y[0], /* W0 */ Y[0 + 1], Y[4], Y[4 + 1], Y[0], Y[0 + 1], Y[4], Y[4 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[8], /* W0 */ Y[8 + 1], Y[12], Y[12 + 1], Y[8], Y[8 + 1], Y[12], Y[12 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_0m (Y[2], /* W2 */ Y[2 + 1], Y[6], Y[6 + 1], Y[2], Y[2 + 1], Y[6], Y[6 + 1], (double) +0.000000000000000, (double) -1.000000000000000); BUTTERFLY_0m (Y[10], /* W2 */ Y[10 + 1], Y[14], Y[14 + 1], Y[10], Y[10 + 1], Y[14], Y[14 + 1], (double) +0.000000000000000, (double) -1.000000000000000); /* perform 1 times fft8 */ BUTTERFLY_10 (Y[0], /* W0 */ Y[0 + 1], Y[8], Y[8 + 1], Y[0], Y[0 + 1], Y[8], Y[8 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_yY (Y[2], /* W1 */ Y[2 + 1], Y[10], Y[10 + 1], Y[2], Y[2 + 1], Y[10], Y[10 + 1], (double) +0.707106781186548, (double) -0.707106781186547); BUTTERFLY_0m (Y[4], /* W2 */ Y[4 + 1], Y[12], Y[12 + 1], Y[4], Y[4 + 1], Y[12], Y[12 + 1], (double) +0.000000000000000, (double) -1.000000000000000); BUTTERFLY_XX (Y[6], /* W3 */ Y[6 + 1], Y[14], Y[14 + 1], Y[6], Y[6 + 1], Y[14], Y[14 + 1], (double) -0.707106781186547, (double) -0.707106781186548); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 8 F S X) **/ static void gsl_power2_fft8synthesis (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* perform 4 times fft2 */ BUTTERFLY_10scale (X[0], X[0 + 1], X[8], X[8 + 1], Y[0], Y[0 + 1], Y[2], Y[2 + 1], 1.0 / (double) 8); BUTTERFLY_10scale (X[4], X[4 + 1], X[12], X[12 + 1], Y[4], Y[4 + 1], Y[6], Y[6 + 1], 1.0 / (double) 8); BUTTERFLY_10scale (X[2], X[2 + 1], X[10], X[10 + 1], Y[8], Y[8 + 1], Y[10], Y[10 + 1], 1.0 / (double) 8); BUTTERFLY_10scale (X[6], X[6 + 1], X[14], X[14 + 1], Y[12], Y[12 + 1], Y[14], Y[14 + 1], 1.0 / (double) 8); /* skipping 2 times fft4 */ /* perform 1 times fft8 */ gsl_power2_fft8synthesis_skip2 (X, Y); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 16 S F F F) **/ static void gsl_power2_fft16synthesis_skip2 (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* skipping 8 times fft2 */ /* perform 4 times fft4 */ BUTTERFLY_10 (Y[0], /* W0 */ Y[0 + 1], Y[4], Y[4 + 1], Y[0], Y[0 + 1], Y[4], Y[4 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[8], /* W0 */ Y[8 + 1], Y[12], Y[12 + 1], Y[8], Y[8 + 1], Y[12], Y[12 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[16], /* W0 */ Y[16 + 1], Y[20], Y[20 + 1], Y[16], Y[16 + 1], Y[20], Y[20 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[24], /* W0 */ Y[24 + 1], Y[28], Y[28 + 1], Y[24], Y[24 + 1], Y[28], Y[28 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_0m (Y[2], /* W4 */ Y[2 + 1], Y[6], Y[6 + 1], Y[2], Y[2 + 1], Y[6], Y[6 + 1], (double) +0.000000000000000, (double) -1.000000000000000); BUTTERFLY_0m (Y[10], /* W4 */ Y[10 + 1], Y[14], Y[14 + 1], Y[10], Y[10 + 1], Y[14], Y[14 + 1], (double) +0.000000000000000, (double) -1.000000000000000); BUTTERFLY_0m (Y[18], /* W4 */ Y[18 + 1], Y[22], Y[22 + 1], Y[18], Y[18 + 1], Y[22], Y[22 + 1], (double) +0.000000000000000, (double) -1.000000000000000); BUTTERFLY_0m (Y[26], /* W4 */ Y[26 + 1], Y[30], Y[30 + 1], Y[26], Y[26 + 1], Y[30], Y[30 + 1], (double) +0.000000000000000, (double) -1.000000000000000); /* perform 2 times fft8 */ BUTTERFLY_10 (Y[0], /* W0 */ Y[0 + 1], Y[8], Y[8 + 1], Y[0], Y[0 + 1], Y[8], Y[8 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[16], /* W0 */ Y[16 + 1], Y[24], Y[24 + 1], Y[16], Y[16 + 1], Y[24], Y[24 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_yY (Y[2], /* W2 */ Y[2 + 1], Y[10], Y[10 + 1], Y[2], Y[2 + 1], Y[10], Y[10 + 1], (double) +0.707106781186548, (double) -0.707106781186547); BUTTERFLY_yY (Y[18], /* W2 */ Y[18 + 1], Y[26], Y[26 + 1], Y[18], Y[18 + 1], Y[26], Y[26 + 1], (double) +0.707106781186548, (double) -0.707106781186547); BUTTERFLY_0m (Y[4], /* W4 */ Y[4 + 1], Y[12], Y[12 + 1], Y[4], Y[4 + 1], Y[12], Y[12 + 1], (double) +0.000000000000000, (double) -1.000000000000000); BUTTERFLY_0m (Y[20], /* W4 */ Y[20 + 1], Y[28], Y[28 + 1], Y[20], Y[20 + 1], Y[28], Y[28 + 1], (double) +0.000000000000000, (double) -1.000000000000000); BUTTERFLY_XX (Y[6], /* W6 */ Y[6 + 1], Y[14], Y[14 + 1], Y[6], Y[6 + 1], Y[14], Y[14 + 1], (double) -0.707106781186547, (double) -0.707106781186548); BUTTERFLY_XX (Y[22], /* W6 */ Y[22 + 1], Y[30], Y[30 + 1], Y[22], Y[22 + 1], Y[30], Y[30 + 1], (double) -0.707106781186547, (double) -0.707106781186548); /* perform 1 times fft16 */ BUTTERFLY_10 (Y[0], /* W0 */ Y[0 + 1], Y[16], Y[16 + 1], Y[0], Y[0 + 1], Y[16], Y[16 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_XY (Y[2], /* W1 */ Y[2 + 1], Y[18], Y[18 + 1], Y[2], Y[2 + 1], Y[18], Y[18 + 1], (double) +0.923879532511287, (double) -0.382683432365090); BUTTERFLY_yY (Y[4], /* W2 */ Y[4 + 1], Y[20], Y[20 + 1], Y[4], Y[4 + 1], Y[20], Y[20 + 1], (double) +0.707106781186548, (double) -0.707106781186547); BUTTERFLY_XY (Y[6], /* W3 */ Y[6 + 1], Y[22], Y[22 + 1], Y[6], Y[6 + 1], Y[22], Y[22 + 1], (double) +0.382683432365090, (double) -0.923879532511287); BUTTERFLY_0m (Y[8], /* W4 */ Y[8 + 1], Y[24], Y[24 + 1], Y[8], Y[8 + 1], Y[24], Y[24 + 1], (double) +0.000000000000000, (double) -1.000000000000000); BUTTERFLY_XY (Y[10], /* W5 */ Y[10 + 1], Y[26], Y[26 + 1], Y[10], Y[10 + 1], Y[26], Y[26 + 1], (double) -0.382683432365090, (double) -0.923879532511287); BUTTERFLY_XX (Y[12], /* W6 */ Y[12 + 1], Y[28], Y[28 + 1], Y[12], Y[12 + 1], Y[28], Y[28 + 1], (double) -0.707106781186547, (double) -0.707106781186548); BUTTERFLY_XY (Y[14], /* W7 */ Y[14 + 1], Y[30], Y[30 + 1], Y[14], Y[14 + 1], Y[30], Y[30 + 1], (double) -0.923879532511287, (double) -0.382683432365090); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 16 F S S X) **/ static void gsl_power2_fft16synthesis (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* perform 8 times fft2 */ BUTTERFLY_10scale (X[0], X[0 + 1], X[16], X[16 + 1], Y[0], Y[0 + 1], Y[2], Y[2 + 1], 1.0 / (double) 16); BUTTERFLY_10scale (X[8], X[8 + 1], X[24], X[24 + 1], Y[4], Y[4 + 1], Y[6], Y[6 + 1], 1.0 / (double) 16); BUTTERFLY_10scale (X[4], X[4 + 1], X[20], X[20 + 1], Y[8], Y[8 + 1], Y[10], Y[10 + 1], 1.0 / (double) 16); BUTTERFLY_10scale (X[12], X[12 + 1], X[28], X[28 + 1], Y[12], Y[12 + 1], Y[14], Y[14 + 1], 1.0 / (double) 16); BUTTERFLY_10scale (X[2], X[2 + 1], X[18], X[18 + 1], Y[16], Y[16 + 1], Y[18], Y[18 + 1], 1.0 / (double) 16); BUTTERFLY_10scale (X[10], X[10 + 1], X[26], X[26 + 1], Y[20], Y[20 + 1], Y[22], Y[22 + 1], 1.0 / (double) 16); BUTTERFLY_10scale (X[6], X[6 + 1], X[22], X[22 + 1], Y[24], Y[24 + 1], Y[26], Y[26 + 1], 1.0 / (double) 16); BUTTERFLY_10scale (X[14], X[14 + 1], X[30], X[30 + 1], Y[28], Y[28 + 1], Y[30], Y[30 + 1], 1.0 / (double) 16); /* skipping 4 times fft4 */ /* skipping 2 times fft8 */ /* perform 1 times fft16 */ gsl_power2_fft16synthesis_skip2 (X, Y); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 32 S F F F F) **/ static void gsl_power2_fft32synthesis_skip2 (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* skipping 16 times fft2 */ /* perform 8 times fft4 */ BUTTERFLY_10 (Y[0], /* W0 */ Y[0 + 1], Y[4], Y[4 + 1], Y[0], Y[0 + 1], Y[4], Y[4 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[8], /* W0 */ Y[8 + 1], Y[12], Y[12 + 1], Y[8], Y[8 + 1], Y[12], Y[12 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[16], /* W0 */ Y[16 + 1], Y[20], Y[20 + 1], Y[16], Y[16 + 1], Y[20], Y[20 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[24], /* W0 */ Y[24 + 1], Y[28], Y[28 + 1], Y[24], Y[24 + 1], Y[28], Y[28 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[32], /* W0 */ Y[32 + 1], Y[36], Y[36 + 1], Y[32], Y[32 + 1], Y[36], Y[36 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[40], /* W0 */ Y[40 + 1], Y[44], Y[44 + 1], Y[40], Y[40 + 1], Y[44], Y[44 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[48], /* W0 */ Y[48 + 1], Y[52], Y[52 + 1], Y[48], Y[48 + 1], Y[52], Y[52 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[56], /* W0 */ Y[56 + 1], Y[60], Y[60 + 1], Y[56], Y[56 + 1], Y[60], Y[60 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_0m (Y[2], /* W8 */ Y[2 + 1], Y[6], Y[6 + 1], Y[2], Y[2 + 1], Y[6], Y[6 + 1], (double) +0.000000000000000, (double) -1.000000000000000); BUTTERFLY_0m (Y[10], /* W8 */ Y[10 + 1], Y[14], Y[14 + 1], Y[10], Y[10 + 1], Y[14], Y[14 + 1], (double) +0.000000000000000, (double) -1.000000000000000); BUTTERFLY_0m (Y[18], /* W8 */ Y[18 + 1], Y[22], Y[22 + 1], Y[18], Y[18 + 1], Y[22], Y[22 + 1], (double) +0.000000000000000, (double) -1.000000000000000); BUTTERFLY_0m (Y[26], /* W8 */ Y[26 + 1], Y[30], Y[30 + 1], Y[26], Y[26 + 1], Y[30], Y[30 + 1], (double) +0.000000000000000, (double) -1.000000000000000); BUTTERFLY_0m (Y[34], /* W8 */ Y[34 + 1], Y[38], Y[38 + 1], Y[34], Y[34 + 1], Y[38], Y[38 + 1], (double) +0.000000000000000, (double) -1.000000000000000); BUTTERFLY_0m (Y[42], /* W8 */ Y[42 + 1], Y[46], Y[46 + 1], Y[42], Y[42 + 1], Y[46], Y[46 + 1], (double) +0.000000000000000, (double) -1.000000000000000); BUTTERFLY_0m (Y[50], /* W8 */ Y[50 + 1], Y[54], Y[54 + 1], Y[50], Y[50 + 1], Y[54], Y[54 + 1], (double) +0.000000000000000, (double) -1.000000000000000); BUTTERFLY_0m (Y[58], /* W8 */ Y[58 + 1], Y[62], Y[62 + 1], Y[58], Y[58 + 1], Y[62], Y[62 + 1], (double) +0.000000000000000, (double) -1.000000000000000); /* perform 4 times fft8 */ BUTTERFLY_10 (Y[0], /* W0 */ Y[0 + 1], Y[8], Y[8 + 1], Y[0], Y[0 + 1], Y[8], Y[8 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[16], /* W0 */ Y[16 + 1], Y[24], Y[24 + 1], Y[16], Y[16 + 1], Y[24], Y[24 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[32], /* W0 */ Y[32 + 1], Y[40], Y[40 + 1], Y[32], Y[32 + 1], Y[40], Y[40 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[48], /* W0 */ Y[48 + 1], Y[56], Y[56 + 1], Y[48], Y[48 + 1], Y[56], Y[56 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_yY (Y[2], /* W4 */ Y[2 + 1], Y[10], Y[10 + 1], Y[2], Y[2 + 1], Y[10], Y[10 + 1], (double) +0.707106781186548, (double) -0.707106781186547); BUTTERFLY_yY (Y[18], /* W4 */ Y[18 + 1], Y[26], Y[26 + 1], Y[18], Y[18 + 1], Y[26], Y[26 + 1], (double) +0.707106781186548, (double) -0.707106781186547); BUTTERFLY_yY (Y[34], /* W4 */ Y[34 + 1], Y[42], Y[42 + 1], Y[34], Y[34 + 1], Y[42], Y[42 + 1], (double) +0.707106781186548, (double) -0.707106781186547); BUTTERFLY_yY (Y[50], /* W4 */ Y[50 + 1], Y[58], Y[58 + 1], Y[50], Y[50 + 1], Y[58], Y[58 + 1], (double) +0.707106781186548, (double) -0.707106781186547); BUTTERFLY_0m (Y[4], /* W8 */ Y[4 + 1], Y[12], Y[12 + 1], Y[4], Y[4 + 1], Y[12], Y[12 + 1], (double) +0.000000000000000, (double) -1.000000000000000); BUTTERFLY_0m (Y[20], /* W8 */ Y[20 + 1], Y[28], Y[28 + 1], Y[20], Y[20 + 1], Y[28], Y[28 + 1], (double) +0.000000000000000, (double) -1.000000000000000); BUTTERFLY_0m (Y[36], /* W8 */ Y[36 + 1], Y[44], Y[44 + 1], Y[36], Y[36 + 1], Y[44], Y[44 + 1], (double) +0.000000000000000, (double) -1.000000000000000); BUTTERFLY_0m (Y[52], /* W8 */ Y[52 + 1], Y[60], Y[60 + 1], Y[52], Y[52 + 1], Y[60], Y[60 + 1], (double) +0.000000000000000, (double) -1.000000000000000); BUTTERFLY_XX (Y[6], /* W12 */ Y[6 + 1], Y[14], Y[14 + 1], Y[6], Y[6 + 1], Y[14], Y[14 + 1], (double) -0.707106781186547, (double) -0.707106781186548); BUTTERFLY_XX (Y[22], /* W12 */ Y[22 + 1], Y[30], Y[30 + 1], Y[22], Y[22 + 1], Y[30], Y[30 + 1], (double) -0.707106781186547, (double) -0.707106781186548); BUTTERFLY_XX (Y[38], /* W12 */ Y[38 + 1], Y[46], Y[46 + 1], Y[38], Y[38 + 1], Y[46], Y[46 + 1], (double) -0.707106781186547, (double) -0.707106781186548); BUTTERFLY_XX (Y[54], /* W12 */ Y[54 + 1], Y[62], Y[62 + 1], Y[54], Y[54 + 1], Y[62], Y[62 + 1], (double) -0.707106781186547, (double) -0.707106781186548); /* perform 2 times fft16 */ BUTTERFLY_10 (Y[0], /* W0 */ Y[0 + 1], Y[16], Y[16 + 1], Y[0], Y[0 + 1], Y[16], Y[16 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_10 (Y[32], /* W0 */ Y[32 + 1], Y[48], Y[48 + 1], Y[32], Y[32 + 1], Y[48], Y[48 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_XY (Y[2], /* W2 */ Y[2 + 1], Y[18], Y[18 + 1], Y[2], Y[2 + 1], Y[18], Y[18 + 1], (double) +0.923879532511287, (double) -0.382683432365090); BUTTERFLY_XY (Y[34], /* W2 */ Y[34 + 1], Y[50], Y[50 + 1], Y[34], Y[34 + 1], Y[50], Y[50 + 1], (double) +0.923879532511287, (double) -0.382683432365090); BUTTERFLY_yY (Y[4], /* W4 */ Y[4 + 1], Y[20], Y[20 + 1], Y[4], Y[4 + 1], Y[20], Y[20 + 1], (double) +0.707106781186548, (double) -0.707106781186547); BUTTERFLY_yY (Y[36], /* W4 */ Y[36 + 1], Y[52], Y[52 + 1], Y[36], Y[36 + 1], Y[52], Y[52 + 1], (double) +0.707106781186548, (double) -0.707106781186547); BUTTERFLY_XY (Y[6], /* W6 */ Y[6 + 1], Y[22], Y[22 + 1], Y[6], Y[6 + 1], Y[22], Y[22 + 1], (double) +0.382683432365090, (double) -0.923879532511287); BUTTERFLY_XY (Y[38], /* W6 */ Y[38 + 1], Y[54], Y[54 + 1], Y[38], Y[38 + 1], Y[54], Y[54 + 1], (double) +0.382683432365090, (double) -0.923879532511287); BUTTERFLY_0m (Y[8], /* W8 */ Y[8 + 1], Y[24], Y[24 + 1], Y[8], Y[8 + 1], Y[24], Y[24 + 1], (double) +0.000000000000000, (double) -1.000000000000000); BUTTERFLY_0m (Y[40], /* W8 */ Y[40 + 1], Y[56], Y[56 + 1], Y[40], Y[40 + 1], Y[56], Y[56 + 1], (double) +0.000000000000000, (double) -1.000000000000000); BUTTERFLY_XY (Y[10], /* W10 */ Y[10 + 1], Y[26], Y[26 + 1], Y[10], Y[10 + 1], Y[26], Y[26 + 1], (double) -0.382683432365090, (double) -0.923879532511287); BUTTERFLY_XY (Y[42], /* W10 */ Y[42 + 1], Y[58], Y[58 + 1], Y[42], Y[42 + 1], Y[58], Y[58 + 1], (double) -0.382683432365090, (double) -0.923879532511287); BUTTERFLY_XX (Y[12], /* W12 */ Y[12 + 1], Y[28], Y[28 + 1], Y[12], Y[12 + 1], Y[28], Y[28 + 1], (double) -0.707106781186547, (double) -0.707106781186548); BUTTERFLY_XX (Y[44], /* W12 */ Y[44 + 1], Y[60], Y[60 + 1], Y[44], Y[44 + 1], Y[60], Y[60 + 1], (double) -0.707106781186547, (double) -0.707106781186548); BUTTERFLY_XY (Y[14], /* W14 */ Y[14 + 1], Y[30], Y[30 + 1], Y[14], Y[14 + 1], Y[30], Y[30 + 1], (double) -0.923879532511287, (double) -0.382683432365090); BUTTERFLY_XY (Y[46], /* W14 */ Y[46 + 1], Y[62], Y[62 + 1], Y[46], Y[46 + 1], Y[62], Y[62 + 1], (double) -0.923879532511287, (double) -0.382683432365090); /* perform 1 times fft32 */ BUTTERFLY_10 (Y[0], /* W0 */ Y[0 + 1], Y[32], Y[32 + 1], Y[0], Y[0 + 1], Y[32], Y[32 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_XY (Y[2], /* W1 */ Y[2 + 1], Y[34], Y[34 + 1], Y[2], Y[2 + 1], Y[34], Y[34 + 1], (double) +0.980785280403230, (double) -0.195090322016128); BUTTERFLY_XY (Y[4], /* W2 */ Y[4 + 1], Y[36], Y[36 + 1], Y[4], Y[4 + 1], Y[36], Y[36 + 1], (double) +0.923879532511287, (double) -0.382683432365090); BUTTERFLY_XY (Y[6], /* W3 */ Y[6 + 1], Y[38], Y[38 + 1], Y[6], Y[6 + 1], Y[38], Y[38 + 1], (double) +0.831469612302545, (double) -0.555570233019602); BUTTERFLY_yY (Y[8], /* W4 */ Y[8 + 1], Y[40], Y[40 + 1], Y[8], Y[8 + 1], Y[40], Y[40 + 1], (double) +0.707106781186548, (double) -0.707106781186547); BUTTERFLY_XY (Y[10], /* W5 */ Y[10 + 1], Y[42], Y[42 + 1], Y[10], Y[10 + 1], Y[42], Y[42 + 1], (double) +0.555570233019602, (double) -0.831469612302545); BUTTERFLY_XY (Y[12], /* W6 */ Y[12 + 1], Y[44], Y[44 + 1], Y[12], Y[12 + 1], Y[44], Y[44 + 1], (double) +0.382683432365090, (double) -0.923879532511287); BUTTERFLY_XY (Y[14], /* W7 */ Y[14 + 1], Y[46], Y[46 + 1], Y[14], Y[14 + 1], Y[46], Y[46 + 1], (double) +0.195090322016128, (double) -0.980785280403230); BUTTERFLY_0m (Y[16], /* W8 */ Y[16 + 1], Y[48], Y[48 + 1], Y[16], Y[16 + 1], Y[48], Y[48 + 1], (double) +0.000000000000000, (double) -1.000000000000000); BUTTERFLY_XY (Y[18], /* W9 */ Y[18 + 1], Y[50], Y[50 + 1], Y[18], Y[18 + 1], Y[50], Y[50 + 1], (double) -0.195090322016128, (double) -0.980785280403230); BUTTERFLY_XY (Y[20], /* W10 */ Y[20 + 1], Y[52], Y[52 + 1], Y[20], Y[20 + 1], Y[52], Y[52 + 1], (double) -0.382683432365090, (double) -0.923879532511287); BUTTERFLY_XY (Y[22], /* W11 */ Y[22 + 1], Y[54], Y[54 + 1], Y[22], Y[22 + 1], Y[54], Y[54 + 1], (double) -0.555570233019602, (double) -0.831469612302545); BUTTERFLY_XX (Y[24], /* W12 */ Y[24 + 1], Y[56], Y[56 + 1], Y[24], Y[24 + 1], Y[56], Y[56 + 1], (double) -0.707106781186547, (double) -0.707106781186548); BUTTERFLY_XY (Y[26], /* W13 */ Y[26 + 1], Y[58], Y[58 + 1], Y[26], Y[26 + 1], Y[58], Y[58 + 1], (double) -0.831469612302545, (double) -0.555570233019602); BUTTERFLY_XY (Y[28], /* W14 */ Y[28 + 1], Y[60], Y[60 + 1], Y[28], Y[28 + 1], Y[60], Y[60 + 1], (double) -0.923879532511287, (double) -0.382683432365090); BUTTERFLY_XY (Y[30], /* W15 */ Y[30 + 1], Y[62], Y[62 + 1], Y[30], Y[30 + 1], Y[62], Y[62 + 1], (double) -0.980785280403230, (double) -0.195090322016129); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 32 F S S S X) **/ static void gsl_power2_fft32synthesis (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* perform 16 times fft2 */ BUTTERFLY_10scale (X[0], X[0 + 1], X[32], X[32 + 1], Y[0], Y[0 + 1], Y[2], Y[2 + 1], 1.0 / (double) 32); BUTTERFLY_10scale (X[16], X[16 + 1], X[48], X[48 + 1], Y[4], Y[4 + 1], Y[6], Y[6 + 1], 1.0 / (double) 32); BUTTERFLY_10scale (X[8], X[8 + 1], X[40], X[40 + 1], Y[8], Y[8 + 1], Y[10], Y[10 + 1], 1.0 / (double) 32); BUTTERFLY_10scale (X[24], X[24 + 1], X[56], X[56 + 1], Y[12], Y[12 + 1], Y[14], Y[14 + 1], 1.0 / (double) 32); BUTTERFLY_10scale (X[4], X[4 + 1], X[36], X[36 + 1], Y[16], Y[16 + 1], Y[18], Y[18 + 1], 1.0 / (double) 32); BUTTERFLY_10scale (X[20], X[20 + 1], X[52], X[52 + 1], Y[20], Y[20 + 1], Y[22], Y[22 + 1], 1.0 / (double) 32); BUTTERFLY_10scale (X[12], X[12 + 1], X[44], X[44 + 1], Y[24], Y[24 + 1], Y[26], Y[26 + 1], 1.0 / (double) 32); BUTTERFLY_10scale (X[28], X[28 + 1], X[60], X[60 + 1], Y[28], Y[28 + 1], Y[30], Y[30 + 1], 1.0 / (double) 32); BUTTERFLY_10scale (X[2], X[2 + 1], X[34], X[34 + 1], Y[32], Y[32 + 1], Y[34], Y[34 + 1], 1.0 / (double) 32); BUTTERFLY_10scale (X[18], X[18 + 1], X[50], X[50 + 1], Y[36], Y[36 + 1], Y[38], Y[38 + 1], 1.0 / (double) 32); BUTTERFLY_10scale (X[10], X[10 + 1], X[42], X[42 + 1], Y[40], Y[40 + 1], Y[42], Y[42 + 1], 1.0 / (double) 32); BUTTERFLY_10scale (X[26], X[26 + 1], X[58], X[58 + 1], Y[44], Y[44 + 1], Y[46], Y[46 + 1], 1.0 / (double) 32); BUTTERFLY_10scale (X[6], X[6 + 1], X[38], X[38 + 1], Y[48], Y[48 + 1], Y[50], Y[50 + 1], 1.0 / (double) 32); BUTTERFLY_10scale (X[22], X[22 + 1], X[54], X[54 + 1], Y[52], Y[52 + 1], Y[54], Y[54 + 1], 1.0 / (double) 32); BUTTERFLY_10scale (X[14], X[14 + 1], X[46], X[46 + 1], Y[56], Y[56 + 1], Y[58], Y[58 + 1], 1.0 / (double) 32); BUTTERFLY_10scale (X[30], X[30 + 1], X[62], X[62 + 1], Y[60], Y[60 + 1], Y[62], Y[62 + 1], 1.0 / (double) 32); /* skipping 8 times fft4 */ /* skipping 4 times fft8 */ /* skipping 2 times fft16 */ /* perform 1 times fft32 */ gsl_power2_fft32synthesis_skip2 (X, Y); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 64 S R R R R F) **/ static void gsl_power2_fft64synthesis_skip2 (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* skipping 32 times fft2 */ /* perform 16 times fft4 */ for (block = 0; block < 128; block += 8) { BUTTERFLY_10 (Y[block + 0], /* W0 */ Y[block + 0 + 1], Y[block + 4], Y[block + 4 + 1], Y[block + 0], Y[block + 0 + 1], Y[block + 4], Y[block + 4 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_0m (Y[block + 2], /* W16 */ Y[block + 2 + 1], Y[block + 6], Y[block + 6 + 1], Y[block + 2], Y[block + 2 + 1], Y[block + 6], Y[block + 6 + 1], (double) +0.000000000000000, (double) -1.000000000000000); } /* perform 8 times fft8 */ for (block = 0; block < 128; block += 16) { BUTTERFLY_10 (Y[block + 0], /* W0 */ Y[block + 0 + 1], Y[block + 8], Y[block + 8 + 1], Y[block + 0], Y[block + 0 + 1], Y[block + 8], Y[block + 8 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_yY (Y[block + 2], /* W8 */ Y[block + 2 + 1], Y[block + 10], Y[block + 10 + 1], Y[block + 2], Y[block + 2 + 1], Y[block + 10], Y[block + 10 + 1], (double) +0.707106781186548, (double) -0.707106781186547); BUTTERFLY_0m (Y[block + 4], /* W16 */ Y[block + 4 + 1], Y[block + 12], Y[block + 12 + 1], Y[block + 4], Y[block + 4 + 1], Y[block + 12], Y[block + 12 + 1], (double) +0.000000000000000, (double) -1.000000000000000); BUTTERFLY_XX (Y[block + 6], /* W24 */ Y[block + 6 + 1], Y[block + 14], Y[block + 14 + 1], Y[block + 6], Y[block + 6 + 1], Y[block + 14], Y[block + 14 + 1], (double) -0.707106781186547, (double) -0.707106781186548); } /* perform 4 times fft16 */ for (block = 0; block < 128; block += 32) { BUTTERFLY_10 (Y[block + 0], /* W0 */ Y[block + 0 + 1], Y[block + 16], Y[block + 16 + 1], Y[block + 0], Y[block + 0 + 1], Y[block + 16], Y[block + 16 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_XY (Y[block + 2], /* W4 */ Y[block + 2 + 1], Y[block + 18], Y[block + 18 + 1], Y[block + 2], Y[block + 2 + 1], Y[block + 18], Y[block + 18 + 1], (double) +0.923879532511287, (double) -0.382683432365090); BUTTERFLY_yY (Y[block + 4], /* W8 */ Y[block + 4 + 1], Y[block + 20], Y[block + 20 + 1], Y[block + 4], Y[block + 4 + 1], Y[block + 20], Y[block + 20 + 1], (double) +0.707106781186548, (double) -0.707106781186547); BUTTERFLY_XY (Y[block + 6], /* W12 */ Y[block + 6 + 1], Y[block + 22], Y[block + 22 + 1], Y[block + 6], Y[block + 6 + 1], Y[block + 22], Y[block + 22 + 1], (double) +0.382683432365090, (double) -0.923879532511287); BUTTERFLY_0m (Y[block + 8], /* W16 */ Y[block + 8 + 1], Y[block + 24], Y[block + 24 + 1], Y[block + 8], Y[block + 8 + 1], Y[block + 24], Y[block + 24 + 1], (double) +0.000000000000000, (double) -1.000000000000000); BUTTERFLY_XY (Y[block + 10], /* W20 */ Y[block + 10 + 1], Y[block + 26], Y[block + 26 + 1], Y[block + 10], Y[block + 10 + 1], Y[block + 26], Y[block + 26 + 1], (double) -0.382683432365090, (double) -0.923879532511287); BUTTERFLY_XX (Y[block + 12], /* W24 */ Y[block + 12 + 1], Y[block + 28], Y[block + 28 + 1], Y[block + 12], Y[block + 12 + 1], Y[block + 28], Y[block + 28 + 1], (double) -0.707106781186547, (double) -0.707106781186548); BUTTERFLY_XY (Y[block + 14], /* W28 */ Y[block + 14 + 1], Y[block + 30], Y[block + 30 + 1], Y[block + 14], Y[block + 14 + 1], Y[block + 30], Y[block + 30 + 1], (double) -0.923879532511287, (double) -0.382683432365090); } /* perform 2 times fft32 */ for (block = 0; block < 128; block += 64) { BUTTERFLY_10 (Y[block + 0], /* W0 */ Y[block + 0 + 1], Y[block + 32], Y[block + 32 + 1], Y[block + 0], Y[block + 0 + 1], Y[block + 32], Y[block + 32 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_XY (Y[block + 2], /* W2 */ Y[block + 2 + 1], Y[block + 34], Y[block + 34 + 1], Y[block + 2], Y[block + 2 + 1], Y[block + 34], Y[block + 34 + 1], (double) +0.980785280403230, (double) -0.195090322016128); BUTTERFLY_XY (Y[block + 4], /* W4 */ Y[block + 4 + 1], Y[block + 36], Y[block + 36 + 1], Y[block + 4], Y[block + 4 + 1], Y[block + 36], Y[block + 36 + 1], (double) +0.923879532511287, (double) -0.382683432365090); BUTTERFLY_XY (Y[block + 6], /* W6 */ Y[block + 6 + 1], Y[block + 38], Y[block + 38 + 1], Y[block + 6], Y[block + 6 + 1], Y[block + 38], Y[block + 38 + 1], (double) +0.831469612302545, (double) -0.555570233019602); BUTTERFLY_yY (Y[block + 8], /* W8 */ Y[block + 8 + 1], Y[block + 40], Y[block + 40 + 1], Y[block + 8], Y[block + 8 + 1], Y[block + 40], Y[block + 40 + 1], (double) +0.707106781186548, (double) -0.707106781186547); BUTTERFLY_XY (Y[block + 10], /* W10 */ Y[block + 10 + 1], Y[block + 42], Y[block + 42 + 1], Y[block + 10], Y[block + 10 + 1], Y[block + 42], Y[block + 42 + 1], (double) +0.555570233019602, (double) -0.831469612302545); BUTTERFLY_XY (Y[block + 12], /* W12 */ Y[block + 12 + 1], Y[block + 44], Y[block + 44 + 1], Y[block + 12], Y[block + 12 + 1], Y[block + 44], Y[block + 44 + 1], (double) +0.382683432365090, (double) -0.923879532511287); BUTTERFLY_XY (Y[block + 14], /* W14 */ Y[block + 14 + 1], Y[block + 46], Y[block + 46 + 1], Y[block + 14], Y[block + 14 + 1], Y[block + 46], Y[block + 46 + 1], (double) +0.195090322016128, (double) -0.980785280403230); BUTTERFLY_0m (Y[block + 16], /* W16 */ Y[block + 16 + 1], Y[block + 48], Y[block + 48 + 1], Y[block + 16], Y[block + 16 + 1], Y[block + 48], Y[block + 48 + 1], (double) +0.000000000000000, (double) -1.000000000000000); BUTTERFLY_XY (Y[block + 18], /* W18 */ Y[block + 18 + 1], Y[block + 50], Y[block + 50 + 1], Y[block + 18], Y[block + 18 + 1], Y[block + 50], Y[block + 50 + 1], (double) -0.195090322016128, (double) -0.980785280403230); BUTTERFLY_XY (Y[block + 20], /* W20 */ Y[block + 20 + 1], Y[block + 52], Y[block + 52 + 1], Y[block + 20], Y[block + 20 + 1], Y[block + 52], Y[block + 52 + 1], (double) -0.382683432365090, (double) -0.923879532511287); BUTTERFLY_XY (Y[block + 22], /* W22 */ Y[block + 22 + 1], Y[block + 54], Y[block + 54 + 1], Y[block + 22], Y[block + 22 + 1], Y[block + 54], Y[block + 54 + 1], (double) -0.555570233019602, (double) -0.831469612302545); BUTTERFLY_XX (Y[block + 24], /* W24 */ Y[block + 24 + 1], Y[block + 56], Y[block + 56 + 1], Y[block + 24], Y[block + 24 + 1], Y[block + 56], Y[block + 56 + 1], (double) -0.707106781186547, (double) -0.707106781186548); BUTTERFLY_XY (Y[block + 26], /* W26 */ Y[block + 26 + 1], Y[block + 58], Y[block + 58 + 1], Y[block + 26], Y[block + 26 + 1], Y[block + 58], Y[block + 58 + 1], (double) -0.831469612302545, (double) -0.555570233019602); BUTTERFLY_XY (Y[block + 28], /* W28 */ Y[block + 28 + 1], Y[block + 60], Y[block + 60 + 1], Y[block + 28], Y[block + 28 + 1], Y[block + 60], Y[block + 60 + 1], (double) -0.923879532511287, (double) -0.382683432365090); BUTTERFLY_XY (Y[block + 30], /* W30 */ Y[block + 30 + 1], Y[block + 62], Y[block + 62 + 1], Y[block + 30], Y[block + 30 + 1], Y[block + 62], Y[block + 62 + 1], (double) -0.980785280403230, (double) -0.195090322016129); } /* perform 1 times fft64 */ BUTTERFLY_10 (Y[0], /* W0 */ Y[0 + 1], Y[64], Y[64 + 1], Y[0], Y[0 + 1], Y[64], Y[64 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_XY (Y[2], /* W1 */ Y[2 + 1], Y[66], Y[66 + 1], Y[2], Y[2 + 1], Y[66], Y[66 + 1], (double) +0.995184726672197, (double) -0.098017140329561); BUTTERFLY_XY (Y[4], /* W2 */ Y[4 + 1], Y[68], Y[68 + 1], Y[4], Y[4 + 1], Y[68], Y[68 + 1], (double) +0.980785280403230, (double) -0.195090322016128); BUTTERFLY_XY (Y[6], /* W3 */ Y[6 + 1], Y[70], Y[70 + 1], Y[6], Y[6 + 1], Y[70], Y[70 + 1], (double) +0.956940335732209, (double) -0.290284677254462); BUTTERFLY_XY (Y[8], /* W4 */ Y[8 + 1], Y[72], Y[72 + 1], Y[8], Y[8 + 1], Y[72], Y[72 + 1], (double) +0.923879532511287, (double) -0.382683432365090); BUTTERFLY_XY (Y[10], /* W5 */ Y[10 + 1], Y[74], Y[74 + 1], Y[10], Y[10 + 1], Y[74], Y[74 + 1], (double) +0.881921264348355, (double) -0.471396736825998); BUTTERFLY_XY (Y[12], /* W6 */ Y[12 + 1], Y[76], Y[76 + 1], Y[12], Y[12 + 1], Y[76], Y[76 + 1], (double) +0.831469612302545, (double) -0.555570233019602); BUTTERFLY_XY (Y[14], /* W7 */ Y[14 + 1], Y[78], Y[78 + 1], Y[14], Y[14 + 1], Y[78], Y[78 + 1], (double) +0.773010453362737, (double) -0.634393284163645); BUTTERFLY_yY (Y[16], /* W8 */ Y[16 + 1], Y[80], Y[80 + 1], Y[16], Y[16 + 1], Y[80], Y[80 + 1], (double) +0.707106781186548, (double) -0.707106781186547); BUTTERFLY_XY (Y[18], /* W9 */ Y[18 + 1], Y[82], Y[82 + 1], Y[18], Y[18 + 1], Y[82], Y[82 + 1], (double) +0.634393284163645, (double) -0.773010453362737); BUTTERFLY_XY (Y[20], /* W10 */ Y[20 + 1], Y[84], Y[84 + 1], Y[20], Y[20 + 1], Y[84], Y[84 + 1], (double) +0.555570233019602, (double) -0.831469612302545); BUTTERFLY_XY (Y[22], /* W11 */ Y[22 + 1], Y[86], Y[86 + 1], Y[22], Y[22 + 1], Y[86], Y[86 + 1], (double) +0.471396736825998, (double) -0.881921264348355); BUTTERFLY_XY (Y[24], /* W12 */ Y[24 + 1], Y[88], Y[88 + 1], Y[24], Y[24 + 1], Y[88], Y[88 + 1], (double) +0.382683432365090, (double) -0.923879532511287); BUTTERFLY_XY (Y[26], /* W13 */ Y[26 + 1], Y[90], Y[90 + 1], Y[26], Y[26 + 1], Y[90], Y[90 + 1], (double) +0.290284677254462, (double) -0.956940335732209); BUTTERFLY_XY (Y[28], /* W14 */ Y[28 + 1], Y[92], Y[92 + 1], Y[28], Y[28 + 1], Y[92], Y[92 + 1], (double) +0.195090322016128, (double) -0.980785280403230); BUTTERFLY_XY (Y[30], /* W15 */ Y[30 + 1], Y[94], Y[94 + 1], Y[30], Y[30 + 1], Y[94], Y[94 + 1], (double) +0.098017140329561, (double) -0.995184726672197); BUTTERFLY_0m (Y[32], /* W16 */ Y[32 + 1], Y[96], Y[96 + 1], Y[32], Y[32 + 1], Y[96], Y[96 + 1], (double) +0.000000000000000, (double) -1.000000000000000); BUTTERFLY_XY (Y[34], /* W17 */ Y[34 + 1], Y[98], Y[98 + 1], Y[34], Y[34 + 1], Y[98], Y[98 + 1], (double) -0.098017140329561, (double) -0.995184726672197); BUTTERFLY_XY (Y[36], /* W18 */ Y[36 + 1], Y[100], Y[100 + 1], Y[36], Y[36 + 1], Y[100], Y[100 + 1], (double) -0.195090322016128, (double) -0.980785280403230); BUTTERFLY_XY (Y[38], /* W19 */ Y[38 + 1], Y[102], Y[102 + 1], Y[38], Y[38 + 1], Y[102], Y[102 + 1], (double) -0.290284677254462, (double) -0.956940335732209); BUTTERFLY_XY (Y[40], /* W20 */ Y[40 + 1], Y[104], Y[104 + 1], Y[40], Y[40 + 1], Y[104], Y[104 + 1], (double) -0.382683432365090, (double) -0.923879532511287); BUTTERFLY_XY (Y[42], /* W21 */ Y[42 + 1], Y[106], Y[106 + 1], Y[42], Y[42 + 1], Y[106], Y[106 + 1], (double) -0.471396736825998, (double) -0.881921264348355); BUTTERFLY_XY (Y[44], /* W22 */ Y[44 + 1], Y[108], Y[108 + 1], Y[44], Y[44 + 1], Y[108], Y[108 + 1], (double) -0.555570233019602, (double) -0.831469612302545); BUTTERFLY_XY (Y[46], /* W23 */ Y[46 + 1], Y[110], Y[110 + 1], Y[46], Y[46 + 1], Y[110], Y[110 + 1], (double) -0.634393284163645, (double) -0.773010453362737); BUTTERFLY_XX (Y[48], /* W24 */ Y[48 + 1], Y[112], Y[112 + 1], Y[48], Y[48 + 1], Y[112], Y[112 + 1], (double) -0.707106781186547, (double) -0.707106781186548); BUTTERFLY_XY (Y[50], /* W25 */ Y[50 + 1], Y[114], Y[114 + 1], Y[50], Y[50 + 1], Y[114], Y[114 + 1], (double) -0.773010453362737, (double) -0.634393284163645); BUTTERFLY_XY (Y[52], /* W26 */ Y[52 + 1], Y[116], Y[116 + 1], Y[52], Y[52 + 1], Y[116], Y[116 + 1], (double) -0.831469612302545, (double) -0.555570233019602); BUTTERFLY_XY (Y[54], /* W27 */ Y[54 + 1], Y[118], Y[118 + 1], Y[54], Y[54 + 1], Y[118], Y[118 + 1], (double) -0.881921264348355, (double) -0.471396736825998); BUTTERFLY_XY (Y[56], /* W28 */ Y[56 + 1], Y[120], Y[120 + 1], Y[56], Y[56 + 1], Y[120], Y[120 + 1], (double) -0.923879532511287, (double) -0.382683432365090); BUTTERFLY_XY (Y[58], /* W29 */ Y[58 + 1], Y[122], Y[122 + 1], Y[58], Y[58 + 1], Y[122], Y[122 + 1], (double) -0.956940335732209, (double) -0.290284677254462); BUTTERFLY_XY (Y[60], /* W30 */ Y[60 + 1], Y[124], Y[124 + 1], Y[60], Y[60 + 1], Y[124], Y[124 + 1], (double) -0.980785280403230, (double) -0.195090322016129); BUTTERFLY_XY (Y[62], /* W31 */ Y[62 + 1], Y[126], Y[126 + 1], Y[62], Y[62 + 1], Y[126], Y[126 + 1], (double) -0.995184726672197, (double) -0.098017140329561); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 64 F S S S S X) **/ static void gsl_power2_fft64synthesis (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* perform 32 times fft2 */ BUTTERFLY_10scale (X[0], X[0 + 1], X[64], X[64 + 1], Y[0], Y[0 + 1], Y[2], Y[2 + 1], 1.0 / (double) 64); BUTTERFLY_10scale (X[32], X[32 + 1], X[96], X[96 + 1], Y[4], Y[4 + 1], Y[6], Y[6 + 1], 1.0 / (double) 64); BUTTERFLY_10scale (X[16], X[16 + 1], X[80], X[80 + 1], Y[8], Y[8 + 1], Y[10], Y[10 + 1], 1.0 / (double) 64); BUTTERFLY_10scale (X[48], X[48 + 1], X[112], X[112 + 1], Y[12], Y[12 + 1], Y[14], Y[14 + 1], 1.0 / (double) 64); BUTTERFLY_10scale (X[8], X[8 + 1], X[72], X[72 + 1], Y[16], Y[16 + 1], Y[18], Y[18 + 1], 1.0 / (double) 64); BUTTERFLY_10scale (X[40], X[40 + 1], X[104], X[104 + 1], Y[20], Y[20 + 1], Y[22], Y[22 + 1], 1.0 / (double) 64); BUTTERFLY_10scale (X[24], X[24 + 1], X[88], X[88 + 1], Y[24], Y[24 + 1], Y[26], Y[26 + 1], 1.0 / (double) 64); BUTTERFLY_10scale (X[56], X[56 + 1], X[120], X[120 + 1], Y[28], Y[28 + 1], Y[30], Y[30 + 1], 1.0 / (double) 64); BUTTERFLY_10scale (X[4], X[4 + 1], X[68], X[68 + 1], Y[32], Y[32 + 1], Y[34], Y[34 + 1], 1.0 / (double) 64); BUTTERFLY_10scale (X[36], X[36 + 1], X[100], X[100 + 1], Y[36], Y[36 + 1], Y[38], Y[38 + 1], 1.0 / (double) 64); BUTTERFLY_10scale (X[20], X[20 + 1], X[84], X[84 + 1], Y[40], Y[40 + 1], Y[42], Y[42 + 1], 1.0 / (double) 64); BUTTERFLY_10scale (X[52], X[52 + 1], X[116], X[116 + 1], Y[44], Y[44 + 1], Y[46], Y[46 + 1], 1.0 / (double) 64); BUTTERFLY_10scale (X[12], X[12 + 1], X[76], X[76 + 1], Y[48], Y[48 + 1], Y[50], Y[50 + 1], 1.0 / (double) 64); BUTTERFLY_10scale (X[44], X[44 + 1], X[108], X[108 + 1], Y[52], Y[52 + 1], Y[54], Y[54 + 1], 1.0 / (double) 64); BUTTERFLY_10scale (X[28], X[28 + 1], X[92], X[92 + 1], Y[56], Y[56 + 1], Y[58], Y[58 + 1], 1.0 / (double) 64); BUTTERFLY_10scale (X[60], X[60 + 1], X[124], X[124 + 1], Y[60], Y[60 + 1], Y[62], Y[62 + 1], 1.0 / (double) 64); BUTTERFLY_10scale (X[2], X[2 + 1], X[66], X[66 + 1], Y[64], Y[64 + 1], Y[66], Y[66 + 1], 1.0 / (double) 64); BUTTERFLY_10scale (X[34], X[34 + 1], X[98], X[98 + 1], Y[68], Y[68 + 1], Y[70], Y[70 + 1], 1.0 / (double) 64); BUTTERFLY_10scale (X[18], X[18 + 1], X[82], X[82 + 1], Y[72], Y[72 + 1], Y[74], Y[74 + 1], 1.0 / (double) 64); BUTTERFLY_10scale (X[50], X[50 + 1], X[114], X[114 + 1], Y[76], Y[76 + 1], Y[78], Y[78 + 1], 1.0 / (double) 64); BUTTERFLY_10scale (X[10], X[10 + 1], X[74], X[74 + 1], Y[80], Y[80 + 1], Y[82], Y[82 + 1], 1.0 / (double) 64); BUTTERFLY_10scale (X[42], X[42 + 1], X[106], X[106 + 1], Y[84], Y[84 + 1], Y[86], Y[86 + 1], 1.0 / (double) 64); BUTTERFLY_10scale (X[26], X[26 + 1], X[90], X[90 + 1], Y[88], Y[88 + 1], Y[90], Y[90 + 1], 1.0 / (double) 64); BUTTERFLY_10scale (X[58], X[58 + 1], X[122], X[122 + 1], Y[92], Y[92 + 1], Y[94], Y[94 + 1], 1.0 / (double) 64); BUTTERFLY_10scale (X[6], X[6 + 1], X[70], X[70 + 1], Y[96], Y[96 + 1], Y[98], Y[98 + 1], 1.0 / (double) 64); BUTTERFLY_10scale (X[38], X[38 + 1], X[102], X[102 + 1], Y[100], Y[100 + 1], Y[102], Y[102 + 1], 1.0 / (double) 64); BUTTERFLY_10scale (X[22], X[22 + 1], X[86], X[86 + 1], Y[104], Y[104 + 1], Y[106], Y[106 + 1], 1.0 / (double) 64); BUTTERFLY_10scale (X[54], X[54 + 1], X[118], X[118 + 1], Y[108], Y[108 + 1], Y[110], Y[110 + 1], 1.0 / (double) 64); BUTTERFLY_10scale (X[14], X[14 + 1], X[78], X[78 + 1], Y[112], Y[112 + 1], Y[114], Y[114 + 1], 1.0 / (double) 64); BUTTERFLY_10scale (X[46], X[46 + 1], X[110], X[110 + 1], Y[116], Y[116 + 1], Y[118], Y[118 + 1], 1.0 / (double) 64); BUTTERFLY_10scale (X[30], X[30 + 1], X[94], X[94 + 1], Y[120], Y[120 + 1], Y[122], Y[122 + 1], 1.0 / (double) 64); BUTTERFLY_10scale (X[62], X[62 + 1], X[126], X[126 + 1], Y[124], Y[124 + 1], Y[126], Y[126 + 1], 1.0 / (double) 64); /* skipping 16 times fft4 */ /* skipping 8 times fft8 */ /* skipping 4 times fft16 */ /* skipping 2 times fft32 */ /* perform 1 times fft64 */ gsl_power2_fft64synthesis_skip2 (X, Y); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 128 S R R R R R F) **/ static void gsl_power2_fft128synthesis_skip2 (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* skipping 64 times fft2 */ /* perform 32 times fft4 */ for (block = 0; block < 256; block += 8) { BUTTERFLY_10 (Y[block + 0], /* W0 */ Y[block + 0 + 1], Y[block + 4], Y[block + 4 + 1], Y[block + 0], Y[block + 0 + 1], Y[block + 4], Y[block + 4 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_0m (Y[block + 2], /* W32 */ Y[block + 2 + 1], Y[block + 6], Y[block + 6 + 1], Y[block + 2], Y[block + 2 + 1], Y[block + 6], Y[block + 6 + 1], (double) +0.000000000000000, (double) -1.000000000000000); } /* perform 16 times fft8 */ for (block = 0; block < 256; block += 16) { BUTTERFLY_10 (Y[block + 0], /* W0 */ Y[block + 0 + 1], Y[block + 8], Y[block + 8 + 1], Y[block + 0], Y[block + 0 + 1], Y[block + 8], Y[block + 8 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_yY (Y[block + 2], /* W16 */ Y[block + 2 + 1], Y[block + 10], Y[block + 10 + 1], Y[block + 2], Y[block + 2 + 1], Y[block + 10], Y[block + 10 + 1], (double) +0.707106781186548, (double) -0.707106781186547); BUTTERFLY_0m (Y[block + 4], /* W32 */ Y[block + 4 + 1], Y[block + 12], Y[block + 12 + 1], Y[block + 4], Y[block + 4 + 1], Y[block + 12], Y[block + 12 + 1], (double) +0.000000000000000, (double) -1.000000000000000); BUTTERFLY_XX (Y[block + 6], /* W48 */ Y[block + 6 + 1], Y[block + 14], Y[block + 14 + 1], Y[block + 6], Y[block + 6 + 1], Y[block + 14], Y[block + 14 + 1], (double) -0.707106781186547, (double) -0.707106781186548); } /* perform 8 times fft16 */ for (block = 0; block < 256; block += 32) { BUTTERFLY_10 (Y[block + 0], /* W0 */ Y[block + 0 + 1], Y[block + 16], Y[block + 16 + 1], Y[block + 0], Y[block + 0 + 1], Y[block + 16], Y[block + 16 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_XY (Y[block + 2], /* W8 */ Y[block + 2 + 1], Y[block + 18], Y[block + 18 + 1], Y[block + 2], Y[block + 2 + 1], Y[block + 18], Y[block + 18 + 1], (double) +0.923879532511287, (double) -0.382683432365090); BUTTERFLY_yY (Y[block + 4], /* W16 */ Y[block + 4 + 1], Y[block + 20], Y[block + 20 + 1], Y[block + 4], Y[block + 4 + 1], Y[block + 20], Y[block + 20 + 1], (double) +0.707106781186548, (double) -0.707106781186547); BUTTERFLY_XY (Y[block + 6], /* W24 */ Y[block + 6 + 1], Y[block + 22], Y[block + 22 + 1], Y[block + 6], Y[block + 6 + 1], Y[block + 22], Y[block + 22 + 1], (double) +0.382683432365090, (double) -0.923879532511287); BUTTERFLY_0m (Y[block + 8], /* W32 */ Y[block + 8 + 1], Y[block + 24], Y[block + 24 + 1], Y[block + 8], Y[block + 8 + 1], Y[block + 24], Y[block + 24 + 1], (double) +0.000000000000000, (double) -1.000000000000000); BUTTERFLY_XY (Y[block + 10], /* W40 */ Y[block + 10 + 1], Y[block + 26], Y[block + 26 + 1], Y[block + 10], Y[block + 10 + 1], Y[block + 26], Y[block + 26 + 1], (double) -0.382683432365090, (double) -0.923879532511287); BUTTERFLY_XX (Y[block + 12], /* W48 */ Y[block + 12 + 1], Y[block + 28], Y[block + 28 + 1], Y[block + 12], Y[block + 12 + 1], Y[block + 28], Y[block + 28 + 1], (double) -0.707106781186547, (double) -0.707106781186548); BUTTERFLY_XY (Y[block + 14], /* W56 */ Y[block + 14 + 1], Y[block + 30], Y[block + 30 + 1], Y[block + 14], Y[block + 14 + 1], Y[block + 30], Y[block + 30 + 1], (double) -0.923879532511287, (double) -0.382683432365090); } /* perform 4 times fft32 */ for (block = 0; block < 256; block += 64) { BUTTERFLY_10 (Y[block + 0], /* W0 */ Y[block + 0 + 1], Y[block + 32], Y[block + 32 + 1], Y[block + 0], Y[block + 0 + 1], Y[block + 32], Y[block + 32 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_XY (Y[block + 2], /* W4 */ Y[block + 2 + 1], Y[block + 34], Y[block + 34 + 1], Y[block + 2], Y[block + 2 + 1], Y[block + 34], Y[block + 34 + 1], (double) +0.980785280403230, (double) -0.195090322016128); BUTTERFLY_XY (Y[block + 4], /* W8 */ Y[block + 4 + 1], Y[block + 36], Y[block + 36 + 1], Y[block + 4], Y[block + 4 + 1], Y[block + 36], Y[block + 36 + 1], (double) +0.923879532511287, (double) -0.382683432365090); BUTTERFLY_XY (Y[block + 6], /* W12 */ Y[block + 6 + 1], Y[block + 38], Y[block + 38 + 1], Y[block + 6], Y[block + 6 + 1], Y[block + 38], Y[block + 38 + 1], (double) +0.831469612302545, (double) -0.555570233019602); BUTTERFLY_yY (Y[block + 8], /* W16 */ Y[block + 8 + 1], Y[block + 40], Y[block + 40 + 1], Y[block + 8], Y[block + 8 + 1], Y[block + 40], Y[block + 40 + 1], (double) +0.707106781186548, (double) -0.707106781186547); BUTTERFLY_XY (Y[block + 10], /* W20 */ Y[block + 10 + 1], Y[block + 42], Y[block + 42 + 1], Y[block + 10], Y[block + 10 + 1], Y[block + 42], Y[block + 42 + 1], (double) +0.555570233019602, (double) -0.831469612302545); BUTTERFLY_XY (Y[block + 12], /* W24 */ Y[block + 12 + 1], Y[block + 44], Y[block + 44 + 1], Y[block + 12], Y[block + 12 + 1], Y[block + 44], Y[block + 44 + 1], (double) +0.382683432365090, (double) -0.923879532511287); BUTTERFLY_XY (Y[block + 14], /* W28 */ Y[block + 14 + 1], Y[block + 46], Y[block + 46 + 1], Y[block + 14], Y[block + 14 + 1], Y[block + 46], Y[block + 46 + 1], (double) +0.195090322016128, (double) -0.980785280403230); BUTTERFLY_0m (Y[block + 16], /* W32 */ Y[block + 16 + 1], Y[block + 48], Y[block + 48 + 1], Y[block + 16], Y[block + 16 + 1], Y[block + 48], Y[block + 48 + 1], (double) +0.000000000000000, (double) -1.000000000000000); BUTTERFLY_XY (Y[block + 18], /* W36 */ Y[block + 18 + 1], Y[block + 50], Y[block + 50 + 1], Y[block + 18], Y[block + 18 + 1], Y[block + 50], Y[block + 50 + 1], (double) -0.195090322016128, (double) -0.980785280403230); BUTTERFLY_XY (Y[block + 20], /* W40 */ Y[block + 20 + 1], Y[block + 52], Y[block + 52 + 1], Y[block + 20], Y[block + 20 + 1], Y[block + 52], Y[block + 52 + 1], (double) -0.382683432365090, (double) -0.923879532511287); BUTTERFLY_XY (Y[block + 22], /* W44 */ Y[block + 22 + 1], Y[block + 54], Y[block + 54 + 1], Y[block + 22], Y[block + 22 + 1], Y[block + 54], Y[block + 54 + 1], (double) -0.555570233019602, (double) -0.831469612302545); BUTTERFLY_XX (Y[block + 24], /* W48 */ Y[block + 24 + 1], Y[block + 56], Y[block + 56 + 1], Y[block + 24], Y[block + 24 + 1], Y[block + 56], Y[block + 56 + 1], (double) -0.707106781186547, (double) -0.707106781186548); BUTTERFLY_XY (Y[block + 26], /* W52 */ Y[block + 26 + 1], Y[block + 58], Y[block + 58 + 1], Y[block + 26], Y[block + 26 + 1], Y[block + 58], Y[block + 58 + 1], (double) -0.831469612302545, (double) -0.555570233019602); BUTTERFLY_XY (Y[block + 28], /* W56 */ Y[block + 28 + 1], Y[block + 60], Y[block + 60 + 1], Y[block + 28], Y[block + 28 + 1], Y[block + 60], Y[block + 60 + 1], (double) -0.923879532511287, (double) -0.382683432365090); BUTTERFLY_XY (Y[block + 30], /* W60 */ Y[block + 30 + 1], Y[block + 62], Y[block + 62 + 1], Y[block + 30], Y[block + 30 + 1], Y[block + 62], Y[block + 62 + 1], (double) -0.980785280403230, (double) -0.195090322016129); } /* perform 2 times fft64 */ for (block = 0; block < 256; block += 128) { BUTTERFLY_10 (Y[block + 0], /* W0 */ Y[block + 0 + 1], Y[block + 64], Y[block + 64 + 1], Y[block + 0], Y[block + 0 + 1], Y[block + 64], Y[block + 64 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_XY (Y[block + 2], /* W2 */ Y[block + 2 + 1], Y[block + 66], Y[block + 66 + 1], Y[block + 2], Y[block + 2 + 1], Y[block + 66], Y[block + 66 + 1], (double) +0.995184726672197, (double) -0.098017140329561); BUTTERFLY_XY (Y[block + 4], /* W4 */ Y[block + 4 + 1], Y[block + 68], Y[block + 68 + 1], Y[block + 4], Y[block + 4 + 1], Y[block + 68], Y[block + 68 + 1], (double) +0.980785280403230, (double) -0.195090322016128); BUTTERFLY_XY (Y[block + 6], /* W6 */ Y[block + 6 + 1], Y[block + 70], Y[block + 70 + 1], Y[block + 6], Y[block + 6 + 1], Y[block + 70], Y[block + 70 + 1], (double) +0.956940335732209, (double) -0.290284677254462); BUTTERFLY_XY (Y[block + 8], /* W8 */ Y[block + 8 + 1], Y[block + 72], Y[block + 72 + 1], Y[block + 8], Y[block + 8 + 1], Y[block + 72], Y[block + 72 + 1], (double) +0.923879532511287, (double) -0.382683432365090); BUTTERFLY_XY (Y[block + 10], /* W10 */ Y[block + 10 + 1], Y[block + 74], Y[block + 74 + 1], Y[block + 10], Y[block + 10 + 1], Y[block + 74], Y[block + 74 + 1], (double) +0.881921264348355, (double) -0.471396736825998); BUTTERFLY_XY (Y[block + 12], /* W12 */ Y[block + 12 + 1], Y[block + 76], Y[block + 76 + 1], Y[block + 12], Y[block + 12 + 1], Y[block + 76], Y[block + 76 + 1], (double) +0.831469612302545, (double) -0.555570233019602); BUTTERFLY_XY (Y[block + 14], /* W14 */ Y[block + 14 + 1], Y[block + 78], Y[block + 78 + 1], Y[block + 14], Y[block + 14 + 1], Y[block + 78], Y[block + 78 + 1], (double) +0.773010453362737, (double) -0.634393284163645); BUTTERFLY_yY (Y[block + 16], /* W16 */ Y[block + 16 + 1], Y[block + 80], Y[block + 80 + 1], Y[block + 16], Y[block + 16 + 1], Y[block + 80], Y[block + 80 + 1], (double) +0.707106781186548, (double) -0.707106781186547); BUTTERFLY_XY (Y[block + 18], /* W18 */ Y[block + 18 + 1], Y[block + 82], Y[block + 82 + 1], Y[block + 18], Y[block + 18 + 1], Y[block + 82], Y[block + 82 + 1], (double) +0.634393284163645, (double) -0.773010453362737); BUTTERFLY_XY (Y[block + 20], /* W20 */ Y[block + 20 + 1], Y[block + 84], Y[block + 84 + 1], Y[block + 20], Y[block + 20 + 1], Y[block + 84], Y[block + 84 + 1], (double) +0.555570233019602, (double) -0.831469612302545); BUTTERFLY_XY (Y[block + 22], /* W22 */ Y[block + 22 + 1], Y[block + 86], Y[block + 86 + 1], Y[block + 22], Y[block + 22 + 1], Y[block + 86], Y[block + 86 + 1], (double) +0.471396736825998, (double) -0.881921264348355); BUTTERFLY_XY (Y[block + 24], /* W24 */ Y[block + 24 + 1], Y[block + 88], Y[block + 88 + 1], Y[block + 24], Y[block + 24 + 1], Y[block + 88], Y[block + 88 + 1], (double) +0.382683432365090, (double) -0.923879532511287); BUTTERFLY_XY (Y[block + 26], /* W26 */ Y[block + 26 + 1], Y[block + 90], Y[block + 90 + 1], Y[block + 26], Y[block + 26 + 1], Y[block + 90], Y[block + 90 + 1], (double) +0.290284677254462, (double) -0.956940335732209); BUTTERFLY_XY (Y[block + 28], /* W28 */ Y[block + 28 + 1], Y[block + 92], Y[block + 92 + 1], Y[block + 28], Y[block + 28 + 1], Y[block + 92], Y[block + 92 + 1], (double) +0.195090322016128, (double) -0.980785280403230); BUTTERFLY_XY (Y[block + 30], /* W30 */ Y[block + 30 + 1], Y[block + 94], Y[block + 94 + 1], Y[block + 30], Y[block + 30 + 1], Y[block + 94], Y[block + 94 + 1], (double) +0.098017140329561, (double) -0.995184726672197); BUTTERFLY_0m (Y[block + 32], /* W32 */ Y[block + 32 + 1], Y[block + 96], Y[block + 96 + 1], Y[block + 32], Y[block + 32 + 1], Y[block + 96], Y[block + 96 + 1], (double) +0.000000000000000, (double) -1.000000000000000); BUTTERFLY_XY (Y[block + 34], /* W34 */ Y[block + 34 + 1], Y[block + 98], Y[block + 98 + 1], Y[block + 34], Y[block + 34 + 1], Y[block + 98], Y[block + 98 + 1], (double) -0.098017140329561, (double) -0.995184726672197); BUTTERFLY_XY (Y[block + 36], /* W36 */ Y[block + 36 + 1], Y[block + 100], Y[block + 100 + 1], Y[block + 36], Y[block + 36 + 1], Y[block + 100], Y[block + 100 + 1], (double) -0.195090322016128, (double) -0.980785280403230); BUTTERFLY_XY (Y[block + 38], /* W38 */ Y[block + 38 + 1], Y[block + 102], Y[block + 102 + 1], Y[block + 38], Y[block + 38 + 1], Y[block + 102], Y[block + 102 + 1], (double) -0.290284677254462, (double) -0.956940335732209); BUTTERFLY_XY (Y[block + 40], /* W40 */ Y[block + 40 + 1], Y[block + 104], Y[block + 104 + 1], Y[block + 40], Y[block + 40 + 1], Y[block + 104], Y[block + 104 + 1], (double) -0.382683432365090, (double) -0.923879532511287); BUTTERFLY_XY (Y[block + 42], /* W42 */ Y[block + 42 + 1], Y[block + 106], Y[block + 106 + 1], Y[block + 42], Y[block + 42 + 1], Y[block + 106], Y[block + 106 + 1], (double) -0.471396736825998, (double) -0.881921264348355); BUTTERFLY_XY (Y[block + 44], /* W44 */ Y[block + 44 + 1], Y[block + 108], Y[block + 108 + 1], Y[block + 44], Y[block + 44 + 1], Y[block + 108], Y[block + 108 + 1], (double) -0.555570233019602, (double) -0.831469612302545); BUTTERFLY_XY (Y[block + 46], /* W46 */ Y[block + 46 + 1], Y[block + 110], Y[block + 110 + 1], Y[block + 46], Y[block + 46 + 1], Y[block + 110], Y[block + 110 + 1], (double) -0.634393284163645, (double) -0.773010453362737); BUTTERFLY_XX (Y[block + 48], /* W48 */ Y[block + 48 + 1], Y[block + 112], Y[block + 112 + 1], Y[block + 48], Y[block + 48 + 1], Y[block + 112], Y[block + 112 + 1], (double) -0.707106781186547, (double) -0.707106781186548); BUTTERFLY_XY (Y[block + 50], /* W50 */ Y[block + 50 + 1], Y[block + 114], Y[block + 114 + 1], Y[block + 50], Y[block + 50 + 1], Y[block + 114], Y[block + 114 + 1], (double) -0.773010453362737, (double) -0.634393284163645); BUTTERFLY_XY (Y[block + 52], /* W52 */ Y[block + 52 + 1], Y[block + 116], Y[block + 116 + 1], Y[block + 52], Y[block + 52 + 1], Y[block + 116], Y[block + 116 + 1], (double) -0.831469612302545, (double) -0.555570233019602); BUTTERFLY_XY (Y[block + 54], /* W54 */ Y[block + 54 + 1], Y[block + 118], Y[block + 118 + 1], Y[block + 54], Y[block + 54 + 1], Y[block + 118], Y[block + 118 + 1], (double) -0.881921264348355, (double) -0.471396736825998); BUTTERFLY_XY (Y[block + 56], /* W56 */ Y[block + 56 + 1], Y[block + 120], Y[block + 120 + 1], Y[block + 56], Y[block + 56 + 1], Y[block + 120], Y[block + 120 + 1], (double) -0.923879532511287, (double) -0.382683432365090); BUTTERFLY_XY (Y[block + 58], /* W58 */ Y[block + 58 + 1], Y[block + 122], Y[block + 122 + 1], Y[block + 58], Y[block + 58 + 1], Y[block + 122], Y[block + 122 + 1], (double) -0.956940335732209, (double) -0.290284677254462); BUTTERFLY_XY (Y[block + 60], /* W60 */ Y[block + 60 + 1], Y[block + 124], Y[block + 124 + 1], Y[block + 60], Y[block + 60 + 1], Y[block + 124], Y[block + 124 + 1], (double) -0.980785280403230, (double) -0.195090322016129); BUTTERFLY_XY (Y[block + 62], /* W62 */ Y[block + 62 + 1], Y[block + 126], Y[block + 126 + 1], Y[block + 62], Y[block + 62 + 1], Y[block + 126], Y[block + 126 + 1], (double) -0.995184726672197, (double) -0.098017140329561); } /* perform 1 times fft128 */ BUTTERFLY_10 (Y[0], /* W0 */ Y[0 + 1], Y[128], Y[128 + 1], Y[0], Y[0 + 1], Y[128], Y[128 + 1], (double) +1.000000000000000, (double) +0.000000000000000); BUTTERFLY_XY (Y[2], /* W1 */ Y[2 + 1], Y[130], Y[130 + 1], Y[2], Y[2 + 1], Y[130], Y[130 + 1], (double) +0.998795456205172, (double) -0.049067674327418); BUTTERFLY_XY (Y[4], /* W2 */ Y[4 + 1], Y[132], Y[132 + 1], Y[4], Y[4 + 1], Y[132], Y[132 + 1], (double) +0.995184726672197, (double) -0.098017140329561); BUTTERFLY_XY (Y[6], /* W3 */ Y[6 + 1], Y[134], Y[134 + 1], Y[6], Y[6 + 1], Y[134], Y[134 + 1], (double) +0.989176509964781, (double) -0.146730474455362); BUTTERFLY_XY (Y[8], /* W4 */ Y[8 + 1], Y[136], Y[136 + 1], Y[8], Y[8 + 1], Y[136], Y[136 + 1], (double) +0.980785280403230, (double) -0.195090322016128); BUTTERFLY_XY (Y[10], /* W5 */ Y[10 + 1], Y[138], Y[138 + 1], Y[10], Y[10 + 1], Y[138], Y[138 + 1], (double) +0.970031253194544, (double) -0.242980179903264); BUTTERFLY_XY (Y[12], /* W6 */ Y[12 + 1], Y[140], Y[140 + 1], Y[12], Y[12 + 1], Y[140], Y[140 + 1], (double) +0.956940335732209, (double) -0.290284677254462); BUTTERFLY_XY (Y[14], /* W7 */ Y[14 + 1], Y[142], Y[142 + 1], Y[14], Y[14 + 1], Y[142], Y[142 + 1], (double) +0.941544065183021, (double) -0.336889853392220); BUTTERFLY_XY (Y[16], /* W8 */ Y[16 + 1], Y[144], Y[144 + 1], Y[16], Y[16 + 1], Y[144], Y[144 + 1], (double) +0.923879532511287, (double) -0.382683432365090); BUTTERFLY_XY (Y[18], /* W9 */ Y[18 + 1], Y[146], Y[146 + 1], Y[18], Y[18 + 1], Y[146], Y[146 + 1], (double) +0.903989293123443, (double) -0.427555093430282); BUTTERFLY_XY (Y[20], /* W10 */ Y[20 + 1], Y[148], Y[148 + 1], Y[20], Y[20 + 1], Y[148], Y[148 + 1], (double) +0.881921264348355, (double) -0.471396736825998); BUTTERFLY_XY (Y[22], /* W11 */ Y[22 + 1], Y[150], Y[150 + 1], Y[22], Y[22 + 1], Y[150], Y[150 + 1], (double) +0.857728610000272, (double) -0.514102744193222); BUTTERFLY_XY (Y[24], /* W12 */ Y[24 + 1], Y[152], Y[152 + 1], Y[24], Y[24 + 1], Y[152], Y[152 + 1], (double) +0.831469612302545, (double) -0.555570233019602); BUTTERFLY_XY (Y[26], /* W13 */ Y[26 + 1], Y[154], Y[154 + 1], Y[26], Y[26 + 1], Y[154], Y[154 + 1], (double) +0.803207531480645, (double) -0.595699304492433); BUTTERFLY_XY (Y[28], /* W14 */ Y[28 + 1], Y[156], Y[156 + 1], Y[28], Y[28 + 1], Y[156], Y[156 + 1], (double) +0.773010453362737, (double) -0.634393284163645); BUTTERFLY_XY (Y[30], /* W15 */ Y[30 + 1], Y[158], Y[158 + 1], Y[30], Y[30 + 1], Y[158], Y[158 + 1], (double) +0.740951125354959, (double) -0.671558954847018); BUTTERFLY_yY (Y[32], /* W16 */ Y[32 + 1], Y[160], Y[160 + 1], Y[32], Y[32 + 1], Y[160], Y[160 + 1], (double) +0.707106781186548, (double) -0.707106781186547); BUTTERFLY_XY (Y[34], /* W17 */ Y[34 + 1], Y[162], Y[162 + 1], Y[34], Y[34 + 1], Y[162], Y[162 + 1], (double) +0.671558954847018, (double) -0.740951125354959); BUTTERFLY_XY (Y[36], /* W18 */ Y[36 + 1], Y[164], Y[164 + 1], Y[36], Y[36 + 1], Y[164], Y[164 + 1], (double) +0.634393284163645, (double) -0.773010453362737); BUTTERFLY_XY (Y[38], /* W19 */ Y[38 + 1], Y[166], Y[166 + 1], Y[38], Y[38 + 1], Y[166], Y[166 + 1], (double) +0.595699304492433, (double) -0.803207531480645); BUTTERFLY_XY (Y[40], /* W20 */ Y[40 + 1], Y[168], Y[168 + 1], Y[40], Y[40 + 1], Y[168], Y[168 + 1], (double) +0.555570233019602, (double) -0.831469612302545); BUTTERFLY_XY (Y[42], /* W21 */ Y[42 + 1], Y[170], Y[170 + 1], Y[42], Y[42 + 1], Y[170], Y[170 + 1], (double) +0.514102744193222, (double) -0.857728610000272); BUTTERFLY_XY (Y[44], /* W22 */ Y[44 + 1], Y[172], Y[172 + 1], Y[44], Y[44 + 1], Y[172], Y[172 + 1], (double) +0.471396736825998, (double) -0.881921264348355); BUTTERFLY_XY (Y[46], /* W23 */ Y[46 + 1], Y[174], Y[174 + 1], Y[46], Y[46 + 1], Y[174], Y[174 + 1], (double) +0.427555093430282, (double) -0.903989293123443); BUTTERFLY_XY (Y[48], /* W24 */ Y[48 + 1], Y[176], Y[176 + 1], Y[48], Y[48 + 1], Y[176], Y[176 + 1], (double) +0.382683432365090, (double) -0.923879532511287); BUTTERFLY_XY (Y[50], /* W25 */ Y[50 + 1], Y[178], Y[178 + 1], Y[50], Y[50 + 1], Y[178], Y[178 + 1], (double) +0.336889853392220, (double) -0.941544065183021); BUTTERFLY_XY (Y[52], /* W26 */ Y[52 + 1], Y[180], Y[180 + 1], Y[52], Y[52 + 1], Y[180], Y[180 + 1], (double) +0.290284677254462, (double) -0.956940335732209); BUTTERFLY_XY (Y[54], /* W27 */ Y[54 + 1], Y[182], Y[182 + 1], Y[54], Y[54 + 1], Y[182], Y[182 + 1], (double) +0.242980179903264, (double) -0.970031253194544); BUTTERFLY_XY (Y[56], /* W28 */ Y[56 + 1], Y[184], Y[184 + 1], Y[56], Y[56 + 1], Y[184], Y[184 + 1], (double) +0.195090322016128, (double) -0.980785280403230); BUTTERFLY_XY (Y[58], /* W29 */ Y[58 + 1], Y[186], Y[186 + 1], Y[58], Y[58 + 1], Y[186], Y[186 + 1], (double) +0.146730474455362, (double) -0.989176509964781); BUTTERFLY_XY (Y[60], /* W30 */ Y[60 + 1], Y[188], Y[188 + 1], Y[60], Y[60 + 1], Y[188], Y[188 + 1], (double) +0.098017140329561, (double) -0.995184726672197); BUTTERFLY_XY (Y[62], /* W31 */ Y[62 + 1], Y[190], Y[190 + 1], Y[62], Y[62 + 1], Y[190], Y[190 + 1], (double) +0.049067674327418, (double) -0.998795456205172); BUTTERFLY_0m (Y[64], /* W32 */ Y[64 + 1], Y[192], Y[192 + 1], Y[64], Y[64 + 1], Y[192], Y[192 + 1], (double) +0.000000000000000, (double) -1.000000000000000); BUTTERFLY_XY (Y[66], /* W33 */ Y[66 + 1], Y[194], Y[194 + 1], Y[66], Y[66 + 1], Y[194], Y[194 + 1], (double) -0.049067674327418, (double) -0.998795456205172); BUTTERFLY_XY (Y[68], /* W34 */ Y[68 + 1], Y[196], Y[196 + 1], Y[68], Y[68 + 1], Y[196], Y[196 + 1], (double) -0.098017140329561, (double) -0.995184726672197); BUTTERFLY_XY (Y[70], /* W35 */ Y[70 + 1], Y[198], Y[198 + 1], Y[70], Y[70 + 1], Y[198], Y[198 + 1], (double) -0.146730474455362, (double) -0.989176509964781); BUTTERFLY_XY (Y[72], /* W36 */ Y[72 + 1], Y[200], Y[200 + 1], Y[72], Y[72 + 1], Y[200], Y[200 + 1], (double) -0.195090322016128, (double) -0.980785280403230); BUTTERFLY_XY (Y[74], /* W37 */ Y[74 + 1], Y[202], Y[202 + 1], Y[74], Y[74 + 1], Y[202], Y[202 + 1], (double) -0.242980179903264, (double) -0.970031253194544); BUTTERFLY_XY (Y[76], /* W38 */ Y[76 + 1], Y[204], Y[204 + 1], Y[76], Y[76 + 1], Y[204], Y[204 + 1], (double) -0.290284677254462, (double) -0.956940335732209); BUTTERFLY_XY (Y[78], /* W39 */ Y[78 + 1], Y[206], Y[206 + 1], Y[78], Y[78 + 1], Y[206], Y[206 + 1], (double) -0.336889853392220, (double) -0.941544065183021); BUTTERFLY_XY (Y[80], /* W40 */ Y[80 + 1], Y[208], Y[208 + 1], Y[80], Y[80 + 1], Y[208], Y[208 + 1], (double) -0.382683432365090, (double) -0.923879532511287); BUTTERFLY_XY (Y[82], /* W41 */ Y[82 + 1], Y[210], Y[210 + 1], Y[82], Y[82 + 1], Y[210], Y[210 + 1], (double) -0.427555093430282, (double) -0.903989293123443); BUTTERFLY_XY (Y[84], /* W42 */ Y[84 + 1], Y[212], Y[212 + 1], Y[84], Y[84 + 1], Y[212], Y[212 + 1], (double) -0.471396736825998, (double) -0.881921264348355); BUTTERFLY_XY (Y[86], /* W43 */ Y[86 + 1], Y[214], Y[214 + 1], Y[86], Y[86 + 1], Y[214], Y[214 + 1], (double) -0.514102744193222, (double) -0.857728610000272); BUTTERFLY_XY (Y[88], /* W44 */ Y[88 + 1], Y[216], Y[216 + 1], Y[88], Y[88 + 1], Y[216], Y[216 + 1], (double) -0.555570233019602, (double) -0.831469612302545); BUTTERFLY_XY (Y[90], /* W45 */ Y[90 + 1], Y[218], Y[218 + 1], Y[90], Y[90 + 1], Y[218], Y[218 + 1], (double) -0.595699304492433, (double) -0.803207531480645); BUTTERFLY_XY (Y[92], /* W46 */ Y[92 + 1], Y[220], Y[220 + 1], Y[92], Y[92 + 1], Y[220], Y[220 + 1], (double) -0.634393284163645, (double) -0.773010453362737); BUTTERFLY_XY (Y[94], /* W47 */ Y[94 + 1], Y[222], Y[222 + 1], Y[94], Y[94 + 1], Y[222], Y[222 + 1], (double) -0.671558954847018, (double) -0.740951125354959); BUTTERFLY_XX (Y[96], /* W48 */ Y[96 + 1], Y[224], Y[224 + 1], Y[96], Y[96 + 1], Y[224], Y[224 + 1], (double) -0.707106781186547, (double) -0.707106781186548); BUTTERFLY_XY (Y[98], /* W49 */ Y[98 + 1], Y[226], Y[226 + 1], Y[98], Y[98 + 1], Y[226], Y[226 + 1], (double) -0.740951125354959, (double) -0.671558954847019); BUTTERFLY_XY (Y[100], /* W50 */ Y[100 + 1], Y[228], Y[228 + 1], Y[100], Y[100 + 1], Y[228], Y[228 + 1], (double) -0.773010453362737, (double) -0.634393284163645); BUTTERFLY_XY (Y[102], /* W51 */ Y[102 + 1], Y[230], Y[230 + 1], Y[102], Y[102 + 1], Y[230], Y[230 + 1], (double) -0.803207531480645, (double) -0.595699304492433); BUTTERFLY_XY (Y[104], /* W52 */ Y[104 + 1], Y[232], Y[232 + 1], Y[104], Y[104 + 1], Y[232], Y[232 + 1], (double) -0.831469612302545, (double) -0.555570233019602); BUTTERFLY_XY (Y[106], /* W53 */ Y[106 + 1], Y[234], Y[234 + 1], Y[106], Y[106 + 1], Y[234], Y[234 + 1], (double) -0.857728610000272, (double) -0.514102744193222); BUTTERFLY_XY (Y[108], /* W54 */ Y[108 + 1], Y[236], Y[236 + 1], Y[108], Y[108 + 1], Y[236], Y[236 + 1], (double) -0.881921264348355, (double) -0.471396736825998); BUTTERFLY_XY (Y[110], /* W55 */ Y[110 + 1], Y[238], Y[238 + 1], Y[110], Y[110 + 1], Y[238], Y[238 + 1], (double) -0.903989293123443, (double) -0.427555093430282); BUTTERFLY_XY (Y[112], /* W56 */ Y[112 + 1], Y[240], Y[240 + 1], Y[112], Y[112 + 1], Y[240], Y[240 + 1], (double) -0.923879532511287, (double) -0.382683432365090); BUTTERFLY_XY (Y[114], /* W57 */ Y[114 + 1], Y[242], Y[242 + 1], Y[114], Y[114 + 1], Y[242], Y[242 + 1], (double) -0.941544065183021, (double) -0.336889853392220); BUTTERFLY_XY (Y[116], /* W58 */ Y[116 + 1], Y[244], Y[244 + 1], Y[116], Y[116 + 1], Y[244], Y[244 + 1], (double) -0.956940335732209, (double) -0.290284677254462); BUTTERFLY_XY (Y[118], /* W59 */ Y[118 + 1], Y[246], Y[246 + 1], Y[118], Y[118 + 1], Y[246], Y[246 + 1], (double) -0.970031253194544, (double) -0.242980179903264); BUTTERFLY_XY (Y[120], /* W60 */ Y[120 + 1], Y[248], Y[248 + 1], Y[120], Y[120 + 1], Y[248], Y[248 + 1], (double) -0.980785280403230, (double) -0.195090322016129); BUTTERFLY_XY (Y[122], /* W61 */ Y[122 + 1], Y[250], Y[250 + 1], Y[122], Y[122 + 1], Y[250], Y[250 + 1], (double) -0.989176509964781, (double) -0.146730474455362); BUTTERFLY_XY (Y[124], /* W62 */ Y[124 + 1], Y[252], Y[252 + 1], Y[124], Y[124 + 1], Y[252], Y[252 + 1], (double) -0.995184726672197, (double) -0.098017140329561); BUTTERFLY_XY (Y[126], /* W63 */ Y[126 + 1], Y[254], Y[254 + 1], Y[126], Y[126 + 1], Y[254], Y[254 + 1], (double) -0.998795456205172, (double) -0.049067674327418); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 128 L S S S S S X) **/ static void gsl_power2_fft128synthesis (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* perform fft2 and bitreverse input */ bitreverse_fft2synthesis (128, X, Y); /* skipping 32 times fft4 */ /* skipping 16 times fft8 */ /* skipping 8 times fft16 */ /* skipping 4 times fft32 */ /* skipping 2 times fft64 */ /* perform 1 times fft128 */ gsl_power2_fft128synthesis_skip2 (X, Y); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 256 S S S S S S X T) **/ static void gsl_power2_fft256synthesis_skip2 (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* skipping 128 times fft2 */ /* skipping 64 times fft4 */ /* skipping 32 times fft8 */ /* skipping 16 times fft16 */ /* skipping 8 times fft32 */ /* skipping 4 times fft64 */ /* perform 2 times fft128 */ gsl_power2_fft128synthesis_skip2 (X, Y); gsl_power2_fft128synthesis_skip2 (X + 256, Y + 256); /* perform 1 times fft256 */ { static const double Wconst256[] = { +0.999698818696204, -0.024541228522912, +0.998795456205172, -0.049067674327418, +0.997290456678690, -0.073564563599667, +0.995184726672197, -0.098017140329561, +0.992479534598710, -0.122410675199216, +0.989176509964781, -0.146730474455362, +0.985277642388941, -0.170961888760301, +0.980785280403230, -0.195090322016128, +0.975702130038529, -0.219101240156870, +0.970031253194544, -0.242980179903264, +0.963776065795440, -0.266712757474898, +0.956940335732209, -0.290284677254462, +0.949528180593037, -0.313681740398892, +0.941544065183021, -0.336889853392220, +0.932992798834739, -0.359895036534988, +0.923879532511287, -0.382683432365090, +0.914209755703531, -0.405241314004990, +0.903989293123443, -0.427555093430282, +0.893224301195515, -0.449611329654607, +0.881921264348355, -0.471396736825998, +0.870086991108711, -0.492898192229784, +0.857728610000272, -0.514102744193222, +0.844853565249707, -0.534997619887097, +0.831469612302545, -0.555570233019602, +0.817584813151584, -0.575808191417845, +0.803207531480645, -0.595699304492433, +0.788346427626606, -0.615231590580627, +0.773010453362737, -0.634393284163645, +0.757208846506485, -0.653172842953777, +0.740951125354959, -0.671558954847018, +0.724247082951467, -0.689540544737067, +0.707106781186548, -0.707106781186547, +0.689540544737067, -0.724247082951467, +0.671558954847018, -0.740951125354959, +0.653172842953777, -0.757208846506484, +0.634393284163645, -0.773010453362737, +0.615231590580627, -0.788346427626606, +0.595699304492433, -0.803207531480645, +0.575808191417845, -0.817584813151584, +0.555570233019602, -0.831469612302545, +0.534997619887097, -0.844853565249707, +0.514102744193222, -0.857728610000272, +0.492898192229784, -0.870086991108711, +0.471396736825998, -0.881921264348355, +0.449611329654607, -0.893224301195515, +0.427555093430282, -0.903989293123443, +0.405241314004990, -0.914209755703531, +0.382683432365090, -0.923879532511287, +0.359895036534988, -0.932992798834739, +0.336889853392220, -0.941544065183021, +0.313681740398892, -0.949528180593037, +0.290284677254462, -0.956940335732209, +0.266712757474898, -0.963776065795440, +0.242980179903264, -0.970031253194544, +0.219101240156870, -0.975702130038529, +0.195090322016128, -0.980785280403230, +0.170961888760301, -0.985277642388941, +0.146730474455362, -0.989176509964781, +0.122410675199216, -0.992479534598710, +0.098017140329561, -0.995184726672197, +0.073564563599667, -0.997290456678690, +0.049067674327418, -0.998795456205172, +0.024541228522912, -0.999698818696204, }; const double *W = Wconst256 - 2; double *Z = Y + 128; for (offset = 0; offset < 512; offset += 512) { BUTTERFLY_10 (Y[offset], Y[offset + 1], Y[offset + 256], Y[offset + 256 + 1], Y[offset], Y[offset + 1], Y[offset + 256], Y[offset + 256 + 1], __1, __0); BUTTERFLY_0m (Z[offset], Z[offset + 1], Z[offset + 256], Z[offset + 256 + 1], Z[offset], Z[offset + 1], Z[offset + 256], Z[offset + 256 + 1], __0, __1); } for (butterfly = 2; butterfly < 128; butterfly += 2) { Wre = W[butterfly]; Wim = W[butterfly + 1]; for (block = 0; block < 512; block += 512) { offset = butterfly + block; BUTTERFLY_XY (Y[offset], Y[offset + 1], Y[offset + 256], Y[offset + 256 + 1], Y[offset], Y[offset + 1], Y[offset + 256], Y[offset + 256 + 1], Wre, Wim); BUTTERFLY_yX (Z[offset], Z[offset + 1], Z[offset + 256], Z[offset + 256 + 1], Z[offset], Z[offset + 1], Z[offset + 256], Z[offset + 256 + 1], Wre, Wim); } } } } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 256 L S S S S S S X) **/ static void gsl_power2_fft256synthesis (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* perform fft2 and bitreverse input */ bitreverse_fft2synthesis (256, X, Y); /* skipping 64 times fft4 */ /* skipping 32 times fft8 */ /* skipping 16 times fft16 */ /* skipping 8 times fft32 */ /* skipping 4 times fft64 */ /* skipping 2 times fft128 */ /* perform 1 times fft256 */ gsl_power2_fft256synthesis_skip2 (X, Y); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 512 S S S S S S X T T) **/ static void gsl_power2_fft512synthesis_skip2 (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* skipping 256 times fft2 */ /* skipping 128 times fft4 */ /* skipping 64 times fft8 */ /* skipping 32 times fft16 */ /* skipping 16 times fft32 */ /* skipping 8 times fft64 */ /* perform 4 times fft128 */ gsl_power2_fft128synthesis_skip2 (X, Y); gsl_power2_fft128synthesis_skip2 (X + 256, Y + 256); gsl_power2_fft128synthesis_skip2 (X + 512, Y + 512); gsl_power2_fft128synthesis_skip2 (X + 768, Y + 768); /* perform 2 times fft256 */ { static const double Wconst256[] = { +0.999698818696204, -0.024541228522912, +0.998795456205172, -0.049067674327418, +0.997290456678690, -0.073564563599667, +0.995184726672197, -0.098017140329561, +0.992479534598710, -0.122410675199216, +0.989176509964781, -0.146730474455362, +0.985277642388941, -0.170961888760301, +0.980785280403230, -0.195090322016128, +0.975702130038529, -0.219101240156870, +0.970031253194544, -0.242980179903264, +0.963776065795440, -0.266712757474898, +0.956940335732209, -0.290284677254462, +0.949528180593037, -0.313681740398892, +0.941544065183021, -0.336889853392220, +0.932992798834739, -0.359895036534988, +0.923879532511287, -0.382683432365090, +0.914209755703531, -0.405241314004990, +0.903989293123443, -0.427555093430282, +0.893224301195515, -0.449611329654607, +0.881921264348355, -0.471396736825998, +0.870086991108711, -0.492898192229784, +0.857728610000272, -0.514102744193222, +0.844853565249707, -0.534997619887097, +0.831469612302545, -0.555570233019602, +0.817584813151584, -0.575808191417845, +0.803207531480645, -0.595699304492433, +0.788346427626606, -0.615231590580627, +0.773010453362737, -0.634393284163645, +0.757208846506485, -0.653172842953777, +0.740951125354959, -0.671558954847018, +0.724247082951467, -0.689540544737067, +0.707106781186548, -0.707106781186547, +0.689540544737067, -0.724247082951467, +0.671558954847018, -0.740951125354959, +0.653172842953777, -0.757208846506484, +0.634393284163645, -0.773010453362737, +0.615231590580627, -0.788346427626606, +0.595699304492433, -0.803207531480645, +0.575808191417845, -0.817584813151584, +0.555570233019602, -0.831469612302545, +0.534997619887097, -0.844853565249707, +0.514102744193222, -0.857728610000272, +0.492898192229784, -0.870086991108711, +0.471396736825998, -0.881921264348355, +0.449611329654607, -0.893224301195515, +0.427555093430282, -0.903989293123443, +0.405241314004990, -0.914209755703531, +0.382683432365090, -0.923879532511287, +0.359895036534988, -0.932992798834739, +0.336889853392220, -0.941544065183021, +0.313681740398892, -0.949528180593037, +0.290284677254462, -0.956940335732209, +0.266712757474898, -0.963776065795440, +0.242980179903264, -0.970031253194544, +0.219101240156870, -0.975702130038529, +0.195090322016128, -0.980785280403230, +0.170961888760301, -0.985277642388941, +0.146730474455362, -0.989176509964781, +0.122410675199216, -0.992479534598710, +0.098017140329561, -0.995184726672197, +0.073564563599667, -0.997290456678690, +0.049067674327418, -0.998795456205172, +0.024541228522912, -0.999698818696204, }; const double *W = Wconst256 - 2; double *Z = Y + 128; for (offset = 0; offset < 1024; offset += 512) { BUTTERFLY_10 (Y[offset], Y[offset + 1], Y[offset + 256], Y[offset + 256 + 1], Y[offset], Y[offset + 1], Y[offset + 256], Y[offset + 256 + 1], __1, __0); BUTTERFLY_0m (Z[offset], Z[offset + 1], Z[offset + 256], Z[offset + 256 + 1], Z[offset], Z[offset + 1], Z[offset + 256], Z[offset + 256 + 1], __0, __1); } for (butterfly = 2; butterfly < 128; butterfly += 2) { Wre = W[butterfly]; Wim = W[butterfly + 1]; for (block = 0; block < 1024; block += 512) { offset = butterfly + block; BUTTERFLY_XY (Y[offset], Y[offset + 1], Y[offset + 256], Y[offset + 256 + 1], Y[offset], Y[offset + 1], Y[offset + 256], Y[offset + 256 + 1], Wre, Wim); BUTTERFLY_yX (Z[offset], Z[offset + 1], Z[offset + 256], Z[offset + 256 + 1], Z[offset], Z[offset + 1], Z[offset + 256], Z[offset + 256 + 1], Wre, Wim); } } } /* perform 1 times fft512 */ { static const double Wconst512[] = { +0.999924701839145, -0.012271538285720, +0.999698818696204, -0.024541228522912, +0.999322384588350, -0.036807222941359, +0.998795456205172, -0.049067674327418, +0.998118112900149, -0.061320736302209, +0.997290456678690, -0.073564563599667, +0.996312612182778, -0.085797312344440, +0.995184726672197, -0.098017140329561, +0.993906970002356, -0.110222207293883, +0.992479534598710, -0.122410675199216, +0.990902635427780, -0.134580708507126, +0.989176509964781, -0.146730474455362, +0.987301418157858, -0.158858143333861, +0.985277642388941, -0.170961888760301, +0.983105487431216, -0.183039887955141, +0.980785280403230, -0.195090322016128, +0.978317370719628, -0.207111376192219, +0.975702130038529, -0.219101240156870, +0.972939952205560, -0.231058108280671, +0.970031253194544, -0.242980179903264, +0.966976471044852, -0.254865659604515, +0.963776065795440, -0.266712757474898, +0.960430519415566, -0.278519689385053, +0.956940335732209, -0.290284677254462, +0.953306040354194, -0.302005949319228, +0.949528180593037, -0.313681740398892, +0.945607325380521, -0.325310292162263, +0.941544065183021, -0.336889853392220, +0.937339011912575, -0.348418680249435, +0.932992798834739, -0.359895036534988, +0.928506080473216, -0.371317193951838, +0.923879532511287, -0.382683432365090, +0.919113851690058, -0.393992040061048, +0.914209755703531, -0.405241314004990, +0.909167983090522, -0.416429560097637, +0.903989293123443, -0.427555093430282, +0.898674465693954, -0.438616238538528, +0.893224301195515, -0.449611329654607, +0.887639620402854, -0.460538710958240, +0.881921264348355, -0.471396736825998, +0.876070094195407, -0.482183772079123, +0.870086991108711, -0.492898192229784, +0.863972856121587, -0.503538383725718, +0.857728610000272, -0.514102744193222, +0.851355193105265, -0.524589682678469, +0.844853565249707, -0.534997619887097, +0.838224705554838, -0.545324988422046, +0.831469612302545, -0.555570233019602, +0.824589302785025, -0.565731810783613, +0.817584813151584, -0.575808191417845, +0.810457198252595, -0.585797857456439, +0.803207531480645, -0.595699304492433, +0.795836904608884, -0.605511041404326, +0.788346427626606, -0.615231590580627, +0.780737228572094, -0.624859488142386, +0.773010453362737, -0.634393284163645, +0.765167265622459, -0.643831542889791, +0.757208846506485, -0.653172842953777, +0.749136394523459, -0.662415777590172, +0.740951125354959, -0.671558954847018, +0.732654271672413, -0.680600997795453, +0.724247082951467, -0.689540544737067, +0.715730825283819, -0.698376249408973, +0.707106781186548, -0.707106781186547, +0.698376249408973, -0.715730825283819, +0.689540544737067, -0.724247082951467, +0.680600997795453, -0.732654271672413, +0.671558954847018, -0.740951125354959, +0.662415777590172, -0.749136394523459, +0.653172842953777, -0.757208846506484, +0.643831542889791, -0.765167265622459, +0.634393284163645, -0.773010453362737, +0.624859488142386, -0.780737228572094, +0.615231590580627, -0.788346427626606, +0.605511041404326, -0.795836904608883, +0.595699304492433, -0.803207531480645, +0.585797857456439, -0.810457198252595, +0.575808191417845, -0.817584813151584, +0.565731810783613, -0.824589302785025, +0.555570233019602, -0.831469612302545, +0.545324988422046, -0.838224705554838, +0.534997619887097, -0.844853565249707, +0.524589682678469, -0.851355193105265, +0.514102744193222, -0.857728610000272, +0.503538383725718, -0.863972856121587, +0.492898192229784, -0.870086991108711, +0.482183772079123, -0.876070094195407, +0.471396736825998, -0.881921264348355, +0.460538710958240, -0.887639620402854, +0.449611329654607, -0.893224301195515, +0.438616238538528, -0.898674465693954, +0.427555093430282, -0.903989293123443, +0.416429560097637, -0.909167983090522, +0.405241314004990, -0.914209755703531, +0.393992040061048, -0.919113851690058, +0.382683432365090, -0.923879532511287, +0.371317193951838, -0.928506080473215, +0.359895036534988, -0.932992798834739, +0.348418680249435, -0.937339011912575, +0.336889853392220, -0.941544065183021, +0.325310292162263, -0.945607325380521, +0.313681740398892, -0.949528180593037, +0.302005949319228, -0.953306040354194, +0.290284677254462, -0.956940335732209, +0.278519689385053, -0.960430519415566, +0.266712757474898, -0.963776065795440, +0.254865659604515, -0.966976471044852, +0.242980179903264, -0.970031253194544, +0.231058108280671, -0.972939952205560, +0.219101240156870, -0.975702130038529, +0.207111376192219, -0.978317370719628, +0.195090322016128, -0.980785280403230, +0.183039887955141, -0.983105487431216, +0.170961888760301, -0.985277642388941, +0.158858143333861, -0.987301418157858, +0.146730474455362, -0.989176509964781, +0.134580708507126, -0.990902635427780, +0.122410675199216, -0.992479534598710, +0.110222207293883, -0.993906970002356, +0.098017140329561, -0.995184726672197, +0.085797312344440, -0.996312612182778, +0.073564563599667, -0.997290456678690, +0.061320736302209, -0.998118112900149, +0.049067674327418, -0.998795456205172, +0.036807222941359, -0.999322384588350, +0.024541228522912, -0.999698818696204, +0.012271538285720, -0.999924701839145, }; const double *W = Wconst512 - 2; double *Z = Y + 256; for (offset = 0; offset < 1024; offset += 1024) { BUTTERFLY_10 (Y[offset], Y[offset + 1], Y[offset + 512], Y[offset + 512 + 1], Y[offset], Y[offset + 1], Y[offset + 512], Y[offset + 512 + 1], __1, __0); BUTTERFLY_0m (Z[offset], Z[offset + 1], Z[offset + 512], Z[offset + 512 + 1], Z[offset], Z[offset + 1], Z[offset + 512], Z[offset + 512 + 1], __0, __1); } for (butterfly = 2; butterfly < 256; butterfly += 2) { Wre = W[butterfly]; Wim = W[butterfly + 1]; for (block = 0; block < 1024; block += 1024) { offset = butterfly + block; BUTTERFLY_XY (Y[offset], Y[offset + 1], Y[offset + 512], Y[offset + 512 + 1], Y[offset], Y[offset + 1], Y[offset + 512], Y[offset + 512 + 1], Wre, Wim); BUTTERFLY_yX (Z[offset], Z[offset + 1], Z[offset + 512], Z[offset + 512 + 1], Z[offset], Z[offset + 1], Z[offset + 512], Z[offset + 512 + 1], Wre, Wim); } } } } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 512 L S S S S S S S X) **/ static void gsl_power2_fft512synthesis (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* perform fft2 and bitreverse input */ bitreverse_fft2synthesis (512, X, Y); /* skipping 128 times fft4 */ /* skipping 64 times fft8 */ /* skipping 32 times fft16 */ /* skipping 16 times fft32 */ /* skipping 8 times fft64 */ /* skipping 4 times fft128 */ /* skipping 2 times fft256 */ /* perform 1 times fft512 */ gsl_power2_fft512synthesis_skip2 (X, Y); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 1024 S S S S S S S S X L) **/ static void gsl_power2_fft1024synthesis_skip2 (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* skipping 512 times fft2 */ /* skipping 256 times fft4 */ /* skipping 128 times fft8 */ /* skipping 64 times fft16 */ /* skipping 32 times fft32 */ /* skipping 16 times fft64 */ /* skipping 8 times fft128 */ /* skipping 4 times fft256 */ /* perform 2 times fft512 */ gsl_power2_fft512synthesis_skip2 (X, Y); gsl_power2_fft512synthesis_skip2 (X + 1024, Y + 1024); /* perform 1 times fft1024 */ for (offset = 0; offset < 2048; offset += 2048) { BUTTERFLY_10 (Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], __1, __0); } Wre = +0.999981175282601; Wim = -0.006135884649154; for (butterfly = 2; butterfly < 512; butterfly += 2) { for (block = 0; block < 2048; block += 2048) { offset = butterfly + block; BUTTERFLY_XY (Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], Wre, Wim); } WMULTIPLY (Wre, Wim, -0.000018824717399, -0.006135884649154); } for (offset = 512; offset < 2048; offset += 2048) { BUTTERFLY_0m (Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], __0, __1); } Wre = -0.006135884649154; Wim = -0.999981175282601; for (butterfly = 514; butterfly < 1024; butterfly += 2) { for (block = 0; block < 2048; block += 2048) { offset = butterfly + block; BUTTERFLY_XY (Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], Wre, Wim); } WMULTIPLY (Wre, Wim, -0.000018824717399, -0.006135884649154); } } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 1024 L S S S S S S S S X) **/ static void gsl_power2_fft1024synthesis (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* perform fft2 and bitreverse input */ bitreverse_fft2synthesis (1024, X, Y); /* skipping 256 times fft4 */ /* skipping 128 times fft8 */ /* skipping 64 times fft16 */ /* skipping 32 times fft32 */ /* skipping 16 times fft64 */ /* skipping 8 times fft128 */ /* skipping 4 times fft256 */ /* skipping 2 times fft512 */ /* perform 1 times fft1024 */ gsl_power2_fft1024synthesis_skip2 (X, Y); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 2048 S S S S S S S S X L L) **/ static void gsl_power2_fft2048synthesis_skip2 (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* skipping 1024 times fft2 */ /* skipping 512 times fft4 */ /* skipping 256 times fft8 */ /* skipping 128 times fft16 */ /* skipping 64 times fft32 */ /* skipping 32 times fft64 */ /* skipping 16 times fft128 */ /* skipping 8 times fft256 */ /* perform 4 times fft512 */ gsl_power2_fft512synthesis_skip2 (X, Y); gsl_power2_fft512synthesis_skip2 (X + 1024, Y + 1024); gsl_power2_fft512synthesis_skip2 (X + 2048, Y + 2048); gsl_power2_fft512synthesis_skip2 (X + 3072, Y + 3072); /* perform 2 times fft1024 */ for (offset = 0; offset < 4096; offset += 2048) { BUTTERFLY_10 (Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], __1, __0); } Wre = +0.999981175282601; Wim = -0.006135884649154; for (butterfly = 2; butterfly < 512; butterfly += 2) { for (block = 0; block < 4096; block += 2048) { offset = butterfly + block; BUTTERFLY_XY (Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], Wre, Wim); } WMULTIPLY (Wre, Wim, -0.000018824717399, -0.006135884649154); } for (offset = 512; offset < 4096; offset += 2048) { BUTTERFLY_0m (Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], __0, __1); } Wre = -0.006135884649154; Wim = -0.999981175282601; for (butterfly = 514; butterfly < 1024; butterfly += 2) { for (block = 0; block < 4096; block += 2048) { offset = butterfly + block; BUTTERFLY_XY (Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], Y[offset], Y[offset + 1], Y[offset + 1024], Y[offset + 1024 + 1], Wre, Wim); } WMULTIPLY (Wre, Wim, -0.000018824717399, -0.006135884649154); } /* perform 1 times fft2048 */ for (offset = 0; offset < 4096; offset += 4096) { BUTTERFLY_10 (Y[offset], Y[offset + 1], Y[offset + 2048], Y[offset + 2048 + 1], Y[offset], Y[offset + 1], Y[offset + 2048], Y[offset + 2048 + 1], __1, __0); } Wre = +0.999995293809576; Wim = -0.003067956762966; for (butterfly = 2; butterfly < 1024; butterfly += 2) { for (block = 0; block < 4096; block += 4096) { offset = butterfly + block; BUTTERFLY_XY (Y[offset], Y[offset + 1], Y[offset + 2048], Y[offset + 2048 + 1], Y[offset], Y[offset + 1], Y[offset + 2048], Y[offset + 2048 + 1], Wre, Wim); } WMULTIPLY (Wre, Wim, -0.000004706190424, -0.003067956762966); } for (offset = 1024; offset < 4096; offset += 4096) { BUTTERFLY_0m (Y[offset], Y[offset + 1], Y[offset + 2048], Y[offset + 2048 + 1], Y[offset], Y[offset + 1], Y[offset + 2048], Y[offset + 2048 + 1], __0, __1); } Wre = -0.003067956762966; Wim = -0.999995293809576; for (butterfly = 1026; butterfly < 2048; butterfly += 2) { for (block = 0; block < 4096; block += 4096) { offset = butterfly + block; BUTTERFLY_XY (Y[offset], Y[offset + 1], Y[offset + 2048], Y[offset + 2048 + 1], Y[offset], Y[offset + 1], Y[offset + 2048], Y[offset + 2048 + 1], Wre, Wim); } WMULTIPLY (Wre, Wim, -0.000004706190424, -0.003067956762966); } } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 2048 L S S S S S S S S S X) **/ static void gsl_power2_fft2048synthesis (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* perform fft2 and bitreverse input */ bitreverse_fft2synthesis (2048, X, Y); /* skipping 512 times fft4 */ /* skipping 256 times fft8 */ /* skipping 128 times fft16 */ /* skipping 64 times fft32 */ /* skipping 32 times fft64 */ /* skipping 16 times fft128 */ /* skipping 8 times fft256 */ /* skipping 4 times fft512 */ /* skipping 2 times fft1024 */ /* perform 1 times fft2048 */ gsl_power2_fft2048synthesis_skip2 (X, Y); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 4096 S S S S S S S S S S X L) **/ static void gsl_power2_fft4096synthesis_skip2 (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* skipping 2048 times fft2 */ /* skipping 1024 times fft4 */ /* skipping 512 times fft8 */ /* skipping 256 times fft16 */ /* skipping 128 times fft32 */ /* skipping 64 times fft64 */ /* skipping 32 times fft128 */ /* skipping 16 times fft256 */ /* skipping 8 times fft512 */ /* skipping 4 times fft1024 */ /* perform 2 times fft2048 */ gsl_power2_fft2048synthesis_skip2 (X, Y); gsl_power2_fft2048synthesis_skip2 (X + 4096, Y + 4096); /* perform 1 times fft4096 */ for (offset = 0; offset < 8192; offset += 8192) { BUTTERFLY_10 (Y[offset], Y[offset + 1], Y[offset + 4096], Y[offset + 4096 + 1], Y[offset], Y[offset + 1], Y[offset + 4096], Y[offset + 4096 + 1], __1, __0); } Wre = +0.999998823451702; Wim = -0.001533980186285; for (butterfly = 2; butterfly < 2048; butterfly += 2) { for (block = 0; block < 8192; block += 8192) { offset = butterfly + block; BUTTERFLY_XY (Y[offset], Y[offset + 1], Y[offset + 4096], Y[offset + 4096 + 1], Y[offset], Y[offset + 1], Y[offset + 4096], Y[offset + 4096 + 1], Wre, Wim); } WMULTIPLY (Wre, Wim, -0.000001176548298, -0.001533980186285); } for (offset = 2048; offset < 8192; offset += 8192) { BUTTERFLY_0m (Y[offset], Y[offset + 1], Y[offset + 4096], Y[offset + 4096 + 1], Y[offset], Y[offset + 1], Y[offset + 4096], Y[offset + 4096 + 1], __0, __1); } Wre = -0.001533980186285; Wim = -0.999998823451702; for (butterfly = 2050; butterfly < 4096; butterfly += 2) { for (block = 0; block < 8192; block += 8192) { offset = butterfly + block; BUTTERFLY_XY (Y[offset], Y[offset + 1], Y[offset + 4096], Y[offset + 4096 + 1], Y[offset], Y[offset + 1], Y[offset + 4096], Y[offset + 4096 + 1], Wre, Wim); } WMULTIPLY (Wre, Wim, -0.000001176548298, -0.001533980186285); } } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 4096 L S S S S S S S S S S X) **/ static void gsl_power2_fft4096synthesis (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* perform fft2 and bitreverse input */ bitreverse_fft2synthesis (4096, X, Y); /* skipping 1024 times fft4 */ /* skipping 512 times fft8 */ /* skipping 256 times fft16 */ /* skipping 128 times fft32 */ /* skipping 64 times fft64 */ /* skipping 32 times fft128 */ /* skipping 16 times fft256 */ /* skipping 8 times fft512 */ /* skipping 4 times fft1024 */ /* skipping 2 times fft2048 */ /* perform 1 times fft4096 */ gsl_power2_fft4096synthesis_skip2 (X, Y); } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 8192 S S S S S S S S S S S X L) **/ static void gsl_power2_fft8192synthesis_skip2 (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* skipping 4096 times fft2 */ /* skipping 2048 times fft4 */ /* skipping 1024 times fft8 */ /* skipping 512 times fft16 */ /* skipping 256 times fft32 */ /* skipping 128 times fft64 */ /* skipping 64 times fft128 */ /* skipping 32 times fft256 */ /* skipping 16 times fft512 */ /* skipping 8 times fft1024 */ /* skipping 4 times fft2048 */ /* perform 2 times fft4096 */ gsl_power2_fft4096synthesis_skip2 (X, Y); gsl_power2_fft4096synthesis_skip2 (X + 8192, Y + 8192); /* perform 1 times fft8192 */ for (offset = 0; offset < 16384; offset += 16384) { BUTTERFLY_10 (Y[offset], Y[offset + 1], Y[offset + 8192], Y[offset + 8192 + 1], Y[offset], Y[offset + 1], Y[offset + 8192], Y[offset + 8192 + 1], __1, __0); } Wre = +0.999999705862882; Wim = -0.000766990318743; for (butterfly = 2; butterfly < 4096; butterfly += 2) { for (block = 0; block < 16384; block += 16384) { offset = butterfly + block; BUTTERFLY_XY (Y[offset], Y[offset + 1], Y[offset + 8192], Y[offset + 8192 + 1], Y[offset], Y[offset + 1], Y[offset + 8192], Y[offset + 8192 + 1], Wre, Wim); } WMULTIPLY (Wre, Wim, -0.000000294137118, -0.000766990318743); } for (offset = 4096; offset < 16384; offset += 16384) { BUTTERFLY_0m (Y[offset], Y[offset + 1], Y[offset + 8192], Y[offset + 8192 + 1], Y[offset], Y[offset + 1], Y[offset + 8192], Y[offset + 8192 + 1], __0, __1); } Wre = -0.000766990318743; Wim = -0.999999705862882; for (butterfly = 4098; butterfly < 8192; butterfly += 2) { for (block = 0; block < 16384; block += 16384) { offset = butterfly + block; BUTTERFLY_XY (Y[offset], Y[offset + 1], Y[offset + 8192], Y[offset + 8192 + 1], Y[offset], Y[offset + 1], Y[offset + 8192], Y[offset + 8192 + 1], Wre, Wim); } WMULTIPLY (Wre, Wim, -0.000000294137118, -0.000766990318743); } } /** ** Generated data ends here **/ /** ** Generated data (by gsl-genfft 8192 L S S S S S S S S S S S X) **/ static void gsl_power2_fft8192synthesis (const double *X, double *Y) { unsigned int butterfly, block, offset; double Wre, Wim; butterfly = block = offset = 0, Wre = Wim = 0.0; /* silence compiler */ /* perform fft2 and bitreverse input */ bitreverse_fft2synthesis (8192, X, Y); /* skipping 2048 times fft4 */ /* skipping 1024 times fft8 */ /* skipping 512 times fft16 */ /* skipping 256 times fft32 */ /* skipping 128 times fft64 */ /* skipping 64 times fft128 */ /* skipping 32 times fft256 */ /* skipping 16 times fft512 */ /* skipping 8 times fft1024 */ /* skipping 4 times fft2048 */ /* skipping 2 times fft4096 */ /* perform 1 times fft8192 */ gsl_power2_fft8192synthesis_skip2 (X, Y); } /** ** Generated data ends here **/ /* public FFT frontends and generic handling of huge fft sizes */ static void gsl_power2_fftc_big (const unsigned int n_values, const double *rivalues_in, double *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); } void gsl_power2_fftac (const unsigned int n_values, const double *rivalues_in, double *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 double *rivalues_in, double *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; } */ } void gsl_power2_fftar (const unsigned int n_values, const double *r_values_in, double *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); }