| /* |
| * Copyright(c)1995,97 Mark Olesen <olesen@me.QueensU.CA> |
| * Queen's Univ at Kingston (Canada) |
| * |
| * Permission to use, copy, modify, and distribute this software for |
| * any purpose without fee is hereby granted, provided that this |
| * entire notice is included in all copies of any software which is |
| * or includes a copy or modification of this software and in all |
| * copies of the supporting documentation for such software. |
| * |
| * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR |
| * IMPLIED WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR QUEEN'S |
| * UNIVERSITY AT KINGSTON MAKES ANY REPRESENTATION OR WARRANTY OF ANY |
| * KIND CONCERNING THE MERCHANTABILITY OF THIS SOFTWARE OR ITS |
| * FITNESS FOR ANY PARTICULAR PURPOSE. |
| * |
| * All of which is to say that you can do what you like with this |
| * source code provided you don't try to sell it as your own and you |
| * include an unaltered copy of this message (including the |
| * copyright). |
| * |
| * It is also implicitly understood that bug fixes and improvements |
| * should make their way back to the general Internet community so |
| * that everyone benefits. |
| * |
| * Changes: |
| * Trivial type modifications by the WebRTC authors. |
| */ |
| |
| |
| /* |
| * File: |
| * WebRtcIsac_Fftn.c |
| * |
| * Public: |
| * WebRtcIsac_Fftn / fftnf (); |
| * |
| * Private: |
| * WebRtcIsac_Fftradix / fftradixf (); |
| * |
| * Descript: |
| * multivariate complex Fourier transform, computed in place |
| * using mixed-radix Fast Fourier Transform algorithm. |
| * |
| * Fortran code by: |
| * RC Singleton, Stanford Research Institute, Sept. 1968 |
| * |
| * translated by f2c (version 19950721). |
| * |
| * int WebRtcIsac_Fftn (int ndim, const int dims[], REAL Re[], REAL Im[], |
| * int iSign, double scaling); |
| * |
| * NDIM = the total number dimensions |
| * DIMS = a vector of array sizes |
| * if NDIM is zero then DIMS must be zero-terminated |
| * |
| * RE and IM hold the real and imaginary components of the data, and return |
| * the resulting real and imaginary Fourier coefficients. Multidimensional |
| * data *must* be allocated contiguously. There is no limit on the number |
| * of dimensions. |
| * |
| * ISIGN = the sign of the complex exponential (ie, forward or inverse FFT) |
| * the magnitude of ISIGN (normally 1) is used to determine the |
| * correct indexing increment (see below). |
| * |
| * SCALING = normalizing constant by which the final result is *divided* |
| * if SCALING == -1, normalize by total dimension of the transform |
| * if SCALING < -1, normalize by the square-root of the total dimension |
| * |
| * example: |
| * tri-variate transform with Re[n1][n2][n3], Im[n1][n2][n3] |
| * |
| * int dims[3] = {n1,n2,n3} |
| * WebRtcIsac_Fftn (3, dims, Re, Im, 1, scaling); |
| * |
| *-----------------------------------------------------------------------* |
| * int WebRtcIsac_Fftradix (REAL Re[], REAL Im[], size_t nTotal, size_t nPass, |
| * size_t nSpan, int iSign, size_t max_factors, |
| * size_t max_perm); |
| * |
| * RE, IM - see above documentation |
| * |
| * Although there is no limit on the number of dimensions, WebRtcIsac_Fftradix() must |
| * be called once for each dimension, but the calls may be in any order. |
| * |
| * NTOTAL = the total number of complex data values |
| * NPASS = the dimension of the current variable |
| * NSPAN/NPASS = the spacing of consecutive data values while indexing the |
| * current variable |
| * ISIGN - see above documentation |
| * |
| * example: |
| * tri-variate transform with Re[n1][n2][n3], Im[n1][n2][n3] |
| * |
| * WebRtcIsac_Fftradix (Re, Im, n1*n2*n3, n1, n1, 1, maxf, maxp); |
| * WebRtcIsac_Fftradix (Re, Im, n1*n2*n3, n2, n1*n2, 1, maxf, maxp); |
| * WebRtcIsac_Fftradix (Re, Im, n1*n2*n3, n3, n1*n2*n3, 1, maxf, maxp); |
| * |
| * single-variate transform, |
| * NTOTAL = N = NSPAN = (number of complex data values), |
| * |
| * WebRtcIsac_Fftradix (Re, Im, n, n, n, 1, maxf, maxp); |
| * |
| * The data can also be stored in a single array with alternating real and |
| * imaginary parts, the magnitude of ISIGN is changed to 2 to give correct |
| * indexing increment, and data [0] and data [1] used to pass the initial |
| * addresses for the sequences of real and imaginary values, |
| * |
| * example: |
| * REAL data [2*NTOTAL]; |
| * WebRtcIsac_Fftradix ( &data[0], &data[1], NTOTAL, nPass, nSpan, 2, maxf, maxp); |
| * |
| * for temporary allocation: |
| * |
| * MAX_FACTORS >= the maximum prime factor of NPASS |
| * MAX_PERM >= the number of prime factors of NPASS. In addition, |
| * if the square-free portion K of NPASS has two or more prime |
| * factors, then MAX_PERM >= (K-1) |
| * |
| * storage in FACTOR for a maximum of 15 prime factors of NPASS. if NPASS |
| * has more than one square-free factor, the product of the square-free |
| * factors must be <= 210 array storage for maximum prime factor of 23 the |
| * following two constants should agree with the array dimensions. |
| * |
| *----------------------------------------------------------------------*/ |
| |
| #include <stdlib.h> |
| #include <math.h> |
| |
| #include "modules/third_party/fft/fft.h" |
| |
| /* double precision routine */ |
| static int |
| WebRtcIsac_Fftradix (double Re[], double Im[], |
| size_t nTotal, size_t nPass, size_t nSpan, int isign, |
| int max_factors, unsigned int max_perm, |
| FFTstr *fftstate); |
| |
| |
| |
| #ifndef M_PI |
| # define M_PI 3.14159265358979323846264338327950288 |
| #endif |
| |
| #ifndef SIN60 |
| # define SIN60 0.86602540378443865 /* sin(60 deg) */ |
| # define COS72 0.30901699437494742 /* cos(72 deg) */ |
| # define SIN72 0.95105651629515357 /* sin(72 deg) */ |
| #endif |
| |
| # define REAL double |
| # define FFTN WebRtcIsac_Fftn |
| # define FFTNS "fftn" |
| # define FFTRADIX WebRtcIsac_Fftradix |
| # define FFTRADIXS "fftradix" |
| |
| |
| int WebRtcIsac_Fftns(unsigned int ndim, const int dims[], |
| double Re[], |
| double Im[], |
| int iSign, |
| double scaling, |
| FFTstr *fftstate) |
| { |
| |
| size_t nSpan, nPass, nTotal; |
| unsigned int i; |
| int ret, max_factors, max_perm; |
| |
| /* |
| * tally the number of elements in the data array |
| * and determine the number of dimensions |
| */ |
| nTotal = 1; |
| if (ndim && dims [0]) |
| { |
| for (i = 0; i < ndim; i++) |
| { |
| if (dims [i] <= 0) |
| { |
| return -1; |
| } |
| nTotal *= dims [i]; |
| } |
| } |
| else |
| { |
| ndim = 0; |
| for (i = 0; dims [i]; i++) |
| { |
| if (dims [i] <= 0) |
| { |
| return -1; |
| } |
| nTotal *= dims [i]; |
| ndim++; |
| } |
| } |
| |
| /* determine maximum number of factors and permuations */ |
| #if 1 |
| /* |
| * follow John Beale's example, just use the largest dimension and don't |
| * worry about excess allocation. May be someone else will do it? |
| */ |
| max_factors = max_perm = 1; |
| for (i = 0; i < ndim; i++) |
| { |
| nSpan = dims [i]; |
| if ((int)nSpan > max_factors) |
| { |
| max_factors = (int)nSpan; |
| } |
| if ((int)nSpan > max_perm) |
| { |
| max_perm = (int)nSpan; |
| } |
| } |
| #else |
| /* use the constants used in the original Fortran code */ |
| max_factors = 23; |
| max_perm = 209; |
| #endif |
| /* loop over the dimensions: */ |
| nPass = 1; |
| for (i = 0; i < ndim; i++) |
| { |
| nSpan = dims [i]; |
| nPass *= nSpan; |
| ret = FFTRADIX (Re, Im, nTotal, nSpan, nPass, iSign, |
| max_factors, max_perm, fftstate); |
| /* exit, clean-up already done */ |
| if (ret) |
| return ret; |
| } |
| |
| /* Divide through by the normalizing constant: */ |
| if (scaling && scaling != 1.0) |
| { |
| if (iSign < 0) iSign = -iSign; |
| if (scaling < 0.0) |
| { |
| scaling = (double)nTotal; |
| if (scaling < -1.0) |
| scaling = sqrt (scaling); |
| } |
| scaling = 1.0 / scaling; /* multiply is often faster */ |
| for (i = 0; i < nTotal; i += iSign) |
| { |
| Re [i] *= scaling; |
| Im [i] *= scaling; |
| } |
| } |
| return 0; |
| } |
| |
| /* |
| * singleton's mixed radix routine |
| * |
| * could move allocation out to WebRtcIsac_Fftn(), but leave it here so that it's |
| * possible to make this a standalone function |
| */ |
| |
| static int FFTRADIX (REAL Re[], |
| REAL Im[], |
| size_t nTotal, |
| size_t nPass, |
| size_t nSpan, |
| int iSign, |
| int max_factors, |
| unsigned int max_perm, |
| FFTstr *fftstate) |
| { |
| int ii, mfactor, kspan, ispan, inc; |
| int j, jc, jf, jj, k, k1, k2, k3, k4, kk, kt, nn, ns, nt; |
| |
| |
| REAL radf; |
| REAL c1, c2, c3, cd, aa, aj, ak, ajm, ajp, akm, akp; |
| REAL s1, s2, s3, sd, bb, bj, bk, bjm, bjp, bkm, bkp; |
| |
| REAL *Rtmp = NULL; /* temp space for real part*/ |
| REAL *Itmp = NULL; /* temp space for imaginary part */ |
| REAL *Cos = NULL; /* Cosine values */ |
| REAL *Sin = NULL; /* Sine values */ |
| |
| REAL s60 = SIN60; /* sin(60 deg) */ |
| REAL c72 = COS72; /* cos(72 deg) */ |
| REAL s72 = SIN72; /* sin(72 deg) */ |
| REAL pi2 = M_PI; /* use PI first, 2 PI later */ |
| |
| |
| fftstate->SpaceAlloced = 0; |
| fftstate->MaxPermAlloced = 0; |
| |
| |
| // initialize to avoid warnings |
| k3 = c2 = c3 = s2 = s3 = 0.0; |
| |
| if (nPass < 2) |
| return 0; |
| |
| /* allocate storage */ |
| if (fftstate->SpaceAlloced < max_factors * sizeof (REAL)) |
| { |
| #ifdef SUN_BROKEN_REALLOC |
| if (!fftstate->SpaceAlloced) /* first time */ |
| { |
| fftstate->SpaceAlloced = max_factors * sizeof (REAL); |
| } |
| else |
| { |
| #endif |
| fftstate->SpaceAlloced = max_factors * sizeof (REAL); |
| #ifdef SUN_BROKEN_REALLOC |
| } |
| #endif |
| } |
| else |
| { |
| /* allow full use of alloc'd space */ |
| max_factors = fftstate->SpaceAlloced / sizeof (REAL); |
| } |
| if (fftstate->MaxPermAlloced < max_perm) |
| { |
| #ifdef SUN_BROKEN_REALLOC |
| if (!fftstate->MaxPermAlloced) /* first time */ |
| else |
| #endif |
| fftstate->MaxPermAlloced = max_perm; |
| } |
| else |
| { |
| /* allow full use of alloc'd space */ |
| max_perm = fftstate->MaxPermAlloced; |
| } |
| |
| /* assign pointers */ |
| Rtmp = (REAL *) fftstate->Tmp0; |
| Itmp = (REAL *) fftstate->Tmp1; |
| Cos = (REAL *) fftstate->Tmp2; |
| Sin = (REAL *) fftstate->Tmp3; |
| |
| /* |
| * Function Body |
| */ |
| inc = iSign; |
| if (iSign < 0) { |
| s72 = -s72; |
| s60 = -s60; |
| pi2 = -pi2; |
| inc = -inc; /* absolute value */ |
| } |
| |
| /* adjust for strange increments */ |
| nt = inc * (int)nTotal; |
| ns = inc * (int)nSpan; |
| kspan = ns; |
| |
| nn = nt - inc; |
| jc = ns / (int)nPass; |
| radf = pi2 * (double) jc; |
| pi2 *= 2.0; /* use 2 PI from here on */ |
| |
| ii = 0; |
| jf = 0; |
| /* determine the factors of n */ |
| mfactor = 0; |
| k = (int)nPass; |
| while (k % 16 == 0) { |
| mfactor++; |
| fftstate->factor [mfactor - 1] = 4; |
| k /= 16; |
| } |
| j = 3; |
| jj = 9; |
| do { |
| while (k % jj == 0) { |
| mfactor++; |
| fftstate->factor [mfactor - 1] = j; |
| k /= jj; |
| } |
| j += 2; |
| jj = j * j; |
| } while (jj <= k); |
| if (k <= 4) { |
| kt = mfactor; |
| fftstate->factor [mfactor] = k; |
| if (k != 1) |
| mfactor++; |
| } else { |
| if (k - (k / 4 << 2) == 0) { |
| mfactor++; |
| fftstate->factor [mfactor - 1] = 2; |
| k /= 4; |
| } |
| kt = mfactor; |
| j = 2; |
| do { |
| if (k % j == 0) { |
| mfactor++; |
| fftstate->factor [mfactor - 1] = j; |
| k /= j; |
| } |
| j = ((j + 1) / 2 << 1) + 1; |
| } while (j <= k); |
| } |
| if (kt) { |
| j = kt; |
| do { |
| mfactor++; |
| fftstate->factor [mfactor - 1] = fftstate->factor [j - 1]; |
| j--; |
| } while (j); |
| } |
| |
| /* test that mfactors is in range */ |
| if (mfactor > FFT_NFACTOR) |
| { |
| return -1; |
| } |
| |
| /* compute fourier transform */ |
| for (;;) { |
| sd = radf / (double) kspan; |
| cd = sin(sd); |
| cd = 2.0 * cd * cd; |
| sd = sin(sd + sd); |
| kk = 0; |
| ii++; |
| |
| switch (fftstate->factor [ii - 1]) { |
| case 2: |
| /* transform for factor of 2 (including rotation factor) */ |
| kspan /= 2; |
| k1 = kspan + 2; |
| do { |
| do { |
| k2 = kk + kspan; |
| ak = Re [k2]; |
| bk = Im [k2]; |
| Re [k2] = Re [kk] - ak; |
| Im [k2] = Im [kk] - bk; |
| Re [kk] += ak; |
| Im [kk] += bk; |
| kk = k2 + kspan; |
| } while (kk < nn); |
| kk -= nn; |
| } while (kk < jc); |
| if (kk >= kspan) |
| goto Permute_Results_Label; /* exit infinite loop */ |
| do { |
| c1 = 1.0 - cd; |
| s1 = sd; |
| do { |
| do { |
| do { |
| k2 = kk + kspan; |
| ak = Re [kk] - Re [k2]; |
| bk = Im [kk] - Im [k2]; |
| Re [kk] += Re [k2]; |
| Im [kk] += Im [k2]; |
| Re [k2] = c1 * ak - s1 * bk; |
| Im [k2] = s1 * ak + c1 * bk; |
| kk = k2 + kspan; |
| } while (kk < (nt-1)); |
| k2 = kk - nt; |
| c1 = -c1; |
| kk = k1 - k2; |
| } while (kk > k2); |
| ak = c1 - (cd * c1 + sd * s1); |
| s1 = sd * c1 - cd * s1 + s1; |
| c1 = 2.0 - (ak * ak + s1 * s1); |
| s1 *= c1; |
| c1 *= ak; |
| kk += jc; |
| } while (kk < k2); |
| k1 += inc + inc; |
| kk = (k1 - kspan + 1) / 2 + jc - 1; |
| } while (kk < (jc + jc)); |
| break; |
| |
| case 4: /* transform for factor of 4 */ |
| ispan = kspan; |
| kspan /= 4; |
| |
| do { |
| c1 = 1.0; |
| s1 = 0.0; |
| do { |
| do { |
| k1 = kk + kspan; |
| k2 = k1 + kspan; |
| k3 = k2 + kspan; |
| akp = Re [kk] + Re [k2]; |
| akm = Re [kk] - Re [k2]; |
| ajp = Re [k1] + Re [k3]; |
| ajm = Re [k1] - Re [k3]; |
| bkp = Im [kk] + Im [k2]; |
| bkm = Im [kk] - Im [k2]; |
| bjp = Im [k1] + Im [k3]; |
| bjm = Im [k1] - Im [k3]; |
| Re [kk] = akp + ajp; |
| Im [kk] = bkp + bjp; |
| ajp = akp - ajp; |
| bjp = bkp - bjp; |
| if (iSign < 0) { |
| akp = akm + bjm; |
| bkp = bkm - ajm; |
| akm -= bjm; |
| bkm += ajm; |
| } else { |
| akp = akm - bjm; |
| bkp = bkm + ajm; |
| akm += bjm; |
| bkm -= ajm; |
| } |
| /* avoid useless multiplies */ |
| if (s1 == 0.0) { |
| Re [k1] = akp; |
| Re [k2] = ajp; |
| Re [k3] = akm; |
| Im [k1] = bkp; |
| Im [k2] = bjp; |
| Im [k3] = bkm; |
| } else { |
| Re [k1] = akp * c1 - bkp * s1; |
| Re [k2] = ajp * c2 - bjp * s2; |
| Re [k3] = akm * c3 - bkm * s3; |
| Im [k1] = akp * s1 + bkp * c1; |
| Im [k2] = ajp * s2 + bjp * c2; |
| Im [k3] = akm * s3 + bkm * c3; |
| } |
| kk = k3 + kspan; |
| } while (kk < nt); |
| |
| c2 = c1 - (cd * c1 + sd * s1); |
| s1 = sd * c1 - cd * s1 + s1; |
| c1 = 2.0 - (c2 * c2 + s1 * s1); |
| s1 *= c1; |
| c1 *= c2; |
| /* values of c2, c3, s2, s3 that will get used next time */ |
| c2 = c1 * c1 - s1 * s1; |
| s2 = 2.0 * c1 * s1; |
| c3 = c2 * c1 - s2 * s1; |
| s3 = c2 * s1 + s2 * c1; |
| kk = kk - nt + jc; |
| } while (kk < kspan); |
| kk = kk - kspan + inc; |
| } while (kk < jc); |
| if (kspan == jc) |
| goto Permute_Results_Label; /* exit infinite loop */ |
| break; |
| |
| default: |
| /* transform for odd factors */ |
| #ifdef FFT_RADIX4 |
| return -1; |
| break; |
| #else /* FFT_RADIX4 */ |
| k = fftstate->factor [ii - 1]; |
| ispan = kspan; |
| kspan /= k; |
| |
| switch (k) { |
| case 3: /* transform for factor of 3 (optional code) */ |
| do { |
| do { |
| k1 = kk + kspan; |
| k2 = k1 + kspan; |
| ak = Re [kk]; |
| bk = Im [kk]; |
| aj = Re [k1] + Re [k2]; |
| bj = Im [k1] + Im [k2]; |
| Re [kk] = ak + aj; |
| Im [kk] = bk + bj; |
| ak -= 0.5 * aj; |
| bk -= 0.5 * bj; |
| aj = (Re [k1] - Re [k2]) * s60; |
| bj = (Im [k1] - Im [k2]) * s60; |
| Re [k1] = ak - bj; |
| Re [k2] = ak + bj; |
| Im [k1] = bk + aj; |
| Im [k2] = bk - aj; |
| kk = k2 + kspan; |
| } while (kk < (nn - 1)); |
| kk -= nn; |
| } while (kk < kspan); |
| break; |
| |
| case 5: /* transform for factor of 5 (optional code) */ |
| c2 = c72 * c72 - s72 * s72; |
| s2 = 2.0 * c72 * s72; |
| do { |
| do { |
| k1 = kk + kspan; |
| k2 = k1 + kspan; |
| k3 = k2 + kspan; |
| k4 = k3 + kspan; |
| akp = Re [k1] + Re [k4]; |
| akm = Re [k1] - Re [k4]; |
| bkp = Im [k1] + Im [k4]; |
| bkm = Im [k1] - Im [k4]; |
| ajp = Re [k2] + Re [k3]; |
| ajm = Re [k2] - Re [k3]; |
| bjp = Im [k2] + Im [k3]; |
| bjm = Im [k2] - Im [k3]; |
| aa = Re [kk]; |
| bb = Im [kk]; |
| Re [kk] = aa + akp + ajp; |
| Im [kk] = bb + bkp + bjp; |
| ak = akp * c72 + ajp * c2 + aa; |
| bk = bkp * c72 + bjp * c2 + bb; |
| aj = akm * s72 + ajm * s2; |
| bj = bkm * s72 + bjm * s2; |
| Re [k1] = ak - bj; |
| Re [k4] = ak + bj; |
| Im [k1] = bk + aj; |
| Im [k4] = bk - aj; |
| ak = akp * c2 + ajp * c72 + aa; |
| bk = bkp * c2 + bjp * c72 + bb; |
| aj = akm * s2 - ajm * s72; |
| bj = bkm * s2 - bjm * s72; |
| Re [k2] = ak - bj; |
| Re [k3] = ak + bj; |
| Im [k2] = bk + aj; |
| Im [k3] = bk - aj; |
| kk = k4 + kspan; |
| } while (kk < (nn-1)); |
| kk -= nn; |
| } while (kk < kspan); |
| break; |
| |
| default: |
| if (k != jf) { |
| jf = k; |
| s1 = pi2 / (double) k; |
| c1 = cos(s1); |
| s1 = sin(s1); |
| if (jf > max_factors){ |
| return -1; |
| } |
| Cos [jf - 1] = 1.0; |
| Sin [jf - 1] = 0.0; |
| j = 1; |
| do { |
| Cos [j - 1] = Cos [k - 1] * c1 + Sin [k - 1] * s1; |
| Sin [j - 1] = Cos [k - 1] * s1 - Sin [k - 1] * c1; |
| k--; |
| Cos [k - 1] = Cos [j - 1]; |
| Sin [k - 1] = -Sin [j - 1]; |
| j++; |
| } while (j < k); |
| } |
| do { |
| do { |
| k1 = kk; |
| k2 = kk + ispan; |
| ak = aa = Re [kk]; |
| bk = bb = Im [kk]; |
| j = 1; |
| k1 += kspan; |
| do { |
| k2 -= kspan; |
| j++; |
| Rtmp [j - 1] = Re [k1] + Re [k2]; |
| ak += Rtmp [j - 1]; |
| Itmp [j - 1] = Im [k1] + Im [k2]; |
| bk += Itmp [j - 1]; |
| j++; |
| Rtmp [j - 1] = Re [k1] - Re [k2]; |
| Itmp [j - 1] = Im [k1] - Im [k2]; |
| k1 += kspan; |
| } while (k1 < k2); |
| Re [kk] = ak; |
| Im [kk] = bk; |
| k1 = kk; |
| k2 = kk + ispan; |
| j = 1; |
| do { |
| k1 += kspan; |
| k2 -= kspan; |
| jj = j; |
| ak = aa; |
| bk = bb; |
| aj = 0.0; |
| bj = 0.0; |
| k = 1; |
| do { |
| k++; |
| ak += Rtmp [k - 1] * Cos [jj - 1]; |
| bk += Itmp [k - 1] * Cos [jj - 1]; |
| k++; |
| aj += Rtmp [k - 1] * Sin [jj - 1]; |
| bj += Itmp [k - 1] * Sin [jj - 1]; |
| jj += j; |
| if (jj > jf) { |
| jj -= jf; |
| } |
| } while (k < jf); |
| k = jf - j; |
| Re [k1] = ak - bj; |
| Im [k1] = bk + aj; |
| Re [k2] = ak + bj; |
| Im [k2] = bk - aj; |
| j++; |
| } while (j < k); |
| kk += ispan; |
| } while (kk < nn); |
| kk -= nn; |
| } while (kk < kspan); |
| break; |
| } |
| |
| /* multiply by rotation factor (except for factors of 2 and 4) */ |
| if (ii == mfactor) |
| goto Permute_Results_Label; /* exit infinite loop */ |
| kk = jc; |
| do { |
| c2 = 1.0 - cd; |
| s1 = sd; |
| do { |
| c1 = c2; |
| s2 = s1; |
| kk += kspan; |
| do { |
| do { |
| ak = Re [kk]; |
| Re [kk] = c2 * ak - s2 * Im [kk]; |
| Im [kk] = s2 * ak + c2 * Im [kk]; |
| kk += ispan; |
| } while (kk < nt); |
| ak = s1 * s2; |
| s2 = s1 * c2 + c1 * s2; |
| c2 = c1 * c2 - ak; |
| kk = kk - nt + kspan; |
| } while (kk < ispan); |
| c2 = c1 - (cd * c1 + sd * s1); |
| s1 += sd * c1 - cd * s1; |
| c1 = 2.0 - (c2 * c2 + s1 * s1); |
| s1 *= c1; |
| c2 *= c1; |
| kk = kk - ispan + jc; |
| } while (kk < kspan); |
| kk = kk - kspan + jc + inc; |
| } while (kk < (jc + jc)); |
| break; |
| #endif /* FFT_RADIX4 */ |
| } |
| } |
| |
| /* permute the results to normal order---done in two stages */ |
| /* permutation for square factors of n */ |
| Permute_Results_Label: |
| fftstate->Perm [0] = ns; |
| if (kt) { |
| k = kt + kt + 1; |
| if (mfactor < k) |
| k--; |
| j = 1; |
| fftstate->Perm [k] = jc; |
| do { |
| fftstate->Perm [j] = fftstate->Perm [j - 1] / fftstate->factor [j - 1]; |
| fftstate->Perm [k - 1] = fftstate->Perm [k] * fftstate->factor [j - 1]; |
| j++; |
| k--; |
| } while (j < k); |
| k3 = fftstate->Perm [k]; |
| kspan = fftstate->Perm [1]; |
| kk = jc; |
| k2 = kspan; |
| j = 1; |
| if (nPass != nTotal) { |
| /* permutation for multivariate transform */ |
| Permute_Multi_Label: |
| do { |
| do { |
| k = kk + jc; |
| do { |
| /* swap Re [kk] <> Re [k2], Im [kk] <> Im [k2] */ |
| ak = Re [kk]; Re [kk] = Re [k2]; Re [k2] = ak; |
| bk = Im [kk]; Im [kk] = Im [k2]; Im [k2] = bk; |
| kk += inc; |
| k2 += inc; |
| } while (kk < (k-1)); |
| kk += ns - jc; |
| k2 += ns - jc; |
| } while (kk < (nt-1)); |
| k2 = k2 - nt + kspan; |
| kk = kk - nt + jc; |
| } while (k2 < (ns-1)); |
| do { |
| do { |
| k2 -= fftstate->Perm [j - 1]; |
| j++; |
| k2 = fftstate->Perm [j] + k2; |
| } while (k2 > fftstate->Perm [j - 1]); |
| j = 1; |
| do { |
| if (kk < (k2-1)) |
| goto Permute_Multi_Label; |
| kk += jc; |
| k2 += kspan; |
| } while (k2 < (ns-1)); |
| } while (kk < (ns-1)); |
| } else { |
| /* permutation for single-variate transform (optional code) */ |
| Permute_Single_Label: |
| do { |
| /* swap Re [kk] <> Re [k2], Im [kk] <> Im [k2] */ |
| ak = Re [kk]; Re [kk] = Re [k2]; Re [k2] = ak; |
| bk = Im [kk]; Im [kk] = Im [k2]; Im [k2] = bk; |
| kk += inc; |
| k2 += kspan; |
| } while (k2 < (ns-1)); |
| do { |
| do { |
| k2 -= fftstate->Perm [j - 1]; |
| j++; |
| k2 = fftstate->Perm [j] + k2; |
| } while (k2 >= fftstate->Perm [j - 1]); |
| j = 1; |
| do { |
| if (kk < k2) |
| goto Permute_Single_Label; |
| kk += inc; |
| k2 += kspan; |
| } while (k2 < (ns-1)); |
| } while (kk < (ns-1)); |
| } |
| jc = k3; |
| } |
| |
| if ((kt << 1) + 1 >= mfactor) |
| return 0; |
| ispan = fftstate->Perm [kt]; |
| /* permutation for square-free factors of n */ |
| j = mfactor - kt; |
| fftstate->factor [j] = 1; |
| do { |
| fftstate->factor [j - 1] *= fftstate->factor [j]; |
| j--; |
| } while (j != kt); |
| kt++; |
| nn = fftstate->factor [kt - 1] - 1; |
| if (nn > (int) max_perm) { |
| return -1; |
| } |
| j = jj = 0; |
| for (;;) { |
| k = kt + 1; |
| k2 = fftstate->factor [kt - 1]; |
| kk = fftstate->factor [k - 1]; |
| j++; |
| if (j > nn) |
| break; /* exit infinite loop */ |
| jj += kk; |
| while (jj >= k2) { |
| jj -= k2; |
| k2 = kk; |
| k++; |
| kk = fftstate->factor [k - 1]; |
| jj += kk; |
| } |
| fftstate->Perm [j - 1] = jj; |
| } |
| /* determine the permutation cycles of length greater than 1 */ |
| j = 0; |
| for (;;) { |
| do { |
| j++; |
| kk = fftstate->Perm [j - 1]; |
| } while (kk < 0); |
| if (kk != j) { |
| do { |
| k = kk; |
| kk = fftstate->Perm [k - 1]; |
| fftstate->Perm [k - 1] = -kk; |
| } while (kk != j); |
| k3 = kk; |
| } else { |
| fftstate->Perm [j - 1] = -j; |
| if (j == nn) |
| break; /* exit infinite loop */ |
| } |
| } |
| max_factors *= inc; |
| /* reorder a and b, following the permutation cycles */ |
| for (;;) { |
| j = k3 + 1; |
| nt -= ispan; |
| ii = nt - inc + 1; |
| if (nt < 0) |
| break; /* exit infinite loop */ |
| do { |
| do { |
| j--; |
| } while (fftstate->Perm [j - 1] < 0); |
| jj = jc; |
| do { |
| kspan = jj; |
| if (jj > max_factors) { |
| kspan = max_factors; |
| } |
| jj -= kspan; |
| k = fftstate->Perm [j - 1]; |
| kk = jc * k + ii + jj; |
| k1 = kk + kspan - 1; |
| k2 = 0; |
| do { |
| k2++; |
| Rtmp [k2 - 1] = Re [k1]; |
| Itmp [k2 - 1] = Im [k1]; |
| k1 -= inc; |
| } while (k1 != (kk-1)); |
| do { |
| k1 = kk + kspan - 1; |
| k2 = k1 - jc * (k + fftstate->Perm [k - 1]); |
| k = -fftstate->Perm [k - 1]; |
| do { |
| Re [k1] = Re [k2]; |
| Im [k1] = Im [k2]; |
| k1 -= inc; |
| k2 -= inc; |
| } while (k1 != (kk-1)); |
| kk = k2 + 1; |
| } while (k != j); |
| k1 = kk + kspan - 1; |
| k2 = 0; |
| do { |
| k2++; |
| Re [k1] = Rtmp [k2 - 1]; |
| Im [k1] = Itmp [k2 - 1]; |
| k1 -= inc; |
| } while (k1 != (kk-1)); |
| } while (jj); |
| } while (j != 1); |
| } |
| return 0; /* exit point here */ |
| } |
| /* ---------------------- end-of-file (c source) ---------------------- */ |
| |
