blob: cbc4dc31eb544ae9cd792dfc4fb8c9e59fe8d021 [file] [log] [blame]
 /* * http://www.kurims.kyoto-u.ac.jp/~ooura/fft.html * Copyright Takuya OOURA, 1996-2001 * * You may use, copy, modify and distribute this code for any purpose (include * commercial use) and without fee. Please refer to this package when you modify * this code. * * Changes: * Trivial type modifications by the WebRTC authors. */ /* Fast Fourier/Cosine/Sine Transform dimension :one data length :power of 2 decimation :frequency radix :4, 2 data :inplace table :use functions cdft: Complex Discrete Fourier Transform rdft: Real Discrete Fourier Transform ddct: Discrete Cosine Transform ddst: Discrete Sine Transform dfct: Cosine Transform of RDFT (Real Symmetric DFT) dfst: Sine Transform of RDFT (Real Anti-symmetric DFT) function prototypes void cdft(int, int, float *, int *, float *); void rdft(int, int, float *, int *, float *); void ddct(int, int, float *, int *, float *); void ddst(int, int, float *, int *, float *); void dfct(int, float *, float *, int *, float *); void dfst(int, float *, float *, int *, float *); -------- Complex DFT (Discrete Fourier Transform) -------- [definition] X[k] = sum_j=0^n-1 x[j]*exp(2*pi*i*j*k/n), 0<=k X[k] = sum_j=0^n-1 x[j]*exp(-2*pi*i*j*k/n), 0<=k ip[0] = 0; // first time only cdft(2*n, 1, a, ip, w); ip[0] = 0; // first time only cdft(2*n, -1, a, ip, w); [parameters] 2*n :data length (int) n >= 1, n = power of 2 a[0...2*n-1] :input/output data (float *) input data a[2*j] = Re(x[j]), a[2*j+1] = Im(x[j]), 0<=j= 2+sqrt(n) strictly, length of ip >= 2+(1<<(int)(log(n+0.5)/log(2))/2). ip[0],ip[1] are pointers of the cos/sin table. w[0...n/2-1] :cos/sin table (float *) w[],ip[] are initialized if ip[0] == 0. [remark] Inverse of cdft(2*n, -1, a, ip, w); is cdft(2*n, 1, a, ip, w); for (j = 0; j <= 2 * n - 1; j++) { a[j] *= 1.0 / n; } . -------- Real DFT / Inverse of Real DFT -------- [definition] RDFT R[k] = sum_j=0^n-1 a[j]*cos(2*pi*j*k/n), 0<=k<=n/2 I[k] = sum_j=0^n-1 a[j]*sin(2*pi*j*k/n), 0 IRDFT (excluding scale) a[k] = (R[0] + R[n/2]*cos(pi*k))/2 + sum_j=1^n/2-1 R[j]*cos(2*pi*j*k/n) + sum_j=1^n/2-1 I[j]*sin(2*pi*j*k/n), 0<=k ip[0] = 0; // first time only rdft(n, 1, a, ip, w); ip[0] = 0; // first time only rdft(n, -1, a, ip, w); [parameters] n :data length (int) n >= 2, n = power of 2 a[0...n-1] :input/output data (float *) output data a[2*k] = R[k], 0<=k input data a[2*j] = R[j], 0<=j= 2+sqrt(n/2) strictly, length of ip >= 2+(1<<(int)(log(n/2+0.5)/log(2))/2). ip[0],ip[1] are pointers of the cos/sin table. w[0...n/2-1] :cos/sin table (float *) w[],ip[] are initialized if ip[0] == 0. [remark] Inverse of rdft(n, 1, a, ip, w); is rdft(n, -1, a, ip, w); for (j = 0; j <= n - 1; j++) { a[j] *= 2.0 / n; } . -------- DCT (Discrete Cosine Transform) / Inverse of DCT -------- [definition] IDCT (excluding scale) C[k] = sum_j=0^n-1 a[j]*cos(pi*j*(k+1/2)/n), 0<=k DCT C[k] = sum_j=0^n-1 a[j]*cos(pi*(j+1/2)*k/n), 0<=k ip[0] = 0; // first time only ddct(n, 1, a, ip, w); ip[0] = 0; // first time only ddct(n, -1, a, ip, w); [parameters] n :data length (int) n >= 2, n = power of 2 a[0...n-1] :input/output data (float *) output data a[k] = C[k], 0<=k= 2+sqrt(n/2) strictly, length of ip >= 2+(1<<(int)(log(n/2+0.5)/log(2))/2). ip[0],ip[1] are pointers of the cos/sin table. w[0...n*5/4-1] :cos/sin table (float *) w[],ip[] are initialized if ip[0] == 0. [remark] Inverse of ddct(n, -1, a, ip, w); is a[0] *= 0.5; ddct(n, 1, a, ip, w); for (j = 0; j <= n - 1; j++) { a[j] *= 2.0 / n; } . -------- DST (Discrete Sine Transform) / Inverse of DST -------- [definition] IDST (excluding scale) S[k] = sum_j=1^n A[j]*sin(pi*j*(k+1/2)/n), 0<=k DST S[k] = sum_j=0^n-1 a[j]*sin(pi*(j+1/2)*k/n), 0 ip[0] = 0; // first time only ddst(n, 1, a, ip, w); ip[0] = 0; // first time only ddst(n, -1, a, ip, w); [parameters] n :data length (int) n >= 2, n = power of 2 a[0...n-1] :input/output data (float *) input data a[j] = A[j], 0 output data a[k] = S[k], 0= 2+sqrt(n/2) strictly, length of ip >= 2+(1<<(int)(log(n/2+0.5)/log(2))/2). ip[0],ip[1] are pointers of the cos/sin table. w[0...n*5/4-1] :cos/sin table (float *) w[],ip[] are initialized if ip[0] == 0. [remark] Inverse of ddst(n, -1, a, ip, w); is a[0] *= 0.5; ddst(n, 1, a, ip, w); for (j = 0; j <= n - 1; j++) { a[j] *= 2.0 / n; } . -------- Cosine Transform of RDFT (Real Symmetric DFT) -------- [definition] C[k] = sum_j=0^n a[j]*cos(pi*j*k/n), 0<=k<=n [usage] ip[0] = 0; // first time only dfct(n, a, t, ip, w); [parameters] n :data length - 1 (int) n >= 2, n = power of 2 a[0...n] :input/output data (float *) output data a[k] = C[k], 0<=k<=n t[0...n/2] :work area (float *) ip[0...*] :work area for bit reversal (int *) length of ip >= 2+sqrt(n/4) strictly, length of ip >= 2+(1<<(int)(log(n/4+0.5)/log(2))/2). ip[0],ip[1] are pointers of the cos/sin table. w[0...n*5/8-1] :cos/sin table (float *) w[],ip[] are initialized if ip[0] == 0. [remark] Inverse of a[0] *= 0.5; a[n] *= 0.5; dfct(n, a, t, ip, w); is a[0] *= 0.5; a[n] *= 0.5; dfct(n, a, t, ip, w); for (j = 0; j <= n; j++) { a[j] *= 2.0 / n; } . -------- Sine Transform of RDFT (Real Anti-symmetric DFT) -------- [definition] S[k] = sum_j=1^n-1 a[j]*sin(pi*j*k/n), 0= 2, n = power of 2 a[0...n-1] :input/output data (float *) output data a[k] = S[k], 0= 2+sqrt(n/4) strictly, length of ip >= 2+(1<<(int)(log(n/4+0.5)/log(2))/2). ip[0],ip[1] are pointers of the cos/sin table. w[0...n*5/8-1] :cos/sin table (float *) w[],ip[] are initialized if ip[0] == 0. [remark] Inverse of dfst(n, a, t, ip, w); is dfst(n, a, t, ip, w); for (j = 1; j <= n - 1; j++) { a[j] *= 2.0 / n; } . Appendix : The cos/sin table is recalculated when the larger table required. w[] and ip[] are compatible with all routines. */ static void makewt(int nw, int *ip, float *w); static void makect(int nc, int *ip, float *c); static void bitrv2(int n, int *ip, float *a); static void bitrv2conj(int n, int *ip, float *a); static void cftfsub(int n, float *a, float *w); static void cftbsub(int n, float *a, float *w); static void cft1st(int n, float *a, float *w); static void cftmdl(int n, int l, float *a, float *w); static void rftfsub(int n, float *a, int nc, float *c); static void rftbsub(int n, float *a, int nc, float *c); #if 0 // Not used. static void dctsub(int n, float *a, int nc, float *c) static void dstsub(int n, float *a, int nc, float *c) #endif void WebRtc_cdft(int n, int isgn, float *a, int *ip, float *w) { if (n > (ip[0] << 2)) { makewt(n >> 2, ip, w); } if (n > 4) { if (isgn >= 0) { bitrv2(n, ip + 2, a); cftfsub(n, a, w); } else { bitrv2conj(n, ip + 2, a); cftbsub(n, a, w); } } else if (n == 4) { cftfsub(n, a, w); } } void WebRtc_rdft(int n, int isgn, float *a, int *ip, float *w) { int nw, nc; float xi; nw = ip[0]; if (n > (nw << 2)) { nw = n >> 2; makewt(nw, ip, w); } nc = ip[1]; if (n > (nc << 2)) { nc = n >> 2; makect(nc, ip, w + nw); } if (isgn >= 0) { if (n > 4) { bitrv2(n, ip + 2, a); cftfsub(n, a, w); rftfsub(n, a, nc, w + nw); } else if (n == 4) { cftfsub(n, a, w); } xi = a[0] - a[1]; a[0] += a[1]; a[1] = xi; } else { a[1] = 0.5f * (a[0] - a[1]); a[0] -= a[1]; if (n > 4) { rftbsub(n, a, nc, w + nw); bitrv2(n, ip + 2, a); cftbsub(n, a, w); } else if (n == 4) { cftfsub(n, a, w); } } } #if 0 // Not used. static void ddct(int n, int isgn, float *a, int *ip, float *w) { int j, nw, nc; float xr; nw = ip[0]; if (n > (nw << 2)) { nw = n >> 2; makewt(nw, ip, w); } nc = ip[1]; if (n > nc) { nc = n; makect(nc, ip, w + nw); } if (isgn < 0) { xr = a[n - 1]; for (j = n - 2; j >= 2; j -= 2) { a[j + 1] = a[j] - a[j - 1]; a[j] += a[j - 1]; } a[1] = a[0] - xr; a[0] += xr; if (n > 4) { rftbsub(n, a, nc, w + nw); bitrv2(n, ip + 2, a); cftbsub(n, a, w); } else if (n == 4) { cftfsub(n, a, w); } } dctsub(n, a, nc, w + nw); if (isgn >= 0) { if (n > 4) { bitrv2(n, ip + 2, a); cftfsub(n, a, w); rftfsub(n, a, nc, w + nw); } else if (n == 4) { cftfsub(n, a, w); } xr = a[0] - a[1]; a[0] += a[1]; for (j = 2; j < n; j += 2) { a[j - 1] = a[j] - a[j + 1]; a[j] += a[j + 1]; } a[n - 1] = xr; } } static void ddst(int n, int isgn, float *a, int *ip, float *w) { int j, nw, nc; float xr; nw = ip[0]; if (n > (nw << 2)) { nw = n >> 2; makewt(nw, ip, w); } nc = ip[1]; if (n > nc) { nc = n; makect(nc, ip, w + nw); } if (isgn < 0) { xr = a[n - 1]; for (j = n - 2; j >= 2; j -= 2) { a[j + 1] = -a[j] - a[j - 1]; a[j] -= a[j - 1]; } a[1] = a[0] + xr; a[0] -= xr; if (n > 4) { rftbsub(n, a, nc, w + nw); bitrv2(n, ip + 2, a); cftbsub(n, a, w); } else if (n == 4) { cftfsub(n, a, w); } } dstsub(n, a, nc, w + nw); if (isgn >= 0) { if (n > 4) { bitrv2(n, ip + 2, a); cftfsub(n, a, w); rftfsub(n, a, nc, w + nw); } else if (n == 4) { cftfsub(n, a, w); } xr = a[0] - a[1]; a[0] += a[1]; for (j = 2; j < n; j += 2) { a[j - 1] = -a[j] - a[j + 1]; a[j] -= a[j + 1]; } a[n - 1] = -xr; } } static void dfct(int n, float *a, float *t, int *ip, float *w) { int j, k, l, m, mh, nw, nc; float xr, xi, yr, yi; nw = ip[0]; if (n > (nw << 3)) { nw = n >> 3; makewt(nw, ip, w); } nc = ip[1]; if (n > (nc << 1)) { nc = n >> 1; makect(nc, ip, w + nw); } m = n >> 1; yi = a[m]; xi = a[0] + a[n]; a[0] -= a[n]; t[0] = xi - yi; t[m] = xi + yi; if (n > 2) { mh = m >> 1; for (j = 1; j < mh; j++) { k = m - j; xr = a[j] - a[n - j]; xi = a[j] + a[n - j]; yr = a[k] - a[n - k]; yi = a[k] + a[n - k]; a[j] = xr; a[k] = yr; t[j] = xi - yi; t[k] = xi + yi; } t[mh] = a[mh] + a[n - mh]; a[mh] -= a[n - mh]; dctsub(m, a, nc, w + nw); if (m > 4) { bitrv2(m, ip + 2, a); cftfsub(m, a, w); rftfsub(m, a, nc, w + nw); } else if (m == 4) { cftfsub(m, a, w); } a[n - 1] = a[0] - a[1]; a[1] = a[0] + a[1]; for (j = m - 2; j >= 2; j -= 2) { a[2 * j + 1] = a[j] + a[j + 1]; a[2 * j - 1] = a[j] - a[j + 1]; } l = 2; m = mh; while (m >= 2) { dctsub(m, t, nc, w + nw); if (m > 4) { bitrv2(m, ip + 2, t); cftfsub(m, t, w); rftfsub(m, t, nc, w + nw); } else if (m == 4) { cftfsub(m, t, w); } a[n - l] = t[0] - t[1]; a[l] = t[0] + t[1]; k = 0; for (j = 2; j < m; j += 2) { k += l << 2; a[k - l] = t[j] - t[j + 1]; a[k + l] = t[j] + t[j + 1]; } l <<= 1; mh = m >> 1; for (j = 0; j < mh; j++) { k = m - j; t[j] = t[m + k] - t[m + j]; t[k] = t[m + k] + t[m + j]; } t[mh] = t[m + mh]; m = mh; } a[l] = t[0]; a[n] = t[2] - t[1]; a[0] = t[2] + t[1]; } else { a[1] = a[0]; a[2] = t[0]; a[0] = t[1]; } } static void dfst(int n, float *a, float *t, int *ip, float *w) { int j, k, l, m, mh, nw, nc; float xr, xi, yr, yi; nw = ip[0]; if (n > (nw << 3)) { nw = n >> 3; makewt(nw, ip, w); } nc = ip[1]; if (n > (nc << 1)) { nc = n >> 1; makect(nc, ip, w + nw); } if (n > 2) { m = n >> 1; mh = m >> 1; for (j = 1; j < mh; j++) { k = m - j; xr = a[j] + a[n - j]; xi = a[j] - a[n - j]; yr = a[k] + a[n - k]; yi = a[k] - a[n - k]; a[j] = xr; a[k] = yr; t[j] = xi + yi; t[k] = xi - yi; } t[0] = a[mh] - a[n - mh]; a[mh] += a[n - mh]; a[0] = a[m]; dstsub(m, a, nc, w + nw); if (m > 4) { bitrv2(m, ip + 2, a); cftfsub(m, a, w); rftfsub(m, a, nc, w + nw); } else if (m == 4) { cftfsub(m, a, w); } a[n - 1] = a[1] - a[0]; a[1] = a[0] + a[1]; for (j = m - 2; j >= 2; j -= 2) { a[2 * j + 1] = a[j] - a[j + 1]; a[2 * j - 1] = -a[j] - a[j + 1]; } l = 2; m = mh; while (m >= 2) { dstsub(m, t, nc, w + nw); if (m > 4) { bitrv2(m, ip + 2, t); cftfsub(m, t, w); rftfsub(m, t, nc, w + nw); } else if (m == 4) { cftfsub(m, t, w); } a[n - l] = t[1] - t[0]; a[l] = t[0] + t[1]; k = 0; for (j = 2; j < m; j += 2) { k += l << 2; a[k - l] = -t[j] - t[j + 1]; a[k + l] = t[j] - t[j + 1]; } l <<= 1; mh = m >> 1; for (j = 1; j < mh; j++) { k = m - j; t[j] = t[m + k] + t[m + j]; t[k] = t[m + k] - t[m + j]; } t[0] = t[m + mh]; m = mh; } a[l] = t[0]; } a[0] = 0; } #endif // Not used. /* -------- initializing routines -------- */ #include static void makewt(int nw, int *ip, float *w) { int j, nwh; float delta, x, y; ip[0] = nw; ip[1] = 1; if (nw > 2) { nwh = nw >> 1; delta = (float)atan(1.0f) / nwh; w[0] = 1; w[1] = 0; w[nwh] = (float)cos(delta * nwh); w[nwh + 1] = w[nwh]; if (nwh > 2) { for (j = 2; j < nwh; j += 2) { x = (float)cos(delta * j); y = (float)sin(delta * j); w[j] = x; w[j + 1] = y; w[nw - j] = y; w[nw - j + 1] = x; } bitrv2(nw, ip + 2, w); } } } static void makect(int nc, int *ip, float *c) { int j, nch; float delta; ip[1] = nc; if (nc > 1) { nch = nc >> 1; delta = (float)atan(1.0f) / nch; c[0] = (float)cos(delta * nch); c[nch] = 0.5f * c[0]; for (j = 1; j < nch; j++) { c[j] = 0.5f * (float)cos(delta * j); c[nc - j] = 0.5f * (float)sin(delta * j); } } } /* -------- child routines -------- */ static void bitrv2(int n, int *ip, float *a) { int j, j1, k, k1, l, m, m2; float xr, xi, yr, yi; ip[0] = 0; l = n; m = 1; while ((m << 3) < l) { l >>= 1; for (j = 0; j < m; j++) { ip[m + j] = ip[j] + l; } m <<= 1; } m2 = 2 * m; if ((m << 3) == l) { for (k = 0; k < m; k++) { for (j = 0; j < k; j++) { j1 = 2 * j + ip[k]; k1 = 2 * k + ip[j]; xr = a[j1]; xi = a[j1 + 1]; yr = a[k1]; yi = a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; j1 += m2; k1 += 2 * m2; xr = a[j1]; xi = a[j1 + 1]; yr = a[k1]; yi = a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; j1 += m2; k1 -= m2; xr = a[j1]; xi = a[j1 + 1]; yr = a[k1]; yi = a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; j1 += m2; k1 += 2 * m2; xr = a[j1]; xi = a[j1 + 1]; yr = a[k1]; yi = a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; } j1 = 2 * k + m2 + ip[k]; k1 = j1 + m2; xr = a[j1]; xi = a[j1 + 1]; yr = a[k1]; yi = a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; } } else { for (k = 1; k < m; k++) { for (j = 0; j < k; j++) { j1 = 2 * j + ip[k]; k1 = 2 * k + ip[j]; xr = a[j1]; xi = a[j1 + 1]; yr = a[k1]; yi = a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; j1 += m2; k1 += m2; xr = a[j1]; xi = a[j1 + 1]; yr = a[k1]; yi = a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; } } } } static void bitrv2conj(int n, int *ip, float *a) { int j, j1, k, k1, l, m, m2; float xr, xi, yr, yi; ip[0] = 0; l = n; m = 1; while ((m << 3) < l) { l >>= 1; for (j = 0; j < m; j++) { ip[m + j] = ip[j] + l; } m <<= 1; } m2 = 2 * m; if ((m << 3) == l) { for (k = 0; k < m; k++) { for (j = 0; j < k; j++) { j1 = 2 * j + ip[k]; k1 = 2 * k + ip[j]; xr = a[j1]; xi = -a[j1 + 1]; yr = a[k1]; yi = -a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; j1 += m2; k1 += 2 * m2; xr = a[j1]; xi = -a[j1 + 1]; yr = a[k1]; yi = -a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; j1 += m2; k1 -= m2; xr = a[j1]; xi = -a[j1 + 1]; yr = a[k1]; yi = -a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; j1 += m2; k1 += 2 * m2; xr = a[j1]; xi = -a[j1 + 1]; yr = a[k1]; yi = -a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; } k1 = 2 * k + ip[k]; a[k1 + 1] = -a[k1 + 1]; j1 = k1 + m2; k1 = j1 + m2; xr = a[j1]; xi = -a[j1 + 1]; yr = a[k1]; yi = -a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; k1 += m2; a[k1 + 1] = -a[k1 + 1]; } } else { a[1] = -a[1]; a[m2 + 1] = -a[m2 + 1]; for (k = 1; k < m; k++) { for (j = 0; j < k; j++) { j1 = 2 * j + ip[k]; k1 = 2 * k + ip[j]; xr = a[j1]; xi = -a[j1 + 1]; yr = a[k1]; yi = -a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; j1 += m2; k1 += m2; xr = a[j1]; xi = -a[j1 + 1]; yr = a[k1]; yi = -a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; } k1 = 2 * k + ip[k]; a[k1 + 1] = -a[k1 + 1]; a[k1 + m2 + 1] = -a[k1 + m2 + 1]; } } } static void cftfsub(int n, float *a, float *w) { int j, j1, j2, j3, l; float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; l = 2; if (n > 8) { cft1st(n, a, w); l = 8; while ((l << 2) < n) { cftmdl(n, l, a, w); l <<= 2; } } if ((l << 2) == n) { for (j = 0; j < l; j += 2) { j1 = j + l; j2 = j1 + l; j3 = j2 + l; x0r = a[j] + a[j1]; x0i = a[j + 1] + a[j1 + 1]; x1r = a[j] - a[j1]; x1i = a[j + 1] - a[j1 + 1]; x2r = a[j2] + a[j3]; x2i = a[j2 + 1] + a[j3 + 1]; x3r = a[j2] - a[j3]; x3i = a[j2 + 1] - a[j3 + 1]; a[j] = x0r + x2r; a[j + 1] = x0i + x2i; a[j2] = x0r - x2r; a[j2 + 1] = x0i - x2i; a[j1] = x1r - x3i; a[j1 + 1] = x1i + x3r; a[j3] = x1r + x3i; a[j3 + 1] = x1i - x3r; } } else { for (j = 0; j < l; j += 2) { j1 = j + l; x0r = a[j] - a[j1]; x0i = a[j + 1] - a[j1 + 1]; a[j] += a[j1]; a[j + 1] += a[j1 + 1]; a[j1] = x0r; a[j1 + 1] = x0i; } } } static void cftbsub(int n, float *a, float *w) { int j, j1, j2, j3, l; float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; l = 2; if (n > 8) { cft1st(n, a, w); l = 8; while ((l << 2) < n) { cftmdl(n, l, a, w); l <<= 2; } } if ((l << 2) == n) { for (j = 0; j < l; j += 2) { j1 = j + l; j2 = j1 + l; j3 = j2 + l; x0r = a[j] + a[j1]; x0i = -a[j + 1] - a[j1 + 1]; x1r = a[j] - a[j1]; x1i = -a[j + 1] + a[j1 + 1]; x2r = a[j2] + a[j3]; x2i = a[j2 + 1] + a[j3 + 1]; x3r = a[j2] - a[j3]; x3i = a[j2 + 1] - a[j3 + 1]; a[j] = x0r + x2r; a[j + 1] = x0i - x2i; a[j2] = x0r - x2r; a[j2 + 1] = x0i + x2i; a[j1] = x1r - x3i; a[j1 + 1] = x1i - x3r; a[j3] = x1r + x3i; a[j3 + 1] = x1i + x3r; } } else { for (j = 0; j < l; j += 2) { j1 = j + l; x0r = a[j] - a[j1]; x0i = -a[j + 1] + a[j1 + 1]; a[j] += a[j1]; a[j + 1] = -a[j + 1] - a[j1 + 1]; a[j1] = x0r; a[j1 + 1] = x0i; } } } static void cft1st(int n, float *a, float *w) { int j, k1, k2; float wk1r, wk1i, wk2r, wk2i, wk3r, wk3i; float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; x0r = a[0] + a[2]; x0i = a[1] + a[3]; x1r = a[0] - a[2]; x1i = a[1] - a[3]; x2r = a[4] + a[6]; x2i = a[5] + a[7]; x3r = a[4] - a[6]; x3i = a[5] - a[7]; a[0] = x0r + x2r; a[1] = x0i + x2i; a[4] = x0r - x2r; a[5] = x0i - x2i; a[2] = x1r - x3i; a[3] = x1i + x3r; a[6] = x1r + x3i; a[7] = x1i - x3r; wk1r = w[2]; x0r = a[8] + a[10]; x0i = a[9] + a[11]; x1r = a[8] - a[10]; x1i = a[9] - a[11]; x2r = a[12] + a[14]; x2i = a[13] + a[15]; x3r = a[12] - a[14]; x3i = a[13] - a[15]; a[8] = x0r + x2r; a[9] = x0i + x2i; a[12] = x2i - x0i; a[13] = x0r - x2r; x0r = x1r - x3i; x0i = x1i + x3r; a[10] = wk1r * (x0r - x0i); a[11] = wk1r * (x0r + x0i); x0r = x3i + x1r; x0i = x3r - x1i; a[14] = wk1r * (x0i - x0r); a[15] = wk1r * (x0i + x0r); k1 = 0; for (j = 16; j < n; j += 16) { k1 += 2; k2 = 2 * k1; wk2r = w[k1]; wk2i = w[k1 + 1]; wk1r = w[k2]; wk1i = w[k2 + 1]; wk3r = wk1r - 2 * wk2i * wk1i; wk3i = 2 * wk2i * wk1r - wk1i; x0r = a[j] + a[j + 2]; x0i = a[j + 1] + a[j + 3]; x1r = a[j] - a[j + 2]; x1i = a[j + 1] - a[j + 3]; x2r = a[j + 4] + a[j + 6]; x2i = a[j + 5] + a[j + 7]; x3r = a[j + 4] - a[j + 6]; x3i = a[j + 5] - a[j + 7]; a[j] = x0r + x2r; a[j + 1] = x0i + x2i; x0r -= x2r; x0i -= x2i; a[j + 4] = wk2r * x0r - wk2i * x0i; a[j + 5] = wk2r * x0i + wk2i * x0r; x0r = x1r - x3i; x0i = x1i + x3r; a[j + 2] = wk1r * x0r - wk1i * x0i; a[j + 3] = wk1r * x0i + wk1i * x0r; x0r = x1r + x3i; x0i = x1i - x3r; a[j + 6] = wk3r * x0r - wk3i * x0i; a[j + 7] = wk3r * x0i + wk3i * x0r; wk1r = w[k2 + 2]; wk1i = w[k2 + 3]; wk3r = wk1r - 2 * wk2r * wk1i; wk3i = 2 * wk2r * wk1r - wk1i; x0r = a[j + 8] + a[j + 10]; x0i = a[j + 9] + a[j + 11]; x1r = a[j + 8] - a[j + 10]; x1i = a[j + 9] - a[j + 11]; x2r = a[j + 12] + a[j + 14]; x2i = a[j + 13] + a[j + 15]; x3r = a[j + 12] - a[j + 14]; x3i = a[j + 13] - a[j + 15]; a[j + 8] = x0r + x2r; a[j + 9] = x0i + x2i; x0r -= x2r; x0i -= x2i; a[j + 12] = -wk2i * x0r - wk2r * x0i; a[j + 13] = -wk2i * x0i + wk2r * x0r; x0r = x1r - x3i; x0i = x1i + x3r; a[j + 10] = wk1r * x0r - wk1i * x0i; a[j + 11] = wk1r * x0i + wk1i * x0r; x0r = x1r + x3i; x0i = x1i - x3r; a[j + 14] = wk3r * x0r - wk3i * x0i; a[j + 15] = wk3r * x0i + wk3i * x0r; } } static void cftmdl(int n, int l, float *a, float *w) { int j, j1, j2, j3, k, k1, k2, m, m2; float wk1r, wk1i, wk2r, wk2i, wk3r, wk3i; float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; m = l << 2; for (j = 0; j < l; j += 2) { j1 = j + l; j2 = j1 + l; j3 = j2 + l; x0r = a[j] + a[j1]; x0i = a[j + 1] + a[j1 + 1]; x1r = a[j] - a[j1]; x1i = a[j + 1] - a[j1 + 1]; x2r = a[j2] + a[j3]; x2i = a[j2 + 1] + a[j3 + 1]; x3r = a[j2] - a[j3]; x3i = a[j2 + 1] - a[j3 + 1]; a[j] = x0r + x2r; a[j + 1] = x0i + x2i; a[j2] = x0r - x2r; a[j2 + 1] = x0i - x2i; a[j1] = x1r - x3i; a[j1 + 1] = x1i + x3r; a[j3] = x1r + x3i; a[j3 + 1] = x1i - x3r; } wk1r = w[2]; for (j = m; j < l + m; j += 2) { j1 = j + l; j2 = j1 + l; j3 = j2 + l; x0r = a[j] + a[j1]; x0i = a[j + 1] + a[j1 + 1]; x1r = a[j] - a[j1]; x1i = a[j + 1] - a[j1 + 1]; x2r = a[j2] + a[j3]; x2i = a[j2 + 1] + a[j3 + 1]; x3r = a[j2] - a[j3]; x3i = a[j2 + 1] - a[j3 + 1]; a[j] = x0r + x2r; a[j + 1] = x0i + x2i; a[j2] = x2i - x0i; a[j2 + 1] = x0r - x2r; x0r = x1r - x3i; x0i = x1i + x3r; a[j1] = wk1r * (x0r - x0i); a[j1 + 1] = wk1r * (x0r + x0i); x0r = x3i + x1r; x0i = x3r - x1i; a[j3] = wk1r * (x0i - x0r); a[j3 + 1] = wk1r * (x0i + x0r); } k1 = 0; m2 = 2 * m; for (k = m2; k < n; k += m2) { k1 += 2; k2 = 2 * k1; wk2r = w[k1]; wk2i = w[k1 + 1]; wk1r = w[k2]; wk1i = w[k2 + 1]; wk3r = wk1r - 2 * wk2i * wk1i; wk3i = 2 * wk2i * wk1r - wk1i; for (j = k; j < l + k; j += 2) { j1 = j + l; j2 = j1 + l; j3 = j2 + l; x0r = a[j] + a[j1]; x0i = a[j + 1] + a[j1 + 1]; x1r = a[j] - a[j1]; x1i = a[j + 1] - a[j1 + 1]; x2r = a[j2] + a[j3]; x2i = a[j2 + 1] + a[j3 + 1]; x3r = a[j2] - a[j3]; x3i = a[j2 + 1] - a[j3 + 1]; a[j] = x0r + x2r; a[j + 1] = x0i + x2i; x0r -= x2r; x0i -= x2i; a[j2] = wk2r * x0r - wk2i * x0i; a[j2 + 1] = wk2r * x0i + wk2i * x0r; x0r = x1r - x3i; x0i = x1i + x3r; a[j1] = wk1r * x0r - wk1i * x0i; a[j1 + 1] = wk1r * x0i + wk1i * x0r; x0r = x1r + x3i; x0i = x1i - x3r; a[j3] = wk3r * x0r - wk3i * x0i; a[j3 + 1] = wk3r * x0i + wk3i * x0r; } wk1r = w[k2 + 2]; wk1i = w[k2 + 3]; wk3r = wk1r - 2 * wk2r * wk1i; wk3i = 2 * wk2r * wk1r - wk1i; for (j = k + m; j < l + (k + m); j += 2) { j1 = j + l; j2 = j1 + l; j3 = j2 + l; x0r = a[j] + a[j1]; x0i = a[j + 1] + a[j1 + 1]; x1r = a[j] - a[j1]; x1i = a[j + 1] - a[j1 + 1]; x2r = a[j2] + a[j3]; x2i = a[j2 + 1] + a[j3 + 1]; x3r = a[j2] - a[j3]; x3i = a[j2 + 1] - a[j3 + 1]; a[j] = x0r + x2r; a[j + 1] = x0i + x2i; x0r -= x2r; x0i -= x2i; a[j2] = -wk2i * x0r - wk2r * x0i; a[j2 + 1] = -wk2i * x0i + wk2r * x0r; x0r = x1r - x3i; x0i = x1i + x3r; a[j1] = wk1r * x0r - wk1i * x0i; a[j1 + 1] = wk1r * x0i + wk1i * x0r; x0r = x1r + x3i; x0i = x1i - x3r; a[j3] = wk3r * x0r - wk3i * x0i; a[j3 + 1] = wk3r * x0i + wk3i * x0r; } } } static void rftfsub(int n, float *a, int nc, float *c) { int j, k, kk, ks, m; float wkr, wki, xr, xi, yr, yi; m = n >> 1; ks = 2 * nc / m; kk = 0; for (j = 2; j < m; j += 2) { k = n - j; kk += ks; wkr = 0.5f - c[nc - kk]; wki = c[kk]; xr = a[j] - a[k]; xi = a[j + 1] + a[k + 1]; yr = wkr * xr - wki * xi; yi = wkr * xi + wki * xr; a[j] -= yr; a[j + 1] -= yi; a[k] += yr; a[k + 1] -= yi; } } static void rftbsub(int n, float *a, int nc, float *c) { int j, k, kk, ks, m; float wkr, wki, xr, xi, yr, yi; a[1] = -a[1]; m = n >> 1; ks = 2 * nc / m; kk = 0; for (j = 2; j < m; j += 2) { k = n - j; kk += ks; wkr = 0.5f - c[nc - kk]; wki = c[kk]; xr = a[j] - a[k]; xi = a[j + 1] + a[k + 1]; yr = wkr * xr + wki * xi; yi = wkr * xi - wki * xr; a[j] -= yr; a[j + 1] = yi - a[j + 1]; a[k] += yr; a[k + 1] = yi - a[k + 1]; } a[m + 1] = -a[m + 1]; } #if 0 // Not used. static void dctsub(int n, float *a, int nc, float *c) { int j, k, kk, ks, m; float wkr, wki, xr; m = n >> 1; ks = nc / n; kk = 0; for (j = 1; j < m; j++) { k = n - j; kk += ks; wkr = c[kk] - c[nc - kk]; wki = c[kk] + c[nc - kk]; xr = wki * a[j] - wkr * a[k]; a[j] = wkr * a[j] + wki * a[k]; a[k] = xr; } a[m] *= c[0]; } static void dstsub(int n, float *a, int nc, float *c) { int j, k, kk, ks, m; float wkr, wki, xr; m = n >> 1; ks = nc / n; kk = 0; for (j = 1; j < m; j++) { k = n - j; kk += ks; wkr = c[kk] - c[nc - kk]; wki = c[kk] + c[nc - kk]; xr = wki * a[k] - wkr * a[j]; a[k] = wkr * a[k] + wki * a[j]; a[j] = xr; } a[m] *= c[0]; } #endif // Not used.