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Diffstat (limited to 'src/sms/OOURA.c')
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diff --git a/src/sms/OOURA.c b/src/sms/OOURA.c new file mode 100644 index 0000000..d88d20d --- /dev/null +++ b/src/sms/OOURA.c @@ -0,0 +1,638 @@ +/* -_-_-_-_-_-_-_-_-_-_-_-_-_-_- Ooura Real DFT -_-_-_-_-_-_-_-_-_-_-_-_-_-_ */ +/* Copyright notice: + This code comes from the "General Purpose FFT Package" that I obtained at + the following website http://www.kurims.kyoto-u.ac.jp/~ooura/fft.html + It is exactly copied from the file fft4g.c, but I have changed the doubles to sfloats. + Here is the copyright notice included in the package: + + Copyright(C) 1996-2001 Takuya OOURA + email: ooura@mmm.t.u-tokyo.ac.jp + download: http://momonga.t.u-tokyo.ac.jp/~ooura/fft.html + You may use, copy, modify this code for any purpose and + without fee. You may distribute this ORIGINAL package. + + The following is documentation of the algorithm included with the source code: + + -------- Real DFT / Inverse of Real DFT -------- + [definition] + <case1> 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<k<n/2 + <case2> 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<n + [usage] + <case1> + ip[0] = 0; // first time only + rdft(n, 1, a, ip, w); + <case2> + 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 (sfloat *) + <case1> + output data + a[2*k] = R[k], 0<=k<n/2 + a[2*k+1] = I[k], 0<k<n/2 + a[1] = R[n/2] + <case2> + input data + a[2*j] = R[j], 0<=j<n/2 + a[2*j+1] = I[j], 0<j<n/2 + a[1] = R[n/2] + ip[0...*] :work area for bit reversal (int *) + length of ip >= 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 (sfloat *) + 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; + } + . +*/ + +#include "OOURA.h" +#include "math.h" /*! \todo (optimize) replace math.h trig functions (table lookup?) */ + +/* ! \brief OOURA Real / Inverse DFT algoriithm + * + * The source code contains documentation from + * the original author. + */ +void rdft(int n, int isgn, sfloat *a, int *ip, sfloat *w) +{ + int nw, nc; + sfloat 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] = 0.5 * (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); + } + } +} + + +void makewt(int nw, int *ip, sfloat *w) +{ + int j, nwh; + sfloat delta, x, y; + + ip[0] = nw; + ip[1] = 1; + if (nw > 2) { + nwh = nw >> 1; + delta = atan(1.0) / nwh; + w[0] = 1; + w[1] = 0; + w[nwh] = cos(delta * nwh); + w[nwh + 1] = w[nwh]; + if (nwh > 2) { + for (j = 2; j < nwh; j += 2) { + x = cos(delta * j); + y = sin(delta * j); + w[j] = x; + w[j + 1] = y; + w[nw - j] = y; + w[nw - j + 1] = x; + } + bitrv2(nw, ip + 2, w); + } + } +} + +void makect(int nc, int *ip, sfloat *c) +{ + int j, nch; + sfloat delta; + + ip[1] = nc; + if (nc > 1) { + nch = nc >> 1; + delta = atan(1.0) / nch; + c[0] = cos(delta * nch); + c[nch] = 0.5 * c[0]; + for (j = 1; j < nch; j++) { + c[j] = 0.5 * cos(delta * j); + c[nc - j] = 0.5 * sin(delta * j); + } + } +} + +void bitrv2(int n, int *ip, sfloat *a) +{ + int j, j1, k, k1, l, m, m2; + sfloat 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; + } + } + } +} + +void cftfsub(int n, sfloat *a, sfloat *w) +{ + int j, j1, j2, j3, l; + sfloat 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; + } + } +} + + +void cftbsub(int n, sfloat *a, sfloat *w) +{ + int j, j1, j2, j3, l; + sfloat 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; + } + } +} + + +void cft1st(int n, sfloat *a, sfloat *w) +{ + int j, k1, k2; + sfloat wk1r, wk1i, wk2r, wk2i, wk3r, wk3i; + sfloat 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; + } +} + + +void cftmdl(int n, int l, sfloat *a, sfloat *w) +{ + int j, j1, j2, j3, k, k1, k2, m, m2; + sfloat wk1r, wk1i, wk2r, wk2i, wk3r, wk3i; + sfloat 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; + } + } +} + + +void rftfsub(int n, sfloat *a, int nc, sfloat *c) +{ + int j, k, kk, ks, m; + sfloat 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 = 0.5 - 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; + } +} + +void rftbsub(int n, sfloat *a, int nc, sfloat *c) +{ + int j, k, kk, ks, m; + sfloat 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 = 0.5 - 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]; +} |