/* Fast Fourier/Cosine/Sine Transform dimension :one data length :power of 2 decimation :frequency radix :split-radix data :inplace table :not 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, double *); void rdft(int, int, double *); void ddct(int, int, double *); void ddst(int, int, double *); void dfct(int, double *); void dfst(int, double *); macro definitions USE_CDFT_PTHREADS : default=not defined CDFT_THREADS_BEGIN_N : must be >= 512, default=8192 CDFT_4THREADS_BEGIN_N : must be >= 512, default=65536 USE_CDFT_WINTHREADS : default=not defined CDFT_THREADS_BEGIN_N : must be >= 512, default=32768 CDFT_4THREADS_BEGIN_N : must be >= 512, default=524288 -------- 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 cdft(2*n, 1, a); cdft(2*n, -1, a); [parameters] 2*n :data length (int) n >= 1, n = power of 2 a[0...2*n-1] :input/output data (double *) input data a[2*j] = Re(x[j]), a[2*j+1] = Im(x[j]), 0<=j 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 rdft(n, 1, a); rdft(n, -1, a); [parameters] n :data length (int) n >= 2, n = power of 2 a[0...n-1] :input/output data (double *) output data a[2*k] = R[k], 0<=k input data a[2*j] = R[j], 0<=j 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 ddct(n, 1, a); ddct(n, -1, a); [parameters] n :data length (int) n >= 2, n = power of 2 a[0...n-1] :input/output data (double *) output data a[k] = C[k], 0<=k 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 ddst(n, 1, a); ddst(n, -1, a); [parameters] n :data length (int) n >= 2, n = power of 2 a[0...n-1] :input/output data (double *) input data a[j] = A[j], 0 output data a[k] = S[k], 0= 2, n = power of 2 a[0...n] :input/output data (double *) output data a[k] = C[k], 0<=k<=n [remark] Inverse of a[0] *= 0.5; a[n] *= 0.5; dfct(n, a); is a[0] *= 0.5; a[n] *= 0.5; dfct(n, a); 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 (double *) output data a[k] = S[k], 0= 0) { cftfsub(n, a); } else { cftbsub(n, a); } } void rdft(int n, int isgn, double *a) { void cftfsub(int n, double *a); void cftbsub(int n, double *a); void rftfsub(int n, double *a); void rftbsub(int n, double *a); double xi; if (isgn >= 0) { if (n > 4) { cftfsub(n, a); rftfsub(n, a); } else if (n == 4) { cftfsub(n, a); } 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); cftbsub(n, a); } else if (n == 4) { cftbsub(n, a); } } } void ddct(int n, int isgn, double *a) { void cftfsub(int n, double *a); void cftbsub(int n, double *a); void rftfsub(int n, double *a); void rftbsub(int n, double *a); void dctsub(int n, double *a); void dctsub4(int n, double *a); int j; double xr; 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); cftbsub(n, a); } else if (n == 4) { cftbsub(n, a); } } if (n > 4) { dctsub(n, a); } else { dctsub4(n, a); } if (isgn >= 0) { if (n > 4) { cftfsub(n, a); rftfsub(n, a); } else if (n == 4) { cftfsub(n, a); } 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; } } void ddst(int n, int isgn, double *a) { void cftfsub(int n, double *a); void cftbsub(int n, double *a); void rftfsub(int n, double *a); void rftbsub(int n, double *a); void dstsub(int n, double *a); void dstsub4(int n, double *a); int j; double xr; 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); cftbsub(n, a); } else if (n == 4) { cftbsub(n, a); } } if (n > 4) { dstsub(n, a); } else { dstsub4(n, a); } if (isgn >= 0) { if (n > 4) { cftfsub(n, a); rftfsub(n, a); } else if (n == 4) { cftfsub(n, a); } 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; } } void dfct(int n, double *a) { void ddct(int n, int isgn, double *a); void bitrv1(int n, double *a); int j, k, m, mh; double xr, xi, yr, yi, an; m = n >> 1; for (j = 0; j < m; j++) { k = n - j; xr = a[j] + a[k]; a[j] -= a[k]; a[k] = xr; } an = a[n]; while (m >= 2) { ddct(m, 1, a); if (m > 2) { bitrv1(m, a); } mh = m >> 1; xi = a[m]; a[m] = a[0]; a[0] = an - xi; an += xi; for (j = 1; j < mh; j++) { k = m - j; xr = a[m + k]; xi = a[m + j]; yr = a[j]; yi = a[k]; a[m + j] = yr; a[m + k] = yi; a[j] = xr - xi; a[k] = xr + xi; } xr = a[mh]; a[mh] = a[m + mh]; a[m + mh] = xr; m = mh; } xi = a[1]; a[1] = a[0]; a[0] = an + xi; a[n] = an - xi; if (n > 2) { bitrv1(n, a); } } void dfst(int n, double *a) { void ddst(int n, int isgn, double *a); void bitrv1(int n, double *a); int j, k, m, mh; double xr, xi, yr, yi; m = n >> 1; for (j = 1; j < m; j++) { k = n - j; xr = a[j] - a[k]; a[j] += a[k]; a[k] = xr; } a[0] = a[m]; while (m >= 2) { ddst(m, 1, a); if (m > 2) { bitrv1(m, a); } mh = m >> 1; for (j = 1; j < mh; j++) { k = m - j; xr = a[m + k]; xi = a[m + j]; yr = a[j]; yi = a[k]; a[m + j] = yr; a[m + k] = yi; a[j] = xr + xi; a[k] = xr - xi; } a[m] = a[0]; a[0] = a[m + mh]; a[m + mh] = a[mh]; m = mh; } a[1] = a[0]; a[0] = 0; if (n > 2) { bitrv1(n, a); } } /* -------- child routines -------- */ #include #ifndef M_PI_2 #define M_PI_2 1.570796326794896619231321691639751442098584699687 #endif #ifndef WR5000 /* cos(M_PI_2*0.5000) */ #define WR5000 0.707106781186547524400844362104849039284835937688 #endif #ifndef WR2500 /* cos(M_PI_2*0.2500) */ #define WR2500 0.923879532511286756128183189396788286822416625863 #endif #ifndef WI2500 /* sin(M_PI_2*0.2500) */ #define WI2500 0.382683432365089771728459984030398866761344562485 #endif #ifndef WR1250 /* cos(M_PI_2*0.1250) */ #define WR1250 0.980785280403230449126182236134239036973933730893 #endif #ifndef WI1250 /* sin(M_PI_2*0.1250) */ #define WI1250 0.195090322016128267848284868477022240927691617751 #endif #ifndef WR3750 /* cos(M_PI_2*0.3750) */ #define WR3750 0.831469612302545237078788377617905756738560811987 #endif #ifndef WI3750 /* sin(M_PI_2*0.3750) */ #define WI3750 0.555570233019602224742830813948532874374937190754 #endif #ifdef USE_CDFT_PTHREADS #define USE_CDFT_THREADS #ifndef CDFT_THREADS_BEGIN_N #define CDFT_THREADS_BEGIN_N 8192 #endif #ifndef CDFT_4THREADS_BEGIN_N #define CDFT_4THREADS_BEGIN_N 65536 #endif #include #include #include #define cdft_thread_t pthread_t #define cdft_thread_create(thp,func,argp) { \ if (pthread_create(thp, NULL, func, (void *) argp) != 0) { \ fprintf(stderr, "cdft thread error\n"); \ exit(1); \ } \ } #define cdft_thread_wait(th) { \ if (pthread_join(th, NULL) != 0) { \ fprintf(stderr, "cdft thread error\n"); \ exit(1); \ } \ } #endif /* USE_CDFT_PTHREADS */ #ifdef USE_CDFT_WINTHREADS #define USE_CDFT_THREADS #ifndef CDFT_THREADS_BEGIN_N #define CDFT_THREADS_BEGIN_N 32768 #endif #ifndef CDFT_4THREADS_BEGIN_N #define CDFT_4THREADS_BEGIN_N 524288 #endif #include #include #include #define cdft_thread_t HANDLE #define cdft_thread_create(thp,func,argp) { \ DWORD thid; \ *(thp) = CreateThread(NULL, 0, (LPTHREAD_START_ROUTINE) func, (LPVOID) argp, 0, &thid); \ if (*(thp) == 0) { \ fprintf(stderr, "cdft thread error\n"); \ exit(1); \ } \ } #define cdft_thread_wait(th) { \ WaitForSingleObject(th, INFINITE); \ CloseHandle(th); \ } #endif /* USE_CDFT_WINTHREADS */ #ifndef CDFT_LOOP_DIV /* control of the CDFT's speed & tolerance */ #define CDFT_LOOP_DIV 32 #endif #ifndef RDFT_LOOP_DIV /* control of the RDFT's speed & tolerance */ #define RDFT_LOOP_DIV 64 #endif #ifndef DCST_LOOP_DIV /* control of the DCT,DST's speed & tolerance */ #define DCST_LOOP_DIV 64 #endif void cftfsub(int n, double *a) { void bitrv2(int n, double *a); void bitrv216(double *a); void bitrv208(double *a); void cftmdl1(int n, double *a); void cftrec4(int n, double *a); void cftleaf(int n, int isplt, double *a); void cftfx41(int n, double *a); void cftf161(double *a); void cftf081(double *a); void cftf040(double *a); void cftx020(double *a); #ifdef USE_CDFT_THREADS void cftrec4_th(int n, double *a); #endif /* USE_CDFT_THREADS */ if (n > 8) { if (n > 32) { cftmdl1(n, a); #ifdef USE_CDFT_THREADS if (n > CDFT_THREADS_BEGIN_N) { cftrec4_th(n, a); } else #endif /* USE_CDFT_THREADS */ if (n > 512) { cftrec4(n, a); } else if (n > 128) { cftleaf(n, 1, a); } else { cftfx41(n, a); } bitrv2(n, a); } else if (n == 32) { cftf161(a); bitrv216(a); } else { cftf081(a); bitrv208(a); } } else if (n == 8) { cftf040(a); } else if (n == 4) { cftx020(a); } } void cftbsub(int n, double *a) { void bitrv2conj(int n, double *a); void bitrv216neg(double *a); void bitrv208neg(double *a); void cftb1st(int n, double *a); void cftrec4(int n, double *a); void cftleaf(int n, int isplt, double *a); void cftfx41(int n, double *a); void cftf161(double *a); void cftf081(double *a); void cftb040(double *a); void cftx020(double *a); #ifdef USE_CDFT_THREADS void cftrec4_th(int n, double *a); #endif /* USE_CDFT_THREADS */ if (n > 8) { if (n > 32) { cftb1st(n, a); #ifdef USE_CDFT_THREADS if (n > CDFT_THREADS_BEGIN_N) { cftrec4_th(n, a); } else #endif /* USE_CDFT_THREADS */ if (n > 512) { cftrec4(n, a); } else if (n > 128) { cftleaf(n, 1, a); } else { cftfx41(n, a); } bitrv2conj(n, a); } else if (n == 32) { cftf161(a); bitrv216neg(a); } else { cftf081(a); bitrv208neg(a); } } else if (n == 8) { cftb040(a); } else if (n == 4) { cftx020(a); } } void bitrv2(int n, double *a) { int j0, k0, j1, k1, l, m, i, j, k, nh; double xr, xi, yr, yi; m = 4; for (l = n >> 2; l > 8; l >>= 2) { m <<= 1; } nh = n >> 1; if (l == 8) { j0 = 0; for (k0 = 0; k0 < m; k0 += 4) { k = k0; for (j = j0; j < j0 + k0; j += 4) { xr = a[j]; xi = a[j + 1]; yr = a[k]; yi = a[k + 1]; a[j] = yr; a[j + 1] = yi; a[k] = xr; a[k + 1] = xi; j1 = j + m; k1 = k + 2 * m; 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 += m; k1 -= m; 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 += m; k1 += 2 * m; 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 += nh; k1 += 2; 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 -= m; k1 -= 2 * m; 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 -= m; k1 += m; 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 -= m; k1 -= 2 * m; 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; k1 += nh; 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 += m; k1 += 2 * m; 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 += m; k1 -= m; 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 += m; k1 += 2 * m; 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 -= nh; k1 -= 2; 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 -= m; k1 -= 2 * m; 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 -= m; k1 += m; 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 -= m; k1 -= 2 * m; 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; for (i = nh >> 1; i > (k ^= i); i >>= 1); } k1 = j0 + k0; j1 = k1 + 2; k1 += nh; 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 += m; k1 += 2 * m; 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 += m; k1 -= m; 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; k1 -= nh; 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 += nh + 2; k1 += nh + 2; 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 -= nh - m; k1 += 2 * m - 2; 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; for (i = nh >> 1; i > (j0 ^= i); i >>= 1); } } else { j0 = 0; for (k0 = 0; k0 < m; k0 += 4) { k = k0; for (j = j0; j < j0 + k0; j += 4) { xr = a[j]; xi = a[j + 1]; yr = a[k]; yi = a[k + 1]; a[j] = yr; a[j + 1] = yi; a[k] = xr; a[k + 1] = xi; j1 = j + m; k1 = k + m; 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 += nh; k1 += 2; 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 -= m; k1 -= m; 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; k1 += nh; 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 += m; k1 += m; 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 -= nh; k1 -= 2; 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 -= m; k1 -= m; 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; for (i = nh >> 1; i > (k ^= i); i >>= 1); } k1 = j0 + k0; j1 = k1 + 2; k1 += nh; 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 += m; k1 += m; 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; for (i = nh >> 1; i > (j0 ^= i); i >>= 1); } } } void bitrv2conj(int n, double *a) { int j0, k0, j1, k1, l, m, i, j, k, nh; double xr, xi, yr, yi; m = 4; for (l = n >> 2; l > 8; l >>= 2) { m <<= 1; } nh = n >> 1; if (l == 8) { j0 = 0; for (k0 = 0; k0 < m; k0 += 4) { k = k0; for (j = j0; j < j0 + k0; j += 4) { xr = a[j]; xi = -a[j + 1]; yr = a[k]; yi = -a[k + 1]; a[j] = yr; a[j + 1] = yi; a[k] = xr; a[k + 1] = xi; j1 = j + m; k1 = k + 2 * m; 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 += m; k1 -= m; 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 += m; k1 += 2 * m; 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 += nh; k1 += 2; 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 -= m; k1 -= 2 * m; 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 -= m; k1 += m; 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 -= m; k1 -= 2 * m; 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; k1 += nh; 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 += m; k1 += 2 * m; 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 += m; k1 -= m; 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 += m; k1 += 2 * m; 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 -= nh; k1 -= 2; 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 -= m; k1 -= 2 * m; 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 -= m; k1 += m; 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 -= m; k1 -= 2 * m; 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; for (i = nh >> 1; i > (k ^= i); i >>= 1); } k1 = j0 + k0; j1 = k1 + 2; k1 += nh; a[j1 - 1] = -a[j1 - 1]; 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; a[k1 + 3] = -a[k1 + 3]; j1 += m; k1 += 2 * m; 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 += m; k1 -= m; 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; k1 -= nh; 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 += nh + 2; k1 += nh + 2; 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 -= nh - m; k1 += 2 * m - 2; a[j1 - 1] = -a[j1 - 1]; 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; a[k1 + 3] = -a[k1 + 3]; for (i = nh >> 1; i > (j0 ^= i); i >>= 1); } } else { j0 = 0; for (k0 = 0; k0 < m; k0 += 4) { k = k0; for (j = j0; j < j0 + k0; j += 4) { xr = a[j]; xi = -a[j + 1]; yr = a[k]; yi = -a[k + 1]; a[j] = yr; a[j + 1] = yi; a[k] = xr; a[k + 1] = xi; j1 = j + m; k1 = k + m; 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 += nh; k1 += 2; 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 -= m; k1 -= m; 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; k1 += nh; 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 += m; k1 += m; 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 -= nh; k1 -= 2; 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 -= m; k1 -= m; 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; for (i = nh >> 1; i > (k ^= i); i >>= 1); } k1 = j0 + k0; j1 = k1 + 2; k1 += nh; a[j1 - 1] = -a[j1 - 1]; 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; a[k1 + 3] = -a[k1 + 3]; j1 += m; k1 += m; a[j1 - 1] = -a[j1 - 1]; 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; a[k1 + 3] = -a[k1 + 3]; for (i = nh >> 1; i > (j0 ^= i); i >>= 1); } } } void bitrv216(double *a) { double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i, x5r, x5i, x7r, x7i, x8r, x8i, x10r, x10i, x11r, x11i, x12r, x12i, x13r, x13i, x14r, x14i; x1r = a[2]; x1i = a[3]; x2r = a[4]; x2i = a[5]; x3r = a[6]; x3i = a[7]; x4r = a[8]; x4i = a[9]; x5r = a[10]; x5i = a[11]; x7r = a[14]; x7i = a[15]; x8r = a[16]; x8i = a[17]; x10r = a[20]; x10i = a[21]; x11r = a[22]; x11i = a[23]; x12r = a[24]; x12i = a[25]; x13r = a[26]; x13i = a[27]; x14r = a[28]; x14i = a[29]; a[2] = x8r; a[3] = x8i; a[4] = x4r; a[5] = x4i; a[6] = x12r; a[7] = x12i; a[8] = x2r; a[9] = x2i; a[10] = x10r; a[11] = x10i; a[14] = x14r; a[15] = x14i; a[16] = x1r; a[17] = x1i; a[20] = x5r; a[21] = x5i; a[22] = x13r; a[23] = x13i; a[24] = x3r; a[25] = x3i; a[26] = x11r; a[27] = x11i; a[28] = x7r; a[29] = x7i; } void bitrv216neg(double *a) { double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i, x5r, x5i, x6r, x6i, x7r, x7i, x8r, x8i, x9r, x9i, x10r, x10i, x11r, x11i, x12r, x12i, x13r, x13i, x14r, x14i, x15r, x15i; x1r = a[2]; x1i = a[3]; x2r = a[4]; x2i = a[5]; x3r = a[6]; x3i = a[7]; x4r = a[8]; x4i = a[9]; x5r = a[10]; x5i = a[11]; x6r = a[12]; x6i = a[13]; x7r = a[14]; x7i = a[15]; x8r = a[16]; x8i = a[17]; x9r = a[18]; x9i = a[19]; x10r = a[20]; x10i = a[21]; x11r = a[22]; x11i = a[23]; x12r = a[24]; x12i = a[25]; x13r = a[26]; x13i = a[27]; x14r = a[28]; x14i = a[29]; x15r = a[30]; x15i = a[31]; a[2] = x15r; a[3] = x15i; a[4] = x7r; a[5] = x7i; a[6] = x11r; a[7] = x11i; a[8] = x3r; a[9] = x3i; a[10] = x13r; a[11] = x13i; a[12] = x5r; a[13] = x5i; a[14] = x9r; a[15] = x9i; a[16] = x1r; a[17] = x1i; a[18] = x14r; a[19] = x14i; a[20] = x6r; a[21] = x6i; a[22] = x10r; a[23] = x10i; a[24] = x2r; a[25] = x2i; a[26] = x12r; a[27] = x12i; a[28] = x4r; a[29] = x4i; a[30] = x8r; a[31] = x8i; } void bitrv208(double *a) { double x1r, x1i, x3r, x3i, x4r, x4i, x6r, x6i; x1r = a[2]; x1i = a[3]; x3r = a[6]; x3i = a[7]; x4r = a[8]; x4i = a[9]; x6r = a[12]; x6i = a[13]; a[2] = x4r; a[3] = x4i; a[6] = x6r; a[7] = x6i; a[8] = x1r; a[9] = x1i; a[12] = x3r; a[13] = x3i; } void bitrv208neg(double *a) { double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i, x5r, x5i, x6r, x6i, x7r, x7i; x1r = a[2]; x1i = a[3]; x2r = a[4]; x2i = a[5]; x3r = a[6]; x3i = a[7]; x4r = a[8]; x4i = a[9]; x5r = a[10]; x5i = a[11]; x6r = a[12]; x6i = a[13]; x7r = a[14]; x7i = a[15]; a[2] = x7r; a[3] = x7i; a[4] = x3r; a[5] = x3i; a[6] = x5r; a[7] = x5i; a[8] = x1r; a[9] = x1i; a[10] = x6r; a[11] = x6i; a[12] = x2r; a[13] = x2i; a[14] = x4r; a[15] = x4i; } void bitrv1(int n, double *a) { int j0, k0, j1, k1, l, m, i, j, k, nh; double x; nh = n >> 1; x = a[1]; a[1] = a[nh]; a[nh] = x; m = 2; for (l = n >> 2; l > 2; l >>= 2) { m <<= 1; } if (l == 2) { j1 = m + 1; k1 = m + nh; x = a[j1]; a[j1] = a[k1]; a[k1] = x; j0 = 0; for (k0 = 2; k0 < m; k0 += 2) { for (i = nh >> 1; i > (j0 ^= i); i >>= 1); k = k0; for (j = j0; j < j0 + k0; j += 2) { x = a[j]; a[j] = a[k]; a[k] = x; j1 = j + m; k1 = k + m; x = a[j1]; a[j1] = a[k1]; a[k1] = x; j1 += nh; k1++; x = a[j1]; a[j1] = a[k1]; a[k1] = x; j1 -= m; k1 -= m; x = a[j1]; a[j1] = a[k1]; a[k1] = x; j1++; k1 += nh; x = a[j1]; a[j1] = a[k1]; a[k1] = x; j1 += m; k1 += m; x = a[j1]; a[j1] = a[k1]; a[k1] = x; j1 -= nh; k1--; x = a[j1]; a[j1] = a[k1]; a[k1] = x; j1 -= m; k1 -= m; x = a[j1]; a[j1] = a[k1]; a[k1] = x; for (i = nh >> 1; i > (k ^= i); i >>= 1); } k1 = j0 + k0; j1 = k1 + 1; k1 += nh; x = a[j1]; a[j1] = a[k1]; a[k1] = x; j1 += m; k1 += m; x = a[j1]; a[j1] = a[k1]; a[k1] = x; } } else { j0 = 0; for (k0 = 2; k0 < m; k0 += 2) { for (i = nh >> 1; i > (j0 ^= i); i >>= 1); k = k0; for (j = j0; j < j0 + k0; j += 2) { x = a[j]; a[j] = a[k]; a[k] = x; j1 = j + nh; k1 = k + 1; x = a[j1]; a[j1] = a[k1]; a[k1] = x; j1++; k1 += nh; x = a[j1]; a[j1] = a[k1]; a[k1] = x; j1 -= nh; k1--; x = a[j1]; a[j1] = a[k1]; a[k1] = x; for (i = nh >> 1; i > (k ^= i); i >>= 1); } k1 = j0 + k0; j1 = k1 + 1; k1 += nh; x = a[j1]; a[j1] = a[k1]; a[k1] = x; } } } void cftb1st(int n, double *a) { int i, i0, j, j0, j1, j2, j3, m, mh; double ew, w1r, w1i, wk1r, wk1i, wk3r, wk3i, wd1r, wd1i, wd3r, wd3i, ss1, ss3; double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; mh = n >> 3; m = 2 * mh; j1 = m; j2 = j1 + m; j3 = j2 + m; x0r = a[0] + a[j2]; x0i = -a[1] - a[j2 + 1]; x1r = a[0] - a[j2]; x1i = -a[1] + a[j2 + 1]; x2r = a[j1] + a[j3]; x2i = a[j1 + 1] + a[j3 + 1]; x3r = a[j1] - a[j3]; x3i = a[j1 + 1] - a[j3 + 1]; a[0] = x0r + x2r; a[1] = x0i - x2i; a[j1] = x0r - x2r; a[j1 + 1] = x0i + x2i; a[j2] = x1r + x3i; a[j2 + 1] = x1i + x3r; a[j3] = x1r - x3i; a[j3 + 1] = x1i - x3r; wd1r = 1; wd1i = 0; wd3r = 1; wd3i = 0; ew = M_PI_2 / m; w1r = cos(2 * ew); w1i = sin(2 * ew); wk1r = w1r; wk1i = w1i; ss1 = 2 * w1i; wk3i = 2 * ss1 * wk1r; wk3r = wk1r - wk3i * wk1i; wk3i = wk1i - wk3i * wk1r; ss3 = 2 * wk3i; i = 0; for (;;) { i0 = i + 4 * CDFT_LOOP_DIV; if (i0 > mh - 4) { i0 = mh - 4; } for (j = i + 2; j < i0; j += 4) { wd1r -= ss1 * wk1i; wd1i += ss1 * wk1r; wd3r -= ss3 * wk3i; wd3i += ss3 * wk3r; j1 = j + m; j2 = j1 + m; j3 = j2 + m; x0r = a[j] + a[j2]; x0i = -a[j + 1] - a[j2 + 1]; x1r = a[j] - a[j2]; x1i = -a[j + 1] + a[j2 + 1]; x2r = a[j1] + a[j3]; x2i = a[j1 + 1] + a[j3 + 1]; x3r = a[j1] - a[j3]; x3i = a[j1 + 1] - a[j3 + 1]; a[j] = x0r + x2r; a[j + 1] = x0i - x2i; a[j1] = x0r - x2r; a[j1 + 1] = x0i + x2i; x0r = x1r + x3i; x0i = x1i + x3r; a[j2] = wk1r * x0r - wk1i * x0i; a[j2 + 1] = wk1r * x0i + wk1i * x0r; x0r = x1r - x3i; x0i = x1i - x3r; a[j3] = wk3r * x0r + wk3i * x0i; a[j3 + 1] = wk3r * x0i - wk3i * x0r; x0r = a[j + 2] + a[j2 + 2]; x0i = -a[j + 3] - a[j2 + 3]; x1r = a[j + 2] - a[j2 + 2]; x1i = -a[j + 3] + a[j2 + 3]; x2r = a[j1 + 2] + a[j3 + 2]; x2i = a[j1 + 3] + a[j3 + 3]; x3r = a[j1 + 2] - a[j3 + 2]; x3i = a[j1 + 3] - a[j3 + 3]; a[j + 2] = x0r + x2r; a[j + 3] = x0i - x2i; a[j1 + 2] = x0r - x2r; a[j1 + 3] = x0i + x2i; x0r = x1r + x3i; x0i = x1i + x3r; a[j2 + 2] = wd1r * x0r - wd1i * x0i; a[j2 + 3] = wd1r * x0i + wd1i * x0r; x0r = x1r - x3i; x0i = x1i - x3r; a[j3 + 2] = wd3r * x0r + wd3i * x0i; a[j3 + 3] = wd3r * x0i - wd3i * x0r; j0 = m - j; j1 = j0 + m; j2 = j1 + m; j3 = j2 + m; x0r = a[j0] + a[j2]; x0i = -a[j0 + 1] - a[j2 + 1]; x1r = a[j0] - a[j2]; x1i = -a[j0 + 1] + a[j2 + 1]; x2r = a[j1] + a[j3]; x2i = a[j1 + 1] + a[j3 + 1]; x3r = a[j1] - a[j3]; x3i = a[j1 + 1] - a[j3 + 1]; a[j0] = x0r + x2r; a[j0 + 1] = x0i - x2i; a[j1] = x0r - x2r; a[j1 + 1] = x0i + x2i; x0r = x1r + x3i; x0i = x1i + x3r; a[j2] = wk1i * x0r - wk1r * x0i; a[j2 + 1] = wk1i * x0i + wk1r * x0r; x0r = x1r - x3i; x0i = x1i - x3r; a[j3] = wk3i * x0r + wk3r * x0i; a[j3 + 1] = wk3i * x0i - wk3r * x0r; x0r = a[j0 - 2] + a[j2 - 2]; x0i = -a[j0 - 1] - a[j2 - 1]; x1r = a[j0 - 2] - a[j2 - 2]; x1i = -a[j0 - 1] + a[j2 - 1]; x2r = a[j1 - 2] + a[j3 - 2]; x2i = a[j1 - 1] + a[j3 - 1]; x3r = a[j1 - 2] - a[j3 - 2]; x3i = a[j1 - 1] - a[j3 - 1]; a[j0 - 2] = x0r + x2r; a[j0 - 1] = x0i - x2i; a[j1 - 2] = x0r - x2r; a[j1 - 1] = x0i + x2i; x0r = x1r + x3i; x0i = x1i + x3r; a[j2 - 2] = wd1i * x0r - wd1r * x0i; a[j2 - 1] = wd1i * x0i + wd1r * x0r; x0r = x1r - x3i; x0i = x1i - x3r; a[j3 - 2] = wd3i * x0r + wd3r * x0i; a[j3 - 1] = wd3i * x0i - wd3r * x0r; wk1r -= ss1 * wd1i; wk1i += ss1 * wd1r; wk3r -= ss3 * wd3i; wk3i += ss3 * wd3r; } if (i0 == mh - 4) { break; } wd1r = cos(ew * i0); wd1i = sin(ew * i0); wd3i = 4 * wd1i * wd1r; wd3r = wd1r - wd3i * wd1i; wd3i = wd1i - wd3i * wd1r; wk1r = w1r * wd1r - w1i * wd1i; wk1i = w1r * wd1i + w1i * wd1r; wk3i = 4 * wk1i * wk1r; wk3r = wk1r - wk3i * wk1i; wk3i = wk1i - wk3i * wk1r; i = i0; } wd1r = WR5000; j0 = mh; j1 = j0 + m; j2 = j1 + m; j3 = j2 + m; x0r = a[j0 - 2] + a[j2 - 2]; x0i = -a[j0 - 1] - a[j2 - 1]; x1r = a[j0 - 2] - a[j2 - 2]; x1i = -a[j0 - 1] + a[j2 - 1]; x2r = a[j1 - 2] + a[j3 - 2]; x2i = a[j1 - 1] + a[j3 - 1]; x3r = a[j1 - 2] - a[j3 - 2]; x3i = a[j1 - 1] - a[j3 - 1]; a[j0 - 2] = x0r + x2r; a[j0 - 1] = x0i - x2i; a[j1 - 2] = x0r - x2r; a[j1 - 1] = x0i + x2i; x0r = x1r + x3i; x0i = x1i + x3r; a[j2 - 2] = wk1r * x0r - wk1i * x0i; a[j2 - 1] = wk1r * x0i + wk1i * x0r; x0r = x1r - x3i; x0i = x1i - x3r; a[j3 - 2] = wk3r * x0r + wk3i * x0i; a[j3 - 1] = wk3r * x0i - wk3i * x0r; x0r = a[j0] + a[j2]; x0i = -a[j0 + 1] - a[j2 + 1]; x1r = a[j0] - a[j2]; x1i = -a[j0 + 1] + a[j2 + 1]; x2r = a[j1] + a[j3]; x2i = a[j1 + 1] + a[j3 + 1]; x3r = a[j1] - a[j3]; x3i = a[j1 + 1] - a[j3 + 1]; a[j0] = x0r + x2r; a[j0 + 1] = x0i - x2i; a[j1] = x0r - x2r; a[j1 + 1] = x0i + x2i; x0r = x1r + x3i; x0i = x1i + x3r; a[j2] = wd1r * (x0r - x0i); a[j2 + 1] = wd1r * (x0i + x0r); x0r = x1r - x3i; x0i = x1i - x3r; a[j3] = -wd1r * (x0r + x0i); a[j3 + 1] = -wd1r * (x0i - x0r); x0r = a[j0 + 2] + a[j2 + 2]; x0i = -a[j0 + 3] - a[j2 + 3]; x1r = a[j0 + 2] - a[j2 + 2]; x1i = -a[j0 + 3] + a[j2 + 3]; x2r = a[j1 + 2] + a[j3 + 2]; x2i = a[j1 + 3] + a[j3 + 3]; x3r = a[j1 + 2] - a[j3 + 2]; x3i = a[j1 + 3] - a[j3 + 3]; a[j0 + 2] = x0r + x2r; a[j0 + 3] = x0i - x2i; a[j1 + 2] = x0r - x2r; a[j1 + 3] = x0i + x2i; x0r = x1r + x3i; x0i = x1i + x3r; a[j2 + 2] = wk1i * x0r - wk1r * x0i; a[j2 + 3] = wk1i * x0i + wk1r * x0r; x0r = x1r - x3i; x0i = x1i - x3r; a[j3 + 2] = wk3i * x0r + wk3r * x0i; a[j3 + 3] = wk3i * x0i - wk3r * x0r; } #ifdef USE_CDFT_THREADS struct cdft_arg_st { int n0; int n; double *a; }; typedef struct cdft_arg_st cdft_arg_t; void cftrec4_th(int n, double *a) { void *cftrec1_th(void *p); void *cftrec2_th(void *p); int i, idiv4, m, nthread; cdft_thread_t th[4]; cdft_arg_t ag[4]; nthread = 2; idiv4 = 0; m = n >> 1; if (n > CDFT_4THREADS_BEGIN_N) { nthread = 4; idiv4 = 1; m >>= 1; } for (i = 0; i < nthread; i++) { ag[i].n0 = n; ag[i].n = m; ag[i].a = &a[i * m]; if (i != idiv4) { cdft_thread_create(&th[i], cftrec1_th, &ag[i]); } else { cdft_thread_create(&th[i], cftrec2_th, &ag[i]); } } for (i = 0; i < nthread; i++) { cdft_thread_wait(th[i]); } } void *cftrec1_th(void *p) { int cfttree(int n, int j, int k, double *a); void cftleaf(int n, int isplt, double *a); void cftmdl1(int n, double *a); int isplt, j, k, m, n, n0; double *a; n0 = ((cdft_arg_t *) p)->n0; n = ((cdft_arg_t *) p)->n; a = ((cdft_arg_t *) p)->a; m = n0; while (m > 512) { m >>= 2; cftmdl1(m, &a[n - m]); } cftleaf(m, 1, &a[n - m]); k = 0; for (j = n - m; j > 0; j -= m) { k++; isplt = cfttree(m, j, k, a); cftleaf(m, isplt, &a[j - m]); } return (void *) 0; } void *cftrec2_th(void *p) { int cfttree(int n, int j, int k, double *a); void cftleaf(int n, int isplt, double *a); void cftmdl2(int n, double *a); int isplt, j, k, m, n, n0; double *a; n0 = ((cdft_arg_t *) p)->n0; n = ((cdft_arg_t *) p)->n; a = ((cdft_arg_t *) p)->a; k = 1; m = n0; while (m > 512) { m >>= 2; k <<= 2; cftmdl2(m, &a[n - m]); } cftleaf(m, 0, &a[n - m]); k >>= 1; for (j = n - m; j > 0; j -= m) { k++; isplt = cfttree(m, j, k, a); cftleaf(m, isplt, &a[j - m]); } return (void *) 0; } #endif /* USE_CDFT_THREADS */ void cftrec4(int n, double *a) { int cfttree(int n, int j, int k, double *a); void cftleaf(int n, int isplt, double *a); void cftmdl1(int n, double *a); int isplt, j, k, m; m = n; while (m > 512) { m >>= 2; cftmdl1(m, &a[n - m]); } cftleaf(m, 1, &a[n - m]); k = 0; for (j = n - m; j > 0; j -= m) { k++; isplt = cfttree(m, j, k, a); cftleaf(m, isplt, &a[j - m]); } } int cfttree(int n, int j, int k, double *a) { void cftmdl1(int n, double *a); void cftmdl2(int n, double *a); int i, isplt, m; if ((k & 3) != 0) { isplt = k & 1; if (isplt != 0) { cftmdl1(n, &a[j - n]); } else { cftmdl2(n, &a[j - n]); } } else { m = n; for (i = k; (i & 3) == 0; i >>= 2) { m <<= 2; } isplt = i & 1; if (isplt != 0) { while (m > 128) { cftmdl1(m, &a[j - m]); m >>= 2; } } else { while (m > 128) { cftmdl2(m, &a[j - m]); m >>= 2; } } } return isplt; } void cftleaf(int n, int isplt, double *a) { void cftmdl1(int n, double *a); void cftmdl2(int n, double *a); void cftf161(double *a); void cftf162(double *a); void cftf081(double *a); void cftf082(double *a); if (n == 512) { cftmdl1(128, a); cftf161(a); cftf162(&a[32]); cftf161(&a[64]); cftf161(&a[96]); cftmdl2(128, &a[128]); cftf161(&a[128]); cftf162(&a[160]); cftf161(&a[192]); cftf162(&a[224]); cftmdl1(128, &a[256]); cftf161(&a[256]); cftf162(&a[288]); cftf161(&a[320]); cftf161(&a[352]); if (isplt != 0) { cftmdl1(128, &a[384]); cftf161(&a[480]); } else { cftmdl2(128, &a[384]); cftf162(&a[480]); } cftf161(&a[384]); cftf162(&a[416]); cftf161(&a[448]); } else { cftmdl1(64, a); cftf081(a); cftf082(&a[16]); cftf081(&a[32]); cftf081(&a[48]); cftmdl2(64, &a[64]); cftf081(&a[64]); cftf082(&a[80]); cftf081(&a[96]); cftf082(&a[112]); cftmdl1(64, &a[128]); cftf081(&a[128]); cftf082(&a[144]); cftf081(&a[160]); cftf081(&a[176]); if (isplt != 0) { cftmdl1(64, &a[192]); cftf081(&a[240]); } else { cftmdl2(64, &a[192]); cftf082(&a[240]); } cftf081(&a[192]); cftf082(&a[208]); cftf081(&a[224]); } } void cftmdl1(int n, double *a) { int i, i0, j, j0, j1, j2, j3, m, mh; double ew, w1r, w1i, wk1r, wk1i, wk3r, wk3i, wd1r, wd1i, wd3r, wd3i, ss1, ss3; double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; mh = n >> 3; m = 2 * mh; j1 = m; j2 = j1 + m; j3 = j2 + m; x0r = a[0] + a[j2]; x0i = a[1] + a[j2 + 1]; x1r = a[0] - a[j2]; x1i = a[1] - a[j2 + 1]; x2r = a[j1] + a[j3]; x2i = a[j1 + 1] + a[j3 + 1]; x3r = a[j1] - a[j3]; x3i = a[j1 + 1] - a[j3 + 1]; a[0] = x0r + x2r; a[1] = x0i + x2i; a[j1] = x0r - x2r; a[j1 + 1] = x0i - x2i; a[j2] = x1r - x3i; a[j2 + 1] = x1i + x3r; a[j3] = x1r + x3i; a[j3 + 1] = x1i - x3r; wd1r = 1; wd1i = 0; wd3r = 1; wd3i = 0; ew = M_PI_2 / m; w1r = cos(2 * ew); w1i = sin(2 * ew); wk1r = w1r; wk1i = w1i; ss1 = 2 * w1i; wk3i = 2 * ss1 * wk1r; wk3r = wk1r - wk3i * wk1i; wk3i = wk1i - wk3i * wk1r; ss3 = 2 * wk3i; i = 0; for (;;) { i0 = i + 4 * CDFT_LOOP_DIV; if (i0 > mh - 4) { i0 = mh - 4; } for (j = i + 2; j < i0; j += 4) { wd1r -= ss1 * wk1i; wd1i += ss1 * wk1r; wd3r -= ss3 * wk3i; wd3i += ss3 * wk3r; j1 = j + m; j2 = j1 + m; j3 = j2 + m; x0r = a[j] + a[j2]; x0i = a[j + 1] + a[j2 + 1]; x1r = a[j] - a[j2]; x1i = a[j + 1] - a[j2 + 1]; x2r = a[j1] + a[j3]; x2i = a[j1 + 1] + a[j3 + 1]; x3r = a[j1] - a[j3]; x3i = a[j1 + 1] - a[j3 + 1]; a[j] = x0r + x2r; a[j + 1] = x0i + x2i; a[j1] = x0r - x2r; a[j1 + 1] = x0i - x2i; x0r = x1r - x3i; x0i = x1i + x3r; a[j2] = wk1r * x0r - wk1i * x0i; a[j2 + 1] = wk1r * x0i + wk1i * x0r; x0r = x1r + x3i; x0i = x1i - x3r; a[j3] = wk3r * x0r + wk3i * x0i; a[j3 + 1] = wk3r * x0i - wk3i * x0r; x0r = a[j + 2] + a[j2 + 2]; x0i = a[j + 3] + a[j2 + 3]; x1r = a[j + 2] - a[j2 + 2]; x1i = a[j + 3] - a[j2 + 3]; x2r = a[j1 + 2] + a[j3 + 2]; x2i = a[j1 + 3] + a[j3 + 3]; x3r = a[j1 + 2] - a[j3 + 2]; x3i = a[j1 + 3] - a[j3 + 3]; a[j + 2] = x0r + x2r; a[j + 3] = x0i + x2i; a[j1 + 2] = x0r - x2r; a[j1 + 3] = x0i - x2i; x0r = x1r - x3i; x0i = x1i + x3r; a[j2 + 2] = wd1r * x0r - wd1i * x0i; a[j2 + 3] = wd1r * x0i + wd1i * x0r; x0r = x1r + x3i; x0i = x1i - x3r; a[j3 + 2] = wd3r * x0r + wd3i * x0i; a[j3 + 3] = wd3r * x0i - wd3i * x0r; j0 = m - j; j1 = j0 + m; j2 = j1 + m; j3 = j2 + m; x0r = a[j0] + a[j2]; x0i = a[j0 + 1] + a[j2 + 1]; x1r = a[j0] - a[j2]; x1i = a[j0 + 1] - a[j2 + 1]; x2r = a[j1] + a[j3]; x2i = a[j1 + 1] + a[j3 + 1]; x3r = a[j1] - a[j3]; x3i = a[j1 + 1] - a[j3 + 1]; a[j0] = x0r + x2r; a[j0 + 1] = x0i + x2i; a[j1] = x0r - x2r; a[j1 + 1] = x0i - x2i; x0r = x1r - x3i; x0i = x1i + x3r; a[j2] = wk1i * x0r - wk1r * x0i; a[j2 + 1] = wk1i * x0i + wk1r * x0r; x0r = x1r + x3i; x0i = x1i - x3r; a[j3] = wk3i * x0r + wk3r * x0i; a[j3 + 1] = wk3i * x0i - wk3r * x0r; x0r = a[j0 - 2] + a[j2 - 2]; x0i = a[j0 - 1] + a[j2 - 1]; x1r = a[j0 - 2] - a[j2 - 2]; x1i = a[j0 - 1] - a[j2 - 1]; x2r = a[j1 - 2] + a[j3 - 2]; x2i = a[j1 - 1] + a[j3 - 1]; x3r = a[j1 - 2] - a[j3 - 2]; x3i = a[j1 - 1] - a[j3 - 1]; a[j0 - 2] = x0r + x2r; a[j0 - 1] = x0i + x2i; a[j1 - 2] = x0r - x2r; a[j1 - 1] = x0i - x2i; x0r = x1r - x3i; x0i = x1i + x3r; a[j2 - 2] = wd1i * x0r - wd1r * x0i; a[j2 - 1] = wd1i * x0i + wd1r * x0r; x0r = x1r + x3i; x0i = x1i - x3r; a[j3 - 2] = wd3i * x0r + wd3r * x0i; a[j3 - 1] = wd3i * x0i - wd3r * x0r; wk1r -= ss1 * wd1i; wk1i += ss1 * wd1r; wk3r -= ss3 * wd3i; wk3i += ss3 * wd3r; } if (i0 == mh - 4) { break; } wd1r = cos(ew * i0); wd1i = sin(ew * i0); wd3i = 4 * wd1i * wd1r; wd3r = wd1r - wd3i * wd1i; wd3i = wd1i - wd3i * wd1r; wk1r = w1r * wd1r - w1i * wd1i; wk1i = w1r * wd1i + w1i * wd1r; wk3i = 4 * wk1i * wk1r; wk3r = wk1r - wk3i * wk1i; wk3i = wk1i - wk3i * wk1r; i = i0; } wd1r = WR5000; j0 = mh; j1 = j0 + m; j2 = j1 + m; j3 = j2 + m; x0r = a[j0 - 2] + a[j2 - 2]; x0i = a[j0 - 1] + a[j2 - 1]; x1r = a[j0 - 2] - a[j2 - 2]; x1i = a[j0 - 1] - a[j2 - 1]; x2r = a[j1 - 2] + a[j3 - 2]; x2i = a[j1 - 1] + a[j3 - 1]; x3r = a[j1 - 2] - a[j3 - 2]; x3i = a[j1 - 1] - a[j3 - 1]; a[j0 - 2] = x0r + x2r; a[j0 - 1] = x0i + x2i; a[j1 - 2] = x0r - x2r; a[j1 - 1] = x0i - x2i; x0r = x1r - x3i; x0i = x1i + x3r; a[j2 - 2] = wk1r * x0r - wk1i * x0i; a[j2 - 1] = wk1r * x0i + wk1i * x0r; x0r = x1r + x3i; x0i = x1i - x3r; a[j3 - 2] = wk3r * x0r + wk3i * x0i; a[j3 - 1] = wk3r * x0i - wk3i * x0r; x0r = a[j0] + a[j2]; x0i = a[j0 + 1] + a[j2 + 1]; x1r = a[j0] - a[j2]; x1i = a[j0 + 1] - a[j2 + 1]; x2r = a[j1] + a[j3]; x2i = a[j1 + 1] + a[j3 + 1]; x3r = a[j1] - a[j3]; x3i = a[j1 + 1] - a[j3 + 1]; a[j0] = x0r + x2r; a[j0 + 1] = x0i + x2i; a[j1] = x0r - x2r; a[j1 + 1] = x0i - x2i; x0r = x1r - x3i; x0i = x1i + x3r; a[j2] = wd1r * (x0r - x0i); a[j2 + 1] = wd1r * (x0i + x0r); x0r = x1r + x3i; x0i = x1i - x3r; a[j3] = -wd1r * (x0r + x0i); a[j3 + 1] = -wd1r * (x0i - x0r); x0r = a[j0 + 2] + a[j2 + 2]; x0i = a[j0 + 3] + a[j2 + 3]; x1r = a[j0 + 2] - a[j2 + 2]; x1i = a[j0 + 3] - a[j2 + 3]; x2r = a[j1 + 2] + a[j3 + 2]; x2i = a[j1 + 3] + a[j3 + 3]; x3r = a[j1 + 2] - a[j3 + 2]; x3i = a[j1 + 3] - a[j3 + 3]; a[j0 + 2] = x0r + x2r; a[j0 + 3] = x0i + x2i; a[j1 + 2] = x0r - x2r; a[j1 + 3] = x0i - x2i; x0r = x1r - x3i; x0i = x1i + x3r; a[j2 + 2] = wk1i * x0r - wk1r * x0i; a[j2 + 3] = wk1i * x0i + wk1r * x0r; x0r = x1r + x3i; x0i = x1i - x3r; a[j3 + 2] = wk3i * x0r + wk3r * x0i; a[j3 + 3] = wk3i * x0i - wk3r * x0r; } void cftmdl2(int n, double *a) { int i, i0, j, j0, j1, j2, j3, m, mh; double ew, w1r, w1i, wn4r, wk1r, wk1i, wk3r, wk3i, wl1r, wl1i, wl3r, wl3i, wd1r, wd1i, wd3r, wd3i, we1r, we1i, we3r, we3i, ss1, ss3; double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y2r, y2i; mh = n >> 3; m = 2 * mh; wn4r = WR5000; j1 = m; j2 = j1 + m; j3 = j2 + m; x0r = a[0] - a[j2 + 1]; x0i = a[1] + a[j2]; x1r = a[0] + a[j2 + 1]; x1i = a[1] - a[j2]; x2r = a[j1] - a[j3 + 1]; x2i = a[j1 + 1] + a[j3]; x3r = a[j1] + a[j3 + 1]; x3i = a[j1 + 1] - a[j3]; y0r = wn4r * (x2r - x2i); y0i = wn4r * (x2i + x2r); a[0] = x0r + y0r; a[1] = x0i + y0i; a[j1] = x0r - y0r; a[j1 + 1] = x0i - y0i; y0r = wn4r * (x3r - x3i); y0i = wn4r * (x3i + x3r); a[j2] = x1r - y0i; a[j2 + 1] = x1i + y0r; a[j3] = x1r + y0i; a[j3 + 1] = x1i - y0r; wl1r = 1; wl1i = 0; wl3r = 1; wl3i = 0; we1r = wn4r; we1i = wn4r; we3r = -wn4r; we3i = -wn4r; ew = M_PI_2 / (2 * m); w1r = cos(2 * ew); w1i = sin(2 * ew); wk1r = w1r; wk1i = w1i; wd1r = wn4r * (w1r - w1i); wd1i = wn4r * (w1i + w1r); ss1 = 2 * w1i; wk3i = 2 * ss1 * wk1r; wk3r = wk1r - wk3i * wk1i; wk3i = wk1i - wk3i * wk1r; ss3 = 2 * wk3i; wd3r = -wn4r * (wk3r - wk3i); wd3i = -wn4r * (wk3i + wk3r); i = 0; for (;;) { i0 = i + 4 * CDFT_LOOP_DIV; if (i0 > mh - 4) { i0 = mh - 4; } for (j = i + 2; j < i0; j += 4) { wl1r -= ss1 * wk1i; wl1i += ss1 * wk1r; wl3r -= ss3 * wk3i; wl3i += ss3 * wk3r; we1r -= ss1 * wd1i; we1i += ss1 * wd1r; we3r -= ss3 * wd3i; we3i += ss3 * wd3r; j1 = j + m; j2 = j1 + m; j3 = j2 + m; x0r = a[j] - a[j2 + 1]; x0i = a[j + 1] + a[j2]; x1r = a[j] + a[j2 + 1]; x1i = a[j + 1] - a[j2]; x2r = a[j1] - a[j3 + 1]; x2i = a[j1 + 1] + a[j3]; x3r = a[j1] + a[j3 + 1]; x3i = a[j1 + 1] - a[j3]; y0r = wk1r * x0r - wk1i * x0i; y0i = wk1r * x0i + wk1i * x0r; y2r = wd1r * x2r - wd1i * x2i; y2i = wd1r * x2i + wd1i * x2r; a[j] = y0r + y2r; a[j + 1] = y0i + y2i; a[j1] = y0r - y2r; a[j1 + 1] = y0i - y2i; y0r = wk3r * x1r + wk3i * x1i; y0i = wk3r * x1i - wk3i * x1r; y2r = wd3r * x3r + wd3i * x3i; y2i = wd3r * x3i - wd3i * x3r; a[j2] = y0r + y2r; a[j2 + 1] = y0i + y2i; a[j3] = y0r - y2r; a[j3 + 1] = y0i - y2i; x0r = a[j + 2] - a[j2 + 3]; x0i = a[j + 3] + a[j2 + 2]; x1r = a[j + 2] + a[j2 + 3]; x1i = a[j + 3] - a[j2 + 2]; x2r = a[j1 + 2] - a[j3 + 3]; x2i = a[j1 + 3] + a[j3 + 2]; x3r = a[j1 + 2] + a[j3 + 3]; x3i = a[j1 + 3] - a[j3 + 2]; y0r = wl1r * x0r - wl1i * x0i; y0i = wl1r * x0i + wl1i * x0r; y2r = we1r * x2r - we1i * x2i; y2i = we1r * x2i + we1i * x2r; a[j + 2] = y0r + y2r; a[j + 3] = y0i + y2i; a[j1 + 2] = y0r - y2r; a[j1 + 3] = y0i - y2i; y0r = wl3r * x1r + wl3i * x1i; y0i = wl3r * x1i - wl3i * x1r; y2r = we3r * x3r + we3i * x3i; y2i = we3r * x3i - we3i * x3r; a[j2 + 2] = y0r + y2r; a[j2 + 3] = y0i + y2i; a[j3 + 2] = y0r - y2r; a[j3 + 3] = y0i - y2i; j0 = m - j; j1 = j0 + m; j2 = j1 + m; j3 = j2 + m; x0r = a[j0] - a[j2 + 1]; x0i = a[j0 + 1] + a[j2]; x1r = a[j0] + a[j2 + 1]; x1i = a[j0 + 1] - a[j2]; x2r = a[j1] - a[j3 + 1]; x2i = a[j1 + 1] + a[j3]; x3r = a[j1] + a[j3 + 1]; x3i = a[j1 + 1] - a[j3]; y0r = wd1i * x0r - wd1r * x0i; y0i = wd1i * x0i + wd1r * x0r; y2r = wk1i * x2r - wk1r * x2i; y2i = wk1i * x2i + wk1r * x2r; a[j0] = y0r + y2r; a[j0 + 1] = y0i + y2i; a[j1] = y0r - y2r; a[j1 + 1] = y0i - y2i; y0r = wd3i * x1r + wd3r * x1i; y0i = wd3i * x1i - wd3r * x1r; y2r = wk3i * x3r + wk3r * x3i; y2i = wk3i * x3i - wk3r * x3r; a[j2] = y0r + y2r; a[j2 + 1] = y0i + y2i; a[j3] = y0r - y2r; a[j3 + 1] = y0i - y2i; x0r = a[j0 - 2] - a[j2 - 1]; x0i = a[j0 - 1] + a[j2 - 2]; x1r = a[j0 - 2] + a[j2 - 1]; x1i = a[j0 - 1] - a[j2 - 2]; x2r = a[j1 - 2] - a[j3 - 1]; x2i = a[j1 - 1] + a[j3 - 2]; x3r = a[j1 - 2] + a[j3 - 1]; x3i = a[j1 - 1] - a[j3 - 2]; y0r = we1i * x0r - we1r * x0i; y0i = we1i * x0i + we1r * x0r; y2r = wl1i * x2r - wl1r * x2i; y2i = wl1i * x2i + wl1r * x2r; a[j0 - 2] = y0r + y2r; a[j0 - 1] = y0i + y2i; a[j1 - 2] = y0r - y2r; a[j1 - 1] = y0i - y2i; y0r = we3i * x1r + we3r * x1i; y0i = we3i * x1i - we3r * x1r; y2r = wl3i * x3r + wl3r * x3i; y2i = wl3i * x3i - wl3r * x3r; a[j2 - 2] = y0r + y2r; a[j2 - 1] = y0i + y2i; a[j3 - 2] = y0r - y2r; a[j3 - 1] = y0i - y2i; wk1r -= ss1 * wl1i; wk1i += ss1 * wl1r; wk3r -= ss3 * wl3i; wk3i += ss3 * wl3r; wd1r -= ss1 * we1i; wd1i += ss1 * we1r; wd3r -= ss3 * we3i; wd3i += ss3 * we3r; } if (i0 == mh - 4) { break; } wl1r = cos(ew * i0); wl1i = sin(ew * i0); wl3i = 4 * wl1i * wl1r; wl3r = wl1r - wl3i * wl1i; wl3i = wl1i - wl3i * wl1r; we1r = wn4r * (wl1r - wl1i); we1i = wn4r * (wl1i + wl1r); we3r = -wn4r * (wl3r - wl3i); we3i = -wn4r * (wl3i + wl3r); wk1r = w1r * wl1r - w1i * wl1i; wk1i = w1r * wl1i + w1i * wl1r; wk3i = 4 * wk1i * wk1r; wk3r = wk1r - wk3i * wk1i; wk3i = wk1i - wk3i * wk1r; wd1r = wn4r * (wk1r - wk1i); wd1i = wn4r * (wk1i + wk1r); wd3r = -wn4r * (wk3r - wk3i); wd3i = -wn4r * (wk3i + wk3r); i = i0; } wl1r = WR2500; wl1i = WI2500; j0 = mh; j1 = j0 + m; j2 = j1 + m; j3 = j2 + m; x0r = a[j0 - 2] - a[j2 - 1]; x0i = a[j0 - 1] + a[j2 - 2]; x1r = a[j0 - 2] + a[j2 - 1]; x1i = a[j0 - 1] - a[j2 - 2]; x2r = a[j1 - 2] - a[j3 - 1]; x2i = a[j1 - 1] + a[j3 - 2]; x3r = a[j1 - 2] + a[j3 - 1]; x3i = a[j1 - 1] - a[j3 - 2]; y0r = wk1r * x0r - wk1i * x0i; y0i = wk1r * x0i + wk1i * x0r; y2r = wd1r * x2r - wd1i * x2i; y2i = wd1r * x2i + wd1i * x2r; a[j0 - 2] = y0r + y2r; a[j0 - 1] = y0i + y2i; a[j1 - 2] = y0r - y2r; a[j1 - 1] = y0i - y2i; y0r = wk3r * x1r + wk3i * x1i; y0i = wk3r * x1i - wk3i * x1r; y2r = wd3r * x3r + wd3i * x3i; y2i = wd3r * x3i - wd3i * x3r; a[j2 - 2] = y0r + y2r; a[j2 - 1] = y0i + y2i; a[j3 - 2] = y0r - y2r; a[j3 - 1] = y0i - y2i; x0r = a[j0] - a[j2 + 1]; x0i = a[j0 + 1] + a[j2]; x1r = a[j0] + a[j2 + 1]; x1i = a[j0 + 1] - a[j2]; x2r = a[j1] - a[j3 + 1]; x2i = a[j1 + 1] + a[j3]; x3r = a[j1] + a[j3 + 1]; x3i = a[j1 + 1] - a[j3]; y0r = wl1r * x0r - wl1i * x0i; y0i = wl1r * x0i + wl1i * x0r; y2r = wl1i * x2r - wl1r * x2i; y2i = wl1i * x2i + wl1r * x2r; a[j0] = y0r + y2r; a[j0 + 1] = y0i + y2i; a[j1] = y0r - y2r; a[j1 + 1] = y0i - y2i; y0r = wl1i * x1r - wl1r * x1i; y0i = wl1i * x1i + wl1r * x1r; y2r = wl1r * x3r - wl1i * x3i; y2i = wl1r * x3i + wl1i * x3r; a[j2] = y0r - y2r; a[j2 + 1] = y0i - y2i; a[j3] = y0r + y2r; a[j3 + 1] = y0i + y2i; x0r = a[j0 + 2] - a[j2 + 3]; x0i = a[j0 + 3] + a[j2 + 2]; x1r = a[j0 + 2] + a[j2 + 3]; x1i = a[j0 + 3] - a[j2 + 2]; x2r = a[j1 + 2] - a[j3 + 3]; x2i = a[j1 + 3] + a[j3 + 2]; x3r = a[j1 + 2] + a[j3 + 3]; x3i = a[j1 + 3] - a[j3 + 2]; y0r = wd1i * x0r - wd1r * x0i; y0i = wd1i * x0i + wd1r * x0r; y2r = wk1i * x2r - wk1r * x2i; y2i = wk1i * x2i + wk1r * x2r; a[j0 + 2] = y0r + y2r; a[j0 + 3] = y0i + y2i; a[j1 + 2] = y0r - y2r; a[j1 + 3] = y0i - y2i; y0r = wd3i * x1r + wd3r * x1i; y0i = wd3i * x1i - wd3r * x1r; y2r = wk3i * x3r + wk3r * x3i; y2i = wk3i * x3i - wk3r * x3r; a[j2 + 2] = y0r + y2r; a[j2 + 3] = y0i + y2i; a[j3 + 2] = y0r - y2r; a[j3 + 3] = y0i - y2i; } void cftfx41(int n, double *a) { void cftf161(double *a); void cftf162(double *a); void cftf081(double *a); void cftf082(double *a); if (n == 128) { cftf161(a); cftf162(&a[32]); cftf161(&a[64]); cftf161(&a[96]); } else { cftf081(a); cftf082(&a[16]); cftf081(&a[32]); cftf081(&a[48]); } } void cftf161(double *a) { double wn4r, wk1r, wk1i, x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i, y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i, y8r, y8i, y9r, y9i, y10r, y10i, y11r, y11i, y12r, y12i, y13r, y13i, y14r, y14i, y15r, y15i; wn4r = WR5000; wk1r = WR2500; wk1i = WI2500; x0r = a[0] + a[16]; x0i = a[1] + a[17]; x1r = a[0] - a[16]; x1i = a[1] - a[17]; x2r = a[8] + a[24]; x2i = a[9] + a[25]; x3r = a[8] - a[24]; x3i = a[9] - a[25]; y0r = x0r + x2r; y0i = x0i + x2i; y4r = x0r - x2r; y4i = x0i - x2i; y8r = x1r - x3i; y8i = x1i + x3r; y12r = x1r + x3i; y12i = x1i - x3r; x0r = a[2] + a[18]; x0i = a[3] + a[19]; x1r = a[2] - a[18]; x1i = a[3] - a[19]; x2r = a[10] + a[26]; x2i = a[11] + a[27]; x3r = a[10] - a[26]; x3i = a[11] - a[27]; y1r = x0r + x2r; y1i = x0i + x2i; y5r = x0r - x2r; y5i = x0i - x2i; x0r = x1r - x3i; x0i = x1i + x3r; y9r = wk1r * x0r - wk1i * x0i; y9i = wk1r * x0i + wk1i * x0r; x0r = x1r + x3i; x0i = x1i - x3r; y13r = wk1i * x0r - wk1r * x0i; y13i = wk1i * x0i + wk1r * x0r; x0r = a[4] + a[20]; x0i = a[5] + a[21]; x1r = a[4] - a[20]; x1i = a[5] - a[21]; x2r = a[12] + a[28]; x2i = a[13] + a[29]; x3r = a[12] - a[28]; x3i = a[13] - a[29]; y2r = x0r + x2r; y2i = x0i + x2i; y6r = x0r - x2r; y6i = x0i - x2i; x0r = x1r - x3i; x0i = x1i + x3r; y10r = wn4r * (x0r - x0i); y10i = wn4r * (x0i + x0r); x0r = x1r + x3i; x0i = x1i - x3r; y14r = wn4r * (x0r + x0i); y14i = wn4r * (x0i - x0r); x0r = a[6] + a[22]; x0i = a[7] + a[23]; x1r = a[6] - a[22]; x1i = a[7] - a[23]; x2r = a[14] + a[30]; x2i = a[15] + a[31]; x3r = a[14] - a[30]; x3i = a[15] - a[31]; y3r = x0r + x2r; y3i = x0i + x2i; y7r = x0r - x2r; y7i = x0i - x2i; x0r = x1r - x3i; x0i = x1i + x3r; y11r = wk1i * x0r - wk1r * x0i; y11i = wk1i * x0i + wk1r * x0r; x0r = x1r + x3i; x0i = x1i - x3r; y15r = wk1r * x0r - wk1i * x0i; y15i = wk1r * x0i + wk1i * x0r; x0r = y12r - y14r; x0i = y12i - y14i; x1r = y12r + y14r; x1i = y12i + y14i; x2r = y13r - y15r; x2i = y13i - y15i; x3r = y13r + y15r; x3i = y13i + y15i; a[24] = x0r + x2r; a[25] = x0i + x2i; a[26] = x0r - x2r; a[27] = x0i - x2i; a[28] = x1r - x3i; a[29] = x1i + x3r; a[30] = x1r + x3i; a[31] = x1i - x3r; x0r = y8r + y10r; x0i = y8i + y10i; x1r = y8r - y10r; x1i = y8i - y10i; x2r = y9r + y11r; x2i = y9i + y11i; x3r = y9r - y11r; x3i = y9i - y11i; a[16] = x0r + x2r; a[17] = x0i + x2i; a[18] = x0r - x2r; a[19] = x0i - x2i; a[20] = x1r - x3i; a[21] = x1i + x3r; a[22] = x1r + x3i; a[23] = x1i - x3r; x0r = y5r - y7i; x0i = y5i + y7r; x2r = wn4r * (x0r - x0i); x2i = wn4r * (x0i + x0r); x0r = y5r + y7i; x0i = y5i - y7r; x3r = wn4r * (x0r - x0i); x3i = wn4r * (x0i + x0r); x0r = y4r - y6i; x0i = y4i + y6r; x1r = y4r + y6i; x1i = y4i - y6r; a[8] = x0r + x2r; a[9] = x0i + x2i; a[10] = x0r - x2r; a[11] = x0i - x2i; a[12] = x1r - x3i; a[13] = x1i + x3r; a[14] = x1r + x3i; a[15] = x1i - x3r; x0r = y0r + y2r; x0i = y0i + y2i; x1r = y0r - y2r; x1i = y0i - y2i; x2r = y1r + y3r; x2i = y1i + y3i; x3r = y1r - y3r; x3i = y1i - y3i; a[0] = x0r + x2r; a[1] = x0i + x2i; a[2] = x0r - x2r; a[3] = x0i - x2i; a[4] = x1r - x3i; a[5] = x1i + x3r; a[6] = x1r + x3i; a[7] = x1i - x3r; } void cftf162(double *a) { double wn4r, wk1r, wk1i, wk2r, wk2i, wk3r, wk3i, x0r, x0i, x1r, x1i, x2r, x2i, y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i, y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i, y8r, y8i, y9r, y9i, y10r, y10i, y11r, y11i, y12r, y12i, y13r, y13i, y14r, y14i, y15r, y15i; wn4r = WR5000; wk1r = WR1250; wk1i = WI1250; wk2r = WR2500; wk2i = WI2500; wk3r = WR3750; wk3i = WI3750; x1r = a[0] - a[17]; x1i = a[1] + a[16]; x0r = a[8] - a[25]; x0i = a[9] + a[24]; x2r = wn4r * (x0r - x0i); x2i = wn4r * (x0i + x0r); y0r = x1r + x2r; y0i = x1i + x2i; y4r = x1r - x2r; y4i = x1i - x2i; x1r = a[0] + a[17]; x1i = a[1] - a[16]; x0r = a[8] + a[25]; x0i = a[9] - a[24]; x2r = wn4r * (x0r - x0i); x2i = wn4r * (x0i + x0r); y8r = x1r - x2i; y8i = x1i + x2r; y12r = x1r + x2i; y12i = x1i - x2r; x0r = a[2] - a[19]; x0i = a[3] + a[18]; x1r = wk1r * x0r - wk1i * x0i; x1i = wk1r * x0i + wk1i * x0r; x0r = a[10] - a[27]; x0i = a[11] + a[26]; x2r = wk3i * x0r - wk3r * x0i; x2i = wk3i * x0i + wk3r * x0r; y1r = x1r + x2r; y1i = x1i + x2i; y5r = x1r - x2r; y5i = x1i - x2i; x0r = a[2] + a[19]; x0i = a[3] - a[18]; x1r = wk3r * x0r - wk3i * x0i; x1i = wk3r * x0i + wk3i * x0r; x0r = a[10] + a[27]; x0i = a[11] - a[26]; x2r = wk1r * x0r + wk1i * x0i; x2i = wk1r * x0i - wk1i * x0r; y9r = x1r - x2r; y9i = x1i - x2i; y13r = x1r + x2r; y13i = x1i + x2i; x0r = a[4] - a[21]; x0i = a[5] + a[20]; x1r = wk2r * x0r - wk2i * x0i; x1i = wk2r * x0i + wk2i * x0r; x0r = a[12] - a[29]; x0i = a[13] + a[28]; x2r = wk2i * x0r - wk2r * x0i; x2i = wk2i * x0i + wk2r * x0r; y2r = x1r + x2r; y2i = x1i + x2i; y6r = x1r - x2r; y6i = x1i - x2i; x0r = a[4] + a[21]; x0i = a[5] - a[20]; x1r = wk2i * x0r - wk2r * x0i; x1i = wk2i * x0i + wk2r * x0r; x0r = a[12] + a[29]; x0i = a[13] - a[28]; x2r = wk2r * x0r - wk2i * x0i; x2i = wk2r * x0i + wk2i * x0r; y10r = x1r - x2r; y10i = x1i - x2i; y14r = x1r + x2r; y14i = x1i + x2i; x0r = a[6] - a[23]; x0i = a[7] + a[22]; x1r = wk3r * x0r - wk3i * x0i; x1i = wk3r * x0i + wk3i * x0r; x0r = a[14] - a[31]; x0i = a[15] + a[30]; x2r = wk1i * x0r - wk1r * x0i; x2i = wk1i * x0i + wk1r * x0r; y3r = x1r + x2r; y3i = x1i + x2i; y7r = x1r - x2r; y7i = x1i - x2i; x0r = a[6] + a[23]; x0i = a[7] - a[22]; x1r = wk1i * x0r + wk1r * x0i; x1i = wk1i * x0i - wk1r * x0r; x0r = a[14] + a[31]; x0i = a[15] - a[30]; x2r = wk3i * x0r - wk3r * x0i; x2i = wk3i * x0i + wk3r * x0r; y11r = x1r + x2r; y11i = x1i + x2i; y15r = x1r - x2r; y15i = x1i - x2i; x1r = y0r + y2r; x1i = y0i + y2i; x2r = y1r + y3r; x2i = y1i + y3i; a[0] = x1r + x2r; a[1] = x1i + x2i; a[2] = x1r - x2r; a[3] = x1i - x2i; x1r = y0r - y2r; x1i = y0i - y2i; x2r = y1r - y3r; x2i = y1i - y3i; a[4] = x1r - x2i; a[5] = x1i + x2r; a[6] = x1r + x2i; a[7] = x1i - x2r; x1r = y4r - y6i; x1i = y4i + y6r; x0r = y5r - y7i; x0i = y5i + y7r; x2r = wn4r * (x0r - x0i); x2i = wn4r * (x0i + x0r); a[8] = x1r + x2r; a[9] = x1i + x2i; a[10] = x1r - x2r; a[11] = x1i - x2i; x1r = y4r + y6i; x1i = y4i - y6r; x0r = y5r + y7i; x0i = y5i - y7r; x2r = wn4r * (x0r - x0i); x2i = wn4r * (x0i + x0r); a[12] = x1r - x2i; a[13] = x1i + x2r; a[14] = x1r + x2i; a[15] = x1i - x2r; x1r = y8r + y10r; x1i = y8i + y10i; x2r = y9r - y11r; x2i = y9i - y11i; a[16] = x1r + x2r; a[17] = x1i + x2i; a[18] = x1r - x2r; a[19] = x1i - x2i; x1r = y8r - y10r; x1i = y8i - y10i; x2r = y9r + y11r; x2i = y9i + y11i; a[20] = x1r - x2i; a[21] = x1i + x2r; a[22] = x1r + x2i; a[23] = x1i - x2r; x1r = y12r - y14i; x1i = y12i + y14r; x0r = y13r + y15i; x0i = y13i - y15r; x2r = wn4r * (x0r - x0i); x2i = wn4r * (x0i + x0r); a[24] = x1r + x2r; a[25] = x1i + x2i; a[26] = x1r - x2r; a[27] = x1i - x2i; x1r = y12r + y14i; x1i = y12i - y14r; x0r = y13r - y15i; x0i = y13i + y15r; x2r = wn4r * (x0r - x0i); x2i = wn4r * (x0i + x0r); a[28] = x1r - x2i; a[29] = x1i + x2r; a[30] = x1r + x2i; a[31] = x1i - x2r; } void cftf081(double *a) { double wn4r, x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i, y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i; wn4r = WR5000; x0r = a[0] + a[8]; x0i = a[1] + a[9]; x1r = a[0] - a[8]; x1i = a[1] - a[9]; x2r = a[4] + a[12]; x2i = a[5] + a[13]; x3r = a[4] - a[12]; x3i = a[5] - a[13]; y0r = x0r + x2r; y0i = x0i + x2i; y2r = x0r - x2r; y2i = x0i - x2i; y1r = x1r - x3i; y1i = x1i + x3r; y3r = x1r + x3i; y3i = x1i - x3r; x0r = a[2] + a[10]; x0i = a[3] + a[11]; x1r = a[2] - a[10]; x1i = a[3] - a[11]; x2r = a[6] + a[14]; x2i = a[7] + a[15]; x3r = a[6] - a[14]; x3i = a[7] - a[15]; y4r = x0r + x2r; y4i = x0i + x2i; y6r = x0r - x2r; y6i = x0i - x2i; x0r = x1r - x3i; x0i = x1i + x3r; x2r = x1r + x3i; x2i = x1i - x3r; y5r = wn4r * (x0r - x0i); y5i = wn4r * (x0r + x0i); y7r = wn4r * (x2r - x2i); y7i = wn4r * (x2r + x2i); a[8] = y1r + y5r; a[9] = y1i + y5i; a[10] = y1r - y5r; a[11] = y1i - y5i; a[12] = y3r - y7i; a[13] = y3i + y7r; a[14] = y3r + y7i; a[15] = y3i - y7r; a[0] = y0r + y4r; a[1] = y0i + y4i; a[2] = y0r - y4r; a[3] = y0i - y4i; a[4] = y2r - y6i; a[5] = y2i + y6r; a[6] = y2r + y6i; a[7] = y2i - y6r; } void cftf082(double *a) { double wn4r, wk1r, wk1i, x0r, x0i, x1r, x1i, y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i, y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i; wn4r = WR5000; wk1r = WR2500; wk1i = WI2500; y0r = a[0] - a[9]; y0i = a[1] + a[8]; y1r = a[0] + a[9]; y1i = a[1] - a[8]; x0r = a[4] - a[13]; x0i = a[5] + a[12]; y2r = wn4r * (x0r - x0i); y2i = wn4r * (x0i + x0r); x0r = a[4] + a[13]; x0i = a[5] - a[12]; y3r = wn4r * (x0r - x0i); y3i = wn4r * (x0i + x0r); x0r = a[2] - a[11]; x0i = a[3] + a[10]; y4r = wk1r * x0r - wk1i * x0i; y4i = wk1r * x0i + wk1i * x0r; x0r = a[2] + a[11]; x0i = a[3] - a[10]; y5r = wk1i * x0r - wk1r * x0i; y5i = wk1i * x0i + wk1r * x0r; x0r = a[6] - a[15]; x0i = a[7] + a[14]; y6r = wk1i * x0r - wk1r * x0i; y6i = wk1i * x0i + wk1r * x0r; x0r = a[6] + a[15]; x0i = a[7] - a[14]; y7r = wk1r * x0r - wk1i * x0i; y7i = wk1r * x0i + wk1i * x0r; x0r = y0r + y2r; x0i = y0i + y2i; x1r = y4r + y6r; x1i = y4i + y6i; a[0] = x0r + x1r; a[1] = x0i + x1i; a[2] = x0r - x1r; a[3] = x0i - x1i; x0r = y0r - y2r; x0i = y0i - y2i; x1r = y4r - y6r; x1i = y4i - y6i; a[4] = x0r - x1i; a[5] = x0i + x1r; a[6] = x0r + x1i; a[7] = x0i - x1r; x0r = y1r - y3i; x0i = y1i + y3r; x1r = y5r - y7r; x1i = y5i - y7i; a[8] = x0r + x1r; a[9] = x0i + x1i; a[10] = x0r - x1r; a[11] = x0i - x1i; x0r = y1r + y3i; x0i = y1i - y3r; x1r = y5r + y7r; x1i = y5i + y7i; a[12] = x0r - x1i; a[13] = x0i + x1r; a[14] = x0r + x1i; a[15] = x0i - x1r; } void cftf040(double *a) { double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; x0r = a[0] + a[4]; x0i = a[1] + a[5]; x1r = a[0] - a[4]; x1i = a[1] - a[5]; x2r = a[2] + a[6]; x2i = a[3] + a[7]; x3r = a[2] - a[6]; x3i = a[3] - a[7]; a[0] = x0r + x2r; a[1] = x0i + x2i; a[2] = x1r - x3i; a[3] = x1i + x3r; a[4] = x0r - x2r; a[5] = x0i - x2i; a[6] = x1r + x3i; a[7] = x1i - x3r; } void cftb040(double *a) { double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; x0r = a[0] + a[4]; x0i = a[1] + a[5]; x1r = a[0] - a[4]; x1i = a[1] - a[5]; x2r = a[2] + a[6]; x2i = a[3] + a[7]; x3r = a[2] - a[6]; x3i = a[3] - a[7]; a[0] = x0r + x2r; a[1] = x0i + x2i; a[2] = x1r + x3i; a[3] = x1i - x3r; a[4] = x0r - x2r; a[5] = x0i - x2i; a[6] = x1r - x3i; a[7] = x1i + x3r; } void cftx020(double *a) { double x0r, x0i; x0r = a[0] - a[2]; x0i = a[1] - a[3]; a[0] += a[2]; a[1] += a[3]; a[2] = x0r; a[3] = x0i; } void rftfsub(int n, double *a) { int i, i0, j, k; double ec, w1r, w1i, wkr, wki, wdr, wdi, ss, xr, xi, yr, yi; ec = 2 * M_PI_2 / n; wkr = 0; wki = 0; wdi = cos(ec); wdr = sin(ec); wdi *= wdr; wdr *= wdr; w1r = 1 - 2 * wdr; w1i = 2 * wdi; ss = 2 * w1i; i = n >> 1; for (;;) { i0 = i - 4 * RDFT_LOOP_DIV; if (i0 < 4) { i0 = 4; } for (j = i - 4; j >= i0; j -= 4) { k = n - j; xr = a[j + 2] - a[k - 2]; xi = a[j + 3] + a[k - 1]; yr = wdr * xr - wdi * xi; yi = wdr * xi + wdi * xr; a[j + 2] -= yr; a[j + 3] -= yi; a[k - 2] += yr; a[k - 1] -= yi; wkr += ss * wdi; wki += ss * (0.5 - wdr); 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; wdr += ss * wki; wdi += ss * (0.5 - wkr); } if (i0 == 4) { break; } wkr = 0.5 * sin(ec * i0); wki = 0.5 * cos(ec * i0); wdr = 0.5 - (wkr * w1r - wki * w1i); wdi = wkr * w1i + wki * w1r; wkr = 0.5 - wkr; i = i0; } xr = a[2] - a[n - 2]; xi = a[3] + a[n - 1]; yr = wdr * xr - wdi * xi; yi = wdr * xi + wdi * xr; a[2] -= yr; a[3] -= yi; a[n - 2] += yr; a[n - 1] -= yi; } void rftbsub(int n, double *a) { int i, i0, j, k; double ec, w1r, w1i, wkr, wki, wdr, wdi, ss, xr, xi, yr, yi; ec = 2 * M_PI_2 / n; wkr = 0; wki = 0; wdi = cos(ec); wdr = sin(ec); wdi *= wdr; wdr *= wdr; w1r = 1 - 2 * wdr; w1i = 2 * wdi; ss = 2 * w1i; i = n >> 1; for (;;) { i0 = i - 4 * RDFT_LOOP_DIV; if (i0 < 4) { i0 = 4; } for (j = i - 4; j >= i0; j -= 4) { k = n - j; xr = a[j + 2] - a[k - 2]; xi = a[j + 3] + a[k - 1]; yr = wdr * xr + wdi * xi; yi = wdr * xi - wdi * xr; a[j + 2] -= yr; a[j + 3] -= yi; a[k - 2] += yr; a[k - 1] -= yi; wkr += ss * wdi; wki += ss * (0.5 - wdr); 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; wdr += ss * wki; wdi += ss * (0.5 - wkr); } if (i0 == 4) { break; } wkr = 0.5 * sin(ec * i0); wki = 0.5 * cos(ec * i0); wdr = 0.5 - (wkr * w1r - wki * w1i); wdi = wkr * w1i + wki * w1r; wkr = 0.5 - wkr; i = i0; } xr = a[2] - a[n - 2]; xi = a[3] + a[n - 1]; yr = wdr * xr + wdi * xi; yi = wdr * xi - wdi * xr; a[2] -= yr; a[3] -= yi; a[n - 2] += yr; a[n - 1] -= yi; } void dctsub(int n, double *a) { int i, i0, j, k, m; double ec, w1r, w1i, wkr, wki, wdr, wdi, ss, xr, xi, yr, yi; ec = M_PI_2 / n; wkr = 0.5; wki = 0.5; w1r = cos(ec); w1i = sin(ec); wdr = 0.5 * (w1r - w1i); wdi = 0.5 * (w1r + w1i); ss = 2 * w1i; m = n >> 1; i = 0; for (;;) { i0 = i + 2 * DCST_LOOP_DIV; if (i0 > m - 2) { i0 = m - 2; } for (j = i + 2; j <= i0; j += 2) { k = n - j; xr = wdi * a[j - 1] - wdr * a[k + 1]; xi = wdr * a[j - 1] + wdi * a[k + 1]; wkr -= ss * wdi; wki += ss * wdr; yr = wki * a[j] - wkr * a[k]; yi = wkr * a[j] + wki * a[k]; wdr -= ss * wki; wdi += ss * wkr; a[k + 1] = xr; a[k] = yr; a[j - 1] = xi; a[j] = yi; } if (i0 == m - 2) { break; } wdr = cos(ec * i0); wdi = sin(ec * i0); wkr = 0.5 * (wdr - wdi); wki = 0.5 * (wdr + wdi); wdr = wkr * w1r - wki * w1i; wdi = wkr * w1i + wki * w1r; i = i0; } xr = wdi * a[m - 1] - wdr * a[m + 1]; a[m - 1] = wdr * a[m - 1] + wdi * a[m + 1]; a[m + 1] = xr; a[m] *= WR5000; } void dstsub(int n, double *a) { int i, i0, j, k, m; double ec, w1r, w1i, wkr, wki, wdr, wdi, ss, xr, xi, yr, yi; ec = M_PI_2 / n; wkr = 0.5; wki = 0.5; w1r = cos(ec); w1i = sin(ec); wdr = 0.5 * (w1r - w1i); wdi = 0.5 * (w1r + w1i); ss = 2 * w1i; m = n >> 1; i = 0; for (;;) { i0 = i + 2 * DCST_LOOP_DIV; if (i0 > m - 2) { i0 = m - 2; } for (j = i + 2; j <= i0; j += 2) { k = n - j; xr = wdi * a[k + 1] - wdr * a[j - 1]; xi = wdr * a[k + 1] + wdi * a[j - 1]; wkr -= ss * wdi; wki += ss * wdr; yr = wki * a[k] - wkr * a[j]; yi = wkr * a[k] + wki * a[j]; wdr -= ss * wki; wdi += ss * wkr; a[j - 1] = xr; a[j] = yr; a[k + 1] = xi; a[k] = yi; } if (i0 == m - 2) { break; } wdr = cos(ec * i0); wdi = sin(ec * i0); wkr = 0.5 * (wdr - wdi); wki = 0.5 * (wdr + wdi); wdr = wkr * w1r - wki * w1i; wdi = wkr * w1i + wki * w1r; i = i0; } xr = wdi * a[m + 1] - wdr * a[m - 1]; a[m + 1] = wdr * a[m + 1] + wdi * a[m - 1]; a[m - 1] = xr; a[m] *= WR5000; } void dctsub4(int n, double *a) { int m; double wki, wdr, wdi, xr; wki = WR5000; m = n >> 1; if (m == 2) { wdr = wki * WI2500; wdi = wki * WR2500; xr = wdi * a[1] - wdr * a[3]; a[1] = wdr * a[1] + wdi * a[3]; a[3] = xr; } a[m] *= wki; } void dstsub4(int n, double *a) { int m; double wki, wdr, wdi, xr; wki = WR5000; m = n >> 1; if (m == 2) { wdr = wki * WI2500; wdi = wki * WR2500; xr = wdi * a[3] - wdr * a[1]; a[3] = wdr * a[3] + wdi * a[1]; a[1] = xr; } a[m] *= wki; }