mirror of https://github.com/AxioDL/boo.git
1353 lines
37 KiB
C
1353 lines
37 KiB
C
/* Copyright Takuya OOURA, 1996-2001.
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You may use, copy, modify and distribute this code for any
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purpose (include commercial use) and without fee. Please
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refer to this package when you modify this code.
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Package home: http://www.kurims.kyoto-u.ac.jp/~ooura/fft.html
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Fast Fourier/Cosine/Sine Transform
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dimension :one
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data length :power of 2
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decimation :frequency
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radix :4, 2
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data :inplace
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table :use
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functions
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cdft: Complex Discrete Fourier Transform
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rdft: Real Discrete Fourier Transform
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ddct: Discrete Cosine Transform
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ddst: Discrete Sine Transform
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dfct: Cosine Transform of RDFT (Real Symmetric DFT)
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dfst: Sine Transform of RDFT (Real Anti-symmetric DFT)
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function prototypes
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void cdft(int, int, double *, int *, double *);
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void rdft(int, int, double *, int *, double *);
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void ddct(int, int, double *, int *, double *);
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void ddst(int, int, double *, int *, double *);
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void dfct(int, double *, double *, int *, double *);
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void dfst(int, double *, double *, int *, double *);
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-------- Complex DFT (Discrete Fourier Transform) --------
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[definition]
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<case1>
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X[k] = sum_j=0^n-1 x[j]*exp(2*pi*i*j*k/n), 0<=k<n
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<case2>
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X[k] = sum_j=0^n-1 x[j]*exp(-2*pi*i*j*k/n), 0<=k<n
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(notes: sum_j=0^n-1 is a summation from j=0 to n-1)
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[usage]
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<case1>
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ip[0] = 0; // first time only
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cdft(2*n, 1, a, ip, w);
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<case2>
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ip[0] = 0; // first time only
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cdft(2*n, -1, a, ip, w);
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[parameters]
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2*n :data length (int)
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n >= 1, n = power of 2
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a[0...2*n-1] :input/output data (double *)
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input data
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a[2*j] = Re(x[j]),
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a[2*j+1] = Im(x[j]), 0<=j<n
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output data
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a[2*k] = Re(X[k]),
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a[2*k+1] = Im(X[k]), 0<=k<n
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ip[0...*] :work area for bit reversal (int *)
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length of ip >= 2+sqrt(n)
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strictly,
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length of ip >=
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2+(1<<(int)(log(n+0.5)/log(2))/2).
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ip[0],ip[1] are pointers of the cos/sin table.
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w[0...n/2-1] :cos/sin table (double *)
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w[],ip[] are initialized if ip[0] == 0.
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[remark]
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Inverse of
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cdft(2*n, -1, a, ip, w);
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is
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cdft(2*n, 1, a, ip, w);
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for (j = 0; j <= 2 * n - 1; j++) {
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a[j] *= 1.0 / n;
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}
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.
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-------- Real DFT / Inverse of Real DFT --------
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[definition]
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<case1> RDFT
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R[k] = sum_j=0^n-1 a[j]*cos(2*pi*j*k/n), 0<=k<=n/2
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I[k] = sum_j=0^n-1 a[j]*sin(2*pi*j*k/n), 0<k<n/2
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<case2> IRDFT (excluding scale)
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a[k] = (R[0] + R[n/2]*cos(pi*k))/2 +
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sum_j=1^n/2-1 R[j]*cos(2*pi*j*k/n) +
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sum_j=1^n/2-1 I[j]*sin(2*pi*j*k/n), 0<=k<n
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[usage]
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<case1>
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ip[0] = 0; // first time only
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rdft(n, 1, a, ip, w);
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<case2>
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ip[0] = 0; // first time only
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rdft(n, -1, a, ip, w);
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[parameters]
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n :data length (int)
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n >= 2, n = power of 2
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a[0...n-1] :input/output data (double *)
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<case1>
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output data
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a[2*k] = R[k], 0<=k<n/2
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a[2*k+1] = I[k], 0<k<n/2
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a[1] = R[n/2]
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<case2>
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input data
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a[2*j] = R[j], 0<=j<n/2
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a[2*j+1] = I[j], 0<j<n/2
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a[1] = R[n/2]
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ip[0...*] :work area for bit reversal (int *)
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length of ip >= 2+sqrt(n/2)
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strictly,
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length of ip >=
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2+(1<<(int)(log(n/2+0.5)/log(2))/2).
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ip[0],ip[1] are pointers of the cos/sin table.
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w[0...n/2-1] :cos/sin table (double *)
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w[],ip[] are initialized if ip[0] == 0.
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[remark]
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Inverse of
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rdft(n, 1, a, ip, w);
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is
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rdft(n, -1, a, ip, w);
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for (j = 0; j <= n - 1; j++) {
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a[j] *= 2.0 / n;
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}
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.
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-------- DCT (Discrete Cosine Transform) / Inverse of DCT --------
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[definition]
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<case1> IDCT (excluding scale)
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C[k] = sum_j=0^n-1 a[j]*cos(pi*j*(k+1/2)/n), 0<=k<n
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<case2> DCT
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C[k] = sum_j=0^n-1 a[j]*cos(pi*(j+1/2)*k/n), 0<=k<n
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[usage]
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<case1>
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ip[0] = 0; // first time only
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ddct(n, 1, a, ip, w);
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<case2>
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ip[0] = 0; // first time only
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ddct(n, -1, a, ip, w);
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[parameters]
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n :data length (int)
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n >= 2, n = power of 2
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a[0...n-1] :input/output data (double *)
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output data
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a[k] = C[k], 0<=k<n
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ip[0...*] :work area for bit reversal (int *)
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length of ip >= 2+sqrt(n/2)
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strictly,
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length of ip >=
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2+(1<<(int)(log(n/2+0.5)/log(2))/2).
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ip[0],ip[1] are pointers of the cos/sin table.
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w[0...n*5/4-1] :cos/sin table (double *)
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w[],ip[] are initialized if ip[0] == 0.
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[remark]
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Inverse of
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ddct(n, -1, a, ip, w);
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is
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a[0] *= 0.5;
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ddct(n, 1, a, ip, w);
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for (j = 0; j <= n - 1; j++) {
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a[j] *= 2.0 / n;
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}
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.
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-------- DST (Discrete Sine Transform) / Inverse of DST --------
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[definition]
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<case1> IDST (excluding scale)
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S[k] = sum_j=1^n A[j]*sin(pi*j*(k+1/2)/n), 0<=k<n
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<case2> DST
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S[k] = sum_j=0^n-1 a[j]*sin(pi*(j+1/2)*k/n), 0<k<=n
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[usage]
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<case1>
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ip[0] = 0; // first time only
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ddst(n, 1, a, ip, w);
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<case2>
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ip[0] = 0; // first time only
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ddst(n, -1, a, ip, w);
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[parameters]
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n :data length (int)
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n >= 2, n = power of 2
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a[0...n-1] :input/output data (double *)
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<case1>
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input data
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a[j] = A[j], 0<j<n
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a[0] = A[n]
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output data
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a[k] = S[k], 0<=k<n
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<case2>
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output data
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a[k] = S[k], 0<k<n
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a[0] = S[n]
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ip[0...*] :work area for bit reversal (int *)
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length of ip >= 2+sqrt(n/2)
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strictly,
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length of ip >=
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2+(1<<(int)(log(n/2+0.5)/log(2))/2).
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ip[0],ip[1] are pointers of the cos/sin table.
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w[0...n*5/4-1] :cos/sin table (double *)
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w[],ip[] are initialized if ip[0] == 0.
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[remark]
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Inverse of
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ddst(n, -1, a, ip, w);
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is
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a[0] *= 0.5;
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ddst(n, 1, a, ip, w);
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for (j = 0; j <= n - 1; j++) {
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a[j] *= 2.0 / n;
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}
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.
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-------- Cosine Transform of RDFT (Real Symmetric DFT) --------
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[definition]
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C[k] = sum_j=0^n a[j]*cos(pi*j*k/n), 0<=k<=n
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[usage]
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ip[0] = 0; // first time only
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dfct(n, a, t, ip, w);
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[parameters]
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n :data length - 1 (int)
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n >= 2, n = power of 2
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a[0...n] :input/output data (double *)
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output data
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a[k] = C[k], 0<=k<=n
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t[0...n/2] :work area (double *)
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ip[0...*] :work area for bit reversal (int *)
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length of ip >= 2+sqrt(n/4)
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strictly,
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length of ip >=
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2+(1<<(int)(log(n/4+0.5)/log(2))/2).
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ip[0],ip[1] are pointers of the cos/sin table.
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w[0...n*5/8-1] :cos/sin table (double *)
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w[],ip[] are initialized if ip[0] == 0.
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[remark]
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Inverse of
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a[0] *= 0.5;
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a[n] *= 0.5;
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dfct(n, a, t, ip, w);
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is
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a[0] *= 0.5;
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a[n] *= 0.5;
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dfct(n, a, t, ip, w);
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for (j = 0; j <= n; j++) {
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a[j] *= 2.0 / n;
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}
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.
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-------- Sine Transform of RDFT (Real Anti-symmetric DFT) --------
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[definition]
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S[k] = sum_j=1^n-1 a[j]*sin(pi*j*k/n), 0<k<n
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[usage]
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ip[0] = 0; // first time only
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dfst(n, a, t, ip, w);
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[parameters]
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n :data length + 1 (int)
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n >= 2, n = power of 2
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a[0...n-1] :input/output data (double *)
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output data
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a[k] = S[k], 0<k<n
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(a[0] is used for work area)
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t[0...n/2-1] :work area (double *)
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ip[0...*] :work area for bit reversal (int *)
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length of ip >= 2+sqrt(n/4)
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strictly,
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length of ip >=
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2+(1<<(int)(log(n/4+0.5)/log(2))/2).
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ip[0],ip[1] are pointers of the cos/sin table.
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w[0...n*5/8-1] :cos/sin table (double *)
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w[],ip[] are initialized if ip[0] == 0.
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[remark]
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Inverse of
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dfst(n, a, t, ip, w);
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is
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dfst(n, a, t, ip, w);
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for (j = 1; j <= n - 1; j++) {
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a[j] *= 2.0 / n;
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}
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.
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Appendix :
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The cos/sin table is recalculated when the larger table required.
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w[] and ip[] are compatible with all routines.
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*/
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#include <math.h>
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#include "fft4g.h"
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#ifdef FFT4G_FLOAT
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#define double float
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#define one_half 0.5f
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#if defined _MSC_VER
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#define sin (float)sin
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#define cos (float)cos
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#define atan (float)atan
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#else
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#define sin sinf
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#define cos cosf
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#define atan atanf
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#endif
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#define cdft lsx_cdft_f
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#define rdft lsx_rdft_f
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#define ddct lsx_ddct_f
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#define ddst lsx_ddst_f
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#define dfct lsx_dfct_f
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#define dfst lsx_dfst_f
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#else
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#define one_half 0.5
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#define cdft lsx_cdft
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#define rdft lsx_rdft
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#define ddct lsx_ddct
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#define ddst lsx_ddst
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#define dfct lsx_dfct
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#define dfst lsx_dfst
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#endif
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static void bitrv2conj(int n, int *ip, double *a);
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static void bitrv2(int n, int *ip, double *a);
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static void cft1st(int n, double *a, double const *w);
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static void cftbsub(int n, double *a, double const *w);
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static void cftfsub(int n, double *a, double const *w);
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static void cftmdl(int n, int l, double *a, double const *w);
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static void dctsub(int n, double *a, int nc, double const *c);
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static void dstsub(int n, double *a, int nc, double const *c);
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static void makect(int nc, int *ip, double *c);
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static void makewt(int nw, int *ip, double *w);
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static void rftbsub(int n, double *a, int nc, double const *c);
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static void rftfsub(int n, double *a, int nc, double const *c);
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void cdft(int n, int isgn, double *a, int *ip, double *w)
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{
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if (n > (ip[0] << 2)) {
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makewt(n >> 2, ip, w);
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}
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if (n > 4) {
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if (isgn >= 0) {
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bitrv2(n, ip + 2, a);
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cftfsub(n, a, w);
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} else {
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bitrv2conj(n, ip + 2, a);
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cftbsub(n, a, w);
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}
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} else if (n == 4) {
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cftfsub(n, a, w);
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}
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}
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void rdft(int n, int isgn, double *a, int *ip, double *w)
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{
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int nw, nc;
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double xi;
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nw = ip[0];
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if (n > (nw << 2)) {
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nw = n >> 2;
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makewt(nw, ip, w);
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}
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nc = ip[1];
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if (n > (nc << 2)) {
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nc = n >> 2;
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makect(nc, ip, w + nw);
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}
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if (isgn >= 0) {
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if (n > 4) {
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bitrv2(n, ip + 2, a);
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cftfsub(n, a, w);
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rftfsub(n, a, nc, w + nw);
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} else if (n == 4) {
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cftfsub(n, a, w);
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}
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xi = a[0] - a[1];
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a[0] += a[1];
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a[1] = xi;
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} else {
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a[1] = one_half * (a[0] - a[1]);
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a[0] -= a[1];
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if (n > 4) {
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rftbsub(n, a, nc, w + nw);
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bitrv2(n, ip + 2, a);
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cftbsub(n, a, w);
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} else if (n == 4) {
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cftfsub(n, a, w);
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}
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}
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}
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void ddct(int n, int isgn, double *a, int *ip, double *w)
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{
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int j, nw, nc;
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double xr;
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nw = ip[0];
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if (n > (nw << 2)) {
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nw = n >> 2;
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makewt(nw, ip, w);
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}
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nc = ip[1];
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if (n > nc) {
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nc = n;
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makect(nc, ip, w + nw);
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}
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if (isgn < 0) {
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xr = a[n - 1];
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for (j = n - 2; j >= 2; j -= 2) {
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a[j + 1] = a[j] - a[j - 1];
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a[j] += a[j - 1];
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}
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a[1] = a[0] - xr;
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a[0] += xr;
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if (n > 4) {
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rftbsub(n, a, nc, w + nw);
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bitrv2(n, ip + 2, a);
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cftbsub(n, a, w);
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} else if (n == 4) {
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cftfsub(n, a, w);
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}
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}
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dctsub(n, a, nc, w + nw);
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if (isgn >= 0) {
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if (n > 4) {
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bitrv2(n, ip + 2, a);
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cftfsub(n, a, w);
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rftfsub(n, a, nc, w + nw);
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} else if (n == 4) {
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cftfsub(n, a, w);
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}
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xr = a[0] - a[1];
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a[0] += a[1];
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for (j = 2; j < n; j += 2) {
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a[j - 1] = a[j] - a[j + 1];
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a[j] += a[j + 1];
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}
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a[n - 1] = xr;
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}
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}
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void ddst(int n, int isgn, double *a, int *ip, double *w)
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{
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int j, nw, nc;
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double xr;
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nw = ip[0];
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if (n > (nw << 2)) {
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nw = n >> 2;
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makewt(nw, ip, w);
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}
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nc = ip[1];
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if (n > nc) {
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nc = n;
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makect(nc, ip, w + nw);
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}
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if (isgn < 0) {
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xr = a[n - 1];
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for (j = n - 2; j >= 2; j -= 2) {
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a[j + 1] = -a[j] - a[j - 1];
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a[j] -= a[j - 1];
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}
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a[1] = a[0] + xr;
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a[0] -= xr;
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if (n > 4) {
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rftbsub(n, a, nc, w + nw);
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bitrv2(n, ip + 2, a);
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cftbsub(n, a, w);
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} else if (n == 4) {
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cftfsub(n, a, w);
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}
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}
|
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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;
|
|
}
|
|
}
|
|
|
|
|
|
void dfct(int n, double *a, double *t, int *ip, double *w)
|
|
{
|
|
int j, k, l, m, mh, nw, nc;
|
|
double 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];
|
|
}
|
|
}
|
|
|
|
|
|
void dfst(int n, double *a, double *t, int *ip, double *w)
|
|
{
|
|
int j, k, l, m, mh, nw, nc;
|
|
double 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;
|
|
}
|
|
|
|
|
|
/* -------- initializing routines -------- */
|
|
|
|
|
|
static void makewt(int nw, int *ip, double *w)
|
|
{
|
|
int j, nwh;
|
|
double delta, x, y;
|
|
|
|
ip[0] = nw;
|
|
ip[1] = 1;
|
|
if (nw > 2) {
|
|
nwh = nw >> 1;
|
|
delta = atan(1.0) / (double)nwh;
|
|
w[0] = 1;
|
|
w[1] = 0;
|
|
w[nwh] = cos(delta * (double)nwh);
|
|
w[nwh + 1] = w[nwh];
|
|
if (nwh > 2) {
|
|
for (j = 2; j < nwh; j += 2) {
|
|
x = cos(delta * (double)j);
|
|
y = sin(delta * (double)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, double *c)
|
|
{
|
|
int j, nch;
|
|
double delta;
|
|
|
|
ip[1] = nc;
|
|
if (nc > 1) {
|
|
nch = nc >> 1;
|
|
delta = atan(1.0) / (double)nch;
|
|
c[0] = cos(delta * (double)nch);
|
|
c[nch] = one_half * c[0];
|
|
for (j = 1; j < nch; j++) {
|
|
c[j] = one_half * cos(delta * (double)j);
|
|
c[nc - j] = one_half * sin(delta * (double)j);
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
/* -------- child routines -------- */
|
|
|
|
|
|
static void bitrv2(int n, int *ip0, double *a)
|
|
{
|
|
int j, j1, k, k1, l, m, m2, ip[1024];
|
|
double xr, xi, yr, yi;
|
|
|
|
(void)ip0;
|
|
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 *ip0, double *a)
|
|
{
|
|
int j, j1, k, k1, l, m, m2, ip[256];
|
|
double xr, xi, yr, yi;
|
|
|
|
(void)ip0;
|
|
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, double *a, double const *w)
|
|
{
|
|
int j, j1, j2, j3, l;
|
|
double 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, double *a, double const *w)
|
|
{
|
|
int j, j1, j2, j3, l;
|
|
double 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, double *a, double const *w)
|
|
{
|
|
int j, k1, k2;
|
|
double wk1r, wk1i, wk2r, wk2i, wk3r, wk3i;
|
|
double 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, double *a, double const *w)
|
|
{
|
|
int j, j1, j2, j3, k, k1, k2, m, m2;
|
|
double wk1r, wk1i, wk2r, wk2i, wk3r, wk3i;
|
|
double 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, double *a, int nc, double const *c)
|
|
{
|
|
int j, k, kk, ks, m;
|
|
double 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 = one_half - 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, double *a, int nc, double const *c)
|
|
{
|
|
int j, k, kk, ks, m;
|
|
double 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 = one_half - 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];
|
|
}
|
|
|
|
|
|
static void dctsub(int n, double *a, int nc, double const *c)
|
|
{
|
|
int j, k, kk, ks, m;
|
|
double 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, double *a, int nc, double const *c)
|
|
{
|
|
int j, k, kk, ks, m;
|
|
double 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];
|
|
}
|