[llvm-commits] CVS: llvm/test/Programs/MultiSource/Benchmarks/FreeBench/pifft/Makefile fftsg.c pifft.c ref.in test.in
Chris Lattner
lattner at cs.uiuc.edu
Sat Oct 11 16:21:03 PDT 2003
Changes in directory llvm/test/Programs/MultiSource/Benchmarks/FreeBench/pifft:
Makefile added (r1.1)
fftsg.c added (r1.1)
pifft.c added (r1.1)
ref.in added (r1.1)
test.in added (r1.1)
---
Log message:
Initial checkin of the FreeBench benchmark suite
---
Diffs of the changes: (+4199 -0)
Index: llvm/test/Programs/MultiSource/Benchmarks/FreeBench/pifft/Makefile
diff -c /dev/null llvm/test/Programs/MultiSource/Benchmarks/FreeBench/pifft/Makefile:1.1
*** /dev/null Sat Oct 11 16:18:59 2003
--- llvm/test/Programs/MultiSource/Benchmarks/FreeBench/pifft/Makefile Sat Oct 11 16:18:48 2003
***************
*** 0 ****
--- 1,12 ----
+ LEVEL = ../../../../../..
+
+ PROG = pifft
+ CPPFLAGS = -DVERSION='"1.00"' -DCOMPDATE="\"today\"" -DCFLAGS='""' -DHOSTNAME="\"thishost\""
+ LDFLAGS = -lm
+ ifdef LARGE_PROBLEM_SIZE
+ RUN_OPTIONS = ref.in
+ else
+ RUN_OPTIONS = test.in
+ endif
+ include $(LEVEL)/test/Programs/MultiSource/Makefile.multisrc
+
Index: llvm/test/Programs/MultiSource/Benchmarks/FreeBench/pifft/fftsg.c
diff -c /dev/null llvm/test/Programs/MultiSource/Benchmarks/FreeBench/pifft/fftsg.c:1.1
*** /dev/null Sat Oct 11 16:18:59 2003
--- llvm/test/Programs/MultiSource/Benchmarks/FreeBench/pifft/fftsg.c Sat Oct 11 16:18:48 2003
***************
*** 0 ****
--- 1,2641 ----
+ /*
+ Fast Fourier/Cosine/Sine Transform
+ dimension :one
+ data length :power of 2
+ decimation :frequency
+ radix :split-radix
+ data :inplace
+ table :use
+ functions
+ cdft: Complex Discrete Fourier Transform
+ rdft: Real Discrete Fourier Transform
+ ddct: Discrete Cosine Transform
+ ddst: Discrete Sine Transform
+ dfct: Cosine Transform of RDFT (Real Symmetric DFT)
+ dfst: Sine Transform of RDFT (Real Anti-symmetric DFT)
+ function prototypes
+ void cdft(int, int, double *, int *, double *);
+ void rdft(int, int, double *, int *, double *);
+ void ddct(int, int, double *, int *, double *);
+ void ddst(int, int, double *, int *, double *);
+ void dfct(int, double *, double *, int *, double *);
+ void dfst(int, double *, double *, int *, double *);
+
+
+ -------- Complex DFT (Discrete Fourier Transform) --------
+ [definition]
+ <case1>
+ X[k] = sum_j=0^n-1 x[j]*exp(2*pi*i*j*k/n), 0<=k<n
+ <case2>
+ X[k] = sum_j=0^n-1 x[j]*exp(-2*pi*i*j*k/n), 0<=k<n
+ (notes: sum_j=0^n-1 is a summation from j=0 to n-1)
+ [usage]
+ <case1>
+ ip[0] = 0; // first time only
+ cdft(2*n, 1, a, ip, w);
+ <case2>
+ ip[0] = 0; // first time only
+ cdft(2*n, -1, a, ip, w);
+ [parameters]
+ 2*n :data length (int)
+ n >= 1, n = power of 2
+ a[0...2*n-1] :input/output data (double *)
+ input data
+ a[2*j] = Re(x[j]),
+ a[2*j+1] = Im(x[j]), 0<=j<n
+ output data
+ a[2*k] = Re(X[k]),
+ a[2*k+1] = Im(X[k]), 0<=k<n
+ ip[0...*] :work area for bit reversal (int *)
+ length of ip >= 2+sqrt(n)
+ strictly,
+ length of ip >=
+ 2+(1<<(int)(log(n+0.5)/log(2))/2).
+ ip[0],ip[1] are pointers of the cos/sin table.
+ w[0...n/2-1] :cos/sin table (double *)
+ w[],ip[] are initialized if ip[0] == 0.
+ [remark]
+ Inverse of
+ cdft(2*n, -1, a, ip, w);
+ is
+ cdft(2*n, 1, a, ip, w);
+ for (j = 0; j <= 2 * n - 1; j++) {
+ a[j] *= 1.0 / n;
+ }
+ .
+
+
+ -------- Real DFT / Inverse of Real DFT --------
+ [definition]
+ <case1> RDFT
+ R[k] = sum_j=0^n-1 a[j]*cos(2*pi*j*k/n), 0<=k<=n/2
+ I[k] = sum_j=0^n-1 a[j]*sin(2*pi*j*k/n), 0<k<n/2
+ <case2> IRDFT (excluding scale)
+ a[k] = (R[0] + R[n/2]*cos(pi*k))/2 +
+ sum_j=1^n/2-1 R[j]*cos(2*pi*j*k/n) +
+ sum_j=1^n/2-1 I[j]*sin(2*pi*j*k/n), 0<=k<n
+ [usage]
+ <case1>
+ ip[0] = 0; // first time only
+ rdft(n, 1, a, ip, w);
+ <case2>
+ ip[0] = 0; // first time only
+ rdft(n, -1, a, ip, w);
+ [parameters]
+ n :data length (int)
+ n >= 2, n = power of 2
+ a[0...n-1] :input/output data (double *)
+ <case1>
+ output data
+ a[2*k] = R[k], 0<=k<n/2
+ a[2*k+1] = I[k], 0<k<n/2
+ a[1] = R[n/2]
+ <case2>
+ input data
+ a[2*j] = R[j], 0<=j<n/2
+ a[2*j+1] = I[j], 0<j<n/2
+ a[1] = R[n/2]
+ ip[0...*] :work area for bit reversal (int *)
+ length of ip >= 2+sqrt(n/2)
+ strictly,
+ length of ip >=
+ 2+(1<<(int)(log(n/2+0.5)/log(2))/2).
+ ip[0],ip[1] are pointers of the cos/sin table.
+ w[0...n/2-1] :cos/sin table (double *)
+ w[],ip[] are initialized if ip[0] == 0.
+ [remark]
+ Inverse of
+ rdft(n, 1, a, ip, w);
+ is
+ rdft(n, -1, a, ip, w);
+ for (j = 0; j <= n - 1; j++) {
+ a[j] *= 2.0 / n;
+ }
+ .
+
+
+ -------- DCT (Discrete Cosine Transform) / Inverse of DCT --------
+ [definition]
+ <case1> IDCT (excluding scale)
+ C[k] = sum_j=0^n-1 a[j]*cos(pi*j*(k+1/2)/n), 0<=k<n
+ <case2> DCT
+ C[k] = sum_j=0^n-1 a[j]*cos(pi*(j+1/2)*k/n), 0<=k<n
+ [usage]
+ <case1>
+ ip[0] = 0; // first time only
+ ddct(n, 1, a, ip, w);
+ <case2>
+ ip[0] = 0; // first time only
+ ddct(n, -1, a, ip, w);
+ [parameters]
+ n :data length (int)
+ n >= 2, n = power of 2
+ a[0...n-1] :input/output data (double *)
+ output data
+ a[k] = C[k], 0<=k<n
+ ip[0...*] :work area for bit reversal (int *)
+ length of ip >= 2+sqrt(n/2)
+ strictly,
+ length of ip >=
+ 2+(1<<(int)(log(n/2+0.5)/log(2))/2).
+ ip[0],ip[1] are pointers of the cos/sin table.
+ w[0...n*5/4-1] :cos/sin table (double *)
+ w[],ip[] are initialized if ip[0] == 0.
+ [remark]
+ Inverse of
+ ddct(n, -1, a, ip, w);
+ is
+ a[0] *= 0.5;
+ ddct(n, 1, a, ip, w);
+ for (j = 0; j <= n - 1; j++) {
+ a[j] *= 2.0 / n;
+ }
+ .
+
+
+ -------- DST (Discrete Sine Transform) / Inverse of DST --------
+ [definition]
+ <case1> IDST (excluding scale)
+ S[k] = sum_j=1^n A[j]*sin(pi*j*(k+1/2)/n), 0<=k<n
+ <case2> DST
+ S[k] = sum_j=0^n-1 a[j]*sin(pi*(j+1/2)*k/n), 0<k<=n
+ [usage]
+ <case1>
+ ip[0] = 0; // first time only
+ ddst(n, 1, a, ip, w);
+ <case2>
+ ip[0] = 0; // first time only
+ ddst(n, -1, a, ip, w);
+ [parameters]
+ n :data length (int)
+ n >= 2, n = power of 2
+ a[0...n-1] :input/output data (double *)
+ <case1>
+ input data
+ a[j] = A[j], 0<j<n
+ a[0] = A[n]
+ output data
+ a[k] = S[k], 0<=k<n
+ <case2>
+ output data
+ a[k] = S[k], 0<k<n
+ a[0] = S[n]
+ ip[0...*] :work area for bit reversal (int *)
+ length of ip >= 2+sqrt(n/2)
+ strictly,
+ length of ip >=
+ 2+(1<<(int)(log(n/2+0.5)/log(2))/2).
+ ip[0],ip[1] are pointers of the cos/sin table.
+ w[0...n*5/4-1] :cos/sin table (double *)
+ w[],ip[] are initialized if ip[0] == 0.
+ [remark]
+ Inverse of
+ ddst(n, -1, a, ip, w);
+ is
+ a[0] *= 0.5;
+ ddst(n, 1, a, ip, w);
+ for (j = 0; j <= n - 1; j++) {
+ a[j] *= 2.0 / n;
+ }
+ .
+
+
+ -------- Cosine Transform of RDFT (Real Symmetric DFT) --------
+ [definition]
+ C[k] = sum_j=0^n a[j]*cos(pi*j*k/n), 0<=k<=n
+ [usage]
+ ip[0] = 0; // first time only
+ dfct(n, a, t, ip, w);
+ [parameters]
+ n :data length - 1 (int)
+ n >= 2, n = power of 2
+ a[0...n] :input/output data (double *)
+ output data
+ a[k] = C[k], 0<=k<=n
+ t[0...n/2] :work area (double *)
+ ip[0...*] :work area for bit reversal (int *)
+ length of ip >= 2+sqrt(n/4)
+ strictly,
+ length of ip >=
+ 2+(1<<(int)(log(n/4+0.5)/log(2))/2).
+ ip[0],ip[1] are pointers of the cos/sin table.
+ w[0...n*5/8-1] :cos/sin table (double *)
+ w[],ip[] are initialized if ip[0] == 0.
+ [remark]
+ Inverse of
+ a[0] *= 0.5;
+ a[n] *= 0.5;
+ dfct(n, a, t, ip, w);
+ is
+ a[0] *= 0.5;
+ a[n] *= 0.5;
+ dfct(n, a, t, ip, w);
+ for (j = 0; j <= n; j++) {
+ a[j] *= 2.0 / n;
+ }
+ .
+
+
+ -------- Sine Transform of RDFT (Real Anti-symmetric DFT) --------
+ [definition]
+ S[k] = sum_j=1^n-1 a[j]*sin(pi*j*k/n), 0<k<n
+ [usage]
+ ip[0] = 0; // first time only
+ dfst(n, a, t, ip, w);
+ [parameters]
+ n :data length + 1 (int)
+ n >= 2, n = power of 2
+ a[0...n-1] :input/output data (double *)
+ output data
+ a[k] = S[k], 0<k<n
+ (a[0] is used for work area)
+ t[0...n/2-1] :work area (double *)
+ ip[0...*] :work area for bit reversal (int *)
+ length of ip >= 2+sqrt(n/4)
+ strictly,
+ length of ip >=
+ 2+(1<<(int)(log(n/4+0.5)/log(2))/2).
+ ip[0],ip[1] are pointers of the cos/sin table.
+ w[0...n*5/8-1] :cos/sin table (double *)
+ w[],ip[] are initialized if ip[0] == 0.
+ [remark]
+ Inverse of
+ dfst(n, a, t, ip, w);
+ is
+ dfst(n, a, t, ip, w);
+ for (j = 1; j <= n - 1; j++) {
+ a[j] *= 2.0 / n;
+ }
+ .
+
+
+ Appendix :
+ The cos/sin table is recalculated when the larger table required.
+ w[] and ip[] are compatible with all routines.
+ */
+
+
+ void cdft(int n, int isgn, double *a, int *ip, double *w)
+ {
+ void makewt(int nw, int *ip, double *w);
+ void cftfsub(int n, double *a, int *ip, int nw, double *w);
+ void cftbsub(int n, double *a, int *ip, int nw, double *w);
+ int nw;
+
+ nw = ip[0];
+ if (n > (nw << 2)) {
+ nw = n >> 2;
+ makewt(nw, ip, w);
+ }
+ if (isgn >= 0) {
+ cftfsub(n, a, ip + 2, nw, w);
+ } else {
+ cftbsub(n, a, ip + 2, nw, w);
+ }
+ }
+
+
+ void rdft(int n, int isgn, double *a, int *ip, double *w)
+ {
+ void makewt(int nw, int *ip, double *w);
+ void makect(int nc, int *ip, double *c);
+ void cftfsub(int n, double *a, int *ip, int nw, double *w);
+ void cftbsub(int n, double *a, int *ip, int nw, double *w);
+ void rftfsub(int n, double *a, int nc, double *c);
+ void rftbsub(int n, double *a, int nc, double *c);
+ int nw, nc;
+ double xi;
+
+ nw = ip[0];
+ if (n > (nw << 2)) {
+ nw = n >> 2;
+ makewt(nw, ip, w);
+ }
+ nc = ip[1];
+ if (n > (nc << 2)) {
+ nc = n >> 2;
+ makect(nc, ip, w + nw);
+ }
+ if (isgn >= 0) {
+ if (n > 4) {
+ cftfsub(n, a, ip + 2, nw, w);
+ rftfsub(n, a, nc, w + nw);
+ } else if (n == 4) {
+ cftfsub(n, a, ip + 2, nw, w);
+ }
+ xi = a[0] - a[1];
+ a[0] += a[1];
+ a[1] = xi;
+ } else {
+ a[1] = 0.5 * (a[0] - a[1]);
+ a[0] -= a[1];
+ if (n > 4) {
+ rftbsub(n, a, nc, w + nw);
+ cftbsub(n, a, ip + 2, nw, w);
+ } else if (n == 4) {
+ cftbsub(n, a, ip + 2, nw, w);
+ }
+ }
+ }
+
+
+ void ddct(int n, int isgn, double *a, int *ip, double *w)
+ {
+ void makewt(int nw, int *ip, double *w);
+ void makect(int nc, int *ip, double *c);
+ void cftfsub(int n, double *a, int *ip, int nw, double *w);
+ void cftbsub(int n, double *a, int *ip, int nw, double *w);
+ void rftfsub(int n, double *a, int nc, double *c);
+ void rftbsub(int n, double *a, int nc, double *c);
+ void dctsub(int n, double *a, int nc, double *c);
+ int j, nw, nc;
+ double xr;
+
+ nw = ip[0];
+ if (n > (nw << 2)) {
+ nw = n >> 2;
+ makewt(nw, ip, w);
+ }
+ nc = ip[1];
+ if (n > nc) {
+ nc = n;
+ makect(nc, ip, w + nw);
+ }
+ if (isgn < 0) {
+ xr = a[n - 1];
+ for (j = n - 2; j >= 2; j -= 2) {
+ a[j + 1] = a[j] - a[j - 1];
+ a[j] += a[j - 1];
+ }
+ a[1] = a[0] - xr;
+ a[0] += xr;
+ if (n > 4) {
+ rftbsub(n, a, nc, w + nw);
+ cftbsub(n, a, ip + 2, nw, w);
+ } else if (n == 4) {
+ cftbsub(n, a, ip + 2, nw, w);
+ }
+ }
+ dctsub(n, a, nc, w + nw);
+ if (isgn >= 0) {
+ if (n > 4) {
+ cftfsub(n, a, ip + 2, nw, w);
+ rftfsub(n, a, nc, w + nw);
+ } else if (n == 4) {
+ cftfsub(n, a, ip + 2, nw, 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 ddst(int n, int isgn, double *a, int *ip, double *w)
+ {
+ void makewt(int nw, int *ip, double *w);
+ void makect(int nc, int *ip, double *c);
+ void cftfsub(int n, double *a, int *ip, int nw, double *w);
+ void cftbsub(int n, double *a, int *ip, int nw, double *w);
+ void rftfsub(int n, double *a, int nc, double *c);
+ void rftbsub(int n, double *a, int nc, double *c);
+ void dstsub(int n, double *a, int nc, double *c);
+ int j, nw, nc;
+ double xr;
+
+ nw = ip[0];
+ if (n > (nw << 2)) {
+ nw = n >> 2;
+ makewt(nw, ip, w);
+ }
+ nc = ip[1];
+ if (n > nc) {
+ nc = n;
+ makect(nc, ip, w + nw);
+ }
+ if (isgn < 0) {
+ xr = a[n - 1];
+ for (j = n - 2; j >= 2; j -= 2) {
+ a[j + 1] = -a[j] - a[j - 1];
+ a[j] -= a[j - 1];
+ }
+ a[1] = a[0] + xr;
+ a[0] -= xr;
+ if (n > 4) {
+ rftbsub(n, a, nc, w + nw);
+ cftbsub(n, a, ip + 2, nw, w);
+ } else if (n == 4) {
+ cftbsub(n, a, ip + 2, nw, w);
+ }
+ }
+ dstsub(n, a, nc, w + nw);
+ if (isgn >= 0) {
+ if (n > 4) {
+ cftfsub(n, a, ip + 2, nw, w);
+ rftfsub(n, a, nc, w + nw);
+ } else if (n == 4) {
+ cftfsub(n, a, ip + 2, nw, 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)
+ {
+ void makewt(int nw, int *ip, double *w);
+ void makect(int nc, int *ip, double *c);
+ void cftfsub(int n, double *a, int *ip, int nw, double *w);
+ void rftfsub(int n, double *a, int nc, double *c);
+ void dctsub(int n, double *a, int nc, double *c);
+ 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) {
+ cftfsub(m, a, ip + 2, nw, w);
+ rftfsub(m, a, nc, w + nw);
+ } else if (m == 4) {
+ cftfsub(m, a, ip + 2, nw, 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) {
+ cftfsub(m, t, ip + 2, nw, w);
+ rftfsub(m, t, nc, w + nw);
+ } else if (m == 4) {
+ cftfsub(m, t, ip + 2, nw, 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)
+ {
+ void makewt(int nw, int *ip, double *w);
+ void makect(int nc, int *ip, double *c);
+ void cftfsub(int n, double *a, int *ip, int nw, double *w);
+ void rftfsub(int n, double *a, int nc, double *c);
+ void dstsub(int n, double *a, int nc, double *c);
+ 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) {
+ cftfsub(m, a, ip + 2, nw, w);
+ rftfsub(m, a, nc, w + nw);
+ } else if (m == 4) {
+ cftfsub(m, a, ip + 2, nw, 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) {
+ cftfsub(m, t, ip + 2, nw, w);
+ rftfsub(m, t, nc, w + nw);
+ } else if (m == 4) {
+ cftfsub(m, t, ip + 2, nw, 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 -------- */
+
+
+ #include <math.h>
+
+ void makewt(int nw, int *ip, double *w)
+ {
+ int j, nwh, nw0, nw1;
+ double delta, wn4r, wk1r, wk1i, wk3r, wk3i;
+
+ ip[0] = nw;
+ ip[1] = 1;
+ if (nw > 2) {
+ nwh = nw >> 1;
+ delta = atan(1.0) / nwh;
+ wn4r = cos(delta * nwh);
+ w[0] = 1;
+ w[1] = wn4r;
+ if (nwh >= 4) {
+ w[2] = 0.5 / cos(delta * 2);
+ w[3] = 0.5 / cos(delta * 6);
+ }
+ for (j = 4; j < nwh; j += 4) {
+ w[j] = cos(delta * j);
+ w[j + 1] = sin(delta * j);
+ w[j + 2] = cos(3 * delta * j);
+ w[j + 3] = sin(3 * delta * j);
+ }
+ nw0 = 0;
+ while (nwh > 2) {
+ nw1 = nw0 + nwh;
+ nwh >>= 1;
+ w[nw1] = 1;
+ w[nw1 + 1] = wn4r;
+ if (nwh >= 4) {
+ wk1r = w[nw0 + 4];
+ wk3r = w[nw0 + 6];
+ w[nw1 + 2] = 0.5 / wk1r;
+ w[nw1 + 3] = 0.5 / wk3r;
+ }
+ for (j = 4; j < nwh; j += 4) {
+ wk1r = w[nw0 + 2 * j];
+ wk1i = w[nw0 + 2 * j + 1];
+ wk3r = w[nw0 + 2 * j + 2];
+ wk3i = w[nw0 + 2 * j + 3];
+ w[nw1 + j] = wk1r;
+ w[nw1 + j + 1] = wk1i;
+ w[nw1 + j + 2] = wk3r;
+ w[nw1 + j + 3] = wk3i;
+ }
+ nw0 = nw1;
+ }
+ }
+ }
+
+
+ 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) / nch;
+ c[0] = cos(delta * nch);
+ c[nch] = 0.5 * c[0];
+ for (j = 1; j < nch; j++) {
+ c[j] = 0.5 * cos(delta * j);
+ c[nc - j] = 0.5 * sin(delta * j);
+ }
+ }
+ }
+
+
+ /* -------- child routines -------- */
+
+
+ #ifndef CDFT_RECURSIVE_N /* length of the recursive FFT mode */
+ #define CDFT_RECURSIVE_N 512 /* <= (L1 cache size) / 16 */
+ #endif
+
+
+ void cftfsub(int n, double *a, int *ip, int nw, double *w)
+ {
+ void bitrv2(int n, int *ip, double *a);
+ void bitrv216(double *a);
+ void bitrv208(double *a);
+ void cftf1st(int n, double *a, double *w);
+ void cftrec1(int n, double *a, int nw, double *w);
+ void cftrec2(int n, double *a, int nw, double *w);
+ void cftexp1(int n, double *a, int nw, double *w);
+ void cftfx41(int n, double *a, int nw, double *w);
+ void cftf161(double *a, double *w);
+ void cftf081(double *a, double *w);
+ void cftf040(double *a);
+ void cftx020(double *a);
+ int m;
+
+ if (n > 32) {
+ m = n >> 2;
+ cftf1st(n, a, &w[nw - m]);
+ if (n > CDFT_RECURSIVE_N) {
+ cftrec1(m, a, nw, w);
+ cftrec2(m, &a[m], nw, w);
+ cftrec1(m, &a[2 * m], nw, w);
+ cftrec1(m, &a[3 * m], nw, w);
+ } else if (m > 32) {
+ cftexp1(n, a, nw, w);
+ } else {
+ cftfx41(n, a, nw, w);
+ }
+ bitrv2(n, ip, a);
+ } else if (n > 8) {
+ if (n == 32) {
+ cftf161(a, &w[nw - 8]);
+ bitrv216(a);
+ } else {
+ cftf081(a, w);
+ bitrv208(a);
+ }
+ } else if (n == 8) {
+ cftf040(a);
+ } else if (n == 4) {
+ cftx020(a);
+ }
+ }
+
+
+ void cftbsub(int n, double *a, int *ip, int nw, double *w)
+ {
+ void bitrv2conj(int n, int *ip, double *a);
+ void bitrv216neg(double *a);
+ void bitrv208neg(double *a);
+ void cftb1st(int n, double *a, double *w);
+ void cftrec1(int n, double *a, int nw, double *w);
+ void cftrec2(int n, double *a, int nw, double *w);
+ void cftexp1(int n, double *a, int nw, double *w);
+ void cftfx41(int n, double *a, int nw, double *w);
+ void cftf161(double *a, double *w);
+ void cftf081(double *a, double *w);
+ void cftb040(double *a);
+ void cftx020(double *a);
+ int m;
+
+ if (n > 32) {
+ m = n >> 2;
+ cftb1st(n, a, &w[nw - m]);
+ if (n > CDFT_RECURSIVE_N) {
+ cftrec1(m, a, nw, w);
+ cftrec2(m, &a[m], nw, w);
+ cftrec1(m, &a[2 * m], nw, w);
+ cftrec1(m, &a[3 * m], nw, w);
+ } else if (m > 32) {
+ cftexp1(n, a, nw, w);
+ } else {
+ cftfx41(n, a, nw, w);
+ }
+ bitrv2conj(n, ip, a);
+ } else if (n > 8) {
+ if (n == 32) {
+ cftf161(a, &w[nw - 8]);
+ bitrv216neg(a);
+ } else {
+ cftf081(a, w);
+ bitrv208neg(a);
+ }
+ } else if (n == 8) {
+ cftb040(a);
+ } else if (n == 4) {
+ cftx020(a);
+ }
+ }
+
+
+ void bitrv2(int n, int *ip, double *a)
+ {
+ int j, j1, k, k1, l, m, m2;
+ double xr, xi, yr, yi;
+
+ ip[0] = 0;
+ l = n;
+ m = 1;
+ while ((m << 3) < l) {
+ l >>= 1;
+ for (j = 0; j < m; j++) {
+ ip[m + j] = ip[j] + l;
+ }
+ m <<= 1;
+ }
+ m2 = 2 * m;
+ if ((m << 3) == l) {
+ for (k = 0; k < m; k++) {
+ for (j = 0; j < k; j++) {
+ j1 = 2 * j + ip[k];
+ k1 = 2 * k + ip[j];
+ xr = a[j1];
+ xi = a[j1 + 1];
+ yr = a[k1];
+ yi = a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ j1 += m2;
+ k1 += 2 * m2;
+ xr = a[j1];
+ xi = a[j1 + 1];
+ yr = a[k1];
+ yi = a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ j1 += m2;
+ k1 -= m2;
+ xr = a[j1];
+ xi = a[j1 + 1];
+ yr = a[k1];
+ yi = a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ j1 += m2;
+ k1 += 2 * m2;
+ xr = a[j1];
+ xi = a[j1 + 1];
+ yr = a[k1];
+ yi = a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ }
+ j1 = 2 * k + m2 + ip[k];
+ k1 = j1 + m2;
+ xr = a[j1];
+ xi = a[j1 + 1];
+ yr = a[k1];
+ yi = a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ }
+ } else {
+ for (k = 1; k < m; k++) {
+ for (j = 0; j < k; j++) {
+ j1 = 2 * j + ip[k];
+ k1 = 2 * k + ip[j];
+ xr = a[j1];
+ xi = a[j1 + 1];
+ yr = a[k1];
+ yi = a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ j1 += m2;
+ k1 += m2;
+ xr = a[j1];
+ xi = a[j1 + 1];
+ yr = a[k1];
+ yi = a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ }
+ }
+ }
+ }
+
+
+ void bitrv2conj(int n, int *ip, double *a)
+ {
+ int j, j1, k, k1, l, m, m2;
+ double xr, xi, yr, yi;
+
+ ip[0] = 0;
+ l = n;
+ m = 1;
+ while ((m << 3) < l) {
+ l >>= 1;
+ for (j = 0; j < m; j++) {
+ ip[m + j] = ip[j] + l;
+ }
+ m <<= 1;
+ }
+ m2 = 2 * m;
+ if ((m << 3) == l) {
+ for (k = 0; k < m; k++) {
+ for (j = 0; j < k; j++) {
+ j1 = 2 * j + ip[k];
+ k1 = 2 * k + ip[j];
+ xr = a[j1];
+ xi = -a[j1 + 1];
+ yr = a[k1];
+ yi = -a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ j1 += m2;
+ k1 += 2 * m2;
+ xr = a[j1];
+ xi = -a[j1 + 1];
+ yr = a[k1];
+ yi = -a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ j1 += m2;
+ k1 -= m2;
+ xr = a[j1];
+ xi = -a[j1 + 1];
+ yr = a[k1];
+ yi = -a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ j1 += m2;
+ k1 += 2 * m2;
+ xr = a[j1];
+ xi = -a[j1 + 1];
+ yr = a[k1];
+ yi = -a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ }
+ k1 = 2 * k + ip[k];
+ a[k1 + 1] = -a[k1 + 1];
+ j1 = k1 + m2;
+ k1 = j1 + m2;
+ xr = a[j1];
+ xi = -a[j1 + 1];
+ yr = a[k1];
+ yi = -a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ k1 += m2;
+ a[k1 + 1] = -a[k1 + 1];
+ }
+ } else {
+ a[1] = -a[1];
+ a[m2 + 1] = -a[m2 + 1];
+ for (k = 1; k < m; k++) {
+ for (j = 0; j < k; j++) {
+ j1 = 2 * j + ip[k];
+ k1 = 2 * k + ip[j];
+ xr = a[j1];
+ xi = -a[j1 + 1];
+ yr = a[k1];
+ yi = -a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ j1 += m2;
+ k1 += m2;
+ xr = a[j1];
+ xi = -a[j1 + 1];
+ yr = a[k1];
+ yi = -a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ }
+ k1 = 2 * k + ip[k];
+ a[k1 + 1] = -a[k1 + 1];
+ a[k1 + m2 + 1] = -a[k1 + m2 + 1];
+ }
+ }
+ }
+
+
+ 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 cftf1st(int n, double *a, double *w)
+ {
+ int j, j0, j1, j2, j3, k, m, mh;
+ double wn4r, csc1, csc3, wk1r, wk1i, wk3r, wk3i,
+ wd1r, wd1i, wd3r, wd3i;
+ double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i,
+ y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i;
+
+ 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;
+ wn4r = w[1];
+ csc1 = w[2];
+ csc3 = w[3];
+ wd1r = 1;
+ wd1i = 0;
+ wd3r = 1;
+ wd3i = 0;
+ k = 0;
+ for (j = 2; j < mh - 2; j += 4) {
+ k += 4;
+ wk1r = csc1 * (wd1r + w[k]);
+ wk1i = csc1 * (wd1i + w[k + 1]);
+ wk3r = csc3 * (wd3r + w[k + 2]);
+ wk3i = csc3 * (wd3i - w[k + 3]);
+ wd1r = w[k];
+ wd1i = w[k + 1];
+ wd3r = w[k + 2];
+ wd3i = -w[k + 3];
+ 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];
+ y0r = a[j + 2] + a[j2 + 2];
+ y0i = a[j + 3] + a[j2 + 3];
+ y1r = a[j + 2] - a[j2 + 2];
+ y1i = a[j + 3] - a[j2 + 3];
+ x2r = a[j1] + a[j3];
+ x2i = a[j1 + 1] + a[j3 + 1];
+ x3r = a[j1] - a[j3];
+ x3i = a[j1 + 1] - a[j3 + 1];
+ y2r = a[j1 + 2] + a[j3 + 2];
+ y2i = a[j1 + 3] + a[j3 + 3];
+ y3r = a[j1 + 2] - a[j3 + 2];
+ y3i = a[j1 + 3] - a[j3 + 3];
+ a[j] = x0r + x2r;
+ a[j + 1] = x0i + x2i;
+ a[j + 2] = y0r + y2r;
+ a[j + 3] = y0i + y2i;
+ a[j1] = x0r - x2r;
+ a[j1 + 1] = x0i - x2i;
+ a[j1 + 2] = y0r - y2r;
+ a[j1 + 3] = y0i - y2i;
+ x0r = x1r - x3i;
+ x0i = x1i + x3r;
+ a[j2] = wk1r * x0r - wk1i * x0i;
+ a[j2 + 1] = wk1r * x0i + wk1i * x0r;
+ x0r = y1r - y3i;
+ x0i = y1i + y3r;
+ a[j2 + 2] = wd1r * x0r - wd1i * x0i;
+ a[j2 + 3] = wd1r * x0i + wd1i * x0r;
+ x0r = x1r + x3i;
+ x0i = x1i - x3r;
+ a[j3] = wk3r * x0r + wk3i * x0i;
+ a[j3 + 1] = wk3r * x0i - wk3i * x0r;
+ x0r = y1r + y3i;
+ x0i = y1i - y3r;
+ 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];
+ y0r = a[j0 - 2] + a[j2 - 2];
+ y0i = a[j0 - 1] + a[j2 - 1];
+ y1r = a[j0 - 2] - a[j2 - 2];
+ y1i = 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];
+ y2r = a[j1 - 2] + a[j3 - 2];
+ y2i = a[j1 - 1] + a[j3 - 1];
+ y3r = a[j1 - 2] - a[j3 - 2];
+ y3i = a[j1 - 1] - a[j3 - 1];
+ a[j0] = x0r + x2r;
+ a[j0 + 1] = x0i + x2i;
+ a[j0 - 2] = y0r + y2r;
+ a[j0 - 1] = y0i + y2i;
+ a[j1] = x0r - x2r;
+ a[j1 + 1] = x0i - x2i;
+ a[j1 - 2] = y0r - y2r;
+ a[j1 - 1] = y0i - y2i;
+ x0r = x1r - x3i;
+ x0i = x1i + x3r;
+ a[j2] = wk1i * x0r - wk1r * x0i;
+ a[j2 + 1] = wk1i * x0i + wk1r * x0r;
+ x0r = y1r - y3i;
+ x0i = y1i + y3r;
+ a[j2 - 2] = wd1i * x0r - wd1r * x0i;
+ a[j2 - 1] = wd1i * x0i + wd1r * x0r;
+ x0r = x1r + x3i;
+ x0i = x1i - x3r;
+ a[j3] = wk3i * x0r + wk3r * x0i;
+ a[j3 + 1] = wk3i * x0i - wk3r * x0r;
+ x0r = y1r + y3i;
+ x0i = y1i - y3r;
+ a[j3 - 2] = wd3i * x0r + wd3r * x0i;
+ a[j3 - 1] = wd3i * x0i - wd3r * x0r;
+ }
+ wk1r = csc1 * (wd1r + wn4r);
+ wk1i = csc1 * (wd1i + wn4r);
+ wk3r = csc3 * (wd3r - wn4r);
+ wk3i = csc3 * (wd3i - wn4r);
+ 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] = wn4r * (x0r - x0i);
+ a[j2 + 1] = wn4r * (x0i + x0r);
+ x0r = x1r + x3i;
+ x0i = x1i - x3r;
+ a[j3] = -wn4r * (x0r + x0i);
+ a[j3 + 1] = -wn4r * (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 cftb1st(int n, double *a, double *w)
+ {
+ int j, j0, j1, j2, j3, k, m, mh;
+ double wn4r, csc1, csc3, wk1r, wk1i, wk3r, wk3i,
+ wd1r, wd1i, wd3r, wd3i;
+ double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i,
+ y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i;
+
+ 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;
+ wn4r = w[1];
+ csc1 = w[2];
+ csc3 = w[3];
+ wd1r = 1;
+ wd1i = 0;
+ wd3r = 1;
+ wd3i = 0;
+ k = 0;
+ for (j = 2; j < mh - 2; j += 4) {
+ k += 4;
+ wk1r = csc1 * (wd1r + w[k]);
+ wk1i = csc1 * (wd1i + w[k + 1]);
+ wk3r = csc3 * (wd3r + w[k + 2]);
+ wk3i = csc3 * (wd3i - w[k + 3]);
+ wd1r = w[k];
+ wd1i = w[k + 1];
+ wd3r = w[k + 2];
+ wd3i = -w[k + 3];
+ 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];
+ y0r = a[j + 2] + a[j2 + 2];
+ y0i = -a[j + 3] - a[j2 + 3];
+ y1r = a[j + 2] - a[j2 + 2];
+ y1i = -a[j + 3] + a[j2 + 3];
+ x2r = a[j1] + a[j3];
+ x2i = a[j1 + 1] + a[j3 + 1];
+ x3r = a[j1] - a[j3];
+ x3i = a[j1 + 1] - a[j3 + 1];
+ y2r = a[j1 + 2] + a[j3 + 2];
+ y2i = a[j1 + 3] + a[j3 + 3];
+ y3r = a[j1 + 2] - a[j3 + 2];
+ y3i = a[j1 + 3] - a[j3 + 3];
+ a[j] = x0r + x2r;
+ a[j + 1] = x0i - x2i;
+ a[j + 2] = y0r + y2r;
+ a[j + 3] = y0i - y2i;
+ a[j1] = x0r - x2r;
+ a[j1 + 1] = x0i + x2i;
+ a[j1 + 2] = y0r - y2r;
+ a[j1 + 3] = y0i + y2i;
+ x0r = x1r + x3i;
+ x0i = x1i + x3r;
+ a[j2] = wk1r * x0r - wk1i * x0i;
+ a[j2 + 1] = wk1r * x0i + wk1i * x0r;
+ x0r = y1r + y3i;
+ x0i = y1i + y3r;
+ a[j2 + 2] = wd1r * x0r - wd1i * x0i;
+ a[j2 + 3] = wd1r * x0i + wd1i * x0r;
+ x0r = x1r - x3i;
+ x0i = x1i - x3r;
+ a[j3] = wk3r * x0r + wk3i * x0i;
+ a[j3 + 1] = wk3r * x0i - wk3i * x0r;
+ x0r = y1r - y3i;
+ x0i = y1i - y3r;
+ 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];
+ y0r = a[j0 - 2] + a[j2 - 2];
+ y0i = -a[j0 - 1] - a[j2 - 1];
+ y1r = a[j0 - 2] - a[j2 - 2];
+ y1i = -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];
+ y2r = a[j1 - 2] + a[j3 - 2];
+ y2i = a[j1 - 1] + a[j3 - 1];
+ y3r = a[j1 - 2] - a[j3 - 2];
+ y3i = a[j1 - 1] - a[j3 - 1];
+ a[j0] = x0r + x2r;
+ a[j0 + 1] = x0i - x2i;
+ a[j0 - 2] = y0r + y2r;
+ a[j0 - 1] = y0i - y2i;
+ a[j1] = x0r - x2r;
+ a[j1 + 1] = x0i + x2i;
+ a[j1 - 2] = y0r - y2r;
+ a[j1 - 1] = y0i + y2i;
+ x0r = x1r + x3i;
+ x0i = x1i + x3r;
+ a[j2] = wk1i * x0r - wk1r * x0i;
+ a[j2 + 1] = wk1i * x0i + wk1r * x0r;
+ x0r = y1r + y3i;
+ x0i = y1i + y3r;
+ a[j2 - 2] = wd1i * x0r - wd1r * x0i;
+ a[j2 - 1] = wd1i * x0i + wd1r * x0r;
+ x0r = x1r - x3i;
+ x0i = x1i - x3r;
+ a[j3] = wk3i * x0r + wk3r * x0i;
+ a[j3 + 1] = wk3i * x0i - wk3r * x0r;
+ x0r = y1r - y3i;
+ x0i = y1i - y3r;
+ a[j3 - 2] = wd3i * x0r + wd3r * x0i;
+ a[j3 - 1] = wd3i * x0i - wd3r * x0r;
+ }
+ wk1r = csc1 * (wd1r + wn4r);
+ wk1i = csc1 * (wd1i + wn4r);
+ wk3r = csc3 * (wd3r - wn4r);
+ wk3i = csc3 * (wd3i - wn4r);
+ 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] = wn4r * (x0r - x0i);
+ a[j2 + 1] = wn4r * (x0i + x0r);
+ x0r = x1r - x3i;
+ x0i = x1i - x3r;
+ a[j3] = -wn4r * (x0r + x0i);
+ a[j3 + 1] = -wn4r * (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 cftrec1(int n, double *a, int nw, double *w)
+ {
+ void cftrec1(int n, double *a, int nw, double *w);
+ void cftrec2(int n, double *a, int nw, double *w);
+ void cftmdl1(int n, double *a, double *w);
+ void cftexp1(int n, double *a, int nw, double *w);
+ int m;
+
+ m = n >> 2;
+ cftmdl1(n, a, &w[nw - 2 * m]);
+ if (n > CDFT_RECURSIVE_N) {
+ cftrec1(m, a, nw, w);
+ cftrec2(m, &a[m], nw, w);
+ cftrec1(m, &a[2 * m], nw, w);
+ cftrec1(m, &a[3 * m], nw, w);
+ } else {
+ cftexp1(n, a, nw, w);
+ }
+ }
+
+
+ void cftrec2(int n, double *a, int nw, double *w)
+ {
+ void cftrec1(int n, double *a, int nw, double *w);
+ void cftrec2(int n, double *a, int nw, double *w);
+ void cftmdl2(int n, double *a, double *w);
+ void cftexp2(int n, double *a, int nw, double *w);
+ int m;
+
+ m = n >> 2;
+ cftmdl2(n, a, &w[nw - n]);
+ if (n > CDFT_RECURSIVE_N) {
+ cftrec1(m, a, nw, w);
+ cftrec2(m, &a[m], nw, w);
+ cftrec1(m, &a[2 * m], nw, w);
+ cftrec2(m, &a[3 * m], nw, w);
+ } else {
+ cftexp2(n, a, nw, w);
+ }
+ }
+
+
+ void cftexp1(int n, double *a, int nw, double *w)
+ {
+ void cftmdl1(int n, double *a, double *w);
+ void cftmdl2(int n, double *a, double *w);
+ void cftfx41(int n, double *a, int nw, double *w);
+ void cftfx42(int n, double *a, int nw, double *w);
+ int j, k, l;
+
+ l = n >> 2;
+ while (l > 128) {
+ for (k = l; k < n; k <<= 2) {
+ for (j = k - l; j < n; j += 4 * k) {
+ cftmdl1(l, &a[j], &w[nw - (l >> 1)]);
+ cftmdl2(l, &a[k + j], &w[nw - l]);
+ cftmdl1(l, &a[2 * k + j], &w[nw - (l >> 1)]);
+ }
+ }
+ cftmdl1(l, &a[n - l], &w[nw - (l >> 1)]);
+ l >>= 2;
+ }
+ for (k = l; k < n; k <<= 2) {
+ for (j = k - l; j < n; j += 4 * k) {
+ cftmdl1(l, &a[j], &w[nw - (l >> 1)]);
+ cftfx41(l, &a[j], nw, w);
+ cftmdl2(l, &a[k + j], &w[nw - l]);
+ cftfx42(l, &a[k + j], nw, w);
+ cftmdl1(l, &a[2 * k + j], &w[nw - (l >> 1)]);
+ cftfx41(l, &a[2 * k + j], nw, w);
+ }
+ }
+ cftmdl1(l, &a[n - l], &w[nw - (l >> 1)]);
+ cftfx41(l, &a[n - l], nw, w);
+ }
+
+
+ void cftexp2(int n, double *a, int nw, double *w)
+ {
+ void cftmdl1(int n, double *a, double *w);
+ void cftmdl2(int n, double *a, double *w);
+ void cftfx41(int n, double *a, int nw, double *w);
+ void cftfx42(int n, double *a, int nw, double *w);
+ int j, k, l, m;
+
+ m = n >> 1;
+ l = n >> 2;
+ while (l > 128) {
+ for (k = l; k < m; k <<= 2) {
+ for (j = k - l; j < m; j += 2 * k) {
+ cftmdl1(l, &a[j], &w[nw - (l >> 1)]);
+ cftmdl1(l, &a[m + j], &w[nw - (l >> 1)]);
+ }
+ for (j = 2 * k - l; j < m; j += 4 * k) {
+ cftmdl2(l, &a[j], &w[nw - l]);
+ cftmdl2(l, &a[m + j], &w[nw - l]);
+ }
+ }
+ l >>= 2;
+ }
+ for (k = l; k < m; k <<= 2) {
+ for (j = k - l; j < m; j += 2 * k) {
+ cftmdl1(l, &a[j], &w[nw - (l >> 1)]);
+ cftfx41(l, &a[j], nw, w);
+ cftmdl1(l, &a[m + j], &w[nw - (l >> 1)]);
+ cftfx41(l, &a[m + j], nw, w);
+ }
+ for (j = 2 * k - l; j < m; j += 4 * k) {
+ cftmdl2(l, &a[j], &w[nw - l]);
+ cftfx42(l, &a[j], nw, w);
+ cftmdl2(l, &a[m + j], &w[nw - l]);
+ cftfx42(l, &a[m + j], nw, w);
+ }
+ }
+ }
+
+
+ void cftmdl1(int n, double *a, double *w)
+ {
+ int j, j0, j1, j2, j3, k, m, mh;
+ double wn4r, wk1r, wk1i, wk3r, wk3i;
+ 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;
+ wn4r = w[1];
+ k = 0;
+ for (j = 2; j < mh; j += 2) {
+ k += 4;
+ wk1r = w[k];
+ wk1i = w[k + 1];
+ wk3r = w[k + 2];
+ wk3i = -w[k + 3];
+ 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;
+ 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;
+ }
+ j0 = mh;
+ 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] = wn4r * (x0r - x0i);
+ a[j2 + 1] = wn4r * (x0i + x0r);
+ x0r = x1r + x3i;
+ x0i = x1i - x3r;
+ a[j3] = -wn4r * (x0r + x0i);
+ a[j3 + 1] = -wn4r * (x0i - x0r);
+ }
+
+
+ void cftmdl2(int n, double *a, double *w)
+ {
+ int j, j0, j1, j2, j3, k, kr, m, mh;
+ double wn4r, wk1r, wk1i, wk3r, wk3i, wd1r, wd1i, wd3r, wd3i;
+ double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y2r, y2i;
+
+ mh = n >> 3;
+ m = 2 * mh;
+ wn4r = w[1];
+ 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;
+ k = 0;
+ kr = 2 * m;
+ for (j = 2; j < mh; j += 2) {
+ k += 4;
+ wk1r = w[k];
+ wk1i = w[k + 1];
+ wk3r = w[k + 2];
+ wk3i = -w[k + 3];
+ kr -= 4;
+ wd1i = w[kr];
+ wd1r = w[kr + 1];
+ wd3i = w[kr + 2];
+ wd3r = -w[kr + 3];
+ 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;
+ 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;
+ }
+ wk1r = w[m];
+ wk1i = w[m + 1];
+ j0 = mh;
+ 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 = wk1r * x0r - wk1i * x0i;
+ y0i = wk1r * x0i + wk1i * 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 = wk1i * x1r - wk1r * x1i;
+ y0i = wk1i * x1i + wk1r * x1r;
+ y2r = wk1r * x3r - wk1i * x3i;
+ y2i = wk1r * x3i + wk1i * x3r;
+ a[j2] = y0r - y2r;
+ a[j2 + 1] = y0i - y2i;
+ a[j3] = y0r + y2r;
+ a[j3 + 1] = y0i + y2i;
+ }
+
+
+ void cftfx41(int n, double *a, int nw, double *w)
+ {
+ void cftf161(double *a, double *w);
+ void cftf162(double *a, double *w);
+ void cftf081(double *a, double *w);
+ void cftf082(double *a, double *w);
+
+ if (n == 128) {
+ cftf161(a, &w[nw - 8]);
+ cftf162(&a[32], &w[nw - 32]);
+ cftf161(&a[64], &w[nw - 8]);
+ cftf161(&a[96], &w[nw - 8]);
+ } else {
+ cftf081(a, &w[nw - 16]);
+ cftf082(&a[16], &w[nw - 16]);
+ cftf081(&a[32], &w[nw - 16]);
+ cftf081(&a[48], &w[nw - 16]);
+ }
+ }
+
+
+ void cftfx42(int n, double *a, int nw, double *w)
+ {
+ void cftf161(double *a, double *w);
+ void cftf162(double *a, double *w);
+ void cftf081(double *a, double *w);
+ void cftf082(double *a, double *w);
+
+ if (n == 128) {
+ cftf161(a, &w[nw - 8]);
+ cftf162(&a[32], &w[nw - 32]);
+ cftf161(&a[64], &w[nw - 8]);
+ cftf162(&a[96], &w[nw - 32]);
+ } else {
+ cftf081(a, &w[nw - 16]);
+ cftf082(&a[16], &w[nw - 16]);
+ cftf081(&a[32], &w[nw - 16]);
+ cftf082(&a[48], &w[nw - 16]);
+ }
+ }
+
+
+ void cftf161(double *a, double *w)
+ {
+ 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 = w[1];
+ wk1i = wn4r * w[2];
+ wk1r = wk1i + w[2];
+ 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 *w)
+ {
+ 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 = w[1];
+ wk1r = w[4];
+ wk1i = w[5];
+ wk3r = w[6];
+ wk3i = w[7];
+ wk2r = w[8];
+ wk2i = w[9];
+ 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 *w)
+ {
+ 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 = w[1];
+ 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 *w)
+ {
+ 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 = w[1];
+ wk1r = w[4];
+ wk1i = w[5];
+ 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[4] = x0r - x2r;
+ a[5] = x0i - x2i;
+ a[2] = x1r - x3i;
+ a[3] = x1i + x3r;
+ 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[4] = x0r - x2r;
+ a[5] = x0i - x2i;
+ a[2] = x1r + x3i;
+ a[3] = x1i - x3r;
+ 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 nc, double *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 = 0.5 - c[nc - kk];
+ wki = c[kk];
+ xr = a[j] - a[k];
+ xi = a[j + 1] + a[k + 1];
+ yr = wkr * xr - wki * xi;
+ yi = wkr * xi + wki * xr;
+ a[j] -= yr;
+ a[j + 1] -= yi;
+ a[k] += yr;
+ a[k + 1] -= yi;
+ }
+ }
+
+
+ void rftbsub(int n, double *a, int nc, double *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 = 0.5 - c[nc - kk];
+ wki = c[kk];
+ xr = a[j] - a[k];
+ xi = a[j + 1] + a[k + 1];
+ yr = wkr * xr + wki * xi;
+ yi = wkr * xi - wki * xr;
+ a[j] -= yr;
+ a[j + 1] -= yi;
+ a[k] += yr;
+ a[k + 1] -= yi;
+ }
+ }
+
+
+ void dctsub(int n, double *a, int nc, double *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];
+ }
+
+
+ void dstsub(int n, double *a, int nc, double *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];
+ }
+
Index: llvm/test/Programs/MultiSource/Benchmarks/FreeBench/pifft/pifft.c
diff -c /dev/null llvm/test/Programs/MultiSource/Benchmarks/FreeBench/pifft/pifft.c:1.1
*** /dev/null Sat Oct 11 16:18:59 2003
--- llvm/test/Programs/MultiSource/Benchmarks/FreeBench/pifft/pifft.c Sat Oct 11 16:18:48 2003
***************
*** 0 ****
--- 1,1544 ----
+ /*
+ ---- calculation of PI(= 3.14159...) using FFT ----
+ by T.Ooura, ver. LG1.1.2-MP1.5 Mar. 1999.
+
+ This is a test program to estimate the performance of
+ the FFT routines: fft4g.c, fft8g.c.
+
+ Example compilation:
+ GNU : gcc -O6 -ffast-math pi_fft.c fftsg.c -lm -o pi_fftsg
+ SUN : cc -fast -xO5 pi_fft.c fft8g.c -lm -o pi_fft8g
+ Microsoft: cl /O2 /G6 pi_fft.c fft4g.c /Fepi_fft4g.exe
+ ...
+ etc.
+ */
+
+ /* Please check the following macros before compiling */
+ #ifndef DBL_ERROR_MARGIN
+ #define DBL_ERROR_MARGIN 0.3 /* must be < 0.5 */
+ #endif
+
+
+ #include <math.h>
+ #include <limits.h>
+ #include <float.h>
+ #include <stdio.h>
+ #include <stdlib.h>
+ #include <time.h>
+
+
+ void mp_load_0(int n, int radix, int out[]);
+ void mp_load_1(int n, int radix, int out[]);
+ void mp_round(int n, int radix, int m, int inout[]);
+ int mp_cmp(int n, int radix, int in1[], int in2[]);
+ void mp_add(int n, int radix, int in1[], int in2[], int out[]);
+ void mp_sub(int n, int radix, int in1[], int in2[], int out[]);
+ void mp_imul(int n, int radix, int in1[], int in2, int out[]);
+ int mp_idiv(int n, int radix, int in1[], int in2, int out[]);
+ void mp_idiv_2(int n, int radix, int in[], int out[]);
+ double mp_mul_radix_test(int n, int radix, int nfft,
+ double tmpfft[], int ip[], double w[]);
+ void mp_mul(int n, int radix, int in1[], int in2[], int out[],
+ int tmp[], int nfft, double tmp1fft[], double tmp2fft[],
+ double tmp3fft[], int ip[], double w[]);
+ void mp_squ(int n, int radix, int in[], int out[], int tmp[],
+ int nfft, double tmp1fft[], double tmp2fft[],
+ int ip[], double w[]);
+ void mp_mulh(int n, int radix, int in1[], int in2[], int out[],
+ int nfft, double in1fft[], double outfft[],
+ int ip[], double w[]);
+ void mp_squh(int n, int radix, int in[], int out[],
+ int nfft, double inoutfft[], int ip[], double w[]);
+ int mp_inv(int n, int radix, int in[], int out[],
+ int tmp1[], int tmp2[], int nfft,
+ double tmp1fft[], double tmp2fft[], int ip[], double w[]);
+ int mp_sqrt(int n, int radix, int in[], int out[],
+ int tmp1[], int tmp2[], int nfft,
+ double tmp1fft[], double tmp2fft[], int ip[], double w[]);
+ void mp_sprintf(int n, int log10_radix, int in[], char out[]);
+ void mp_sscanf(int n, int log10_radix, char in[], int out[]);
+
+
+ int main(int argc, char *argv[])
+ {
+ int nfft, log2_nfft, radix, log10_radix, n, npow, nprc;
+ double err, n_op;
+ int *a, *b, *c, *e, *i1, *i2, *ip;
+ double *d1, *d2, *d3, *w;
+ char *dgt;
+ FILE *f_in;
+
+ fprintf(stderr,"Compile date: %s\n", COMPDATE);
+ fprintf(stderr,"Compiler switches: %s\n", CFLAGS);
+
+ if (argc!=2)
+ exit(1);
+
+ printf("PI calculation to estimate the FFT benchmarks\n");
+
+ f_in = fopen(argv[1], "r");
+ if (f_in==NULL) {
+ fprintf(stderr,"ERROR: Could not open indata file.\n");
+ exit(1);
+ }
+ fscanf(f_in, "%d", &nfft);
+
+ printf("initializing...\n");
+ for (log2_nfft = 1; (1 << log2_nfft) < nfft; log2_nfft++);
+ nfft = 1 << log2_nfft;
+ n = nfft + 2;
+ ip = (int *) malloc((3 + (int) sqrt(0.5 * nfft)) * sizeof(int));
+ w = (double *) malloc(nfft / 2 * sizeof(double));
+ a = (int *) malloc((n + 2) * sizeof(int));
+ b = (int *) malloc((n + 2) * sizeof(int));
+ c = (int *) malloc((n + 2) * sizeof(int));
+ e = (int *) malloc((n + 2) * sizeof(int));
+ i1 = (int *) malloc((n + 2) * sizeof(int));
+ i2 = (int *) malloc((n + 2) * sizeof(int));
+ d1 = (double *) malloc((nfft + 2) * sizeof(double));
+ d2 = (double *) malloc((nfft + 2) * sizeof(double));
+ d3 = (double *) malloc((nfft + 2) * sizeof(double));
+ if (d3 == NULL) {
+ fprintf(stderr,"Allocation Failure!\n");
+ exit(1);
+ }
+ ip[0] = 0;
+ /* ---- radix test ---- */
+ log10_radix = 1;
+ radix = 10;
+ err = mp_mul_radix_test(n, radix, nfft, d1, ip, w);
+ err += DBL_EPSILON * (n * radix * radix / 4);
+ while (100 * err < DBL_ERROR_MARGIN && radix <= INT_MAX / 20) {
+ err *= 100;
+ log10_radix++;
+ radix *= 10;
+ }
+ printf("nfft= %d\nradix= %d\n", nfft, radix);
+ printf("calculating %d digits of PI...\n", log10_radix * (n - 2));
+
+ /*
+ * ---- a formula based on the AGM (Arithmetic-Geometric Mean) ----
+ * c = sqrt(0.125);
+ * a = 1 + 3 * c;
+ * b = sqrt(a);
+ * e = b - 0.625;
+ * b = 2 * b;
+ * c = e - c;
+ * a = a + e;
+ * npow = 4;
+ * do {
+ * npow = 2 * npow;
+ * e = (a + b) / 2;
+ * b = sqrt(a * b);
+ * e = e - b;
+ * b = 2 * b;
+ * c = c - e;
+ * a = e + b;
+ * } while (e > SQRT_SQRT_EPSILON);
+ * e = e * e / 4;
+ * a = a + b;
+ * pi = (a * a - e - e / 2) / (a * c - e) / npow;
+ * ---- modification ----
+ * This is a modified version of Gauss-Legendre formula
+ * (by T.Ooura). It is faster than original version.
+ * ---- reference ----
+ * 1. E.Salamin,
+ * Computation of PI Using Arithmetic-Geometric Mean,
+ * Mathematics of Computation, Vol.30 1976.
+ * 2. R.P.Brent,
+ * Fast Multiple-Precision Evaluation of Elementary Functions,
+ * J. ACM 23 1976.
+ * 3. D.Takahasi, Y.Kanada,
+ * Calculation of PI to 51.5 Billion Decimal Digits on
+ * Distributed Memoriy Parallel Processors,
+ * Transactions of Information Processing Society of Japan,
+ * Vol.39 No.7 1998.
+ * 4. T.Ooura,
+ * Improvement of the PI Calculation Algorithm and
+ * Implementation of Fast Multiple-Precision Computation,
+ * Information Processing Society of Japan SIG Notes,
+ * 98-HPC-74, 1998.
+ */
+ /* ---- c = sqrt(0.125) ---- */
+ mp_sscanf(n, log10_radix, "0.125", a);
+ mp_sqrt(n, radix, a, c, i1, i2, nfft, d1, d2, ip, w);
+ /* ---- a = 1 + 3 * c ---- */
+ mp_imul(n, radix, c, 3, e);
+ mp_sscanf(n, log10_radix, "1", a);
+ mp_add(n, radix, a, e, a);
+ /* ---- b = sqrt(a) ---- */
+ mp_sqrt(n, radix, a, b, i1, i2, nfft, d1, d2, ip, w);
+ /* ---- e = b - 0.625 ---- */
+ mp_sscanf(n, log10_radix, "0.625", e);
+ mp_sub(n, radix, b, e, e);
+ /* ---- b = 2 * b ---- */
+ mp_add(n, radix, b, b, b);
+ /* ---- c = e - c ---- */
+ mp_sub(n, radix, e, c, c);
+ /* ---- a = a + e ---- */
+ mp_add(n, radix, a, e, a);
+ printf("AGM iteration\n");
+ npow = 4;
+ do {
+ npow *= 2;
+ /* ---- e = (a + b) / 2 ---- */
+ mp_add(n, radix, a, b, e);
+ mp_idiv_2(n, radix, e, e);
+ /* ---- b = sqrt(a * b) ---- */
+ mp_mul(n, radix, a, b, a, i1, nfft, d1, d2, d3, ip, w);
+ mp_sqrt(n, radix, a, b, i1, i2, nfft, d1, d2, ip, w);
+ /* ---- e = e - b ---- */
+ mp_sub(n, radix, e, b, e);
+ /* ---- b = 2 * b ---- */
+ mp_add(n, radix, b, b, b);
+ /* ---- c = c - e ---- */
+ mp_sub(n, radix, c, e, c);
+ /* ---- a = e + b ---- */
+ mp_add(n, radix, e, b, a);
+ /* ---- convergence check ---- */
+ nprc = -e[1];
+ if (e[0] == 0) {
+ nprc = n;
+ }
+ printf("precision= %d\n", 4 * nprc * log10_radix);
+ } while (4 * nprc <= n);
+ /* ---- e = e * e / 4 (half precision) ---- */
+ mp_idiv_2(n, radix, e, e);
+ mp_squh(n, radix, e, e, nfft, d1, ip, w);
+ /* ---- a = a + b ---- */
+ mp_add(n, radix, a, b, a);
+ /* ---- a = (a * a - e - e / 2) / (a * c - e) / npow ---- */
+ mp_mul(n, radix, a, c, c, i1, nfft, d1, d2, d3, ip, w);
+ mp_sub(n, radix, c, e, c);
+ mp_inv(n, radix, c, b, i1, i2, nfft, d1, d2, ip, w);
+ mp_squ(n, radix, a, a, i1, nfft, d1, d2, ip, w);
+ mp_sub(n, radix, a, e, a);
+ mp_idiv_2(n, radix, e, e);
+ mp_sub(n, radix, a, e, a);
+ mp_mul(n, radix, a, b, a, i1, nfft, d1, d2, d3, ip, w);
+ mp_idiv(n, radix, a, npow, a);
+
+ /* ---- output ---- */
+ free(d3);
+ free(d2);
+ free(d1);
+ dgt = (char *) malloc((log10_radix * n + 32) * sizeof(char));
+ mp_sprintf(n - 1, log10_radix, a, dgt);
+
+ printf("%s\n", dgt);
+
+ free(dgt);
+ free(i2);
+ free(i1);
+ free(e);
+ free(c);
+ free(b);
+ free(a);
+ free(w);
+ free(ip);
+ /* ---- benchmark ---- */
+ n_op = 50.0 * nfft * log2_nfft * log2_nfft;
+ printf("floating point operation: %g op.\n", n_op);
+
+ return 0;
+ }
+
+
+ /* -------- multiple precision routines -------- */
+
+
+ #include <math.h>
+ #include <float.h>
+ #include <stdio.h>
+
+ /* ---- floating point format ----
+ data := data[0] * pow(radix, data[1]) *
+ (data[2] + data[3]/radix + data[4]/radix/radix + ...),
+ data[0] : sign (1;data>0, -1;data<0, 0;data==0)
+ data[1] : exponent (0;data==0)
+ data[2...n+1] : digits
+ ---- function prototypes ----
+ void mp_load_0(int n, int radix, int out[]);
+ void mp_load_1(int n, int radix, int out[]);
+ void mp_round(int n, int radix, int m, int inout[]);
+ int mp_cmp(int n, int radix, int in1[], int in2[]);
+ void mp_add(int n, int radix, int in1[], int in2[], int out[]);
+ void mp_sub(int n, int radix, int in1[], int in2[], int out[]);
+ void mp_imul(int n, int radix, int in1[], int in2, int out[]);
+ int mp_idiv(int n, int radix, int in1[], int in2, int out[]);
+ void mp_idiv_2(int n, int radix, int in[], int out[]);
+ double mp_mul_radix_test(int n, int radix, int nfft,
+ double tmpfft[], int ip[], double w[]);
+ void mp_mul(int n, int radix, int in1[], int in2[], int out[],
+ int tmp[], int nfft, double tmp1fft[], double tmp2fft[],
+ double tmp3fft[], int ip[], double w[]);
+ void mp_squ(int n, int radix, int in[], int out[], int tmp[],
+ int nfft, double tmp1fft[], double tmp2fft[],
+ int ip[], double w[]);
+ void mp_mulh(int n, int radix, int in1[], int in2[], int out[],
+ int nfft, double in1fft[], double outfft[],
+ int ip[], double w[]);
+ void mp_squh(int n, int radix, int in[], int out[],
+ int nfft, double inoutfft[], int ip[], double w[]);
+ int mp_inv(int n, int radix, int in[], int out[],
+ int tmp1[], int tmp2[], int nfft,
+ double tmp1fft[], double tmp2fft[], int ip[], double w[]);
+ int mp_sqrt(int n, int radix, int in[], int out[],
+ int tmp1[], int tmp2[], int nfft,
+ double tmp1fft[], double tmp2fft[], int ip[], double w[]);
+ void mp_sprintf(int n, int log10_radix, int in[], char out[]);
+ void mp_sscanf(int n, int log10_radix, char in[], int out[]);
+ ----
+ */
+
+
+ /* -------- mp_load routines -------- */
+
+
+ void mp_load_0(int n, int radix, int out[])
+ {
+ int j;
+
+ for (j = 0; j <= n + 1; j++) {
+ out[j] = 0;
+ }
+ }
+
+
+ void mp_load_1(int n, int radix, int out[])
+ {
+ int j;
+
+ out[0] = 1;
+ out[1] = 0;
+ out[2] = 1;
+ for (j = 3; j <= n + 1; j++) {
+ out[j] = 0;
+ }
+ }
+
+
+ void mp_round(int n, int radix, int m, int inout[])
+ {
+ int j, x;
+
+ if (m < n) {
+ for (j = n + 1; j > m + 2; j--) {
+ inout[j] = 0;
+ }
+ x = 2 * inout[m + 2];
+ inout[m + 2] = 0;
+ if (x >= radix) {
+ for (j = m + 1; j >= 2; j--) {
+ x = inout[j] + 1;
+ if (x < radix) {
+ inout[j] = x;
+ break;
+ }
+ inout[j] = 0;
+ }
+ if (x >= radix) {
+ inout[2] = 1;
+ inout[1]++;
+ }
+ }
+ }
+ }
+
+
+ /* -------- mp_add routines -------- */
+
+
+ int mp_cmp(int n, int radix, int in1[], int in2[])
+ {
+ int mp_unsgn_cmp(int n, int in1[], int in2[]);
+
+ if (in1[0] > in2[0]) {
+ return 1;
+ } else if (in1[0] < in2[0]) {
+ return -1;
+ }
+ return in1[0] * mp_unsgn_cmp(n, &in1[1], &in2[1]);
+ }
+
+
+ void mp_add(int n, int radix, int in1[], int in2[], int out[])
+ {
+ int mp_unsgn_cmp(int n, int in1[], int in2[]);
+ int mp_unexp_add(int n, int radix, int expdif,
+ int in1[], int in2[], int out[]);
+ int mp_unexp_sub(int n, int radix, int expdif,
+ int in1[], int in2[], int out[]);
+ int outsgn, outexp, expdif;
+
+ expdif = in1[1] - in2[1];
+ outexp = in1[1];
+ if (expdif < 0) {
+ outexp = in2[1];
+ }
+ outsgn = in1[0] * in2[0];
+ if (outsgn >= 0) {
+ if (outsgn > 0) {
+ outsgn = in1[0];
+ } else {
+ outsgn = in1[0] + in2[0];
+ outexp = in1[1] + in2[1];
+ expdif = 0;
+ }
+ if (expdif >= 0) {
+ outexp += mp_unexp_add(n, radix, expdif,
+ &in1[2], &in2[2], &out[2]);
+ } else {
+ outexp += mp_unexp_add(n, radix, -expdif,
+ &in2[2], &in1[2], &out[2]);
+ }
+ } else {
+ outsgn = mp_unsgn_cmp(n, &in1[1], &in2[1]);
+ if (outsgn >= 0) {
+ expdif = mp_unexp_sub(n, radix, expdif,
+ &in1[2], &in2[2], &out[2]);
+ } else {
+ expdif = mp_unexp_sub(n, radix, -expdif,
+ &in2[2], &in1[2], &out[2]);
+ }
+ outexp -= expdif;
+ outsgn *= in1[0];
+ if (expdif == n) {
+ outsgn = 0;
+ }
+ }
+ if (outsgn == 0) {
+ outexp = 0;
+ }
+ out[0] = outsgn;
+ out[1] = outexp;
+ }
+
+
+ void mp_sub(int n, int radix, int in1[], int in2[], int out[])
+ {
+ int mp_unsgn_cmp(int n, int in1[], int in2[]);
+ int mp_unexp_add(int n, int radix, int expdif,
+ int in1[], int in2[], int out[]);
+ int mp_unexp_sub(int n, int radix, int expdif,
+ int in1[], int in2[], int out[]);
+ int outsgn, outexp, expdif;
+
+ expdif = in1[1] - in2[1];
+ outexp = in1[1];
+ if (expdif < 0) {
+ outexp = in2[1];
+ }
+ outsgn = in1[0] * in2[0];
+ if (outsgn <= 0) {
+ if (outsgn < 0) {
+ outsgn = in1[0];
+ } else {
+ outsgn = in1[0] - in2[0];
+ outexp = in1[1] + in2[1];
+ expdif = 0;
+ }
+ if (expdif >= 0) {
+ outexp += mp_unexp_add(n, radix, expdif,
+ &in1[2], &in2[2], &out[2]);
+ } else {
+ outexp += mp_unexp_add(n, radix, -expdif,
+ &in2[2], &in1[2], &out[2]);
+ }
+ } else {
+ outsgn = mp_unsgn_cmp(n, &in1[1], &in2[1]);
+ if (outsgn >= 0) {
+ expdif = mp_unexp_sub(n, radix, expdif,
+ &in1[2], &in2[2], &out[2]);
+ } else {
+ expdif = mp_unexp_sub(n, radix, -expdif,
+ &in2[2], &in1[2], &out[2]);
+ }
+ outexp -= expdif;
+ outsgn *= in1[0];
+ if (expdif == n) {
+ outsgn = 0;
+ }
+ }
+ if (outsgn == 0) {
+ outexp = 0;
+ }
+ out[0] = outsgn;
+ out[1] = outexp;
+ }
+
+
+ /* -------- mp_add child routines -------- */
+
+
+ int mp_unsgn_cmp(int n, int in1[], int in2[])
+ {
+ int j, cmp;
+
+ cmp = 0;
+ for (j = 0; j <= n && cmp == 0; j++) {
+ cmp = in1[j] - in2[j];
+ }
+ if (cmp > 0) {
+ cmp = 1;
+ } else if (cmp < 0) {
+ cmp = -1;
+ }
+ return cmp;
+ }
+
+
+ int mp_unexp_add(int n, int radix, int expdif,
+ int in1[], int in2[], int out[])
+ {
+ int j, x, carry;
+
+ carry = 0;
+ if (expdif == 0 && in1[0] + in2[0] >= radix) {
+ x = in1[n - 1] + in2[n - 1];
+ carry = x >= radix ? -1 : 0;
+ for (j = n - 1; j > 0; j--) {
+ x = in1[j - 1] + in2[j - 1] - carry;
+ carry = x >= radix ? -1 : 0;
+ out[j] = x - (radix & carry);
+ }
+ out[0] = -carry;
+ } else {
+ if (expdif > n) {
+ expdif = n;
+ }
+ for (j = n - 1; j >= expdif; j--) {
+ x = in1[j] + in2[j - expdif] - carry;
+ carry = x >= radix ? -1 : 0;
+ out[j] = x - (radix & carry);
+ }
+ for (j = expdif - 1; j >= 0; j--) {
+ x = in1[j] - carry;
+ carry = x >= radix ? -1 : 0;
+ out[j] = x - (radix & carry);
+ }
+ if (carry != 0) {
+ for (j = n - 1; j > 0; j--) {
+ out[j] = out[j - 1];
+ }
+ out[0] = -carry;
+ }
+ }
+ return -carry;
+ }
+
+
+ int mp_unexp_sub(int n, int radix, int expdif,
+ int in1[], int in2[], int out[])
+ {
+ int j, x, borrow, ncancel;
+
+ if (expdif > n) {
+ expdif = n;
+ }
+ borrow = 0;
+ for (j = n - 1; j >= expdif; j--) {
+ x = in1[j] - in2[j - expdif] + borrow;
+ borrow = x < 0 ? -1 : 0;
+ out[j] = x + (radix & borrow);
+ }
+ for (j = expdif - 1; j >= 0; j--) {
+ x = in1[j] + borrow;
+ borrow = x < 0 ? -1 : 0;
+ out[j] = x + (radix & borrow);
+ }
+ ncancel = 0;
+ for (j = 0; j < n && out[j] == 0; j++) {
+ ncancel = j + 1;
+ }
+ if (ncancel > 0 && ncancel < n) {
+ for (j = 0; j < n - ncancel; j++) {
+ out[j] = out[j + ncancel];
+ }
+ for (j = n - ncancel; j < n; j++) {
+ out[j] = 0;
+ }
+ }
+ return ncancel;
+ }
+
+
+ /* -------- mp_imul routines -------- */
+
+
+ void mp_imul(int n, int radix, int in1[], int in2, int out[])
+ {
+ void mp_unsgn_imul(int n, double dradix, int in1[], double din2, int out[]);
+
+ if (in2 > 0) {
+ out[0] = in1[0];
+ } else if (in2 < 0) {
+ out[0] = -in1[0];
+ in2 = -in2;
+ } else {
+ out[0] = 0;
+ }
+ mp_unsgn_imul(n, radix, &in1[1], in2, &out[1]);
+ if (out[0] == 0) {
+ out[1] = 0;
+ }
+ }
+
+
+ int mp_idiv(int n, int radix, int in1[], int in2, int out[])
+ {
+ void mp_load_0(int n, int radix, int out[]);
+ void mp_unsgn_idiv(int n, double dradix, int in1[], double din2,
+ int out[]);
+
+ if (in2 == 0) {
+ return -1;
+ }
+ if (in2 > 0) {
+ out[0] = in1[0];
+ } else {
+ out[0] = -in1[0];
+ in2 = -in2;
+ }
+ if (in1[0] == 0) {
+ mp_load_0(n, radix, out);
+ return 0;
+ }
+ mp_unsgn_idiv(n, radix, &in1[1], in2, &out[1]);
+ return 0;
+ }
+
+
+ void mp_idiv_2(int n, int radix, int in[], int out[])
+ {
+ int j, ix, carry, shift;
+
+ out[0] = in[0];
+ shift = 0;
+ if (in[2] == 1) {
+ shift = 1;
+ }
+ out[1] = in[1] - shift;
+ carry = -shift;
+ for (j = 2; j <= n + 1 - shift; j++) {
+ ix = in[j + shift] + (radix & carry);
+ carry = -(ix & 1);
+ out[j] = ix >> 1;
+ }
+ if (shift > 0) {
+ out[n + 1] = (radix & carry) >> 1;
+ }
+ }
+
+
+ /* -------- mp_imul child routines -------- */
+
+
+ void mp_unsgn_imul(int n, double dradix, int in1[], double din2,
+ int out[])
+ {
+ int j, carry, shift;
+ double x, d1_radix;
+
+ d1_radix = 1.0 / dradix;
+ carry = 0;
+ for (j = n; j >= 1; j--) {
+ x = din2 * in1[j] + carry + 0.5;
+ carry = (int) (d1_radix * x);
+ out[j] = (int) (x - dradix * carry);
+ }
+ shift = 0;
+ x = carry + 0.5;
+ while (x > 1) {
+ x *= d1_radix;
+ shift++;
+ }
+ out[0] = in1[0] + shift;
+ if (shift > 0) {
+ while (shift > n) {
+ carry = (int) (d1_radix * carry + 0.5);
+ shift--;
+ }
+ for (j = n; j >= shift + 1; j--) {
+ out[j] = out[j - shift];
+ }
+ for (j = shift; j >= 1; j--) {
+ x = carry + 0.5;
+ carry = (int) (d1_radix * x);
+ out[j] = (int) (x - dradix * carry);
+ }
+ }
+ }
+
+
+ void mp_unsgn_idiv(int n, double dradix, int in1[], double din2, int out[])
+ {
+ int j, ix, carry, shift;
+ double x, d1_in2;
+
+ d1_in2 = 1.0 / din2;
+ shift = 0;
+ x = 0;
+ do {
+ shift++;
+ x *= dradix;
+ if (shift <= n) {
+ x += in1[shift];
+ }
+ } while (x < din2 - 0.5);
+ x += 0.5;
+ ix = (int) (d1_in2 * x);
+ carry = (int) (x - din2 * ix);
+ out[1] = ix;
+ shift--;
+ out[0] = in1[0] - shift;
+ if (shift >= n) {
+ shift = n - 1;
+ }
+ for (j = 2; j <= n - shift; j++) {
+ x = in1[j + shift] + dradix * carry + 0.5;
+ ix = (int) (d1_in2 * x);
+ carry = (int) (x - din2 * ix);
+ out[j] = ix;
+ }
+ for (j = n - shift + 1; j <= n; j++) {
+ x = dradix * carry + 0.5;
+ ix = (int) (d1_in2 * x);
+ carry = (int) (x - din2 * ix);
+ out[j] = ix;
+ }
+ }
+
+
+ /* -------- mp_mul routines -------- */
+
+
+ double mp_mul_radix_test(int n, int radix, int nfft,
+ double tmpfft[], int ip[], double w[])
+ {
+ void rdft(int n, int isgn, double *a, int *ip, double *w);
+ void mp_mul_csqu(int nfft, double dinout[]);
+ double mp_mul_d2i_test(int radix, int nfft, double din[]);
+ int j, ndata, radix_2;
+
+ ndata = (nfft >> 1) + 1;
+ if (ndata > n) {
+ ndata = n;
+ }
+ tmpfft[nfft + 1] = radix - 1;
+ for (j = nfft; j > ndata; j--) {
+ tmpfft[j] = 0;
+ }
+ radix_2 = (radix + 1) / 2;
+ for (j = ndata; j > 2; j--) {
+ tmpfft[j] = radix_2;
+ }
+ tmpfft[2] = radix;
+ tmpfft[1] = radix - 1; tmpfft[0] = 0;
+ rdft(nfft, 1, &tmpfft[1], ip, w);
+ mp_mul_csqu(nfft, tmpfft);
+ rdft(nfft, -1, &tmpfft[1], ip, w);
+ return 2 * mp_mul_d2i_test(radix, nfft, tmpfft);
+ }
+
+
+ void mp_mul(int n, int radix, int in1[], int in2[], int out[],
+ int tmp[], int nfft, double tmp1fft[], double tmp2fft[],
+ double tmp3fft[], int ip[], double w[])
+ {
+ void mp_add(int n, int radix, int in1[], int in2[], int out[]);
+ void rdft(int n, int isgn, double *a, int *ip, double *w);
+ void mp_mul_i2d(int n, int radix, int nfft, int shift,
+ int in[], double dout[]);
+ void mp_mul_cmul(int nfft, double din[], double dinout[]);
+ void mp_mul_cmuladd(int nfft, double din1[], double din2[],
+ double dinout[]);
+ void mp_mul_d2i(int n, int radix, int nfft, double din[], int out[]);
+ int n_h, shift;
+
+ shift = (nfft >> 1) + 1;
+ while (n > shift) {
+ if (in1[shift + 2] + in2[shift + 2] != 0) {
+ break;
+ }
+ shift++;
+ }
+ n_h = n / 2 + 1;
+ if (n_h < n - shift) {
+ n_h = n - shift;
+ }
+ /* ---- tmp3fft = (upper) in1 * (lower) in2 ---- */
+ mp_mul_i2d(n, radix, nfft, 0, in1, tmp1fft);
+ rdft(nfft, 1, &tmp1fft[1], ip, w);
+ mp_mul_i2d(n, radix, nfft, shift, in2, tmp3fft);
+ rdft(nfft, 1, &tmp3fft[1], ip, w);
+ mp_mul_cmul(nfft, tmp1fft, tmp3fft);
+ /* ---- tmp = (upper) in1 * (upper) in2 ---- */
+ mp_mul_i2d(n, radix, nfft, 0, in2, tmp2fft);
+ rdft(nfft, 1, &tmp2fft[1], ip, w);
+ mp_mul_cmul(nfft, tmp2fft, tmp1fft);
+ rdft(nfft, -1, &tmp1fft[1], ip, w);
+ mp_mul_d2i(n, radix, nfft, tmp1fft, tmp);
+ /* ---- tmp3fft += (upper) in2 * (lower) in1 ---- */
+ mp_mul_i2d(n, radix, nfft, shift, in1, tmp1fft);
+ rdft(nfft, 1, &tmp1fft[1], ip, w);
+ mp_mul_cmuladd(nfft, tmp1fft, tmp2fft, tmp3fft);
+ /* ---- out = tmp + tmp3fft ---- */
+ rdft(nfft, -1, &tmp3fft[1], ip, w);
+ mp_mul_d2i(n_h, radix, nfft, tmp3fft, out);
+ mp_add(n, radix, out, tmp, out);
+ }
+
+
+ void mp_squ(int n, int radix, int in[], int out[], int tmp[],
+ int nfft, double tmp1fft[], double tmp2fft[],
+ int ip[], double w[])
+ {
+ void mp_add(int n, int radix, int in1[], int in2[], int out[]);
+ void rdft(int n, int isgn, double *a, int *ip, double *w);
+ void mp_mul_i2d(int n, int radix, int nfft, int shift,
+ int in[], double dout[]);
+ void mp_mul_cmul(int nfft, double din[], double dinout[]);
+ void mp_mul_csqu(int nfft, double dinout[]);
+ void mp_mul_d2i(int n, int radix, int nfft, double din[], int out[]);
+ int n_h, shift;
+
+ shift = (nfft >> 1) + 1;
+ while (n > shift) {
+ if (in[shift + 2] != 0) {
+ break;
+ }
+ shift++;
+ }
+ n_h = n / 2 + 1;
+ if (n_h < n - shift) {
+ n_h = n - shift;
+ }
+ /* ---- tmp = 2 * (upper) in * (lower) in ---- */
+ mp_mul_i2d(n, radix, nfft, 0, in, tmp1fft);
+ rdft(nfft, 1, &tmp1fft[1], ip, w);
+ mp_mul_i2d(n, radix, nfft, shift, in, tmp2fft);
+ rdft(nfft, 1, &tmp2fft[1], ip, w);
+ mp_mul_cmul(nfft, tmp1fft, tmp2fft);
+ rdft(nfft, -1, &tmp2fft[1], ip, w);
+ mp_mul_d2i(n_h, radix, nfft, tmp2fft, tmp);
+ mp_add(n_h, radix, tmp, tmp, tmp);
+ /* ---- out = tmp + ((upper) in)^2 ---- */
+ mp_mul_csqu(nfft, tmp1fft);
+ rdft(nfft, -1, &tmp1fft[1], ip, w);
+ mp_mul_d2i(n, radix, nfft, tmp1fft, out);
+ mp_add(n, radix, out, tmp, out);
+ }
+
+
+ void mp_mulh(int n, int radix, int in1[], int in2[], int out[],
+ int nfft, double in1fft[], double outfft[], int ip[], double w[])
+ {
+ void rdft(int n, int isgn, double *a, int *ip, double *w);
+ void mp_mul_i2d(int n, int radix, int nfft, int shift,
+ int in[], double dout[]);
+ void mp_mul_cmul(int nfft, double din[], double dinout[]);
+ void mp_mul_d2i(int n, int radix, int nfft, double din[], int out[]);
+
+ mp_mul_i2d(n, radix, nfft, 0, in1, in1fft);
+ rdft(nfft, 1, &in1fft[1], ip, w);
+ mp_mul_i2d(n, radix, nfft, 0, in2, outfft);
+ rdft(nfft, 1, &outfft[1], ip, w);
+ mp_mul_cmul(nfft, in1fft, outfft);
+ rdft(nfft, -1, &outfft[1], ip, w);
+ mp_mul_d2i(n, radix, nfft, outfft, out);
+ }
+
+
+ void mp_mulh_use_in1fft(int n, int radix, double in1fft[],
+ int shift, int in2[], int out[], int nfft, double outfft[],
+ int ip[], double w[])
+ {
+ void rdft(int n, int isgn, double *a, int *ip, double *w);
+ void mp_mul_i2d(int n, int radix, int nfft, int shift,
+ int in[], double dout[]);
+ void mp_mul_cmul(int nfft, double din[], double dinout[]);
+ void mp_mul_d2i(int n, int radix, int nfft, double din[], int out[]);
+
+ while (n > shift) {
+ if (in2[shift + 2] != 0) {
+ break;
+ }
+ shift++;
+ }
+ mp_mul_i2d(n, radix, nfft, shift, in2, outfft);
+ rdft(nfft, 1, &outfft[1], ip, w);
+ mp_mul_cmul(nfft, in1fft, outfft);
+ rdft(nfft, -1, &outfft[1], ip, w);
+ mp_mul_d2i(n, radix, nfft, outfft, out);
+ }
+
+
+ void mp_squh(int n, int radix, int in[], int out[],
+ int nfft, double inoutfft[], int ip[], double w[])
+ {
+ void rdft(int n, int isgn, double *a, int *ip, double *w);
+ void mp_mul_i2d(int n, int radix, int nfft, int shift,
+ int in[], double dout[]);
+ void mp_mul_csqu(int nfft, double dinout[]);
+ void mp_mul_d2i(int n, int radix, int nfft, double din[], int out[]);
+
+ mp_mul_i2d(n, radix, nfft, 0, in, inoutfft);
+ rdft(nfft, 1, &inoutfft[1], ip, w);
+ mp_mul_csqu(nfft, inoutfft);
+ rdft(nfft, -1, &inoutfft[1], ip, w);
+ mp_mul_d2i(n, radix, nfft, inoutfft, out);
+ }
+
+
+ void mp_squh_use_in1fft(int n, int radix, double inoutfft[], int out[],
+ int nfft, int ip[], double w[])
+ {
+ void rdft(int n, int isgn, double *a, int *ip, double *w);
+ void mp_mul_csqu(int nfft, double dinout[]);
+ void mp_mul_d2i(int n, int radix, int nfft, double din[], int out[]);
+
+ mp_mul_csqu(nfft, inoutfft);
+ rdft(nfft, -1, &inoutfft[1], ip, w);
+ mp_mul_d2i(n, radix, nfft, inoutfft, out);
+ }
+
+
+ /* -------- mp_mul child routines -------- */
+
+
+ void mp_mul_i2d(int n, int radix, int nfft, int shift,
+ int in[], double dout[])
+ {
+ int j, x, carry, ndata, radix_2, topdgt;
+
+ ndata = 0;
+ topdgt = 0;
+ if (n > shift) {
+ topdgt = in[shift + 2];
+ ndata = (nfft >> 1) + 1;
+ if (ndata > n - shift) {
+ ndata = n - shift;
+ }
+ }
+ dout[nfft + 1] = in[0] * topdgt;
+ for (j = nfft; j > ndata; j--) {
+ dout[j] = 0;
+ }
+ /* ---- abs(dout[j]) <= radix/2 (to keep FFT precision) ---- */
+ if (ndata > 1) {
+ radix_2 = radix / 2;
+ carry = 0;
+ for (j = ndata + 1; j > 3; j--) {
+ x = in[j + shift] - carry;
+ carry = x >= radix_2 ? -1 : 0;
+ dout[j - 1] = x - (radix & carry);
+ }
+ dout[2] = in[shift + 3] - carry;
+ }
+ dout[1] = topdgt;
+ dout[0] = in[1] - shift;
+ }
+
+
+ void mp_mul_cmul(int nfft, double din[], double dinout[])
+ {
+ int j;
+ double xr, xi, yr, yi;
+
+ dinout[0] += din[0];
+ dinout[1] *= din[1];
+ dinout[2] *= din[2];
+ for (j = 3; j < nfft; j += 2) {
+ xr = din[j];
+ xi = din[j + 1];
+ yr = dinout[j];
+ yi = dinout[j + 1];
+ dinout[j] = xr * yr - xi * yi;
+ dinout[j + 1] = xr * yi + xi * yr;
+ }
+ dinout[nfft + 1] *= din[nfft + 1];
+ }
+
+
+ void mp_mul_cmuladd(int nfft, double din1[], double din2[],
+ double dinout[])
+ {
+ int j;
+ double xr, xi, yr, yi;
+
+ dinout[1] += din1[1] * din2[1];
+ dinout[2] += din1[2] * din2[2];
+ for (j = 3; j < nfft; j += 2) {
+ xr = din1[j];
+ xi = din1[j + 1];
+ yr = din2[j];
+ yi = din2[j + 1];
+ dinout[j] += xr * yr - xi * yi;
+ dinout[j + 1] += xr * yi + xi * yr;
+ }
+ dinout[nfft + 1] += din1[nfft + 1] * din2[nfft + 1];
+ }
+
+
+ void mp_mul_csqu(int nfft, double dinout[])
+ {
+ int j;
+ double xr, xi;
+
+ dinout[0] *= 2;
+ dinout[1] *= dinout[1];
+ dinout[2] *= dinout[2];
+ for (j = 3; j < nfft; j += 2) {
+ xr = dinout[j];
+ xi = dinout[j + 1];
+ dinout[j] = xr * xr - xi * xi;
+ dinout[j + 1] = 2 * xr * xi;
+ }
+ dinout[nfft + 1] *= dinout[nfft + 1];
+ }
+
+
+ void mp_mul_d2i(int n, int radix, int nfft, double din[], int out[])
+ {
+ int j, carry, carry1, carry2, shift, ndata;
+ double x, scale, d1_radix, d1_radix2, pow_radix, topdgt;
+
+ scale = 2.0 / nfft;
+ d1_radix = 1.0 / radix;
+ d1_radix2 = d1_radix * d1_radix;
+ topdgt = din[nfft + 1];
+ x = topdgt < 0 ? -topdgt : topdgt;
+ shift = x + 0.5 >= radix ? 1 : 0;
+ /* ---- correction of cyclic convolution of din[1] ---- */
+ x *= nfft * 0.5;
+ din[nfft + 1] = din[1] - x;
+ din[1] = x;
+ /* ---- output of digits ---- */
+ ndata = n;
+ if (n > nfft + 1 + shift) {
+ ndata = nfft + 1 + shift;
+ for (j = n + 1; j > ndata + 1; j--) {
+ out[j] = 0;
+ }
+ }
+ x = 0;
+ pow_radix = 1;
+ for (j = ndata + 1 - shift; j <= nfft + 1; j++) {
+ x += pow_radix * din[j];
+ pow_radix *= d1_radix;
+ if (pow_radix < DBL_EPSILON) {
+ break;
+ }
+ }
+ x = d1_radix2 * (scale * x + 0.5);
+ carry2 = ((int) x) - 1;
+ carry = (int) (radix * (x - carry2) + 0.5);
+ for (j = ndata; j > 1; j--) {
+ x = d1_radix2 * (scale * din[j - shift] + carry + 0.5);
+ carry = carry2;
+ carry2 = ((int) x) - 1;
+ x = radix * (x - carry2);
+ carry1 = (int) x;
+ out[j + 1] = (int) (radix * (x - carry1));
+ carry += carry1;
+ }
+ x = carry + ((double) radix) * carry2 + 0.5;
+ if (shift == 0) {
+ x += scale * din[1];
+ }
+ carry = (int) (d1_radix * x);
+ out[2] = (int) (x - ((double) radix) * carry);
+ if (carry > 0) {
+ for (j = n + 1; j > 2; j--) {
+ out[j] = out[j - 1];
+ }
+ out[2] = carry;
+ shift++;
+ }
+ /* ---- output of exp, sgn ---- */
+ x = din[0] + shift + 0.5;
+ shift = ((int) x) - 1;
+ out[1] = shift + ((int) (x - shift));
+ out[0] = topdgt > 0.5 ? 1 : -1;
+ if (out[2] == 0) {
+ out[0] = 0;
+ out[1] = 0;
+ }
+ }
+
+
+ double mp_mul_d2i_test(int radix, int nfft, double din[])
+ {
+ int j, carry, carry1, carry2;
+ double x, scale, d1_radix, d1_radix2, err;
+
+ scale = 2.0 / nfft;
+ d1_radix = 1.0 / radix;
+ d1_radix2 = d1_radix * d1_radix;
+ /* ---- correction of cyclic convolution of din[1] ---- */
+ x = din[nfft + 1] * nfft * 0.5;
+ if (x < 0) {
+ x = -x;
+ }
+ din[nfft + 1] = din[1] - x;
+ /* ---- check of digits ---- */
+ err = 0;
+ carry = 0;
+ carry2 = 0;
+ for (j = nfft + 1; j > 1; j--) {
+ x = d1_radix2 * (scale * din[j] + carry + 0.5);
+ carry = carry2;
+ carry2 = ((int) x) - 1;
+ x = radix * (x - carry2);
+ carry1 = (int) x;
+ x = radix * (x - carry1);
+ carry += carry1;
+ x = x - 0.5 - ((int) x);
+ if (x > err) {
+ err = x;
+ } else if (-x > err) {
+ err = -x;
+ }
+ }
+ return err;
+ }
+
+
+ /* -------- mp_inv routines -------- */
+
+
+ int mp_inv(int n, int radix, int in[], int out[],
+ int tmp1[], int tmp2[], int nfft,
+ double tmp1fft[], double tmp2fft[], int ip[], double w[])
+ {
+ int mp_get_nfft_init(int radix, int nfft_max);
+ void mp_inv_init(int n, int radix, int in[], int out[]);
+ int mp_inv_newton(int n, int radix, int in[], int inout[],
+ int tmp1[], int tmp2[], int nfft, double tmp1fft[],
+ double tmp2fft[], int ip[], double w[]);
+ int n_nwt, nfft_nwt, thr, prc;
+
+ if (in[0] == 0) {
+ return -1;
+ }
+ nfft_nwt = mp_get_nfft_init(radix, nfft);
+ n_nwt = nfft_nwt + 2;
+ if (n_nwt > n) {
+ n_nwt = n;
+ }
+ mp_inv_init(n_nwt, radix, in, out);
+ thr = 8;
+ do {
+ n_nwt = nfft_nwt + 2;
+ if (n_nwt > n) {
+ n_nwt = n;
+ }
+ prc = mp_inv_newton(n_nwt, radix, in, out,
+ tmp1, tmp2, nfft_nwt, tmp1fft, tmp2fft, ip, w);
+ #ifdef DEBUG
+ printf("n=%d, nfft=%d, prc=%d\n", n_nwt, nfft_nwt, prc);
+ #endif
+ if (thr * nfft_nwt >= nfft) {
+ thr = 0;
+ if (2 * prc <= n_nwt - 2) {
+ nfft_nwt >>= 1;
+ }
+ } else {
+ if (3 * prc < n_nwt - 2) {
+ nfft_nwt >>= 1;
+ }
+ }
+ nfft_nwt <<= 1;
+ } while (nfft_nwt <= nfft);
+ return 0;
+ }
+
+
+ int mp_sqrt(int n, int radix, int in[], int out[],
+ int tmp1[], int tmp2[], int nfft,
+ double tmp1fft[], double tmp2fft[], int ip[], double w[])
+ {
+ void mp_load_0(int n, int radix, int out[]);
+ int mp_get_nfft_init(int radix, int nfft_max);
+ void mp_sqrt_init(int n, int radix, int in[], int out[], int out_rev[]);
+ int mp_sqrt_newton(int n, int radix, int in[], int inout[],
+ int inout_rev[], int tmp[], int nfft, double tmp1fft[],
+ double tmp2fft[], int ip[], double w[], int *n_tmp1fft);
+ int n_nwt, nfft_nwt, thr, prc, n_tmp1fft;
+
+ if (in[0] < 0) {
+ return -1;
+ } else if (in[0] == 0) {
+ mp_load_0(n, radix, out);
+ return 0;
+ }
+ nfft_nwt = mp_get_nfft_init(radix, nfft);
+ n_nwt = nfft_nwt + 2;
+ if (n_nwt > n) {
+ n_nwt = n;
+ }
+ mp_sqrt_init(n_nwt, radix, in, out, tmp1);
+ n_tmp1fft = 0;
+ thr = 8;
+ do {
+ n_nwt = nfft_nwt + 2;
+ if (n_nwt > n) {
+ n_nwt = n;
+ }
+ prc = mp_sqrt_newton(n_nwt, radix, in, out,
+ tmp1, tmp2, nfft_nwt, tmp1fft, tmp2fft,
+ ip, w, &n_tmp1fft);
+ #ifdef DEBUG
+ printf("n=%d, nfft=%d, prc=%d\n", n_nwt, nfft_nwt, prc);
+ #endif
+ if (thr * nfft_nwt >= nfft) {
+ thr = 0;
+ if (2 * prc <= n_nwt - 2) {
+ nfft_nwt >>= 1;
+ }
+ } else {
+ if (3 * prc < n_nwt - 2) {
+ nfft_nwt >>= 1;
+ }
+ }
+ nfft_nwt <<= 1;
+ } while (nfft_nwt <= nfft);
+ return 0;
+ }
+
+
+ /* -------- mp_inv child routines -------- */
+
+
+ int mp_get_nfft_init(int radix, int nfft_max)
+ {
+ int nfft_init;
+ double r;
+
+ r = radix;
+ nfft_init = 1;
+ do {
+ r *= r;
+ nfft_init <<= 1;
+ } while (DBL_EPSILON * r < 1 && nfft_init < nfft_max);
+ return nfft_init;
+ }
+
+
+ void mp_inv_init(int n, int radix, int in[], int out[])
+ {
+ void mp_unexp_d2mp(int n, int radix, double din, int out[]);
+ double mp_unexp_mp2d(int n, int radix, int in[]);
+ int outexp;
+ double din;
+
+ out[0] = in[0];
+ outexp = -in[1];
+ din = 1.0 / mp_unexp_mp2d(n, radix, &in[2]);
+ while (din < 1) {
+ din *= radix;
+ outexp--;
+ }
+ out[1] = outexp;
+ mp_unexp_d2mp(n, radix, din, &out[2]);
+ }
+
+
+ void mp_sqrt_init(int n, int radix, int in[], int out[], int out_rev[])
+ {
+ void mp_unexp_d2mp(int n, int radix, double din, int out[]);
+ double mp_unexp_mp2d(int n, int radix, int in[]);
+ int outexp;
+ double din;
+
+ out[0] = 1;
+ out_rev[0] = 1;
+ outexp = in[1];
+ din = mp_unexp_mp2d(n, radix, &in[2]);
+ if (outexp % 2 != 0) {
+ din *= radix;
+ outexp--;
+ }
+ outexp /= 2;
+ din = sqrt(din);
+ if (din < 1) {
+ din *= radix;
+ outexp--;
+ }
+ out[1] = outexp;
+ mp_unexp_d2mp(n, radix, din, &out[2]);
+ outexp = -outexp;
+ din = 1.0 / din;
+ while (din < 1) {
+ din *= radix;
+ outexp--;
+ }
+ out_rev[1] = outexp;
+ mp_unexp_d2mp(n, radix, din, &out_rev[2]);
+ }
+
+
+ void mp_unexp_d2mp(int n, int radix, double din, int out[])
+ {
+ int j, x;
+
+ for (j = 0; j < n; j++) {
+ x = (int) din;
+ if (x >= radix) {
+ x = radix - 1;
+ din = radix;
+ }
+ din = radix * (din - x);
+ out[j] = x;
+ }
+ }
+
+
+ double mp_unexp_mp2d(int n, int radix, int in[])
+ {
+ int j;
+ double d1_radix, dout;
+
+ d1_radix = 1.0 / radix;
+ dout = 0;
+ for (j = n - 1; j >= 0; j--) {
+ dout = d1_radix * dout + in[j];
+ }
+ return dout;
+ }
+
+
+ int mp_inv_newton(int n, int radix, int in[], int inout[],
+ int tmp1[], int tmp2[], int nfft, double tmp1fft[],
+ double tmp2fft[], int ip[], double w[])
+ {
+ void mp_load_1(int n, int radix, int out[]);
+ void mp_round(int n, int radix, int m, int inout[]);
+ void mp_add(int n, int radix, int in1[], int in2[], int out[]);
+ void mp_sub(int n, int radix, int in1[], int in2[], int out[]);
+ void mp_mulh(int n, int radix, int in1[], int in2[], int out[],
+ int nfft, double in1fft[], double outfft[],
+ int ip[], double w[]);
+ void mp_mulh_use_in1fft(int n, int radix, double in1fft[],
+ int shift, int in2[], int out[], int nfft, double outfft[],
+ int ip[], double w[]);
+ int n_h, shift, prc;
+
+ shift = (nfft >> 1) + 1;
+ n_h = n / 2 + 1;
+ if (n_h < n - shift) {
+ n_h = n - shift;
+ }
+ /* ---- tmp1 = inout * (upper) in (half to normal precision) ---- */
+ mp_round(n, radix, shift, inout);
+ mp_mulh(n, radix, inout, in, tmp1,
+ nfft, tmp1fft, tmp2fft, ip, w);
+ /* ---- tmp2 = 1 - tmp1 ---- */
+ mp_load_1(n, radix, tmp2);
+ mp_sub(n, radix, tmp2, tmp1, tmp2);
+ /* ---- tmp2 -= inout * (lower) in (half precision) ---- */
+ mp_mulh_use_in1fft(n, radix, tmp1fft, shift, in, tmp1,
+ nfft, tmp2fft, ip, w);
+ mp_sub(n_h, radix, tmp2, tmp1, tmp2);
+ /* ---- get precision ---- */
+ prc = -tmp2[1];
+ if (tmp2[0] == 0) {
+ prc = nfft + 1;
+ }
+ /* ---- tmp2 *= inout (half precision) ---- */
+ mp_mulh_use_in1fft(n_h, radix, tmp1fft, 0, tmp2, tmp2,
+ nfft, tmp2fft, ip, w);
+ /* ---- inout += tmp2 ---- */
+ mp_add(n, radix, inout, tmp2, inout);
+ return prc;
+ }
+
+
+ int mp_sqrt_newton(int n, int radix, int in[], int inout[],
+ int inout_rev[], int tmp[], int nfft, double tmp1fft[],
+ double tmp2fft[], int ip[], double w[], int *n_tmp1fft)
+ {
+ void mp_round(int n, int radix, int m, int inout[]);
+ void mp_add(int n, int radix, int in1[], int in2[], int out[]);
+ void mp_sub(int n, int radix, int in1[], int in2[], int out[]);
+ void mp_idiv_2(int n, int radix, int in[], int out[]);
+ void mp_mulh(int n, int radix, int in1[], int in2[], int out[],
+ int nfft, double in1fft[], double outfft[], int ip[], double w[]);
+ void mp_squh(int n, int radix, int in[], int out[],
+ int nfft, double inoutfft[], int ip[], double w[]);
+ void mp_squh_use_in1fft(int n, int radix, double inoutfft[], int out[],
+ int nfft, int ip[], double w[]);
+ int n_h, nfft_h, shift, prc;
+
+ nfft_h = nfft >> 1;
+ shift = nfft_h + 1;
+ if (nfft_h < 2) {
+ nfft_h = 2;
+ }
+ n_h = n / 2 + 1;
+ if (n_h < n - shift) {
+ n_h = n - shift;
+ }
+ /* ---- tmp = inout_rev^2 (1/4 to half precision) ---- */
+ mp_round(n_h, radix, (nfft_h >> 1) + 1, inout_rev);
+ if (*n_tmp1fft != nfft_h) {
+ mp_squh(n_h, radix, inout_rev, tmp,
+ nfft_h, tmp1fft, ip, w);
+ } else {
+ mp_squh_use_in1fft(n_h, radix, tmp1fft, tmp,
+ nfft_h, ip, w);
+ }
+ /* ---- tmp = inout_rev - inout * tmp (half precision) ---- */
+ mp_round(n, radix, shift, inout);
+ mp_mulh(n_h, radix, inout, tmp, tmp,
+ nfft, tmp1fft, tmp2fft, ip, w);
+ mp_sub(n_h, radix, inout_rev, tmp, tmp);
+ /* ---- inout_rev += tmp ---- */
+ mp_add(n_h, radix, inout_rev, tmp, inout_rev);
+ /* ---- tmp = in - inout^2 (half to normal precision) ---- */
+ mp_squh_use_in1fft(n, radix, tmp1fft, tmp,
+ nfft, ip, w);
+ mp_sub(n, radix, in, tmp, tmp);
+ /* ---- get precision ---- */
+ prc = in[1] - tmp[1];
+ if (in[2] > tmp[2]) {
+ prc++;
+ }
+ if (tmp[0] == 0) {
+ prc = nfft + 1;
+ }
+ /* ---- tmp = tmp * inout_rev / 2 (half precision) ---- */
+ mp_round(n_h, radix, shift, inout_rev);
+ mp_mulh(n_h, radix, inout_rev, tmp, tmp,
+ nfft, tmp1fft, tmp2fft, ip, w);
+ *n_tmp1fft = nfft;
+ mp_idiv_2(n_h, radix, tmp, tmp);
+ /* ---- inout += tmp ---- */
+ mp_add(n, radix, inout, tmp, inout);
+ return prc;
+ }
+
+
+ /* -------- mp_io routines -------- */
+
+
+ void mp_sprintf(int n, int log10_radix, int in[], char out[])
+ {
+ int j, k, x, y, outexp, shift;
+
+ if (in[0] < 0) {
+ *out++ = '-';
+ }
+ x = in[2];
+ shift = log10_radix;
+ for (k = log10_radix; k > 0; k--) {
+ y = x % 10;
+ x /= 10;
+ out[k] = '0' + y;
+ if (y != 0) {
+ shift = k;
+ }
+ }
+ out[0] = out[shift];
+ out[1] = '.';
+ for (k = 1; k <= log10_radix - shift; k++) {
+ out[k + 1] = out[k + shift];
+ }
+ outexp = log10_radix - shift;
+ out += outexp + 2;
+ for (j = 3; j <= n + 1; j++) {
+ x = in[j];
+ for (k = log10_radix - 1; k >= 0; k--) {
+ y = x % 10;
+ x /= 10;
+ out[k] = '0' + y;
+ }
+ out += log10_radix;
+ }
+ *out++ = 'e';
+ outexp += log10_radix * in[1];
+ sprintf(out, "%d", outexp);
+ }
+
+
+ void mp_sscanf(int n, int log10_radix, char in[], int out[])
+ {
+ char *s;
+ int j, x, outexp, outexp_mod;
+
+ while (*in == ' ') {
+ in++;
+ }
+ out[0] = 1;
+ if (*in == '-') {
+ out[0] = -1;
+ in++;
+ } else if (*in == '+') {
+ in++;
+ }
+ while (*in == ' ' || *in == '0') {
+ in++;
+ }
+ outexp = 0;
+ for (s = in; *s != '\0'; s++) {
+ if (*s == 'e' || *s == 'E' || *s == 'd' || *s == 'D') {
+ if (sscanf(++s, "%d", &outexp) != 1) {
+ outexp = 0;
+ }
+ break;
+ }
+ }
+ if (*in == '.') {
+ do {
+ outexp--;
+ while (*++in == ' ');
+ } while (*in == '0' && *in != '\0');
+ } else if (*in != '\0') {
+ s = in;
+ while (*++s == ' ');
+ while (*s >= '0' && *s <= '9' && *s != '\0') {
+ outexp++;
+ while (*++s == ' ');
+ }
+ }
+ x = outexp / log10_radix;
+ outexp_mod = outexp - log10_radix * x;
+ if (outexp_mod < 0) {
+ x--;
+ outexp_mod += log10_radix;
+ }
+ out[1] = x;
+ x = 0;
+ j = 2;
+ for (s = in; *s != '\0'; s++) {
+ if (*s == '.' || *s == ' ') {
+ continue;
+ }
+ if (*s < '0' || *s > '9') {
+ break;
+ }
+ x = 10 * x + (*s - '0');
+ if (--outexp_mod < 0) {
+ if (j > n + 1) {
+ break;
+ }
+ out[j++] = x;
+ x = 0;
+ outexp_mod = log10_radix - 1;
+ }
+ }
+ while (outexp_mod-- >= 0) {
+ x *= 10;
+ }
+ while (j <= n + 1) {
+ out[j++] = x;
+ x = 0;
+ }
+ if (out[2] == 0) {
+ out[0] = 0;
+ out[1] = 0;
+ }
+ }
+
+
Index: llvm/test/Programs/MultiSource/Benchmarks/FreeBench/pifft/ref.in
diff -c /dev/null llvm/test/Programs/MultiSource/Benchmarks/FreeBench/pifft/ref.in:1.1
*** /dev/null Sat Oct 11 16:18:59 2003
--- llvm/test/Programs/MultiSource/Benchmarks/FreeBench/pifft/ref.in Sat Oct 11 16:18:48 2003
***************
*** 0 ****
--- 1 ----
+ 1048576
Index: llvm/test/Programs/MultiSource/Benchmarks/FreeBench/pifft/test.in
diff -c /dev/null llvm/test/Programs/MultiSource/Benchmarks/FreeBench/pifft/test.in:1.1
*** /dev/null Sat Oct 11 16:18:59 2003
--- llvm/test/Programs/MultiSource/Benchmarks/FreeBench/pifft/test.in Sat Oct 11 16:18:49 2003
***************
*** 0 ****
--- 1 ----
+ 16384
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