source: tags/arb-6.0/GDE/MAFFT/mafft-7.055-with-extensions/core/fft.c

#include "mltaln.h"
#include "mtxutl.h"

/*
  from "C gengo niyoru saishin algorithm jiten" ISBN4-87408-414-1 Haruhiko Okumura
*/
static void make_sintbl(int n, float sintbl[])
{
        int i, n2, n4, n8;
        double c, s, dc, ds, t;

        n2 = n / 2;  n4 = n / 4;  n8 = n / 8;
        t = sin(PI / n);
        dc = 2 * t * t;  ds = sqrt(dc * (2 - dc));
        t = 2 * dc;  c = sintbl[n4] = 1;  s = sintbl[0] = 0;
        for (i = 1; i < n8; i++) {
                c -= dc;  dc += t * c;
                s += ds;  ds -= t * s;
                sintbl[i] = s;  sintbl[n4 - i] = c;
        }
        if (n8 != 0) sintbl[n8] = sqrt(0.5);
        for (i = 0; i < n4; i++)
                sintbl[n2 - i] = sintbl[i];
        for (i = 0; i < n2 + n4; i++)
                sintbl[i + n2] = - sintbl[i];
}
/*
  {\tt fft()}.
*/
static void make_bitrev(int n, int bitrev[])
{
        int i, j, k, n2;

        n2 = n / 2;  i = j = 0;
        for ( ; ; ) {
                bitrev[i] = j;
                if (++i >= n) break;
                k = n2;
                while (k <= j) {  j -= k;  k /= 2;  }
                j += k;
        }
}
/*
*/
int fft(int n, Fukusosuu *x, int freeflag)
{
        static TLS int    last_n = 0;    /*  {\tt n} */
        static TLS int   *bitrev = NULL; /*  */
        static TLS float *sintbl = NULL; /*  */
        int i, j, k, ik, h, d, k2, n4, inverse;
        float t, s, c, dR, dI;

                if (freeflag)
                {
                        if (bitrev) free(bitrev); bitrev = NULL;
                        if (sintbl) free(sintbl); sintbl = NULL;
                        return( 0 );
                }

        /*  */
        if (n < 0) {
                n = -n;  inverse = 1;  /*  */
        } else inverse = 0;
        n4 = n / 4;
        if (n != last_n || n == 0) {
                last_n = n;
#if 0
                if (sintbl != NULL) {
                                        free(sintbl);
                                        sintbl = NULL;
                                }
                if (bitrev != NULL) {
                                        free(bitrev);
                                        bitrev = NULL;
                                }
                if (n == 0) return 0;  /*  */
                sintbl = (float *)malloc((n + n4) * sizeof(float));
                bitrev = (int *)malloc(n * sizeof(int));
#else /* by T. Nishiyama */
                                sintbl = realloc(sintbl, (n + n4) * sizeof(float));
                                bitrev = realloc(bitrev, n * sizeof(int));
#endif
                if (sintbl == NULL || bitrev == NULL) {
                        fprintf(stderr, "\n");  return 1;
                }
                make_sintbl(n, sintbl);
                make_bitrev(n, bitrev);
        }
        for (i = 0; i < n; i++) {    /*  */
                j = bitrev[i];
                if (i < j) {
                        t = x[i].R;  x[i].R = x[j].R;  x[j].R = t;
                        t = x[i].I;  x[i].I = x[j].I;  x[j].I = t;
                }
        }
        for (k = 1; k < n; k = k2) {    /*  */
#if 0
                                fprintf( stderr, "%d / %d\n", k, n );
#endif
                h = 0;  k2 = k + k;  d = n / k2;
                for (j = 0; j < k; j++) {
#if 0
                                        if( j % 1 == 0 )
                                                fprintf( stderr, "%d / %d\r", j, k );
#endif
                        c = sintbl[h + n4];
                        if (inverse) s = - sintbl[h];
                        else         s =   sintbl[h];
                        for (i = j; i < n; i += k2) {
#if 0
                                                                if( k>=4194000 ) fprintf( stderr, "in loop %d -  %d < %d, k2=%d\r", j, i, n, k2 );
#endif
                                ik = i + k;
                                dR = s * x[ik].I + c * x[ik].R;
                                dI = c * x[ik].I - s * x[ik].R;
                                x[ik].R = x[i].R - dR;  x[i].R += dR;
                                x[ik].I = x[i].I - dI;  x[i].I += dI;
                        }
                        h += d;
                }
        }
        if (! inverse)    /* n */
                for (i = 0; i < n; i++) {  x[i].R /= n;  x[i].I /= n;  }
        return 0;  /*  */
}