cannam@127: /*
cannam@127:  * Copyright (c) 2003, 2007-14 Matteo Frigo
cannam@127:  * Copyright (c) 2003, 2007-14 Massachusetts Institute of Technology
cannam@127:  *
cannam@127:  * This program is free software; you can redistribute it and/or modify
cannam@127:  * it under the terms of the GNU General Public License as published by
cannam@127:  * the Free Software Foundation; either version 2 of the License, or
cannam@127:  * (at your option) any later version.
cannam@127:  *
cannam@127:  * This program is distributed in the hope that it will be useful,
cannam@127:  * but WITHOUT ANY WARRANTY; without even the implied warranty of
cannam@127:  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
cannam@127:  * GNU General Public License for more details.
cannam@127:  *
cannam@127:  * You should have received a copy of the GNU General Public License
cannam@127:  * along with this program; if not, write to the Free Software
cannam@127:  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
cannam@127:  *
cannam@127:  */
cannam@127: 
cannam@127: 
cannam@127: /* trigonometric functions */
cannam@127: #include "ifftw.h"
cannam@127: #include <math.h>
cannam@127: 
cannam@127: #if defined(TRIGREAL_IS_LONG_DOUBLE)
cannam@127: #  define COS cosl
cannam@127: #  define SIN sinl
cannam@127: #  define KTRIG(x) (x##L)
cannam@127: #  if defined(HAVE_DECL_SINL) && !HAVE_DECL_SINL
cannam@127:      extern long double sinl(long double x);
cannam@127: #  endif
cannam@127: #  if defined(HAVE_DECL_COSL) && !HAVE_DECL_COSL
cannam@127:      extern long double cosl(long double x);
cannam@127: #  endif
cannam@127: #elif defined(TRIGREAL_IS_QUAD)
cannam@127: #  define COS cosq
cannam@127: #  define SIN sinq
cannam@127: #  define KTRIG(x) (x##Q)
cannam@127:    extern __float128 sinq(__float128 x);
cannam@127:    extern __float128 cosq(__float128 x);
cannam@127: #else
cannam@127: #  define COS cos
cannam@127: #  define SIN sin
cannam@127: #  define KTRIG(x) (x)
cannam@127: #endif
cannam@127: 
cannam@127: static const trigreal K2PI =
cannam@127:     KTRIG(6.2831853071795864769252867665590057683943388);
cannam@127: #define by2pi(m, n) ((K2PI * (m)) / (n))
cannam@127: 
cannam@127: /*
cannam@127:  * Improve accuracy by reducing x to range [0..1/8]
cannam@127:  * before multiplication by 2 * PI.
cannam@127:  */
cannam@127: 
cannam@127: static void real_cexp(INT m, INT n, trigreal *out)
cannam@127: {
cannam@127:      trigreal theta, c, s, t;
cannam@127:      unsigned octant = 0;
cannam@127:      INT quarter_n = n;
cannam@127: 
cannam@127:      n += n; n += n;
cannam@127:      m += m; m += m;
cannam@127: 
cannam@127:      if (m < 0) m += n;
cannam@127:      if (m > n - m) { m = n - m; octant |= 4; }
cannam@127:      if (m - quarter_n > 0) { m = m - quarter_n; octant |= 2; }
cannam@127:      if (m > quarter_n - m) { m = quarter_n - m; octant |= 1; }
cannam@127: 
cannam@127:      theta = by2pi(m, n);
cannam@127:      c = COS(theta); s = SIN(theta);
cannam@127: 
cannam@127:      if (octant & 1) { t = c; c = s; s = t; }
cannam@127:      if (octant & 2) { t = c; c = -s; s = t; }
cannam@127:      if (octant & 4) { s = -s; }
cannam@127: 
cannam@127:      out[0] = c; 
cannam@127:      out[1] = s; 
cannam@127: }
cannam@127: 
cannam@127: static INT choose_twshft(INT n)
cannam@127: {
cannam@127:      INT log2r = 0;
cannam@127:      while (n > 0) {
cannam@127: 	  ++log2r;
cannam@127: 	  n /= 4;
cannam@127:      }
cannam@127:      return log2r;
cannam@127: }
cannam@127: 
cannam@127: static void cexpl_sqrtn_table(triggen *p, INT m, trigreal *res)
cannam@127: {
cannam@127:      m += p->n * (m < 0);
cannam@127: 
cannam@127:      {
cannam@127: 	  INT m0 = m & p->twmsk;
cannam@127: 	  INT m1 = m >> p->twshft;
cannam@127: 	  trigreal wr0 = p->W0[2 * m0];
cannam@127: 	  trigreal wi0 = p->W0[2 * m0 + 1];
cannam@127: 	  trigreal wr1 = p->W1[2 * m1];
cannam@127: 	  trigreal wi1 = p->W1[2 * m1 + 1];
cannam@127: 
cannam@127: 	  res[0] = wr1 * wr0 - wi1 * wi0;
cannam@127: 	  res[1] = wi1 * wr0 + wr1 * wi0;
cannam@127:      }
cannam@127: }
cannam@127: 
cannam@127: /* multiply (xr, xi) by exp(FFT_SIGN * 2*pi*i*m/n) */
cannam@127: static void rotate_sqrtn_table(triggen *p, INT m, R xr, R xi, R *res)
cannam@127: {
cannam@127:      m += p->n * (m < 0);
cannam@127: 
cannam@127:      {
cannam@127: 	  INT m0 = m & p->twmsk;
cannam@127: 	  INT m1 = m >> p->twshft;
cannam@127: 	  trigreal wr0 = p->W0[2 * m0];
cannam@127: 	  trigreal wi0 = p->W0[2 * m0 + 1];
cannam@127: 	  trigreal wr1 = p->W1[2 * m1];
cannam@127: 	  trigreal wi1 = p->W1[2 * m1 + 1];
cannam@127: 	  trigreal wr = wr1 * wr0 - wi1 * wi0;
cannam@127: 	  trigreal wi = wi1 * wr0 + wr1 * wi0;
cannam@127: 
cannam@127: #if FFT_SIGN == -1
cannam@127: 	  res[0] = xr * wr + xi * wi;
cannam@127: 	  res[1] = xi * wr - xr * wi;
cannam@127: #else
cannam@127: 	  res[0] = xr * wr - xi * wi;
cannam@127: 	  res[1] = xi * wr + xr * wi;
cannam@127: #endif
cannam@127:      }
cannam@127: }
cannam@127: 
cannam@127: static void cexpl_sincos(triggen *p, INT m, trigreal *res)
cannam@127: {
cannam@127:      real_cexp(m, p->n, res);
cannam@127: }
cannam@127: 
cannam@127: static void cexp_zero(triggen *p, INT m, R *res)
cannam@127: {
cannam@127:      UNUSED(p); UNUSED(m);
cannam@127:      res[0] = 0;
cannam@127:      res[1] = 0;
cannam@127: }
cannam@127: 
cannam@127: static void cexpl_zero(triggen *p, INT m, trigreal *res)
cannam@127: {
cannam@127:      UNUSED(p); UNUSED(m);
cannam@127:      res[0] = 0;
cannam@127:      res[1] = 0;
cannam@127: }
cannam@127: 
cannam@127: static void cexp_generic(triggen *p, INT m, R *res)
cannam@127: {
cannam@127:      trigreal resl[2];
cannam@127:      p->cexpl(p, m, resl);
cannam@127:      res[0] = (R)resl[0];
cannam@127:      res[1] = (R)resl[1];
cannam@127: }
cannam@127: 
cannam@127: static void rotate_generic(triggen *p, INT m, R xr, R xi, R *res)
cannam@127: {
cannam@127:      trigreal w[2];
cannam@127:      p->cexpl(p, m, w);
cannam@127:      res[0] = xr * w[0] - xi * (FFT_SIGN * w[1]);
cannam@127:      res[1] = xi * w[0] + xr * (FFT_SIGN * w[1]);
cannam@127: }
cannam@127: 
cannam@127: triggen *X(mktriggen)(enum wakefulness wakefulness, INT n)
cannam@127: {
cannam@127:      INT i, n0, n1;
cannam@127:      triggen *p = (triggen *)MALLOC(sizeof(*p), TWIDDLES);
cannam@127: 
cannam@127:      p->n = n;
cannam@127:      p->W0 = p->W1 = 0;
cannam@127:      p->cexp = 0;
cannam@127:      p->rotate = 0;
cannam@127: 
cannam@127:      switch (wakefulness) {
cannam@127: 	 case SLEEPY:
cannam@127: 	      A(0 /* can't happen */);
cannam@127: 	      break;
cannam@127: 
cannam@127: 	 case AWAKE_SQRTN_TABLE: {
cannam@127: 	      INT twshft = choose_twshft(n);
cannam@127: 
cannam@127: 	      p->twshft = twshft;
cannam@127: 	      p->twradix = ((INT)1) << twshft;
cannam@127: 	      p->twmsk = p->twradix - 1;
cannam@127: 
cannam@127: 	      n0 = p->twradix;
cannam@127: 	      n1 = (n + n0 - 1) / n0;
cannam@127: 
cannam@127: 	      p->W0 = (trigreal *)MALLOC(n0 * 2 * sizeof(trigreal), TWIDDLES);
cannam@127: 	      p->W1 = (trigreal *)MALLOC(n1 * 2 * sizeof(trigreal), TWIDDLES);
cannam@127: 
cannam@127: 	      for (i = 0; i < n0; ++i) 
cannam@127: 		   real_cexp(i, n, p->W0 + 2 * i);
cannam@127: 
cannam@127: 	      for (i = 0; i < n1; ++i) 
cannam@127: 		   real_cexp(i * p->twradix, n, p->W1 + 2 * i);
cannam@127: 
cannam@127: 	      p->cexpl = cexpl_sqrtn_table;
cannam@127: 	      p->rotate = rotate_sqrtn_table;
cannam@127: 	      break;
cannam@127: 	 }
cannam@127: 
cannam@127: 	 case AWAKE_SINCOS: 
cannam@127: 	      p->cexpl = cexpl_sincos;
cannam@127: 	      break;
cannam@127: 
cannam@127: 	 case AWAKE_ZERO: 
cannam@127: 	      p->cexp = cexp_zero;
cannam@127: 	      p->cexpl = cexpl_zero;
cannam@127: 	      break;
cannam@127:      }
cannam@127: 
cannam@127:      if (!p->cexp) {
cannam@127: 	  if (sizeof(trigreal) == sizeof(R))
cannam@127: 	       p->cexp = (void (*)(triggen *, INT, R *))p->cexpl;
cannam@127: 	  else
cannam@127: 	       p->cexp = cexp_generic;
cannam@127:      }
cannam@127:      if (!p->rotate)     
cannam@127: 	       p->rotate = rotate_generic;
cannam@127:      return p;
cannam@127: }
cannam@127: 
cannam@127: void X(triggen_destroy)(triggen *p)
cannam@127: {
cannam@127:      X(ifree0)(p->W0);
cannam@127:      X(ifree0)(p->W1);
cannam@127:      X(ifree)(p);
cannam@127: }