Chris@42: /*
Chris@42:  * Copyright (c) 2003, 2007-14 Matteo Frigo
Chris@42:  * Copyright (c) 2003, 2007-14 Massachusetts Institute of Technology
Chris@42:  *
Chris@42:  * This program is free software; you can redistribute it and/or modify
Chris@42:  * it under the terms of the GNU General Public License as published by
Chris@42:  * the Free Software Foundation; either version 2 of the License, or
Chris@42:  * (at your option) any later version.
Chris@42:  *
Chris@42:  * This program is distributed in the hope that it will be useful,
Chris@42:  * but WITHOUT ANY WARRANTY; without even the implied warranty of
Chris@42:  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
Chris@42:  * GNU General Public License for more details.
Chris@42:  *
Chris@42:  * You should have received a copy of the GNU General Public License
Chris@42:  * along with this program; if not, write to the Free Software
Chris@42:  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
Chris@42:  *
Chris@42:  */
Chris@42: 
Chris@42: #include "dft.h"
Chris@42: 
Chris@42: /*
Chris@42:  * Compute transforms of prime sizes using Rader's trick: turn them
Chris@42:  * into convolutions of size n - 1, which you then perform via a pair
Chris@42:  * of FFTs.
Chris@42:  */
Chris@42: 
Chris@42: typedef struct {
Chris@42:      solver super;
Chris@42: } S;
Chris@42: 
Chris@42: typedef struct {
Chris@42:      plan_dft super;
Chris@42: 
Chris@42:      plan *cld1, *cld2;
Chris@42:      R *omega;
Chris@42:      INT n, g, ginv;
Chris@42:      INT is, os;
Chris@42:      plan *cld_omega;
Chris@42: } P;
Chris@42: 
Chris@42: static rader_tl *omegas = 0;
Chris@42: 
Chris@42: static R *mkomega(enum wakefulness wakefulness, plan *p_, INT n, INT ginv)
Chris@42: {
Chris@42:      plan_dft *p = (plan_dft *) p_;
Chris@42:      R *omega;
Chris@42:      INT i, gpower;
Chris@42:      trigreal scale;
Chris@42:      triggen *t;
Chris@42: 
Chris@42:      if ((omega = X(rader_tl_find)(n, n, ginv, omegas)))
Chris@42: 	  return omega;
Chris@42: 
Chris@42:      omega = (R *)MALLOC(sizeof(R) * (n - 1) * 2, TWIDDLES);
Chris@42: 
Chris@42:      scale = n - 1.0; /* normalization for convolution */
Chris@42: 
Chris@42:      t = X(mktriggen)(wakefulness, n);
Chris@42:      for (i = 0, gpower = 1; i < n-1; ++i, gpower = MULMOD(gpower, ginv, n)) {
Chris@42: 	  trigreal w[2];
Chris@42: 	  t->cexpl(t, gpower, w);
Chris@42: 	  omega[2*i] = w[0] / scale;
Chris@42: 	  omega[2*i+1] = FFT_SIGN * w[1] / scale;
Chris@42:      }
Chris@42:      X(triggen_destroy)(t);
Chris@42:      A(gpower == 1);
Chris@42: 
Chris@42:      p->apply(p_, omega, omega + 1, omega, omega + 1);
Chris@42: 
Chris@42:      X(rader_tl_insert)(n, n, ginv, omega, &omegas);
Chris@42:      return omega;
Chris@42: }
Chris@42: 
Chris@42: static void free_omega(R *omega)
Chris@42: {
Chris@42:      X(rader_tl_delete)(omega, &omegas);
Chris@42: }
Chris@42: 
Chris@42: 
Chris@42: /***************************************************************************/
Chris@42: 
Chris@42: /* Below, we extensively use the identity that fft(x*)* = ifft(x) in
Chris@42:    order to share data between forward and backward transforms and to
Chris@42:    obviate the necessity of having separate forward and backward
Chris@42:    plans.  (Although we often compute separate plans these days anyway
Chris@42:    due to the differing strides, etcetera.)
Chris@42: 
Chris@42:    Of course, since the new FFTW gives us separate pointers to
Chris@42:    the real and imaginary parts, we could have instead used the
Chris@42:    fft(r,i) = ifft(i,r) form of this identity, but it was easier to
Chris@42:    reuse the code from our old version. */
Chris@42: 
Chris@42: static void apply(const plan *ego_, R *ri, R *ii, R *ro, R *io)
Chris@42: {
Chris@42:      const P *ego = (const P *) ego_;
Chris@42:      INT is, os;
Chris@42:      INT k, gpower, g, r;
Chris@42:      R *buf;
Chris@42:      R r0 = ri[0], i0 = ii[0];
Chris@42: 
Chris@42:      r = ego->n; is = ego->is; os = ego->os; g = ego->g; 
Chris@42:      buf = (R *) MALLOC(sizeof(R) * (r - 1) * 2, BUFFERS);
Chris@42: 
Chris@42:      /* First, permute the input, storing in buf: */
Chris@42:      for (gpower = 1, k = 0; k < r - 1; ++k, gpower = MULMOD(gpower, g, r)) {
Chris@42: 	  R rA, iA;
Chris@42: 	  rA = ri[gpower * is];
Chris@42: 	  iA = ii[gpower * is];
Chris@42: 	  buf[2*k] = rA; buf[2*k + 1] = iA;
Chris@42:      }
Chris@42:      /* gpower == g^(r-1) mod r == 1 */;
Chris@42: 
Chris@42: 
Chris@42:      /* compute DFT of buf, storing in output (except DC): */
Chris@42:      {
Chris@42: 	    plan_dft *cld = (plan_dft *) ego->cld1;
Chris@42: 	    cld->apply(ego->cld1, buf, buf+1, ro+os, io+os);
Chris@42:      }
Chris@42: 
Chris@42:      /* set output DC component: */
Chris@42:      {
Chris@42: 	  ro[0] = r0 + ro[os];
Chris@42: 	  io[0] = i0 + io[os];
Chris@42:      }
Chris@42: 
Chris@42:      /* now, multiply by omega: */
Chris@42:      {
Chris@42: 	  const R *omega = ego->omega;
Chris@42: 	  for (k = 0; k < r - 1; ++k) {
Chris@42: 	       E rB, iB, rW, iW;
Chris@42: 	       rW = omega[2*k];
Chris@42: 	       iW = omega[2*k+1];
Chris@42: 	       rB = ro[(k+1)*os];
Chris@42: 	       iB = io[(k+1)*os];
Chris@42: 	       ro[(k+1)*os] = rW * rB - iW * iB;
Chris@42: 	       io[(k+1)*os] = -(rW * iB + iW * rB);
Chris@42: 	  }
Chris@42:      }
Chris@42:      
Chris@42:      /* this will add input[0] to all of the outputs after the ifft */
Chris@42:      ro[os] += r0;
Chris@42:      io[os] -= i0;
Chris@42: 
Chris@42:      /* inverse FFT: */
Chris@42:      {
Chris@42: 	    plan_dft *cld = (plan_dft *) ego->cld2;
Chris@42: 	    cld->apply(ego->cld2, ro+os, io+os, buf, buf+1);
Chris@42:      }
Chris@42:      
Chris@42:      /* finally, do inverse permutation to unshuffle the output: */
Chris@42:      {
Chris@42: 	  INT ginv = ego->ginv;
Chris@42: 	  gpower = 1;
Chris@42: 	  for (k = 0; k < r - 1; ++k, gpower = MULMOD(gpower, ginv, r)) {
Chris@42: 	       ro[gpower * os] = buf[2*k];
Chris@42: 	       io[gpower * os] = -buf[2*k+1];
Chris@42: 	  }
Chris@42: 	  A(gpower == 1);
Chris@42:      }
Chris@42: 
Chris@42: 
Chris@42:      X(ifree)(buf);
Chris@42: }
Chris@42: 
Chris@42: /***************************************************************************/
Chris@42: 
Chris@42: static void awake(plan *ego_, enum wakefulness wakefulness)
Chris@42: {
Chris@42:      P *ego = (P *) ego_;
Chris@42: 
Chris@42:      X(plan_awake)(ego->cld1, wakefulness);
Chris@42:      X(plan_awake)(ego->cld2, wakefulness);
Chris@42:      X(plan_awake)(ego->cld_omega, wakefulness);
Chris@42: 
Chris@42:      switch (wakefulness) {
Chris@42: 	 case SLEEPY:
Chris@42: 	      free_omega(ego->omega);
Chris@42: 	      ego->omega = 0;
Chris@42: 	      break;
Chris@42: 	 default:
Chris@42: 	      ego->g = X(find_generator)(ego->n);
Chris@42: 	      ego->ginv = X(power_mod)(ego->g, ego->n - 2, ego->n);
Chris@42: 	      A(MULMOD(ego->g, ego->ginv, ego->n) == 1);
Chris@42: 
Chris@42: 	      ego->omega = mkomega(wakefulness,
Chris@42: 				   ego->cld_omega, ego->n, ego->ginv);
Chris@42: 	      break;
Chris@42:      }
Chris@42: }
Chris@42: 
Chris@42: static void destroy(plan *ego_)
Chris@42: {
Chris@42:      P *ego = (P *) ego_;
Chris@42:      X(plan_destroy_internal)(ego->cld_omega);
Chris@42:      X(plan_destroy_internal)(ego->cld2);
Chris@42:      X(plan_destroy_internal)(ego->cld1);
Chris@42: }
Chris@42: 
Chris@42: static void print(const plan *ego_, printer *p)
Chris@42: {
Chris@42:      const P *ego = (const P *)ego_;
Chris@42:      p->print(p, "(dft-rader-%D%ois=%oos=%(%p%)",
Chris@42:               ego->n, ego->is, ego->os, ego->cld1);
Chris@42:      if (ego->cld2 != ego->cld1)
Chris@42:           p->print(p, "%(%p%)", ego->cld2);
Chris@42:      if (ego->cld_omega != ego->cld1 && ego->cld_omega != ego->cld2)
Chris@42:           p->print(p, "%(%p%)", ego->cld_omega);
Chris@42:      p->putchr(p, ')');
Chris@42: }
Chris@42: 
Chris@42: static int applicable(const solver *ego_, const problem *p_,
Chris@42: 		      const planner *plnr)
Chris@42: {
Chris@42:      const problem_dft *p = (const problem_dft *) p_;
Chris@42:      UNUSED(ego_);
Chris@42:      return (1
Chris@42: 	     && p->sz->rnk == 1
Chris@42: 	     && p->vecsz->rnk == 0
Chris@42: 	     && CIMPLIES(NO_SLOWP(plnr), p->sz->dims[0].n > RADER_MAX_SLOW)
Chris@42: 	     && X(is_prime)(p->sz->dims[0].n)
Chris@42: 
Chris@42: 	     /* proclaim the solver SLOW if p-1 is not easily factorizable.
Chris@42: 		Bluestein should take care of this case. */
Chris@42: 	     && CIMPLIES(NO_SLOWP(plnr), X(factors_into_small_primes)(p->sz->dims[0].n - 1))
Chris@42: 	  );
Chris@42: }
Chris@42: 
Chris@42: static int mkP(P *pln, INT n, INT is, INT os, R *ro, R *io,
Chris@42: 	       planner *plnr)
Chris@42: {
Chris@42:      plan *cld1 = (plan *) 0;
Chris@42:      plan *cld2 = (plan *) 0;
Chris@42:      plan *cld_omega = (plan *) 0;
Chris@42:      R *buf = (R *) 0;
Chris@42: 
Chris@42:      /* initial allocation for the purpose of planning */
Chris@42:      buf = (R *) MALLOC(sizeof(R) * (n - 1) * 2, BUFFERS);
Chris@42: 
Chris@42:      cld1 = X(mkplan_f_d)(plnr, 
Chris@42: 			  X(mkproblem_dft_d)(X(mktensor_1d)(n - 1, 2, os),
Chris@42: 					     X(mktensor_1d)(1, 0, 0),
Chris@42: 					     buf, buf + 1, ro + os, io + os),
Chris@42: 			  NO_SLOW, 0, 0);
Chris@42:      if (!cld1) goto nada;
Chris@42: 
Chris@42:      cld2 = X(mkplan_f_d)(plnr, 
Chris@42: 			  X(mkproblem_dft_d)(X(mktensor_1d)(n - 1, os, 2),
Chris@42: 					     X(mktensor_1d)(1, 0, 0),
Chris@42: 					     ro + os, io + os, buf, buf + 1),
Chris@42: 			  NO_SLOW, 0, 0);
Chris@42: 
Chris@42:      if (!cld2) goto nada;
Chris@42: 
Chris@42:      /* plan for omega array */
Chris@42:      cld_omega = X(mkplan_f_d)(plnr, 
Chris@42: 			       X(mkproblem_dft_d)(X(mktensor_1d)(n - 1, 2, 2),
Chris@42: 						  X(mktensor_1d)(1, 0, 0),
Chris@42: 						  buf, buf + 1, buf, buf + 1),
Chris@42: 			       NO_SLOW, ESTIMATE, 0);
Chris@42:      if (!cld_omega) goto nada;
Chris@42: 
Chris@42:      /* deallocate buffers; let awake() or apply() allocate them for real */
Chris@42:      X(ifree)(buf);
Chris@42:      buf = 0;
Chris@42: 
Chris@42:      pln->cld1 = cld1;
Chris@42:      pln->cld2 = cld2;
Chris@42:      pln->cld_omega = cld_omega;
Chris@42:      pln->omega = 0;
Chris@42:      pln->n = n;
Chris@42:      pln->is = is;
Chris@42:      pln->os = os;
Chris@42: 
Chris@42:      X(ops_add)(&cld1->ops, &cld2->ops, &pln->super.super.ops);
Chris@42:      pln->super.super.ops.other += (n - 1) * (4 * 2 + 6) + 6;
Chris@42:      pln->super.super.ops.add += (n - 1) * 2 + 4;
Chris@42:      pln->super.super.ops.mul += (n - 1) * 4;
Chris@42: 
Chris@42:      return 1;
Chris@42: 
Chris@42:  nada:
Chris@42:      X(ifree0)(buf);
Chris@42:      X(plan_destroy_internal)(cld_omega);
Chris@42:      X(plan_destroy_internal)(cld2);
Chris@42:      X(plan_destroy_internal)(cld1);
Chris@42:      return 0;
Chris@42: }
Chris@42: 
Chris@42: static plan *mkplan(const solver *ego, const problem *p_, planner *plnr)
Chris@42: {
Chris@42:      const problem_dft *p = (const problem_dft *) p_;
Chris@42:      P *pln;
Chris@42:      INT n;
Chris@42:      INT is, os;
Chris@42: 
Chris@42:      static const plan_adt padt = {
Chris@42: 	  X(dft_solve), awake, print, destroy
Chris@42:      };
Chris@42: 
Chris@42:      if (!applicable(ego, p_, plnr))
Chris@42: 	  return (plan *) 0;
Chris@42: 
Chris@42:      n = p->sz->dims[0].n;
Chris@42:      is = p->sz->dims[0].is;
Chris@42:      os = p->sz->dims[0].os;
Chris@42: 
Chris@42:      pln = MKPLAN_DFT(P, &padt, apply);
Chris@42:      if (!mkP(pln, n, is, os, p->ro, p->io, plnr)) {
Chris@42: 	  X(ifree)(pln);
Chris@42: 	  return (plan *) 0;
Chris@42:      }
Chris@42:      return &(pln->super.super);
Chris@42: }
Chris@42: 
Chris@42: static solver *mksolver(void)
Chris@42: {
Chris@42:      static const solver_adt sadt = { PROBLEM_DFT, mkplan, 0 };
Chris@42:      S *slv = MKSOLVER(S, &sadt);
Chris@42:      return &(slv->super);
Chris@42: }
Chris@42: 
Chris@42: void X(dft_rader_register)(planner *p)
Chris@42: {
Chris@42:      REGISTER_SOLVER(p, mksolver());
Chris@42: }