cannam@167: /* cannam@167: * Copyright (c) 2003, 2007-14 Matteo Frigo cannam@167: * Copyright (c) 2003, 2007-14 Massachusetts Institute of Technology cannam@167: * cannam@167: * This program is free software; you can redistribute it and/or modify cannam@167: * it under the terms of the GNU General Public License as published by cannam@167: * the Free Software Foundation; either version 2 of the License, or cannam@167: * (at your option) any later version. cannam@167: * cannam@167: * This program is distributed in the hope that it will be useful, cannam@167: * but WITHOUT ANY WARRANTY; without even the implied warranty of cannam@167: * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the cannam@167: * GNU General Public License for more details. cannam@167: * cannam@167: * You should have received a copy of the GNU General Public License cannam@167: * along with this program; if not, write to the Free Software cannam@167: * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA cannam@167: * cannam@167: */ cannam@167: cannam@167: cannam@167: /* Do an R{E,O}DFT11 problem via an R2HC problem of the same *odd* size, cannam@167: with some permutations and post-processing, as described in: cannam@167: cannam@167: S. C. Chan and K. L. Ho, "Fast algorithms for computing the cannam@167: discrete cosine transform," IEEE Trans. Circuits Systems II: cannam@167: Analog & Digital Sig. Proc. 39 (3), 185--190 (1992). cannam@167: cannam@167: (For even sizes, see reodft11e-radix2.c.) cannam@167: cannam@167: This algorithm is related to the 8 x n prime-factor-algorithm (PFA) cannam@167: decomposition of the size 8n "logical" DFT corresponding to the cannam@167: R{EO}DFT11. cannam@167: cannam@167: Aside from very confusing notation (several symbols are redefined cannam@167: from one line to the next), be aware that this paper has some cannam@167: errors. In particular, the signs are wrong in Eqs. (34-35). Also, cannam@167: Eqs. (36-37) should be simply C(k) = C(2k + 1 mod N), and similarly cannam@167: for S (or, equivalently, the second cases should have 2*N - 2*k - 1 cannam@167: instead of N - k - 1). Note also that in their definition of the cannam@167: DFT, similarly to FFTW's, the exponent's sign is -1, but they cannam@167: forgot to correspondingly multiply S (the sine terms) by -1. cannam@167: */ cannam@167: cannam@167: #include "reodft/reodft.h" cannam@167: cannam@167: typedef struct { cannam@167: solver super; cannam@167: } S; cannam@167: cannam@167: typedef struct { cannam@167: plan_rdft super; cannam@167: plan *cld; cannam@167: INT is, os; cannam@167: INT n; cannam@167: INT vl; cannam@167: INT ivs, ovs; cannam@167: rdft_kind kind; cannam@167: } P; cannam@167: cannam@167: static DK(SQRT2, +1.4142135623730950488016887242096980785696718753769); cannam@167: cannam@167: #define SGN_SET(x, i) ((i) % 2 ? -(x) : (x)) cannam@167: cannam@167: static void apply_re11(const plan *ego_, R *I, R *O) cannam@167: { cannam@167: const P *ego = (const P *) ego_; cannam@167: INT is = ego->is, os = ego->os; cannam@167: INT i, n = ego->n, n2 = n/2; cannam@167: INT iv, vl = ego->vl; cannam@167: INT ivs = ego->ivs, ovs = ego->ovs; cannam@167: R *buf; cannam@167: cannam@167: buf = (R *) MALLOC(sizeof(R) * n, BUFFERS); cannam@167: cannam@167: for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) { cannam@167: { cannam@167: INT m; cannam@167: for (i = 0, m = n2; m < n; ++i, m += 4) cannam@167: buf[i] = I[is * m]; cannam@167: for (; m < 2 * n; ++i, m += 4) cannam@167: buf[i] = -I[is * (2*n - m - 1)]; cannam@167: for (; m < 3 * n; ++i, m += 4) cannam@167: buf[i] = -I[is * (m - 2*n)]; cannam@167: for (; m < 4 * n; ++i, m += 4) cannam@167: buf[i] = I[is * (4*n - m - 1)]; cannam@167: m -= 4 * n; cannam@167: for (; i < n; ++i, m += 4) cannam@167: buf[i] = I[is * m]; cannam@167: } cannam@167: cannam@167: { /* child plan: R2HC of size n */ cannam@167: plan_rdft *cld = (plan_rdft *) ego->cld; cannam@167: cld->apply((plan *) cld, buf, buf); cannam@167: } cannam@167: cannam@167: /* FIXME: strength-reduce loop by 4 to eliminate ugly sgn_set? */ cannam@167: for (i = 0; i + i + 1 < n2; ++i) { cannam@167: INT k = i + i + 1; cannam@167: E c1, s1; cannam@167: E c2, s2; cannam@167: c1 = buf[k]; cannam@167: c2 = buf[k + 1]; cannam@167: s2 = buf[n - (k + 1)]; cannam@167: s1 = buf[n - k]; cannam@167: cannam@167: O[os * i] = SQRT2 * (SGN_SET(c1, (i+1)/2) + cannam@167: SGN_SET(s1, i/2)); cannam@167: O[os * (n - (i+1))] = SQRT2 * (SGN_SET(c1, (n-i)/2) - cannam@167: SGN_SET(s1, (n-(i+1))/2)); cannam@167: cannam@167: O[os * (n2 - (i+1))] = SQRT2 * (SGN_SET(c2, (n2-i)/2) - cannam@167: SGN_SET(s2, (n2-(i+1))/2)); cannam@167: O[os * (n2 + (i+1))] = SQRT2 * (SGN_SET(c2, (n2+i+2)/2) + cannam@167: SGN_SET(s2, (n2+(i+1))/2)); cannam@167: } cannam@167: if (i + i + 1 == n2) { cannam@167: E c, s; cannam@167: c = buf[n2]; cannam@167: s = buf[n - n2]; cannam@167: O[os * i] = SQRT2 * (SGN_SET(c, (i+1)/2) + cannam@167: SGN_SET(s, i/2)); cannam@167: O[os * (n - (i+1))] = SQRT2 * (SGN_SET(c, (i+2)/2) + cannam@167: SGN_SET(s, (i+1)/2)); cannam@167: } cannam@167: O[os * n2] = SQRT2 * SGN_SET(buf[0], (n2+1)/2); cannam@167: } cannam@167: cannam@167: X(ifree)(buf); cannam@167: } cannam@167: cannam@167: /* like for rodft01, rodft11 is obtained from redft11 by cannam@167: reversing the input and flipping the sign of every other output. */ cannam@167: static void apply_ro11(const plan *ego_, R *I, R *O) cannam@167: { cannam@167: const P *ego = (const P *) ego_; cannam@167: INT is = ego->is, os = ego->os; cannam@167: INT i, n = ego->n, n2 = n/2; cannam@167: INT iv, vl = ego->vl; cannam@167: INT ivs = ego->ivs, ovs = ego->ovs; cannam@167: R *buf; cannam@167: cannam@167: buf = (R *) MALLOC(sizeof(R) * n, BUFFERS); cannam@167: cannam@167: for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) { cannam@167: { cannam@167: INT m; cannam@167: for (i = 0, m = n2; m < n; ++i, m += 4) cannam@167: buf[i] = I[is * (n - 1 - m)]; cannam@167: for (; m < 2 * n; ++i, m += 4) cannam@167: buf[i] = -I[is * (m - n)]; cannam@167: for (; m < 3 * n; ++i, m += 4) cannam@167: buf[i] = -I[is * (3*n - 1 - m)]; cannam@167: for (; m < 4 * n; ++i, m += 4) cannam@167: buf[i] = I[is * (m - 3*n)]; cannam@167: m -= 4 * n; cannam@167: for (; i < n; ++i, m += 4) cannam@167: buf[i] = I[is * (n - 1 - m)]; cannam@167: } cannam@167: cannam@167: { /* child plan: R2HC of size n */ cannam@167: plan_rdft *cld = (plan_rdft *) ego->cld; cannam@167: cld->apply((plan *) cld, buf, buf); cannam@167: } cannam@167: cannam@167: /* FIXME: strength-reduce loop by 4 to eliminate ugly sgn_set? */ cannam@167: for (i = 0; i + i + 1 < n2; ++i) { cannam@167: INT k = i + i + 1; cannam@167: INT j; cannam@167: E c1, s1; cannam@167: E c2, s2; cannam@167: c1 = buf[k]; cannam@167: c2 = buf[k + 1]; cannam@167: s2 = buf[n - (k + 1)]; cannam@167: s1 = buf[n - k]; cannam@167: cannam@167: O[os * i] = SQRT2 * (SGN_SET(c1, (i+1)/2 + i) + cannam@167: SGN_SET(s1, i/2 + i)); cannam@167: O[os * (n - (i+1))] = SQRT2 * (SGN_SET(c1, (n-i)/2 + i) - cannam@167: SGN_SET(s1, (n-(i+1))/2 + i)); cannam@167: cannam@167: j = n2 - (i+1); cannam@167: O[os * j] = SQRT2 * (SGN_SET(c2, (n2-i)/2 + j) - cannam@167: SGN_SET(s2, (n2-(i+1))/2 + j)); cannam@167: O[os * (n2 + (i+1))] = SQRT2 * (SGN_SET(c2, (n2+i+2)/2 + j) + cannam@167: SGN_SET(s2, (n2+(i+1))/2 + j)); cannam@167: } cannam@167: if (i + i + 1 == n2) { cannam@167: E c, s; cannam@167: c = buf[n2]; cannam@167: s = buf[n - n2]; cannam@167: O[os * i] = SQRT2 * (SGN_SET(c, (i+1)/2 + i) + cannam@167: SGN_SET(s, i/2 + i)); cannam@167: O[os * (n - (i+1))] = SQRT2 * (SGN_SET(c, (i+2)/2 + i) + cannam@167: SGN_SET(s, (i+1)/2 + i)); cannam@167: } cannam@167: O[os * n2] = SQRT2 * SGN_SET(buf[0], (n2+1)/2 + n2); cannam@167: } cannam@167: cannam@167: X(ifree)(buf); cannam@167: } cannam@167: cannam@167: static void awake(plan *ego_, enum wakefulness wakefulness) cannam@167: { cannam@167: P *ego = (P *) ego_; cannam@167: X(plan_awake)(ego->cld, wakefulness); cannam@167: } cannam@167: cannam@167: static void destroy(plan *ego_) cannam@167: { cannam@167: P *ego = (P *) ego_; cannam@167: X(plan_destroy_internal)(ego->cld); cannam@167: } cannam@167: cannam@167: static void print(const plan *ego_, printer *p) cannam@167: { cannam@167: const P *ego = (const P *) ego_; cannam@167: p->print(p, "(%se-r2hc-odd-%D%v%(%p%))", cannam@167: X(rdft_kind_str)(ego->kind), ego->n, ego->vl, ego->cld); cannam@167: } cannam@167: cannam@167: static int applicable0(const solver *ego_, const problem *p_) cannam@167: { cannam@167: const problem_rdft *p = (const problem_rdft *) p_; cannam@167: UNUSED(ego_); cannam@167: cannam@167: return (1 cannam@167: && p->sz->rnk == 1 cannam@167: && p->vecsz->rnk <= 1 cannam@167: && p->sz->dims[0].n % 2 == 1 cannam@167: && (p->kind[0] == REDFT11 || p->kind[0] == RODFT11) cannam@167: ); cannam@167: } cannam@167: cannam@167: static int applicable(const solver *ego, const problem *p, const planner *plnr) cannam@167: { cannam@167: return (!NO_SLOWP(plnr) && applicable0(ego, p)); cannam@167: } cannam@167: cannam@167: static plan *mkplan(const solver *ego_, const problem *p_, planner *plnr) cannam@167: { cannam@167: P *pln; cannam@167: const problem_rdft *p; cannam@167: plan *cld; cannam@167: R *buf; cannam@167: INT n; cannam@167: opcnt ops; cannam@167: cannam@167: static const plan_adt padt = { cannam@167: X(rdft_solve), awake, print, destroy cannam@167: }; cannam@167: cannam@167: if (!applicable(ego_, p_, plnr)) cannam@167: return (plan *)0; cannam@167: cannam@167: p = (const problem_rdft *) p_; cannam@167: cannam@167: n = p->sz->dims[0].n; cannam@167: buf = (R *) MALLOC(sizeof(R) * n, BUFFERS); cannam@167: cannam@167: cld = X(mkplan_d)(plnr, X(mkproblem_rdft_1_d)(X(mktensor_1d)(n, 1, 1), cannam@167: X(mktensor_0d)(), cannam@167: buf, buf, R2HC)); cannam@167: X(ifree)(buf); cannam@167: if (!cld) cannam@167: return (plan *)0; cannam@167: cannam@167: pln = MKPLAN_RDFT(P, &padt, p->kind[0]==REDFT11 ? apply_re11:apply_ro11); cannam@167: pln->n = n; cannam@167: pln->is = p->sz->dims[0].is; cannam@167: pln->os = p->sz->dims[0].os; cannam@167: pln->cld = cld; cannam@167: pln->kind = p->kind[0]; cannam@167: cannam@167: X(tensor_tornk1)(p->vecsz, &pln->vl, &pln->ivs, &pln->ovs); cannam@167: cannam@167: X(ops_zero)(&ops); cannam@167: ops.add = n - 1; cannam@167: ops.mul = n; cannam@167: ops.other = 4*n; cannam@167: cannam@167: X(ops_zero)(&pln->super.super.ops); cannam@167: X(ops_madd2)(pln->vl, &ops, &pln->super.super.ops); cannam@167: X(ops_madd2)(pln->vl, &cld->ops, &pln->super.super.ops); cannam@167: cannam@167: return &(pln->super.super); cannam@167: } cannam@167: cannam@167: /* constructor */ cannam@167: static solver *mksolver(void) cannam@167: { cannam@167: static const solver_adt sadt = { PROBLEM_RDFT, mkplan, 0 }; cannam@167: S *slv = MKSOLVER(S, &sadt); cannam@167: return &(slv->super); cannam@167: } cannam@167: cannam@167: void X(reodft11e_r2hc_odd_register)(planner *p) cannam@167: { cannam@167: REGISTER_SOLVER(p, mksolver()); cannam@167: }