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: /* Do an R{E,O}DFT11 problem via an R2HC problem of the same *odd* size, cannam@127: with some permutations and post-processing, as described in: cannam@127: cannam@127: S. C. Chan and K. L. Ho, "Fast algorithms for computing the cannam@127: discrete cosine transform," IEEE Trans. Circuits Systems II: cannam@127: Analog & Digital Sig. Proc. 39 (3), 185--190 (1992). cannam@127: cannam@127: (For even sizes, see reodft11e-radix2.c.) cannam@127: cannam@127: This algorithm is related to the 8 x n prime-factor-algorithm (PFA) cannam@127: decomposition of the size 8n "logical" DFT corresponding to the cannam@127: R{EO}DFT11. cannam@127: cannam@127: Aside from very confusing notation (several symbols are redefined cannam@127: from one line to the next), be aware that this paper has some cannam@127: errors. In particular, the signs are wrong in Eqs. (34-35). Also, cannam@127: Eqs. (36-37) should be simply C(k) = C(2k + 1 mod N), and similarly cannam@127: for S (or, equivalently, the second cases should have 2*N - 2*k - 1 cannam@127: instead of N - k - 1). Note also that in their definition of the cannam@127: DFT, similarly to FFTW's, the exponent's sign is -1, but they cannam@127: forgot to correspondingly multiply S (the sine terms) by -1. cannam@127: */ cannam@127: cannam@127: #include "reodft.h" cannam@127: cannam@127: typedef struct { cannam@127: solver super; cannam@127: } S; cannam@127: cannam@127: typedef struct { cannam@127: plan_rdft super; cannam@127: plan *cld; cannam@127: INT is, os; cannam@127: INT n; cannam@127: INT vl; cannam@127: INT ivs, ovs; cannam@127: rdft_kind kind; cannam@127: } P; cannam@127: cannam@127: static DK(SQRT2, +1.4142135623730950488016887242096980785696718753769); cannam@127: cannam@127: #define SGN_SET(x, i) ((i) % 2 ? -(x) : (x)) cannam@127: cannam@127: static void apply_re11(const plan *ego_, R *I, R *O) cannam@127: { cannam@127: const P *ego = (const P *) ego_; cannam@127: INT is = ego->is, os = ego->os; cannam@127: INT i, n = ego->n, n2 = n/2; cannam@127: INT iv, vl = ego->vl; cannam@127: INT ivs = ego->ivs, ovs = ego->ovs; cannam@127: R *buf; cannam@127: cannam@127: buf = (R *) MALLOC(sizeof(R) * n, BUFFERS); cannam@127: cannam@127: for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) { cannam@127: { cannam@127: INT m; cannam@127: for (i = 0, m = n2; m < n; ++i, m += 4) cannam@127: buf[i] = I[is * m]; cannam@127: for (; m < 2 * n; ++i, m += 4) cannam@127: buf[i] = -I[is * (2*n - m - 1)]; cannam@127: for (; m < 3 * n; ++i, m += 4) cannam@127: buf[i] = -I[is * (m - 2*n)]; cannam@127: for (; m < 4 * n; ++i, m += 4) cannam@127: buf[i] = I[is * (4*n - m - 1)]; cannam@127: m -= 4 * n; cannam@127: for (; i < n; ++i, m += 4) cannam@127: buf[i] = I[is * m]; cannam@127: } cannam@127: cannam@127: { /* child plan: R2HC of size n */ cannam@127: plan_rdft *cld = (plan_rdft *) ego->cld; cannam@127: cld->apply((plan *) cld, buf, buf); cannam@127: } cannam@127: cannam@127: /* FIXME: strength-reduce loop by 4 to eliminate ugly sgn_set? */ cannam@127: for (i = 0; i + i + 1 < n2; ++i) { cannam@127: INT k = i + i + 1; cannam@127: E c1, s1; cannam@127: E c2, s2; cannam@127: c1 = buf[k]; cannam@127: c2 = buf[k + 1]; cannam@127: s2 = buf[n - (k + 1)]; cannam@127: s1 = buf[n - k]; cannam@127: cannam@127: O[os * i] = SQRT2 * (SGN_SET(c1, (i+1)/2) + cannam@127: SGN_SET(s1, i/2)); cannam@127: O[os * (n - (i+1))] = SQRT2 * (SGN_SET(c1, (n-i)/2) - cannam@127: SGN_SET(s1, (n-(i+1))/2)); cannam@127: cannam@127: O[os * (n2 - (i+1))] = SQRT2 * (SGN_SET(c2, (n2-i)/2) - cannam@127: SGN_SET(s2, (n2-(i+1))/2)); cannam@127: O[os * (n2 + (i+1))] = SQRT2 * (SGN_SET(c2, (n2+i+2)/2) + cannam@127: SGN_SET(s2, (n2+(i+1))/2)); cannam@127: } cannam@127: if (i + i + 1 == n2) { cannam@127: E c, s; cannam@127: c = buf[n2]; cannam@127: s = buf[n - n2]; cannam@127: O[os * i] = SQRT2 * (SGN_SET(c, (i+1)/2) + cannam@127: SGN_SET(s, i/2)); cannam@127: O[os * (n - (i+1))] = SQRT2 * (SGN_SET(c, (i+2)/2) + cannam@127: SGN_SET(s, (i+1)/2)); cannam@127: } cannam@127: O[os * n2] = SQRT2 * SGN_SET(buf[0], (n2+1)/2); cannam@127: } cannam@127: cannam@127: X(ifree)(buf); cannam@127: } cannam@127: cannam@127: /* like for rodft01, rodft11 is obtained from redft11 by cannam@127: reversing the input and flipping the sign of every other output. */ cannam@127: static void apply_ro11(const plan *ego_, R *I, R *O) cannam@127: { cannam@127: const P *ego = (const P *) ego_; cannam@127: INT is = ego->is, os = ego->os; cannam@127: INT i, n = ego->n, n2 = n/2; cannam@127: INT iv, vl = ego->vl; cannam@127: INT ivs = ego->ivs, ovs = ego->ovs; cannam@127: R *buf; cannam@127: cannam@127: buf = (R *) MALLOC(sizeof(R) * n, BUFFERS); cannam@127: cannam@127: for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) { cannam@127: { cannam@127: INT m; cannam@127: for (i = 0, m = n2; m < n; ++i, m += 4) cannam@127: buf[i] = I[is * (n - 1 - m)]; cannam@127: for (; m < 2 * n; ++i, m += 4) cannam@127: buf[i] = -I[is * (m - n)]; cannam@127: for (; m < 3 * n; ++i, m += 4) cannam@127: buf[i] = -I[is * (3*n - 1 - m)]; cannam@127: for (; m < 4 * n; ++i, m += 4) cannam@127: buf[i] = I[is * (m - 3*n)]; cannam@127: m -= 4 * n; cannam@127: for (; i < n; ++i, m += 4) cannam@127: buf[i] = I[is * (n - 1 - m)]; cannam@127: } cannam@127: cannam@127: { /* child plan: R2HC of size n */ cannam@127: plan_rdft *cld = (plan_rdft *) ego->cld; cannam@127: cld->apply((plan *) cld, buf, buf); cannam@127: } cannam@127: cannam@127: /* FIXME: strength-reduce loop by 4 to eliminate ugly sgn_set? */ cannam@127: for (i = 0; i + i + 1 < n2; ++i) { cannam@127: INT k = i + i + 1; cannam@127: INT j; cannam@127: E c1, s1; cannam@127: E c2, s2; cannam@127: c1 = buf[k]; cannam@127: c2 = buf[k + 1]; cannam@127: s2 = buf[n - (k + 1)]; cannam@127: s1 = buf[n - k]; cannam@127: cannam@127: O[os * i] = SQRT2 * (SGN_SET(c1, (i+1)/2 + i) + cannam@127: SGN_SET(s1, i/2 + i)); cannam@127: O[os * (n - (i+1))] = SQRT2 * (SGN_SET(c1, (n-i)/2 + i) - cannam@127: SGN_SET(s1, (n-(i+1))/2 + i)); cannam@127: cannam@127: j = n2 - (i+1); cannam@127: O[os * j] = SQRT2 * (SGN_SET(c2, (n2-i)/2 + j) - cannam@127: SGN_SET(s2, (n2-(i+1))/2 + j)); cannam@127: O[os * (n2 + (i+1))] = SQRT2 * (SGN_SET(c2, (n2+i+2)/2 + j) + cannam@127: SGN_SET(s2, (n2+(i+1))/2 + j)); cannam@127: } cannam@127: if (i + i + 1 == n2) { cannam@127: E c, s; cannam@127: c = buf[n2]; cannam@127: s = buf[n - n2]; cannam@127: O[os * i] = SQRT2 * (SGN_SET(c, (i+1)/2 + i) + cannam@127: SGN_SET(s, i/2 + i)); cannam@127: O[os * (n - (i+1))] = SQRT2 * (SGN_SET(c, (i+2)/2 + i) + cannam@127: SGN_SET(s, (i+1)/2 + i)); cannam@127: } cannam@127: O[os * n2] = SQRT2 * SGN_SET(buf[0], (n2+1)/2 + n2); cannam@127: } cannam@127: cannam@127: X(ifree)(buf); cannam@127: } cannam@127: cannam@127: static void awake(plan *ego_, enum wakefulness wakefulness) cannam@127: { cannam@127: P *ego = (P *) ego_; cannam@127: X(plan_awake)(ego->cld, wakefulness); cannam@127: } cannam@127: cannam@127: static void destroy(plan *ego_) cannam@127: { cannam@127: P *ego = (P *) ego_; cannam@127: X(plan_destroy_internal)(ego->cld); cannam@127: } cannam@127: cannam@127: static void print(const plan *ego_, printer *p) cannam@127: { cannam@127: const P *ego = (const P *) ego_; cannam@127: p->print(p, "(%se-r2hc-odd-%D%v%(%p%))", cannam@127: X(rdft_kind_str)(ego->kind), ego->n, ego->vl, ego->cld); cannam@127: } cannam@127: cannam@127: static int applicable0(const solver *ego_, const problem *p_) cannam@127: { cannam@127: const problem_rdft *p = (const problem_rdft *) p_; cannam@127: UNUSED(ego_); cannam@127: cannam@127: return (1 cannam@127: && p->sz->rnk == 1 cannam@127: && p->vecsz->rnk <= 1 cannam@127: && p->sz->dims[0].n % 2 == 1 cannam@127: && (p->kind[0] == REDFT11 || p->kind[0] == RODFT11) cannam@127: ); cannam@127: } cannam@127: cannam@127: static int applicable(const solver *ego, const problem *p, const planner *plnr) cannam@127: { cannam@127: return (!NO_SLOWP(plnr) && applicable0(ego, p)); cannam@127: } cannam@127: cannam@127: static plan *mkplan(const solver *ego_, const problem *p_, planner *plnr) cannam@127: { cannam@127: P *pln; cannam@127: const problem_rdft *p; cannam@127: plan *cld; cannam@127: R *buf; cannam@127: INT n; cannam@127: opcnt ops; cannam@127: cannam@127: static const plan_adt padt = { cannam@127: X(rdft_solve), awake, print, destroy cannam@127: }; cannam@127: cannam@127: if (!applicable(ego_, p_, plnr)) cannam@127: return (plan *)0; cannam@127: cannam@127: p = (const problem_rdft *) p_; cannam@127: cannam@127: n = p->sz->dims[0].n; cannam@127: buf = (R *) MALLOC(sizeof(R) * n, BUFFERS); cannam@127: cannam@127: cld = X(mkplan_d)(plnr, X(mkproblem_rdft_1_d)(X(mktensor_1d)(n, 1, 1), cannam@127: X(mktensor_0d)(), cannam@127: buf, buf, R2HC)); cannam@127: X(ifree)(buf); cannam@127: if (!cld) cannam@127: return (plan *)0; cannam@127: cannam@127: pln = MKPLAN_RDFT(P, &padt, p->kind[0]==REDFT11 ? apply_re11:apply_ro11); cannam@127: pln->n = n; cannam@127: pln->is = p->sz->dims[0].is; cannam@127: pln->os = p->sz->dims[0].os; cannam@127: pln->cld = cld; cannam@127: pln->kind = p->kind[0]; cannam@127: cannam@127: X(tensor_tornk1)(p->vecsz, &pln->vl, &pln->ivs, &pln->ovs); cannam@127: cannam@127: X(ops_zero)(&ops); cannam@127: ops.add = n - 1; cannam@127: ops.mul = n; cannam@127: ops.other = 4*n; cannam@127: cannam@127: X(ops_zero)(&pln->super.super.ops); cannam@127: X(ops_madd2)(pln->vl, &ops, &pln->super.super.ops); cannam@127: X(ops_madd2)(pln->vl, &cld->ops, &pln->super.super.ops); cannam@127: cannam@127: return &(pln->super.super); cannam@127: } cannam@127: cannam@127: /* constructor */ cannam@127: static solver *mksolver(void) cannam@127: { cannam@127: static const solver_adt sadt = { PROBLEM_RDFT, mkplan, 0 }; cannam@127: S *slv = MKSOLVER(S, &sadt); cannam@127: return &(slv->super); cannam@127: } cannam@127: cannam@127: void X(reodft11e_r2hc_odd_register)(planner *p) cannam@127: { cannam@127: REGISTER_SOLVER(p, mksolver()); cannam@127: }