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pffft_priv_impl.h
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/* Copyright (c) 2013 Julien Pommier ( [email protected] )
Copyright (c) 2020 Hayati Ayguen ( [email protected] )
Copyright (c) 2020 Dario Mambro ( [email protected] )
Based on original fortran 77 code from FFTPACKv4 from NETLIB
(http://www.netlib.org/fftpack), authored by Dr Paul Swarztrauber
of NCAR, in 1985.
As confirmed by the NCAR fftpack software curators, the following
FFTPACKv5 license applies to FFTPACKv4 sources. My changes are
released under the same terms.
FFTPACK license:
http://www.cisl.ucar.edu/css/software/fftpack5/ftpk.html
Copyright (c) 2004 the University Corporation for Atmospheric
Research ("UCAR"). All rights reserved. Developed by NCAR's
Computational and Information Systems Laboratory, UCAR,
www.cisl.ucar.edu.
Redistribution and use of the Software in source and binary forms,
with or without modification, is permitted provided that the
following conditions are met:
- Neither the names of NCAR's Computational and Information Systems
Laboratory, the University Corporation for Atmospheric Research,
nor the names of its sponsors or contributors may be used to
endorse or promote products derived from this Software without
specific prior written permission.
- Redistributions of source code must retain the above copyright
notices, this list of conditions, and the disclaimer below.
- Redistributions in binary form must reproduce the above copyright
notice, this list of conditions, and the disclaimer below in the
documentation and/or other materials provided with the
distribution.
THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE CONTRIBUTORS OR COPYRIGHT
HOLDERS BE LIABLE FOR ANY CLAIM, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY, WHETHER IN AN
ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE
SOFTWARE.
PFFFT : a Pretty Fast FFT.
This file is largerly based on the original FFTPACK implementation, modified in
order to take advantage of SIMD instructions of modern CPUs.
*/
/* this file requires architecture specific preprocessor definitions
* it's only for library internal use
*/
/* define own constants required to turn off g++ extensions .. */
#ifndef M_PI
#define M_PI 3.14159265358979323846 /* pi */
#endif
#ifndef M_SQRT2
#define M_SQRT2 1.41421356237309504880 /* sqrt(2) */
#endif
int FUNC_SIMD_SIZE() { return SIMD_SZ; }
const char * FUNC_SIMD_ARCH() { return VARCH; }
/*
passf2 and passb2 has been merged here, fsign = -1 for passf2, +1 for passb2
*/
static NEVER_INLINE(void) passf2_ps(int ido, int l1, const v4sf *cc, v4sf *ch, const float *wa1, float fsign) {
int k, i;
int l1ido = l1*ido;
if (ido <= 2) {
for (k=0; k < l1ido; k += ido, ch += ido, cc+= 2*ido) {
ch[0] = VADD(cc[0], cc[ido+0]);
ch[l1ido] = VSUB(cc[0], cc[ido+0]);
ch[1] = VADD(cc[1], cc[ido+1]);
ch[l1ido + 1] = VSUB(cc[1], cc[ido+1]);
}
} else {
for (k=0; k < l1ido; k += ido, ch += ido, cc += 2*ido) {
for (i=0; i<ido-1; i+=2) {
v4sf tr2 = VSUB(cc[i+0], cc[i+ido+0]);
v4sf ti2 = VSUB(cc[i+1], cc[i+ido+1]);
v4sf wr = LD_PS1(wa1[i]), wi = VMUL(LD_PS1(fsign), LD_PS1(wa1[i+1]));
ch[i] = VADD(cc[i+0], cc[i+ido+0]);
ch[i+1] = VADD(cc[i+1], cc[i+ido+1]);
VCPLXMUL(tr2, ti2, wr, wi);
ch[i+l1ido] = tr2;
ch[i+l1ido+1] = ti2;
}
}
}
}
/*
passf3 and passb3 has been merged here, fsign = -1 for passf3, +1 for passb3
*/
static NEVER_INLINE(void) passf3_ps(int ido, int l1, const v4sf *cc, v4sf *ch,
const float *wa1, const float *wa2, float fsign) {
static const float taur = -0.5f;
float taui = 0.866025403784439f*fsign;
int i, k;
v4sf tr2, ti2, cr2, ci2, cr3, ci3, dr2, di2, dr3, di3;
int l1ido = l1*ido;
float wr1, wi1, wr2, wi2;
assert(ido > 2);
for (k=0; k< l1ido; k += ido, cc+= 3*ido, ch +=ido) {
for (i=0; i<ido-1; i+=2) {
tr2 = VADD(cc[i+ido], cc[i+2*ido]);
cr2 = VADD(cc[i], SVMUL(taur,tr2));
ch[i] = VADD(cc[i], tr2);
ti2 = VADD(cc[i+ido+1], cc[i+2*ido+1]);
ci2 = VADD(cc[i +1], SVMUL(taur,ti2));
ch[i+1] = VADD(cc[i+1], ti2);
cr3 = SVMUL(taui, VSUB(cc[i+ido], cc[i+2*ido]));
ci3 = SVMUL(taui, VSUB(cc[i+ido+1], cc[i+2*ido+1]));
dr2 = VSUB(cr2, ci3);
dr3 = VADD(cr2, ci3);
di2 = VADD(ci2, cr3);
di3 = VSUB(ci2, cr3);
wr1=wa1[i], wi1=fsign*wa1[i+1], wr2=wa2[i], wi2=fsign*wa2[i+1];
VCPLXMUL(dr2, di2, LD_PS1(wr1), LD_PS1(wi1));
ch[i+l1ido] = dr2;
ch[i+l1ido + 1] = di2;
VCPLXMUL(dr3, di3, LD_PS1(wr2), LD_PS1(wi2));
ch[i+2*l1ido] = dr3;
ch[i+2*l1ido+1] = di3;
}
}
} /* passf3 */
static NEVER_INLINE(void) passf4_ps(int ido, int l1, const v4sf *cc, v4sf *ch,
const float *wa1, const float *wa2, const float *wa3, float fsign) {
/* isign == -1 for forward transform and +1 for backward transform */
int i, k;
v4sf ci2, ci3, ci4, cr2, cr3, cr4, ti1, ti2, ti3, ti4, tr1, tr2, tr3, tr4;
int l1ido = l1*ido;
if (ido == 2) {
for (k=0; k < l1ido; k += ido, ch += ido, cc += 4*ido) {
tr1 = VSUB(cc[0], cc[2*ido + 0]);
tr2 = VADD(cc[0], cc[2*ido + 0]);
ti1 = VSUB(cc[1], cc[2*ido + 1]);
ti2 = VADD(cc[1], cc[2*ido + 1]);
ti4 = VMUL(VSUB(cc[1*ido + 0], cc[3*ido + 0]), LD_PS1(fsign));
tr4 = VMUL(VSUB(cc[3*ido + 1], cc[1*ido + 1]), LD_PS1(fsign));
tr3 = VADD(cc[ido + 0], cc[3*ido + 0]);
ti3 = VADD(cc[ido + 1], cc[3*ido + 1]);
ch[0*l1ido + 0] = VADD(tr2, tr3);
ch[0*l1ido + 1] = VADD(ti2, ti3);
ch[1*l1ido + 0] = VADD(tr1, tr4);
ch[1*l1ido + 1] = VADD(ti1, ti4);
ch[2*l1ido + 0] = VSUB(tr2, tr3);
ch[2*l1ido + 1] = VSUB(ti2, ti3);
ch[3*l1ido + 0] = VSUB(tr1, tr4);
ch[3*l1ido + 1] = VSUB(ti1, ti4);
}
} else {
for (k=0; k < l1ido; k += ido, ch+=ido, cc += 4*ido) {
for (i=0; i<ido-1; i+=2) {
float wr1, wi1, wr2, wi2, wr3, wi3;
tr1 = VSUB(cc[i + 0], cc[i + 2*ido + 0]);
tr2 = VADD(cc[i + 0], cc[i + 2*ido + 0]);
ti1 = VSUB(cc[i + 1], cc[i + 2*ido + 1]);
ti2 = VADD(cc[i + 1], cc[i + 2*ido + 1]);
tr4 = VMUL(VSUB(cc[i + 3*ido + 1], cc[i + 1*ido + 1]), LD_PS1(fsign));
ti4 = VMUL(VSUB(cc[i + 1*ido + 0], cc[i + 3*ido + 0]), LD_PS1(fsign));
tr3 = VADD(cc[i + ido + 0], cc[i + 3*ido + 0]);
ti3 = VADD(cc[i + ido + 1], cc[i + 3*ido + 1]);
ch[i] = VADD(tr2, tr3);
cr3 = VSUB(tr2, tr3);
ch[i + 1] = VADD(ti2, ti3);
ci3 = VSUB(ti2, ti3);
cr2 = VADD(tr1, tr4);
cr4 = VSUB(tr1, tr4);
ci2 = VADD(ti1, ti4);
ci4 = VSUB(ti1, ti4);
wr1=wa1[i], wi1=fsign*wa1[i+1];
VCPLXMUL(cr2, ci2, LD_PS1(wr1), LD_PS1(wi1));
wr2=wa2[i], wi2=fsign*wa2[i+1];
ch[i + l1ido] = cr2;
ch[i + l1ido + 1] = ci2;
VCPLXMUL(cr3, ci3, LD_PS1(wr2), LD_PS1(wi2));
wr3=wa3[i], wi3=fsign*wa3[i+1];
ch[i + 2*l1ido] = cr3;
ch[i + 2*l1ido + 1] = ci3;
VCPLXMUL(cr4, ci4, LD_PS1(wr3), LD_PS1(wi3));
ch[i + 3*l1ido] = cr4;
ch[i + 3*l1ido + 1] = ci4;
}
}
}
} /* passf4 */
/*
passf5 and passb5 has been merged here, fsign = -1 for passf5, +1 for passb5
*/
static NEVER_INLINE(void) passf5_ps(int ido, int l1, const v4sf *cc, v4sf *ch,
const float *wa1, const float *wa2,
const float *wa3, const float *wa4, float fsign) {
static const float tr11 = .309016994374947f;
const float ti11 = .951056516295154f*fsign;
static const float tr12 = -.809016994374947f;
const float ti12 = .587785252292473f*fsign;
/* Local variables */
int i, k;
v4sf ci2, ci3, ci4, ci5, di3, di4, di5, di2, cr2, cr3, cr5, cr4, ti2, ti3,
ti4, ti5, dr3, dr4, dr5, dr2, tr2, tr3, tr4, tr5;
float wr1, wi1, wr2, wi2, wr3, wi3, wr4, wi4;
#define cc_ref(a_1,a_2) cc[(a_2-1)*ido + a_1 + 1]
#define ch_ref(a_1,a_3) ch[(a_3-1)*l1*ido + a_1 + 1]
assert(ido > 2);
for (k = 0; k < l1; ++k, cc += 5*ido, ch += ido) {
for (i = 0; i < ido-1; i += 2) {
ti5 = VSUB(cc_ref(i , 2), cc_ref(i , 5));
ti2 = VADD(cc_ref(i , 2), cc_ref(i , 5));
ti4 = VSUB(cc_ref(i , 3), cc_ref(i , 4));
ti3 = VADD(cc_ref(i , 3), cc_ref(i , 4));
tr5 = VSUB(cc_ref(i-1, 2), cc_ref(i-1, 5));
tr2 = VADD(cc_ref(i-1, 2), cc_ref(i-1, 5));
tr4 = VSUB(cc_ref(i-1, 3), cc_ref(i-1, 4));
tr3 = VADD(cc_ref(i-1, 3), cc_ref(i-1, 4));
ch_ref(i-1, 1) = VADD(cc_ref(i-1, 1), VADD(tr2, tr3));
ch_ref(i , 1) = VADD(cc_ref(i , 1), VADD(ti2, ti3));
cr2 = VADD(cc_ref(i-1, 1), VADD(SVMUL(tr11, tr2),SVMUL(tr12, tr3)));
ci2 = VADD(cc_ref(i , 1), VADD(SVMUL(tr11, ti2),SVMUL(tr12, ti3)));
cr3 = VADD(cc_ref(i-1, 1), VADD(SVMUL(tr12, tr2),SVMUL(tr11, tr3)));
ci3 = VADD(cc_ref(i , 1), VADD(SVMUL(tr12, ti2),SVMUL(tr11, ti3)));
cr5 = VADD(SVMUL(ti11, tr5), SVMUL(ti12, tr4));
ci5 = VADD(SVMUL(ti11, ti5), SVMUL(ti12, ti4));
cr4 = VSUB(SVMUL(ti12, tr5), SVMUL(ti11, tr4));
ci4 = VSUB(SVMUL(ti12, ti5), SVMUL(ti11, ti4));
dr3 = VSUB(cr3, ci4);
dr4 = VADD(cr3, ci4);
di3 = VADD(ci3, cr4);
di4 = VSUB(ci3, cr4);
dr5 = VADD(cr2, ci5);
dr2 = VSUB(cr2, ci5);
di5 = VSUB(ci2, cr5);
di2 = VADD(ci2, cr5);
wr1=wa1[i], wi1=fsign*wa1[i+1], wr2=wa2[i], wi2=fsign*wa2[i+1];
wr3=wa3[i], wi3=fsign*wa3[i+1], wr4=wa4[i], wi4=fsign*wa4[i+1];
VCPLXMUL(dr2, di2, LD_PS1(wr1), LD_PS1(wi1));
ch_ref(i - 1, 2) = dr2;
ch_ref(i, 2) = di2;
VCPLXMUL(dr3, di3, LD_PS1(wr2), LD_PS1(wi2));
ch_ref(i - 1, 3) = dr3;
ch_ref(i, 3) = di3;
VCPLXMUL(dr4, di4, LD_PS1(wr3), LD_PS1(wi3));
ch_ref(i - 1, 4) = dr4;
ch_ref(i, 4) = di4;
VCPLXMUL(dr5, di5, LD_PS1(wr4), LD_PS1(wi4));
ch_ref(i - 1, 5) = dr5;
ch_ref(i, 5) = di5;
}
}
#undef ch_ref
#undef cc_ref
}
static NEVER_INLINE(void) radf2_ps(int ido, int l1, const v4sf * RESTRICT cc, v4sf * RESTRICT ch, const float *wa1) {
static const float minus_one = -1.f;
int i, k, l1ido = l1*ido;
for (k=0; k < l1ido; k += ido) {
v4sf a = cc[k], b = cc[k + l1ido];
ch[2*k] = VADD(a, b);
ch[2*(k+ido)-1] = VSUB(a, b);
}
if (ido < 2) return;
if (ido != 2) {
for (k=0; k < l1ido; k += ido) {
for (i=2; i<ido; i+=2) {
v4sf tr2 = cc[i - 1 + k + l1ido], ti2 = cc[i + k + l1ido];
v4sf br = cc[i - 1 + k], bi = cc[i + k];
VCPLXMULCONJ(tr2, ti2, LD_PS1(wa1[i - 2]), LD_PS1(wa1[i - 1]));
ch[i + 2*k] = VADD(bi, ti2);
ch[2*(k+ido) - i] = VSUB(ti2, bi);
ch[i - 1 + 2*k] = VADD(br, tr2);
ch[2*(k+ido) - i -1] = VSUB(br, tr2);
}
}
if (ido % 2 == 1) return;
}
for (k=0; k < l1ido; k += ido) {
ch[2*k + ido] = SVMUL(minus_one, cc[ido-1 + k + l1ido]);
ch[2*k + ido-1] = cc[k + ido-1];
}
} /* radf2 */
static NEVER_INLINE(void) radb2_ps(int ido, int l1, const v4sf *cc, v4sf *ch, const float *wa1) {
static const float minus_two=-2;
int i, k, l1ido = l1*ido;
v4sf a,b,c,d, tr2, ti2;
for (k=0; k < l1ido; k += ido) {
a = cc[2*k]; b = cc[2*(k+ido) - 1];
ch[k] = VADD(a, b);
ch[k + l1ido] =VSUB(a, b);
}
if (ido < 2) return;
if (ido != 2) {
for (k = 0; k < l1ido; k += ido) {
for (i = 2; i < ido; i += 2) {
a = cc[i-1 + 2*k]; b = cc[2*(k + ido) - i - 1];
c = cc[i+0 + 2*k]; d = cc[2*(k + ido) - i + 0];
ch[i-1 + k] = VADD(a, b);
tr2 = VSUB(a, b);
ch[i+0 + k] = VSUB(c, d);
ti2 = VADD(c, d);
VCPLXMUL(tr2, ti2, LD_PS1(wa1[i - 2]), LD_PS1(wa1[i - 1]));
ch[i-1 + k + l1ido] = tr2;
ch[i+0 + k + l1ido] = ti2;
}
}
if (ido % 2 == 1) return;
}
for (k = 0; k < l1ido; k += ido) {
a = cc[2*k + ido-1]; b = cc[2*k + ido];
ch[k + ido-1] = VADD(a,a);
ch[k + ido-1 + l1ido] = SVMUL(minus_two, b);
}
} /* radb2 */
static void radf3_ps(int ido, int l1, const v4sf * RESTRICT cc, v4sf * RESTRICT ch,
const float *wa1, const float *wa2) {
static const float taur = -0.5f;
static const float taui = 0.866025403784439f;
int i, k, ic;
v4sf ci2, di2, di3, cr2, dr2, dr3, ti2, ti3, tr2, tr3, wr1, wi1, wr2, wi2;
for (k=0; k<l1; k++) {
cr2 = VADD(cc[(k + l1)*ido], cc[(k + 2*l1)*ido]);
ch[3*k*ido] = VADD(cc[k*ido], cr2);
ch[(3*k+2)*ido] = SVMUL(taui, VSUB(cc[(k + l1*2)*ido], cc[(k + l1)*ido]));
ch[ido-1 + (3*k + 1)*ido] = VADD(cc[k*ido], SVMUL(taur, cr2));
}
if (ido == 1) return;
for (k=0; k<l1; k++) {
for (i=2; i<ido; i+=2) {
ic = ido - i;
wr1 = LD_PS1(wa1[i - 2]); wi1 = LD_PS1(wa1[i - 1]);
dr2 = cc[i - 1 + (k + l1)*ido]; di2 = cc[i + (k + l1)*ido];
VCPLXMULCONJ(dr2, di2, wr1, wi1);
wr2 = LD_PS1(wa2[i - 2]); wi2 = LD_PS1(wa2[i - 1]);
dr3 = cc[i - 1 + (k + l1*2)*ido]; di3 = cc[i + (k + l1*2)*ido];
VCPLXMULCONJ(dr3, di3, wr2, wi2);
cr2 = VADD(dr2, dr3);
ci2 = VADD(di2, di3);
ch[i - 1 + 3*k*ido] = VADD(cc[i - 1 + k*ido], cr2);
ch[i + 3*k*ido] = VADD(cc[i + k*ido], ci2);
tr2 = VADD(cc[i - 1 + k*ido], SVMUL(taur, cr2));
ti2 = VADD(cc[i + k*ido], SVMUL(taur, ci2));
tr3 = SVMUL(taui, VSUB(di2, di3));
ti3 = SVMUL(taui, VSUB(dr3, dr2));
ch[i - 1 + (3*k + 2)*ido] = VADD(tr2, tr3);
ch[ic - 1 + (3*k + 1)*ido] = VSUB(tr2, tr3);
ch[i + (3*k + 2)*ido] = VADD(ti2, ti3);
ch[ic + (3*k + 1)*ido] = VSUB(ti3, ti2);
}
}
} /* radf3 */
static void radb3_ps(int ido, int l1, const v4sf *RESTRICT cc, v4sf *RESTRICT ch,
const float *wa1, const float *wa2)
{
static const float taur = -0.5f;
static const float taui = 0.866025403784439f;
static const float taui_2 = 0.866025403784439f*2;
int i, k, ic;
v4sf ci2, ci3, di2, di3, cr2, cr3, dr2, dr3, ti2, tr2;
for (k=0; k<l1; k++) {
tr2 = cc[ido-1 + (3*k + 1)*ido]; tr2 = VADD(tr2,tr2);
cr2 = VMADD(LD_PS1(taur), tr2, cc[3*k*ido]);
ch[k*ido] = VADD(cc[3*k*ido], tr2);
ci3 = SVMUL(taui_2, cc[(3*k + 2)*ido]);
ch[(k + l1)*ido] = VSUB(cr2, ci3);
ch[(k + 2*l1)*ido] = VADD(cr2, ci3);
}
if (ido == 1) return;
for (k=0; k<l1; k++) {
for (i=2; i<ido; i+=2) {
ic = ido - i;
tr2 = VADD(cc[i - 1 + (3*k + 2)*ido], cc[ic - 1 + (3*k + 1)*ido]);
cr2 = VMADD(LD_PS1(taur), tr2, cc[i - 1 + 3*k*ido]);
ch[i - 1 + k*ido] = VADD(cc[i - 1 + 3*k*ido], tr2);
ti2 = VSUB(cc[i + (3*k + 2)*ido], cc[ic + (3*k + 1)*ido]);
ci2 = VMADD(LD_PS1(taur), ti2, cc[i + 3*k*ido]);
ch[i + k*ido] = VADD(cc[i + 3*k*ido], ti2);
cr3 = SVMUL(taui, VSUB(cc[i - 1 + (3*k + 2)*ido], cc[ic - 1 + (3*k + 1)*ido]));
ci3 = SVMUL(taui, VADD(cc[i + (3*k + 2)*ido], cc[ic + (3*k + 1)*ido]));
dr2 = VSUB(cr2, ci3);
dr3 = VADD(cr2, ci3);
di2 = VADD(ci2, cr3);
di3 = VSUB(ci2, cr3);
VCPLXMUL(dr2, di2, LD_PS1(wa1[i-2]), LD_PS1(wa1[i-1]));
ch[i - 1 + (k + l1)*ido] = dr2;
ch[i + (k + l1)*ido] = di2;
VCPLXMUL(dr3, di3, LD_PS1(wa2[i-2]), LD_PS1(wa2[i-1]));
ch[i - 1 + (k + 2*l1)*ido] = dr3;
ch[i + (k + 2*l1)*ido] = di3;
}
}
} /* radb3 */
static NEVER_INLINE(void) radf4_ps(int ido, int l1, const v4sf *RESTRICT cc, v4sf * RESTRICT ch,
const float * RESTRICT wa1, const float * RESTRICT wa2, const float * RESTRICT wa3)
{
static const float minus_hsqt2 = (float)-0.7071067811865475;
int i, k, l1ido = l1*ido;
{
const v4sf *RESTRICT cc_ = cc, * RESTRICT cc_end = cc + l1ido;
v4sf * RESTRICT ch_ = ch;
while (cc < cc_end) {
/* this loop represents between 25% and 40% of total radf4_ps cost ! */
v4sf a0 = cc[0], a1 = cc[l1ido];
v4sf a2 = cc[2*l1ido], a3 = cc[3*l1ido];
v4sf tr1 = VADD(a1, a3);
v4sf tr2 = VADD(a0, a2);
ch[2*ido-1] = VSUB(a0, a2);
ch[2*ido ] = VSUB(a3, a1);
ch[0 ] = VADD(tr1, tr2);
ch[4*ido-1] = VSUB(tr2, tr1);
cc += ido; ch += 4*ido;
}
cc = cc_; ch = ch_;
}
if (ido < 2) return;
if (ido != 2) {
for (k = 0; k < l1ido; k += ido) {
const v4sf * RESTRICT pc = (v4sf*)(cc + 1 + k);
for (i=2; i<ido; i += 2, pc += 2) {
int ic = ido - i;
v4sf wr, wi, cr2, ci2, cr3, ci3, cr4, ci4;
v4sf tr1, ti1, tr2, ti2, tr3, ti3, tr4, ti4;
cr2 = pc[1*l1ido+0];
ci2 = pc[1*l1ido+1];
wr=LD_PS1(wa1[i - 2]);
wi=LD_PS1(wa1[i - 1]);
VCPLXMULCONJ(cr2,ci2,wr,wi);
cr3 = pc[2*l1ido+0];
ci3 = pc[2*l1ido+1];
wr = LD_PS1(wa2[i-2]);
wi = LD_PS1(wa2[i-1]);
VCPLXMULCONJ(cr3, ci3, wr, wi);
cr4 = pc[3*l1ido];
ci4 = pc[3*l1ido+1];
wr = LD_PS1(wa3[i-2]);
wi = LD_PS1(wa3[i-1]);
VCPLXMULCONJ(cr4, ci4, wr, wi);
/* at this point, on SSE, five of "cr2 cr3 cr4 ci2 ci3 ci4" should be loaded in registers */
tr1 = VADD(cr2,cr4);
tr4 = VSUB(cr4,cr2);
tr2 = VADD(pc[0],cr3);
tr3 = VSUB(pc[0],cr3);
ch[i - 1 + 4*k] = VADD(tr1,tr2);
ch[ic - 1 + 4*k + 3*ido] = VSUB(tr2,tr1); /* at this point tr1 and tr2 can be disposed */
ti1 = VADD(ci2,ci4);
ti4 = VSUB(ci2,ci4);
ch[i - 1 + 4*k + 2*ido] = VADD(ti4,tr3);
ch[ic - 1 + 4*k + 1*ido] = VSUB(tr3,ti4); /* dispose tr3, ti4 */
ti2 = VADD(pc[1],ci3);
ti3 = VSUB(pc[1],ci3);
ch[i + 4*k] = VADD(ti1, ti2);
ch[ic + 4*k + 3*ido] = VSUB(ti1, ti2);
ch[i + 4*k + 2*ido] = VADD(tr4, ti3);
ch[ic + 4*k + 1*ido] = VSUB(tr4, ti3);
}
}
if (ido % 2 == 1) return;
}
for (k=0; k<l1ido; k += ido) {
v4sf a = cc[ido-1 + k + l1ido], b = cc[ido-1 + k + 3*l1ido];
v4sf c = cc[ido-1 + k], d = cc[ido-1 + k + 2*l1ido];
v4sf ti1 = SVMUL(minus_hsqt2, VADD(a, b));
v4sf tr1 = SVMUL(minus_hsqt2, VSUB(b, a));
ch[ido-1 + 4*k] = VADD(tr1, c);
ch[ido-1 + 4*k + 2*ido] = VSUB(c, tr1);
ch[4*k + 1*ido] = VSUB(ti1, d);
ch[4*k + 3*ido] = VADD(ti1, d);
}
} /* radf4 */
static NEVER_INLINE(void) radb4_ps(int ido, int l1, const v4sf * RESTRICT cc, v4sf * RESTRICT ch,
const float * RESTRICT wa1, const float * RESTRICT wa2, const float *RESTRICT wa3)
{
static const float minus_sqrt2 = (float)-1.414213562373095;
static const float two = 2.f;
int i, k, l1ido = l1*ido;
v4sf ci2, ci3, ci4, cr2, cr3, cr4, ti1, ti2, ti3, ti4, tr1, tr2, tr3, tr4;
{
const v4sf *RESTRICT cc_ = cc, * RESTRICT ch_end = ch + l1ido;
v4sf *ch_ = ch;
while (ch < ch_end) {
v4sf a = cc[0], b = cc[4*ido-1];
v4sf c = cc[2*ido], d = cc[2*ido-1];
tr3 = SVMUL(two,d);
tr2 = VADD(a,b);
tr1 = VSUB(a,b);
tr4 = SVMUL(two,c);
ch[0*l1ido] = VADD(tr2, tr3);
ch[2*l1ido] = VSUB(tr2, tr3);
ch[1*l1ido] = VSUB(tr1, tr4);
ch[3*l1ido] = VADD(tr1, tr4);
cc += 4*ido; ch += ido;
}
cc = cc_; ch = ch_;
}
if (ido < 2) return;
if (ido != 2) {
for (k = 0; k < l1ido; k += ido) {
const v4sf * RESTRICT pc = (v4sf*)(cc - 1 + 4*k);
v4sf * RESTRICT ph = (v4sf*)(ch + k + 1);
for (i = 2; i < ido; i += 2) {
tr1 = VSUB(pc[i], pc[4*ido - i]);
tr2 = VADD(pc[i], pc[4*ido - i]);
ti4 = VSUB(pc[2*ido + i], pc[2*ido - i]);
tr3 = VADD(pc[2*ido + i], pc[2*ido - i]);
ph[0] = VADD(tr2, tr3);
cr3 = VSUB(tr2, tr3);
ti3 = VSUB(pc[2*ido + i + 1], pc[2*ido - i + 1]);
tr4 = VADD(pc[2*ido + i + 1], pc[2*ido - i + 1]);
cr2 = VSUB(tr1, tr4);
cr4 = VADD(tr1, tr4);
ti1 = VADD(pc[i + 1], pc[4*ido - i + 1]);
ti2 = VSUB(pc[i + 1], pc[4*ido - i + 1]);
ph[1] = VADD(ti2, ti3); ph += l1ido;
ci3 = VSUB(ti2, ti3);
ci2 = VADD(ti1, ti4);
ci4 = VSUB(ti1, ti4);
VCPLXMUL(cr2, ci2, LD_PS1(wa1[i-2]), LD_PS1(wa1[i-1]));
ph[0] = cr2;
ph[1] = ci2; ph += l1ido;
VCPLXMUL(cr3, ci3, LD_PS1(wa2[i-2]), LD_PS1(wa2[i-1]));
ph[0] = cr3;
ph[1] = ci3; ph += l1ido;
VCPLXMUL(cr4, ci4, LD_PS1(wa3[i-2]), LD_PS1(wa3[i-1]));
ph[0] = cr4;
ph[1] = ci4; ph = ph - 3*l1ido + 2;
}
}
if (ido % 2 == 1) return;
}
for (k=0; k < l1ido; k+=ido) {
int i0 = 4*k + ido;
v4sf c = cc[i0-1], d = cc[i0 + 2*ido-1];
v4sf a = cc[i0+0], b = cc[i0 + 2*ido+0];
tr1 = VSUB(c,d);
tr2 = VADD(c,d);
ti1 = VADD(b,a);
ti2 = VSUB(b,a);
ch[ido-1 + k + 0*l1ido] = VADD(tr2,tr2);
ch[ido-1 + k + 1*l1ido] = SVMUL(minus_sqrt2, VSUB(ti1, tr1));
ch[ido-1 + k + 2*l1ido] = VADD(ti2, ti2);
ch[ido-1 + k + 3*l1ido] = SVMUL(minus_sqrt2, VADD(ti1, tr1));
}
} /* radb4 */
static void radf5_ps(int ido, int l1, const v4sf * RESTRICT cc, v4sf * RESTRICT ch,
const float *wa1, const float *wa2, const float *wa3, const float *wa4)
{
static const float tr11 = .309016994374947f;
static const float ti11 = .951056516295154f;
static const float tr12 = -.809016994374947f;
static const float ti12 = .587785252292473f;
/* System generated locals */
int cc_offset, ch_offset;
/* Local variables */
int i, k, ic;
v4sf ci2, di2, ci4, ci5, di3, di4, di5, ci3, cr2, cr3, dr2, dr3, dr4, dr5,
cr5, cr4, ti2, ti3, ti5, ti4, tr2, tr3, tr4, tr5;
int idp2;
#define cc_ref(a_1,a_2,a_3) cc[((a_3)*l1 + (a_2))*ido + a_1]
#define ch_ref(a_1,a_2,a_3) ch[((a_3)*5 + (a_2))*ido + a_1]
/* Parameter adjustments */
ch_offset = 1 + ido * 6;
ch -= ch_offset;
cc_offset = 1 + ido * (1 + l1);
cc -= cc_offset;
/* Function Body */
for (k = 1; k <= l1; ++k) {
cr2 = VADD(cc_ref(1, k, 5), cc_ref(1, k, 2));
ci5 = VSUB(cc_ref(1, k, 5), cc_ref(1, k, 2));
cr3 = VADD(cc_ref(1, k, 4), cc_ref(1, k, 3));
ci4 = VSUB(cc_ref(1, k, 4), cc_ref(1, k, 3));
ch_ref(1, 1, k) = VADD(cc_ref(1, k, 1), VADD(cr2, cr3));
ch_ref(ido, 2, k) = VADD(cc_ref(1, k, 1), VADD(SVMUL(tr11, cr2), SVMUL(tr12, cr3)));
ch_ref(1, 3, k) = VADD(SVMUL(ti11, ci5), SVMUL(ti12, ci4));
ch_ref(ido, 4, k) = VADD(cc_ref(1, k, 1), VADD(SVMUL(tr12, cr2), SVMUL(tr11, cr3)));
ch_ref(1, 5, k) = VSUB(SVMUL(ti12, ci5), SVMUL(ti11, ci4));
/* printf("pffft: radf5, k=%d ch_ref=%f, ci4=%f\n", k, ch_ref(1, 5, k), ci4); */
}
if (ido == 1) {
return;
}
idp2 = ido + 2;
for (k = 1; k <= l1; ++k) {
for (i = 3; i <= ido; i += 2) {
ic = idp2 - i;
dr2 = LD_PS1(wa1[i-3]); di2 = LD_PS1(wa1[i-2]);
dr3 = LD_PS1(wa2[i-3]); di3 = LD_PS1(wa2[i-2]);
dr4 = LD_PS1(wa3[i-3]); di4 = LD_PS1(wa3[i-2]);
dr5 = LD_PS1(wa4[i-3]); di5 = LD_PS1(wa4[i-2]);
VCPLXMULCONJ(dr2, di2, cc_ref(i-1, k, 2), cc_ref(i, k, 2));
VCPLXMULCONJ(dr3, di3, cc_ref(i-1, k, 3), cc_ref(i, k, 3));
VCPLXMULCONJ(dr4, di4, cc_ref(i-1, k, 4), cc_ref(i, k, 4));
VCPLXMULCONJ(dr5, di5, cc_ref(i-1, k, 5), cc_ref(i, k, 5));
cr2 = VADD(dr2, dr5);
ci5 = VSUB(dr5, dr2);
cr5 = VSUB(di2, di5);
ci2 = VADD(di2, di5);
cr3 = VADD(dr3, dr4);
ci4 = VSUB(dr4, dr3);
cr4 = VSUB(di3, di4);
ci3 = VADD(di3, di4);
ch_ref(i - 1, 1, k) = VADD(cc_ref(i - 1, k, 1), VADD(cr2, cr3));
ch_ref(i, 1, k) = VSUB(cc_ref(i, k, 1), VADD(ci2, ci3));
tr2 = VADD(cc_ref(i - 1, k, 1), VADD(SVMUL(tr11, cr2), SVMUL(tr12, cr3)));
ti2 = VSUB(cc_ref(i, k, 1), VADD(SVMUL(tr11, ci2), SVMUL(tr12, ci3)));
tr3 = VADD(cc_ref(i - 1, k, 1), VADD(SVMUL(tr12, cr2), SVMUL(tr11, cr3)));
ti3 = VSUB(cc_ref(i, k, 1), VADD(SVMUL(tr12, ci2), SVMUL(tr11, ci3)));
tr5 = VADD(SVMUL(ti11, cr5), SVMUL(ti12, cr4));
ti5 = VADD(SVMUL(ti11, ci5), SVMUL(ti12, ci4));
tr4 = VSUB(SVMUL(ti12, cr5), SVMUL(ti11, cr4));
ti4 = VSUB(SVMUL(ti12, ci5), SVMUL(ti11, ci4));
ch_ref(i - 1, 3, k) = VSUB(tr2, tr5);
ch_ref(ic - 1, 2, k) = VADD(tr2, tr5);
ch_ref(i, 3, k) = VADD(ti2, ti5);
ch_ref(ic, 2, k) = VSUB(ti5, ti2);
ch_ref(i - 1, 5, k) = VSUB(tr3, tr4);
ch_ref(ic - 1, 4, k) = VADD(tr3, tr4);
ch_ref(i, 5, k) = VADD(ti3, ti4);
ch_ref(ic, 4, k) = VSUB(ti4, ti3);
}
}
#undef cc_ref
#undef ch_ref
} /* radf5 */
static void radb5_ps(int ido, int l1, const v4sf *RESTRICT cc, v4sf *RESTRICT ch,
const float *wa1, const float *wa2, const float *wa3, const float *wa4)
{
static const float tr11 = .309016994374947f;
static const float ti11 = .951056516295154f;
static const float tr12 = -.809016994374947f;
static const float ti12 = .587785252292473f;
int cc_offset, ch_offset;
/* Local variables */
int i, k, ic;
v4sf ci2, ci3, ci4, ci5, di3, di4, di5, di2, cr2, cr3, cr5, cr4, ti2, ti3,
ti4, ti5, dr3, dr4, dr5, dr2, tr2, tr3, tr4, tr5;
int idp2;
#define cc_ref(a_1,a_2,a_3) cc[((a_3)*5 + (a_2))*ido + a_1]
#define ch_ref(a_1,a_2,a_3) ch[((a_3)*l1 + (a_2))*ido + a_1]
/* Parameter adjustments */
ch_offset = 1 + ido * (1 + l1);
ch -= ch_offset;
cc_offset = 1 + ido * 6;
cc -= cc_offset;
/* Function Body */
for (k = 1; k <= l1; ++k) {
ti5 = VADD(cc_ref(1, 3, k), cc_ref(1, 3, k));
ti4 = VADD(cc_ref(1, 5, k), cc_ref(1, 5, k));
tr2 = VADD(cc_ref(ido, 2, k), cc_ref(ido, 2, k));
tr3 = VADD(cc_ref(ido, 4, k), cc_ref(ido, 4, k));
ch_ref(1, k, 1) = VADD(cc_ref(1, 1, k), VADD(tr2, tr3));
cr2 = VADD(cc_ref(1, 1, k), VADD(SVMUL(tr11, tr2), SVMUL(tr12, tr3)));
cr3 = VADD(cc_ref(1, 1, k), VADD(SVMUL(tr12, tr2), SVMUL(tr11, tr3)));
ci5 = VADD(SVMUL(ti11, ti5), SVMUL(ti12, ti4));
ci4 = VSUB(SVMUL(ti12, ti5), SVMUL(ti11, ti4));
ch_ref(1, k, 2) = VSUB(cr2, ci5);
ch_ref(1, k, 3) = VSUB(cr3, ci4);
ch_ref(1, k, 4) = VADD(cr3, ci4);
ch_ref(1, k, 5) = VADD(cr2, ci5);
}
if (ido == 1) {
return;
}
idp2 = ido + 2;
for (k = 1; k <= l1; ++k) {
for (i = 3; i <= ido; i += 2) {
ic = idp2 - i;
ti5 = VADD(cc_ref(i , 3, k), cc_ref(ic , 2, k));
ti2 = VSUB(cc_ref(i , 3, k), cc_ref(ic , 2, k));
ti4 = VADD(cc_ref(i , 5, k), cc_ref(ic , 4, k));
ti3 = VSUB(cc_ref(i , 5, k), cc_ref(ic , 4, k));
tr5 = VSUB(cc_ref(i-1, 3, k), cc_ref(ic-1, 2, k));
tr2 = VADD(cc_ref(i-1, 3, k), cc_ref(ic-1, 2, k));
tr4 = VSUB(cc_ref(i-1, 5, k), cc_ref(ic-1, 4, k));
tr3 = VADD(cc_ref(i-1, 5, k), cc_ref(ic-1, 4, k));
ch_ref(i - 1, k, 1) = VADD(cc_ref(i-1, 1, k), VADD(tr2, tr3));
ch_ref(i, k, 1) = VADD(cc_ref(i, 1, k), VADD(ti2, ti3));
cr2 = VADD(cc_ref(i-1, 1, k), VADD(SVMUL(tr11, tr2), SVMUL(tr12, tr3)));
ci2 = VADD(cc_ref(i , 1, k), VADD(SVMUL(tr11, ti2), SVMUL(tr12, ti3)));
cr3 = VADD(cc_ref(i-1, 1, k), VADD(SVMUL(tr12, tr2), SVMUL(tr11, tr3)));
ci3 = VADD(cc_ref(i , 1, k), VADD(SVMUL(tr12, ti2), SVMUL(tr11, ti3)));
cr5 = VADD(SVMUL(ti11, tr5), SVMUL(ti12, tr4));
ci5 = VADD(SVMUL(ti11, ti5), SVMUL(ti12, ti4));
cr4 = VSUB(SVMUL(ti12, tr5), SVMUL(ti11, tr4));
ci4 = VSUB(SVMUL(ti12, ti5), SVMUL(ti11, ti4));
dr3 = VSUB(cr3, ci4);
dr4 = VADD(cr3, ci4);
di3 = VADD(ci3, cr4);
di4 = VSUB(ci3, cr4);
dr5 = VADD(cr2, ci5);
dr2 = VSUB(cr2, ci5);
di5 = VSUB(ci2, cr5);
di2 = VADD(ci2, cr5);
VCPLXMUL(dr2, di2, LD_PS1(wa1[i-3]), LD_PS1(wa1[i-2]));
VCPLXMUL(dr3, di3, LD_PS1(wa2[i-3]), LD_PS1(wa2[i-2]));
VCPLXMUL(dr4, di4, LD_PS1(wa3[i-3]), LD_PS1(wa3[i-2]));
VCPLXMUL(dr5, di5, LD_PS1(wa4[i-3]), LD_PS1(wa4[i-2]));
ch_ref(i-1, k, 2) = dr2; ch_ref(i, k, 2) = di2;
ch_ref(i-1, k, 3) = dr3; ch_ref(i, k, 3) = di3;
ch_ref(i-1, k, 4) = dr4; ch_ref(i, k, 4) = di4;
ch_ref(i-1, k, 5) = dr5; ch_ref(i, k, 5) = di5;
}
}
#undef cc_ref
#undef ch_ref
} /* radb5 */
static NEVER_INLINE(v4sf *) rfftf1_ps(int n, const v4sf *input_readonly, v4sf *work1, v4sf *work2,
const float *wa, const int *ifac) {
v4sf *in = (v4sf*)input_readonly;
v4sf *out = (in == work2 ? work1 : work2);
int nf = ifac[1], k1;
int l2 = n;
int iw = n-1;
assert(in != out && work1 != work2);
for (k1 = 1; k1 <= nf; ++k1) {
int kh = nf - k1;
int ip = ifac[kh + 2];
int l1 = l2 / ip;
int ido = n / l2;
iw -= (ip - 1)*ido;
switch (ip) {
case 5: {
int ix2 = iw + ido;
int ix3 = ix2 + ido;
int ix4 = ix3 + ido;
radf5_ps(ido, l1, in, out, &wa[iw], &wa[ix2], &wa[ix3], &wa[ix4]);
} break;
case 4: {
int ix2 = iw + ido;
int ix3 = ix2 + ido;
radf4_ps(ido, l1, in, out, &wa[iw], &wa[ix2], &wa[ix3]);
} break;
case 3: {
int ix2 = iw + ido;
radf3_ps(ido, l1, in, out, &wa[iw], &wa[ix2]);
} break;
case 2:
radf2_ps(ido, l1, in, out, &wa[iw]);
break;
default:
assert(0);
break;
}
l2 = l1;
if (out == work2) {
out = work1; in = work2;
} else {
out = work2; in = work1;
}
}
return in; /* this is in fact the output .. */
} /* rfftf1 */
static NEVER_INLINE(v4sf *) rfftb1_ps(int n, const v4sf *input_readonly, v4sf *work1, v4sf *work2,
const float *wa, const int *ifac) {
v4sf *in = (v4sf*)input_readonly;
v4sf *out = (in == work2 ? work1 : work2);
int nf = ifac[1], k1;
int l1 = 1;
int iw = 0;
assert(in != out);
for (k1=1; k1<=nf; k1++) {
int ip = ifac[k1 + 1];
int l2 = ip*l1;
int ido = n / l2;
switch (ip) {
case 5: {
int ix2 = iw + ido;
int ix3 = ix2 + ido;
int ix4 = ix3 + ido;
radb5_ps(ido, l1, in, out, &wa[iw], &wa[ix2], &wa[ix3], &wa[ix4]);
} break;
case 4: {
int ix2 = iw + ido;
int ix3 = ix2 + ido;
radb4_ps(ido, l1, in, out, &wa[iw], &wa[ix2], &wa[ix3]);
} break;
case 3: {
int ix2 = iw + ido;
radb3_ps(ido, l1, in, out, &wa[iw], &wa[ix2]);
} break;
case 2:
radb2_ps(ido, l1, in, out, &wa[iw]);
break;
default:
assert(0);
break;
}
l1 = l2;
iw += (ip - 1)*ido;
if (out == work2) {
out = work1; in = work2;
} else {
out = work2; in = work1;
}
}
return in; /* this is in fact the output .. */
}
static int decompose(int n, int *ifac, const int *ntryh) {
int nl = n, nf = 0, i, j = 0;
for (j=0; ntryh[j]; ++j) {
int ntry = ntryh[j];
while (nl != 1) {
int nq = nl / ntry;
int nr = nl - ntry * nq;
if (nr == 0) {
ifac[2+nf++] = ntry;
nl = nq;
if (ntry == 2 && nf != 1) {
for (i = 2; i <= nf; ++i) {
int ib = nf - i + 2;
ifac[ib + 1] = ifac[ib];
}
ifac[2] = 2;
}
} else break;
}
}
ifac[0] = n;
ifac[1] = nf;
return nf;
}
static void rffti1_ps(int n, float *wa, int *ifac)
{
static const int ntryh[] = { 4,2,3,5,0 };
int k1, j, ii;
int nf = decompose(n,ifac,ntryh);
float argh = (2*(float)M_PI) / n;
int is = 0;
int nfm1 = nf - 1;
int l1 = 1;
for (k1 = 1; k1 <= nfm1; k1++) {
int ip = ifac[k1 + 1];
int ld = 0;
int l2 = l1*ip;
int ido = n / l2;
int ipm = ip - 1;
for (j = 1; j <= ipm; ++j) {
float argld;
int i = is, fi=0;
ld += l1;
argld = ld*argh;
for (ii = 3; ii <= ido; ii += 2) {
i += 2;
fi += 1;
wa[i - 2] = FUNC_COS(fi*argld);
wa[i - 1] = FUNC_SIN(fi*argld);
}
is += ido;
}
l1 = l2;
}
} /* rffti1 */
static void cffti1_ps(int n, float *wa, int *ifac)
{
static const int ntryh[] = { 5,3,4,2,0 };
int k1, j, ii;
int nf = decompose(n,ifac,ntryh);
float argh = (2*(float)M_PI) / n;
int i = 1;
int l1 = 1;
for (k1=1; k1<=nf; k1++) {
int ip = ifac[k1+1];
int ld = 0;
int l2 = l1*ip;
int ido = n / l2;
int idot = ido + ido + 2;
int ipm = ip - 1;
for (j=1; j<=ipm; j++) {
float argld;
int i1 = i, fi = 0;
wa[i-1] = 1;
wa[i] = 0;
ld += l1;
argld = ld*argh;
for (ii = 4; ii <= idot; ii += 2) {
i += 2;
fi += 1;
wa[i-1] = FUNC_COS(fi*argld);
wa[i] = FUNC_SIN(fi*argld);
}
if (ip > 5) {
wa[i1-1] = wa[i-1];
wa[i1] = wa[i];
}
}
l1 = l2;
}
} /* cffti1 */
static v4sf *cfftf1_ps(int n, const v4sf *input_readonly, v4sf *work1, v4sf *work2, const float *wa, const int *ifac, int isign) {
v4sf *in = (v4sf*)input_readonly;
v4sf *out = (in == work2 ? work1 : work2);
int nf = ifac[1], k1;
int l1 = 1;
int iw = 0;
assert(in != out && work1 != work2);
for (k1=2; k1<=nf+1; k1++) {
int ip = ifac[k1];
int l2 = ip*l1;
int ido = n / l2;
int idot = ido + ido;
switch (ip) {
case 5: {
int ix2 = iw + idot;
int ix3 = ix2 + idot;
int ix4 = ix3 + idot;
passf5_ps(idot, l1, in, out, &wa[iw], &wa[ix2], &wa[ix3], &wa[ix4], isign);
} break;
case 4: {
int ix2 = iw + idot;
int ix3 = ix2 + idot;
passf4_ps(idot, l1, in, out, &wa[iw], &wa[ix2], &wa[ix3], isign);
} break;
case 2: {
passf2_ps(idot, l1, in, out, &wa[iw], isign);
} break;
case 3: {
int ix2 = iw + idot;
passf3_ps(idot, l1, in, out, &wa[iw], &wa[ix2], isign);
} break;
default:
assert(0);
}
l1 = l2;
iw += (ip - 1)*idot;
if (out == work2) {
out = work1; in = work2;
} else {
out = work2; in = work1;
}