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cosmotool/external/sharp/libsharp/sharp_legendre.c

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Updated libsharp to commit 0787838ab3ec8afc0c28b98479a321ffba388980
2016-11-04 18:14:49 +01:00
/* DO NOT EDIT. md5sum of source: d9499375a254cbf1e7903a249a8676ff *//*
NOTE NOTE NOTE
This file is edited in sharp_legendre.c.in which is then preprocessed.
Do not make manual modifications to sharp_legendre.c.
NOTE NOTE NOTE
*/
/*
* This file is part of libsharp.
*
* Redistribution and use in source and binary forms, with or without
* met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* 3. Neither the name of the copyright holder nor the names of its
* contributors may be used to endorse or promote products derived from
* this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
* HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
/*! \file sharp_legendre.c.in
*
* Copyright (C) 2015 University of Oslo
* \author Dag Sverre Seljebotn
*/
#ifndef NO_LEGENDRE
#if (VLEN==8)
#error This code is not tested with MIC; please compile with -DNO_LEGENDRE
/* ...or test it (it probably works) and remove this check */
#endif
#ifndef SHARP_LEGENDRE_CS
#define SHARP_LEGENDRE_CS 4
#endif
#define MAX_CS 6
#if (SHARP_LEGENDRE_CS > MAX_CS)
#error (SHARP_LEGENDRE_CS > MAX_CS)
#endif
#include "sharp_legendre.h"
#include "sharp_vecsupport.h"
#include <malloc.h>
static void legendre_transform_vec1(double *recfacs, double *bl, ptrdiff_t lmax,
double xarr[(1) * VLEN],
double out[(1) * VLEN]) {
Tv P_0, Pm1_0, Pm2_0, x0, y0;
Tv W1, W2, b, R;
ptrdiff_t l;
x0 = vloadu(xarr + 0 * VLEN);
Pm1_0 = vload(1.0);
P_0 = x0;
b = vload(*bl);
y0 = vmul(Pm1_0, b);
b = vload(*(bl + 1));
vfmaeq(y0, P_0, b);
for (l = 2; l <= lmax; ++l) {
b = vload(*(bl + l));
R = vload(*(recfacs + l));
/*
P = x * Pm1 + recfacs[l] * (x * Pm1 - Pm2)
*/
Pm2_0 = Pm1_0; Pm1_0 = P_0;
W1 = vmul(x0, Pm1_0);
W2 = W1;
W2 = vsub(W2, Pm2_0);
P_0 = W1;
vfmaeq(P_0, W2, R);
vfmaeq(y0, P_0, b);
}
vstoreu(out + 0 * VLEN, y0);
}
static void legendre_transform_vec2(double *recfacs, double *bl, ptrdiff_t lmax,
double xarr[(2) * VLEN],
double out[(2) * VLEN]) {
Tv P_0, Pm1_0, Pm2_0, x0, y0;
Tv P_1, Pm1_1, Pm2_1, x1, y1;
Tv W1, W2, b, R;
ptrdiff_t l;
x0 = vloadu(xarr + 0 * VLEN);
Pm1_0 = vload(1.0);
P_0 = x0;
b = vload(*bl);
y0 = vmul(Pm1_0, b);
x1 = vloadu(xarr + 1 * VLEN);
Pm1_1 = vload(1.0);
P_1 = x1;
b = vload(*bl);
y1 = vmul(Pm1_1, b);
b = vload(*(bl + 1));
vfmaeq(y0, P_0, b);
vfmaeq(y1, P_1, b);
for (l = 2; l <= lmax; ++l) {
b = vload(*(bl + l));
R = vload(*(recfacs + l));
/*
P = x * Pm1 + recfacs[l] * (x * Pm1 - Pm2)
*/
Pm2_0 = Pm1_0; Pm1_0 = P_0;
W1 = vmul(x0, Pm1_0);
W2 = W1;
W2 = vsub(W2, Pm2_0);
P_0 = W1;
vfmaeq(P_0, W2, R);
vfmaeq(y0, P_0, b);
Pm2_1 = Pm1_1; Pm1_1 = P_1;
W1 = vmul(x1, Pm1_1);
W2 = W1;
W2 = vsub(W2, Pm2_1);
P_1 = W1;
vfmaeq(P_1, W2, R);
vfmaeq(y1, P_1, b);
}
vstoreu(out + 0 * VLEN, y0);
vstoreu(out + 1 * VLEN, y1);
}
static void legendre_transform_vec3(double *recfacs, double *bl, ptrdiff_t lmax,
double xarr[(3) * VLEN],
double out[(3) * VLEN]) {
Tv P_0, Pm1_0, Pm2_0, x0, y0;
Tv P_1, Pm1_1, Pm2_1, x1, y1;
Tv P_2, Pm1_2, Pm2_2, x2, y2;
Tv W1, W2, b, R;
ptrdiff_t l;
x0 = vloadu(xarr + 0 * VLEN);
Pm1_0 = vload(1.0);
P_0 = x0;
b = vload(*bl);
y0 = vmul(Pm1_0, b);
x1 = vloadu(xarr + 1 * VLEN);
Pm1_1 = vload(1.0);
P_1 = x1;
b = vload(*bl);
y1 = vmul(Pm1_1, b);
x2 = vloadu(xarr + 2 * VLEN);
Pm1_2 = vload(1.0);
P_2 = x2;
b = vload(*bl);
y2 = vmul(Pm1_2, b);
b = vload(*(bl + 1));
vfmaeq(y0, P_0, b);
vfmaeq(y1, P_1, b);
vfmaeq(y2, P_2, b);
for (l = 2; l <= lmax; ++l) {
b = vload(*(bl + l));
R = vload(*(recfacs + l));
/*
P = x * Pm1 + recfacs[l] * (x * Pm1 - Pm2)
*/
Pm2_0 = Pm1_0; Pm1_0 = P_0;
W1 = vmul(x0, Pm1_0);
W2 = W1;
W2 = vsub(W2, Pm2_0);
P_0 = W1;
vfmaeq(P_0, W2, R);
vfmaeq(y0, P_0, b);
Pm2_1 = Pm1_1; Pm1_1 = P_1;
W1 = vmul(x1, Pm1_1);
W2 = W1;
W2 = vsub(W2, Pm2_1);
P_1 = W1;
vfmaeq(P_1, W2, R);
vfmaeq(y1, P_1, b);
Pm2_2 = Pm1_2; Pm1_2 = P_2;
W1 = vmul(x2, Pm1_2);
W2 = W1;
W2 = vsub(W2, Pm2_2);
P_2 = W1;
vfmaeq(P_2, W2, R);
vfmaeq(y2, P_2, b);
}
vstoreu(out + 0 * VLEN, y0);
vstoreu(out + 1 * VLEN, y1);
vstoreu(out + 2 * VLEN, y2);
}
static void legendre_transform_vec4(double *recfacs, double *bl, ptrdiff_t lmax,
double xarr[(4) * VLEN],
double out[(4) * VLEN]) {
Tv P_0, Pm1_0, Pm2_0, x0, y0;
Tv P_1, Pm1_1, Pm2_1, x1, y1;
Tv P_2, Pm1_2, Pm2_2, x2, y2;
Tv P_3, Pm1_3, Pm2_3, x3, y3;
Tv W1, W2, b, R;
ptrdiff_t l;
x0 = vloadu(xarr + 0 * VLEN);
Pm1_0 = vload(1.0);
P_0 = x0;
b = vload(*bl);
y0 = vmul(Pm1_0, b);
x1 = vloadu(xarr + 1 * VLEN);
Pm1_1 = vload(1.0);
P_1 = x1;
b = vload(*bl);
y1 = vmul(Pm1_1, b);
x2 = vloadu(xarr + 2 * VLEN);
Pm1_2 = vload(1.0);
P_2 = x2;
b = vload(*bl);
y2 = vmul(Pm1_2, b);
x3 = vloadu(xarr + 3 * VLEN);
Pm1_3 = vload(1.0);
P_3 = x3;
b = vload(*bl);
y3 = vmul(Pm1_3, b);
b = vload(*(bl + 1));
vfmaeq(y0, P_0, b);
vfmaeq(y1, P_1, b);
vfmaeq(y2, P_2, b);
vfmaeq(y3, P_3, b);
for (l = 2; l <= lmax; ++l) {
b = vload(*(bl + l));
R = vload(*(recfacs + l));
/*
P = x * Pm1 + recfacs[l] * (x * Pm1 - Pm2)
*/
Pm2_0 = Pm1_0; Pm1_0 = P_0;
W1 = vmul(x0, Pm1_0);
W2 = W1;
W2 = vsub(W2, Pm2_0);
P_0 = W1;
vfmaeq(P_0, W2, R);
vfmaeq(y0, P_0, b);
Pm2_1 = Pm1_1; Pm1_1 = P_1;
W1 = vmul(x1, Pm1_1);
W2 = W1;
W2 = vsub(W2, Pm2_1);
P_1 = W1;
vfmaeq(P_1, W2, R);
vfmaeq(y1, P_1, b);
Pm2_2 = Pm1_2; Pm1_2 = P_2;
W1 = vmul(x2, Pm1_2);
W2 = W1;
W2 = vsub(W2, Pm2_2);
P_2 = W1;
vfmaeq(P_2, W2, R);
vfmaeq(y2, P_2, b);
Pm2_3 = Pm1_3; Pm1_3 = P_3;
W1 = vmul(x3, Pm1_3);
W2 = W1;
W2 = vsub(W2, Pm2_3);
P_3 = W1;
vfmaeq(P_3, W2, R);
vfmaeq(y3, P_3, b);
}
vstoreu(out + 0 * VLEN, y0);
vstoreu(out + 1 * VLEN, y1);
vstoreu(out + 2 * VLEN, y2);
vstoreu(out + 3 * VLEN, y3);
}
static void legendre_transform_vec5(double *recfacs, double *bl, ptrdiff_t lmax,
double xarr[(5) * VLEN],
double out[(5) * VLEN]) {
Tv P_0, Pm1_0, Pm2_0, x0, y0;
Tv P_1, Pm1_1, Pm2_1, x1, y1;
Tv P_2, Pm1_2, Pm2_2, x2, y2;
Tv P_3, Pm1_3, Pm2_3, x3, y3;
Tv P_4, Pm1_4, Pm2_4, x4, y4;
Tv W1, W2, b, R;
ptrdiff_t l;
x0 = vloadu(xarr + 0 * VLEN);
Pm1_0 = vload(1.0);
P_0 = x0;
b = vload(*bl);
y0 = vmul(Pm1_0, b);
x1 = vloadu(xarr + 1 * VLEN);
Pm1_1 = vload(1.0);
P_1 = x1;
b = vload(*bl);
y1 = vmul(Pm1_1, b);
x2 = vloadu(xarr + 2 * VLEN);
Pm1_2 = vload(1.0);
P_2 = x2;
b = vload(*bl);
y2 = vmul(Pm1_2, b);
x3 = vloadu(xarr + 3 * VLEN);
Pm1_3 = vload(1.0);
P_3 = x3;
b = vload(*bl);
y3 = vmul(Pm1_3, b);
x4 = vloadu(xarr + 4 * VLEN);
Pm1_4 = vload(1.0);
P_4 = x4;
b = vload(*bl);
y4 = vmul(Pm1_4, b);
b = vload(*(bl + 1));
vfmaeq(y0, P_0, b);
vfmaeq(y1, P_1, b);
vfmaeq(y2, P_2, b);
vfmaeq(y3, P_3, b);
vfmaeq(y4, P_4, b);
for (l = 2; l <= lmax; ++l) {
b = vload(*(bl + l));
R = vload(*(recfacs + l));
/*
P = x * Pm1 + recfacs[l] * (x * Pm1 - Pm2)
*/
Pm2_0 = Pm1_0; Pm1_0 = P_0;
W1 = vmul(x0, Pm1_0);
W2 = W1;
W2 = vsub(W2, Pm2_0);
P_0 = W1;
vfmaeq(P_0, W2, R);
vfmaeq(y0, P_0, b);
Pm2_1 = Pm1_1; Pm1_1 = P_1;
W1 = vmul(x1, Pm1_1);
W2 = W1;
W2 = vsub(W2, Pm2_1);
P_1 = W1;
vfmaeq(P_1, W2, R);
vfmaeq(y1, P_1, b);
Pm2_2 = Pm1_2; Pm1_2 = P_2;
W1 = vmul(x2, Pm1_2);
W2 = W1;
W2 = vsub(W2, Pm2_2);
P_2 = W1;
vfmaeq(P_2, W2, R);
vfmaeq(y2, P_2, b);
Pm2_3 = Pm1_3; Pm1_3 = P_3;
W1 = vmul(x3, Pm1_3);
W2 = W1;
W2 = vsub(W2, Pm2_3);
P_3 = W1;
vfmaeq(P_3, W2, R);
vfmaeq(y3, P_3, b);
Pm2_4 = Pm1_4; Pm1_4 = P_4;
W1 = vmul(x4, Pm1_4);
W2 = W1;
W2 = vsub(W2, Pm2_4);
P_4 = W1;
vfmaeq(P_4, W2, R);
vfmaeq(y4, P_4, b);
}
vstoreu(out + 0 * VLEN, y0);
vstoreu(out + 1 * VLEN, y1);
vstoreu(out + 2 * VLEN, y2);
vstoreu(out + 3 * VLEN, y3);
vstoreu(out + 4 * VLEN, y4);
}
static void legendre_transform_vec6(double *recfacs, double *bl, ptrdiff_t lmax,
double xarr[(6) * VLEN],
double out[(6) * VLEN]) {
Tv P_0, Pm1_0, Pm2_0, x0, y0;
Tv P_1, Pm1_1, Pm2_1, x1, y1;
Tv P_2, Pm1_2, Pm2_2, x2, y2;
Tv P_3, Pm1_3, Pm2_3, x3, y3;
Tv P_4, Pm1_4, Pm2_4, x4, y4;
Tv P_5, Pm1_5, Pm2_5, x5, y5;
Tv W1, W2, b, R;
ptrdiff_t l;
x0 = vloadu(xarr + 0 * VLEN);
Pm1_0 = vload(1.0);
P_0 = x0;
b = vload(*bl);
y0 = vmul(Pm1_0, b);
x1 = vloadu(xarr + 1 * VLEN);
Pm1_1 = vload(1.0);
P_1 = x1;
b = vload(*bl);
y1 = vmul(Pm1_1, b);
x2 = vloadu(xarr + 2 * VLEN);
Pm1_2 = vload(1.0);
P_2 = x2;
b = vload(*bl);
y2 = vmul(Pm1_2, b);
x3 = vloadu(xarr + 3 * VLEN);
Pm1_3 = vload(1.0);
P_3 = x3;
b = vload(*bl);
y3 = vmul(Pm1_3, b);
x4 = vloadu(xarr + 4 * VLEN);
Pm1_4 = vload(1.0);
P_4 = x4;
b = vload(*bl);
y4 = vmul(Pm1_4, b);
x5 = vloadu(xarr + 5 * VLEN);
Pm1_5 = vload(1.0);
P_5 = x5;
b = vload(*bl);
y5 = vmul(Pm1_5, b);
b = vload(*(bl + 1));
vfmaeq(y0, P_0, b);
vfmaeq(y1, P_1, b);
vfmaeq(y2, P_2, b);
vfmaeq(y3, P_3, b);
vfmaeq(y4, P_4, b);
vfmaeq(y5, P_5, b);
for (l = 2; l <= lmax; ++l) {
b = vload(*(bl + l));
R = vload(*(recfacs + l));
/*
P = x * Pm1 + recfacs[l] * (x * Pm1 - Pm2)
*/
Pm2_0 = Pm1_0; Pm1_0 = P_0;
W1 = vmul(x0, Pm1_0);
W2 = W1;
W2 = vsub(W2, Pm2_0);
P_0 = W1;
vfmaeq(P_0, W2, R);
vfmaeq(y0, P_0, b);
Pm2_1 = Pm1_1; Pm1_1 = P_1;
W1 = vmul(x1, Pm1_1);
W2 = W1;
W2 = vsub(W2, Pm2_1);
P_1 = W1;
vfmaeq(P_1, W2, R);
vfmaeq(y1, P_1, b);
Pm2_2 = Pm1_2; Pm1_2 = P_2;
W1 = vmul(x2, Pm1_2);
W2 = W1;
W2 = vsub(W2, Pm2_2);
P_2 = W1;
vfmaeq(P_2, W2, R);
vfmaeq(y2, P_2, b);
Pm2_3 = Pm1_3; Pm1_3 = P_3;
W1 = vmul(x3, Pm1_3);
W2 = W1;
W2 = vsub(W2, Pm2_3);
P_3 = W1;
vfmaeq(P_3, W2, R);
vfmaeq(y3, P_3, b);
Pm2_4 = Pm1_4; Pm1_4 = P_4;
W1 = vmul(x4, Pm1_4);
W2 = W1;
W2 = vsub(W2, Pm2_4);
P_4 = W1;
vfmaeq(P_4, W2, R);
vfmaeq(y4, P_4, b);
Pm2_5 = Pm1_5; Pm1_5 = P_5;
W1 = vmul(x5, Pm1_5);
W2 = W1;
W2 = vsub(W2, Pm2_5);
P_5 = W1;
vfmaeq(P_5, W2, R);
vfmaeq(y5, P_5, b);
}
vstoreu(out + 0 * VLEN, y0);
vstoreu(out + 1 * VLEN, y1);
vstoreu(out + 2 * VLEN, y2);
vstoreu(out + 3 * VLEN, y3);
vstoreu(out + 4 * VLEN, y4);
vstoreu(out + 5 * VLEN, y5);
}
static void legendre_transform_vec1_s(float *recfacs, float *bl, ptrdiff_t lmax,
float xarr[(1) * VLEN_s],
float out[(1) * VLEN_s]) {
Tv_s P_0, Pm1_0, Pm2_0, x0, y0;
Tv_s W1, W2, b, R;
ptrdiff_t l;
x0 = vloadu_s(xarr + 0 * VLEN_s);
Pm1_0 = vload_s(1.0);
P_0 = x0;
b = vload_s(*bl);
y0 = vmul_s(Pm1_0, b);
b = vload_s(*(bl + 1));
vfmaeq_s(y0, P_0, b);
for (l = 2; l <= lmax; ++l) {
b = vload_s(*(bl + l));
R = vload_s(*(recfacs + l));
/*
P = x * Pm1 + recfacs[l] * (x * Pm1 - Pm2)
*/
Pm2_0 = Pm1_0; Pm1_0 = P_0;
W1 = vmul_s(x0, Pm1_0);
W2 = W1;
W2 = vsub_s(W2, Pm2_0);
P_0 = W1;
vfmaeq_s(P_0, W2, R);
vfmaeq_s(y0, P_0, b);
}
vstoreu_s(out + 0 * VLEN_s, y0);
}
static void legendre_transform_vec2_s(float *recfacs, float *bl, ptrdiff_t lmax,
float xarr[(2) * VLEN_s],
float out[(2) * VLEN_s]) {
Tv_s P_0, Pm1_0, Pm2_0, x0, y0;
Tv_s P_1, Pm1_1, Pm2_1, x1, y1;
Tv_s W1, W2, b, R;
ptrdiff_t l;
x0 = vloadu_s(xarr + 0 * VLEN_s);
Pm1_0 = vload_s(1.0);
P_0 = x0;
b = vload_s(*bl);
y0 = vmul_s(Pm1_0, b);
x1 = vloadu_s(xarr + 1 * VLEN_s);
Pm1_1 = vload_s(1.0);
P_1 = x1;
b = vload_s(*bl);
y1 = vmul_s(Pm1_1, b);
b = vload_s(*(bl + 1));
vfmaeq_s(y0, P_0, b);
vfmaeq_s(y1, P_1, b);
for (l = 2; l <= lmax; ++l) {
b = vload_s(*(bl + l));
R = vload_s(*(recfacs + l));
/*
P = x * Pm1 + recfacs[l] * (x * Pm1 - Pm2)
*/
Pm2_0 = Pm1_0; Pm1_0 = P_0;
W1 = vmul_s(x0, Pm1_0);
W2 = W1;
W2 = vsub_s(W2, Pm2_0);
P_0 = W1;
vfmaeq_s(P_0, W2, R);
vfmaeq_s(y0, P_0, b);
Pm2_1 = Pm1_1; Pm1_1 = P_1;
W1 = vmul_s(x1, Pm1_1);
W2 = W1;
W2 = vsub_s(W2, Pm2_1);
P_1 = W1;
vfmaeq_s(P_1, W2, R);
vfmaeq_s(y1, P_1, b);
}
vstoreu_s(out + 0 * VLEN_s, y0);
vstoreu_s(out + 1 * VLEN_s, y1);
}
static void legendre_transform_vec3_s(float *recfacs, float *bl, ptrdiff_t lmax,
float xarr[(3) * VLEN_s],
float out[(3) * VLEN_s]) {
Tv_s P_0, Pm1_0, Pm2_0, x0, y0;
Tv_s P_1, Pm1_1, Pm2_1, x1, y1;
Tv_s P_2, Pm1_2, Pm2_2, x2, y2;
Tv_s W1, W2, b, R;
ptrdiff_t l;
x0 = vloadu_s(xarr + 0 * VLEN_s);
Pm1_0 = vload_s(1.0);
P_0 = x0;
b = vload_s(*bl);
y0 = vmul_s(Pm1_0, b);
x1 = vloadu_s(xarr + 1 * VLEN_s);
Pm1_1 = vload_s(1.0);
P_1 = x1;
b = vload_s(*bl);
y1 = vmul_s(Pm1_1, b);
x2 = vloadu_s(xarr + 2 * VLEN_s);
Pm1_2 = vload_s(1.0);
P_2 = x2;
b = vload_s(*bl);
y2 = vmul_s(Pm1_2, b);
b = vload_s(*(bl + 1));
vfmaeq_s(y0, P_0, b);
vfmaeq_s(y1, P_1, b);
vfmaeq_s(y2, P_2, b);
for (l = 2; l <= lmax; ++l) {
b = vload_s(*(bl + l));
R = vload_s(*(recfacs + l));
/*
P = x * Pm1 + recfacs[l] * (x * Pm1 - Pm2)
*/
Pm2_0 = Pm1_0; Pm1_0 = P_0;
W1 = vmul_s(x0, Pm1_0);
W2 = W1;
W2 = vsub_s(W2, Pm2_0);
P_0 = W1;
vfmaeq_s(P_0, W2, R);
vfmaeq_s(y0, P_0, b);
Pm2_1 = Pm1_1; Pm1_1 = P_1;
W1 = vmul_s(x1, Pm1_1);
W2 = W1;
W2 = vsub_s(W2, Pm2_1);
P_1 = W1;
vfmaeq_s(P_1, W2, R);
vfmaeq_s(y1, P_1, b);
Pm2_2 = Pm1_2; Pm1_2 = P_2;
W1 = vmul_s(x2, Pm1_2);
W2 = W1;
W2 = vsub_s(W2, Pm2_2);
P_2 = W1;
vfmaeq_s(P_2, W2, R);
vfmaeq_s(y2, P_2, b);
}
vstoreu_s(out + 0 * VLEN_s, y0);
vstoreu_s(out + 1 * VLEN_s, y1);
vstoreu_s(out + 2 * VLEN_s, y2);
}
static void legendre_transform_vec4_s(float *recfacs, float *bl, ptrdiff_t lmax,
float xarr[(4) * VLEN_s],
float out[(4) * VLEN_s]) {
Tv_s P_0, Pm1_0, Pm2_0, x0, y0;
Tv_s P_1, Pm1_1, Pm2_1, x1, y1;
Tv_s P_2, Pm1_2, Pm2_2, x2, y2;
Tv_s P_3, Pm1_3, Pm2_3, x3, y3;
Tv_s W1, W2, b, R;
ptrdiff_t l;
x0 = vloadu_s(xarr + 0 * VLEN_s);
Pm1_0 = vload_s(1.0);
P_0 = x0;
b = vload_s(*bl);
y0 = vmul_s(Pm1_0, b);
x1 = vloadu_s(xarr + 1 * VLEN_s);
Pm1_1 = vload_s(1.0);
P_1 = x1;
b = vload_s(*bl);
y1 = vmul_s(Pm1_1, b);
x2 = vloadu_s(xarr + 2 * VLEN_s);
Pm1_2 = vload_s(1.0);
P_2 = x2;
b = vload_s(*bl);
y2 = vmul_s(Pm1_2, b);
x3 = vloadu_s(xarr + 3 * VLEN_s);
Pm1_3 = vload_s(1.0);
P_3 = x3;
b = vload_s(*bl);
y3 = vmul_s(Pm1_3, b);
b = vload_s(*(bl + 1));
vfmaeq_s(y0, P_0, b);
vfmaeq_s(y1, P_1, b);
vfmaeq_s(y2, P_2, b);
vfmaeq_s(y3, P_3, b);
for (l = 2; l <= lmax; ++l) {
b = vload_s(*(bl + l));
R = vload_s(*(recfacs + l));
/*
P = x * Pm1 + recfacs[l] * (x * Pm1 - Pm2)
*/
Pm2_0 = Pm1_0; Pm1_0 = P_0;
W1 = vmul_s(x0, Pm1_0);
W2 = W1;
W2 = vsub_s(W2, Pm2_0);
P_0 = W1;
vfmaeq_s(P_0, W2, R);
vfmaeq_s(y0, P_0, b);
Pm2_1 = Pm1_1; Pm1_1 = P_1;
W1 = vmul_s(x1, Pm1_1);
W2 = W1;
W2 = vsub_s(W2, Pm2_1);
P_1 = W1;
vfmaeq_s(P_1, W2, R);
vfmaeq_s(y1, P_1, b);
Pm2_2 = Pm1_2; Pm1_2 = P_2;
W1 = vmul_s(x2, Pm1_2);
W2 = W1;
W2 = vsub_s(W2, Pm2_2);
P_2 = W1;
vfmaeq_s(P_2, W2, R);
vfmaeq_s(y2, P_2, b);
Pm2_3 = Pm1_3; Pm1_3 = P_3;
W1 = vmul_s(x3, Pm1_3);
W2 = W1;
W2 = vsub_s(W2, Pm2_3);
P_3 = W1;
vfmaeq_s(P_3, W2, R);
vfmaeq_s(y3, P_3, b);
}
vstoreu_s(out + 0 * VLEN_s, y0);
vstoreu_s(out + 1 * VLEN_s, y1);
vstoreu_s(out + 2 * VLEN_s, y2);
vstoreu_s(out + 3 * VLEN_s, y3);
}
static void legendre_transform_vec5_s(float *recfacs, float *bl, ptrdiff_t lmax,
float xarr[(5) * VLEN_s],
float out[(5) * VLEN_s]) {
Tv_s P_0, Pm1_0, Pm2_0, x0, y0;
Tv_s P_1, Pm1_1, Pm2_1, x1, y1;
Tv_s P_2, Pm1_2, Pm2_2, x2, y2;
Tv_s P_3, Pm1_3, Pm2_3, x3, y3;
Tv_s P_4, Pm1_4, Pm2_4, x4, y4;
Tv_s W1, W2, b, R;
ptrdiff_t l;
x0 = vloadu_s(xarr + 0 * VLEN_s);
Pm1_0 = vload_s(1.0);
P_0 = x0;
b = vload_s(*bl);
y0 = vmul_s(Pm1_0, b);
x1 = vloadu_s(xarr + 1 * VLEN_s);
Pm1_1 = vload_s(1.0);
P_1 = x1;
b = vload_s(*bl);
y1 = vmul_s(Pm1_1, b);
x2 = vloadu_s(xarr + 2 * VLEN_s);
Pm1_2 = vload_s(1.0);
P_2 = x2;
b = vload_s(*bl);
y2 = vmul_s(Pm1_2, b);
x3 = vloadu_s(xarr + 3 * VLEN_s);
Pm1_3 = vload_s(1.0);
P_3 = x3;
b = vload_s(*bl);
y3 = vmul_s(Pm1_3, b);
x4 = vloadu_s(xarr + 4 * VLEN_s);
Pm1_4 = vload_s(1.0);
P_4 = x4;
b = vload_s(*bl);
y4 = vmul_s(Pm1_4, b);
b = vload_s(*(bl + 1));
vfmaeq_s(y0, P_0, b);
vfmaeq_s(y1, P_1, b);
vfmaeq_s(y2, P_2, b);
vfmaeq_s(y3, P_3, b);
vfmaeq_s(y4, P_4, b);
for (l = 2; l <= lmax; ++l) {
b = vload_s(*(bl + l));
R = vload_s(*(recfacs + l));
/*
P = x * Pm1 + recfacs[l] * (x * Pm1 - Pm2)
*/
Pm2_0 = Pm1_0; Pm1_0 = P_0;
W1 = vmul_s(x0, Pm1_0);
W2 = W1;
W2 = vsub_s(W2, Pm2_0);
P_0 = W1;
vfmaeq_s(P_0, W2, R);
vfmaeq_s(y0, P_0, b);
Pm2_1 = Pm1_1; Pm1_1 = P_1;
W1 = vmul_s(x1, Pm1_1);
W2 = W1;
W2 = vsub_s(W2, Pm2_1);
P_1 = W1;
vfmaeq_s(P_1, W2, R);
vfmaeq_s(y1, P_1, b);
Pm2_2 = Pm1_2; Pm1_2 = P_2;
W1 = vmul_s(x2, Pm1_2);
W2 = W1;
W2 = vsub_s(W2, Pm2_2);
P_2 = W1;
vfmaeq_s(P_2, W2, R);
vfmaeq_s(y2, P_2, b);
Pm2_3 = Pm1_3; Pm1_3 = P_3;
W1 = vmul_s(x3, Pm1_3);
W2 = W1;
W2 = vsub_s(W2, Pm2_3);
P_3 = W1;
vfmaeq_s(P_3, W2, R);
vfmaeq_s(y3, P_3, b);
Pm2_4 = Pm1_4; Pm1_4 = P_4;
W1 = vmul_s(x4, Pm1_4);
W2 = W1;
W2 = vsub_s(W2, Pm2_4);
P_4 = W1;
vfmaeq_s(P_4, W2, R);
vfmaeq_s(y4, P_4, b);
}
vstoreu_s(out + 0 * VLEN_s, y0);
vstoreu_s(out + 1 * VLEN_s, y1);
vstoreu_s(out + 2 * VLEN_s, y2);
vstoreu_s(out + 3 * VLEN_s, y3);
vstoreu_s(out + 4 * VLEN_s, y4);
}
static void legendre_transform_vec6_s(float *recfacs, float *bl, ptrdiff_t lmax,
float xarr[(6) * VLEN_s],
float out[(6) * VLEN_s]) {
Tv_s P_0, Pm1_0, Pm2_0, x0, y0;
Tv_s P_1, Pm1_1, Pm2_1, x1, y1;
Tv_s P_2, Pm1_2, Pm2_2, x2, y2;
Tv_s P_3, Pm1_3, Pm2_3, x3, y3;
Tv_s P_4, Pm1_4, Pm2_4, x4, y4;
Tv_s P_5, Pm1_5, Pm2_5, x5, y5;
Tv_s W1, W2, b, R;
ptrdiff_t l;
x0 = vloadu_s(xarr + 0 * VLEN_s);
Pm1_0 = vload_s(1.0);
P_0 = x0;
b = vload_s(*bl);
y0 = vmul_s(Pm1_0, b);
x1 = vloadu_s(xarr + 1 * VLEN_s);
Pm1_1 = vload_s(1.0);
P_1 = x1;
b = vload_s(*bl);
y1 = vmul_s(Pm1_1, b);
x2 = vloadu_s(xarr + 2 * VLEN_s);
Pm1_2 = vload_s(1.0);
P_2 = x2;
b = vload_s(*bl);
y2 = vmul_s(Pm1_2, b);
x3 = vloadu_s(xarr + 3 * VLEN_s);
Pm1_3 = vload_s(1.0);
P_3 = x3;
b = vload_s(*bl);
y3 = vmul_s(Pm1_3, b);
x4 = vloadu_s(xarr + 4 * VLEN_s);
Pm1_4 = vload_s(1.0);
P_4 = x4;
b = vload_s(*bl);
y4 = vmul_s(Pm1_4, b);
x5 = vloadu_s(xarr + 5 * VLEN_s);
Pm1_5 = vload_s(1.0);
P_5 = x5;
b = vload_s(*bl);
y5 = vmul_s(Pm1_5, b);
b = vload_s(*(bl + 1));
vfmaeq_s(y0, P_0, b);
vfmaeq_s(y1, P_1, b);
vfmaeq_s(y2, P_2, b);
vfmaeq_s(y3, P_3, b);
vfmaeq_s(y4, P_4, b);
vfmaeq_s(y5, P_5, b);
for (l = 2; l <= lmax; ++l) {
b = vload_s(*(bl + l));
R = vload_s(*(recfacs + l));
/*
P = x * Pm1 + recfacs[l] * (x * Pm1 - Pm2)
*/
Pm2_0 = Pm1_0; Pm1_0 = P_0;
W1 = vmul_s(x0, Pm1_0);
W2 = W1;
W2 = vsub_s(W2, Pm2_0);
P_0 = W1;
vfmaeq_s(P_0, W2, R);
vfmaeq_s(y0, P_0, b);
Pm2_1 = Pm1_1; Pm1_1 = P_1;
W1 = vmul_s(x1, Pm1_1);
W2 = W1;
W2 = vsub_s(W2, Pm2_1);
P_1 = W1;
vfmaeq_s(P_1, W2, R);
vfmaeq_s(y1, P_1, b);
Pm2_2 = Pm1_2; Pm1_2 = P_2;
W1 = vmul_s(x2, Pm1_2);
W2 = W1;
W2 = vsub_s(W2, Pm2_2);
P_2 = W1;
vfmaeq_s(P_2, W2, R);
vfmaeq_s(y2, P_2, b);
Pm2_3 = Pm1_3; Pm1_3 = P_3;
W1 = vmul_s(x3, Pm1_3);
W2 = W1;
W2 = vsub_s(W2, Pm2_3);
P_3 = W1;
vfmaeq_s(P_3, W2, R);
vfmaeq_s(y3, P_3, b);
Pm2_4 = Pm1_4; Pm1_4 = P_4;
W1 = vmul_s(x4, Pm1_4);
W2 = W1;
W2 = vsub_s(W2, Pm2_4);
P_4 = W1;
vfmaeq_s(P_4, W2, R);
vfmaeq_s(y4, P_4, b);
Pm2_5 = Pm1_5; Pm1_5 = P_5;
W1 = vmul_s(x5, Pm1_5);
W2 = W1;
W2 = vsub_s(W2, Pm2_5);
P_5 = W1;
vfmaeq_s(P_5, W2, R);
vfmaeq_s(y5, P_5, b);
}
vstoreu_s(out + 0 * VLEN_s, y0);
vstoreu_s(out + 1 * VLEN_s, y1);
vstoreu_s(out + 2 * VLEN_s, y2);
vstoreu_s(out + 3 * VLEN_s, y3);
vstoreu_s(out + 4 * VLEN_s, y4);
vstoreu_s(out + 5 * VLEN_s, y5);
}
void sharp_legendre_transform_recfac(double *r, ptrdiff_t lmax) {
/* (l - 1) / l, for l >= 2 */
ptrdiff_t l;
r[0] = 0;
r[1] = 1;
for (l = 2; l <= lmax; ++l) {
r[l] = (double)(l - 1) / (double)l;
}
}
void sharp_legendre_transform_recfac_s(float *r, ptrdiff_t lmax) {
/* (l - 1) / l, for l >= 2 */
ptrdiff_t l;
r[0] = 0;
r[1] = 1;
for (l = 2; l <= lmax; ++l) {
r[l] = (float)(l - 1) / (float)l;
}
}
/*
Compute sum_l b_l P_l(x_i) for all i.
*/
#define LEN (SHARP_LEGENDRE_CS * VLEN)
#define LEN_s (SHARP_LEGENDRE_CS * VLEN_s)
void sharp_legendre_transform(double *bl,
double *recfac,
ptrdiff_t lmax,
double *x, double *out, ptrdiff_t nx) {
double xchunk[MAX_CS * VLEN], outchunk[MAX_CS * LEN];
int compute_recfac;
ptrdiff_t i, j, len;
compute_recfac = (recfac == NULL);
if (compute_recfac) {
recfac = malloc(sizeof(double) * (lmax + 1));
sharp_legendre_transform_recfac(recfac, lmax);
}
for (j = 0; j != LEN; ++j) xchunk[j] = 0;
for (i = 0; i < nx; i += LEN) {
len = (i + (LEN) <= nx) ? (LEN) : (nx - i);
for (j = 0; j != len; ++j) xchunk[j] = x[i + j];
switch ((len + VLEN - 1) / VLEN) {
case 6: legendre_transform_vec6(recfac, bl, lmax, xchunk, outchunk); break;
case 5: legendre_transform_vec5(recfac, bl, lmax, xchunk, outchunk); break;
case 4: legendre_transform_vec4(recfac, bl, lmax, xchunk, outchunk); break;
case 3: legendre_transform_vec3(recfac, bl, lmax, xchunk, outchunk); break;
case 2: legendre_transform_vec2(recfac, bl, lmax, xchunk, outchunk); break;
case 1:
case 0:
legendre_transform_vec1(recfac, bl, lmax, xchunk, outchunk); break;
}
for (j = 0; j != len; ++j) out[i + j] = outchunk[j];
}
if (compute_recfac) {
free(recfac);
}
}
void sharp_legendre_transform_s(float *bl,
float *recfac,
ptrdiff_t lmax,
float *x, float *out, ptrdiff_t nx) {
float xchunk[MAX_CS * VLEN_s], outchunk[MAX_CS * LEN_s];
int compute_recfac;
ptrdiff_t i, j, len;
compute_recfac = (recfac == NULL);
if (compute_recfac) {
recfac = malloc(sizeof(float) * (lmax + 1));
sharp_legendre_transform_recfac_s(recfac, lmax);
}
for (j = 0; j != LEN_s; ++j) xchunk[j] = 0;
for (i = 0; i < nx; i += LEN_s) {
len = (i + (LEN_s) <= nx) ? (LEN_s) : (nx - i);
for (j = 0; j != len; ++j) xchunk[j] = x[i + j];
switch ((len + VLEN_s - 1) / VLEN_s) {
case 6: legendre_transform_vec6_s(recfac, bl, lmax, xchunk, outchunk); break;
case 5: legendre_transform_vec5_s(recfac, bl, lmax, xchunk, outchunk); break;
case 4: legendre_transform_vec4_s(recfac, bl, lmax, xchunk, outchunk); break;
case 3: legendre_transform_vec3_s(recfac, bl, lmax, xchunk, outchunk); break;
case 2: legendre_transform_vec2_s(recfac, bl, lmax, xchunk, outchunk); break;
case 1:
case 0:
legendre_transform_vec1_s(recfac, bl, lmax, xchunk, outchunk); break;
}
for (j = 0; j != len; ++j) out[i + j] = outchunk[j];
}
if (compute_recfac) {
free(recfac);
}
}
#endif
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