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Matthieu Schaller authoredMatthieu Schaller authored
kernel.h 20.33 KiB
/*******************************************************************************
* This file is part of SWIFT.
* Copyright (c) 2012 Pedro Gonnet (pedro.gonnet@durham.ac.uk)
* Matthieu Schaller (matthieu.schaller@durham.ac.uk)
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published
* by the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*
******************************************************************************/
#ifndef SWIFT_KERNEL_H
#define SWIFT_KERNEL_H
/* Includes. */
#include "const.h"
#include "inline.h"
#include "vector.h"
/**
* @file kernel.h
* @brief SPH kernel functions. Compute W(x,h) and the gradient of W(x,h),
* as well as the blending function used for gravity.
*/
/* Gravity kernel stuff
* -----------------------------------------------------------------------------------------------
*/
/* The gravity kernel is defined as a degree 6 polynomial in the distance
r. The resulting value should be post-multiplied with r^-3, resulting
in a polynomial with terms ranging from r^-3 to r^3, which are
sufficient to model both the direct potential as well as the splines
near the origin. */
/* Coefficients for the gravity kernel. */
#define kernel_grav_degree 6
#define kernel_grav_ivals 2
#define kernel_grav_scale (2 * const_iepsilon)
static float kernel_grav_coeffs
[(kernel_grav_degree + 1) * (kernel_grav_ivals + 1)] = {
32.0f * const_iepsilon6, -192.0f / 5.0f * const_iepsilon5,
0.0f, 32.0f / 3.0f * const_iepsilon3,
0.0f, 0.0f,
0.0f, -32.0f / 3.0f * const_iepsilon6,
192.0f / 5.0f * const_iepsilon5, -48.0f * const_iepsilon4,
64.0f / 3.0f * const_iepsilon3, 0.0f,
0.0f, -1.0f / 15.0f,
0.0f, 0.0f,
0.0f, 0.0f,
0.0f, 0.0f,
1.0f};
/**
* @brief Computes the gravity cubic spline for a given distance x.
*/
__attribute__((always_inline)) INLINE static void kernel_grav_eval(float x,
float *W) {
int ind = fmin(x * kernel_grav_scale, kernel_grav_ivals);
float *coeffs = &kernel_grav_coeffs[ind * (kernel_grav_degree + 1)];
float w = coeffs[0] * x + coeffs[1]; for (int k = 2; k <= kernel_grav_degree; k++) w = x * w + coeffs[k];
*W = w;
}
#ifdef VECTORIZE
/**
* @brief Computes the gravity cubic spline for a given distance x (Vectorized
* version).
*/
__attribute__((always_inline))
INLINE static void kernel_grav_eval_vec(vector *x, vector *w) {
vector ind, c[kernel_grav_degree + 1];
int j, k;
/* Load x and get the interval id. */
ind.m = vec_ftoi(vec_fmin(x->v * vec_set1(kernel_grav_scale),
vec_set1((float)kernel_grav_ivals)));
/* load the coefficients. */
for (k = 0; k < VEC_SIZE; k++)
for (j = 0; j < kernel_grav_degree + 1; j++)
c[j].f[k] = kernel_grav_coeffs[ind.i[k] * (kernel_grav_degree + 1) + j];
/* Init the iteration for Horner's scheme. */
w->v = (c[0].v * x->v) + c[1].v;
/* And we're off! */
for (int k = 2; k <= kernel_grav_degree; k++) w->v = (x->v * w->v) + c[k].v;
}
#endif
/* Blending function stuff
* --------------------------------------------------------------------------------------------
*/
/* Coefficients for the blending function. */
#define blender_degree 3
#define blender_ivals 3
#define blender_scale 4.0f
static float blender_coeffs[(blender_degree + 1) * (blender_ivals + 1)] = {
0.0f, 0.0f, 0.0f, 1.0f, -32.0f, 24.0f, -6.0f, 1.5f,
-32.0f, 72.0f, -54.0f, 13.5f, 0.0f, 0.0f, 0.0f, 0.0f};
/**
* @brief Computes the cubic spline blender for a given distance x.
*/
__attribute__((always_inline)) INLINE static void blender_eval(float x,
float *W) {
int ind = fmin(x * blender_scale, blender_ivals);
float *coeffs = &blender_coeffs[ind * (blender_degree + 1)];
float w = coeffs[0] * x + coeffs[1];
for (int k = 2; k <= blender_degree; k++) w = x * w + coeffs[k];
*W = w;
}
/**
* @brief Computes the cubic spline blender and its derivative for a given
* distance x.
*/
__attribute__((always_inline)) INLINE static void blender_deval(float x,
float *W,
float *dW_dx) {
int ind = fminf(x * blender_scale, blender_ivals);
float *coeffs = &blender_coeffs[ind * (blender_degree + 1)]; float w = coeffs[0] * x + coeffs[1];
float dw_dx = coeffs[0];
for (int k = 2; k <= blender_degree; k++) {
dw_dx = dw_dx * x + w;
w = x * w + coeffs[k];
}
*W = w;
*dW_dx = dw_dx;
}
#ifdef VECTORIZE
/**
* @brief Computes the cubic spline blender and its derivative for a given
* distance x (Vectorized version). Gives a sensible answer only if x<2.
*/
__attribute__((always_inline)) INLINE static void blender_eval_vec(vector *x,
vector *w) {
vector ind, c[blender_degree + 1];
int j, k;
/* Load x and get the interval id. */
ind.m = vec_ftoi(
vec_fmin(x->v * vec_set1(blender_scale), vec_set1((float)blender_ivals)));
/* load the coefficients. */
for (k = 0; k < VEC_SIZE; k++)
for (j = 0; j < blender_degree + 1; j++)
c[j].f[k] = blender_coeffs[ind.i[k] * (blender_degree + 1) + j];
/* Init the iteration for Horner's scheme. */
w->v = (c[0].v * x->v) + c[1].v;
/* And we're off! */
for (int k = 2; k <= blender_degree; k++) w->v = (x->v * w->v) + c[k].v;
}
/**
* @brief Computes the cubic spline blender and its derivative for a given
* distance x (Vectorized version). Gives a sensible answer only if x<2.
*/
__attribute__((always_inline))
INLINE static void blender_deval_vec(vector *x, vector *w, vector *dw_dx) {
vector ind, c[blender_degree + 1];
int j, k;
/* Load x and get the interval id. */
ind.m = vec_ftoi(
vec_fmin(x->v * vec_set1(blender_scale), vec_set1((float)blender_ivals)));
/* load the coefficients. */
for (k = 0; k < VEC_SIZE; k++)
for (j = 0; j < blender_degree + 1; j++)
c[j].f[k] = blender_coeffs[ind.i[k] * (blender_degree + 1) + j];
/* Init the iteration for Horner's scheme. */
w->v = (c[0].v * x->v) + c[1].v;
dw_dx->v = c[0].v;
/* And we're off! */
for (int k = 2; k <= blender_degree; k++) {
dw_dx->v = (dw_dx->v * x->v) + w->v;
w->v = (x->v * w->v) + c[k].v;
}
}
#endif
/* --------------------------------------------------------------------------------------------------------------------
*/
#if defined(CUBIC_SPLINE_KERNEL)
/* --------------------------------------------------------------------------------------------------------------------
*/
/* Coefficients for the kernel. */
#define kernel_name "Cubic spline"
#define kernel_degree 3
#define kernel_ivals 2
#define kernel_gamma 2.0f
#define kernel_gamma2 4.0f
#define kernel_gamma3 8.0f
#define kernel_igamma 0.5f
#define kernel_nwneigh \
(4.0 / 3.0 * M_PI *const_eta_kernel *const_eta_kernel *const_eta_kernel * \
6.0858f)
static float kernel_coeffs[(kernel_degree + 1) * (kernel_ivals + 1)]
__attribute__((aligned(16))) = {
3.0 / 4.0 * M_1_PI, -3.0 / 2.0 * M_1_PI, 0.0, M_1_PI,
-0.25 * M_1_PI, 3.0 / 2.0 * M_1_PI, -3.0 * M_1_PI, M_2_PI,
0.0, 0.0, 0.0, 0.0};
#define kernel_root (kernel_coeffs[kernel_degree])
#define kernel_wroot (4.0 / 3.0 * M_PI *kernel_coeffs[kernel_degree])
/**
* @brief Computes the cubic spline kernel and its derivative for a given
* distance x. Gives a sensible answer only if x<2.
*/
__attribute__((always_inline)) INLINE static void kernel_deval(float x,
float *W,
float *dW_dx) {
int ind = fminf(x, kernel_ivals);
float *coeffs = &kernel_coeffs[ind * (kernel_degree + 1)];
float w = coeffs[0] * x + coeffs[1];
float dw_dx = coeffs[0];
for (int k = 2; k <= kernel_degree; k++) {
dw_dx = dw_dx * x + w;
w = x * w + coeffs[k];
}
*W = w;
*dW_dx = dw_dx;
}
#ifdef VECTORIZE
/**
* @brief Computes the cubic spline kernel and its derivative for a given
* distance x (Vectorized version). Gives a sensible answer only if x<2.
*/
__attribute__((always_inline))
INLINE static void kernel_deval_vec(vector *x, vector *w, vector *dw_dx) {
vector ind, c[kernel_degree + 1];
int j, k;
/* Load x and get the interval id. */
ind.m = vec_ftoi(vec_fmin(x->v, vec_set1((float)kernel_ivals)));
/* load the coefficients. */
for (k = 0; k < VEC_SIZE; k++)
for (j = 0; j < kernel_degree + 1; j++)
c[j].f[k] = kernel_coeffs[ind.i[k] * (kernel_degree + 1) + j];
/* Init the iteration for Horner's scheme. */
w->v = (c[0].v * x->v) + c[1].v;
dw_dx->v = c[0].v;
/* And we're off! */
for (int k = 2; k <= kernel_degree; k++) {
dw_dx->v = (dw_dx->v * x->v) + w->v;
w->v = (x->v * w->v) + c[k].v;
}
}
#endif
/**
* @brief Computes the cubic spline kernel for a given distance x. Gives a
* sensible answer only if x<2.
*/
__attribute__((always_inline)) INLINE static void kernel_eval(float x,
float *W) {
int ind = fmin(x, kernel_ivals);
float *coeffs = &kernel_coeffs[ind * (kernel_degree + 1)];
float w = coeffs[0] * x + coeffs[1];
for (int k = 2; k <= kernel_degree; k++) w = x * w + coeffs[k];
*W = w;
}
/* --------------------------------------------------------------------------------------------------------------------
*/
#elif defined(QUARTIC_SPLINE_KERNEL)
/* --------------------------------------------------------------------------------------------------------------------
*/
/* Coefficients for the kernel. */
#define kernel_name "Quartic spline"
#define kernel_degree 4
#define kernel_ivals 3
#define kernel_gamma 2.5f
#define kernel_gamma2 6.25f
#define kernel_gamma3 15.625f
#define kernel_igamma 0.4f
#define kernel_nwneigh \
(4.0 / 3.0 * M_PI *const_eta_kernel *const_eta_kernel *const_eta_kernel * \
8.2293f)
static float kernel_coeffs[(kernel_degree + 1) * (kernel_ivals + 1)]
__attribute__((aligned(16))) = {
3.0 / 10.0 * M_1_PI, 0.0, -3.0 / 4.0 * M_1_PI,
0.0, 23.0 / 32.0 * M_1_PI, -1.0 / 5.0 * M_1_PI,
M_1_PI, -3.0 / 2.0 * M_1_PI, 0.25 * M_1_PI,
11.0 / 16.0 * M_1_PI, 1.0 / 20.0 * M_1_PI, -0.5 * M_1_PI,
15.0 / 8.0 * M_1_PI, -25.0 / 8.0 * M_1_PI, 125.0 / 64.0 * M_1_PI,
0.0, 0.0, 0.0,
0.0, 0.0};
#define kernel_root (kernel_coeffs[kernel_degree])
#define kernel_wroot (4.0 / 3.0 * M_PI *kernel_coeffs[kernel_degree])
/**
* @brief Computes the quartic spline kernel and its derivative for a given
* distance x. Gives a sensible answer only if x<2.5
*/
__attribute__((always_inline)) INLINE static void kernel_deval(float x,
float *W,
float *dW_dx) {
int ind = fminf(x + 0.5, kernel_ivals);
float *coeffs = &kernel_coeffs[ind * (kernel_degree + 1)];
float w = coeffs[0] * x + coeffs[1];
float dw_dx = coeffs[0]; for (int k = 2; k <= kernel_degree; k++) {
dw_dx = dw_dx * x + w;
w = x * w + coeffs[k];
}
*W = w;
*dW_dx = dw_dx;
}
#ifdef VECTORIZE
/**
* @brief Computes the quartic spline kernel and its derivative for a given
* distance x (Vectorized version). Gives a sensible answer only if x<2.5
*/
__attribute__((always_inline))
INLINE static void kernel_deval_vec(vector *x, vector *w, vector *dw_dx) {
vector ind, c[kernel_degree + 1];
int j, k;
/* Load x and get the interval id. */
ind.m = vec_ftoi(vec_fmin(x->v + 0.5f, vec_set1((float)kernel_ivals)));
/* load the coefficients. */
for (k = 0; k < VEC_SIZE; k++)
for (j = 0; j < kernel_degree + 1; j++)
c[j].f[k] = kernel_coeffs[ind.i[k] * (kernel_degree + 1) + j];
/* Init the iteration for Horner's scheme. */
w->v = (c[0].v * x->v) + c[1].v;
dw_dx->v = c[0].v;
/* And we're off! */
for (int k = 2; k <= kernel_degree; k++) {
dw_dx->v = (dw_dx->v * x->v) + w->v;
w->v = (x->v * w->v) + c[k].v;
}
}
#endif
/**
* @brief Computes the quartic spline kernel for a given distance x. Gives a
* sensible answer only if x<2.5
*/
__attribute__((always_inline)) INLINE static void kernel_eval(float x,
float *W) {
int ind = fmin(x + 0.5f, kernel_ivals);
float *coeffs = &kernel_coeffs[ind * (kernel_degree + 1)];
float w = coeffs[0] * x + coeffs[1];
for (int k = 2; k <= kernel_degree; k++) w = x * w + coeffs[k];
*W = w;
}
/* --------------------------------------------------------------------------------------------------------------------
*/
#elif defined(QUINTIC_SPLINE_KERNEL)
/* --------------------------------------------------------------------------------------------------------------------
*/
/* Coefficients for the kernel. */
#define kernel_name "Quintic spline"
#define kernel_degree 5
#define kernel_ivals 3
#define kernel_gamma 3.f
#define kernel_gamma2 9.f#define kernel_gamma3 27.f
#define kernel_igamma 1.0f / 3.0f
#define kernel_nwneigh \
(4.0 / 3.0 * M_PI *const_eta_kernel *const_eta_kernel *const_eta_kernel * \
10.5868f)
static float kernel_coeffs[(kernel_degree + 1) * (kernel_ivals + 1)]
__attribute__((aligned(16))) = {
-1.0 / 12.0 * M_1_PI, 1.0 / 4.0 * M_1_PI, 0.0,
-1.0 / 2.0 * M_1_PI, 0.0, 11.0 / 20.0 * M_1_PI,
1.0 / 24.0 * M_1_PI, -3.0 / 8.0 * M_1_PI, 5.0 / 4.0 * M_1_PI,
-7.0 / 4.0 * M_1_PI, 5.0 / 8.0 * M_1_PI, 17.0 / 40.0 * M_1_PI,
-1.0 / 120.0 * M_1_PI, 1.0 / 8.0 * M_1_PI, -3.0 / 4.0 * M_1_PI,
9.0 / 4.0 * M_1_PI, -27.0 / 8.0 * M_1_PI, 81.0 / 40.0 * M_1_PI,
0.0, 0.0, 0.0,
0.0, 0.0, 0.0};
#define kernel_root (kernel_coeffs[kernel_degree])
#define kernel_wroot (4.0 / 3.0 * M_PI *kernel_coeffs[kernel_degree])
/**
* @brief Computes the quintic spline kernel and its derivative for a given
* distance x. Gives a sensible answer only if x<3.
*/
__attribute__((always_inline)) INLINE static void kernel_deval(float x,
float *W,
float *dW_dx) {
int ind = fminf(x, kernel_ivals);
float *coeffs = &kernel_coeffs[ind * (kernel_degree + 1)];
float w = coeffs[0] * x + coeffs[1];
float dw_dx = coeffs[0];
for (int k = 2; k <= kernel_degree; k++) {
dw_dx = dw_dx * x + w;
w = x * w + coeffs[k];
}
*W = w;
*dW_dx = dw_dx;
}
#ifdef VECTORIZE
/**
* @brief Computes the quintic spline kernel and its derivative for a given
* distance x (Vectorized version). Gives a sensible answer only if x<3.
*/
__attribute__((always_inline))
INLINE static void kernel_deval_vec(vector *x, vector *w, vector *dw_dx) {
vector ind, c[kernel_degree + 1];
int j, k;
/* Load x and get the interval id. */
ind.m = vec_ftoi(vec_fmin(x->v, vec_set1((float)kernel_ivals)));
/* load the coefficients. */
for (k = 0; k < VEC_SIZE; k++)
for (j = 0; j < kernel_degree + 1; j++)
c[j].f[k] = kernel_coeffs[ind.i[k] * (kernel_degree + 1) + j];
/* Init the iteration for Horner's scheme. */
w->v = (c[0].v * x->v) + c[1].v;
dw_dx->v = c[0].v;
/* And we're off! */
for (int k = 2; k <= kernel_degree; k++) {
dw_dx->v = (dw_dx->v * x->v) + w->v;
w->v = (x->v * w->v) + c[k].v;
}
}
#endif
/**
* @brief Computes the quintic spline kernel for a given distance x. Gives a
* sensible answer only if x<3.
*/
__attribute__((always_inline)) INLINE static void kernel_eval(float x,
float *W) {
int ind = fmin(x, kernel_ivals);
float *coeffs = &kernel_coeffs[ind * (kernel_degree + 1)];
float w = coeffs[0] * x + coeffs[1];
for (int k = 2; k <= kernel_degree; k++) w = x * w + coeffs[k];
*W = w;
}
/* --------------------------------------------------------------------------------------------------------------------
*/
#elif defined(WENDLAND_C2_KERNEL)
/* --------------------------------------------------------------------------------------------------------------------
*/
/* Coefficients for the kernel. */
#define kernel_name "Wendland C2"
#define kernel_degree 5
#define kernel_ivals 1
#define kernel_gamma 2.f
#define kernel_gamma2 4.f
#define kernel_gamma3 8.f
#define kernel_igamma 0.5f
#define kernel_nwneigh \
(4.0 / 3.0 * M_PI *const_eta_kernel *const_eta_kernel *const_eta_kernel * \
7.261825f)
static float kernel_coeffs[(kernel_degree + 1) * (kernel_ivals + 1)]
__attribute__((aligned(16))) = {
0.05222272f, -0.39167037f, 1.04445431f, -1.04445431f, 0.f, 0.41778173f,
0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f};
#define kernel_root (kernel_coeffs[kernel_degree])
#define kernel_wroot (4.0 / 3.0 * M_PI *kernel_coeffs[kernel_degree])
/**
* @brief Computes the quintic spline kernel and its derivative for a given
* distance x. Gives a sensible answer only if x<1.
*/
__attribute__((always_inline)) INLINE static void kernel_deval(float x,
float *W,
float *dW_dx) {
int ind = fminf(0.5f * x, kernel_ivals);
float *coeffs = &kernel_coeffs[ind * (kernel_degree + 1)];
float w = coeffs[0] * x + coeffs[1];
float dw_dx = coeffs[0];
for (int k = 2; k <= kernel_degree; k++) {
dw_dx = dw_dx * x + w;
w = x * w + coeffs[k];
}
*W = w;
*dW_dx = dw_dx;
}
#ifdef VECTORIZE
/**
* @brief Computes the Wendland C2 kernel and its derivative for a given
* distance x (Vectorized version). Gives a sensible answer only if x<1.
*/
__attribute__((always_inline)) INLINE static void kernel_deval_vec(vector *x, vector *w, vector *dw_dx) {
vector ind, c[kernel_degree + 1];
int j, k;
/* Load x and get the interval id. */
ind.m = vec_ftoi(vec_fmin(0.5f * x->v, vec_set1((float)kernel_ivals)));
/* load the coefficients. */
for (k = 0; k < VEC_SIZE; k++)
for (j = 0; j < kernel_degree + 1; j++)
c[j].f[k] = kernel_coeffs[ind.i[k] * (kernel_degree + 1) + j];
/* Init the iteration for Horner's scheme. */
w->v = (c[0].v * x->v) + c[1].v;
dw_dx->v = c[0].v;
/* And we're off! */
for (int k = 2; k <= kernel_degree; k++) {
dw_dx->v = (dw_dx->v * x->v) + w->v;
w->v = (x->v * w->v) + c[k].v;
}
}
#endif
/**
* @brief Computes the Wendland C2 kernel for a given distance x. Gives a
* sensible answer only if x<1.
*/
__attribute__((always_inline)) INLINE static void kernel_eval(float x,
float *W) {
int ind = fmin(0.5f * x, kernel_ivals);
float *coeffs = &kernel_coeffs[ind * (kernel_degree + 1)];
float w = coeffs[0] * x + coeffs[1];
for (int k = 2; k <= kernel_degree; k++) w = x * w + coeffs[k];
*W = w;
}
/* --------------------------------------------------------------------------------------------------------------------
*/
#else
/* --------------------------------------------------------------------------------------------------------------------
*/
#error "A kernel function must be chosen in const.h !!"
#endif // Kernel choice
/* Some cross-check functions */
void SPH_kernel_dump(int N);
void gravity_kernel_dump(float r_max, int N);
#endif // SWIFT_KERNEL_H