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Commit f266036d authored by Matthieu Schaller's avatar Matthieu Schaller
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src/kernel_hydro.h
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/* Includes. */
#include "const.h"
#include "error.h"
#include "inline.h"
#include "vector.h"
#if defined(CUBIC_SPLINE_KERNEL)
/* --------------------------------------------------------------------------------------------------------------------
*/
/* ----------------------------------------------------------------------------- */
#if defined(CUBIC_SPLINE_KERNEL)
/* Coefficients for the kernel. */
#define kernel_name "Cubic spline"
#define kernel_name "Cubic spline (M4)"
#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)
#define kernel_gamma 1.825742
#define kernel_constant 16. * M_1_PI
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)
+48.f * M_1_PI, -48.f * M_1_PI, 0.f, +8.f * M_1_PI,
-16.f * M_1_PI, +48.f * M_1_PI, -48.f * M_1_PI, +16.f * M_1_PI,
0.f, 0.f, 0.f, 0.f};
/* --------------------------------------------------------------------------------------------------------------------
*/
/* ----------------------------------------------------------------------------- */
#elif defined(WENDLAND_C2_KERNEL)
/* Coefficients for the kernel. */
#define kernel_name "Quintic spline"
#define kernel_name "Wendland C2"
#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)
#define kernel_ivals 1
#define kernel_gamma 1.936492
#define kernel_constant 10.5 * M_1_PI
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])
42.f * M_1_PI, -157.5f * M_1_PI, 210.f * M_1_PI, -105.f * M_1_PI,
0.f, 10.5f * M_1_PI, 0.f, 0.f,
0.f, 0.f, 0.f, 0.f};
/**
* @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.
*/
/* ----------------------------------------------------------------------------- */
#else
__attribute__((always_inline))
INLINE static void kernel_deval_vec(vector *x, vector *w, vector *dw_dx) {
#error "A kernel function must be chosen in const.h !!"
vector ind, c[kernel_degree + 1];
int j, k;
#endif
/* Load x and get the interval id. */
ind.m = vec_ftoi(vec_fmin(x->v, vec_set1((float)kernel_ivals)));
/* Ok, now comes the real deal. */
/* 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];
/* First some powers of gamma = H/h */
#define kernel_gamma2 kernel_gamma *kernel_gamma
#define kernel_gamma3 kernel_gamma2 *kernel_gamma
#define kernel_gamma4 kernel_gamma3 *kernel_gamma
#define kernel_igamma 1. / kernel_gamma
#define kernel_igamma2 kernel_igamma *kernel_igamma
#define kernel_igamma3 kernel_igamma2 *kernel_igamma
#define kernel_igamma4 kernel_igamma3 *kernel_igamma
/* Init the iteration for Horner's scheme. */
w->v = (c[0].v * x->v) + c[1].v;
dw_dx->v = c[0].v;
/* Some powers of eta */
#define kernel_eta3 const_eta_kernel *const_eta_kernel *const_eta_kernel
/* 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;
}
}
/* The number of neighbours (i.e. N_ngb) */
#define kernel_nwneigh 4.0 * M_PI *kernel_gamma3 *kernel_eta3 / 3.0
#endif
/* Kernel self contribution (i.e. W(0,h)) */
#define kernel_root (kernel_coeffs[kernel_degree]) * kernel_igamma3
/**
* @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)
/* --------------------------------------------------------------------------------------------------------------------
* @brief Computes the kernel function and its derivative.
*
* Return 0 if $u > \\gamma = H/h$
*
* @param u The ratio of the distance to the smoothing length $u = x/h$.
* @param W (return) The value of the kernel function $W(x,h)$.
* @param dW_dx (return) The norm of the gradient of $|\\nabla W(x,h)|$.
*/
__attribute__((always_inline)) INLINE static void kernel_deval(
float u, float *const W, float *const dW_dx) {
/* 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])
/* Go to the range [0,1[ from [0,H[ */
const float x = u * kernel_igamma;
/**
* @brief Computes the quintic spline kernel and its derivative for a given
* distance x. Gives a sensible answer only if x<1.
*/
/* Pick the correct branch of the kernel */
const int ind = (int)fminf(x * (float)kernel_ivals, kernel_ivals);
const float *const coeffs = &kernel_coeffs[ind * (kernel_degree + 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)];
/* First two terms of the polynomial ... */
float w = coeffs[0] * x + coeffs[1];
float dw_dx = coeffs[0];
/* ... and the rest of them */
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;
}
/* Return everything */
*W = w * kernel_igamma3;
*dW_dx = dw_dx * kernel_igamma4;
}
#endif
/**
* @brief Computes the Wendland C2 kernel for a given distance x. Gives a
* sensible answer only if x<1.
* @brief Computes the kernel function.
*
* @param u The ratio of the distance to the smoothing length $u = x/h$.
* @param W (return) The value of the kernel function $W(x,h)$.
*/
__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 *const W) {
const int ind = fminf(x * 0.5f, kernel_ivals);
const float *const 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 hydro_kernel_dump(int N);
......
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