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kernel_fast_lean.h
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kernel_fast_lean.h
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#ifndef kernel_fast_lean_h
#define kernel_fast_lean_h
#include "exafmm.h"
#include <iostream>
#include <math.h> /*isnan, sqrt, atan2 */
#include <stdio.h> /*printf */
#include "vectorclass/vectorclass.h"
#ifndef DOUBLE_P2P
#define NSIMD 16
#else
#define NSIMD 8
#endif
#ifdef MINIBALL
#include "miniball.hpp"
#endif
#ifdef SIMD_M2L
#include "kernel_rotate_two_arrays.h"
#else
#include "kernel_rotate.h"
#endif
namespace exafmm
{
real_t t_design[64 * 3] = {
-.3345022001069780, .2559037493280540, -.9069848671303380,
.2559037493281330, -.9069848671303220, -.3345022001069590,
.3345022001069660, -.2559037493280760, -.9069848671303360,
-.9069848671303240, -.3345022001070400, .2559037493280210,
-.2559037493280450, -.9069848671303130, .3345022001070510,
-.9069848671303130, .3345022001069890, -.2559037493281280,
-.2559037493280770, .9069848671303280, -.3345022001069860,
.9069848671303340, .3345022001069990, .2559037493280370,
.2559037493280530, .9069848671303270, .3345022001070080,
.9069848671303220, -.3345022001070060, -.2559037493280710,
-.3345022001070360, -.2559037493280360, .9069848671303210,
.3345022001069960, .2559037493281340, .9069848671303080,
.1812453816504250, .1532808703053070, -.9714191095654030,
.1532808703053200, -.9714191095653860, .1812453816505030,
-.1812453816503960, -.1532808703053140, -.9714191095654070,
-.9714191095654200, .1812453816504160, .1532808703052080,
-.1532808703052110, -.9714191095654300, -.1812453816503590,
-.9714191095653910, -.1812453816504850, -.1532808703053120,
-.1532808703053150, .9714191095654040, .1812453816504130,
.9714191095654130, -.1812453816504040, .1532808703052690,
.1532808703052900, .9714191095654090, -.1812453816504040,
.9714191095653960, .1812453816504510, -.1532808703053180,
.1812453816504140, -.1532808703051840, .9714191095654240,
-.1812453816504980, .1532808703053040, .9714191095653890,
-.5671272467360530, .2239533904880130, .7925979844148650,
.2239533904880520, .7925979844149510, -.5671272467359180,
.5671272467359560, -.2239533904879880, .7925979844149420,
.7925979844149380, -.5671272467359511, .2239533904880140,
-.2239533904880400, .7925979844149330, .5671272467359481,
.7925979844149070, .5671272467359810, -.2239533904880470,
-.2239533904880380, -.7925979844149900, -.5671272467358700,
-.7925979844149520, .5671272467359360, .2239533904880050,
.2239533904880500, -.7925979844148791, .5671272467360200,
-.7925979844148781, -.5671272467360270, -.2239533904880330,
-.5671272467359670, -.2239533904880070, -.7925979844149290,
.5671272467359780, .2239533904879970, -.7925979844149240,
-0.6608756503404201, -.5307337939386410, -.8449580307443481,
-.5307337939385640, -.8449580307444050, -0.6608756503393801,
0.6608756503400100, .5307337939386150, -.8449580307443680,
-.8449580307443810, -0.6608756503398400, -.5307337939385970,
.5307337939386250, -.8449580307443620, 0.6608756503400000,
-.8449580307444290, 0.6608756503394300, .5307337939385250,
.5307337939386140, .8449580307443740, -0.6608756503393801,
.8449580307443800, 0.6608756503393200, -.5307337939386040,
-.5307337939386390, .8449580307443550, 0.6608756503397401,
.8449580307443840, -0.6608756503398600, .5307337939385910,
-0.6608756503402601, .5307337939385840, .8449580307443860,
0.6608756503400399, -.5307337939385089, .8449580307444350,
.6566234254592690, -.3208553693050780, -.6825668532284860,
-.3208553693049820, -.6825668532284280, .6566234254593770,
-.6566234254592740, .3208553693050560, -.6825668532284920,
-.6825668532284440, .6566234254593130, -.3208553693050770,
.3208553693049670, -.6825668532284750, -.6566234254593351,
-.6825668532284180, -.6566234254593410, .3208553693050760,
.3208553693050100, .6825668532284710, .6566234254593180,
.6825668532284540, -.6566234254593000, -.3208553693050810,
-.3208553693049920, .6825668532284720, -.6566234254593259,
.6825668532284560, .6566234254593050, .3208553693050690,
.6566234254593371, .3208553693050400, .6825668532284380,
-.6566234254593390, -.3208553693050600, .6825668532284270,
-.5773502691896160, -.5773502691896200, -.5773502691896411,
.5773502691896250, .5773502691896060, -.5773502691896460,
.5773502691896440, -.5773502691895930, .5773502691896401,
-.5773502691896371, .5773502691896250, .5773502691896160
};
real_t oddOrEventable[EXPANSION + 1];
real_t factorial_table[2*EXPANSION+1];
real_t inverse_factorial_table[2*EXPANSION+1];
real_t factorial_coef[EXPANSION + 1][EXPANSION + 1];
real_t factorial_coef_inv[EXPANSION + 1][EXPANSION + 1];
real_t factorial_coef_oned[(EXPANSION + 1) * (EXPANSION + 1)];
real_t factorial_coef_inv_oned[(EXPANSION + 1) * (EXPANSION + 1)];
real_t combinator_coef[EXPANSION + 1][EXPANSION + 1];
const complex_t R(1., 0.); //!<Real unit
const complex_t I(0., 1.); //!<Imaginary unit
real_t norm(real_t * X)
{
return X[0] * X[0] + X[1] * X[1] + X[2] * X[2];
}
int oddOrEven(int n)
{
return (((n) & 1) == 1) ? -1 : 1;
}
void initKernel()
{
NTERM = (P + 1) * (P + 1);
factorial_table[0] = 1.0;
inverse_factorial_table[0] = 1.0;
for(int i = 1; i < EXPANSION*2; i++)
{
factorial_table[i] = (real_t) i *factorial_table[i - 1];
inverse_factorial_table[i] = 1 / factorial_table[i];
}
for(int i = 0; i <= P; i++)
{
for(int j = 0; j <= P; j++)
{
factorial_coef[i][j] = factorial_table[i + j] * factorial_table[i - j];
factorial_coef_inv[i][j] = 1.0 / factorial_coef[i][j];
if(j <= i)
combinator_coef[i][j] =
factorial_table[i] * inverse_factorial_table[j] * inverse_factorial_table[i - j];
}
oddOrEventable[i] = oddOrEven(i);
}
for(int n = 0; n <= P; n++)
{
int index_start = n * n + n;
factorial_coef_oned[index_start] = factorial_coef[n][0];
factorial_coef_inv_oned[index_start] = factorial_coef_inv[n][0];
for(int m = 1; m <= n; m++)
{
factorial_coef_oned[index_start + m] = factorial_coef[n][m];
factorial_coef_oned[index_start - m] = factorial_coef[n][m];
factorial_coef_inv_oned[index_start + m] = factorial_coef_inv[n][m];
factorial_coef_inv_oned[index_start - m] = factorial_coef_inv[n][m];
}
}
}
void real_2_complex(real_t * real_arr, complex_t * complex_arr, int order)
{
for(int n = 0; n <= order; n++)
{
int index_start = n * n + n;
complex_arr[index_start] = complex_t(real_arr[index_start], 0);
real_t oddevenfac = -1;
for(int m = 1; m <= n; m++)
{
complex_arr[index_start - m] = complex_t(real_arr[index_start + m] * oddevenfac,
-real_arr[index_start - m] * oddevenfac);
complex_arr[index_start + m] = complex_t(real_arr[index_start + m], real_arr[index_start - m]);
oddevenfac *= -1;
}
}
}
void complex_2_real(complex_t * complex_arr, real_t * real_arr, int order)
{
for(int n = 0; n <= order; n++)
{
int index_start = n * n + n;
real_arr[index_start] = std::real(complex_arr[index_start]);
for(int m = 1; m <= n; m++)
{
real_arr[index_start - m] = std::imag(complex_arr[index_start + m]);
real_arr[index_start + m] = std::real(complex_arr[index_start + m]);
}
}
}
void make_Tnm(real_t * dX, complex_t * Tnm, int Order)
{
real_t r2 = norm(dX);
real_t invr2 = 1 / r2;
Tnm[0] = complex_t(sqrt(invr2), 0);
for(int n = 1; n <= Order; n++)
{
int n2 = n * n;
int ind = n2 + n + n;
Tnm[ind] = Tnm[n2 - 1] * complex_t(dX[0] * (2 * n - 1) * invr2, dX[1] * (2 * n - 1) * invr2);
if(n > 0)
{
int m, m2, indexstart = n2 - n, indexnew = n2 + n;
if(n > 1)
{
for(m = 0; m < n - 1; m++)
{
m2 = m * m;
Tnm[indexnew + m] =
invr2 * (2 * n - 1.) * dX[2] * Tnm[indexstart + m] -
invr2 * ((n - 1) * (n - 1) * (n > 1) - m * m) * Tnm[n2 - 3 * n + 2 + m];
}
}
m = n - 1;
Tnm[indexnew + m] = invr2 * (2 * n - 1.) * dX[2] * Tnm[indexstart + m];
}
real_t oddoreven = -1;
for(int m = 1; m <= n; m++)
{
Tnm[n2 + n - m] = std::conj(Tnm[n2 + n + m] * oddoreven);
oddoreven *= -1;
}
}
}
void make_Gnm(real_t * dX, complex_t * Gnm, int Order)
{
real_t r2 = norm(dX);
Gnm[0] = complex_t(1, 0);
for(int n = 1; n <= Order; n++)
{
int n2 = n * n;
int ind = n2 + n + n;
Gnm[ind] = Gnm[n2 - 1] * complex_t(dX[0] / (2 * n), dX[1] / (2 * n));
int m, m2, indexstart = n2 - n, indexnew = n2 + n;
for(m = 0; m < n - 1; m++)
{
m2 = n2 - m * m;
Gnm[indexnew + m] =
(2 * n - 1.) / m2 * dX[2] * Gnm[indexstart + m] - r2 / m2 * Gnm[n2 - 3 * n + 2 + m];
}
Gnm[indexnew + n - 1] = dX[2] * Gnm[indexstart + n - 1];
real_t oddoreven = -1;
for(int m = 1; m <= n; m++)
{
Gnm[indexnew - m] = std::conj(Gnm[indexnew + m] * oddoreven);
oddoreven *= -1;
}
}
}
void P2P_simple(Cell * Ci, Cell * Cj)
{
if(Ci->has_sink)
{
Body *Bi = Ci->BODY;
Body *Bj = Cj->BODY;
int ni = Ci->NBODY;
int nj = Cj->NBODY;
#if SIMD_P2P
if(ni > NSIMD)
{
int nii = (ni + NSIMD - 1) & (-NSIMD);
#ifndef DOUBLE_P2P
float Xi[nii] __attribute__ ((aligned(64)));
float Yi[nii] __attribute__ ((aligned(64)));
float Zi[nii] __attribute__ ((aligned(64)));
#else
double Xi[nii] __attribute__ ((aligned(64)));
double Yi[nii] __attribute__ ((aligned(64)));
double Zi[nii] __attribute__ ((aligned(64)));
#endif
for(int k = 0; k < ni; k++)
{
Xi[k] = -Bi[k].X[0];
Yi[k] = -Bi[k].X[1];
Zi[k] = -Bi[k].X[2];
}
#ifndef DOUBLE_P2P
Vec16f xi, yi, zi, r, mj;
Vec16f invR, factor1, fac1, dx, dy, dz, r2;
Vec16f ax, ay, az, pot;
#else
Vec8d xi, yi, zi, r, mj;
Vec8d invR, factor1, fac1, dx, dy, dz, r2;
Vec8d ax, ay, az, pot;
#endif
for(int i = 0; i < nii; i = i + NSIMD)
{
xi.load(Xi + i);
yi.load(Yi + i);
zi.load(Zi + i);
ax = 0, ay = 0, az = 0, pot = 0;
for(int j = 0; j < nj; j++)
{
if(!Bj[j].issource)
continue;
mj = Bj[j].q;
dx = Bj[j].X[0] + xi;
dy = Bj[j].X[1] + yi;
dz = Bj[j].X[2] + zi;
r2 = dx * dx + dy * dy + dz * dz;
mj = select(r2 > 0, mj, 0);
r2 = select(r2 > 0, r2, 1e38);
r = sqrt(r2);
invR = 1 / r;
mj *= invR;
pot += mj;
factor1 = mj * (invR * invR);
ax += dx * factor1;
ay += dy * factor1;
az += dz * factor1;
}
for(int k = 0; (k < NSIMD) && (i + k < ni); k++)
{
if(Bi[i + k].issink)
{
#pragma omp atomic
Bi[i + k].p += (real_t) pot[k];
#pragma omp atomic
Bi[i + k].F[0] += (real_t) ax[k];
#pragma omp atomic
Bi[i + k].F[1] += (real_t) ay[k];
#pragma omp atomic
Bi[i + k].F[2] += (real_t) az[k];
}
}
}
}
else
{
// do not use vectorized version if n1*n2 too small
for(int i = 0; i < ni; i++)
{
if(!Bi[i].issink)
continue;
real_t ax = 0;
real_t ay = 0;
real_t az = 0;
real_t pot = 0;
for(int j = 0; j < nj; j++)
{
if(!Bj[j].issource)
continue;
for(int d = 0; d < 3; d++)
{
dX[d] = Bj[j].X[d] - Bi[i].X[d];
}
real_t R2 = norm(dX);
if(R2 > 0)
{
real_t R = sqrt(R2);
real_t invR2 = 1 / R2;
real_t invR = Bj[j].q * sqrt(invR2) * Bj[j].issource;
pot += invR;
for(int d = 0; d < 3; d++)
dX[d] *= invR2 * invR;
ax += dX[0];
ay += dX[1];
az += dX[2];
}
}
#pragma omp atomic
Bi[i].p += (real_t) pot;
#pragma omp atomic
Bi[i].F[0] += (real_t) ax;
#pragma omp atomic
Bi[i].F[1] += (real_t) ay;
#pragma omp atomic
Bi[i].F[2] += (real_t) az;
}
}
#else
// do not use vectorized version if n1*n2 too small
for(int i = 0; i < ni; i++)
{
real_t ax = 0;
real_t ay = 0;
real_t az = 0;
real_t pot = 0;
for(int j = 0; j < nj; j++)
{
for(int d = 0; d < 3; d++)
dX[d] = Bi[i].X[d] - Bj[j].X[d];
real_t R2 = norm(dX);
if(R2 > 0)
{
real_t R = sqrt(R2);
real_t invR2 = 1.0 / R2;
real_t invR = Bj[j].q * sqrt(invR2) * Bj[j].issource;
pot += invR;
for(int d = 0; d < 3; d++)
dX[d] *= invR2 * invR;
ax += dX[0];
ay += dX[1];
az += dX[2];
}
}
if(Bi[i].issink)
{
#pragma omp atomic
Bi[i].p += pot;
#pragma omp atomic
Bi[i].F[0] -= ax;
#pragma omp atomic
Bi[i].F[1] -= ay;
#pragma omp atomic
Bi[i].F[2] -= az;
}
}
#endif
}
}
void P2P(Cell * Ci, Cell * Cj)
{
if(Ci->has_sink)
{
Body *Bi = Ci->BODY;
Body *Bj = Cj->BODY;
int ni = Ci->NBODY;
int nj = Cj->NBODY;
real_t delta_t;
#if SIMD_P2P
int nii = (ni + NSIMD - 1) & (-NSIMD);
#ifndef DOUBLE_P2P
float Mi[nii] __attribute__ ((aligned(64)));
float Xi[nii] __attribute__ ((aligned(64)));
float Yi[nii] __attribute__ ((aligned(64)));
float Zi[nii] __attribute__ ((aligned(64)));
float VXi[nii] __attribute__ ((aligned(64)));
float VYi[nii] __attribute__ ((aligned(64)));
float VZi[nii] __attribute__ ((aligned(64)));
#else
double Mi[nii] __attribute__ ((aligned(64)));
double Xi[nii] __attribute__ ((aligned(64)));
double Yi[nii] __attribute__ ((aligned(64)));
double Zi[nii] __attribute__ ((aligned(64)));
double VXi[nii] __attribute__ ((aligned(64)));
double VYi[nii] __attribute__ ((aligned(64)));
double VZi[nii] __attribute__ ((aligned(64)));
#endif
for(int k = 0; k < ni; k++)
{
Mi[k] = Bi[k].q;
Xi[k] = -Bi[k].X[0];
Yi[k] = -Bi[k].X[1];
Zi[k] = -Bi[k].X[2];
VXi[k] = -Bi[k].V[0];
VYi[k] = -Bi[k].V[1];
VZi[k] = -Bi[k].V[2];
}
#ifndef DOUBLE_P2P
Vec16f mi, xi, yi, zi, vxi, vyi, vzi, r2, v2, vdotdr2, r, mj;
Vec16f invR, factor1, fac1, dx, dy, dz, dvx, dvy, dvz;
Vec16f ax, ay, az, pot, timestep, tau, dtau;
#else
Vec8d mi, xi, yi, zi, vxi, vyi, vzi, r2, v2, vdotdr2, r, mj;
Vec8d invR, factor1, fac1, dx, dy, dz, dvx, dvy, dvz;
Vec8d ax, ay, az, pot, timestep, tau, dtau;
#endif
for(int i = 0; i < nii; i = i + NSIMD)
{
mi.load(Mi + i);
xi.load(Xi + i);
yi.load(Yi + i);
zi.load(Zi + i);
vxi.load(VXi + i);
vyi.load(VYi + i);
vzi.load(VZi + i);
ax = 0, ay = 0, az = 0, pot = 0, timestep = 1e38;
for(int j = 0; j < nj; j++){
mj = Bj[j].q;
dx = xi + Bj[j].X[0];
dy = yi + Bj[j].X[1];
dz = zi + Bj[j].X[2];
dvx = vxi + Bj[j].V[0];
dvy = vyi + Bj[j].V[1];
dvz = vzi + Bj[j].V[2];
r2 = dx * dx + dy * dy + dz * dz;
v2 = dvx * dvx + dvy * dvy + dvz * dvz + 1e-20;
mj = select(r2 > 0, mj, 0);
mi += mj;
r2 = select(r2 > 0, r2, 1e38);
vdotdr2 = (dx * dvx + dy * dvy + dz * dvz) / r2;
r = sqrt(r2);
invR = 1 / r;
tau = dt_param / M_SQRT2 * r * sqrt(r / mi);
dtau = 3 * tau * vdotdr2 / 2;
dtau = select(dtau < 1, dtau, 1);
tau /= (1 - dtau / 2);
timestep = min(tau, timestep);
tau = dt_param * r / sqrt(v2);
dtau = tau * vdotdr2 * (1 + mi / (v2 * r));
dtau = select(dtau < 1, dtau, 1);
tau /= (1 - dtau / 2);
timestep = min(tau, timestep);
mj *= invR;
if(Bj[j].issource)
{
pot += mj;
factor1 = mj * (invR * invR);
ax += dx * factor1;
ay += dy * factor1;
az += dz * factor1;
}
}
timestep *= timestep;
timestep *= timestep;
timestep = (real_t) 1 / timestep;
for(int k = 0; (k < NSIMD) && (i + k < ni); k++)
{
if(Bi[i + k].issink)
{
#pragma omp atomic
Bi[i + k].p += (real_t) pot[k];
#pragma omp atomic
Bi[i + k].F[0] += (real_t) ax[k];
#pragma omp atomic
Bi[i + k].F[1] += (real_t) ay[k];
#pragma omp atomic
Bi[i + k].F[2] += (real_t) az[k];
#pragma omp atomic
Bi[i + k].timestep += (real_t) timestep[k];
}
}
}
#else
for(int i = 0; i < ni; i++)
{
real_t ax = 0;
real_t ay = 0;
real_t az = 0;
real_t pot = 0;
real_t timestep = 1e38;
for(int j = 0; j < nj; j++)
{
for(int d = 0; d < 3; d++)
{
dX[d] = Bj[j].X[d] - Bi[i].X[d];
dV[d] = Bj[j].V[d] - Bi[i].V[d];
}
real_t R2 = norm(dX);
if(R2 > 0)
{
real_t R = sqrt(R2);
real_t vdotdr2;
real_t v2 = norm(dV);
vdotdr2 = (dX[0] * dV[0] + dX[1] * dV[1] + dX[2] * dV[2]) / R2;
real_t tau = dt_param / M_SQRT2 * sqrt(R * R2 / (Bi[i].q + Bj[j].q));
real_t dtau = 3 * tau * vdotdr2 / 2;
if(dtau > 1)
dtau = 1;
tau /= (1 - dtau / 2);
if(tau < timestep)
timestep = tau;
if(v2 > 0)
{
tau = dt_param * R / sqrt(v2);
dtau = tau * vdotdr2 * (1 + (Bi[i].q + Bj[j].q) / (v2 * R));
if(dtau > 1)
dtau = 1;
tau /= (1 - dtau / 2);
if(tau < timestep)
timestep = tau;
}
real_t invR2 = 1.0 / R2;
real_t invR = Bj[j].q * sqrt(invR2) * Bj[j].issource;
pot += invR;
for(int d = 0; d < 3; d++)
dX[d] *= invR2 * invR;
ax += dX[0];
ay += dX[1];
az += dX[2];
}
}
timestep *= timestep;
timestep *= timestep;
timestep = (real_t)1 / timestep;
if(Bi[i].issink)
{
#pragma omp atomic
Bi[i].p += pot;
#pragma omp atomic
Bi[i].F[0] += ax;
#pragma omp atomic
Bi[i].F[1] += ay;
#pragma omp atomic
Bi[i].F[2] += az;
#pragma omp atomic
Bi[i].timestep += timestep;
}
}
#endif
}
}
void P2M(Cell * C)
{
real_t min_acc = 1e30;
#ifndef MINIBALL
if(C->NBODY > 0)
{
real_t comx = 0, comy = 0, comz = 0, totalq = 0;
for(Body * B = C->BODY; B != C->BODY + C->NBODY; B++)
{
comx += B->X[0] * B->q;
comy += B->X[1] * B->q;
comz += B->X[2] * B->q;
totalq += B->q;
}
comx /= totalq;
comy /= totalq;
comz /= totalq;
C->X[0] = comx;
C->X[1] = comy;
C->X[2] = comz;
C->cell_mass = totalq;
}
else
{
C->R = 1e-6;
}
#else
if(C->NBODY > 0)
{
std::list < std::vector < real_t > >lp;
for(Body * B = C->BODY; B != C->BODY + C->NBODY; B++)
{
std::vector < real_t > p(3);
p[0] = B->X[0];
p[1] = B->X[1];
p[2] = B->X[2];
lp.push_back(p);
}
// define the types of iterators through the points and their coordinates
typedef std::list < std::vector < real_t > >::const_iterator PointIterator;
typedef std::vector < real_t >::const_iterator CoordIterator;
typedef Miniball::Miniball < Miniball::CoordAccessor < PointIterator, CoordIterator > >MB;
MB mb(3, lp.begin(), lp.end());
real_t rminball = sqrt(mb.squared_radius());
const real_t *center = mb.center();
//use rminball as R
C->X[0] = center[0];
C->X[1] = center[1];
C->X[2] = center[2];
C->R = rminball + 1e-6;
}
else
{
C->R = 1e-6;
}
#endif
complex_t c_multipole[NTERM];
#ifndef MINIBALL
max_r2 = 1e-6 * C->R * C->R;
#endif
for(Body * B = C->BODY; B != C->BODY + C->NBODY; B++)
{
for(int d = 0; d < 3; d++)
{
dX[d] = B->X[d] - C->X[d];
}
#ifndef MINIBALL
max_r2 = fmax(max_r2, norm(dX));
#endif
min_acc = fmin(B->acc_old, min_acc);
if(B->issink)
C->has_sink = true;
complex_t Gnm[NTERM];
make_Gnm(&dX[0], &Gnm[0], P);
for(int indice = 0; indice < NTERM; indice++)
c_multipole[indice] += (B->q * B->issource) * Gnm[indice];
}
real_t r_multipole[NTERM];
complex_2_real(&c_multipole[0], &r_multipole[0], P);
for(int indice = 0; indice < NTERM; indice++)
C->M[indice] += r_multipole[indice];
C->min_acc = min_acc;
#ifndef MINIBALL
C->R = sqrt(max_r2);
#endif
}
void M2M(Cell * Ci)
{
real_t min_acc = 1e30;
#ifndef MINIBALL
if(Ci->NCHILD > 0)
{
real_t comx = 0, comy = 0, comz = 0, totalq = 0;
for(Cell * Cj = Ci->CHILD; Cj != Ci->CHILD + Ci->NCHILD; Cj++)
{
comx += Cj->X[0] * Cj->cell_mass;
comy += Cj->X[1] * Cj->cell_mass;
comz += Cj->X[2] * Cj->cell_mass;
totalq += Cj->cell_mass;
min_acc = fmin(Cj->min_acc, min_acc);
if(Cj->has_sink)
Ci->has_sink = true;
}
comx /= totalq;
comy /= totalq;
comz /= totalq;
real_t max_r = 1e-10;
for(Cell * Cj = Ci->CHILD; Cj != Ci->CHILD + Ci->NCHILD; Cj++)
{
for(int d = 0; d < 3; d++)
dX[d] = Cj->X[d] - Ci->X[d];
max_r = fmax(max_r, sqrt(norm(dX)) + Cj->R);
}
Ci->R = max_r;
Ci->min_acc = min_acc;
Ci->X[0] = comx;
Ci->X[1] = comy;
Ci->X[2] = comz;
Ci->cell_mass = totalq;
}
else
{
Ci->R = 1e-6;
Ci->min_acc = min_acc;
}
#else
if(Ci->NCHILD > 0)
{
std::list < std::vector < real_t > >lp;
for(Cell * ci = Ci->CHILD; ci != Ci->CHILD + Ci->NCHILD; ci++)
{
min_acc = fmin(ci->min_acc, min_acc);
if(ci->has_sink)
Ci->has_sink = true;
if(ci->NCHILD == 0)
{ //leaves, just use bodies to get R_max
for(Body * B = ci->BODY; B != ci->BODY + ci->NBODY; B++)
{
std::vector < real_t > p(3);
p[0] = B->X[0];
p[1] = B->X[1];
p[2] = B->X[2];
lp.push_back(p);
}
}
else
{
// use granddaughers information to get R_max with a
// precomputed t-design of a sphere with 64 points.
for(Cell * cii = ci->CHILD; cii != ci->CHILD + ci->NCHILD; cii++)
{
for(int k = 0; k < 64; k++)
{
std::vector < real_t > p(3);
p[0] = cii->X[0] + cii->R * t_design[3 * k + 0];
p[1] = cii->X[1] + cii->R * t_design[3 * k + 1];
p[2] = cii->X[2] + cii->R * t_design[3 * k + 2];
lp.push_back(p);
}
}
}
}
typedef std::list < std::vector < real_t > >::const_iterator PointIterator;
typedef std::vector < real_t >::const_iterator CoordIterator;
typedef Miniball::Miniball < Miniball::CoordAccessor < PointIterator, CoordIterator > >MB;
MB mb(3, lp.begin(), lp.end());
real_t rminball = sqrt(mb.squared_radius());
const real_t *center = mb.center();
Ci->X[0] = center[0];
Ci->X[1] = center[1];
Ci->X[2] = center[2];
Ci->R = rminball + 1e-6;
Ci->min_acc = min_acc;
}
else
{
Ci->R = 1e-6;
Ci->min_acc = min_acc;
}
#endif
complex_t c_multipole[NTERM];
for(int i = 0; i < NTERM; i++)
{
c_multipole[i] = 0;
}
for(Cell * Cj = Ci->CHILD; Cj != Ci->CHILD + Ci->NCHILD; Cj++)
{
for(int d = 0; d < 3; d++)
{
dX[d] = Cj->X[d] - Ci->X[d];
}
real_t r_multipole_Cj[NTERM];
complex_t c_multipole_Cj[NTERM];
for(int i = 0; i < NTERM; i++)
{
r_multipole_Cj[i] = Cj->M[i];
c_multipole_Cj[i] = 0;
}
real_2_complex(r_multipole_Cj, c_multipole_Cj, P);
complex_t Gnm[NTERM];
make_Gnm(&dX[0], &Gnm[0], P);
for(int n = 0; n <= P; n++)
{
for(int m = 0; m <= n; m++)
{
int indice = n * n + n + m;
for(int k = 0; k <= n; k++)
for(int l = std::max(-k, m - n + k); l <= std::min(k, m + n - k); l++)
c_multipole[indice] +=
c_multipole_Cj[(n - k) * (n - k) + (n - k) + (m - l)] * Gnm[k * k + k + l];
}
}
}
real_t r_multipole[NTERM];
complex_2_real(c_multipole, r_multipole, P);
for(int indice = 0; indice < NTERM; indice++)
Ci->M[indice] += r_multipole[indice];
}
void L2L(Cell * Ci)
{
real_t r_local_Ci[NTERM];
complex_t c_local_Ci[NTERM];
for(int indice = 0; indice < NTERM; indice++)
r_local_Ci[indice] = Ci->L[indice];
real_2_complex(r_local_Ci, c_local_Ci, P);
for(Cell * Cj = Ci->CHILD; Cj != Ci->CHILD + Ci->NCHILD; Cj++)
{
for(int d = 0; d < 3; d++)
dX[d] = Ci->X[d] - Cj->X[d];
complex_t c_local[NTERM];
for(int indice = 0; indice < NTERM; indice++)
c_local[indice] = 0.0;
complex_t Gnm[NTERM];
make_Gnm(&dX[0], &Gnm[0], P);
for(int i = 0; i < NTERM; i++)
Gnm[i] = std::conj(Gnm[i]);
for(int n = 0; n <= P; n++)
{
for(int m = 0; m <= n; m++)
{
int indice = n * n + n + m;
for(int k = 0; k <= P - n; k++)
for(int l = -k; l <= k; l++)
c_local[indice] += c_local_Ci[(n + k) * (n + k) + (n + k) + (m + l)] * Gnm[k * k + k + l];
}
}
real_t r_local[NTERM];
complex_2_real(c_local, r_local, P);
for(int indice = 0; indice < NTERM; indice++)
Cj->L[indice] += r_local[indice];
}
}
void L2P(Cell * Ci)
{
real_t r_local_Ci[NTERM];
complex_t c_local_Ci[NTERM];
for(int indice = 0; indice < NTERM; indice++)
r_local_Ci[indice] = Ci->L[indice];
real_2_complex(r_local_Ci, c_local_Ci, P);
for(Body * B = Ci->BODY; B != Ci->BODY + Ci->NBODY; B++)
{