void drnorm(RngEngine* rng, double* buffer, BlasInt* n, BlasInt* isAligned,
RngErrorType* info) {
UNUSED(isAligned);
if (*n > 0) {
#if defined(USE_RNG_BOX_MULLER)
for (BlasInt iter = 0; iter < *n; iter += 2) {
double x = 2.0 * M_PI * dsfmt_genrand_close_open(&(rng->m_dsfmt));
double z = sqrt(-log(dsfmt_genrand_close_open(&(rng->m_dsfmt))));
double c = cos(x);
buffer[iter] = z * c;
if (iter + 1 < *n) {
double s = sin(x);
buffer[iter + 1] = z * s;
}
}
#elif defined(USE_RNG_MARSAGLIA)
for (BlasInt iter = 0; iter < *n; ++iter) {
double x, y, r;
do {
x = 2.0 * dsfmt_genrand_close_open(&(rng->m_dsfmt)) - 1.0;
y = 2.0 * dsfmt_genrand_close_open(&(rng->m_dsfmt)) - 1.0;
r = x * x + y * y;
} while (r >= 1 || r == 0);
buffer[iter] = x * sqrt(- 2.0 * log(r) / r);
}
#endif
}
*info = 0;
}
Color Phong::color(const SIMD::Point &p, const SIMD::Matrix &m, const SIMD::Vec &in, Scene &scene, size_t depth, dsfmt_t &dsfmt) const
{
const SIMD::Vec u = m[0], v = m[1], n = m[2];
Color ret;
ret.add(c_emit);
if(n.dot(in) > 0)
return ret;
RT_FLOAT xi = dsfmt_genrand_close_open(&dsfmt);
if(diffuse > xi)
{
// Cosine weighted random hemisphere sampling
// from smallpt by Kevin Beason
RT_FLOAT r1=2*M_PI*dsfmt_genrand_close_open(&dsfmt), r2=dsfmt_genrand_close_open(&dsfmt), r2s=std::sqrt(r2);
SIMD::Vec d = u*std::cos(r1)*r2s + v*std::sin(r1)*r2s + n*std::sqrt(1-r2);
d.normalize();
// End of CWRHS
Raytracer::Color lambda = c_diffuse;
lambda.mult(scene.radiance(SIMD::Ray(p, d), depth+1, dsfmt));
ret.add(lambda);
}
else if(diffuse+specular > xi)
{
// Importance sampling of Phong reflection model by Jason Lawrence
SIMD::Vec u, v, out = in-2*in.dot(n)*n, d;
if(std::abs(out[0]) > 0.1)
u = SIMD::Vec(0, 1, 0).cross(out);
else
u = SIMD::Vec(1, 0, 0).cross(out);
u.normalize();
v = out.cross(u);
do
{
RT_FLOAT cos_theta = std::pow(dsfmt_genrand_close_open(&dsfmt), 1/(spec_pow+2)), phi = 2*M_PI*dsfmt_genrand_close_open(&dsfmt);
RT_FLOAT sin_theta = std::sqrt(1-cos_theta*cos_theta);
d = u*std::cos(phi)*sin_theta+v*std::sin(phi)*sin_theta+out*cos_theta;
}
while(d.dot(n) < 0);
d.normalize();
// End of ISoPRM
Color lambda = scene.radiance(SIMD::Ray(p, d), depth+1, dsfmt);
lambda.mult(c_specular);
ret.add(lambda);
}
return ret;
}
int main(int argc, char* argv[]) {
int i, inside, seed;
double x, y, pi;
const long n_steps = 1000000000;
dsfmt_t dsfmt;
seed = 142857;
inside = 0;
dsfmt_init_gen_rand(&dsfmt, seed);
for (i = 0; i < n_steps; i++) {
x = dsfmt_genrand_close_open(&dsfmt);
y = dsfmt_genrand_close_open(&dsfmt);
if (x * x + y * y < 1.0) {
inside++;
}
}
pi = (double)inside / n_steps * 4;
printf("%.10g\n", pi);
return 0;
}
void drunif(RngEngine* rng, double* buffer, BlasInt* n, BlasInt* isAligned,
RngErrorType* info) {
if ((*isAligned == 0) || (*n == 1)) {
for (BlasInt iter = 0; iter < *n; ++iter) {
buffer[iter] = dsfmt_genrand_close_open(&(rng->m_dsfmt));
}
} else if (*n > 1) {
dsfmt_fill_array_close_open(&(rng->m_dsfmt), buffer, *n);
}
*info = 0;
}
double tls_rand()
{
/* Setup PRNG state for current thread. */
UNUSED(pthread_once(&tls_prng_once, tls_prng_init));
/* Create PRNG state if not exists. */
dsfmt_t* s = pthread_getspecific(tls_prng_key);
if (!s) {
/* Initialize seed from system PRNG generator. */
uint32_t seed = 0;
FILE *fp = fopen("/dev/urandom", "r");
if (fp == NULL) {
fp = fopen("/dev/random", "r");
}
if (fp != NULL) {
if (fread(&seed, sizeof(uint32_t), 1, fp) != 1) {
fclose(fp);
fp = NULL;
}
}
if (fp == NULL) {
fprintf(stderr, "error: PRNG: cannot seed from "
"/dev/urandom, seeding from local time\n");
struct timeval tv;
if (gettimeofday(&tv, NULL) == 0) {
seed = (uint32_t)(tv.tv_sec ^ tv.tv_usec);
} else {
/* Last resort. */
seed = (uint32_t)time(NULL);
}
} else {
fclose(fp);
}
/* Initialize PRNG state. */
#ifdef HAVE_POSIX_MEMALIGN
if (posix_memalign((void **)&s, 16, sizeof(dsfmt_t)) != 0) {
fprintf(stderr, "error: PRNG: not enough memory\n");
return .0;
}
#else
if ((s = malloc(sizeof(dsfmt_t))) == NULL) {
fprintf(stderr, "error: PRNG: not enough memory\n");
return .0;
}
#endif
dsfmt_init_gen_rand(s, seed);
UNUSED(pthread_setspecific(tls_prng_key, s));
}
return dsfmt_genrand_close_open(s);
}
static size_t sample1(const double *probs, size_t n, dsfmt_t * dsfmt)
{
size_t i;
double u = dsfmt_genrand_close_open(dsfmt);
double sum = 0;
for (i = 0; i < n - 1; i++) {
sum += probs[i];
if (sum >= u)
break;
}
return i;
}
/**
*
*
* @param X
*
* @author Takahiro Misawa (The University of Tokyo)
* @author Kazuyoshi Yoshimi (The University of Tokyo)
* @return
*/
int Lanczos_EigenValue(struct BindStruct *X)
{
fprintf(stdoutMPI, "%s", cLogLanczos_EigenValueStart);
FILE *fp;
char sdt[D_FileNameMax],sdt_2[D_FileNameMax];
int stp, iproc;
long int i,iv,i_max;
unsigned long int i_max_tmp, sum_i_max;
int k_exct,Target;
int iconv=-1;
double beta1,alpha1; //beta,alpha1 should be real
double complex temp1,temp2;
double complex cbeta1;
double E[5],ebefor;
int mythread;
// for GC
double dnorm;
double complex cdnorm;
long unsigned int u_long_i;
dsfmt_t dsfmt;
#ifdef lapack
double **tmp_mat;
double *tmp_E;
int int_i,int_j,mfint[7];
#endif
sprintf(sdt_2, cFileNameLanczosStep, X->Def.CDataFileHead);
i_max=X->Check.idim_max;
k_exct = X->Def.k_exct;
if(initial_mode == 0){
sum_i_max = SumMPI_li(X->Check.idim_max);
X->Large.iv = (sum_i_max / 2 + X->Def.initial_iv) % sum_i_max + 1;
iv=X->Large.iv;
fprintf(stdoutMPI, " initial_mode=%d normal: iv = %ld i_max=%ld k_exct =%d \n\n",initial_mode,iv,i_max,k_exct);
#pragma omp parallel for default(none) private(i) shared(v0, v1) firstprivate(i_max)
for(i = 1; i <= i_max; i++){
v0[i]=0.0;
v1[i]=0.0;
}
sum_i_max = 0;
for (iproc = 0; iproc < nproc; iproc++) {
i_max_tmp = BcastMPI_li(iproc, i_max);
if (sum_i_max <= iv && iv < sum_i_max + i_max_tmp) {
if (myrank == iproc) {
v1[iv - sum_i_max+1] = 1.0;
if (X->Def.iInitialVecType == 0) {
v1[iv - sum_i_max+1] += 1.0*I;
v1[iv - sum_i_max+1] /= sqrt(2.0);
}
}/*if (myrank == iproc)*/
}/*if (sum_i_max <= iv && iv < sum_i_max + i_max_tmp)*/
sum_i_max += i_max_tmp;
}/*for (iproc = 0; iproc < nproc; iproc++)*/
}/*if(initial_mode == 0)*/
else if(initial_mode==1){
iv = X->Def.initial_iv;
fprintf(stdoutMPI, " initial_mode=%d (random): iv = %ld i_max=%ld k_exct =%d \n\n",initial_mode,iv,i_max,k_exct);
#pragma omp parallel default(none) private(i, u_long_i, mythread, dsfmt) \
shared(v0, v1, iv, X, nthreads, myrank) firstprivate(i_max)
{
#pragma omp for
for (i = 1; i <= i_max; i++) {
v0[i] = 0.0;
}
/*
Initialise MT
*/
#ifdef _OPENMP
mythread = omp_get_thread_num();
#else
mythread = 0;
#endif
u_long_i = 123432 + labs(iv) + mythread + nthreads * myrank;
dsfmt_init_gen_rand(&dsfmt, u_long_i);
if (X->Def.iInitialVecType == 0) {
#pragma omp for
for (i = 1; i <= i_max; i++)
v1[i] = 2.0*(dsfmt_genrand_close_open(&dsfmt) - 0.5) + 2.0*(dsfmt_genrand_close_open(&dsfmt) - 0.5)*I;
}
else {
#pragma omp for
for (i = 1; i <= i_max; i++)
v1[i] = 2.0*(dsfmt_genrand_close_open(&dsfmt) - 0.5);
}
}/*#pragma omp parallel*/
cdnorm=0.0;
#pragma omp parallel for default(none) private(i) shared(v1, i_max) reduction(+: cdnorm)
for(i=1;i<=i_max;i++){
cdnorm += conj(v1[i])*v1[i];
}
cdnorm = SumMPI_dc(cdnorm);
dnorm=creal(cdnorm);
dnorm=sqrt(dnorm);
#pragma omp parallel for default(none) private(i) shared(v1) firstprivate(i_max, dnorm)
for(i=1;i<=i_max;i++){
v1[i] = v1[i]/dnorm;
}
}/*else if(initial_mode==1)*/
//Eigenvalues by Lanczos method
TimeKeeper(X, cFileNameTimeKeep, cLanczos_EigenValueStart, "a");
mltply(X, v0, v1);
stp=1;
TimeKeeperWithStep(X, cFileNameTimeKeep, cLanczos_EigenValueStep, "a", stp);
alpha1=creal(X->Large.prdct) ;// alpha = v^{\dag}*H*v
alpha[1]=alpha1;
cbeta1=0.0;
#pragma omp parallel for reduction(+:cbeta1) default(none) private(i) shared(v0, v1) firstprivate(i_max, alpha1)
for(i = 1; i <= i_max; i++){
cbeta1+=conj(v0[i]-alpha1*v1[i])*(v0[i]-alpha1*v1[i]);
}
cbeta1 = SumMPI_dc(cbeta1);
beta1=creal(cbeta1);
beta1=sqrt(beta1);
beta[1]=beta1;
ebefor=0;
/*
Set Maximum number of loop to the dimention of the Wavefunction
*/
i_max_tmp = SumMPI_li(i_max);
if(i_max_tmp < X->Def.Lanczos_max){
X->Def.Lanczos_max = i_max_tmp;
}
if(i_max_tmp < X->Def.LanczosTarget){
X->Def.LanczosTarget = i_max_tmp;
}
if(i_max_tmp == 1){
E[1]=alpha[1];
vec12(alpha,beta,stp,E,X);
X->Large.itr=stp;
X->Phys.Target_energy=E[k_exct];
iconv=0;
fprintf(stdoutMPI," LanczosStep E[1] \n");
fprintf(stdoutMPI," stp=%d %.10lf \n",stp,E[1]);
}
else{
#ifdef lapack
fprintf(stdoutMPI, " LanczosStep E[1] E[2] E[3] E[4] E_Max/Nsite\n");
#else
fprintf(stdoutMPI, " LanczosStep E[1] E[2] E[3] E[4] \n");
#endif
for(stp = 2; stp <= X->Def.Lanczos_max; stp++){
#pragma omp parallel for default(none) private(i,temp1, temp2) shared(v0, v1) firstprivate(i_max, alpha1, beta1)
for(i=1;i<=i_max;i++){
temp1 = v1[i];
temp2 = (v0[i]-alpha1*v1[i])/beta1;
v0[i] = -beta1*temp1;
v1[i] = temp2;
}
mltply(X, v0, v1);
TimeKeeperWithStep(X, cFileNameTimeKeep, cLanczos_EigenValueStep, "a", stp);
alpha1=creal(X->Large.prdct);
alpha[stp]=alpha1;
cbeta1=0.0;
#pragma omp parallel for reduction(+:cbeta1) default(none) private(i) shared(v0, v1) firstprivate(i_max, alpha1)
for(i=1;i<=i_max;i++){
cbeta1+=conj(v0[i]-alpha1*v1[i])*(v0[i]-alpha1*v1[i]);
}
cbeta1 = SumMPI_dc(cbeta1);
beta1=creal(cbeta1);
beta1=sqrt(beta1);
beta[stp]=beta1;
Target = X->Def.LanczosTarget;
if(stp==2){
#ifdef lapack
d_malloc2(tmp_mat,stp,stp);
d_malloc1(tmp_E,stp+1);
for(int_i=0;int_i<stp;int_i++){
for(int_j=0;int_j<stp;int_j++){
tmp_mat[int_i][int_j] = 0.0;
}
}
tmp_mat[0][0] = alpha[1];
tmp_mat[0][1] = beta[1];
tmp_mat[1][0] = beta[1];
tmp_mat[1][1] = alpha[2];
DSEVvalue(stp,tmp_mat,tmp_E);
E[1] = tmp_E[0];
E[2] = tmp_E[1];
E[3] = tmp_E[2];
E[4] = tmp_E[3];
d_free1(tmp_E,stp+1);
d_free2(tmp_mat,stp,stp);
#else
bisec(alpha,beta,stp,E,4,eps_Bisec);
#endif
ebefor=E[Target];
childfopenMPI(sdt_2,"w", &fp);
#ifdef lapack
fprintf(stdoutMPI, " stp = %d %.10lf %.10lf xxxxxxxxxx xxxxxxxxx xxxxxxxxx \n",stp,E[1],E[2]);
fprintf(fp, "LanczosStep E[1] E[2] E[3] E[4] E_Max/Nsite\n");
fprintf(fp, "stp = %d %.10lf %.10lf xxxxxxxxxx xxxxxxxxx xxxxxxxxx \n",stp,E[1],E[2]);
#else
fprintf(stdoutMPI, " stp = %d %.10lf %.10lf xxxxxxxxxx xxxxxxxxx \n",stp,E[1],E[2]);
fprintf(fp, "LanczosStep E[1] E[2] E[3] E[4] \n");
fprintf(fp,"stp = %d %.10lf %.10lf xxxxxxxxxx xxxxxxxxx \n",stp,E[1],E[2]);
#endif
fclose(fp);
}
if(stp>2 && stp%2==0){
childfopenMPI(sdt_2,"a", &fp);
#ifdef lapack
d_malloc2(tmp_mat,stp,stp);
d_malloc1(tmp_E,stp+1);
for(int_i=0;int_i<stp;int_i++){
for(int_j=0;int_j<stp;int_j++){
tmp_mat[int_i][int_j] = 0.0;
}
}
tmp_mat[0][0] = alpha[1];
tmp_mat[0][1] = beta[1];
for(int_i=1;int_i<stp-1;int_i++){
tmp_mat[int_i][int_i] = alpha[int_i+1];
tmp_mat[int_i][int_i+1] = beta[int_i+1];
tmp_mat[int_i][int_i-1] = beta[int_i];
}
tmp_mat[int_i][int_i] = alpha[int_i+1];
tmp_mat[int_i][int_i-1] = beta[int_i];
DSEVvalue(stp,tmp_mat,tmp_E);
E[1] = tmp_E[0];
E[2] = tmp_E[1];
E[3] = tmp_E[2];
E[4] = tmp_E[3];
E[0] = tmp_E[stp-1];
d_free1(tmp_E,stp+1);
d_free2(tmp_mat,stp,stp);
fprintf(stdoutMPI, " stp = %d %.10lf %.10lf %.10lf %.10lf %.10lf\n",stp,E[1],E[2],E[3],E[4],E[0]/(double)X->Def.NsiteMPI);
fprintf(fp,"stp=%d %.10lf %.10lf %.10lf %.10lf %.10lf\n",stp,E[1],E[2],E[3],E[4],E[0]/(double)X->Def.NsiteMPI);
#else
bisec(alpha,beta,stp,E,4,eps_Bisec);
fprintf(stdoutMPI, " stp = %d %.10lf %.10lf %.10lf %.10lf \n",stp,E[1],E[2],E[3],E[4]);
fprintf(fp,"stp=%d %.10lf %.10lf %.10lf %.10lf\n",stp,E[1],E[2],E[3],E[4]);
#endif
fclose(fp);
if(fabs((E[Target]-ebefor)/E[Target])<eps_Lanczos || fabs(beta[stp])<pow(10.0, -14)){
vec12(alpha,beta,stp,E,X);
X->Large.itr=stp;
X->Phys.Target_energy=E[k_exct];
iconv=0;
break;
}
ebefor=E[Target];
}
}
}
sprintf(sdt,cFileNameTimeKeep,X->Def.CDataFileHead);
if(iconv!=0){
sprintf(sdt, cLogLanczos_EigenValueNotConverged);
return -1;
}
TimeKeeper(X, cFileNameTimeKeep, cLanczos_EigenValueFinish, "a");
fprintf(stdoutMPI, "%s", cLogLanczos_EigenValueEnd);
return 0;
}
double eqdist() {
return dsfmt_genrand_close_open(&g_dsfmt);
}
static void gen_random_uuid(uint8_t *uuid, dsfmt_t *state)
{
double rand[2] = {dsfmt_genrand_close_open(state) * DBL_MAX,
dsfmt_genrand_close_open(state) * DBL_MAX};
memcpy(uuid, rand, 16);
}
/**
*
*
* @param X
* @author Takahiro Misawa (The University of Tokyo)
* @author Kazuyoshi Yoshimi (The University of Tokyo)
*/
void Lanczos_EigenVector(struct BindStruct *X){
printf("%s", cLogLanczos_EigenVectorStart);
int i,j,i_max,iv;
int k_exct;
double beta1,alpha1,dnorm, dnorm_inv;
double complex temp1,temp2;
// for GC
long unsigned int u_long_i;
dsfmt_t dsfmt;
k_exct = X->Def.k_exct;
iv=X->Large.iv;
i_max=X->Check.idim_max;
//Eigenvectors by Lanczos method
//initialization: initialization should be identical to that of Lanczos_EigenValue.c
#pragma omp parallel for default(none) private(i) shared(v0, v1, vg) firstprivate(i_max)
for(i=1;i<=i_max;i++){
v0[i]=0.0+0.0*I;
v1[i]=0.0+0.0*I;
vg[i]=0.0+0.0*I;
}
if(initial_mode == 0){
v1[iv]=1.0;
vg[iv]=vec[k_exct][1];
}else if(initial_mode==1){
iv = X->Def.initial_iv;
u_long_i = 123432 + abs(iv);
dsfmt_init_gen_rand(&dsfmt, u_long_i);
for(i = 1; i <= i_max; i++){
v1[i]=2.0*(dsfmt_genrand_close_open(&dsfmt)-0.5)+2.0*(dsfmt_genrand_close_open(&dsfmt)-0.5)*I;
}
dnorm=0;
#pragma omp parallel for default(none) private(i) shared(v1, i_max) reduction(+: dnorm)
for(i=1;i<=i_max;i++){
dnorm += conj(v1[i])*v1[i];
}
dnorm=sqrt(dnorm);
dnorm_inv=1.0/dnorm;
#pragma omp parallel for default(none) private(i) shared(v1,vg,vec,k_exct) firstprivate(i_max, dnorm_inv)
for(i=1;i<=i_max;i++){
v1[i] = v1[i]*dnorm_inv;
vg[i] = v1[i]*vec[k_exct][1];
}
}
mltply(X, v0, v1);
alpha1=alpha[1];
beta1=beta[1];
#pragma omp parallel for default(none) private(j) shared(vec, v0, v1, vg) firstprivate(alpha1, beta1, i_max, k_exct)
for(j=1;j<=i_max;j++){
vg[j]+=vec[k_exct][2]*(v0[j]-alpha1*v1[j])/beta1;
}
//iteration
for(i=2;i<=X->Large.itr-1;i++){
#pragma omp parallel for default(none) private(j, temp1, temp2) shared(v0, v1) firstprivate(i_max, alpha1, beta1)
for(j=1;j<=i_max;j++){
temp1=v1[j];
temp2=(v0[j]-alpha1*v1[j])/beta1;
v0[j]=-beta1*temp1;
v1[j]=temp2;
}
mltply(X, v0, v1);
alpha1 = alpha[i];
beta1 = beta[i];
#pragma omp parallel for default(none) private(j) shared(vec, v0, v1, vg) firstprivate(alpha1, beta1, i_max, k_exct, i)
for(j=1;j<=i_max;j++){
vg[j] += vec[k_exct][i+1]*(v0[j]-alpha1*v1[j])/beta1;
}
}
#pragma omp parallel for default(none) private(j) shared(v0, vg) firstprivate(i_max)
for(j=1;j<=i_max;j++){
v0[j] = vg[j];
}
//normalization
dnorm=0.0;
#pragma omp parallel for default(none) reduction(+:dnorm) private(j) shared(v0) firstprivate(i_max)
for(j=1;j<=i_max;j++){
dnorm += conj(v0[j])*v0[j];
}
dnorm=sqrt(dnorm);
dnorm_inv=dnorm;
#pragma omp parallel for default(none) private(j) shared(v0) firstprivate(i_max, dnorm_inv)
for(j=1;j<=i_max;j++){
v0[j] = v0[j]*dnorm_inv;
}
TimeKeeper(X, cFileNameTimeKeep, cLanczos_EigenVectorFinish, "a");
printf("%s", cLogLanczos_EigenVectorEnd);
}