void h_ode_set_safe(const real safein) {
/* pre-condition */
BI_ASSERT(safein > BI_REAL(0.001) && safein < BI_REAL(1.0));
h_safe = safein;
h_safe1 = BI_REAL(1.0) / safein;
h_logsafe = bi::log(safein);
}
void h_ode_init() {
h_ode_set_h0(BI_REAL(1.0e-2));
h_ode_set_rtoler(BI_REAL(1.0e-7));
h_ode_set_atoler(BI_REAL(1.0e-7));
h_ode_set_uround(BI_REAL(1.0e-16));
h_ode_set_safe(BI_REAL(0.9));
h_ode_set_facl(BI_REAL(0.2));
h_ode_set_facr(BI_REAL(10.0));
h_ode_set_beta(BI_REAL(0.04));
h_ode_set_nsteps(1000);
}
void h_ode_set_beta(const real betain) {
/* pre-condition */
BI_ASSERT(betain >= 0.0 && betain <= BI_REAL(0.2));
h_beta = betain;
h_expo1 = BI_REAL(0.2) - betain*BI_REAL(0.75);
h_expo = BI_REAL(0.5)*(BI_REAL(0.2) - betain*BI_REAL(0.75));
}
void bi::RK43IntegratorHost<B,S,T1>::update(const T1 t1, const T1 t2,
State<B,ON_HOST>& s) {
/* pre-condition */
BI_ASSERT(t1 < t2);
typedef typename temp_host_vector<real>::type vector_type;
typedef Pa<ON_HOST,B,host,host,host,host> PX;
typedef RK43VisitorHost<B,S,S,real,PX,real> Visitor;
static const int N = block_size<S>::value;
const int P = s.size();
#pragma omp parallel
{
vector_type r1(N), r2(N), err(N), old(N);
real t, h, e, e2, logfacold, logfac11, fac;
int n, id, p;
PX pax;
#pragma omp for
for (p = 0; p < P; ++p) {
t = t1;
h = h_h0;
logfacold = bi::log(BI_REAL(1.0e-4));
n = 0;
host_load<B,S>(s, p, old);
r1 = old;
/* integrate */
while (t < t2 && n < h_nsteps) {
if (BI_REAL(0.1)*bi::abs(h) <= bi::abs(t)*h_uround) {
// step size too small
}
if (t + BI_REAL(1.01)*h - t2 > BI_REAL(0.0)) {
h = t2 - t;
if (h <= BI_REAL(0.0)) {
t = t2;
break;
}
}
/* stages */
Visitor::stage1(t, h, s, p, pax, r1.buf(), r2.buf(), err.buf());
host_store<B,S>(s, p, r1);
Visitor::stage2(t, h, s, p, pax, r1.buf(), r2.buf(), err.buf());
host_store<B,S>(s, p, r2);
Visitor::stage3(t, h, s, p, pax, r1.buf(), r2.buf(), err.buf());
host_store<B,S>(s, p, r1);
Visitor::stage4(t, h, s, p, pax, r1.buf(), r2.buf(), err.buf());
host_store<B,S>(s, p, r2);
Visitor::stage5(t, h, s, p, pax, r1.buf(), r2.buf(), err.buf());
host_store<B,S>(s, p, r1);
/* compute error */
e2 = BI_REAL(0.0);
for (id = 0; id < N; ++id) {
e = err(id)*h/(h_atoler + h_rtoler*bi::max(bi::abs(old(id)), bi::abs(r1(id))));
e2 += e*e;
}
e2 /= N;
if (e2 <= BI_REAL(1.0)) {
/* accept */
t += h;
if (t < t2) {
old = r1;
}
} else {
/* reject */
r1 = old;
host_store<B,S>(s, p, old);
}
/* compute next step size */
if (t < t2) {
logfac11 = h_expo*bi::log(e2);
if (e2 > BI_REAL(1.0)) {
/* step was rejected */
h *= bi::max(h_facl, bi::exp(h_logsafe - logfac11));
} else {
/* step was accepted */
fac = bi::exp(h_beta*logfacold + h_logsafe - logfac11); // Lund-stabilization
fac = bi::min(h_facr, bi::max(h_facl, fac)); // bound
h *= fac;
logfacold = BI_REAL(0.5)*bi::log(bi::max(e2, BI_REAL(1.0e-8)));
}
}
++n;
}
}
}
}
void bi::DOPRI5IntegratorHost<B,S,T1>::update(const T1 t1, const T1 t2,
State<B,ON_HOST>& s) {
/* pre-condition */
BI_ASSERT(t1 < t2);
typedef host_vector_reference<real> vector_reference_type;
typedef Pa<ON_HOST,B,host,host,host,host> PX;
typedef DOPRI5VisitorHost<B,S,S,real,PX,real> Visitor;
static const int N = block_size<S>::value;
const int P = s.size();
#pragma omp parallel
{
real buf[10*N]; // use of dynamic array faster than heap allocation
vector_reference_type x0(buf, N);
vector_reference_type x1(buf + N, N);
vector_reference_type x2(buf + 2*N, N);
vector_reference_type x3(buf + 3*N, N);
vector_reference_type x4(buf + 4*N, N);
vector_reference_type x5(buf + 5*N, N);
vector_reference_type x6(buf + 6*N, N);
vector_reference_type err(buf + 7*N, N);
vector_reference_type k1(buf + 8*N, N);
vector_reference_type k7(buf + 9*N, N);
real t, h, e, e2, logfacold, logfac11, fac;
int n, id, p;
bool k1in;
PX pax;
#pragma omp for
for (p = 0; p < P; ++p) {
t = t1;
h = h_h0;
logfacold = bi::log(BI_REAL(1.0e-4));
k1in = false;
n = 0;
host_load<B,S>(s, p, x0);
/* integrate */
while (t < t2 && n < h_nsteps) {
if (BI_REAL(0.1)*bi::abs(h) <= bi::abs(t)*h_uround) {
// step size too small
}
if (t + BI_REAL(1.01)*h - t2 > BI_REAL(0.0)) {
h = t2 - t;
if (h <= BI_REAL(0.0)) {
t = t2;
break;
}
}
/* stages */
Visitor::stage1(t, h, s, p, pax, x0.buf(), x1.buf(), x2.buf(), x3.buf(), x4.buf(), x5.buf(), x6.buf(), k1.buf(), err.buf(), k1in);
k1in = true; // can reuse from previous iteration in future
host_store<B,S>(s, p, x1);
Visitor::stage2(t, h, s, p, pax, x0.buf(), x2.buf(), x3.buf(), x4.buf(), x5.buf(), x6.buf(), err.buf());
host_store<B,S>(s, p, x2);
Visitor::stage3(t, h, s, p, pax, x0.buf(), x3.buf(), x4.buf(), x5.buf(), x6.buf(), err.buf());
host_store<B,S>(s, p, x3);
Visitor::stage4(t, h, s, p, pax, x0.buf(), x4.buf(), x5.buf(), x6.buf(), err.buf());
host_store<B,S>(s, p, x4);
Visitor::stage5(t, h, s, p, pax, x0.buf(), x5.buf(), x6.buf(), err.buf());
host_store<B,S>(s, p, x5);
Visitor::stage6(t, h, s, p, pax, x0.buf(), x6.buf(), err.buf());
/* compute error */
Visitor::stageErr(t, h, s, p, pax, x0.buf(), x6.buf(), k7.buf(), err.buf());
e2 = 0.0;
for (id = 0; id < N; ++id) {
e = err(id)*h/(h_atoler + h_rtoler*bi::max(bi::abs(x0(id)), bi::abs(x6(id))));
e2 += e*e;
}
e2 /= N;
/* accept/reject */
if (e2 <= BI_REAL(1.0)) {
/* accept */
t += h;
x0.swap(x6);
k1.swap(k7);
}
host_store<B,S>(s, p, x0);
/* compute next step size */
if (t < t2) {
logfac11 = h_expo*bi::log(e2);
if (e2 > BI_REAL(1.0)) {
/* step was rejected */
h *= bi::max(h_facl, bi::exp(h_logsafe - logfac11));
} else {
/* step was accepted */
fac = bi::exp(h_beta*logfacold + h_logsafe - logfac11); // Lund-stabilization
fac = bi::min(h_facr, bi::max(h_facl, fac)); // bound
h *= fac;
logfacold = BI_REAL(0.5)*bi::log(bi::max(e2, BI_REAL(1.0e-8)));
}
}
++n;
}
}
}
}
BI_FORCE_INLINE inline const bi::sse_real bi::operator-(const bi::sse_real& o) {
return BI_SSE_XOR_P(BI_SSE_SET1_P(BI_REAL(-0.0)), o.packed);
}
void h_ode_set_facr(const real facrin) {
h_facr = facrin;
h_facc2 = BI_REAL(1.0) / facrin;
}
void h_ode_set_facl(const real faclin) {
h_facl = faclin;
h_facc1 = BI_REAL(1.0) / faclin;
}
void h_ode_set_uround(const real uroundin) {
/* pre-condition */
BI_ASSERT(uroundin > BI_REAL(1.0e-19) && uroundin < BI_REAL(1.0));
h_uround = uroundin;
}