/** Integrated generalized Lagrange basis polynomials
* B_j(y) := r^(j+1) (IntBasisPoly(p,j,y) - IntBasisPoly(p,j,-1))
* satisfies the 2p+1 Hermite interpolation conditions
* B_j^k(-1) = delta(k,j), for k=0,...,p,
* B_j^k(1) = 0, for k=1,...,p. (the function value at y=-1 is not interpolated)
* Analogously, we get the derivates at y=1 via
* C_j(y) := (-r)^(j+1) (IntBasisPoly(p,j,-y) - IntBasisPoly(p,j,1))
* that satisfies the 2p+1 Hermite interpolation conditions
* C_j^k(-1) = 0, for k=0,...,p,
* C_j^k(1) = delta(k,j), for k=1,...,p.
* */
static fcs_float IntBasisPoly(fcs_int p, fcs_int j, fcs_float y)
{
fcs_int k,l;
fcs_float sum1=0.0, sum2=0.0;
for (l=0; l<=p; l++) {
sum1 = 0.0;
for (k=0; k<=p-j-1; k++) {
sum1 += binom(p+k-1,k)*fak(j+k)/fak(j+k+1+l)*fcs_pow((1.0+y)/2.0,(fcs_float)k);
}
sum2 += fcs_pow(1.0+y,(fcs_float)l)*fcs_pow(1.0-y,(fcs_float)(p-l))/fak(p-l)*sum1;
}
return sum2 * fak(p)/fak(j)/(1<<p)*fcs_pow(1.0+y,(fcs_float)(j+1)); /* 1<<p = 2^p */
}
int main(int argc, char *argv[]) {
unsigned v = 7;
if (argc > 1)
v = atoi(argv[1]);
printf("%u! = %u\n", v, fak(v));
}
void fak(int x,unsigned long int *y)
{
if(x){
*y *=x;
x--;
fak(x,y);
}
}
/** basis polynomial for regularized kernel */
double BasisPoly(int m, int r, double xx)
{
int k;
double sum=0.0;
for (k=0; k<=m-r; k++) {
sum+=binom(m+k,k)*pow((xx+1.0)/2.0,(double)k);
}
return sum*pow((xx+1.0),(double)r)*pow(1.0-xx,(double)(m+1))/(1<<(m+1))/fak(r); /* 1<<(m+1) = 2^(m+1) */
}
int main() {
using t=std::integral_constant<std::size_t, fak(7)>;
using f0=std::integral_constant<std::size_t, a[0]>;
using f1=std::integral_constant<std::size_t, a[1]>;
using f2=std::integral_constant<std::size_t, a[2]>;
using f3=std::integral_constant<std::size_t, a[3]>;
std::cout << f0{} << " " << f1{} << f2{} << f3{} << std::endl;
}
int main()
{
int x;
unsigned long int y = 1, *p_y;
p_y = &y;
printf("zadej cislo vypocitam faktorial\n");
scanf("%d",&x);
fak(x,p_y);
printf("%lu\n",y);
return 0;
}
int main(int argc, char **argv){
int a = A;
char feld[3][4];
char (*ptr)[] = feld;
feld[0][0] = 88;
setFeld(ptr);
fak(&a);
return EXIT_SUCCESS;
}
unsigned fak(unsigned n) {
if (n == 0)
return 1;
return fak(n-1) * n;
}
/** binomial coefficient */
double binom(int n, int m)
{
return fak(n)/fak(m)/fak(n-m);
}
/** factorial */
double fak(int n)
{
if (n<=1) return 1.0;
else return (double)n*fak(n-1);
}
/* series for erf computation via series expansion */
static double erfseries(int i)
{
return (2*i+1)*fak(i);
}
void calculator::run()
{
abort = false;
if( (mprec == 0) | (mpar == 0) )
return;
qDebug() << "Parameter" << mpar << "Precision" << mprec << "Mode" << mmode;
mp::mp_init(mprec+2);
mp::mpsetprec(mprec);
mp::mpsetoutputprec(mprec);
time.start();
switch( mmode ) {
case montecarlo : {
mpar = pow(10, mpar);
quint64 walk = mpar/1000;
quint64 hits = 0;
double x,y;
if( walk == 0 ) walk = 1;
for(quint64 current=1;current<=mpar;current++) {
x=genrand_real3();
y=genrand_real3();
if( x*x+y*y <= 1 )
hits++;
if( current % walk == 0 )
emit update(1000*current/mpar);
if( abort )
break;
}
mp_real pi = mp_real(hits)/mp_real(mpar)*4;
mresult = QString::fromStdString(pi.to_string());
break;
}
case montemin1 : {
mpar = pow(10, mpar)-1;
quint64 walk = mpar/1000;
quint64 hits = 0;
double x,y;
if( walk == 0 ) walk = 1;
for(quint64 current=1;current<=mpar;current++) {
x=genrand_real3();
y=genrand_real3();
if( x*x+y*y <= 1 )
hits++;
if( current % walk == 0 )
emit update(1000*current/mpar);
if( abort )
break;
}
mp_real pi = mp_real(hits)/mp_real(mpar)*4;
mresult = QString::fromStdString(pi.to_string());
break;
}
case subdivide : {
mp_real x, a;
mpar = pow(10, mpar);
quint64 walk = mpar/1000;
quint64 current = 0;
a=0;
mp_real real_par(mpar);
x=1/(real_par*0.5);
while( x < 1 ) {
current++;
a+=1*sqrt(1-(x*x))/real_par;
x+=(1/real_par);
if( current % walk == 0)
emit update(current/walk);
if( abort )
break;
}
mp_real pi = a*4;
mresult = QString::fromStdString(pi.to_string());
break;
}
case grid : {
quint64 res = pow(10, mpar);
quint32 walk = res/1000+1;
quint64 hits = 0;
quint64 x = 0, y = res;
while( y > 0 )
{
while( x*x+y*y <= res )
x++;
hits += x;
if( y % walk == 0 ) emit update((res-y)/(walk+1));
y--;
if( abort )
break;
}
mp_real pi = mp_real(hits)/mp_real(res)*4;
mresult = QString::fromStdString(pi.to_string());
break;
}
case bbp : {
mp_real pi;
for(quint32 step=0;step<=mpar;step++) {
pi += ((mp_real(4)/mp_real(8*step+1))-(mp_real(2)/mp_real(8*step+4))-(mp_real(1)/mp_real(8*step+5))-(mp_real(1)/mp_real(8*step+6)))/(pow(mp_real(16),(int)step));
emit update(1000*step/mpar);
if( abort )
break;
}
mresult = QString::fromStdString(pi.to_string());
break;
}
case chudnovsky : {
mp_real temp;
for(quint32 step=0;step<=mpar;step++) {
mp_real upper = fak(6*step)*(13591409+545140134*mp_real(step))*pow(-1,step);
mp_real lower = pow(640320,mp_real(3*step)+1.5)*(fak(3*step)*pow(fak(step),3)+0.0);
temp += upper/lower;
emit update(1000*step/mpar);
if( abort )
break;
}
mp_real pi = mp_real(1)/(temp*12);
mresult = QString::fromStdString(pi.to_string());
break;
}
case polygon : {
mp_real pi_min = mp_real(mpar)/2*sin(2*mp_real::_pi/mp_real(mpar));
mp_real pi_max = mp_real(mpar)*tan(mp_real::_pi/mp_real(mpar));
mp_real pi_mid = (pi_min+pi_max)/2;
mresult = QString::fromStdString(pi_min.to_string())+" < Pi < "+QString::fromStdString(pi_max.to_string()) +"\nPi = "+QString::fromStdString(pi_mid.to_string());
break;
}
}
duration = time.elapsed();
mp::mp_finalize();
}
/** Generalized Lagrange basis polynomials (including derivatives up to degree p)
* B_j(y) := r^j BasisPoly(p,j,y)
* satisfies the 2p+2 Hermite interpolation conditions
* B_j^k(-1) = delta(k,j), for k=0,...,p,
* B_j^k(1) = 0, for k=0,...,p.
* I.e., each B_j(y) is equal to 1 in the j-th derivative at y=-1 and zero in all other interpolation points.
* Analogously, we get the derivates at y=1 via
* C_j(y) := (-r)^j BasisPoly(p,j,-y)
* that satisfies the 2p+2 Hermite interpolation conditions
* C_j^k(-1) = 0, for k=0,...,p,
* C_j^k(1) = delta(k,j), for k=0,...,p.
* */
static fcs_float BasisPoly(fcs_int p, fcs_int j, fcs_float y)
{
fcs_int k;
fcs_float sum=0.0;
for (k=0; k<=p-j; k++) {
sum+=binom(p+k,k)*fcs_pow((y+1.0)/2.0,(fcs_float)k);
}
return sum*fcs_pow((y+1.0),(fcs_float)j)*fcs_pow(1.0-y,(fcs_float)(p+1))/(1<<(p+1))/fak(j); /* 1<<(p+1) = 2^(p+1) */
}
/** binomial coefficient */
static fcs_float binom(fcs_int n, fcs_int m)
{
return fak(n)/fak(m)/fak(n-m);
}
/** factorial */
static fcs_float fak(fcs_int n)
{
if (n<=1) return 1.0;
else return (fcs_float)n*fak(n-1);
}
