real bump(real x, real y)
{
real cxs = cosr(x); cxs *= cxs;
real cys = cosr(y); cys *= cys;
return fabsr((cxs*cxs + cys*cys - 2*cxs*cys) / sqrtr(x*x+2*y*y));
}
void
tformsetangle(Tform *t, real angle) {
real c = cosr(angle);
real s = sinr(angle);
t->col1.x = c;
t->col2.x = -s;
t->col1.y = s;
t->col2.y = c;
}
/* n inner lobatto nodes (excluding -1,1) */
static void lobatto_nodes_aux(real *z, int n)
{
int i,j,np=n+1;
for(i=0; i<=n/2-1; ++i) {
real ox, x = cosr( (n-i)*PI/np );
do {
ox = x;
x -= legendre_d1(np,x)/legendre_d2(np,x);
} while(fabsr(x-ox)>-x*EPS);
z[i] = x - legendre_d1(np,x)/legendre_d2(np,x);
}
if(n&1) z[n/2]=0;
for(j=(n+1)/2,i=n/2-1; j<n; ++j,--i) z[j]=-z[i];
}
/* n nodes */
void gauss_nodes(real *z, int n)
{
int i,j;
for(i=0; i<=n/2-1; ++i) {
real ox, x = cosr( (2*n-2*i-1)*(PI/2)/n );
do {
ox = x;
x -= legendre(n,x)/legendre_d1(n,x);
} while(fabsr(x-ox)>-x*EPS);
z[i] = x - legendre(n,x)/legendre_d1(n,x);
}
if(n&1) z[n/2]=0;
for(j=(n+1)/2,i=n/2-1; j<n; ++j,--i) z[j]=-z[i];
}
real randn()
{
static bool prepped = false;
static real prepped_result = 0;
if (prepped)
{
prepped = false;
return prepped_result;
}
else
{
real u1 = randf(), u2 = randf();
real len = sqrtr(-2 * logr(u1));
prepped = true;
prepped_result = len * sinr(2*M_PI*u2);
return len * cosr(2*M_PI*u2);
}
}
