eigenmath/tchebychevU.cpp

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2005-07-30 21:37:29 +02:00
//-----------------------------------------------------------------------------
//
// Author : philippe.billet@noos.fr
//
// tchebychevU polynomial U(x,n+1)=2*x*U(n,x)-U(x,n-1) U(x,0)=1,U(x,1)=2*x
//
// Input: tos-2 x (can be a symbol or expr)
//
// tos-1 n
//
// Output: Result on stack
//
//-----------------------------------------------------------------------------
#include "stdafx.h"
#include "defs.h"
static void ytchebychevU(void);
static void ytchebychevU2(int);
void
eval_tchebychevU(void)
{
push(cadr(p1));
eval();
push(caddr(p1));
eval();
tchebychevU();
}
void
tchebychevU(void)
{
save();
ytchebychevU();
restore();
}
#define X p1
#define N p2
#define Y p3
#define Y1 p4
#define Y0 p5
static void
ytchebychevU(void)
{
int n;
N = pop();
X = pop();
push(N);
n = pop_integer();
if (n < 0) {
push_symbol(TCHEBYCHEVU);
push(X);
push(N);
list(3);
return;
}
if (n == 0) {
push_integer(1);
return;
}
if (issymbol(X))
ytchebychevU2(n-1);
else {
Y = X; // do this when X is an expr
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X = symbol(SECRETX);
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ytchebychevU2(n-1);
X = Y;
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push(symbol(SECRETX));
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push(X);
subst();
eval();
}
}
static void
ytchebychevU2(int n)
{
int i;
push(X);
push_integer(2);
multiply();
push_integer(1);
Y1 = pop();
for (i = 0; i < n; i++) {
Y0 = Y1;
Y1 = pop();
push(X);
push(Y1);
multiply();
push_integer(2);
multiply();
push(Y0);
subtract();
}
}
static char *s[] = {
"tchebychevU(x,n)",
"tchebychevU(x,n)",
"tchebychevU(x,0)-1",
"0",
"tchebychevU(x,1)-2*x",
"0",
"tchebychevU(x,2)-(4x^2-1)",
"0",
"tchebychevU(x,3)-(8*x^3-4*x)",
"0",
"tchebychevU(x,4)-(16*x^4-12*x^2+1)",
"0",
};
void
test_tchebychevU(void)
{
test(__FILE__, s, sizeof s / sizeof (char *));
}