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