147 lines
1.9 KiB
C++
147 lines
1.9 KiB
C++
//-----------------------------------------------------------------------------
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//
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// Hermite polynomial
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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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void
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hermite(void)
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{
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save();
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yyhermite();
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restore();
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}
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// uses the recurrence relation H(x,n+1)=2*x*H(x,n)-2*n*H(x,n-1)
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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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void
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yyhermite(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(HERMITE);
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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 (issymbol(X))
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yyhermite2(n);
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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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yyhermite2(n);
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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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void
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yyhermite2(int n)
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{
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int i;
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push_integer(1);
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push_integer(0);
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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(i);
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push(Y0);
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multiply();
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subtract();
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push_integer(2);
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multiply();
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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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"hermite(x,n)",
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"hermite(x,n)",
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"hermite(x,0)-1",
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"0",
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"hermite(x,1)-2*x",
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"0",
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"hermite(x,2)-(4*x^2-2)",
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"0",
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"hermite(x,3)-(8*x^3-12*x)",
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"0",
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"hermite(x,4)-(16*x^4-48*x^2+12)",
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"0",
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"hermite(x,5)-(32*x^5-160*x^3+120*x)",
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"0",
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"hermite(x,6)-(64*x^6-480*x^4+720*x^2-120)",
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"0",
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"hermite(x,7)-(128*x^7-1344*x^5+3360*x^3-1680*x)",
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"0",
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"hermite(x,8)-(256*x^8-3584*x^6+13440*x^4-13440*x^2+1680)",
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"0",
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"hermite(x,9)-(512*x^9-9216*x^7+48384*x^5-80640*x^3+30240*x)",
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"0",
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"hermite(x,10)-(1024*x^10-23040*x^8+161280*x^6-403200*x^4+302400*x^2-30240)",
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"0",
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"hermite(a-b,10)-eval(subst(a-b,x,hermite(x,10)))",
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"0",
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};
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void
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test_hermite(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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