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- //-----------------------------------------------------------------------------
- //
- // Hermite polynomial
- //
- // Input: tos-2 x (can be a symbol or expr)
- //
- // tos-1 n
- //
- // Output: Result on stack
- //
- //-----------------------------------------------------------------------------
- #include "stdafx.h"
- #include "defs.h"
- void
- hermite(void)
- {
- save();
- yyhermite();
- restore();
- }
- // uses the recurrence relation H(x,n+1)=2*x*H(x,n)-2*n*H(x,n-1)
- #define X p1
- #define N p2
- #define Y p3
- #define Y1 p4
- #define Y0 p5
- void
- yyhermite(void)
- {
- int n;
- N = pop();
- X = pop();
- push(N);
- n = pop_integer();
- if (n < 0) {
- push_symbol(HERMITE);
- push(X);
- push(N);
- list(3);
- return;
- }
- if (issymbol(X))
- yyhermite2(n);
- else {
- Y = X; // do this when X is an expr
- X = symbol(SECRETX);
- yyhermite2(n);
- X = Y;
- push(symbol(SECRETX));
- push(X);
- subst();
- eval();
- }
- }
- void
- yyhermite2(int n)
- {
- int i;
- push_integer(1);
- push_integer(0);
- Y1 = pop();
- for (i = 0; i < n; i++) {
- Y0 = Y1;
- Y1 = pop();
- push(X);
- push(Y1);
- multiply();
- push_integer(i);
- push(Y0);
- multiply();
- subtract();
- push_integer(2);
- multiply();
- }
- }
- #if SELFTEST
- static char *s[] = {
- "hermite(x,n)",
- "hermite(x,n)",
- "hermite(x,0)-1",
- "0",
- "hermite(x,1)-2*x",
- "0",
- "hermite(x,2)-(4*x^2-2)",
- "0",
- "hermite(x,3)-(8*x^3-12*x)",
- "0",
- "hermite(x,4)-(16*x^4-48*x^2+12)",
- "0",
- "hermite(x,5)-(32*x^5-160*x^3+120*x)",
- "0",
- "hermite(x,6)-(64*x^6-480*x^4+720*x^2-120)",
- "0",
- "hermite(x,7)-(128*x^7-1344*x^5+3360*x^3-1680*x)",
- "0",
- "hermite(x,8)-(256*x^8-3584*x^6+13440*x^4-13440*x^2+1680)",
- "0",
- "hermite(x,9)-(512*x^9-9216*x^7+48384*x^5-80640*x^3+30240*x)",
- "0",
- "hermite(x,10)-(1024*x^10-23040*x^8+161280*x^6-403200*x^4+302400*x^2-30240)",
- "0",
- "hermite(a-b,10)-eval(subst(a-b,x,hermite(x,10)))",
- "0",
- };
- void
- test_hermite(void)
- {
- test(__FILE__, s, sizeof s / sizeof (char *));
- }
- #endif
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