151 lines
1.7 KiB
C++
151 lines
1.7 KiB
C++
/* Taylor expansion of a function
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push(F)
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push(X)
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push(N)
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push(A)
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taylor()
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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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eval_taylor(void)
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{
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// 1st arg
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p1 = cdr(p1);
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push(car(p1));
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eval();
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// 2nd arg
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p1 = cdr(p1);
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push(car(p1));
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eval();
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p2 = pop();
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if (p2 == symbol(NIL))
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guess();
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else
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push(p2);
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// 3rd arg
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p1 = cdr(p1);
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push(car(p1));
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eval();
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p2 = pop();
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if (p2 == symbol(NIL))
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push_integer(24); // default number of terms
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else
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push(p2);
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// 4th arg
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p1 = cdr(p1);
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push(car(p1));
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eval();
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p2 = pop();
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if (p2 == symbol(NIL))
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push_integer(0); // default expansion point
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else
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push(p2);
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taylor();
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}
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#define F p1
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#define X p2
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#define N p3
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#define A p4
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#define C p5
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void
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taylor(void)
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{
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int i, k;
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save();
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A = pop();
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N = pop();
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X = pop();
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F = pop();
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push(N);
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k = pop_integer();
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if (k == (int) 0x80000000) {
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push_symbol(TAYLOR);
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push(F);
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push(X);
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push(N);
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push(A);
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list(5);
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restore();
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return;
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}
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push(F); // f(a)
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push(X);
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push(A);
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subst();
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eval();
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push_integer(1);
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C = pop();
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for (i = 1; i <= k; i++) {
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push(F); // f = f'
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push(X);
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derivative();
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F = pop();
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if (iszero(F))
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break;
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push(C); // c = c * (x - a)
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push(X);
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push(A);
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subtract();
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multiply();
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C = pop();
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push(F); // f(a)
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push(X);
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push(A);
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subst();
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eval();
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push(C);
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multiply();
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push_integer(i);
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factorial();
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divide();
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add();
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}
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restore();
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}
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#if SELFTEST
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static char *s[] = {
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"taylor(1/(5+4*cos(x)),x,6,0)-(1/9+2/81*x^2+5/1458*x^4+49/131220*x^6)",
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"0",
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"taylor(1/(5+4*cos(x)),x,6)-(1/9+2/81*x^2+5/1458*x^4+49/131220*x^6)",
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"0",
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};
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void
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test_taylor(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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