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