130 lines
1.6 KiB
C++
130 lines
1.6 KiB
C++
#include "stdafx.h"
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//-----------------------------------------------------------------------------
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//
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// Generate a Taylor expansion for expr.
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//
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// Input: tos-4 expr
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//
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// tos-3 function var
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//
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// tos-2 number of terms
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//
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// tos-1 expansion point
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//
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// Output: Result on stack
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//
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// Example:
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//
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// taylor(cos(x),x,8,a)
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//
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// tos-4 cos(x)
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//
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// tos-3 x
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//
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// tos-2 8
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//
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// tos-1 a
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//
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//-----------------------------------------------------------------------------
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#include "defs.h"
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static void __taylor(void);
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void
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taylor(void)
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{
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save();
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__taylor();
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restore();
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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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static void
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__taylor(void)
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{
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int i, k;
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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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if (X->k != SYM)
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stop("taylor: symbol expected, 2nd arg is not a symbol");
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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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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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evalat();
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C = _one;
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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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evalat();
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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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}
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static char *s[] = {
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"taylor(1/(5+4*cos(x)),x,6,0)",
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"1/9+2/81*x^2+5/1458*x^4+49/131220*x^6",
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"taylor(1/(5+4*cos(x)),x,6)",
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"1/9+2/81*x^2+5/1458*x^4+49/131220*x^6",
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"taylor(ln(x),x,8)",
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"undefined function",
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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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