«Exercise» Numeric Est. of Smooth Functions

/prog/ Exercise

Write an implementation of that gives the numeric approximation of a smooth function (infinitely differentiable) such as tangent(x), cosine(x), or log(x) with an adjustable level of precision in a desired programming language.  Please briefly describe the method or algorithm used in your code to approximate the function. If desired, it is acceptable to not reply.

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Function e^x
Method Maclaurin
Language ANSI C

#include <stdio.h>
double e(double e, int p)
{
    double x=1,y=1; int i=1,j=1;
    for(;i<p;++i) {
        y*=e,j*=i;
        x+=y/j;
    }
    return x;
}
int main()
{
    double x = 1;
    int p = 11;
    printf("e^%f ≈ %.8f\n| Error | ≤ %f^%d/%d!\n", x, e(x,p), x, ++p, p);
}


ackermann 0 = 0
ackermann 1 = 1
ackermann n = ackermann (n-1) + ackermann (n-2)