C中的未知数学系列

Question

Does anybody have any idea what this code does? I suspect it has something to do with Taylor series, but I'm not sure since I don't really know what Taylor series is. However, it could be anything. I'm really not sure.

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
int main() {
  double x, y, a;
  int n;
  int z;
  x = 25.0;
  if (z < 0) {
    z = 1;
    x = -x;
  } else
    z = 0;
  n = 0;
  a = 1;
  y = 1;
  for (n = n + 1; n < 20; n++) {
    a = a * x / n;
    y = y + a;
    printf("%i \t %.20g \t %g \n", n, y, a);
  }
  if (z) {
    x = -x;
    y = 1.0 / y;
  }
  printf("%i \t %.20g \t %g \n", n, y, a);
  return 0;
}

Answer 1

Enable compiler warnings.

if (z < 0) { is a coding error. @Pablo .

It certainly should be

if (x < 0) {

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Unrolling

  n = 0;
  a = 1;
  y = 1;
  for (n = n + 1; n < 20; n++) {
    a = a * x / n;
    y = y + a;

The terms are

  y = 1 + x/1 + x*x/(1*2) + x*x*x/(1*2*3) + ....  pow(x,20)/(1*2*3*...*20)

Review Taylor series to discern which one.

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BTW, For x==25 , code Taylor's series does not converge enough. Either more terms are needed or better - an alternate/additional approach is needed.