Approximation of error-function erf(x)

Question

The code beyond approximates the error-function erf(x) with following formular \$erf(x)=1-(a_1t+a_2t^2+a_3t^3)e^{-x^2})\$ for \$x\geq0\$ inclusive the identity \$erf(-x)=-erf(x)\$.

1. Is it okay to end the program in the middle of a code with exit(EXIT_FAILURE)? I just tried to avoid it and came to following solution, where the program always ends with return 0 at the end of the main-programm: https://codepaste.net/ek8ed5 So the question is whats's the more correct way?

(I hope a moderator can paste this code section in here please, because somehow I didn't make it work to show it as nicely formatted code, sorry!)

2. What else can I improve?

.

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define p 0.47047
#define a_1 0.3480242
#define a_2 -0.0958798
#define a_3 0.7478556
double ErrorFunction(double x);
int main(void)
{
 double x = 0;
 do
 {
 printf("Enter any value x to show erf(x): ");
 if (scanf_s("%lf", &x) != 1)
 {
 printf("error: invalid input\n");
 exit(EXIT_FAILURE);
 }
 else
 {
 printf("\n erf(x)=%f\n\n", ErrorFunction(x));
 }
 } while (x != 0);
 return 0;
}
double ErrorFunction(double x)
{
 double t = 0;
 if (x < 0)
 {
 x = -x;
 t = 1 / (1 + p*x);
 return -(1 - (a_1*t + a_2*t*t + a_3*t*t*t)*exp(-(x*x)));
 }
 else
 {
 t = 1 / (1 + p*x);
 return 1 - (a_1*t + a_2*t*t + a_3*t*t*t)*exp(-(x*x));
 }
}

Answer 1

• DRY. Actual computations are repeated twice, which is always a signal for improvement:

  if (x < 0) {
   t = 1 / (1 - p*x);
  } else {
   t = 1 / (1 + p*x);
  }
  result = compute_the_formula(t, x);
  if (x < 0) {
   result = -result;
  }
  return result;
  

• Try to cut down multiplications. Instead of

  a_1*t + a_2*t*t + a_3*t*t*t
  

  consider

  t*(a_1 + t*(a2 + t*a_3)))
  

  Three multiplications instead of original six is not only faster, but generally more accurate.

• physics: Thanks. 1. Actually I should really implement erf(-x)=-erf(x) according to this exercise. And it is also called identity.
• physics: 2. I.e. the less multiplications you have the more accurate it is, because you have less rounding errors?
• physics: 3. What do you say to my v1- and v2-main() in my starting post (codepaste.net)?

Answer 2

double ErrorFunction(double x);

Would erf be a better name?

---

 if (scanf_s("%lf", &x) != 1)

 printf("\n erf(x)=%f\n\n", ErrorFunction(x));

Why the inconsistency between %lf and %f?

---

Following up on a comment you made to another answer:

Actually I should really implement erf(-x)=-erf(x) according to this exercise

The best way to do that from the point of view of 1) self-documenting code; 2) not accidentally breaking it in maintenance is

double ErrorFunction(double x)
{
 if (x < 0) return -ErrorFunction(-x);
 ...

• physics: Oh yeah that is good idea! So I only have one code line that computes my approximation instead ot two! 1. I didn't use erf as name, because I got this compiler warning: docs.microsoft.com/en-us/cpp/error-messages/compiler-warnings/… or is it ok to ignore this one? I thought that you always should avoid any compiler Warnings. (I use VS 2017)
• physics: 2. I used %fin my printf, because it makes no difference to %lfby using it in a printf and I got the advice from here too: codereview.stackexchange.com/questions/160846/… (point 5)
• physics: And when are you trying to use it on 'scanf' it won't work, because pointers aren't promoted to anything, but variables are. (stackoverflow.com/questions/210590/…) But I guess i should always stick to the same %? I. e. %lffor doubles, %ffor floats etc.
• Peter Taylor: @physics, 1. Makes sense that the logical name is already used. Still, I'd favour namespacing the name. In extremis, my_erf. 2. Fair enough. Gareth knows C better than I do.