gcc - Strange behaviour of macros C/C++

Question

I'm using some macros, and observing some strange behaviour.

I've defined PI as a constant, and then used it in macros to convert degrees to radians and radians to degrees. Degrees to radians works fine, but radians to degrees does not:

piTest.cpp:

#include <cmath>
#include <iostream>
using namespace std;

#define PI atan(1) * 4
#define radians(deg)  deg * PI / 180
#define degrees(rad)  rad * 180 / PI

int main()
{
  cout << "pi: " << PI << endl;
  cout << "PI, in degrees: " << degrees(PI) << endl;
  cout << "45 degrees, in rad: " << radians(45) << endl;
  cout << "PI * 180 / PI: " << (PI * 180 / PI) << endl;
  cout << "3.14159 * 180 / 3.14159: " << (3.14159 * 180 / 3.14159) << endl;
  cout << "PI * 180 / 3.14159: " << (PI * 180 / 3.14159) << endl;
  cout << "3.14159 * 180 / PI: " << (3.14159 * 180 / PI) << endl;

  return 0;

}

When I compile and run, I get the following output:

pi: 3.14159
PI, in degrees: 2880
45 degrees, in rad: 0.785398
PI * 180 / PI: 2880
3.14159 * 180 / 3.14159: 180
PI * 180 / 3.14159: 180
3.14159 * 180 / PI: 2880

It seems like my constant PI works in the numerator, but not the denominator. I've observed the same behaviour in C. I'm running gcc version 4.6.3

Can anyone explain why I'm getting this behaviour?

Answer 1

Macros are (relatively simple) textual substitutions.

Use parentheses in your definitions (both to enclose the macro itself and the macro arguments):

#define PI (atan(1) * 4)
#define radians(deg)  ((deg) * PI / 180)
#define degrees(rad)  ((rad) * 180 / PI)