YJL

1   The error: M_PI undeclared

I’ve seen the following error many times, whenever I felt that I should code project foobar in Standard C, and every time it was thrown at me by gcc, I usually have to re-think what solution I should take. By re-think, I meant re-search on the Internet.

test.c:22:18: error: 'M_PI' undeclared (first use in this function)
   printf("%f\n", M_PI);

2   Standards define no mathematical constants

The error message is pretty clear, apparently, M_PI is not declared as stated. The question is why do so many people use it and we get the error during the compilation.

A quick and simple answer is M_PI and other mathematics constants, such as M_E for Euler’s number, are not in Standard C and C++. From Trigonometric Functions in the GNU C Library’s manual:

The math library normally defines M_PI to a double approximation of pi. If strict ISO and/or POSIX compliance² are requested this constant is not defined, but you can easily define it yourself:

According to Predefined Mathematical Constants also in the GNU C Library’s manual:

These constants come from the Unix98 standard and were also available in 4.4BSD; therefore they are only defined if _XOPEN_SOURCE=500, or a more general feature select macro, is defined. The default set of features includes these constants. See Feature Test Macros.

UNIX 98 is the Single UNIX Specification version 2, back in 1997, and 4.4BSD in 1993, these constants go back for at least three decades, no wonder we all use them.

It seems these commonly used mathematical constants never are part of the standards, they have never been defined ever since the first standard, C89. I wonder why? Maybe there is a principle to prevent them from being included, some MUST NOT or SHOULD NOT? Since I have never read the standard, I’d not know, but if there is one, please quote for me. Or, perhaps, math.h is laid out to be only the “declarations for math functions” as the first line of GNU C Library’s implementation states.

However, I am more curious about why no M_2PI — not to be confused with M_2_PI, $2/\pi$ — isn’t $2\pi$ quite commonly used?

One more thing, it’s strange that Wikipedia has no mentions about these non-standard constants but only the mathematical functions, when lots of people are looking for a definition from math.h.

3   C++ on GNU/Linux

Although I have never coded in C++, while writing this post, I found out there is a strange behavior, the _GNU_SOURCE is defined as shown below:

% cpp -xc++ -std=c++98 -dD /dev/null | grep -B1 GNU_SOURCE
# 1 "<command-line>"
#define _GNU_SOURCE 1
$ clang -E -xc++ -std=c++98 -dM /dev/null | grep GNU_SOURCE
#define _GNU_SOURCE 1

As you can see in the issued command, I didn’t define the macro, _GNU_SOURCE, however, it showed up under the <command-line> section. The GNU C++ Library’s FAQ has an entry explaining it:

_XOPEN_SOURCE and _GNU_SOURCE are always defined?

On Solaris, g++ (but not gcc) always defines the preprocessor macro _XOPEN_SOURCE. On GNU/Linux, the same happens with _GNU_SOURCE. (This is not an exhaustive list; other macros and other platforms are also affected.)

[…]

Since almost all the Linux distributions are with GNU tools and libraries, that is GNU/Linux, in this case, the GNU C Library, it’s unavoidable that if you code in C++, you have actually enabled GNU extensions. If you ain’t aware of it, you could be writing a code that’s not as portable as you may think.

Also on lwn.net, Jonathan Wakely (jwakely) posted on 2014-03-13:

To confuse things a bit, G++ unconditionally defines _GNU_SOURCE on systems using glibc, because the C++ standard library wants to be able to make use of GNU extensions, so uses the “give me everything” approach.

[…]

It’s been more than a year, if there is a fix, then I haven’t seen it. Considering it’s the GNU C Library, and I use Gentoo Linux, therefore I don’t expect to see the fix at least for a year from my end. Nonetheless, since I hardly code in C or C++, I don’t even bother to check.

4   Solutions

#ifndef M_PI
#define M_PI  3.14159265358979323846
#endif

#define M_PIl 3.141592653589793238462643383279502884L

const double M_PI = 3.14159265358979323846;

const long double M_PIl = 3.141592653589793238462643383279502884L;

const auto M_PI = 3.1415926535897932384;

const auto M_PIl = 3.141592653589793238462643383279502884L;

double M_PI;
long double M_PIl

int
main(int argc, char *argv[])
{
  M_PI = acos(-1.0);
  M_PIl = acosl(-1.0);
  /* ... */
}

#if __STDC_VERSION__ >= 199901L
  // ..
#endif

const double M_PI = acos(-1.0);
const long double M_PIl = acosl(-1.0);

const auto M_PI = acos(-1.0);
const auto M_PIl = acosl(-1.0);

#undef __STRICT_ANSI__
#define _USE_MATH_DEFINES
#include <math.h>

#undef __STRICT_ANSI__
#define _USE_MATH_DEFINES
#include <cmath>

#define _XOPEN_SOURCE
#include <math.h>

#define _XOPEN_SOURCE
#include <cmath>