### 19.1 Predefined Mathematical Constants

The header `math.h` defines several useful mathematical constants. All values are defined as preprocessor macros starting with `M_`. The values provided are:

`M_E`
  The base of natural logarithms.
`M_LOG2E`
  The logarithm to base `2` of `M_E`.
`M_LOG10E`
  The logarithm to base `10` of `M_E`.
`M_LN2`
  The natural logarithm of `2`.
`M_LN10`
  The natural logarithm of `10`.
`M_PI`
  Pi, the ratio of a circle's circumference to its diameter.
`M_PI_2`
  Pi divided by two.
`M_PI_4`
  Pi divided by four.
`M_1_PI`
  The reciprocal of pi (1/pi)
`M_2_PI`
  Two times the reciprocal of pi.
`M_2_SQRTPI`
  Two times the reciprocal of the square root of pi.
`M_SQRT2`
  The square root of two.
`M_SQRT1_2`
  The reciprocal of the square root of two (also the square root of 1/2).

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

All values are of type `double`. As an extension, the GNU C Library also defines these constants with type `long double`. The `long double` macros have a lowercase ‘`l`’ appended to their names: `M_El`, `M_PIl`, and so forth. These are only available if `_GNU_SOURCE` is defined.

Note: Some programs use a constant named `PI` which has the same value as `M_PI`. This constant is not standard; it may have appeared in some old AT&T headers, and is mentioned in Stroustrup's book on C++. It infringes on the user's name space, so the GNU C Library does not define it. Fixing programs written to expect it is simple: replace `PI` with `M_PI` throughout, or put ‘`-DPI=M_PI`’ on the compiler command line.