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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:


The base of natural logarithms.


The logarithm to base 2 of M_E.


The logarithm to base 10 of M_E.


The natural logarithm of 2.


The natural logarithm of 10.


Pi, the ratio of a circle’s circumference to its diameter.


Pi divided by two.


Pi divided by four.


The reciprocal of pi (1/pi)


Two times the reciprocal of pi.


Two times the reciprocal of the square root of pi.


The square root of two.


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 _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.

Likewise, the GNU C Library also defines these constants with the types _FloatN and _FloatNx for the machines that have support for such types enabled (see Mathematics) and if _GNU_SOURCE is defined. When available, the macros names are appended with ‘fN’ or ‘fNx’, such as ‘f128’ for the type _Float128.

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.

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