# Floating Numbers¶

## Approximate Reals¶

Felix has three floating types:

Felix C Suffix Positive Infinity
float float f FINFINITY
double double float d DINFINITY
ldouble long double float l LINFINITY

where the d suffix can be omitted. The lexical rules are

regdef decimal_string = digit (underscore ? digit) *;
regdef hexadecimal_string = hexdigit (underscore ? hexdigit) *;

regdef decimal_fractional_constant =
decimal_string '.' decimal_string;

("0x" |"0X")

regdef decimal_exponent = ('E'|'e') ('+'|'-')? decimal_string;
regdef binary_exponent = ('P'|'p') ('+'|'-')? decimal_string;

regdef floating_suffix = 'L' | 'l' | 'F' | 'f' | 'D' | 'd';
regdef floating_literal =
(
decimal_fractional_constant decimal_exponent ? |
)
floating_suffix ?;


This is consistent with ISO C, except that underscores may be used to separate digits, and a decimal point is required and must be surrounded by digits. Therefore 0. and .0 are not permissible floating literals.

IEEE NaN (Not a Number) values can be checked for with the function isnan. IEEE Infinity values can be checked for with the function isinf.

## Approximate Complex¶

Felix has three complex types based on C++ complex<T> where T is one of the three floating types.

Felix C++
fcomplex ::std::complex<float>
dcomplex ::std::complex<double>
lcomplex ::std::complex<long double>

### Constructors¶

Complex numbers can be constructed using the typedef name complex and two arguments of the same floating real type, or the typedef name polar and two arguments of the same floating real type. These construct a complex number in Cartesian and Polar coordinates, respectively.

## Approximate Quaternion¶

Felix provides a single type quaternion which is based on float double. It is defined in the library module Quaternion which should be opened to use it.