6.2.5 Syntax of numerical constants

The syntax of the written representations for numbers is described formally in Formal syntax. Note that case is not significant in numerical constants.

A number can be written in binary, octal, decimal, or hexadecimal by the use of a radix prefix. The radix prefixes are #b (binary), #o (octal), #d (decimal), and #x (hexadecimal). With no radix prefix, a number is assumed to be expressed in decimal.

A numerical constant can be specified to be either exact or inexact by a prefix. The prefixes are #e for exact, and #i for inexact. An exactness prefix can appear before or after any radix prefix that is used. If the written representation of a number has no exactness prefix, the constant is inexact if it contains a decimal point or an exponent. Otherwise, it is exact.

In systems with inexact numbers of varying precisions it can be useful to specify the precision of a constant. For this purpose, implementations may accept numerical constants written with an exponent marker that indicates the desired precision of the inexact representation. If so, the letter s, f, d, or l, meaning short, single, double, or long precision, respectively, can be used in place of e. The default precision has at least as much precision as double, but implementations may allow this default to be set by the user.

3.14159265358979F0
        Round to single — 3.141593
0.6L0
        Extend to long — .600000000000000

The numbers positive infinity, negative infinity, and NaN are written +inf.0, -inf.0 and +nan.0 respectively. NaN may also be written -nan.0. The use of signs in the written representation does not necessarily reflect the underlying sign of the NaN value, if any. Implementations are not required to support these numbers, but if they do, they must do so in general conformance with IEEE 754. However, implementations are not required to support signaling NaNs, nor to provide a way to distinguish between different NaNs.

There are two notations provided for non-real complex numbers: the rectangular notation a+bi, where a is the real part and b is the imaginary part; and the polar notation r@θ where r is the magnitude and θ is the phase (angle) in radians. These are related by the equation \(a + bi = r \cos\theta + (r \sin\theta)i\). All of a, b, r, and θ are real numbers.