#### 12.2.4 float [System Class]

#### Class Precedence List::

float,

real,

number, t

#### Description::

A float is a mathematical rational (but not a Common Lisp rational) of the form s\cdot f\cdot b^e-p, where s is +1 or -1, the sign; b is an integer greater than~1, the base or radix of the representation; p is a positive integer, the precision (in base-b digits) of the float; f is a positive integer between b^p-1 and b^p-1 (inclusive), the significand; and e is an integer, the exponent. The value of p and the range of~e depends on the implementation and on the type of float within that implementation. In addition, there is a floating-point zero; depending on the implementation, there can also be a “minus zero”. If there is no minus zero, then 0.0 and~-0.0 are both interpreted as simply a floating-point zero. `(= 0.0 -0.0)` is always true. If there is a minus zero, `(eql -0.0 0.0)` is false, otherwise it is true.

[Reviewer Note by Barmar: What about IEEE NaNs and infinities?]

[Reviewer Note by RWK: In the following, what is the “ordering”? precision? range? Can there be additional subtypes of float or does “others” in the list of four?]

The types short-float, single-float, double-float, and long-float are subtypes of type float. Any two of them must be either disjoint types or the same type; if the same type, then any other types between them in the above ordering must also be the same type. For example, if the type single-float and the type long-float are the same type, then the type double-float must be the same type also.

#### Compound Type Specifier Kind::

Abbreviating.

#### Compound Type Specifier Syntax::

(`float`{`[`lower-limit [upper-limit]`]`})

#### Compound Type Specifier Arguments::

lower-limit, upper-limit—interval designators for type float. The defaults for each of lower-limit and upper-limit is the symbol *.

#### Compound Type Specifier Description::

This denotes the floats on the interval described by lower-limit and upper-limit.

#### See Also::

Figure~2–9, Constructing Numbers from Tokens, Printing Floats

#### Notes::

Note that all mathematical integers are representable not only as Common Lisp reals, but also as complex floats. For example, possible representations of the mathematical number 1 include the integer `1`, the float `1.0`, or the complex `#C(1.0 0.0)`.