System Class float

Class Precedence List:

Description:

A float is a mathematical rational (but not a Common Lisp rational) of the form $s·f·b^{e-p}$, 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: Barmar: What about IEEE NaNs and infinities?

!!!Reviewer: 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?

2.15.0 12The 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:

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, Section 2.3.2 (Constructing Numbers from Tokens), Section 22.1.3.1.3 (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).