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bignum

bignum Type

Supertypes:

bignum, integer, rational, real, number, t

Description:

The type bignum is defined to be exactly (and integer (not fixnum)).

=, /=, <, >, <=, >

Expanded Reference: bignum​

Type Checking​

A bignum is an integer too large to be represented as a fixnum. The type bignum is equivalent to (and integer (not fixnum)).

(typep 1 'bignum)
=> NIL
(typep most-positive-fixnum 'bignum)
=> NIL
(typep (1+ most-positive-fixnum) 'bignum)
=> T
(typep (1- most-negative-fixnum) 'bignum)
=> T

Relationship to fixnum and integer​

Every integer is either a fixnum or a bignum. These two types are an exhaustive partition of the integer type.

(subtypep 'bignum 'integer)
=> T
=> T
(type-of (1+ most-positive-fixnum))
;; => impl-dependent
(type-of (expt 2 100))
;; => impl-dependent
(integerp (expt 2 100))
=> T

Arbitrary Precision​

Common Lisp bignums provide arbitrary precision arithmetic. There is no upper bound on the size of a bignum, limited only by available memory.

(expt 2 128)
=> 340282366920938463463374607431768211456

(* most-positive-fixnum most-positive-fixnum)
;; => impl-dependent

Performance Note​

Bignum arithmetic is typically slower than fixnum arithmetic because fixnums can use native machine instructions while bignums require multi-word operations. Keeping values within fixnum range when possible improves performance.

;; Checking if a value is a fixnum for performance-sensitive code
(typep 42 'fixnum)
=> T
(typep (expt 10 20) 'fixnum)
=> NIL