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Status: Passed Jan 89 X3J13, as amended


References: CLtL p. 14, 34, 43, 231


Edit History: Version 1, 11-Jul-88, Sandra Loosemore

Version 2, 15-Sep-88, Masinter

Version 3, 23-Sep-88, Masinter

Version 4, 7-Dec-88, Masinter (two proposals)

Version 5, 16-Mar-89, Masinter (incorporate amendments)

Version 6, 17-Mar-89, Masinter (incorporate amendments correctly)

Problem Description:

Implementations of Common Lisp are required to support two disjoint

subsets of integers, fixnums and bignums, with the promise that

fixnums have a more efficient representation. However, nothing is

guaranteed about the range of integers which are fixnums: "Exactly

which integers are fixnums is implementation-dependent; typically they

will be those integers in the range -2**n to 2**n - 1, inclusive, for

some n not less than 15."

There are few uses of the fixnum type that are portable, given the

current definition. In particular, many programmers use FIXNUM type

declarations where they really mean "small integer".

While most Common Lisp implementations have a FIXNUM range

which is a subset of integers represeted and operated on most

efficiently, many also have several other subranges. The

partitioning of INTEGER into BIGNUM and FIXNUM is merely

confusing in these implementations, and not useful.

CLtL p14 and p34 disagree about BIGNUM. One says that

FIXNUM and BIGNUM are an exhaustive partition of the

integer space, the other says they might not be!


(1) Change the description of the type FIXNUM to reflect that it is

required to be a supertype of (SIGNED-BYTE 16).

(2) Define BIGNUM to be exactly (AND INTEGER (NOT FIXNUM))



Consider an implementation with three numeric representations:

Fast (INTEGER -1024 1023)

Immediate 29 bits

Extended Multi-precision

Such an implementation would have to define

FIXNUM to be (OR Fast Immediate). BIGNUM

would then refer to multi-precision integers.


Many programmers already use FIXNUM to mean "small integer"; this

proposal makes this usage portable.

However, there is little portable use for the type BIGNUM, and it

is inconsistent with many current implementation techniques.

Removing it is an incompatible change for a weak reason.

Current Practice:

Xerox Common Lisp has 17-bit fixnums. Most other Common Lisp

implementations have fixnum ranges of 24 bits or larger. We know

of no implementation that currently violates the proposed minimum


Several existing Common Lisp implementations have more than two

representations for integers, such that the FIXNUM/BIGNUM distinction

is confusing; they define BIGNUM to cover all of the larger number


Cost to implementors:

Slight. All implementations we know of already define FIXNUMs to be at

least 16 bits.

Cost to users:



The FIXNUM type specifier would have a portable interpretation.

The language would be less confusing.


There was little consensus on whether to leave BIGNUM in the language.

Earlier discussion of a related proposal contained several other more

controversial components (adding a constant MAX-INTEGER-LENGTH, allowing

MOST-POSITIVE-FIXNUM to be NIL as well as an integer.) This proposal

is an attempt to address the part that cleanup committee seemed to agree


It is possible that an implementation have a single representation for all

integers, and no way to identify any efficient range of integers. Those

implementations might need to set MOST-POSITIVE-FIXNUM

and MOST-NEGATIVE-FIXNUM to arbitrary values, consistent with

the requirement that (SIGNED-BYTE 16) is a subtype of FIXNUM.

Other alternatives considered (and not necessarily mutually exclusive

with this proposal):

remove the FIXNUM type specifier entirely, while leaving a way

to query what is the most efficient range of integers

leave the range of FIXNUMs unconstrained and introduce a

SMALL-INTEGER type with a fixed range (but no promises about

efficiency) .

It might be possible to specify the required performance behavior

of FIXNUMs more concretely, e.g., specify that the basic integer operations

use algorithms that are not proportional to the size of the data; it

should be just about as fast to add numbers in the middle of the fixnum

range as it is to add, say, 10 and 11. This might be a useful way to


the intent of the FIXNUM range, if not its specification.

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