Status: Passed Jan 89 X3J13, as amended
References: CLtL p. 14, 34, 43, 231
Category: CHANGE, CLARIFICATION
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)
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))
(3) require that (<= ARRAY-DIMENSION-LIMIT MOST-POSITIVE-FIXNUM)
Consider an implementation with three numeric representations:
Fast (INTEGER -1024 1023)
Immediate 29 bits
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.
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
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.