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The range of values for an integer depends on the machine. The range is -8388608 to 8388607 (24 bits; i.e., to ) on most machines, but on others it is -16777216 to 16777215 (25 bits), or -33554432 to 33554431 (26 bits). All of the examples shown below assume an integer has 24 bits.
The Lisp reader reads numbers as a sequence of digits with an optional sign.
1 ; The integer 1. +1 ; Also the integer 1. -1 ; The integer -1. 16777217 ; Also the integer 1, due to overflow. 0 ; The number 0. -0 ; The number 0. 1. ; The integer 1.
To understand how various functions work on integers, especially the bitwise operators (see section Bitwise Operations on Integers), it is often helpful to view the numbers in their binary form.
In 24 bit binary, the decimal integer 5 looks like this:
0000 0000 0000 0000 0000 0101
(We have inserted spaces between groups of 4 bits, and two spaces between groups of 8 bits, to make the binary integer easier to read.)
The integer -1 looks like this:
1111 1111 1111 1111 1111 1111
-1 is represented as 24 ones. (This is called two's complement notation.)
The negative integer, -5, is creating by subtracting 4 from -1. In binary, the decimal integer 4 is 100. Consequently, -5 looks like this:
1111 1111 1111 1111 1111 1011
In this implementation, the largest 24 bit binary integer is the decimal integer 8,388,607. In binary, this number looks like this:
0111 1111 1111 1111 1111 1111
Since the arithmetic functions do not check whether integers go outside their range, when you add 1 to 8,388,607, the value is negative integer -8,388,608:
(+ 1 8388607)
=> -8388608
=> 1000 0000 0000 0000 0000 0000
Many of the following functions accept markers for arguments as well as integers. (See section Markers.) More precisely, the actual parameters to such functions may be either integers or markers, which is why we often give these parameters the name int-or-marker. When the actual parameter is a marker, the position value of the marker is used and the buffer of the marker is ignored.
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