3.1 Integer Basics

The range of values for an integer depends on the machine. The minimum range is −536,870,912 to 536,870,911 (30 bits; i.e., −2**29 to 2**29 − 1), but many machines provide a wider range. Many examples in this chapter assume the minimum integer width of 30 bits. The Lisp reader reads an integer as a sequence of digits with optional initial sign and optional final period. An integer that is out of the Emacs range is treated as a floating-point number.

      1               ; The integer 1.
      1.              ; The integer 1.
     +1               ; Also the integer 1.
     -1               ; The integer −1.
      9000000000000000000
                      ; The floating-point number 9e18.
      0               ; The integer 0.
     -0               ; The integer 0.

The syntax for integers in bases other than 10 uses ‘#’ followed by a letter that specifies the radix: ‘b’ for binary, ‘o’ for octal, ‘x’ for hex, or ‘radixr’ to specify radix radix. Case is not significant for the letter that specifies the radix. Thus, ‘#binteger’ reads integer in binary, and ‘#radixrinteger’ reads integer in radix radix. Allowed values of radix run from 2 to 36. For example:

     #b101100 ⇒ 44
     #o54 ⇒ 44
     #x2c ⇒ 44
     #24r1k ⇒ 44

To understand how various functions work on integers, especially the bitwise operators (see Bitwise Operations), it is often helpful to view the numbers in their binary form.

In 30-bit binary, the decimal integer 5 looks like this:

     0000...000101 (30 bits total)

(The ‘...’ stands for enough bits to fill out a 30-bit word; in this case, ‘...’ stands for twenty 0 bits. Later examples also use the ‘...’ notation to make binary integers easier to read.)

The integer −1 looks like this:

     1111...111111 (30 bits total)

−1 is represented as 30 ones. (This is called two's complement notation.)

Subtracting 4 from −1 returns the negative integer −5. In binary, the decimal integer 4 is 100. Consequently, −5 looks like this:

     1111...111011 (30 bits total)

In this implementation, the largest 30-bit binary integer is 536,870,911 in decimal. In binary, it looks like this:

     0111...111111 (30 bits total)

Since the arithmetic functions do not check whether integers go outside their range, when you add 1 to 536,870,911, the value is the negative integer −536,870,912:

     (+ 1 536870911)
          ⇒ -536870912
          ⇒ 1000...000000 (30 bits total)

Many of the functions described in this chapter accept markers for arguments in place of numbers. (See Markers.) Since the actual arguments to such functions may be either numbers or markers, we often give these arguments the name number-or-marker. When the argument value is a marker, its position value is used and its buffer is ignored.

In Emacs Lisp, text characters are represented by integers. Any integer between zero and the value of (max-char), inclusive, is considered to be valid as a character. See Character Codes.