Emacs Lisp

3.1 Integer Basics

The Lisp reader reads an integer as a nonempty sequence of decimal digits with optional initial sign and optional final period.

 1               ; The integer 1.
 1.              ; The integer 1.
+1               ; Also the integer 1.
-1               ; The integer -1.
 0               ; The integer 0.
-0               ; The integer 0.

The syntax for integers in bases other than 10 consists of ‘#’ followed by a radix indication followed by one or more digits. The radix indications are ‘b’ for binary, ‘o’ for octal, ‘x’ for hex, and ‘radixr’ for radix radix. Thus, ‘#binteger’ reads integer in binary, and ‘#radixrinteger’ reads integer in radix radix. Allowed values of radix run from 2 to 36, and allowed digits are the first radix characters taken from ‘0’–‘9’, ‘A’–‘Z’. Letter case is ignored and there is no initial sign or final period. 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 on Integers), it is often helpful to view the numbers in their binary form.

In binary, the decimal integer 5 looks like this:

…000101

(The ellipsis ‘…’ stands for a conceptually infinite number of bits that match the leading bit; here, an infinite number of 0 bits. Later examples also use this ‘…’ notation.)

The integer -1 looks like this:

…111111

-1 is represented as all 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:

…111011

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.

Integers in Emacs Lisp are not limited to the machine word size. Under the hood, though, there are two kinds of integers: smaller ones, called fixnums, and larger ones, called bignums. Although Emacs Lisp code ordinarily should not depend on whether an integer is a fixnum or a bignum, older Emacs versions support only fixnums, some functions in Emacs still accept only fixnums, and older Emacs Lisp code may have trouble when given bignums. For example, while older Emacs Lisp code could safely compare integers for numeric equality with eq, the presence of bignums means that equality predicates like eql and = should now be used to compare integers.

The range of values for bignums is limited by the amount of main memory, by machine characteristics such as the size of the word used to represent a bignum’s exponent, and by the integer-width variable. These limits are typically much more generous than the limits for fixnums. A bignum is never numerically equal to a fixnum; Emacs always represents an integer in fixnum range as a fixnum, not a bignum.

The range of values for a fixnum 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.

Variable: most-positive-fixnum ¶

The value of this variable is the greatest “small” integer that Emacs Lisp can handle. Typical values are 2**29 - 1 on 32-bit and 2**61 - 1 on 64-bit platforms.

Variable: most-negative-fixnum ¶

The value of this variable is the numerically least “small” integer that Emacs Lisp can handle. It is negative. Typical values are -2**29 on 32-bit and -2**61 on 64-bit platforms.

Variable: integer-width ¶

The value of this variable is a nonnegative integer that controls whether Emacs signals a range error when a large integer would be calculated. Integers with absolute values less than 2**n, where n is this variable’s value, do not signal a range error. Attempts to create larger integers typically signal a range error, although there might be no signal if a larger integer can be created cheaply. Setting this variable to a large number can be costly if a computation creates huge integers.

3.2 Floating-Point Basics

Floating-point numbers are useful for representing numbers that are not integral. The range of floating-point numbers is the same as the range of the C data type double on the machine you are using. On almost all computers supported by Emacs, this is IEEE binary64 floating point format, which is standardized by IEEE Std 754-2019 and is discussed further in David Goldberg’s paper “What Every Computer Scientist Should Know About Floating-Point Arithmetic”. On modern platforms, floating-point operations follow the IEEE-754 standard closely; however, results are not always rounded correctly on some systems, notably 32-bit x86.

On some old computer systems, Emacs may not use IEEE floating-point. We know of one such system on which Emacs runs correctly, but does not follow IEEE-754: the VAX running NetBSD using GCC 10.4.0, where the VAX ‘D_Floating’ format is used instead. IBM System/370-derived mainframes and their XL/C compiler are also capable of utilizing a hexadecimal floating point format, but Emacs has not yet been built in such a configuration.

The read syntax for floating-point numbers requires either a decimal point, an exponent, or both. Optional signs (‘+’ or ‘-’) precede the number and its exponent. For example, ‘1500.0’, ‘+15e2’, ‘15.0e+2’, ‘+1500000e-3’, and ‘.15e4’ are five ways of writing a floating-point number whose value is 1500. They are all equivalent. Like Common Lisp, Emacs Lisp requires at least one digit after a decimal point in a floating-point number that does not have an exponent; ‘1500.’ is an integer, not a floating-point number.

Emacs Lisp treats -0.0 as numerically equal to ordinary zero with respect to numeric comparisons like =. This follows the IEEE floating-point standard, which says -0.0 and 0.0 are numerically equal even though other operations can distinguish them.

The IEEE floating-point standard supports positive infinity and negative infinity as floating-point values. It also provides for a class of values called NaN, or “not a number”; numerical functions return such values in cases where there is no correct answer. For example, (/ 0.0 0.0) returns a NaN. A NaN is never numerically equal to any value, not even to itself. NaNs carry a sign and a significand, and non-numeric functions treat two NaNs as equal when their signs and significands agree. Significands of NaNs are machine-dependent, as are the digits in their string representation.

NaNs are not available on systems which do not use IEEE floating-point arithmetic; if the read syntax for a NaN is used on a VAX, for example, the reader signals an error.

When NaNs and signed zeros are involved, non-numeric functions like eql, equal, sxhash-eql, sxhash-equal and gethash determine whether values are indistinguishable, not whether they are numerically equal. For example, when x and y are the same NaN, (equal x y) returns t whereas (= x y) uses numeric comparison and returns nil; conversely, (equal 0.0 -0.0) returns nil whereas (= 0.0 -0.0) returns t.

Here are read syntaxes for these special floating-point values:

infinity

‘1.0e+INF’ and ‘-1.0e+INF’

not-a-number

‘0.0e+NaN’ and ‘-0.0e+NaN’

The following functions are specialized for handling floating-point numbers:

Function: isnan x ¶

This predicate returns t if its floating-point argument is a NaN, nil otherwise.

Function: frexp x ¶

This function returns a cons cell (s . e), where s and e are respectively the significand and exponent of the floating-point number x.

If x is finite, then s is a floating-point number between 0.5 (inclusive) and 1.0 (exclusive), e is an integer, and x = s * 2**e. If x is zero or infinity, then s is the same as x. If x is a NaN, then s is also a NaN. If x is zero, then e is 0.

Function: ldexp s e ¶

Given a numeric significand s and an integer exponent e, this function returns the floating point number s * 2**e.

Function: copysign x1 x2 ¶

This function copies the sign of x2 to the value of x1, and returns the result. x1 and x2 must be floating point.

Function: logb x ¶

This function returns the binary exponent of x. More precisely, if x is finite and nonzero, the value is the logarithm base 2 of |x|, rounded down to an integer. If x is zero or infinite, the value is infinity; if x is a NaN, the value is a NaN.

(logb 10)
     ⇒ 3
(logb 10.0e20)
     ⇒ 69
(logb 0)
     ⇒ -1.0e+INF

3.3 Type Predicates for Numbers

The functions in this section test for numbers, or for a specific type of number. The functions integerp and floatp can take any type of Lisp object as argument (they would not be of much use otherwise), but the zerop predicate requires a number as its argument. See also integer-or-marker-p and number-or-marker-p, in Predicates on Markers.

Function: bignump object ¶

This predicate tests whether its argument is a large integer, and returns t if so, nil otherwise. Unlike small integers, large integers can be = or eql even if they are not eq.

Function: fixnump object ¶

This predicate tests whether its argument is a small integer, and returns t if so, nil otherwise. Small integers can be compared with eq.

Function: floatp object ¶

This predicate tests whether its argument is floating point and returns t if so, nil otherwise.

Function: integerp object ¶

This predicate tests whether its argument is an integer, and returns t if so, nil otherwise.

Function: numberp object ¶

This predicate tests whether its argument is a number (either integer or floating point), and returns t if so, nil otherwise.

Function: natnump object ¶

This predicate (whose name comes from the phrase “natural number”) tests to see whether its argument is a nonnegative integer, and returns t if so, nil otherwise. 0 is considered non-negative.

wholenump is a synonym for natnump.

Function: zerop number ¶

This predicate tests whether its argument is zero, and returns t if so, nil otherwise. The argument must be a number.

(zerop x) is equivalent to (= x 0).

3.4 Comparison of Numbers

To test numbers for numerical equality, you should normally use = instead of non-numeric comparison predicates like eq, eql and equal. Distinct floating-point and large integer objects can be numerically equal. If you use eq to compare them, you test whether they are the same object; if you use eql or equal, you test whether their values are indistinguishable. In contrast, = uses numeric comparison, and sometimes returns t when a non-numeric comparison would return nil and vice versa. See Floating-Point Basics.

In Emacs Lisp, if two fixnums are numerically equal, they are the same Lisp object. That is, eq is equivalent to = on fixnums. It is sometimes convenient to use eq for comparing an unknown value with a fixnum, because eq does not report an error if the unknown value is not a number—it accepts arguments of any type. By contrast, = signals an error if the arguments are not numbers or markers. However, it is better programming practice to use = if you can, even for comparing integers.

Sometimes it is useful to compare numbers with eql or equal, which treat two numbers as equal if they have the same data type (both integers, or both floating point) and the same value. By contrast, = can treat an integer and a floating-point number as equal. See Equality Predicates.

There is another wrinkle: because floating-point arithmetic is not exact, it is often a bad idea to check for equality of floating-point values. Usually it is better to test for approximate equality. Here’s a function to do this:

(defvar fuzz-factor 1.0e-6)
(defun approx-equal (x y)
  (or (= x y)
      (< (/ (abs (- x y))
            (max (abs x) (abs y)))
         fuzz-factor)))

Function: = number-or-marker &rest number-or-markers ¶

This function tests whether all its arguments are numerically equal, and returns t if so, nil otherwise.

Function: eql value1 value2 ¶

This function acts like eq except when both arguments are numbers. It compares numbers by type and numeric value, so that (eql 1.0 1) returns nil, but (eql 1.0 1.0) and (eql 1 1) both return t. This can be used to compare large integers as well as small ones. Floating-point values with the same sign, exponent and fraction are eql. This differs from numeric comparison: (eql 0.0 -0.0) returns nil and (eql 0.0e+NaN 0.0e+NaN) returns t, whereas = does the opposite.

Function: /= number-or-marker1 number-or-marker2 ¶

This function tests whether its arguments are numerically equal, and returns t if they are not, and nil if they are.

Function: < number-or-marker &rest number-or-markers ¶

This function tests whether each argument is strictly less than the following argument. It returns t if so, nil otherwise.

Function: <= number-or-marker &rest number-or-markers ¶

This function tests whether each argument is less than or equal to the following argument. It returns t if so, nil otherwise.

Function: > number-or-marker &rest number-or-markers ¶

This function tests whether each argument is strictly greater than the following argument. It returns t if so, nil otherwise.

Function: >= number-or-marker &rest number-or-markers ¶

This function tests whether each argument is greater than or equal to the following argument. It returns t if so, nil otherwise.

Function: max number-or-marker &rest numbers-or-markers ¶

This function returns the largest of its arguments.

(max 20)
     ⇒ 20
(max 1 2.5)
     ⇒ 2.5
(max 1 3 2.5)
     ⇒ 3

Function: min number-or-marker &rest numbers-or-markers ¶

This function returns the smallest of its arguments.

(min -4 1)
     ⇒ -4

Function: abs number ¶

This function returns the absolute value of number.

3.5 Numeric Conversions

To convert an integer to floating point, use the function float.

Function: float number ¶

This returns number converted to floating point. If number is already floating point, float returns it unchanged.

There are four functions to convert floating-point numbers to integers; they differ in how they round. All accept an argument number and an optional argument divisor. Both arguments may be integers or floating-point numbers. divisor may also be nil. If divisor is nil or omitted, these functions convert number to an integer, or return it unchanged if it already is an integer. If divisor is non-nil, they divide number by divisor and convert the result to an integer. If divisor is zero (whether integer or floating point), Emacs signals an arith-error error.

Function: truncate number &optional divisor ¶

This returns number, converted to an integer by rounding towards zero.

(truncate 1.2)
     ⇒ 1
(truncate 1.7)
     ⇒ 1
(truncate -1.2)
     ⇒ -1
(truncate -1.7)
     ⇒ -1

Function: floor number &optional divisor ¶

This returns number, converted to an integer by rounding downward (towards negative infinity).

If divisor is specified, this uses the kind of division operation that corresponds to mod, rounding downward.

(floor 1.2)
     ⇒ 1
(floor 1.7)
     ⇒ 1
(floor -1.2)
     ⇒ -2
(floor -1.7)
     ⇒ -2
(floor 5.99 3)
     ⇒ 1

Function: ceiling number &optional divisor ¶

This returns number, converted to an integer by rounding upward (towards positive infinity).

(ceiling 1.2)
     ⇒ 2
(ceiling 1.7)
     ⇒ 2
(ceiling -1.2)
     ⇒ -1
(ceiling -1.7)
     ⇒ -1

Function: round number &optional divisor ¶

This returns number, converted to an integer by rounding towards the nearest integer. Rounding a value equidistant between two integers returns the even integer.

(round 1.2)
     ⇒ 1
(round 1.7)
     ⇒ 2
(round -1.2)
     ⇒ -1
(round -1.7)
     ⇒ -2

3.6 Arithmetic Operations

Emacs Lisp provides the traditional four arithmetic operations (addition, subtraction, multiplication, and division), as well as remainder and modulus functions, and functions to add or subtract 1. Except for %, each of these functions accepts both integer and floating-point arguments, and returns a floating-point number if any argument is floating point.

Function: 1+ number-or-marker ¶

This function returns number-or-marker plus 1. For example,

(setq foo 4)
     ⇒ 4
(1+ foo)
     ⇒ 5

This function is not analogous to the C operator ++—it does not increment a variable. It just computes a sum. Thus, if we continue,

foo
     ⇒ 4

If you want to increment the variable, you must use setq, like this:

(setq foo (1+ foo))
     ⇒ 5

Function: 1- number-or-marker ¶

This function returns number-or-marker minus 1.

Function: + &rest numbers-or-markers ¶

This function adds its arguments together. When given no arguments, + returns 0.

(+)
     ⇒ 0
(+ 1)
     ⇒ 1
(+ 1 2 3 4)
     ⇒ 10

Function: - &optional number-or-marker &rest more-numbers-or-markers ¶

The - function serves two purposes: negation and subtraction. When - has a single argument, the value is the negative of the argument. When there are multiple arguments, - subtracts each of the more-numbers-or-markers from number-or-marker, cumulatively. If there are no arguments, the result is 0.

(- 10 1 2 3 4)
     ⇒ 0
(- 10)
     ⇒ -10
(-)
     ⇒ 0

Function: * &rest numbers-or-markers ¶

This function multiplies its arguments together, and returns the product. When given no arguments, * returns 1.

(*)
     ⇒ 1
(* 1)
     ⇒ 1
(* 1 2 3 4)
     ⇒ 24

Function: / number &rest divisors ¶

With one or more divisors, this function divides number by each divisor in divisors in turn, and returns the quotient. With no divisors, this function returns 1/number, i.e., the multiplicative inverse of number. Each argument may be a number or a marker.

If all the arguments are integers, the result is an integer, obtained by rounding the quotient towards zero after each division.

(/ 6 2)
     ⇒ 3

(/ 5 2)
     ⇒ 2

(/ 5.0 2)
     ⇒ 2.5

(/ 5 2.0)
     ⇒ 2.5

(/ 5.0 2.0)
     ⇒ 2.5

(/ 4.0)
     ⇒ 0.25

(/ 4)
     ⇒ 0

(/ 25 3 2)
     ⇒ 4

(/ -17 6)
     ⇒ -2

If you divide an integer by the integer 0, Emacs signals an arith-error error (see Errors). On systems using IEEE-754 floating-point, floating-point division of a nonzero number by zero yields either positive or negative infinity (see Floating-Point Basics); otherwise, an arith-error is signaled as usual.

Function: % dividend divisor ¶

This function returns the integer remainder after division of dividend by divisor. The arguments must be integers or markers.

For any two integers dividend and divisor,

(+ (% dividend divisor)
   (* (/ dividend divisor) divisor))

always equals dividend if divisor is nonzero.

(% 9 4)
     ⇒ 1
(% -9 4)
     ⇒ -1
(% 9 -4)
     ⇒ 1
(% -9 -4)
     ⇒ -1

Function: mod dividend divisor ¶

This function returns the value of dividend modulo divisor; in other words, the remainder after division of dividend by divisor, but with the same sign as divisor. The arguments must be numbers or markers.

Unlike %, mod permits floating-point arguments; it rounds the quotient downward (towards minus infinity) to an integer, and uses that quotient to compute the remainder.

If divisor is zero, mod signals an arith-error error if both arguments are integers, and returns a NaN otherwise.

(mod 9 4)
     ⇒ 1

(mod -9 4)
     ⇒ 3

(mod 9 -4)
     ⇒ -3

(mod -9 -4)
     ⇒ -1

(mod 5.5 2.5)
     ⇒ .5

For any two numbers dividend and divisor,

(+ (mod dividend divisor)
   (* (floor dividend divisor) divisor))

always equals dividend, subject to rounding error if either argument is floating point and to an arith-error if dividend is an integer and divisor is 0. For floor, see Numeric Conversions.

3.7 Rounding Operations

The functions ffloor, fceiling, fround, and ftruncate take a floating-point argument and return a floating-point result whose value is a nearby integer. ffloor returns the nearest integer below; fceiling, the nearest integer above; ftruncate, the nearest integer in the direction towards zero; fround, the nearest integer.

Function: ffloor float ¶

This function rounds float to the next lower integral value, and returns that value as a floating-point number.

Function: fceiling float ¶

This function rounds float to the next higher integral value, and returns that value as a floating-point number.

Function: ftruncate float ¶

This function rounds float towards zero to an integral value, and returns that value as a floating-point number.

Function: fround float ¶

This function rounds float to the nearest integral value, and returns that value as a floating-point number. Rounding a value equidistant between two integers returns the even integer.

3.8 Bitwise Operations on Integers

In a computer, an integer is represented as a binary number, a sequence of bits (digits which are either zero or one). Conceptually the bit sequence is infinite on the left, with the most-significant bits being all zeros or all ones. A bitwise operation acts on the individual bits of such a sequence. For example, shifting moves the whole sequence left or right one or more places, reproducing the same pattern moved over.

The bitwise operations in Emacs Lisp apply only to integers.

Function: ash integer1 count ¶

ash (arithmetic shift) shifts the bits in integer1 to the left count places, or to the right if count is negative. Left shifts introduce zero bits on the right; right shifts discard the rightmost bits. Considered as an integer operation, ash multiplies integer1 by 2**count, and then converts the result to an integer by rounding downward, toward minus infinity.

Here are examples of ash, shifting a pattern of bits one place to the left and to the right. These examples show only the low-order bits of the binary pattern; leading bits all agree with the highest-order bit shown. As you can see, shifting left by one is equivalent to multiplying by two, whereas shifting right by one is equivalent to dividing by two and then rounding toward minus infinity.

(ash 7 1) ⇒ 14
;; Decimal 7 becomes decimal 14.
…000111
     ⇒
…001110

(ash 7 -1) ⇒ 3
…000111
     ⇒
…000011

(ash -7 1) ⇒ -14
…111001
     ⇒
…110010

(ash -7 -1) ⇒ -4
…111001
     ⇒
…111100

Here are examples of shifting left or right by two bits:

                  ;         binary values
(ash 5 2)         ;   5  =  …000101
     ⇒ 20         ;      =  …010100
(ash -5 2)        ;  -5  =  …111011
     ⇒ -20        ;      =  …101100

(ash 5 -2)
     ⇒ 1          ;      =  …000001

(ash -5 -2)
     ⇒ -2         ;      =  …111110

Function: lsh integer1 count ¶

lsh, which is an abbreviation for logical shift, shifts the bits in integer1 to the left count places, or to the right if count is negative, bringing zeros into the vacated bits. If count is negative, then integer1 must be either a fixnum or a positive bignum, and lsh treats a negative fixnum as if it were unsigned by subtracting twice most-negative-fixnum before shifting, producing a nonnegative result. This quirky behavior dates back to when Emacs supported only fixnums; nowadays ash is a better choice.

As lsh behaves like ash except when integer1 and count1 are both negative, the following examples focus on these exceptional cases. These examples assume 30-bit fixnums.

                 ;      binary values
(ash -7 -1)      ; -7 = …111111111111111111111111111001
     ⇒ -4        ;    = …111111111111111111111111111100
(lsh -7 -1)
     ⇒ 536870908 ;    = …011111111111111111111111111100

(ash -5 -2)      ; -5 = …111111111111111111111111111011
     ⇒ -2        ;    = …111111111111111111111111111110
(lsh -5 -2)
     ⇒ 268435454 ;    = …001111111111111111111111111110

Function: logand &rest ints-or-markers ¶

This function returns the bitwise AND of the arguments: the nth bit is 1 in the result if, and only if, the nth bit is 1 in all the arguments.

For example, using 4-bit binary numbers, the bitwise AND of 13 and 12 is 12: 1101 combined with 1100 produces 1100. In both the binary numbers, the leftmost two bits are both 1 so the leftmost two bits of the returned value are both 1. However, for the rightmost two bits, each is 0 in at least one of the arguments, so the rightmost two bits of the returned value are both 0.

Therefore,

(logand 13 12)
     ⇒ 12

If logand is not passed any argument, it returns a value of -1. This number is an identity element for logand because its binary representation consists entirely of ones. If logand is passed just one argument, it returns that argument.

                   ;        binary values

(logand 14 13)     ; 14  =  …001110
                   ; 13  =  …001101
     ⇒ 12         ; 12  =  …001100

(logand 14 13 4)   ; 14  =  …001110
                   ; 13  =  …001101
                   ;  4  =  …000100
     ⇒ 4          ;  4  =  …000100

(logand)
     ⇒ -1         ; -1  =  …111111

Function: logior &rest ints-or-markers ¶

This function returns the bitwise inclusive OR of its arguments: the nth bit is 1 in the result if, and only if, the nth bit is 1 in at least one of the arguments. If there are no arguments, the result is 0, which is an identity element for this operation. If logior is passed just one argument, it returns that argument.

                   ;        binary values

(logior 12 5)      ; 12  =  …001100
                   ;  5  =  …000101
     ⇒ 13         ; 13  =  …001101

(logior 12 5 7)    ; 12  =  …001100
                   ;  5  =  …000101
                   ;  7  =  …000111
     ⇒ 15         ; 15  =  …001111

Function: logxor &rest ints-or-markers ¶

This function returns the bitwise exclusive OR of its arguments: the nth bit is 1 in the result if, and only if, the nth bit is 1 in an odd number of the arguments. If there are no arguments, the result is 0, which is an identity element for this operation. If logxor is passed just one argument, it returns that argument.

                   ;        binary values

(logxor 12 5)      ; 12  =  …001100
                   ;  5  =  …000101
     ⇒ 9          ;  9  =  …001001

(logxor 12 5 7)    ; 12  =  …001100
                   ;  5  =  …000101
                   ;  7  =  …000111
     ⇒ 14         ; 14  =  …001110

Function: lognot integer ¶

This function returns the bitwise complement of its argument: the nth bit is one in the result if, and only if, the nth bit is zero in integer, and vice-versa. The result equals -1 - integer.

(lognot 5)
     ⇒ -6
;;  5  =  …000101
;; becomes
;; -6  =  …111010

Function: logcount integer ¶

This function returns the Hamming weight of integer: the number of ones in the binary representation of integer. If integer is negative, it returns the number of zero bits in its two’s complement binary representation. The result is always nonnegative.

(logcount 43)     ;  43 = …000101011
     ⇒ 4
(logcount -43)    ; -43 = …111010101
     ⇒ 3

3.9 Standard Mathematical Functions

These mathematical functions allow integers as well as floating-point numbers as arguments.

Function: sin arg ¶

Function: cos arg ¶

Function: tan arg ¶

These are the basic trigonometric functions, with argument arg measured in radians.

Function: asin arg ¶

The value of (asin arg) is a number between -pi/2 and pi/2 (inclusive) whose sine is arg. If arg is out of range (outside [-1, 1]), asin returns a NaN.

Function: acos arg ¶

The value of (acos arg) is a number between 0 and pi (inclusive) whose cosine is arg. If arg is out of range (outside [-1, 1]), acos returns a NaN.

Function: atan y &optional x ¶

The value of (atan y) is a number between -pi/2 and pi/2 (exclusive) whose tangent is y. If the optional second argument x is given, the value of (atan y x) is the angle in radians between the vector [x, y] and the X axis.

Function: exp arg ¶

This is the exponential function; it returns e to the power arg.

Function: log arg &optional base ¶

This function returns the logarithm of arg, with base base. If you don’t specify base, the natural base e is used. If arg or base is negative, log returns a NaN.

Function: expt x y ¶

This function returns x raised to power y. If both arguments are integers and y is nonnegative, the result is an integer; in this case, overflow signals an error, so watch out. If x is a finite negative number and y is a finite non-integer, expt returns a NaN.

Function: sqrt arg ¶

This returns the square root of arg. If arg is finite and less than zero, sqrt returns a NaN.

In addition, Emacs defines the following common mathematical constants:

Variable: float-e ¶

The mathematical constant e (2.71828…).

Variable: float-pi ¶

The mathematical constant pi (3.14159…).

3.10 Random Numbers

A deterministic computer program cannot generate true random numbers. For most purposes, pseudo-random numbers suffice. A series of pseudo-random numbers is generated in a deterministic fashion. The numbers are not truly random, but they have certain properties that mimic a random series. For example, all possible values occur equally often in a pseudo-random series.

Pseudo-random numbers are generated from a seed value. Starting from any given seed, the random function always generates the same sequence of numbers. By default, Emacs initializes the random seed at startup, in such a way that the sequence of values of random (with overwhelming likelihood) differs in each Emacs run. The random seed is typically initialized from system entropy; however, on obsolescent platforms lacking entropy pools, the seed is taken from less-random volatile data such as the current time.

Sometimes you want the random number sequence to be repeatable. For example, when debugging a program whose behavior depends on the random number sequence, it is helpful to get the same behavior in each program run. To make the sequence repeat, execute (random ""). This sets the seed to a constant value for your particular Emacs executable (though it may differ for other Emacs builds). You can use other strings to choose various seed values.

Function: random &optional limit ¶

This function returns a pseudo-random integer. Repeated calls return a series of pseudo-random integers.

If limit is a positive integer, the value is chosen to be nonnegative and less than limit. Otherwise, the value might be any fixnum, i.e., any integer from most-negative-fixnum through most-positive-fixnum (see Integer Basics).

If limit is a string, it means to choose a new seed based on the string’s contents. This causes later calls to random to return a reproducible sequence of results.

If limit is t, it means to choose a new seed as if Emacs were restarting. This causes later calls to random to return an unpredictable sequence of results.

If you need a random nonce for cryptographic purposes, using random is typically not the best approach, for several reasons:

• Although you can use (random t) to consult system entropy, doing so can adversely affect other parts of your program that benefit from reproducible results.
• The system-dependent pseudo-random number generator (PRNG) used by random is not necessarily suitable for cryptography.
• A call to (random t) does not give direct access to system entropy; the entropy is passed through the system-dependent PRNG, thus possibly biasing the results.
• On typical platforms the random seed contains only 32 bits, which is typically narrower than an Emacs fixnum, and is not nearly enough for cryptographic purposes.
• A (random t) call leaves information about the nonce scattered about Emacs’s internal state, increasing the size of the internal attack surface.
• On obsolescent platforms lacking entropy pools, (random t) is seeded from a cryptographically weak source.

4.1 String and Character Basics

A character is a Lisp object which represents a single character of text. In Emacs Lisp, characters are simply integers; whether an integer is a character or not is determined only by how it is used. See Character Codes, for details about character representation in Emacs.

A string is a fixed sequence of characters. It is a type of sequence called an array, meaning that its length is fixed and cannot be altered once it is created (see Sequences, Arrays, and Vectors). Unlike in C, Emacs Lisp strings are not terminated by a distinguished character code.

Since strings are arrays, and therefore sequences as well, you can operate on them with the general array and sequence functions documented in Sequences, Arrays, and Vectors. For example, you can access individual characters in a string using the function aref (see Functions that Operate on Arrays).

There are two text representations for non-ASCII characters in Emacs strings (and in buffers): unibyte and multibyte. For most Lisp programming, you don’t need to be concerned with these two representations. See Text Representations, for details.

Sometimes key sequences are represented as unibyte strings. When a unibyte string is a key sequence, string elements in the range 128 to 255 represent meta characters (which are large integers) rather than character codes in the range 128 to 255. Strings cannot hold characters that have the hyper, super or alt modifiers; they can hold ASCII control characters, but no other control characters. They do not distinguish case in ASCII control characters. If you want to store such characters in a sequence, such as a key sequence, you must use a vector instead of a string. See Character Type, for more information about keyboard input characters.

Strings are useful for holding regular expressions. You can also match regular expressions against strings with string-match (see Regular Expression Searching). The functions match-string (see Simple Match Data Access) and replace-match (see Replacing the Text that Matched) are useful for decomposing and modifying strings after matching regular expressions against them.

Like a buffer, a string can contain text properties for the characters in it, as well as the characters themselves. See Text Properties. All the Lisp primitives that copy text from strings to buffers or other strings also copy the properties of the characters being copied.

See Text, for information about functions that display strings or copy them into buffers. See Character Type, and String Type, for information about the syntax of characters and strings. See Non-ASCII Characters, for functions to convert between text representations and to encode and decode character codes. Also, note that length should not be used for computing the width of a string on display; use string-width (see Size of Displayed Text) instead.

4.2 Predicates for Strings

For more information about general sequence and array predicates, see Sequences, Arrays, and Vectors, and Arrays.

Function: stringp object ¶

This function returns t if object is a string, nil otherwise.

Function: string-or-null-p object ¶

This function returns t if object is a string or nil. It returns nil otherwise.

Function: char-or-string-p object ¶

This function returns t if object is a string or a character (i.e., an integer), nil otherwise.

4.3 Creating Strings

The following functions create strings, either from scratch, or by putting strings together, or by taking them apart. (For functions that create strings based on the modified contents of other strings, like string-replace and replace-regexp-in-string, see Search and Replace.)

Function: make-string count character &optional multibyte ¶

This function returns a string made up of count repetitions of character. If count is negative, an error is signaled.

(make-string 5 ?x)
     ⇒ "xxxxx"
(make-string 0 ?x)
     ⇒ ""

Normally, if character is an ASCII character, the result is a unibyte string. But if the optional argument multibyte is non-nil, the function will produce a multibyte string instead. This is useful when you later need to concatenate the result with non-ASCII strings or replace some of its characters with non-ASCII characters.

Other functions to compare with this one include make-vector (see Vectors) and make-list (see Building Cons Cells and Lists).

Function: string &rest characters ¶

This returns a string containing the characters characters.

(string ?a ?b ?c)
     ⇒ "abc"

Function: substring string &optional start end ¶

This function returns a new string which consists of those characters from string in the range from (and including) the character at the index start up to (but excluding) the character at the index end. The first character is at index zero. With one argument, this function just copies string.

(substring "abcdefg" 0 3)
     ⇒ "abc"

In the above example, the index for ‘a’ is 0, the index for ‘b’ is 1, and the index for ‘c’ is 2. The index 3—which is the fourth character in the string—marks the character position up to which the substring is copied. Thus, ‘abc’ is copied from the string "abcdefg".

A negative number counts from the end of the string, so that -1 signifies the index of the last character of the string. For example:

(substring "abcdefg" -3 -1)
     ⇒ "ef"

In this example, the index for ‘e’ is -3, the index for ‘f’ is -2, and the index for ‘g’ is -1. Therefore, ‘e’ and ‘f’ are included, and ‘g’ is excluded.

When nil is used for end, it stands for the length of the string. Thus,

(substring "abcdefg" -3 nil)
     ⇒ "efg"

Omitting the argument end is equivalent to specifying nil. It follows that (substring string 0) returns a copy of all of string.

(substring "abcdefg" 0)
     ⇒ "abcdefg"

But we recommend copy-sequence for this purpose (see Sequences).

If the characters copied from string have text properties, the properties are copied into the new string also. See Text Properties.

substring also accepts a vector for the first argument. For example:

(substring [a b (c) "d"] 1 3)
     ⇒ [b (c)]

A wrong-type-argument error is signaled if start is not an integer or if end is neither an integer nor nil. An args-out-of-range error is signaled if start indicates a character following end, or if either integer is out of range for string.

Contrast this function with buffer-substring (see Examining Buffer Contents), which returns a string containing a portion of the text in the current buffer. The beginning of a string is at index 0, but the beginning of a buffer is at index 1.

Function: substring-no-properties string &optional start end ¶

This works like substring but discards all text properties from the value. Also, start may be omitted or nil, which is equivalent to 0. Thus, (substring-no-properties string) returns a copy of string, with all text properties removed.

Function: concat &rest sequences ¶

This function returns a string consisting of the characters in the arguments passed to it (along with their text properties, if any). The arguments may be strings, lists of numbers, or vectors of numbers; they are not themselves changed. If concat receives no arguments, it returns an empty string.

(concat "abc" "-def")
     ⇒ "abc-def"
(concat "abc" (list 120 121) [122])
     ⇒ "abcxyz"
;; nil is an empty sequence.
(concat "abc" nil "-def")
     ⇒ "abc-def"
(concat "The " "quick brown " "fox.")
     ⇒ "The quick brown fox."
(concat)
     ⇒ ""

This function does not always allocate a new string. Callers are advised not rely on the result being a new string nor on it being eq to an existing string.

In particular, mutating the returned value may inadvertently change another string, alter a constant string in the program, or even raise an error. To obtain a string that you can safely mutate, use copy-sequence on the result.

For information about other concatenation functions, see the description of mapconcat in Mapping Functions, vconcat in Functions for Vectors, and append in Building Cons Cells and Lists. For concatenating individual command-line arguments into a string to be used as a shell command, see combine-and-quote-strings.

Function: split-string string &optional separators omit-nulls trim ¶

This function splits string into substrings based on the regular expression separators (see Regular Expressions). Each match for separators defines a splitting point; the substrings between splitting points are made into a list, which is returned.

If separators is nil (or omitted), the default is the value of split-string-default-separators and the function behaves as if omit-nulls were t.

If omit-nulls is nil (or omitted), the result contains null strings whenever there are two consecutive matches for separators, or a match is adjacent to the beginning or end of string. If omit-nulls is t, these null strings are omitted from the result.

If the optional argument trim is non-nil, it should be a regular expression to match text to trim from the beginning and end of each substring. If trimming makes the substring empty, it is treated as null.

If you need to split a string into a list of individual command-line arguments suitable for call-process or start-process, see split-string-and-unquote.

Examples:

(split-string "  two words ")
     ⇒ ("two" "words")

The result is not ("" "two" "words" ""), which would rarely be useful. If you need such a result, use an explicit value for separators:

(split-string "  two words "
              split-string-default-separators)
     ⇒ ("" "two" "words" "")

(split-string "Soup is good food" "o")
     ⇒ ("S" "up is g" "" "d f" "" "d")
(split-string "Soup is good food" "o" t)
     ⇒ ("S" "up is g" "d f" "d")
(split-string "Soup is good food" "o+")
     ⇒ ("S" "up is g" "d f" "d")

Empty matches do count, except that split-string will not look for a final empty match when it already reached the end of the string using a non-empty match or when string is empty:

(split-string "aooob" "o*")
     ⇒ ("" "a" "" "b" "")
(split-string "ooaboo" "o*")
     ⇒ ("" "" "a" "b" "")
(split-string "" "")
     ⇒ ("")

However, when separators can match the empty string, omit-nulls is usually t, so that the subtleties in the three previous examples are rarely relevant:

(split-string "Soup is good food" "o*" t)
     ⇒ ("S" "u" "p" " " "i" "s" " " "g" "d" " " "f" "d")
(split-string "Nice doggy!" "" t)
     ⇒ ("N" "i" "c" "e" " " "d" "o" "g" "g" "y" "!")
(split-string "" "" t)
     ⇒ nil

Somewhat odd, but predictable, behavior can occur for certain “non-greedy” values of separators that can prefer empty matches over non-empty matches. Again, such values rarely occur in practice:

(split-string "ooo" "o*" t)
     ⇒ nil
(split-string "ooo" "\\|o+" t)
     ⇒ ("o" "o" "o")

Variable: split-string-default-separators ¶

The default value of separators for split-string. Its usual value is "[ \f\t\n\r\v]+".

Function: string-clean-whitespace string ¶

Clean up the whitespace in string by collapsing stretches of whitespace to a single space character, as well as removing all whitespace from the start and the end of string.

Function: string-trim-left string &optional regexp ¶

Remove the leading text that matches regexp from string. regexp defaults to ‘[ \t\n\r]+’.

Function: string-trim-right string &optional regexp ¶

Remove the trailing text that matches regexp from string. regexp defaults to ‘[ \t\n\r]+’.

Function: string-trim string &optional trim-left trim-right ¶

Remove the leading text that matches trim-left and trailing text that matches trim-right from string. Both regexps default to ‘[ \t\n\r]+’.

Function: string-fill string length ¶

Attempt to Word-wrap string so that no lines are longer than length. Filling is done on whitespace boundaries only. If there are individual words that are longer than length, these will not be shortened.

Function: string-limit string length &optional end coding-system ¶

If string is shorter than length characters, string is returned as is. Otherwise, return a substring of string consisting of the first length characters. If the optional end parameter is given, return a string of the length last characters instead.

If coding-system is non-nil, string will be encoded before limiting, and the result will be a unibyte string that’s shorter than length bytes. If string contains characters that are encoded into several bytes (for instance, when using utf-8), the resulting unibyte string is never truncated in the middle of a character representation.

This function measures the string length in characters or bytes, and thus is generally inappropriate if you need to shorten strings for display purposes; use truncate-string-to-width or window-text-pixel-size or string-glyph-split instead (see Size of Displayed Text).

Function: string-lines string &optional omit-nulls keep-newlines ¶

Split string into a list of strings on newline boundaries. If the optional argument omit-nulls is non-nil, remove empty lines from the results. If the optional argument keep-newlines is non-nil, don’t remove the trailing newlines from the result strings.

Function: string-pad string length &optional padding start ¶

Pad string to be of the given length using padding as the padding character. padding defaults to the space character. If string is longer than length, no padding is done. If start is nil or omitted, the padding is appended to the characters of string, and if it’s non-nil, the padding is prepended to string’s characters.

Function: string-chop-newline string ¶

Remove the final newline, if any, from string.

4.4 Modifying Strings

You can alter the contents of a mutable string via operations described in this section. See Mutability.

The most basic way to alter the contents of an existing string is with aset (see Functions that Operate on Arrays). (aset string idx char) stores char into string at character index idx. It will automatically convert a pure-ASCII string to a multibyte string (see Text Representations) if needed, but we recommend to always make sure string is multibyte (e.g., by using string-to-multibyte, see Converting Text Representations), if char is a non-ASCII character, not a raw byte.

A more powerful function is store-substring:

Function: store-substring string idx obj ¶

This function alters part of the contents of the specified string, by storing obj starting at character index idx. The argument obj may be either a character (in which case the function behaves exactly as aset) or a (smaller) string. If obj is a multibyte string, we recommend to make sure string is also multibyte, even if it’s pure-ASCII.

Since it is impossible to change the number of characters in an existing string, it is an error if obj consists of more characters than would fit in string starting at character index idx.

To clear out a string that contained a password, use clear-string:

Function: clear-string string ¶

This makes string a unibyte string and clears its contents to zeros. It may also change string’s length.

4.5 Comparison of Characters and Strings

Function: char-equal character1 character2 ¶

This function returns t if the arguments represent the same character, nil otherwise. This function ignores differences in case if case-fold-search is non-nil.

(char-equal ?x ?x)
     ⇒ t
(let ((case-fold-search nil))
  (char-equal ?x ?X))
     ⇒ nil

Function: string= string1 string2 ¶

This function returns t if the characters of the two strings match exactly. Symbols are also allowed as arguments, in which case the symbol names are used. Case is always significant, regardless of case-fold-search.

This function is equivalent to equal for comparing two strings (see Equality Predicates). In particular, the text properties of the two strings are ignored; use equal-including-properties if you need to distinguish between strings that differ only in their text properties. However, unlike equal, if either argument is not a string or symbol, string= signals an error.

(string= "abc" "abc")
     ⇒ t
(string= "abc" "ABC")
     ⇒ nil
(string= "ab" "ABC")
     ⇒ nil

A unibyte and a multibyte string are equal in the sense of string= if and only if they contain the same sequence of character codes all being in the range 0–127 (ASCII). See Text Representations.

Function: string-equal string1 string2 ¶

string-equal is another name for string=.

Function: string-equal-ignore-case string1 string2 ¶

string-equal-ignore-case compares strings ignoring case differences, like char-equal when case-fold-search is t.

Function: string-collate-equalp string1 string2 &optional locale ignore-case ¶

This function returns t if string1 and string2 are equal with respect to the collation rules of the specified locale, which defaults to your current system locale. A collation rule is not only determined by the lexicographic order of the characters contained in string1 and string2, but also by further rules about relations between these characters. Usually, it is defined by the locale environment with which Emacs is running and by the Standard C library against which Emacs was linked³.

For example, characters with different code points but the same meaning, like different grave accent Unicode characters, might, in some locales, be considered as equal:

(string-collate-equalp (string ?\uFF40) (string ?\u1FEF))
     ⇒ t

The optional argument locale, a string, overrides the setting of your current locale identifier for collation. The value is system dependent; a locale "en_US.UTF-8" is applicable on POSIX systems, while it would be, e.g., "enu_USA.1252" on MS-Windows systems.

If ignore-case is non-nil, characters are compared case-insensitively, by converting them to lower-case. However, if the underlying system library doesn’t provide locale-specific collation rules, this function falls back to string-equal, in which case the ignore-case argument is ignored, and the comparison will always be case-sensitive.

To emulate Unicode-compliant collation on MS-Windows systems, bind w32-collate-ignore-punctuation to a non-nil value, since the codeset part of the locale cannot be "UTF-8" on MS-Windows.

If your system does not support a locale environment, this function behaves like string-equal.

Do not use this function to compare file names for equality, as filesystems generally don’t honor linguistic equivalence of strings that collation implements.

Function: string< string1 string2 ¶

This function compares two strings a character at a time. It scans both the strings at the same time to find the first pair of corresponding characters that do not match. If the lesser character of these two is the character from string1, then string1 is less, and this function returns t. If the lesser character is the one from string2, then string1 is greater, and this function returns nil. If the two strings match entirely, the value is nil.

Pairs of characters are compared according to their character codes. Keep in mind that lower case letters have higher numeric values in the ASCII character set than their upper case counterparts; digits and many punctuation characters have a lower numeric value than upper case letters. An ASCII character is less than any non-ASCII character; a unibyte non-ASCII character is always less than any multibyte non-ASCII character (see Text Representations).

(string< "abc" "abd")
     ⇒ t
(string< "abd" "abc")
     ⇒ nil
(string< "123" "abc")
     ⇒ t

When the strings have different lengths, and they match up to the length of string1, then the result is t. If they match up to the length of string2, the result is nil. A string of no characters is less than any other string.

(string< "" "abc")
     ⇒ t
(string< "ab" "abc")
     ⇒ t
(string< "abc" "")
     ⇒ nil
(string< "abc" "ab")
     ⇒ nil
(string< "" "")
     ⇒ nil

Symbols are also allowed as arguments, in which case their print names are compared.

Function: string-lessp string1 string2 ¶

string-lessp is another name for string<.

Function: string-greaterp string1 string2 ¶

This function returns the result of comparing string1 and string2 in the opposite order, i.e., it is equivalent to calling (string-lessp string2 string1).

Function: string-collate-lessp string1 string2 &optional locale ignore-case ¶

This function returns t if string1 is less than string2 in collation order of the specified locale, which defaults to your current system locale. A collation order is not only determined by the lexicographic order of the characters contained in string1 and string2, but also by further rules about relations between these characters. Usually, it is defined by the locale environment with which Emacs is running, and by the Standard C library against which Emacs was linked.

For example, punctuation and whitespace characters might be ignored for sorting (see Sequences):

(sort (list "11" "12" "1 1" "1 2" "1.1" "1.2") 'string-collate-lessp)
     ⇒ ("11" "1 1" "1.1" "12" "1 2" "1.2")

This behavior is system-dependent; e.g., punctuation and whitespace are never ignored on Cygwin, regardless of locale.

The optional argument locale, a string, overrides the setting of your current locale identifier for collation. The value is system dependent; a locale "en_US.UTF-8" is applicable on POSIX systems, while it would be, e.g., "enu_USA.1252" on MS-Windows systems. The locale value of "POSIX" or "C" lets string-collate-lessp behave like string-lessp:

(sort (list "11" "12" "1 1" "1 2" "1.1" "1.2")
      (lambda (s1 s2) (string-collate-lessp s1 s2 "POSIX")))
     ⇒ ("1 1" "1 2" "1.1" "1.2" "11" "12")

If ignore-case is non-nil, characters are compared case-insensitively, by converting them to lower-case. However, if the underlying system library doesn’t provide locale-specific collation rules, this function falls back to string-lessp, in which case the ignore-case argument is ignored, and the comparison will always be case-sensitive.

To emulate Unicode-compliant collation on MS-Windows systems, bind w32-collate-ignore-punctuation to a non-nil value, since the codeset part of the locale cannot be "UTF-8" on MS-Windows.

If your system does not support a locale environment, this function behaves like string-lessp.

Function: string-version-lessp string1 string2 ¶

This function compares strings lexicographically, except it treats sequences of numerical characters as if they comprised a base-ten number, and then compares the numbers. So ‘foo2.png’ is “smaller” than ‘foo12.png’ according to this predicate, even if ‘12’ is lexicographically “smaller” than ‘2’.

Function: string-prefix-p string1 string2 &optional ignore-case ¶

This function returns non-nil if string1 is a prefix of string2; i.e., if string2 starts with string1. If the optional argument ignore-case is non-nil, the comparison ignores case differences.

Function: string-suffix-p suffix string &optional ignore-case ¶

This function returns non-nil if suffix is a suffix of string; i.e., if string ends with suffix. If the optional argument ignore-case is non-nil, the comparison ignores case differences.

Function: string-search needle haystack &optional start-pos ¶

Return the position of the first instance of needle in haystack, both of which are strings. If start-pos is non-nil, start searching from that position in haystack. Return nil if no match was found. This function only considers the characters in the strings when doing the comparison; text properties are ignored. Matching is always case-sensitive.

Function: compare-strings string1 start1 end1 string2 start2 end2 &optional ignore-case ¶

This function compares a specified part of string1 with a specified part of string2. The specified part of string1 runs from index start1 (inclusive) up to index end1 (exclusive); nil for start1 means the start of the string, while nil for end1 means the length of the string. Likewise, the specified part of string2 runs from index start2 up to index end2.

The strings are compared by the numeric values of their characters. For instance, str1 is considered less than str2 if its first differing character has a smaller numeric value. If ignore-case is non-nil, characters are converted to upper-case, using the current buffer’s case-table (see The Case Table), before comparing them. Unibyte strings are converted to multibyte for comparison (see Text Representations), so that a unibyte string and its conversion to multibyte are always regarded as equal.

If the specified portions of the two strings match, the value is t. Otherwise, the value is an integer which indicates how many leading characters agree, and which string is less. Its absolute value is one plus the number of characters that agree at the beginning of the two strings. The sign is negative if string1 (or its specified portion) is less.

Function: string-distance string1 string2 &optional bytecompare ¶

This function returns the Levenshtein distance between the source string string1 and the target string string2. The Levenshtein distance is the number of single-character changes—deletions, insertions, or replacements—required to transform the source string into the target string; it is one possible definition of the edit distance between strings.

Letter-case of the strings is significant for the computed distance, but their text properties are ignored. If the optional argument bytecompare is non-nil, the function calculates the distance in terms of bytes instead of characters. The byte-wise comparison uses the internal Emacs representation of characters, so it will produce inaccurate results for multibyte strings that include raw bytes (see Text Representations); make the strings unibyte by encoding them (see Explicit Encoding and Decoding) if you need accurate results with raw bytes.

Function: assoc-string key alist &optional case-fold ¶

This function works like assoc, except that key must be a string or symbol, and comparison is done using compare-strings. Symbols are converted to strings before testing. If case-fold is non-nil, key and the elements of alist are converted to upper-case before comparison. Unlike assoc, this function can also match elements of the alist that are strings or symbols rather than conses. In particular, alist can be a list of strings or symbols rather than an actual alist. See Association Lists.

See also the function compare-buffer-substrings in Comparing Text, for a way to compare text in buffers. The function string-match, which matches a regular expression against a string, can be used for a kind of string comparison; see Regular Expression Searching.

4.6 Conversion of Characters and Strings

This section describes functions for converting between characters, strings and integers. format (see Formatting Strings) and prin1-to-string (see Output Functions) can also convert Lisp objects into strings. read-from-string (see Input Functions) can convert a string representation of a Lisp object into an object. The functions string-to-multibyte and string-to-unibyte convert the text representation of a string (see Converting Text Representations).

See Documentation, for functions that produce textual descriptions of text characters and general input events (single-key-description and text-char-description). These are used primarily for making help messages.

Function: number-to-string number ¶

This function returns a string consisting of the printed base-ten representation of number. The returned value starts with a minus sign if the argument is negative.

(number-to-string 256)
     ⇒ "256"

(number-to-string -23)
     ⇒ "-23"

(number-to-string -23.5)
     ⇒ "-23.5"

int-to-string is a semi-obsolete alias for this function.

See also the function format in Formatting Strings.

Function: string-to-number string &optional base ¶

This function returns the numeric value of the characters in string. If base is non-nil, it must be an integer between 2 and 16 (inclusive), and integers are converted in that base. If base is nil, then base ten is used. Floating-point conversion only works in base ten; we have not implemented other radices for floating-point numbers, because that would be much more work and does not seem useful.

The parsing skips spaces and tabs at the beginning of string, then reads as much of string as it can interpret as a number in the given base. (On some systems it ignores other whitespace at the beginning, not just spaces and tabs.) If string cannot be interpreted as a number, this function returns 0.

(string-to-number "256")
     ⇒ 256
(string-to-number "25 is a perfect square.")
     ⇒ 25
(string-to-number "X256")
     ⇒ 0
(string-to-number "-4.5")
     ⇒ -4.5
(string-to-number "1e5")
     ⇒ 100000.0

string-to-int is an obsolete alias for this function.

Function: char-to-string character ¶

This function returns a new string containing one character, character. This function is semi-obsolete because the function string is more general. See Creating Strings.

Function: string-to-char string ¶

This function returns the first character in string. This is mostly identical to (aref string 0), except that it returns 0 if the string is empty. (The value is also 0 when the first character of string is the null character, ASCII code 0.) This function may be eliminated in the future if it does not seem useful enough to retain.

Here are some other functions that can convert to or from a string:

concat

This function converts a vector or a list into a string. See Creating Strings.

vconcat

This function converts a string into a vector. See Functions for Vectors.

append

This function converts a string into a list. See Building Cons Cells and Lists.

byte-to-string

This function converts a byte of character data into a unibyte string. See Converting Text Representations.

4.7 Formatting Strings

Formatting means constructing a string by substituting computed values at various places in a constant string. This constant string controls how the other values are printed, as well as where they appear; it is called a format string.

Formatting is often useful for computing messages to be displayed. In fact, the functions message and error provide the same formatting feature described here; they differ from format-message only in how they use the result of formatting.

Function: format string &rest objects ¶

This function returns a string equal to string, replacing any format specifications with encodings of the corresponding objects. The arguments objects are the computed values to be formatted.

The characters in string, other than the format specifications, are copied directly into the output, including their text properties, if any. Any text properties of the format specifications are copied to the produced string representations of the argument objects.

The output string need not be newly-allocated. For example, if x is the string "foo", the expressions (eq x (format x)) and (eq x (format "%s" x)) might both yield t.

Function: format-message string &rest objects ¶

This function acts like format, except it also converts any grave accents (`) and apostrophes (') in string as per the value of text-quoting-style.

Typically grave accent and apostrophe in the format translate to matching curved quotes, e.g., "Missing `%s'" might result in "Missing ‘foo’". See Text Quoting Style, for how to influence or inhibit this translation.

A format specification is a sequence of characters beginning with a ‘%’. Thus, if there is a ‘%d’ in string, the format function replaces it with the printed representation of one of the values to be formatted (one of the arguments objects). For example:

(format "The value of fill-column is %d." fill-column)
     ⇒ "The value of fill-column is 72."

Since format interprets ‘%’ characters as format specifications, you should never pass an arbitrary string as the first argument. This is particularly true when the string is generated by some Lisp code. Unless the string is known to never include any ‘%’ characters, pass "%s", described below, as the first argument, and the string as the second, like this:

  (format "%s" arbitrary-string)

Certain format specifications require values of particular types. If you supply a value that doesn’t fit the requirements, an error is signaled.

Here is a table of valid format specifications:

‘%s’

Replace the specification with the printed representation of the object, made without quoting (that is, using princ, not prin1—see Output Functions). Thus, strings are represented by their contents alone, with no ‘"’ characters, and symbols appear without ‘\’ characters.

If the object is a string, its text properties are copied into the output. The text properties of the ‘%s’ itself are also copied, but those of the object take priority.

‘%S’

Replace the specification with the printed representation of the object, made with quoting (that is, using prin1—see Output Functions). Thus, strings are enclosed in ‘"’ characters, and ‘\’ characters appear where necessary before special characters.

‘%o’ ¶

Replace the specification with the base-eight representation of an integer. Negative integers are formatted in a platform-dependent way. The object can also be a floating-point number that is formatted as an integer, dropping any fraction.

‘%d’

Replace the specification with the base-ten representation of a signed integer. The object can also be a floating-point number that is formatted as an integer, dropping any fraction.

‘%x’ ¶

‘%X’

Replace the specification with the base-sixteen representation of an integer. Negative integers are formatted in a platform-dependent way. ‘%x’ uses lower case and ‘%X’ uses upper case. The object can also be a floating-point number that is formatted as an integer, dropping any fraction.

‘%c’

Replace the specification with the character which is the value given.

‘%e’

Replace the specification with the exponential notation for a floating-point number.

‘%f’

Replace the specification with the decimal-point notation for a floating-point number.

‘%g’

Replace the specification with notation for a floating-point number, using either exponential notation or decimal-point notation. The exponential notation is used if the exponent would be less than -4 or greater than or equal to the precision (default: 6). By default, trailing zeros are removed from the fractional portion of the result and a decimal-point character appears only if it is followed by a digit.

‘%%’

Replace the specification with a single ‘%’. This format specification is unusual in that its only form is plain ‘%%’ and that it does not use a value. For example, (format "%% %d" 30) returns "% 30".

Any other format character results in an ‘Invalid format operation’ error.

Here are several examples, which assume the typical text-quoting-style settings:

(format "The octal value of %d is %o,
         and the hex value is %x." 18 18 18)
     ⇒ "The octal value of 18 is 22,
         and the hex value is 12."

(format-message
 "The name of this buffer is ‘%s’." (buffer-name))
     ⇒ "The name of this buffer is ‘strings.texi’."

(format-message
 "The buffer object prints as `%s'." (current-buffer))
     ⇒ "The buffer object prints as ‘strings.texi’."

By default, format specifications correspond to successive values from objects. Thus, the first format specification in string uses the first such value, the second format specification uses the second such value, and so on. Any extra format specifications (those for which there are no corresponding values) cause an error. Any extra values to be formatted are ignored.

A format specification can have a field number, which is a decimal number immediately after the initial ‘%’, followed by a literal dollar sign ‘$’. It causes the format specification to convert the argument with the given number instead of the next argument. Field numbers start at 1. A format can contain either numbered or unnumbered format specifications but not both, except that ‘%%’ can be mixed with numbered specifications.

(format "%2$s, %3$s, %%, %1$s" "x" "y" "z")
     ⇒ "y, z, %, x"

After the ‘%’ and any field number, you can put certain flag characters.

The flag ‘+’ inserts a plus sign before a nonnegative number, so that it always has a sign. A space character as flag inserts a space before a nonnegative number. (Otherwise, nonnegative numbers start with the first digit.) These flags are useful for ensuring that nonnegative and negative numbers use the same number of columns. They are ignored except for ‘%d’, ‘%e’, ‘%f’, ‘%g’, and if both flags are used, ‘+’ takes precedence.

The flag ‘#’ specifies an alternate form which depends on the format in use. For ‘%o’, it ensures that the result begins with a ‘0’. For ‘%x’ and ‘%X’, it prefixes nonzero results with ‘0x’ or ‘0X’. For ‘%e’ and ‘%f’, the ‘#’ flag means include a decimal point even if the precision is zero. For ‘%g’, it always includes a decimal point, and also forces any trailing zeros after the decimal point to be left in place where they would otherwise be removed.

The flag ‘0’ ensures that the padding consists of ‘0’ characters instead of spaces. This flag is ignored for non-numerical specification characters like ‘%s’, ‘%S’ and ‘%c’. These specification characters accept the ‘0’ flag, but still pad with spaces.

The flag ‘-’ causes any padding inserted by the width, if specified, to be inserted on the right rather than the left. If both ‘-’ and ‘0’ are present, the ‘0’ flag is ignored.

(format "%06d is padded on the left with zeros" 123)
     ⇒ "000123 is padded on the left with zeros"

(format "'%-6d' is padded on the right" 123)
     ⇒ "'123   ' is padded on the right"

(format "The word '%-7s' actually has %d letters in it."
        "foo" (length "foo"))
     ⇒ "The word 'foo    ' actually has 3 letters in it."

A specification can have a width, which is a decimal number that appears after any field number and flags. If the printed representation of the object contains fewer characters than this width, format extends it with padding. Any padding introduced by the width normally consists of spaces inserted on the left:

(format "%5d is padded on the left with spaces" 123)
     ⇒ "  123 is padded on the left with spaces"

If the width is too small, format does not truncate the object’s printed representation. Thus, you can use a width to specify a minimum spacing between columns with no risk of losing information. In the following two examples, ‘%7s’ specifies a minimum width of 7. In the first case, the string inserted in place of ‘%7s’ has only 3 letters, and needs 4 blank spaces as padding. In the second case, the string "specification" is 13 letters wide but is not truncated.

(format "The word '%7s' has %d letters in it."
        "foo" (length "foo"))
     ⇒ "The word '    foo' has 3 letters in it."
(format "The word '%7s' has %d letters in it."
        "specification" (length "specification"))
     ⇒ "The word 'specification' has 13 letters in it."

All the specification characters allow an optional precision after the field number, flags and width, if present. The precision is a decimal-point ‘.’ followed by a digit-string. For the floating-point specifications (‘%e’ and ‘%f’), the precision specifies how many digits following the decimal point to show; if zero, the decimal-point itself is also omitted. For ‘%g’, the precision specifies how many significant digits to show (significant digits are the first digit before the decimal point and all the digits after it). If the precision of %g is zero or unspecified, it is treated as 1. For ‘%s’ and ‘%S’, the precision truncates the string to the given width, so ‘%.3s’ shows only the first three characters of the representation for object. For other specification characters, the effect of precision is what the local library functions of the printf family produce.

If you plan to use read later on the formatted string to retrieve a copy of the formatted value, use a specification that lets read reconstruct the value. To format numbers in this reversible way you can use ‘%s’ and ‘%S’, to format just integers you can also use ‘%d’, and to format just nonnegative integers you can also use ‘#x%x’ and ‘#o%o’. Other formats may be problematic; for example, ‘%d’ and ‘%g’ can mishandle NaNs and can lose precision and type, and ‘#x%x’ and ‘#o%o’ can mishandle negative integers. See Input Functions.

The functions described in this section accept a fixed set of specification characters. The next section describes a function format-spec which can accept custom specification characters, such as ‘%a’ or ‘%z’.

4.8 Custom Format Strings

Sometimes it is useful to allow users and Lisp programs alike to control how certain text is generated via custom format control strings. For example, a format string could control how to display someone’s forename, surname, and email address. Using the function format described in the previous section, the format string could be something like "%s %s <%s>". This approach quickly becomes impractical, however, as it can be unclear which specification character corresponds to which piece of information.

A more convenient format string for such cases would be something like "%f %l <%e>", where each specification character carries more semantic information and can easily be rearranged relative to other specification characters, making such format strings more easily customizable by the user.

The function format-spec described in this section performs a similar function to format, except it operates on format control strings that use arbitrary specification characters.

Function: format-spec template spec-alist &optional ignore-missing split ¶

This function returns a string produced from the format string template according to conversions specified in spec-alist, which is an alist (see Association Lists) of the form (letter . replacement). Each specification %letter in template will be replaced by replacement when formatting the resulting string.

The characters in template, other than the format specifications, are copied directly into the output, including their text properties, if any. Any text properties of the format specifications are copied to their replacements.

Using an alist to specify conversions gives rise to some useful properties:

• If spec-alist contains more unique letter keys than there are unique specification characters in template, the unused keys are simply ignored.
• If spec-alist contains more than one association with the same letter, the closest one to the start of the list is used.
• If template contains the same specification character more than once, then the same replacement found in spec-alist is used as a basis for all of that character’s substitutions.
• The order of specifications in template need not correspond to the order of associations in spec-alist.

REPLACEMENT can also be a function taking no arguments, and returning a string to be used for the replacement. It will only be called when the corresponding LETTER is used in the TEMPLATE. This is useful, for example, to avoid prompting for input unless it is needed.

The optional argument ignore-missing indicates how to handle specification characters in template that are not found in spec-alist. If it is nil or omitted, the function signals an error; if it is ignore, those format specifications are left verbatim in the output, including their text properties, if any; if it is delete, those format specifications are removed from the output; any other non-nil value is handled like ignore, but any occurrences of ‘%%’ are also left verbatim in the output.

If the optional argument split is non-nil, instead of returning a single string, format-spec will split the result into a list of strings, based on where the substitutions were performed. For instance:

(format-spec "foo %b bar" '((?b . "zot")) nil t)
     ⇒ ("foo " "zot" " bar")

The syntax of format specifications accepted by format-spec is similar, but not identical, to that accepted by format. In both cases, a format specification is a sequence of characters beginning with ‘%’ and ending with an alphabetic letter such as ‘s’.

Unlike format, which assigns specific meanings to a fixed set of specification characters, format-spec accepts arbitrary specification characters and treats them all equally. For example:

(setq my-site-info
      (list (cons ?s system-name)
            (cons ?t (symbol-name system-type))
            (cons ?c system-configuration)
            (cons ?v emacs-version)
            (cons ?e invocation-name)
            (cons ?p (number-to-string (emacs-pid)))
            (cons ?a user-mail-address)
            (cons ?n user-full-name)))

(format-spec "%e %v (%c)" my-site-info)
     ⇒ "emacs 27.1 (x86_64-pc-linux-gnu)"

(format-spec "%n <%a>" my-site-info)
     ⇒ "Emacs Developers <emacs-devel@gnu.org>"

A format specification can include any number of the following flag characters immediately after the ‘%’ to modify aspects of the substitution.

‘0’

This flag causes any padding specified by the width to consist of ‘0’ characters instead of spaces.

‘-’

This flag causes any padding specified by the width to be inserted on the right rather than the left.

‘<’

This flag causes the substitution to be truncated on the left to the given width and precision, if specified.

‘>’

This flag causes the substitution to be truncated on the right to the given width and precision, if specified.

‘^’

This flag converts the substituted text to upper case (see Case Conversion in Lisp).

‘_ (underscore)’

This flag converts the substituted text to lower case (see Case Conversion in Lisp).

The result of using contradictory flags (for instance, both upper and lower case) is undefined.

As is the case with format, a format specification can include a width, which is a decimal number that appears after any flags, and a precision, which is a decimal-point ‘.’ followed by a decimal number that appears after any flags and width.

If a substitution contains fewer characters than its specified width, it is padded on the left:

(format-spec "%8a is padded on the left with spaces"
             '((?a . "alpha")))
     ⇒ "   alpha is padded on the left with spaces"

If a substitution contains more characters than its specified precision, it is truncated on the right:

(format-spec "%.2a is truncated on the right"
             '((?a . "alpha")))
     ⇒ "al is truncated on the right"

Here is a more complicated example that combines several aforementioned features:

(setq my-battery-info
      (list (cons ?p "73")      ; Percentage
            (cons ?L "Battery") ; Status
            (cons ?t "2:23")    ; Remaining time
            (cons ?c "24330")   ; Capacity
            (cons ?r "10.6")))  ; Rate of discharge

(format-spec "%>^-3L : %3p%% (%05t left)" my-battery-info)
     ⇒ "BAT :  73% (02:23 left)"

(format-spec "%>^-3L : %3p%% (%05t left)"
             (cons (cons ?L "AC")
                   my-battery-info))
     ⇒ "AC  :  73% (02:23 left)"

As the examples in this section illustrate, format-spec is often used for selectively formatting an assortment of different pieces of information. This is useful in programs that provide user-customizable format strings, as the user can choose to format with a regular syntax and in any desired order only a subset of the information that the program makes available.

4.9 Case Conversion in Lisp

The character case functions change the case of single characters or of the contents of strings. The functions normally convert only alphabetic characters (the letters ‘A’ through ‘Z’ and ‘a’ through ‘z’, as well as non-ASCII letters); other characters are not altered. You can specify a different case conversion mapping by specifying a case table (see The Case Table).

These functions do not modify the strings that are passed to them as arguments.

The examples below use the characters ‘X’ and ‘x’ which have ASCII codes 88 and 120 respectively.

Function: downcase string-or-char ¶

This function converts string-or-char, which should be either a character or a string, to lower case.

When string-or-char is a string, this function returns a new string in which each letter in the argument that is upper case is converted to lower case. When string-or-char is a character, this function returns the corresponding lower case character (an integer); if the original character is lower case, or is not a letter, the return value is equal to the original character.

(downcase "The cat in the hat")
     ⇒ "the cat in the hat"

(downcase ?X)
     ⇒ 120

Function: upcase string-or-char ¶

This function converts string-or-char, which should be either a character or a string, to upper case.

When string-or-char is a string, this function returns a new string in which each letter in the argument that is lower case is converted to upper case. When string-or-char is a character, this function returns the corresponding upper case character (an integer); if the original character is upper case, or is not a letter, the return value is equal to the original character.

(upcase "The cat in the hat")
     ⇒ "THE CAT IN THE HAT"

(upcase ?x)
     ⇒ 88

Function: capitalize string-or-char ¶

This function capitalizes strings or characters. If string-or-char is a string, the function returns a new string whose contents are a copy of string-or-char in which each word has been capitalized. This means that the first character of each word is converted to upper case, and the rest are converted to lower case.

The definition of a word is any sequence of consecutive characters that are assigned to the word constituent syntax class in the current syntax table (see Table of Syntax Classes).

When string-or-char is a character, this function does the same thing as upcase.

(capitalize "The cat in the hat")
     ⇒ "The Cat In The Hat"

(capitalize "THE 77TH-HATTED CAT")
     ⇒ "The 77th-Hatted Cat"

(capitalize ?x)
     ⇒ 88