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GNU Emacs supports two numeric data types: *integers* and
*floating point numbers*. Integers are whole numbers such as
-3, 0, 7, 13, and 511. Their values are exact. Floating point
numbers are numbers with fractional parts, such as -4.5, 0.0, or
2.71828. They can also be expressed in exponential notation: 1.5e2
equals 150; in this example, ``e2`' stands for ten to the second
power, and that is multiplied by 1.5. Floating point values are not
exact; they have a fixed, limited amount of precision.

3.1 Integer Basics | Representation and range of integers. | |

3.2 Floating Point Basics | Representation and range of floating point. | |

3.3 Type Predicates for Numbers | Testing for numbers. | |

3.4 Comparison of Numbers | Equality and inequality predicates. | |

3.5 Numeric Conversions | Converting float to integer and vice versa. | |

3.6 Arithmetic Operations | How to add, subtract, multiply and divide. | |

3.7 Rounding Operations | Explicitly rounding floating point numbers. | |

3.8 Bitwise Operations on Integers | Logical and, or, not, shifting. | |

3.9 Standard Mathematical Functions | Trig, exponential and logarithmic functions. | |

3.10 Random Numbers | Obtaining random integers, predictable or not. |

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The range of values for an integer depends on the machine. The minimum range is -134217728 to 134217727 (28 bits; i.e., -2**27 to 2**27 - 1), but some machines may provide a wider range. Many examples in this chapter assume an integer has 28 bits.

The Lisp reader reads an integer as a sequence of 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. 268435457 ; Also the integer 1, due to overflow. 0 ; The integer 0. -0 ; The integer 0. |

In addition, the Lisp reader recognizes a syntax for integers in
bases other than 10: ``#B integer`' reads

To understand how various functions work on integers, especially the bitwise operators (see section 3.8 Bitwise Operations on Integers), it is often helpful to view the numbers in their binary form.

In 28-bit binary, the decimal integer 5 looks like this:

0000 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 1111 |

-1 is represented as 28 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 1111 1011 |

In this implementation, the largest 28-bit binary integer value is 134,217,727 in decimal. In binary, it looks like this:

0111 1111 1111 1111 1111 1111 1111 |

Since the arithmetic functions do not check whether integers go outside their range, when you add 1 to 134,217,727, the value is the negative integer -134,217,728:

(+ 1 134217727) => -134217728 => 1000 0000 0000 0000 0000 0000 0000 |

Many of the functions described in this chapter accept markers for
arguments in place of numbers. (See section 31. 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.

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Floating point numbers are useful for representing numbers that are
not integral. The precise range of floating point numbers is
machine-specific; it is the same as the range of the C data type
`double`

on the machine you are using.

The read-syntax for floating point numbers requires either a decimal
point (with at least one digit following), an exponent, or both. For
example, ``1500.0`', ``15e2`', ``15.0e2`', ``1.5e3`', and
``.15e4`' are five ways of writing a floating point number whose
value is 1500. They are all equivalent. You can also use a minus sign
to write negative floating point numbers, as in ``-1.0`'.

Most modern computers support the IEEE floating point standard, which
provides for 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, `(sqrt -1.0)`

returns a
NaN. For practical purposes, there's no significant difference between
different NaN values in Emacs Lisp, and there's no rule for precisely
which NaN value should be used in a particular case, so Emacs Lisp
doesn't try to distinguish them. Here are the read syntaxes for
these special floating point values:

- positive infinity
- `
`1.0e+INF`' - negative infinity
- `
`-1.0e+INF`' - Not-a-number
- `
`0.0e+NaN`'.

In addition, the value `-0.0`

is distinguishable from ordinary
zero in IEEE floating point (although `equal`

and `=`

consider
them equal values).

You can use `logb`

to extract the binary exponent of a floating
point number (or estimate the logarithm of an integer):

__Function:__**logb***number*- This function returns the binary exponent of
`number`. More precisely, the value is the logarithm of`number`base 2, rounded down to an integer.(logb 10) => 3 (logb 10.0e20) => 69

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The functions in this section test whether the argument is a number or
whether it is a certain sort of number. The functions `integerp`

and `floatp`

can take any type of Lisp object as argument (the
predicates 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
31.2 Predicates on Markers.

__Function:__**floatp***object*- This predicate tests whether its argument is a floating point
number and returns
`t`

if so,`nil`

otherwise.`floatp`

does not exist in Emacs versions 18 and earlier.

__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:__**wholenump***object*-
The
`wholenump`

predicate (whose name comes from the phrase "whole-number-p") tests to see whether its argument is a nonnegative integer, and returns`t`

if so,`nil`

otherwise. 0 is considered non-negative.

__Function:__**zerop***number*- This predicate tests whether its argument is zero, and returns
`t`

if so,`nil`

otherwise. The argument must be a number.These two forms are equivalent:

`(zerop x)`

==`(= x 0)`

.

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To test numbers for numerical equality, you should normally use
`=`

, not `eq`

. There can be many distinct floating point
number objects with the same numeric value. If you use `eq`

to
compare them, then you test whether two values are the same
*object*. By contrast, `=`

compares only the numeric values
of the objects.

At present, each integer value has a unique Lisp object in Emacs Lisp.
Therefore, `eq`

is equivalent to `=`

where integers are
concerned. It is sometimes convenient to use `eq`

for comparing an
unknown value with an integer, 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 a good idea to use `=`

if you
can, even for comparing integers, just in case we change the
representation of integers in a future Emacs version.

Sometimes it is useful to compare numbers with `equal`

; it treats
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.

There is another wrinkle: because floating point arithmetic is not exact, it is often a bad idea to check for equality of two 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 (and (= x 0) (= y 0)) (< (/ (abs (- x y)) (max (abs x) (abs y))) fuzz-factor))) |

Common Lisp note:Comparing numbers in Common Lisp always requires`=`

because Common Lisp implements multi-word integers, and two distinct integer objects can have the same numeric value. Emacs Lisp can have just one integer object for any given value because it has a limited range of integer values.

__Function:__**=***number-or-marker1 number-or-marker2*- This function tests whether its arguments are numerically equal, and
returns
`t`

if so,`nil`

otherwise.

__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-marker1 number-or-marker2*- This function tests whether its first argument is strictly less than
its second argument. It returns
`t`

if so,`nil`

otherwise.

__Function:__**<=***number-or-marker1 number-or-marker2*- This function tests whether its first argument is less than or equal
to its second argument. It returns
`t`

if so,`nil`

otherwise.

__Function:__**>***number-or-marker1 number-or-marker2*- This function tests whether its first argument is strictly greater
than its second argument. It returns
`t`

if so,`nil`

otherwise.

__Function:__**>=***number-or-marker1 number-or-marker2*- This function tests whether its first argument is greater than or
equal to its second 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.
If any of the argument is floating-point, the value is returned
as floating point, even if it was given as an integer.
(max 20) => 20 (max 1 2.5) => 2.5 (max 1 3 2.5) => 3.0

__Function:__**min***number-or-marker &rest numbers-or-markers*- This function returns the smallest of its arguments.
If any of the argument is floating-point, the value is returned
as floating point, even if it was given as an integer.
(min -4 1) => -4

__Function:__**abs***number*- This function returns the absolute value of
`number`.

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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 a floating point number,`float`

returns it unchanged.

There are four functions to convert floating point numbers to integers; they differ in how they round. These functions accept integer arguments also, and return such arguments unchanged.

__Function:__**truncate***number*- 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,`floor`

divides`number`by`divisor`and then converts to an integer; this uses the kind of division operation that corresponds to`mod`

, rounding downward. An`arith-error`

results if`divisor`is 0.(floor 1.2) => 1 (floor 1.7) => 1 (floor -1.2) => -2 (floor -1.7) => -2 (floor 5.99 3) => 1

__Function:__**ceiling***number*- 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*- This returns
`number`, converted to an integer by rounding towards the nearest integer. Rounding a value equidistant between two integers may choose the integer closer to zero, or it may prefer an even integer, depending on your machine.(round 1.2) => 1 (round 1.7) => 2 (round -1.2) => -1 (round -1.7) => -2

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Emacs Lisp provides the traditional four arithmetic operations: addition, subtraction, multiplication, and division. Remainder and modulus functions supplement the division functions. The functions to add or subtract 1 are provided because they are traditional in Lisp and commonly used.

All of these functions except `%`

return a floating point value
if any argument is floating.

It is important to note that in Emacs Lisp, arithmetic functions
do not check for overflow. Thus `(1+ 134217727)`

may evaluate to
-134217728, depending on your hardware.

__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:__**/***dividend divisor &rest divisors*- This function divides
`dividend`by`divisor`and returns the quotient. If there are additional arguments`divisors`, then it divides`dividend`by each divisor in turn. Each argument may be a number or a marker.If all the arguments are integers, then the result is an integer too. This means the result has to be rounded. On most machines, the result is rounded towards zero after each division, but some machines may round differently with negative arguments. This is because the Lisp function

`/`

is implemented using the C division operator, which also permits machine-dependent rounding. As a practical matter, all known machines round in the standard fashion.If you divide an integer by 0, an

`arith-error`

error is signaled. (See section 10.5.3 Errors.) Floating point division by zero returns either infinity or a NaN if your machine supports IEEE floating point; otherwise, it signals an`arith-error`

error.(/ 6 2) => 3 (/ 5 2) => 2 (/ 5.0 2) => 2.5 (/ 5 2.0) => 2.5 (/ 5.0 2.0) => 2.5 (/ 25 3 2) => 4 (/ -17 6) => -2

The result of

`(/ -17 6)`

could in principle be -3 on some machines.

__Function:__**%***dividend divisor*-
This function returns the integer remainder after division of
`dividend`by`divisor`. The arguments must be integers or markers.For negative arguments, the remainder is in principle machine-dependent since the quotient is; but in practice, all known machines behave alike.

An

`arith-error`

results if`divisor`is 0.(% 9 4) => 1 (% -9 4) => -1 (% 9 -4) => 1 (% -9 -4) => -1

For any two integers

`dividend`and`divisor`,(+ (%

`dividend``divisor`) (* (/`dividend``divisor`)`divisor`))always equals

`dividend`.

__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`

returns a well-defined result for negative arguments. It also permits floating point arguments; it rounds the quotient downward (towards minus infinity) to an integer, and uses that quotient to compute the remainder.An

`arith-error`

results if`divisor`is 0.(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. For`floor`

, see 3.5 Numeric Conversions.

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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.

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In a computer, an integer is represented as a binary number, a
sequence of *bits* (digits which are either zero or one). 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:__**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,`lsh`

shifts zeros into the leftmost (most-significant) bit, producing a positive result even if`integer1`is negative. Contrast this with`ash`

, below.Here are two examples of

`lsh`

, shifting a pattern of bits one place to the left. We show only the low-order eight bits of the binary pattern; the rest are all zero.(lsh 5 1) => 10 ;; Decimal 5 becomes decimal 10. 00000101 => 00001010 (lsh 7 1) => 14 ;; Decimal 7 becomes decimal 14. 00000111 => 00001110

As the examples illustrate, shifting the pattern of bits one place to the left produces a number that is twice the value of the previous number.

Shifting a pattern of bits two places to the left produces results like this (with 8-bit binary numbers):

(lsh 3 2) => 12 ;; Decimal 3 becomes decimal 12. 00000011 => 00001100

On the other hand, shifting one place to the right looks like this:

(lsh 6 -1) => 3 ;; Decimal 6 becomes decimal 3. 00000110 => 00000011 (lsh 5 -1) => 2 ;; Decimal 5 becomes decimal 2. 00000101 => 00000010

As the example illustrates, shifting one place to the right divides the value of a positive integer by two, rounding downward.

The function

`lsh`

, like all Emacs Lisp arithmetic functions, does not check for overflow, so shifting left can discard significant bits and change the sign of the number. For example, left shifting 134,217,727 produces -2 on a 28-bit machine:(lsh 134217727 1) ; left shift => -2

In binary, in the 28-bit implementation, the argument looks like this:

;; Decimal 134,217,727 0111 1111 1111 1111 1111 1111 1111

which becomes the following when left shifted:

;; Decimal -2 1111 1111 1111 1111 1111 1111 1110

__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.`ash`

gives the same results as`lsh`

except when`integer1`and`count`are both negative. In that case,`ash`

puts ones in the empty bit positions on the left, while`lsh`

puts zeros in those bit positions.Thus, with

`ash`

, shifting the pattern of bits one place to the right looks like this:(ash -6 -1) => -3 ;; Decimal -6 becomes decimal -3. 1111 1111 1111 1111 1111 1111 1010 => 1111 1111 1111 1111 1111 1111 1101

In contrast, shifting the pattern of bits one place to the right with

`lsh`

looks like this:(lsh -6 -1) => 134217725 ;; Decimal -6 becomes decimal 134,217,725. 1111 1111 1111 1111 1111 1111 1010 => 0111 1111 1111 1111 1111 1111 1101

Here are other examples:

; 28-bit binary values (lsh 5 2) ; 5 = 0000 0000 0000 0000 0000 0000 0101 => 20 ; = 0000 0000 0000 0000 0000 0001 0100 (ash 5 2) => 20 (lsh -5 2) ; -5 = 1111 1111 1111 1111 1111 1111 1011 => -20 ; = 1111 1111 1111 1111 1111 1110 1100 (ash -5 2) => -20 (lsh 5 -2) ; 5 = 0000 0000 0000 0000 0000 0000 0101 => 1 ; = 0000 0000 0000 0000 0000 0000 0001 (ash 5 -2) => 1 (lsh -5 -2) ; -5 = 1111 1111 1111 1111 1111 1111 1011 => 4194302 ; = 0011 1111 1111 1111 1111 1111 1110 (ash -5 -2) ; -5 = 1111 1111 1111 1111 1111 1111 1011 => -2 ; = 1111 1111 1111 1111 1111 1111 1110

__Function:__**logand***&rest ints-or-markers*-
This function returns the "logical and" of the arguments: the
`n`th bit is set in the result if, and only if, the`n`th bit is set in all the arguments. ("Set" means that the value of the bit is 1 rather than 0.)For example, using 4-bit binary numbers, the "logical and" of 13 and 12 is 12: 1101 combined with 1100 produces 1100. In both the binary numbers, the leftmost two bits are set (i.e., they are 1's), so the leftmost two bits of the returned value are set. However, for the rightmost two bits, each is zero in at least one of the arguments, so the rightmost two bits of the returned value are 0's.

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.; 28-bit binary values (logand 14 13) ; 14 = 0000 0000 0000 0000 0000 0000 1110 ; 13 = 0000 0000 0000 0000 0000 0000 1101 => 12 ; 12 = 0000 0000 0000 0000 0000 0000 1100 (logand 14 13 4) ; 14 = 0000 0000 0000 0000 0000 0000 1110 ; 13 = 0000 0000 0000 0000 0000 0000 1101 ; 4 = 0000 0000 0000 0000 0000 0000 0100 => 4 ; 4 = 0000 0000 0000 0000 0000 0000 0100 (logand) => -1 ; -1 = 1111 1111 1111 1111 1111 1111 1111

__Function:__**logior***&rest ints-or-markers*-
This function returns the "inclusive or" of its arguments: the
`n`th bit is set in the result if, and only if, the`n`th bit is set in at least one of the arguments. If there are no arguments, the result is zero, which is an identity element for this operation. If`logior`

is passed just one argument, it returns that argument.; 28-bit binary values (logior 12 5) ; 12 = 0000 0000 0000 0000 0000 0000 1100 ; 5 = 0000 0000 0000 0000 0000 0000 0101 => 13 ; 13 = 0000 0000 0000 0000 0000 0000 1101 (logior 12 5 7) ; 12 = 0000 0000 0000 0000 0000 0000 1100 ; 5 = 0000 0000 0000 0000 0000 0000 0101 ; 7 = 0000 0000 0000 0000 0000 0000 0111 => 15 ; 15 = 0000 0000 0000 0000 0000 0000 1111

__Function:__**logxor***&rest ints-or-markers*-
This function returns the "exclusive or" of its arguments: the
`n`th bit is set in the result if, and only if, the`n`th bit is set 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.; 28-bit binary values (logxor 12 5) ; 12 = 0000 0000 0000 0000 0000 0000 1100 ; 5 = 0000 0000 0000 0000 0000 0000 0101 => 9 ; 9 = 0000 0000 0000 0000 0000 0000 1001 (logxor 12 5 7) ; 12 = 0000 0000 0000 0000 0000 0000 1100 ; 5 = 0000 0000 0000 0000 0000 0000 0101 ; 7 = 0000 0000 0000 0000 0000 0000 0111 => 14 ; 14 = 0000 0000 0000 0000 0000 0000 1110

__Function:__**lognot***integer*-
This function returns the logical complement of its argument: the
`n`th bit is one in the result if, and only if, the`n`th bit is zero in`integer`, and vice-versa.(lognot 5) => -6 ;; 5 = 0000 0000 0000 0000 0000 0000 0101 ;; becomes ;; -6 = 1111 1111 1111 1111 1111 1111 1010

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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 ordinary trigonometric functions, with argument measured in radians.

__Function:__**asin***arg*- The value of
`(asin`

is a number between -pi/2 and pi/2 (inclusive) whose sine is`arg`)`arg`; if, however,`arg`is out of range (outside [-1, 1]), then the result is a NaN.

__Function:__**acos***arg*- The value of
`(acos`

is a number between 0 and pi (inclusive) whose cosine is`arg`)`arg`; if, however,`arg`is out of range (outside [-1, 1]), then the result is a NaN.

__Function:__**atan***arg*- The value of
`(atan`

is a number between -pi/2 and pi/2 (exclusive) whose tangent is`arg`)`arg`.

__Function:__**exp***arg*- This is the exponential function; it returns
*e*to the power`arg`.*e*is a fundamental mathematical constant also called the base of natural logarithms.

__Function:__**log***arg &optional base*- This function returns the logarithm of
`arg`, with base`base`. If you don't specify`base`, the base*e*is used. If`arg`is negative, the result is a NaN.

__Function:__**log10***arg*- This function returns the logarithm of
`arg`, with base 10. If`arg`is negative, the result is a NaN.`(log10`

==`x`)`(log`

, at least approximately.`x`10)

__Function:__**expt***x y*- This function returns
`x`raised to power`y`. If both arguments are integers and`y`is positive, the result is an integer; in this case, it is truncated to fit the range of possible integer values.

__Function:__**sqrt***arg*- This returns the square root of
`arg`. If`arg`is negative, the value is a NaN.

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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.

In Emacs, pseudo-random numbers are generated from a "seed" number.
Starting from any given seed, the `random`

function always
generates the same sequence of numbers. Emacs always starts with the
same seed value, so the sequence of values of `random`

is actually
the same in each Emacs run! For example, in one operating system, the
first call to `(random)`

after you start Emacs always returns
-1457731, and the second one always returns -7692030. This
repeatability is helpful for debugging.

If you want random numbers that don't always come out the same, execute
`(random t)`

. This chooses a new seed based on the current time of
day and on Emacs's process ID number.

__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`.If

`limit`is`t`

, it means to choose a new seed based on the current time of day and on Emacs's process ID number.On some machines, any integer representable in Lisp may be the result of

`random`

. On other machines, the result can never be larger than a certain maximum or less than a certain (negative) minimum.

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