Standard Library: Math and Numeric Functions • arl

Examples on this page may reference functions from other stdlib modules without showing explicit (import ...) statements. In the REPL or your own code, you will need to import non-prelude modules before using their exports — see Importing modules.

Arithmetic Helpers

%

Modulo helper using R %%.

Signature: (% x y)

Parameters: - x — Dividend - y — Divisor

Examples:

arl> (% 10 3)   ; => 1
#> 1
arl> (% 17 5)   ; => 2
#> 2

inc

Increment numeric value by n (default 1).

Signature: (inc x [n 1])

Parameters: - x — Number to increment - n — Amount to add (default 1)

Examples:

arl> (inc 5)       ; => 6
#> 6
arl> (inc 5 3)     ; => 8
#> 8

See also: dec

dec

Decrement numeric value by n (default 1).

Signature: (dec x [n 1])

Parameters: - x — Number to decrement - n — Amount to subtract (default 1)

Examples:

arl> (dec 5)       ; => 4
#> 4
arl> (dec 5 3)     ; => 2
#> 2

See also: inc

clamp

Clamp numeric value x to the inclusive range [lo, hi].

Signature: (clamp x lo hi)

Parameters: - x — Value to clamp - lo — Lower bound (inclusive) - hi — Upper bound (inclusive)

Examples:

arl> (clamp 5 0 10)   ; => 5
#> 5
arl> (clamp -3 0 10)  ; => 0
#> 0
arl> (clamp 15 0 10)  ; => 10
#> 10

See also: within?

within?

Return #t if x is within the inclusive range [lo, hi].

Signature: (within? x lo hi)

Parameters: - x — Value to test - lo — Lower bound (inclusive) - hi — Upper bound (inclusive)

Examples:

arl> (within? 5 0 10)   ; => #t
#> TRUE
arl> (within? -3 0 10)  ; => #f
#> FALSE
arl> (within? 10 0 10)  ; => #t
#> TRUE

See also: clamp

signum

Return sign of x: -1, 0, or 1.

Signature: (signum x)

Parameters: - x — Numeric value

Examples:

arl> (signum 42)    ; => 1
#> 1
arl> (signum -5)    ; => -1
#> -1
arl> (signum 0)     ; => 0
#> 0

Power and Roots

expt

Return base raised to power.

Signature: (expt base power)

Parameters: - base — Base number - power — Exponent

Examples:

arl> (expt 2 10)   ; => 1024
#> 1024
arl> (expt 3 3)    ; => 27
#> 27

Integer Division

quotient

Return integer quotient of x divided by y.

Signature: (quotient x y)

Parameters: - x — Dividend - y — Divisor

Examples:

arl> (quotient 10 3)   ; => 3
#> 3
arl> (quotient -10 3)  ; => -3
#> -3

See also: remainder, modulo

remainder

Return remainder of x divided by y (same sign as x).

Signature: (remainder x y)

Parameters: - x — Dividend - y — Divisor

Examples:

arl> (remainder 10 3)   ; => 1
#> 1
arl> (remainder -10 3)  ; => -1
#> -1

See also: quotient, modulo

modulo

Return modulo of x and y (same sign as y).

Signature: (modulo x y)

Parameters: - x — Dividend - y — Divisor

Examples:

arl> (modulo 10 3)    ; => 1
#> 1
arl> (modulo -10 3)   ; => 2
#> 2

See also: quotient, remainder, %

Number Theory

gcd

Return greatest common divisor of arguments.

Signature: (gcd a b ...)

Parameters: - args — Two or more integers

Examples:

arl> (gcd 12 8)      ; => 4
#> 4
arl> (gcd 12 8 6)    ; => 2
#> 2

See also: lcm

lcm

Return least common multiple of arguments.

Signature: (lcm a b ...)

Parameters: - args — Two or more integers

Examples:

arl> (lcm 4 6)       ; => 12
#> 12
arl> (lcm 3 4 5)     ; => 60
#> 60

See also: gcd

Complex Number Utilities

make-rectangular

Construct a complex number from real and imaginary parts.

Signature: (make-rectangular real imag)

Parameters: - real — Real component - imag — Imaginary component

Examples:

arl> (make-rectangular 3 4)  ; => 3+4i
#> 3+4i

See also: make-polar, real-part, imag-part

make-polar

Construct a complex number from polar coordinates (magnitude and angle).

Signature: (make-polar magnitude angle)

Parameters: - magnitude — Distance from origin - angle — Angle in radians

Examples:

arl> (make-polar 5 0)      ; => 5+0i
#> 5+0i

See also: make-rectangular, magnitude, angle

real-part

Extract the real part of a complex number.

Signature: (real-part z)

Parameters: - z — Complex number

Examples:

arl> (real-part (make-rectangular 3 4))  ; => 3.0
#> 3

See also: imag-part, make-rectangular

imag-part

Extract the imaginary part of a complex number.

Signature: (imag-part z)

Parameters: - z — Complex number

Examples:

arl> (imag-part (make-rectangular 3 4))  ; => 4.0
#> 4

See also: real-part, make-rectangular

magnitude

Compute the magnitude (modulus) of a complex number.

Signature: (magnitude z)

Parameters: - z — Complex number

Examples:

arl> (magnitude (make-rectangular 3 4))  ; => 5.0
#> 5

See also: angle, make-polar

angle

Compute the angle (argument) of a complex number.

Signature: (angle z)

Parameters: - z — Complex number

Examples:

arl> (angle (make-rectangular 1 1))  ; => 0.7853981633974483 (pi/4)
#> 0.785398163397448

See also: magnitude, make-polar