aiken/math
This module contains some basic Math utilities. Standard arithmetic operations on integers are available through native operators:
| Operator | Description |
|---|---|
+ | Arithmetic sum |
- | Arithmetic difference |
/ | Whole division |
* | Arithmetic multiplication |
% | Remainder by whole division |
Here are a few examples:
1 + 1 // 2
10 - 2 // 8
40 / 14 // 2
3 * 4 // 12
10 % 3 // 1Functions
abs(self: Int) -> Int
Calculate the absolute value of an integer.
math.abs(-42) == 42
math.abs(14) == 14
clamp(self: Int, min: Int, max: Int) -> Int
Restrict the value of an integer between two min and max bounds
math.clamp(14, min: 0, max: 10) == 10
gcd(x: Int, y: Int) -> Int
The greatest common divisor of two integers.
math.gcd(42, 14) == 14
math.gcd(14, 42) == 14
math.gcd(0, 0) == 0
is_sqrt(self: Int, x: Int) -> Bool
Checks if an integer has a given integer square root x. The check has constant time complexity (O(1)).
math.is_sqrt(0, 0)
math.is_sqrt(25, 5)
! math.is_sqrt(25, -5)
math.is_sqrt(44203, 210)
log(self: Int, base: Int) -> Int
The logarithm in base b of an element using integer divisions.
math.log(10, base: 2) == 3
math.log(42, base: 2) == 5
math.log(42, base: 3) == 3
math.log(5, base: 0) == 0
math.log(4, base: 4) == 1
math.log(4, base: 42) == 0
max(a: Int, b: Int) -> Int
Return the maximum of two integers.
min(a: Int, b: Int) -> Int
Return the minimum of two integers.
pow(self: Int, e: Int) -> Int
Calculates a number to the power of e using the exponentiation by
squaring method.
math.pow(3, 5) == 243
math.pow(7, 2) == 49
math.pow(3, -4) == 0
math.pow(0, 0) == 1
math.pow(513, 3) == 135005697
pow2(e: Int) -> Int
Calculates the power of 2 for a given exponent e. Much cheaper than
using pow(2, _) for small exponents (0 < e < 256).
math.pow2(-2) == 0
math.pow2(0) == 1
math.pow2(1) == 2
math.pow2(4) == 16
math.pow2(42) == 4398046511104
sqrt(self: Int) -> Option<Int>
Calculates the square root of an integer using the Babylonian method. This returns either the exact result or the smallest integer nearest to the square root.
Returns None for negative values.
math.sqrt(0) == Some(0)
math.sqrt(25) == Some(5)
math.sqrt(44203) == Some(210)
math.sqrt(-42) == None