MATH

Math Module

Usage

To use the math module, import it into your Vint script:

import math

You can then call functions and access constants from the module:

println(math.PI())
println(math.sqrt(16))

Contents

This module provides a wide range of mathematical functions and constants, including:

  • Basic Mathematical Functions
  • Hyperbolic & Trigonometric Functions
  • Exponential & Logarithmic Functions
  • Rounding & Comparison Functions

Here is a complete list of the available functions and constants:

Constants

  • PI: Represents the mathematical constant π (3.14159...).
  • e: Represents Euler's Number (2.71828...).
  • phi: Represents the Golden Ratio (1.61803...).
  • ln10: Represents the natural logarithm of 10.
  • ln2: Represents the natural logarithm of 2.
  • log10e: Represents the base-10 logarithm of e.
  • log2e: Represents the base-2 logarithm of e.
  • sqrt1_2: Represents the square root of 1/2.
  • sqrt2: Represents the square root of 2.
  • sqrt3: Represents the square root of 3.
  • sqrt5: Represents the square root of 5.
  • EPSILON: Represents a very small number, often used for float comparisons.

Functions

abs(n)

  • Description: Calculates the absolute value of a number.
  • Example: math.abs(-42) returns 42.

acos(n)

  • Description: Calculates the arccosine (inverse cosine) of a number in radians.
  • Example: math.acos(0.5) returns 1.047....

acosh(n)

  • Description: Calculates the inverse hyperbolic cosine of a number.
  • Example: math.acosh(2.0) returns 1.316....

asin(n)

  • Description: Calculates the arcsine (inverse sine) of a number in radians.
  • Example: math.asin(0.5) returns 0.523....

asinh(n)

  • Description: Calculates the inverse hyperbolic sine of a number.
  • Example: math.asinh(2.0) returns 1.443....

atan(n)

  • Description: Calculates the arctangent (inverse tangent) of a number in radians.
  • Example: math.atan(1.0) returns 0.785....

atan2(y, x)

  • Description: Calculates the arctangent of the quotient of its arguments (y/x) in radians.
  • Example: math.atan2(1.0, 1.0) returns 0.785....

atanh(n)

  • Description: Calculates the inverse hyperbolic tangent of a number.
  • Example: math.atanh(0.5) returns 0.549....

cbrt(n)

  • Description: Calculates the cube root of a number.
  • Example: math.cbrt(8) returns 2.0.

ceil(n)

  • Description: Rounds a number up to the nearest integer.
  • Example: math.ceil(4.3) returns 5.

cos(n)

  • Description: Calculates the cosine of an angle (in radians).
  • Example: math.cos(0.0) returns 1.0.

cosh(n)

  • Description: Calculates the hyperbolic cosine of a number.
  • Example: math.cosh(0.0) returns 1.0.

exp(n)

  • Description: Calculates e raised to the power of n.
  • Example: math.exp(2.0) returns 7.389....

expm1(n)

  • Description: Calculates e raised to the power of a number, minus 1.
  • Example: math.expm1(1.0) returns 1.718....

factorial(n)

  • Description: Calculates the factorial of a non-negative integer.
  • Example: math.factorial(5) returns 120.

floor(n)

  • Description: Rounds a number down to the nearest integer.
  • Example: math.floor(4.7) returns 4.

hypot(numbers)

  • Description: Calculates the square root of the sum of the squares of the numbers in an array.
  • Example: math.hypot([3, 4]) returns 5.0.

log10(n)

  • Description: Calculates the base-10 logarithm of a number.
  • Example: math.log10(100.0) returns 2.0.

log1p(n)

  • Description: Calculates the natural logarithm of 1 plus the given number.
  • Example: math.log1p(1.0) returns 0.693....

log2(n)

  • Description: Calculates the base-2 logarithm of a number.
  • Example: math.log2(8) returns 3.0.

max(numbers)

  • Description: Finds the maximum value in an array of numbers.
  • Example: math.max([4, 2, 9, 5]) returns 9.0.

min(numbers)

  • Description: Finds the minimum value in an array of numbers.
  • Example: math.min([4, 2, 9, 5]) returns 2.0.

random()

  • Description: Returns a random floating-point number between 0.0 and 1.0.
  • Example: math.random() returns a value like 0.12345....

round(n)

  • Description: Rounds a floating-point number to the nearest integer.
  • Example: math.round(4.6) returns 5.

root(x, n)

  • Description: Calculates the nth root of a number x.
  • Example: math.root(27, 3) returns 3.0.

sign(n)

  • Description: Returns the sign of a number (-1 for negative, 0 for zero, 1 for positive).
  • Example: math.sign(-5) returns -1.

sin(n)

  • Description: Calculates the sine of an angle (in radians).
  • Example: math.sin(1.0) returns 0.841....

sinh(n)

  • Description: Calculates the hyperbolic sine of a number.
  • Example: math.sinh(1.0) returns 1.175....

sqrt(n)

  • Description: Calculates the square root of a number.
  • Example: math.sqrt(4) returns 2.0.

tan(n)

  • Description: Calculates the tangent of an angle (in radians).
  • Example: math.tan(1.0) returns 1.557....

tanh(n)

  • Description: Calculates the hyperbolic tangent of a number.
  • Example: math.tanh(1.0) returns 0.761....

Statistics Functions

mean(array)

  • Description: Calculates the arithmetic mean (average) of an array of numbers.
  • Example: math.mean([1, 2, 3, 4, 5]) returns 3.0.

median(array)

  • Description: Calculates the median (middle value) of an array of numbers.
  • Example: math.median([1, 2, 3, 4, 5]) returns 3.0.
  • Note: For even-length arrays, returns the average of the two middle values.

variance(array)

  • Description: Calculates the variance of an array of numbers.
  • Example: math.variance([1, 2, 3, 4, 5]) returns 2.0.

stddev(array)

  • Description: Calculates the standard deviation of an array of numbers.
  • Example: math.stddev([1, 2, 3, 4, 5]) returns 1.414....

Complex Numbers

complex(real, imag)

  • Description: Creates a complex number with the given real and imaginary parts.
  • Returns: A dictionary with real and imag keys.
  • Example: 
    let c = math.complex(3, 4)
print(c["real"])  // 3
print(c["imag"])  // 4

abs(n) (extended)

  • Description: Also works with complex numbers to calculate magnitude.
  • Example: 
    let c = math.complex(3, 4)
math.abs(c)  // returns 5.0

Arbitrary Precision

bigint(value)

  • Description: Creates a big integer representation for arbitrary precision arithmetic.
  • Parameters: A string or integer representing a large number.
  • Returns: A dictionary with value (string) and type ("bigint") keys.
  • Example: 
    let big = math.bigint("999999999999999999999")
print(big["value"])  // "999999999999999999999"

Linear Algebra

dot(array1, array2)

  • Description: Calculates the dot product of two vectors (arrays).
  • Example: math.dot([1, 2, 3], [4, 5, 6]) returns 32.0.

cross(array1, array2)

  • Description: Calculates the cross product of two 3D vectors.
  • Example: math.cross([1, 2, 3], [4, 5, 6]) returns [-3, 6, -3].

magnitude(array)

  • Description: Calculates the magnitude (length) of a vector.
  • Example: math.magnitude([3, 4]) returns 5.0.

Numerical Methods

gcd(a, b)

  • Description: Calculates the greatest common divisor of two integers.
  • Example: math.gcd(48, 18) returns 6.

lcm(a, b)

  • Description: Calculates the least common multiple of two integers.
  • Example: math.lcm(12, 15) returns 60.

clamp(value, min, max)

  • Description: Clamps a value between a minimum and maximum.
  • Example: math.clamp(15, 0, 10) returns 10.0.

lerp(start, end, t)

  • Description: Linear interpolation between two values.
  • Parameters: start and end values, and t (0.0 to 1.0) as the interpolation factor.
  • Example: math.lerp(0, 10, 0.5) returns 5.0.