math

The math package has the usual mathematical functions.

println math::sqrt(2)            # 1.4142135623730951
println math::pow(2, 10)         # 1024
println math::hypot(3, 4)        # 5
println math::round(3.14159, 2)  # 3.14
println math::floor(3.7)         # 3
println math::abs(-42)           # 42
println math::log10(1000)        # 3

The functions accept integers and floats alike. Those that compute a float, such as sqrt and floor, return a float even for an integer argument.

Group	Functions
Powers and roots	`sqrt`, `cbrt`, `pow`, `exp`, `expm1`, `hypot`
Logarithms	`log`, `log2`, `log10`, `log1p`
Trigonometry	`sin`, `cos`, `tan`, `asin`, `acos`, `atan`, `atan2`, `sinh`, `cosh`, `tanh`
Rounding	`floor`, `ceil`, `round`, `trunc`
Comparison	`abs`, `fmax`, `fmin`, `fdim`, `copysign`, `nextafter`
Division	`fmod`, `remainder`, `divmod`, `ediv`, `emod`
Classification	`isfinite`, `isinf`, `isnan`, `isnormal`
Special functions	`erf`, `erfc`, `lgamma`, `tgamma`
Random	`random`, `random_set`
Primes	`listprimes`, `nthprime`
Precision	`epsilon`, `eps`

Constants

math::PI, math::E and math::TAU (2π) hold the usual constants:

println math::PI                        # 3.141592653589793
println math::E                         # 2.718281828459045
println math::cos(math::PI)             # -1

Primes

listprimes(limit) returns the primes up to limit, and nthprime(n) the n-th prime, counting from 1:

println math::listprimes(20)   # [2, 3, 5, 7, 11, 13, 17, 19]
println math::nthprime(10)     # 29

Random numbers

random(low, high) returns a random number between the bounds: an integer for integer bounds, a float for float bounds. random_set(low, high, count) returns a list of random integers.

roll = math::random(1, 6)
println roll.between(1, 6)                    # true
println math::random_set(1, 100, 5).size()    # 5

For realistic fake data, see faker.

Euclidean division

ediv and emod perform Euclidean division, whose remainder is never negative, unlike %. divmod returns both as a list.

println -7 % 2                # -1
println math::emod(-7, 2)     # 1
println math::ediv(-7, 2)     # -4
println math::divmod(-7, 2)   # [-4, 1]

They satisfy dividend == divisor * ediv(dividend, divisor) + emod(dividend, divisor).

For statistics such as mean, median and standard deviation, see stat.

Constants

Name	Value	Description
`math::PI`	`3.141592653589793`	The ratio of a circle's circumference to its diameter, `3.141592653589793`.
`math::E`	`2.718281828459045`	Euler's number, the base of the natural logarithm, `2.718281828459045`.
`math::TAU`	`6.283185307179586`	The ratio of a circle's circumference to its radius (`2 * PI`), `6.283185307179586`.

Functions

`math::epsilon`

math::epsilon()

Gets the smallest difference from 1.0 that a floating-point type can accurately represent.

Returns float — The machine epsilon value.

`math::eps`

math::eps(n = 9)

Returns a decimal epsilon value of the form 1e-n.

Parameter	Type	Default	Description
`n`	`integer`	`9`	The exponent (must be between 1 and 15, default `9`).

Returns float — A floating-point value of 0.1 ** n.

`math::random`

math::random(_valueX, _valueY)

Gets a random number between x and y.

Parameter	Type	Default	Description
`_valueX`	`integer\|float`		The lower bound.
`_valueY`	`integer\|float`		The upper bound.

Returns integer|float — A random number in the range [_valueX, _valueY].

`math::random_set`

math::random_set(_range_start, _range_end, _size)

Gets a random set of unique numbers within a given range.

Parameter	Type	Description
`_range_start`	`integer\|float`	The lower bound.
`_range_end`	`integer\|float`	The upper bound.
`_size`	`integer`	The number of unique values to generate.

Returns list — A list of _size unique random numbers, or [] if the range is invalid.

`math::listprimes`

math::listprimes(_limit)

Gets a list of prime numbers up to a limit.

Parameter	Type	Default	Description
`_limit`	`integer`		The upper bound (inclusive).

Returns list — A list of prime numbers up to _limit.

`math::nthprime`

math::nthprime(_n)

Gets the n-th prime number.

Parameter	Type	Default	Description
`_n`	`integer`		The 1-based index of the prime to retrieve.

Returns integer — The n-th prime number.

`math::sin`

math::sin(_value)

Computes the sine of a number.

Parameter	Type	Default	Description
`_value`	`integer\|float`		The angle in radians.

Returns float — The sine of _value.

`math::cos`

math::cos(_value)

Computes the cosine of a number.

Parameter	Type	Default	Description
`_value`	`integer\|float`		The angle in radians.

Returns float — The cosine of _value.

`math::tan`

math::tan(_value)

Computes the tangent of a number.

Parameter	Type	Default	Description
`_value`	`integer\|float`		The angle in radians.

Returns float — The tangent of _value.

`math::asin`

math::asin(_value)

Computes the arc sine of a number.

Parameter	Type	Default	Description
`_value`	`integer\|float`		A value in the range `[-1, 1]`.

Returns float — The arc sine of _value in radians.

`math::acos`

math::acos(_value)

Computes the arc cosine of a number.

Parameter	Type	Default	Description
`_value`	`integer\|float`		A value in the range `[-1, 1]`.

Returns float — The arc cosine of _value in radians.

`math::atan`

math::atan(_value)

Computes the arc tangent of a number.

Parameter	Type	Default	Description
`_value`	`integer\|float`		The number.

Returns float — The arc tangent of _value in radians.

`math::atan2`

math::atan2(_valueY, _valueX)

Computes the arc tangent of y / x, handling quadrants correctly.

Parameter	Type	Default	Description
`_valueY`	`integer\|float`		The y coordinate.
`_valueX`	`integer\|float`		The x coordinate.

Returns float — The angle in radians between the positive x-axis and the point (x, y).

`math::sinh`

math::sinh(_value)

Computes the hyperbolic sine of a number.

Parameter	Type	Default	Description
`_value`	`integer\|float`		The number.

Returns float — The hyperbolic sine of _value.

`math::cosh`

math::cosh(_value)

Computes the hyperbolic cosine of a number.

Parameter	Type	Default	Description
`_value`	`integer\|float`		The number.

Returns float — The hyperbolic cosine of _value.

`math::tanh`

math::tanh(_value)

Computes the hyperbolic tangent of a number.

Parameter	Type	Default	Description
`_value`	`integer\|float`		The number.

Returns float — The hyperbolic tangent of _value.

`math::log`

math::log(_value)

Computes the natural logarithm (base e) of a number.

Parameter	Type	Default	Description
`_value`	`integer\|float`		The number.

Returns float — The natural logarithm of _value.

`math::log2`

math::log2(_value)

Computes the base-2 logarithm of a number.

Parameter	Type	Default	Description
`_value`	`integer\|float`		The number.

Returns float — The base-2 logarithm of _value.

`math::log10`

math::log10(_value)

Computes the base-10 logarithm of a number.

Parameter	Type	Default	Description
`_value`	`integer\|float`		The number.

Returns float — The base-10 logarithm of _value.

`math::log1p`

math::log1p(_value)

Computes log(1 + x) accurately for small values of x.

Parameter	Type	Default	Description
`_value`	`integer\|float`		The number x.

Returns float — The value of log(1 + x).

`math::sqrt`

math::sqrt(_value)

Computes the square root of a number.

Parameter	Type	Default	Description
`_value`	`integer\|float`		The number.

Returns float — The square root of _value.

`math::cbrt`

math::cbrt(_value)

Computes the cube root of a number.

Parameter	Type	Default	Description
`_value`	`integer\|float`		The number.

Returns float — The cube root of _value.

`math::fmod`

math::fmod(_valueX, _valueY)

Computes the floating-point remainder of x / y.

Parameter	Type	Default	Description
`_valueX`	`integer\|float`		The dividend x.
`_valueY`	`integer\|float`		The divisor y.

Returns float — The remainder of x / y.

`math::hypot`

math::hypot(_valueX, _valueY)

Computes sqrt(x**2 + y**2) without undue overflow or underflow.

Parameter	Type	Default	Description
`_valueX`	`integer\|float`		The number x.
`_valueY`	`integer\|float`		The number y.

Returns float — The Euclidean distance from the origin to (x, y).

`math::isfinite`

math::isfinite(_value)

Checks if a value is a finite floating-point number.

Parameter	Type	Default	Description
`_value`	`integer\|float`		The number to test.

Returns boolean — true if _value is finite.

`math::isinf`

math::isinf(_value)

Checks if a value is positive or negative infinity.

Parameter	Type	Default	Description
`_value`	`integer\|float`		The number to test.

Returns boolean — true if _value is infinite.

`math::isnan`

math::isnan(_value)

Checks if a value is NaN (Not a Number).

Parameter	Type	Default	Description
`_value`	`integer\|float`		The number to test.

Returns boolean — true if _value is NaN.

`math::isnormal`

math::isnormal(_value)

Checks if a value is a normal floating-point number.

Parameter	Type	Default	Description
`_value`	`integer\|float`		The number to test.

Returns boolean — true if _value is a normal FP number (not zero, subnormal, infinite, or NaN).

`math::floor`

math::floor(_value)

Rounds x down to the largest integer not greater than x.

Parameter	Type	Default	Description
`_value`	`integer\|float`		The number x.

Returns float — The floor of _value.

`math::ceil`

math::ceil(_value)

Rounds x up to the smallest integer not less than x.

Parameter	Type	Default	Description
`_value`	`integer\|float`		The number x.

Returns float — The ceiling of _value.

`math::round`

math::round(_value: float, _digits: integer = 0)

Rounds a double-precision floating-point value to a specified number of fractional digits, and rounds midpoint values to the nearest even number.

Parameter	Type	Default	Description
`_value`	`float`		The value.
`_digits`	`integer`	`0`	The fractional digits.

Returns float — The rounded value.

`math::trunc`

math::trunc(_value)

Truncates x to the integer part, rounding towards zero.

Parameter	Type	Default	Description
`_value`	`integer\|float`		The number x.

Returns float — The truncated value.

`math::remainder`

math::remainder(_valueX, _valueY)

Computes the IEEE 754 floating-point remainder of x / y.

Parameter	Type	Default	Description
`_valueX`	`integer\|float`		The dividend x.
`_valueY`	`integer\|float`		The divisor y.

Returns float — The IEEE 754 remainder of x / y.

`math::exp`

math::exp(_value)

Computes e raised to the power of x.

Parameter	Type	Default	Description
`_value`	`integer\|float`		The exponent x.

Returns float — The value of e ** x.

`math::expm1`

math::expm1(_value)

Computes e raised to the power of x, minus 1.

Parameter	Type	Default	Description
`_value`	`integer\|float`		The exponent x.

Returns float — The value of e ** x - 1, accurate for small x.

`math::erf`

math::erf(_value)

Computes the error function of a number.

Parameter	Type	Default	Description
`_value`	`integer\|float`		The number.

Returns float — The error function value erf(_value).

`math::erfc`

math::erfc(_value)

Computes the complementary error function of a number.

Parameter	Type	Default	Description
`_value`	`integer\|float`		The number.

Returns float — The complementary error function value 1 - erf(_value).

`math::lgamma`

math::lgamma(_value)

Computes the natural logarithm of the absolute value of the gamma function.

Parameter	Type	Default	Description
`_value`	`integer\|float`		The number.

Returns float — The value of log(|gamma(_value)|).

`math::tgamma`

math::tgamma(_value)

Computes the gamma function of a number.

Parameter	Type	Default	Description
`_value`	`integer\|float`		The number.

Returns float — The gamma function value gamma(_value).

`math::copysign`

math::copysign(_valueX, _valueY)

Copies the sign of y to x.

Parameter	Type	Default	Description
`_valueX`	`integer\|float`		The magnitude source.
`_valueY`	`integer\|float`		The sign source.

Returns float — A value with the magnitude of x and the sign of y.

`math::nextafter`

math::nextafter(_valueX, _valueY)

Gets the next representable floating-point value after x towards y.

Parameter	Type	Default	Description
`_valueX`	`integer\|float`		The starting value.
`_valueY`	`integer\|float`		The direction.

Returns float — The next representable FP value from x towards y.

`math::fmax`

math::fmax(_valueX, _valueY)

Returns the larger of two numbers.

Parameter	Type	Default	Description
`_valueX`	`integer\|float`		The first number.
`_valueY`	`integer\|float`		The second number.

Returns integer|float — The maximum of x and y.

`math::fmin`

math::fmin(_valueX, _valueY)

Returns the smaller of two numbers.

Parameter	Type	Default	Description
`_valueX`	`integer\|float`		The first number.
`_valueY`	`integer\|float`		The second number.

Returns integer|float — The minimum of x and y.

`math::fdim`

math::fdim(_valueX, _valueY)

Returns the positive difference between x and y.

Parameter	Type	Default	Description
`_valueX`	`integer\|float`		The first number.
`_valueY`	`integer\|float`		The second number.

Returns float — max(x - y, 0).

`math::pow`

math::pow(_valueX, _valueY)

Raises x to the power of y.

Parameter	Type	Default	Description
`_valueX`	`integer\|float`		The base.
`_valueY`	`integer\|float`		The exponent.

Returns float — The value of x ** y.

`math::abs`

math::abs(_value)

Returns the absolute value of a number.

Parameter	Type	Default	Description
`_value`	`integer\|float`		The number.

Returns integer|float — The absolute value of _value.

`math::ediv`

math::ediv(_dividend, _divisor)

Computes the Euclidean quotient of _dividend divided by _divisor.

Parameter	Type	Default	Description
`_dividend`	`integer\|float`		The dividend.
`_divisor`	`integer\|float`		The divisor (must not be zero).

Returns integer — The Euclidean quotient.

`math::emod`

math::emod(_dividend, _divisor)

Computes the Euclidean remainder of _dividend divided by _divisor.

Parameter	Type	Default	Description
`_dividend`	`integer\|float`		The dividend.
`_divisor`	`integer\|float`		The divisor (must not be zero).

Returns integer — The Euclidean remainder.

`math::divmod`

math::divmod(_dividend, _divisor)

Performs Euclidean division and returns both the quotient and remainder.

Parameter	Type	Default	Description
`_dividend`	`integer\|float`		The dividend.
`_divisor`	`integer\|float`		The divisor (must not be zero).

Returns list — A two-element list [quotient, remainder].