//// Functions for working with floats.
////
//// ## Float representation
////
//// Floats are represented as 64 bit floating point numbers on both the Erlang
//// and JavaScript runtimes. The floating point behaviour is native to their
//// respective runtimes, so their exact behaviour will be slightly different on
//// the two runtimes.
////
//// ### Infinity and NaN
////
//// Under the JavaScript runtime, exceeding the maximum (or minimum)
//// representable value for a floating point value will result in Infinity (or
//// -Infinity). Should you try to divide two infinities you will get NaN as a
//// result.
////
//// When running on BEAM, exceeding the maximum (or minimum) representable
//// value for a floating point value will raise an error.
////
//// ## Division by zero
////
//// Gleam runs on the Erlang virtual machine, which does not follow the IEEE
//// 754 standard for floating point arithmetic and does not have an `Infinity`
//// value.  In Erlang division by zero results in a crash, however Gleam does
//// not have partial functions and operators in core so instead division by zero
//// returns zero, a behaviour taken from Pony, Coq, and Lean.
////
//// This may seem unexpected at first, but it is no less mathematically valid
//// than crashing or returning a special value. Division by zero is undefined
//// in mathematics.

import gleam/order.{type Order}

/// Attempts to parse a string as a `Float`, returning `Error(Nil)` if it was
/// not possible.
///
/// ## Examples
///
/// ```gleam
/// assert parse("2.3") == Ok(2.3)
/// ```
///
/// ```gleam
/// assert parse("ABC") == Error(Nil)
/// ```
///
@external(erlang, "gleam_stdlib", "parse_float")
@external(javascript, "../gleam_stdlib.mjs", "parse_float")
pub fn parse(string: String) -> Result(Float, Nil)

/// Returns the string representation of the provided `Float`.
///
/// ## Examples
///
/// ```gleam
/// assert to_string(2.3) == "2.3"
/// ```
///
@external(erlang, "gleam_stdlib", "float_to_string")
@external(javascript, "../gleam_stdlib.mjs", "float_to_string")
pub fn to_string(x: Float) -> String

/// Restricts a float between two bounds.
///
/// Note: If the `min` argument is larger than the `max` argument then they
/// will be swapped, so the minimum bound is always lower than the maximum
/// bound.
///
///
/// ## Examples
///
/// ```gleam
/// assert clamp(1.2, min: 1.4, max: 1.6) == 1.4
/// ```
///
/// ```gleam
/// assert clamp(1.2, min: 1.4, max: 0.6) == 1.2
/// ```
///
pub fn clamp(x: Float, min min_bound: Float, max max_bound: Float) -> Float {
  case min_bound >=. max_bound {
    True -> x |> min(min_bound) |> max(max_bound)
    False -> x |> min(max_bound) |> max(min_bound)
  }
}

/// Compares two `Float`s, returning an `Order`:
/// `Lt` for lower than, `Eq` for equals, or `Gt` for greater than.
///
/// ## Examples
///
/// ```gleam
/// assert compare(2.0, 2.3) == Lt
/// ```
///
/// To handle
/// [Floating Point Imprecision](https://en.wikipedia.org/wiki/Floating-point_arithmetic#Accuracy_problems)
/// you may use [`loosely_compare`](#loosely_compare) instead.
///
pub fn compare(a: Float, with b: Float) -> Order {
  case a == b {
    True -> order.Eq
    False ->
      case a <. b {
        True -> order.Lt
        False -> order.Gt
      }
  }
}

/// Compares two `Float`s within a tolerance, returning an `Order`:
/// `Lt` for lower than, `Eq` for equals, or `Gt` for greater than.
///
/// This function allows Float comparison while handling
/// [Floating Point Imprecision](https://en.wikipedia.org/wiki/Floating-point_arithmetic#Accuracy_problems).
///
/// Notice: For `Float`s the tolerance won't be exact:
/// `5.3 - 5.0` is not exactly `0.3`.
///
/// ## Examples
///
/// ```gleam
/// assert loosely_compare(5.0, with: 5.3, tolerating: 0.5) == Eq
/// ```
///
/// If you want to check only for equality you may use
/// [`loosely_equals`](#loosely_equals) instead.
///
pub fn loosely_compare(
  a: Float,
  with b: Float,
  tolerating tolerance: Float,
) -> Order {
  let difference = absolute_value(a -. b)
  case difference <=. tolerance {
    True -> order.Eq
    False -> compare(a, b)
  }
}

/// Checks for equality of two `Float`s within a tolerance,
/// returning a `Bool`.
///
/// This function allows Float comparison while handling
/// [Floating Point Imprecision](https://en.wikipedia.org/wiki/Floating-point_arithmetic#Accuracy_problems).
///
/// Notice: For `Float`s the tolerance won't be exact:
/// `5.3 - 5.0` is not exactly `0.3`.
///
/// ## Examples
///
/// ```gleam
/// assert loosely_equals(5.0, with: 5.3, tolerating: 0.5)
/// ```
///
/// ```gleam
/// assert !loosely_equals(5.0, with: 5.1, tolerating: 0.1)
/// ```
///
pub fn loosely_equals(
  a: Float,
  with b: Float,
  tolerating tolerance: Float,
) -> Bool {
  let difference = absolute_value(a -. b)
  difference <=. tolerance
}

/// Compares two `Float`s, returning the smaller of the two.
///
/// ## Examples
///
/// ```gleam
/// assert min(2.0, 2.3) == 2.0
/// ```
///
pub fn min(a: Float, b: Float) -> Float {
  case a <. b {
    True -> a
    False -> b
  }
}

/// Compares two `Float`s, returning the larger of the two.
///
/// ## Examples
///
/// ```gleam
/// assert max(2.0, 2.3) == 2.3
/// ```
///
pub fn max(a: Float, b: Float) -> Float {
  case a >. b {
    True -> a
    False -> b
  }
}

/// Rounds the value to the next highest whole number as a `Float`.
///
/// ## Examples
///
/// ```gleam
/// assert ceiling(2.3) == 3.0
/// ```
///
@external(erlang, "math", "ceil")
@external(javascript, "../gleam_stdlib.mjs", "ceiling")
pub fn ceiling(x: Float) -> Float

/// Rounds the value to the next lowest whole number as a `Float`.
///
/// ## Examples
///
/// ```gleam
/// assert floor(2.3) == 2.0
/// ```
///
@external(erlang, "math", "floor")
@external(javascript, "../gleam_stdlib.mjs", "floor")
pub fn floor(x: Float) -> Float

/// Rounds the value to the nearest whole number as an `Int`.
///
/// ## Examples
///
/// ```gleam
/// assert round(2.3) == 2
/// ```
///
/// ```gleam
/// assert round(2.5) == 3
/// ```
///
@external(erlang, "erlang", "round")
pub fn round(x: Float) -> Int {
  case x >=. 0.0 {
    True -> js_round(x)
    False -> 0 - js_round(negate(x))
  }
}

@external(javascript, "../gleam_stdlib.mjs", "round")
fn js_round(a: Float) -> Int

/// Returns the value as an `Int`, truncating all decimal digits.
///
/// ## Examples
///
/// ```gleam
/// assert truncate(2.4343434847383438) == 2
/// ```
///
@external(erlang, "erlang", "trunc")
@external(javascript, "../gleam_stdlib.mjs", "truncate")
pub fn truncate(x: Float) -> Int

/// Converts the value to a given precision as a `Float`.
/// The precision is the number of allowed decimal places.
/// Negative precisions are allowed and force rounding
/// to the nearest tenth, hundredth, thousandth etc.
///
/// ## Examples
///
/// ```gleam
/// assert to_precision(2.43434348473, 2) == 2.43
/// ```
///
/// ```gleam
/// assert to_precision(547890.453444, -3) == 548000.0
/// ```
///
pub fn to_precision(x: Float, precision: Int) -> Float {
  case precision <= 0 {
    True -> {
      let factor = do_power(10.0, do_to_float(-precision))
      do_to_float(round(x /. factor)) *. factor
    }
    False -> {
      let factor = do_power(10.0, do_to_float(precision))
      do_to_float(round(x *. factor)) /. factor
    }
  }
}

@external(erlang, "erlang", "float")
@external(javascript, "../gleam_stdlib.mjs", "identity")
fn do_to_float(a: Int) -> Float

/// Returns the absolute value of the input as a `Float`.
///
/// ## Examples
///
/// ```gleam
/// assert absolute_value(-12.5) == 12.5
/// ```
///
/// ```gleam
/// assert absolute_value(10.2) == 10.2
/// ```
///
pub fn absolute_value(x: Float) -> Float {
  case x >=. 0.0 {
    True -> x
    False -> 0.0 -. x
  }
}

/// Returns the result of the base being raised to the power of the
/// exponent, as a `Float`.
///
/// ## Examples
///
/// ```gleam
/// assert power(2.0, -1.0) == Ok(0.5)
/// ```
///
/// ```gleam
/// assert power(2.0, 2.0) == Ok(4.0)
/// ```
///
/// ```gleam
/// assert power(8.0, 1.5) == Ok(22.627416997969522)
/// ```
///
/// ```gleam
/// assert 4.0 |> power(of: 2.0) == Ok(16.0)
/// ```
///
/// ```gleam
/// assert power(-1.0, 0.5) == Error(Nil)
/// ```
///
pub fn power(base: Float, of exponent: Float) -> Result(Float, Nil) {
  let fractional: Bool = ceiling(exponent) -. exponent >. 0.0
  // In the following check:
  // 1. If the base is negative and the exponent is fractional then
  //    return an error as it will otherwise be an imaginary number
  // 2. If the base is 0 and the exponent is negative then the expression
  //    is equivalent to the exponent divided by 0 and an error should be
  //    returned
  case base <. 0.0 && fractional || base == 0.0 && exponent <. 0.0 {
    True -> Error(Nil)
    False -> Ok(do_power(base, exponent))
  }
}

@external(erlang, "math", "pow")
@external(javascript, "../gleam_stdlib.mjs", "power")
fn do_power(a: Float, b: Float) -> Float

/// Returns the square root of the input as a `Float`.
///
/// ## Examples
///
/// ```gleam
/// assert square_root(4.0) == Ok(2.0)
/// ```
///
/// ```gleam
/// assert square_root(-16.0) == Error(Nil)
/// ```
///
pub fn square_root(x: Float) -> Result(Float, Nil) {
  power(x, 0.5)
}

/// Returns the negative of the value provided.
///
/// ## Examples
///
/// ```gleam
/// assert negate(1.0) == -1.0
/// ```
///
pub fn negate(x: Float) -> Float {
  -1.0 *. x
}

/// Sums a list of `Float`s.
///
/// ## Example
///
/// ```gleam
/// assert sum([1.0, 2.2, 3.3]) == 6.5
/// ```
///
pub fn sum(numbers: List(Float)) -> Float {
  sum_loop(numbers, 0.0)
}

fn sum_loop(numbers: List(Float), initial: Float) -> Float {
  case numbers {
    [first, ..rest] -> sum_loop(rest, first +. initial)
    [] -> initial
  }
}

/// Multiplies a list of `Float`s and returns the product.
///
/// ## Example
///
/// ```gleam
/// assert product([2.5, 3.2, 4.2]) == 33.6
/// ```
///
pub fn product(numbers: List(Float)) -> Float {
  product_loop(numbers, 1.0)
}

fn product_loop(numbers: List(Float), initial: Float) -> Float {
  case numbers {
    [first, ..rest] -> product_loop(rest, first *. initial)
    [] -> initial
  }
}

/// Generates a random float between the given zero (inclusive) and one
/// (exclusive).
///
/// On Erlang this updates the random state in the process dictionary.
/// See: <https://www.erlang.org/doc/man/rand.html#uniform-0>
///
/// ## Examples
///
/// ```gleam
/// random()
/// // -> 0.646355926896028
/// ```
///
@external(erlang, "rand", "uniform")
@external(javascript, "../gleam_stdlib.mjs", "random_uniform")
pub fn random() -> Float

/// Computes the modulo of a float division of inputs as a `Result`.
///
/// Returns division of the inputs as a `Result`: If the given divisor equals
/// `0`, this function returns an `Error`.
///
/// The computed value will always have the same sign as the `divisor`.
///
/// ## Examples
///
/// ```gleam
/// assert modulo(13.3, by: 3.3) == Ok(0.1)
/// ```
///
/// ```gleam
/// assert modulo(-13.3, by: 3.3) == Ok(3.2)
/// ```
///
/// ```gleam
/// assert modulo(13.3, by: -3.3) == Ok(-3.2)
/// ```
///
/// ```gleam
/// assert modulo(-13.3, by: -3.3) == Ok(-0.1)
/// ```
///
pub fn modulo(dividend: Float, by divisor: Float) -> Result(Float, Nil) {
  case divisor {
    0.0 -> Error(Nil)
    _ -> Ok(dividend -. floor(dividend /. divisor) *. divisor)
  }
}

/// Returns division of the inputs as a `Result`.
///
/// ## Examples
///
/// ```gleam
/// assert divide(0.0, 1.0) == Ok(0.0)
/// ```
///
/// ```gleam
/// assert divide(1.0, 0.0) == Error(Nil)
/// ```
///
pub fn divide(a: Float, by b: Float) -> Result(Float, Nil) {
  case b {
    0.0 -> Error(Nil)
    b -> Ok(a /. b)
  }
}

/// Adds two floats together.
///
/// It's the function equivalent of the `+.` operator.
/// This function is useful in higher order functions or pipes.
///
/// ## Examples
///
/// ```gleam
/// assert add(1.0, 2.0) == 3.0
/// ```
///
/// ```gleam
/// import gleam/list
///
/// assert list.fold([1.0, 2.0, 3.0], 0.0, add) == 6.0
/// ```
///
/// ```gleam
/// assert 3.0 |> add(2.0) == 5.0
/// ```
///
pub fn add(a: Float, b: Float) -> Float {
  a +. b
}

/// Multiplies two floats together.
///
/// It's the function equivalent of the `*.` operator.
/// This function is useful in higher order functions or pipes.
///
/// ## Examples
///
/// ```gleam
/// assert multiply(2.0, 4.0) == 8.0
/// ```
///
/// ```gleam
/// import gleam/list
///
/// assert list.fold([2.0, 3.0, 4.0], 1.0, multiply) == 24.0
/// ```
///
/// ```gleam
/// assert 3.0 |> multiply(2.0) == 6.0
/// ```
///
pub fn multiply(a: Float, b: Float) -> Float {
  a *. b
}

/// Subtracts one float from another.
///
/// It's the function equivalent of the `-.` operator.
/// This function is useful in higher order functions or pipes.
///
/// ## Examples
///
/// ```gleam
/// assert subtract(3.0, 1.0) == 2.0
/// ```
///
/// ```gleam
/// import gleam/list
///
/// assert list.fold([1.0, 2.0, 3.0], 10.0, subtract) == 4.0
/// ```
///
/// ```gleam
/// assert 3.0 |> subtract(_, 2.0) == 1.0
/// ```
///
/// ```gleam
/// assert 3.0 |> subtract(2.0, _) == -1.0
/// ```
///
pub fn subtract(a: Float, b: Float) -> Float {
  a -. b
}

/// Returns the natural logarithm (base e) of the given `Float` as a `Result`. If the
/// input is less than or equal to 0, returns `Error(Nil)`.
///
/// ## Examples
///
/// ```gleam
/// assert logarithm(1.0) == Ok(0.0)
/// ```
///
/// ```gleam
/// assert logarithm(2.718281828459045) == Ok(1.0)
/// ```
///
/// ```gleam
/// assert logarithm(0.0) == Error(Nil)
/// ```
///
/// ```gleam
/// assert logarithm(-1.0) == Error(Nil)
/// ```
///
pub fn logarithm(x: Float) -> Result(Float, Nil) {
  // In the following check:
  // 1. If x is negative then return an error as the natural logarithm
  //    of a negative number is undefined (would be a complex number)
  // 2. If x is 0 then return an error as the natural logarithm of 0
  //    approaches negative infinity
  case x <=. 0.0 {
    True -> Error(Nil)
    False -> Ok(do_log(x))
  }
}

@external(erlang, "math", "log")
@external(javascript, "../gleam_stdlib.mjs", "log")
fn do_log(x: Float) -> Float

/// Returns e (Euler's number) raised to the power of the given exponent, as
/// a `Float`.
///
/// ## Examples
///
/// ```gleam
/// assert exponential(0.0) == Ok(1.0)
/// ```
///
/// ```gleam
/// assert exponential(1.0) == Ok(2.718281828459045)
/// ```
///
/// ```gleam
/// assert exponential(-1.0) == Ok(0.36787944117144233)
/// ```
///
@external(erlang, "math", "exp")
@external(javascript, "../gleam_stdlib.mjs", "exp")
pub fn exponential(x: Float) -> Float