(ns math
  "Erlang :math module — mathematical functions.

   In CljElixir: (math/sqrt 2), (math/pow 2 10), etc.
   All functions return floats.")

(defn pi
  "Returns the value of pi.
   (math/pi) ;=> 3.141592653589793"
  [])

(defn e
  "Returns Euler's number.
   (math/e) ;=> 2.718281828459045"
  [])

(defn tau
  "Returns tau (2*pi).
   (math/tau) ;=> 6.283185307179586"
  [])

;; --- Powers & Roots ---

(defn pow
  "Returns `x` raised to `y`.
   (math/pow 2 10) ;=> 1024.0"
  [x y])

(defn sqrt
  "Returns the square root.
   (math/sqrt 4) ;=> 2.0"
  [x])

(defn exp
  "Returns e^x.
   (math/exp 1) ;=> 2.718281828459045"
  [x])

(defn log
  "Returns the natural logarithm (base e).
   (math/log 2.718281828459045) ;=> 1.0"
  [x])

(defn log2
  "Returns the base-2 logarithm.
   (math/log2 1024) ;=> 10.0"
  [x])

(defn log10
  "Returns the base-10 logarithm.
   (math/log10 1000) ;=> 3.0"
  [x])

;; --- Trigonometry ---

(defn sin
  "Returns the sine (radians).
   (math/sin (/ (math/pi) 2)) ;=> 1.0"
  [x])

(defn cos
  "Returns the cosine (radians).
   (math/cos 0) ;=> 1.0"
  [x])

(defn tan
  "Returns the tangent (radians).
   (math/tan 0) ;=> 0.0"
  [x])

(defn asin
  "Returns the arcsine (radians).
   (math/asin 1) ;=> 1.5707963267948966"
  [x])

(defn acos
  "Returns the arccosine (radians).
   (math/acos 1) ;=> 0.0"
  [x])

(defn atan
  "Returns the arctangent (radians).
   (math/atan 1) ;=> 0.7853981633974483"
  [x])

(defn atan2
  "Returns the two-argument arctangent (radians).
   (math/atan2 1 1) ;=> 0.7853981633974483"
  [y x])

;; --- Hyperbolic ---

(defn sinh
  "Returns the hyperbolic sine."
  [x])

(defn cosh
  "Returns the hyperbolic cosine."
  [x])

(defn tanh
  "Returns the hyperbolic tangent."
  [x])

(defn asinh
  "Returns the inverse hyperbolic sine."
  [x])

(defn acosh
  "Returns the inverse hyperbolic cosine."
  [x])

(defn atanh
  "Returns the inverse hyperbolic tangent."
  [x])

;; --- Rounding ---

(defn ceil
  "Returns the smallest integer >= x (as float).
   (math/ceil 3.2) ;=> 4.0"
  [x])

(defn floor
  "Returns the largest integer <= x (as float).
   (math/floor 3.8) ;=> 3.0"
  [x])

(defn fmod
  "Returns the floating-point remainder of x/y.
   (math/fmod 10.0 3.0) ;=> 1.0"
  [x y])

(defn erf
  "Returns the error function.
   (math/erf 1) ;=> 0.8427007929497149"
  [x])

(defn erfc
  "Returns the complementary error function."
  [x])