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(.module: {#.doc "Common mathematical constants and functions."}
[lux #*])
## [Values]
(do-template [<name> <value> <doc>]
[(def: #export <name>
{#.doc <doc>}
Frac
<value>)]
[e +2.7182818284590452354 "The base of the natural logarithm."]
[pi +3.14159265358979323846 "The ratio of a circle's circumference to its diameter."]
[tau +6.28318530717958647692 "The ratio of a circle's circumference to its radius."]
)
(do-template [<name> <method>]
[(def: #export (<name> input)
(-> Frac Frac)
(<method> input))]
[cos "jvm invokestatic:java.lang.Math:cos:double"]
[sin "jvm invokestatic:java.lang.Math:sin:double"]
[tan "jvm invokestatic:java.lang.Math:tan:double"]
[acos "jvm invokestatic:java.lang.Math:acos:double"]
[asin "jvm invokestatic:java.lang.Math:asin:double"]
[atan "jvm invokestatic:java.lang.Math:atan:double"]
[exp "jvm invokestatic:java.lang.Math:exp:double"]
[log "jvm invokestatic:java.lang.Math:log:double"]
[ceil "jvm invokestatic:java.lang.Math:ceil:double"]
[floor "jvm invokestatic:java.lang.Math:floor:double"]
)
(def: #export (round input)
(-> Frac Frac)
(let [floored (floor input)
diff (f/- floored input)]
(cond (f/> +0.5 diff)
(f/+ +1.0 floored)
(f/< -0.5 diff)
(f/+ -1.0 floored)
## else
floored)))
(def: #export (pow param subject)
(-> Frac Frac Frac)
("jvm invokestatic:java.lang.Math:pow:double,double" subject param))
(def: #export (atan2 param subject)
(-> Frac Frac Frac)
(cond (f/> +0.0 param)
(atan (f// param subject))
(f/< +0.0 param)
(if (f/>= +0.0 subject)
(|> subject (f// param) atan (f/+ pi))
(|> subject (f// param) atan (f/- pi)))
## (f/= +0.0 param)
(cond (f/> +0.0 subject)
(|> pi (f// +2.0))
(f/< +0.0 subject)
(|> pi (f// -2.0))
## (f/= +0.0 subject)
(f// +0.0 +0.0))))
(def: #export (log' base input)
(-> Frac Frac Frac)
(f// (log base)
(log input)))
(def: #export (factorial n)
(-> Nat Nat)
(loop [acc 1
n n]
(if (n/<= 1 n)
acc
(recur (n/* n acc) (dec n)))))
(def: #export (hypotenuse catA catB)
(-> Frac Frac Frac)
(pow +0.5 (f/+ (pow +2.0 catA)
(pow +2.0 catB))))
(do-template [<type> <mod> <gcd> <lcm> <zero> <*> </> <->]
[(def: #export (<gcd> a b)
{#.doc "Greatest Common Divisor."}
(-> <type> <type> <type>)
(case b
<zero> a
_ (<gcd> b (<mod> b a))))
(def: #export (<lcm> a b)
{#.doc "Least Common Multiple."}
(-> <type> <type> <type>)
(case [a b]
(^or [_ <zero>] [<zero> _])
<zero>
_
(|> a (</> (<gcd> a b)) (<*> b))
))]
[Nat n/mod n/gcd n/lcm 0 n/* n// n/-]
[Int i/mod i/gcd i/lcm +0 i/* i// i/-]
)
## Hyperbolic functions
## https://en.wikipedia.org/wiki/Hyperbolic_function#Definitions
(do-template [<name> <comp> <inverse>]
[(def: #export (<name> x)
(-> Frac Frac)
(|> (exp x) (<comp> (exp (f/* -1.0 x))) (f// +2.0)))
(def: #export (<inverse> x)
(-> Frac Frac)
(|> +2.0 (f// (|> (exp x) (<comp> (exp (f/* -1.0 x)))))))]
[sinh f/- csch]
[cosh f/+ sech]
)
(do-template [<name> <top> <bottom>]
[(def: #export (<name> x)
(-> Frac Frac)
(let [e+ (exp x)
e- (exp (f/* -1.0 x))
sinh' (|> e+ (f/- e-))
cosh' (|> e+ (f/+ e-))]
(|> <top> (f// <bottom>))))]
[tanh sinh' cosh']
[coth cosh' sinh']
)
## https://en.wikipedia.org/wiki/Inverse_hyperbolic_functions#Definitions_in_terms_of_logarithms
(do-template [<name> <comp>]
[(def: #export (<name> x)
(-> Frac Frac)
(|> x (pow +2.0) (<comp> +1.0) (pow +0.5) (f/+ x) log))]
[asinh f/+]
[acosh f/-]
)
(do-template [<name> <base> <diff>]
[(def: #export (<name> x)
(-> Frac Frac)
(let [x+ (|> <base> (f/+ <diff>))
x- (|> <base> (f/- <diff>))]
(|> x+ (f// x-) log (f// +2.0))))]
[atanh +1.0 x]
[acoth x +1.0]
)
(do-template [<name> <op>]
[(def: #export (<name> x)
(-> Frac Frac)
(let [x^2 (|> x (pow +2.0))]
(|> +1.0 (<op> x^2) (pow +0.5) (f/+ +1.0) (f// x) log)))]
[asech f/-]
[acsch f/+]
)
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