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|
(.module: {#.doc "Common mathematical constants and functions."}
[library
[lux #*
["@" target]
[math
[number
["n" nat]
["i" int]]]]])
(template [<name> <value> <doc>]
[(def: .public <name>
{#.doc <doc>}
<value>)]
[e +2.7182818284590452354 "The base of the natural logarithm."]
... ["π is wrong!" by Bob Palais](https://www.math.utah.edu/~palais/pi.html)
[pi +3.14159265358979323846 "The ratio of a circle's circumference to its diameter."]
... [The Tau Manifesto](https://tauday.com/tau-manifesto)
[tau +6.28318530717958647692 "The ratio of a circle's circumference to its radius."]
)
(for {@.old
(as_is (template [<name> <method>]
[(def: .public (<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"]
[root/2 "jvm invokestatic:java.lang.Math:sqrt:double"]
[root/3 "jvm invokestatic:java.lang.Math:cbrt:double"]
)
(def: .public (pow param subject)
(-> Frac Frac Frac)
("jvm invokestatic:java.lang.Math:pow:double,double" subject param)))
@.jvm
(as_is (template: (!double value)
[(|> value
(:as (primitive "java.lang.Double"))
"jvm object cast")])
(template: (!frac value)
[(|> value
"jvm object cast"
(: (primitive "java.lang.Double"))
(:as Frac))])
(template [<name> <method>]
[(def: .public <name>
(-> Frac Frac)
(|>> !double
["D"]
("jvm member invoke static" [] "java.lang.Math" <method> [])
!frac))]
[cos "cos"]
[sin "sin"]
[tan "tan"]
[acos "acos"]
[asin "asin"]
[atan "atan"]
[exp "exp"]
[log "log"]
[ceil "ceil"]
[floor "floor"]
[root/2 "sqrt"]
[root/3 "cbrt"]
)
(def: .public (pow param subject)
(-> Frac Frac Frac)
(|> ("jvm member invoke static" [] "java.lang.Math" "pow" []
["D" (!double subject)] ["D" (!double param)])
!frac)))
@.js
(as_is (template [<name> <method>]
[(def: .public <name>
(-> Frac Frac)
(|>> ("js apply" ("js constant" <method>))
(:as Frac)))]
[cos "Math.cos"]
[sin "Math.sin"]
[tan "Math.tan"]
[acos "Math.acos"]
[asin "Math.asin"]
[atan "Math.atan"]
[exp "Math.exp"]
[log "Math.log"]
[ceil "Math.ceil"]
[floor "Math.floor"]
[root/2 "Math.sqrt"]
[root/3 "Math.cbrt"]
)
(def: .public (pow param subject)
(-> Frac Frac Frac)
(:as Frac ("js apply" ("js constant" "Math.pow") subject param))))
@.python
(as_is (template [<name> <method>]
[(def: .public <name>
(-> Frac Frac)
(|>> ("python object do" <method> ("python import" "math"))
(:as Frac)))]
[cos "cos"]
[sin "sin"]
[tan "tan"]
[acos "acos"]
[asin "asin"]
[atan "atan"]
[exp "exp"]
[log "log"]
[ceil "ceil"]
[floor "floor"]
[root/2 "sqrt"]
)
(def: .public (pow param subject)
(-> Frac Frac Frac)
(:as Frac ("python object do" "pow" ("python import" "math") subject param)))
(def: .public root/3
(-> Frac Frac)
(..pow ("lux f64 /" +3.0 +1.0))))
@.lua
(as_is (template [<name> <method>]
[(def: .public <name>
(-> Frac Frac)
(|>> ("lua apply" ("lua constant" <method>))
(:as Frac)))]
[cos "math.cos"]
[sin "math.sin"]
[tan "math.tan"]
[acos "math.acos"]
[asin "math.asin"]
[atan "math.atan"]
[exp "math.exp"]
[log "math.log"]
[ceil "math.ceil"]
[floor "math.floor"]
[root/2 "math.sqrt"]
)
(def: .public (pow param subject)
(-> Frac Frac Frac)
("lua power" param subject))
(def: .public root/3
(-> Frac Frac)
(..pow ("lux f64 /" +3.0 +1.0))))
@.ruby
(as_is (template [<name> <method>]
[(def: .public <name>
(-> Frac Frac)
(|>> ("ruby apply" ("ruby constant" <method>))
(:as Frac)))]
[cos "Math.cos"]
[sin "Math.sin"]
[tan "Math.tan"]
[acos "Math.acos"]
[asin "Math.asin"]
[atan "Math.atan"]
[exp "Math.exp"]
[log "Math.log"]
[root/2 "Math.sqrt"]
[root/3 "Math.cbrt"]
)
(template [<name> <method>]
[(def: .public <name>
(-> Frac Frac)
(|>> ("ruby object do" <method>)
(:as Int)
("lux i64 f64")))]
[ceil "ceil"]
[floor "floor"]
)
(def: .public (pow param subject)
(-> Frac Frac Frac)
(:as Frac ("ruby object do" "**" subject param))))
@.php
(as_is (template [<name> <method>]
[(def: .public <name>
(-> Frac Frac)
(|>> ("php apply" ("php constant" <method>))
(:as Frac)))]
[cos "cos"]
[sin "sin"]
[tan "tan"]
[acos "acos"]
[asin "asin"]
[atan "atan"]
[exp "exp"]
[log "log"]
[ceil "ceil"]
[floor "floor"]
[root/2 "sqrt"]
)
(def: .public (pow param subject)
(-> Frac Frac Frac)
(:as Frac ("php apply" ("php constant" "pow") subject param)))
(def: .public root/3
(-> Frac Frac)
(..pow ("lux f64 /" +3.0 +1.0))))
@.scheme
(as_is (template [<name> <method>]
[(def: .public <name>
(-> Frac Frac)
(|>> ("scheme apply" ("scheme constant" <method>))
(:as Frac)))]
[cos "cos"]
[sin "sin"]
[tan "tan"]
[acos "acos"]
[asin "asin"]
[atan "atan"]
[exp "exp"]
[log "log"]
[ceil "ceiling"]
[floor "floor"]
[root/2 "sqrt"]
)
(def: .public (pow param subject)
(-> Frac Frac Frac)
(:as Frac ("scheme apply" ("scheme constant" "expt") subject param)))
(def: .public root/3
(-> Frac Frac)
(..pow ("lux f64 /" +3.0 +1.0))))
})
(def: .public (round input)
(-> Frac Frac)
(let [floored (floor input)
diff ("lux f64 -" floored input)]
(cond ("lux f64 <" diff +0.5)
("lux f64 +" +1.0 floored)
("lux f64 <" -0.5 diff)
("lux f64 +" -1.0 floored)
... else
floored)))
(def: .public (atan/2 x y)
(-> Frac Frac Frac)
(cond ("lux f64 <" x +0.0)
(..atan ("lux f64 /" x y))
("lux f64 <" +0.0 x)
(if (or ("lux f64 <" y +0.0)
("lux f64 =" +0.0 y))
(|> y ("lux f64 /" x) atan ("lux f64 +" pi))
(|> y ("lux f64 /" x) atan ("lux f64 -" pi)))
... ("lux f64 =" +0.0 x)
(cond ("lux f64 <" y +0.0)
(|> pi ("lux f64 /" +2.0))
("lux f64 <" +0.0 y)
(|> pi ("lux f64 /" -2.0))
... ("lux f64 =" +0.0 y)
("lux f64 /" +0.0 +0.0))))
(def: .public (log' base input)
(-> Frac Frac Frac)
("lux f64 /"
(..log base)
(..log input)))
(def: .public (factorial n)
(-> Nat Nat)
(loop [acc 1
n n]
(if (n.<= 1 n)
acc
(recur (n.* n acc) (-- n)))))
(def: .public (hypotenuse catA catB)
(-> Frac Frac Frac)
(..pow +0.5 ("lux f64 +"
(..pow +2.0 catA)
(..pow +2.0 catB))))
... Hyperbolic functions
... https://en.wikipedia.org/wiki/Hyperbolic_function#Definitions
(template [<name> <comp> <inverse>]
[(def: .public (<name> x)
(-> Frac Frac)
(|> (..exp x) (<comp> (..exp ("lux f64 *" -1.0 x))) ("lux f64 /" +2.0)))
(def: .public (<inverse> x)
(-> Frac Frac)
(|> +2.0 ("lux f64 /" (|> (..exp x) (<comp> (..exp ("lux f64 *" -1.0 x)))))))]
[sinh "lux f64 -" csch]
[cosh "lux f64 +" sech]
)
(template [<name> <top> <bottom>]
[(def: .public (<name> x)
(-> Frac Frac)
(let [e+ (exp x)
e- (exp ("lux f64 *" -1.0 x))
sinh' (|> e+ ("lux f64 -" e-))
cosh' (|> e+ ("lux f64 +" e-))]
(|> <top> ("lux f64 /" <bottom>))))]
[tanh sinh' cosh']
[coth cosh' sinh']
)
... https://en.wikipedia.org/wiki/Inverse_hyperbolic_functions#Definitions_in_terms_of_logarithms
(template [<name> <comp>]
[(def: .public (<name> x)
(-> Frac Frac)
(|> x (pow +2.0) (<comp> +1.0) (pow +0.5) ("lux f64 +" x) log))]
[asinh "lux f64 +"]
[acosh "lux f64 -"]
)
(template [<name> <base> <diff>]
[(def: .public (<name> x)
(-> Frac Frac)
(let [x+ (|> <base> ("lux f64 +" <diff>))
x- (|> <base> ("lux f64 -" <diff>))]
(|> x+ ("lux f64 /" x-) log ("lux f64 /" +2.0))))]
[atanh +1.0 x]
[acoth x +1.0]
)
(template [<name> <op>]
[(def: .public (<name> x)
(-> Frac Frac)
(let [x^2 (|> x (pow +2.0))]
(|> +1.0 (<op> x^2) (pow +0.5) ("lux f64 +" +1.0) ("lux f64 /" x) log)))]
[asech "lux f64 -"]
[acsch "lux f64 +"]
)
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