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(.module:
[library
[lux #*
["_" test (#+ Test)]
[abstract
[monad (#+ do)]]
[macro
["." template]]
[math
["." random (#+ Random)]
[number
["n" nat]
["i" int]
["f" frac]]]]]
[\\library
["." /]]
["." / #_
["#." infix]
["#." modulus]
["#." modular]
["#." number]
["#." logic #_
["#/." continuous]
["#/." fuzzy]]])
(def: margin_of_error
+0.0000001)
(def: (trigonometric_symmetry forward backward angle)
(-> (-> Frac Frac) (-> Frac Frac) Frac Bit)
(let [normal (|> angle forward backward)]
(|> normal forward backward (f.approximately? ..margin_of_error normal))))
(def: #export test
Test
(<| (_.covering /._)
($_ _.and
(do {! random.monad}
[#let [~= (f.approximately? ..margin_of_error)]
angle (|> random.safe_frac (\ ! map (f.* /.tau)))]
($_ _.and
(_.cover [/.sin /.asin]
(trigonometric_symmetry /.sin /.asin angle))
(_.cover [/.cos /.acos]
(trigonometric_symmetry /.cos /.acos angle))
(_.cover [/.tan /.atan]
(trigonometric_symmetry /.tan /.atan angle))
(_.cover [/.tau]
(and (and (~= +0.0 (/.sin /.tau))
(~= +1.0 (/.cos /.tau)))
(and (~= +0.0 (/.sin (f./ +2.0 /.tau)))
(~= -1.0 (/.cos (f./ +2.0 /.tau))))
(and (~= +1.0 (/.sin (f./ +4.0 /.tau)))
(~= +0.0 (/.cos (f./ +4.0 /.tau))))
(and (~= -1.0 (/.sin (f.* +3.0 (f./ +4.0 /.tau))))
(~= +0.0 (/.cos (f.* +3.0 (f./ +4.0 /.tau)))))
(let [x2+y2 (f.+ (/.pow +2.0 (/.sin angle))
(/.pow +2.0 (/.cos angle)))]
(~= +1.0 x2+y2))))
(_.cover [/.pi]
(~= (f./ +2.0 /.tau) /.pi))
))
(do {! random.monad}
[sample (|> random.safe_frac (\ ! map (f.* +1000.0)))]
($_ _.and
(_.cover [/.ceil]
(let [ceil'd (/.ceil sample)]
(and (|> ceil'd f.int i.frac (f.= ceil'd))
(f.>= sample ceil'd)
(f.<= +1.0 (f.- sample ceil'd)))))
(_.cover [/.floor]
(let [floor'd (/.floor sample)]
(and (|> floor'd f.int i.frac (f.= floor'd))
(f.<= sample floor'd)
(f.<= +1.0 (f.- floor'd sample)))))
(_.cover [/.round]
(let [round'd (/.round sample)]
(and (|> round'd f.int i.frac (f.= round'd))
(f.<= +1.0 (f.abs (f.- sample round'd))))))
(_.cover [/.root/2]
(let [sample (f.abs sample)]
(|> sample
/.root/2
(/.pow +2.0)
(f.approximately? ..margin_of_error sample))))
(_.cover [/.root/3]
(|> sample
/.root/3
(/.pow +3.0)
(f.approximately? ..margin_of_error sample)))
))
(do {! random.monad}
[#let [~= (f.approximately? ..margin_of_error)]
sample (\ ! map (f.* +10.0) random.safe_frac)
power (\ ! map (|>> (n.% 10) inc n.frac) random.nat)]
($_ _.and
(_.cover [/.exp /.log]
(|> sample /.exp /.log (f.approximately? +0.000000000000001 sample)))
(_.cover [/.e]
(~= +1.0 (/.log /.e)))
(_.cover [/.pow /.log']
(let [sample (f.abs sample)]
(|> sample
(/.pow power)
(/.log' sample)
(~= power))))
))
(do {! random.monad}
[#let [~= (f.approximately? ..margin_of_error)]
angle (\ ! map (f.* /.tau) random.safe_frac)
sample (\ ! map f.abs random.safe_frac)
big (\ ! map (f.* +1,000,000,000.00) random.safe_frac)]
(template.let [(odd! <function>)
[(_.cover [<function>]
(~= (f.negate (<function> angle))
(<function> (f.negate angle))))]
(even! <function>)
[(_.cover [<function>]
(~= (<function> angle)
(<function> (f.negate angle))))]
(inverse! <left> <right> <input>)
[(_.cover [<left> <right>]
(~= (<right> <input>)
(<left> (f./ <input> +1.0))))]]
($_ _.and
(odd! /.sinh)
(even! /.cosh)
(odd! /.tanh)
(odd! /.coth)
(even! /.sech)
(odd! /.csch)
(inverse! /.acosh /.asech sample)
(inverse! /.asinh /.acsch sample)
(inverse! /.atanh /.acoth big)
)))
(do {! random.monad}
[x (\ ! map (|>> (f.* +10.0) f.abs) random.safe_frac)
y (\ ! map (|>> (f.* +10.0) f.abs) random.safe_frac)]
(_.cover [/.hypotenuse]
(let [h (/.hypotenuse x y)]
(and (f.>= x h)
(f.>= y h)))))
(do {! random.monad}
[#let [~= (f.approximately? ..margin_of_error)
tau/4 (f./ +4.0 /.tau)]
x (\ ! map (f.* tau/4) random.safe_frac)
y (\ ! map (f.* tau/4) random.safe_frac)]
(_.cover [/.atan/2]
(let [expected (/.atan/2 x y)
actual (if (f.> +0.0 x)
(/.atan (f./ x y))
(if (f.< +0.0 y)
(f.- /.pi (/.atan (f./ x y)))
(f.+ /.pi (/.atan (f./ x y)))))]
(and (~= expected actual)
(~= tau/4 (/.atan/2 +0.0 (f.abs y)))
(~= (f.negate tau/4) (/.atan/2 +0.0 (f.negate (f.abs y))))
(f.not_a_number? (/.atan/2 +0.0 +0.0))))))
(do {! random.monad}
[of (\ ! map (|>> (n.% 10) inc) random.nat)]
(_.cover [/.factorial]
(and (n.= 1 (/.factorial 0))
(|> (/.factorial of) (n.% of) (n.= 0)))))
/infix.test
/modulus.test
/modular.test
/number.test
/logic/continuous.test
/logic/fuzzy.test
)))
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