diff options
Diffstat (limited to '')
| -rw-r--r-- | stdlib/source/test/lux/data/color.lux | 12 | ||||
| -rw-r--r-- | stdlib/source/test/lux/math.lux | 252 | ||||
| -rw-r--r-- | stdlib/source/test/lux/math/infix.lux | 33 | ||||
| -rw-r--r-- | stdlib/source/test/lux/math/number/complex.lux | 13 | ||||
| -rw-r--r-- | stdlib/source/test/lux/math/number/frac.lux | 145 |
5 files changed, 282 insertions, 173 deletions
diff --git a/stdlib/source/test/lux/data/color.lux b/stdlib/source/test/lux/data/color.lux index 8df8e5813..a8b175c3a 100644 --- a/stdlib/source/test/lux/data/color.lux +++ b/stdlib/source/test/lux/data/color.lux @@ -11,15 +11,13 @@ [data [collection ["[0]" list]]] - [macro - ["[0]" template]] - ["[0]" math + [math ["[0]" random {"+" Random}] [number ["n" nat] - ["[0]" int] ["f" frac] - ["r" rev]]]]] + ["r" rev] + ["[0]" int]]]]] [\\library ["[0]" /]]) @@ -34,11 +32,11 @@ (def: square (-> Frac Frac) - (math.pow +2.0)) + (f.pow +2.0)) (def: square_root (-> Frac Frac) - (math.pow +0.5)) + (f.pow +0.5)) (def: (distance/1 from to) (-> Frac Frac Frac) diff --git a/stdlib/source/test/lux/math.lux b/stdlib/source/test/lux/math.lux index aeadbf093..6b5c9749e 100644 --- a/stdlib/source/test/lux/math.lux +++ b/stdlib/source/test/lux/math.lux @@ -4,6 +4,8 @@ ["_" test {"+" Test}] [abstract [monad {"+" do}]] + [data + ["[0]" bit ("[1]#[0]" equivalence)]] [macro ["[0]" template]] [math @@ -11,7 +13,10 @@ [number ["n" nat] ["i" int] - ["f" frac]]]]] + ["r" rev] + ["f" frac] + ["[0]" ratio {"+" Ratio}] + ["[0]" complex {"+" Complex}]]]]] [\\library ["[0]" /]] ["[0]" / "_" @@ -23,152 +28,117 @@ ["[1]/[0]" continuous] ["[1]/[0]" fuzzy]]]) -(def: margin_of_error - +0.0000001) +(def: ratio/0 + Ratio + [ratio.#numerator 0 ratio.#denominator 1]) -(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: complex/0 + Complex + [complex.#real +0.0 complex.#imaginary +0.0]) (def: .public test Test (<| (_.covering /._) - ($_ _.and - (do [! random.monad] - [.let [~= (f.approximately? ..margin_of_error)] - angle (|> random.safe_frac (# ! each (f.* /.tau)))] - ($_ _.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 (# ! each (f.* +1000.0)))] - ($_ _.and - (_.cover [/.ceil] - (let [ceil'd (/.ceil sample)] - (and (|> ceil'd f.int i.frac (f.= ceil'd)) - (f.>= sample ceil'd) - (f.<= +1.0 (f.- sample ceil'd))))) - (_.cover [/.floor] - (let [floor'd (/.floor sample)] - (and (|> floor'd f.int i.frac (f.= floor'd)) - (f.<= sample floor'd) - (f.<= +1.0 (f.- floor'd sample))))) - (_.cover [/.round] - (let [round'd (/.round sample)] - (and (|> round'd f.int i.frac (f.= round'd)) - (f.<= +1.0 (f.abs (f.- sample round'd)))))) - (_.cover [/.root/2] - (let [sample (f.abs sample)] - (|> sample - /.root/2 - (/.pow +2.0) - (f.approximately? ..margin_of_error sample)))) - (_.cover [/.root/3] - (|> sample - /.root/3 - (/.pow +3.0) - (f.approximately? ..margin_of_error sample))) - )) - (do [! random.monad] - [.let [~= (f.approximately? ..margin_of_error)] - sample (# ! each (f.* +10.0) random.safe_frac) - power (# ! each (|>> (n.% 10) ++ n.frac) random.nat)] - ($_ _.and - (_.cover [/.exp /.log] - (|> sample /.exp /.log (f.approximately? +0.000000000000001 sample))) - (_.cover [/.e] - (~= +1.0 (/.log /.e))) - (_.cover [/.pow /.log_by] - (let [sample (f.abs sample)] - (|> sample - (/.pow power) - (/.log_by sample) - (~= power)))) - )) - (do [! random.monad] - [.let [~= (f.approximately? ..margin_of_error)] - angle (# ! each (f.* /.tau) random.safe_frac) - sample (# ! each f.abs random.safe_frac) - big (# ! each (f.* +1,000,000,000.00) random.safe_frac)] - (template.let [(odd! <function>) - [(_.cover [<function>] - (~= (f.opposite (<function> angle)) - (<function> (f.opposite angle))))] + (do random.monad + [parameterN (random.only (|>> (n.= 0) not) random.nat) + subjectN random.nat - (even! <function>) - [(_.cover [<function>] - (~= (<function> angle) - (<function> (f.opposite angle))))] + parameterI (random.only (|>> (i.= +0) not) random.int) + subjectI random.int - (inverse! <left> <right> <input>) - [(_.cover [<left> <right>] - (~= (<right> <input>) - (<left> (f./ <input> +1.0))))]] - ($_ _.and - (odd! /.sinh) - (even! /.cosh) - (odd! /.tanh) - (odd! /.coth) - (even! /.sech) - (odd! /.csch) + parameterR (random.only (|>> (r.= .0) not) random.rev) + subjectR random.rev - (inverse! /.acosh /.asech sample) - (inverse! /.asinh /.acsch sample) - (inverse! /.atanh /.acoth big) - ))) - (do [! random.monad] - [x (# ! each (|>> (f.* +10.0) f.abs) random.safe_frac) - y (# ! each (|>> (f.* +10.0) f.abs) random.safe_frac)] - (_.cover [/.hypotenuse] - (let [h (/.hypotenuse x y)] - (and (f.>= x h) - (f.>= y h))))) - (do [! random.monad] - [.let [~= (f.approximately? ..margin_of_error) - tau/4 (f./ +4.0 /.tau)] - x (# ! each (f.* tau/4) random.safe_frac) - y (# ! each (f.* tau/4) random.safe_frac)] - (_.cover [/.atan/2] - (let [expected (/.atan/2 x y) - actual (if (f.> +0.0 x) - (/.atan (f./ x y)) - (if (f.< +0.0 y) - (f.- /.pi (/.atan (f./ x y))) - (f.+ /.pi (/.atan (f./ x y)))))] - (and (~= expected actual) - (~= tau/4 (/.atan/2 +0.0 (f.abs y))) - (~= (f.opposite tau/4) (/.atan/2 +0.0 (f.opposite (f.abs y)))) - (f.not_a_number? (/.atan/2 +0.0 +0.0)))))) - (do [! random.monad] - [of (# ! each (|>> (n.% 10) ++) random.nat)] - (_.cover [/.factorial] - (and (n.= 1 (/.factorial 0)) - (|> (/.factorial of) (n.% of) (n.= 0))))) + parameterF (random.only (|>> (f.= +0.0) not) random.safe_frac) + subjectF random.safe_frac - /infix.test - /modulus.test - /modular.test - /number.test - /logic/continuous.test - /logic/fuzzy.test - ))) + parameter/ (random.only (|>> (ratio.= ratio/0) not) random.ratio) + subject/ random.ratio + + parameterC (random.only (|>> (complex.= complex/0) not) random.complex) + subjectC random.complex]) + (`` ($_ _.and + (~~ (template [</> <scenarios>'] + [(_.cover [</>] + (with_expansions [<scenarios> (template.spliced <scenarios>')] + (`` (and (~~ (template [<=> <//> <parameter> <subject>] + [(<=> (<//> <parameter> <subject>) + (</> <parameter> <subject>))] + + <scenarios>))))))] + + [/.+ [[n.= n.+ parameterN subjectN] + [i.= i.+ parameterI subjectI] + [r.= r.+ parameterR subjectR] + [f.= f.+ parameterF subjectF] + [ratio.= ratio.+ parameter/ subject/] + [complex.= complex.+ parameterC subjectC]]] + [/.- [[n.= n.- parameterN subjectN] + [i.= i.- parameterI subjectI] + [r.= r.- parameterR subjectR] + [f.= f.- parameterF subjectF] + [ratio.= ratio.- parameter/ subject/] + [complex.= complex.- parameterC subjectC]]] + [/.* [[n.= n.* parameterN subjectN] + [i.= i.* parameterI subjectI] + [r.= r.* parameterR subjectR] + [f.= f.* parameterF subjectF] + [ratio.= ratio.* parameter/ subject/] + [complex.= complex.* parameterC subjectC]]] + [/./ [[n.= n./ parameterN subjectN] + [i.= i./ parameterI subjectI] + [r.= r./ parameterR subjectR] + [f.= f./ parameterF subjectF] + [ratio.= ratio./ parameter/ subject/] + [complex.= complex./ parameterC subjectC]]] + [/.% [[n.= n.% parameterN subjectN] + [i.= i.% parameterI subjectI] + [r.= r.% parameterR subjectR] + [f.= f.% parameterF subjectF] + [ratio.= ratio.% parameter/ subject/] + [complex.= complex.% parameterC subjectC]]] + )) + (~~ (template [</> <scenarios>'] + [(_.cover [</>] + (with_expansions [<scenarios> (template.spliced <scenarios>')] + (`` (and (~~ (template [<//> <parameter> <subject>] + [(bit#= (<//> <parameter> <subject>) + (</> <parameter> <subject>))] + + <scenarios>))))))] + + [/.= [[n.= parameterN subjectN] + [i.= parameterI subjectI] + [r.= parameterR subjectR] + [f.= parameterF subjectF] + [ratio.= parameter/ subject/] + [complex.= parameterC subjectC]]] + [/.< [[n.< parameterN subjectN] + [i.< parameterI subjectI] + [r.< parameterR subjectR] + [f.< parameterF subjectF] + [ratio.< parameter/ subject/]]] + [/.<= [[n.<= parameterN subjectN] + [i.<= parameterI subjectI] + [r.<= parameterR subjectR] + [f.<= parameterF subjectF] + [ratio.<= parameter/ subject/]]] + [/.> [[n.> parameterN subjectN] + [i.> parameterI subjectI] + [r.> parameterR subjectR] + [f.> parameterF subjectF] + [ratio.> parameter/ subject/]]] + [/.>= [[n.>= parameterN subjectN] + [i.>= parameterI subjectI] + [r.>= parameterR subjectR] + [f.>= parameterF subjectF] + [ratio.>= parameter/ subject/]]] + )) + + /infix.test + /modulus.test + /modular.test + /number.test + /logic/continuous.test + /logic/fuzzy.test + )))) diff --git a/stdlib/source/test/lux/math/infix.lux b/stdlib/source/test/lux/math/infix.lux index f52e6dd5f..709a24b0b 100644 --- a/stdlib/source/test/lux/math/infix.lux +++ b/stdlib/source/test/lux/math/infix.lux @@ -1,19 +1,18 @@ (.using - [library - [lux "*" - ["_" test {"+" Test}] - [abstract - [monad {"+" do}]] - [data - ["[0]" bit ("[1]#[0]" equivalence)]] - [math - ["[0]" random] - [number - ["n" nat] - ["f" frac]]]]] - [\\library - ["[0]" / - ["[0]" //]]]) + [library + [lux "*" + ["_" test {"+" Test}] + [abstract + [monad {"+" do}]] + [data + ["[0]" bit ("[1]#[0]" equivalence)]] + [math + ["[0]" random] + [number + ["n" nat] + ["f" frac]]]]] + [\\library + ["[0]" /]]) (def: .public test Test @@ -30,8 +29,8 @@ (/.infix subject)) unary_functions! - (f.= (//.sin angle) - (/.infix [//.sin angle])) + (f.= (f.sin angle) + (/.infix [f.sin angle])) binary_functions! (n.= (n.gcd parameter subject) diff --git a/stdlib/source/test/lux/math/number/complex.lux b/stdlib/source/test/lux/math/number/complex.lux index 53b8982a2..bfee3adcc 100644 --- a/stdlib/source/test/lux/math/number/complex.lux +++ b/stdlib/source/test/lux/math/number/complex.lux @@ -1,18 +1,15 @@ (.using [library [lux "*" - ["%" data/text/format {"+" format}] ["_" test {"+" Test}] [abstract [monad {"+" do}] [\\specification - ["$[0]" equivalence] - ["$[0]" order] - ["$[0]" codec]]] + ["$[0]" equivalence]]] [data [collection ["[0]" list ("[1]#[0]" functor)]]] - ["[0]" math + [math ["[0]" random {"+" Random}]]]] [\\library ["[0]" / @@ -161,8 +158,8 @@ (let [rem (/.% y x) quotient (|> x (/.- rem) (/./ y)) floored (|> quotient - (revised /.#real math.floor) - (revised /.#imaginary math.floor))] + (revised /.#real f.floor) + (revised /.#imaginary f.floor))] (/.approximately? +0.000000000001 x (|> quotient (/.* y) (/.+ rem))))) @@ -192,7 +189,7 @@ (let [signum_abs (|> x /.signum /.abs)] (or (f.= +0.0 signum_abs) (f.= +1.0 signum_abs) - (f.= (math.pow +0.5 +2.0) signum_abs)))) + (f.= (f.pow +0.5 +2.0) signum_abs)))) (_.cover [/.opposite] (let [own_inverse! (let [there (/.opposite x) diff --git a/stdlib/source/test/lux/math/number/frac.lux b/stdlib/source/test/lux/math/number/frac.lux index f78b23afd..77453c6f2 100644 --- a/stdlib/source/test/lux/math/number/frac.lux +++ b/stdlib/source/test/lux/math/number/frac.lux @@ -14,6 +14,8 @@ ["$[0]" codec]]] [data ["[0]" bit ("[1]#[0]" equivalence)]] + [macro + ["[0]" template]] [math ["[0]" random {"+" Random}]]]] [\\library @@ -126,6 +128,148 @@ @.jvm (as_is <jvm>) (as_is))) +(def: margin_of_error + +0.0000001) + +(def: (trigonometric_symmetry forward backward angle) + (-> (-> Frac Frac) (-> Frac Frac) Frac Bit) + (let [normal (|> angle forward backward)] + (|> normal forward backward (/.approximately? ..margin_of_error normal)))) + +(def: test|math + Test + ($_ _.and + (do [! random.monad] + [.let [~= (/.approximately? ..margin_of_error)] + angle (|> random.safe_frac (# ! each (/.* /.tau)))] + ($_ _.and + (_.cover [/.sin /.asin] + (trigonometric_symmetry /.sin /.asin angle)) + (_.cover [/.cos /.acos] + (trigonometric_symmetry /.cos /.acos angle)) + (_.cover [/.tan /.atan] + (trigonometric_symmetry /.tan /.atan angle)) + (_.cover [/.tau] + (and (and (~= +0.0 (/.sin /.tau)) + (~= +1.0 (/.cos /.tau))) + (and (~= +0.0 (/.sin (/./ +2.0 /.tau))) + (~= -1.0 (/.cos (/./ +2.0 /.tau)))) + (and (~= +1.0 (/.sin (/./ +4.0 /.tau))) + (~= +0.0 (/.cos (/./ +4.0 /.tau)))) + (and (~= -1.0 (/.sin (/.* +3.0 (/./ +4.0 /.tau)))) + (~= +0.0 (/.cos (/.* +3.0 (/./ +4.0 /.tau))))) + (let [x2+y2 (/.+ (/.pow +2.0 (/.sin angle)) + (/.pow +2.0 (/.cos angle)))] + (~= +1.0 x2+y2)))) + (_.cover [/.pi] + (~= (/./ +2.0 /.tau) /.pi)) + )) + (do [! random.monad] + [sample (|> random.safe_frac (# ! each (/.* +1000.0)))] + ($_ _.and + (_.cover [/.ceil] + (let [ceil'd (/.ceil sample)] + (and (|> ceil'd /.int i.frac (/.= ceil'd)) + (/.>= sample ceil'd) + (/.<= +1.0 (/.- sample ceil'd))))) + (_.cover [/.floor] + (let [floor'd (/.floor sample)] + (and (|> floor'd /.int i.frac (/.= floor'd)) + (/.<= sample floor'd) + (/.<= +1.0 (/.- floor'd sample))))) + (_.cover [/.round] + (let [round'd (/.round sample)] + (and (|> round'd /.int i.frac (/.= round'd)) + (/.<= +1.0 (/.abs (/.- sample round'd)))))) + (_.cover [/.root/2] + (let [sample (/.abs sample)] + (|> sample + /.root/2 + (/.pow +2.0) + (/.approximately? ..margin_of_error sample)))) + (_.cover [/.root/3] + (|> sample + /.root/3 + (/.pow +3.0) + (/.approximately? ..margin_of_error sample))) + )) + (do [! random.monad] + [.let [~= (/.approximately? ..margin_of_error)] + sample (# ! each (/.* +10.0) random.safe_frac) + power (# ! each (|>> (n.% 10) ++ n.frac) random.nat)] + ($_ _.and + (_.cover [/.exp /.log] + (|> sample /.exp /.log (/.approximately? +0.000000000000001 sample))) + (_.cover [/.e] + (~= +1.0 (/.log /.e))) + (_.cover [/.pow /.log_by] + (let [sample (/.abs sample)] + (|> sample + (/.pow power) + (/.log_by sample) + (~= power)))) + )) + (do [! random.monad] + [.let [~= (/.approximately? ..margin_of_error)] + angle (# ! each (/.* /.tau) random.safe_frac) + sample (# ! each /.abs random.safe_frac) + big (# ! each (/.* +1,000,000,000.00) random.safe_frac)] + (template.let [(odd! <function>) + [(_.cover [<function>] + (~= (/.opposite (<function> angle)) + (<function> (/.opposite angle))))] + + (even! <function>) + [(_.cover [<function>] + (~= (<function> angle) + (<function> (/.opposite angle))))] + + (inverse! <left> <right> <input>) + [(_.cover [<left> <right>] + (~= (<right> <input>) + (<left> (/./ <input> +1.0))))]] + ($_ _.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 (# ! each (|>> (/.* +10.0) /.abs) random.safe_frac) + y (# ! each (|>> (/.* +10.0) /.abs) random.safe_frac)] + (_.cover [/.hypotenuse] + (let [h (/.hypotenuse x y)] + (and (/.>= x h) + (/.>= y h))))) + (do [! random.monad] + [.let [~= (/.approximately? ..margin_of_error) + tau/4 (/./ +4.0 /.tau)] + x (# ! each (/.* tau/4) random.safe_frac) + y (# ! each (/.* tau/4) random.safe_frac)] + (_.cover [/.atan/2] + (let [expected (/.atan/2 x y) + actual (if (/.> +0.0 x) + (/.atan (/./ x y)) + (if (/.< +0.0 y) + (/.- /.pi (/.atan (/./ x y))) + (/.+ /.pi (/.atan (/./ x y)))))] + (and (~= expected actual) + (~= tau/4 (/.atan/2 +0.0 (/.abs y))) + (~= (/.opposite tau/4) (/.atan/2 +0.0 (/.opposite (/.abs y)))) + (/.not_a_number? (/.atan/2 +0.0 +0.0)))))) + (do [! random.monad] + [of (# ! each (|>> (n.% 10) ++) random.nat)] + (_.cover [/.factorial] + (and (n.= 1 (/.factorial 0)) + (|> (/.factorial of) (n.% of) (n.= 0))))) + )) + (def: .public test Test (<| (_.covering /._) @@ -242,4 +386,5 @@ ..predicate ..conversion ..signature + ..test|math ))) |