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|
... This Source Code Form is subject to the terms of the Mozilla Public License, v. 2.0.
... If a copy of the MPL was not distributed with this file, You can obtain one at https://mozilla.org/MPL/2.0/.
(.require
[library
[lux (.except)
["[0]" ffi]
[abstract
[monad (.only do)]
["[0]" hash
["[1]T" \\test]]
["[0]" codec
["[1]T" \\test]]
["[0]" equivalence
["[1]T" \\test]]
["[0]" order
["[1]T" \\test]]
["[0]" monoid
["[1]T" \\test]]]
[data
["[0]" bit (.use "[1]#[0]" equivalence)]]
[math
["[0]" random (.only Random)]
["[0]" arithmetic
["[1]T" \\test]]]
[meta
[macro
["[0]" template]]
[compiler
["@" target]]]
[test
["_" property (.only Test)]]]]
[\\library
["[0]" / (.only)
[// (.except)
["n" nat]
["i" int]
["r" rev]
["[0]" i64]]]])
(def random
(Random Frac)
(of random.monad each (|>> (i.% +1,000,000) i.frac) random.int))
(def constant
Test
(do random.monad
[sample random.safe_frac]
(all _.and
(_.coverage [/.biggest]
(/.<= /.biggest sample))
(_.coverage [/.positive_infinity]
(/.< /.positive_infinity sample))
(_.coverage [/.smallest]
(bit#= (/.positive? sample)
(/.>= /.smallest sample)))
(_.coverage [/.negative_infinity]
(/.> /.negative_infinity sample))
(_.coverage [/.not_a_number /.not_a_number?]
(and (/.not_a_number? /.not_a_number)
(not (or (/.= /.not_a_number sample)
(/.not_a_number? sample)))))
)))
(def predicate
Test
(do [! random.monad]
[sample ..random
shift (of ! each /.abs ..random)]
(all _.and
(_.coverage [/.negative?]
(bit#= (/.negative? sample)
(/.< +0.0 sample)))
(_.coverage [/.positive?]
(bit#= (/.positive? sample)
(/.> +0.0 sample)))
(_.coverage [/.zero?]
(bit#= (/.zero? sample)
(/.= +0.0 sample)))
(_.coverage [/.approximately?]
(and (/.approximately? /.smallest sample sample)
(/.approximately? (/.+ +1.0 shift) sample (/.+ shift sample))))
(_.coverage [/.number?]
(and (not (/.number? /.not_a_number))
(not (/.number? /.positive_infinity))
(not (/.number? /.negative_infinity))
(/.number? sample)))
)))
(def conversion
Test
(all _.and
(do [! random.monad]
[expected (of ! each (n.% 1,000,000) random.nat)]
(_.coverage [/.nat]
(|> expected n.frac /.nat (n.= expected))))
(do [! random.monad]
[expected (of ! each (i.% +1,000,000) random.int)]
(_.coverage [/.int]
(|> expected i.frac /.int (i.= expected))))
(do [! random.monad]
[expected (of ! each (|>> (i64.left_shifted 52) .rev)
random.nat)]
(_.coverage [/.rev]
(|> expected r.frac /.rev (r.= expected))))
))
(def signature
Test
(`` (all _.and
(_.for [/.equivalence /.=]
(equivalenceT.spec /.equivalence random.safe_frac))
(_.for [/.hash]
(hashT.spec /.hash random.frac))
(_.for [/.order /.<]
(orderT.spec /.order random.safe_frac))
(,, (with_template [<composite> <monoid>]
[(_.for [<monoid> <composite>]
(monoidT.spec /.equivalence <monoid> ..random))]
[/.+ /.addition]
[/.* /.multiplication]
[/.min /.minimum]
[/.max /.maximum]
))
(,, (with_template [<codec>]
[(_.for [<codec>]
(codecT.spec /.equivalence <codec> random.safe_frac))]
[/.binary] [/.octal] [/.decimal] [/.hex]
))
(_.for [/.arithmetic]
(arithmeticT.spec /.equivalence /.arithmetic random.safe_frac))
)))
(with_expansions [<jvm> (these (ffi.import java/lang/Double
"[1]::[0]"
("static" doubleToRawLongBits [double] long)
("static" longBitsToDouble [long] double)))]
(for @.old (these <jvm>)
@.jvm (these <jvm>)
(these)))
(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
(all _.and
(do [! random.monad]
[.let [~= (/.approximately? ..margin_of_error)]
angle (|> random.safe_frac (of ! each (/.* /.tau)))]
(all _.and
(_.coverage [/.sin /.asin]
(trigonometric_symmetry /.sin /.asin angle))
(_.coverage [/.cos /.acos]
(trigonometric_symmetry /.cos /.acos angle))
(_.coverage [/.tan /.atan]
(trigonometric_symmetry /.tan /.atan angle))
(_.coverage [/.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))))
(_.coverage [/.pi]
(~= (/./ +2.0 /.tau) /.pi))
))
(do [! random.monad]
[sample (|> random.safe_frac (of ! each (/.* +1000.0)))]
(all _.and
(_.coverage [/.ceil]
(let [ceil'd (/.ceil sample)]
(and (|> ceil'd /.int i.frac (/.= ceil'd))
(/.>= sample ceil'd)
(/.<= +1.0 (/.- sample ceil'd)))))
(_.coverage [/.floor]
(let [floor'd (/.floor sample)]
(and (|> floor'd /.int i.frac (/.= floor'd))
(/.<= sample floor'd)
(/.<= +1.0 (/.- floor'd sample)))))
(_.coverage [/.round]
(let [round'd (/.round sample)]
(and (|> round'd /.int i.frac (/.= round'd))
(/.<= +1.0 (/.abs (/.- sample round'd))))))
(_.coverage [/.root_2]
(let [sample (/.abs sample)]
(|> sample
/.root_2
(/.pow +2.0)
(/.approximately? ..margin_of_error sample))))
(_.coverage [/.root_3]
(|> sample
/.root_3
(/.pow +3.0)
(/.approximately? ..margin_of_error sample)))
))
(do [! random.monad]
[.let [~= (/.approximately? ..margin_of_error)]
sample (of ! each (/.* +10.0) random.safe_frac)
power (of ! each (|>> (n.% 10) ++ n.frac) random.nat)]
(all _.and
(_.coverage [/.exp /.log]
(|> sample /.exp /.log (/.approximately? +0.000000000000001 sample)))
(_.coverage [/.e]
(~= +1.0 (/.log /.e)))
(_.coverage [/.pow /.log_by]
(let [sample (/.abs sample)]
(|> sample
(/.pow power)
(/.log_by sample)
(~= power))))
))
(do [! random.monad]
[.let [~= (/.approximately? ..margin_of_error)]
angle (of ! each (/.* /.tau) random.safe_frac)
sample (of ! each /.abs random.safe_frac)
big (of ! each (/.* +1,000,000,000.00) random.safe_frac)]
(template.let [(odd! <function>)
[(_.coverage [<function>]
(~= (/.opposite (<function> angle))
(<function> (/.opposite angle))))]
(even! <function>)
[(_.coverage [<function>]
(~= (<function> angle)
(<function> (/.opposite angle))))]
(inverse! <left> <right> <input>)
[(_.coverage [<left> <right>]
(~= (<right> <input>)
(<left> (/./ <input> +1.0))))]]
(all _.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 (of ! each (|>> (/.* +10.0) /.abs) random.safe_frac)
y (of ! each (|>> (/.* +10.0) /.abs) random.safe_frac)]
(_.coverage [/.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 (of ! each (/.* tau/4) random.safe_frac)
y (of ! each (/.* tau/4) random.safe_frac)]
(_.coverage [/.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 (of ! each (|>> (n.% 10) ++) random.nat)]
(_.coverage [/.factorial]
(and (n.= 1 (/.factorial 0))
(|> (/.factorial of) (n.% of) (n.= 0)))))
))
(def .public test
Test
(<| (_.covering /._)
(_.for [.Frac .F64 .Double])
(all _.and
(do random.monad
[left random.safe_frac
right random.safe_frac]
(all _.and
(_.coverage [/.>]
(bit#= (/.> left right)
(/.< right left)))
(_.coverage [/.<= /.>=]
(bit#= (/.<= left right)
(/.>= right left)))
))
(do random.monad
[sample random.safe_frac]
(all _.and
(_.coverage [/.-]
(and (/.= +0.0 (/.- sample sample))
(/.= sample (/.- +0.0 sample))
(/.= (/.opposite sample)
(/.- sample +0.0))))
(_.coverage [/./]
(and (/.= +1.0 (/./ sample sample))
(/.= sample (/./ +1.0 sample))))
(_.coverage [/.abs]
(bit#= (/.> sample (/.abs sample))
(/.negative? sample)))
(_.coverage [/.signum]
(/.= (/.abs sample)
(/.* (/.signum sample) sample)))
))
(do random.monad
[left (random.only (|>> (/.= +0.0) not)
..random)
right ..random]
(all _.and
(_.coverage [/.%]
(let [rem (/.% left right)
div (|> right (/.- rem) (/./ left))]
(/.= right
(|> div (/.* left) (/.+ rem)))))
(_.coverage [/./%]
(let [[div rem] (/./% left right)]
(and (/.= div (/./ left right))
(/.= rem (/.% left right)))))
(_.coverage [/.mod]
(or (and (/.= +0.0 (/.% left right))
(/.= +0.0 (/.mod left right)))
(and (/.= (/.signum left)
(/.signum (/.mod left right)))
(/.= (/.signum right)
(/.signum (/.% left right)))
(if (/.= (/.signum left) (/.signum right))
(/.= (/.% left right)
(/.mod left right))
(/.= (/.+ left (/.% left right))
(/.mod left right))))))
))
(with_expansions [<jvm> (all _.and
(let [test (is (-> Frac Bit)
(function (_ value)
(n.= (.nat (ffi.of_long (java/lang/Double::doubleToRawLongBits (ffi.as_double value))))
(/.bits value))))]
(do random.monad
[sample random.frac]
(_.coverage [/.bits]
(and (test sample)
(test /.biggest)
(test /.smallest)
(test /.not_a_number)
(test /.positive_infinity)
(test /.negative_infinity)))))
(do random.monad
[sample random.i64]
(_.coverage [/.of_bits]
(let [expected (ffi.of_double (java/lang/Double::longBitsToDouble (ffi.as_long sample)))
actual (/.of_bits sample)]
(or (/.= expected actual)
(and (/.not_a_number? expected)
(/.not_a_number? actual))))))
)]
(for @.old <jvm>
@.jvm <jvm>
(let [test (is (-> Frac Bit)
(function (_ expected)
(let [actual (|> expected /.bits /.of_bits)]
(or (/.= expected actual)
(and (/.not_a_number? expected)
(/.not_a_number? actual))))))]
(do random.monad
[sample random.frac]
(_.coverage [/.bits /.of_bits]
(and (test sample)
(test /.biggest)
(test /.smallest)
(test /.not_a_number)
(test /.positive_infinity)
(test /.negative_infinity)))))))
(do random.monad
[expected random.safe_frac]
(_.coverage [/.opposite]
(let [subtraction!
(/.= +0.0 (/.+ (/.opposite expected) expected))
inverse!
(|> expected /.opposite /.opposite (/.= expected))]
(and subtraction!
inverse!))))
(do [! random.monad]
[it (of ! each /.abs random.safe_frac)]
(_.coverage [/.degree]
(/.> it
(/.degree it))))
(do [! random.monad]
[it (of ! each /.abs random.safe_frac)]
(_.coverage [/.percentage /.permille /.permyriad]
(and (/.> it
(/.percentage it))
(/.> (/.percentage it)
(/.permille it))
(/.> (/.permille it)
(/.permyriad it)))))
..constant
..predicate
..conversion
..signature
..test|math
)))
|
