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(.module:
[library
[lux #*
["_" test (#+ Test)]
[abstract
[monad (#+ do)]
[\\specification
["$." equivalence]
["$." hash]
["$." order]
["$." enum]
["$." interval]
["$." monoid]
["$." codec]]]
[data
["." bit ("#\." equivalence)]]
[math
["." random (#+ Random)]]]]
[\\library
["." /
[//
["n" nat]
["f" frac]
["." i64]]]])
(def: signature
Test
(`` ($_ _.and
(_.for [/.equivalence /.=]
($equivalence.spec /.equivalence random.int))
(_.for [/.hash]
($hash.spec /.hash random.int))
(_.for [/.order /.<]
($order.spec /.order random.int))
(_.for [/.enum]
($enum.spec /.enum random.int))
(_.for [/.interval]
($interval.spec /.interval random.int))
(~~ (template [<compose> <monoid>]
[(_.for [<monoid> <compose>]
($monoid.spec /.equivalence <monoid> random.int))]
[/.+ /.addition]
[/.* /.multiplication]
[/.min /.minimum]
[/.max /.maximum]
))
(~~ (template [<codec>]
[(_.for [<codec>]
($codec.spec /.equivalence <codec> random.int))]
[/.binary] [/.octal] [/.decimal] [/.hex]
))
)))
(def: predicate
Test
(do {! random.monad}
[sample random.int]
($_ _.and
(_.cover [/.negative?]
(bit\= (/.negative? sample)
(/.< +0 sample)))
(_.cover [/.positive?]
(bit\= (/.positive? sample)
(/.> +0 sample)))
(_.cover [/.zero?]
(bit\= (/.zero? sample)
(/.= +0 sample)))
(_.cover [/.even? /.odd?]
(bit\= (/.even? sample)
(not (/.odd? sample))))
)))
(def: #export test
Test
(<| (_.covering /._)
(_.for [.Int])
($_ _.and
(do random.monad
[sample random.int]
($_ _.and
(_.cover [/.-]
(and (/.= +0 (/.- sample sample))
(/.= sample (/.- +0 sample))
(/.= (/.negate sample)
(/.- sample +0))))
(_.cover [/./]
(and (/.= +1 (/./ sample sample))
(/.= sample (/./ +1 sample))))
(_.cover [/.abs]
(bit\= (/.> sample (/.abs sample))
(/.negative? sample)))
(_.cover [/.signum]
(/.= (/.abs sample)
(/.* (/.signum sample) sample)))
))
(do random.monad
[left random.int
right random.int]
($_ _.and
(_.cover [/.>]
(bit\= (/.> left right)
(/.< right left)))
(_.cover [/.<= /.>=]
(bit\= (/.<= left right)
(/.>= right left)))
))
(do random.monad
[left (random.only (|>> (/.= +0) not)
random.int)
right random.int]
($_ _.and
(_.cover [/.%]
(let [rem (/.% left right)
div (|> right (/.- rem) (/./ left))]
(/.= right
(|> div (/.* left) (/.+ rem)))))
(_.cover [/./%]
(let [[div rem] (/./% left right)]
(and (/.= div (/./ left right))
(/.= rem (/.% left right)))))
(_.cover [/.mod]
(and (/.= (/.signum left)
(/.signum (/.mod left right)))
(/.= (/.signum right)
(/.signum (/.% left right)))
(if (/.= (/.signum left) (/.signum right))
(/.= (/.% left right)
(/.mod left right))
(or (and (/.= +0 (/.% left right))
(/.= +0 (/.mod left right)))
(/.= (/.+ left (/.% left right))
(/.mod left right))))))
))
(do {! random.monad}
[#let [random (|> random.int
(\ ! map (/.% +1,000))
(random.only (|>> (/.= +0) not)))]
left random
right random]
($_ _.and
(_.cover [/.gcd]
(let [gcd (/.gcd left right)]
(and (/.= +0 (/.% gcd left))
(/.= +0 (/.% gcd right)))))
(_.cover [/.extended_gcd]
(let [[[left_k right_k] gcd] (/.extended_gcd left right)
same_gcd!
(/.= gcd
(/.gcd left right))
bezout_identity!
(/.= gcd
(/.+ (/.* left_k left)
(/.* right_k right)))]
(and same_gcd!
bezout_identity!)))
(_.cover [/.co_prime?]
(bit\= (/.= +1 (/.gcd left right))
(/.co_prime? left right)))
(_.cover [/.lcm]
(let [lcm (/.lcm left right)]
(and (/.= +0 (/.% left lcm))
(/.= +0 (/.% right lcm)))))
))
(do random.monad
[expected random.int]
(_.cover [/.negate]
(let [subtraction!
(/.= +0 (/.+ (/.negate expected) expected))
inverse!
(|> expected /.negate /.negate (/.= expected))]
(and subtraction!
inverse!))))
(do {! random.monad}
[expected (\ ! map (/.% +1,000,000) random.int)]
(_.cover [/.frac]
(|> expected /.frac f.int (/.= expected))))
(do {! random.monad}
[pattern random.int
idx (\ ! map (n.% i64.width) random.nat)]
(_.cover [/.right_shift]
(let [nullity!
(/.= pattern (/.right_shift 0 pattern))
idempotency!
(/.= pattern (/.right_shift i64.width pattern))
sign_mask (i64.left_shift (dec i64.width) 1)
mantissa_mask (i64.not sign_mask)
sign_preservation!
(/.= (i64.and sign_mask pattern)
(i64.and sign_mask (/.right_shift idx pattern)))
mantissa_parity!
(/.= (i64.and mantissa_mask (i64.right_shift idx pattern))
(i64.and mantissa_mask (/.right_shift idx pattern)))]
(and nullity!
idempotency!
sign_preservation!
mantissa_parity!))))
..predicate
..signature
)))
|
