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|
(.require
[library
[lux (.except)
["_" test (.only Test)]
[abstract
[monad (.only do)]
[\\specification
["$[0]" equivalence]
["$[0]" hash]
["$[0]" order]
["$[0]" enum]
["$[0]" interval]
["$[0]" monoid]
["$[0]" codec]]]
[data
["[0]" bit (.use "[1]#[0]" equivalence)]]
[math
["[0]" random (.only Random)]]]]
[\\library
["[0]" / (.only)
[//
["n" nat]
["f" frac]
["[0]" i64]]]])
(def signature
Test
(`` (all _.and
(_.for [/.equivalence /.=]
($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))
(,, (with_template [<monoid>]
[(_.for [<monoid>]
($monoid.spec /.equivalence <monoid> random.int))]
[/.addition]
[/.multiplication]
[/.minimum]
[/.maximum]
))
(,, (with_template [<codec>]
[(_.for [<codec>]
($codec.spec /.equivalence <codec> random.int))]
[/.binary] [/.octal] [/.decimal] [/.hex]
))
)))
(def predicate
Test
(do [! random.monad]
[sample random.int]
(all _.and
(_.coverage [/.negative?]
(bit#= (/.negative? sample)
(/.< +0 sample)))
(_.coverage [/.positive?]
(bit#= (/.positive? sample)
(/.> +0 sample)))
(_.coverage [/.zero?]
(bit#= (/.zero? sample)
(/.= +0 sample)))
(_.coverage [/.even? /.odd?]
(bit#= (/.even? sample)
(not (/.odd? sample))))
)))
(def .public test
Test
(<| (_.covering /._)
(_.for [.Int])
(let [(open "/#[0]") /.interval])
(all _.and
(do random.monad
[sample random.int
left random.int
right random.int]
(all _.and
(_.coverage [/.+]
(and (/.= (/.+ left right)
(/.+ right left))
(/.= sample (/.+ +0 sample))))
(_.coverage [/.-]
(and (/.= +0 (/.- sample sample))
(/.= sample (/.- +0 sample))
(/.= (/.opposite sample)
(/.- sample +0))
(/.= /#bottom
(/.- /#bottom +0))))
(_.coverage [/.*]
(and (/.= (/.* left right)
(/.* right left))
(/.= sample (/.* +1 sample))
(/.= /#bottom
(/.* -1 /#bottom))))
(_.coverage [/./]
(and (/.= +1 (/./ sample sample))
(/.= sample (/./ +1 sample))
(/.= /#bottom
(/./ -1 /#bottom))))
(_.coverage [/.abs]
(bit#= (/.> sample (/.abs sample))
(/.negative? sample)))
(_.coverage [/.signum]
(/.= (/.abs sample)
(/.* (/.signum sample) sample)))
(_.coverage [/.min]
(and (/.= (/.min left right)
(/.min right left))
(/.= sample
(/.min /#top sample))
(/.= /#bottom
(/.min /#bottom sample))))
(_.coverage [/.max]
(and (/.= (/.max left right)
(/.max right left))
(/.= /#top
(/.max /#top sample))
(/.= sample
(/.max /#bottom sample))))
))
(do random.monad
[left random.int
right random.int]
(all _.and
(_.coverage [/.>]
(bit#= (/.> left right)
(/.< right left)))
(_.coverage [/.<= /.>=]
(bit#= (/.<= left right)
(/.>= right left)))
))
(do random.monad
[left (random.only (|>> (/.= +0) not)
random.int)
right random.int]
(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]
(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
(at ! each (/.% +1,000))
(random.only (|>> (/.= +0) not)))]
left random
right random]
(all _.and
(_.coverage [/.gcd]
(let [gcd (/.gcd left right)]
(and (/.= +0 (/.% gcd left))
(/.= +0 (/.% gcd right)))))
(_.coverage [/.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!)))
(_.coverage [/.co_prime?]
(bit#= (/.= +1 (/.gcd left right))
(/.co_prime? left right)))
(_.coverage [/.lcm]
(let [lcm (/.lcm left right)]
(and (/.= +0 (/.% left lcm))
(/.= +0 (/.% right lcm)))))
))
(do random.monad
[expected random.int]
(_.coverage [/.opposite]
(let [subtraction!
(/.= +0 (/.+ (/.opposite expected) expected))
inverse!
(|> expected /.opposite /.opposite (/.= expected))]
(and subtraction!
inverse!))))
(do [! random.monad]
[expected (at ! each (/.% +1,000,000) random.int)
sample random.int]
(_.coverage [/.frac]
(and (|> expected /.frac f.int (/.= expected))
(f.number? (/.frac sample)))))
(do [! random.monad]
[pattern random.int
idx (at ! each (n.% i64.width) random.nat)]
(_.coverage [/.right_shifted]
(let [nullity!
(/.= pattern (/.right_shifted 0 pattern))
idempotency!
(/.= pattern (/.right_shifted i64.width pattern))
sign_mask (i64.left_shifted (-- i64.width) 1)
mantissa_mask (-- (i64.left_shifted (n.- idx i64.width) 1))
co_mantissa_mask (i64.not mantissa_mask)
sign_preservation!
(/.= (i64.and sign_mask pattern)
(i64.and sign_mask (/.right_shifted idx pattern)))
mantissa_parity!
(/.= (i64.and mantissa_mask (i64.right_shifted idx pattern))
(i64.and mantissa_mask (/.right_shifted idx pattern)))
co_mantissa_disparity!
(or (n.= 0 idx)
(and (/.= +0 (i64.and co_mantissa_mask (i64.right_shifted idx pattern)))
(/.= (if (/.< +0 pattern)
(.int co_mantissa_mask)
+0)
(i64.and co_mantissa_mask (/.right_shifted idx pattern)))))]
(and nullity!
idempotency!
sign_preservation!
mantissa_parity!
co_mantissa_disparity!
))))
..predicate
..signature
)))
|
