diff options
Diffstat (limited to 'stdlib/source/test/lux/math')
| -rw-r--r-- | stdlib/source/test/lux/math/logic/continuous.lux | 186 | ||||
| -rw-r--r-- | stdlib/source/test/lux/math/logic/fuzzy.lux | 454 | ||||
| -rw-r--r-- | stdlib/source/test/lux/math/modular.lux | 148 | ||||
| -rw-r--r-- | stdlib/source/test/lux/math/modulus.lux | 88 | ||||
| -rw-r--r-- | stdlib/source/test/lux/math/number.lux | 188 | ||||
| -rw-r--r-- | stdlib/source/test/lux/math/number/complex.lux | 336 | ||||
| -rw-r--r-- | stdlib/source/test/lux/math/number/frac.lux | 616 | ||||
| -rw-r--r-- | stdlib/source/test/lux/math/number/i16.lux | 44 | ||||
| -rw-r--r-- | stdlib/source/test/lux/math/number/i32.lux | 44 | ||||
| -rw-r--r-- | stdlib/source/test/lux/math/number/i64.lux | 368 | ||||
| -rw-r--r-- | stdlib/source/test/lux/math/number/i8.lux | 44 | ||||
| -rw-r--r-- | stdlib/source/test/lux/math/number/int.lux | 410 | ||||
| -rw-r--r-- | stdlib/source/test/lux/math/number/nat.lux | 230 | ||||
| -rw-r--r-- | stdlib/source/test/lux/math/number/ratio.lux | 166 | ||||
| -rw-r--r-- | stdlib/source/test/lux/math/number/rev.lux | 304 |
15 files changed, 1813 insertions, 1813 deletions
diff --git a/stdlib/source/test/lux/math/logic/continuous.lux b/stdlib/source/test/lux/math/logic/continuous.lux index 6b313d6a8..b4d9993d5 100644 --- a/stdlib/source/test/lux/math/logic/continuous.lux +++ b/stdlib/source/test/lux/math/logic/continuous.lux @@ -1,17 +1,17 @@ (.using - [library - [lux "*" - ["_" test {"+" Test}] - [abstract - [monad {"+" do}] - [\\specification - ["$[0]" monoid]]] - [math - ["[0]" random] - [number - ["r" rev]]]]] - [\\library - ["[0]" /]]) + [library + [lux "*" + ["_" test {"+" Test}] + [abstract + [monad {"+" do}] + [\\specification + ["$[0]" monoid]]] + [math + ["[0]" random] + [number + ["r" rev]]]]] + [\\library + ["[0]" /]]) (def: .public test Test @@ -20,96 +20,96 @@ [left random.rev mid random.rev right random.rev] - (`` ($_ _.and - (~~ (template [<monoid>] - [(_.for [<monoid>] - ($monoid.spec r.= <monoid> random.rev))] - - [/.disjunction] - [/.conjunction] - )) - - (_.cover [/.true /.false] - (let [true=max! - (r.= /.false (++ /.true)) + (`` (all _.and + (~~ (template [<monoid>] + [(_.for [<monoid>] + ($monoid.spec r.= <monoid> random.rev))] + + [/.disjunction] + [/.conjunction] + )) + + (_.cover [/.true /.false] + (let [true=max! + (r.= /.false (++ /.true)) - false=min! - (r.= /.true (-- /.false))] - (and true=max! - false=min!))) - (_.cover [/.or] - (let [identity! - (r.= left (/.or /.false left)) + false=min! + (r.= /.true (-- /.false))] + (and true=max! + false=min!))) + (_.cover [/.or] + (let [identity! + (r.= left (/.or /.false left)) - annihilation! - (r.= /.true (/.or /.true left)) - - idempotence! - (r.= left (/.or left left)) - - associativity! - (r.= ($_ /.or left mid right) - (_$ /.or left mid right))] - (and identity! annihilation! + (r.= /.true (/.or /.true left)) + idempotence! - associativity! - (let [l|r (/.or left right)] - (and (r.>= left l|r) - (r.>= right l|r)))))) - (_.cover [/.and] - (let [identity! - (r.= left (/.and /.true left)) + (r.= left (/.or left left)) - annihilation! - (r.= /.false (/.and /.false left)) - - idempotence! - (r.= left (/.and left left)) + associativity! + (r.= (all /.or left mid right) + (.left /.or left mid right))] + (and identity! + annihilation! + idempotence! + associativity! + (let [l|r (/.or left right)] + (and (r.>= left l|r) + (r.>= right l|r)))))) + (_.cover [/.and] + (let [identity! + (r.= left (/.and /.true left)) - associativity! - (r.= ($_ /.and left mid right) - (_$ /.and left mid right))] - (and identity! annihilation! + (r.= /.false (/.and /.false left)) + idempotence! - associativity! - (let [l&r (/.and left right)] - (and (r.<= left l&r) - (r.<= right l&r)))))) - (_.cover [/.not] - (let [inverses! - (and (r.= /.false (/.not /.true)) - (r.= /.true (/.not /.false))) + (r.= left (/.and left left)) - double_negation! - (r.= left (/.not (/.not left))) + associativity! + (r.= (all /.and left mid right) + (.left /.and left mid right))] + (and identity! + annihilation! + idempotence! + associativity! + (let [l&r (/.and left right)] + (and (r.<= left l&r) + (r.<= right l&r)))))) + (_.cover [/.not] + (let [inverses! + (and (r.= /.false (/.not /.true)) + (r.= /.true (/.not /.false))) - de_morgan! - (and (r.= (/.not (/.or left right)) - (/.and (/.not left) (/.not right))) - (r.= (/.not (/.and left right)) - (/.or (/.not left) (/.not right))))] - (and inverses! double_negation! - de_morgan!))) - (_.cover [/.implies] - (let [modus_tollens! - (r.= (/.implies right left) - (/.implies (/.not left) (/.not right)))] - (and modus_tollens!))) - (_.cover [/.=] - (let [trivial! - (and (r.= /.true (/.= /.true /.true)) - (r.= /.true (/.= /.false /.false)) + (r.= left (/.not (/.not left))) + + de_morgan! + (and (r.= (/.not (/.or left right)) + (/.and (/.not left) (/.not right))) + (r.= (/.not (/.and left right)) + (/.or (/.not left) (/.not right))))] + (and inverses! + double_negation! + de_morgan!))) + (_.cover [/.implies] + (let [modus_tollens! + (r.= (/.implies right left) + (/.implies (/.not left) (/.not right)))] + (and modus_tollens!))) + (_.cover [/.=] + (let [trivial! + (and (r.= /.true (/.= /.true /.true)) + (r.= /.true (/.= /.false /.false)) - (r.= /.false (/.= /.true /.false))) + (r.= /.false (/.= /.true /.false))) - common! - (and (r.>= left - (/.= left left)) - (r.>= right - (/.= right right)))] - (and trivial! - common!))) - ))))) + common! + (and (r.>= left + (/.= left left)) + (r.>= right + (/.= right right)))] + (and trivial! + common!))) + ))))) diff --git a/stdlib/source/test/lux/math/logic/fuzzy.lux b/stdlib/source/test/lux/math/logic/fuzzy.lux index a79d72805..d954d22e7 100644 --- a/stdlib/source/test/lux/math/logic/fuzzy.lux +++ b/stdlib/source/test/lux/math/logic/fuzzy.lux @@ -27,12 +27,12 @@ Test (do random.monad [sample random.rev] - ($_ _.and - (_.cover [/.empty] - (r.= //.false (/.empty sample))) - (_.cover [/.full] - (r.= //.true (/.full sample))) - ))) + (all _.and + (_.cover [/.empty] + (r.= //.false (/.empty sample))) + (_.cover [/.full] + (r.= //.true (/.full sample))) + ))) (def: simple Test @@ -46,40 +46,40 @@ .let [bottom (r.min threshold_0 threshold_1) top (r.max threshold_0 threshold_1)]] - ($_ _.and - (_.cover [/.gradient] - (let [ascending! - (let [set (/.gradient bottom top)] - (and (r.= //.false (set bottom)) - (r.= //.true (set top)) - (let [membership (set sample)] - (cond (r.<= bottom sample) - (r.= //.false membership) - - (r.>= top sample) - (r.= //.true membership) - - (r.> //.false membership))))) - - descending! - (let [set (/.gradient top bottom)] - (and (r.= //.true (set bottom)) - (r.= //.false (set top)) - (let [membership (set sample)] - (cond (r.<= bottom sample) - (r.= //.true membership) - - (r.>= top sample) - (r.= //.false membership) - - (r.> //.false membership)))))] - (and ascending! - descending!))) - (_.cover [/.membership] - (let [set (/.gradient bottom top)] - (r.= (set sample) - (/.membership set sample)))) - ))) + (all _.and + (_.cover [/.gradient] + (let [ascending! + (let [set (/.gradient bottom top)] + (and (r.= //.false (set bottom)) + (r.= //.true (set top)) + (let [membership (set sample)] + (cond (r.<= bottom sample) + (r.= //.false membership) + + (r.>= top sample) + (r.= //.true membership) + + (r.> //.false membership))))) + + descending! + (let [set (/.gradient top bottom)] + (and (r.= //.true (set bottom)) + (r.= //.false (set top)) + (let [membership (set sample)] + (cond (r.<= bottom sample) + (r.= //.true membership) + + (r.>= top sample) + (r.= //.false membership) + + (r.> //.false membership)))))] + (and ascending! + descending!))) + (_.cover [/.membership] + (let [set (/.gradient bottom top)] + (r.= (set sample) + (/.membership set sample)))) + ))) (def: composition Test @@ -100,68 +100,68 @@ .let [bottom_set (/.gradient bottom middle_bottom) top_set (/.gradient middle_top top)]] - ($_ _.and - (_.cover [/.union] - (let [set (/.gradient bottom top)] - (and (r.= (/.membership set sample) - (/.membership (/.union /.empty set) sample)) - (r.= (/.membership /.full sample) - (/.membership (/.union /.full set) sample)) - - (r.>= (/.membership bottom_set sample) - (/.membership (/.union bottom_set top_set) sample)) - (r.>= (/.membership top_set sample) - (/.membership (/.union bottom_set top_set) sample))))) - (_.cover [/.intersection] - (let [set (/.gradient bottom top)] - (and (r.= (/.membership /.empty sample) - (/.membership (/.intersection /.empty set) sample)) - (r.= (/.membership set sample) - (/.membership (/.intersection /.full set) sample)) - - (r.<= (/.membership bottom_set sample) - (/.membership (/.intersection bottom_set top_set) sample)) - (r.<= (/.membership top_set sample) - (/.membership (/.intersection bottom_set top_set) sample))))) - (_.cover [/.complement] - (let [set (/.gradient bottom top) - - trivial! - (and (r.= (/.membership /.full sample) - (/.membership (/.complement /.empty) sample)) - (r.= (/.membership /.empty sample) - (/.membership (/.complement /.full) sample))) - - common! - (and (r.>= (/.membership set sample) - (/.membership (/.union set (/.complement set)) sample)) - (r.<= (/.membership set sample) - (/.membership (/.intersection set (/.complement set)) sample))) - - de_morgan! - (and (r.= (/.membership (/.complement (/.union bottom_set top_set)) - sample) - (/.membership (/.intersection (/.complement bottom_set) (/.complement top_set)) - sample)) - (r.= (/.membership (/.complement (/.intersection bottom_set top_set)) - sample) - (/.membership (/.union (/.complement bottom_set) (/.complement top_set)) - sample)))] - (and trivial! + (all _.and + (_.cover [/.union] + (let [set (/.gradient bottom top)] + (and (r.= (/.membership set sample) + (/.membership (/.union /.empty set) sample)) + (r.= (/.membership /.full sample) + (/.membership (/.union /.full set) sample)) + + (r.>= (/.membership bottom_set sample) + (/.membership (/.union bottom_set top_set) sample)) + (r.>= (/.membership top_set sample) + (/.membership (/.union bottom_set top_set) sample))))) + (_.cover [/.intersection] + (let [set (/.gradient bottom top)] + (and (r.= (/.membership /.empty sample) + (/.membership (/.intersection /.empty set) sample)) + (r.= (/.membership set sample) + (/.membership (/.intersection /.full set) sample)) + + (r.<= (/.membership bottom_set sample) + (/.membership (/.intersection bottom_set top_set) sample)) + (r.<= (/.membership top_set sample) + (/.membership (/.intersection bottom_set top_set) sample))))) + (_.cover [/.complement] + (let [set (/.gradient bottom top) + + trivial! + (and (r.= (/.membership /.full sample) + (/.membership (/.complement /.empty) sample)) + (r.= (/.membership /.empty sample) + (/.membership (/.complement /.full) sample))) + common! - de_morgan!))) - (_.cover [/.difference] - (let [set (/.gradient bottom top)] - (and (r.= (/.membership set sample) - (/.membership (/.difference /.empty set) sample)) - (r.= (/.membership /.empty sample) - (/.membership (/.difference /.full set) sample)) - - (r.<= (/.membership top_set sample) - (/.membership (/.difference bottom_set top_set) sample)) - (r.<= (/.membership bottom_set sample) - (/.membership (/.difference bottom_set top_set) sample))))) - ))) + (and (r.>= (/.membership set sample) + (/.membership (/.union set (/.complement set)) sample)) + (r.<= (/.membership set sample) + (/.membership (/.intersection set (/.complement set)) sample))) + + de_morgan! + (and (r.= (/.membership (/.complement (/.union bottom_set top_set)) + sample) + (/.membership (/.intersection (/.complement bottom_set) (/.complement top_set)) + sample)) + (r.= (/.membership (/.complement (/.intersection bottom_set top_set)) + sample) + (/.membership (/.union (/.complement bottom_set) (/.complement top_set)) + sample)))] + (and trivial! + common! + de_morgan!))) + (_.cover [/.difference] + (let [set (/.gradient bottom top)] + (and (r.= (/.membership set sample) + (/.membership (/.difference /.empty set) sample)) + (r.= (/.membership /.empty sample) + (/.membership (/.difference /.full set) sample)) + + (r.<= (/.membership top_set sample) + (/.membership (/.difference bottom_set top_set) sample)) + (r.<= (/.membership bottom_set sample) + (/.membership (/.difference bottom_set top_set) sample))))) + ))) (def: geometric Test @@ -181,111 +181,111 @@ _ {.#None}))))] - ($_ _.and - (_.cover [/.triangle] - (let [reference (/.triangle bottom middle_bottom top) - - irrelevant_order! - (list.every? (function (_ set) - (r.= (/.membership reference sample) - (/.membership set sample))) - (list (/.triangle bottom top middle_bottom) - (/.triangle middle_bottom bottom top) - (/.triangle middle_bottom top bottom) - (/.triangle top bottom middle_bottom) - (/.triangle top middle_bottom bottom))) - - middle_maximum! - (r.= //.true (/.membership reference middle_bottom)) - - boundary_minima! - (and (r.= //.false (/.membership reference bottom)) - (r.= //.false (/.membership reference top))) - - inside_range! - (bit#= (r.> //.false (/.membership reference sample)) - (and (r.> bottom sample) - (r.< top sample))) - - outside_range! - (bit#= (r.= //.false (/.membership reference sample)) - (or (r.<= bottom sample) - (r.>= top sample)))] - (and irrelevant_order! + (all _.and + (_.cover [/.triangle] + (let [reference (/.triangle bottom middle_bottom top) + + irrelevant_order! + (list.every? (function (_ set) + (r.= (/.membership reference sample) + (/.membership set sample))) + (list (/.triangle bottom top middle_bottom) + (/.triangle middle_bottom bottom top) + (/.triangle middle_bottom top bottom) + (/.triangle top bottom middle_bottom) + (/.triangle top middle_bottom bottom))) + middle_maximum! + (r.= //.true (/.membership reference middle_bottom)) + boundary_minima! + (and (r.= //.false (/.membership reference bottom)) + (r.= //.false (/.membership reference top))) + inside_range! - outside_range!))) - (_.cover [/.trapezoid] - (let [reference (/.trapezoid bottom middle_bottom middle_top top) - - irrelevant_order! - (list.every? (function (_ set) - (r.= (/.membership reference sample) - (/.membership set sample))) - (let [r0 bottom - r1 middle_bottom - r2 middle_top - r3 top] - (list (/.trapezoid r0 r1 r2 r3) - (/.trapezoid r0 r1 r3 r2) - (/.trapezoid r0 r2 r1 r3) - (/.trapezoid r0 r2 r3 r1) - (/.trapezoid r0 r3 r1 r2) - (/.trapezoid r0 r3 r2 r1) - - (/.trapezoid r1 r0 r2 r3) - (/.trapezoid r1 r0 r3 r2) - (/.trapezoid r1 r2 r0 r3) - (/.trapezoid r1 r2 r3 r0) - (/.trapezoid r1 r3 r0 r2) - (/.trapezoid r1 r3 r2 r0) - - (/.trapezoid r2 r0 r1 r3) - (/.trapezoid r2 r0 r3 r1) - (/.trapezoid r2 r1 r0 r3) - (/.trapezoid r2 r1 r3 r0) - (/.trapezoid r2 r3 r0 r1) - (/.trapezoid r2 r3 r1 r0) - - (/.trapezoid r3 r0 r1 r2) - (/.trapezoid r3 r0 r2 r1) - (/.trapezoid r3 r1 r0 r2) - (/.trapezoid r3 r1 r2 r0) - (/.trapezoid r3 r2 r0 r1) - (/.trapezoid r3 r2 r1 r0) - ))) - - middle_maxima! - (and (r.= //.true (/.membership reference middle_bottom)) - (r.= //.true (/.membership reference middle_top))) - - boundary_minima! - (and (r.= //.false (/.membership reference bottom)) - (r.= //.false (/.membership reference top))) - - inside_range! - (bit#= (r.> //.false (/.membership reference sample)) - (and (r.> bottom sample) - (r.< top sample))) - - outside_range! - (bit#= (r.= //.false (/.membership reference sample)) - (or (r.<= bottom sample) - (r.>= top sample))) - - - inside_inner_range! - (bit#= (r.= //.true (/.membership reference sample)) - (and (r.<= middle_top sample) - (r.>= middle_bottom sample)))] - (and irrelevant_order! + (bit#= (r.> //.false (/.membership reference sample)) + (and (r.> bottom sample) + (r.< top sample))) + + outside_range! + (bit#= (r.= //.false (/.membership reference sample)) + (or (r.<= bottom sample) + (r.>= top sample)))] + (and irrelevant_order! + middle_maximum! + boundary_minima! + inside_range! + outside_range!))) + (_.cover [/.trapezoid] + (let [reference (/.trapezoid bottom middle_bottom middle_top top) + + irrelevant_order! + (list.every? (function (_ set) + (r.= (/.membership reference sample) + (/.membership set sample))) + (let [r0 bottom + r1 middle_bottom + r2 middle_top + r3 top] + (list (/.trapezoid r0 r1 r2 r3) + (/.trapezoid r0 r1 r3 r2) + (/.trapezoid r0 r2 r1 r3) + (/.trapezoid r0 r2 r3 r1) + (/.trapezoid r0 r3 r1 r2) + (/.trapezoid r0 r3 r2 r1) + + (/.trapezoid r1 r0 r2 r3) + (/.trapezoid r1 r0 r3 r2) + (/.trapezoid r1 r2 r0 r3) + (/.trapezoid r1 r2 r3 r0) + (/.trapezoid r1 r3 r0 r2) + (/.trapezoid r1 r3 r2 r0) + + (/.trapezoid r2 r0 r1 r3) + (/.trapezoid r2 r0 r3 r1) + (/.trapezoid r2 r1 r0 r3) + (/.trapezoid r2 r1 r3 r0) + (/.trapezoid r2 r3 r0 r1) + (/.trapezoid r2 r3 r1 r0) + + (/.trapezoid r3 r0 r1 r2) + (/.trapezoid r3 r0 r2 r1) + (/.trapezoid r3 r1 r0 r2) + (/.trapezoid r3 r1 r2 r0) + (/.trapezoid r3 r2 r0 r1) + (/.trapezoid r3 r2 r1 r0) + ))) + middle_maxima! + (and (r.= //.true (/.membership reference middle_bottom)) + (r.= //.true (/.membership reference middle_top))) + boundary_minima! + (and (r.= //.false (/.membership reference bottom)) + (r.= //.false (/.membership reference top))) + inside_range! + (bit#= (r.> //.false (/.membership reference sample)) + (and (r.> bottom sample) + (r.< top sample))) + outside_range! - inside_inner_range!))) - )))) + (bit#= (r.= //.false (/.membership reference sample)) + (or (r.<= bottom sample) + (r.>= top sample))) + + + inside_inner_range! + (bit#= (r.= //.true (/.membership reference sample)) + (and (r.<= middle_top sample) + (r.>= middle_bottom sample)))] + (and irrelevant_order! + middle_maxima! + boundary_minima! + inside_range! + outside_range! + inside_inner_range!))) + )))) (def: discrete Test @@ -294,15 +294,15 @@ .let [under? (n.< threshold) set (set.of_list n.hash (list threshold))] sample random.nat] - ($_ _.and - (_.cover [/.of_predicate] - (bit#= (r.= //.true (/.membership (/.of_predicate under?) sample)) - (under? sample))) - (_.cover [/.of_set] - (and (r.= //.true (/.membership (/.of_set set) threshold)) - (bit#= (r.= //.true (/.membership (/.of_set set) sample)) - (set.member? set sample)))) - ))) + (all _.and + (_.cover [/.of_predicate] + (bit#= (r.= //.true (/.membership (/.of_predicate under?) sample)) + (under? sample))) + (_.cover [/.of_set] + (and (r.= //.true (/.membership (/.of_set set) threshold)) + (bit#= (r.= //.true (/.membership (/.of_set set) sample)) + (set.member? set sample)))) + ))) (def: gradient (Random [[Rev Rev] (Fuzzy Rev)]) @@ -323,14 +323,14 @@ [[_ set] ..gradient threshold random.rev sample random.rev] - ($_ _.and - (_.cover [/.predicate] - (bit#= (not ((/.predicate threshold set) sample)) - (r.< threshold (/.membership set sample)))) - (_.cover [/.cut] - (bit#= (r.= //.false (/.membership (/.cut threshold set) sample)) - (r.< threshold (/.membership set sample)))) - ))) + (all _.and + (_.cover [/.predicate] + (bit#= (not ((/.predicate threshold set) sample)) + (r.< threshold (/.membership set sample)))) + (_.cover [/.cut] + (bit#= (r.= //.false (/.membership (/.cut threshold set) sample)) + (r.< threshold (/.membership set sample)))) + ))) (def: .public test Test @@ -344,14 +344,14 @@ (def: (= left right) (r.= (left sample) (right sample)))))]] - ($_ _.and - (_.for [/.functor] - ($contravariant.spec equivalence fuzzy /.functor)) - - ..trivial - ..simple - ..composition - ..geometric - ..discrete - ..threshold - )))) + (all _.and + (_.for [/.functor] + ($contravariant.spec equivalence fuzzy /.functor)) + + ..trivial + ..simple + ..composition + ..geometric + ..discrete + ..threshold + )))) diff --git a/stdlib/source/test/lux/math/modular.lux b/stdlib/source/test/lux/math/modular.lux index 243603132..535ba1048 100644 --- a/stdlib/source/test/lux/math/modular.lux +++ b/stdlib/source/test/lux/math/modular.lux @@ -47,78 +47,78 @@ ($//.random +1,000,000)) subject (..random subject##%) another (..random subject##%)] - (`` ($_ _.and - (_.for [/.equivalence /.=] - ($equivalence.spec /.equivalence (..random subject##%))) - (_.for [/.order /.<] - ($order.spec /.order (..random subject##%))) - (~~ (template [<composite> <monoid>] - [(_.for [<monoid> <composite>] - ($monoid.spec /.equivalence (<monoid> subject##%) (..random subject##%)))] - - [/.+ /.addition] - [/.* /.multiplication] - )) - (_.for [/.codec] - ($codec.spec /.equivalence (/.codec subject##%) (..random subject##%))) + (`` (all _.and + (_.for [/.equivalence /.=] + ($equivalence.spec /.equivalence (..random subject##%))) + (_.for [/.order /.<] + ($order.spec /.order (..random subject##%))) + (~~ (template [<composite> <monoid>] + [(_.for [<monoid> <composite>] + ($monoid.spec /.equivalence (<monoid> subject##%) (..random subject##%)))] + + [/.+ /.addition] + [/.* /.multiplication] + )) + (_.for [/.codec] + ($codec.spec /.equivalence (/.codec subject##%) (..random subject##%))) - (_.cover [/.incorrect_modulus] - (case (|> param - (# (/.codec param##%) encoded) - (# (/.codec subject##%) decoded)) - {try.#Failure error} - (exception.match? /.incorrect_modulus error) - - {try.#Success _} - false)) - (_.cover [/.modulus] - (and (type#= (type_of (/.modulus subject)) - (type_of (/.modulus subject))) - (not (type#= (type_of (/.modulus subject)) - (type_of (/.modulus param)))))) - (_.cover [/.modular /.value] - (/.= subject - (/.modular (/.modulus subject) (/.value subject)))) - (_.cover [/.>] - (bit#= (/.> another subject) - (/.< subject another))) - (_.cover [/.<= /.>=] - (bit#= (/.<= another subject) - (/.>= subject another))) - (_.cover [/.-] - (let [zero (/.modular (/.modulus subject) +0)] - (and (/.= zero - (/.- subject subject)) - (/.= subject - (/.- zero subject))))) - (_.cover [/.inverse] - (let [one (/.modular (/.modulus subject) +1) - co_prime? (i.co_prime? (//.divisor (/.modulus subject)) - (/.value subject))] - (case (/.inverse subject) - {.#Some subject^-1} - (and co_prime? - (|> subject - (/.* subject^-1) - (/.= one))) - - {.#None} - (not co_prime?)))) - (_.cover [/.adapter] - (<| (try.else false) - (do try.monad - [copy##% (//.modulus (//.divisor subject##%)) - adapt (/.adapter subject##% copy##%)] - (in (|> subject - /.value - (/.modular copy##%) - adapt - (/.= subject)))))) - (_.cover [/.moduli_are_not_equal] - (case (/.adapter subject##% param##%) - {try.#Failure error} - (exception.match? /.moduli_are_not_equal error) - - {try.#Success _} - false)) - ))))) + (_.cover [/.incorrect_modulus] + (case (|> param + (# (/.codec param##%) encoded) + (# (/.codec subject##%) decoded)) + {try.#Failure error} + (exception.match? /.incorrect_modulus error) + + {try.#Success _} + false)) + (_.cover [/.modulus] + (and (type#= (type_of (/.modulus subject)) + (type_of (/.modulus subject))) + (not (type#= (type_of (/.modulus subject)) + (type_of (/.modulus param)))))) + (_.cover [/.modular /.value] + (/.= subject + (/.modular (/.modulus subject) (/.value subject)))) + (_.cover [/.>] + (bit#= (/.> another subject) + (/.< subject another))) + (_.cover [/.<= /.>=] + (bit#= (/.<= another subject) + (/.>= subject another))) + (_.cover [/.-] + (let [zero (/.modular (/.modulus subject) +0)] + (and (/.= zero + (/.- subject subject)) + (/.= subject + (/.- zero subject))))) + (_.cover [/.inverse] + (let [one (/.modular (/.modulus subject) +1) + co_prime? (i.co_prime? (//.divisor (/.modulus subject)) + (/.value subject))] + (case (/.inverse subject) + {.#Some subject^-1} + (and co_prime? + (|> subject + (/.* subject^-1) + (/.= one))) + + {.#None} + (not co_prime?)))) + (_.cover [/.adapter] + (<| (try.else false) + (do try.monad + [copy##% (//.modulus (//.divisor subject##%)) + adapt (/.adapter subject##% copy##%)] + (in (|> subject + /.value + (/.modular copy##%) + adapt + (/.= subject)))))) + (_.cover [/.moduli_are_not_equal] + (case (/.adapter subject##% param##%) + {try.#Failure error} + (exception.match? /.moduli_are_not_equal error) + + {try.#Success _} + false)) + ))))) diff --git a/stdlib/source/test/lux/math/modulus.lux b/stdlib/source/test/lux/math/modulus.lux index fbb7bd563..71dd3b81b 100644 --- a/stdlib/source/test/lux/math/modulus.lux +++ b/stdlib/source/test/lux/math/modulus.lux @@ -1,22 +1,22 @@ (.using - [library - [lux "*" - ["_" test {"+" Test}] - ["[0]" meta] - [abstract - [monad {"+" do}]] - [control - ["[0]" try] - ["[0]" exception]] - [math - ["[0]" random {"+" Random}] - [number - ["i" int]]] - [macro - [syntax {"+" syntax:}] - ["[0]" code]]]] - [\\library - ["[0]" /]]) + [library + [lux "*" + ["_" test {"+" Test}] + ["[0]" meta] + [abstract + [monad {"+" do}]] + [control + ["[0]" try] + ["[0]" exception]] + [math + ["[0]" random {"+" Random}] + [number + ["i" int]]] + [macro + [syntax {"+" syntax:}] + ["[0]" code]]]] + [\\library + ["[0]" /]]) (syntax: (|divisor| []) (do meta.monad @@ -39,30 +39,30 @@ [divisor random.int modulus (..random +1,000,000) dividend random.int] - ($_ _.and - (_.cover [/.modulus /.divisor] - (case (/.modulus divisor) - {try.#Success modulus} - (i.= divisor (/.divisor modulus)) - - {try.#Failure error} - (i.= +0 divisor))) - (_.cover [/.zero_cannot_be_a_modulus] - (case (/.modulus +0) - {try.#Failure error} - (exception.match? /.zero_cannot_be_a_modulus error) + (all _.and + (_.cover [/.modulus /.divisor] + (case (/.modulus divisor) + {try.#Success modulus} + (i.= divisor (/.divisor modulus)) + + {try.#Failure error} + (i.= +0 divisor))) + (_.cover [/.zero_cannot_be_a_modulus] + (case (/.modulus +0) + {try.#Failure error} + (exception.match? /.zero_cannot_be_a_modulus error) - {try.#Success modulus} - false)) - (_.cover [/.literal] - (with_expansions [<divisor> (|divisor|)] - (i.= <divisor> (/.divisor (/.literal <divisor>))))) - (_.cover [/.=] - (with_expansions [<divisor> (|divisor|)] - (/.= (/.literal <divisor>) - (/.literal <divisor>)))) - (_.cover [/.congruent?] - (and (/.congruent? modulus dividend dividend) - (or (not (/.congruent? modulus dividend (++ dividend))) - (i.= +1 (/.divisor modulus))))) - )))) + {try.#Success modulus} + false)) + (_.cover [/.literal] + (with_expansions [<divisor> (|divisor|)] + (i.= <divisor> (/.divisor (/.literal <divisor>))))) + (_.cover [/.=] + (with_expansions [<divisor> (|divisor|)] + (/.= (/.literal <divisor>) + (/.literal <divisor>)))) + (_.cover [/.congruent?] + (and (/.congruent? modulus dividend dividend) + (or (not (/.congruent? modulus dividend (++ dividend))) + (i.= +1 (/.divisor modulus))))) + )))) diff --git a/stdlib/source/test/lux/math/number.lux b/stdlib/source/test/lux/math/number.lux index beaa84aa6..94df83848 100644 --- a/stdlib/source/test/lux/math/number.lux +++ b/stdlib/source/test/lux/math/number.lux @@ -1,28 +1,28 @@ (.using - [library - [lux "*" - ["_" test {"+" Test}] - [control - ["[0]" try]] - [data - ["[0]" text]]]] - [\\library - ["[0]" / - ["n" nat] - ["i" int] - ["r" rev] - ["f" frac]]] - ["[0]" / "_" - ["[1][0]" i8] - ["[1][0]" i16] - ["[1][0]" i32] - ["[1][0]" i64] - ["[1][0]" nat] - ["[1][0]" int] - ["[1][0]" rev] - ["[1][0]" frac] - ["[1][0]" ratio] - ["[1][0]" complex]]) + [library + [lux "*" + ["_" test {"+" Test}] + [control + ["[0]" try]] + [data + ["[0]" text]]]] + [\\library + ["[0]" / + ["n" nat] + ["i" int] + ["r" rev] + ["f" frac]]] + ["[0]" / "_" + ["[1][0]" i8] + ["[1][0]" i16] + ["[1][0]" i32] + ["[1][0]" i64] + ["[1][0]" nat] + ["[1][0]" int] + ["[1][0]" rev] + ["[1][0]" frac] + ["[1][0]" ratio] + ["[1][0]" complex]]) (def: clean_commas (-> Text Text) @@ -31,73 +31,73 @@ (def: .public test Test (<| (_.covering /._) - ($_ _.and - (_.cover [/.bin] - (`` (and (~~ (template [<=> <codec> <number>] - [(case (# <codec> decoded (..clean_commas <number>)) - {try.#Success actual} - (<=> (/.bin <number>) actual) - - {try.#Failure error} - false)] - - [n.= n.binary "11,00,10,01"] - - [i.= i.binary "+11,00,10,01"] - [i.= i.binary "-11,00,10,01"] - - [r.= r.binary ".11,00,10,01"] - - [f.= f.binary "+11,00.10,01"] - [f.= f.binary "-11,00.10,01"] - ))))) - (_.cover [/.oct] - (`` (and (~~ (template [<=> <codec> <number>] - [(case (# <codec> decoded (..clean_commas <number>)) - {try.#Success actual} - (<=> (/.oct <number>) actual) - - {try.#Failure error} - false)] - - [n.= n.octal "615,243"] - - [i.= i.octal "+615,243"] - [i.= i.octal "-615,243"] - - [r.= r.octal ".615,243"] - - [f.= f.octal "+61,52.43"] - [f.= f.octal "-61,52.43"] - ))))) - (_.cover [/.hex] - (`` (and (~~ (template [<=> <codec> <number>] - [(case (# <codec> decoded (..clean_commas <number>)) - {try.#Success actual} - (<=> (/.hex <number>) actual) - - {try.#Failure error} - false)] - - [n.= n.hex "dead,BEEF"] - - [i.= i.hex "+dead,BEEF"] - [i.= i.hex "-dead,BEEF"] - - [r.= r.hex ".dead,BEEF"] - - [f.= f.hex "+dead,BE.EF"] - [f.= f.hex "-dead,BE.EF"] - ))))) - - /i8.test - /i16.test - /i32.test - /i64.test - /nat.test - /int.test - /rev.test - /frac.test - /ratio.test - /complex.test - ))) + (all _.and + (_.cover [/.bin] + (`` (and (~~ (template [<=> <codec> <number>] + [(case (# <codec> decoded (..clean_commas <number>)) + {try.#Success actual} + (<=> (/.bin <number>) actual) + + {try.#Failure error} + false)] + + [n.= n.binary "11,00,10,01"] + + [i.= i.binary "+11,00,10,01"] + [i.= i.binary "-11,00,10,01"] + + [r.= r.binary ".11,00,10,01"] + + [f.= f.binary "+11,00.10,01"] + [f.= f.binary "-11,00.10,01"] + ))))) + (_.cover [/.oct] + (`` (and (~~ (template [<=> <codec> <number>] + [(case (# <codec> decoded (..clean_commas <number>)) + {try.#Success actual} + (<=> (/.oct <number>) actual) + + {try.#Failure error} + false)] + + [n.= n.octal "615,243"] + + [i.= i.octal "+615,243"] + [i.= i.octal "-615,243"] + + [r.= r.octal ".615,243"] + + [f.= f.octal "+61,52.43"] + [f.= f.octal "-61,52.43"] + ))))) + (_.cover [/.hex] + (`` (and (~~ (template [<=> <codec> <number>] + [(case (# <codec> decoded (..clean_commas <number>)) + {try.#Success actual} + (<=> (/.hex <number>) actual) + + {try.#Failure error} + false)] + + [n.= n.hex "dead,BEEF"] + + [i.= i.hex "+dead,BEEF"] + [i.= i.hex "-dead,BEEF"] + + [r.= r.hex ".dead,BEEF"] + + [f.= f.hex "+dead,BE.EF"] + [f.= f.hex "-dead,BE.EF"] + ))))) + + /i8.test + /i16.test + /i32.test + /i64.test + /nat.test + /int.test + /rev.test + /frac.test + /ratio.test + /complex.test + ))) diff --git a/stdlib/source/test/lux/math/number/complex.lux b/stdlib/source/test/lux/math/number/complex.lux index 7bdc17274..a705bbb0e 100644 --- a/stdlib/source/test/lux/math/number/complex.lux +++ b/stdlib/source/test/lux/math/number/complex.lux @@ -49,78 +49,78 @@ (do random.monad [real ..dimension imaginary ..dimension] - ($_ _.and - (_.cover [/.complex] - (and (let [r+i (/.complex real imaginary)] - (and (f.= real (the /.#real r+i)) - (f.= imaginary (the /.#imaginary r+i)))) - (let [r+i (/.complex real)] - (and (f.= real (the /.#real r+i)) - (f.= +0.0 (the /.#imaginary r+i)))))) - (_.cover [/.approximately?] - (/.approximately? ..margin_of_error - (/.complex real imaginary) - (/.complex real imaginary))) - (_.cover [/.not_a_number?] - (and (/.not_a_number? (/.complex f.not_a_number imaginary)) - (/.not_a_number? (/.complex real f.not_a_number)))) - ))) + (all _.and + (_.cover [/.complex] + (and (let [r+i (/.complex real imaginary)] + (and (f.= real (the /.#real r+i)) + (f.= imaginary (the /.#imaginary r+i)))) + (let [r+i (/.complex real)] + (and (f.= real (the /.#real r+i)) + (f.= +0.0 (the /.#imaginary r+i)))))) + (_.cover [/.approximately?] + (/.approximately? ..margin_of_error + (/.complex real imaginary) + (/.complex real imaginary))) + (_.cover [/.not_a_number?] + (and (/.not_a_number? (/.complex f.not_a_number imaginary)) + (/.not_a_number? (/.complex real f.not_a_number)))) + ))) (def: constant Test (do random.monad [sample ..random dimension ..dimension] - ($_ _.and - (_.cover [/.zero] - (/.= /.zero (/.* /.zero sample))) - (_.cover [/.+one] - (/.= sample (/.* /.+one sample))) - (_.cover [/.-one] - (and (/.= /.zero - (/.+ sample - (/.* /.-one sample))) - (/.= sample (/.* /.-one (/.* /.-one sample))))) - (_.cover [/.i] - (and (/.= (/.complex +0.0 dimension) - (/.* /.i (/.complex dimension))) - (/.= (/.* /.-one sample) - (/.* /.i (/.* /.i sample))))) - ))) + (all _.and + (_.cover [/.zero] + (/.= /.zero (/.* /.zero sample))) + (_.cover [/.+one] + (/.= sample (/.* /.+one sample))) + (_.cover [/.-one] + (and (/.= /.zero + (/.+ sample + (/.* /.-one sample))) + (/.= sample (/.* /.-one (/.* /.-one sample))))) + (_.cover [/.i] + (and (/.= (/.complex +0.0 dimension) + (/.* /.i (/.complex dimension))) + (/.= (/.* /.-one sample) + (/.* /.i (/.* /.i sample))))) + ))) (def: absolute_value&argument Test (do random.monad [real ..dimension imaginary ..dimension] - ($_ _.and - (_.cover [/.abs] - (let [normal! - (let [r+i (/.complex real imaginary)] - (and (f.>= (f.abs real) (/.abs r+i)) - (f.>= (f.abs imaginary) (/.abs r+i)))) + (all _.and + (_.cover [/.abs] + (let [normal! + (let [r+i (/.complex real imaginary)] + (and (f.>= (f.abs real) (/.abs r+i)) + (f.>= (f.abs imaginary) (/.abs r+i)))) - not_a_number! - (and (f.not_a_number? (/.abs (/.complex f.not_a_number imaginary))) - (f.not_a_number? (/.abs (/.complex real f.not_a_number)))) - - infinity! - (and (f.= f.positive_infinity (/.abs (/.complex f.positive_infinity imaginary))) - (f.= f.positive_infinity (/.abs (/.complex real f.positive_infinity))) - (f.= f.positive_infinity (/.abs (/.complex f.negative_infinity imaginary))) - (f.= f.positive_infinity (/.abs (/.complex real f.negative_infinity))))] - (and normal! not_a_number! - infinity!))) - ... https://en.wikipedia.org/wiki/Argument_(complex_analysis)#Identities - (_.cover [/.argument] - (let [sample (/.complex real imaginary)] - (or (/.= /.zero sample) - (/.approximately? ..margin_of_error - sample - (/.*' (/.abs sample) - (/.exp (/.* /.i (/.complex (/.argument sample))))))))) - ))) + (and (f.not_a_number? (/.abs (/.complex f.not_a_number imaginary))) + (f.not_a_number? (/.abs (/.complex real f.not_a_number)))) + + infinity! + (and (f.= f.positive_infinity (/.abs (/.complex f.positive_infinity imaginary))) + (f.= f.positive_infinity (/.abs (/.complex real f.positive_infinity))) + (f.= f.positive_infinity (/.abs (/.complex f.negative_infinity imaginary))) + (f.= f.positive_infinity (/.abs (/.complex real f.negative_infinity))))] + (and normal! + not_a_number! + infinity!))) + ... https://en.wikipedia.org/wiki/Argument_(complex_analysis)#Identities + (_.cover [/.argument] + (let [sample (/.complex real imaginary)] + (or (/.= /.zero sample) + (/.approximately? ..margin_of_error + sample + (/.*' (/.abs sample) + (/.exp (/.* /.i (/.complex (/.argument sample))))))))) + ))) (def: number Test @@ -128,81 +128,81 @@ [x ..random y ..random factor ..dimension] - ($_ _.and - (_.cover [/.+] - (let [z (/.+ y x)] - (and (/.= z - (/.complex (f.+ (the /.#real y) - (the /.#real x)) - (f.+ (the /.#imaginary y) - (the /.#imaginary x))))))) - (_.cover [/.-] - (let [normal! - (let [z (/.- y x)] - (and (/.= z - (/.complex (f.- (the /.#real y) - (the /.#real x)) - (f.- (the /.#imaginary y) - (the /.#imaginary x)))))) + (all _.and + (_.cover [/.+] + (let [z (/.+ y x)] + (and (/.= z + (/.complex (f.+ (the /.#real y) + (the /.#real x)) + (f.+ (the /.#imaginary y) + (the /.#imaginary x))))))) + (_.cover [/.-] + (let [normal! + (let [z (/.- y x)] + (and (/.= z + (/.complex (f.- (the /.#real y) + (the /.#real x)) + (f.- (the /.#imaginary y) + (the /.#imaginary x)))))) - inverse! - (and (|> x (/.+ y) (/.- y) (/.approximately? ..margin_of_error x)) - (|> x (/.- y) (/.+ y) (/.approximately? ..margin_of_error x)))] - (and normal! - inverse!))) - (_.cover [/.* /./] - (|> x (/.* y) (/./ y) (/.approximately? ..margin_of_error x))) - (_.cover [/.*' /./'] - (|> x (/.*' factor) (/./' factor) (/.approximately? ..margin_of_error x))) - (_.cover [/.%] - (let [rem (/.% y x) - quotient (|> x (/.- rem) (/./ y)) - floored (|> quotient - (revised /.#real f.floor) - (revised /.#imaginary f.floor))] - (/.approximately? +0.000000000001 - x - (|> quotient (/.* y) (/.+ rem))))) - ))) + inverse! + (and (|> x (/.+ y) (/.- y) (/.approximately? ..margin_of_error x)) + (|> x (/.- y) (/.+ y) (/.approximately? ..margin_of_error x)))] + (and normal! + inverse!))) + (_.cover [/.* /./] + (|> x (/.* y) (/./ y) (/.approximately? ..margin_of_error x))) + (_.cover [/.*' /./'] + (|> x (/.*' factor) (/./' factor) (/.approximately? ..margin_of_error x))) + (_.cover [/.%] + (let [rem (/.% y x) + quotient (|> x (/.- rem) (/./ y)) + floored (|> quotient + (revised /.#real f.floor) + (revised /.#imaginary f.floor))] + (/.approximately? +0.000000000001 + x + (|> quotient (/.* y) (/.+ rem))))) + ))) (def: conjugate&reciprocal&signum&negation Test (do random.monad [x ..random] - ($_ _.and - (_.cover [/.conjugate] - (let [cx (/.conjugate x)] - (and (f.= (the /.#real x) - (the /.#real cx)) - (f.= (f.opposite (the /.#imaginary x)) - (the /.#imaginary cx))))) - (_.cover [/.reciprocal] - (let [reciprocal! - (|> x (/.* (/.reciprocal x)) (/.approximately? ..margin_of_error /.+one)) - - own_inverse! - (|> x /.reciprocal /.reciprocal (/.approximately? ..margin_of_error x))] - (and reciprocal! - own_inverse!))) - (_.cover [/.signum] - ... Absolute value of signum is always root_2(2), 1 or 0. - (let [signum_abs (|> x /.signum /.abs)] - (or (f.= +0.0 signum_abs) - (f.= +1.0 signum_abs) - (f.= (f.pow +0.5 +2.0) signum_abs)))) - (_.cover [/.opposite] - (let [own_inverse! - (let [there (/.opposite x) - back_again (/.opposite there)] - (and (not (/.= there x)) - (/.= back_again x))) + (all _.and + (_.cover [/.conjugate] + (let [cx (/.conjugate x)] + (and (f.= (the /.#real x) + (the /.#real cx)) + (f.= (f.opposite (the /.#imaginary x)) + (the /.#imaginary cx))))) + (_.cover [/.reciprocal] + (let [reciprocal! + (|> x (/.* (/.reciprocal x)) (/.approximately? ..margin_of_error /.+one)) + + own_inverse! + (|> x /.reciprocal /.reciprocal (/.approximately? ..margin_of_error x))] + (and reciprocal! + own_inverse!))) + (_.cover [/.signum] + ... Absolute value of signum is always root_2(2), 1 or 0. + (let [signum_abs (|> x /.signum /.abs)] + (or (f.= +0.0 signum_abs) + (f.= +1.0 signum_abs) + (f.= (f.pow +0.5 +2.0) signum_abs)))) + (_.cover [/.opposite] + (let [own_inverse! + (let [there (/.opposite x) + back_again (/.opposite there)] + (and (not (/.= there x)) + (/.= back_again x))) - absolute! - (f.= (/.abs x) - (/.abs (/.opposite x)))] - (and own_inverse! - absolute!))) - ))) + absolute! + (f.= (/.abs x) + (/.abs (/.opposite x)))] + (and own_inverse! + absolute!))) + ))) (def: (trigonometric_symmetry forward backward angle) (-> (-> /.Complex /.Complex) (-> /.Complex /.Complex) /.Complex Bit) @@ -213,45 +213,45 @@ Test (do [! random.monad] [angle ..angle] - ($_ _.and - (_.cover [/.sin /.asin] - (trigonometric_symmetry /.sin /.asin angle)) - (_.cover [/.cos /.acos] - (trigonometric_symmetry /.cos /.acos angle)) - (_.cover [/.tan /.atan] - (trigonometric_symmetry /.tan /.atan angle))))) + (all _.and + (_.cover [/.sin /.asin] + (trigonometric_symmetry /.sin /.asin angle)) + (_.cover [/.cos /.acos] + (trigonometric_symmetry /.cos /.acos angle)) + (_.cover [/.tan /.atan] + (trigonometric_symmetry /.tan /.atan angle))))) (def: hyperbolic Test (do [! random.monad] [angle ..angle] - ($_ _.and - (_.cover [/.sinh] - (/.approximately? ..margin_of_error - (|> angle (/.* /.i) /.sin (/.* /.i) (/.* /.-one)) - (/.sinh angle))) - (_.cover [/.cosh] - (/.approximately? ..margin_of_error - (|> angle (/.* /.i) /.cos) - (/.cosh angle))) - (_.cover [/.tanh] - (/.approximately? ..margin_of_error - (|> angle (/.* /.i) /.tan (/.* /.i) (/.* /.-one)) - (/.tanh angle))) - ))) + (all _.and + (_.cover [/.sinh] + (/.approximately? ..margin_of_error + (|> angle (/.* /.i) /.sin (/.* /.i) (/.* /.-one)) + (/.sinh angle))) + (_.cover [/.cosh] + (/.approximately? ..margin_of_error + (|> angle (/.* /.i) /.cos) + (/.cosh angle))) + (_.cover [/.tanh] + (/.approximately? ..margin_of_error + (|> angle (/.* /.i) /.tan (/.* /.i) (/.* /.-one)) + (/.tanh angle))) + ))) (def: exponentiation&logarithm Test (do random.monad [x ..random] - ($_ _.and - (_.cover [/.pow /.root_2] - (|> x (/.pow (/.complex +2.0)) /.root_2 (/.approximately? ..margin_of_error x))) - (_.cover [/.pow'] - (|> x (/.pow' +2.0) (/.pow' +0.5) (/.approximately? ..margin_of_error x))) - (_.cover [/.log /.exp] - (|> x /.log /.exp (/.approximately? ..margin_of_error x))) - ))) + (all _.and + (_.cover [/.pow /.root_2] + (|> x (/.pow (/.complex +2.0)) /.root_2 (/.approximately? ..margin_of_error x))) + (_.cover [/.pow'] + (|> x (/.pow' +2.0) (/.pow' +0.5) (/.approximately? ..margin_of_error x))) + (_.cover [/.log /.exp] + (|> x /.log /.exp (/.approximately? ..margin_of_error x))) + ))) (def: root Test @@ -268,17 +268,17 @@ Test (<| (_.covering /._) (_.for [/.Complex]) - ($_ _.and - (_.for [/.= /.equivalence] - ($equivalence.spec /.equivalence ..random)) + (all _.and + (_.for [/.= /.equivalence] + ($equivalence.spec /.equivalence ..random)) - ..construction - ..constant - ..absolute_value&argument - ..number - ..conjugate&reciprocal&signum&negation - ..trigonometry - ..hyperbolic - ..exponentiation&logarithm - ..root - ))) + ..construction + ..constant + ..absolute_value&argument + ..number + ..conjugate&reciprocal&signum&negation + ..trigonometry + ..hyperbolic + ..exponentiation&logarithm + ..root + ))) diff --git a/stdlib/source/test/lux/math/number/frac.lux b/stdlib/source/test/lux/math/number/frac.lux index 22f56af05..66334e80c 100644 --- a/stdlib/source/test/lux/math/number/frac.lux +++ b/stdlib/source/test/lux/math/number/frac.lux @@ -34,91 +34,91 @@ Test (do random.monad [sample random.safe_frac] - ($_ _.and - (_.cover [/.biggest] - (/.<= /.biggest sample)) - (_.cover [/.positive_infinity] - (/.< /.positive_infinity sample)) - (_.cover [/.smallest] - (bit#= (/.positive? sample) - (/.>= /.smallest sample))) - (_.cover [/.negative_infinity] - (/.> /.negative_infinity sample)) - (_.cover [/.not_a_number /.not_a_number?] - (and (/.not_a_number? /.not_a_number) - (not (or (/.= /.not_a_number sample) - (/.not_a_number? sample))))) - ))) + (all _.and + (_.cover [/.biggest] + (/.<= /.biggest sample)) + (_.cover [/.positive_infinity] + (/.< /.positive_infinity sample)) + (_.cover [/.smallest] + (bit#= (/.positive? sample) + (/.>= /.smallest sample))) + (_.cover [/.negative_infinity] + (/.> /.negative_infinity sample)) + (_.cover [/.not_a_number /.not_a_number?] + (and (/.not_a_number? /.not_a_number) + (not (or (/.= /.not_a_number sample) + (/.not_a_number? sample))))) + ))) (def: predicate Test (do [! random.monad] [sample ..random shift (# ! each /.abs ..random)] - ($_ _.and - (_.cover [/.negative?] - (bit#= (/.negative? sample) - (/.< +0.0 sample))) - (_.cover [/.positive?] - (bit#= (/.positive? sample) - (/.> +0.0 sample))) - (_.cover [/.zero?] - (bit#= (/.zero? sample) - (/.= +0.0 sample))) - (_.cover [/.approximately?] - (and (/.approximately? /.smallest sample sample) - (/.approximately? (/.+ +1.0 shift) sample (/.+ shift sample)))) - (_.cover [/.number?] - (and (not (/.number? /.not_a_number)) - (not (/.number? /.positive_infinity)) - (not (/.number? /.negative_infinity)) - (/.number? sample))) - ))) + (all _.and + (_.cover [/.negative?] + (bit#= (/.negative? sample) + (/.< +0.0 sample))) + (_.cover [/.positive?] + (bit#= (/.positive? sample) + (/.> +0.0 sample))) + (_.cover [/.zero?] + (bit#= (/.zero? sample) + (/.= +0.0 sample))) + (_.cover [/.approximately?] + (and (/.approximately? /.smallest sample sample) + (/.approximately? (/.+ +1.0 shift) sample (/.+ shift sample)))) + (_.cover [/.number?] + (and (not (/.number? /.not_a_number)) + (not (/.number? /.positive_infinity)) + (not (/.number? /.negative_infinity)) + (/.number? sample))) + ))) (def: conversion Test - ($_ _.and - (do [! random.monad] - [expected (# ! each (n.% 1,000,000) random.nat)] - (_.cover [/.nat] - (|> expected n.frac /.nat (n.= expected)))) - (do [! random.monad] - [expected (# ! each (i.% +1,000,000) random.int)] - (_.cover [/.int] - (|> expected i.frac /.int (i.= expected)))) - (do [! random.monad] - [expected (# ! each (|>> (i64.left_shifted 52) .rev) - random.nat)] - (_.cover [/.rev] - (|> expected r.frac /.rev (r.= expected)))) - )) + (all _.and + (do [! random.monad] + [expected (# ! each (n.% 1,000,000) random.nat)] + (_.cover [/.nat] + (|> expected n.frac /.nat (n.= expected)))) + (do [! random.monad] + [expected (# ! each (i.% +1,000,000) random.int)] + (_.cover [/.int] + (|> expected i.frac /.int (i.= expected)))) + (do [! random.monad] + [expected (# ! each (|>> (i64.left_shifted 52) .rev) + random.nat)] + (_.cover [/.rev] + (|> expected r.frac /.rev (r.= expected)))) + )) (def: signature Test - (`` ($_ _.and - (_.for [/.equivalence /.=] - ($equivalence.spec /.equivalence random.safe_frac)) - (_.for [/.hash] - ($hash.spec /.hash random.frac)) - (_.for [/.order /.<] - ($order.spec /.order random.safe_frac)) - (~~ (template [<composite> <monoid>] - [(_.for [<monoid> <composite>] - ($monoid.spec /.equivalence <monoid> ..random))] + (`` (all _.and + (_.for [/.equivalence /.=] + ($equivalence.spec /.equivalence random.safe_frac)) + (_.for [/.hash] + ($hash.spec /.hash random.frac)) + (_.for [/.order /.<] + ($order.spec /.order random.safe_frac)) + (~~ (template [<composite> <monoid>] + [(_.for [<monoid> <composite>] + ($monoid.spec /.equivalence <monoid> ..random))] - [/.+ /.addition] - [/.* /.multiplication] + [/.+ /.addition] + [/.* /.multiplication] - [/.min /.minimum] - [/.max /.maximum] - )) - (~~ (template [<codec>] - [(_.for [<codec>] - ($codec.spec /.equivalence <codec> random.safe_frac))] + [/.min /.minimum] + [/.max /.maximum] + )) + (~~ (template [<codec>] + [(_.for [<codec>] + ($codec.spec /.equivalence <codec> random.safe_frac))] - [/.binary] [/.octal] [/.decimal] [/.hex] - )) - ))) + [/.binary] [/.octal] [/.decimal] [/.hex] + )) + ))) (with_expansions [<jvm> (these (ffi.import: java/lang/Double "[1]::[0]" @@ -138,253 +138,253 @@ (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)] + (all _.and + (do [! random.monad] + [.let [~= (/.approximately? ..margin_of_error)] + angle (|> random.safe_frac (# ! each (/.* /.tau)))] + (all _.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)))] + (all _.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_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))))] + /.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)] + (all _.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))))] + (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! <left> <right> <input>) + [(_.cover [<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 (# ! 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))))) - )) + (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 /._) (_.for [.Frac]) - ($_ _.and - (do random.monad - [left random.safe_frac - right random.safe_frac] - ($_ _.and - (_.cover [/.>] - (bit#= (/.> left right) - (/.< right left))) - (_.cover [/.<= /.>=] - (bit#= (/.<= left right) - (/.>= right left))) - )) - (do random.monad - [sample random.safe_frac] - ($_ _.and - (_.cover [/.-] - (and (/.= +0.0 (/.- sample sample)) - (/.= sample (/.- +0.0 sample)) - (/.= (/.opposite sample) - (/.- sample +0.0)))) - (_.cover [/./] - (and (/.= +1.0 (/./ sample sample)) - (/.= sample (/./ +1.0 sample)))) - (_.cover [/.abs] - (bit#= (/.> sample (/.abs sample)) - (/.negative? sample))) - (_.cover [/.signum] - (/.= (/.abs sample) - (/.* (/.signum sample) sample))) - )) - (do random.monad - [left (random.only (|>> (/.= +0.0) not) - ..random) - right ..random] - ($_ _.and - (_.cover [/.%] - (let [rem (/.% left right) - div (|> right (/.- rem) (/./ left))] - (/.= right - (|> div (/.* left) (/.+ rem))))) - (_.cover [/./%] - (let [[div rem] (/./% left right)] - (and (/.= div (/./ left right)) - (/.= rem (/.% left right))))) - (_.cover [/.mod] - (or (and (/.= +0.0 (/.% left right)) - (/.= +0.0 (/.mod left right))) - (and (/.= (/.signum left) - (/.signum (/.mod left right))) - (/.= (/.signum right) - (/.signum (/.% left right))) - (if (/.= (/.signum left) (/.signum right)) - (/.= (/.% left right) - (/.mod left right)) - (/.= (/.+ left (/.% left right)) - (/.mod left right)))))) - )) - (with_expansions [<jvm> ($_ _.and - (let [test (is (-> Frac Bit) - (function (_ value) - (n.= (.nat (ffi.of_long (java/lang/Double::doubleToRawLongBits (ffi.as_double value)))) - (/.bits value))))] + (all _.and + (do random.monad + [left random.safe_frac + right random.safe_frac] + (all _.and + (_.cover [/.>] + (bit#= (/.> left right) + (/.< right left))) + (_.cover [/.<= /.>=] + (bit#= (/.<= left right) + (/.>= right left))) + )) + (do random.monad + [sample random.safe_frac] + (all _.and + (_.cover [/.-] + (and (/.= +0.0 (/.- sample sample)) + (/.= sample (/.- +0.0 sample)) + (/.= (/.opposite sample) + (/.- sample +0.0)))) + (_.cover [/./] + (and (/.= +1.0 (/./ sample sample)) + (/.= sample (/./ +1.0 sample)))) + (_.cover [/.abs] + (bit#= (/.> sample (/.abs sample)) + (/.negative? sample))) + (_.cover [/.signum] + (/.= (/.abs sample) + (/.* (/.signum sample) sample))) + )) + (do random.monad + [left (random.only (|>> (/.= +0.0) not) + ..random) + right ..random] + (all _.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] + (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] + (_.cover [/.bits] + (and (test sample) + (test /.biggest) + (test /.smallest) + (test /.not_a_number) + (test /.positive_infinity) + (test /.negative_infinity))))) (do random.monad - [sample random.frac] - (_.cover [/.bits] - (and (test sample) - (test /.biggest) - (test /.smallest) - (test /.not_a_number) - (test /.positive_infinity) - (test /.negative_infinity))))) - (do random.monad - [sample random.i64] - (_.cover [/.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] - (_.cover [/.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] - (_.cover [/.opposite] - (let [subtraction! - (/.= +0.0 (/.+ (/.opposite expected) expected)) + [sample random.i64] + (_.cover [/.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] + (_.cover [/.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] + (_.cover [/.opposite] + (let [subtraction! + (/.= +0.0 (/.+ (/.opposite expected) expected)) - inverse! - (|> expected /.opposite /.opposite (/.= expected))] - (and subtraction! - inverse!)))) + inverse! + (|> expected /.opposite /.opposite (/.= expected))] + (and subtraction! + inverse!)))) - ..constant - ..predicate - ..conversion - ..signature - ..test|math - ))) + ..constant + ..predicate + ..conversion + ..signature + ..test|math + ))) diff --git a/stdlib/source/test/lux/math/number/i16.lux b/stdlib/source/test/lux/math/number/i16.lux index b8d99c061..8321376d8 100644 --- a/stdlib/source/test/lux/math/number/i16.lux +++ b/stdlib/source/test/lux/math/number/i16.lux @@ -1,18 +1,18 @@ (.using - [library - [lux "*" - ["_" test {"+" Test}] - [abstract - [monad {"+" do}] - [\\specification - ["$[0]" equivalence]]] - [math - ["[0]" random {"+" Random}]]]] - [\\library - ["[0]" / - ["/[1]" // "_" - ["i" int] - ["[1][0]" i64]]]]) + [library + [lux "*" + ["_" test {"+" Test}] + [abstract + [monad {"+" do}] + [\\specification + ["$[0]" equivalence]]] + [math + ["[0]" random {"+" Random}]]]] + [\\library + ["[0]" / + ["/[1]" // "_" + ["i" int] + ["[1][0]" i64]]]]) (def: .public random (Random /.I16) @@ -28,11 +28,11 @@ .int ++)] expected (# ! each (i.% limit) random.int)] - ($_ _.and - (_.for [/.equivalence] - ($equivalence.spec /.equivalence ..random)) - - (_.cover [/.i16 /.i64 /.width] - (let [actual (|> expected .i64 /.i16 /.i64)] - (# //i64.equivalence = expected actual))) - )))) + (all _.and + (_.for [/.equivalence] + ($equivalence.spec /.equivalence ..random)) + + (_.cover [/.i16 /.i64 /.width] + (let [actual (|> expected .i64 /.i16 /.i64)] + (# //i64.equivalence = expected actual))) + )))) diff --git a/stdlib/source/test/lux/math/number/i32.lux b/stdlib/source/test/lux/math/number/i32.lux index 4d44e5d24..ed7e88201 100644 --- a/stdlib/source/test/lux/math/number/i32.lux +++ b/stdlib/source/test/lux/math/number/i32.lux @@ -1,18 +1,18 @@ (.using - [library - [lux "*" - ["_" test {"+" Test}] - [abstract - [monad {"+" do}] - [\\specification - ["$[0]" equivalence]]] - [math - ["[0]" random {"+" Random}]]]] - [\\library - ["[0]" / - ["/[1]" // "_" - ["i" int] - ["[1][0]" i64]]]]) + [library + [lux "*" + ["_" test {"+" Test}] + [abstract + [monad {"+" do}] + [\\specification + ["$[0]" equivalence]]] + [math + ["[0]" random {"+" Random}]]]] + [\\library + ["[0]" / + ["/[1]" // "_" + ["i" int] + ["[1][0]" i64]]]]) (def: .public random (Random /.I32) @@ -28,11 +28,11 @@ .int ++)] expected (# ! each (i.% limit) random.int)] - ($_ _.and - (_.for [/.equivalence] - ($equivalence.spec /.equivalence ..random)) - - (_.cover [/.i32 /.i64 /.width] - (let [actual (|> expected .i64 /.i32 /.i64)] - (# //i64.equivalence = expected actual))) - )))) + (all _.and + (_.for [/.equivalence] + ($equivalence.spec /.equivalence ..random)) + + (_.cover [/.i32 /.i64 /.width] + (let [actual (|> expected .i64 /.i32 /.i64)] + (# //i64.equivalence = expected actual))) + )))) diff --git a/stdlib/source/test/lux/math/number/i64.lux b/stdlib/source/test/lux/math/number/i64.lux index ec6b56f7e..805c212b1 100644 --- a/stdlib/source/test/lux/math/number/i64.lux +++ b/stdlib/source/test/lux/math/number/i64.lux @@ -23,51 +23,51 @@ (do [! random.monad] [pattern random.nat idx (# ! each (n.% /.width) random.nat)] - ($_ _.and - (_.cover [/.one? /.one] - (if (/.one? idx pattern) - (#= pattern (/.one idx pattern)) - (not (#= pattern (/.one idx pattern))))) - (_.cover [/.zero? /.zero] - (if (/.zero? idx pattern) - (#= pattern (/.zero idx pattern)) - (not (#= pattern (/.zero idx pattern))))) - (_.cover [/.flipped] - (#= (/.flipped idx pattern) - (if (/.one? idx pattern) - (/.zero idx pattern) - (/.one idx pattern)))) - (_.cover [/.bit] - (bit#= (/.zero? idx pattern) - (#= /.false (/.and (/.bit idx) pattern)))) - ))) + (all _.and + (_.cover [/.one? /.one] + (if (/.one? idx pattern) + (#= pattern (/.one idx pattern)) + (not (#= pattern (/.one idx pattern))))) + (_.cover [/.zero? /.zero] + (if (/.zero? idx pattern) + (#= pattern (/.zero idx pattern)) + (not (#= pattern (/.zero idx pattern))))) + (_.cover [/.flipped] + (#= (/.flipped idx pattern) + (if (/.one? idx pattern) + (/.zero idx pattern) + (/.one idx pattern)))) + (_.cover [/.bit] + (bit#= (/.zero? idx pattern) + (#= /.false (/.and (/.bit idx) pattern)))) + ))) (def: shift Test (do [! random.monad] [pattern random.nat] - ($_ _.and - (do ! - [idx (# ! each (|>> (n.% (-- /.width)) ++) random.nat)] - (_.cover [/.left_shifted /.right_shifted] - (let [nullity! - (and (#= pattern (/.left_shifted 0 pattern)) - (#= pattern (/.right_shifted 0 pattern))) + (all _.and + (do ! + [idx (# ! each (|>> (n.% (-- /.width)) ++) random.nat)] + (_.cover [/.left_shifted /.right_shifted] + (let [nullity! + (and (#= pattern (/.left_shifted 0 pattern)) + (#= pattern (/.right_shifted 0 pattern))) - idempotency! - (and (#= pattern (/.left_shifted /.width pattern)) - (#= pattern (/.right_shifted /.width pattern))) - - movement! - (let [shift (n.- idx /.width)] - (#= (/.and (/.mask idx) pattern) - (|> pattern - (/.left_shifted shift) - (/.right_shifted shift))))] - (and nullity! idempotency! - movement!)))) - ))) + (and (#= pattern (/.left_shifted /.width pattern)) + (#= pattern (/.right_shifted /.width pattern))) + + movement! + (let [shift (n.- idx /.width)] + (#= (/.and (/.mask idx) pattern) + (|> pattern + (/.left_shifted shift) + (/.right_shifted shift))))] + (and nullity! + idempotency! + movement!)))) + ))) (def: mask Test @@ -76,47 +76,47 @@ [pattern random.nat idx (# ! each (n.% /.width) random.nat) signed random.int] - ($_ _.and - (_.cover [/.sign] - (bit#= (#= (.i64 0) (/.and /.sign signed)) - (i.positive? signed))) - (_.cover [/.mask] - (let [mask (/.mask idx) - idempotency! (#= (/.and mask pattern) - (/.and mask (/.and mask pattern))) + (all _.and + (_.cover [/.sign] + (bit#= (#= (.i64 0) (/.and /.sign signed)) + (i.positive? signed))) + (_.cover [/.mask] + (let [mask (/.mask idx) + idempotency! (#= (/.and mask pattern) + (/.and mask (/.and mask pattern))) - limit (++ (.nat mask)) - limit! (if (n.< limit pattern) - (#= pattern (/.and mask pattern)) - (n.< limit (/.and mask pattern))) + limit (++ (.nat mask)) + limit! (if (n.< limit pattern) + (#= pattern (/.and mask pattern)) + (n.< limit (/.and mask pattern))) - empty! (#= /.false (/.mask 0)) - full! (#= /.true (/.mask /.width))] - (and idempotency! - limit! + empty! (#= /.false (/.mask 0)) + full! (#= /.true (/.mask /.width))] + (and idempotency! + limit! - empty! - full!))) - (do ! - [size (# ! each (n.% /.width) random.nat) - .let [spare (n.- size /.width)] - offset (# ! each (n.% spare) random.nat)] - (_.cover [/.region] - (case size - 0 (#= /.false (/.region offset size)) - _ (#= (|> pattern - ... NNNNYYYYNNNN - (/.right_shifted offset) - ... ____NNNNYYYY - (/.left_shifted spare) - ... YYYY________ - (/.right_shifted spare) - ... ________YYYY - (/.left_shifted offset) - ... ____YYYY____ - ) - (/.and (/.region offset size) pattern))))) - )))) + empty! + full!))) + (do ! + [size (# ! each (n.% /.width) random.nat) + .let [spare (n.- size /.width)] + offset (# ! each (n.% spare) random.nat)] + (_.cover [/.region] + (case size + 0 (#= /.false (/.region offset size)) + _ (#= (|> pattern + ... NNNNYYYYNNNN + (/.right_shifted offset) + ... ____NNNNYYYY + (/.left_shifted spare) + ... YYYY________ + (/.right_shifted spare) + ... ________YYYY + (/.left_shifted offset) + ... ____YYYY____ + ) + (/.and (/.region offset size) pattern))))) + )))) (def: sub Test @@ -139,25 +139,25 @@ (-> (-> I64 (I64 size)) (Random (I64 size)))) (function (_ narrow) (# random.functor each narrow random.i64)))]] - ($_ _.and - ($equivalence.spec (# sub sub_equivalence) (random (# sub narrow))) - (_.cover [/.sub] - (let [actual (|> expected .i64 (# sub narrow) (# sub wide))] - (#= expected actual))) - )))))) + (all _.and + ($equivalence.spec (# sub sub_equivalence) (random (# sub narrow))) + (_.cover [/.sub] + (let [actual (|> expected .i64 (# sub narrow) (# sub wide))] + (#= expected actual))) + )))))) (def: signature Test - ($_ _.and - (_.for [/.equivalence] - ($equivalence.spec /.equivalence random.i64)) - (_.for [/.hash] - ($hash.spec /.hash random.i64)) - (_.for [/.disjunction] - ($monoid.spec n.equivalence /.disjunction random.nat)) - (_.for [/.conjunction] - ($monoid.spec n.equivalence /.conjunction random.nat)) - )) + (all _.and + (_.for [/.equivalence] + ($equivalence.spec /.equivalence random.i64)) + (_.for [/.hash] + ($hash.spec /.hash random.i64)) + (_.for [/.disjunction] + ($monoid.spec n.equivalence /.disjunction random.nat)) + (_.for [/.conjunction] + ($monoid.spec n.equivalence /.conjunction random.nat)) + )) (def: .public test Test @@ -166,100 +166,100 @@ (do [! random.monad] [pattern random.nat idx (# ! each (n.% /.width) random.nat)] - ($_ _.and - (_.cover [/.width /.bits_per_byte /.bytes_per_i64] - (and (n.= /.bytes_per_i64 - (n./ /.bits_per_byte /.width)) - (n.= /.bits_per_byte - (n./ /.bytes_per_i64 /.width)))) - (_.cover [/.false] - (n.= 0 (/.ones /.false))) - (_.cover [/.or] - (and (#= /.true (/.or /.true pattern)) - (#= pattern (/.or /.false pattern)))) - (_.cover [/.true] - (n.= /.width (/.ones /.true))) - (_.cover [/.and] - (and (#= pattern (/.and /.true pattern)) - (#= /.false (/.and /.false pattern)))) - (_.cover [/.not] - (and (#= /.false - (/.and pattern - (/.not pattern))) - (#= /.true - (/.or pattern - (/.not pattern))))) - (_.cover [/.xor] - (and (#= /.true - (/.xor pattern - (/.not pattern))) - (#= /.false - (/.xor pattern - pattern)))) - (_.cover [/.ones] - (let [zero&one! - (if (/.one? idx pattern) - (n.= (-- (/.ones pattern)) (/.ones (/.zero idx pattern))) - (n.= (++ (/.ones pattern)) (/.ones (/.one idx pattern)))) - - complementarity! - (n.= /.width - (n.+ (/.ones pattern) - (/.ones (/.not pattern))))] - (and zero&one! - complementarity!))) - (_.cover [/.left_rotated /.right_rotated] - (let [false! - (and (#= /.false (/.left_rotated idx /.false)) - (#= /.false (/.right_rotated idx /.false))) - - true! - (and (#= /.true (/.left_rotated idx /.true)) - (#= /.true (/.right_rotated idx /.true))) - - inverse! - (and (|> pattern - (/.left_rotated idx) - (/.right_rotated idx) - (#= pattern)) - (|> pattern - (/.right_rotated idx) - (/.left_rotated idx) - (#= pattern))) + (all _.and + (_.cover [/.width /.bits_per_byte /.bytes_per_i64] + (and (n.= /.bytes_per_i64 + (n./ /.bits_per_byte /.width)) + (n.= /.bits_per_byte + (n./ /.bytes_per_i64 /.width)))) + (_.cover [/.false] + (n.= 0 (/.ones /.false))) + (_.cover [/.or] + (and (#= /.true (/.or /.true pattern)) + (#= pattern (/.or /.false pattern)))) + (_.cover [/.true] + (n.= /.width (/.ones /.true))) + (_.cover [/.and] + (and (#= pattern (/.and /.true pattern)) + (#= /.false (/.and /.false pattern)))) + (_.cover [/.not] + (and (#= /.false + (/.and pattern + (/.not pattern))) + (#= /.true + (/.or pattern + (/.not pattern))))) + (_.cover [/.xor] + (and (#= /.true + (/.xor pattern + (/.not pattern))) + (#= /.false + (/.xor pattern + pattern)))) + (_.cover [/.ones] + (let [zero&one! + (if (/.one? idx pattern) + (n.= (-- (/.ones pattern)) (/.ones (/.zero idx pattern))) + (n.= (++ (/.ones pattern)) (/.ones (/.one idx pattern)))) - nullity! - (and (|> pattern - (/.left_rotated 0) - (#= pattern)) - (|> pattern - (/.right_rotated 0) - (#= pattern))) + complementarity! + (n.= /.width + (n.+ (/.ones pattern) + (/.ones (/.not pattern))))] + (and zero&one! + complementarity!))) + (_.cover [/.left_rotated /.right_rotated] + (let [false! + (and (#= /.false (/.left_rotated idx /.false)) + (#= /.false (/.right_rotated idx /.false))) - futility! - (and (|> pattern - (/.left_rotated /.width) - (#= pattern)) - (|> pattern - (/.right_rotated /.width) - (#= pattern)))] - (and false! true! + (and (#= /.true (/.left_rotated idx /.true)) + (#= /.true (/.right_rotated idx /.true))) + inverse! + (and (|> pattern + (/.left_rotated idx) + (/.right_rotated idx) + (#= pattern)) + (|> pattern + (/.right_rotated idx) + (/.left_rotated idx) + (#= pattern))) + nullity! - futility!))) - (_.cover [/.reversed] - (and (|> pattern /.reversed /.reversed (#= pattern)) - (or (|> pattern /.reversed (#= pattern) not) - (let [high (/.and (hex "FFFFFFFF00000000") - pattern) - low (/.and (hex "00000000FFFFFFFF") - pattern)] - (#= (/.reversed high) - low))))) - - ..bit - ..shift - ..mask - ..sub - ..signature - )))) + (and (|> pattern + (/.left_rotated 0) + (#= pattern)) + (|> pattern + (/.right_rotated 0) + (#= pattern))) + + futility! + (and (|> pattern + (/.left_rotated /.width) + (#= pattern)) + (|> pattern + (/.right_rotated /.width) + (#= pattern)))] + (and false! + true! + inverse! + nullity! + futility!))) + (_.cover [/.reversed] + (and (|> pattern /.reversed /.reversed (#= pattern)) + (or (|> pattern /.reversed (#= pattern) not) + (let [high (/.and (hex "FFFFFFFF00000000") + pattern) + low (/.and (hex "00000000FFFFFFFF") + pattern)] + (#= (/.reversed high) + low))))) + + ..bit + ..shift + ..mask + ..sub + ..signature + )))) diff --git a/stdlib/source/test/lux/math/number/i8.lux b/stdlib/source/test/lux/math/number/i8.lux index 6e20a2117..3994b5433 100644 --- a/stdlib/source/test/lux/math/number/i8.lux +++ b/stdlib/source/test/lux/math/number/i8.lux @@ -1,18 +1,18 @@ (.using - [library - [lux "*" - ["_" test {"+" Test}] - [abstract - [monad {"+" do}] - [\\specification - ["$[0]" equivalence]]] - [math - ["[0]" random {"+" Random}]]]] - [\\library - ["[0]" / - ["/[1]" // "_" - ["i" int] - ["[1][0]" i64]]]]) + [library + [lux "*" + ["_" test {"+" Test}] + [abstract + [monad {"+" do}] + [\\specification + ["$[0]" equivalence]]] + [math + ["[0]" random {"+" Random}]]]] + [\\library + ["[0]" / + ["/[1]" // "_" + ["i" int] + ["[1][0]" i64]]]]) (def: .public random (Random /.I8) @@ -28,11 +28,11 @@ .int ++)] expected (# ! each (i.% limit) random.int)] - ($_ _.and - (_.for [/.equivalence] - ($equivalence.spec /.equivalence ..random)) - - (_.cover [/.i8 /.i64 /.width] - (let [actual (|> expected .i64 /.i8 /.i64)] - (# //i64.equivalence = expected actual))) - )))) + (all _.and + (_.for [/.equivalence] + ($equivalence.spec /.equivalence ..random)) + + (_.cover [/.i8 /.i64 /.width] + (let [actual (|> expected .i64 /.i8 /.i64)] + (# //i64.equivalence = expected actual))) + )))) diff --git a/stdlib/source/test/lux/math/number/int.lux b/stdlib/source/test/lux/math/number/int.lux index 4a6b893f4..9265507e7 100644 --- a/stdlib/source/test/lux/math/number/int.lux +++ b/stdlib/source/test/lux/math/number/int.lux @@ -25,230 +25,230 @@ (def: signature Test - (`` ($_ _.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] - ($interval.spec /.interval random.int)) - (~~ (template [<monoid>] - [(_.for [<monoid>] - ($monoid.spec /.equivalence <monoid> random.int))] - - [/.addition] - [/.multiplication] + (`` (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] + ($interval.spec /.interval random.int)) + (~~ (template [<monoid>] + [(_.for [<monoid>] + ($monoid.spec /.equivalence <monoid> random.int))] + + [/.addition] + [/.multiplication] - [/.minimum] - [/.maximum] - )) - (~~ (template [<codec>] - [(_.for [<codec>] - ($codec.spec /.equivalence <codec> random.int))] + [/.minimum] + [/.maximum] + )) + (~~ (template [<codec>] + [(_.for [<codec>] + ($codec.spec /.equivalence <codec> random.int))] - [/.binary] [/.octal] [/.decimal] [/.hex] - )) - ))) + [/.binary] [/.octal] [/.decimal] [/.hex] + )) + ))) (def: predicate Test (do [! random.monad] [sample random.int] - ($_ _.and - (_.cover [/.negative?] - (bit#= (/.negative? sample) - (/.< +0 sample))) - (_.cover [/.positive?] - (bit#= (/.positive? sample) - (/.> +0 sample))) - (_.cover [/.zero?] - (bit#= (/.zero? sample) - (/.= +0 sample))) - (_.cover [/.even? /.odd?] - (bit#= (/.even? sample) - (not (/.odd? sample)))) - ))) + (all _.and + (_.cover [/.negative?] + (bit#= (/.negative? sample) + (/.< +0 sample))) + (_.cover [/.positive?] + (bit#= (/.positive? sample) + (/.> +0 sample))) + (_.cover [/.zero?] + (bit#= (/.zero? sample) + (/.= +0 sample))) + (_.cover [/.even? /.odd?] + (bit#= (/.even? sample) + (not (/.odd? sample)))) + ))) (def: .public test Test (<| (_.covering /._) (_.for [.Int]) (let [(open "/#[0]") /.interval]) - ($_ _.and - (do random.monad - [sample random.int - left random.int - right random.int] - ($_ _.and - (_.cover [/.+] - (and (/.= (/.+ left right) - (/.+ right left)) - (/.= sample (/.+ +0 sample)))) - (_.cover [/.-] - (and (/.= +0 (/.- sample sample)) - (/.= sample (/.- +0 sample)) - (/.= (/.opposite sample) - (/.- sample +0)) - (/.= /#bottom - (/.- /#bottom +0)))) - (_.cover [/.*] - (and (/.= (/.* left right) - (/.* right left)) - (/.= sample (/.* +1 sample)) - (/.= /#bottom - (/.* -1 /#bottom)))) - (_.cover [/./] - (and (/.= +1 (/./ sample sample)) - (/.= sample (/./ +1 sample)) - (/.= /#bottom - (/./ -1 /#bottom)))) - (_.cover [/.abs] - (bit#= (/.> sample (/.abs sample)) - (/.negative? sample))) - (_.cover [/.signum] - (/.= (/.abs sample) - (/.* (/.signum sample) sample))) - (_.cover [/.min] - (and (/.= (/.min left right) - (/.min right left)) - (/.= sample - (/.min /#top sample)) - (/.= /#bottom - (/.min /#bottom sample)))) - (_.cover [/.max] - (and (/.= (/.max left right) - (/.max right left)) - (/.= /#top - (/.max /#top sample)) - (/.= sample - (/.max /#bottom sample)))) - )) - (do random.monad - [left random.int - right random.int] - ($_ _.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] - ($_ _.and - (_.cover [/.%] - (let [rem (/.% left right) - div (|> right (/.- rem) (/./ left))] - (/.= right - (|> div (/.* left) (/.+ rem))))) - (_.cover [/./%] - (let [[div rem] (/./% left right)] - (and (/.= div (/./ left right)) - (/.= rem (/.% left right))))) - (_.cover [/.mod] - (and (/.= (/.signum left) - (/.signum (/.mod left right))) - (/.= (/.signum right) - (/.signum (/.% left right))) - (if (/.= (/.signum left) (/.signum right)) - (/.= (/.% left right) - (/.mod left right)) - (or (and (/.= +0 (/.% left right)) - (/.= +0 (/.mod left right))) - (/.= (/.+ left (/.% left right)) - (/.mod left right)))))) - )) - (do [! random.monad] - [.let [random (|> random.int - (# ! each (/.% +1,000)) - (random.only (|>> (/.= +0) not)))] - left random - right random] - ($_ _.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) + (all _.and + (do random.monad + [sample random.int + left random.int + right random.int] + (all _.and + (_.cover [/.+] + (and (/.= (/.+ left right) + (/.+ right left)) + (/.= sample (/.+ +0 sample)))) + (_.cover [/.-] + (and (/.= +0 (/.- sample sample)) + (/.= sample (/.- +0 sample)) + (/.= (/.opposite sample) + (/.- sample +0)) + (/.= /#bottom + (/.- /#bottom +0)))) + (_.cover [/.*] + (and (/.= (/.* left right) + (/.* right left)) + (/.= sample (/.* +1 sample)) + (/.= /#bottom + (/.* -1 /#bottom)))) + (_.cover [/./] + (and (/.= +1 (/./ sample sample)) + (/.= sample (/./ +1 sample)) + (/.= /#bottom + (/./ -1 /#bottom)))) + (_.cover [/.abs] + (bit#= (/.> sample (/.abs sample)) + (/.negative? sample))) + (_.cover [/.signum] + (/.= (/.abs sample) + (/.* (/.signum sample) sample))) + (_.cover [/.min] + (and (/.= (/.min left right) + (/.min right left)) + (/.= sample + (/.min /#top sample)) + (/.= /#bottom + (/.min /#bottom sample)))) + (_.cover [/.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 + (_.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] + (all _.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 + (# ! each (/.% +1,000)) + (random.only (|>> (/.= +0) not)))] + left random + right random] + (all _.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 [/.opposite] - (let [subtraction! - (/.= +0 (/.+ (/.opposite expected) expected)) + 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 [/.opposite] + (let [subtraction! + (/.= +0 (/.+ (/.opposite expected) expected)) - inverse! - (|> expected /.opposite /.opposite (/.= expected))] - (and subtraction! - inverse!)))) - (do [! random.monad] - [expected (# ! each (/.% +1,000,000) random.int) - sample random.int] - (_.cover [/.frac] - (and (|> expected /.frac f.int (/.= expected)) - (f.number? (/.frac sample))))) - (do [! random.monad] - [pattern random.int - idx (# ! each (n.% i64.width) random.nat)] - (_.cover [/.right_shifted] - (let [nullity! - (/.= pattern (/.right_shifted 0 pattern)) + inverse! + (|> expected /.opposite /.opposite (/.= expected))] + (and subtraction! + inverse!)))) + (do [! random.monad] + [expected (# ! each (/.% +1,000,000) random.int) + sample random.int] + (_.cover [/.frac] + (and (|> expected /.frac f.int (/.= expected)) + (f.number? (/.frac sample))))) + (do [! random.monad] + [pattern random.int + idx (# ! each (n.% i64.width) random.nat)] + (_.cover [/.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))) + idempotency! + (/.= pattern (/.right_shifted i64.width pattern)) - mantissa_parity! - (/.= (i64.and mantissa_mask (i64.right_shifted idx pattern)) - (i64.and mantissa_mask (/.right_shifted idx 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) - 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! + (/.= (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 - ))) + ..predicate + ..signature + ))) diff --git a/stdlib/source/test/lux/math/number/nat.lux b/stdlib/source/test/lux/math/number/nat.lux index f236a7aa6..05c248337 100644 --- a/stdlib/source/test/lux/math/number/nat.lux +++ b/stdlib/source/test/lux/math/number/nat.lux @@ -1,132 +1,132 @@ (.using - [library - [lux "*" - ["_" test {"+" Test}] - [abstract - [monad {"+" do}] - [\\specification - ["$[0]" equivalence] - ["$[0]" hash] - ["$[0]" order] - ["$[0]" enum] - ["$[0]" interval] - ["$[0]" monoid] - ["$[0]" codec]]] - [data - ["[0]" bit ("[1]#[0]" equivalence)]] - [math - ["[0]" random]]]] - [\\library - ["[0]" / - [// - ["f" frac]]]]) + [library + [lux "*" + ["_" test {"+" Test}] + [abstract + [monad {"+" do}] + [\\specification + ["$[0]" equivalence] + ["$[0]" hash] + ["$[0]" order] + ["$[0]" enum] + ["$[0]" interval] + ["$[0]" monoid] + ["$[0]" codec]]] + [data + ["[0]" bit ("[1]#[0]" equivalence)]] + [math + ["[0]" random]]]] + [\\library + ["[0]" / + [// + ["f" frac]]]]) (def: signature Test - (`` ($_ _.and - (_.for [/.equivalence /.=] - ($equivalence.spec /.equivalence random.nat)) - (_.for [/.hash] - ($hash.spec /.hash random.nat)) - (_.for [/.order /.<] - ($order.spec /.order random.nat)) - (_.for [/.enum] - ($enum.spec /.enum random.nat)) - (_.for [/.interval] - ($interval.spec /.interval random.nat)) - (~~ (template [<composite> <monoid>] - [(_.for [<monoid> <composite>] - ($monoid.spec /.equivalence <monoid> random.nat))] - - [/.+ /.addition] - [/.* /.multiplication] + (`` (all _.and + (_.for [/.equivalence /.=] + ($equivalence.spec /.equivalence random.nat)) + (_.for [/.hash] + ($hash.spec /.hash random.nat)) + (_.for [/.order /.<] + ($order.spec /.order random.nat)) + (_.for [/.enum] + ($enum.spec /.enum random.nat)) + (_.for [/.interval] + ($interval.spec /.interval random.nat)) + (~~ (template [<composite> <monoid>] + [(_.for [<monoid> <composite>] + ($monoid.spec /.equivalence <monoid> random.nat))] + + [/.+ /.addition] + [/.* /.multiplication] - [/.min /.minimum] - [/.max /.maximum] - )) - (~~ (template [<codec>] - [(_.for [<codec>] - ($codec.spec /.equivalence <codec> random.nat))] + [/.min /.minimum] + [/.max /.maximum] + )) + (~~ (template [<codec>] + [(_.for [<codec>] + ($codec.spec /.equivalence <codec> random.nat))] - [/.binary] [/.octal] [/.decimal] [/.hex] - )) - ))) + [/.binary] [/.octal] [/.decimal] [/.hex] + )) + ))) (def: predicate Test (do [! random.monad] [sample random.nat] - ($_ _.and - (_.cover [/.even? /.odd?] - (bit#= (/.even? sample) - (not (/.odd? sample)))) - ))) + (all _.and + (_.cover [/.even? /.odd?] + (bit#= (/.even? sample) + (not (/.odd? sample)))) + ))) (def: .public test Test (<| (_.covering /._) (_.for [.Nat]) - ($_ _.and - (do random.monad - [sample random.nat] - ($_ _.and - (_.cover [/.-] - (and (/.= 0 (/.- sample sample)) - (/.= sample (/.- 0 sample)))) - (_.cover [/./] - (and (/.= 1 (/./ sample sample)) - (/.= sample (/./ 1 sample)))) - )) - (do random.monad - [left random.nat - right random.nat] - ($_ _.and - (_.cover [/.>] - (bit#= (/.> left right) - (/.< right left))) - (_.cover [/.<= /.>=] - (bit#= (/.<= left right) - (/.>= right left))) - )) - (do random.monad - [left (random.only (|>> (/.= 0) not) - random.nat) - right random.nat] - ($_ _.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))))) - )) - (do [! random.monad] - [.let [random (# ! each (|>> (/.% 1,000) ++) random.nat)] - left random - right random] - ($_ _.and - (_.cover [/.gcd] - (let [gcd (/.gcd left right)] - (and (/.= 0 (/.% gcd left)) - (/.= 0 (/.% gcd right))))) - (_.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 (# ! each (/.% 1,000,000) random.nat) - sample random.nat] - (_.cover [/.frac] - (and (|> expected /.frac f.nat (/.= expected)) - (f.number? (/.frac sample))))) + (all _.and + (do random.monad + [sample random.nat] + (all _.and + (_.cover [/.-] + (and (/.= 0 (/.- sample sample)) + (/.= sample (/.- 0 sample)))) + (_.cover [/./] + (and (/.= 1 (/./ sample sample)) + (/.= sample (/./ 1 sample)))) + )) + (do random.monad + [left random.nat + right random.nat] + (all _.and + (_.cover [/.>] + (bit#= (/.> left right) + (/.< right left))) + (_.cover [/.<= /.>=] + (bit#= (/.<= left right) + (/.>= right left))) + )) + (do random.monad + [left (random.only (|>> (/.= 0) not) + random.nat) + right random.nat] + (all _.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))))) + )) + (do [! random.monad] + [.let [random (# ! each (|>> (/.% 1,000) ++) random.nat)] + left random + right random] + (all _.and + (_.cover [/.gcd] + (let [gcd (/.gcd left right)] + (and (/.= 0 (/.% gcd left)) + (/.= 0 (/.% gcd right))))) + (_.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 (# ! each (/.% 1,000,000) random.nat) + sample random.nat] + (_.cover [/.frac] + (and (|> expected /.frac f.nat (/.= expected)) + (f.number? (/.frac sample))))) - ..predicate - ..signature - ))) + ..predicate + ..signature + ))) diff --git a/stdlib/source/test/lux/math/number/ratio.lux b/stdlib/source/test/lux/math/number/ratio.lux index d9c1c1ba8..a5af79e0b 100644 --- a/stdlib/source/test/lux/math/number/ratio.lux +++ b/stdlib/source/test/lux/math/number/ratio.lux @@ -38,90 +38,90 @@ Test (<| (_.covering /._) (_.for [/.Ratio]) - (`` ($_ _.and - (_.for [/.equivalence /.=] - ($equivalence.spec /.equivalence ..random)) - (_.for [/.order /.<] - ($order.spec /.order ..random)) - (~~ (template [<composite> <monoid>] - [(_.for [<monoid> <composite>] - ($monoid.spec /.equivalence <monoid> ..random))] + (`` (all _.and + (_.for [/.equivalence /.=] + ($equivalence.spec /.equivalence ..random)) + (_.for [/.order /.<] + ($order.spec /.order ..random)) + (~~ (template [<composite> <monoid>] + [(_.for [<monoid> <composite>] + ($monoid.spec /.equivalence <monoid> ..random))] - [/.+ /.addition] - [/.* /.multiplication] - )) - (_.for [/.codec] - ($codec.spec /.equivalence /.codec ..random)) + [/.+ /.addition] + [/.* /.multiplication] + )) + (_.for [/.codec] + ($codec.spec /.equivalence /.codec ..random)) - (do random.monad - [.let [(open "#[0]") /.equivalence] - denom/0 ..part - denom/1 ..part] - (_.cover [/.ratio] - (#= (/.ratio 0 denom/0) - (/.ratio 0 denom/1)))) - (do random.monad - [numerator ..part - denominator (random.only (|>> (n#= 1) not) - ..part)] - (_.cover [/.nat] - (let [only_numerator! - (|> (/.ratio numerator) - /.nat - (maybe#each (n#= numerator)) - (maybe.else false)) + (do random.monad + [.let [(open "#[0]") /.equivalence] + denom/0 ..part + denom/1 ..part] + (_.cover [/.ratio] + (#= (/.ratio 0 denom/0) + (/.ratio 0 denom/1)))) + (do random.monad + [numerator ..part + denominator (random.only (|>> (n#= 1) not) + ..part)] + (_.cover [/.nat] + (let [only_numerator! + (|> (/.ratio numerator) + /.nat + (maybe#each (n#= numerator)) + (maybe.else false)) - denominator_1! - (|> (/.ratio numerator 1) - /.nat - (maybe#each (n#= numerator)) - (maybe.else false)) - - with_denominator! - (case (/.nat (/.ratio numerator denominator)) - {.#Some factor} - (and (n.= 0 (n.% denominator numerator)) - (n.= numerator (n.* factor denominator))) - - {.#None} - (not (n.= 0 (n.% denominator numerator))))] - (and only_numerator! denominator_1! - with_denominator!)))) - (do random.monad - [sample ..random] - ($_ _.and - (_.cover [/.-] - (and (/.= (/.ratio 0) (/.- sample sample)) - (/.= sample (/.- (/.ratio 0) sample)))) - (_.cover [/./] - (and (/.= (/.ratio 1) (/./ sample sample)) - (/.= sample (/./ (/.ratio 1) sample)))) - (_.cover [/.reciprocal] - (/.= (/.ratio 1) - (/.* sample (/.reciprocal sample)))) - )) - (do random.monad - [left (random.only (|>> (/.= (/.ratio 0)) not) - ..random) - right ..random] - (_.cover [/.%] - (let [rem (/.% left right) - div (|> right (/.- rem) (/./ left))] - (and (/.= right - (|> div (/.* left) (/.+ rem))) - (case (/.nat div) - {.#Some _} true - {.#None} false))))) - (do random.monad - [left ..random - right ..random] - ($_ _.and - (_.cover [/.>] - (bit#= (/.> left right) - (/.< right left))) - (_.cover [/.<= /.>=] - (bit#= (/.<= left right) - (/.>= right left))) - )) - )))) + (|> (/.ratio numerator 1) + /.nat + (maybe#each (n#= numerator)) + (maybe.else false)) + + with_denominator! + (case (/.nat (/.ratio numerator denominator)) + {.#Some factor} + (and (n.= 0 (n.% denominator numerator)) + (n.= numerator (n.* factor denominator))) + + {.#None} + (not (n.= 0 (n.% denominator numerator))))] + (and only_numerator! + denominator_1! + with_denominator!)))) + (do random.monad + [sample ..random] + (all _.and + (_.cover [/.-] + (and (/.= (/.ratio 0) (/.- sample sample)) + (/.= sample (/.- (/.ratio 0) sample)))) + (_.cover [/./] + (and (/.= (/.ratio 1) (/./ sample sample)) + (/.= sample (/./ (/.ratio 1) sample)))) + (_.cover [/.reciprocal] + (/.= (/.ratio 1) + (/.* sample (/.reciprocal sample)))) + )) + (do random.monad + [left (random.only (|>> (/.= (/.ratio 0)) not) + ..random) + right ..random] + (_.cover [/.%] + (let [rem (/.% left right) + div (|> right (/.- rem) (/./ left))] + (and (/.= right + (|> div (/.* left) (/.+ rem))) + (case (/.nat div) + {.#Some _} true + {.#None} false))))) + (do random.monad + [left ..random + right ..random] + (all _.and + (_.cover [/.>] + (bit#= (/.> left right) + (/.< right left))) + (_.cover [/.<= /.>=] + (bit#= (/.<= left right) + (/.>= right left))) + )) + )))) diff --git a/stdlib/source/test/lux/math/number/rev.lux b/stdlib/source/test/lux/math/number/rev.lux index 88473533d..7fe3c86dd 100644 --- a/stdlib/source/test/lux/math/number/rev.lux +++ b/stdlib/source/test/lux/math/number/rev.lux @@ -1,167 +1,167 @@ (.using - [library - [lux "*" - ["_" test {"+" Test}] - [abstract - [monad {"+" do}] - [\\specification - ["$[0]" equivalence] - ["$[0]" hash] - ["$[0]" order] - ["$[0]" enum] - ["$[0]" interval] - ["$[0]" monoid] - ["$[0]" codec]]] - [data - ["[0]" bit ("[1]#[0]" equivalence)]] - [math - ["[0]" random]]]] - [\\library - ["[0]" / - [// {"+" hex} - ["n" nat] - ["f" frac] - ["[0]" i64 ("[1]#[0]" hash)]]]]) + [library + [lux "*" + ["_" test {"+" Test}] + [abstract + [monad {"+" do}] + [\\specification + ["$[0]" equivalence] + ["$[0]" hash] + ["$[0]" order] + ["$[0]" enum] + ["$[0]" interval] + ["$[0]" monoid] + ["$[0]" codec]]] + [data + ["[0]" bit ("[1]#[0]" equivalence)]] + [math + ["[0]" random]]]] + [\\library + ["[0]" / + [// {"+" hex} + ["n" nat] + ["f" frac] + ["[0]" i64 ("[1]#[0]" hash)]]]]) (def: signature Test - (`` ($_ _.and - (_.for [/.equivalence /.=] - ($equivalence.spec /.equivalence random.rev)) - (_.for [/.hash] - ($hash.spec /.hash random.rev)) - (_.for [/.order /.<] - ($order.spec /.order random.rev)) - (_.for [/.enum] - ($enum.spec /.enum random.rev)) - (_.for [/.interval] - ($interval.spec /.interval random.rev)) - (~~ (template [<composite> <monoid>] - [(_.for [<monoid> <composite>] - ($monoid.spec /.equivalence <monoid> random.rev))] + (`` (all _.and + (_.for [/.equivalence /.=] + ($equivalence.spec /.equivalence random.rev)) + (_.for [/.hash] + ($hash.spec /.hash random.rev)) + (_.for [/.order /.<] + ($order.spec /.order random.rev)) + (_.for [/.enum] + ($enum.spec /.enum random.rev)) + (_.for [/.interval] + ($interval.spec /.interval random.rev)) + (~~ (template [<composite> <monoid>] + [(_.for [<monoid> <composite>] + ($monoid.spec /.equivalence <monoid> random.rev))] - [/.+ /.addition] + [/.+ /.addition] - [/.min /.minimum] - [/.max /.maximum] - )) - (~~ (template [<codec>] - [(_.for [<codec>] - ($codec.spec /.equivalence <codec> random.rev))] + [/.min /.minimum] + [/.max /.maximum] + )) + (~~ (template [<codec>] + [(_.for [<codec>] + ($codec.spec /.equivalence <codec> random.rev))] - [/.binary] [/.octal] [/.decimal] [/.hex] - )) - ))) + [/.binary] [/.octal] [/.decimal] [/.hex] + )) + ))) (def: .public test Test (<| (_.covering /._) (_.for [.Rev]) - (`` ($_ _.and - (~~ (template [<half> <whole>] - [(_.cover [<half>] - (/.= <whole> - (/.+ <half> <half>)))] + (`` (all _.and + (~~ (template [<half> <whole>] + [(_.cover [<half>] + (/.= <whole> + (/.+ <half> <half>)))] - [/./1 (-- /./1)] - [/./2 .0] - [/./4 /./2] - [/./8 /./4] - [/./16 /./8] - [/./32 /./16] - [/./64 /./32] - [/./128 /./64] - [/./256 /./128] - [/./512 /./256] - [/./1024 /./512] - [/./2048 /./1024] - [/./4096 /./2048] - )) - (do random.monad - [sample random.rev] - (_.cover [/.-] - (and (/.= .0 (/.- sample sample)) - (/.= sample (/.- .0 sample))))) - (do [! random.monad] - [left random.rev - right random.rev] - (_.cover [/.*] - (and (/.< left (/.* left right)) - (/.< right (/.* left right))))) - (do [! random.monad] - [.let [dividend (# ! each (i64.and (hex "FFFF")) - random.rev) - divisor (# ! each (|>> (i64.and (hex "F")) - (i64.or (hex "1")) - (i64.right_rotated 8) - .rev) - random.nat)] - dividend (random.only (/.> .0) dividend) - divisor/0 divisor - divisor/1 (random.only (|>> (/.= divisor/0) not) - divisor) - scale (# ! each (|>> (n.% 10) ++) - random.nat)] - ($_ _.and - (_.cover [/./] - (bit#= (/.< divisor/0 divisor/1) - (/.> (/./ divisor/0 dividend) (/./ divisor/1 dividend)))) - (_.cover [/.%] - (# i64.equivalence = - (.i64 (n.% (.nat divisor/0) (.nat dividend))) - (.i64 (/.% divisor/0 dividend)))) - (_.cover [/.up /.down] - (let [symmetry! - (|> dividend - (/.up scale) - (/.down scale) - (/.= dividend)) + [/./1 (-- /./1)] + [/./2 .0] + [/./4 /./2] + [/./8 /./4] + [/./16 /./8] + [/./32 /./16] + [/./64 /./32] + [/./128 /./64] + [/./256 /./128] + [/./512 /./256] + [/./1024 /./512] + [/./2048 /./1024] + [/./4096 /./2048] + )) + (do random.monad + [sample random.rev] + (_.cover [/.-] + (and (/.= .0 (/.- sample sample)) + (/.= sample (/.- .0 sample))))) + (do [! random.monad] + [left random.rev + right random.rev] + (_.cover [/.*] + (and (/.< left (/.* left right)) + (/.< right (/.* left right))))) + (do [! random.monad] + [.let [dividend (# ! each (i64.and (hex "FFFF")) + random.rev) + divisor (# ! each (|>> (i64.and (hex "F")) + (i64.or (hex "1")) + (i64.right_rotated 8) + .rev) + random.nat)] + dividend (random.only (/.> .0) dividend) + divisor/0 divisor + divisor/1 (random.only (|>> (/.= divisor/0) not) + divisor) + scale (# ! each (|>> (n.% 10) ++) + random.nat)] + (all _.and + (_.cover [/./] + (bit#= (/.< divisor/0 divisor/1) + (/.> (/./ divisor/0 dividend) (/./ divisor/1 dividend)))) + (_.cover [/.%] + (# i64.equivalence = + (.i64 (n.% (.nat divisor/0) (.nat dividend))) + (.i64 (/.% divisor/0 dividend)))) + (_.cover [/.up /.down] + (let [symmetry! + (|> dividend + (/.up scale) + (/.down scale) + (/.= dividend)) - discrete_division! - (/.= (/.% (.rev scale) dividend) - (/.- (|> dividend - (/.down scale) - (/.up scale)) - dividend))] - (and symmetry! - discrete_division!))) - (_.cover [/.ratio] - (|> dividend - (/.up scale) - (/.ratio dividend) - (n.= scale))) - )) - (do [! random.monad] - [dividend random.rev - divisor (random.only (|>> (/.= .0) not) - random.rev)] - (_.cover [/./%] - (let [[quotient remainder] (/./% divisor dividend)] - (and (/.= (/./ divisor dividend) quotient) - (/.= (/.% divisor dividend) remainder))))) - (do random.monad - [left random.rev - right random.rev] - ($_ _.and - (_.cover [/.>] - (bit#= (/.> left right) - (/.< right left))) - (_.cover [/.<= /.>=] - (bit#= (/.<= left right) - (/.>= right left))) - )) - (do random.monad - [sample random.nat] - (_.cover [/.reciprocal] - (/.= (/.reciprocal sample) - (|> sample /.reciprocal .nat /.reciprocal .nat /.reciprocal)))) - (do [! random.monad] - [expected (# ! each (|>> f.abs (f.% +1.0)) - random.safe_frac) - sample random.rev] - (_.cover [/.frac] - (and (|> expected f.rev /.frac (f.= expected)) - (f.number? (/.frac sample))))) + discrete_division! + (/.= (/.% (.rev scale) dividend) + (/.- (|> dividend + (/.down scale) + (/.up scale)) + dividend))] + (and symmetry! + discrete_division!))) + (_.cover [/.ratio] + (|> dividend + (/.up scale) + (/.ratio dividend) + (n.= scale))) + )) + (do [! random.monad] + [dividend random.rev + divisor (random.only (|>> (/.= .0) not) + random.rev)] + (_.cover [/./%] + (let [[quotient remainder] (/./% divisor dividend)] + (and (/.= (/./ divisor dividend) quotient) + (/.= (/.% divisor dividend) remainder))))) + (do random.monad + [left random.rev + right random.rev] + (all _.and + (_.cover [/.>] + (bit#= (/.> left right) + (/.< right left))) + (_.cover [/.<= /.>=] + (bit#= (/.<= left right) + (/.>= right left))) + )) + (do random.monad + [sample random.nat] + (_.cover [/.reciprocal] + (/.= (/.reciprocal sample) + (|> sample /.reciprocal .nat /.reciprocal .nat /.reciprocal)))) + (do [! random.monad] + [expected (# ! each (|>> f.abs (f.% +1.0)) + random.safe_frac) + sample random.rev] + (_.cover [/.frac] + (and (|> expected f.rev /.frac (f.= expected)) + (f.number? (/.frac sample))))) - ..signature - )))) + ..signature + )))) |