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# Tester that checks primitives on random arguments
opts ← {
help ← 1↓"
Fuzz testing. Options:
-h, --help: Print this message and exit
-b: Maximum bound (1e3)
-n: Number of iterations (100)
-t: Element type (0 3 4 5 6)
-p: Primitives: both | mon%dy | mon%dy%both
Any number of types or bounds can be given; all combinations are tested."
o ← "-h"‿"--help"‿"-b"‿"-n"‿"-t"‿"-p"
oo ← (≠o) = oi ← o ⊐ a←•args
•Exit∘•Out∘help⍟(∨´2⊸>) oi
opts ← 2↓o≠⊸↑ a ⊔˜ (¬-˜⊢× oi⊏˜ ↕∘≠⌈`∘׬)oo
bounds‿num‿types‿prims ⇐ •BQN¨¨⌾(¯1⊸↓) opts
"Only one iteration number can be given" ! 1≥≠num
num ↩ ≠◶⟨100,+´⟩ num
types ↩ 0‿3‿4‿5‿6⍟(0=≠) types
bounds ↩ ⟨1e3⟩⍟(0=≠) bounds
prims ↩ ((⊢-˜¬×+`+2×·¬∨´)'%'⊸=)¨⊸(⊔○∾) prims
"At most three %-separated primitive groups allowed" ! 3≥≠prims
arith ← ∾`"+-×÷⋆√⌊⌈¬|"‿"∧∨≤<>≥=≠"
Pr ← {
𝕩 ↩ 2 (↑((¬∘∊/⊣)∾⊢)¨⊏) 3 ↑ 𝕩
"Only arithmetic primitives supported" ! ∧´∾𝕩∊¨arith
𝕩
}
monArith‿dyArith ⇐ •BQN∘⥊¨¨ prims ↩ (0<≠)◶arith‿Pr prims
}
Squeeze‿ListVariations‿Variation‿ClearRefs ← •internal
Range ← (•MakeRand 2).Range
Rand ← {𝕨 Range 1⌈𝕩}
_randChoose ← { Rand∘(≠𝕗)◶𝕗 }
_randUnbounded ← { 𝕊⊸+⍟(1=-)⟜Rand 𝕗 }
RandRank ← 4 _randUnbounded
# Prime factorization
⟨Factor⟩ ← {
p ← (¬∘∊/⊣)⟜(⥊×⌜˜)2↓↕m←60
Pr ← {m<𝕩}◶{𝕩↑p}‿{ m↩(טm)⌊2×𝕩 ⋄ p∾↩1↓/1(m⥊0<↕)⊸∧´p ⋄ Pr 𝕩 }
Factor ⇐ {
!(1=•Type𝕩)∧(𝕩=⌊𝕩)∧0<𝕩
∧ 𝕩 {(0<≠∘⊢)◶⟨⥊⊣,⊢∾𝕊⟩⍟(>⟜1)˜⟜(𝕨÷×´)𝕩/˜0=𝕩|𝕨} Pr ⌈√𝕩
}
}
Sigmoid ← (40≤|)◶⟨1(-÷+)˜⋆,×⟩
# Generate 𝕨 positive (not zero) integers summing to 𝕩
RandPart ← {k←𝕨 ⋄ n←𝕩
RU ← Range∘0 # Random float in [0,1]
# Vitter, "An Efficient Algorithm for Sequential Random Sampling"
vPrime ← @
# Add or reject each possibility individually
MethodA ← {k←𝕩
v ← RU@
1 { (𝕨×-⟜k⊸÷n-𝕩) (⊣𝕊1+⊢)⍟(v<⊣) 𝕩 } 0
}
# Compute number of skipped possibilities
MethodD ← {k←𝕩
RvP ← k√RU # Generate new vPrime
kn ← k-1 # k for next iteration
qu1 ← n-kn
Sk ← {vP←𝕩
s ← ⌊ x ← { 𝕊∘RvP⍟(qu1⊸≤) n׬𝕩 } vP
y1 ← kn √ (n ÷ qu1) × RU@
vPrime ↩ y1 × (1-x÷n) × qu1 (⊣÷-) s
Cont ← {
y2 ← ×´ kn (((n-1)-↕∘⌊) (⊣÷-) ⌈) 𝕩
(n(⊣÷-)x) < y1 × kn√y2
}
Cont◶⟨{ vPrime↩@ ⋄ 𝕩 }, 𝕊 RvP⟩⍟(1<vPrime) s
}
Sk RvP⍟(@⊸≡) vPrime
}
Gen ← {𝕤
alphaInv ← 13 # Used to choose A or D
M ← {n≤alphaInv×𝕩}◶MethodD‿{vPrime↩@ ⋄ (M↩MethodA)𝕩}
seq ← { n-↩1+s←M𝕩 ⋄ s }¨ k-↕k-1
last ← ⌊n×RU⍟(@⊸≡)vPrime
1 + seq ∾ last
}
0⊸<◶↕‿Gen k
}
# 𝕩 is maximum bound plus 1 for both functions
⟨RandBound,RandShape⟩ ← {
RandBound ⇐ ⟨
Rand # Uniform
Rand 128⊸⌊ # Small
(0⌈-⟜1) ⌊ Rand∘(1⌈⌈)⌾((2⋆3+⊢)⁼) + ¯7+Rand∘15 # Near power of two
⟩_randChoose
Augment ← {
d ← 1+⌊𝕨÷1⌈×´𝕩 # Maximum bound that can be added, plus 1
C ← 10⊸+ Rand⊸< 1.2⊸√ # Decide whether to add
d (𝕨 𝕊 ⟨∾,∾˜⟩_randChoose⟜RandBound˜)⍟(C⊣) 𝕩
}
Combine ← ⟨
Rand∘≠⊸⌽ (2+Rand∘≠)⊸{×´¨𝕨↑(𝕨|↕∘≠)⊸⊔𝕩}∘⊢ # Random number of groups
×´¨ (⊐·Rand¨⥊˜∘≠)⊸⊔∘⊢ # Distribute randomly
⟩_randChoose
RandShape ⇐ ⊢ Augment ⟨
⊢ (⊢ ⌊∘× ⊢ ≠⊸√ (Sigmoid⊸÷1⌈×´⊸÷˜)) · Rand¨ (RandRank⌈√<Rand)⊸⥊
⊢ Combine⟜Factor 1⌈RandBound
⟩_randChoose
}
# 𝕨 is 2⋆⁼bits in type; 𝕩 is shape
⟨RandArith,RandChar,RandIndex⟩ ← {
RandInt ← { (1⊸<⊸×m÷2) -˜ 𝕩 Rand m←2⋆2⋆𝕨 }
floats ← ⟨2⋆¯1074,2⋆¯1022,(2-2⋆¯52)×2⋆1023⟩
RandFloat ← ⟨
(floats∾2⋆0‿8‿32‿100)_randChoose × Range⟜0 - 2÷˜Rand∘3
⊢ (Rand⟜≠⊏⊢) (Rand(⊣≥⌈´⊸⌊)3+Rand∘+)˜∘≠⊸/∘(∾⟜-0∾floats∾∞)
⟩_randChoose
RandTyped ← =⟜6◶⟨RandInt,RandFloat⊣⟩
RN ← (0⌈-⟜1) ⌊ 1‿RandRank‿RandBound _randChoose
RandSplit ← ⌽⍟(Rand∘2) (-≍⊢)⟜RN
Combine ← (⍋Rand˜∘≠)⊸⊏⍟(Rand∘2) ∾
_Rec_ ← {
S ← {𝕨R𝕩}
R ← ⟨
𝔽 # Random
∧‿∨_randChoose 𝔽 # Sort
⊢ ⟨⥊,RandPart˜⟜≠/⊢⟩_randChoose S⟜(1⌈RN) # Repeat
Combine <⊸(𝔾‿⊢_randChoose⊸S¨)⟜RandSplit # Partition
⟩{ 8⊸≤◶⟨0,Rand∘(≠𝕗)⟩◶𝕗 }
⊢ ⥊ R⟜(×´⥊)
}
RandArith ⇐ Squeeze RandTyped _Rec_ Rand
ContractRange ← (⟨≍⟜0,0≍-⟩_randChoose·RN-˜´)⊸+
RandInterval ← (⊑∘⊣ + -˜´⊸(Rand˜)) _Rec_ ContractRange
RandIndex ⇐ Squeeze (0⊸≍ ⊣ ·!0⊸<)⊸RandInterval
ch_end ← 17×2⋆16 ⋄ surr ← (2⋆11)×27+↕2
RandChar ⇐ Squeeze @ + ·(1≠surr⊸⍋)⊸× (0≍ch_end⌊2⋆2⋆⊣)⊸RandInterval
}
_testConsistent_ ← {Match←𝔾
v ← <˘⍉> (5⌊´≠¨)⊸((Rand⟜≠⊏⊢)¨) ListVariations¨ a←𝕨≍○<𝕩
(ClearRefs@) ⊢ (∧´ ⊏ Match¨ 1⊸↓) (𝕨 (𝔽⊑∘⊢)⊘(𝔽´⊢) Variation¨⟜a)¨ v
}
FlatMatch ← ≡◶⟨∧´∘⥊=∨∧○(≠˜),1⟩
TestMonArith ← opts.monArith{
(0<≠f←𝕗) ⊑ 1‿{
_t ← { ! 𝕏 _testConsistent_ FlatMatch 𝕗 }
(𝕨 RandArith RandShape 𝕩)_t¨ f
}
}
RandDyShape ← {
Prefix ← (∨`⌾⌽ 𝕩 ≥ ×`)⊸/ (Rand 1+≠)⊸↑
(Rand 2) ⌽ ≍○<⟜Prefix RandShape 𝕩
}
TestDyArith ← opts.dyArith{
(0<≠f←𝕗) ⊑ 1‿{
sh ← RandDyShape 𝕩
_t ← { ! 𝕏 _testConsistent_ FlatMatch´ 𝕗 }
(𝕨⊸RandArith¨ sh)_t¨ f
{
k←𝕩
p‿m‿n ← (∊/⊣)⟜f¨ ⟨+⟩‿⟨-⟩‿⟨¬⟩
rca ← ⟨RandChar,RandArith⟩
Fit ← -⟜(@+1-˜17×2⋆16)⌈-⟜@⌊⊢
{ (⌽⍟(Rand 2) -∘Fit⟜-` rca{k𝕎𝕩}¨sh)_t 𝕩 }¨ p
{ s←Rand 2⋄(Fit`⍟s(⊣`⍟(¬s)rca){k𝕎𝕩}¨sh)_t 𝕩 }¨ m
{ s←Rand 2⋄((1+Fit)`⍟s(⊣`⍟(¬s)rca){k𝕎𝕩}¨sh)_t 𝕩 }¨ n
}⍟(0⊸<∧≤⟜5) 𝕨
}
}
t←opts.types ⋄ b←opts.num/opts.bounds
t TestMonArith⌜ b
t TestDyArith ⌜ b
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