1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
|
# 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
prims ↩ 2 (↑((¬∘∊/⊣)∾⊢)¨⊏) 3 ↑ 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(-÷+)˜⋆,×⟩
# 𝕨 positive (not zero) integers summing to 𝕩
RandPart ← { ¬⟜» (𝕨-1) (∧∘Rand∾1-˜⊢) 𝕩¬𝕨 }
# 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
}
RandShape1 ← 1⊸∾⍟(0=≠) RandShape
# 𝕨 is 2⋆⁼bits in type; 𝕩 is shape
gen ← {
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⟜(×´⥊)
}
Arith ⇐ Squeeze RandTyped _Rec_ Rand
ContractRange ← (⟨≍⟜0,0≍-⟩_randChoose·RN-˜´)⊸+
RandInterval ← (⊑∘⊣ + -˜´⊸(Rand˜)) _Rec_ ContractRange
Index ⇐ Squeeze (0⊸≍ ⊣ ·!0⊸<)⊸RandInterval
ch_end ← 17×2⋆16 ⋄ surr ← (2⋆11)×27+↕2
Char ⇐ Squeeze @ + ·(1≠surr⊸⍋)⊸× (0≍ch_end⌊2⋆2⋆⊣)⊸RandInterval
Struct ⇐ ⊢ ⥊ =⟜6◶⟨RandInt‿(@+(ch_end⌊2⋆2⋆⊣)⊸Rand˜)_randChoose,RandFloat⊢⟩⟜(×´⥊)
}
_testConsistent_ ← {Match←𝔾
v ← <˘⍉> (5⌊´≠¨)⊸((Rand⟜≠⊏⊢)¨) ListVariations¨ a←𝕨≍○<𝕩
(ClearRefs@) ⊢ (∧´ ⊏ Match¨ 1⊸↓) (𝕨 (𝔽⊑∘⊢)⊘(𝔽´⊢) Variation¨⟜a)¨ v
}
FlatMatch ← ≡◶⟨∧´∘⥊=∨∧○(≠˜),1⟩
_testMonArith ← {
(𝕨 gen.Arith RandShape 𝕩)⊸{ ! 𝕏 _testConsistent_ FlatMatch 𝕨 }¨ 𝕗
}
RandDyShape ← {
Prefix ← (∨`⌾⌽ 𝕩 ≥ ×`)⊸/ (Rand 1+≠)⊸↑
(Rand 2) ⌽ ≍○<⟜Prefix RandShape 𝕩
}
_testDyArith ← {f←𝕗
ch ← 0<+´≠¨ pmn ← (∊⟜f⥊¨⊢) +‿-‿¬
{
sh ← RandDyShape 𝕩
_t ← { ! 𝕏 _testConsistent_ FlatMatch´ 𝕗 }
(𝕨⊸gen.Arith¨ sh)_t¨ f
{
k←𝕩
rca ← ⟨gen.Char,gen.Arith⟩{k𝕎𝕩}¨sh
Fit ← -⟜(@+1-˜17×2⋆16)⌈-⟜@⌊⊢
⟨⌽⍟(Rand 2)-∘Fit⟜-`,Fit`,(1+Fit)`⟩ { (𝕎rca)_t 𝕩 }¨¨ pmn
{ (sh (k gen.Char ⊣)⌾(1⊸⊑) rca)_t¨ 𝕩 }⍟(0<≠) ∾1↓pmn
}⍟(ch∧0⊸<∧≤⟜5) 𝕨
}
}
_testMonStruct ← { # ⥊≍⌽⍉⊏
k ← 3|1+ ⌽‿⊏ ⊐ 𝕗
sh ← k ⊏ {𝕏𝕨}` (1+⌈´k) ↑ ⟨RandShape 𝕩, 1⊸∾⍟(0=≠), 1⊸⌈⌾⊑⟩
((⊐sh) ⊏ 𝕨⊸gen.Struct¨ ⍷sh) { ! 𝕏 _testConsistent_ FlatMatch 𝕨 }¨ 𝕗
}
_testDyStruct ← { # ⥊↑↓↕⌽⍉ (no overtake)
d ← 𝕨 gen.Struct sh ← RandShape 𝕩
l ← RandShape 𝕩
RR ← ≍ ⟨⊑⊸+,⊢´⊸-⟩_randChoose RandBound∘¬˜
RT ← -RR¨⊢
p‿r ← <˘⍉> ⟨⟨⥊,(0∾1⊸↓)⍟(sh>○(0=×´)⊢)∘l⟩, ⟨↓,l‿RT _randChoose⟩
⟨⌽,RT+˜⟩, ⟨↑,RT⟩, ⟨↕,0 RR¨ 1⊸+⟩, ⟨⍉,(⍋⊏⊐)Rand˜∘≠⟩⟩
(r⊏˜p⊐𝕗) { ! (𝕎sh) 𝕏 _testConsistent_ FlatMatch d }¨ 𝕗
}
_testDim ← { # ≠=≢
(𝕨 gen.Struct RandShape 𝕩)⊸{ ! 𝕏 _testConsistent_ ≡ 𝕨 }¨ 𝕗
}
_testCombine ← { # ≍∾«»
a ← 𝕨 gen.Struct sh ← RandShape1 𝕩
bs ← (RandBound 1⊸+)⌾⊑⍟({≍}≠𝕗) sh
swap ← (Rand 2)⊑{𝔽}‿˜
((⊐bs) ⊏ 𝕨⊸gen.Struct¨ ⍷bs) { ! a 𝕏 _testConsistent_ FlatMatch _swap 𝕨 }¨ 𝕗
}
_testMonSearch ← { # ⊐⊒∊⍷∧∨⍋⍒
(𝕨 gen.Arith RandShape1 𝕩)⊸{ ! 𝕏 _testConsistent_ FlatMatch 𝕨 }¨ 𝕗
}
_testDySearch ← { # ⊐⊒∊⍋⍒
sh ← RandShape1 𝕩
k ← ⍋‿⍒⊐𝕗
a‿b ← 𝕨⊸gen.Arith¨ ⟨sh, (0⊸<◶⟨-⟜⌊RandShape∘𝕩,RandShape⟩·⌊𝕩÷1⌈×´)⊸∾ 1↓sh⟩
as ← (⊐k) ⊏ {𝕏a}¨(⍷k)⊏∧‿∨‿⊢
as { ! 𝕨 𝕏 _testConsistent_ FlatMatch b }¨ {𝕏˜}⍟(∊˙⊸=)¨ 𝕗
}
cases ← ⟨
⟨∾`"+-×÷⋆√⌊⌈¬|"‿"∧∨≤<>≥=≠", testMonArith‿testDyArith⟩
⟨"⥊≍⌽⍉⊏"‿"⥊↑↓↕⌽⍉", testMonStruct‿testDyStruct⟩ # Monadic «» hard to test
⟨"≠=≢"‿"", testDim‿@⟩
⟨""‿"≍∾«»", @‿testCombine⟩
⟨"⊐⊒∊⍷∧∨⍋⍒"‿"⊐⊒∊⍋⍒", testMonSearch‿testDySearch⟩
⟩
MakeTests ← {
prim‿test ← <∘>˘ ⍉> 𝕨
m ← 𝕩 ∊¨⎉1 prim
((∾"Unsupported primitives: "‿"%"∾¨/¨⟜𝕩) ! 0˙)⍟(∨´∨´¨) ¬∨˝m
p ← •BQN∘⥊¨¨ 𝕩
t ← <∘{t←2⊑𝕩⋄(/´2↑𝕩)_t}˘ (∨´¨⊏˘)⊸/ ⍉>⥊¨⟨m,p˙˘m,test⟩
1 {𝕎⊢𝕏}´ t
}
pr ← (⊑⊑cases)⍟(0=·+´≠¨) opts.prims
opts.types (cases MakeTests pr)⌜ opts.num/opts.bounds
|
