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# Tester that checks primitives on random arguments
Range β (β’MakeRand 2).Range
Rand β {π¨ Range 1βπ©}
_randChoose β { Randβ(β π)βΆπ }
_randUnbounded β { πβΈ+β(1=-)βRand π }
RandRank β 4 _randUnbounded
# Prime factorization
β¨Factorβ© β {
p β (Β¬ββ/β£)β(β₯ΓβΛ)2ββmβ60
Pr β {m<π©}βΆ{π©βp}βΏ{ mβ©(ΓΛm)β2Γπ© β pβΎβ©1β/1(mβ₯0<β)βΈβ§Β΄p β Pr π© }
Factor β {
!(1=β’Typeπ©)β§(π©=βπ©)β§0<π©
β§ π© {(0<β ββ’)βΆβ¨β₯β£,β’βΎπβ©β(>β1)Λβ(π¨Γ·ΓΒ΄)π©/Λ0=π©|π¨} Pr ββπ©
}
}
Sigmoid β (40β€|)βΆβ¨1(-Γ·+)Λβ,Γβ©
# π© is maximum bound plus 1 for both functions
β¨RandBound,RandShapeβ© β {
RandBound β β¨
Rand # Uniform
Rand 128βΈβ # Small
(0β-β1) β Randβ(1ββ)βΎ((2β3+β’)βΌ) + Β―7+Randβ15 # Near power of two
β©_randChoose
Augment β {
d β 1+βπ¨Γ·1βΓΒ΄π© # Maximum bound that can be added, plus 1
C β 10βΈ+ RandβΈ< 1.2βΈβ # Decide whether to add
d (π¨ π β¨βΎ,βΎΛβ©_randChooseβRandBoundΛ)β(Cβ£) π©
}
Combine β β¨
Randββ βΈβ½ (2+Randββ )βΈ{Γ´¨π¨β(π¨|βββ )βΈβπ©}ββ’ # Random number of groups
Γ´¨ (βΒ·RandΒ¨β₯Λββ )βΈβββ’ # Distribute randomly
β©_randChoose
RandShape β β’ Augment β¨
β’ (β’ ββΓ β’ β βΈβ (SigmoidβΈΓ·1βΓΒ΄βΈΓ·Λ)) Β· RandΒ¨ (RandRankββ<Rand)βΈβ₯
β’ CombineβFactor 1βRandBound
β©_randChoose
}
# π¨ is 2ββΌbits in type; π© is shape
β¨RandArithβ© β {
RandInt β { (1βΈ<βΈΓmΓ·2) -Λ π© Rand mβ2β2βπ¨ }
floats β β¨2βΒ―1074,2βΒ―1022,(2-2βΒ―52)Γ2β1023β©
RandFloat β β¨
(floatsβΎ2β0βΏ8βΏ32βΏ100)_randChoose Γ Rangeβ0 - 2Γ·ΛRandβ3
β’ (Randββ ββ’) (Rand(β£β₯βΒ΄βΈβ)3+Randβ+)Λββ βΈ/β(βΎβ-0βΎfloatsβΎβ)
β©_randChoose
RandTyped β =β6βΆβ¨RandInt,RandFloatβ£β©
RN β (0β-β1) β 1βΏRandRankβΏRandBound _randChoose
RandSplit β β½β(Randβ2) (-ββ’)βRN
Combine β (βRandΛββ )βΈββ(Randβ2) βΎ
RL β {π¨RandListπ©}
RandList β β¨
RandTyped # Random
β§βΏβ¨_randChoose RandTyped # Sort
β’ β₯ RLβ(1βRN) # Repeat
Combine RandβΏβ’_randChooseβΈRLΒ¨βRandSplit # Partition
β©{ 8βΈβ€βΆβ¨0,Randβ(β π)β©βΆπ }
RandArith β β’internal.Squeeze β’ β₯ RandListβ(ΓΒ΄)
}
# π© is bound
RandMonArith β RandArithβRandShape
RandDyArith β {
Prefix β (β¨`βΎβ½ π© β₯ Γ`)βΈ/ (Rand 1+β )βΈβ
π¨βΈRandArithΒ¨ (Rand 2) β½ ββ<βPrefix RandShape π©
}
types β 0βΏ3βΏ4βΏ5βΏ6
types { ! (π¨+π©)β‘βΆβ¨β§Β΄ββ₯=β¨β§β(β Λ),1β©π¨--π© }Β΄βRandDyArithβ 100β₯1e3
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