(Modular ^) vs. (^ then mod)

[Pedro Fortuny Ayuso <fortunypedro@uniovi.es>]

Hi,

I am doing quite a few (millions) of modular powers and
additions like shown below. Is it natural that the Mod
operation takes longer than the operation without Mod?
It may be as simple as "yes, pretty normal" but somehow
I expected the operation with the Mods to be faster,
but I may well be quite wrong.

Thank you,


Pedro.
---- Pari session
? #
   timer = 1 (on)
? n = 120
time = 0 ms.
? s=[0,0;0,0];
time = 0 ms.
? for(a=0,n-1, for(b=0, n-1, for(c=0, n-1, s=s+[a,b;0,c]^n)))
time = 12,315 ms.
? s=[0,0;0,0];
time = 0 ms.
? for(a=0,n-1, for(b=0, n-1, for(c=0, n-1, s=s+[Mod(a,n),Mod(b,n);0,Mod(c,n)]^n)))
time = 18,268 ms.
? s=[0,0;0,0];
time = 0 ms.
? for(a=0,n-1, for(b=0, n-1, for(c=0, n-1, s=s+Mod([a,b;0,c]^n,n))))
time = 13,896 ms.



-- 
Pedro Fortuny Ayuso
http://pfortuny.net

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EPIG, Campus de Viesques, Gijon
Dpto. de Matematicas
Universidad de Oviedo

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