Hi,
we can show that
(x/3) = (x/2) - (x/4) + (x/8) - (x/16) + .... infinity
Proof:
let s1 = (x/2)+(x/8)+(x/32)+...infinity = (x/2)/(1-(1/4)) [Geometric
Progression , common Ratio(r) = 1/4]
& s2 = (x/4)+(x/16)+(x/64)+...infinity = (x/4)/(1-(1/4)) [Geometric
Progression , common Ratio(r) = 1/4]
now s1-s2 upon simplifying becomes (x/3)
Implementation:
x1=x>>1;
x2=x>>2;
s1=x1;
s2=x2;
while(x1 || x2){
s1+=x1>>2;
s2+=x2>>2;
x1>>=2;
x2>>=2;
}
return s1-s2;
If the number is not divisible by 3 the answer returned is the least integer
function of (x/3)
correct me if i am wrong...
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