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refactor updating multiples into separate common function

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filifa
2025-10-07 17:49:39 -04:00
parent 26c197318e
commit 30ad962cfd
2 changed files with 38 additions and 19 deletions
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25
internal/lib/sieve/divisors.go
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@@ -30,24 +30,6 @@ func pow(base uint, exp uint) uint {
return result
}
func updateMultiples(sieve []uint, x uint, p uint, n uint) {
for q := p; ; q *= p {
// sigma_x(a*b) = sigma_x(a) * sigma_x(b) if gcd(a,b) = 1
for i := 2 * q; i < n; i += q {
if i%(p*q) != 0 {
sieve[i] *= sieve[q]
}
}
if p*q >= n {
break
}
// sigma_x(p^k) = p^(kx) + sigma_x(p^(k-1))
sieve[p*q] = pow(p*q, x) + sieve[q]
}
}
/*
Divisors computes sigma_x(k) for k=1 to n, where sigma_x is the divisor sum function. x sets the power each divisor is raised to.
*/
@@ -68,7 +50,12 @@ func Divisors(n uint, x uint, buflen uint) chan uint {
}
sieve[i] = pow(i, x) + 1
updateMultiples(sieve, x, i, n)
for j := i; i*j < n; j *= i {
// sigma_x(p^k) = p^(kx) + sigma_x(p^(k-1))
sieve[i*j] = pow(i*j, x) + sieve[j]
}
updateMultiples(sieve, i, n)
ch <- sieve[i]
}
}()