mathtools/internal/lib/sieve/qresidue.go

63 lines
1.5 KiB
Go

/*
Copyright © 2025 filifa
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
package sieve
func updatePowersOfTwo(sieve []uint, n uint) {
for q := uint(8); 2*q < n; q *= 2 {
sieve[2*q] = 2 * sieve[q]
}
}
func updatePowersOfOddPrimes(sieve []uint, p uint, n uint) {
for q := p; p*q < n; q *= p {
sieve[p*q] = (p*q - q) / 2
}
}
/*
QuadraticResidues computes the number of quadratic residues modulo k for k=1 to n.
*/
func QuadraticResidues(n uint, buflen uint) chan uint {
sieve := make([]uint, n)
for i := uint(0); i < n; i++ {
sieve[i] = 1
}
ch := make(chan uint, buflen)
go func() {
defer close(ch)
for i := uint(0); i < n; i++ {
if i == 0 || i == 1 || i == 4 || i == 6 || i == 8 || i == 12 || i == 24 || sieve[i] != 1 {
ch <- sieve[i]
continue
}
if i == 2 {
updatePowersOfTwo(sieve, n)
} else {
sieve[i] = (i - 1) / 2
updatePowersOfOddPrimes(sieve, i, n)
}
updateMultiples(sieve, i, n, false)
ch <- sieve[i]
}
}()
return ch
}