add quadratic residues sieve

internal/lib/sieve/qresidue.go

@@ -0,0 +1,62 @@
+/*
+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
+}