move sieves to subpackage

internal/lib/sieve/divisors.go

@@ -0,0 +1,78 @@
+/*
+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 pow(base uint, exp uint) uint {
+	result := uint(1)
+	for exp > 0 {
+		if exp%2 == 1 {
+			result *= base
+		}
+
+		exp >>= 1
+		base *= base
+	}
+
+	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
+		}
+		println(q)
+
+		// sigma_x(p^k) = p^(kx) + sigma_x(p^(k-1))
+		sieve[p*q] = pow(p*q, x) + sieve[q]
+	}
+}
+
+/*
+DivisorSieve 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.
+*/
+func DivisorsSieve(n uint, x uint, buflen uint) chan uint {
+	sieve := make([]uint, n)
+	sieve[0] = 0
+	for i := uint(1); 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 || sieve[i] != 1 {
+				ch <- sieve[i]
+				continue
+			}
+
+			sieve[i] = pow(i, x) + 1
+			updateMultiples(sieve, x, i, n)
+			ch <- sieve[i]
+		}
+	}()
+
+	return ch
+}

internal/lib/sieve/mobius.go

@@ -0,0 +1,50 @@
+/*
+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
+
+/*
+MobiusSieve computes mobius(k) for k=1 to n, where mobius is the Mobius function.
+*/
+func MobiusSieve(n uint, buflen uint) chan int {
+	sieve := make([]int, n)
+	for i := 0; i < int(n); i++ {
+		sieve[i] = i
+	}
+
+	ch := make(chan int, buflen)
+	go func() {
+		defer close(ch)
+		for i := 0; i < int(n); i++ {
+			if i == 0 || i == 1 || sieve[i] != i {
+				ch <- sieve[i]
+				continue
+			}
+
+			ch <- -1
+
+			for j := 2 * i; j < int(n); j += i {
+				if j%(i*i) == 0 {
+					sieve[j] = 0
+				}
+
+				sieve[j] /= -i
+			}
+		}
+	}()
+
+	return ch
+}

internal/lib/sieve/primeOmega.go

@@ -0,0 +1,63 @@
+/*
+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 primeOmegaUpdateMultiples(sieve []uint, p uint, n uint, multiplicity bool) {
+	for q := p; ; q *= p {
+		// omega(a*b) = omega(a) + omega(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
+		}
+
+		if multiplicity {
+			sieve[p*q] = 1 + sieve[q]
+		}
+	}
+}
+
+/*
+PrimeOmegaSieve computes omega(k) for k=1 to n, where omega is the prime omega function. If multiplicity is true, factors are counted with multiplicity.
+*/
+func PrimeOmegaSieve(n uint, multiplicity bool, buflen uint) chan uint {
+	sieve := make([]uint, n)
+	for i := uint(0); i < n; i++ {
+		sieve[i] = 0
+	}
+
+	ch := make(chan uint, buflen)
+	go func() {
+		defer close(ch)
+		for i := uint(0); i < n; i++ {
+			if i == 0 || i == 1 || sieve[i] != 0 {
+				ch <- sieve[i]
+				continue
+			}
+
+			sieve[i] = 1
+			primeOmegaUpdateMultiples(sieve, i, n, multiplicity)
+			ch <- sieve[i]
+		}
+	}()
+
+	return ch
+}

internal/lib/sieve/radical.go

@@ -0,0 +1,63 @@
+/*
+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 radicalUpdateMultiples(sieve []uint, p uint, n uint) {
+	for q := p; ; q *= p {
+		// rad(a*b) = rad(a) * rad(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
+		}
+
+		// rad(p^k) = rad(p)
+		sieve[p*q] = sieve[q]
+	}
+}
+
+/*
+RadicalSieve computes rad(k) for k=1 to n, where rad(n) is the radical of n.
+*/
+func RadicalSieve(n uint, buflen uint) chan uint {
+	sieve := make([]uint, n)
+	sieve[0] = 0
+	for i := uint(1); 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 || sieve[i] != 1 {
+				ch <- sieve[i]
+				continue
+			}
+
+			sieve[i] = i
+			radicalUpdateMultiples(sieve, i, n)
+			ch <- sieve[i]
+		}
+	}()
+
+	return ch
+}

internal/lib/sieve/totient.go

@@ -0,0 +1,46 @@
+/*
+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
+
+/*
+TotientSieve computes totient(k) for k=1 to n, where totient is Euler's totient function. buflen sets the buffer length of the returned channel. Larger buffer lengths can result in better performance at the cost of higher memory usage.
+*/
+func TotientSieve(n uint, buflen uint) chan uint {
+	totients := make([]uint, n)
+	totients[0] = 0
+	totients[1] = 1
+	for i := uint(2); i < n; i++ {
+		totients[i] = i - 1
+	}
+
+	ch := make(chan uint, buflen)
+	go func() {
+		defer close(ch)
+		for i := uint(0); i < n; i++ {
+			ch <- totients[i]
+			if i == 0 || i == 1 || totients[i] != i-1 {
+				continue
+			}
+
+			for j := 2 * i; j < n; j += i {
+				totients[j] -= totients[j] / i
+			}
+		}
+	}()
+
+	return ch
+}