mathtools/internal/lib/totient.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 lib

/*
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
}