make same performance improvements to all sieve commands

internal/lib/divisors.go

@@ -51,15 +51,16 @@ func updateMultiples(sieve []uint, x uint, p uint, n uint) {
 /*
 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) chan uint {
+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)
+	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]
@@ -70,8 +71,6 @@ func DivisorsSieve(n uint, x uint) chan uint {
 			updateMultiples(sieve, x, i, n)
 			ch <- sieve[i]
 		}
-
-		close(ch)
 	}()
 
 	return ch

internal/lib/mobius.go

@@ -19,14 +19,15 @@ package lib
 /*
 MobiusSieve computes mobius(k) for k=1 to n, where mobius is the Mobius function.
 */
-func MobiusSieve(n uint) chan int {
+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)
+	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]
@@ -43,8 +44,6 @@ func MobiusSieve(n uint) chan int {
 				sieve[j] /= -i
 			}
 		}
-
-		close(ch)
 	}()
 
 	return ch

internal/lib/primeOmega.go

@@ -38,14 +38,15 @@ func primeOmegaUpdateMultiples(sieve []uint, p uint, n uint, multiplicity bool)
 /*
 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) chan uint {
+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)
+	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]
@@ -56,8 +57,6 @@ func PrimeOmegaSieve(n uint, multiplicity bool) chan uint {
 			primeOmegaUpdateMultiples(sieve, i, n, multiplicity)
 			ch <- sieve[i]
 		}
-
-		close(ch)
 	}()
 
 	return ch