From 592fadb6d7f1fc9b25da2babff9b579bd18bc05e Mon Sep 17 00:00:00 2001
From: filifa <filifa.breath652@8alias.com>
Date: Fri, 5 Dec 2025 22:29:56 -0500
Subject: [PATCH] clean up

---
 internal/lib/sieve/qresidue.go | 33 ++++++++++++++++++---------------
 1 file changed, 18 insertions(+), 15 deletions(-)

diff --git a/internal/lib/sieve/qresidue.go b/internal/lib/sieve/qresidue.go
index b09840d..3be8582 100644
--- a/internal/lib/sieve/qresidue.go
+++ b/internal/lib/sieve/qresidue.go
@@ -18,21 +18,21 @@ package sieve
 
 // NOTE: these formulas come from https://web.archive.org/web/20151224013638/http://www.maa.org/sites/default/files/Walter_D22068._Stangl.pdf
 
-func updatePowersOfTwoCoprime(sieve []uint, n uint) {
+func qrPowersOfTwoCoprime(sieve []uint, n uint) {
 	for q := uint(8); 2*q < n; q *= 2 {
 		// q(2^n) = 2^(n-3) for n >= 3
 		sieve[2*q] = 2 * sieve[q]
 	}
 }
 
-func updatePowersOfOddPrimesCoprime(sieve []uint, p uint, n uint) {
+func qrPowersOfOddPrimesCoprime(sieve []uint, p uint, n uint) {
 	for q := p; p*q < n; q *= p {
 		// q(p^n) = (p^n - p^(n-1)) / 2
 		sieve[p*q] = (p*q - q) / 2
 	}
 }
 
-func updatePowersOfTwo(sieve []uint, n uint) {
+func qrPowersOfTwo(sieve []uint, n uint) {
 	k := 1
 	for q := uint(1); 2*q < n; q *= 2 {
 		if k%2 == 0 {
@@ -47,13 +47,10 @@ func updatePowersOfTwo(sieve []uint, n uint) {
 	}
 }
 
-func updatePowersOfOddPrimes(sieve []uint, p uint, n uint) {
-	k := 2
-	for q := p; p*q < n; q *= p {
-		if p == q {
-			// s(p^2) = (p^2 - p + 2) / 2
-			sieve[p*q] = (p*p - p + 2) / 2
-		} else if k%2 == 0 {
+func qrPowersOfOddPrimes(sieve []uint, p uint, n uint) {
+	k := 3
+	for q := p * p; p*q < n; q *= p {
+		if k%2 == 0 {
 			// s(p^n) = (p^(n+1) + p + 2) / (2*(p+1)) for even n
 			sieve[p*q] = (p*p*q + p + 2) / (2 * (p + 1))
 		} else {
@@ -68,7 +65,7 @@ func updatePowersOfOddPrimes(sieve []uint, p uint, n uint) {
 /*
 QuadraticResidues computes the number of quadratic residues modulo k for k=1 to n.
 
-see https://oeis.org/A046073
+see https://oeis.org/A000224 and https://oeis.org/A046073
 */
 func QuadraticResidues(n uint, coprime bool, buflen uint) chan uint {
 	sieve := make([]uint, n)
@@ -97,10 +94,11 @@ func sieveQRCoprime(sieve []uint, n uint, ch chan uint) {
 		}
 
 		if i == 2 {
-			updatePowersOfTwoCoprime(sieve, n)
+			qrPowersOfTwoCoprime(sieve, n)
 		} else {
+			// q(p) = (p - 1) / 2
 			sieve[i] = (i - 1) / 2
-			updatePowersOfOddPrimesCoprime(sieve, i, n)
+			qrPowersOfOddPrimesCoprime(sieve, i, n)
 		}
 
 		updateMultiples(sieve, i, n, false)
@@ -116,10 +114,15 @@ func sieveQR(sieve []uint, n uint, ch chan uint) {
 		}
 
 		if i == 2 {
-			updatePowersOfTwo(sieve, n)
+			qrPowersOfTwo(sieve, n)
 		} else {
+			// s(p) = (p + 1) / 2
 			sieve[i] = (i + 1) / 2
-			updatePowersOfOddPrimes(sieve, i, n)
+			if i*i < n {
+				// s(p^2) = (p^2 - p + 2) / 2
+				sieve[i*i] = (i*i - i + 2) / 2
+			}
+			qrPowersOfOddPrimes(sieve, i, n)
 		}
 
 		updateMultiples(sieve, i, n, false)