From 7d554fb945c3f3f827bfefa02f6093acee3ae61d Mon Sep 17 00:00:00 2001
From: filifa <filifa.breath652@8alias.com>
Date: Tue, 19 Aug 2025 22:35:15 -0400
Subject: [PATCH] optimize a bunch

---
 cmd/primitiveRoot.go | 43 +++++++++++++++++++++----------------------
 1 file changed, 21 insertions(+), 22 deletions(-)

diff --git a/cmd/primitiveRoot.go b/cmd/primitiveRoot.go
index 99b8eb0..04f969b 100644
--- a/cmd/primitiveRoot.go
+++ b/cmd/primitiveRoot.go
@@ -28,40 +28,39 @@ import (
 var modulus string
 var tpf []string
 
+func totient(n *big.Int) *big.Int {
+	total := big.NewInt(0)
+	for a := big.NewInt(1); a.Cmp(n) == -1; a.Add(a, big.NewInt(1)) {
+		gcd := new(big.Int).GCD(nil, nil, a, n)
+		if gcd.Cmp(big.NewInt(1)) == 0 {
+			total.Add(total, big.NewInt(1))
+		}
+	}
+
+	return total
+}
+
 func computeNaive(modulus *big.Int) (*big.Int, error) {
 	if modulus.Cmp(big.NewInt(1)) == 0 {
 		return big.NewInt(0), nil
 	}
 
-	coprimes := make(map[string]bool)
-	for a := big.NewInt(1); a.Cmp(modulus) == -1; a.Add(a, big.NewInt(1)) {
-		gcd := new(big.Int).GCD(nil, nil, a, modulus)
-		if gcd.Cmp(big.NewInt(1)) != 0 {
+	phi := totient(modulus)
+
+	for g := big.NewInt(1); g.Cmp(modulus) == -1; g.Add(g, big.NewInt(1)) {
+		tmp := new(big.Int).GCD(nil, nil, g, modulus)
+		if tmp.Cmp(big.NewInt(1)) != 0 {
 			continue
 		}
 
-		coprimes[a.Text(10)] = true
-	}
-
-	for g := big.NewInt(1); g.Cmp(modulus) == -1; g.Add(g, big.NewInt(1)) {
-		e := big.NewInt(1)
-		exps := make(map[string]big.Int)
-		for k := big.NewInt(1); k.Cmp(modulus) == -1; k.Add(k, big.NewInt(1)) {
+		e := new(big.Int).Set(g)
+		var k *big.Int
+		for k = big.NewInt(1); e.Cmp(big.NewInt(1)) != 0; k.Add(k, big.NewInt(1)) {
 			e.Mul(e, g)
 			e.Mod(e, modulus)
-			exps[e.Text(10)] = *k
 		}
 
-		isPrimitive := true
-		for a := range coprimes {
-			_, ok := exps[a]
-			if !ok {
-				isPrimitive = false
-				break
-			}
-		}
-
-		if isPrimitive {
+		if k.Cmp(phi) == 0 {
 			return g, nil
 		}
 	}