From 2fcb8474454f613cde693a63771ad8e6cde47c67 Mon Sep 17 00:00:00 2001
From: Chip Hogg <chogg@aurora.tech>
Date: Tue, 12 Nov 2024 16:29:51 -0500
Subject: [PATCH] Express D's flag as "is positive"

It's harder to reason about a negative.  This code just reads better.
---
 au/code/au/utility/probable_primes.hh           | 16 ++++++++++------
 au/code/au/utility/test/probable_primes_test.cc |  4 ++--
 2 files changed, 12 insertions(+), 8 deletions(-)

diff --git a/au/code/au/utility/probable_primes.hh b/au/code/au/utility/probable_primes.hh
index 99d6d284..fb9715fb 100644
--- a/au/code/au/utility/probable_primes.hh
+++ b/au/code/au/utility/probable_primes.hh
@@ -185,16 +185,20 @@ constexpr int jacobi_symbol(int64_t raw_a, uint64_t n) {
     return jacobi_symbol_positive_numerator(a, n, result);
 }
 
+// The "D" parameter in the Strong Lucas probable prime test.
+//
+// Default construction produces the first value to try according to Selfridge's parameter
+// selection.  Calling `increment()` on this will successively produce the next parameter to try.
 struct LucasDParameter {
     uint64_t mag = 5u;
-    bool is_neg = false;
+    bool is_positive = true;
 
     friend constexpr int as_int(const LucasDParameter &D) {
-        return bool_sign(!D.is_neg) * static_cast<int>(D.mag);
+        return bool_sign(D.is_positive) * static_cast<int>(D.mag);
     }
     friend constexpr void increment(LucasDParameter &D) {
         D.mag += 2u;
-        D.is_neg = !D.is_neg;
+        D.is_positive = !D.is_positive;
     }
 };
 
@@ -205,7 +209,7 @@ struct LucasDParameter {
 // Requires that `n` is *not* a perfect square.
 //
 constexpr LucasDParameter find_first_D_with_jacobi_symbol_neg_one(uint64_t n) {
-    LucasDParameter D{5u, false};
+    LucasDParameter D{};
     while (jacobi_symbol(as_int(D), n) != -1) {
         increment(D);
     }
@@ -232,7 +236,7 @@ constexpr LucasSequenceElement double_strong_lucas_index(const LucasSequenceElem
     uint64_t V_squared = mul_mod(V, V, n);
     uint64_t D_U_squared = mul_mod(D.mag, mul_mod(U, U, n), n);
     uint64_t V2 =
-        D.is_neg ? sub_mod(V_squared, D_U_squared, n) : add_mod(V_squared, D_U_squared, n);
+        D.is_positive ? add_mod(V_squared, D_U_squared, n) : sub_mod(V_squared, D_U_squared, n);
     V2 = half_mod_odd(V2, n);
 
     return LucasSequenceElement{
@@ -251,7 +255,7 @@ constexpr LucasSequenceElement increment_strong_lucas_index(const LucasSequenceE
     auto U2 = half_mod_odd(add_mod(U, V, n), n);
 
     const auto D_U = mul_mod(D.mag, U, n);
-    auto V2 = D.is_neg ? sub_mod(V, D_U, n) : add_mod(V, D_U, n);
+    auto V2 = D.is_positive ? add_mod(V, D_U, n) : sub_mod(V, D_U, n);
     V2 = half_mod_odd(V2, n);
 
     return LucasSequenceElement{U2, V2};
diff --git a/au/code/au/utility/test/probable_primes_test.cc b/au/code/au/utility/test/probable_primes_test.cc
index 9f167be9..8f150dd7 100644
--- a/au/code/au/utility/test/probable_primes_test.cc
+++ b/au/code/au/utility/test/probable_primes_test.cc
@@ -223,8 +223,8 @@ std::vector<uint64_t> strong_lucas_pseudoprimes() {
 }
 
 TEST(LucasDParameter, CanConvertToInt) {
-    EXPECT_EQ(as_int(LucasDParameter{5u, false}), 5);
-    EXPECT_EQ(as_int(LucasDParameter{7u, true}), -7);
+    EXPECT_EQ(as_int(LucasDParameter{5u, true}), 5);
+    EXPECT_EQ(as_int(LucasDParameter{7u, false}), -7);
 }
 
 TEST(StrongLucas, AllPrimeNumbersAreProbablyPrime) {