From 46d2036560113fba693bf7a487062cca34328130 Mon Sep 17 00:00:00 2001
From: Paul <paulxicao7@gmail.com>
Date: Sat, 25 Oct 2025 14:31:37 +0200
Subject: [PATCH 1/5] use auxiliary variables as in documented formula

---
 src/lib.rs | 9 ++++++---
 1 file changed, 6 insertions(+), 3 deletions(-)

diff --git a/src/lib.rs b/src/lib.rs
index 661b67b..90da77f 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -793,9 +793,12 @@ impl<T: Clone + Num + MulAdd<Output = T>> MulAdd<Complex<T>> for Complex<T> {
 
     #[inline]
     fn mul_add(self, other: Complex<T>, add: Complex<T>) -> Complex<T> {
-        let re = self.re.clone().mul_add(other.re.clone(), add.re)
-            - (self.im.clone() * other.im.clone()); // FIXME: use mulsub when available in rust
-        let im = self.re.mul_add(other.im, self.im.mul_add(other.re, add.im));
+        let (a, b) = (self.re, self.im);
+        let (c, d) = (other.re, other.im);
+        let (e, f) = (add.re, add.im);
+
+        let re = a.clone().mul_add(c.clone(), e) - (b.clone() * d.clone()); // FIXME: use mulsub when available in rust
+        let im = a.mul_add(d, b.mul_add(c, f));
         Complex::new(re, im)
     }
 }

From d2481a0089d6de45abca437a48fe8dd4b0f69ef5 Mon Sep 17 00:00:00 2001
From: Paul <paulxicao7@gmail.com>
Date: Sat, 25 Oct 2025 14:42:01 +0200
Subject: [PATCH 2/5] recommended impl from #148

---
 src/lib.rs | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/src/lib.rs b/src/lib.rs
index 90da77f..65e4744 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -797,7 +797,9 @@ impl<T: Clone + Num + MulAdd<Output = T>> MulAdd<Complex<T>> for Complex<T> {
         let (c, d) = (other.re, other.im);
         let (e, f) = (add.re, add.im);
 
-        let re = a.clone().mul_add(c.clone(), e) - (b.clone() * d.clone()); // FIXME: use mulsub when available in rust
+        let re = a
+            .clone()
+            .mul_add(c.clone(), -b.clone().mul_add(d.clone(), -e)); // FIXME: use mulsub when available in rust
         let im = a.mul_add(d, b.mul_add(c, f));
         Complex::new(re, im)
     }

From d984ef847263084b18f36087a4c954296d2443a5 Mon Sep 17 00:00:00 2001
From: Paul <paulxicao7@gmail.com>
Date: Sat, 25 Oct 2025 14:42:31 +0200
Subject: [PATCH 3/5] update method documentation formula

---
 src/lib.rs | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/lib.rs b/src/lib.rs
index 65e4744..d7628e7 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -787,7 +787,7 @@ impl<T: Clone + Num> Mul<Complex<T>> for Complex<T> {
     }
 }
 
-// (a + i b) * (c + i d) + (e + i f) == ((a*c + e) - b*d) + i (a*d + (b*c + f))
+// (a + i b) * (c + i d) + (e + i f) == (a*c - (b*d - e)) + i (a*d + (b*c + f))
 impl<T: Clone + Num + MulAdd<Output = T>> MulAdd<Complex<T>> for Complex<T> {
     type Output = Complex<T>;
 

From 00ac3a20ac5ab11d7efb3f55eee2053b85a6a104 Mon Sep 17 00:00:00 2001
From: Paul <paulxicao7@gmail.com>
Date: Sat, 25 Oct 2025 14:45:00 +0200
Subject: [PATCH 4/5] add trait bound

---
 src/lib.rs | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/src/lib.rs b/src/lib.rs
index d7628e7..261e95b 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -788,7 +788,7 @@ impl<T: Clone + Num> Mul<Complex<T>> for Complex<T> {
 }
 
 // (a + i b) * (c + i d) + (e + i f) == (a*c - (b*d - e)) + i (a*d + (b*c + f))
-impl<T: Clone + Num + MulAdd<Output = T>> MulAdd<Complex<T>> for Complex<T> {
+impl<T: Clone + Num + MulAdd<Output = T> + Neg<Output = T>> MulAdd<Complex<T>> for Complex<T> {
     type Output = Complex<T>;
 
     #[inline]
@@ -804,7 +804,9 @@ impl<T: Clone + Num + MulAdd<Output = T>> MulAdd<Complex<T>> for Complex<T> {
         Complex::new(re, im)
     }
 }
-impl<'a, 'b, T: Clone + Num + MulAdd<Output = T>> MulAdd<&'b Complex<T>> for &'a Complex<T> {
+impl<'a, 'b, T: Clone + Num + MulAdd<Output = T> + Neg<Output = T>> MulAdd<&'b Complex<T>>
+    for &'a Complex<T>
+{
     type Output = Complex<T>;
 
     #[inline]

From bed1daac07ea9beeb11b923a669aa06d21dd0c9c Mon Sep 17 00:00:00 2001
From: Paul <paulxicao7@gmail.com>
Date: Sat, 25 Oct 2025 14:45:46 +0200
Subject: [PATCH 5/5] move trait bounds into where clause

---
 src/lib.rs | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/src/lib.rs b/src/lib.rs
index 261e95b..094f738 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -788,7 +788,10 @@ impl<T: Clone + Num> Mul<Complex<T>> for Complex<T> {
 }
 
 // (a + i b) * (c + i d) + (e + i f) == (a*c - (b*d - e)) + i (a*d + (b*c + f))
-impl<T: Clone + Num + MulAdd<Output = T> + Neg<Output = T>> MulAdd<Complex<T>> for Complex<T> {
+impl<T> MulAdd<Complex<T>> for Complex<T>
+where
+    T: Clone + Num + MulAdd<Output = T> + Neg<Output = T>,
+{
     type Output = Complex<T>;
 
     #[inline]