From 61aad93f8dea749f327372839fbd53c3f02f392d Mon Sep 17 00:00:00 2001
From: Quaternions <krakow20@gmail.com>
Date: Thu, 29 Aug 2024 18:29:04 -0700
Subject: [PATCH] sqrt: closed loop over bit shift

---
 fixed_wide/src/fixed_wide_traits.rs | 24 ++++++------------------
 1 file changed, 6 insertions(+), 18 deletions(-)

diff --git a/fixed_wide/src/fixed_wide_traits.rs b/fixed_wide/src/fixed_wide_traits.rs
index d34419c..0c8e9d8 100644
--- a/fixed_wide/src/fixed_wide_traits.rs
+++ b/fixed_wide/src/fixed_wide_traits.rs
@@ -69,30 +69,18 @@ impl<const CHUNKS:usize,Frac:Unsigned> Fixed<CHUNKS,Frac>
 		//sqrt
 		//0110.0000
 		//pow2 = 0100.0000
-		let mut pow2=Self{
-			bits:BInt::<CHUNKS>::ONE.shl(((((CHUNKS as i32*64-Frac::I32-(self.bits.leading_zeros() as i32)+1)>>1)+Frac::I32) as u32).saturating_sub(1)),
-			frac:PhantomData,
-		};
+		let max_shift=((((CHUNKS as i32*64-Frac::I32-(self.bits.leading_zeros() as i32)+1)>>1)+Frac::I32) as u32).saturating_sub(1);
 		let mut result=Self::ZERO;
 
 		//cheat to make the types match
 		let wide_self=self.wide_mul(Fixed::<CHUNKS,Frac>::ONE);
-		loop{
-			//TODO: closed loop over bit shift exponent rather than pow2
-			if pow2==Self::ZERO{
-				break result;
+		for shift in (0..=max_shift).rev(){
+			let new_result=result|(Fixed::<CHUNKS,Frac>::EPSILON<<shift);
+			if new_result.wide_mul(new_result)<=wide_self{
+				result=new_result;
 			}
-			//TODO: flip a single bit instead of adding a power of 2
-			let new_result=result+pow2;
-			//note that the implicit truncation in the multiply
-			//means that the algorithm can return a result which squares to a number greater than the input.
-			match wide_self.cmp(&new_result.wide_mul(new_result)){
-				core::cmp::Ordering::Less=>(),
-				core::cmp::Ordering::Equal=>break new_result,
-				core::cmp::Ordering::Greater=>result=new_result,
-			}
-			pow2>>=1;
 		}
+		result
 	}
 	pub fn sqrt(self)->Self{
 		if self<Self::ZERO{