fix(stores): Actually check a vector is a unit vector/normalized

Instead of just summing the components to see if they equal 1.0, take
the actual magnitude/p-norm of the vector and check that is
approximately 1.0.

Note that this shouldn't change the order of results except in edge
cases if I am too lax with the precision of the equality
comparison. However it should improve performance for normalized
vectors which were being misclassified.

Author: richiejp

backend/go/stores/store.go

@@ -311,12 +311,16 @@ func (s *Store) StoresGet(opts *pb.StoresGetOptions) (pb.StoresGetResult, error)
 }
 
 func isNormalized(k []float32) bool {
-	var sum float32
+	var sum float64
+
 	for _, v := range k {
-		sum += v
+		v64 := float64(v)
+		sum += v64*v64
 	}
 
-	return sum == 1.0
+	s := math.Sqrt(sum)
+
+	return s >= 0.99 && s <= 1.01
 }
 
 // TODO: This we could replace with handwritten SIMD code
@@ -328,7 +332,7 @@ func normalizedCosineSimilarity(k1, k2 []float32) float32 {
 		dot += k1[i] * k2[i]
 	}
 
-	assert(dot >= -1 && dot <= 1, fmt.Sprintf("dot = %f", dot))
+	assert(dot >= -1.01 && dot <= 1.01, fmt.Sprintf("dot = %f", dot))
 
 	// 2.0 * (1.0 - dot) would be the Euclidean distance
 	return dot
@@ -418,7 +422,7 @@ func cosineSimilarity(k1, k2 []float32, mag1 float64) float32 {
 
 	sim := float32(dot / (mag1 * math.Sqrt(mag2)))
 
-	assert(sim >= -1 && sim <= 1, fmt.Sprintf("sim = %f", sim))
+	assert(sim >= -1.01 && sim <= 1.01, fmt.Sprintf("sim = %f", sim))
 
 	return sim
 }