diff --git a/src/popsift/s_desc_norm_l2.h b/src/popsift/s_desc_norm_l2.h
index 96a161d4..b067d71f 100644
--- a/src/popsift/s_desc_norm_l2.h
+++ b/src/popsift/s_desc_norm_l2.h
@@ -50,24 +50,10 @@ void NormalizeL2::normalize( const float* src_desc, float* dst_desc, const bool
     float4 descr;
     descr = ptr4[threadIdx.x];
 
-#if POPSIFT_IS_DEFINED(POPSIFT_HAVE_NORMF)
-    // normf() is an elegant function: sqrt(sum_0^127{v^2})
-    // It exists from CUDA 7.5 but the trouble with CUB on the GTX 980 Ti forces
-    // us to with CUDA 7.0 right now
-
     float norm;
 
-    if( threadIdx.x == 0 ) {
-        norm = rnormf( 128, src_desc ); // 1/sqrt(sum of squares)
-    }
-    __syncthreads();
-    norm = popsift::shuffle( norm, 0 );
-
-    descr.x = min( descr.x*norm, 0.2f );
-    descr.y = min( descr.y*norm, 0.2f );
-    descr.z = min( descr.z*norm, 0.2f );
-    descr.w = min( descr.w*norm, 0.2f );
-
+    // 32 threads compute 4 squares each, then shuffle to performing a addition by
+    // reduction for the sum of 128 squares, result in thread 0
     norm = descr.x * descr.x
          + descr.y * descr.y
          + descr.z * descr.z
@@ -77,34 +63,25 @@ void NormalizeL2::normalize( const float* src_desc, float* dst_desc, const bool
     norm += popsift::shuffle_down( norm,  4 );
     norm += popsift::shuffle_down( norm,  2 );
     norm += popsift::shuffle_down( norm,  1 );
-    if( threadIdx.x == 0 ) {
-        // norm = __fsqrt_rn( norm );
-        // norm = __fdividef( 512.0f, norm );
-        norm = __frsqrt_rn( norm ); // inverse square root
-        norm = scalbnf( norm, d_consts.norm_multi );
-    }
-#else // not HAVE_NORMF
-    float norm;
 
-    norm = descr.x * descr.x
-         + descr.y * descr.y
-         + descr.z * descr.z
-         + descr.w * descr.w;
-    norm += popsift::shuffle_down( norm, 16 );
-    norm += popsift::shuffle_down( norm,  8 );
-    norm += popsift::shuffle_down( norm,  4 );
-    norm += popsift::shuffle_down( norm,  2 );
-    norm += popsift::shuffle_down( norm,  1 );
     if( threadIdx.x == 0 ) {
+        // compute 1 / sqrt(sum) in round-to-nearest even mode in thread 0
         norm = __frsqrt_rn( norm );
     }
+
+    // spread the inverted norm from thread 0 to all threads in the warp
     norm = popsift::shuffle( norm,  0 );
 
+    // quasi-normalize all 128 floats
     descr.x = min( descr.x*norm, 0.2f );
     descr.y = min( descr.y*norm, 0.2f );
     descr.z = min( descr.z*norm, 0.2f );
     descr.w = min( descr.w*norm, 0.2f );
 
+    // Repeat the procedure, but also add a multiplier. E.g., if the user wants to
+    // descriptors as bytes rather than floats, multiply by 256 - or even by 512
+    // for better accuracy, which is OK because a point cannot be a keypoint if more
+    // than half of its gradient is in a single direction.
     norm = descr.x * descr.x
          + descr.y * descr.y
          + descr.z * descr.z
@@ -114,13 +91,12 @@ void NormalizeL2::normalize( const float* src_desc, float* dst_desc, const bool
     norm += popsift::shuffle_down( norm,  4 );
     norm += popsift::shuffle_down( norm,  2 );
     norm += popsift::shuffle_down( norm,  1 );
+
     if( threadIdx.x == 0 ) {
-        // norm = __fsqrt_rn( norm );
-        // norm = __fdividef( 512.0f, norm );
         norm = __frsqrt_rn( norm ); // inverse square root
         norm = scalbnf( norm, d_consts.norm_multi );
     }
-#endif // HAVE_NORMF
+
     norm = popsift::shuffle( norm,  0 );
 
     descr.x = descr.x * norm;