upgrade horizontal sum in distance_single_code for PQ/IVFPQ (#2830)

Summary:
Pull Request resolved: facebookresearch/faiss#2830

17 cycles per AVX2 horizontal sum instead of 19

Reviewed By: mdouze

Differential Revision: D45244153

fbshipit-source-id: 15accba2e8b4f12725dba41696c302e72f61c2db

Author: BZO95

faiss/impl/code_distance/code_distance-avx2.h

@@ -17,21 +17,19 @@
 
 namespace {
 
-// Computes a horizontal sum over an __m256 register
-inline float horizontal_sum(const __m256 reg) {
-    const __m256 h0 = _mm256_hadd_ps(reg, reg);
-    const __m256 h1 = _mm256_hadd_ps(h0, h0);
-
-    // extract high and low __m128 regs from __m256
-    const __m128 h2 = _mm256_extractf128_ps(h1, 1);
-    const __m128 h3 = _mm256_castps256_ps128(h1);
-
-    // get a final hsum into all 4 regs
-    const __m128 h4 = _mm_add_ss(h2, h3);
+inline float horizontal_sum(const __m128 v) {
+    const __m128 v0 = _mm_shuffle_ps(v, v, _MM_SHUFFLE(0, 0, 3, 2));
+    const __m128 v1 = _mm_add_ps(v, v0);
+    __m128 v2 = _mm_shuffle_ps(v1, v1, _MM_SHUFFLE(0, 0, 0, 1));
+    const __m128 v3 = _mm_add_ps(v1, v2);
+    return _mm_cvtss_f32(v3);
+}
 
-    // extract f[0] from __m128
-    const float hsum = _mm_cvtss_f32(h4);
-    return hsum;
+// Computes a horizontal sum over an __m256 register
+inline float horizontal_sum(const __m256 v) {
+    const __m128 v0 =
+            _mm_add_ps(_mm256_castps256_ps128(v), _mm256_extractf128_ps(v, 1));
+    return horizontal_sum(v0);
 }
 
 } // namespace