Fixed some performance issues in DTW.

Co-authored-by: Jyrki Alakuijala <jyrki.alakuijala@gmail.com>

cpp/zimt/dtw.cc

@@ -66,26 +66,18 @@ float HwyMin(hwy::Span<const float> span) {
   return min;
 }
 
-float HwyDeltaNorm(hwy::Span<const float> span_a, hwy::Span<const float> span_b,
-                   float order, float max) {
-  if (max == 0) {
-    return 0;
-  }
-
+float HwyDeltaNorm(hwy::Span<const float> span_a,
+                   hwy::Span<const float> span_b) {
   CHECK_EQ(span_a.size(), span_b.size());
 
-  const Vec order_vec = Set(d, order);
-  const Vec max_reciprocal = Div(Set(d, 1), Set(d, max));
   double sum = 0;
   for (size_t index = 0; index < span_a.size(); index += Lanes(d)) {
     const Vec delta =
         Sub(Load(d, span_a.data() + index), Load(d, span_b.data() + index));
-    const Vec downscaled_values = Mul(delta, max_reciprocal);
-    const Vec pows = Exp(d, Mul(order_vec, Log(d, downscaled_values)));
-    sum += static_cast<double>(ReduceSum(d, pows));
+    const Vec square = Mul(delta, delta);
+    sum += static_cast<double>(ReduceSum(d, square));
   }
-  return static_cast<float>(max *
-                            std::pow(sum, 1 / static_cast<double>(order)));
+  return static_cast<float>(std::sqrt(sum));
 }
 
 }  // namespace HWY_NAMESPACE
@@ -120,20 +112,12 @@ std::vector<std::pair<size_t, size_t>> DTWSlice(
     hwy::AlignedNDArray<float, 2>& cost_matrix) {
   CHECK_EQ(cost_matrix.shape()[0], spec_a.shape()[0]);
   CHECK_EQ(cost_matrix.shape()[1], spec_b.shape()[0]);
-  std::vector<float> max_a(spec_a.shape()[0]);
-  std::vector<float> min_a(spec_a.shape()[0]);
-  std::vector<float> max_b(spec_b.shape()[0]);
-  std::vector<float> min_b(spec_b.shape()[0]);
   for (size_t spec_b_index = 0; spec_b_index < spec_b.shape()[0];
        ++spec_b_index) {
-    max_b[spec_b_index] = HWY_DYNAMIC_DISPATCH(HwyMax)(spec_b[{spec_b_index}]);
-    min_b[spec_b_index] = HWY_DYNAMIC_DISPATCH(HwyMin)(spec_b[{spec_b_index}]);
     cost_matrix[{0}][spec_b_index] = std::numeric_limits<float>::infinity();
   }
   for (size_t spec_a_index = 1; spec_a_index < spec_a.shape()[0];
        ++spec_a_index) {
-    max_a[spec_a_index] = HWY_DYNAMIC_DISPATCH(HwyMax)(spec_a[{spec_a_index}]);
-    min_a[spec_a_index] = HWY_DYNAMIC_DISPATCH(HwyMin)(spec_a[{spec_a_index}]);
     for (size_t spec_b_index = 0; spec_b_index < spec_b.shape()[0];
          ++spec_b_index) {
       cost_matrix[{spec_a_index}][spec_b_index] =
@@ -145,11 +129,8 @@ std::vector<std::pair<size_t, size_t>> DTWSlice(
        ++spec_a_index) {
     for (size_t spec_b_index = 1; spec_b_index < spec_b.shape()[0];
          ++spec_b_index) {
-      const float max_delta =
-          std::max(std::abs(max_a[spec_a_index] - min_b[spec_b_index]),
-                   std::abs(max_b[spec_b_index] - min_a[spec_a_index]));
       const float cost = HWY_DYNAMIC_DISPATCH(HwyDeltaNorm)(
-          spec_a[{spec_a_index}], spec_b[{spec_b_index}], 2.0, max_delta);
+          spec_a[{spec_a_index}], spec_b[{spec_b_index}]);
       cost_matrix[{spec_a_index}][spec_b_index] =
           cost +
           std::min(cost_matrix[{spec_a_index - 1}][spec_b_index - 1],