quantize_stats: print rmse and max error as fraction of <x> (#21)

This allows for a better comparison between different models
or different tensors of the same model where the magnitude of
the model weights may differ.

Co-authored-by: Iwan Kawrakow <[email protected]>

examples/quantize-stats/quantize-stats.cpp

@@ -40,6 +40,7 @@ struct error_stats {
     size_t num_samples;
     double total_error;
     double max_error;
+    double sum_x2;
     uint64_t error_histogram[HISTOGRAM_BUCKETS];
 };
 
@@ -89,6 +90,7 @@ static void update_error_stats(int64_t nelements, const float * input, const flo
         double diff = input[i] - output[i];
         stats.total_error += diff * diff;
         stats.max_error = fmax(fabs(diff), stats.max_error);
+        stats.sum_x2 += input[i]*input[i];
         stats.error_histogram[std::max(std::min((size_t) floor(fabs(diff) / HISTOGRAM_RANGE * HISTOGRAM_BUCKETS), HISTOGRAM_BUCKETS-1), (size_t) 0)]++;
     }
     stats.num_samples += nelements;
@@ -97,6 +99,7 @@ static void update_error_stats(int64_t nelements, const float * input, const flo
 static void combine_error_stats(error_stats & into, const error_stats & from) {
     into.num_samples += from.num_samples;
     into.total_error += from.total_error;
+    into.sum_x2      += from.sum_x2;
     if (from.max_error > into.max_error) into.max_error = from.max_error;
     for (size_t i=0; i<HISTOGRAM_BUCKETS; ++i) into.error_histogram[i] += from.error_histogram[i];
 }
@@ -116,9 +119,11 @@ static double find_quantile(const error_stats & stats, double quantile) {
 
 static void print_error_stats(const std::string & name, const error_stats & stats, bool print_histogram) {
     double rmse = sqrt(stats.total_error / (double) stats.num_samples);
+    double av_x = sqrt(stats.sum_x2 / (double) stats.num_samples);
     double median = find_quantile(stats, .5);
     double pct95 = find_quantile(stats, .95);
-    printf("%-50s: rmse %.8f, maxerr %.8f, 95pct<%.4f, median<%.4f\n", name.c_str(), rmse, stats.max_error, pct95, median);
+    printf("%-40s: rmse %.8f, %.6f  maxerr %.8f, %.6f  95pct<%.4f,  median<%.4f\n", name.c_str(), rmse, rmse/av_x,
+            stats.max_error, stats.max_error/av_x, pct95, median);
     if (print_histogram) {
         printf("Error distribution:\n");
         for (size_t i = 0; i < HISTOGRAM_BUCKETS; i++) {