Add a UMA histogram for a user's device scale at startup.

chrome/browser/metrics/chrome_browser_main_extra_parts_metrics.cc

Index: chrome/browser/metrics/chrome_browser_main_extra_parts_metrics.cc
diff --git a/chrome/browser/metrics/chrome_browser_main_extra_parts_metrics.cc b/chrome/browser/metrics/chrome_browser_main_extra_parts_metrics.cc
index b1af95d46c49e1f16df919098bf4be74ca4560cc..08a3db2e79b2d225f3e81907531a843f4e5af604 100644
--- a/chrome/browser/metrics/chrome_browser_main_extra_parts_metrics.cc
+++ b/chrome/browser/metrics/chrome_browser_main_extra_parts_metrics.cc
@@ -54,6 +54,7 @@
 #include "base/win/windows_version.h"
 #include "chrome/browser/shell_integration_win.h"
 #include "chrome/installer/util/google_update_settings.h"
+#include "ui/display/win/dpi.h"
 #endif  // defined(OS_WIN)
 
 namespace {
@@ -271,6 +272,18 @@ void RecordTouchEventState() {
                             UMA_TOUCH_EVENTS_STATE_COUNT);
 }
 
+#if defined(OS_WIN)
+void RecordDeviceScale() {
+  // Clamp the reported value so that if it's wildly out-of-band we won't send
+  // it to the backend.
+  const int scale = std::min(
+      std::max(std::floor(display::win::GetUnforcedDeviceScaleFactor() * 100),
+               0.f),
+      1000.f);

[Ilya Sherman, 2016/07/16 00:43:10]

nit: I think you want 0 and 1000 instead of 0.f and 1000.f, since the final
result is an int.

[Bret, 2016/07/16 01:22:35]

std::floor returns a float and std::min/max require their arguments to be the
same type. Doing this seemed slightly less silly than doing
static_cast<int>(std::floor(etc)) because the value is still unclamped.

+  UMA_HISTOGRAM_SPARSE_SLOWLY("UI.DeviceScale", scale);
+}
+#endif

[Ilya Sherman, 2016/07/16 00:43:10]

Could you please find a different location for recording this metric? 
chrome_browser_main_extra_parts_metrics isn't intended for reporting all kinds
of unrelated metrics; otherwise, it'd end up an overwhelmingly large, hairy
file.

[Bret, 2016/07/16 01:22:35]

Done. Moved into dpi.cc initialization.

+
 #if defined(USE_OZONE) || defined(USE_X11)
 
 // Asynchronously records the touch event state when the ui::DeviceDataManager
@@ -356,6 +369,7 @@ void ChromeBrowserMainExtraPartsMetrics::PostBrowserStart() {
       FROM_HERE, base::Bind(&RecordStartupMetricsOnBlockingPool),
       kStartupMetricsGatheringDelay);
 #if defined(OS_WIN)
+  RecordDeviceScale();
   content::BrowserThread::PostDelayedTask(
       content::BrowserThread::IO, FROM_HERE,
       base::Bind(&shell_integration::win::RecordIsPinnedToTaskbarHistogram),