backend/native: Calculate refresh rate in double-precision

The old calculation was introduced to improve the precision
with commit c16a5ec1cf14d67ee8100afd31a2e85e7003f9a8.

Here, I call the calculation as "revision 2", and the
calculation even older as "revision 1", and the new
calculation introduced with this commit as "reivion 3".

Revision 2 has two problems:
1. The calculation is mixed with fixed-point numbers and
   floating-point numbers.

To overcome the precision loss of fixed-point numbers division,
it first "calculates refresh rate in milliHz first for extra
precision", but this requires converting the value back to Hz.
An extra calculation has performance and precision costs.
It is also hard to understand for programmers.

2. The calculation has a bias.

In the process, it does:
refresh += (drm_mode->vtotal / 2);
It prevents the value from being rounded to a smaller value in
a fixed-point integer arithmetics, but it only adds a small
bias (0.0005) and consumes some fraction bits for
floating point arithmetic.

Revision 3, introduced with this commit always uses
double-precision floating-point values for true precision and
to ease understanding of this code. It also removes the bias.

Another change is that it now has two internal values, numerator
and denominator. Revision 1 also calculated those two values
first, and later performed a division with them, which minimizes
the precision loss caused by divisions. This method has risks of
overflowing the two values and revision 1 caused problems due to
that, but revision 3 won't thanks to double-precision. Therefore,
revision 3 will theoretically have the result identical with
the calculation with infinite-precision.

Part-of: <https://gitlab.gnome.org/GNOME/mutter/-/merge_requests/1737>

1 files changed, 11 insertions, 12 deletions

diff --git a/src/backends/native/meta-kms-utils.c b/src/backends/native/meta-kms-utils.c
index 11df09be8..1c58db83d 100644
--- a/src/backends/native/meta-kms-utils.c
+++ b/src/backends/native/meta-kms-utils.c
@@ -33,19 +33,18 @@
 float
 meta_calculate_drm_mode_refresh_rate (const drmModeModeInfo *drm_mode)
 {
-  float refresh = 0.0;
+  double numerator;
+  double denominator;
 
-  if (drm_mode->htotal > 0 && drm_mode->vtotal > 0)
-    {
-      /* Calculate refresh rate in milliHz first for extra precision. */
-      refresh = (drm_mode->clock * 1000000LL) / drm_mode->htotal;
-      refresh += (drm_mode->vtotal / 2);
-      refresh /= drm_mode->vtotal;
-      if (drm_mode->vscan > 1)
-        refresh /= drm_mode->vscan;
-      refresh /= 1000.0;
-    }
-  return refresh;
+  if (drm_mode->htotal <= 0 || drm_mode->vtotal <= 0)
+    return 0.0;
+
+  numerator = drm_mode->clock * 1000.0;
+  denominator = (double) drm_mode->vtotal * drm_mode->htotal;
+  if (drm_mode->vscan > 1)
+    denominator *= drm_mode->vscan;
+
+  return numerator / denominator;
 }
 
 /**