Fix rounding errors with float timestamps

When converting from float to (TICKS . HZ) form, do the
conversion exactly.  When converting from (TICKS . HZ) form to
float, round to even precisely.  This way, successfully
converting a float to (TICKS . HZ) and back yields a value
numerically equal to the original.
* src/timefns.c (flt_radix_power_size): New constant.
(flt_radix_power): New static var.
(decode_float_time): Convert the exact numeric value rather
than guessing TIMESPEC_HZ resolution.
(s_ns_to_double): Remove; no longer needed.
(frac_to_double): New function.
(decode_ticks_hz): It is now the caller’s responsibility to
pass a valid TICKS and HZ.  All callers changed.
Use frac_to_double to round (TICKS . HZ) precisely.
(decode_time_components): When decoding nil, use
decode_ticks_hz since it rounds precisely.
(syms_of_timefns): Initialize flt_radix_power.
* test/src/timefns-tests.el (float-time-precision): New test.

1 files changed, 18 insertions, 0 deletions

diff --git a/test/src/timefns-tests.el b/test/src/timefns-tests.el
index feb8fc7905e..1b1032deaa1 100644
--- a/test/src/timefns-tests.el
+++ b/test/src/timefns-tests.el
@@ -150,3 +150,21 @@
     (should (time-equal-p
              (encode-time '(29 31 17 30 4 2019 2 t 7200 0))
              '(23752 27217))))
+
+(ert-deftest float-time-precision ()
+  (should (< 0 (float-time '(1 . 10000000000))))
+  (should (< (float-time '(-1 . 10000000000)) 0))
+
+  (let ((x 1.0))
+    (while (not (zerop x))
+      (dolist (multiplier '(-1.9 -1.5 -1.1 -1 1 1.1 1.5 1.9))
+        (let ((xmult (* x multiplier)))
+          (should (= xmult (float-time (time-convert xmult t))))))
+      (setq x (/ x 2))))
+
+  (let ((x 1.0))
+    (while (ignore-errors (time-convert x t))
+      (dolist (divisor '(-1.9 -1.5 -1.1 -1 1 1.1 1.5 1.9))
+        (let ((xdiv (/ x divisor)))
+          (should (= xdiv (float-time (time-convert xdiv t))))))
+      (setq x (* x 2)))))