bug in xtime.h

[Bruno Haible]

Hi Paul,

This formula in xtime.h caught my attention:

xtime_sec (xtime_t t)
{
  return (t < 0
          ? (t + XTIME_PRECISION - 1) / XTIME_PRECISION - 1
          : xtime_nonnegative_sec (t));
} 

Let's look at its behaviour for t < 0.

It looks wrong for two reasons:

1) This function is supposed to be constant on intervals of
length XTIME_PRECISION - 1. However, it is also constant on
the interval   [ -2*XTIME_PRECISION+2 , -1 ], which is
nearly twice as long.

2) For all integral t, the equation
      t = XTIME_PRECISION * (t / XTIME_PRECISION) + (t % XTIME_PRECISION)
holds. For negative t, the function

xtime_nsec (xtime_t t)
{
  long int ns = t % XTIME_PRECISION;
  if (ns < 0)
    ns += XTIME_PRECISION;
  return ns;
}

applies a positive correction to the second summand in more than 99% of the
cases. To compensate, a negative correction of the first summand should
occur in more than 99% of the cases. But the formula

   (t + XTIME_PRECISION - 1) / XTIME_PRECISION - 1

applies a negative correction only in less than 1% of the cases.


Here's a suggested fix. And a simplification in xtime_make.


2019-12-22  Bruno Haible  <br...@clisp.org>

        gethrxtime: Fix a bug in xtime_sec().
        * lib/xtime.h (xtime_make): Simplify.
        (xtime_sec): Fix an off-by-one error in 99.9999998% of the negative t
        cases.

diff --git a/lib/xtime.h b/lib/xtime.h
index 77f1c30..5e0ae89 100644
--- a/lib/xtime.h
+++ b/lib/xtime.h
@@ -42,12 +42,13 @@ extern "C" {
 XTIME_INLINE xtime_t
 xtime_make (xtime_t s, long int ns)
 {
-  const long int giga = 1000 * 1000 * 1000;
-  s += ns / giga;
-  ns %= giga;
   return XTIME_PRECISION * s + ns;
 }
 
+/* The following functions split an extended time value:
+   T = XTIME_PRECISION * xtime_sec (T) + xtime_nsec (T)
+   with  0 <= xtime_nsec (T) < XTIME_PRECISION.  */
+
 /* Return the number of seconds in T, which must be nonnegative.  */
 XTIME_INLINE xtime_t
 xtime_nonnegative_sec (xtime_t t)
@@ -60,7 +61,7 @@ XTIME_INLINE xtime_t
 xtime_sec (xtime_t t)
 {
   return (t < 0
-          ? (t + XTIME_PRECISION - 1) / XTIME_PRECISION - 1
+          ? (t + 1) / XTIME_PRECISION - 1
           : xtime_nonnegative_sec (t));
 }