time: test and fix Time.Round, Duration.Round for d > 2⁶²

Round uses r+r < d to decide whether the remainder is
above or below half of d (to decide whether to round up or down).
This is wrong when r+r wraps negative, because it looks < d
but is really > d.

No one will ever care about rounding to a multiple of
d > 2⁶² (about 146 years), but might as well get it right.

Fixes #19807.

Change-Id: I1b55a742dc36e02a7465bc778bf5dd74fe71f7c0
Reviewed-on: https://go-review.googlesource.com/39151
Run-TryBot: Russ Cox <rsc@golang.org>
Reviewed-by: Rob Pike <r@golang.org>
Reviewed-by: David Chase <drchase@google.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>

src/time/time.go

@@ -798,6 +798,12 @@ func (d Duration) Truncate(m Duration) Duration {
 	return d - d%m
 }
 
+// lessThanHalf reports whether x+x < y but avoids overflow,
+// assuming x and y are both positive (Duration is signed).
+func lessThanHalf(x, y Duration) bool {
+	return uint64(x)+uint64(x) < uint64(y)
+}
+
 // Round returns the result of rounding d to the nearest multiple of m.
 // The rounding behavior for halfway values is to round away from zero.
 // If the result exceeds the maximum (or minimum)
@@ -811,7 +817,7 @@ func (d Duration) Round(m Duration) Duration {
 	r := d % m
 	if d < 0 {
 		r = -r
-		if r+r < m {
+		if lessThanHalf(r, m) {
 			return d + r
 		}
 		if d1 := d - m + r; d1 < d {
@@ -819,7 +825,7 @@ func (d Duration) Round(m Duration) Duration {
 		}
 		return minDuration // overflow
 	}
-	if r+r < m {
+	if lessThanHalf(r, m) {
 		return d - r
 	}
 	if d1 := d + m - r; d1 > d {
@@ -1400,7 +1406,7 @@ func (t Time) Round(d Duration) Time {
 		return t
 	}
 	_, r := div(t, d)
-	if r+r < d {
+	if lessThanHalf(r, d) {
 		return t.Add(-r)
 	}
 	return t.Add(d - r)

src/time/time_test.go

@@ -233,6 +233,7 @@ var truncateRoundTests = []struct {
 	{Date(-1, January, 1, 12, 15, 31, 5e8, UTC), 3},
 	{Date(2012, January, 1, 12, 15, 30, 5e8, UTC), Second},
 	{Date(2012, January, 1, 12, 15, 31, 5e8, UTC), Second},
+	{Unix(-19012425939, 649146258), 7435029458905025217}, // 5.8*d rounds to 6*d, but .8*d+.8*d < 0 < d
 }
 
 func TestTruncateRound(t *testing.T) {
@@ -1107,6 +1108,7 @@ var durationRoundTests = []struct {
 	{9e18, 5e18, 1<<63 - 1},
 	{-8e18, 3e18, -9e18},
 	{-9e18, 5e18, -1 << 63},
+	{3<<61 - 1, 3 << 61, 3 << 61},
 }
 
 func TestDurationRound(t *testing.T) {