diff --git a/go/mysql/datetime/datetime.go b/go/mysql/datetime/datetime.go
index 7a532818cc8..1673a71d662 100644
--- a/go/mysql/datetime/datetime.go
+++ b/go/mysql/datetime/datetime.go
@@ -245,7 +245,14 @@ func (d Date) Hash(h *vthash.Hasher) {
 }
 
 func (d Date) Weekday() time.Weekday {
-	return d.ToStdTime(time.Local).Weekday()
+	// Go considers 0000-01-01 day as Saturday, while
+	// MySQL considers it to be Sunday, now 0000-02-29 exists in
+	// Go but not in MySQL so it balances out after that
+	wd := d.ToStdTime(time.Local).Weekday()
+	if d.Year() == 0 && d.Month() <= 2 {
+		wd = (wd + 1) % 7
+	}
+	return wd
 }
 
 func (d Date) Yearday() int {
diff --git a/go/mysql/datetime/helpers.go b/go/mysql/datetime/helpers.go
index c199844df19..b91114fd791 100644
--- a/go/mysql/datetime/helpers.go
+++ b/go/mysql/datetime/helpers.go
@@ -245,7 +245,7 @@ func daysIn(m time.Month, year int) int {
 }
 
 func isLeap(year int) bool {
-	return year%4 == 0 && (year%100 != 0 || year%400 == 0)
+	return year%4 == 0 && (year%100 != 0 || year%400 == 0) && (year != 0)
 }
 
 func daysInYear(year int) int {
diff --git a/go/vt/vtgate/evalengine/fn_time.go b/go/vt/vtgate/evalengine/fn_time.go
index ecb1fedc135..319f8d1b328 100644
--- a/go/vt/vtgate/evalengine/fn_time.go
+++ b/go/vt/vtgate/evalengine/fn_time.go
@@ -341,6 +341,10 @@ func convertTz(dt datetime.DateTime, from, to *time.Location) (datetime.DateTime
 	if err != nil {
 		return datetime.DateTime{}, false
 	}
+
+	if ts.Unix() < 0 || ts.Unix() >= maxUnixtime {
+		return dt, true
+	}
 	return datetime.NewDateTimeFromStd(ts.In(to)), true
 }
 
@@ -504,7 +508,7 @@ func (b *builtinDayOfWeek) eval(env *ExpressionEnv) (eval, error) {
 	if d == nil || d.isZero() {
 		return nil, nil
 	}
-	return newEvalInt64(int64(d.dt.Date.ToStdTime(env.currentTimezone()).Weekday() + 1)), nil
+	return newEvalInt64(int64(d.dt.Date.Weekday() + 1)), nil
 }
 
 func (call *builtinDayOfWeek) compile(c *compiler) (ctype, error) {
@@ -1494,6 +1498,10 @@ func dateTimeUnixTimestamp(env *ExpressionEnv, date eval) evalNumeric {
 	}
 
 	ts := dt.dt.ToStdTime(env.now)
+	if ts.Unix() < 0 || ts.Unix() >= maxUnixtime {
+		return newEvalInt64(0)
+	}
+
 	if dt.prec == 0 {
 		return newEvalInt64(ts.Unix())
 	}
diff --git a/go/vt/vtgate/evalengine/testcases/inputs.go b/go/vt/vtgate/evalengine/testcases/inputs.go
index f5fa75854e0..b4a558d1145 100644
--- a/go/vt/vtgate/evalengine/testcases/inputs.go
+++ b/go/vt/vtgate/evalengine/testcases/inputs.go
@@ -108,7 +108,7 @@ var inputConversions = []string{
 	"'20000101103458foo'", "'20000101103458.1234foo'", "'20000101103458.123456foo'", "'20000101foo'", "'103458foo'", "'103458.123456foo'",
 	"time '-10:04:58'", "time '-31:34:58'", "time '-32:34:58'",
 	"time '-101:34:58'", "time '-5 10:34:58'",
-	"'10:04:58'", "'101:34:58'", "'5 10:34:58'", "'2000-01-01'", "'2000-01-01 12:34:58'",
+	"'10:04:58'", "'101:34:58'", "'5 10:34:58'", "'2000-01-01'", "'2000-01-01 12:34:58'", "'0000-02-29'", "'0000-01-03'", "'1969-02-18'", "'1970-01-01 00:00:01'", "'3001-02-19 00:00:00'", "'3001-02-18 23:59:59'",
 	"cast(0 as json)", "cast(1 as json)",
 	"cast(true as json)", "cast(false as json)",
 	"cast('{}' as json)", "cast('[]' as json)",