math/cmplx: prevent infinite loop in tanSeries

The condition to determine if any further iterations are needed is
evaluated to false in case it encounters a NaN. Instead, flip the
condition to keep looping until the factor is greater than the machine
roundoff error.

Updates #17577

Change-Id: I058abe73fcd49d3ae4e2f7b33020437cc8f290c3
Reviewed-on: https://go-review.googlesource.com/31952
Reviewed-by: Robert Griesemer <gri@golang.org>

src/math/cmplx/cmath_test.go

@@ -759,6 +759,14 @@ func TestTanh(t *testing.T) {
 	}
 }
 
+// See issue 17577
+func TestInfiniteLoopIntanSeries(t *testing.T) {
+	want := Inf()
+	if got := Cot(0); got != want {
+		t.Errorf("Cot(0): got %g, want %g", got, want)
+	}
+}
+
 func BenchmarkAbs(b *testing.B) {
 	for i := 0; i < b.N; i++ {
 		Abs(complex(2.5, 3.5))

src/math/cmplx/tan.go

@@ -139,7 +139,9 @@ func tanSeries(z complex128) float64 {
 		t = y2 - x2
 		t /= f
 		d += t
-		if math.Abs(t/d) <= MACHEP {
+		if !(math.Abs(t/d) > MACHEP) {
+			// Caution: Use ! and > instead of <= for correct behavior if t/d is NaN.
+			// See issue 17577.
 			break
 		}
 	}