diff --git a/src/math/cmplx/asin.go b/src/math/cmplx/asin.go
index 61880a257d..062f324ce2 100644
--- a/src/math/cmplx/asin.go
+++ b/src/math/cmplx/asin.go
@@ -49,11 +49,8 @@ import "math"
 
 // Asin returns the inverse sine of x.
 func Asin(x complex128) complex128 {
-	if imag(x) == 0 {
-		if math.Abs(real(x)) > 1 {
-			return complex(math.Pi/2, 0) // DOMAIN error
-		}
-		return complex(math.Asin(real(x)), 0)
+	if imag(x) == 0 && math.Abs(real(x)) <= 1 {
+		return complex(math.Asin(real(x)), imag(x))
 	}
 	ct := complex(-imag(x), real(x)) // i * x
 	xx := x * x
@@ -65,12 +62,8 @@ func Asin(x complex128) complex128 {
 
 // Asinh returns the inverse hyperbolic sine of x.
 func Asinh(x complex128) complex128 {
-	// TODO check range
-	if imag(x) == 0 {
-		if math.Abs(real(x)) > 1 {
-			return complex(math.Pi/2, 0) // DOMAIN error
-		}
-		return complex(math.Asinh(real(x)), 0)
+	if imag(x) == 0 && math.Abs(real(x)) <= 1 {
+		return complex(math.Asinh(real(x)), imag(x))
 	}
 	xx := x * x
 	x1 := complex(1+real(xx), imag(xx)) // 1 + x*x
@@ -140,10 +133,6 @@ func Acosh(x complex128) complex128 {
 
 // Atan returns the inverse tangent of x.
 func Atan(x complex128) complex128 {
-	if real(x) == 0 && imag(x) > 1 {
-		return NaN()
-	}
-
 	x2 := real(x) * real(x)
 	a := 1 - x2 - imag(x)*imag(x)
 	if a == 0 {
diff --git a/src/math/cmplx/cmath_test.go b/src/math/cmplx/cmath_test.go
index 7a5c485a31..8d705622fd 100644
--- a/src/math/cmplx/cmath_test.go
+++ b/src/math/cmplx/cmath_test.go
@@ -435,6 +435,24 @@ var tanhSC = []complex128{
 	NaN(),
 }
 
+// branch cut continuity checks
+// points on each axis at |z| > 1 are checked for one-sided continuity from both the positive and negative side
+// all possible branch cuts for the elementary functions are at one of these points
+
+var zero = 0.0
+var eps = 1.0 / (1 << 53)
+
+var branchPoints = [][2]complex128{
+	{complex(2.0, zero), complex(2.0, eps)},
+	{complex(2.0, -zero), complex(2.0, -eps)},
+	{complex(-2.0, zero), complex(-2.0, eps)},
+	{complex(-2.0, -zero), complex(-2.0, -eps)},
+	{complex(zero, 2.0), complex(eps, 2.0)},
+	{complex(-zero, 2.0), complex(-eps, 2.0)},
+	{complex(zero, -2.0), complex(eps, -2.0)},
+	{complex(-zero, -2.0), complex(-eps, -2.0)},
+}
+
 // functions borrowed from pkg/math/all_test.go
 func tolerance(a, b, e float64) bool {
 	d := a - b
@@ -508,6 +526,11 @@ func TestAcos(t *testing.T) {
 			t.Errorf("Acos(%g) = %g, want %g", vcAcosSC[i], f, acosSC[i])
 		}
 	}
+	for _, pt := range branchPoints {
+		if f0, f1 := Acos(pt[0]), Acos(pt[1]); !cVeryclose(f0, f1) {
+			t.Errorf("Acos(%g) not continuous, got %g want %g", pt[0], f0, f1)
+		}
+	}
 }
 func TestAcosh(t *testing.T) {
 	for i := 0; i < len(vc); i++ {
@@ -520,6 +543,11 @@ func TestAcosh(t *testing.T) {
 			t.Errorf("Acosh(%g) = %g, want %g", vcAcoshSC[i], f, acoshSC[i])
 		}
 	}
+	for _, pt := range branchPoints {
+		if f0, f1 := Acosh(pt[0]), Acosh(pt[1]); !cVeryclose(f0, f1) {
+			t.Errorf("Acosh(%g) not continuous, got %g want %g", pt[0], f0, f1)
+		}
+	}
 }
 func TestAsin(t *testing.T) {
 	for i := 0; i < len(vc); i++ {
@@ -532,6 +560,11 @@ func TestAsin(t *testing.T) {
 			t.Errorf("Asin(%g) = %g, want %g", vcAsinSC[i], f, asinSC[i])
 		}
 	}
+	for _, pt := range branchPoints {
+		if f0, f1 := Asin(pt[0]), Asin(pt[1]); !cVeryclose(f0, f1) {
+			t.Errorf("Asin(%g) not continuous, got %g want %g", pt[0], f0, f1)
+		}
+	}
 }
 func TestAsinh(t *testing.T) {
 	for i := 0; i < len(vc); i++ {
@@ -544,6 +577,11 @@ func TestAsinh(t *testing.T) {
 			t.Errorf("Asinh(%g) = %g, want %g", vcAsinhSC[i], f, asinhSC[i])
 		}
 	}
+	for _, pt := range branchPoints {
+		if f0, f1 := Asinh(pt[0]), Asinh(pt[1]); !cVeryclose(f0, f1) {
+			t.Errorf("Asinh(%g) not continuous, got %g want %g", pt[0], f0, f1)
+		}
+	}
 }
 func TestAtan(t *testing.T) {
 	for i := 0; i < len(vc); i++ {
@@ -556,6 +594,11 @@ func TestAtan(t *testing.T) {
 			t.Errorf("Atan(%g) = %g, want %g", vcAtanSC[i], f, atanSC[i])
 		}
 	}
+	for _, pt := range branchPoints {
+		if f0, f1 := Atan(pt[0]), Atan(pt[1]); !cVeryclose(f0, f1) {
+			t.Errorf("Atan(%g) not continuous, got %g want %g", pt[0], f0, f1)
+		}
+	}
 }
 func TestAtanh(t *testing.T) {
 	for i := 0; i < len(vc); i++ {
@@ -568,6 +611,11 @@ func TestAtanh(t *testing.T) {
 			t.Errorf("Atanh(%g) = %g, want %g", vcAtanhSC[i], f, atanhSC[i])
 		}
 	}
+	for _, pt := range branchPoints {
+		if f0, f1 := Atanh(pt[0]), Atanh(pt[1]); !cVeryclose(f0, f1) {
+			t.Errorf("Atanh(%g) not continuous, got %g want %g", pt[0], f0, f1)
+		}
+	}
 }
 func TestConj(t *testing.T) {
 	for i := 0; i < len(vc); i++ {
@@ -635,6 +683,11 @@ func TestLog(t *testing.T) {
 			t.Errorf("Log(%g) = %g, want %g", vcLogSC[i], f, logSC[i])
 		}
 	}
+	for _, pt := range branchPoints {
+		if f0, f1 := Log(pt[0]), Log(pt[1]); !cVeryclose(f0, f1) {
+			t.Errorf("Log(%g) not continuous, got %g want %g", pt[0], f0, f1)
+		}
+	}
 }
 func TestLog10(t *testing.T) {
 	for i := 0; i < len(vc); i++ {
@@ -685,6 +738,11 @@ func TestPow(t *testing.T) {
 			t.Errorf("Pow(%g, %g) = %g, want %g", vcPowSC[i][0], vcPowSC[i][0], f, powSC[i])
 		}
 	}
+	for _, pt := range branchPoints {
+		if f0, f1 := Pow(pt[0], 0.1), Pow(pt[1], 0.1); !cVeryclose(f0, f1) {
+			t.Errorf("Pow(%g, 0.1) not continuous, got %g want %g", pt[0], f0, f1)
+		}
+	}
 }
 func TestRect(t *testing.T) {
 	for i := 0; i < len(vc); i++ {
@@ -733,6 +791,11 @@ func TestSqrt(t *testing.T) {
 			t.Errorf("Sqrt(%g) = %g, want %g", vcSqrtSC[i], f, sqrtSC[i])
 		}
 	}
+	for _, pt := range branchPoints {
+		if f0, f1 := Sqrt(pt[0]), Sqrt(pt[1]); !cVeryclose(f0, f1) {
+			t.Errorf("Sqrt(%g) not continuous, got %g want %g", pt[0], f0, f1)
+		}
+	}
 }
 func TestTan(t *testing.T) {
 	for i := 0; i < len(vc); i++ {
diff --git a/src/math/cmplx/sqrt.go b/src/math/cmplx/sqrt.go
index 72f81e907c..0fbdcdedd3 100644
--- a/src/math/cmplx/sqrt.go
+++ b/src/math/cmplx/sqrt.go
@@ -57,13 +57,14 @@ import "math"
 // The result r is chosen so that real(r) ≥ 0 and imag(r) has the same sign as imag(x).
 func Sqrt(x complex128) complex128 {
 	if imag(x) == 0 {
+		// Ensure that imag(r) has the same sign as imag(x) for imag(x) == signed zero.
 		if real(x) == 0 {
-			return complex(0, 0)
+			return complex(0, imag(x))
 		}
 		if real(x) < 0 {
-			return complex(0, math.Sqrt(-real(x)))
+			return complex(0, math.Copysign(math.Sqrt(-real(x)), imag(x)))
 		}
-		return complex(math.Sqrt(real(x)), 0)
+		return complex(math.Sqrt(real(x)), imag(x))
 	}
 	if real(x) == 0 {
 		if imag(x) < 0 {