diff --git a/lib/msun/src/catrig.c b/lib/msun/src/catrig.c
index ebfe3567c168..b304f213fa6d 100644
--- a/lib/msun/src/catrig.c
+++ b/lib/msun/src/catrig.c
@@ -469,8 +469,13 @@ clog_for_large_values(double complex z)
 
 	/*
 	 * Avoid overflow in hypot() when x and y are both very large.
-	 * Divide x and y by E, and then add 1 to the logarithm.  This depends
-	 * on E being larger than sqrt(2).
+	 * Divide x and y by E, and then add 1 to the logarithm.  This
+	 * depends on E being larger than sqrt(2), since the return value of
+	 * hypot cannot overflow if neither argument is greater in magnitude
+	 * than 1/sqrt(2) of the maximum value of the return type.  Likewise
+	 * this determines the necessary threshold for using this method
+	 * (however, actually use 1/2 instead as it is simpler).
+	 *
 	 * Dividing by E causes an insignificant loss of accuracy; however
 	 * this method is still poor since it is uneccessarily slow.
 	 */
diff --git a/lib/msun/src/catrigl.c b/lib/msun/src/catrigl.c
index 41357e864456..b79857082700 100644
--- a/lib/msun/src/catrigl.c
+++ b/lib/msun/src/catrigl.c
@@ -57,10 +57,15 @@ __FBSDID("$FreeBSD$");
 #undef signbit
 #define signbit(x)	(__builtin_signbitl(x))
 
+#if LDBL_MAX_EXP != 0x4000
+#error "Unsupported long double format"
+#endif
+
 static const long double
 A_crossover =		10,
 B_crossover =		0.6417,
 FOUR_SQRT_MIN =		0x1p-8189L,
+HALF_MAX =		0x1p16383L,
 QUARTER_SQRT_MAX =	0x1p8189L,
 RECIP_EPSILON =		1 / LDBL_EPSILON,
 SQRT_MIN =		0x1p-8191L;
@@ -307,7 +312,7 @@ clog_for_large_values(long double complex z)
 		ay = t;
 	}
 
-	if (ax > LDBL_MAX / 2)
+	if (ax > HALF_MAX)
 		return (CMPLXL(logl(hypotl(x / m_e, y / m_e)) + 1,
 		    atan2l(y, x)));
 
diff --git a/lib/msun/src/s_csqrtl.c b/lib/msun/src/s_csqrtl.c
index ea2ef27b5088..01cc4090e964 100644
--- a/lib/msun/src/s_csqrtl.c
+++ b/lib/msun/src/s_csqrtl.c
@@ -42,8 +42,16 @@ __FBSDID("$FreeBSD$");
  */
 #pragma	STDC CX_LIMITED_RANGE	ON
 
-/* We risk spurious overflow for components >= LDBL_MAX / (1 + sqrt(2)). */
-#define	THRESH	(LDBL_MAX / 2.414213562373095048801688724209698L)
+/*
+ * We risk spurious overflow for components >= LDBL_MAX / (1 + sqrt(2)).
+ * Rather than determining the fully precise value at which we might
+ * overflow, just use a threshold of approximately LDBL_MAX / 4.
+ */
+#if LDBL_MAX_EXP != 0x4000
+#error "Unsupported long double format"
+#else
+#define	THRESH	0x1p16382L
+#endif
 
 long double complex
 csqrtl(long double complex z)