diff --git a/lib/Support/APFloat.cpp b/lib/Support/APFloat.cpp
index 34bc6b6dd6b..676e2d4ba00 100644
--- a/lib/Support/APFloat.cpp
+++ b/lib/Support/APFloat.cpp
@@ -3546,11 +3546,14 @@ void APFloat::toString(SmallVectorImpl<char> &Str,
   // Set FormatPrecision if zero.  We want to do this before we
   // truncate trailing zeros, as those are part of the precision.
   if (!FormatPrecision) {
-    // It's an interesting question whether to use the nominal
-    // precision or the active precision here for denormals.
+    // We use enough digits so the number can be round-tripped back to an
+    // APFloat. The formula comes from "How to Print Floating-Point Numbers
+    // Accurately" by Steele and White.
+    // FIXME: Using a formula based purely on the precision is conservative;
+    // we can print fewer digits depending on the actual value being printed.
 
-    // FormatPrecision = ceil(significandBits / lg_2(10))
-    FormatPrecision = (semantics->precision * 59 + 195) / 196;
+    // FormatPrecision = 2 + floor(significandBits / lg_2(10))
+    FormatPrecision = 2 + semantics->precision * 59 / 196;
   }
 
   // Ignore trailing binary zeros.
diff --git a/unittests/ADT/APFloatTest.cpp b/unittests/ADT/APFloatTest.cpp
index 3b69de2a52f..e57c8d4b931 100644
--- a/unittests/ADT/APFloatTest.cpp
+++ b/unittests/ADT/APFloatTest.cpp
@@ -866,10 +866,11 @@ TEST(APFloatTest, toString) {
   ASSERT_EQ("0.0101", convertToString(1.01E-2, 5, 2));
   ASSERT_EQ("0.0101", convertToString(1.01E-2, 4, 2));
   ASSERT_EQ("1.01E-2", convertToString(1.01E-2, 5, 1));
-  ASSERT_EQ("0.7853981633974483", convertToString(0.78539816339744830961, 0, 3));
-  ASSERT_EQ("4.940656458412465E-324", convertToString(4.9406564584124654e-324, 0, 3));
-  ASSERT_EQ("873.1834", convertToString(873.1834, 0, 1));
-  ASSERT_EQ("8.731834E+2", convertToString(873.1834, 0, 0));
+  ASSERT_EQ("0.78539816339744828", convertToString(0.78539816339744830961, 0, 3));
+  ASSERT_EQ("4.9406564584124654E-324", convertToString(4.9406564584124654e-324, 0, 3));
+  ASSERT_EQ("873.18340000000001", convertToString(873.1834, 0, 1));
+  ASSERT_EQ("8.7318340000000001E+2", convertToString(873.1834, 0, 0));
+  ASSERT_EQ("1.7976931348623157E+308", convertToString(1.7976931348623157E+308, 0, 0));
 }
 
 TEST(APFloatTest, toInteger) {