diff --git a/src/LogarithmicIntegral.cpp b/src/LogarithmicIntegral.cpp
index d5d661cc..3548c27f 100644
--- a/src/LogarithmicIntegral.cpp
+++ b/src/LogarithmicIntegral.cpp
@@ -227,7 +227,7 @@ int64_t Li(int64_t x)
 {
 #if defined(HAVE_FLOAT128)
   double long_double_mantissa_bits = std::numeric_limits<long double>::digits;
-  if (x > 1e10 && std::log2(x) >= long_double_mantissa_bits - 3)
+  if (x > 1e10 && std::log2(x) >= long_double_mantissa_bits - 4)
     return (int64_t) ::Li((__float128) x);
 #endif
   return (int64_t) ::Li((long double) x);
@@ -239,10 +239,10 @@ int64_t Li_inverse(int64_t x)
   if (x > 1e10)
   {
     double logx = std::log(x);
-    double n = (double) x * logx * logx * logx;
+    double n = (double) x * logx * logx;
     double long_double_mantissa_bits = std::numeric_limits<long double>::digits;
 
-    if (std::log2(n) >= long_double_mantissa_bits)
+    if (std::log2(n) >= long_double_mantissa_bits - 4)
     {
       __float128 res = ::Li_inverse((__float128) x);
       if (res > (__float128) std::numeric_limits<int64_t>::max())
@@ -266,7 +266,7 @@ int128_t Li(int128_t x)
 {
 #if defined(HAVE_FLOAT128)
   double long_double_mantissa_bits = std::numeric_limits<long double>::digits;
-  if (x > 1e10 && std::log2(x) >= long_double_mantissa_bits - 3)
+  if (x > 1e10 && std::log2(x) >= long_double_mantissa_bits - 4)
     return (int128_t) ::Li((__float128) x);
 #endif
   return (int128_t) ::Li((long double) x);
@@ -278,10 +278,10 @@ int128_t Li_inverse(int128_t x)
   if (x > 1e10)
   {
     double logx = std::log(x);
-    double n = (double) x * logx * logx * logx;
+    double n = (double) x * logx * logx;
     double long_double_mantissa_bits = std::numeric_limits<long double>::digits;
 
-    if (std::log2(n) >= long_double_mantissa_bits)
+    if (std::log2(n) >= long_double_mantissa_bits - 4)
     {
       __float128 res = ::Li_inverse((__float128) x);
       if (res > (__float128) std::numeric_limits<int128_t>::max())
diff --git a/src/RiemannR.cpp b/src/RiemannR.cpp
index 922539d8..3790032c 100644
--- a/src/RiemannR.cpp
+++ b/src/RiemannR.cpp
@@ -551,7 +551,7 @@ int64_t RiemannR(int64_t x)
 {
 #if defined(HAVE_FLOAT128)
   double long_double_mantissa_bits = std::numeric_limits<long double>::digits;
-  if (x > 1e10 && std::log2(x) >= long_double_mantissa_bits - 3)
+  if (x > 1e10 && std::log2(x) >= long_double_mantissa_bits - 4)
     return (int64_t) ::RiemannR((__float128) x);
 #endif
   return (int64_t) ::RiemannR((long double) x);
@@ -563,10 +563,10 @@ int64_t RiemannR_inverse(int64_t x)
   if (x > 1e10)
   {
     double logx = std::log(x);
-    double n = (double) x * logx * logx * logx;
+    double n = (double) x * logx * logx;
     double long_double_mantissa_bits = std::numeric_limits<long double>::digits;
 
-    if (std::log2(n) >= long_double_mantissa_bits)
+    if (std::log2(n) >= long_double_mantissa_bits - 4)
     {
       __float128 res = ::RiemannR_inverse((__float128) x);
       if (res > (__float128) std::numeric_limits<int64_t>::max())
@@ -590,7 +590,7 @@ int128_t RiemannR(int128_t x)
 {
 #if defined(HAVE_FLOAT128)
   double long_double_mantissa_bits = std::numeric_limits<long double>::digits;
-  if (x > 1e10 && std::log2(x) >= long_double_mantissa_bits - 3)
+  if (x > 1e10 && std::log2(x) >= long_double_mantissa_bits - 4)
     return (int128_t) ::RiemannR((__float128) x);
 #endif
   return (int128_t) ::RiemannR((long double) x);
@@ -602,10 +602,10 @@ int128_t RiemannR_inverse(int128_t x)
   if (x > 1e10)
   {
     double logx = std::log(x);
-    double n = (double) x * logx * logx * logx;
+    double n = (double) x * logx * logx;
     double long_double_mantissa_bits = std::numeric_limits<long double>::digits;
 
-    if (std::log2(n) >= long_double_mantissa_bits)
+    if (std::log2(n) >= long_double_mantissa_bits - 4)
     {
       __float128 res = ::RiemannR_inverse((__float128) x);
       if (res > (__float128) std::numeric_limits<int128_t>::max())