From 08896769659975f1f9288ccbc58f57cd1558b9e2 Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Fri, 22 Mar 2024 19:28:43 +0100
Subject: [PATCH] Improve bounds near 0

---
 src/RiemannR.cpp | 12 ++++--------
 1 file changed, 4 insertions(+), 8 deletions(-)

diff --git a/src/RiemannR.cpp b/src/RiemannR.cpp
index 5d58ce5a9..da733b0cc 100644
--- a/src/RiemannR.cpp
+++ b/src/RiemannR.cpp
@@ -201,7 +201,7 @@ T initialNthPrimeApprox(T x)
 template <typename T>
 T RiemannR(T x)
 {
-  if (x < T(0.1))
+  if (x < T(1e-5))
     return 0;
 
   T epsilon = std::numeric_limits<T>::epsilon();
@@ -240,12 +240,12 @@ T RiemannR(T x)
 template <typename T>
 T RiemannR_inverse(T x)
 {
+  if (x < 1)
+    return 0;
+
   T t = initialNthPrimeApprox(x);
   T old_term = std::numeric_limits<T>::infinity();
 
-  if (x < 3)
-    return t;
-
   // The condition i < ITERS is required in case the computation
   // does not converge. This happened on Linux i386 where
   // the precision of the libc math functions is very limited.
@@ -274,8 +274,6 @@ namespace primesieve {
 
 long double RiemannR(long double x)
 {
-  if (x <= 100)
-    return ::RiemannR((float) x);
   if (x <= 1e8)
     return ::RiemannR((double) x);
   else
@@ -284,8 +282,6 @@ long double RiemannR(long double x)
 
 long double RiemannR_inverse(long double x)
 {
-  if (x <= 100)
-    return ::RiemannR_inverse((float) x);
   if (x <= 1e8)
     return ::RiemannR_inverse((double) x);
   else