Use the Gram series for calculating Ri (#144)

RiemannR(x) = 1 + \sum_{k=1}^{∞} ln(x)^k / (zeta(k + 1) * k * k!)
kimwalisch · Feb 9, 2024 · 29051b9 · 29051b9
1 parent 55a1d06
commit 29051b9
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diff --git a/include/primesieve/forward.hpp b/include/primesieve/forward.hpp
@@ -18,6 +18,7 @@ namespace primesieve {
 
 extern const Array<uint64_t, 65> bitValues;
 extern const Array<uint64_t, 64> bruijnBitValues;
+extern const Array<long double, 128> zetaInv;
 
 int get_num_threads();
 int get_sieve_size();

diff --git a/include/primesieve/nthPrimeApprox.hpp b/include/primesieve/nthPrimeApprox.hpp
@@ -12,9 +12,6 @@
 
 namespace primesieve {
 
-Vector<int32_t> generate_moebius(int64_t max);
-uint64_t Li(uint64_t x);
-uint64_t Li_inverse(uint64_t x);
 uint64_t Ri(uint64_t x);
 uint64_t Ri_inverse(uint64_t x);
 uint64_t primePiApprox(uint64_t x);

diff --git a/src/LookupTables.cpp b/src/LookupTables.cpp
@@ -107,4 +107,140 @@ const WheelInit wheel210Init[210] =
   { 1, 47 }, { 0, 47 }
 };
 
+/// Precomputed values of zetaInv[k] = 1 / zeta(k + 1).
+/// Used in the calculation of the Riemann R function and its derivative.
+/// These values are calculated up to a precision of 128 bits.
+///
+const Array<long double, 128> zetaInv =
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+
 } // namespace