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Use a faster series for calculating the Riemann R function #144

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Feb 9, 2024
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Use a faster series for calculating the Riemann R function #144

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1 change: 1 addition & 0 deletions include/primesieve/forward.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -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();
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3 changes: 0 additions & 3 deletions include/primesieve/nthPrimeApprox.hpp
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Expand Up @@ -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);
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136 changes: 136 additions & 0 deletions src/LookupTables.cpp
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Expand Up @@ -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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0.83190737258070746868312627882153073442L,
0.92393840292159016702375049404068247277L,
0.96438734042926245912643658844498457124L,
0.98295259226458041980489656499392413295L,
0.99171985583844431042818593149755069165L,
0.99593920112551514683483647280554532401L,
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0.99999999999999999999999999999999999991L,
1.00000000000000000000000000000000000000L,
1.00000000000000000000000000000000000000L,
1.00000000000000000000000000000000000000L,
1.00000000000000000000000000000000000000L,
1.00000000000000000000000000000000000000L
};

} // namespace
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