Add options: --RiemannR && --R-inverse

doc/primesieve.txt

@@ -62,6 +62,12 @@ OPTIONS
 *-q, --quiet*::
 	Quiet mode, prints less output.
 
+*-R, --RiemannR*::
+	Approximate PrimePi(x) using the Riemann R function: R(x).
+
+*--R-inverse*::
+	Approximate the nth prime using the inverse Riemann R function: R^-1(x).
+
 *-s, --size*='SIZE'::
 	Set the size of the sieve array in KiB, 16 \<= 'SIZE' \<= 8192. By default
 	primesieve uses a sieve size that matches your CPU's L1 cache size (per

src/app/cmdoptions.cpp

@@ -3,7 +3,7 @@
 /// @brief  Parse command-line options for the primesieve console
 ///         (terminal) application.
 ///
-/// Copyright (C) 2022 Kim Walisch, <[email protected]>
+/// Copyright (C) 2024 Kim Walisch, <[email protected]>
 ///
 /// This file is distributed under the BSD License. See the COPYING
 /// file in the top level directory.
@@ -44,6 +44,8 @@ enum OptionID
   OPTION_DISTANCE,
   OPTION_PRINT,
   OPTION_QUIET,
+  OPTION_R,
+  OPTION_R_INVERSE,
   OPTION_SIZE,
   OPTION_TEST,
   OPTION_THREADS,
@@ -380,6 +382,9 @@ CmdOptions parseOptions(int argc, char* argv[])
     { "--print",     std::make_pair(OPTION_PRINT, OPTIONAL_PARAM) },
     { "-q",          std::make_pair(OPTION_QUIET, NO_PARAM) },
     { "--quiet",     std::make_pair(OPTION_QUIET, NO_PARAM) },
+    { "-R",          std::make_pair(OPTION_R, NO_PARAM) },
+    { "--RiemannR",  std::make_pair(OPTION_R, NO_PARAM) },
+    { "--R-inverse", std::make_pair(OPTION_R_INVERSE, NO_PARAM) },
     { "-s",          std::make_pair(OPTION_SIZE, REQUIRED_PARAM) },
     { "--size",      std::make_pair(OPTION_SIZE, REQUIRED_PARAM) },
     { "--test",      std::make_pair(OPTION_TEST, NO_PARAM) },
@@ -408,6 +413,8 @@ CmdOptions parseOptions(int argc, char* argv[])
       case OPTION_QUIET:     opts.quiet = true; break;
       case OPTION_NTH_PRIME: opts.nthPrime = true; break;
       case OPTION_NO_STATUS: opts.status = false; break;
+      case OPTION_R:         opts.RiemannR = true; break;
+      case OPTION_R_INVERSE: opts.RiemannR_inverse = true; break;
       case OPTION_TIME:      opts.time = true; break;
       case OPTION_NUMBER:    opts.numbers.push_back(opt.getValue<uint64_t>()); break;
       case OPTION_HELP:      help(/* exitCode */ 0); break;

src/app/cmdoptions.hpp

@@ -1,7 +1,7 @@
 ///
 /// @file  cmdoptions.hpp
 ///
-/// Copyright (C) 2023 Kim Walisch, <[email protected]>
+/// Copyright (C) 2024 Kim Walisch, <[email protected]>
 ///
 /// This file is distributed under the BSD License. See the COPYING
 /// file in the top level directory.
@@ -21,6 +21,8 @@ struct CmdOptions
   int threads = 0;
   bool quiet = false;
   bool nthPrime = false;
+  bool RiemannR = false;
+  bool RiemannR_inverse = false;
   bool status = true;
   bool time = false;
 };

src/app/help.cpp

@@ -39,6 +39,10 @@ void help(int exitCode)
     "                      print twin primes: -p2 or --print=2,\n"
     "                      print prime triplets: -p3 or --print=3, ...\n"
     "  -q, --quiet         Quiet mode, prints less output.\n"
+    "  -R, --RiemannR      Riemann R function, very accurate\n"
+    "                      approximation of PrimePi(x).\n"
+    "      --R-inverse     Inverse Riemann R function, very accurate\n"
+    "                      approximation of the nth prime.\n"
     "  -s, --size=SIZE     Set the sieve size in KiB, SIZE <= 8192.\n"
     "                      By default primesieve uses a sieve size that\n"
     "                      matches your CPU's L1 cache size (per core) or is\n"

src/app/main.cpp

@@ -2,13 +2,14 @@
 /// @file   main.cpp
 /// @brief  primesieve console application.
 ///
-/// Copyright (C) 2023 Kim Walisch, <[email protected]>
+/// Copyright (C) 2024 Kim Walisch, <[email protected]>
 ///
 /// This file is distributed under the BSD License. See the COPYING
 /// file in the top level directory.
 ///
 
 #include <primesieve/ParallelSieve.hpp>
+#include <primesieve/nthPrimeApprox.hpp>
 #include <primesieve/Vector.hpp>
 #include "cmdoptions.hpp"
 
@@ -136,6 +137,10 @@ int main(int argc, char* argv[])
 
     if (opt.nthPrime)
       nthPrime(opt);
+    else if (opt.RiemannR)
+      std::cout << Ri(opt.numbers[0]) << std::endl;
+    else if (opt.RiemannR_inverse)
+      std::cout << Ri_inverse(opt.numbers[0]) << std::endl;
     else
       sieve(opt);
   }