time q=10007

**************** precomputations

air:~ languasc$ cd /Users/languasc/Documents/LANGUASCO/matematica/lavori/\[55\]Euler-kronecker-constants/programmi-finali/for_precomputations 
air:for_precomputations languasc$ gp
                  GP/PARI CALCULATOR Version 2.11.0 (released)
          i386 running darwin (x86-64/GMP-6.1.2 kernel) 64-bit version
       compiled: Aug 11 2018, Apple LLVM version 9.1.0 (clang-902.0.39.2)
                            threading engine: single
                 (readline v6.3 enabled, extended help enabled)

                     Copyright (C) 2000-2018 The PARI Group

PARI/GP is free software, covered by the GNU General Public License, and comes 
WITHOUT ANY WARRANTY WHATSOEVER.

Type ? for help, \q to quit.
Type ?17 for how to get moral (and possibly technical) support.

parisize = 8000000, primelimit = 500000
? \r mainEK.gp 
? mainEK(10007)
Computing the primitive root for q = 10007 and saving on file
Now you can call the precomputation programs
Precomputation time (I/O excluded): 0 min, 0 sec, 0 millisec
? quit

air:for_precomputations languasc$ ./m_preclngamma.out
x = 0
y = 10005
Precomputation lngamma-values for q = 10007 and saving on file
Precomputation time (I/O included): 0 min, 0 sec, 436 millisec

air:for_precomputations languasc$ ./m_precpsi.out
x = 0
y = 10005
Precomputation psi-values for q = 10007 and saving on file
Precomputation time (I/O included): 0 min, 0 sec, 248 millisec

air:for_precomputations languasc$ ./m_precT.out
x = 0
y = 10005
Precomputation T-values for q = 10007 and saving on file
Precomputation time (I/O included): 1 min, 15 sec, 172 millisec

air:for_precomputations languasc$ ./m_precS.out
x = 0
y = 10005
Precomputation S-values for q = 10007 and saving on file
Precomputation time (I/O included): 1 min, 33 sec, 772 millisec

**************** fft comput

air:10007 languasc$ ./EK-T-fftw.out 
********** A. LANGUASCO  *********** 
Computation of the Euler-Kronecker constant with the T function. [DOUBLE PRECISION]
Acquiring q from file: q = 10007
Acquiring precomputed values for T(a/q). Done
Acquiring precomputed values for psi(a/q). Done

EK(10007) = 12.664612

FFT - computation time (I/O excluded): 
0.000000 min. 0.000000 sec. 1.188000 millisec. 
********** END PROGRAM  *********** 
air:10007 languasc$ ./EK-T-fftwl.out 
********** A. LANGUASCO  *********** 
Computation of the Euler-Kronecker constant with the T function. [LONG DOUBLE PRECISION]
Acquiring q from file: q = 10007
Acquiring precomputed values for T(a/q). Done
Acquiring precomputed values for psi(a/q). Done

EK(10007) = 12.664612

FFT - computation time (I/O excluded): 
0.000000 min. 0.000000 sec. 5.171000 millisec. 
********** END PROGRAM  *********** 


air:10007 languasc$ ./EK-S-fftw.out 
********** A. LANGUASCO  *********** 
Computation of the Euler-Kronecker constant with the S function. [DOUBLE PRECISION]
Acquiring q from file: q = 10007
Acquiring precomputed values for S(a/q). Done
Acquiring precomputed values for log(gamma(a/q)). Done
Building the sequence g^k%q. Done

EK(10007)^+ = 11.060162
EK(10007) = 12.664612

FFT - computation time (I/O excluded): 
0.000000 min. 0.000000 sec. 2.039000 millisec. 
********** END PROGRAM  *********** 
air:10007 languasc$ ./EK-S-fftwl.out 
********** A. LANGUASCO  *********** 
Computation of the Euler-Kronecker constant with the S function. [LONG DOUBLE PRECISION]
Acquiring q from file: q = 10007
Acquiring precomputed values for S(a/q). Done
Acquiring precomputed values for log(gamma(a/q)). Done
Building the sequence g^k%q. Done

EK(10007)^+ = 11.060162
EK(10007) = 12.664612

FFT - computation time (I/O excluded): 
0.000000 min. 0.000000 sec. 8.260000 millisec. 
********** END PROGRAM  *********** 
 
on OPtiplex:

********** A. LANGUASCO and L. RIGHI *********** 
Computation of the Euler-Kronecker constan with the T function. [QUADRUPLE PRECISION]
Acquiring q from file: q = 10007
Acquiring precomputed values for T(a/q). Done
Acquiring precomputed values for psi(a/q). Done

EK(10007) = +12.66461200456069233248                      

FFT - computation time (I/O excluded): 
0.000000 min. 0.000000 sec. 93.721000 millisec. 
********** END PROGRAM  *********** 


********** A. LANGUASCO and L. RIGHI *********** 
Computation of the Euler-Kronecker constant with the S function. [QUADRUPLE PRECISION]
Acquiring q from file: q = 10007
Acquiring precomputed values for S(a/q). Done
Acquiring precomputed values for log(gamma(a/q)). Done
Building the sequence g^k%q. Done

EK(10007)^+ = +11.06016247590230393618                      

EK(10007) = +12.66461200456035177426                      

FFT - computation time (I/O excluded): 
0.000000 min. 0.000000 sec. 140.569000 millisec. 
********** END PROGRAM  *********** 

***********  SIZE of the precomp files  *************

primroot : 8 bytes

precompsi,precomplngamma, precompT, precompS: about 420 KB each 

***********  TOTAL COMPUTATION TIME q=10007  *************

TIMES S:
precomplngamma: 436 millisec
precompS:  1 min, 33 sec, 772 millisec
FFT singleprec: 2.039000 millisec. 
FFT doubleprec: 8.260000 millisec.
total (single): 1 min, 34 sec, 209 millisec.
total (double): 1 min, 34 sec, 217 millisec.


TIMES T
precomppsi:  248 millisec
precompT: 1 min, 15 sec, 172 millisec
FFT singleprec: 1.188000 millisec. 
FFT doubleprec: 5.171000 millisec. 
total (single):  1 min, 15 sec, 422 millisec
total (double): 1 min, 15 sec, 426 millisec

*********** 

