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https://github.com/vale981/arb
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multithreaded refinement of zeta zeros; tweak example program
This commit is contained in:
Fredrik Johansson
parent
8e2436c7a1
commit
31578cdefe
3 changed files with 63 additions and 37 deletions
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@ -10,6 +10,7 @@
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(at your option) any later version. See <http://www.gnu.org/licenses/>.
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*/
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#include "flint/thread_support.h"
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#include "acb_dirichlet.h"
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#include "arb_calc.h"
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@ -1376,6 +1377,20 @@ _acb_dirichlet_exact_zeta_nzeros(fmpz_t res, const arf_t t)
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exact_zeta_multi_nzeros(res, t, 1);
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}
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typedef struct
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{
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arb_ptr res;
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arf_interval_ptr p;
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slong prec;
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}
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work_t;
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static void
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refinement_worker(slong i, work_t * work)
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{
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_acb_dirichlet_refine_hardy_z_zero(work->res + i, &(work->p[i].a), &(work->p[i].b), work->prec);
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}
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void
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acb_dirichlet_hardy_z_zeros(arb_ptr res, const fmpz_t n, slong len, slong prec)
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{
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@ -1390,13 +1405,15 @@ acb_dirichlet_hardy_z_zeros(arb_ptr res, const fmpz_t n, slong len, slong prec)
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}
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else
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{
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slong i;
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work_t work;
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arf_interval_ptr p = _arf_interval_vec_init(len);
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acb_dirichlet_isolate_hardy_z_zeros(p, n, len);
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for (i = 0; i < len; i++)
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{
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_acb_dirichlet_refine_hardy_z_zero(res + i, &p[i].a, &p[i].b, prec);
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}
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work.res = res;
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work.p = p;
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work.prec = prec;
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flint_parallel_do((do_func_t) refinement_worker, &work, len, -1, FLINT_PARALLEL_STRIDED);
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_arf_interval_vec_clear(p, len);
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}
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}
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@ -53,41 +53,37 @@ zeta_zeros.c
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This program computes one or several consecutive zeros of the
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Riemann zeta function on the critical line::
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> build/examples/zeta_zeros -num 10 -digits 30
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Computing 10 zeros starting with zero #1, with prec = 102 bits...
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cpu/wall(s): 0.01 0.009
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virt/peak/res/peak(MB): 21.30 21.30 7.32 7.32
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14.1347251417346937904572519836
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21.0220396387715549926284795939
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25.0108575801456887632137909926
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30.4248761258595132103118975306
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32.9350615877391896906623689641
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37.5861781588256712572177634807
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40.9187190121474951873981269146
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43.3270732809149995194961221654
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48.0051508811671597279424727494
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49.7738324776723021819167846786
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> build/examples/zeta_zeros -n 1 -count 10 -digits 30
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1 14.1347251417346937904572519836
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2 21.0220396387715549926284795939
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3 25.0108575801456887632137909926
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4 30.4248761258595132103118975306
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5 32.9350615877391896906623689641
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6 37.5861781588256712572177634807
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7 40.9187190121474951873981269146
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8 43.3270732809149995194961221654
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9 48.0051508811671597279424727494
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10 49.7738324776723021819167846786
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cpu/wall(s): 0.01 0.01
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virt/peak/res/peak(MB): 21.28 21.28 7.29 7.29
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Five zeros starting with the millionth::
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> build/examples/zeta_zeros -start 1000000 -num 5 -digits 20
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Computing 5 zeros starting with zero #1000000, with prec = 69 bits...
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cpu/wall(s): 0.029 0.029
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virt/peak/res/peak(MB): 21.16 21.16 5.82 5.82
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600269.67701244495552
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600270.30109071169866
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600270.74787059436613
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600271.48637367364820
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600271.76148042593778
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> build/examples/zeta_zeros -n 1000000 -count 5 -digits 20
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1000000 600269.67701244495552
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1000001 600270.30109071169866
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1000002 600270.74787059436613
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1000003 600271.48637367364820
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1000004 600271.76148042593778
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cpu/wall(s): 0.03 0.03
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virt/peak/res/peak(MB): 21.41 21.41 7.41 7.41
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The program supports the following options::
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zeta_zeros [-start n] [-num n] [-threads t] [-digits d] [-suppress] [-gradual] [-stream]
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zeta_zeros [-n n] [-count n] [-prec n] [-digits n] [-threads n] [-platt] [-noplatt] [-v] [-verbose] [-h] [-help]
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With ``-platt``, Platt's algorithm is used, which may be faster when
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computing many zeros of large index simultaneously.
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With ``-stream``, the zeros are computed and output one
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by one instead of simultaneously.
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bernoulli.c
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-------------------------------------------------------------------------------
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@ -13,7 +13,7 @@ void print_zeros(arb_srcptr p, const fmpz_t n, slong len, slong digits)
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{
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fmpz_print(k);
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flint_printf("\t");
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arb_printn(p+i, digits, 0);
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arb_printn(p+i, digits, ARB_STR_NO_RADIUS);
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flint_printf("\n");
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fmpz_add_ui(k, k, 1);
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}
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@ -22,7 +22,7 @@ void print_zeros(arb_srcptr p, const fmpz_t n, slong len, slong digits)
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void print_help()
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{
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flint_printf("zeta_zeros [-n n] [-count n] [-prec n] [-threads n] "
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flint_printf("zeta_zeros [-n n] [-count n] [-prec n] [-digits n] [-threads n] "
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"[-platt] [-noplatt] [-v] [-verbose] [-h] [-help]\n\n");
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flint_printf("Reports the imaginary parts of consecutive nontrivial zeros "
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"of the Riemann zeta function.\n");
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@ -49,7 +49,7 @@ int main(int argc, char *argv[])
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int verbose = 0;
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int platt = 0;
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int noplatt = 0;
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slong i, buffersize, prec;
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slong i, buffersize, prec, digits;
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fmpz_t requested, count, nstart, n;
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arb_ptr p;
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@ -71,6 +71,7 @@ int main(int argc, char *argv[])
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fmpz_set_si(requested, -1);
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buffersize = max_buffersize;
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prec = -1;
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digits = 2;
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for (i = 1; i < argc; i++)
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{
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@ -122,6 +123,17 @@ int main(int argc, char *argv[])
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{
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requires_value(argc, argv, i);
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prec = atol(argv[i+1]);
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digits = prec / 3.32192809488736 + 1;
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if (prec < 2)
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{
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invalid_value(argv, i);
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}
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}
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else if (!strcmp(argv[i], "-digits"))
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{
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requires_value(argc, argv, i);
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digits = atol(argv[i+1]);
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prec = digits * 3.32192809488736 + 3;
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if (prec < 2)
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{
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invalid_value(argv, i);
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@ -173,6 +185,7 @@ int main(int argc, char *argv[])
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{
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prec = 64 + fmpz_clog_ui(nstart, 2);
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if (platt) prec *= 2;
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digits = prec / 3.32192809488736 + 1;
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}
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if (verbose)
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@ -225,7 +238,7 @@ int main(int argc, char *argv[])
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num = FLINT_MIN(1 << fmpz_get_si(iter), num);
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}
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acb_dirichlet_hardy_z_zeros(p, n, num, prec);
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print_zeros(p, n, num, prec*0.3 + 2);
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print_zeros(p, n, num, digits);
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fmpz_add_si(n, n, num);
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fmpz_add_si(count, count, num);
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fmpz_add_si(iter, iter, 1);
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@ -259,7 +272,7 @@ int main(int argc, char *argv[])
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"is wrong with the internal tuning parameters.");
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flint_abort();
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}
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print_zeros(p, n, found, prec*0.3 + 2);
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print_zeros(p, n, found, digits);
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fmpz_add_si(n, n, found);
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fmpz_add_si(count, count, found);
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}
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@ -274,6 +287,6 @@ int main(int argc, char *argv[])
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fmpz_clear(requested);
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fmpz_clear(count);
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flint_cleanup();
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flint_cleanup_master();
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return 0;
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}
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