Mercurial > octave-antonio
view scripts/specfun/primes.m @ 14868:5d3a684236b0
maint: Use Octave coding conventions for cuddling parentheses in scripts directory
* lin2mu.m, loadaudio.m, wavread.m, accumarray.m, bicubic.m, celldisp.m,
colon.m, cplxpair.m, dblquad.m, divergence.m, genvarname.m, gradient.m,
int2str.m, interp1.m, interp1q.m, interp2.m, interpn.m, loadobj.m, nthargout.m,
__isequal__.m, __splinen__.m, quadgk.m, quadl.m, quadv.m, rat.m, rot90.m,
rotdim.m, saveobj.m, subsindex.m, triplequad.m, delaunay3.m, griddata.m,
inpolygon.m, tsearchn.m, voronoi.m, get_first_help_sentence.m, which.m,
gray2ind.m, pink.m, dlmwrite.m, strread.m, textread.m, textscan.m, housh.m,
ishermitian.m, issymmetric.m, krylov.m, logm.m, null.m, rref.m,
compare_versions.m, copyfile.m, dump_prefs.m, edit.m, fileparts.m,
getappdata.m, isappdata.m, movefile.m, orderfields.m, parseparams.m,
__xzip__.m, rmappdata.m, setappdata.m, swapbytes.m, unpack.m, ver.m, fminbnd.m,
fminunc.m, fsolve.m, glpk.m, lsqnonneg.m, qp.m, sqp.m, configure_make.m,
copy_files.m, describe.m, get_description.m, get_forge_pkg.m, install.m,
installed_packages.m, is_architecture_dependent.m, load_package_dirs.m,
print_package_description.m, rebuild.m, repackage.m, save_order.m, shell.m,
allchild.m, ancestor.m, area.m, axes.m, axis.m, clabel.m, close.m, colorbar.m,
comet.m, comet3.m, contour.m, cylinder.m, ezmesh.m, ezsurf.m, findobj.m,
fplot.m, hist.m, isocolors.m, isonormals.m, isosurface.m, isprop.m, legend.m,
mesh.m, meshz.m, pareto.m, pcolor.m, peaks.m, plot3.m, plotmatrix.m, plotyy.m,
polar.m, print.m, __add_datasource__.m, __add_default_menu__.m,
__axes_limits__.m, __bar__.m, __clabel__.m, __contour__.m, __errcomm__.m,
__errplot__.m, __ezplot__.m, __file_filter__.m, __fltk_print__.m,
__ghostscript__.m, __gnuplot_print__.m, __go_draw_axes__.m,
__go_draw_figure__.m, __interp_cube__.m, __marching_cube__.m, __patch__.m,
__pie__.m, __plt__.m, __print_parse_opts__.m, __quiver__.m, __scatter__.m,
__stem__.m, __tight_eps_bbox__.m, __uigetdir_fltk__.m, __uigetfile_fltk__.m,
__uiputfile_fltk__.m, quiver.m, quiver3.m, rectangle.m, refreshdata.m,
ribbon.m, scatter.m, semilogy.m, shading.m, slice.m, subplot.m, surface.m,
surfl.m, surfnorm.m, text.m, uigetfile.m, uiputfile.m, whitebg.m, deconv.m,
mkpp.m, pchip.m, polyaffine.m, polyder.m, polygcd.m, polyout.m, polyval.m,
ppint.m, ppjumps.m, ppval.m, residue.m, roots.m, spline.m, splinefit.m,
addpref.m, getpref.m, setpref.m, ismember.m, setxor.m, arch_fit.m, arch_rnd.m,
arch_test.m, autoreg_matrix.m, diffpara.m, fftconv.m, filter2.m, hanning.m,
hurst.m, periodogram.m, triangle_sw.m, sinc.m, spectral_xdf.m, spencer.m,
stft.m, synthesis.m, unwrap.m, yulewalker.m, bicgstab.m, gmres.m, pcg.m, pcr.m,
__sprand_impl__.m, speye.m, spfun.m, sprandn.m, spstats.m, svds.m,
treelayout.m, treeplot.m, bessel.m, factor.m, legendre.m, perms.m, primes.m,
magic.m, toeplitz.m, corr.m, cov.m, mean.m, median.m, mode.m, qqplot.m,
quantile.m, ranks.m, zscore.m, logistic_regression_likelihood.m,
bartlett_test.m, chisquare_test_homogeneity.m, chisquare_test_independence.m,
kolmogorov_smirnov_test.m, run_test.m, u_test.m, wilcoxon_test.m, z_test.m,
z_test_2.m, bin2dec.m, dec2base.m, mat2str.m, strcat.m, strchr.m, strjust.m,
strtok.m, substr.m, untabify.m, assert.m, demo.m, example.m, fail.m, speed.m,
test.m, now.m: Use Octave coding conventions for cuddling parentheses in
scripts directory.
author | Rik <octave@nomad.inbox5.com> |
---|---|
date | Tue, 17 Jul 2012 07:08:39 -0700 |
parents | f3d52523cde1 |
children | d63878346099 |
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## Copyright (C) 2000-2012 Paul Kienzle ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {Function File} {} primes (@var{n}) ## ## Return all primes up to @var{n}. ## ## The algorithm used is the Sieve of Eratosthenes. ## ## Note that if you need a specific number of primes you can use the ## fact that the distance from one prime to the next is, on average, ## proportional to the logarithm of the prime. Integrating, one finds ## that there are about @math{k} primes less than ## @tex ## $k \log (5 k)$. ## @end tex ## @ifnottex ## k*log (5*k). ## @end ifnottex ## @seealso{list_primes, isprime} ## @end deftypefn ## Author: Paul Kienzle ## Author: Francesco Potortì ## Author: Dirk Laurie function x = primes (n) if (nargin != 1) print_usage (); endif if (! isscalar (n)) error ("primes: N must be a scalar"); endif if (n > 100000) ## Optimization: 1/6 less memory, and much faster (asymptotically) ## 100000 happens to be the cross-over point for Paul's machine; ## below this the more direct code below is faster. At the limit ## of memory in Paul's machine, this saves .7 seconds out of 7 for ## n = 3e6. Hardly worthwhile, but Dirk reports better numbers. lenm = floor ((n+1)/6); # length of the 6n-1 sieve lenp = floor ((n-1)/6); # length of the 6n+1 sieve sievem = true (1, lenm); # assume every number of form 6n-1 is prime sievep = true (1, lenp); # assume every number of form 6n+1 is prime for i = 1:(sqrt (n)+1)/6 # check up to sqrt (n) if (sievem(i)) # if i is prime, eliminate multiples of i sievem(7*i-1:6*i-1:lenm) = false; sievep(5*i-1:6*i-1:lenp) = false; endif # if i is prime, eliminate multiples of i if (sievep(i)) sievep(7*i+1:6*i+1:lenp) = false; sievem(5*i+1:6*i+1:lenm) = false; endif endfor x = sort ([2, 3, 6*find(sievem)-1, 6*find(sievep)+1]); elseif (n > 352) # nothing magical about 352; must be >2 len = floor ((n-1)/2); # length of the sieve sieve = true (1, len); # assume every odd number is prime for i = 1:(sqrt (n)-1)/2 # check up to sqrt (n) if (sieve(i)) # if i is prime, eliminate multiples of i sieve(3*i+1:2*i+1:len) = false; # do it endif endfor x = [2, 1+2*find(sieve)]; # primes remaining after sieve else a = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, ... 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, ... 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, ... 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, ... 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, ... 293, 307, 311, 313, 317, 331, 337, 347, 349]; x = a(a <= n); endif endfunction %!assert (size (primes (350)), [1, 70]) %!assert (primes (357)(end), 353) %!error primes () %!error primes (1, 2)