Mercurial > octave-antonio

annotate scripts/specfun/primes.m @ 20162:2645f9ef8c88 stable

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
doc: Update more docstrings to have one sentence summary as first line. Reviewed specfun, special-matrix, testfun, and time script directories. * scripts/specfun/expint.m, scripts/specfun/isprime.m, scripts/specfun/legendre.m, scripts/specfun/primes.m, scripts/specfun/reallog.m, scripts/specfun/realsqrt.m, scripts/special-matrix/gallery.m, scripts/special-matrix/hadamard.m, scripts/special-matrix/hankel.m, scripts/special-matrix/hilb.m, scripts/special-matrix/invhilb.m, scripts/special-matrix/magic.m, scripts/special-matrix/pascal.m, scripts/special-matrix/rosser.m, scripts/special-matrix/toeplitz.m, scripts/special-matrix/vander.m, scripts/special-matrix/wilkinson.m, scripts/testfun/assert.m, scripts/testfun/demo.m, scripts/testfun/example.m, scripts/testfun/fail.m, scripts/testfun/rundemos.m, scripts/testfun/runtests.m, scripts/testfun/speed.m, scripts/time/asctime.m, scripts/time/calendar.m, scripts/time/clock.m, scripts/time/ctime.m, scripts/time/datenum.m, scripts/time/datestr.m, scripts/time/datevec.m, scripts/time/etime.m, scripts/time/is_leap_year.m, scripts/time/now.m, scripts/time/weekday.m: Update more docstrings to have one sentence summary as first line.
author Rik <rik@octave.org>
date Sun, 03 May 2015 17:00:11 -0700
parents 4197fc428c7d
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
19697
4197fc428c7d maint: Update copyright notices for 2015.
John W. Eaton <jwe@octave.org>
parents: 19152
diff changeset
1 ## Copyright (C) 2000-2015 Paul Kienzle
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
2 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
3 ## This file is part of Octave.
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
4 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
5 ## Octave is free software; you can redistribute it and/or modify it
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
6 ## under the terms of the GNU General Public License as published by
7016
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe]
jwe
parents: 5827
diff changeset
7 ## the Free Software Foundation; either version 3 of the License, or (at
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe]
jwe
parents: 5827
diff changeset
8 ## your option) any later version.
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
9 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
10 ## Octave is distributed in the hope that it will be useful, but
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
13 ## General Public License for more details.
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
14 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
15 ## You should have received a copy of the GNU General Public License
7016
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe]
jwe
parents: 5827
diff changeset
16 ## along with Octave; see the file COPYING. If not, see
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe]
jwe
parents: 5827
diff changeset
17 ## <http://www.gnu.org/licenses/>.
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
18
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
19 ## -*- texinfo -*-
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
20 ## @deftypefn {Function File} {} primes (@var{n})
11587
c792872f8942 all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
21 ## Return all primes up to @var{n}.
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
22 ##
20162
2645f9ef8c88 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19697
diff changeset
23 ## The output data class (double, single, uint32, etc.) is the same as the
2645f9ef8c88 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19697
diff changeset
24 ## input class of @var{n}. The algorithm used is the Sieve of Eratosthenes.
9141
c1fff751b5a8 Update section 17.1 (Utility Functions) of arith.txi
Rik <rdrider0-list@yahoo.com>
parents: 8920
diff changeset
25 ##
20162
2645f9ef8c88 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19697
diff changeset
26 ## Notes: If you need a specific number of primes you can use the fact that the
2645f9ef8c88 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19697
diff changeset
27 ## distance from one prime to the next is, on average, proportional to the
2645f9ef8c88 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19697
diff changeset
28 ## logarithm of the prime. Integrating, one finds that there are about
2645f9ef8c88 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19697
diff changeset
29 ## @math{k} primes less than
9165
8c71a86c4bf4 Update section 17.5 (Utility Functions) of arith.txi
Rik <rdrider0-list@yahoo.com>
parents: 9141
diff changeset
30 ## @tex
8c71a86c4bf4 Update section 17.5 (Utility Functions) of arith.txi
Rik <rdrider0-list@yahoo.com>
parents: 9141
diff changeset
31 ## $k \log (5 k)$.
8c71a86c4bf4 Update section 17.5 (Utility Functions) of arith.txi
Rik <rdrider0-list@yahoo.com>
parents: 9141
diff changeset
32 ## @end tex
8c71a86c4bf4 Update section 17.5 (Utility Functions) of arith.txi
Rik <rdrider0-list@yahoo.com>
parents: 9141
diff changeset
33 ## @ifnottex
14868
5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory
Rik <octave@nomad.inbox5.com>
parents: 14363
diff changeset
34 ## k*log (5*k).
9165
8c71a86c4bf4 Update section 17.5 (Utility Functions) of arith.txi
Rik <rdrider0-list@yahoo.com>
parents: 9141
diff changeset
35 ## @end ifnottex
19096
90dd85369c2e primes.m: Overhaul function.
Rik <rik@octave.org>
parents: 17744
diff changeset
36 ##
20162
2645f9ef8c88 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19697
diff changeset
37 ## See also @code{list_primes} if you need a specific number @var{n} of primes.
9165
8c71a86c4bf4 Update section 17.5 (Utility Functions) of arith.txi
Rik <rdrider0-list@yahoo.com>
parents: 9141
diff changeset
38 ## @seealso{list_primes, isprime}
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
39 ## @end deftypefn
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
40
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
41 ## Author: Paul Kienzle
11472
1740012184f9 Use uppercase for variable names in error() strings to match Info documentation. Only m-files done.
Rik <octave@nomad.inbox5.com>
parents: 11469
diff changeset
42 ## Author: Francesco Potortì
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
43 ## Author: Dirk Laurie
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
44
19096
90dd85369c2e primes.m: Overhaul function.
Rik <rik@octave.org>
parents: 17744
diff changeset
45 function p = primes (n)
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
46
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
47 if (nargin != 1)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
48 print_usage ();
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
49 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
50
11469
c776f063fefe Overhaul m-script files to use common variable name between code and documentation.
Rik <octave@nomad.inbox5.com>
parents: 10791
diff changeset
51 if (! isscalar (n))
11472
1740012184f9 Use uppercase for variable names in error() strings to match Info documentation. Only m-files done.
Rik <octave@nomad.inbox5.com>
parents: 11469
diff changeset
52 error ("primes: N must be a scalar");
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
53 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
54
19096
90dd85369c2e primes.m: Overhaul function.
Rik <rik@octave.org>
parents: 17744
diff changeset
55 if (n > 100e3)
8506
bc982528de11 comment style fixes
John W. Eaton <jwe@octave.org>
parents: 7017
diff changeset
56 ## Optimization: 1/6 less memory, and much faster (asymptotically)
19096
90dd85369c2e primes.m: Overhaul function.
Rik <rik@octave.org>
parents: 17744
diff changeset
57 ## 100K happens to be the cross-over point for Paul's machine;
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
58 ## below this the more direct code below is faster. At the limit
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
59 ## of memory in Paul's machine, this saves .7 seconds out of 7 for
11469
c776f063fefe Overhaul m-script files to use common variable name between code and documentation.
Rik <octave@nomad.inbox5.com>
parents: 10791
diff changeset
60 ## n = 3e6. Hardly worthwhile, but Dirk reports better numbers.
c776f063fefe Overhaul m-script files to use common variable name between code and documentation.
Rik <octave@nomad.inbox5.com>
parents: 10791
diff changeset
61 lenm = floor ((n+1)/6); # length of the 6n-1 sieve
c776f063fefe Overhaul m-script files to use common variable name between code and documentation.
Rik <octave@nomad.inbox5.com>
parents: 10791
diff changeset
62 lenp = floor ((n-1)/6); # length of the 6n+1 sieve
10657
c6833d31f34e optimize primes and isprime
Jaroslav Hajek <highegg@gmail.com>
parents: 10549
diff changeset
63 sievem = true (1, lenm); # assume every number of form 6n-1 is prime
c6833d31f34e optimize primes and isprime
Jaroslav Hajek <highegg@gmail.com>
parents: 10549
diff changeset
64 sievep = true (1, lenp); # assume every number of form 6n+1 is prime
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
65
14868
5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory
Rik <octave@nomad.inbox5.com>
parents: 14363
diff changeset
66 for i = 1:(sqrt (n)+1)/6 # check up to sqrt (n)
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
67 if (sievem(i)) # if i is prime, eliminate multiples of i
10657
c6833d31f34e optimize primes and isprime
Jaroslav Hajek <highegg@gmail.com>
parents: 10549
diff changeset
68 sievem(7*i-1:6*i-1:lenm) = false;
c6833d31f34e optimize primes and isprime
Jaroslav Hajek <highegg@gmail.com>
parents: 10549
diff changeset
69 sievep(5*i-1:6*i-1:lenp) = false;
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
70 endif # if i is prime, eliminate multiples of i
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
71 if (sievep(i))
10657
c6833d31f34e optimize primes and isprime
Jaroslav Hajek <highegg@gmail.com>
parents: 10549
diff changeset
72 sievep(7*i+1:6*i+1:lenp) = false;
c6833d31f34e optimize primes and isprime
Jaroslav Hajek <highegg@gmail.com>
parents: 10549
diff changeset
73 sievem(5*i+1:6*i+1:lenm) = false;
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
74 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
75 endfor
19096
90dd85369c2e primes.m: Overhaul function.
Rik <rik@octave.org>
parents: 17744
diff changeset
76 p = sort ([2, 3, 6*find(sievem)-1, 6*find(sievep)+1]);
90dd85369c2e primes.m: Overhaul function.
Rik <rik@octave.org>
parents: 17744
diff changeset
77 elseif (n > 352) # nothing magical about 352; must be > 2
11469
c776f063fefe Overhaul m-script files to use common variable name between code and documentation.
Rik <octave@nomad.inbox5.com>
parents: 10791
diff changeset
78 len = floor ((n-1)/2); # length of the sieve
10657
c6833d31f34e optimize primes and isprime
Jaroslav Hajek <highegg@gmail.com>
parents: 10549
diff changeset
79 sieve = true (1, len); # assume every odd number is prime
14868
5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory
Rik <octave@nomad.inbox5.com>
parents: 14363
diff changeset
80 for i = 1:(sqrt (n)-1)/2 # check up to sqrt (n)
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
81 if (sieve(i)) # if i is prime, eliminate multiples of i
10657
c6833d31f34e optimize primes and isprime
Jaroslav Hajek <highegg@gmail.com>
parents: 10549
diff changeset
82 sieve(3*i+1:2*i+1:len) = false; # do it
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
83 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
84 endfor
19096
90dd85369c2e primes.m: Overhaul function.
Rik <rik@octave.org>
parents: 17744
diff changeset
85 p = [2, 1+2*find(sieve)]; # primes remaining after sieve
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
86 else
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
87 a = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, ...
10549
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 9165
diff changeset
88 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, ...
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 9165
diff changeset
89 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, ...
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 9165
diff changeset
90 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, ...
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 9165
diff changeset
91 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, ...
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 9165
diff changeset
92 293, 307, 311, 313, 317, 331, 337, 347, 349];
19096
90dd85369c2e primes.m: Overhaul function.
Rik <rik@octave.org>
parents: 17744
diff changeset
93 p = a(a <= n);
90dd85369c2e primes.m: Overhaul function.
Rik <rik@octave.org>
parents: 17744
diff changeset
94 endif
90dd85369c2e primes.m: Overhaul function.
Rik <rik@octave.org>
parents: 17744
diff changeset
95
90dd85369c2e primes.m: Overhaul function.
Rik <rik@octave.org>
parents: 17744
diff changeset
96 if (! isa (n, "double"))
90dd85369c2e primes.m: Overhaul function.
Rik <rik@octave.org>
parents: 17744
diff changeset
97 cast (p, class (n));
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
98 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
99
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
100 endfunction
12815
918610ea2f34 codesprint: new tests for specfun directory
John W. Eaton <jwe@octave.org>
parents: 11587
diff changeset
101
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
102
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
103 %!assert (size (primes (350)), [1, 70])
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
104 %!assert (primes (357)(end), 353)
12815
918610ea2f34 codesprint: new tests for specfun directory
John W. Eaton <jwe@octave.org>
parents: 11587
diff changeset
105
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
106 %!error primes ()
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
107 %!error primes (1, 2)
19104
fbe5a2dd64ae primes.m: Fix failing BIST test introduced in cset 90dd85369c2e.
Rik <rik@octave.org>
parents: 19096
diff changeset
108 %!error <N must be a scalar> primes (ones (2,2))
12815
918610ea2f34 codesprint: new tests for specfun directory
John W. Eaton <jwe@octave.org>
parents: 11587
diff changeset
109