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Fix octave header includes in audiodevinfo * audiodevinfo.cc: change includes to use local octave headers
author Vytautas Jančauskas <unaudio@gmail.com>
date Wed, 11 Sep 2013 21:32:14 +0300
parents 5d3a684236b0
children d63878346099
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1 ## Copyright (C) 2000-2012 Paul Kienzle
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {} primes (@var{n})
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21 ##
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22 ## Return all primes up to @var{n}.
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23 ##
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24 ## The algorithm used is the Sieve of Eratosthenes.
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25 ##
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26 ## Note that if you need a specific number of primes you can use the
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27 ## fact that the distance from one prime to the next is, on average,
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28 ## proportional to the logarithm of the prime. Integrating, one finds
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29 ## that there are about @math{k} primes less than
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30 ## @tex
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31 ## $k \log (5 k)$.
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32 ## @end tex
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33 ## @ifnottex
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34 ## k*log (5*k).
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35 ## @end ifnottex
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36 ## @seealso{list_primes, isprime}
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37 ## @end deftypefn
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38
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39 ## Author: Paul Kienzle
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40 ## Author: Francesco Potortì
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41 ## Author: Dirk Laurie
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42
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43 function x = primes (n)
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44
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45 if (nargin != 1)
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46 print_usage ();
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47 endif
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48
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49 if (! isscalar (n))
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50 error ("primes: N must be a scalar");
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51 endif
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52
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53 if (n > 100000)
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54 ## Optimization: 1/6 less memory, and much faster (asymptotically)
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55 ## 100000 happens to be the cross-over point for Paul's machine;
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56 ## below this the more direct code below is faster. At the limit
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57 ## of memory in Paul's machine, this saves .7 seconds out of 7 for
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58 ## n = 3e6. Hardly worthwhile, but Dirk reports better numbers.
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59 lenm = floor ((n+1)/6); # length of the 6n-1 sieve
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60 lenp = floor ((n-1)/6); # length of the 6n+1 sieve
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61 sievem = true (1, lenm); # assume every number of form 6n-1 is prime
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62 sievep = true (1, lenp); # assume every number of form 6n+1 is prime
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63
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64 for i = 1:(sqrt (n)+1)/6 # check up to sqrt (n)
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65 if (sievem(i)) # if i is prime, eliminate multiples of i
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66 sievem(7*i-1:6*i-1:lenm) = false;
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67 sievep(5*i-1:6*i-1:lenp) = false;
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68 endif # if i is prime, eliminate multiples of i
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69 if (sievep(i))
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70 sievep(7*i+1:6*i+1:lenp) = false;
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71 sievem(5*i+1:6*i+1:lenm) = false;
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72 endif
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73 endfor
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74 x = sort ([2, 3, 6*find(sievem)-1, 6*find(sievep)+1]);
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75 elseif (n > 352) # nothing magical about 352; must be >2
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76 len = floor ((n-1)/2); # length of the sieve
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77 sieve = true (1, len); # assume every odd number is prime
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78 for i = 1:(sqrt (n)-1)/2 # check up to sqrt (n)
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79 if (sieve(i)) # if i is prime, eliminate multiples of i
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80 sieve(3*i+1:2*i+1:len) = false; # do it
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81 endif
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82 endfor
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83 x = [2, 1+2*find(sieve)]; # primes remaining after sieve
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84 else
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85 a = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, ...
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86 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, ...
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87 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, ...
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88 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, ...
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89 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, ...
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90 293, 307, 311, 313, 317, 331, 337, 347, 349];
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91 x = a(a <= n);
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92 endif
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93
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94 endfunction
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97 %!assert (size (primes (350)), [1, 70])
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98 %!assert (primes (357)(end), 353)
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99
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100 %!error primes ()
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101 %!error primes (1, 2)
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102