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primes.m: Fix failing BIST test introduced in cset 90dd85369c2e. * primes.m: Fix failing BIST test introduced in cset 90dd85369c2e.
author Rik <rik@octave.org>
date Sat, 20 Sep 2014 10:43:47 -0700
parents 90dd85369c2e
children 0f9c5a15c8fa
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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1 ## Copyright (C) 2000-2013 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 ## Return all primes up to @var{n}.
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22 ##
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23 ## The output data class (double, single, uint32, etc.) is the same as
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24 ## the input class of @var{n}. The algorithm used is the Sieve of
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25 ## Eratosthenes.
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26 ##
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27 ## Notes: If you need a specific number of primes you can use the
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28 ## fact that the distance from one prime to the next is, on average,
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29 ## proportional to the logarithm of the prime. Integrating, one finds
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30 ## that there are about @math{k} primes less than
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31 ## @tex
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32 ## $k \log (5 k)$.
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33 ## @end tex
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34 ## @ifnottex
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35 ## k*log (5*k).
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36 ## @end ifnottex
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37 ##
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38 ## See also @code{list_primes} if you need a specific number @var{n} of
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39 ## primes.
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40 ## @seealso{list_primes, isprime}
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41 ## @end deftypefn
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42
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43 ## Author: Paul Kienzle
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44 ## Author: Francesco Potortì
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45 ## Author: Dirk Laurie
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46
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47 function p = primes (n)
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48
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49 if (nargin != 1)
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50 print_usage ();
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51 endif
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52
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53 if (! isscalar (n))
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54 error ("primes: N must be a scalar");
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55 endif
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56
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57 if (n > 100e3)
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58 ## Optimization: 1/6 less memory, and much faster (asymptotically)
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59 ## 100K happens to be the cross-over point for Paul's machine;
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60 ## below this the more direct code below is faster. At the limit
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61 ## of memory in Paul's machine, this saves .7 seconds out of 7 for
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62 ## n = 3e6. Hardly worthwhile, but Dirk reports better numbers.
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63 lenm = floor ((n+1)/6); # length of the 6n-1 sieve
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64 lenp = floor ((n-1)/6); # length of the 6n+1 sieve
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65 sievem = true (1, lenm); # assume every number of form 6n-1 is prime
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66 sievep = true (1, lenp); # assume every number of form 6n+1 is prime
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67
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68 for i = 1:(sqrt (n)+1)/6 # check up to sqrt (n)
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69 if (sievem(i)) # if i is prime, eliminate multiples of i
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70 sievem(7*i-1:6*i-1:lenm) = false;
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71 sievep(5*i-1:6*i-1:lenp) = false;
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72 endif # if i is prime, eliminate multiples of i
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73 if (sievep(i))
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74 sievep(7*i+1:6*i+1:lenp) = false;
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75 sievem(5*i+1:6*i+1:lenm) = false;
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76 endif
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77 endfor
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78 p = sort ([2, 3, 6*find(sievem)-1, 6*find(sievep)+1]);
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79 elseif (n > 352) # nothing magical about 352; must be > 2
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80 len = floor ((n-1)/2); # length of the sieve
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81 sieve = true (1, len); # assume every odd number is prime
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82 for i = 1:(sqrt (n)-1)/2 # check up to sqrt (n)
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83 if (sieve(i)) # if i is prime, eliminate multiples of i
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84 sieve(3*i+1:2*i+1:len) = false; # do it
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85 endif
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86 endfor
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87 p = [2, 1+2*find(sieve)]; # primes remaining after sieve
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88 else
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89 a = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, ...
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90 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, ...
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91 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, ...
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92 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, ...
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93 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, ...
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94 293, 307, 311, 313, 317, 331, 337, 347, 349];
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95 p = a(a <= n);
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96 endif
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97
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98 if (! isa (n, "double"))
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99 cast (p, class (n));
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100 endif
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101
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102 endfunction
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103
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104
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105 %!assert (size (primes (350)), [1, 70])
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106 %!assert (primes (357)(end), 353)
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107
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108 %!error primes ()
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109 %!error primes (1, 2)
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110 %!error <N must be a scalar> primes (ones (2,2))
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111