Mercurial > octave-dspies
view scripts/specfun/primes.m @ 19010:3fb030666878 draft default tip dspies
Added special-case logical-indexing function
* logical-index.h (New file) : Logical-indexing function. May be called on
octave_value types via call_bool_index
* nz-iterators.h : Add base-class nz_iterator for iterator types. Array has
template bool for whether to internally store row-col or compute on the fly
Add skip_ahead method which skips forward to the next nonzero after its
argument
Add flat_index for computing octave_idx_type index of current position (with
assertion failure in the case of overflow)
Move is_zero to separate file
* ov-base-diag.cc, ov-base-mat.cc, ov-base-sparse.cc, ov-perm.cc
(do_index_op): Add call to call_bool_index in logical-index.h
* Array.h : Move forward-declaration for array_iterator to separate header file
* dim-vector.cc (dim_max): Refers to idx-bounds.h (max_idx)
* array-iter-decl.h (New file): Header file for forward declaration of
array-iterator
* direction.h : Add constants fdirc and bdirc to avoid having to reconstruct
them
* dv-utils.h, dv-utils.cc (New files) :
Utility functions for querying and constructing dim-vectors
* idx-bounds.h (New file) :
Utility constants and functions for determining whether things will overflow
the maximum allowed bounds
* interp-idx.h (New function : to_flat_idx) : Converts row-col pair to linear
index of octave_idx_type
* is-zero.h (New file) : Function for determining whether an element is zero
* logical-index.tst : Add tests for correct return-value dimensions and large
sparse matrix behavior
author | David Spies <dnspies@gmail.com> |
---|---|
date | Fri, 25 Jul 2014 13:39:31 -0600 |
parents | d63878346099 |
children |
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## Copyright (C) 2000-2013 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)