This is an automated email from the git hooks/post-receive script. ppm-guest pushed a commit to annotated tag v0.35 in repository libmath-prime-util-perl.

commit 31afb1b2e42e0286eba085fde9f4e5daedc3e788 Author: Dana Jacobsen <d...@acm.org> Date: Fri Dec 6 18:16:56 2013 -0800 Documentation updates --- lib/Math/Prime/Util.pm | 26 ++++++++++++-------------- 1 file changed, 12 insertions(+), 14 deletions(-) diff --git a/lib/Math/Prime/Util.pm b/lib/Math/Prime/Util.pm index 8a431f3..b0df220 100644 --- a/lib/Math/Prime/Util.pm +++ b/lib/Math/Prime/Util.pm @@ -2180,6 +2180,7 @@ sub prime_count_approx { # Method 10^10 %error 10^19 %error # ----------------- ------------ ------------ + # n/(log(n)-1) .22% .06% # average bounds .01% .0002% # li(n) .0007% .00000004% # li(n)-li(n^.5)/2 .0004% .00000001% @@ -2906,8 +2907,8 @@ handles iterating across bigints. Returns the Prime Count function C<Pi(n)>, also called C<primepi> in some math packages. When given two arguments, it returns the inclusive -count of primes between the ranges (e.g. C<(13,17)> returns 2, C<14,17> -and C<13,16> return 1, and C<14,16> returns 0). +count of primes between the ranges. E.g. C<(13,17)> returns 2, C<(14,17)> +and C<(13,16)> return 1, C<(14,16)> returns 0. The current implementation decides based on the ranges whether to use a segmented sieve with a fast bit count, or the extended LMO algorithm. @@ -2924,8 +2925,8 @@ The extended LMO method has complexity approximately C<O(b^(2/3)) + O(a^(2/3))>, and also uses low memory. A calculation of C<Pi(10^14)> completes in a few seconds, C<Pi(10^15)> in well under a minute, and C<Pi(10^16)> in about one minute. In -contrast, even primesieve using 12 cores would take over a week on this -same computer to determine C<Pi(10^16)>. +contrast, even parallel primesieve would take over a week on a +similar machine to determine C<Pi(10^16)>. Also see the function L</prime_count_approx> which gives a very good approximation to the prime count, and L</prime_count_lower> and @@ -2988,14 +2989,13 @@ the upper and lower bounds. Returns the prime that lies in index C<n> in the array of prime numbers. Put another way, this returns the smallest C<p> such that C<Pi(p) E<gt>= n>. -For relatively small inputs (below 2 million or so), this does a sieve over +For relatively small inputs (below 1 million or so), this does a sieve over a range containing the nth prime, then counts up to the number. This is fairly -efficient in time and memory. For larger values, a binary search is performed -between the Dusart 2010 bounds using Riemann's R function, then a fast -prime counting method is used to calculate the count up to that point, then -sieving is done in the typically small difference zone. +efficient in time and memory. For larger values, create a low-biased estimate +using the inverse logarithmic integral, use a fast prime count, then sieve in +the small difference. -While this method is hundreds of times faster than generating primes, and +While this method is thousands of times faster than generating primes, and doesn't involve big tables of precomputed values, it still can take a fair amount of time for large inputs. Calculating the C<10^12th> prime takes about 1 second, the C<10^13th> prime takes under 10 seconds, and the @@ -3003,10 +3003,8 @@ C<10^14th> prime (3475385758524527) takes under one minute. Think about whether a bound or approximation would be acceptable, as they can be computed analytically. -If the bigint or bignum module is not in use, this will generate an overflow -exception if the number requested would result in a prime that cannot fit in -a native type. If bigints are in use, then the calculation will proceed, -though it will be exceedingly slow. A later version of +If the result is larger than a native integer size (32-bit or 64-bit), the +result will take a very long time. A later version of L<Math::Prime::Util::GMP> may include this functionality which would help for 32-bit machines. -- Alioth's /usr/local/bin/git-commit-notice on /srv/git.debian.org/git/pkg-perl/packages/libmath-prime-util-perl.git _______________________________________________ Pkg-perl-cvs-commits mailing list Pkg-perl-cvs-commits@lists.alioth.debian.org http://lists.alioth.debian.org/cgi-bin/mailman/listinfo/pkg-perl-cvs-commits