Re: How to count
- To: mathgroup at smc.vnet.net
- Subject: [mg125760] Re: How to count
- From: Costa Bravo <q13a27tt at aol.com>
- Date: Sun, 1 Apr 2012 03:36:30 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <jl14ig$l5e$1@smc.vnet.net> <jl3uuf$3kp$1@smc.vnet.net>
Daniel Lichtblau Wolfram Research danl at wolfram.com wrote: > bottom = 100000; > Timing[bb = Table[Ceiling[Exp[LogGamma[N[n+1,n]]/2]], > {n,bottom,10*bottom,bottom}];] > > Out[16]= {671.196962, Null} My computer needs more time {1256.916, Null} Let's test a better solution n = 100000; {Timing[lg2 = Exp[LogGamma[N[n + 1, n]]/2];], Precision[lg2]} {Timing[lg2 = N[Exp[LogGamma[n + 1]/2], n];], Precision[lg2]} {Timing[lg2 = Exp[N[LogGamma[n + 1]/2, n]];], Precision[lg2]} {{9.048, Null}, 556568.58} {{3.338, Null}, 100000.} {{0.593, Null}, 99994.11} (* !!! *) surprising result for n = 1 000 000 n = 1000000; {Timing[lg2 = Exp[LogGamma[N[n + 1, n]]/2];], Precision[lg2]} {Timing[lg2 = N[Exp[LogGamma[n + 1]/2], n];], Precision[lg2]} {Timing[lg2 = Exp[N[LogGamma[n + 1]/2, n]];], Precision[lg2]} {{218.557, Null}, 6.5657032*10^6} {{217.528, Null}, 1.*10^6} (* !!! *) {{27.877, Null}, 999993.19} The new version of the original expression bottom = 10^5; Timing[bb1 = Table[Ceiling[Exp[N[LogGamma[n + 1]/2, n]]], {n, bottom, 10*bottom, bottom}];] {126.034, Null} 10 times faster !! -- Costa