Re: For loop problem in mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg90237] Re: [mg90163] For loop problem in mathematica*From*: DrMajorBob <drmajorbob at att.net>*Date*: Thu, 3 Jul 2008 06:10:22 -0400 (EDT)*References*: <11203311.1214991822381.JavaMail.root@m08>*Reply-to*: drmajorbob at longhorns.com

I see nothing "catastrophic" about a 10-million-long For taking considerable time to complete. (x = 0; For[i = 1, i < 10000000, i++, x = N[x + 1/(i^2), 53]]; N[Sqrt[6*x], 25]) // Timing {67.2293, 3.141592558096821157357751} (x = Sum[1/i^2, {i, 1, n}]; N[Sqrt[6 x /. n -> Infinity], 25]) // Timing {0.004447, 3.141592653589793238462643} N[Pi, 25] // Timing {0.000024, 3.141592653589793238462643} As written, your code created Rational numbers with very large denominators. For instance: (x = 0; For[i = 1, i < 100, i++, x = x + 1/(i^2)]; N[Sqrt[6*x], 25]) // Timing {0.002248, 3.131980747244362801857815} N@Log[10, #] &@Through[{Numerator, Denominator}@x] {81.9002, 81.6867} or (x = 0; For[i = 1, i < 1000, i++, x = x + 1/(i^2)]; N[Sqrt[6*x], 25]) // Timing {0.015289, 3.140637100985938301795880} N@Log[10, #] &@Through[{Numerator, Denominator}@x] {865.922, 865.706} and (x = 0; For[i = 1, i < 10000, i++, x = x + 1/(i^2)]; N[Sqrt[6*x], 25]) // Timing {0.211607, 3.141497154397622340592830} N@Log[10, #] &@Through[{Numerator, Denominator}@x] {8692.74, 8692.52} Notice that almost 9 thousand digit in the denominator isn't enough to get 25-digit accuracy in Pi. Bobby On Tue, 01 Jul 2008 05:59:02 -0500, PhysNova <skhoshbinfar at gmail.com> wrote: > Hi, > i wrote a simple program of evaluating Pi number in M6 to test cpu > computation timing, to do this a simple for loop > > was used: > > x=0;For[i = 1, i < 10,000,000, i++, x = x + 1/(i^2)];N[Sqrt(6*x),25]// > Timing > > the result was catastrophe! it take few minuates. but i first expect > to do this very simple job in few > > seconds.computation time is just satisfactory up to 100000 cycle. > > could anyone interperet this falut? > our get an idea to improve the result? > > Tanks > > -- DrMajorBob at longhorns.com