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 fast accurate Kneser sexp algorithm sheldonison Long Time Fellow Posts: 641 Threads: 22 Joined: Oct 2008 07/23/2011, 12:54 PM (This post was last modified: 11/21/2011, 09:34 PM by sheldonison.) (07/23/2011, 05:48 AM)deepblue Wrote: Is it continuous at 1/2? I got... sexp(1/2)=1.6376... sexp(1/2+10^-30)=1.6489...You're using the initial seed approximation, which is a three term taylor series, along with iterative logs/exps. After initialization, you need to "loop" through iteratively calculating the Kneser theta mapping. After 13 iterations (which takes about 4 seconds), you'll get results accurate to 110 binary bits. Code:```gp > init(exp(1));loop    base          2.71828182845904523536029    fixed point   0.318131505204764135312654 + 1.33723570143068940890116*I    Pseudo Period 4.44695072006700782711228 + 1.05793999115693918376341*I generating superf taylor series; inverse Schroder equation, scnt 235 generating isuperf taylor series; Schroder equation, scnt 235 sexp(-0.5)= 0.49855114028767537891166401244655 1=loopcnt  8.842977061 Riemann/sexp binary precision bits sexp(-0.5)= 0.49856330616566898032298548529033 2=loopcnt  17.67523398 Riemann/sexp binary precision bits sexp(-0.5)= 0.49856328805247482985620720695870 3=loopcnt  26.43624250 Riemann/sexp binary precision bits sexp(-0.5)= 0.49856328794127685577078081234199 4=loopcnt  35.02171218 Riemann/sexp binary precision bits sexp(-0.5)= 0.49856328794111357966546850464454 5=loopcnt  43.44600587 Riemann/sexp binary precision bits sexp(-0.5)= 0.49856328794111443478679527238125 6=loopcnt  52.16036487 Riemann/sexp binary precision bits sexp(-0.5)= 0.49856328794111443467429889486618 7=loopcnt  60.48849684 Riemann/sexp binary precision bits sexp(-0.5)= 0.49856328794111443467961715088127 8=loopcnt  69.25315295 Riemann/sexp binary precision bits sexp(-0.5)= 0.49856328794111443467961906029415 9=loopcnt  77.65865208 Riemann/sexp binary precision bits sexp(-0.5)= 0.49856328794111443467961909246830 10=loopcnt  86.52036006 Riemann/sexp binary precision bits sexp(-0.5)= 0.49856328794111443467961909249278 11=loopcnt  94.54807694 Riemann/sexp binary precision bits sexp(-0.5)= 0.49856328794111443467961909249313 12=loopcnt  102.8988830 Riemann/sexp binary precision bits sexp(-0.5)= 0.49856328794111443467961909249313 13=loopcnt  110.6414599 Riemann/sexp binary precision bits %1 = 1```Code:```gp > sexp(0.5) %2 = 1.6463542337511945809719240315921 gp > sexp(0.5+1E-30) %3 = 1.6463542337511945809719240315937 gp >```The separate "init(b)" routine from the "loop" routine is a little confusing. Originally, the kneser.gp program was more of an experiment, although I kind of like to be able to initialize for a base, and see the fixed point, and the pseudo period, before doing the loop. Sometimes I want to manually control the looping.... Anyway, I could change the program in one of two ways that would make it simpler. Both changes I'm thinking of involve putting the "loop;" at the end of the init routine, so that anytime you initialize for a given base, via "init(b)", the program automatically loops through with the current precision, generating the sexp(z) series. Then the question becomes what to do when kneser.gp is first loaded into pari-gp. Since the loop only takes 4-5 seconds for base e, "\p 67", I could have the program fully initialize for base e when it loads, going through the loop of thirteen iterations. Or, I could completely remove the partial initialization for base e when the program loads. Any opinions, as to which makes more sense? - Sheldon For the most recent code version: go to the Nov 21st, 2011 thread. « Next Oldest | Next Newest »

 Messages In This Thread fast accurate Kneser sexp algorithm - by sheldonison - 08/07/2010, 06:53 AM The pari-GP code - by sheldonison - 08/07/2010, 09:17 PM RE: fast accurate Knesser sexp algorithm - by bo198214 - 08/08/2010, 03:54 PM RE: fast accurate Knesser sexp algorithm - by sheldonison - 08/08/2010, 06:46 PM RE: fast accurate Kneser sexp algorithm - by nuninho1980 - 08/15/2010, 12:09 AM updated kneser.gp code - by sheldonison - 08/19/2010, 02:35 AM RE: updated kneser.gp code - by nuninho1980 - 08/19/2010, 12:08 PM RE: updated kneser.gp code - by sheldonison - 08/20/2010, 01:05 AM RE: fast accurate Kneser sexp algorithm - by sheldonison - 10/14/2010, 10:00 PM RE: fast accurate Kneser sexp algorithm - by nuninho1980 - 10/15/2010, 04:03 PM RE: fast accurate Kneser sexp algorithm - by sheldonison - 10/15/2010, 09:20 PM kneser.gp modified for large bases - by sheldonison - 10/19/2010, 03:33 AM small update to allow more flexibility, faster - by sheldonison - 10/30/2010, 09:47 PM update to support B

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