# 6,000,000 Digit Computation of CMRB

6,000,000 Digit Computation of CMRB

Print["Start time is ",ds=DateString[],"."];prec=6000000;(**Numberofrequireddecimals.*.*)ClearSystemCache[];T0=SessionTime[];expM[pre_]:=Module[{a,d,s,k,bb,c,end,iprec,xvals,x,pc,cores=16(*=4*numberofphysicalcores*),tsize=2^7,chunksize,start=1,ll,ctab,pr=Floor[1.005pre]},chunksize=cores*tsize;n=Floor[1.32pr];end=Ceiling[n/chunksize];Print["Iterations required: ",n];Print["Will give ",end," time estimates, each more accurate than the previous."];Print["Will stop at ",end*chunksize," iterations to ensure precision of around ",pr," decimal places."];Print[];d=ChebyshevT[n,3];{b,c,s}={SetPrecision[-1,1.1*n],-d,0};iprec=Ceiling[pr/27];Do[xvals=Flatten[ParallelTable[Table[ll=start+j*tsize+l;x=N[E^(Log[ll]/(ll)),iprec];pc=iprec;While[pc<pr/4,pc=Min[3pc,pr/4];x=SetPrecision[x,pc];y=x^ll-ll;x=x(1-2y/((ll+1)y+2llll));];(**N[Exp[Log[ll]/ll],pr/4]**)x=SetPrecision[x,pr];xll=x^ll;z=(ll-xll)/xll;t=2ll-1;t2=t^2;x=x*(1+SetPrecision[4.5,pr](ll-1)/t2+(ll+1)z/(2llt)-SetPrecision[13.5,pr]ll(ll-1)1/(3llt2+t^3z));(**N[Exp[Log[ll]/ll],pr]**)x,{l,0,tsize-1}],{j,0,cores-1},Method"EvaluationsPerKernel"32]];ctab=ParallelTable[Table[c=b-c;ll=start+l-2;b*=2(ll+n)(ll-n)/((ll+1)(2ll+1));c,{l,chunksize}],Method"EvaluationsPerKernel"16];s+=ctab.(xvals-1);start+=chunksize;st=SessionTime[]-T0;kc=k*chunksize;ti=(st)/(kc+10^-4)*(n)/(3600)/(24);If[kc>1,Print["As of ",DateString[]," there were ",kc," iterations done in ",N[st,5]," seconds. That is ",N[kc/st,5]," iterations/s. ",N[kc/(end*chunksize)*100,7],"% complete."," It should take ",N[ti,6]," days or ",N[ti*24*3600,4],"s, and finish ",DatePlus[ds,ti],"."]];Print[];,{k,0,end-1}];N[-s/d,pr]];t2=Timing[MRB1=expM[prec];];Print["Finished on ",DateString[],". Proccessor and actual time were ",t2[[1]]," and ",SessionTime[]-T0," s. respectively"];Print["Enter MRB1 to print ",Floor[Precision[MRB1]]," digits. The error from a 5,000,000 or more digit calculation that used a different method is "];N[MRB-MRB1,20]

In[]:=

Start time is Fri 11 Sep 2020 21:41:41.

Iterations required: 7959598

Will give 3887 time estimates, each more accurate than the previous.

Will stop at 7960576 iterations to ensure precision of around 6029999 decimal places.

As of Fri 11 Sep 2020 23:34:58 there were 2048 iterations done in 6796.6 seconds. That is 0.30133 iterations/s. 0.02572678% complete. It should take 305.732 days or 2.642×s, and finish Wed 14 Jul 2021 15:15:35.

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As of Sat 12 Sep 2020 00:33:00 there were 4096 iterations done in 10279. seconds. That is 0.39849 iterations/s. 0.05145356% complete. It should take 231.185 days or 1.997×s, and finish Sat 1 May 2021 02:08:09.

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As of Sat 12 Sep 2020 01:31:00 there were 6144 iterations done in 13759. seconds. That is 0.44654 iterations/s. 0.07718034% complete. It should take 206.308 days or 1.782×s, and finish Tue 6 Apr 2021 05:04:34.

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As of Sat 12 Sep 2020 02:29:24 there were 8192 iterations done in 17263. seconds. That is 0.47454 iterations/s. 0.1029071% complete. It should take 194.136 days or 1.677×s, and finish Thu 25 Mar 2021 00:57:15.

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As of Sat 12 Sep 2020 03:30:10 there were 10240 iterations done in 20908. seconds. That is 0.48976 iterations/s. 0.1286339% complete. It should take 188.103 days or 1.625×s, and finish Fri 19 Mar 2021 00:10:32.

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As of Sat 12 Sep 2020 04:31:07 there were 12288 iterations done in 24566. seconds. That is 0.50021 iterations/s. 0.1543607% complete. It should take 184.173 days or 1.591×s, and finish Mon 15 Mar 2021 01:51:07.

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As of Sat 12 Sep 2020 05:30:33 there were 14336 iterations done in 28131. seconds. That is 0.50961 iterations/s. 0.1800875% complete. It should take 180.776 days or 1.562×s, and finish Thu 11 Mar 2021 16:18:25.

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As of Sat 12 Sep 2020 06:30:23 there were 16384 iterations done in 31722. seconds. That is 0.51649 iterations/s. 0.2058143% complete. It should take 178.368 days or 1.541×s, and finish Tue 9 Mar 2021 06:31:30.

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As of Sat 12 Sep 2020 07:29:34 there were 18432 iterations done in 35272. seconds. That is 0.52256 iterations/s. 0.2315410% complete. It should take 176.295 days or 1.523×s, and finish Sun 7 Mar 2021 04:47:05.

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As of Sat 12 Sep 2020 08:28:50 there were 20480 iterations done in 38829. seconds. That is 0.52744 iterations/s. 0.2572678% complete. It should take 174.663 days or 1.509×s, and finish Fri 5 Mar 2021 13:36:09.

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As of Sat 12 Sep 2020 09:28:33 there were 22528 iterations done in 42411. seconds. That is 0.53118 iterations/s. 0.2829946% complete. It should take 173.435 days or 1.498×s, and finish Thu 4 Mar 2021 08:08:03.

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As of Sat 12 Sep 2020 10:27:38 there were 24576 iterations done in 45957. seconds. That is 0.53476 iterations/s. 0.3087214% complete. It should take 172.272 days or 1.488×s, and finish Wed 3 Mar 2021 04:13:22.

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As of Sat 12 Sep 2020 11:27:37 there were 26624 iterations done in 49556. seconds. That is 0.53725 iterations/s. 0.3344482% complete. It should take 171.475 days or 1.482×s, and finish Tue 2 Mar 2021 09:05:02.

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As of Sat 12 Sep 2020 12:27:55 there were 28672 iterations done in 53174. seconds. That is 0.53921 iterations/s. 0.3601749% complete. It should take 170.850 days or 1.476×s, and finish Mon 1 Mar 2021 18:06:07.

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As of Sat 12 Sep 2020 13:32:09 there were 30720 iterations done in 57028. seconds. That is 0.53868 iterations/s. 0.3859017% complete. It should take 171.019 days or 1.478×s, and finish Mon 1 Mar 2021 22:09:38.

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As of Sat 12 Sep 2020 14:31:43 there were 32768 iterations done in 60601. seconds. That is 0.54071 iterations/s. 0.4116285% complete. It should take 170.377 days or 1.472×s, and finish Mon 1 Mar 2021 06:43:57.

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As of Sat 12 Sep 2020 15:31:50 there were 34816 iterations done in 64209. seconds. That is 0.54223 iterations/s. 0.4373553% complete. It should take 169.900 days or 1.468×s, and finish Sun 28 Feb 2021 19:17:01.

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As of Sat 12 Sep 2020 16:32:59 there were 36864 iterations done in 67877. seconds. That is 0.54310 iterations/s. 0.4630821% complete. It should take 169.629 days or 1.466×s, and finish Sun 28 Feb 2021 12:46:52.

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