In[]:=
Print["Start time is ",ds=DateString[],"."];prec=10000000;(*Numberofrequireddecimals.*)ClearSystemCache[];T0=SessionTime[];(*Sixth–orderPadékernelforn^(1/n)*)Clear[RootPade6];RootPade6[n_Integer,prec_Integer]:=Module[{x,pc,z,t,N0=n,A1,A2,A3,B1,B2},(*initialseedatmodestprecision*)x=N[N0^(1/N0),13];pc=Precision[x];While[pc<prec,pc=Min[6pc,prec];x=SetPrecision[x,pc];(*coefficientswithcurrentworkingprecisionpc*)A1=SetPrecision[3(2N0+1)/(5N0),pc];A2=SetPrecision[3(N0+1)(2N0+1)/(20N0^2),pc];A3=SetPrecision[(N0+1)(2N0+1)/(60N0^3),pc];B1=SetPrecision[2(3N0-1)/(5N0),pc];B2=SetPrecision[(2N0-1)(3N0-1)/(20N0^2),pc];(*residualz_i=(n-x^n)/x^n*)t=x^N0;z=(N0-t)/t;(*6th–orderPadéupdate*)x=x*(1+A1z+A2z^2+A3z^3)/(1+B1z+B2z^2);];N[x,prec]]expM[pre_]:=Module[{a,d,s,k,bb,c,end,xvals,x,pc,cores=12,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."];d=ChebyshevT[n,3];{b,c,s}={SetPrecision[-1,1.1*n],-d,0};Do[xvals=Flatten[ParallelTable[Table[ll=start+j*tsize+l;(*solekernelforll^(1/ll)atprecisionpr*)x=RootPade6[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[kc," iterations done in ",N[st,4]," seconds."," Should take ",N[ti,4]," days or ",N[ti*24*3600,4],"s, finish ",DatePlus[ds,ti],"."]];,{k,0,end-1}];N[-s/d,pr]]t2=Timing[MRB=expM[prec];];Print["Finished on ",DateString[],". Processor time was ",t2[[1]]," s."];Print["error= ",N[mtest-MRB,20]];Print["Enter MRB to print ",Floor[Precision[MRB]]," digits"];
Start time is Sat 17 Jan 2026 15:40:05.
Iterations required: 13265998
Will give 8637 time estimates, each more accurate than the previous.
Will stop at 13266432 iterations to ensure precision of around 10049999 decimal places.
1536 iterations done in 6436. seconds. Should take 643.3 days or 5.558×s, finish Fri 22 Oct 2027 23:29:54.
7
10
3072 iterations done in 9709. seconds. Should take 485.2 days or 4.193×s, finish Mon 17 May 2027 21:30:53.
7
10
4608 iterations done in 1.300× seconds. Should take 433.1 days or 3.742×s, finish Fri 26 Mar 2027 17:43:47.
4
10
7
10
6144 iterations done in 1.628× seconds. Should take 407.0 days or 3.516×s, finish Sun 28 Feb 2027 14:34:16.
4
10
7
10
7680 iterations done in 1.958× seconds. Should take 391.4 days or 3.382×s, finish Sat 13 Feb 2027 01:56:03.
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10
9216 iterations done in 2.289× seconds. Should take 381.3 days or 3.295×s, finish Wed 3 Feb 2027 00:03:43.
4
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10
10752 iterations done in 2.621× seconds. Should take 374.3 days or 3.234×s, finish Tue 26 Jan 2027 22:29:32.
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7
10
12288 iterations done in 2.955× seconds. Should take 369.2 days or 3.190×s, finish Thu 21 Jan 2027 20:33:41.
4
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10
13824 iterations done in 3.288× seconds. Should take 365.2 days or 3.156×s, finish Sun 17 Jan 2027 21:28:33.
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15360 iterations done in 3.621× seconds. Should take 362.0 days or 3.128×s, finish Thu 14 Jan 2027 15:43:33.
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10
16896 iterations done in 3.955× seconds. Should take 359.4 days or 3.105×s, finish Tue 12 Jan 2027 01:44:39.
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7
10
18432 iterations done in 4.291× seconds. Should take 357.4 days or 3.088×s, finish Sun 10 Jan 2027 02:19:41.
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10
19968 iterations done in 4.624× seconds. Should take 355.6 days or 3.072×s, finish Fri 8 Jan 2027 05:40:09.
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10
21504 iterations done in 4.962× seconds. Should take 354.3 days or 3.061×s, finish Wed 6 Jan 2027 22:29:18.
4
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10
23040 iterations done in 5.302× seconds. Should take 353.3 days or 3.053×s, finish Tue 5 Jan 2027 23:09:12.
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24576 iterations done in 5.639× seconds. Should take 352.3 days or 3.044×s, finish Mon 4 Jan 2027 22:21:19.
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26112 iterations done in 5.975× seconds. Should take 351.3 days or 3.035×s, finish Sun 3 Jan 2027 23:05:24.
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10
27648 iterations done in 6.312× seconds. Should take 350.5 days or 3.029×s, finish Sun 3 Jan 2027 04:32:45.
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10
29184 iterations done in 6.649× seconds. Should take 349.8 days or 3.023×s, finish Sat 2 Jan 2027 11:40:06.
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30720 iterations done in 6.988× seconds. Should take 349.3 days or 3.018×s, finish Fri 1 Jan 2027 22:17:44.
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32256 iterations done in 7.324× seconds. Should take 348.6 days or 3.012×s, finish Fri 1 Jan 2027 07:12:46.
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33792 iterations done in 7.663× seconds. Should take 348.2 days or 3.008×s, finish Thu 31 Dec 2026 19:44:05.
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35328 iterations done in 7.997× seconds. Should take 347.6 days or 3.003×s, finish Thu 31 Dec 2026 04:58:49.
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29184 iterations done in 7.917× seconds. Should take 416.5 days or 3.599×s, finish Fri 5 Mar 2027 09:11:00.
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30720 iterations done in 8.340× seconds. Should take 416.8 days or 3.601×s, finish Fri 5 Mar 2027 15:58:54.
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32256 iterations done in 8.765× seconds. Should take 417.2 days or 3.605×s, finish Sat 6 Mar 2027 01:49:17.
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33792 iterations done in 9.182× seconds. Should take 417.2 days or 3.605×s, finish Sat 6 Mar 2027 01:34:02.
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35328 iterations done in 9.603× seconds. Should take 417.4 days or 3.606×s, finish Sat 6 Mar 2027 05:01:08.
4
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10
36864 iterations done in 1.002× seconds. Should take 417.5 days or 3.607×s, finish Sat 6 Mar 2027 08:46:24.
5
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