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=4,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 Mon 12 Jan 2026 20:21:50.
Iterations required: 13265998
Will give 25911 time estimates, each more accurate than the previous.
Will stop at 13266432 iterations to ensure precision of around 10049999 decimal places.
512 iterations done in 2494. seconds. Should take 748.1 days or 6.463×s, finish Sun 30 Jan 2028 21:48:00.
7
10
1024 iterations done in 3793. seconds. Should take 568.8 days or 4.914×s, finish Wed 4 Aug 2027 14:31:12.
7
10
1536 iterations done in 5107. seconds. Should take 510.5 days or 4.411×s, finish Mon 7 Jun 2027 08:02:43.
7
10
2048 iterations done in 6421. seconds. Should take 481.4 days or 4.159×s, finish Sun 9 May 2027 05:10:01.
7
10
2560 iterations done in 7746. seconds. Should take 464.6 days or 4.014×s, finish Thu 22 Apr 2027 10:46:37.
7
10
3072 iterations done in 9074. seconds. Should take 453.5 days or 3.918×s, finish Sun 11 Apr 2027 08:27:31.
7
10
3584 iterations done in 1.041× seconds. Should take 446.2 days or 3.855×s, finish Sun 4 Apr 2027 00:51:16.
4
10
7
10
4096 iterations done in 1.174× seconds. Should take 440.2 days or 3.804×s, finish Mon 29 Mar 2027 02:14:39.
4
10
7
10
4608 iterations done in 1.309× seconds. Should take 436.0 days or 3.767×s, finish Wed 24 Mar 2027 21:10:24.
4
10
7
10
5120 iterations done in 1.442× seconds. Should take 432.5 days or 3.736×s, finish Sun 21 Mar 2027 07:21:42.
4
10
7
10
5632 iterations done in 1.577× seconds. Should take 429.8 days or 3.714×s, finish Thu 18 Mar 2027 16:37:15.
4
10
7
10
6144 iterations done in 1.710× seconds. Should take 427.3 days or 3.692×s, finish Tue 16 Mar 2027 04:38:54.
4
10
7
10
6656 iterations done in 1.845× seconds. Should take 425.5 days or 3.677×s, finish Sun 14 Mar 2027 08:52:50.
4
10
7
10
7168 iterations done in 1.979× seconds. Should take 424.0 days or 3.663×s, finish Fri 12 Mar 2027 19:19:50.
4
10
7
10
7680 iterations done in 2.115× seconds. Should take 422.8 days or 3.653×s, finish Thu 11 Mar 2027 16:34:33.
4
10
7
10
8192 iterations done in 2.249× seconds. Should take 421.4 days or 3.641×s, finish Wed 10 Mar 2027 07:00:52.
4
10
7
10
8704 iterations done in 2.383× seconds. Should take 420.4 days or 3.632×s, finish Tue 9 Mar 2027 06:10:01.
4
10
7
10
9216 iterations done in 2.518× seconds. Should take 419.5 days or 3.624×s, finish Mon 8 Mar 2027 07:52:51.
4
10
7
10
9728 iterations done in 2.654× seconds. Should take 418.8 days or 3.619×s, finish Sun 7 Mar 2027 16:44:59.
4
10
7
10
10240 iterations done in 2.788× seconds. Should take 418.1 days or 3.612×s, finish Sat 6 Mar 2027 22:46:10.
4
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7
10
10752 iterations done in 2.924× seconds. Should take 417.6 days or 3.608×s, finish Sat 6 Mar 2027 11:04:03.
4
10
7
10
11264 iterations done in 3.060× seconds. Should take 417.2 days or 3.604×s, finish Sat 6 Mar 2027 00:03:00.
4
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7
10
11776 iterations done in 3.198× seconds. Should take 416.9 days or 3.602×s, finish Fri 5 Mar 2027 19:04:04.
4
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7
10
12288 iterations done in 3.333× seconds. Should take 416.4 days or 3.598×s, finish Fri 5 Mar 2027 06:56:50.
4
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7
10
12800 iterations done in 3.469× seconds. Should take 416.1 days or 3.595×s, finish Thu 4 Mar 2027 23:20:02.
4
10
7
10
13312 iterations done in 3.605× seconds. Should take 415.8 days or 3.593×s, finish Thu 4 Mar 2027 16:26:35.
4
10
7
10
13824 iterations done in 3.743× seconds. Should take 415.7 days or 3.592×s, finish Thu 4 Mar 2027 13:48:23.
4
10
7
10
14336 iterations done in 3.879× seconds. Should take 415.5 days or 3.590×s, finish Thu 4 Mar 2027 08:11:09.
4
10
7
10
14848 iterations done in 4.017× seconds. Should take 415.4 days or 3.589×s, finish Thu 4 Mar 2027 05:43:38.
4
10
7
10
15360 iterations done in 4.155× seconds. Should take 415.3 days or 3.588×s, finish Thu 4 Mar 2027 03:33:45.
4
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7
10
15872 iterations done in 4.293× seconds. Should take 415.3 days or 3.588×s, finish Thu 4 Mar 2027 04:21:35.
4
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7
10
16384 iterations done in 4.429× seconds. Should take 415.0 days or 3.586×s, finish Wed 3 Mar 2027 21:13:58.
4
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7
10
16896 iterations done in 4.565× seconds. Should take 414.9 days or 3.584×s, finish Wed 3 Mar 2027 17:16:03.
4
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7
10