In[]:=
Print["Start time is ",ds=DateString[],"."];​​prec=100000;​​(**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 precsion of around ",pr," decimal places."];d=ChebyshevT[n,3];​​{b,c,s}={SetPrecision[-1,1.1*n],-d,0};​​iprec=Ceiling[pr/6912];​​Do[xvals=Flatten[Parallelize[Table[Table[ll=start+j*tsize+l;​​x=N[E^(Log[ll]/(ll)),iprec];​​pc=iprec;​​While[pc<pr/1024,pc=Min[3pc,pr/1024];​​x=SetPrecision[x,pc];​​y=x^ll-ll;​​x=x(1-2y/((ll+1)y+2llll));];​​(**N[Exp[Log[ll]/ll],pr/1024]**)x=SetPrecision[x,pr/256];​​xll=x^ll;z=(ll-xll)/xll;​​t=2ll-1;t2=t^2;​​x=x*(1+SetPrecision[4.5,pr/256](ll-1)/t2+(ll+1)z/(2llt)-SetPrecision[13.5,pr/256]ll(ll-1)1/(3llt2+t^3z));(*N[Exp[Log[ll]/ll],pr/256]*)x=SetPrecision[x,pr/64];​​xll=x^ll;z=(ll-xll)/xll;​​t=2ll-1;t2=t^2;​​x=x*(1+SetPrecision[4.5,pr/64](ll-1)/t2+(ll+1)z/(2llt)-SetPrecision[13.5,pr/64]ll(ll-1)1/(3llt2+t^3z));(**N[Exp[Log[ll]/ll],pr/64]**)x=SetPrecision[x,pr/16];​​xll=x^ll;z=(ll-xll)/xll;​​t=2ll-1;t2=t^2;​​x=x*(1+SetPrecision[4.5,pr/16](ll-1)/t2+(ll+1)z/(2llt)-SetPrecision[13.5,pr/16]ll(ll-1)1/(3llt2+t^3z));(**N[Exp[Log[ll]/ll],pr/16]**)x=SetPrecision[x,pr/4];​​xll=x^ll;z=(ll-xll)/xll;​​t=2ll-1;t2=t^2;​​x=x*(1+SetPrecision[4.5,pr/4](ll-1)/t2+(ll+1)z/(2llt)-SetPrecision[13.5,pr/4]ll(ll-1)1/(3llt2+t^3z));(**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}]]];​​ctab=ParallelTable[Table[c=b-c;​​ll=start+l-2;​​b*=2(ll+n)(ll-n)/((ll+1)(2ll+1));​​c,{l,chunksize}],Method"Automatic"];​​s+=ctab.(xvals-1);​​start+=chunksize;​​st=SessionTime[]-T0;kc=k*chunksize;​​ti=(st)/(kc+10^-4)*(n)/(3600)/(24);​​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[MRBtest2=expM[prec];];Print["Finished on ",DateString[],". Proccessor time was ",t2[[1]]," s."];Print["Actual time was ",st];​​(*Print[*)MRBtest2(*]*)(*Remove(**)orenterMRBtest2toprintoutput*);Print["Enter MRBtest2 to print ",Floor[Precision[MRBtest2]]," digits"];Print["If you saved m3M, the difference between this and 3,014,991 known digits is ",N[MRBtest2-m3M,10]]
Start time is Wed 7 Dec 2022 00:38:55.
Iterations required: 132658
Will give 65 time estimates, each more accurate than the previous.
Will stop at 133120 iterations to ensure precsion of around 100499 decimal places.
0 iterations done in 9.449 seconds. Should take 1.451×
5
10
days or 1.253×
10
10
s, finish Sun 16 Feb 2420 03:16:39.
2048 iterations done in 19.28 seconds. Should take 0.01445 days or 1249.s, finish Wed 7 Dec 2022 00:59:43.
4096 iterations done in 29.30 seconds. Should take 0.01098 days or 948.8s, finish Wed 7 Dec 2022 00:54:43.
6144 iterations done in 39.35 seconds. Should take 0.009834 days or 849.7s, finish Wed 7 Dec 2022 00:53:04.
8192 iterations done in 49.36 seconds. Should take 0.009251 days or 799.3s, finish Wed 7 Dec 2022 00:52:14.
10240 iterations done in 59.42 seconds. Should take 0.008910 days or 769.8s, finish Wed 7 Dec 2022 00:51:44.
12288 iterations done in 69.40 seconds. Should take 0.008672 days or 749.2s, finish Wed 7 Dec 2022 00:51:24.
14336 iterations done in 79.38 seconds. Should take 0.008501 days or 734.5s, finish Wed 7 Dec 2022 00:51:09.
16384 iterations done in 89.12 seconds. Should take 0.008352 days or 721.6s, finish Wed 7 Dec 2022 00:50:56.
18432 iterations done in 98.88 seconds. Should take 0.008237 days or 711.7s, finish Wed 7 Dec 2022 00:50:46.
20480 iterations done in 108.6 seconds. Should take 0.008142 days or 703.5s, finish Wed 7 Dec 2022 00:50:38.
22528 iterations done in 118.5 seconds. Should take 0.008076 days or 697.8s, finish Wed 7 Dec 2022 00:50:32.
24576 iterations done in 128.3 seconds. Should take 0.008016 days or 692.5s, finish Wed 7 Dec 2022 00:50:27.
26624 iterations done in 138.2 seconds. Should take 0.007970 days or 688.6s, finish Wed 7 Dec 2022 00:50:23.
28672 iterations done in 148.1 seconds. Should take 0.007931 days or 685.3s, finish Wed 7 Dec 2022 00:50:20.
30720 iterations done in 158.0 seconds. Should take 0.007897 days or 682.3s, finish Wed 7 Dec 2022 00:50:17.
32768 iterations done in 167.9 seconds. Should take 0.007865 days or 679.6s, finish Wed 7 Dec 2022 00:50:14.
34816 iterations done in 177.7 seconds. Should take 0.007838 days or 677.2s, finish Wed 7 Dec 2022 00:50:12.
36864 iterations done in 187.5 seconds. Should take 0.007810 days or 674.8s, finish Wed 7 Dec 2022 00:50:09.
38912 iterations done in 197.3 seconds. Should take 0.007786 days or 672.7s, finish Wed 7 Dec 2022 00:50:07.
40960 iterations done in 207.0 seconds. Should take 0.007760 days or 670.5s, finish Wed 7 Dec 2022 00:50:05.
43008 iterations done in 216.8 seconds. Should take 0.007740 days or 668.7s, finish Wed 7 Dec 2022 00:50:03.
45056 iterations done in 226.5 seconds. Should take 0.007718 days or 666.8s, finish Wed 7 Dec 2022 00:50:01.
47104 iterations done in 236.3 seconds. Should take 0.007702 days or 665.5s, finish Wed 7 Dec 2022 00:50:00.
49152 iterations done in 245.9 seconds. Should take 0.007680 days or 663.6s, finish Wed 7 Dec 2022 00:49:58.
51200 iterations done in 255.5 seconds. Should take 0.007661 days or 661.9s, finish Wed 7 Dec 2022 00:49:56.
53248 iterations done in 265.2 seconds. Should take 0.007647 days or 660.7s, finish Wed 7 Dec 2022 00:49:55.
55296 iterations done in 275.1 seconds. Should take 0.007640 days or 660.1s, finish Wed 7 Dec 2022 00:49:55.
57344 iterations done in 284.9 seconds. Should take 0.007628 days or 659.0s, finish Wed 7 Dec 2022 00:49:54.
59392 iterations done in 294.8 seconds. Should take 0.007621 days or 658.4s, finish Wed 7 Dec 2022 00:49:53.
61440 iterations done in 304.7 seconds. Should take 0.007613 days or 657.8s, finish Wed 7 Dec 2022 00:49:52.
63488 iterations done in 314.5 seconds. Should take 0.007606 days or 657.2s, finish Wed 7 Dec 2022 00:49:52.
65536 iterations done in 324.2 seconds. Should take 0.007595 days or 656.2s, finish Wed 7 Dec 2022 00:49:51.
67584 iterations done in 334.0 seconds. Should take 0.007589 days or 655.7s, finish Wed 7 Dec 2022 00:49:50.
69632 iterations done in 343.7 seconds. Should take 0.007578 days or 654.8s, finish Wed 7 Dec 2022 00:49:49.
71680 iterations done in 353.5 seconds. Should take 0.007573 days or 654.3s, finish Wed 7 Dec 2022 00:49:49.
73728 iterations done in 363.2 seconds. Should take 0.007564 days or 653.5s, finish Wed 7 Dec 2022 00:49:48.
75776 iterations done in 373.0 seconds. Should take 0.007558 days or 653.0s, finish Wed 7 Dec 2022 00:49:48.
77824 iterations done in 382.7 seconds. Should take 0.007550 days or 652.3s, finish Wed 7 Dec 2022 00:49:47.
79872 iterations done in 392.4 seconds. Should take 0.007543 days or 651.7s, finish Wed 7 Dec 2022 00:49:46.
81920 iterations done in 402.0 seconds. Should take 0.007535 days or 651.1s, finish Wed 7 Dec 2022 00:49:46.
83968 iterations done in 411.8 seconds. Should take 0.007529 days or 650.5s, finish Wed 7 Dec 2022 00:49:45.
86016 iterations done in 421.5 seconds. Should take 0.007523 days or 650.0s, finish Wed 7 Dec 2022 00:49:45.
88064 iterations done in 431.2 seconds. Should take 0.007518 days or 649.6s, finish Wed 7 Dec 2022 00:49:44.
90112 iterations done in 440.7 seconds. Should take 0.007510 days or 648.8s, finish Wed 7 Dec 2022 00:49:43.
92160 iterations done in 450.4 seconds. Should take 0.007504 days or 648.3s, finish Wed 7 Dec 2022 00:49:43.
94208 iterations done in 460.0 seconds. Should take 0.007497 days or 647.7s, finish Wed 7 Dec 2022 00:49:42.
96256 iterations done in 469.8 seconds. Should take 0.007493 days or 647.4s, finish Wed 7 Dec 2022 00:49:42.
98304 iterations done in 479.3 seconds. Should take 0.007486 days or 646.8s, finish Wed 7 Dec 2022 00:49:41.
100352 iterations done in 489.0 seconds. Should take 0.007481 days or 646.4s, finish Wed 7 Dec 2022 00:49:41.
102400 iterations done in 498.6 seconds. Should take 0.007476 days or 645.9s, finish Wed 7 Dec 2022 00:49:40.
104448 iterations done in 508.4 seconds. Should take 0.007473 days or 645.7s, finish Wed 7 Dec 2022 00:49:40.
106496 iterations done in 518.2 seconds. Should take 0.007471 days or 645.5s, finish Wed 7 Dec 2022 00:49:40.
108544 iterations done in 527.9 seconds. Should take 0.007468 days or 645.2s, finish Wed 7 Dec 2022 00:49:40.
110592 iterations done in 537.7 seconds. Should take 0.007465 days or 644.9s, finish Wed 7 Dec 2022 00:49:39.
112640 iterations done in 547.3 seconds. Should take 0.007460 days or 644.5s, finish Wed 7 Dec 2022 00:49:39.
114688 iterations done in 556.9 seconds. Should take 0.007455 days or 644.1s, finish Wed 7 Dec 2022 00:49:39.
116736 iterations done in 566.4 seconds. Should take 0.007450 days or 643.7s, finish Wed 7 Dec 2022 00:49:38.
118784 iterations done in 575.8 seconds. Should take 0.007443 days or 643.1s, finish Wed 7 Dec 2022 00:49:38.
120832 iterations done in 585.4 seconds. Should take 0.007439 days or 642.7s, finish Wed 7 Dec 2022 00:49:37.
122880 iterations done in 594.9 seconds. Should take 0.007433 days or 642.2s, finish Wed 7 Dec 2022 00:49:37.
124928 iterations done in 604.4 seconds. Should take 0.007429 days or 641.8s, finish Wed 7 Dec 2022 00:49:36.
126976 iterations done in 614.1 seconds. Should take 0.007425 days or 641.6s, finish Wed 7 Dec 2022 00:49:36.
129024 iterations done in 623.6 seconds. Should take 0.007421 days or 641.2s, finish Wed 7 Dec 2022 00:49:36.
131072 iterations done in 632.8 seconds. Should take 0.007413 days or 640.5s, finish Wed 7 Dec 2022 00:49:35.
Finished on Wed 7 Dec 2022 00:49:28. Proccessor time was 282.266 s.
Actual time was 632.8139346
Enter MRBtest2 to print 100493 digits
If you saved m3M, the difference between this and 3,014,991 known digits is 0.×
-100494
10
In[]:=
632/60.
Out[]=
10.5333
In[]:=
282/60.
Out[]=
4.7