Science Forums 2

[CraigD]

Originally Posted by Qfwfq

If you really find it important to improve precision on that computation you could always contruct an ad hoc numeric type or use a language which handles higher precision, perhaps Craig's favourite language would suit the purpose.

All of my favorite hand-made calculators are exact precision integer and rational number based, but I could cobble together trig and logarithm approximating functions to some defined precision pretty quickly, and solve



Using a simple binary search. An answer to a couple of thousand decimal digits precision shouldn’t be too hard.

I’ve lotsa work today, and play plans for tonight, but hopefully can post a result late tonight or tomorrow. As a teaser, here’s an approximation of using a common infinite series,

ZL HPM
s X=2
s A=0,(B,C)=X,(D,E)=1 F CT=1:1 D RD(.I,C,D),RA(.A,A,I),RM(.C,C,B),RM(.C,C,B),RA(.E,E,1),RM(.D,D,E),RA(.E,E,1),RM(.D,D,"-"_E) W CT,". ",A," =~",@A,! R R
1. 2/1 =~2
2. 2/31 =~.6666666666666666667
3. 14/151 =~.933333333333333333
4. 286/3151 =~.9079365079365079365
5. 2578/28351 =~.9093474426807760141
6. 141782/1559251 =~.9092961359628026295
7. 5529506/60810751 =~.9092974515196737419
8. 580598114/6385128751 =~.9092974264614476255
...
31. 53824986296478094273294897582567285743149004618784793429340024238/59194037845657181864228121483295877940276107097847234991455078125 =~.9092974268256816954

31 iterations gives about 65 digits precision.