[R] Ramanujan and the accuracy of floating point computations - using Rmpfr in R

[Aditya Singh]

Ravi

1. You may want to check the sqrt too.

2. Why not take log and try?

Aditya



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On Thu 2 Jul, 2015 10:18 AM PDT Boris Steipe wrote:

>Just a wild guess, but did you check exactly which operations are actually done to high precision? Obviously you will need high-resolution representations of pi and e to get an improved result.
>
>B.
>
>
>
>On Jul 2, 2015, at 10:28 AM, Ravi Varadhan <ravi.varadhan at jhu.edu> wrote:
>
>> Hi,
>> 
>> Ramanujan supposedly discovered that the number, 163, has this interesting property that exp(sqrt(163)*pi), which is obviously a transcendental number, is real close to an integer (close to 10^(-12)).
>> 
>> If I compute this using the Wolfram alpha engine, I get:
>> 262537412640768743.99999999999925007259719818568887935385...
>> 
>> When I do this in R 3.1.1 (64-bit windows), I get:
>> 262537412640768256.0000
>> 
>> The absolute error between the exact and R's value is 488, with a relative error of about 1.9x10^(-15).
>> 
>> In order to replicate Wolfram Alpha, I tried doing this in "Rmfpr" but I am unable to get accurate results:
>> 
>> library(Rmpfr)
>> 
>> 
>> exp(sqrt(163) * mpfr(pi, 120))
>> 
>> 1 'mpfr' number of precision  120   bits
>> 
>> [1] 262537412640767837.08771354274620169031
>> 
>> The above answer is not only inaccurate, but it is actually worse than the answer using the usual double precision.  Any thoughts as to what I am doing wrong?
>> 
>> Thank you,
>> Ravi
>> 
>> 
>> 
>> 	[[alternative HTML version deleted]]
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>______________________________________________
>R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
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