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

[Boris Steipe]

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
> 
> 
> 
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