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

[Jeff Newmiller]

I don't know much about Rmpfr, but it doesn't look like your "pi" or "sqrt" or "exp" are being handled by that package, so I am not really seeing why your result should be more accurate when you have loaded that package.
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Sent from my phone. Please excuse my brevity.

On July 2, 2015 7:28:19 AM PDT, 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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>
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