Ramanujan and the accuracy of floating point computations - using Rmpfr in R
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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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 [[alternative HTML version deleted]]
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