[R-pkg-devel] How to get arbitrary precise inputs from R for an Rcpp package?

[Khue Tran]

Hi,

I am trying to create an Rcpp package that involves arbitrary precise
calculations. The function to calculate e^x below with 100 digits precision
works well with integers, but for decimals, since the input is a double,
the result differs a lot from the arbitrary precise result I got on
Wolfram.

I understand the results are different since 0.1 cannot be represented
precisely in binary with limited bits. It is possible to enter 1 then 10
and get the multiprecision division of these two integers to attain a more
precise 0.1 in C++, but this method won't work on a large scale. Thus, I am
looking for a general solution to get more precise inputs?

The dummy example is as follows:

library(Rcpp)

sourceCpp(code = '
#include <boost/multiprecision/cpp_dec_float.hpp>
#include <boost/math/special_functions/expm1.hpp>

// [[Rcpp::depends(BH)]]
// [[Rcpp::export]]
std::string calculateExp100(double x) {
  boost::multiprecision::cpp_dec_float_100 bx = x;
  boost::multiprecision::cpp_dec_float_100 expx = exp(bx);
  return expx.str(50);
}
')

[1] represents the R output and [W] for Wolfram results

calculateExp100(1) # Agrees with Wolfram answer all the way to the last
digit
[1] "2.7182818284590452353602874713526624977572470937"
[W] 2.7182818284590452353602874713526624977572470936999595749669676277...

calculateExp100(0.1) # Differs pretty significantly from Wolfram's answer
[1] "1.1051709180756476309466388234587796577416634163742"
[W] 1.1051709180756476248117078264902466682245471947375187187928632894...

I am currently trying to get precise inputs by taking strings instead of
numbers then writing a function to decompose the string into a rational
with the denominator in the form of 10^(-n) where n is the number of
decimal places. I am not sure if this is the only way or if there is a
better method out there that I do not know of, so if you can think of a
general way to get precise inputs from users, it will be greatly
appreciated!

Thank you!
Best,
Khue Tran

-- 
*Khue B. Tran (she/her/hers)*
tran3 using kenyon.edu | +1 (220) - 203 - 9306 | LinkedIn
<https://www.linkedin.com/in/tranbaokhue/>
Mathematics and Music Double Major, Kenyon College '25

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