Just for your info:
> exp(mpfr("0.1", 152))
1 'mpfr' number of precision 152 bits
[1] 1.1051709180756476248117078264902466682245471948
So it looks like your approach of parsing the numbers yourself makes sense.
You can find the R parser here:
https://github.com/wch/r-source/blob/b64422334a8269535718efd9a1f969c94b103056/src/main/gram.y#L2577-L2705
I don't know how much of that you want to replicate, but I suppose
handling the weird cases (e.g. 0x1p1) the way R does will make it easier
for your users.
Duncan Murdoch
On 2024-07-18 4:29 p.m., Khue Tran wrote:
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
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