使用 boost lib 的更高精度浮点数(高于 16 位)

问题描述

我正在模拟物理实验，所以我需要非常高的浮点精度(超过 16 位).我使用 Boost.Multiprecision，但是无论我尝试什么，我都无法获得高于 16 位的精度.我用C++和eclipse编译器运行模拟，例如:

I am running a simulation of physical experiments, so I need really high floating point precision (more than 16 digits). I use Boost.Multiprecision, however I can't get a precision higher than 16 digits, no matter what I tried. I run the simulation with C++ and eclipse compiler, for example:

#include <boost/math/constants/constants.hpp>
#include <boost/multiprecision/cpp_dec_float.hpp>
#include <iostream>
#include <limits>

using boost::multiprecision::cpp_dec_float_50;

void main()
{
    cpp_dec_float_50 my_num= cpp_dec_float_50(0.123456789123456789123456789);
    std::cout.precision(std::numeric_limits<cpp_dec_float_50>::digits10);
    std::cout << my_num << std::endl;
}

输出为:

0.12345678912345678379658409085095627233386039733887
                   ^

但应该是:

0.123456789123456789123456789

如您所见，在 16 位数字之后是不正确的.为什么?

As you can see, after 16 digits it is incorrect. Why?

推荐答案

您的问题在这里:

cpp_dec_float_50 my_num = cpp_dec_float_50(0.123456789123456789123456789);
                                            ^ // This number is a double!

编译器不使用任意精度的浮点文字，而是使用 IEEE-754 doubles，它们具有有限精度.在这种情况下，与您所写数字最接近的 double 是:

The compiler does not use arbitrary-precision floating point literals, and instead uses IEEE-754 doubles, which have finite precision. In this case, the closest double to the number you have written is:

0.1234567891234567837965840908509562723338603973388671875

并将其打印到小数点后 50 位确实可以提供您正在观察的输出.

And printing it to the 50th decimal does indeed give the output you are observing.

您想要的是从字符串构造任意精度的浮点数(演示)::>

What you want is to construct your arbitrary-precision float from a string instead (demo):

#include <boost/math/constants/constants.hpp>
#include <boost/multiprecision/cpp_dec_float.hpp>
#include <iostream>
#include <limits>

using boost::multiprecision::cpp_dec_float_50;

int main() {
    cpp_dec_float_50 my_num = cpp_dec_float_50("0.123456789123456789123456789");
    std::cout.precision(std::numeric_limits<cpp_dec_float_50>::digits10);
    std::cout << my_num << std::endl;
}

输出:

0.123456789123456789123456789

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