为什么将浮点表示与精度结合起来不起作用？

Question

WHy is below code not giving proper output till requested precision? Please note that since i am using std::fixed so i am expecting precision to be representing digits after decimal points. Hope thats correct?

#include <iostream>
#include <limits>
#include <cmath>
#include <iomanip>

int main()
{
    double d3 = 50388143.0682372156805328369140625;
    std::cout << "d3 = " << d3 << std::endl; 
    std::cout << std::setprecision(17) << std::fixed << "d3 = " << d3 << std::endl; 
    std::cout << std::setprecision(20) << std::fixed << "d3 = " << d3 << std::endl; 
}

Produces output as

d3 = 5.03881e+07
d3 = 50388143.06823721528053284   // See its different than original floating point
d3 = 50388143.06823721528053283691 // See its different than original floating point

Why isn't the output coming as

d3 = 5.03881e+07
d3 = 50388143.06823721568053283
d3 = 50388143.06823721568053283691

I was expecting the output digits to match with input digits till requested precision but its not the case. Why so?

Answer 1

d3 does not have the value OP expects.

---

double is typically a 64-bit object and so can exactly represent about 2 ⁶⁴ different values.

50388143.0682372156805328369140625 is not one of them.

Typical double is encoded as an integer (less than 2 ⁵³ ) times some power of 2. See dyadic rational .

The closest double is 1690745520189437 * pow(2,-25) or

50388143.068237215_2805328369140625   // closest double
50388143.068237215_6805328369140625   // OP's original code.
50388143.068237222_731113433837890625 // next best double

Printing 50388143.068237215_2802805328369140625 with setprecision(17) is expected to be:

50388143.06823721528053284

as seen by OP.