问如何计算32位浮点感应器？

EN

#include <iostream>
#include <iomanip>

/*
https://en.wikipedia.org/wiki/Machine_epsilon#How_to_determine_machine_epsilon
*/

typedef union
{
    int32_t i32;
    float   f32;
} fi32_t;

float float_epsilon(float nbr)
{
    fi32_t flt;
    flt.f32 = nbr;
    flt.i32++;
    return (flt.f32 - nbr);
}

int main()
{
    // How to calculate 32-bit floating-point epsilon?

    const float one {1.}, ten_mills {10e6};
    std::cout << "epsilon for number " << one << " is:\n"
        << std::fixed << std::setprecision(25)
        << float_epsilon(one)
        << std::defaultfloat << "\n\n";

    std::cout << "epsilon for number " << ten_mills << " is:\n"
        << std::fixed << std::setprecision(25)
        << float_epsilon(ten_mills)
        << std::defaultfloat << "\n\n";


    // In book Game Engine Architecture : "..., let’s say we use a
    // floating-point variable to track absolute game time in seconds.
    // How long can we run our game before the magnitude of our clock
    // variable gets so large that adding 1/30th of a second to it no
    // longer changes its value? The answer is roughly 12.9 days."
    // Why 12.9 days, how to calculate it ?

    const float one_30th {1.f/30}, day_sec {60*60*24};
    float time_sec {}, time_sec_old {};

    while ((time_sec += one_30th) > time_sec_old)
    {
        time_sec_old = time_sec;
    }

    std::cout << "We can run our game for "
        << std::fixed << std::setprecision(5)
        << (time_sec / day_sec)
        << std::defaultfloat << " days.\n";


    return EXIT_SUCCESS;
}

epsilon for number 1 is:
0.0000001192092895507812500

epsilon for number 10000000 is:
1.0000000000000000000000000

We can run our game for 12.13630 days.