A fast method to round a double to a 32-bit int explained

Question

When reading Lua\'s source code, I noticed that Lua uses a macro to round a double to a 32-bit int. I extracted the macro

Answer 1

Here is a simpler implementation of the above Lua trick:

/**
 * Round to the nearest integer.
 * for tie-breaks: round half to even (bankers' rounding)
 * Only works for inputs in the range: [-2^51, 2^51]
 */
inline double rint(double d)
{
    double x = 6755399441055744.0;  // 2^51 + 2^52
    return d + x - x;
}

The trick works for numbers with absolute value < 2 ^ 51.

This is a little program to test it: ideone.com

#include 

int main()
{
    // round to nearest integer
    printf("%.1f, %.1f\n", rint(-12345678.3), rint(-12345678.9));

    // test tie-breaking rule
    printf("%.1f, %.1f, %.1f, %.1f\n", rint(-24.5), rint(-23.5), rint(23.5), rint(24.5));      
    return 0;
}

// output:
// -12345678.0, -12345679.0
// -24.0, -24.0, 24.0, 24.0