float.cpp

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

#define HALF_EXPONENT 5
#define HALF_FRACTION (16-HALF_EXPONENT-1)

#define SINGLE_EXPONENT 8
#define SINGLE_FRACTION (32-SINGLE_EXPONENT-1)

#define DOUBLE_EXPONENT 11
#define DOUBLE_FRACTION (64-DOUBLE_EXPONENT-1)

double resolve(double v, int exponent, int fraction) {
    auto raw = *(uint64_t *)&v;
    auto me = (uint64_t(1)<<DOUBLE_EXPONENT) - 1;
    auto mf = (uint64_t(1)<<DOUBLE_FRACTION) - 1;
    auto s = (raw >> (DOUBLE_EXPONENT+DOUBLE_FRACTION)) & 1;
    auto e = (raw >> DOUBLE_FRACTION & me) - (me>>1);
    auto f = 1.0 + double(raw & mf)/mf;

    auto nme = (uint64_t(1)<<exponent) - 1;
    auto nmf = (uint64_t(1)<<fraction) - 1;
    auto ne = e + (nme>>1);
    auto nf = static_cast<uint64_t>((f - 1.0) * (nmf+1));
    auto layout = s << (exponent + fraction) | ne << fraction | nf;
    
    // auto min = pow(2, 1 - (nme>>1)) * (1.0/(nmf+1));
    auto max = pow(2, (nme-1) - (nme>>1))*(1.0+double(nmf)/(nmf+1));
    
    printf("%.8f %.8f %#llx MAX=%.8f [%lld,%llu]\n",  v, pow(2, e)*(1.0+double(nf)/(nmf+1)), layout, max, 1 - (nme>>1), (nme-1) - (nme>>1));
    return 0;
}

int main(int argc, char* argv[]) {
    for (auto i = 1; i < argc; i++)
    {
        double v = atof(argv[i]);
        printf("%.8f %#016llx\n", v, *(uint64_t *)&v);
        resolve(v, DOUBLE_EXPONENT, DOUBLE_FRACTION);
        resolve(v, SINGLE_EXPONENT, SINGLE_FRACTION);
        resolve(v, HALF_EXPONENT, HALF_FRACTION);
    }
    
    return 0;
}