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std::ilogb

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int ilogb( float arg );
 ( C++11)
int ilogb( double arg );
 ( C++11)
int ilogb( long double arg );
 ( C++11)
double ilogb( Integral arg );
 ( C++11)
#define FP_ILOGB0 /*implementation-defined*/
 ( C++11)
#define FP_ILOGBNAN /*implementation-defined*/
 ( C++11)

Extracts the value of the exponent from the floating-point argument arg, and returns it as a signed integer value. Formally, the result is the integral part of log
r|arg| as a signed integral value, for non-zero arg, where r is std::numeric_limits<T>::radix and T is the floating-point type of arg.

arg
:
floating point value
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The floating-point exponent, cast to integer, as if by static_cast<int>(std::logb(arg)).

, arg , FP_ILOGB0 .
:
Domain or range error may occur if arg is zero, FP_ILOGB0 is returned in that case.
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, arg , MAX_INT .
:
Domain or range error may occur if arg is infinite, MAX_INT is returned in that case.
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, arg NaN, FP_ILOGBNAN .
:
Domain or range error may occur if arg is NaN, FP_ILOGBNAN is returned in that case.
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int, .
:
If the result cannot be represented as int, the result is undefined.
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std::ilogb 1 std::frexp - : e std::ilogb, |arg*r-e
| 1 r ( 1 2), e std::frexp, |arg*2-e
| 0.5 1.
:
The value of the exponent returned by std::ilogb is always 1 less than the exponent retuned by std::frexp because of the different normalization requirements: for the exponent e returned by std::ilogb, |arg*r-e
| is between 1 and r (typically between 1 and 2), but for the exponent e returned by std::frexp, |arg*2-e
| is between 0.5 and 1.
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Compares different floating-point decomposition functions
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#include <iostream>
#include <cmath>
#include <limits>
int main()
{
    double f = 123.45;
    std::cout << "Given the number " << f << " or " << std::hexfloat
              << f << std::defaultfloat << " in hex,\n";

    double f3;
    double f2 = std::modf(f, &f3);
    std::cout << "modf() makes " << f3 << " + " << f2 << '\n';

    int i;
    f2 = std::frexp(f, &i);
    std::cout << "frexp() makes " << f2 << " * 2^" << i << '\n';

    i = std::ilogb(f);
    std::cout << "logb()/ilogb() make " << f/std::scalbn(1.0, i) << " * "
              << std::numeric_limits<double>::radix
              << "^" << std::ilogb(f) << '\n';
}

: 

Given the number 123.45 or 0x1.edccccccccccdp+6 in hex,
modf() makes 123 + 0.45
frexp() makes 0.964453 * 2^7
logb()/ilogb() make 1.92891 * 2^6

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