std::logb

float       logb( float arg );

double      logb( double arg );

long double logb( long double arg );

double      logb( IntegralType arg );

Formally, the unbiased exponent is the signed integral part of log
r|arg| (returned by this function as a floating-point value), for non-zero arg, where r is std::numeric_limits<T>::radix and T is the floating-point type of arg. If arg is subnormal, it is treated as though it was normalized.

Parameters

Return value

If no errors occur, the unbiased exponent of arg is returned as a signed floating-point value.

If a domain error occurs, an implementation-defined value is returned.

If a pole error occurs, -HUGE_VAL, -HUGE_VALF, or -HUGE_VALL is returned.

Error handling

Errors are reported as specified in math_errhandling.

Domain or range error may occur if arg is zero.

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

• If arg is ±0, -∞ is returned and FE_DIVBYZERO is raised.
• If arg is ±∞, +∞ is returned
• If arg is NaN, NaN is returned.
• In all other cases, the result is exact (FE_INEXACT is never raised) and the current rounding mode is ignored

Notes

POSIX requires that a pole error occurs if arg is ±0.

The value of the exponent returned by std::logb is always 1 less than the exponent retuned by std::frexp because of the different normalization requirements: for the exponent e returned by std::logb, |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.

Example

#include <iostream>
#include <cmath>
#include <limits>
#include <cfenv>
#pragma STDC FENV_ACCESS ON
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';
 
    // error handling
    std::feclearexcept(FE_ALL_EXCEPT);
    std::cout << "logb(0) = " << std::logb(0) << '\n';
    if(std::fetestexcept(FE_DIVBYZERO))
        std::cout << "    FE_DIVBYZERO raised\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
logb(0) = -Inf
    FE_DIVBYZERO raised

See also