Logb

Defined in header <cmath>.

Description

Extracts the value of the unbiased radix-independent exponent from the floating-point argument num, and returns it as a floating-point value.
​The library provides overloads of std::logb for all cv-unqualified floating-point types as the type of the parameter num  (since C++23).

​Additional Overloads are provided for all integer types, which are treated as double.

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

Declarations

C++23

// 1)
constexpr /* floating-point-type */
            logb ( /* floating-point-type */ num );
// 2)
constexpr float logbf( float num );
// 3)
constexpr long double logbl( long double num );

Additional Overloads

// 4)
template< class Integer >
constexpr double logb ( Integer num );

C++11

// 1)
float logb ( float num );
// 2)
double logb ( double num );
// 3)
long double logb ( long double num );
// 4)
float logbf( float num );
// 5)
long double logbl( long double num );

Additional Overloads

// 6)
template< class Integer >
double logb ( Integer num );

Parameters

​num - floating-point or integer value

Return value

If no errors occur, the unbiased exponent of num 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 num is zero.

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

If num is ±0, -∞ is returned and FE_DIVBYZERO is raised If num is ±∞, +∞ is returned If num 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 num is ±0.

The value of the exponent returned by std::logb is always 1 less than the exponent returned by std::frexp because of the different normalization requirements: for the exponent e returned by std::logb, |num*r-e| is between 1 and r (typically between 1 and 2), but for the exponent e returned by std::frexp, |num*2-e| is between 0.5 and 1.

The additional overloads are not required to be provided exactly as Additional Overloads. They only need to be sufficient to ensure that for their argument num of integer type,
std::logb(num) has the same effect as std::logb(static_cast<double>(num)).

Examples

#include <cfenv>
#include <cmath>
#include <iostream>
#include <limits>
 
// #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";
}

Possible Result

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