std::logb, std::logbf, std::logbl

Defined in header `<cmath>`
float logb ( float arg );	(1)	(since C++11) (constexpr since C++23)
float logbf( float arg );	(2)	(since C++11) (constexpr since C++23)
double logb ( double arg );	(3)	(since C++11) (constexpr since C++23)
long double logb ( long double arg );	(4)	(since C++11) (constexpr since C++23)
long double logbl( long double arg );	(5)	(since C++11) (constexpr since C++23)
double logb ( IntegralType arg );	(6)	(since C++11) (constexpr since C++23)

1-5) Extracts the value of the unbiased radix-independent exponent from the floating-point argument arg, and returns it as a floating-point value.

6) A set of overloads or a function template accepting an argument of any integral type. Equivalent to (3) (the argument is cast to double).

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

arg

-

floating point value

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 returned 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

Compares different floating-point decomposition functions

Run this code

#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";
}

Possible output:

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

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frexpfrexpffrexpl (C++11)(C++11)	decomposes a number into significand and a power of 2 (function)
ilogbilogbfilogbl (C++11)(C++11)(C++11)	extracts exponent of the number (function)
scalbnscalbnfscalbnlscalblnscalblnfscalblnl (C++11)(C++11)(C++11)(C++11)(C++11)(C++11)	multiplies a number by FLT_RADIX raised to a power (function)