std::logb,std::logbf,std::logbl(3)

NAME
std::logb,std::logbf,std::logbl - std::logb,std::logbf,std::logbl

Synopsis
   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

See also
   frexp
   frexpf decomposes a number into significand and a power of 2
   frexpl (function)
   (C++11)
   (C++11)
   ilogb
   ilogbf
   ilogbl extracts exponent of the number
   (C++11) (function)
   (C++11)
   (C++11)
   scalbn
   scalbnf
   scalbnl
   scalbln
   scalblnf
   scalblnl multiplies a number by FLT_RADIX raised to a power
   (C++11) (function)
   (C++11)
   (C++11)
   (C++11)
   (C++11)
   (C++11)