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

1-3) 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.(since C++23)

S) The SIMD overload performs an element-wise std::logb on v_num.

(See math-floating-point and deduced-simd-t for their definitions.)

(since C++26)

A) Additional overloads are provided for all integer types, which are treated as double.

(since C++11)

Formally, the unbiased exponent is the signed integral part of logr|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.

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 (A). 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)).

[edit] Example

Compares different floating-point decomposition functions:

Run this code

#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 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