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# std::logb

From cppreference.com
< cpp‎ | numeric‎ | math

Defined in header `<cmath>` |  |
float logb( float arg ); | (1) | (since C++11)
double logb( double arg ); | (2) | (since C++11)
long double logb( long double arg ); | (3) | (since C++11)
double logb( Integral arg ); | (4) | (since C++11)

1-3) Extracts the value of the unbiased radix-independent exponent from the floating-point argument `arg`, and returns it as a floating-point value.
4) A set of overloads or a function template accepting an argument of any integral type. Equivalent to (2) (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.

### [edit] Parameters

arg | - | floating point value

### [edit] 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.

### [edit] 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

### [edit] 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.

### [edit] 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

### [edit] See also

frexp | decomposes a number into significand and a power of 2 (function) [edit]
ilogb (C++11) | extracts exponent of the number (function) [edit]
scalbn scalbln (C++11)(C++11) | multiplies a number by FLT_RADIX raised to a power (function) [edit]
C documentation for logb

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