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# std::ilogb

From cppreference.com
< cpp‎ | numeric‎ | math

Defined in header `<cmath>` |  |
int ilogb( float arg ); | (1) | (since C++11)
int ilogb( double arg ); | (2) | (since C++11)
int ilogb( long double arg ); | (3) | (since C++11)
int ilogb( Integral arg ); | (4) | (since C++11)
#define FP_ILOGB0 /*implementation-defined*/ | (5) | (since C++11)
#define FP_ILOGBNAN /*implementation-defined*/ | (6) | (since C++11)

1-3) Extracts the value of the unbiased exponent from the floating-point argument `arg`, and returns it as a signed integer 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).
5) Expands to integer constant expression whose value is either INT_MIN or -INT_MAX.
6) Expands to integer constant expression whose value is either INT_MIN or +INT_MAX.

Formally, the unbiased exponent is the integral part of log
r|arg| as a signed integral value, for non-zero `arg`, where `r` is std::numeric_limits<T>::radix and `T` is the floating-point type of `arg`.

### [edit] Parameters

arg | - | floating point value

### [edit] Return value

If no errors occur, the unbiased exponent of `arg` is returned as a signed int value.

If `arg` is zero, FP_ILOGB0 is returned.

If `arg` is infinite, INT_MAX is returned.

If `arg` is a NaN, FP_ILOGBNAN is returned.

If the correct result is greater than INT_MAX or smaller than INT_MIN, the return value is unspecified.

### [edit] Error handling

Errors are reported as specified in math_errhandling

A domain error or range error may occur if `arg` is zero, infinite, or NaN.

If the correct result is greater than INT_MAX or smaller than INT_MIN, a domain error or a range error may occur

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

- If the correct result is greater than INT_MAX or smaller than INT_MIN, FE_INVALID is raised.
- If `arg` is ±0, ±∞, or NaN, FE_INVALID is raised.
- In all other cases, the result is exact (FE_INEXACT is never raised) and the current rounding mode is ignored

### [edit] Notes

If `arg` is not zero, infinite, or NaN, the value returned is exactly equivalent to static_cast<int>(std::logb(arg))

POSIX requires that a domain error occurs if `arg` is zero, infinite, NaN, or if the correct result is outside of the range of int.

POSIX also requires that, on XSI-conformant systems, the value returned when the correct result is greater than INT_MAX is INT_MAX and the value returned when the correct result is less than INT_MIN is INT_MIN.

The correct result can be represented as int on all known implementations. For overflow to occur, INT_MAX must be less than LDBL_MAX_EXP*log2(FLT_RADIX) or INT_MIN must be greater than LDBL_MIN_EXP-LDBL_MANT_DIG)*log2(FLT_RADIX).

The value of the exponent returned by `std::ilogb` is always 1 less than the exponent retuned by std::frexp because of the different normalization requirements: for the exponent `e` returned by `std::ilogb`, |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 << "ilogb(0) = " << std::ilogb(0) << '\n';
        if(std::fetestexcept(FE_INVALID))
            std::cout << "    FE_INVALID 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
    ilogb(0) = -2147483648
        FE_INVALID raised

### [edit] See also

frexp | decomposes a number into significand and a power of 2 (function) [edit]
logb (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 ilogb

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