std::ilogb, std::ilogbf, std::ilogbl

Defined in header `<cmath>`
int ilogb ( float arg ); int ilogbf( float arg );	(1)	(since C++11) (constexpr since C++23)
int ilogb ( double arg );	(2)	(since C++11) (constexpr since C++23)
int ilogb ( long double arg ); int ilogbl( long double arg );	(3)	(since C++11) (constexpr since C++23)
int ilogb ( IntegralType arg );	(4)	(since C++11) (constexpr since C++23)
#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.

Parameters

arg

-

floating point value

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.

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

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.

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

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gcd (C++17)
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frexpfrexpffrexpl (C++11)(C++11)	decomposes a number into significand and a power of 2 (function)
logblogbflogbl (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)