std::ilogb

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ilogb
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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.

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),

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

See also

 decomposes a number into significand and a power of 2
(function)
(C++11)
 extracts exponent of the number
(function)
(C++11)(C++11)
 multiplies a number by FLT_RADIX raised to a power
(function)
C documentation for ilogb
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