# std::frexp

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< cpp‎ | numeric‎ | math

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

1-3) Decomposes given floating point value `arg` into a normalized fraction and an integral power of two.
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).

### Parameters

arg | - | floating point value
exp | - | pointer to integer value to store the exponent to

### Return value

If `arg` is zero, returns zero and stores zero in `*exp`.

Otherwise (if `arg` is not zero), if no errors occur, returns the value `x` in the range `(-1;-0.5], [0.5; 1)` and stores an integer value in *exp such that x×2(*exp)
=arg

If the value to be stored in `*exp` is outside the range of int, the behavior is unspecified.

If `arg` is not a floating-point number, the behavior is unspecified.

### Error handling

This function is not subject to any errors specified in math_errhandling

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

- If `arg` is ±0, it is returned, unmodified, and `0` is stored in *exp.
- If `arg` is ±∞, it is returned, and an unspecified value is stored in *exp.
- If `arg` is NaN, NaN is returned, and an unspecified value is stored in *exp.
- No floating-point exceptions are raised.
- If FLT_RADIX is 2 (or a power of 2), the returned value is exact, the current rounding mode is ignored

### Notes

On a binary system (where FLT_RADIX is `2`), `frexp` may be implemented as

    {
        *exp = (value == 0) ? 0 : (int)(1 + std::logb(value));
        return std::scalbn(value, -(*exp));
    }

The function `std::frexp`, together with its dual, std::ldexp, can be used to manipulate the representation of a floating-point number without direct bit manipulations.

### Example

Compares different floating-point decomposition functions

Run this code

    #include <iostream>
    #include <cmath>
    #include <limits>

    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';
    }

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

### See also

ldexp | multiplies a number by 2 raised to a power (function)
logb (C++11) | extracts exponent of the number (function)
ilogb (C++11) | extracts exponent of the number (function)
modf | decomposes a number into integer and fractional parts (function)
C documentation for frexp

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