std::frexp

Defined in header <cmath>

1	`float` `frexp(` `float` `arg,` `int*` `exp` `);`

(1)

1	`double` `frexp(` `double` `arg,` `int*` `exp` `);`

(2)

1	`long` `double` `frexp(` `long` `double` `arg,` `int*` `exp` `);`

(3)

1	`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.

#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

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`