# frexp, frexpf, frexpl

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< c‎ | numeric‎ | math

Defined in header `<math.h>` |  |
float frexpf( float arg, int* exp ); | (1) | (since C99)
double frexp( double arg, int* exp ); | (2) |
long double frexpl( long double arg, int* exp ); | (3) | (since C99)
Defined in header `<tgmath.h>` |  |
#define frexp( arg, exp ) | (4) | (since C99)

1-3) Decomposes given floating point value `x` into a normalized fraction and an integral power of two.
4) Type-generic macro: If `arg` has type long double, `frexpl` is called. Otherwise, if `arg` has integer type or the type double, `frexp` is called. Otherwise, `frexpf` is called, respectively.

### 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 + logb(value));
        return scalbn(value, -(*exp));
    }

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

### Example

Run this code

    #include <stdio.h>
    #include <math.h>
    #include <float.h>

    int main(void)
    {
        double f = 123.45;
        printf("Given the number %.2f or %a in hex,\n", f, f);

        double f3;
        double f2 = modf(f, &f3);
        printf("modf() makes %.0f + %.2f\n", f3, f2);

        int i;
        f2 = frexp(f, &i);
        printf("frexp() makes %f * 2^%d\n", f2, i);

        i = ilogb(f);
        printf("logb()/ilogb() make %f * %d^%d\n", f/scalbn(1.0, i), FLT_RADIX, i);
    }

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

### References

- C11 standard (ISO/IEC 9899:2011):

  - 7.12.6.4 The frexp functions (p: 243)

  - 7.25 Type-generic math <tgmath.h> (p: 373-375)

  - F.10.3.4 The frexp functions (p: 521)

- C99 standard (ISO/IEC 9899:1999):

  - 7.12.6.4 The frexp functions (p: 224)

  - 7.22 Type-generic math <tgmath.h> (p: 335-337)

  - F.9.3.4 The frexp functions (p: 458)

- C89/C90 standard (ISO/IEC 9899:1990):

  - 4.5.4.2 The frexp function

### See also

ldexp ldexpf ldexpl (C99)(C99) | multiplies a number by 2 raised to a power (function)
logb logbf logbl (C99)(C99)(C99) | extracts exponent of the given number (function)
ilogb ilogbf ilogbl (C99)(C99)(C99) | extracts exponent of the given number (function)
modf modff modfl (C99)(C99) | breaks a number into integer and fractional parts (function)

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