# exp, expf, expl

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< c‎ | numeric‎ | math

Defined in header `<math.h>` |  |
float expf( float arg ); | (1) | (since C99)
double exp( double arg ); | (2) |
long double expl( long double arg ); | (3) | (since C99)
Defined in header `<tgmath.h>` |  |
#define exp( arg ) | (4) | (since C99)

1-3) Computes the e (Euler's number, `2.7182818`) raised to the given power `arg`.
4) Type-generic macro: If `arg` has type long double, `expl` is called. Otherwise, if `arg` has integer type or the type double, `exp` is called. Otherwise, `expf` is called. If `arg` is complex or imaginary, then the macro invokes the corresponding complex function (cexpf, cexp, cexpl).

### Parameters

arg | - | floating point value

### Return value

If no errors occur, the base-e exponential of `arg` (earg
) is returned.

If a range error due to overflow occurs, `+HUGE_VAL`, `+HUGE_VALF`, or `+HUGE_VALL` is returned.

If a range error occurs due to underflow, the correct result (after rounding) is returned.

### Error handling

Errors are reported as specified in math_errhandling.

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

- If the argument is ±0, 1 is returned
- If the argument is -∞, +0 is returned
- If the argument is +∞, +∞ is returned
- If the argument is NaN, NaN is returned

### Notes

For IEEE-compatible type double, overflow is guaranteed if 709.8 < arg, and underflow is guaranteed if arg < -708.4.

### Example

Run this code

    #include <stdio.h>
    #include <math.h>
    #include <float.h>
    #include <errno.h>
    #include <fenv.h>
    #pragma STDC FENV_ACCESS ON
    int main(void)
    {
        printf("exp(1) = %f\n", exp(1));
        printf("FV of $100, continuously compounded at 3%% for 1 year = %f\n",
                100*exp(0.03));
        // special values
        printf("exp(-0) = %f\n", exp(-0.0));
        printf("exp(-Inf) = %f\n", exp(-INFINITY));
        //error handling
        errno = 0; feclearexcept(FE_ALL_EXCEPT);
        printf("exp(710) = %f\n", exp(710));
        if(errno == ERANGE) perror("    errno == ERANGE");
        if(fetestexcept(FE_OVERFLOW)) puts("    FE_OVERFLOW raised");
    }

Possible output:

    exp(1) = 2.718282
    FV of $100, continuously compounded at 3% for 1 year = 103.045453
    exp(-0) = 1.000000
    exp(-Inf) = 0.000000
    exp(710) = inf
        errno == ERANGE: Numerical result out of range
        FE_OVERFLOW raised

### References

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

  - 7.12.6.1 The exp functions (p: 242)

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

  - F.10.3.1 The exp functions (p: 520)

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

  - 7.12.6.1 The exp functions (p: 223)

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

  - F.9.3.1 The exp functions (p: 458)

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

  - 4.5.4.1 The exp function

### See also

exp2 exp2f exp2l (C99)(C99)(C99) | computes 2 raised to the given power (2x) (function)
expm1 expm1f expm1l (C99)(C99)(C99) | computes e raised to the given power, minus one (ex-1) (function)
log logf logl (C99)(C99) | computes natural (base-e) logarithm (ln(x)) (function)
cexp cexpf cexpl (C99)(C99)(C99) | computes the complex base-e exponential (function)
C++ documentation for exp

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