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exp

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

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#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:

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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

(C99)(C99)(C99)
 computes 2 raised to the given power (2x)
(function)
(C99)(C99)(C99)
 computes e raised to the given power, minus one (ex-1)
(function)
(C99)(C99)
 computes natural (base-e) logarithm (ln(x))
(function)
(C99)(C99)(C99)
 computes the complex base-e exponential
(function)
C++ documentation for exp
doc_C_Language
doc_C_Language
2025-01-10 15:47:30
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