The Open Group Base Specifications Issue 7
IEEE Std 1003.1, 2013 Edition
Copyright © 2001-2013 The IEEE and The Open Group

#### NAME

> exp, expf, expl - exponential function

#### SYNOPSIS

> ``#include <math.h>
> double exp(double` x`);
> float expf(float` x`);
> long double expl(long double` x`);
> ``

#### DESCRIPTION

> [CX] The functionality described on this reference page is aligned with the ISO C standard. Any conflict between the requirements described here and the ISO C standard is unintentional. This volume of POSIX.1-2008 defers to the ISO C standard.

> These functions shall compute the base- e exponential of x.

> An application wishing to check for error situations should set errno to zero and call feclearexcept(FE_ALL_EXCEPT) before calling these functions. On return, if errno is non-zero or fetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has occurred.

#### RETURN VALUE

> Upon successful completion, these functions shall return the exponential value of x.

> If the correct value would cause overflow, a range error shall occur and exp(), expf(), and expl() shall return the value of the macro HUGE_VAL, HUGE_VALF, and HUGE_VALL, respectively.

> If the correct value would cause underflow, [MXX] and is not representable, a range error may occur, and exp(), expf(), and expl() shall return [MXX] 0.0, or (if the IEC 60559 Floating-Point option is not supported) an implementation-defined value no greater in magnitude than DBL_MIN, FLT_MIN, and LDBL_MIN, respectively.

> [MX] If x is NaN, a NaN shall be returned.

> If x is ±0, 1 shall be returned.

> If x is -Inf, +0 shall be returned.

> If x is +Inf, x shall be returned.

> [MXX] If the correct value would cause underflow, and is representable, a range error may occur and the correct value shall be returned.

#### ERRORS

> These functions shall fail if:

> Range Error
>   The result overflows.

>   If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then errno shall be set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the overflow floating-point exception shall be raised.

> These functions may fail if:

> Range Error
>   The result underflows.

>   If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then errno shall be set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the underflow floating-point exception shall be raised.

The following sections are informative.

#### EXAMPLES

> ##### Computing the Density of the Standard Normal Distribution

> This function shows an implementation for the density of the standard normal distribution using exp(). This example uses the constant M_PI which is part of the XSI option.

>     #include <math.h>

>     double
>     normal_density (double x)
>     {
>         return exp(-x*x/2) / sqrt (2*M_PI);
>     }

#### APPLICATION USAGE

> Note that for IEEE Std 754-1985 double, 709.8 < x implies exp(x) has overflowed. The value x < -708.4 implies exp(x) has underflowed.

> On error, the expressions (math_errhandling & MATH_ERRNO) and (math_errhandling & MATH_ERREXCEPT) are independent of each other, but at least one of them must be non-zero.

#### RATIONALE

> None.

#### FUTURE DIRECTIONS

> None.

#### SEE ALSO

> feclearexcept, fetestexcept, isnan, log

> XBD Treatment of Error Conditions for Mathematical Functions, <math.h>

#### CHANGE HISTORY

> First released in Issue 1. Derived from Issue 1 of the SVID.

#### Issue 5

> The DESCRIPTION is updated to indicate how an application should check for an error. This text was previously published in the APPLICATION USAGE section.

#### Issue 6

> The expf() and expl() functions are added for alignment with the ISO/IEC 9899:1999 standard.

> The DESCRIPTION, RETURN VALUE, ERRORS, and APPLICATION USAGE sections are revised to align with the ISO/IEC 9899:1999 standard.

> IEC 60559:1989 standard floating-point extensions over the ISO/IEC 9899:1999 standard are marked.

> IEEE Std 1003.1-2001/Cor 2-2004, item XSH/TC2/D6/26 is applied, adding the example to the EXAMPLES section.

#### Issue 7

> POSIX.1-2008, Technical Corrigendum 1, XSH/TC1-2008/0106 [68] and XSH/TC1-2008/0107 [68] are applied.

End of informative text.

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