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.

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.