IEEE Std 1003.1, 2013 Edition

Copyright © 2001-2013 The IEEE and The Open Group

exp, expf, expl - exponential function

#include <math.h>

double exp(doublex);

float expf(floatx);

long double expl(long doublex);

^{[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-

eexponential ofx.An application wishing to check for error situations should set

errnoto zero and callfeclearexcept(FE_ALL_EXCEPT) before calling these functions. On return, iferrnois non-zero orfetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has occurred.

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(), andexpl() 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, andexp(),expf(), andexpl() 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]}Ifxis NaN, a NaN shall be returned.If

xis ±0, 1 shall be returned.If

xis -Inf, +0 shall be returned.If

xis +Inf,xshall 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.

These functions shall fail if:

- Range Error
- The result overflows.
If the integer expression (

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

## 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); }

Note that for IEEE Std 754-1985

double, 709.8 <ximpliesexp(x) has overflowed. The valuex< -708.4 impliesexp(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.

None.

None.

feclearexcept,fetestexcept,isnan,logXBD

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

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

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

The

expf() andexpl() 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.

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

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