# exp (3p)

# PROLOG

This manual page is part of the POSIX Programmer's Manual. The Linux implementation of this interface may differ (consult the corresponding Linux manual page for details of Linux behavior), or the interface may not be implemented on Linux.# NAME

exp, expf, expl — exponential function# SYNOPSIS

#include <math.h>

double exp(doublex); float expf(floatx); long double expl(long doublex);

# DESCRIPTION

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, and is not representable, a range error may occur, and

*exp*(),

*expf*(), and

*expl*() shall return 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. 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. 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 (

These functions may fail if:
*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.- 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*()*The Base Definitions volume of POSIX.1‐2008,*

*log*()*Section 4.19*,

*Treatment of Error Conditions for Mathematical Functions*,

**<math.h>**