
EXPM1(P) POSIX Programmer's Manual EXPM1(P)
NAME
expm1, expm1f, expm1l  compute exponential functions
SYNOPSIS
#include <math.h>
double expm1(double x);
float expm1f(float x);
long double expm1l(long double x);
DESCRIPTION
These functions shall compute e**x1.0.
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 nonzero,
an error has occurred.
RETURN VALUE
Upon successful completion, these functions return e**x1.0.
If the correct value would cause overflow, a range error shall occur and expm1(),
expm1f(), and expm1l() shall return the value of the macro HUGE_VAL, HUGE_VALF, and
HUGE_VALL, respectively.
If x is NaN, a NaN shall be returned.
If x is +0, +0 shall be returned.
If x is Inf, 1 shall be returned.
If x is +Inf, x shall be returned.
If x is subnormal, a range error may occur and x should be returned.
ERRORS
These functions shall fail if:
Range Error
The result overflows.
If the integer expression (math_errhandling & MATH_ERRNO) is nonzero, then errno shall be
set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non
zero, then the overflow floatingpoint exception shall be raised.
These functions may fail if:
Range Error
The value of x is subnormal.
If the integer expression (math_errhandling & MATH_ERRNO) is nonzero, then errno shall be
set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non
zero, then the underflow floatingpoint exception shall be raised.
The following sections are informative.
EXAMPLES
None.
APPLICATION USAGE
The value of expm1(x) may be more accurate than exp(x)1.0 for small values of x.
The expm1() and log1p() functions are useful for financial calculations of ((1+x)**n1)/x,
namely:
expm1(n * log1p(x))/x
when x is very small (for example, when calculating small daily interest rates). These
functions also simplify writing accurate inverse hyperbolic functions.
For IEEE Std 7541985 double, 709.8 < x implies expm1( x) has overflowed.
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 nonzero.
RATIONALE
None.
FUTURE DIRECTIONS
None.
SEE ALSO
exp() , feclearexcept() , fetestexcept() , ilogb() , log1p() , the Base Definitions volume
of IEEE Std 1003.12001, Section 4.18, Treatment of Error Conditions for Mathematical
Functions, <math.h>
COPYRIGHT
Portions of this text are reprinted and reproduced in electronic form from IEEE Std
1003.1, 2003 Edition, Standard for Information Technology  Portable Operating System
Interface (POSIX), The Open Group Base Specifications Issue 6, Copyright (C) 20012003 by
the Institute of Electrical and Electronics Engineers, Inc and The Open Group. In the
event of any discrepancy between this version and the original IEEE and The Open Group
Standard, the original IEEE and The Open Group Standard is the referee document. The orig
inal Standard can be obtained online at http://www.opengroup.org/unix/online.html .
IEEE/The Open Group 2003 EXPM1(P) 
