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**x-1.0.
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 non-zero, an error has
occurred.
RETURN VALUE
Upon successful completion, these functions return e**x-1.0.
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 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 value of x is subnormal.
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
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)**n-1)/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 754-1985 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 non-zero.
RATIONALE
None.
FUTURE DIRECTIONS
None.
SEE ALSO
exp() , feclearexcept() , fetestexcept() , ilogb() , log1p() , the Base
Definitions volume of IEEE Std 1003.1-2001, 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) 2001-2003 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 original Standard can be obtained online
at http://www.opengroup.org/unix/online.html .