expm1 (3p)  Linux Manuals
expm1: compute exponential functions
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
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 nonzero 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 nonzero, 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 nonzero, then the underflow floatingpoint exception shall be raised.
The following sections are informative.
EXAMPLES
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
FUTURE DIRECTIONS
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 original Standard can be obtained online at http://www.opengroup.org/unix/online.html .
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>