EXPM1(3P)                                           POSIX Programmer's Manual                                          EXPM1(3P)



PROLOG
       This  manual  page is part of the POSIX Programmer's Manual.  The Linux implementation of this interface may differ (con-
       sult 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**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  inte-
       ger  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  inte-
       ger  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,  Copy-
       right (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.open-
       group.org/unix/online.html .



IEEE/The Open Group                                           2003                                                     EXPM1(3P)