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 .