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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 (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**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  inter-
       est  rates).  These  functions  also  simplify writing accurate inverse
       hyperbolic functions.
       For IEEE Std 754-1985 double, 709.8 < x implies  expm1(  x)  has  over-
       flowed.
       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 Def-
       initions 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 .

IEEE/The Open Group                  2003                            EXPM1(3P)