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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 dif-
       fer (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 feclearex-
       cept(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 excep-
       tion 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 indepen-
       dent 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, Stan-
       dard for Information Technology -- Portable Operating System Interface (POSIX), The Open Group Base  Specifica-
       tions  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 Stan-
       dard,  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)