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

       The functionality described on this reference page is aligned with the ISO C standard. Any
       conflict between the requirements described here and the ISO C standard is  unintentional.
       This volume of POSIX.1‐2008 defers to the ISO C standard.

       These functions shall compute ex−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 ex−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.

       If x is not returned, expm1(), expm1f(), and  expm1l()  shall  return  an  implementation-
       defined value no greater in magnitude than DBL_MIN, FLT_MIN, and LDBL_MIN, respectively.

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 POSIX.1‐2008, Section 4.19, 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, 2013 Edition, Standard for Information Technology  --  Portable  Operating  System
       Interface  (POSIX),  The Open Group Base Specifications Issue 7, Copyright (C) 2013 by the
       Institute of Electrical and Electronics Engineers, Inc  and  The  Open  Group.   (This  is
       POSIX.1-2008  with  the  2013  Technical  Corrigendum  1  applied.)  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.unix.org/online.html .

       Any typographical or formatting errors that appear in this page are most  likely  to  have
       been  introduced  during  the conversion of the source files to man page format. To report
       such errors, see https://www.kernel.org/doc/man-pages/reporting_bugs.html .