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
       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.1-2017
       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.

       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.1-2017, Section 4.20, Treatment of
       Error Conditions for Mathematical Functions, <math.h>

COPYRIGHT
       Portions of this text are reprinted and reproduced in electronic form
       from IEEE Std 1003.1-2017, Standard for Information Technology --
       Portable Operating System Interface (POSIX), The Open Group Base
       Specifications Issue 7, 2018 Edition, Copyright (C) 2018 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 .

       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 .

IEEE/The Open Group                  2017                            EXPM1(3P)