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.TH EXPM1 "3P" 2013 "IEEE/The Open Group" "POSIX Programmer's Manual"
.SH 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.

.SH NAME
expm1,
expm1f,
expm1l
\(em compute exponential functions
.SH SYNOPSIS
.LP
.nf
#include <math.h>
.P
double expm1(double \fIx\fP);
float expm1f(float \fIx\fP);
long double expm1l(long double \fIx\fP);
.fi
.SH 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\(hy2008 defers to the ISO\ C standard.
.P
These functions shall compute \fIe\u\s-3x\s+3\d\fR\(mi1.0.
.P
An application wishing to check for error situations should set
.IR errno
to zero and call
.IR feclearexcept (FE_ALL_EXCEPT)
before calling these functions. On return, if
.IR errno
is non-zero or \fIfetestexcept\fR(FE_INVALID | FE_DIVBYZERO |
FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has occurred.
.SH "RETURN VALUE"
Upon successful completion, these functions return
\fIe\s-3\ux\d\s+3\fR\(mi1.0.
.P
If the correct value would cause overflow, a range error shall occur
and
\fIexpm1\fR(),
\fIexpm1f\fR(),
and
\fIexpm1l\fR()
shall return the value of the macro HUGE_VAL, HUGE_VALF, and HUGE_VALL,
respectively.
.P
If
.IR x
is NaN, a NaN shall be returned.
.P
If
.IR x
is \(+-0, \(+-0 shall be returned.
.P
If
.IR x
is \(miInf, \(mi1 shall be returned.
.P
If
.IR x
is +Inf,
.IR x
shall be returned.
.P
If
.IR x
is subnormal, a range error may occur
.br
and
.IR x
should be returned.
.P
If
.IR x
is not returned,
\fIexpm1\fR(),
\fIexpm1f\fR(),
and
\fIexpm1l\fR()
shall return an implementation-defined value no greater in magnitude
than DBL_MIN, FLT_MIN, and LDBL_MIN, respectively.
.SH ERRORS
These functions shall fail if:
.IP "Range\ Error" 12
The result overflows.
.RS 12 
.P
If the integer expression (\fImath_errhandling\fR & MATH_ERRNO) is
non-zero, then
.IR errno
shall be set to
.BR [ERANGE] .
If the integer expression (\fImath_errhandling\fR & MATH_ERREXCEPT) is
non-zero, then the overflow floating-point exception shall be raised.
.RE
.P
These functions may fail if:
.IP "Range\ Error" 12
The value of
.IR x
is subnormal.
.RS 12 
.P
If the integer expression (\fImath_errhandling\fR & MATH_ERRNO) is
non-zero, then
.IR errno
shall be set to
.BR [ERANGE] .
If the integer expression (\fImath_errhandling\fR & MATH_ERREXCEPT) is
non-zero, then the underflow floating-point exception shall be raised.
.RE
.LP
.IR "The following sections are informative."
.SH EXAMPLES
None.
.SH "APPLICATION USAGE"
The value of
.IR expm1 ( x )
may be more accurate than
.IR exp ( x )\(mi1.0
for small values of
.IR x .
.P
The
\fIexpm1\fR()
and
\fIlog1p\fR()
functions are useful for financial calculations of
((1+\fIx\fR)\u\s-3\fIn\fR\s+3\d\(mi1)/\fIx\fR, namely:
.sp
.RS 4
.nf
\fB
expm1(\fIn\fP * log1p(\fIx\fP))/\fIx\fP
.fi \fR
.P
.RE
.P
when
.IR x
is very small (for example, when calculating small daily interest
rates). These functions also simplify writing accurate inverse
hyperbolic functions.
.P
For IEEE\ Std\ 754\(hy1985
.BR double ,
709.8 <
.IR x
implies
.IR expm1 (\c
.IR x )
has overflowed.
.P
On error, the expressions (\fImath_errhandling\fR & MATH_ERRNO) and
(\fImath_errhandling\fR & MATH_ERREXCEPT) are independent of each
other, but at least one of them must be non-zero.
.SH RATIONALE
None.
.SH "FUTURE DIRECTIONS"
None.
.SH "SEE ALSO"
.IR "\fIexp\fR\^(\|)",
.IR "\fIfeclearexcept\fR\^(\|)",
.IR "\fIfetestexcept\fR\^(\|)",
.IR "\fIilogb\fR\^(\|)",
.IR "\fIlog1p\fR\^(\|)"
.P
The Base Definitions volume of POSIX.1\(hy2008,
.IR "Section 4.19" ", " "Treatment of Error Conditions for Mathematical Functions",
.IR "\fB<math.h>\fP"
.SH 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 .

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