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'\" et
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.TH EXPM1 "3P" 2013 "IEEE/The Open Group" "POSIX Programmer's Manual"
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.SH PROLOG
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This manual page is part of the POSIX Programmer's Manual.
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The Linux implementation of this interface may differ (consult
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the corresponding Linux manual page for details of Linux behavior),
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or the interface may not be implemented on Linux.
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.SH NAME
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expm1,
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expm1f,
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expm1l
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\(em compute exponential functions
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.SH SYNOPSIS
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.LP
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.nf
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#include <math.h>
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.P
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double expm1(double \fIx\fP);
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float expm1f(float \fIx\fP);
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long double expm1l(long double \fIx\fP);
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.fi
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.SH DESCRIPTION
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The functionality described on this reference page is aligned with the
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ISO\ C standard. Any conflict between the requirements described here and the
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ISO\ C standard is unintentional. This volume of POSIX.1\(hy2008 defers to the ISO\ C standard.
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.P
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These functions shall compute \fIe\u\s-3x\s+3\d\fR\(mi1.0.
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.P
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An application wishing to check for error situations should set
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.IR errno
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to zero and call
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.IR feclearexcept (FE_ALL_EXCEPT)
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before calling these functions. On return, if
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.IR errno
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is non-zero or \fIfetestexcept\fR(FE_INVALID | FE_DIVBYZERO |
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FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has occurred.
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.SH "RETURN VALUE"
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Upon successful completion, these functions return
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\fIe\s-3\ux\d\s+3\fR\(mi1.0.
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.P
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If the correct value would cause overflow, a range error shall occur
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and
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\fIexpm1\fR(),
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\fIexpm1f\fR(),
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and
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\fIexpm1l\fR()
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shall return the value of the macro HUGE_VAL, HUGE_VALF, and HUGE_VALL,
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respectively.
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.P
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If
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.IR x
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is NaN, a NaN shall be returned.
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.P
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If
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.IR x
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is \(+-0, \(+-0 shall be returned.
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.P
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If
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.IR x
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is \(miInf, \(mi1 shall be returned.
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.P
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If
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.IR x
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is +Inf,
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.IR x
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shall be returned.
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.P
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If
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.IR x
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is subnormal, a range error may occur
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.br
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and
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.IR x
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should be returned.
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.P
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If
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.IR x
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is not returned,
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\fIexpm1\fR(),
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\fIexpm1f\fR(),
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and
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\fIexpm1l\fR()
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shall return an implementation-defined value no greater in magnitude
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than DBL_MIN, FLT_MIN, and LDBL_MIN, respectively.
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.SH ERRORS
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These functions shall fail if:
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.IP "Range\ Error" 12
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The result overflows.
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.RS 12
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.P
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If the integer expression (\fImath_errhandling\fR & MATH_ERRNO) is
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non-zero, then
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.IR errno
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shall be set to
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.BR [ERANGE] .
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If the integer expression (\fImath_errhandling\fR & MATH_ERREXCEPT) is
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non-zero, then the overflow floating-point exception shall be raised.
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.RE
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.P
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These functions may fail if:
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.IP "Range\ Error" 12
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The value of
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.IR x
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is subnormal.
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.RS 12
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.P
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If the integer expression (\fImath_errhandling\fR & MATH_ERRNO) is
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non-zero, then
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.IR errno
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shall be set to
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.BR [ERANGE] .
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If the integer expression (\fImath_errhandling\fR & MATH_ERREXCEPT) is
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non-zero, then the underflow floating-point exception shall be raised.
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.RE
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.LP
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.IR "The following sections are informative."
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.SH EXAMPLES
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None.
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.SH "APPLICATION USAGE"
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The value of
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.IR expm1 ( x )
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may be more accurate than
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.IR exp ( x )\(mi1.0
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for small values of
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.IR x .
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.P
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The
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\fIexpm1\fR()
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and
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\fIlog1p\fR()
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functions are useful for financial calculations of
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((1+\fIx\fR)\u\s-3\fIn\fR\s+3\d\(mi1)/\fIx\fR, namely:
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.sp
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.RS 4
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.nf
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\fB
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expm1(\fIn\fP * log1p(\fIx\fP))/\fIx\fP
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.fi \fR
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.P
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.RE
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.P
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when
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.IR x
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is very small (for example, when calculating small daily interest
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rates). These functions also simplify writing accurate inverse
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hyperbolic functions.
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.P
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For IEEE\ Std\ 754\(hy1985
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.BR double ,
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709.8 <
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.IR x
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implies
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.IR expm1 (\c
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.IR x )
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has overflowed.
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.P
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On error, the expressions (\fImath_errhandling\fR & MATH_ERRNO) and
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(\fImath_errhandling\fR & MATH_ERREXCEPT) are independent of each
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other, but at least one of them must be non-zero.
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.SH RATIONALE
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None.
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.SH "FUTURE DIRECTIONS"
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None.
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.SH "SEE ALSO"
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.IR "\fIexp\fR\^(\|)",
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.IR "\fIfeclearexcept\fR\^(\|)",
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.IR "\fIfetestexcept\fR\^(\|)",
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.IR "\fIilogb\fR\^(\|)",
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.IR "\fIlog1p\fR\^(\|)"
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.P
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The Base Definitions volume of POSIX.1\(hy2008,
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.IR "Section 4.19" ", " "Treatment of Error Conditions for Mathematical Functions",
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.IR "\fB<math.h>\fP"
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.SH COPYRIGHT
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Portions of this text are reprinted and reproduced in electronic form
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from IEEE Std 1003.1, 2013 Edition, Standard for Information Technology
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-- Portable Operating System Interface (POSIX), The Open Group Base
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Specifications Issue 7, Copyright (C) 2013 by the Institute of
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Electrical and Electronics Engineers, Inc and The Open Group.
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(This is POSIX.1-2008 with the 2013 Technical Corrigendum 1 applied.) In the
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event of any discrepancy between this version and the original IEEE and
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The Open Group Standard, the original IEEE and The Open Group Standard
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is the referee document. The original Standard can be obtained online at
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http://www.unix.org/online.html .
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Any typographical or formatting errors that appear
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in this page are most likely
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to have been introduced during the conversion of the source files to
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man page format. To report such errors, see
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https://www.kernel.org/doc/man-pages/reporting_bugs.html .
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