mirror of https://github.com/mkerrisk/man-pages
126 lines
3.8 KiB
Plaintext
126 lines
3.8 KiB
Plaintext
.\" Copyright (c) 2001-2003 The Open Group, All Rights Reserved
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.TH "EXPM1" 3P 2003 "IEEE/The Open Group" "POSIX Programmer's Manual"
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.\" expm1
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.SH NAME
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expm1, expm1f, expm1l \- compute exponential functions
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.SH SYNOPSIS
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.LP
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\fB#include <math.h>
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.br
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.sp
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double expm1(double\fP \fIx\fP\fB);
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.br
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float expm1f(float\fP \fIx\fP\fB);
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.br
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long double expm1l(long double\fP \fIx\fP\fB);
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.br
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\fP
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.SH DESCRIPTION
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.LP
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These functions shall compute \fIe**x\fP-1.0.
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.LP
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An application wishing to check for error situations should set \fIerrno\fP
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to zero and call
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\fIfeclearexcept\fP(FE_ALL_EXCEPT) before calling these functions.
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On return, if \fIerrno\fP is non-zero or
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\fIfetestexcept\fP(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW)
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is non-zero, an error has occurred.
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.SH RETURN VALUE
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.LP
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Upon successful completion, these functions return \fIe**x\fP-1.0.
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.LP
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If the correct value would cause overflow, a range error shall occur
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and \fIexpm1\fP(), \fIexpm1f\fP(), and \fIexpm1l\fP()
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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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.LP
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If
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\fIx\fP is NaN, a NaN shall be returned.
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.LP
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If \fIx\fP is \(+-0, \(+-0 shall be returned.
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.LP
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If \fIx\fP is -Inf, -1 shall be returned.
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.LP
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If \fIx\fP is +Inf, \fIx\fP shall be returned.
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.LP
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If \fIx\fP is subnormal, a range error may occur and \fIx\fP should
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be returned.
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.SH ERRORS
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.LP
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These functions shall fail if:
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.TP 7
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Range\ Error
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The result overflows.
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.LP
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If the integer expression (math_errhandling & MATH_ERRNO) is non-zero,
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then \fIerrno\fP shall be set to [ERANGE]. If the
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integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero,
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then the overflow floating-point exception shall be
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raised.
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.sp
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.LP
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These functions may fail if:
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.TP 7
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Range\ Error
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The value of \fIx\fP is subnormal.
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.LP
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If the integer expression (math_errhandling & MATH_ERRNO) is non-zero,
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then \fIerrno\fP shall be set to [ERANGE]. If the
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integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero,
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then the underflow floating-point exception shall be
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raised.
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.sp
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.LP
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\fIThe following sections are informative.\fP
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.SH EXAMPLES
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.LP
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None.
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.SH APPLICATION USAGE
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.LP
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The value of \fIexpm1\fP(\fIx\fP) may be more accurate than \fIexp\fP(\fIx\fP)-1.0
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for small values of \fIx\fP.
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.LP
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The \fIexpm1\fP() and \fIlog1p\fP() functions are useful for financial
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calculations of
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((1+\fIx\fP)**\fIn\fP-1)/\fIx\fP, namely:
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.sp
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.RS
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.nf
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\fBexpm1(\fP\fIn\fP \fB* log1p(\fP\fIx\fP\fB))/\fP\fIx\fP
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.fi
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.RE
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.LP
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when \fIx\fP is very small (for example, when calculating small daily
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interest rates). These functions also simplify writing
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accurate inverse hyperbolic functions.
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.LP
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For IEEE\ Std\ 754-1985 \fBdouble\fP, 709.8 < \fIx\fP implies \fIexpm1\fP(
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\fIx\fP) has overflowed.
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.LP
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On error, the expressions (math_errhandling & MATH_ERRNO) and (math_errhandling
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& MATH_ERREXCEPT) are independent of
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each other, but at least one of them must be non-zero.
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.SH RATIONALE
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.LP
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None.
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.SH FUTURE DIRECTIONS
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.LP
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None.
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.SH SEE ALSO
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.LP
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\fIexp\fP() , \fIfeclearexcept\fP() , \fIfetestexcept\fP() , \fIilogb\fP()
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, \fIlog1p\fP() ,
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the Base Definitions volume of IEEE\ Std\ 1003.1-2001, Section 4.18,
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Treatment of Error Conditions for Mathematical Functions, \fI<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, 2003 Edition, Standard for Information Technology
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-- Portable Operating System Interface (POSIX), The Open Group Base
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Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of
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Electrical and Electronics Engineers, Inc and The Open Group. 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.opengroup.org/unix/online.html .
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