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authorJeff Johnston <jjohnstn@redhat.com>2008-12-22 21:48:04 +0000
committerJeff Johnston <jjohnstn@redhat.com>2008-12-22 21:48:04 +0000
commitca0430d7306e5099f39fbf8b264d6b66ffc2e998 (patch)
tree7e4a7d92e7756e8734304595b8ee9a74de0d3e06 /libm.html
parent2008-10-28 Jeff Johnston <jjohnstn@redhat.com> (diff)
2008-12-22 Jeff Johnston <jjohnstn@redhat.com>
* COPYING.LIBGLOSS: Updated for 1.17.0 snapshot. * COPYING.NEWLIB: Ditto. * README: Ditto. * libc.html: Ditto. * libm.html: Ditto. * news.html: Ditto.
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1<HTML> 1<div class="node">
2<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> 2<p><hr>
3<!-- Created on January, 30 2004 by texi2html 1.64 --> 3<a name="Top"></a>
4<!-- 4Up:&nbsp;<a rel="up" accesskey="u" href="#dir">(dir)</a>
5Written by: Lionel Cons <Lionel.Cons@cern.ch> (original author) 5
6 Karl Berry <karl@freefriends.org> 6</div>
7 Olaf Bachmann <obachman@mathematik.uni-kl.de> 7
8 and many others. 8<h2 class="unnumbered">Top</h2>
9Maintained by: Olaf Bachmann <obachman@mathematik.uni-kl.de> 9
10Send bugs and suggestions to <texi2html@mathematik.uni-kl.de> 10<html lang="en">
11 11<head>
12--> 12<title>Untitled</title>
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14<TITLE>The Red Hat newlib C Math Library: </TITLE> 14<meta name="description" content="Untitled">
15 15<meta name="generator" content="makeinfo 4.12">
16<META NAME="description" CONTENT="The Red Hat newlib C Math Library: "> 16<link title="Top" rel="top" href="#Top">
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24<BODY LANG="" BGCOLOR="#FFFFFF" TEXT="#000000" LINK="#0000FF" VLINK="#800080" ALINK="#FF0000"> 24 pre.smallexample { font-size:smaller }
25 25 pre.smalllisp { font-size:smaller }
26<A NAME="SEC_Top"></A> 26 span.sc { font-variant:small-caps }
27<h1>The Red Hat newlib C Math Library: </h1> 27 span.roman { font-family:serif; font-weight:normal; }
28<h2>Full Configuration</h2> 28 span.sansserif { font-family:sans-serif; font-weight:normal; }
29<h2><code>libm</code> 1.13.0</h2> 29--></style>
30<h2>January 30, 2004 </h2> 30</head>
31<address>{Steve Chamberlain}</address> 31<body>
32<address>{Roland Pesch}</address> 32<ul class="menu">
33<address>{Red Hat Support}</address> 33<li><a accesskey="1" href="#Math">Math</a>: The mathematical functions (`math.h').
34<address>{Jeff Johnston}</address> 34<li><a accesskey="2" href="#Reentrancy">Reentrancy</a>: The functions in libm are not reentrant by default.
35<p> 35<li><a accesskey="3" href="#Index">Index</a>
36<p><hr><p> 36</ul>
37<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> 37
38<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD> 38<div class="node">
39<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD> 39<p><hr>
40<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD> 40<a name="Math"></a>
41<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD> 41Next:&nbsp;<a rel="next" accesskey="n" href="#Reentrancy">Reentrancy</a>,
42</TR></TABLE> 42Previous:&nbsp;<a rel="previous" accesskey="p" href="#Top">Top</a>,
43<H1>Red Hat newlib C Library: libm</H1></P><P> 43Up:&nbsp;<a rel="up" accesskey="u" href="#Top">Top</a>
44 44
45<BLOCKQUOTE><TABLE BORDER=0 CELLSPACING=0> 45</div>
46<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC1">1. Mathematical Functions (<TT>`math.h'</TT>)</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">The mathematical functions (`math.h').</TD></TR> 46
47<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC42">2. Reentrancy Properties of <CODE>libm</CODE></A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">The functions in libm are not reentrant by default.</TD></TR> 47<h2 class="chapter">1 Mathematical Functions (<samp><span class="file">math.h</span></samp>)</h2>
48<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC43">Index</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP"></TD></TR> 48
49</TABLE></BLOCKQUOTE> 49<p>This chapter groups a wide variety of mathematical functions. The
50<P> 50corresponding definitions and declarations are in <samp><span class="file">math.h</span></samp>.
51 51Two definitions from <samp><span class="file">math.h</span></samp> are of particular interest.
52<HR SIZE=1> 52
53<A NAME="SEC1"></A> 53 <ol type=1 start=1>
54<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> 54<li>The representation of infinity as a <code>double</code> is defined as
55<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top"> &lt; </A>]</TD> 55<code>HUGE_VAL</code>; this number is returned on overflow by many functions.
56<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC2"> &gt; </A>]</TD> 56
57<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD> 57 <li>The structure <code>exception</code> is used when you write customized error
58<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top"> Up </A>]</TD>
59<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &gt;&gt; </A>]</TD>
60<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD>
61<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD>
62<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
63<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
64</TR></TABLE>
65<A NAME="Math"></A>
66<H1> 1. Mathematical Functions (<TT>`math.h'</TT>) </H1>
67<!--docid::SEC1::-->
68<P>
69
70This chapter groups a wide variety of mathematical functions. The
71corresponding definitions and declarations are in <TT>`math.h'</TT>.
72Two definitions from <TT>`math.h'</TT> are of particular interest.
73</P><P>
74
75<OL>
76<LI>
77The representation of infinity as a <CODE>double</CODE> is defined as
78<CODE>HUGE_VAL</CODE>; this number is returned on overflow by many functions.
79<P>
80
81<LI>
82The structure <CODE>exception</CODE> is used when you write customized error
83handlers for the mathematical functions. You can customize error 58handlers for the mathematical functions. You can customize error
84handling for most of these functions by defining your own version of 59handling for most of these functions by defining your own version of
85<CODE>matherr</CODE>; see the section on <CODE>matherr</CODE> for details. 60<code>matherr</code>; see the section on <code>matherr</code> for details.
86</OL> 61 </ol>
87<P> 62
88 63 <p><a name="index-system-calls-1"></a><a name="index-support-subroutines-2"></a><a name="index-stubs-3"></a><a name="index-OS-stubs-4"></a>Since the error handling code calls <code>fputs</code>, the mathematical
89<A NAME="IDX1"></A>
90<A NAME="IDX2"></A>
91<A NAME="IDX3"></A>
92<A NAME="IDX4"></A>
93Since the error handling code calls <CODE>fputs</CODE>, the mathematical
94subroutines require stubs or minimal implementations for the same list 64subroutines require stubs or minimal implementations for the same list
95of OS subroutines as <CODE>fputs</CODE>: <CODE>close</CODE>, <CODE>fstat</CODE>, 65of OS subroutines as <code>fputs</code>: <code>close</code>, <code>fstat</code>,
96<CODE>isatty</CODE>, <CODE>lseek</CODE>, <CODE>read</CODE>, <CODE>sbrk</CODE>, <CODE>write</CODE>. 66<code>isatty</code>, <code>lseek</code>, <code>read</code>, <code>sbrk</code>, <code>write</code>.
97See section `System Calls' in <CITE>The Cygnus C Support Library</CITE>, 67See <a href="libc.html#syscalls">System Calls</a>,
98for a discussion and for sample minimal implementations of these support 68for a discussion and for sample minimal implementations of these support
99subroutines. 69subroutines.
100</P><P>
101 70
102Alternative declarations of the mathematical functions, which exploit 71 <p>Alternative declarations of the mathematical functions, which exploit
103specific machine capabilities to operate faster--but generally have 72specific machine capabilities to operate faster&mdash;but generally have
104less error checking and may reflect additional limitations on some 73less error checking and may reflect additional limitations on some
105machines--are available when you include <TT>`fastmath.h'</TT> instead of 74machines&mdash;are available when you include <samp><span class="file">fastmath.h</span></samp> instead of
106<TT>`math.h'</TT>. 75<samp><span class="file">math.h</span></samp>.
107</P><P> 76
108 77<ul class="menu">
109<BLOCKQUOTE><TABLE BORDER=0 CELLSPACING=0> 78<li><a accesskey="1" href="#version">version</a>: Version of library
110<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC2">1.1 Version of library</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP"></TD></TR> 79<li><a accesskey="2" href="#acos">acos</a>: Arccosine
111<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC3">1.2 <CODE>acos</CODE>, <CODE>acosf</CODE>---arc cosine</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Arccosine</TD></TR> 80<li><a accesskey="3" href="#acosh">acosh</a>: Inverse hyperbolic cosine
112<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC4">1.3 <CODE>acosh</CODE>, <CODE>acoshf</CODE>---inverse hyperbolic cosine</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Inverse hyperbolic cosine</TD></TR> 81<li><a accesskey="4" href="#asin">asin</a>: Arcsine
113<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC5">1.4 <CODE>asin</CODE>, <CODE>asinf</CODE>---arc sine</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Arcsine</TD></TR> 82<li><a accesskey="5" href="#asinh">asinh</a>: Inverse hyperbolic sine
114<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC6">1.5 <CODE>asinh</CODE>, <CODE>asinhf</CODE>---inverse hyperbolic sine</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Inverse hyperbolic sine</TD></TR> 83<li><a accesskey="6" href="#atan">atan</a>: Arctangent
115<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC7">1.6 <CODE>atan</CODE>, <CODE>atanf</CODE>---arc tangent</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Arctangent</TD></TR> 84<li><a accesskey="7" href="#atan2">atan2</a>: Arctangent of y/x
116<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC8">1.7 <CODE>atan2</CODE>, <CODE>atan2f</CODE>---arc tangent of y/x</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Arctangent of y/x</TD></TR> 85<li><a accesskey="8" href="#atanh">atanh</a>: Inverse hyperbolic tangent
117<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC9">1.8 <CODE>atanh</CODE>, <CODE>atanhf</CODE>---inverse hyperbolic tangent</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Inverse hyperbolic tangent</TD></TR> 86<li><a accesskey="9" href="#jN">jN</a>: Bessel functions (jN, yN)
118<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC10">1.9 <CODE>jN</CODE>,<CODE>jNf</CODE>,<CODE>yN</CODE>,<CODE>yNf</CODE>---Bessel functions</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Bessel functions (jN, yN)</TD></TR> 87<li><a href="#cbrt">cbrt</a>: Cube root
119<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC31">1.30 <CODE>cbrt</CODE>, <CODE>cbrtf</CODE>---cube root</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Cube root</TD></TR> 88<li><a href="#copysign">copysign</a>: Sign of Y, magnitude of X
120<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC32">1.31 <CODE>copysign</CODE>, <CODE>copysignf</CODE>---sign of <VAR>y</VAR>, magnitude of <VAR>x</VAR></A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Sign of Y, magnitude of X</TD></TR> 89<li><a href="#cosh">cosh</a>: Hyperbolic cosine
121<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC11">1.10 <CODE>cosh</CODE>, <CODE>coshf</CODE>---hyperbolic cosine</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Hyperbolic cosine</TD></TR> 90<li><a href="#erf">erf</a>: Error function (erf, erfc)
122<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC12">1.11 <CODE>erf</CODE>, <CODE>erff</CODE>, <CODE>erfc</CODE>, <CODE>erfcf</CODE>---error function</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Error function (erf, erfc)</TD></TR> 91<li><a href="#exp">exp</a>: Exponential
123<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC13">1.12 <CODE>exp</CODE>, <CODE>expf</CODE>---exponential</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Exponential</TD></TR> 92<li><a href="#expm1">expm1</a>: Exponential of x, - 1
124<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC33">1.32 <CODE>expm1</CODE>, <CODE>expm1f</CODE>---exponential minus 1</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Exponential of x, - 1</TD></TR> 93<li><a href="#fabs">fabs</a>: Absolute value (magnitude)
125<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC14">1.13 <CODE>fabs</CODE>, <CODE>fabsf</CODE>---absolute value (magnitude)</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Absolute value (magnitude)</TD></TR> 94<li><a href="#floor">floor</a>: Floor and ceiling (floor, ceil)
126<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC15">1.14 <CODE>floor</CODE>, <CODE>floorf</CODE>, <CODE>ceil</CODE>, <CODE>ceilf</CODE>---floor and ceiling</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Floor and ceiling (floor, ceil)</TD></TR> 95<li><a href="#fmod">fmod</a>: Floating-point remainder (modulo)
127<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC16">1.15 <CODE>fmod</CODE>, <CODE>fmodf</CODE>---floating-point remainder (modulo)</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Floating-point remainder (modulo)</TD></TR> 96<li><a href="#frexp">frexp</a>: Split floating-point number
128<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC17">1.16 <CODE>frexp</CODE>, <CODE>frexpf</CODE>---split floating-point number</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Split floating-point number</TD></TR> 97<li><a href="#gamma">gamma</a>: Logarithmic gamma function
129<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC18">1.17 <CODE>gamma</CODE>, <CODE>gammaf</CODE>, <CODE>lgamma</CODE>, <CODE>lgammaf</CODE>, <CODE>gamma_r</CODE>,</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Logarithmic gamma function</TD></TR> 98<li><a href="#hypot">hypot</a>: Distance from origin
130<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC19">1.18 <CODE>hypot</CODE>, <CODE>hypotf</CODE>---distance from origin</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Distance from origin</TD></TR> 99<li><a href="#ilogb">ilogb</a>: Get exponent
131<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC34">1.33 <CODE>ilogb</CODE>, <CODE>ilogbf</CODE>---get exponent of floating-point number</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Get exponent</TD></TR> 100<li><a href="#infinity">infinity</a>: Floating infinity
132<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC35">1.34 <CODE>infinity</CODE>, <CODE>infinityf</CODE>---representation of infinity</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Floating infinity</TD></TR> 101<li><a href="#isnan">isnan</a>: Check type of number
133<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC20">1.19 <CODE>isnan</CODE>,<CODE>isnanf</CODE>,<CODE>isinf</CODE>,<CODE>isinff</CODE>,<CODE>finite</CODE>,<CODE>finitef</CODE>---test for exceptional numbers</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Check type of number</TD></TR> 102<li><a href="#ldexp">ldexp</a>: Load exponent
134<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC21">1.20 <CODE>ldexp</CODE>, <CODE>ldexpf</CODE>---load exponent</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Load exponent</TD></TR> 103<li><a href="#log">log</a>: Natural logarithms
135<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC22">1.21 <CODE>log</CODE>, <CODE>logf</CODE>---natural logarithms</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Natural logarithms</TD></TR> 104<li><a href="#log10">log10</a>: Base 10 logarithms
136<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC23">1.22 <CODE>log10</CODE>, <CODE>log10f</CODE>---base 10 logarithms</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Base 10 logarithms</TD></TR> 105<li><a href="#log1p">log1p</a>: Log of 1 + X
137<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC36">1.35 <CODE>log1p</CODE>, <CODE>log1pf</CODE>---log of <CODE>1 + <VAR>x</VAR></CODE></A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Log of 1 + X</TD></TR> 106<li><a href="#matherr">matherr</a>: Modifiable math error handler
138<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC37">1.36 <CODE>matherr</CODE>---modifiable math error handler</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Modifiable math error handler</TD></TR> 107<li><a href="#modf">modf</a>: Split fractional and integer parts
139<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC38">1.37 <CODE>modf</CODE>, <CODE>modff</CODE>---split fractional and integer parts</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Split fractional and integer parts</TD></TR> 108<li><a href="#nan">nan</a>: Floating Not a Number
140<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC39">1.38 <CODE>nan</CODE>, <CODE>nanf</CODE>---representation of "Not a Number"</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Floating Not a Number</TD></TR> 109<li><a href="#nextafter">nextafter</a>: Get next representable number
141<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC40">1.39 <CODE>nextafter</CODE>, <CODE>nextafterf</CODE>---get next number</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Get next representable number</TD></TR> 110<li><a href="#pow">pow</a>: X to the power Y
142<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC24">1.23 <CODE>pow</CODE>, <CODE>powf</CODE>---x to the power y</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">X to the power Y</TD></TR> 111<li><a href="#remainder">remainder</a>: remainder of X divided by Y
143<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC25">1.24 <CODE>remainder</CODE>, <CODE>remainderf</CODE>---round and remainder</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">remainder of X divided by Y</TD></TR> 112<li><a href="#scalbn">scalbn</a>: scalbn
144<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC41">1.40 <CODE>scalbn</CODE>, <CODE>scalbnf</CODE>---scale by power of two</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">scalbn</TD></TR> 113<li><a href="#sin">sin</a>: Sine or cosine (sin, cos)
145<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC27">1.26 <CODE>sin</CODE>, <CODE>sinf</CODE>, <CODE>cos</CODE>, <CODE>cosf</CODE>---sine or cosine</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Sine or cosine (sin, cos)</TD></TR> 114<li><a href="#sinh">sinh</a>: Hyperbolic sine
146<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC28">1.27 <CODE>sinh</CODE>, <CODE>sinhf</CODE>---hyperbolic sine</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Hyperbolic sine</TD></TR> 115<li><a href="#sqrt">sqrt</a>: Positive square root
147<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC26">1.25 <CODE>sqrt</CODE>, <CODE>sqrtf</CODE>---positive square root</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Positive square root</TD></TR> 116<li><a href="#tan">tan</a>: Tangent
148<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC29">1.28 <CODE>tan</CODE>, <CODE>tanf</CODE>---tangent</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Tangent</TD></TR> 117<li><a href="#tanh">tanh</a>: Hyperbolic tangent
149<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC30">1.29 <CODE>tanh</CODE>, <CODE>tanhf</CODE>---hyperbolic tangent</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Hyperbolic tangent</TD></TR> 118</ul>
150</TABLE></BLOCKQUOTE> 119
151<P> 120<div class="node">
152 121<p><hr>
153<A NAME="version"></A> 122<a name="version"></a>
154<HR SIZE="6"> 123Next:&nbsp;<a rel="next" accesskey="n" href="#acos">acos</a>,
155<A NAME="SEC2"></A> 124Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
156<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> 125
157<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> &lt; </A>]</TD> 126</div>
158<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC3"> &gt; </A>]</TD> 127
159<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD> 128<h3 class="section">1.1 Version of library</h3>
160<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD> 129
161<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &gt;&gt; </A>]</TD> 130<p>There are four different versions of the math library routines: IEEE,
162<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD>
163<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD>
164<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
165<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
166</TR></TABLE>
167<H2> 1.1 Version of library </H2>
168<!--docid::SEC2::-->
169<P>
170
171There are four different versions of the math library routines: IEEE,
172POSIX, X/Open, or SVID. The version may be selected at runtime by 131POSIX, X/Open, or SVID. The version may be selected at runtime by
173setting the global variable <CODE>_LIB_VERSION</CODE>, defined in 132setting the global variable <code>_LIB_VERSION</code>, defined in
174<TT>`math.h'</TT>. It may be set to one of the following constants defined 133<samp><span class="file">math.h</span></samp>. It may be set to one of the following constants defined
175in <TT>`math.h'</TT>: <CODE>_IEEE_</CODE>, <CODE>_POSIX_</CODE>, <CODE>_XOPEN_</CODE>, or 134in <samp><span class="file">math.h</span></samp>: <code>_IEEE_</code>, <code>_POSIX_</code>, <code>_XOPEN_</code>, or
176<CODE>_SVID_</CODE>. The <CODE>_LIB_VERSION</CODE> variable is not specific to any 135<code>_SVID_</code>. The <code>_LIB_VERSION</code> variable is not specific to any
177thread, and changing it will affect all threads. 136thread, and changing it will affect all threads.
178</P><P>
179 137
180The versions of the library differ only in how errors are handled. 138 <p>The versions of the library differ only in how errors are handled.
181</P><P>
182 139
183In IEEE mode, the <CODE>matherr</CODE> function is never called, no warning 140 <p>In IEEE mode, the <code>matherr</code> function is never called, no warning
184messages are printed, and <CODE>errno</CODE> is never set. 141messages are printed, and <code>errno</code> is never set.
185</P><P>
186 142
187In POSIX mode, <CODE>errno</CODE> is set correctly, but the <CODE>matherr</CODE> 143 <p>In POSIX mode, <code>errno</code> is set correctly, but the <code>matherr</code>
188function is never called and no warning messages are printed. 144function is never called and no warning messages are printed.
189</P><P>
190 145
191In X/Open mode, <CODE>errno</CODE> is set correctly, and <CODE>matherr</CODE> is 146 <p>In X/Open mode, <code>errno</code> is set correctly, and <code>matherr</code> is
192called, but warning message are not printed. 147called, but warning message are not printed.
193</P><P>
194 148
195In SVID mode, functions which overflow return 3.40282346638528860e+38, 149 <p>In SVID mode, functions which overflow return 3.40282346638528860e+38,
196the maximum single-precision floating-point value, rather than infinity. 150the maximum single-precision floating-point value, rather than infinity.
197Also, <CODE>errno</CODE> is set correctly, <CODE>matherr</CODE> is called, and, if 151Also, <code>errno</code> is set correctly, <code>matherr</code> is called, and, if
198<CODE>matherr</CODE> returns 0, warning messages are printed for some errors. 152<code>matherr</code> returns 0, warning messages are printed for some errors.
199For example, by default <SAMP>`log(-1.0)'</SAMP> writes this message on standard 153For example, by default &lsquo;<samp><span class="samp">log(-1.0)</span></samp>&rsquo; writes this message on standard
200error output: 154error output:
201</P><P> 155
202 156<pre class="example"> log: DOMAIN error
203<TABLE><tr><td>&nbsp;</td><td class=example><pre>log: DOMAIN error 157</pre>
204</pre></td></tr></table></P><P> 158 <p>The library is set to X/Open mode by default.
205 159
206The library is set to X/Open mode by default. 160<div class="node">
207</P><P> 161<p><hr>
208 162<a name="acos"></a>
209<A NAME="acos"></A> 163Next:&nbsp;<a rel="next" accesskey="n" href="#acosh">acosh</a>,
210<HR SIZE="6"> 164Previous:&nbsp;<a rel="previous" accesskey="p" href="#version">version</a>,
211<A NAME="SEC3"></A> 165Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
212<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> 166
213<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC2"> &lt; </A>]</TD> 167</div>
214<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC4"> &gt; </A>]</TD> 168
215<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC4"> &lt;&lt; </A>]</TD> 169<h3 class="section">1.2 <code>acos</code>, <code>acosf</code>&mdash;arc cosine</h3>
216<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD> 170
217<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &gt;&gt; </A>]</TD> 171<p><a name="index-acos-5"></a><a name="index-acosf-6"></a><strong>Synopsis</strong>
218<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD> 172<pre class="example"> #include &lt;math.h&gt;
219<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD> 173 double acos(double <var>x</var>);
220<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD> 174 float acosf(float <var>x</var>);
221<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD> 175
222</TR></TABLE> 176</pre>
223<H2> 1.2 <CODE>acos</CODE>, <CODE>acosf</CODE>---arc cosine </H2> 177 <p><strong>Description</strong><br>
224<!--docid::SEC3::--> 178
225<STRONG>Synopsis</STRONG> 179 <p><code>acos</code> computes the inverse cosine (arc cosine) of the input value.
226<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62; 180Arguments to <code>acos</code> must be in the range &minus;1 to 1.
227double acos(double <VAR>x</VAR>); 181
228float acosf(float <VAR>x</VAR>); 182 <p><code>acosf</code> is identical to <code>acos</code>, except that it performs
229 183its calculations on <code>floats</code>.
230</pre></td></tr></table><STRONG>Description</STRONG><BR> 184
231<P> 185 <p><br>
232 186<strong>Returns</strong><br>
233<CODE>acos</CODE> computes the inverse cosine (arc cosine) of the input value. 187<code>acos</code> and <code>acosf</code> return values in radians, in the range of 0 to pi.
234Arguments to <CODE>acos</CODE> must be in the range -1 to 1. 188
235</P><P> 189 <p>If <var>x</var> is not between &minus;1 and 1, the returned value is NaN
236 190(not a number) the global variable <code>errno</code> is set to <code>EDOM</code>, and a
237<CODE>acosf</CODE> is identical to <CODE>acos</CODE>, except that it performs 191<code>DOMAIN error</code> message is sent as standard error output.
238its calculations on <CODE>floats</CODE>. 192
239</P><P> 193 <p>You can modify error handling for these functions using <code>matherr</code>.
240 194
241<BR> 195 <p><br>
242<STRONG>Returns</STRONG><BR> 196
243<CODE>acos</CODE> and <CODE>acosf</CODE> return values in radians, in the range of 0 to pi. 197<div class="node">
244</P><P> 198<p><hr>
245 199<a name="acosh"></a>
246If <VAR>x</VAR> is not between -1 and 1, the returned value is NaN 200Next:&nbsp;<a rel="next" accesskey="n" href="#asin">asin</a>,
247(not a number) the global variable <CODE>errno</CODE> is set to <CODE>EDOM</CODE>, and a 201Previous:&nbsp;<a rel="previous" accesskey="p" href="#acos">acos</a>,
248<CODE>DOMAIN error</CODE> message is sent as standard error output. 202Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
249</P><P> 203
250 204</div>
251You can modify error handling for these functions using <CODE>matherr</CODE>. 205
252</P><P> 206<h3 class="section">1.3 <code>acosh</code>, <code>acoshf</code>&mdash;inverse hyperbolic cosine</h3>
253 207
254<BR> 208<p><a name="index-acosh-7"></a><a name="index-acoshf-8"></a><strong>Synopsis</strong>
255</P><P> 209<pre class="example"> #include &lt;math.h&gt;
256 210 double acosh(double <var>x</var>);
257<A NAME="acosh"></A> 211 float acoshf(float <var>x</var>);
258<HR SIZE="6"> 212
259<A NAME="SEC4"></A> 213</pre>
260<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> 214 <p><strong>Description</strong><br>
261<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC3"> &lt; </A>]</TD> 215<code>acosh</code> calculates the inverse hyperbolic cosine of <var>x</var>.
262<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC5"> &gt; </A>]</TD> 216<code>acosh</code> is defined as
263<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC5"> &lt;&lt; </A>]</TD> 217<pre class="smallexample"> log(<var>x</var> + sqrt(<var>x</var>*<var>x</var>-1))
264<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD> 218</pre>
265<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &gt;&gt; </A>]</TD> 219 <p><var>x</var> must be a number greater than or equal to 1.
266<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD> 220
267<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD> 221 <p><code>acoshf</code> is identical, other than taking and returning floats.
268<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD> 222
269<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD> 223 <p><br>
270</TR></TABLE> 224<strong>Returns</strong><br>
271<H2> 1.3 <CODE>acosh</CODE>, <CODE>acoshf</CODE>---inverse hyperbolic cosine </H2> 225<code>acosh</code> and <code>acoshf</code> return the calculated value. If <var>x</var>
272<!--docid::SEC4::--> 226less than 1, the return value is NaN and <code>errno</code> is set to <code>EDOM</code>.
273<STRONG>Synopsis</STRONG> 227
274<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62; 228 <p>You can change the error-handling behavior with the non-ANSI
275double acosh(double <VAR>x</VAR>); 229<code>matherr</code> function.
276float acoshf(float <VAR>x</VAR>); 230
277 231 <p><br>
278</pre></td></tr></table><STRONG>Description</STRONG><BR> 232<strong>Portability</strong><br>
279<CODE>acosh</CODE> calculates the inverse hyperbolic cosine of <VAR>x</VAR>. 233Neither <code>acosh</code> nor <code>acoshf</code> are ANSI C. They are not recommended
280<CODE>acosh</CODE> is defined as
281<TABLE><tr><td>&nbsp;</td><td class=smallexample><FONT SIZE=-1><pre> log(<VAR>x</VAR> + sqrt(<VAR>x</VAR>*<VAR>x</VAR>-1))
282</FONT></pre></td></tr></table><P>
283
284<VAR>x</VAR> must be a number greater than or equal to 1.
285</P><P>
286
287<CODE>acoshf</CODE> is identical, other than taking and returning floats.
288</P><P>
289
290<BR>
291<STRONG>Returns</STRONG><BR>
292<CODE>acosh</CODE> and <CODE>acoshf</CODE> return the calculated value. If <VAR>x</VAR>
293less than 1, the return value is NaN and <CODE>errno</CODE> is set to <CODE>EDOM</CODE>.
294</P><P>
295
296You can change the error-handling behavior with the non-ANSI
297<CODE>matherr</CODE> function.
298</P><P>
299
300<BR>
301<STRONG>Portability</STRONG><BR>
302Neither <CODE>acosh</CODE> nor <CODE>acoshf</CODE> are ANSI C. They are not recommended
303for portable programs. 234for portable programs.
304</P><P> 235
305 236 <p><br>
306<BR> 237
307</P><P> 238<div class="node">
308 239<p><hr>
309<A NAME="asin"></A> 240<a name="asin"></a>
310<HR SIZE="6"> 241Next:&nbsp;<a rel="next" accesskey="n" href="#asinh">asinh</a>,
311<A NAME="SEC5"></A> 242Previous:&nbsp;<a rel="previous" accesskey="p" href="#acosh">acosh</a>,
312<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> 243Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
313<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC4"> &lt; </A>]</TD> 244
314<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC6"> &gt; </A>]</TD> 245</div>
315<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC6"> &lt;&lt; </A>]</TD> 246
316<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD> 247<h3 class="section">1.4 <code>asin</code>, <code>asinf</code>&mdash;arc sine</h3>
317<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &gt;&gt; </A>]</TD> 248
318<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD> 249<p><a name="index-asin-9"></a><a name="index-asinf-10"></a><strong>Synopsis</strong>
319<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD> 250<pre class="example"> #include &lt;math.h&gt;
320<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD> 251 double asin(double <var>x</var>);
321<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD> 252 float asinf(float <var>x</var>);
322</TR></TABLE> 253
323<H2> 1.4 <CODE>asin</CODE>, <CODE>asinf</CODE>---arc sine </H2> 254</pre>
324<!--docid::SEC5::--> 255 <p><strong>Description</strong><br>
325<STRONG>Synopsis</STRONG> 256
326<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62; 257 <p><code>asin</code> computes the inverse sine (arc sine) of the argument <var>x</var>.
327double asin(double <VAR>x</VAR>); 258Arguments to <code>asin</code> must be in the range &minus;1 to 1.
328float asinf(float <VAR>x</VAR>); 259
329 260 <p><code>asinf</code> is identical to <code>asin</code>, other than taking and
330</pre></td></tr></table><STRONG>Description</STRONG><BR>
331<P>
332
333<CODE>asin</CODE> computes the inverse sine (arc sine) of the argument <VAR>x</VAR>.
334Arguments to <CODE>asin</CODE> must be in the range -1 to 1.
335</P><P>
336
337<CODE>asinf</CODE> is identical to <CODE>asin</CODE>, other than taking and
338returning floats. 261returning floats.
339</P><P> 262
340 263 <p>You can modify error handling for these routines using <code>matherr</code>.
341You can modify error handling for these routines using <CODE>matherr</CODE>. 264
342</P><P> 265 <p><br>
343 266<strong>Returns</strong><br>
344<BR> 267<code>asin</code> returns values in radians, in the range of -pi/2 to pi/2.
345<STRONG>Returns</STRONG><BR> 268
346<CODE>asin</CODE> returns values in radians, in the range of -pi/2 to pi/2. 269 <p>If <var>x</var> is not in the range &minus;1 to 1, <code>asin</code> and <code>asinf</code>
347</P><P> 270return NaN (not a number), set the global variable <code>errno</code> to
348 271<code>EDOM</code>, and issue a <code>DOMAIN error</code> message.
349If <VAR>x</VAR> is not in the range -1 to 1, <CODE>asin</CODE> and <CODE>asinf</CODE> 272
350return NaN (not a number), set the global variable <CODE>errno</CODE> to 273 <p>You can change this error treatment using <code>matherr</code>.
351<CODE>EDOM</CODE>, and issue a <CODE>DOMAIN error</CODE> message. 274
352</P><P> 275 <p><br>
353 276
354You can change this error treatment using <CODE>matherr</CODE>. 277<div class="node">
355</P><P> 278<p><hr>
356 279<a name="asinh"></a>
357<BR> 280Next:&nbsp;<a rel="next" accesskey="n" href="#atan">atan</a>,
358</P><P> 281Previous:&nbsp;<a rel="previous" accesskey="p" href="#asin">asin</a>,
359 282Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
360<A NAME="asinh"></A> 283
361<HR SIZE="6"> 284</div>
362<A NAME="SEC6"></A> 285
363<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> 286<h3 class="section">1.5 <code>asinh</code>, <code>asinhf</code>&mdash;inverse hyperbolic sine</h3>
364<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC5"> &lt; </A>]</TD> 287
365<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC7"> &gt; </A>]</TD> 288<p><a name="index-asinh-11"></a><a name="index-asinhf-12"></a><strong>Synopsis</strong>
366<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC7"> &lt;&lt; </A>]</TD> 289<pre class="example"> #include &lt;math.h&gt;
367<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD> 290 double asinh(double <var>x</var>);
368<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &gt;&gt; </A>]</TD> 291 float asinhf(float <var>x</var>);
369<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD> 292
370<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD> 293</pre>
371<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD> 294 <p><strong>Description</strong><br>
372<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD> 295<code>asinh</code> calculates the inverse hyperbolic sine of <var>x</var>.
373</TR></TABLE> 296<code>asinh</code> is defined as
374<H2> 1.5 <CODE>asinh</CODE>, <CODE>asinhf</CODE>---inverse hyperbolic sine </H2> 297<pre class="smallexample"> sgn(<var>x</var>) * log(abs(<var>x</var>) + sqrt(1+<var>x</var>*<var>x</var>))
375<!--docid::SEC6::--> 298</pre>
376<STRONG>Synopsis</STRONG> 299 <p><code>asinhf</code> is identical, other than taking and returning floats.
377<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62; 300
378double asinh(double <VAR>x</VAR>); 301 <p><br>
379float asinhf(float <VAR>x</VAR>); 302<strong>Returns</strong><br>
380 303<code>asinh</code> and <code>asinhf</code> return the calculated value.
381</pre></td></tr></table><STRONG>Description</STRONG><BR> 304
382<CODE>asinh</CODE> calculates the inverse hyperbolic sine of <VAR>x</VAR>. 305 <p><br>
383<CODE>asinh</CODE> is defined as 306<strong>Portability</strong><br>
384<TABLE><tr><td>&nbsp;</td><td class=smallexample><FONT SIZE=-1><pre> sgn(<VAR>x</VAR>) * log(abs(<VAR>x</VAR>) + sqrt(1+<VAR>x</VAR>*<VAR>x</VAR>)) 307Neither <code>asinh</code> nor <code>asinhf</code> are ANSI C.
385</FONT></pre></td></tr></table><P> 308
386 309 <p><br>
387<CODE>asinhf</CODE> is identical, other than taking and returning floats. 310
388</P><P> 311<div class="node">
389 312<p><hr>
390<BR> 313<a name="atan"></a>
391<STRONG>Returns</STRONG><BR> 314Next:&nbsp;<a rel="next" accesskey="n" href="#atan2">atan2</a>,
392<CODE>asinh</CODE> and <CODE>asinhf</CODE> return the calculated value. 315Previous:&nbsp;<a rel="previous" accesskey="p" href="#asinh">asinh</a>,
393</P><P> 316Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
394 317
395<BR> 318</div>
396<STRONG>Portability</STRONG><BR> 319
397Neither <CODE>asinh</CODE> nor <CODE>asinhf</CODE> are ANSI C. 320<h3 class="section">1.6 <code>atan</code>, <code>atanf</code>&mdash;arc tangent</h3>
398</P><P> 321
399 322<p><a name="index-atan-13"></a><a name="index-atanf-14"></a><strong>Synopsis</strong>
400<BR> 323<pre class="example"> #include &lt;math.h&gt;
401</P><P> 324 double atan(double <var>x</var>);
402 325 float atanf(float <var>x</var>);
403<A NAME="atan"></A> 326
404<HR SIZE="6"> 327</pre>
405<A NAME="SEC7"></A> 328 <p><strong>Description</strong><br>
406<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> 329
407<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC6"> &lt; </A>]</TD> 330 <p><code>atan</code> computes the inverse tangent (arc tangent) of the input value.
408<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC8"> &gt; </A>]</TD> 331
409<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC8"> &lt;&lt; </A>]</TD> 332 <p><code>atanf</code> is identical to <code>atan</code>, save that it operates on <code>floats</code>.
410<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD> 333
411<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &gt;&gt; </A>]</TD> 334 <p><br>
412<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD> 335<strong>Returns</strong><br>
413<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD> 336<code>atan</code> returns a value in radians, in the range of -pi/2 to pi/2.
414<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD> 337
415<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD> 338 <p><br>
416</TR></TABLE> 339<strong>Portability</strong><br>
417<H2> 1.6 <CODE>atan</CODE>, <CODE>atanf</CODE>---arc tangent </H2> 340<code>atan</code> is ANSI C. <code>atanf</code> is an extension.
418<!--docid::SEC7::--> 341
419<STRONG>Synopsis</STRONG> 342 <p><br>
420<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62; 343
421double atan(double <VAR>x</VAR>); 344<div class="node">
422float atanf(float <VAR>x</VAR>); 345<p><hr>
423 346<a name="atan2"></a>
424</pre></td></tr></table><STRONG>Description</STRONG><BR> 347Next:&nbsp;<a rel="next" accesskey="n" href="#atanh">atanh</a>,
425<P> 348Previous:&nbsp;<a rel="previous" accesskey="p" href="#atan">atan</a>,
426 349Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
427<CODE>atan</CODE> computes the inverse tangent (arc tangent) of the input value. 350
428</P><P> 351</div>
429 352
430<CODE>atanf</CODE> is identical to <CODE>atan</CODE>, save that it operates on <CODE>floats</CODE>. 353<h3 class="section">1.7 <code>atan2</code>, <code>atan2f</code>&mdash;arc tangent of y/x</h3>
431</P><P> 354
432 355<p><a name="index-atan2-15"></a><a name="index-atan2f-16"></a><strong>Synopsis</strong>
433<BR> 356<pre class="example"> #include &lt;math.h&gt;
434<STRONG>Returns</STRONG><BR> 357 double atan2(double <var>y</var>,double <var>x</var>);
435<CODE>atan</CODE> returns a value in radians, in the range of -pi/2 to pi/2. 358 float atan2f(float <var>y</var>,float <var>x</var>);
436</P><P> 359
437 360</pre>
438<BR> 361 <p><strong>Description</strong><br>
439<STRONG>Portability</STRONG><BR> 362
440<CODE>atan</CODE> is ANSI C. <CODE>atanf</CODE> is an extension. 363 <p><code>atan2</code> computes the inverse tangent (arc tangent) of <var>y</var>/<var>x</var>.
441</P><P> 364<code>atan2</code> produces the correct result even for angles near
442 365pi/2 or -pi/2
443<BR> 366(that is, when <var>x</var> is near 0).
444</P><P> 367
445 368 <p><code>atan2f</code> is identical to <code>atan2</code>, save that it takes and returns
446<A NAME="atan2"></A> 369<code>float</code>.
447<HR SIZE="6"> 370
448<A NAME="SEC8"></A> 371 <p><br>
449<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> 372<strong>Returns</strong><br>
450<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC7"> &lt; </A>]</TD> 373<code>atan2</code> and <code>atan2f</code> return a value in radians, in the range of
451<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC9"> &gt; </A>]</TD>
452<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC9"> &lt;&lt; </A>]</TD>
453<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
454<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &gt;&gt; </A>]</TD>
455<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD>
456<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD>
457<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
458<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
459</TR></TABLE>
460<H2> 1.7 <CODE>atan2</CODE>, <CODE>atan2f</CODE>---arc tangent of y/x </H2>
461<!--docid::SEC8::-->
462<STRONG>Synopsis</STRONG>
463<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
464double atan2(double <VAR>y</VAR>,double <VAR>x</VAR>);
465float atan2f(float <VAR>y</VAR>,float <VAR>x</VAR>);
466
467</pre></td></tr></table><STRONG>Description</STRONG><BR>
468<P>
469
470<CODE>atan2</CODE> computes the inverse tangent (arc tangent) of <VAR>y</VAR>/<VAR>x</VAR>.
471<CODE>atan2</CODE> produces the correct result even for angles near
472pi/2 or -pi/2
473(that is, when <VAR>x</VAR> is near 0).
474</P><P>
475
476<CODE>atan2f</CODE> is identical to <CODE>atan2</CODE>, save that it takes and returns
477<CODE>float</CODE>.
478</P><P>
479
480<BR>
481<STRONG>Returns</STRONG><BR>
482<CODE>atan2</CODE> and <CODE>atan2f</CODE> return a value in radians, in the range of
483-pi to pi. 374-pi to pi.
484</P><P> 375
485 376 <p>You can modify error handling for these functions using <code>matherr</code>.
486If both <VAR>x</VAR> and <VAR>y</VAR> are 0.0, <CODE>atan2</CODE> causes a <CODE>DOMAIN</CODE> error. 377
487</P><P> 378 <p><br>
488 379<strong>Portability</strong><br>
489You can modify error handling for these functions using <CODE>matherr</CODE>. 380<code>atan2</code> is ANSI C. <code>atan2f</code> is an extension.
490</P><P> 381
491 382 <p><br>
492<BR> 383
493<STRONG>Portability</STRONG><BR> 384<div class="node">
494<CODE>atan2</CODE> is ANSI C. <CODE>atan2f</CODE> is an extension. 385<p><hr>
495</P><P> 386<a name="atanh"></a>
496 387Next:&nbsp;<a rel="next" accesskey="n" href="#jN">jN</a>,
497<BR> 388Previous:&nbsp;<a rel="previous" accesskey="p" href="#atan2">atan2</a>,
498</P><P> 389Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
499 390
500<A NAME="atanh"></A> 391</div>
501<HR SIZE="6"> 392
502<A NAME="SEC9"></A> 393<h3 class="section">1.8 <code>atanh</code>, <code>atanhf</code>&mdash;inverse hyperbolic tangent</h3>
503<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> 394
504<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC8"> &lt; </A>]</TD> 395<p><a name="index-atanh-17"></a><a name="index-atanhf-18"></a><strong>Synopsis</strong>
505<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC10"> &gt; </A>]</TD> 396<pre class="example"> #include &lt;math.h&gt;
506<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC10"> &lt;&lt; </A>]</TD> 397 double atanh(double <var>x</var>);
507<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD> 398 float atanhf(float <var>x</var>);
508<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &gt;&gt; </A>]</TD> 399
509<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD> 400</pre>
510<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD> 401 <p><strong>Description</strong><br>
511<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD> 402<code>atanh</code> calculates the inverse hyperbolic tangent of <var>x</var>.
512<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD> 403
513</TR></TABLE> 404 <p><code>atanhf</code> is identical, other than taking and returning
514<H2> 1.8 <CODE>atanh</CODE>, <CODE>atanhf</CODE>---inverse hyperbolic tangent </H2> 405<code>float</code> values.
515<!--docid::SEC9::--> 406
516<STRONG>Synopsis</STRONG> 407 <p><br>
517<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62; 408<strong>Returns</strong><br>
518double atanh(double <VAR>x</VAR>); 409<code>atanh</code> and <code>atanhf</code> return the calculated value.
519float atanhf(float <VAR>x</VAR>); 410
520 411 <p>If
521</pre></td></tr></table><STRONG>Description</STRONG><BR> 412<pre class="smallexample"> <var>x</var>|
522<CODE>atanh</CODE> calculates the inverse hyperbolic tangent of <VAR>x</VAR>. 413</pre>
523<P> 414 <p>is greater than 1, the global <code>errno</code> is set to <code>EDOM</code> and
524 415the result is a NaN. A <code>DOMAIN error</code> is reported.
525<CODE>atanhf</CODE> is identical, other than taking and returning 416
526<CODE>float</CODE> values. 417 <p>If
527</P><P> 418<pre class="smallexample"> <var>x</var>|
528 419</pre>
529<BR> 420 <p>is 1, the global <code>errno</code> is set to <code>EDOM</code>; and the result is
530<STRONG>Returns</STRONG><BR> 421infinity with the same sign as <code>x</code>. A <code>SING error</code> is reported.
531<CODE>atanh</CODE> and <CODE>atanhf</CODE> return the calculated value. 422
532</P><P> 423 <p>You can modify the error handling for these routines using
533 424<code>matherr</code>.
534If 425
535<TABLE><tr><td>&nbsp;</td><td class=smallexample><FONT SIZE=-1><pre><VAR>x</VAR>| 426 <p><br>
536</FONT></pre></td></tr></table>is greater than 1, the global <CODE>errno</CODE> is set to <CODE>EDOM</CODE> and 427<strong>Portability</strong><br>
537the result is a NaN. A <CODE>DOMAIN error</CODE> is reported. 428Neither <code>atanh</code> nor <code>atanhf</code> are ANSI C.
538</P><P> 429
539 430 <p><br>
540If 431
541<TABLE><tr><td>&nbsp;</td><td class=smallexample><FONT SIZE=-1><pre><VAR>x</VAR>| 432<div class="node">
542</FONT></pre></td></tr></table>is 1, the global <CODE>errno</CODE> is set to <CODE>EDOM</CODE>; and the result is 433<p><hr>
543infinity with the same sign as <CODE>x</CODE>. A <CODE>SING error</CODE> is reported. 434<a name="jN"></a>
544</P><P> 435Next:&nbsp;<a rel="next" accesskey="n" href="#cbrt">cbrt</a>,
545 436Previous:&nbsp;<a rel="previous" accesskey="p" href="#atanh">atanh</a>,
546You can modify the error handling for these routines using 437Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
547<CODE>matherr</CODE>. 438
548</P><P> 439</div>
549 440
550<BR> 441<h3 class="section">1.9 <code>jN</code>, <code>jNf</code>, <code>yN</code>, <code>yNf</code>&mdash;Bessel functions</h3>
551<STRONG>Portability</STRONG><BR> 442
552Neither <CODE>atanh</CODE> nor <CODE>atanhf</CODE> are ANSI C. 443<p><a name="index-j0-19"></a><a name="index-j0f-20"></a><a name="index-j1-21"></a><a name="index-j1f-22"></a><a name="index-jn-23"></a><a name="index-jnf-24"></a><a name="index-y0-25"></a><a name="index-y0f-26"></a><a name="index-y1-27"></a><a name="index-y1f-28"></a><a name="index-yn-29"></a><a name="index-ynf-30"></a><strong>Synopsis</strong>
553</P><P> 444<pre class="example"> #include &lt;math.h&gt;
554 445 double j0(double <var>x</var>);
555<BR> 446 float j0f(float <var>x</var>);
556</P><P> 447 double j1(double <var>x</var>);
557 448 float j1f(float <var>x</var>);
558<A NAME="jN"></A> 449 double jn(int <var>n</var>, double <var>x</var>);
559<HR SIZE="6"> 450 float jnf(int <var>n</var>, float <var>x</var>);
560<A NAME="SEC10"></A> 451 double y0(double <var>x</var>);
561<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> 452 float y0f(float <var>x</var>);
562<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC9"> &lt; </A>]</TD> 453 double y1(double <var>x</var>);
563<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC11"> &gt; </A>]</TD> 454 float y1f(float <var>x</var>);
564<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD> 455 double yn(int <var>n</var>, double <var>x</var>);
565<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD> 456 float ynf(int <var>n</var>, float <var>x</var>);
566<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &gt;&gt; </A>]</TD> 457
567<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD> 458</pre>
568<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD> 459 <p><strong>Description</strong><br>
569<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
570<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
571</TR></TABLE>
572<H2> 1.9 <CODE>jN</CODE>,<CODE>jNf</CODE>,<CODE>yN</CODE>,<CODE>yNf</CODE>---Bessel functions </H2>
573<!--docid::SEC10::-->
574<STRONG>Synopsis</STRONG>
575<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
576double j0(double <VAR>x</VAR>);
577float j0f(float <VAR>x</VAR>);
578double j1(double <VAR>x</VAR>);
579float j1f(float <VAR>x</VAR>);
580double jn(int <VAR>n</VAR>, double <VAR>x</VAR>);
581float jnf(int <VAR>n</VAR>, float <VAR>x</VAR>);
582double y0(double <VAR>x</VAR>);
583float y0f(float <VAR>x</VAR>);
584double y1(double <VAR>x</VAR>);
585float y1f(float <VAR>x</VAR>);
586double yn(int <VAR>n</VAR>, double <VAR>x</VAR>);
587float ynf(int <VAR>n</VAR>, float <VAR>x</VAR>);
588
589</pre></td></tr></table><STRONG>Description</STRONG><BR>
590The Bessel functions are a family of functions that solve the 460The Bessel functions are a family of functions that solve the
591differential equation 461differential equation
592<TABLE><tr><td>&nbsp;</td><td class=smallexample><FONT SIZE=-1><pre> 2 2 2 462<pre class="smallexample"> 2 2 2
593 x y'' + xy' + (x - p )y = 0 463 x y'' + xy' + (x - p )y = 0
594</FONT></pre></td></tr></table>These functions have many applications in engineering and physics. 464</pre>
595<P> 465 <p>These functions have many applications in engineering and physics.
596 466
597<CODE>jn</CODE> calculates the Bessel function of the first kind of order 467 <p><code>jn</code> calculates the Bessel function of the first kind of order
598<VAR>n</VAR>. <CODE>j0</CODE> and <CODE>j1</CODE> are special cases for order 0 and order 468<var>n</var>. <code>j0</code> and <code>j1</code> are special cases for order 0 and order
5991 respectively. 4691 respectively.
600</P><P>
601 470
602Similarly, <CODE>yn</CODE> calculates the Bessel function of the second kind of 471 <p>Similarly, <code>yn</code> calculates the Bessel function of the second kind of
603order <VAR>n</VAR>, and <CODE>y0</CODE> and <CODE>y1</CODE> are special cases for order 0 and 472order <var>n</var>, and <code>y0</code> and <code>y1</code> are special cases for order 0 and
6041. 4731.
605</P><P>
606 474
607<CODE>jnf</CODE>, <CODE>j0f</CODE>, <CODE>j1f</CODE>, <CODE>ynf</CODE>, <CODE>y0f</CODE>, and <CODE>y1f</CODE> perform the 475 <p><code>jnf</code>, <code>j0f</code>, <code>j1f</code>, <code>ynf</code>, <code>y0f</code>, and <code>y1f</code> perform the
608same calculations, but on <CODE>float</CODE> rather than <CODE>double</CODE> values. 476same calculations, but on <code>float</code> rather than <code>double</code> values.
609</P><P>
610 477
611<BR> 478 <p><br>
612<STRONG>Returns</STRONG><BR> 479<strong>Returns</strong><br>
613The value of each Bessel function at <VAR>x</VAR> is returned. 480The value of each Bessel function at <var>x</var> is returned.
614</P><P>
615 481
616<BR> 482 <p><br>
617<STRONG>Portability</STRONG><BR> 483<strong>Portability</strong><br>
618None of the Bessel functions are in ANSI C. 484None of the Bessel functions are in ANSI C.
619</P><P> 485
620 486 <p><br>
621<BR> 487
622</P><P> 488<div class="node">
623 489<p><hr>
624<A NAME="cosh"></A> 490<a name="cbrt"></a>
625<HR SIZE="6"> 491Next:&nbsp;<a rel="next" accesskey="n" href="#copysign">copysign</a>,
626<A NAME="SEC11"></A> 492Previous:&nbsp;<a rel="previous" accesskey="p" href="#jN">jN</a>,
627<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> 493Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
628<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC10"> &lt; </A>]</TD> 494
629<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC12"> &gt; </A>]</TD> 495</div>
630<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC3"> &lt;&lt; </A>]</TD> 496
631<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD> 497<h3 class="section">1.10 <code>cbrt</code>, <code>cbrtf</code>&mdash;cube root</h3>
632<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &gt;&gt; </A>]</TD> 498
633<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD> 499<p><a name="index-cbrt-31"></a><a name="index-cbrtf-32"></a><strong>Synopsis</strong>
634<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD> 500<pre class="example"> #include &lt;math.h&gt;
635<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD> 501 double cbrt(double <var>x</var>);
636<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD> 502 float cbrtf(float <var>x</var>);
637</TR></TABLE> 503
638<H2> 1.10 <CODE>cosh</CODE>, <CODE>coshf</CODE>---hyperbolic cosine </H2> 504</pre>
639<!--docid::SEC11::--> 505 <p><strong>Description</strong><br>
640<STRONG>Synopsis</STRONG> 506<code>cbrt</code> computes the cube root of the argument.
641<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62; 507
642double cosh(double <VAR>x</VAR>); 508 <p><br>
643float coshf(float <VAR>x</VAR>) 509<strong>Returns</strong><br>
644 510The cube root is returned.
645</pre></td></tr></table><STRONG>Description</STRONG><BR> 511
646<P> 512 <p><br>
647 513<strong>Portability</strong><br>
648<CODE>cosh</CODE> computes the hyperbolic cosine of the argument <VAR>x</VAR>. 514<code>cbrt</code> is in System V release 4. <code>cbrtf</code> is an extension.
649<CODE>cosh(<VAR>x</VAR>)</CODE> is defined as 515
650<TABLE><tr><td>&nbsp;</td><td class=smallexample><FONT SIZE=-1><pre> (exp(x) + exp(-x))/2 516 <p><br>
651</FONT></pre></td></tr></table></P><P> 517
652 518<div class="node">
653Angles are specified in radians. 519<p><hr>
654<CODE>coshf</CODE> is identical, save that it takes and returns <CODE>float</CODE>. 520<a name="copysign"></a>
655</P><P> 521Next:&nbsp;<a rel="next" accesskey="n" href="#cosh">cosh</a>,
656 522Previous:&nbsp;<a rel="previous" accesskey="p" href="#cbrt">cbrt</a>,
657<BR> 523Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
658<STRONG>Returns</STRONG><BR> 524
525</div>
526
527<h3 class="section">1.11 <code>copysign</code>, <code>copysignf</code>&mdash;sign of <var>y</var>, magnitude of <var>x</var></h3>
528
529<p><a name="index-copysign-33"></a><a name="index-copysignf-34"></a><strong>Synopsis</strong>
530<pre class="example"> #include &lt;math.h&gt;
531 double copysign (double <var>x</var>, double <var>y</var>);
532 float copysignf (float <var>x</var>, float <var>y</var>);
533
534</pre>
535 <p><strong>Description</strong><br>
536<code>copysign</code> constructs a number with the magnitude (absolute value)
537of its first argument, <var>x</var>, and the sign of its second argument,
538<var>y</var>.
539
540 <p><code>copysignf</code> does the same thing; the two functions differ only in
541the type of their arguments and result.
542
543 <p><br>
544<strong>Returns</strong><br>
545<code>copysign</code> returns a <code>double</code> with the magnitude of
546<var>x</var> and the sign of <var>y</var>.
547<code>copysignf</code> returns a <code>float</code> with the magnitude of
548<var>x</var> and the sign of <var>y</var>.
549
550 <p><br>
551<strong>Portability</strong><br>
552<code>copysign</code> is not required by either ANSI C or the System V Interface
553Definition (Issue 2).
554
555 <p><br>
556
557<div class="node">
558<p><hr>
559<a name="cosh"></a>
560Next:&nbsp;<a rel="next" accesskey="n" href="#erf">erf</a>,
561Previous:&nbsp;<a rel="previous" accesskey="p" href="#copysign">copysign</a>,
562Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
563
564</div>
565
566<h3 class="section">1.12 <code>cosh</code>, <code>coshf</code>&mdash;hyperbolic cosine</h3>
567
568<p><strong>Synopsis</strong>
569<pre class="example"> #include &lt;math.h&gt;
570 double cosh(double <var>x</var>);
571 float coshf(float <var>x</var>)
572
573</pre>
574 <p><strong>Description</strong><br>
575
576 <p><code>cosh</code> computes the hyperbolic cosine of the argument <var>x</var>.
577<code>cosh(</code><var>x</var><code>)</code> is defined as
578<pre class="smallexample"> (exp(x) + exp(-x))/2
579</pre>
580 <p>Angles are specified in radians.
581<code>coshf</code> is identical, save that it takes and returns <code>float</code>.
582
583 <p><br>
584<strong>Returns</strong><br>
659The computed value is returned. When the correct value would create 585The computed value is returned. When the correct value would create
660an overflow, <CODE>cosh</CODE> returns the value <CODE>HUGE_VAL</CODE> with the 586an overflow, <code>cosh</code> returns the value <code>HUGE_VAL</code> with the
661appropriate sign, and the global value <CODE>errno</CODE> is set to <CODE>ERANGE</CODE>. 587appropriate sign, and the global value <code>errno</code> is set to <code>ERANGE</code>.
662</P><P> 588
663 589 <p>You can modify error handling for these functions using the
664You can modify error handling for these functions using the 590function <code>matherr</code>.
665function <CODE>matherr</CODE>. 591
666</P><P> 592 <p><br>
667 593<strong>Portability</strong><br>
668<BR> 594<code>cosh</code> is ANSI.
669<STRONG>Portability</STRONG><BR> 595<code>coshf</code> is an extension.
670<CODE>cosh</CODE> is ANSI. 596
671<CODE>coshf</CODE> is an extension. 597 <p><br>
672</P><P> 598
673 599<div class="node">
674<BR> 600<p><hr>
675</P><P> 601<a name="erf"></a>
676 602Next:&nbsp;<a rel="next" accesskey="n" href="#exp">exp</a>,
677<A NAME="erf"></A> 603Previous:&nbsp;<a rel="previous" accesskey="p" href="#cosh">cosh</a>,
678<HR SIZE="6"> 604Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
679<A NAME="SEC12"></A> 605
680<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> 606</div>
681<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC11"> &lt; </A>]</TD> 607
682<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC13"> &gt; </A>]</TD> 608<h3 class="section">1.13 <code>erf</code>, <code>erff</code>, <code>erfc</code>, <code>erfcf</code>&mdash;error function</h3>
683<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC3"> &lt;&lt; </A>]</TD> 609
684<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD> 610<p><a name="index-erf-35"></a><a name="index-erff-36"></a><a name="index-erfc-37"></a><a name="index-erfcf-38"></a><strong>Synopsis</strong>
685<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &gt;&gt; </A>]</TD> 611<pre class="example"> #include &lt;math.h&gt;
686<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD> 612 double erf(double <var>x</var>);
687<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD> 613 float erff(float <var>x</var>);
688<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD> 614 double erfc(double <var>x</var>);
689<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD> 615 float erfcf(float <var>x</var>);
690</TR></TABLE> 616</pre>
691<H2> 1.11 <CODE>erf</CODE>, <CODE>erff</CODE>, <CODE>erfc</CODE>, <CODE>erfcf</CODE>---error function </H2> 617 <p><strong>Description</strong><br>
692<!--docid::SEC12::--> 618<code>erf</code> calculates an approximation to the &ldquo;error function&rdquo;,
693<STRONG>Synopsis</STRONG>
694<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
695double erf(double <VAR>x</VAR>);
696float erff(float <VAR>x</VAR>);
697double erfc(double <VAR>x</VAR>);
698float erfcf(float <VAR>x</VAR>);
699</pre></td></tr></table><STRONG>Description</STRONG><BR>
700<CODE>erf</CODE> calculates an approximation to the "error function",
701which estimates the probability that an observation will fall within 619which estimates the probability that an observation will fall within
702<VAR>x</VAR> standard deviations of the mean (assuming a normal 620<var>x</var> standard deviations of the mean (assuming a normal
703distribution). 621distribution).
704<P>
705 622
706<CODE>erfc</CODE> calculates the complementary probability; that is, 623 <p><code>erfc</code> calculates the complementary probability; that is,
707<CODE>erfc(<VAR>x</VAR>)</CODE> is <CODE>1 - erf(<VAR>x</VAR>)</CODE>. <CODE>erfc</CODE> is computed directly, 624<code>erfc(</code><var>x</var><code>)</code> is <code>1 - erf(</code><var>x</var><code>)</code>. <code>erfc</code> is computed directly,
708so that you can use it to avoid the loss of precision that would 625so that you can use it to avoid the loss of precision that would
709result from subtracting large probabilities (on large <VAR>x</VAR>) from 1. 626result from subtracting large probabilities (on large <var>x</var>) from 1.
710</P><P>
711 627
712<CODE>erff</CODE> and <CODE>erfcf</CODE> differ from <CODE>erf</CODE> and <CODE>erfc</CODE> only in the 628 <p><code>erff</code> and <code>erfcf</code> differ from <code>erf</code> and <code>erfc</code> only in the
713argument and result types. 629argument and result types.
714</P><P> 630
715 631 <p><br>
716<BR> 632<strong>Returns</strong><br>
717<STRONG>Returns</STRONG><BR> 633For positive arguments, <code>erf</code> and all its variants return a
718For positive arguments, <CODE>erf</CODE> and all its variants return a 634probability&mdash;a number between 0 and 1.
719probability--a number between 0 and 1. 635
720</P><P> 636 <p><br>
721 637<strong>Portability</strong><br>
722<BR> 638None of the variants of <code>erf</code> are ANSI C.
723<STRONG>Portability</STRONG><BR> 639
724None of the variants of <CODE>erf</CODE> are ANSI C. 640 <p><br>
725</P><P> 641
726 642<div class="node">
727<BR> 643<p><hr>
728</P><P> 644<a name="exp"></a>
729 645Next:&nbsp;<a rel="next" accesskey="n" href="#expm1">expm1</a>,
730<A NAME="exp"></A> 646Previous:&nbsp;<a rel="previous" accesskey="p" href="#erf">erf</a>,
731<HR SIZE="6"> 647Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
732<A NAME="SEC13"></A> 648
733<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> 649</div>
734<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC12"> &lt; </A>]</TD> 650
735<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC14"> &gt; </A>]</TD> 651<h3 class="section">1.14 <code>exp</code>, <code>expf</code>&mdash;exponential</h3>
736<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC3"> &lt;&lt; </A>]</TD> 652
737<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD> 653<p><a name="index-exp-39"></a><a name="index-expf-40"></a><strong>Synopsis</strong>
738<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &gt;&gt; </A>]</TD> 654<pre class="example"> #include &lt;math.h&gt;
739<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD> 655 double exp(double <var>x</var>);
740<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD> 656 float expf(float <var>x</var>);
741<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD> 657
742<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD> 658</pre>
743</TR></TABLE> 659 <p><strong>Description</strong><br>
744<H2> 1.12 <CODE>exp</CODE>, <CODE>expf</CODE>---exponential </H2> 660<code>exp</code> and <code>expf</code> calculate the exponential of <var>x</var>, that is,
745<!--docid::SEC13::--> 661e raised to the power <var>x</var> (where e
746<STRONG>Synopsis</STRONG>
747<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
748double exp(double <VAR>x</VAR>);
749float expf(float <VAR>x</VAR>);
750
751</pre></td></tr></table><STRONG>Description</STRONG><BR>
752<CODE>exp</CODE> and <CODE>expf</CODE> calculate the exponential of <VAR>x</VAR>, that is,
753e raised to the power <VAR>x</VAR> (where e
754is the base of the natural system of logarithms, approximately 2.71828). 662is the base of the natural system of logarithms, approximately 2.71828).
755<P>
756 663
757You can use the (non-ANSI) function <CODE>matherr</CODE> to specify 664 <p>You can use the (non-ANSI) function <code>matherr</code> to specify
758error handling for these functions. 665error handling for these functions.
759</P><P> 666
760 667 <p><br>
761<BR> 668<strong>Returns</strong><br>
762<STRONG>Returns</STRONG><BR> 669On success, <code>exp</code> and <code>expf</code> return the calculated value.
763On success, <CODE>exp</CODE> and <CODE>expf</CODE> return the calculated value. 670If the result underflows, the returned value is <code>0</code>. If the
764If the result underflows, the returned value is <CODE>0</CODE>. If the 671result overflows, the returned value is <code>HUGE_VAL</code>. In
765result overflows, the returned value is <CODE>HUGE_VAL</CODE>. In 672either case, <code>errno</code> is set to <code>ERANGE</code>.
766either case, <CODE>errno</CODE> is set to <CODE>ERANGE</CODE>. 673
767</P><P> 674 <p><br>
768 675<strong>Portability</strong><br>
769<BR> 676<code>exp</code> is ANSI C. <code>expf</code> is an extension.
770<STRONG>Portability</STRONG><BR> 677
771<CODE>exp</CODE> is ANSI C. <CODE>expf</CODE> is an extension. 678 <p><br>
772</P><P> 679
773 680<div class="node">
774<BR> 681<p><hr>
775</P><P> 682<a name="expm1"></a>
776 683Next:&nbsp;<a rel="next" accesskey="n" href="#fabs">fabs</a>,
777<A NAME="fabs"></A> 684Previous:&nbsp;<a rel="previous" accesskey="p" href="#exp">exp</a>,
778<HR SIZE="6"> 685Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
779<A NAME="SEC14"></A> 686
780<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> 687</div>
781<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC13"> &lt; </A>]</TD> 688
782<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC15"> &gt; </A>]</TD> 689<h3 class="section">1.15 <code>expm1</code>, <code>expm1f</code>&mdash;exponential minus 1</h3>
783<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC3"> &lt;&lt; </A>]</TD> 690
784<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD> 691<p><a name="index-expm1-41"></a><a name="index-expm1f-42"></a><strong>Synopsis</strong>
785<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &gt;&gt; </A>]</TD> 692<pre class="example"> #include &lt;math.h&gt;
786<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD> 693 double expm1(double <var>x</var>);
787<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD> 694 float expm1f(float <var>x</var>);
788<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD> 695
789<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD> 696</pre>
790</TR></TABLE> 697 <p><strong>Description</strong><br>
791<H2> 1.13 <CODE>fabs</CODE>, <CODE>fabsf</CODE>---absolute value (magnitude) </H2> 698<code>expm1</code> and <code>expm1f</code> calculate the exponential of <var>x</var>
792<!--docid::SEC14::--> 699and subtract 1, that is,
793<STRONG>Synopsis</STRONG> 700e raised to the power <var>x</var> minus 1 (where e
794<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62; 701is the base of the natural system of logarithms, approximately
795double fabs(double <VAR>x</VAR>); 7022.71828). The result is accurate even for small values of
796float fabsf(float <VAR>x</VAR>); 703<var>x</var>, where using <code>exp(</code><var>x</var><code>)-1</code> would lose many
797 704significant digits.
798</pre></td></tr></table><STRONG>Description</STRONG><BR> 705
799<CODE>fabs</CODE> and <CODE>fabsf</CODE> calculate 706 <p><br>
800the absolute value (magnitude) of the argument <VAR>x</VAR>, by direct 707<strong>Returns</strong><br>
801manipulation of the bit representation of <VAR>x</VAR>. 708e raised to the power <var>x</var>, minus 1.
802<P> 709
803 710 <p><br>
804<BR> 711<strong>Portability</strong><br>
805<STRONG>Returns</STRONG><BR> 712Neither <code>expm1</code> nor <code>expm1f</code> is required by ANSI C or by
713the System V Interface Definition (Issue 2).
714
715 <p><br>
716
717<div class="node">
718<p><hr>
719<a name="fabs"></a>
720Next:&nbsp;<a rel="next" accesskey="n" href="#floor">floor</a>,
721Previous:&nbsp;<a rel="previous" accesskey="p" href="#expm1">expm1</a>,
722Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
723
724</div>
725
726<h3 class="section">1.16 <code>fabs</code>, <code>fabsf</code>&mdash;absolute value (magnitude)</h3>
727
728<p><a name="index-fabs-43"></a><a name="index-fabsf-44"></a><strong>Synopsis</strong>
729<pre class="example"> #include &lt;math.h&gt;
730 double fabs(double <var>x</var>);
731 float fabsf(float <var>x</var>);
732
733</pre>
734 <p><strong>Description</strong><br>
735<code>fabs</code> and <code>fabsf</code> calculate
736the absolute value (magnitude) of the argument <var>x</var>, by direct
737manipulation of the bit representation of <var>x</var>.
738
739 <p><br>
740<strong>Returns</strong><br>
806The calculated value is returned. No errors are detected. 741The calculated value is returned. No errors are detected.
807</P><P> 742
808 743 <p><br>
809<BR> 744<strong>Portability</strong><br>
810<STRONG>Portability</STRONG><BR> 745<code>fabs</code> is ANSI.
811<CODE>fabs</CODE> is ANSI. 746<code>fabsf</code> is an extension.
812<CODE>fabsf</CODE> is an extension. 747
813</P><P> 748 <p><br>
814 749
815<BR> 750<div class="node">
816</P><P> 751<p><hr>
817 752<a name="floor"></a>
818<A NAME="floor"></A> 753Next:&nbsp;<a rel="next" accesskey="n" href="#fmod">fmod</a>,
819<HR SIZE="6"> 754Previous:&nbsp;<a rel="previous" accesskey="p" href="#fabs">fabs</a>,
820<A NAME="SEC15"></A> 755Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
821<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> 756
822<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC14"> &lt; </A>]</TD> 757</div>
823<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC16"> &gt; </A>]</TD> 758
824<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC3"> &lt;&lt; </A>]</TD> 759<h3 class="section">1.17 <code>floor</code>, <code>floorf</code>, <code>ceil</code>, <code>ceilf</code>&mdash;floor and ceiling</h3>
825<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD> 760
826<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &gt;&gt; </A>]</TD> 761<p><a name="index-floor-45"></a><a name="index-floorf-46"></a><a name="index-ceil-47"></a><a name="index-ceilf-48"></a><strong>Synopsis</strong>
827<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD> 762<pre class="example"> #include &lt;math.h&gt;
828<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD> 763 double floor(double <var>x</var>);
829<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD> 764 float floorf(float <var>x</var>);
830<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD> 765 double ceil(double <var>x</var>);
831</TR></TABLE> 766 float ceilf(float <var>x</var>);
832<H2> 1.14 <CODE>floor</CODE>, <CODE>floorf</CODE>, <CODE>ceil</CODE>, <CODE>ceilf</CODE>---floor and ceiling </H2> 767
833<!--docid::SEC15::--> 768</pre>
834<STRONG>Synopsis</STRONG> 769 <p><strong>Description</strong><br>
835<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62; 770<code>floor</code> and <code>floorf</code> find
836double floor(double <VAR>x</VAR>); 771the nearest integer less than or equal to <var>x</var>.
837float floorf(float <VAR>x</VAR>); 772<code>ceil</code> and <code>ceilf</code> find
838double ceil(double <VAR>x</VAR>); 773the nearest integer greater than or equal to <var>x</var>.
839float ceilf(float <VAR>x</VAR>); 774
840 775 <p><br>
841</pre></td></tr></table><STRONG>Description</STRONG><BR> 776<strong>Returns</strong><br>
842<CODE>floor</CODE> and <CODE>floorf</CODE> find 777<code>floor</code> and <code>ceil</code> return the integer result as a double.
843the nearest integer less than or equal to <VAR>x</VAR>. 778<code>floorf</code> and <code>ceilf</code> return the integer result as a float.
844<CODE>ceil</CODE> and <CODE>ceilf</CODE> find 779
845the nearest integer greater than or equal to <VAR>x</VAR>. 780 <p><br>
846<P> 781<strong>Portability</strong><br>
847 782<code>floor</code> and <code>ceil</code> are ANSI.
848<BR> 783<code>floorf</code> and <code>ceilf</code> are extensions.
849<STRONG>Returns</STRONG><BR> 784
850<CODE>floor</CODE> and <CODE>ceil</CODE> return the integer result as a double. 785 <p><br>
851<CODE>floorf</CODE> and <CODE>ceilf</CODE> return the integer result as a float. 786
852</P><P> 787<div class="node">
853 788<p><hr>
854<BR> 789<a name="fmod"></a>
855<STRONG>Portability</STRONG><BR> 790Next:&nbsp;<a rel="next" accesskey="n" href="#frexp">frexp</a>,
856<CODE>floor</CODE> and <CODE>ceil</CODE> are ANSI. 791Previous:&nbsp;<a rel="previous" accesskey="p" href="#floor">floor</a>,
857<CODE>floorf</CODE> and <CODE>ceilf</CODE> are extensions. 792Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
858</P><P> 793
859 794</div>
860<BR> 795
861</P><P> 796<h3 class="section">1.18 <code>fmod</code>, <code>fmodf</code>&mdash;floating-point remainder (modulo)</h3>
862 797
863<A NAME="fmod"></A> 798<p><a name="index-fmod-49"></a><a name="index-fmodf-50"></a><strong>Synopsis</strong>
864<HR SIZE="6"> 799<pre class="example"> #include &lt;math.h&gt;
865<A NAME="SEC16"></A> 800 double fmod(double <var>x</var>, double <var>y</var>)
866<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> 801 float fmodf(float <var>x</var>, float <var>y</var>)
867<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC15"> &lt; </A>]</TD> 802
868<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC17"> &gt; </A>]</TD> 803</pre>
869<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC3"> &lt;&lt; </A>]</TD> 804 <p><strong>Description</strong><br>
870<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD> 805The <code>fmod</code> and <code>fmodf</code> functions compute the floating-point
871<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &gt;&gt; </A>]</TD> 806remainder of <var>x</var>/<var>y</var> (<var>x</var> modulo <var>y</var>).
872<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD> 807
873<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD> 808 <p><br>
874<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD> 809<strong>Returns</strong><br>
875<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD> 810The <code>fmod</code> function returns the value
876</TR></TABLE> 811<var>x</var>-<var>i</var>*<var>y</var>,
877<H2> 1.15 <CODE>fmod</CODE>, <CODE>fmodf</CODE>---floating-point remainder (modulo) </H2> 812for the largest integer <var>i</var> such that, if <var>y</var> is nonzero, the
878<!--docid::SEC16::--> 813result has the same sign as <var>x</var> and magnitude less than the
879<STRONG>Synopsis</STRONG> 814magnitude of <var>y</var>.
880<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62; 815
881double fmod(double <VAR>x</VAR>, double <VAR>y</VAR>) 816 <p><code>fmod(</code><var>x</var><code>,0)</code> returns NaN, and sets <code>errno</code> to <code>EDOM</code>.
882float fmodf(float <VAR>x</VAR>, float <VAR>y</VAR>) 817
883 818 <p>You can modify error treatment for these functions using <code>matherr</code>.
884</pre></td></tr></table><STRONG>Description</STRONG><BR> 819
885The <CODE>fmod</CODE> and <CODE>fmodf</CODE> functions compute the floating-point 820 <p><br>
886remainder of <VAR>x</VAR>/<VAR>y</VAR> (<VAR>x</VAR> modulo <VAR>y</VAR>). 821<strong>Portability</strong><br>
887<P> 822<code>fmod</code> is ANSI C. <code>fmodf</code> is an extension.
888 823
889<BR> 824 <p><br>
890<STRONG>Returns</STRONG><BR> 825
891The <CODE>fmod</CODE> function returns the value 826<div class="node">
892<VAR>x</VAR>-<VAR>i</VAR>*<VAR>y</VAR>, 827<p><hr>
893for the largest integer <VAR>i</VAR> such that, if <VAR>y</VAR> is nonzero, the 828<a name="frexp"></a>
894result has the same sign as <VAR>x</VAR> and magnitude less than the 829Next:&nbsp;<a rel="next" accesskey="n" href="#gamma">gamma</a>,
895magnitude of <VAR>y</VAR>. 830Previous:&nbsp;<a rel="previous" accesskey="p" href="#fmod">fmod</a>,
896</P><P> 831Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
897 832
898<CODE>fmod(<VAR>x</VAR>,0)</CODE> returns NaN, and sets <CODE>errno</CODE> to <CODE>EDOM</CODE>. 833</div>
899</P><P> 834
900 835<h3 class="section">1.19 <code>frexp</code>, <code>frexpf</code>&mdash;split floating-point number</h3>
901You can modify error treatment for these functions using <CODE>matherr</CODE>. 836
902</P><P> 837<p><a name="index-frexp-51"></a><a name="index-frexpf-52"></a><strong>Synopsis</strong>
903 838<pre class="example"> #include &lt;math.h&gt;
904<BR> 839 double frexp(double <var>val</var>, int *<var>exp</var>);
905<STRONG>Portability</STRONG><BR> 840 float frexpf(float <var>val</var>, int *<var>exp</var>);
906<CODE>fmod</CODE> is ANSI C. <CODE>fmodf</CODE> is an extension. 841
907</P><P> 842</pre>
908 843 <p><strong>Description</strong><br>
909<BR> 844All nonzero, normal numbers can be described as <var>m</var> * 2**<var>p</var>.
910</P><P> 845<code>frexp</code> represents the double <var>val</var> as a mantissa <var>m</var>
911 846and a power of two <var>p</var>. The resulting mantissa will always
912<A NAME="frexp"></A> 847be greater than or equal to <code>0.5</code>, and less than <code>1.0</code> (as
913<HR SIZE="6"> 848long as <var>val</var> is nonzero). The power of two will be stored
914<A NAME="SEC17"></A> 849in <code>*</code><var>exp</var>.
915<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> 850
916<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC16"> &lt; </A>]</TD> 851 <p><var>m</var> and <var>p</var> are calculated so that
917<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC18"> &gt; </A>]</TD> 852<var>val</var> is <var>m</var> times <code>2</code> to the power <var>p</var>.
918<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC3"> &lt;&lt; </A>]</TD> 853
919<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD> 854 <p><code>frexpf</code> is identical, other than taking and returning
920<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &gt;&gt; </A>]</TD>
921<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD>
922<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD>
923<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
924<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
925</TR></TABLE>
926<H2> 1.16 <CODE>frexp</CODE>, <CODE>frexpf</CODE>---split floating-point number </H2>
927<!--docid::SEC17::-->
928<STRONG>Synopsis</STRONG>
929<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
930double frexp(double <VAR>val</VAR>, int *<VAR>exp</VAR>);
931float frexpf(float <VAR>val</VAR>, int *<VAR>exp</VAR>);
932
933</pre></td></tr></table><STRONG>Description</STRONG><BR>
934All nonzero, normal numbers can be described as <VAR>m</VAR> * 2**<VAR>p</VAR>.
935<CODE>frexp</CODE> represents the double <VAR>val</VAR> as a mantissa <VAR>m</VAR>
936and a power of two <VAR>p</VAR>. The resulting mantissa will always
937be greater than or equal to <CODE>0.5</CODE>, and less than <CODE>1.0</CODE> (as
938long as <VAR>val</VAR> is nonzero). The power of two will be stored
939in <CODE>*</CODE><VAR>exp</VAR>.
940<P>
941
942<VAR>m</VAR> and <VAR>p</VAR> are calculated so that
943<VAR>val</VAR> is <VAR>m</VAR> times <CODE>2</CODE> to the power <VAR>p</VAR>.
944</P><P>
945
946<CODE>frexpf</CODE> is identical, other than taking and returning
947floats rather than doubles. 855floats rather than doubles.
948</P><P> 856
949 857 <p><br>
950<BR> 858<strong>Returns</strong><br>
951<STRONG>Returns</STRONG><BR> 859<code>frexp</code> returns the mantissa <var>m</var>. If <var>val</var> is <code>0</code>, infinity,
952<CODE>frexp</CODE> returns the mantissa <VAR>m</VAR>. If <VAR>val</VAR> is <CODE>0</CODE>, infinity, 860or Nan, <code>frexp</code> will set <code>*</code><var>exp</var> to <code>0</code> and return <var>val</var>.
953or Nan, <CODE>frexp</CODE> will set <CODE>*</CODE><VAR>exp</VAR> to <CODE>0</CODE> and return <VAR>val</VAR>. 861
954</P><P> 862 <p><br>
955 863<strong>Portability</strong><br>
956<BR> 864<code>frexp</code> is ANSI.
957<STRONG>Portability</STRONG><BR> 865<code>frexpf</code> is an extension.
958<CODE>frexp</CODE> is ANSI. 866
959<CODE>frexpf</CODE> is an extension. 867 <p><br>
960</P><P> 868
961 869<div class="node">
962<BR> 870<p><hr>
963</P><P> 871<a name="gamma"></a>
964 872Next:&nbsp;<a rel="next" accesskey="n" href="#hypot">hypot</a>,
965<A NAME="gamma"></A> 873Previous:&nbsp;<a rel="previous" accesskey="p" href="#frexp">frexp</a>,
966<HR SIZE="6"> 874Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
967<A NAME="SEC18"></A> 875
968<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> 876</div>
969<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC17"> &lt; </A>]</TD> 877
970<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC19"> &gt; </A>]</TD> 878<h3 class="section">1.20 <code>gamma</code>, <code>gammaf</code>, <code>lgamma</code>, <code>lgammaf</code>, <code>gamma_r</code>,</h3>
971<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC3"> &lt;&lt; </A>]</TD> 879
972<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD> 880<p><a name="index-gamma-53"></a><a name="index-gammaf-54"></a><a name="index-lgamma-55"></a><a name="index-lgammaf-56"></a><a name="index-gamma_005fr-57"></a><a name="index-gammaf_005fr-58"></a><a name="index-lgamma_005fr-59"></a><a name="index-lgammaf_005fr-60"></a><strong>Synopsis</strong>
973<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &gt;&gt; </A>]</TD> 881<pre class="example"> #include &lt;math.h&gt;
974<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD> 882 double gamma(double <var>x</var>);
975<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD> 883 float gammaf(float <var>x</var>);
976<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD> 884 double lgamma(double <var>x</var>);
977<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD> 885 float lgammaf(float <var>x</var>);
978</TR></TABLE> 886 double gamma_r(double <var>x</var>, int *<var>signgamp</var>);
979<H2> 1.17 <CODE>gamma</CODE>, <CODE>gammaf</CODE>, <CODE>lgamma</CODE>, <CODE>lgammaf</CODE>, <CODE>gamma_r</CODE>, </H2> 887 float gammaf_r(float <var>x</var>, int *<var>signgamp</var>);
980<!--docid::SEC18::--> 888 double lgamma_r(double <var>x</var>, int *<var>signgamp</var>);
981<STRONG>Synopsis</STRONG> 889 float lgammaf_r(float <var>x</var>, int *<var>signgamp</var>);
982<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62; 890
983double gamma(double <VAR>x</VAR>); 891</pre>
984float gammaf(float <VAR>x</VAR>); 892 <p><strong>Description</strong><br>
985double lgamma(double <VAR>x</VAR>); 893<code>gamma</code> calculates
986float lgammaf(float <VAR>x</VAR>); 894the natural logarithm of the gamma function of <var>x</var>. The gamma function
987double gamma_r(double <VAR>x</VAR>, int *<VAR>signgamp</VAR>); 895(<code>exp(gamma(</code><var>x</var><code>))</code>) is a generalization of factorial, and retains
988float gammaf_r(float <VAR>x</VAR>, int *<VAR>signgamp</VAR>); 896the property that
989double lgamma_r(double <VAR>x</VAR>, int *<VAR>signgamp</VAR>); 897<code>exp(gamma(N))</code> is equivalent to <code>N*exp(gamma(N-1))</code>.
990float lgammaf_r(float <VAR>x</VAR>, int *<VAR>signgamp</VAR>);
991
992</pre></td></tr></table><STRONG>Description</STRONG><BR>
993<CODE>gamma</CODE> calculates
994the natural logarithm of the gamma function of <VAR>x</VAR>. The gamma function
995(<CODE>exp(gamma(<VAR>x</VAR>))</CODE>) is a generalization of factorial, and retains
996the property that
997<CODE>exp(gamma(N))</CODE> is equivalent to <CODE>N*exp(gamma(N-1))</CODE>.
998Accordingly, the results of the gamma function itself grow very 898Accordingly, the results of the gamma function itself grow very
999quickly. <CODE>gamma</CODE> is defined as 899quickly. <code>gamma</code> is defined as
1000the natural log of the gamma function, rather than the gamma function 900the natural log of the gamma function, rather than the gamma function
1001itself, 901itself,
1002to extend the useful range of results representable. 902to extend the useful range of results representable.
1003<P>
1004 903
1005The sign of the result is returned in the global variable <CODE>signgam</CODE>, 904 <p>The sign of the result is returned in the global variable <code>signgam</code>,
1006which is declared in math.h. 905which is declared in math.h.
1007</P><P>
1008 906
1009<CODE>gammaf</CODE> performs the same calculation as <CODE>gamma</CODE>, but uses and 907 <p><code>gammaf</code> performs the same calculation as <code>gamma</code>, but uses and
1010returns <CODE>float</CODE> values. 908returns <code>float</code> values.
1011</P><P>
1012 909
1013<CODE>lgamma</CODE> and <CODE>lgammaf</CODE> are alternate names for <CODE>gamma</CODE> and 910 <p><code>lgamma</code> and <code>lgammaf</code> are alternate names for <code>gamma</code> and
1014<CODE>gammaf</CODE>. The use of <CODE>lgamma</CODE> instead of <CODE>gamma</CODE> is a reminder 911<code>gammaf</code>. The use of <code>lgamma</code> instead of <code>gamma</code> is a reminder
1015that these functions compute the log of the gamma function, rather 912that these functions compute the log of the gamma function, rather
1016than the gamma function itself. 913than the gamma function itself.
1017</P><P>
1018 914
1019The functions <CODE>gamma_r</CODE>, <CODE>gammaf_r</CODE>, <CODE>lgamma_r</CODE>, and 915 <p>The functions <code>gamma_r</code>, <code>gammaf_r</code>, <code>lgamma_r</code>, and
1020<CODE>lgammaf_r</CODE> are just like <CODE>gamma</CODE>, <CODE>gammaf</CODE>, <CODE>lgamma</CODE>, and 916<code>lgammaf_r</code> are just like <code>gamma</code>, <code>gammaf</code>, <code>lgamma</code>, and
1021<CODE>lgammaf</CODE>, respectively, but take an additional argument. This 917<code>lgammaf</code>, respectively, but take an additional argument. This
1022additional argument is a pointer to an integer. This additional 918additional argument is a pointer to an integer. This additional
1023argument is used to return the sign of the result, and the global 919argument is used to return the sign of the result, and the global
1024variable <CODE>signgam</CODE> is not used. These functions may be used for 920variable <code>signgam</code> is not used. These functions may be used for
1025reentrant calls (but they will still set the global variable <CODE>errno</CODE> 921reentrant calls (but they will still set the global variable <code>errno</code>
1026if an error occurs). 922if an error occurs).
1027</P><P> 923
1028 924 <p><br>
1029<BR> 925<strong>Returns</strong><br>
1030<STRONG>Returns</STRONG><BR> 926Normally, the computed result is returned.
1031Normally, the computed result is returned. 927
1032</P><P> 928 <p>When <var>x</var> is a nonpositive integer, <code>gamma</code> returns <code>HUGE_VAL</code>
1033 929and <code>errno</code> is set to <code>EDOM</code>. If the result overflows, <code>gamma</code>
1034When <VAR>x</VAR> is a nonpositive integer, <CODE>gamma</CODE> returns <CODE>HUGE_VAL</CODE> 930returns <code>HUGE_VAL</code> and <code>errno</code> is set to <code>ERANGE</code>.
1035and <CODE>errno</CODE> is set to <CODE>EDOM</CODE>. If the result overflows, <CODE>gamma</CODE> 931
1036returns <CODE>HUGE_VAL</CODE> and <CODE>errno</CODE> is set to <CODE>ERANGE</CODE>. 932 <p>You can modify this error treatment using <code>matherr</code>.
1037</P><P> 933
1038 934 <p><br>
1039You can modify this error treatment using <CODE>matherr</CODE>. 935<strong>Portability</strong><br>
1040</P><P> 936Neither <code>gamma</code> nor <code>gammaf</code> is ANSI C.
1041 937<br>
1042<BR> 938
1043<STRONG>Portability</STRONG><BR> 939<div class="node">
1044Neither <CODE>gamma</CODE> nor <CODE>gammaf</CODE> is ANSI C. 940<p><hr>
1045<BR> 941<a name="hypot"></a>
1046</P><P> 942Next:&nbsp;<a rel="next" accesskey="n" href="#ilogb">ilogb</a>,
1047 943Previous:&nbsp;<a rel="previous" accesskey="p" href="#gamma">gamma</a>,
1048<A NAME="hypot"></A> 944Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
1049<HR SIZE="6"> 945
1050<A NAME="SEC19"></A> 946</div>
1051<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> 947
1052<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC18"> &lt; </A>]</TD> 948<h3 class="section">1.21 <code>hypot</code>, <code>hypotf</code>&mdash;distance from origin</h3>
1053<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC20"> &gt; </A>]</TD> 949
1054<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC3"> &lt;&lt; </A>]</TD> 950<p><a name="index-hypot-61"></a><a name="index-hypotf-62"></a><strong>Synopsis</strong>
1055<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD> 951<pre class="example"> #include &lt;math.h&gt;
1056<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &gt;&gt; </A>]</TD> 952 double hypot(double <var>x</var>, double <var>y</var>);
1057<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD> 953 float hypotf(float <var>x</var>, float <var>y</var>);
1058<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD> 954
1059<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD> 955</pre>
1060<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD> 956 <p><strong>Description</strong><br>
1061</TR></TABLE> 957<code>hypot</code> calculates the Euclidean distance
1062<H2> 1.18 <CODE>hypot</CODE>, <CODE>hypotf</CODE>---distance from origin </H2> 958<code>sqrt(</code><var>x</var><code>*</code><var>x</var><code> + </code><var>y</var><code>*</code><var>y</var><code>)</code>
1063<!--docid::SEC19::-->
1064<STRONG>Synopsis</STRONG>
1065<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1066double hypot(double <VAR>x</VAR>, double <VAR>y</VAR>);
1067float hypotf(float <VAR>x</VAR>, float <VAR>y</VAR>);
1068
1069</pre></td></tr></table><STRONG>Description</STRONG><BR>
1070<CODE>hypot</CODE> calculates the Euclidean distance
1071<CODE>sqrt(<VAR>x</VAR>*<VAR>x</VAR> + <VAR>y</VAR>*<VAR>y</VAR>)</CODE>
1072between the origin (0,0) and a point represented by the 959between the origin (0,0) and a point represented by the
1073Cartesian coordinates (<VAR>x</VAR>,<VAR>y</VAR>). <CODE>hypotf</CODE> differs only 960Cartesian coordinates (<var>x</var>,<var>y</var>). <code>hypotf</code> differs only
1074in the type of its arguments and result. 961in the type of its arguments and result.
1075<P>
1076 962
1077<BR> 963 <p><br>
1078<STRONG>Returns</STRONG><BR> 964<strong>Returns</strong><br>
1079Normally, the distance value is returned. On overflow, 965Normally, the distance value is returned. On overflow,
1080<CODE>hypot</CODE> returns <CODE>HUGE_VAL</CODE> and sets <CODE>errno</CODE> to 966<code>hypot</code> returns <code>HUGE_VAL</code> and sets <code>errno</code> to
1081<CODE>ERANGE</CODE>. 967<code>ERANGE</code>.
1082</P><P> 968
1083 969 <p>You can change the error treatment with <code>matherr</code>.
1084You can change the error treatment with <CODE>matherr</CODE>. 970
1085</P><P> 971 <p><br>
1086 972<strong>Portability</strong><br>
1087<BR> 973<code>hypot</code> and <code>hypotf</code> are not ANSI C.
1088<STRONG>Portability</STRONG><BR> 974<br>
1089<CODE>hypot</CODE> and <CODE>hypotf</CODE> are not ANSI C. 975
1090<BR> 976<div class="node">
1091</P><P> 977<p><hr>
1092 978<a name="ilogb"></a>
1093<A NAME="isnan"></A> 979Next:&nbsp;<a rel="next" accesskey="n" href="#infinity">infinity</a>,
1094<HR SIZE="6"> 980Previous:&nbsp;<a rel="previous" accesskey="p" href="#hypot">hypot</a>,
1095<A NAME="SEC20"></A> 981Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
1096<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> 982
1097<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC19"> &lt; </A>]</TD> 983</div>
1098<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC21"> &gt; </A>]</TD> 984
1099<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC3"> &lt;&lt; </A>]</TD> 985<h3 class="section">1.22 <code>ilogb</code>, <code>ilogbf</code>&mdash;get exponent of floating-point number</h3>
1100<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD> 986
1101<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &gt;&gt; </A>]</TD> 987<p><a name="index-ilogb-63"></a><a name="index-ilogbf-64"></a><strong>Synopsis</strong>
1102<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD> 988<pre class="example"> #include &lt;math.h&gt;
1103<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD> 989 int ilogb(double <var>val</var>);
1104<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD> 990 int ilogbf(float <var>val</var>);
1105<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD> 991
1106</TR></TABLE> 992</pre>
1107<H2> 1.19 <CODE>isnan</CODE>,<CODE>isnanf</CODE>,<CODE>isinf</CODE>,<CODE>isinff</CODE>,<CODE>finite</CODE>,<CODE>finitef</CODE>---test for exceptional numbers </H2> 993 <p><strong>Description</strong><br>
1108<!--docid::SEC20::--> 994
1109<STRONG>Synopsis</STRONG> 995 <p>All nonzero, normal numbers can be described as <var>m</var> *
1110<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;ieeefp.h&#62; 9962**<var>p</var>. <code>ilogb</code> and <code>ilogbf</code> examine the argument
1111int isnan(double <VAR>arg</VAR>); 997<var>val</var>, and return <var>p</var>. The functions <code>frexp</code> and
1112int isinf(double <VAR>arg</VAR>); 998<code>frexpf</code> are similar to <code>ilogb</code> and <code>ilogbf</code>, but also
1113int finite(double <VAR>arg</VAR>); 999return <var>m</var>.
1114int isnanf(float <VAR>arg</VAR>); 1000
1115int isinff(float <VAR>arg</VAR>); 1001 <p><br>
1116int finitef(float <VAR>arg</VAR>); 1002<strong>Returns</strong><br>
1117 1003
1118</pre></td></tr></table><STRONG>Description</STRONG><BR> 1004 <p><code>ilogb</code> and <code>ilogbf</code> return the power of two used to form the
1005floating-point argument. If <var>val</var> is <code>0</code>, they return <code>-
1006INT_MAX</code> (<code>INT_MAX</code> is defined in limits.h). If <var>val</var> is
1007infinite, or NaN, they return <code>INT_MAX</code>.
1008
1009 <p><br>
1010<strong>Portability</strong><br>
1011Neither <code>ilogb</code> nor <code>ilogbf</code> is required by ANSI C or by
1012the System V Interface Definition (Issue 2).
1013<br>
1014
1015<div class="node">
1016<p><hr>
1017<a name="infinity"></a>
1018Next:&nbsp;<a rel="next" accesskey="n" href="#isnan">isnan</a>,
1019Previous:&nbsp;<a rel="previous" accesskey="p" href="#ilogb">ilogb</a>,
1020Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
1021
1022</div>
1023
1024<h3 class="section">1.23 <code>infinity</code>, <code>infinityf</code>&mdash;representation of infinity</h3>
1025
1026<p><a name="index-infinity-65"></a><a name="index-infinityf-66"></a><strong>Synopsis</strong>
1027<pre class="example"> #include &lt;math.h&gt;
1028 double infinity(void);
1029 float infinityf(void);
1030
1031</pre>
1032 <p><strong>Description</strong><br>
1033<code>infinity</code> and <code>infinityf</code> return the special number IEEE
1034infinity in double- and single-precision arithmetic
1035respectively.
1036
1037 <p><br>
1038
1039<div class="node">
1040<p><hr>
1041<a name="isnan"></a>
1042Next:&nbsp;<a rel="next" accesskey="n" href="#ldexp">ldexp</a>,
1043Previous:&nbsp;<a rel="previous" accesskey="p" href="#infinity">infinity</a>,
1044Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
1045
1046</div>
1047
1048<h3 class="section">1.24 <code>isnan</code>, <code>isnanf</code>, <code>isinf</code>, <code>isinff</code>, <code>finite</code>, <code>finitef</code>&mdash;test for exceptional numbers</h3>
1049
1050<p><a name="index-isnan-67"></a><a name="index-isinf-68"></a><a name="index-finite-69"></a><a name="index-isnanf-70"></a><a name="index-isinff-71"></a><a name="index-finitef-72"></a><strong>Synopsis</strong>
1051<pre class="example"> #include &lt;ieeefp.h&gt;
1052 int isnan(double <var>arg</var>);
1053 int isinf(double <var>arg</var>);
1054 int finite(double <var>arg</var>);
1055 int isnanf(float <var>arg</var>);
1056 int isinff(float <var>arg</var>);
1057 int finitef(float <var>arg</var>);
1058
1059</pre>
1060 <p><strong>Description</strong><br>
1119These functions provide information on the floating-point 1061These functions provide information on the floating-point
1120argument supplied. 1062argument supplied.
1121<P>
1122
1123There are five major number formats -
1124<DL COMPACT>
1125
1126<DT><CODE>zero</CODE>
1127<DD>a number which contains all zero bits.
1128<DT><CODE>subnormal</CODE>
1129<DD>Is used to represent number with a zero exponent, but a nonzero fraction.
1130<DT><CODE>normal</CODE>
1131<DD>A number with an exponent, and a fraction
1132<DT><CODE>infinity</CODE>
1133<DD>A number with an all 1's exponent and a zero fraction.
1134<DT><CODE>NAN</CODE>
1135<DD>A number with an all 1's exponent and a nonzero fraction.
1136<P>
1137
1138</DL>
1139<P>
1140
1141<CODE>isnan</CODE> returns 1 if the argument is a nan. <CODE>isinf</CODE>
1142returns 1 if the argument is infinity. <CODE>finite</CODE> returns 1 if the
1143argument is zero, subnormal or normal.
1144The <CODE>isnanf</CODE>, <CODE>isinff</CODE> and <CODE>finitef</CODE> perform the same
1145operations as their <CODE>isnan</CODE>, <CODE>isinf</CODE> and <CODE>finite</CODE>
1146counterparts, but on single-precision floating-point numbers.
1147</P><P>
1148
1149<BR>
1150</P><P>
1151
1152<A NAME="ldexp"></A>
1153<HR SIZE="6">
1154<A NAME="SEC21"></A>
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1165</TR></TABLE>
1166<H2> 1.20 <CODE>ldexp</CODE>, <CODE>ldexpf</CODE>---load exponent </H2>
1167<!--docid::SEC21::-->
1168<STRONG>Synopsis</STRONG>
1169<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1170double ldexp(double <VAR>val</VAR>, int <VAR>exp</VAR>);
1171float ldexpf(float <VAR>val</VAR>, int <VAR>exp</VAR>);
1172
1173</pre></td></tr></table><STRONG>Description</STRONG><BR>
1174<CODE>ldexp</CODE> calculates the value
1175<VAR>val</VAR> times 2 to the power <VAR>exp</VAR>.
1176<CODE>ldexpf</CODE> is identical, save that it takes and returns <CODE>float</CODE>
1177rather than <CODE>double</CODE> values.
1178<P>
1179
1180<BR>
1181<STRONG>Returns</STRONG><BR>
1182<CODE>ldexp</CODE> returns the calculated value.
1183</P><P>
1184
1185Underflow and overflow both set <CODE>errno</CODE> to <CODE>ERANGE</CODE>.
1186On underflow, <CODE>ldexp</CODE> and <CODE>ldexpf</CODE> return 0.0.
1187On overflow, <CODE>ldexp</CODE> returns plus or minus <CODE>HUGE_VAL</CODE>.
1188</P><P>
1189
1190<BR>
1191<STRONG>Portability</STRONG><BR>
1192<CODE>ldexp</CODE> is ANSI, <CODE>ldexpf</CODE> is an extension.
1193</P><P>
1194
1195<BR>
1196</P><P>
1197
1198<A NAME="log"></A>
1199<HR SIZE="6">
1200<A NAME="SEC22"></A>
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1211</TR></TABLE>
1212<H2> 1.21 <CODE>log</CODE>, <CODE>logf</CODE>---natural logarithms </H2>
1213<!--docid::SEC22::-->
1214<STRONG>Synopsis</STRONG>
1215<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1216double log(double <VAR>x</VAR>);
1217float logf(float <VAR>x</VAR>);
1218
1219</pre></td></tr></table><STRONG>Description</STRONG><BR>
1220Return the natural logarithm of <VAR>x</VAR>, that is, its logarithm base e
1221(where e is the base of the natural system of logarithms, 2.71828<small>...</small>).
1222<CODE>log</CODE> and <CODE>logf</CODE> are identical save for the return and argument types.
1223<P>
1224
1225You can use the (non-ANSI) function <CODE>matherr</CODE> to specify error
1226handling for these functions.
1227</P><P>
1228
1229<BR>
1230<STRONG>Returns</STRONG><BR>
1231Normally, returns the calculated value. When <VAR>x</VAR> is zero, the
1232returned value is <CODE>-HUGE_VAL</CODE> and <CODE>errno</CODE> is set to <CODE>ERANGE</CODE>.
1233When <VAR>x</VAR> is negative, the returned value is <CODE>-HUGE_VAL</CODE> and
1234<CODE>errno</CODE> is set to <CODE>EDOM</CODE>. You can control the error behavior via
1235<CODE>matherr</CODE>.
1236</P><P>
1237
1238<BR>
1239<STRONG>Portability</STRONG><BR>
1240<CODE>log</CODE> is ANSI, <CODE>logf</CODE> is an extension.
1241</P><P>
1242
1243<BR>
1244</P><P>
1245
1246<A NAME="log10"></A>
1247<HR SIZE="6">
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1259</TR></TABLE>
1260<H2> 1.22 <CODE>log10</CODE>, <CODE>log10f</CODE>---base 10 logarithms </H2>
1261<!--docid::SEC23::-->
1262<STRONG>Synopsis</STRONG>
1263<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1264double log10(double <VAR>x</VAR>);
1265float log10f(float <VAR>x</VAR>);
1266
1267</pre></td></tr></table><STRONG>Description</STRONG><BR>
1268<CODE>log10</CODE> returns the base 10 logarithm of <VAR>x</VAR>.
1269It is implemented as <CODE>log(<VAR>x</VAR>) / log(10)</CODE>.
1270<P>
1271
1272<CODE>log10f</CODE> is identical, save that it takes and returns <CODE>float</CODE> values.
1273</P><P>
1274
1275<BR>
1276<STRONG>Returns</STRONG><BR>
1277<CODE>log10</CODE> and <CODE>log10f</CODE> return the calculated value.
1278</P><P>
1279
1280See the description of <CODE>log</CODE> for information on errors.
1281</P><P>
1282
1283<BR>
1284<STRONG>Portability</STRONG><BR>
1285<CODE>log10</CODE> is ANSI C. <CODE>log10f</CODE> is an extension.
1286</P><P>
1287
1288<BR>
1289</P><P>
1290
1291<A NAME="pow"></A>
1292<HR SIZE="6">
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1301<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD>
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1304</TR></TABLE>
1305<H2> 1.23 <CODE>pow</CODE>, <CODE>powf</CODE>---x to the power y </H2>
1306<!--docid::SEC24::-->
1307<STRONG>Synopsis</STRONG>
1308<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1309double pow(double <VAR>x</VAR>, double <VAR>y</VAR>);
1310float pow(float <VAR>x</VAR>, float <VAR>y</VAR>);
1311
1312</pre></td></tr></table><STRONG>Description</STRONG><BR>
1313<CODE>pow</CODE> and <CODE>powf</CODE> calculate <VAR>x</VAR> raised to the exponent <VAR>y</VAR>.
1314<P>
1315
1316<BR>
1317<STRONG>Returns</STRONG><BR>
1318On success, <CODE>pow</CODE> and <CODE>powf</CODE> return the value calculated.
1319</P><P>
1320
1321When the argument values would produce overflow, <CODE>pow</CODE>
1322returns <CODE>HUGE_VAL</CODE> and set <CODE>errno</CODE> to <CODE>ERANGE</CODE>. If the
1323argument <VAR>x</VAR> passed to <CODE>pow</CODE> or <CODE>powf</CODE> is a negative
1324noninteger, and <VAR>y</VAR> is also not an integer, then <CODE>errno</CODE>
1325is set to <CODE>EDOM</CODE>. If <VAR>x</VAR> and <VAR>y</VAR> are both 0, then
1326<CODE>pow</CODE> and <CODE>powf</CODE> return <CODE>1</CODE>.
1327</P><P>
1328
1329You can modify error handling for these functions using <CODE>matherr</CODE>.
1330</P><P>
1331
1332<BR>
1333<STRONG>Portability</STRONG><BR>
1334<CODE>pow</CODE> is ANSI C. <CODE>powf</CODE> is an extension.
1335<BR>
1336</P><P>
1337
1338<A NAME="remainder"></A>
1339<HR SIZE="6">
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1351</TR></TABLE>
1352<H2> 1.24 <CODE>remainder</CODE>, <CODE>remainderf</CODE>---round and remainder </H2>
1353<!--docid::SEC25::-->
1354<STRONG>Synopsis</STRONG>
1355<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1356double remainder(double <VAR>x</VAR>, double <VAR>y</VAR>);
1357float remainderf(float <VAR>x</VAR>, float <VAR>y</VAR>);
1358
1359</pre></td></tr></table><STRONG>Description</STRONG><BR>
1360<CODE>remainder</CODE> and <CODE>remainderf</CODE> find the remainder of
1361<VAR>x</VAR>/<VAR>y</VAR>; this value is in the range -<VAR>y</VAR>/2 .. +<VAR>y</VAR>/2.
1362<P>
1363
1364<BR>
1365<STRONG>Returns</STRONG><BR>
1366<CODE>remainder</CODE> returns the integer result as a double.
1367</P><P>
1368
1369<BR>
1370<STRONG>Portability</STRONG><BR>
1371<CODE>remainder</CODE> is a System V release 4.
1372<CODE>remainderf</CODE> is an extension.
1373</P><P>
1374
1375<BR>
1376</P><P>
1377
1378<A NAME="sqrt"></A>
1379<HR SIZE="6">
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1391</TR></TABLE>
1392<H2> 1.25 <CODE>sqrt</CODE>, <CODE>sqrtf</CODE>---positive square root </H2>
1393<!--docid::SEC26::-->
1394<STRONG>Synopsis</STRONG>
1395<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1396double sqrt(double <VAR>x</VAR>);
1397float sqrtf(float <VAR>x</VAR>);
1398
1399</pre></td></tr></table><STRONG>Description</STRONG><BR>
1400<CODE>sqrt</CODE> computes the positive square root of the argument.
1401You can modify error handling for this function with
1402<CODE>matherr</CODE>.
1403<P>
1404
1405<BR>
1406<STRONG>Returns</STRONG><BR>
1407On success, the square root is returned. If <VAR>x</VAR> is real and
1408positive, then the result is positive. If <VAR>x</VAR> is real and
1409negative, the global value <CODE>errno</CODE> is set to <CODE>EDOM</CODE> (domain error).
1410</P><P>
1411
1412<BR>
1413<STRONG>Portability</STRONG><BR>
1414<CODE>sqrt</CODE> is ANSI C. <CODE>sqrtf</CODE> is an extension.
1415</P><P>
1416
1417<BR>
1418</P><P>
1419
1420<A NAME="sin"></A>
1421<HR SIZE="6">
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1433</TR></TABLE>
1434<H2> 1.26 <CODE>sin</CODE>, <CODE>sinf</CODE>, <CODE>cos</CODE>, <CODE>cosf</CODE>---sine or cosine </H2>
1435<!--docid::SEC27::-->
1436<STRONG>Synopsis</STRONG>
1437<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1438double sin(double <VAR>x</VAR>);
1439float sinf(float <VAR>x</VAR>);
1440double cos(double <VAR>x</VAR>);
1441float cosf(float <VAR>x</VAR>);
1442
1443</pre></td></tr></table><STRONG>Description</STRONG><BR>
1444<CODE>sin</CODE> and <CODE>cos</CODE> compute (respectively) the sine and cosine
1445of the argument <VAR>x</VAR>. Angles are specified in radians.
1446<P>
1447
1448<CODE>sinf</CODE> and <CODE>cosf</CODE> are identical, save that they take and
1449return <CODE>float</CODE> values.
1450</P><P>
1451
1452<BR>
1453<STRONG>Returns</STRONG><BR>
1454The sine or cosine of <VAR>x</VAR> is returned.
1455</P><P>
1456
1457<BR>
1458<STRONG>Portability</STRONG><BR>
1459<CODE>sin</CODE> and <CODE>cos</CODE> are ANSI C.
1460<CODE>sinf</CODE> and <CODE>cosf</CODE> are extensions.
1461</P><P>
1462
1463<BR>
1464</P><P>
1465
1466<A NAME="sinh"></A>
1467<HR SIZE="6">
1468<A NAME="SEC28"></A>
1469<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
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1478<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
1479</TR></TABLE>
1480<H2> 1.27 <CODE>sinh</CODE>, <CODE>sinhf</CODE>---hyperbolic sine </H2>
1481<!--docid::SEC28::-->
1482<STRONG>Synopsis</STRONG>
1483<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1484double sinh(double <VAR>x</VAR>);
1485float sinhf(float <VAR>x</VAR>);
1486
1487</pre></td></tr></table><STRONG>Description</STRONG><BR>
1488<CODE>sinh</CODE> computes the hyperbolic sine of the argument <VAR>x</VAR>.
1489Angles are specified in radians. <CODE>sinh</CODE>(<VAR>x</VAR>) is defined as
1490<TABLE><tr><td>&nbsp;</td><td class=smallexample><FONT SIZE=-1><pre> (exp(<VAR>x</VAR>) - exp(-<VAR>x</VAR>))/2
1491</FONT></pre></td></tr></table><P>
1492
1493<CODE>sinhf</CODE> is identical, save that it takes and returns <CODE>float</CODE> values.
1494</P><P>
1495
1496<BR>
1497<STRONG>Returns</STRONG><BR>
1498The hyperbolic sine of <VAR>x</VAR> is returned.
1499</P><P>
1500
1501When the correct result is too large to be representable (an
1502overflow), <CODE>sinh</CODE> returns <CODE>HUGE_VAL</CODE> with the
1503appropriate sign, and sets the global value <CODE>errno</CODE> to
1504<CODE>ERANGE</CODE>.
1505</P><P>
1506
1507You can modify error handling for these functions with <CODE>matherr</CODE>.
1508</P><P>
1509
1510<BR>
1511<STRONG>Portability</STRONG><BR>
1512<CODE>sinh</CODE> is ANSI C.
1513<CODE>sinhf</CODE> is an extension.
1514</P><P>
1515
1516<BR>
1517</P><P>
1518
1519<A NAME="tan"></A>
1520<HR SIZE="6">
1521<A NAME="SEC29"></A>
1522<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
1523<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC28"> &lt; </A>]</TD>
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1527<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &gt;&gt; </A>]</TD>
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1529<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD>
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1531<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
1532</TR></TABLE>
1533<H2> 1.28 <CODE>tan</CODE>, <CODE>tanf</CODE>---tangent </H2>
1534<!--docid::SEC29::-->
1535<STRONG>Synopsis</STRONG>
1536<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1537double tan(double <VAR>x</VAR>);
1538float tanf(float <VAR>x</VAR>);
1539
1540</pre></td></tr></table><STRONG>Description</STRONG><BR>
1541<CODE>tan</CODE> computes the tangent of the argument <VAR>x</VAR>.
1542Angles are specified in radians.
1543<P>
1544
1545<CODE>tanf</CODE> is identical, save that it takes and returns <CODE>float</CODE> values.
1546</P><P>
1547
1548<BR>
1549<STRONG>Returns</STRONG><BR>
1550The tangent of <VAR>x</VAR> is returned.
1551</P><P>
1552
1553<BR>
1554<STRONG>Portability</STRONG><BR>
1555<CODE>tan</CODE> is ANSI. <CODE>tanf</CODE> is an extension.
1556</P><P>
1557
1558<BR>
1559</P><P>
1560
1561<A NAME="tanh"></A>
1562<HR SIZE="6">
1563<A NAME="SEC30"></A>
1564<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
1565<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC29"> &lt; </A>]</TD>
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1571<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD>
1572<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
1573<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
1574</TR></TABLE>
1575<H2> 1.29 <CODE>tanh</CODE>, <CODE>tanhf</CODE>---hyperbolic tangent </H2>
1576<!--docid::SEC30::-->
1577<STRONG>Synopsis</STRONG>
1578<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1579double tanh(double <VAR>x</VAR>);
1580float tanhf(float <VAR>x</VAR>);
1581
1582</pre></td></tr></table><STRONG>Description</STRONG><BR>
1583<P>
1584
1585<CODE>tanh</CODE> computes the hyperbolic tangent of
1586the argument <VAR>x</VAR>. Angles are specified in radians.
1587</P><P>
1588
1589<CODE>tanh(<VAR>x</VAR>)</CODE> is defined as
1590<TABLE><tr><td>&nbsp;</td><td class=smallexample><FONT SIZE=-1><pre> sinh(<VAR>x</VAR>)/cosh(<VAR>x</VAR>)
1591</FONT></pre></td></tr></table><CODE>tanhf</CODE> is identical, save that it takes and returns <CODE>float</CODE> values.
1592</P><P>
1593
1594<BR>
1595<STRONG>Returns</STRONG><BR>
1596The hyperbolic tangent of <VAR>x</VAR> is returned.
1597</P><P>
1598
1599<BR>
1600<STRONG>Portability</STRONG><BR>
1601<CODE>tanh</CODE> is ANSI C. <CODE>tanhf</CODE> is an extension.
1602</P><P>
1603
1604<BR>
1605<A NAME="cbrt"></A>
1606<HR SIZE="6">
1607<A NAME="SEC31"></A>
1608<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
1609<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC30"> &lt; </A>]</TD>
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1615<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD>
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1618</TR></TABLE>
1619<H2> 1.30 <CODE>cbrt</CODE>, <CODE>cbrtf</CODE>---cube root </H2>
1620<!--docid::SEC31::-->
1621<STRONG>Synopsis</STRONG>
1622<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1623double cbrt(double <VAR>x</VAR>);
1624float cbrtf(float <VAR>x</VAR>);
1625
1626</pre></td></tr></table><STRONG>Description</STRONG><BR>
1627<CODE>cbrt</CODE> computes the cube root of the argument.
1628<P>
1629
1630<BR>
1631<STRONG>Returns</STRONG><BR>
1632The cube root is returned.
1633</P><P>
1634
1635<BR>
1636<STRONG>Portability</STRONG><BR>
1637<CODE>cbrt</CODE> is in System V release 4. <CODE>cbrtf</CODE> is an extension.
1638</P><P>
1639
1640<BR>
1641<A NAME="copysign"></A>
1642<HR SIZE="6">
1643<A NAME="SEC32"></A>
1644<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
1645<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC31"> &lt; </A>]</TD>
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1651<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD>
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1653<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
1654</TR></TABLE>
1655<H2> 1.31 <CODE>copysign</CODE>, <CODE>copysignf</CODE>---sign of <VAR>y</VAR>, magnitude of <VAR>x</VAR> </H2>
1656<!--docid::SEC32::-->
1657<STRONG>Synopsis</STRONG>
1658<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1659double copysign (double <VAR>x</VAR>, double <VAR>y</VAR>);
1660float copysignf (float <VAR>x</VAR>, float <VAR>y</VAR>);
1661
1662</pre></td></tr></table><STRONG>Description</STRONG><BR>
1663<CODE>copysign</CODE> constructs a number with the magnitude (absolute value)
1664of its first argument, <VAR>x</VAR>, and the sign of its second argument,
1665<VAR>y</VAR>.
1666<P>
1667
1668<CODE>copysignf</CODE> does the same thing; the two functions differ only in
1669the type of their arguments and result.
1670</P><P>
1671
1672<BR>
1673<STRONG>Returns</STRONG><BR>
1674<CODE>copysign</CODE> returns a <CODE>double</CODE> with the magnitude of
1675<VAR>x</VAR> and the sign of <VAR>y</VAR>.
1676<CODE>copysignf</CODE> returns a <CODE>float</CODE> with the magnitude of
1677<VAR>x</VAR> and the sign of <VAR>y</VAR>.
1678</P><P>
1679
1680<BR>
1681<STRONG>Portability</STRONG><BR>
1682<CODE>copysign</CODE> is not required by either ANSI C or the System V Interface
1683Definition (Issue 2).
1684</P><P>
1685
1686<BR>
1687<A NAME="expm1"></A>
1688<HR SIZE="6">
1689<A NAME="SEC33"></A>
1690<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
1691<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC32"> &lt; </A>]</TD>
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1697<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD>
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1700</TR></TABLE>
1701<H2> 1.32 <CODE>expm1</CODE>, <CODE>expm1f</CODE>---exponential minus 1 </H2>
1702<!--docid::SEC33::-->
1703<STRONG>Synopsis</STRONG>
1704<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1705double expm1(double <VAR>x</VAR>);
1706float expm1f(float <VAR>x</VAR>);
1707
1708</pre></td></tr></table><STRONG>Description</STRONG><BR>
1709<CODE>expm1</CODE> and <CODE>expm1f</CODE> calculate the exponential of <VAR>x</VAR>
1710and subtract 1, that is,
1711e raised to the power <VAR>x</VAR> minus 1 (where e
1712is the base of the natural system of logarithms, approximately
17132.71828). The result is accurate even for small values of
1714<VAR>x</VAR>, where using <CODE>exp(<VAR>x</VAR>)-1</CODE> would lose many
1715significant digits.
1716<P>
1717 1063
1718<BR> 1064 <p>There are five major number formats:
1719<STRONG>Returns</STRONG><BR> 1065 <dl>
1720e raised to the power <VAR>x</VAR>, minus 1. 1066<dt><code>zero</code><dd>A number which contains all zero bits.
1721</P><P> 1067<br><dt><code>subnormal</code><dd>A number with a zero exponent but a nonzero fraction.
1068<br><dt><code>normal</code><dd>A number with an exponent and a fraction.
1069<br><dt><code>infinity</code><dd>A number with an all 1's exponent and a zero fraction.
1070<br><dt><code>NAN</code><dd>A number with an all 1's exponent and a nonzero fraction.
1071
1072 </dl>
1073
1074 <p><code>isnan</code> returns 1 if the argument is a nan. <code>isinf</code>
1075returns 1 if the argument is infinity. <code>finite</code> returns 1 if the
1076argument is zero, subnormal or normal.
1077The <code>isnanf</code>, <code>isinff</code> and <code>finitef</code> functions perform the same
1078operations as their <code>isnan</code>, <code>isinf</code> and <code>finite</code>
1079counterparts, but on single-precision floating-point numbers.
1722 1080
1723<BR> 1081 <p>It should be noted that the C99 standard dictates that <code>isnan</code>
1724<STRONG>Portability</STRONG><BR> 1082and <code>isinf</code> are macros that operate on multiple types of
1725Neither <CODE>expm1</CODE> nor <CODE>expm1f</CODE> is required by ANSI C or by 1083floating-point. The SUSv2 standard declares <code>isnan</code> as
1726the System V Interface Definition (Issue 2). 1084a function taking double. Newlib has decided to declare
1727</P><P> 1085them both as macros in math.h and as functions in ieeefp.h.
1728 1086
1729<BR> 1087 <p><br>
1730<A NAME="ilogb"></A> 1088
1731<HR SIZE="6"> 1089<div class="node">
1732<A NAME="SEC34"></A> 1090<p><hr>
1733<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> 1091<a name="ldexp"></a>
1734<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC33"> &lt; </A>]</TD> 1092Next:&nbsp;<a rel="next" accesskey="n" href="#log">log</a>,
1735<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC35"> &gt; </A>]</TD> 1093Previous:&nbsp;<a rel="previous" accesskey="p" href="#isnan">isnan</a>,
1736<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC5"> &lt;&lt; </A>]</TD> 1094Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
1737<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD> 1095
1738<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &gt;&gt; </A>]</TD> 1096</div>
1739<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD> 1097
1740<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD> 1098<h3 class="section">1.25 <code>ldexp</code>, <code>ldexpf</code>&mdash;load exponent</h3>
1741<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD> 1099
1742<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD> 1100<p><a name="index-ldexp-73"></a><a name="index-ldexpf-74"></a><strong>Synopsis</strong>
1743</TR></TABLE> 1101<pre class="example"> #include &lt;math.h&gt;
1744<H2> 1.33 <CODE>ilogb</CODE>, <CODE>ilogbf</CODE>---get exponent of floating-point number </H2> 1102 double ldexp(double <var>val</var>, int <var>exp</var>);
1745<!--docid::SEC34::--> 1103 float ldexpf(float <var>val</var>, int <var>exp</var>);
1746<STRONG>Synopsis</STRONG> 1104
1747<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62; 1105</pre>
1748int ilogb(double <VAR>val</VAR>); 1106 <p><strong>Description</strong><br>
1749int ilogbf(float <VAR>val</VAR>); 1107<code>ldexp</code> calculates the value
1750 1108<var>val</var> times 2 to the power <var>exp</var>.
1751</pre></td></tr></table><STRONG>Description</STRONG><BR> 1109<code>ldexpf</code> is identical, save that it takes and returns <code>float</code>
1752<P> 1110rather than <code>double</code> values.
1753 1111
1754All nonzero, normal numbers can be described as <VAR>m</VAR> * 1112 <p><br>
17552**<VAR>p</VAR>. <CODE>ilogb</CODE> and <CODE>ilogbf</CODE> examine the argument 1113<strong>Returns</strong><br>
1756<VAR>val</VAR>, and return <VAR>p</VAR>. The functions <CODE>frexp</CODE> and 1114<code>ldexp</code> returns the calculated value.
1757<CODE>frexpf</CODE> are similar to <CODE>ilogb</CODE> and <CODE>ilogbf</CODE>, but also 1115
1758return <VAR>m</VAR>. 1116 <p>Underflow and overflow both set <code>errno</code> to <code>ERANGE</code>.
1759</P><P> 1117On underflow, <code>ldexp</code> and <code>ldexpf</code> return 0.0.
1760 1118On overflow, <code>ldexp</code> returns plus or minus <code>HUGE_VAL</code>.
1761<BR> 1119
1762<STRONG>Returns</STRONG><BR> 1120 <p><br>
1763</P><P> 1121<strong>Portability</strong><br>
1764 1122<code>ldexp</code> is ANSI. <code>ldexpf</code> is an extension.
1765<CODE>ilogb</CODE> and <CODE>ilogbf</CODE> return the power of two used to form the 1123
1766floating-point argument. If <VAR>val</VAR> is <CODE>0</CODE>, they return <CODE>- 1124 <p><br>
1767INT_MAX</CODE> (<CODE>INT_MAX</CODE> is defined in limits.h). If <VAR>val</VAR> is 1125
1768infinite, or NaN, they return <CODE>INT_MAX</CODE>. 1126<div class="node">
1769</P><P> 1127<p><hr>
1770 1128<a name="log"></a>
1771<BR> 1129Next:&nbsp;<a rel="next" accesskey="n" href="#log10">log10</a>,
1772<STRONG>Portability</STRONG><BR> 1130Previous:&nbsp;<a rel="previous" accesskey="p" href="#ldexp">ldexp</a>,
1773Neither <CODE>ilogb</CODE> nor <CODE>ilogbf</CODE> is required by ANSI C or by 1131Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
1774the System V Interface Definition (Issue 2). 1132
1775<BR> 1133</div>
1776<A NAME="infinity"></A> 1134
1777<HR SIZE="6"> 1135<h3 class="section">1.26 <code>log</code>, <code>logf</code>&mdash;natural logarithms</h3>
1778<A NAME="SEC35"></A> 1136
1779<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> 1137<p><a name="index-log-75"></a><a name="index-logf-76"></a><strong>Synopsis</strong>
1780<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC34"> &lt; </A>]</TD> 1138<pre class="example"> #include &lt;math.h&gt;
1781<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC36"> &gt; </A>]</TD> 1139 double log(double <var>x</var>);
1782<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC5"> &lt;&lt; </A>]</TD> 1140 float logf(float <var>x</var>);
1783<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD> 1141
1784<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &gt;&gt; </A>]</TD> 1142</pre>
1785<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD> 1143 <p><strong>Description</strong><br>
1786<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD> 1144Return the natural logarithm of <var>x</var>, that is, its logarithm base e
1787<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD> 1145(where e is the base of the natural system of logarithms, 2.71828<small class="dots">...</small>).
1788<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD> 1146<code>log</code> and <code>logf</code> are identical save for the return and argument types.
1789</TR></TABLE> 1147
1790<H2> 1.34 <CODE>infinity</CODE>, <CODE>infinityf</CODE>---representation of infinity </H2> 1148 <p>You can use the (non-ANSI) function <code>matherr</code> to specify error
1791<!--docid::SEC35::--> 1149handling for these functions.
1792<STRONG>Synopsis</STRONG> 1150
1793<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62; 1151 <p><br>
1794double infinity(void); 1152<strong>Returns</strong><br>
1795float infinityf(void); 1153Normally, returns the calculated value. When <var>x</var> is zero, the
1796 1154returned value is <code>-HUGE_VAL</code> and <code>errno</code> is set to <code>ERANGE</code>.
1797</pre></td></tr></table><STRONG>Description</STRONG><BR> 1155When <var>x</var> is negative, the returned value is NaN (not a number) and
1798<CODE>infinity</CODE> and <CODE>infinityf</CODE> return the special number IEEE 1156<code>errno</code> is set to <code>EDOM</code>. You can control the error behavior via
1799infinity in double- and single-precision arithmetic 1157<code>matherr</code>.
1800respectively. 1158
1801<P> 1159 <p><br>
1802 1160<strong>Portability</strong><br>
1803<BR> 1161<code>log</code> is ANSI. <code>logf</code> is an extension.
1804<A NAME="log1p"></A> 1162
1805<HR SIZE="6"> 1163 <p><br>
1806<A NAME="SEC36"></A> 1164
1807<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> 1165<div class="node">
1808<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC35"> &lt; </A>]</TD> 1166<p><hr>
1809<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC37"> &gt; </A>]</TD> 1167<a name="log10"></a>
1810<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC5"> &lt;&lt; </A>]</TD> 1168Next:&nbsp;<a rel="next" accesskey="n" href="#log1p">log1p</a>,
1811<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD> 1169Previous:&nbsp;<a rel="previous" accesskey="p" href="#log">log</a>,
1812<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &gt;&gt; </A>]</TD> 1170Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
1813<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD> 1171
1814<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD> 1172</div>
1815<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD> 1173
1816<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD> 1174<h3 class="section">1.27 <code>log10</code>, <code>log10f</code>&mdash;base 10 logarithms</h3>
1817</TR></TABLE> 1175
1818<H2> 1.35 <CODE>log1p</CODE>, <CODE>log1pf</CODE>---log of <CODE>1 + <VAR>x</VAR></CODE> </H2> 1176<p><a name="index-log10-77"></a><a name="index-log10f-78"></a><strong>Synopsis</strong>
1819<!--docid::SEC36::--> 1177<pre class="example"> #include &lt;math.h&gt;
1820<STRONG>Synopsis</STRONG> 1178 double log10(double <var>x</var>);
1821<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62; 1179 float log10f(float <var>x</var>);
1822double log1p(double <VAR>x</VAR>); 1180
1823float log1pf(float <VAR>x</VAR>); 1181</pre>
1824 1182 <p><strong>Description</strong><br>
1825</pre></td></tr></table><STRONG>Description</STRONG><BR> 1183<code>log10</code> returns the base 10 logarithm of <var>x</var>.
1826<CODE>log1p</CODE> calculates 1184It is implemented as <code>log(</code><var>x</var><code>) / log(10)</code>.
1827the natural logarithm of <CODE>1+<VAR>x</VAR></CODE>. You can use <CODE>log1p</CODE> rather 1185
1828than `<CODE>log(1+<VAR>x</VAR>)</CODE>' for greater precision when <VAR>x</VAR> is very 1186 <p><code>log10f</code> is identical, save that it takes and returns <code>float</code> values.
1187
1188 <p><br>
1189<strong>Returns</strong><br>
1190<code>log10</code> and <code>log10f</code> return the calculated value.
1191
1192 <p>See the description of <code>log</code> for information on errors.
1193
1194 <p><br>
1195<strong>Portability</strong><br>
1196<code>log10</code> is ANSI C. <code>log10f</code> is an extension.
1197
1198 <p><br>
1199
1200<div class="node">
1201<p><hr>
1202<a name="log1p"></a>
1203Next:&nbsp;<a rel="next" accesskey="n" href="#matherr">matherr</a>,
1204Previous:&nbsp;<a rel="previous" accesskey="p" href="#log10">log10</a>,
1205Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
1206
1207</div>
1208
1209<h3 class="section">1.28 <code>log1p</code>, <code>log1pf</code>&mdash;log of <code>1 + </code><var>x</var></h3>
1210
1211<p><a name="index-log1p-79"></a><a name="index-log1pf-80"></a><strong>Synopsis</strong>
1212<pre class="example"> #include &lt;math.h&gt;
1213 double log1p(double <var>x</var>);
1214 float log1pf(float <var>x</var>);
1215
1216</pre>
1217 <p><strong>Description</strong><br>
1218<code>log1p</code> calculates
1219the natural logarithm of <code>1+</code><var>x</var>. You can use <code>log1p</code> rather
1220than `<code>log(1+</code><var>x</var><code>)</code>' for greater precision when <var>x</var> is very
1829small. 1221small.
1830<P>
1831 1222
1832<CODE>log1pf</CODE> calculates the same thing, but accepts and returns 1223 <p><code>log1pf</code> calculates the same thing, but accepts and returns
1833<CODE>float</CODE> values rather than <CODE>double</CODE>. 1224<code>float</code> values rather than <code>double</code>.
1834</P><P>
1835 1225
1836<BR> 1226 <p><br>
1837<STRONG>Returns</STRONG><BR> 1227<strong>Returns</strong><br>
1838<CODE>log1p</CODE> returns a <CODE>double</CODE>, the natural log of <CODE>1+<VAR>x</VAR></CODE>. 1228<code>log1p</code> returns a <code>double</code>, the natural log of <code>1+</code><var>x</var>.
1839<CODE>log1pf</CODE> returns a <CODE>float</CODE>, the natural log of <CODE>1+<VAR>x</VAR></CODE>. 1229<code>log1pf</code> returns a <code>float</code>, the natural log of <code>1+</code><var>x</var>.
1840</P><P>
1841 1230
1842<BR> 1231 <p><br>
1843<STRONG>Portability</STRONG><BR> 1232<strong>Portability</strong><br>
1844Neither <CODE>log1p</CODE> nor <CODE>log1pf</CODE> is required by ANSI C or by the System V 1233Neither <code>log1p</code> nor <code>log1pf</code> is required by ANSI C or by the System V
1845Interface Definition (Issue 2). 1234Interface Definition (Issue 2).
1846</P><P> 1235
1847 1236 <p><br>
1848<BR> 1237
1849<A NAME="matherr"></A> 1238<div class="node">
1850<HR SIZE="6"> 1239<p><hr>
1851<A NAME="SEC37"></A> 1240<a name="matherr"></a>
1852<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> 1241Next:&nbsp;<a rel="next" accesskey="n" href="#modf">modf</a>,
1853<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC36"> &lt; </A>]</TD> 1242Previous:&nbsp;<a rel="previous" accesskey="p" href="#log1p">log1p</a>,
1854<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC38"> &gt; </A>]</TD> 1243Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
1855<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC5"> &lt;&lt; </A>]</TD> 1244
1856<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD> 1245</div>
1857<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &gt;&gt; </A>]</TD> 1246
1858<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD> 1247<h3 class="section">1.29 <code>matherr</code>&mdash;modifiable math error handler</h3>
1859<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD> 1248
1860<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD> 1249<p><a name="index-matherr-81"></a><strong>Synopsis</strong>
1861<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD> 1250<pre class="example"> #include &lt;math.h&gt;
1862</TR></TABLE> 1251 int matherr(struct exception *<var>e</var>);
1863<H2> 1.36 <CODE>matherr</CODE>---modifiable math error handler </H2> 1252
1864<!--docid::SEC37::--> 1253</pre>
1865<STRONG>Synopsis</STRONG> 1254 <p><strong>Description</strong><br>
1866<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62; 1255<code>matherr</code> is called whenever a math library function generates an error.
1867int matherr(struct exception *<VAR>e</VAR>); 1256You can replace <code>matherr</code> by your own subroutine to customize
1868 1257error treatment. The customized <code>matherr</code> must return 0 if
1869</pre></td></tr></table><STRONG>Description</STRONG><BR>
1870<CODE>matherr</CODE> is called whenever a math library function generates an error.
1871You can replace <CODE>matherr</CODE> by your own subroutine to customize
1872error treatment. The customized <CODE>matherr</CODE> must return 0 if
1873it fails to resolve the error, and non-zero if the error is resolved. 1258it fails to resolve the error, and non-zero if the error is resolved.
1874<P> 1259
1875 1260 <p>When <code>matherr</code> returns a nonzero value, no error message is printed
1876When <CODE>matherr</CODE> returns a nonzero value, no error message is printed 1261and the value of <code>errno</code> is not modified. You can accomplish either
1877and the value of <CODE>errno</CODE> is not modified. You can accomplish either 1262or both of these things in your own <code>matherr</code> using the information
1878or both of these things in your own <CODE>matherr</CODE> using the information 1263passed in the structure <code>*</code><var>e</var>.
1879passed in the structure <CODE>*<VAR>e</VAR></CODE>. 1264
1880</P><P> 1265 <p>This is the <code>exception</code> structure (defined in `<code>math.h</code>'):
1881 1266<pre class="smallexample"> struct exception {
1882This is the <CODE>exception</CODE> structure (defined in `<CODE>math.h</CODE>'): 1267 int type;
1883<TABLE><tr><td>&nbsp;</td><td class=smallexample><FONT SIZE=-1><pre> struct exception { 1268 char *name;
1884 int type; 1269 double arg1, arg2, retval;
1885 char *name; 1270 int err;
1886 double arg1, arg2, retval; 1271 };
1887 int err; 1272</pre>
1888 }; 1273 <p>The members of the exception structure have the following meanings:
1889</FONT></pre></td></tr></table></P><P> 1274 <dl>
1890 1275<dt><code>type</code><dd>The type of mathematical error that occured; macros encoding error
1891The members of the exception structure have the following meanings: 1276types are also defined in `<code>math.h</code>'.
1892<DL COMPACT> 1277
1893 1278 <br><dt><code>name</code><dd>a pointer to a null-terminated string holding the
1894<DT><CODE>type</CODE>
1895<DD>The type of mathematical error that occured; macros encoding error
1896types are also defined in `<CODE>math.h</CODE>'.
1897<P>
1898
1899<DT><CODE>name</CODE>
1900<DD>a pointer to a null-terminated string holding the
1901name of the math library function where the error occurred. 1279name of the math library function where the error occurred.
1902<P>
1903 1280
1904<DT><CODE>arg1, arg2</CODE> 1281 <br><dt><code>arg1, arg2</code><dd>The arguments which caused the error.
1905<DD>The arguments which caused the error.
1906<P>
1907 1282
1908<DT><CODE>retval</CODE> 1283 <br><dt><code>retval</code><dd>The error return value (what the calling function will return).
1909<DD>The error return value (what the calling function will return).
1910<P>
1911 1284
1912<DT><CODE>err</CODE> 1285 <br><dt><code>err</code><dd>If set to be non-zero, this is the new value assigned to <code>errno</code>.
1913<DD>If set to be non-zero, this is the new value assigned to <CODE>errno</CODE>. 1286</dl>
1914</DL>
1915<P>
1916 1287
1917The error types defined in `<CODE>math.h</CODE>' represent possible mathematical 1288 <p>The error types defined in `<code>math.h</code>' represent possible mathematical
1918errors as follows: 1289errors as follows:
1919</P><P>
1920
1921<DL COMPACT>
1922 1290
1923<DT><CODE>DOMAIN</CODE> 1291 <dl>
1924<DD>An argument was not in the domain of the function; e.g. <CODE>log(-1.0)</CODE>. 1292<dt><code>DOMAIN</code><dd>An argument was not in the domain of the function; e.g. <code>log(-1.0)</code>.
1925<P>
1926 1293
1927<DT><CODE>SING</CODE> 1294 <br><dt><code>SING</code><dd>The requested calculation would result in a singularity; e.g. <code>pow(0.0,-2.0)</code>
1928<DD>The requested calculation would result in a singularity; e.g. <CODE>pow(0.0,-2.0)</CODE>
1929<P>
1930 1295
1931<DT><CODE>OVERFLOW</CODE> 1296 <br><dt><code>OVERFLOW</code><dd>A calculation would produce a result too large to represent; e.g.
1932<DD>A calculation would produce a result too large to represent; e.g. 1297<code>exp(1000.0)</code>.
1933<CODE>exp(1000.0)</CODE>.
1934<P>
1935 1298
1936<DT><CODE>UNDERFLOW</CODE> 1299 <br><dt><code>UNDERFLOW</code><dd>A calculation would produce a result too small to represent; e.g.
1937<DD>A calculation would produce a result too small to represent; e.g. 1300<code>exp(-1000.0)</code>.
1938<CODE>exp(-1000.0)</CODE>.
1939<P>
1940 1301
1941<DT><CODE>TLOSS</CODE> 1302 <br><dt><code>TLOSS</code><dd>Total loss of precision. The result would have no significant digits;
1942<DD>Total loss of precision. The result would have no significant digits; 1303e.g. <code>sin(10e70)</code>.
1943e.g. <CODE>sin(10e70)</CODE>.
1944<P>
1945 1304
1946<DT><CODE>PLOSS</CODE> 1305 <br><dt><code>PLOSS</code><dd>Partial loss of precision.
1947<DD>Partial loss of precision. 1306</dl>
1948</DL>
1949<P>
1950 1307
1951<BR> 1308 <p><br>
1952<STRONG>Returns</STRONG><BR> 1309<strong>Returns</strong><br>
1953The library definition for <CODE>matherr</CODE> returns <CODE>0</CODE> in all cases. 1310The library definition for <code>matherr</code> returns <code>0</code> in all cases.
1954</P><P>
1955 1311
1956You can change the calling function's result from a customized <CODE>matherr</CODE> 1312 <p>You can change the calling function's result from a customized <code>matherr</code>
1957by modifying <CODE>e-&#62;retval</CODE>, which propagates backs to the caller. 1313by modifying <code>e-&gt;retval</code>, which propagates backs to the caller.
1958</P><P>
1959 1314
1960If <CODE>matherr</CODE> returns <CODE>0</CODE> (indicating that it was not able to resolve 1315 <p>If <code>matherr</code> returns <code>0</code> (indicating that it was not able to resolve
1961the error) the caller sets <CODE>errno</CODE> to an appropriate value, and prints 1316the error) the caller sets <code>errno</code> to an appropriate value, and prints
1962an error message. 1317an error message.
1963</P><P> 1318
1964 1319 <p><br>
1965<BR> 1320<strong>Portability</strong><br>
1966<STRONG>Portability</STRONG><BR> 1321<code>matherr</code> is not ANSI C.
1967<CODE>matherr</CODE> is not ANSI C. 1322
1968</P><P> 1323 <p><br>
1969 1324
1970<BR> 1325<div class="node">
1971<A NAME="modf"></A> 1326<p><hr>
1972<HR SIZE="6"> 1327<a name="modf"></a>
1973<A NAME="SEC38"></A> 1328Next:&nbsp;<a rel="next" accesskey="n" href="#nan">nan</a>,
1974<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> 1329Previous:&nbsp;<a rel="previous" accesskey="p" href="#matherr">matherr</a>,
1975<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC37"> &lt; </A>]</TD> 1330Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
1976<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC39"> &gt; </A>]</TD> 1331
1977<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC5"> &lt;&lt; </A>]</TD> 1332</div>
1978<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD> 1333
1979<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &gt;&gt; </A>]</TD> 1334<h3 class="section">1.30 <code>modf</code>, <code>modff</code>&mdash;split fractional and integer parts</h3>
1980<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD> 1335
1981<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD> 1336<p><a name="index-modf-82"></a><a name="index-modff-83"></a><strong>Synopsis</strong>
1982<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD> 1337<pre class="example"> #include &lt;math.h&gt;
1983<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD> 1338 double modf(double <var>val</var>, double *<var>ipart</var>);
1984</TR></TABLE> 1339 float modff(float <var>val</var>, float *<var>ipart</var>);
1985<H2> 1.37 <CODE>modf</CODE>, <CODE>modff</CODE>---split fractional and integer parts </H2> 1340
1986<!--docid::SEC38::--> 1341</pre>
1987<STRONG>Synopsis</STRONG> 1342 <p><strong>Description</strong><br>
1988<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62; 1343<code>modf</code> splits the double <var>val</var> apart into an integer part
1989double modf(double <VAR>val</VAR>, double *<VAR>ipart</VAR>);
1990float modff(float <VAR>val</VAR>, float *<VAR>ipart</VAR>);
1991
1992</pre></td></tr></table><STRONG>Description</STRONG><BR>
1993<CODE>modf</CODE> splits the double <VAR>val</VAR> apart into an integer part
1994and a fractional part, returning the fractional part and 1344and a fractional part, returning the fractional part and
1995storing the integer part in <CODE>*<VAR>ipart</VAR></CODE>. No rounding 1345storing the integer part in <code>*</code><var>ipart</var>. No rounding
1996whatsoever is done; the sum of the integer and fractional 1346whatsoever is done; the sum of the integer and fractional
1997parts is guaranteed to be exactly equal to <VAR>val</VAR>. That 1347parts is guaranteed to be exactly equal to <var>val</var>. That
1998is, if . <VAR>realpart</VAR> = modf(<VAR>val</VAR>, &#38;<VAR>intpart</VAR>); then 1348is, if <var>realpart</var> = modf(<var>val</var>, &amp;<var>intpart</var>); then
1999`<CODE><VAR>realpart</VAR>+<VAR>intpart</VAR></CODE>' is the same as <VAR>val</VAR>. 1349`<var>realpart</var><code>+</code><var>intpart</var>' is the same as <var>val</var>.
2000<CODE>modff</CODE> is identical, save that it takes and returns 1350<code>modff</code> is identical, save that it takes and returns
2001<CODE>float</CODE> rather than <CODE>double</CODE> values. 1351<code>float</code> rather than <code>double</code> values.
2002<P> 1352
2003 1353 <p><br>
2004<BR> 1354<strong>Returns</strong><br>
2005<STRONG>Returns</STRONG><BR>
2006The fractional part is returned. Each result has the same 1355The fractional part is returned. Each result has the same
2007sign as the supplied argument <VAR>val</VAR>. 1356sign as the supplied argument <var>val</var>.
2008</P><P> 1357
2009 1358 <p><br>
2010<BR> 1359<strong>Portability</strong><br>
2011<STRONG>Portability</STRONG><BR> 1360<code>modf</code> is ANSI C. <code>modff</code> is an extension.
2012<CODE>modf</CODE> is ANSI C. <CODE>modff</CODE> is an extension. 1361
2013</P><P> 1362 <p><br>
2014 1363
2015<BR> 1364<div class="node">
2016<A NAME="nan"></A> 1365<p><hr>
2017<HR SIZE="6"> 1366<a name="nan"></a>
2018<A NAME="SEC39"></A> 1367Next:&nbsp;<a rel="next" accesskey="n" href="#nextafter">nextafter</a>,
2019<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> 1368Previous:&nbsp;<a rel="previous" accesskey="p" href="#modf">modf</a>,
2020<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC38"> &lt; </A>]</TD> 1369Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
2021<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC40"> &gt; </A>]</TD> 1370
2022<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC5"> &lt;&lt; </A>]</TD> 1371</div>
2023<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD> 1372
2024<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &gt;&gt; </A>]</TD> 1373<h3 class="section">1.31 <code>nan</code>, <code>nanf</code>&mdash;representation of &ldquo;Not a Number&rdquo;</h3>
2025<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD> 1374
2026<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD> 1375<p><a name="index-nan-84"></a><a name="index-nanf-85"></a><strong>Synopsis</strong>
2027<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD> 1376<pre class="example"> #include &lt;math.h&gt;
2028<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD> 1377 double nan(const char *);
2029</TR></TABLE> 1378 float nanf(const char *);
2030<H2> 1.38 <CODE>nan</CODE>, <CODE>nanf</CODE>---representation of "Not a Number" </H2> 1379
2031<!--docid::SEC39::--> 1380</pre>
2032<STRONG>Synopsis</STRONG> 1381 <p><strong>Description</strong><br>
2033<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62; 1382<code>nan</code> and <code>nanf</code> return an IEEE NaN (Not a Number) in
2034double nan(const char *);
2035float nanf(const char *);
2036
2037</pre></td></tr></table><STRONG>Description</STRONG><BR>
2038<CODE>nan</CODE> and <CODE>nanf</CODE> return an IEEE NaN (Not a Number) in
2039double- and single-precision arithmetic respectively. The 1383double- and single-precision arithmetic respectively. The
2040argument is currently disregarded. 1384argument is currently disregarded.
2041<P> 1385
2042 1386 <p><br>
2043<BR> 1387
2044<A NAME="nextafter"></A> 1388<div class="node">
2045<HR SIZE="6"> 1389<p><hr>
2046<A NAME="SEC40"></A> 1390<a name="nextafter"></a>
2047<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> 1391Next:&nbsp;<a rel="next" accesskey="n" href="#pow">pow</a>,
2048<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC39"> &lt; </A>]</TD> 1392Previous:&nbsp;<a rel="previous" accesskey="p" href="#nan">nan</a>,
2049<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC41"> &gt; </A>]</TD> 1393Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
2050<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC5"> &lt;&lt; </A>]</TD> 1394
2051<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD> 1395</div>
2052<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &gt;&gt; </A>]</TD> 1396
2053<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD> 1397<h3 class="section">1.32 <code>nextafter</code>, <code>nextafterf</code>&mdash;get next number</h3>
2054<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD> 1398
2055<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD> 1399<p><a name="index-nextafter-86"></a><a name="index-nextafterf-87"></a><strong>Synopsis</strong>
2056<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD> 1400<pre class="example"> #include &lt;math.h&gt;
2057</TR></TABLE> 1401 double nextafter(double <var>val</var>, double <var>dir</var>);
2058<H2> 1.39 <CODE>nextafter</CODE>, <CODE>nextafterf</CODE>---get next number </H2> 1402 float nextafterf(float <var>val</var>, float <var>dir</var>);
2059<!--docid::SEC40::--> 1403
2060<STRONG>Synopsis</STRONG> 1404</pre>
2061<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62; 1405 <p><strong>Description</strong><br>
2062double nextafter(double <VAR>val</VAR>, double <VAR>dir</VAR>); 1406<code>nextafter</code> returns the double-precision floating-point number
2063float nextafterf(float <VAR>val</VAR>, float <VAR>dir</VAR>); 1407closest to <var>val</var> in the direction toward <var>dir</var>. <code>nextafterf</code>
2064
2065</pre></td></tr></table><STRONG>Description</STRONG><BR>
2066<CODE>nextafter</CODE> returns the double-precision floating-point number
2067closest to <VAR>val</VAR> in the direction toward <VAR>dir</VAR>. <CODE>nextafterf</CODE>
2068performs the same operation in single precision. For example, 1408performs the same operation in single precision. For example,
2069<CODE>nextafter(0.0,1.0)</CODE> returns the smallest positive number which is 1409<code>nextafter(0.0,1.0)</code> returns the smallest positive number which is
2070representable in double precision. 1410representable in double precision.
2071<P>
2072 1411
2073<BR> 1412 <p><br>
2074<STRONG>Returns</STRONG><BR> 1413<strong>Returns</strong><br>
2075Returns the next closest number to <VAR>val</VAR> in the direction toward 1414Returns the next closest number to <var>val</var> in the direction toward
2076<VAR>dir</VAR>. 1415<var>dir</var>.
2077</P><P>
2078 1416
2079<BR> 1417 <p><br>
2080<STRONG>Portability</STRONG><BR> 1418<strong>Portability</strong><br>
2081Neither <CODE>nextafter</CODE> nor <CODE>nextafterf</CODE> is required by ANSI C 1419Neither <code>nextafter</code> nor <code>nextafterf</code> is required by ANSI C
2082or by the System V Interface Definition (Issue 2). 1420or by the System V Interface Definition (Issue 2).
2083</P><P> 1421
2084 1422 <p><br>
2085<BR> 1423
2086<A NAME="scalbn"></A> 1424<div class="node">
2087<HR SIZE="6"> 1425<p><hr>
2088<A NAME="SEC41"></A> 1426<a name="pow"></a>
2089<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> 1427Next:&nbsp;<a rel="next" accesskey="n" href="#remainder">remainder</a>,
2090<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC40"> &lt; </A>]</TD> 1428Previous:&nbsp;<a rel="previous" accesskey="p" href="#nextafter">nextafter</a>,
2091<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &gt; </A>]</TD> 1429Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
2092<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC6"> &lt;&lt; </A>]</TD> 1430
2093<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD> 1431</div>
2094<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &gt;&gt; </A>]</TD> 1432
2095<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD> 1433<h3 class="section">1.33 <code>pow</code>, <code>powf</code>&mdash;x to the power y</h3>
2096<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD> 1434
2097<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD> 1435<p><a name="index-pow-88"></a><a name="index-powf-89"></a><strong>Synopsis</strong>
2098<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD> 1436<pre class="example"> #include &lt;math.h&gt;
2099</TR></TABLE> 1437 double pow(double <var>x</var>, double <var>y</var>);
2100<H2> 1.40 <CODE>scalbn</CODE>, <CODE>scalbnf</CODE>---scale by power of two </H2> 1438 float powf(float <var>x</var>, float <var>y</var>);
2101<!--docid::SEC41::--> 1439
2102<STRONG>Synopsis</STRONG> 1440</pre>
2103<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62; 1441 <p><strong>Description</strong><br>
2104double scalbn(double <VAR>x</VAR>, int <VAR>y</VAR>); 1442<code>pow</code> and <code>powf</code> calculate <var>x</var> raised to the exponent <var>y</var>.
2105float scalbnf(float <VAR>x</VAR>, int <VAR>y</VAR>); 1443
2106 1444 <p><br>
2107</pre></td></tr></table><STRONG>Description</STRONG><BR> 1445<strong>Returns</strong><br>
2108<CODE>scalbn</CODE> and <CODE>scalbnf</CODE> scale <VAR>x</VAR> by <VAR>n</VAR>, returning <VAR>x</VAR> times 1446On success, <code>pow</code> and <code>powf</code> return the value calculated.
21092 to the power <VAR>n</VAR>. The result is computed by manipulating the 1447
1448 <p>When the argument values would produce overflow, <code>pow</code>
1449returns <code>HUGE_VAL</code> and set <code>errno</code> to <code>ERANGE</code>. If the
1450argument <var>x</var> passed to <code>pow</code> or <code>powf</code> is a negative
1451noninteger, and <var>y</var> is also not an integer, then <code>errno</code>
1452is set to <code>EDOM</code>. If <var>x</var> and <var>y</var> are both 0, then
1453<code>pow</code> and <code>powf</code> return <code>1</code>.
1454
1455 <p>You can modify error handling for these functions using <code>matherr</code>.
1456
1457 <p><br>
1458<strong>Portability</strong><br>
1459<code>pow</code> is ANSI C. <code>powf</code> is an extension.
1460<br>
1461
1462<div class="node">
1463<p><hr>
1464<a name="remainder"></a>
1465Next:&nbsp;<a rel="next" accesskey="n" href="#scalbn">scalbn</a>,
1466Previous:&nbsp;<a rel="previous" accesskey="p" href="#pow">pow</a>,
1467Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
1468
1469</div>
1470
1471<h3 class="section">1.34 <code>remainder</code>, <code>remainderf</code>&mdash;round and remainder</h3>
1472
1473<p><a name="index-remainder-90"></a><a name="index-remainderf-91"></a><strong>Synopsis</strong>
1474<pre class="example"> #include &lt;math.h&gt;
1475 double remainder(double <var>x</var>, double <var>y</var>);
1476 float remainderf(float <var>x</var>, float <var>y</var>);
1477
1478</pre>
1479 <p><strong>Description</strong><br>
1480<code>remainder</code> and <code>remainderf</code> find the remainder of
1481<var>x</var>/<var>y</var>; this value is in the range -<var>y</var>/2 .. +<var>y</var>/2.
1482
1483 <p><br>
1484<strong>Returns</strong><br>
1485<code>remainder</code> returns the integer result as a double.
1486
1487 <p><br>
1488<strong>Portability</strong><br>
1489<code>remainder</code> is a System V release 4.
1490<code>remainderf</code> is an extension.
1491
1492 <p><br>
1493
1494<div class="node">
1495<p><hr>
1496<a name="scalbn"></a>
1497Next:&nbsp;<a rel="next" accesskey="n" href="#sin">sin</a>,
1498Previous:&nbsp;<a rel="previous" accesskey="p" href="#remainder">remainder</a>,
1499Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
1500
1501</div>
1502
1503<h3 class="section">1.35 <code>scalbn</code>, <code>scalbnf</code>&mdash;scale by power of two</h3>
1504
1505<p><a name="index-scalbn-92"></a><a name="index-scalbnf-93"></a><strong>Synopsis</strong>
1506<pre class="example"> #include &lt;math.h&gt;
1507 double scalbn(double <var>x</var>, int <var>y</var>);
1508 float scalbnf(float <var>x</var>, int <var>y</var>);
1509
1510</pre>
1511 <p><strong>Description</strong><br>
1512<code>scalbn</code> and <code>scalbnf</code> scale <var>x</var> by <var>n</var>, returning <var>x</var> times
15132 to the power <var>n</var>. The result is computed by manipulating the
2110exponent, rather than by actually performing an exponentiation or 1514exponent, rather than by actually performing an exponentiation or
2111multiplication. 1515multiplication.
2112<P>
2113 1516
2114<BR> 1517 <p><br>
2115<STRONG>Returns</STRONG><BR> 1518<strong>Returns</strong><br>
2116<VAR>x</VAR> times 2 to the power <VAR>n</VAR>. 1519<var>x</var> times 2 to the power <var>n</var>.
2117</P><P>
2118 1520
2119<BR> 1521 <p><br>
2120<STRONG>Portability</STRONG><BR> 1522<strong>Portability</strong><br>
2121Neither <CODE>scalbn</CODE> nor <CODE>scalbnf</CODE> is required by ANSI C or by the System V 1523Neither <code>scalbn</code> nor <code>scalbnf</code> is required by ANSI C or by the System V
2122Interface Definition (Issue 2). 1524Interface Definition (Issue 2).
2123</P><P> 1525
2124 1526 <p><br>
2125<BR> 1527
2126</P><P> 1528<div class="node">
2127 1529<p><hr>
2128<A NAME="Reentrancy"></A> 1530<a name="sqrt"></a>
2129<HR SIZE="6"> 1531Next:&nbsp;<a rel="next" accesskey="n" href="#tan">tan</a>,
2130<A NAME="SEC42"></A> 1532Previous:&nbsp;<a rel="previous" accesskey="p" href="#sinh">sinh</a>,
2131<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> 1533Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
2132<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC41"> &lt; </A>]</TD> 1534
2133<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43"> &gt; </A>]</TD> 1535</div>
2134<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD> 1536
2135<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top"> Up </A>]</TD> 1537<h3 class="section">1.36 <code>sqrt</code>, <code>sqrtf</code>&mdash;positive square root</h3>
2136<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD> 1538
2137<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD> 1539<p><a name="index-sqrt-94"></a><a name="index-sqrtf-95"></a><strong>Synopsis</strong>
2138<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD> 1540<pre class="example"> #include &lt;math.h&gt;
2139<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD> 1541 double sqrt(double <var>x</var>);
2140<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD> 1542 float sqrtf(float <var>x</var>);
2141</TR></TABLE> 1543
2142<H1> 2. Reentrancy Properties of <CODE>libm</CODE> </H1> 1544</pre>
2143<!--docid::SEC42::--> 1545 <p><strong>Description</strong><br>
2144<P> 1546<code>sqrt</code> computes the positive square root of the argument.
2145 1547You can modify error handling for this function with
2146<A NAME="IDX5"></A> 1548<code>matherr</code>.
2147<A NAME="IDX6"></A> 1549
2148When a libm function detects an exceptional case, <CODE>errno</CODE> may be 1550 <p><br>
2149set, the <CODE>matherr</CODE> function may be called, and a error message 1551<strong>Returns</strong><br>
1552On success, the square root is returned. If <var>x</var> is real and
1553positive, then the result is positive. If <var>x</var> is real and
1554negative, the global value <code>errno</code> is set to <code>EDOM</code> (domain error).
1555
1556 <p><br>
1557<strong>Portability</strong><br>
1558<code>sqrt</code> is ANSI C. <code>sqrtf</code> is an extension.
1559
1560 <p><br>
1561
1562<div class="node">
1563<p><hr>
1564<a name="sin"></a>
1565Next:&nbsp;<a rel="next" accesskey="n" href="#sinh">sinh</a>,
1566Previous:&nbsp;<a rel="previous" accesskey="p" href="#scalbn">scalbn</a>,
1567Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
1568
1569</div>
1570
1571<h3 class="section">1.37 <code>sin</code>, <code>sinf</code>, <code>cos</code>, <code>cosf</code>&mdash;sine or cosine</h3>
1572
1573<p><a name="index-sin-96"></a><a name="index-sinf-97"></a><a name="index-cos-98"></a><a name="index-cosf-99"></a><strong>Synopsis</strong>
1574<pre class="example"> #include &lt;math.h&gt;
1575 double sin(double <var>x</var>);
1576 float sinf(float <var>x</var>);
1577 double cos(double <var>x</var>);
1578 float cosf(float <var>x</var>);
1579
1580</pre>
1581 <p><strong>Description</strong><br>
1582<code>sin</code> and <code>cos</code> compute (respectively) the sine and cosine
1583of the argument <var>x</var>. Angles are specified in radians.
1584
1585 <p><code>sinf</code> and <code>cosf</code> are identical, save that they take and
1586return <code>float</code> values.
1587
1588 <p><br>
1589<strong>Returns</strong><br>
1590The sine or cosine of <var>x</var> is returned.
1591
1592 <p><br>
1593<strong>Portability</strong><br>
1594<code>sin</code> and <code>cos</code> are ANSI C.
1595<code>sinf</code> and <code>cosf</code> are extensions.
1596
1597 <p><br>
1598
1599<div class="node">
1600<p><hr>
1601<a name="sinh"></a>
1602Next:&nbsp;<a rel="next" accesskey="n" href="#sqrt">sqrt</a>,
1603Previous:&nbsp;<a rel="previous" accesskey="p" href="#sin">sin</a>,
1604Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
1605
1606</div>
1607
1608<h3 class="section">1.38 <code>sinh</code>, <code>sinhf</code>&mdash;hyperbolic sine</h3>
1609
1610<p><a name="index-sinh-100"></a><a name="index-sinhf-101"></a><strong>Synopsis</strong>
1611<pre class="example"> #include &lt;math.h&gt;
1612 double sinh(double <var>x</var>);
1613 float sinhf(float <var>x</var>);
1614
1615</pre>
1616 <p><strong>Description</strong><br>
1617<code>sinh</code> computes the hyperbolic sine of the argument <var>x</var>.
1618Angles are specified in radians. <code>sinh</code>(<var>x</var>) is defined as
1619<pre class="smallexample"> (exp(<var>x</var>) - exp(-<var>x</var>))/2
1620</pre>
1621 <p><code>sinhf</code> is identical, save that it takes and returns <code>float</code> values.
1622
1623 <p><br>
1624<strong>Returns</strong><br>
1625The hyperbolic sine of <var>x</var> is returned.
1626
1627 <p>When the correct result is too large to be representable (an
1628overflow), <code>sinh</code> returns <code>HUGE_VAL</code> with the
1629appropriate sign, and sets the global value <code>errno</code> to
1630<code>ERANGE</code>.
1631
1632 <p>You can modify error handling for these functions with <code>matherr</code>.
1633
1634 <p><br>
1635<strong>Portability</strong><br>
1636<code>sinh</code> is ANSI C.
1637<code>sinhf</code> is an extension.
1638
1639 <p><br>
1640
1641<div class="node">
1642<p><hr>
1643<a name="tan"></a>
1644Next:&nbsp;<a rel="next" accesskey="n" href="#tanh">tanh</a>,
1645Previous:&nbsp;<a rel="previous" accesskey="p" href="#sqrt">sqrt</a>,
1646Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
1647
1648</div>
1649
1650<h3 class="section">1.39 <code>tan</code>, <code>tanf</code>&mdash;tangent</h3>
1651
1652<p><a name="index-tan-102"></a><a name="index-tanf-103"></a><strong>Synopsis</strong>
1653<pre class="example"> #include &lt;math.h&gt;
1654 double tan(double <var>x</var>);
1655 float tanf(float <var>x</var>);
1656
1657</pre>
1658 <p><strong>Description</strong><br>
1659<code>tan</code> computes the tangent of the argument <var>x</var>.
1660Angles are specified in radians.
1661
1662 <p><code>tanf</code> is identical, save that it takes and returns <code>float</code> values.
1663
1664 <p><br>
1665<strong>Returns</strong><br>
1666The tangent of <var>x</var> is returned.
1667
1668 <p><br>
1669<strong>Portability</strong><br>
1670<code>tan</code> is ANSI. <code>tanf</code> is an extension.
1671
1672 <p><br>
1673
1674<div class="node">
1675<p><hr>
1676<a name="tanh"></a>
1677Previous:&nbsp;<a rel="previous" accesskey="p" href="#tan">tan</a>,
1678Up:&nbsp;<a rel="up" accesskey="u" href="#Math">Math</a>
1679
1680</div>
1681
1682<h3 class="section">1.40 <code>tanh</code>, <code>tanhf</code>&mdash;hyperbolic tangent</h3>
1683
1684<p><a name="index-tanh-104"></a><a name="index-tanhf-105"></a><strong>Synopsis</strong>
1685<pre class="example"> #include &lt;math.h&gt;
1686 double tanh(double <var>x</var>);
1687 float tanhf(float <var>x</var>);
1688
1689</pre>
1690 <p><strong>Description</strong><br>
1691
1692 <p><code>tanh</code> computes the hyperbolic tangent of
1693the argument <var>x</var>. Angles are specified in radians.
1694
1695 <p><code>tanh(</code><var>x</var><code>)</code> is defined as
1696<pre class="smallexample"> sinh(<var>x</var>)/cosh(<var>x</var>)
1697</pre>
1698 <p><code>tanhf</code> is identical, save that it takes and returns <code>float</code> values.
1699
1700 <p><br>
1701<strong>Returns</strong><br>
1702The hyperbolic tangent of <var>x</var> is returned.
1703
1704 <p><br>
1705<strong>Portability</strong><br>
1706<code>tanh</code> is ANSI C. <code>tanhf</code> is an extension.
1707
1708 <p><br>
1709
1710<div class="node">
1711<p><hr>
1712<a name="Reentrancy"></a>
1713Next:&nbsp;<a rel="next" accesskey="n" href="#Index">Index</a>,
1714Previous:&nbsp;<a rel="previous" accesskey="p" href="#Math">Math</a>,
1715Up:&nbsp;<a rel="up" accesskey="u" href="#Top">Top</a>
1716
1717</div>
1718
1719<h2 class="chapter">2 Reentrancy Properties of <code>libm</code></h2>
1720
1721<p><a name="index-reentrancy-106"></a><a name="index-g_t_0040code_007bmatherr_007d-and-reentrancy-107"></a>When a libm function detects an exceptional case, <code>errno</code> may be
1722set, the <code>matherr</code> function may be called, and a error message
2150may be written to the standard error stream. This behavior may not 1723may be written to the standard error stream. This behavior may not
2151be reentrant. 1724be reentrant.
2152</P><P>
2153 1725
2154With reentrant C libraries like the Red Hat newlib C library, <CODE>errno</CODE> is 1726<!-- The exact behavior depends on the currently selected error handling -->
1727<!-- mode (IEEE, POSIX, X/Open, or SVID). -->
1728 <p>With reentrant C libraries like the Red Hat newlib C library, <code>errno</code> is
2155a macro which expands to the per-thread error value. This makes it thread 1729a macro which expands to the per-thread error value. This makes it thread
2156safe. 1730safe.
2157</P><P>
2158 1731
2159When the user provides his own <CODE>matherr</CODE> function it must be 1732 <p>When the user provides his own <code>matherr</code> function it must be
2160reentrant for the math library as a whole to be reentrant. 1733reentrant for the math library as a whole to be reentrant.
2161</P><P>
2162 1734
2163In normal debugged programs, there are usually no math subroutine 1735 <p>In normal debugged programs, there are usually no math subroutine
2164errors--and therefore no assignments to <CODE>errno</CODE> and no <CODE>matherr</CODE> 1736errors&mdash;and therefore no assignments to <code>errno</code> and no <code>matherr</code>
2165calls; in that situation, the math functions behave reentrantly. 1737calls; in that situation, the math functions behave reentrantly.
2166</P><P> 1738
2167 1739<div class="node">
2168<A NAME="Index"></A> 1740<p><hr>
2169<HR SIZE="6"> 1741<a name="Index"></a>
2170<A NAME="SEC43"></A> 1742Previous:&nbsp;<a rel="previous" accesskey="p" href="#Reentrancy">Reentrancy</a>,
2171<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> 1743Up:&nbsp;<a rel="up" accesskey="u" href="#Top">Top</a>
2172<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &lt; </A>]</TD> 1744
2173<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt; ]</TD> 1745</div>
2174<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD> 1746
2175<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top"> Up </A>]</TD> 1747<h2 class="unnumbered">Index</h2>
2176<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD> 1748
2177<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD> 1749<ul class="index-cp" compact>
2178<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD> 1750<li><a href="#index-acos-5"><code>acos</code></a>: <a href="#acos">acos</a></li>
2179<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD> 1751<li><a href="#index-acosf-6"><code>acosf</code></a>: <a href="#acos">acos</a></li>
2180<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD> 1752<li><a href="#index-acosh-7"><code>acosh</code></a>: <a href="#acosh">acosh</a></li>
2181</TR></TABLE> 1753<li><a href="#index-acoshf-8"><code>acoshf</code></a>: <a href="#acosh">acosh</a></li>
2182<H1> Index </H1> 1754<li><a href="#index-asin-9"><code>asin</code></a>: <a href="#asin">asin</a></li>
2183<!--docid::SEC43::--> 1755<li><a href="#index-asinf-10"><code>asinf</code></a>: <a href="#asin">asin</a></li>
2184<table><tr><th valign=top>Jump to: &nbsp; </th><td><A HREF="libm.html#cp_A" style="text-decoration:none"><b>A</b></A> 1756<li><a href="#index-asinh-11"><code>asinh</code></a>: <a href="#asinh">asinh</a></li>
2185 &nbsp; 1757<li><a href="#index-asinhf-12"><code>asinhf</code></a>: <a href="#asinh">asinh</a></li>
2186<A HREF="libm.html#cp_C" style="text-decoration:none"><b>C</b></A> 1758<li><a href="#index-atan-13"><code>atan</code></a>: <a href="#atan">atan</a></li>
2187 &nbsp; 1759<li><a href="#index-atan2-15"><code>atan2</code></a>: <a href="#atan2">atan2</a></li>
2188<A HREF="libm.html#cp_E" style="text-decoration:none"><b>E</b></A> 1760<li><a href="#index-atan2f-16"><code>atan2f</code></a>: <a href="#atan2">atan2</a></li>
2189 &nbsp; 1761<li><a href="#index-atanf-14"><code>atanf</code></a>: <a href="#atan">atan</a></li>
2190<A HREF="libm.html#cp_F" style="text-decoration:none"><b>F</b></A> 1762<li><a href="#index-atanh-17"><code>atanh</code></a>: <a href="#atanh">atanh</a></li>
2191 &nbsp; 1763<li><a href="#index-atanhf-18"><code>atanhf</code></a>: <a href="#atanh">atanh</a></li>
2192<A HREF="libm.html#cp_G" style="text-decoration:none"><b>G</b></A> 1764<li><a href="#index-cbrt-31"><code>cbrt</code></a>: <a href="#cbrt">cbrt</a></li>
2193 &nbsp; 1765<li><a href="#index-cbrtf-32"><code>cbrtf</code></a>: <a href="#cbrt">cbrt</a></li>
2194<A HREF="libm.html#cp_H" style="text-decoration:none"><b>H</b></A> 1766<li><a href="#index-ceil-47"><code>ceil</code></a>: <a href="#floor">floor</a></li>
2195 &nbsp; 1767<li><a href="#index-ceilf-48"><code>ceilf</code></a>: <a href="#floor">floor</a></li>
2196<A HREF="libm.html#cp_I" style="text-decoration:none"><b>I</b></A> 1768<li><a href="#index-copysign-33"><code>copysign</code></a>: <a href="#copysign">copysign</a></li>
2197 &nbsp; 1769<li><a href="#index-copysignf-34"><code>copysignf</code></a>: <a href="#copysign">copysign</a></li>
2198<A HREF="libm.html#cp_J" style="text-decoration:none"><b>J</b></A> 1770<li><a href="#index-cos-98"><code>cos</code></a>: <a href="#sin">sin</a></li>
2199 &nbsp; 1771<li><a href="#index-cosf-99"><code>cosf</code></a>: <a href="#sin">sin</a></li>
2200<A HREF="libm.html#cp_L" style="text-decoration:none"><b>L</b></A> 1772<li><a href="#index-erf-35"><code>erf</code></a>: <a href="#erf">erf</a></li>
2201 &nbsp; 1773<li><a href="#index-erfc-37"><code>erfc</code></a>: <a href="#erf">erf</a></li>
2202<A HREF="libm.html#cp_M" style="text-decoration:none"><b>M</b></A> 1774<li><a href="#index-erfcf-38"><code>erfcf</code></a>: <a href="#erf">erf</a></li>
2203 &nbsp; 1775<li><a href="#index-erff-36"><code>erff</code></a>: <a href="#erf">erf</a></li>
2204<A HREF="libm.html#cp_N" style="text-decoration:none"><b>N</b></A> 1776<li><a href="#index-exp-39"><code>exp</code></a>: <a href="#exp">exp</a></li>
2205 &nbsp; 1777<li><a href="#index-expf-40"><code>expf</code></a>: <a href="#exp">exp</a></li>
2206<A HREF="libm.html#cp_O" style="text-decoration:none"><b>O</b></A> 1778<li><a href="#index-expm1-41"><code>expm1</code></a>: <a href="#expm1">expm1</a></li>
2207 &nbsp; 1779<li><a href="#index-expm1f-42"><code>expm1f</code></a>: <a href="#expm1">expm1</a></li>
2208<A HREF="libm.html#cp_P" style="text-decoration:none"><b>P</b></A> 1780<li><a href="#index-fabs-43"><code>fabs</code></a>: <a href="#fabs">fabs</a></li>
2209 &nbsp; 1781<li><a href="#index-fabsf-44"><code>fabsf</code></a>: <a href="#fabs">fabs</a></li>
2210<A HREF="libm.html#cp_R" style="text-decoration:none"><b>R</b></A> 1782<li><a href="#index-finite-69"><code>finite</code></a>: <a href="#isnan">isnan</a></li>
2211 &nbsp; 1783<li><a href="#index-finitef-72"><code>finitef</code></a>: <a href="#isnan">isnan</a></li>
2212<A HREF="libm.html#cp_S" style="text-decoration:none"><b>S</b></A> 1784<li><a href="#index-floor-45"><code>floor</code></a>: <a href="#floor">floor</a></li>
2213 &nbsp; 1785<li><a href="#index-floorf-46"><code>floorf</code></a>: <a href="#floor">floor</a></li>
2214<A HREF="libm.html#cp_T" style="text-decoration:none"><b>T</b></A> 1786<li><a href="#index-fmod-49"><code>fmod</code></a>: <a href="#fmod">fmod</a></li>
2215 &nbsp; 1787<li><a href="#index-fmodf-50"><code>fmodf</code></a>: <a href="#fmod">fmod</a></li>
2216<A HREF="libm.html#cp_Y" style="text-decoration:none"><b>Y</b></A> 1788<li><a href="#index-frexp-51"><code>frexp</code></a>: <a href="#frexp">frexp</a></li>
2217 &nbsp; 1789<li><a href="#index-frexpf-52"><code>frexpf</code></a>: <a href="#frexp">frexp</a></li>
2218</td></tr></table><br><P></P> 1790<li><a href="#index-gamma-53"><code>gamma</code></a>: <a href="#gamma">gamma</a></li>
2219<TABLE border=0> 1791<li><a href="#index-gamma_005fr-57"><code>gamma_r</code></a>: <a href="#gamma">gamma</a></li>
2220<TR><TD></TD><TH ALIGN=LEFT>Index Entry</TH><TH ALIGN=LEFT> Section</TH></TR> 1792<li><a href="#index-gammaf-54"><code>gammaf</code></a>: <a href="#gamma">gamma</a></li>
2221<TR><TD COLSPAN=3> <HR></TD></TR> 1793<li><a href="#index-gammaf_005fr-58"><code>gammaf_r</code></a>: <a href="#gamma">gamma</a></li>
2222<TR><TH><A NAME="cp_A"></A>A</TH><TD></TD><TD></TD></TR> 1794<li><a href="#index-hypot-61"><code>hypot</code></a>: <a href="#hypot">hypot</a></li>
2223<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC3"><CODE>acos</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC3">1.2 <CODE>acos</CODE>, <CODE>acosf</CODE>---arc cosine</A></TD></TR> 1795<li><a href="#index-hypotf-62"><code>hypotf</code></a>: <a href="#hypot">hypot</a></li>
2224<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC3"><CODE>acosf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC3">1.2 <CODE>acos</CODE>, <CODE>acosf</CODE>---arc cosine</A></TD></TR> 1796<li><a href="#index-ilogb-63"><code>ilogb</code></a>: <a href="#ilogb">ilogb</a></li>
2225<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC4"><CODE>acosh</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC4">1.3 <CODE>acosh</CODE>, <CODE>acoshf</CODE>---inverse hyperbolic cosine</A></TD></TR> 1797<li><a href="#index-ilogbf-64"><code>ilogbf</code></a>: <a href="#ilogb">ilogb</a></li>
2226<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC4"><CODE>acoshf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC4">1.3 <CODE>acosh</CODE>, <CODE>acoshf</CODE>---inverse hyperbolic cosine</A></TD></TR> 1798<li><a href="#index-infinity-65"><code>infinity</code></a>: <a href="#infinity">infinity</a></li>
2227<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC5"><CODE>asin</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC5">1.4 <CODE>asin</CODE>, <CODE>asinf</CODE>---arc sine</A></TD></TR> 1799<li><a href="#index-infinityf-66"><code>infinityf</code></a>: <a href="#infinity">infinity</a></li>
2228<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC5"><CODE>asinf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC5">1.4 <CODE>asin</CODE>, <CODE>asinf</CODE>---arc sine</A></TD></TR> 1800<li><a href="#index-isinf-68"><code>isinf</code></a>: <a href="#isnan">isnan</a></li>
2229<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC6"><CODE>asinh</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC6">1.5 <CODE>asinh</CODE>, <CODE>asinhf</CODE>---inverse hyperbolic sine</A></TD></TR> 1801<li><a href="#index-isinff-71"><code>isinff</code></a>: <a href="#isnan">isnan</a></li>
2230<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC6"><CODE>asinhf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC6">1.5 <CODE>asinh</CODE>, <CODE>asinhf</CODE>---inverse hyperbolic sine</A></TD></TR> 1802<li><a href="#index-isnan-67"><code>isnan</code></a>: <a href="#isnan">isnan</a></li>
2231<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC7"><CODE>atan</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC7">1.6 <CODE>atan</CODE>, <CODE>atanf</CODE>---arc tangent</A></TD></TR> 1803<li><a href="#index-isnanf-70"><code>isnanf</code></a>: <a href="#isnan">isnan</a></li>
2232<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC8"><CODE>atan2</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC8">1.7 <CODE>atan2</CODE>, <CODE>atan2f</CODE>---arc tangent of y/x</A></TD></TR> 1804<li><a href="#index-j0-19"><code>j0</code></a>: <a href="#jN">jN</a></li>
2233<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC8"><CODE>atan2f</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC8">1.7 <CODE>atan2</CODE>, <CODE>atan2f</CODE>---arc tangent of y/x</A></TD></TR> 1805<li><a href="#index-j0f-20"><code>j0f</code></a>: <a href="#jN">jN</a></li>
2234<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC7"><CODE>atanf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC7">1.6 <CODE>atan</CODE>, <CODE>atanf</CODE>---arc tangent</A></TD></TR> 1806<li><a href="#index-j1-21"><code>j1</code></a>: <a href="#jN">jN</a></li>
2235<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC9"><CODE>atanh</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC9">1.8 <CODE>atanh</CODE>, <CODE>atanhf</CODE>---inverse hyperbolic tangent</A></TD></TR> 1807<li><a href="#index-j1f-22"><code>j1f</code></a>: <a href="#jN">jN</a></li>
2236<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC9"><CODE>atanhf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC9">1.8 <CODE>atanh</CODE>, <CODE>atanhf</CODE>---inverse hyperbolic tangent</A></TD></TR> 1808<li><a href="#index-jn-23"><code>jn</code></a>: <a href="#jN">jN</a></li>
2237<TR><TD COLSPAN=3> <HR></TD></TR> 1809<li><a href="#index-jnf-24"><code>jnf</code></a>: <a href="#jN">jN</a></li>
2238<TR><TH><A NAME="cp_C"></A>C</TH><TD></TD><TD></TD></TR> 1810<li><a href="#index-ldexp-73"><code>ldexp</code></a>: <a href="#ldexp">ldexp</a></li>
2239<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC31"><CODE>cbrt</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC31">1.30 <CODE>cbrt</CODE>, <CODE>cbrtf</CODE>---cube root</A></TD></TR> 1811<li><a href="#index-ldexpf-74"><code>ldexpf</code></a>: <a href="#ldexp">ldexp</a></li>
2240<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC31"><CODE>cbrtf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC31">1.30 <CODE>cbrt</CODE>, <CODE>cbrtf</CODE>---cube root</A></TD></TR> 1812<li><a href="#index-lgamma-55"><code>lgamma</code></a>: <a href="#gamma">gamma</a></li>
2241<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC15"><CODE>ceil</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC15">1.14 <CODE>floor</CODE>, <CODE>floorf</CODE>, <CODE>ceil</CODE>, <CODE>ceilf</CODE>---floor and ceiling</A></TD></TR> 1813<li><a href="#index-lgamma_005fr-59"><code>lgamma_r</code></a>: <a href="#gamma">gamma</a></li>
2242<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC15"><CODE>ceilf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC15">1.14 <CODE>floor</CODE>, <CODE>floorf</CODE>, <CODE>ceil</CODE>, <CODE>ceilf</CODE>---floor and ceiling</A></TD></TR> 1814<li><a href="#index-lgammaf-56"><code>lgammaf</code></a>: <a href="#gamma">gamma</a></li>
2243<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC32"><CODE>copysign</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC32">1.31 <CODE>copysign</CODE>, <CODE>copysignf</CODE>---sign of <VAR>y</VAR>, magnitude of <VAR>x</VAR></A></TD></TR> 1815<li><a href="#index-lgammaf_005fr-60"><code>lgammaf_r</code></a>: <a href="#gamma">gamma</a></li>
2244<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC32"><CODE>copysignf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC32">1.31 <CODE>copysign</CODE>, <CODE>copysignf</CODE>---sign of <VAR>y</VAR>, magnitude of <VAR>x</VAR></A></TD></TR> 1816<li><a href="#index-log-75"><code>log</code></a>: <a href="#log">log</a></li>
2245<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC27"><CODE>cos</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC27">1.26 <CODE>sin</CODE>, <CODE>sinf</CODE>, <CODE>cos</CODE>, <CODE>cosf</CODE>---sine or cosine</A></TD></TR> 1817<li><a href="#index-log10-77"><code>log10</code></a>: <a href="#log10">log10</a></li>
2246<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC27"><CODE>cosf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC27">1.26 <CODE>sin</CODE>, <CODE>sinf</CODE>, <CODE>cos</CODE>, <CODE>cosf</CODE>---sine or cosine</A></TD></TR> 1818<li><a href="#index-log10f-78"><code>log10f</code></a>: <a href="#log10">log10</a></li>
2247<TR><TD COLSPAN=3> <HR></TD></TR> 1819<li><a href="#index-log1p-79"><code>log1p</code></a>: <a href="#log1p">log1p</a></li>
2248<TR><TH><A NAME="cp_E"></A>E</TH><TD></TD><TD></TD></TR> 1820<li><a href="#index-log1pf-80"><code>log1pf</code></a>: <a href="#log1p">log1p</a></li>
2249<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC12"><CODE>erf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC12">1.11 <CODE>erf</CODE>, <CODE>erff</CODE>, <CODE>erfc</CODE>, <CODE>erfcf</CODE>---error function</A></TD></TR> 1821<li><a href="#index-logf-76"><code>logf</code></a>: <a href="#log">log</a></li>
2250<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC12"><CODE>erfc</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC12">1.11 <CODE>erf</CODE>, <CODE>erff</CODE>, <CODE>erfc</CODE>, <CODE>erfcf</CODE>---error function</A></TD></TR> 1822<li><a href="#index-matherr-81"><code>matherr</code></a>: <a href="#matherr">matherr</a></li>
2251<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC12"><CODE>erfcf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC12">1.11 <CODE>erf</CODE>, <CODE>erff</CODE>, <CODE>erfc</CODE>, <CODE>erfcf</CODE>---error function</A></TD></TR> 1823<li><a href="#index-g_t_0040code_007bmatherr_007d-and-reentrancy-107"><code>matherr</code> and reentrancy</a>: <a href="#Reentrancy">Reentrancy</a></li>
2252<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC12"><CODE>erff</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC12">1.11 <CODE>erf</CODE>, <CODE>erff</CODE>, <CODE>erfc</CODE>, <CODE>erfcf</CODE>---error function</A></TD></TR> 1824<li><a href="#index-modf-82"><code>modf</code></a>: <a href="#modf">modf</a></li>
2253<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC13"><CODE>exp</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC13">1.12 <CODE>exp</CODE>, <CODE>expf</CODE>---exponential</A></TD></TR> 1825<li><a href="#index-modff-83"><code>modff</code></a>: <a href="#modf">modf</a></li>
2254<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC13"><CODE>expf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC13">1.12 <CODE>exp</CODE>, <CODE>expf</CODE>---exponential</A></TD></TR> 1826<li><a href="#index-nan-84"><code>nan</code></a>: <a href="#nan">nan</a></li>
2255<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC33"><CODE>expm1</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC33">1.32 <CODE>expm1</CODE>, <CODE>expm1f</CODE>---exponential minus 1</A></TD></TR> 1827<li><a href="#index-nanf-85"><code>nanf</code></a>: <a href="#nan">nan</a></li>
2256<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC33"><CODE>expm1f</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC33">1.32 <CODE>expm1</CODE>, <CODE>expm1f</CODE>---exponential minus 1</A></TD></TR> 1828<li><a href="#index-nextafter-86"><code>nextafter</code></a>: <a href="#nextafter">nextafter</a></li>
2257<TR><TD COLSPAN=3> <HR></TD></TR> 1829<li><a href="#index-nextafterf-87"><code>nextafterf</code></a>: <a href="#nextafter">nextafter</a></li>
2258<TR><TH><A NAME="cp_F"></A>F</TH><TD></TD><TD></TD></TR> 1830<li><a href="#index-OS-stubs-4">OS stubs</a>: <a href="#Math">Math</a></li>
2259<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC14"><CODE>fabs</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC14">1.13 <CODE>fabs</CODE>, <CODE>fabsf</CODE>---absolute value (magnitude)</A></TD></TR> 1831<li><a href="#index-pow-88"><code>pow</code></a>: <a href="#pow">pow</a></li>
2260<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC14"><CODE>fabsf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC14">1.13 <CODE>fabs</CODE>, <CODE>fabsf</CODE>---absolute value (magnitude)</A></TD></TR> 1832<li><a href="#index-powf-89"><code>powf</code></a>: <a href="#pow">pow</a></li>
2261<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC20"><CODE>finite</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC20">1.19 <CODE>isnan</CODE>,<CODE>isnanf</CODE>,<CODE>isinf</CODE>,<CODE>isinff</CODE>,<CODE>finite</CODE>,<CODE>finitef</CODE>---test for exceptional numbers</A></TD></TR> 1833<li><a href="#index-reentrancy-106">reentrancy</a>: <a href="#Reentrancy">Reentrancy</a></li>
2262<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC20"><CODE>finitef</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC20">1.19 <CODE>isnan</CODE>,<CODE>isnanf</CODE>,<CODE>isinf</CODE>,<CODE>isinff</CODE>,<CODE>finite</CODE>,<CODE>finitef</CODE>---test for exceptional numbers</A></TD></TR> 1834<li><a href="#index-remainder-90"><code>remainder</code></a>: <a href="#remainder">remainder</a></li>
2263<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC15"><CODE>floor</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC15">1.14 <CODE>floor</CODE>, <CODE>floorf</CODE>, <CODE>ceil</CODE>, <CODE>ceilf</CODE>---floor and ceiling</A></TD></TR> 1835<li><a href="#index-remainderf-91"><code>remainderf</code></a>: <a href="#remainder">remainder</a></li>
2264<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC15"><CODE>floorf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC15">1.14 <CODE>floor</CODE>, <CODE>floorf</CODE>, <CODE>ceil</CODE>, <CODE>ceilf</CODE>---floor and ceiling</A></TD></TR> 1836<li><a href="#index-scalbn-92"><code>scalbn</code></a>: <a href="#scalbn">scalbn</a></li>
2265<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC16"><CODE>fmod</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC16">1.15 <CODE>fmod</CODE>, <CODE>fmodf</CODE>---floating-point remainder (modulo)</A></TD></TR> 1837<li><a href="#index-scalbnf-93"><code>scalbnf</code></a>: <a href="#scalbn">scalbn</a></li>
2266<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC16"><CODE>fmodf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC16">1.15 <CODE>fmod</CODE>, <CODE>fmodf</CODE>---floating-point remainder (modulo)</A></TD></TR> 1838<li><a href="#index-sin-96"><code>sin</code></a>: <a href="#sin">sin</a></li>
2267<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC17"><CODE>frexp</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC17">1.16 <CODE>frexp</CODE>, <CODE>frexpf</CODE>---split floating-point number</A></TD></TR> 1839<li><a href="#index-sinf-97"><code>sinf</code></a>: <a href="#sin">sin</a></li>
2268<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC17"><CODE>frexpf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC17">1.16 <CODE>frexp</CODE>, <CODE>frexpf</CODE>---split floating-point number</A></TD></TR> 1840<li><a href="#index-sinh-100"><code>sinh</code></a>: <a href="#sinh">sinh</a></li>
2269<TR><TD COLSPAN=3> <HR></TD></TR> 1841<li><a href="#index-sinhf-101"><code>sinhf</code></a>: <a href="#sinh">sinh</a></li>
2270<TR><TH><A NAME="cp_G"></A>G</TH><TD></TD><TD></TD></TR> 1842<li><a href="#index-sqrt-94"><code>sqrt</code></a>: <a href="#sqrt">sqrt</a></li>
2271<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC18"><CODE>gamma</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC18">1.17 <CODE>gamma</CODE>, <CODE>gammaf</CODE>, <CODE>lgamma</CODE>, <CODE>lgammaf</CODE>, <CODE>gamma_r</CODE>,</A></TD></TR> 1843<li><a href="#index-sqrtf-95"><code>sqrtf</code></a>: <a href="#sqrt">sqrt</a></li>
2272<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC18"><CODE>gamma_r</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC18">1.17 <CODE>gamma</CODE>, <CODE>gammaf</CODE>, <CODE>lgamma</CODE>, <CODE>lgammaf</CODE>, <CODE>gamma_r</CODE>,</A></TD></TR> 1844<li><a href="#index-stubs-3">stubs</a>: <a href="#Math">Math</a></li>
2273<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC18"><CODE>gammaf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC18">1.17 <CODE>gamma</CODE>, <CODE>gammaf</CODE>, <CODE>lgamma</CODE>, <CODE>lgammaf</CODE>, <CODE>gamma_r</CODE>,</A></TD></TR> 1845<li><a href="#index-support-subroutines-2">support subroutines</a>: <a href="#Math">Math</a></li>
2274<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC18"><CODE>gammaf_r</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC18">1.17 <CODE>gamma</CODE>, <CODE>gammaf</CODE>, <CODE>lgamma</CODE>, <CODE>lgammaf</CODE>, <CODE>gamma_r</CODE>,</A></TD></TR> 1846<li><a href="#index-system-calls-1">system calls</a>: <a href="#Math">Math</a></li>
2275<TR><TD COLSPAN=3> <HR></TD></TR> 1847<li><a href="#index-tan-102"><code>tan</code></a>: <a href="#tan">tan</a></li>
2276<TR><TH><A NAME="cp_H"></A>H</TH><TD></TD><TD></TD></TR> 1848<li><a href="#index-tanf-103"><code>tanf</code></a>: <a href="#tan">tan</a></li>
2277<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC19"><CODE>hypot</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC19">1.18 <CODE>hypot</CODE>, <CODE>hypotf</CODE>---distance from origin</A></TD></TR> 1849<li><a href="#index-tanh-104"><code>tanh</code></a>: <a href="#tanh">tanh</a></li>
2278<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC19"><CODE>hypotf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC19">1.18 <CODE>hypot</CODE>, <CODE>hypotf</CODE>---distance from origin</A></TD></TR> 1850<li><a href="#index-tanhf-105"><code>tanhf</code></a>: <a href="#tanh">tanh</a></li>
2279<TR><TD COLSPAN=3> <HR></TD></TR> 1851<li><a href="#index-y0-25"><code>y0</code></a>: <a href="#jN">jN</a></li>
2280<TR><TH><A NAME="cp_I"></A>I</TH><TD></TD><TD></TD></TR> 1852<li><a href="#index-y0f-26"><code>y0f</code></a>: <a href="#jN">jN</a></li>
2281<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC34"><CODE>ilogb</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC34">1.33 <CODE>ilogb</CODE>, <CODE>ilogbf</CODE>---get exponent of floating-point number</A></TD></TR> 1853<li><a href="#index-y1-27"><code>y1</code></a>: <a href="#jN">jN</a></li>
2282<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC34"><CODE>ilogbf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC34">1.33 <CODE>ilogb</CODE>, <CODE>ilogbf</CODE>---get exponent of floating-point number</A></TD></TR> 1854<li><a href="#index-y1f-28"><code>y1f</code></a>: <a href="#jN">jN</a></li>
2283<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC35"><CODE>infinity</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC35">1.34 <CODE>infinity</CODE>, <CODE>infinityf</CODE>---representation of infinity</A></TD></TR> 1855<li><a href="#index-yn-29"><code>yn</code></a>: <a href="#jN">jN</a></li>
2284<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC35"><CODE>infinityf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC35">1.34 <CODE>infinity</CODE>, <CODE>infinityf</CODE>---representation of infinity</A></TD></TR> 1856<li><a href="#index-ynf-30"><code>ynf</code></a>: <a href="#jN">jN</a></li>
2285<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC20"><CODE>isinf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC20">1.19 <CODE>isnan</CODE>,<CODE>isnanf</CODE>,<CODE>isinf</CODE>,<CODE>isinff</CODE>,<CODE>finite</CODE>,<CODE>finitef</CODE>---test for exceptional numbers</A></TD></TR> 1857</ul>
2286<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC20"><CODE>isinff</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC20">1.19 <CODE>isnan</CODE>,<CODE>isnanf</CODE>,<CODE>isinf</CODE>,<CODE>isinff</CODE>,<CODE>finite</CODE>,<CODE>finitef</CODE>---test for exceptional numbers</A></TD></TR> 1858<div class="contents">
2287<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC20"><CODE>isnan</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC20">1.19 <CODE>isnan</CODE>,<CODE>isnanf</CODE>,<CODE>isinf</CODE>,<CODE>isinff</CODE>,<CODE>finite</CODE>,<CODE>finitef</CODE>---test for exceptional numbers</A></TD></TR> 1859<h2>Table of Contents</h2>
2288<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC20"><CODE>isnanf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC20">1.19 <CODE>isnan</CODE>,<CODE>isnanf</CODE>,<CODE>isinf</CODE>,<CODE>isinff</CODE>,<CODE>finite</CODE>,<CODE>finitef</CODE>---test for exceptional numbers</A></TD></TR> 1860<ul>
2289<TR><TD COLSPAN=3> <HR></TD></TR> 1861<li><a name="toc_Top" href="#Top">Top</a>
2290<TR><TH><A NAME="cp_J"></A>J</TH><TD></TD><TD></TD></TR> 1862<li><a name="toc_Math" href="#Math">1 Mathematical Functions (<samp><span class="file">math.h</span></samp>)</a>
2291<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC10"><CODE>j0</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC10">1.9 <CODE>jN</CODE>,<CODE>jNf</CODE>,<CODE>yN</CODE>,<CODE>yNf</CODE>---Bessel functions</A></TD></TR> 1863<ul>
2292<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC10"><CODE>j0f</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC10">1.9 <CODE>jN</CODE>,<CODE>jNf</CODE>,<CODE>yN</CODE>,<CODE>yNf</CODE>---Bessel functions</A></TD></TR> 1864<li><a href="#version">1.1 Version of library</a>
2293<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC10"><CODE>j1</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC10">1.9 <CODE>jN</CODE>,<CODE>jNf</CODE>,<CODE>yN</CODE>,<CODE>yNf</CODE>---Bessel functions</A></TD></TR> 1865<li><a href="#acos">1.2 <code>acos</code>, <code>acosf</code>&mdash;arc cosine</a>
2294<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC10"><CODE>j1f</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC10">1.9 <CODE>jN</CODE>,<CODE>jNf</CODE>,<CODE>yN</CODE>,<CODE>yNf</CODE>---Bessel functions</A></TD></TR> 1866<li><a href="#acosh">1.3 <code>acosh</code>, <code>acoshf</code>&mdash;inverse hyperbolic cosine</a>
2295<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC10"><CODE>jn</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC10">1.9 <CODE>jN</CODE>,<CODE>jNf</CODE>,<CODE>yN</CODE>,<CODE>yNf</CODE>---Bessel functions</A></TD></TR> 1867<li><a href="#asin">1.4 <code>asin</code>, <code>asinf</code>&mdash;arc sine</a>
2296<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC10"><CODE>jnf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC10">1.9 <CODE>jN</CODE>,<CODE>jNf</CODE>,<CODE>yN</CODE>,<CODE>yNf</CODE>---Bessel functions</A></TD></TR> 1868<li><a href="#asinh">1.5 <code>asinh</code>, <code>asinhf</code>&mdash;inverse hyperbolic sine</a>
2297<TR><TD COLSPAN=3> <HR></TD></TR> 1869<li><a href="#atan">1.6 <code>atan</code>, <code>atanf</code>&mdash;arc tangent</a>
2298<TR><TH><A NAME="cp_L"></A>L</TH><TD></TD><TD></TD></TR> 1870<li><a href="#atan2">1.7 <code>atan2</code>, <code>atan2f</code>&mdash;arc tangent of y/x</a>
2299<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC21"><CODE>ldexp</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC21">1.20 <CODE>ldexp</CODE>, <CODE>ldexpf</CODE>---load exponent</A></TD></TR> 1871<li><a href="#atanh">1.8 <code>atanh</code>, <code>atanhf</code>&mdash;inverse hyperbolic tangent</a>
2300<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC21"><CODE>ldexpf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC21">1.20 <CODE>ldexp</CODE>, <CODE>ldexpf</CODE>---load exponent</A></TD></TR> 1872<li><a href="#jN">1.9 <code>jN</code>, <code>jNf</code>, <code>yN</code>, <code>yNf</code>&mdash;Bessel functions</a>
2301<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC18"><CODE>lgamma</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC18">1.17 <CODE>gamma</CODE>, <CODE>gammaf</CODE>, <CODE>lgamma</CODE>, <CODE>lgammaf</CODE>, <CODE>gamma_r</CODE>,</A></TD></TR> 1873<li><a href="#cbrt">1.10 <code>cbrt</code>, <code>cbrtf</code>&mdash;cube root</a>
2302<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC18"><CODE>lgamma_r</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC18">1.17 <CODE>gamma</CODE>, <CODE>gammaf</CODE>, <CODE>lgamma</CODE>, <CODE>lgammaf</CODE>, <CODE>gamma_r</CODE>,</A></TD></TR> 1874<li><a href="#copysign">1.11 <code>copysign</code>, <code>copysignf</code>&mdash;sign of <var>y</var>, magnitude of <var>x</var></a>
2303<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC18"><CODE>lgammaf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC18">1.17 <CODE>gamma</CODE>, <CODE>gammaf</CODE>, <CODE>lgamma</CODE>, <CODE>lgammaf</CODE>, <CODE>gamma_r</CODE>,</A></TD></TR> 1875<li><a href="#cosh">1.12 <code>cosh</code>, <code>coshf</code>&mdash;hyperbolic cosine</a>
2304<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC18"><CODE>lgammaf_r</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC18">1.17 <CODE>gamma</CODE>, <CODE>gammaf</CODE>, <CODE>lgamma</CODE>, <CODE>lgammaf</CODE>, <CODE>gamma_r</CODE>,</A></TD></TR> 1876<li><a href="#erf">1.13 <code>erf</code>, <code>erff</code>, <code>erfc</code>, <code>erfcf</code>&mdash;error function</a>
2305<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC22"><CODE>log</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC22">1.21 <CODE>log</CODE>, <CODE>logf</CODE>---natural logarithms</A></TD></TR> 1877<li><a href="#exp">1.14 <code>exp</code>, <code>expf</code>&mdash;exponential</a>
2306<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC23"><CODE>log10</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC23">1.22 <CODE>log10</CODE>, <CODE>log10f</CODE>---base 10 logarithms</A></TD></TR> 1878<li><a href="#expm1">1.15 <code>expm1</code>, <code>expm1f</code>&mdash;exponential minus 1</a>
2307<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC23"><CODE>log10f</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC23">1.22 <CODE>log10</CODE>, <CODE>log10f</CODE>---base 10 logarithms</A></TD></TR> 1879<li><a href="#fabs">1.16 <code>fabs</code>, <code>fabsf</code>&mdash;absolute value (magnitude)</a>
2308<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC36"><CODE>log1p</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC36">1.35 <CODE>log1p</CODE>, <CODE>log1pf</CODE>---log of <CODE>1 + <VAR>x</VAR></CODE></A></TD></TR> 1880<li><a href="#floor">1.17 <code>floor</code>, <code>floorf</code>, <code>ceil</code>, <code>ceilf</code>&mdash;floor and ceiling</a>
2309<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC36"><CODE>log1pf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC36">1.35 <CODE>log1p</CODE>, <CODE>log1pf</CODE>---log of <CODE>1 + <VAR>x</VAR></CODE></A></TD></TR> 1881<li><a href="#fmod">1.18 <code>fmod</code>, <code>fmodf</code>&mdash;floating-point remainder (modulo)</a>
2310<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC22"><CODE>logf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC22">1.21 <CODE>log</CODE>, <CODE>logf</CODE>---natural logarithms</A></TD></TR> 1882<li><a href="#frexp">1.19 <code>frexp</code>, <code>frexpf</code>&mdash;split floating-point number</a>
2311<TR><TD COLSPAN=3> <HR></TD></TR> 1883<li><a href="#gamma">1.20 <code>gamma</code>, <code>gammaf</code>, <code>lgamma</code>, <code>lgammaf</code>, <code>gamma_r</code>,</a>
2312<TR><TH><A NAME="cp_M"></A>M</TH><TD></TD><TD></TD></TR> 1884<li><a href="#hypot">1.21 <code>hypot</code>, <code>hypotf</code>&mdash;distance from origin</a>
2313<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC37"><CODE>matherr</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC37">1.36 <CODE>matherr</CODE>---modifiable math error handler</A></TD></TR> 1885<li><a href="#ilogb">1.22 <code>ilogb</code>, <code>ilogbf</code>&mdash;get exponent of floating-point number</a>
2314<TR><TD></TD><TD valign=top><A HREF="libm.html#IDX6"><CODE>matherr</CODE> and reentrancy</A></TD><TD valign=top><A HREF="libm.html#SEC42">2. Reentrancy Properties of <CODE>libm</CODE></A></TD></TR> 1886<li><a href="#infinity">1.23 <code>infinity</code>, <code>infinityf</code>&mdash;representation of infinity</a>
2315<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC38"><CODE>modf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC38">1.37 <CODE>modf</CODE>, <CODE>modff</CODE>---split fractional and integer parts</A></TD></TR> 1887<li><a href="#isnan">1.24 <code>isnan</code>, <code>isnanf</code>, <code>isinf</code>, <code>isinff</code>, <code>finite</code>, <code>finitef</code>&mdash;test for exceptional numbers</a>
2316<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC38"><CODE>modff</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC38">1.37 <CODE>modf</CODE>, <CODE>modff</CODE>---split fractional and integer parts</A></TD></TR> 1888<li><a href="#ldexp">1.25 <code>ldexp</code>, <code>ldexpf</code>&mdash;load exponent</a>
2317<TR><TD COLSPAN=3> <HR></TD></TR> 1889<li><a href="#log">1.26 <code>log</code>, <code>logf</code>&mdash;natural logarithms</a>
2318<TR><TH><A NAME="cp_N"></A>N</TH><TD></TD><TD></TD></TR> 1890<li><a href="#log10">1.27 <code>log10</code>, <code>log10f</code>&mdash;base 10 logarithms</a>
2319<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC39"><CODE>nan</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC39">1.38 <CODE>nan</CODE>, <CODE>nanf</CODE>---representation of "Not a Number"</A></TD></TR> 1891<li><a href="#log1p">1.28 <code>log1p</code>, <code>log1pf</code>&mdash;log of <code>1 + </code><var>x</var></a>
2320<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC39"><CODE>nanf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC39">1.38 <CODE>nan</CODE>, <CODE>nanf</CODE>---representation of "Not a Number"</A></TD></TR> 1892<li><a href="#matherr">1.29 <code>matherr</code>&mdash;modifiable math error handler</a>
2321<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC40"><CODE>nextafter</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC40">1.39 <CODE>nextafter</CODE>, <CODE>nextafterf</CODE>---get next number</A></TD></TR> 1893<li><a href="#modf">1.30 <code>modf</code>, <code>modff</code>&mdash;split fractional and integer parts</a>
2322<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC40"><CODE>nextafterf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC40">1.39 <CODE>nextafter</CODE>, <CODE>nextafterf</CODE>---get next number</A></TD></TR> 1894<li><a href="#nan">1.31 <code>nan</code>, <code>nanf</code>&mdash;representation of &ldquo;Not a Number&rdquo;</a>
2323<TR><TD COLSPAN=3> <HR></TD></TR> 1895<li><a href="#nextafter">1.32 <code>nextafter</code>, <code>nextafterf</code>&mdash;get next number</a>
2324<TR><TH><A NAME="cp_O"></A>O</TH><TD></TD><TD></TD></TR> 1896<li><a href="#pow">1.33 <code>pow</code>, <code>powf</code>&mdash;x to the power y</a>
2325<TR><TD></TD><TD valign=top><A HREF="libm.html#IDX4">OS stubs</A></TD><TD valign=top><A HREF="libm.html#SEC1">1. Mathematical Functions (<TT>`math.h'</TT>)</A></TD></TR> 1897<li><a href="#remainder">1.34 <code>remainder</code>, <code>remainderf</code>&mdash;round and remainder</a>
2326<TR><TD COLSPAN=3> <HR></TD></TR> 1898<li><a href="#scalbn">1.35 <code>scalbn</code>, <code>scalbnf</code>&mdash;scale by power of two</a>
2327<TR><TH><A NAME="cp_P"></A>P</TH><TD></TD><TD></TD></TR> 1899<li><a href="#sqrt">1.36 <code>sqrt</code>, <code>sqrtf</code>&mdash;positive square root</a>
2328<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC24"><CODE>pow</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC24">1.23 <CODE>pow</CODE>, <CODE>powf</CODE>---x to the power y</A></TD></TR> 1900<li><a href="#sin">1.37 <code>sin</code>, <code>sinf</code>, <code>cos</code>, <code>cosf</code>&mdash;sine or cosine</a>
2329<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC24"><CODE>powf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC24">1.23 <CODE>pow</CODE>, <CODE>powf</CODE>---x to the power y</A></TD></TR> 1901<li><a href="#sinh">1.38 <code>sinh</code>, <code>sinhf</code>&mdash;hyperbolic sine</a>
2330<TR><TD COLSPAN=3> <HR></TD></TR> 1902<li><a href="#tan">1.39 <code>tan</code>, <code>tanf</code>&mdash;tangent</a>
2331<TR><TH><A NAME="cp_R"></A>R</TH><TD></TD><TD></TD></TR> 1903<li><a href="#tanh">1.40 <code>tanh</code>, <code>tanhf</code>&mdash;hyperbolic tangent</a>
2332<TR><TD></TD><TD valign=top><A HREF="libm.html#IDX5">reentrancy</A></TD><TD valign=top><A HREF="libm.html#SEC42">2. Reentrancy Properties of <CODE>libm</CODE></A></TD></TR> 1904</li></ul>
2333<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC25"><CODE>remainder</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC25">1.24 <CODE>remainder</CODE>, <CODE>remainderf</CODE>---round and remainder</A></TD></TR> 1905<li><a name="toc_Reentrancy" href="#Reentrancy">2 Reentrancy Properties of <code>libm</code></a>
2334<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC25"><CODE>remainderf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC25">1.24 <CODE>remainder</CODE>, <CODE>remainderf</CODE>---round and remainder</A></TD></TR> 1906<li><a name="toc_Index" href="#Index">Index</a>
2335<TR><TD COLSPAN=3> <HR></TD></TR> 1907</li></ul>
2336<TR><TH><A NAME="cp_S"></A>S</TH><TD></TD><TD></TD></TR> 1908</div>
2337<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC41"><CODE>scalbn</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC41">1.40 <CODE>scalbn</CODE>, <CODE>scalbnf</CODE>---scale by power of two</A></TD></TR> 1909
2338<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC41"><CODE>scalbnf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC41">1.40 <CODE>scalbn</CODE>, <CODE>scalbnf</CODE>---scale by power of two</A></TD></TR> 1910</body></html>
2339<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC27"><CODE>sin</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC27">1.26 <CODE>sin</CODE>, <CODE>sinf</CODE>, <CODE>cos</CODE>, <CODE>cosf</CODE>---sine or cosine</A></TD></TR> 1911
2340<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC27"><CODE>sinf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC27">1.26 <CODE>sin</CODE>, <CODE>sinf</CODE>, <CODE>cos</CODE>, <CODE>cosf</CODE>---sine or cosine</A></TD></TR>
2341<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC28"><CODE>sinh</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC28">1.27 <CODE>sinh</CODE>, <CODE>sinhf</CODE>---hyperbolic sine</A></TD></TR>
2342<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC28"><CODE>sinhf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC28">1.27 <CODE>sinh</CODE>, <CODE>sinhf</CODE>---hyperbolic sine</A></TD></TR>
2343<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC26"><CODE>sqrt</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC26">1.25 <CODE>sqrt</CODE>, <CODE>sqrtf</CODE>---positive square root</A></TD></TR>
2344<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC26"><CODE>sqrtf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC26">1.25 <CODE>sqrt</CODE>, <CODE>sqrtf</CODE>---positive square root</A></TD></TR>
2345<TR><TD></TD><TD valign=top><A HREF="libm.html#IDX3">stubs</A></TD><TD valign=top><A HREF="libm.html#SEC1">1. Mathematical Functions (<TT>`math.h'</TT>)</A></TD></TR>
2346<TR><TD></TD><TD valign=top><A HREF="libm.html#IDX2">support subroutines</A></TD><TD valign=top><A HREF="libm.html#SEC1">1. Mathematical Functions (<TT>`math.h'</TT>)</A></TD></TR>
2347<TR><TD></TD><TD valign=top><A HREF="libm.html#IDX1">system calls</A></TD><TD valign=top><A HREF="libm.html#SEC1">1. Mathematical Functions (<TT>`math.h'</TT>)</A></TD></TR>
2348<TR><TD COLSPAN=3> <HR></TD></TR>
2349<TR><TH><A NAME="cp_T"></A>T</TH><TD></TD><TD></TD></TR>
2350<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC29"><CODE>tan</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC29">1.28 <CODE>tan</CODE>, <CODE>tanf</CODE>---tangent</A></TD></TR>
2351<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC29"><CODE>tanf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC29">1.28 <CODE>tan</CODE>, <CODE>tanf</CODE>---tangent</A></TD></TR>
2352<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC30"><CODE>tanh</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC30">1.29 <CODE>tanh</CODE>, <CODE>tanhf</CODE>---hyperbolic tangent</A></TD></TR>
2353<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC30"><CODE>tanhf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC30">1.29 <CODE>tanh</CODE>, <CODE>tanhf</CODE>---hyperbolic tangent</A></TD></TR>
2354<TR><TD COLSPAN=3> <HR></TD></TR>
2355<TR><TH><A NAME="cp_Y"></A>Y</TH><TD></TD><TD></TD></TR>
2356<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC10"><CODE>y0</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC10">1.9 <CODE>jN</CODE>,<CODE>jNf</CODE>,<CODE>yN</CODE>,<CODE>yNf</CODE>---Bessel functions</A></TD></TR>
2357<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC10"><CODE>y0f</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC10">1.9 <CODE>jN</CODE>,<CODE>jNf</CODE>,<CODE>yN</CODE>,<CODE>yNf</CODE>---Bessel functions</A></TD></TR>
2358<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC10"><CODE>y1</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC10">1.9 <CODE>jN</CODE>,<CODE>jNf</CODE>,<CODE>yN</CODE>,<CODE>yNf</CODE>---Bessel functions</A></TD></TR>
2359<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC10"><CODE>y1f</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC10">1.9 <CODE>jN</CODE>,<CODE>jNf</CODE>,<CODE>yN</CODE>,<CODE>yNf</CODE>---Bessel functions</A></TD></TR>
2360<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC10"><CODE>yn</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC10">1.9 <CODE>jN</CODE>,<CODE>jNf</CODE>,<CODE>yN</CODE>,<CODE>yNf</CODE>---Bessel functions</A></TD></TR>
2361<TR><TD></TD><TD valign=top><A HREF="libm.html#SEC10"><CODE>ynf</CODE></A></TD><TD valign=top><A HREF="libm.html#SEC10">1.9 <CODE>jN</CODE>,<CODE>jNf</CODE>,<CODE>yN</CODE>,<CODE>yNf</CODE>---Bessel functions</A></TD></TR>
2362<TR><TD COLSPAN=3> <HR></TD></TR>
2363</TABLE><P></P><table><tr><th valign=top>Jump to: &nbsp; </th><td><A HREF="libm.html#cp_A" style="text-decoration:none"><b>A</b></A>
2364 &nbsp;
2365<A HREF="libm.html#cp_C" style="text-decoration:none"><b>C</b></A>
2366 &nbsp;
2367<A HREF="libm.html#cp_E" style="text-decoration:none"><b>E</b></A>
2368 &nbsp;
2369<A HREF="libm.html#cp_F" style="text-decoration:none"><b>F</b></A>
2370 &nbsp;
2371<A HREF="libm.html#cp_G" style="text-decoration:none"><b>G</b></A>
2372 &nbsp;
2373<A HREF="libm.html#cp_H" style="text-decoration:none"><b>H</b></A>
2374 &nbsp;
2375<A HREF="libm.html#cp_I" style="text-decoration:none"><b>I</b></A>
2376 &nbsp;
2377<A HREF="libm.html#cp_J" style="text-decoration:none"><b>J</b></A>
2378 &nbsp;
2379<A HREF="libm.html#cp_L" style="text-decoration:none"><b>L</b></A>
2380 &nbsp;
2381<A HREF="libm.html#cp_M" style="text-decoration:none"><b>M</b></A>
2382 &nbsp;
2383<A HREF="libm.html#cp_N" style="text-decoration:none"><b>N</b></A>
2384 &nbsp;
2385<A HREF="libm.html#cp_O" style="text-decoration:none"><b>O</b></A>
2386 &nbsp;
2387<A HREF="libm.html#cp_P" style="text-decoration:none"><b>P</b></A>
2388 &nbsp;
2389<A HREF="libm.html#cp_R" style="text-decoration:none"><b>R</b></A>
2390 &nbsp;
2391<A HREF="libm.html#cp_S" style="text-decoration:none"><b>S</b></A>
2392 &nbsp;
2393<A HREF="libm.html#cp_T" style="text-decoration:none"><b>T</b></A>
2394 &nbsp;
2395<A HREF="libm.html#cp_Y" style="text-decoration:none"><b>Y</b></A>
2396 &nbsp;
2397</td></tr></table><br><P>
2398
2399<HR SIZE="6">
2400<A NAME="SEC_Contents"></A>
2401<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
2402<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD>
2403<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD>
2404<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
2405<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
2406</TR></TABLE>
2407<H1>Table of Contents</H1>
2408<UL>
2409<A NAME="TOC1" HREF="libm.html#SEC1">1. Mathematical Functions (<TT>`math.h'</TT>)</A>
2410<BR>
2411<UL>
2412<A NAME="TOC2" HREF="libm.html#SEC2">1.1 Version of library</A>
2413<BR>
2414<A NAME="TOC3" HREF="libm.html#SEC3">1.2 <CODE>acos</CODE>, <CODE>acosf</CODE>---arc cosine</A>
2415<BR>
2416<A NAME="TOC4" HREF="libm.html#SEC4">1.3 <CODE>acosh</CODE>, <CODE>acoshf</CODE>---inverse hyperbolic cosine</A>
2417<BR>
2418<A NAME="TOC5" HREF="libm.html#SEC5">1.4 <CODE>asin</CODE>, <CODE>asinf</CODE>---arc sine</A>
2419<BR>
2420<A NAME="TOC6" HREF="libm.html#SEC6">1.5 <CODE>asinh</CODE>, <CODE>asinhf</CODE>---inverse hyperbolic sine</A>
2421<BR>
2422<A NAME="TOC7" HREF="libm.html#SEC7">1.6 <CODE>atan</CODE>, <CODE>atanf</CODE>---arc tangent</A>
2423<BR>
2424<A NAME="TOC8" HREF="libm.html#SEC8">1.7 <CODE>atan2</CODE>, <CODE>atan2f</CODE>---arc tangent of y/x</A>
2425<BR>
2426<A NAME="TOC9" HREF="libm.html#SEC9">1.8 <CODE>atanh</CODE>, <CODE>atanhf</CODE>---inverse hyperbolic tangent</A>
2427<BR>
2428<A NAME="TOC10" HREF="libm.html#SEC10">1.9 <CODE>jN</CODE>,<CODE>jNf</CODE>,<CODE>yN</CODE>,<CODE>yNf</CODE>---Bessel functions</A>
2429<BR>
2430<A NAME="TOC11" HREF="libm.html#SEC11">1.10 <CODE>cosh</CODE>, <CODE>coshf</CODE>---hyperbolic cosine</A>
2431<BR>
2432<A NAME="TOC12" HREF="libm.html#SEC12">1.11 <CODE>erf</CODE>, <CODE>erff</CODE>, <CODE>erfc</CODE>, <CODE>erfcf</CODE>---error function</A>
2433<BR>
2434<A NAME="TOC13" HREF="libm.html#SEC13">1.12 <CODE>exp</CODE>, <CODE>expf</CODE>---exponential</A>
2435<BR>
2436<A NAME="TOC14" HREF="libm.html#SEC14">1.13 <CODE>fabs</CODE>, <CODE>fabsf</CODE>---absolute value (magnitude)</A>
2437<BR>
2438<A NAME="TOC15" HREF="libm.html#SEC15">1.14 <CODE>floor</CODE>, <CODE>floorf</CODE>, <CODE>ceil</CODE>, <CODE>ceilf</CODE>---floor and ceiling</A>
2439<BR>
2440<A NAME="TOC16" HREF="libm.html#SEC16">1.15 <CODE>fmod</CODE>, <CODE>fmodf</CODE>---floating-point remainder (modulo)</A>
2441<BR>
2442<A NAME="TOC17" HREF="libm.html#SEC17">1.16 <CODE>frexp</CODE>, <CODE>frexpf</CODE>---split floating-point number</A>
2443<BR>
2444<A NAME="TOC18" HREF="libm.html#SEC18">1.17 <CODE>gamma</CODE>, <CODE>gammaf</CODE>, <CODE>lgamma</CODE>, <CODE>lgammaf</CODE>, <CODE>gamma_r</CODE>,</A>
2445<BR>
2446<A NAME="TOC19" HREF="libm.html#SEC19">1.18 <CODE>hypot</CODE>, <CODE>hypotf</CODE>---distance from origin</A>
2447<BR>
2448<A NAME="TOC20" HREF="libm.html#SEC20">1.19 <CODE>isnan</CODE>,<CODE>isnanf</CODE>,<CODE>isinf</CODE>,<CODE>isinff</CODE>,<CODE>finite</CODE>,<CODE>finitef</CODE>---test for exceptional numbers</A>
2449<BR>
2450<A NAME="TOC21" HREF="libm.html#SEC21">1.20 <CODE>ldexp</CODE>, <CODE>ldexpf</CODE>---load exponent</A>
2451<BR>
2452<A NAME="TOC22" HREF="libm.html#SEC22">1.21 <CODE>log</CODE>, <CODE>logf</CODE>---natural logarithms</A>
2453<BR>
2454<A NAME="TOC23" HREF="libm.html#SEC23">1.22 <CODE>log10</CODE>, <CODE>log10f</CODE>---base 10 logarithms</A>
2455<BR>
2456<A NAME="TOC24" HREF="libm.html#SEC24">1.23 <CODE>pow</CODE>, <CODE>powf</CODE>---x to the power y</A>
2457<BR>
2458<A NAME="TOC25" HREF="libm.html#SEC25">1.24 <CODE>remainder</CODE>, <CODE>remainderf</CODE>---round and remainder</A>
2459<BR>
2460<A NAME="TOC26" HREF="libm.html#SEC26">1.25 <CODE>sqrt</CODE>, <CODE>sqrtf</CODE>---positive square root</A>
2461<BR>
2462<A NAME="TOC27" HREF="libm.html#SEC27">1.26 <CODE>sin</CODE>, <CODE>sinf</CODE>, <CODE>cos</CODE>, <CODE>cosf</CODE>---sine or cosine</A>
2463<BR>
2464<A NAME="TOC28" HREF="libm.html#SEC28">1.27 <CODE>sinh</CODE>, <CODE>sinhf</CODE>---hyperbolic sine</A>
2465<BR>
2466<A NAME="TOC29" HREF="libm.html#SEC29">1.28 <CODE>tan</CODE>, <CODE>tanf</CODE>---tangent</A>
2467<BR>
2468<A NAME="TOC30" HREF="libm.html#SEC30">1.29 <CODE>tanh</CODE>, <CODE>tanhf</CODE>---hyperbolic tangent</A>
2469<BR>
2470<A NAME="TOC31" HREF="libm.html#SEC31">1.30 <CODE>cbrt</CODE>, <CODE>cbrtf</CODE>---cube root</A>
2471<BR>
2472<A NAME="TOC32" HREF="libm.html#SEC32">1.31 <CODE>copysign</CODE>, <CODE>copysignf</CODE>---sign of <VAR>y</VAR>, magnitude of <VAR>x</VAR></A>
2473<BR>
2474<A NAME="TOC33" HREF="libm.html#SEC33">1.32 <CODE>expm1</CODE>, <CODE>expm1f</CODE>---exponential minus 1</A>
2475<BR>
2476<A NAME="TOC34" HREF="libm.html#SEC34">1.33 <CODE>ilogb</CODE>, <CODE>ilogbf</CODE>---get exponent of floating-point number</A>
2477<BR>
2478<A NAME="TOC35" HREF="libm.html#SEC35">1.34 <CODE>infinity</CODE>, <CODE>infinityf</CODE>---representation of infinity</A>
2479<BR>
2480<A NAME="TOC36" HREF="libm.html#SEC36">1.35 <CODE>log1p</CODE>, <CODE>log1pf</CODE>---log of <CODE>1 + <VAR>x</VAR></CODE></A>
2481<BR>
2482<A NAME="TOC37" HREF="libm.html#SEC37">1.36 <CODE>matherr</CODE>---modifiable math error handler</A>
2483<BR>
2484<A NAME="TOC38" HREF="libm.html#SEC38">1.37 <CODE>modf</CODE>, <CODE>modff</CODE>---split fractional and integer parts</A>
2485<BR>
2486<A NAME="TOC39" HREF="libm.html#SEC39">1.38 <CODE>nan</CODE>, <CODE>nanf</CODE>---representation of "Not a Number"</A>
2487<BR>
2488<A NAME="TOC40" HREF="libm.html#SEC40">1.39 <CODE>nextafter</CODE>, <CODE>nextafterf</CODE>---get next number</A>
2489<BR>
2490<A NAME="TOC41" HREF="libm.html#SEC41">1.40 <CODE>scalbn</CODE>, <CODE>scalbnf</CODE>---scale by power of two</A>
2491<BR>
2492</UL>
2493<A NAME="TOC42" HREF="libm.html#SEC42">2. Reentrancy Properties of <CODE>libm</CODE></A>
2494<BR>
2495<A NAME="TOC43" HREF="libm.html#SEC43">Index</A>
2496<BR>
2497</UL>
2498<HR SIZE=1>
2499<A NAME="SEC_OVERVIEW"></A>
2500<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
2501<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD>
2502<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD>
2503<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
2504<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
2505</TR></TABLE>
2506<H1>Short Table of Contents</H1>
2507<BLOCKQUOTE>
2508<A NAME="TOC1" HREF="libm.html#SEC1">1. Mathematical Functions (<TT>`math.h'</TT>)</A>
2509<BR>
2510<A NAME="TOC42" HREF="libm.html#SEC42">2. Reentrancy Properties of <CODE>libm</CODE></A>
2511<BR>
2512<A NAME="TOC43" HREF="libm.html#SEC43">Index</A>
2513<BR>
2514
2515</BLOCKQUOTE>
2516<HR SIZE=1>
2517<A NAME="SEC_About"></A>
2518<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
2519<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Top">Top</A>]</TD>
2520<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_Contents">Contents</A>]</TD>
2521<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
2522<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
2523</TR></TABLE>
2524<H1>About this document</H1>
2525This document was generated by <I>Jeff Johnston</I> on <I>January, 30 2004</I>
2526using <A HREF="http://www.mathematik.uni-kl.de/~obachman/Texi2html
2527"><I>texi2html</I></A>
2528<P></P>
2529The buttons in the navigation panels have the following meaning:
2530<P></P>
2531<table border = "1">
2532<TR>
2533<TH> Button </TH>
2534<TH> Name </TH>
2535<TH> Go to </TH>
2536<TH> From 1.2.3 go to</TH>
2537</TR>
2538<TR>
2539<TD ALIGN="CENTER">
2540 [ &lt; ] </TD>
2541<TD ALIGN="CENTER">
2542Back
2543</TD>
2544<TD>
2545previous section in reading order
2546</TD>
2547<TD>
25481.2.2
2549</TD>
2550</TR>
2551<TR>
2552<TD ALIGN="CENTER">
2553 [ &gt; ] </TD>
2554<TD ALIGN="CENTER">
2555Forward
2556</TD>
2557<TD>
2558next section in reading order
2559</TD>
2560<TD>
25611.2.4
2562</TD>
2563</TR>
2564<TR>
2565<TD ALIGN="CENTER">
2566 [ &lt;&lt; ] </TD>
2567<TD ALIGN="CENTER">
2568FastBack
2569</TD>
2570<TD>
2571previous or up-and-previous section
2572</TD>
2573<TD>
25741.1
2575</TD>
2576</TR>
2577<TR>
2578<TD ALIGN="CENTER">
2579 [ Up ] </TD>
2580<TD ALIGN="CENTER">
2581Up
2582</TD>
2583<TD>
2584up section
2585</TD>
2586<TD>
25871.2
2588</TD>
2589</TR>
2590<TR>
2591<TD ALIGN="CENTER">
2592 [ &gt;&gt; ] </TD>
2593<TD ALIGN="CENTER">
2594FastForward
2595</TD>
2596<TD>
2597next or up-and-next section
2598</TD>
2599<TD>
26001.3
2601</TD>
2602</TR>
2603<TR>
2604<TD ALIGN="CENTER">
2605 [Top] </TD>
2606<TD ALIGN="CENTER">
2607Top
2608</TD>
2609<TD>
2610cover (top) of document
2611</TD>
2612<TD>
2613 &nbsp;
2614</TD>
2615</TR>
2616<TR>
2617<TD ALIGN="CENTER">
2618 [Contents] </TD>
2619<TD ALIGN="CENTER">
2620Contents
2621</TD>
2622<TD>
2623table of contents
2624</TD>
2625<TD>
2626 &nbsp;
2627</TD>
2628</TR>
2629<TR>
2630<TD ALIGN="CENTER">
2631 [Index] </TD>
2632<TD ALIGN="CENTER">
2633Index
2634</TD>
2635<TD>
2636concept index
2637</TD>
2638<TD>
2639 &nbsp;
2640</TD>
2641</TR>
2642<TR>
2643<TD ALIGN="CENTER">
2644 [ ? ] </TD>
2645<TD ALIGN="CENTER">
2646About
2647</TD>
2648<TD>
2649this page
2650</TD>
2651<TD>
2652 &nbsp;
2653</TD>
2654</TR>
2655</TABLE>
2656<P></P>
2657where the <STRONG> Example </STRONG> assumes that the current position
2658is at <STRONG> Subsubsection One-Two-Three </STRONG> of a document of
2659the following structure:
2660<UL>
2661<LI> 1. Section One </LI>
2662<UL>
2663<LI>1.1 Subsection One-One</LI>
2664<UL>
2665<LI> ... </LI>
2666</UL>
2667<LI>1.2 Subsection One-Two</LI>
2668<UL>
2669<LI>1.2.1 Subsubsection One-Two-One
2670</LI><LI>1.2.2 Subsubsection One-Two-Two
2671</LI><LI>1.2.3 Subsubsection One-Two-Three &nbsp; &nbsp; <STRONG>
2672&lt;== Current Position </STRONG>
2673</LI><LI>1.2.4 Subsubsection One-Two-Four
2674</LI></UL>
2675<LI>1.3 Subsection One-Three</LI>
2676<UL>
2677<LI> ... </LI>
2678</UL>
2679<LI>1.4 Subsection One-Four</LI>
2680</UL>
2681</UL>
2682
2683<HR SIZE=1>
2684<BR>
2685<FONT SIZE="-1">
2686This document was generated
2687by <I>Jeff Johnston</I> on <I>January, 30 2004</I>
2688using <A HREF="http://www.mathematik.uni-kl.de/~obachman/Texi2html
2689"><I>texi2html</I></A>
2690
2691</BODY>
2692</HTML>
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