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authorJeff Johnston <jjohnstn@redhat.com>2003-05-02 19:28:40 +0000
committerJeff Johnston <jjohnstn@redhat.com>2003-05-02 19:28:40 +0000
commit3da4f434ddf94259eca6d5f3a7a2a07026a465fd (patch)
treeaa944d0d84d27569ff0ec56bac8120072d8ce392 /libm.html
parent2003-02-03 Jeff Johnston <jjohnstn@redhat.com> (diff)
2003-05-02 Jeff Johnston <jjohnstn@redhat.com>
* COPYING.NEWLIB: New file from up to date sources. * info.html: Updated to use COPYING.NEWLIB. * README: Updated to 1.11.0. * libc.html: Ditto. * libc_toc.html: Ditto. * libm.html: Ditto. * libm_toc.html: Ditto.
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1<HTML> 1<HTML>
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3<!-- Created on May, 2 2003 by texi2html 1.64 -->
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5Written by: Lionel Cons <Lionel.Cons@cern.ch> (original author)
6 Karl Berry <karl@freefriends.org>
7 Olaf Bachmann <obachman@mathematik.uni-kl.de>
8 and many others.
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3<!-- Created by texi2html 1.56k from /home/fitzsim/sources/src-newlib-devel/src/newlib/libm/libm.texinfo on 21 July 2002 --> 14<TITLE>The Red Hat newlib C Math Library: </TITLE>
4 15
5<TITLE>The Red Hat newlib C Math Library</TITLE> 16<META NAME="description" CONTENT="The Red Hat newlib C Math Library: ">
6</HEAD> 17<META NAME="keywords" CONTENT="The Red Hat newlib C Math Library: ">
7<BODY> 18<META NAME="resource-type" CONTENT="document">
8<H1>The Red Hat newlib C Math Library</H1> 19<META NAME="distribution" CONTENT="global">
9<H2><CODE>libm</CODE> 1.10.0</H2> 20<META NAME="Generator" CONTENT="texi2html 1.64">
10<H2>July 2002</H2>
11<ADDRESS>{Steve Chamberlain}</ADDRESS>
12<ADDRESS>{Roland Pesch}</ADDRESS>
13<ADDRESS>{Red Hat Support}</ADDRESS>
14<ADDRESS>{Jeff Johnston}</ADDRESS>
15<P>
16<P><HR><P>
17
18<P>
19Copyright (C) 1992, 1993, 1994-2002 Red Hat, Inc.
20
21
22<P>
23<TT>`libm'</TT> includes software developed at SunPro, a Sun Microsystems,
24Inc. business. Permission to use, copy, modify, and distribute this
25software is freely granted, provided that this notice is preserved.
26
27
28<P>
29Permission is granted to make and distribute verbatim copies of
30this manual provided the copyright notice and this permission notice
31are preserved on all copies.
32
33
34<P>
35Permission is granted to copy and distribute modified versions of this
36manual under the conditions for verbatim copying, subject to the terms
37of the GNU General Public License, which includes the provision that the
38entire resulting derived work is distributed under the terms of a
39permission notice identical to this one.
40 21
22</HEAD>
41 23
24<BODY LANG="" BGCOLOR="#FFFFFF" TEXT="#000000" LINK="#0000FF" VLINK="#800080" ALINK="#FF0000">
25<h1>The Red Hat newlib C Math Library: </h1>
26<h2>Full Configuration</h2>
27<h2><code>libm</code> 1.11.0</h2>
28<h2>May, 2 2003 </h2>
29<address>{Steve Chamberlain}</address>
30<address>{Roland Pesch}</address>
31<address>{Red Hat Support}</address>
32<address>{Jeff Johnston}</address>
33<p>
34<p><hr><p>
35<A NAME="SEC1"></A>
36<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
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43<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
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45<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
46</TR></TABLE>
47<P>
48
49<BLOCKQUOTE><TABLE BORDER=0 CELLSPACING=0>
50<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>
51<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>
52<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>
53</TABLE></BLOCKQUOTE>
54<P>
55
56<A NAME="Math"></A>
57<H1> 1. Mathematical Functions (<TT>`math.h'</TT>) </H1>
58<!--docid::SEC1::-->
42<P> 59<P>
43Permission is granted to copy and distribute translations of this manual
44into another language, under the above conditions for modified versions.
45
46
47
48 60
49<H1><A NAME="SEC1" HREF="libm_toc.html#TOC1">Mathematical Functions (<TT>`math.h'</TT>)</A></H1>
50
51<P>
52This chapter groups a wide variety of mathematical functions. The 61This chapter groups a wide variety of mathematical functions. The
53corresponding definitions and declarations are in <TT>`math.h'</TT>. 62corresponding definitions and declarations are in <TT>`math.h'</TT>.
54Two definitions from <TT>`math.h'</TT> are of particular interest. 63Two definitions from <TT>`math.h'</TT> are of particular interest.
55 64</P><P>
56
57 65
58<OL> 66<OL>
59<LI> 67<LI>
60
61The representation of infinity as a <CODE>double</CODE> is defined as 68The representation of infinity as a <CODE>double</CODE> is defined as
62<CODE>HUGE_VAL</CODE>; this number is returned on overflow by many functions. 69<CODE>HUGE_VAL</CODE>; this number is returned on overflow by many functions.
70<P>
63 71
64<LI> 72<LI>
65
66The structure <CODE>exception</CODE> is used when you write customized error 73The structure <CODE>exception</CODE> is used when you write customized error
67handlers for the mathematical functions. You can customize error 74handlers for the mathematical functions. You can customize error
68handling for most of these functions by defining your own version of 75handling for most of these functions by defining your own version of
69<CODE>matherr</CODE>; see the section on <CODE>matherr</CODE> for details. 76<CODE>matherr</CODE>; see the section on <CODE>matherr</CODE> for details.
70</OL> 77</OL>
71
72<P> 78<P>
79
73<A NAME="IDX1"></A> 80<A NAME="IDX1"></A>
74<A NAME="IDX2"></A> 81<A NAME="IDX2"></A>
75<A NAME="IDX3"></A> 82<A NAME="IDX3"></A>
@@ -81,21 +88,77 @@ of OS subroutines as <CODE>fputs</CODE>: <CODE>close</CODE>, <CODE>fstat</CODE>,
81See section `System Calls' in <CITE>The Cygnus C Support Library</CITE>, 88See section `System Calls' in <CITE>The Cygnus C Support Library</CITE>,
82for a discussion and for sample minimal implementations of these support 89for a discussion and for sample minimal implementations of these support
83subroutines. 90subroutines.
91</P><P>
84 92
85
86<P>
87Alternative declarations of the mathematical functions, which exploit 93Alternative declarations of the mathematical functions, which exploit
88specific machine capabilities to operate faster--but generally have 94specific machine capabilities to operate faster--but generally have
89less error checking and may reflect additional limitations on some 95less error checking and may reflect additional limitations on some
90machines--are available when you include <TT>`fastmath.h'</TT> instead of 96machines--are available when you include <TT>`fastmath.h'</TT> instead of
91<TT>`math.h'</TT>. 97<TT>`math.h'</TT>.
92 98</P><P>
93 99
94 100<BLOCKQUOTE><TABLE BORDER=0 CELLSPACING=0>
95 101<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>
96<H2><A NAME="SEC2" HREF="libm_toc.html#TOC2">Version of library</A></H2> 102<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>
97 103<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>
104<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>
105<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>
106<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>
107<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>
108<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>
109<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>
110<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>
111<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>
112<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>
113<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>
114<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>
115<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>
116<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>
117<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>
118<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>
119<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>
120<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>
121<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>
122<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>
123<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>
124<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>
125<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>
126<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>
127<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>
128<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>
129<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>
130<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>
131<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC39">1.38 <CODE>nan</CODE>, <CODE>nanf</CODE>---representation of infinity</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Floating Not a Number</TD></TR>
132<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>
133<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>
134<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>
135<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="libm.html#SEC41">1.40 <CODE>scalbn</CODE>, <CODE>scalbnf</CODE>---scale by integer</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">scalbn</TD></TR>
136<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>
137<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>
138<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>
139<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>
140<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>
141</TABLE></BLOCKQUOTE>
142<P>
143
144<A NAME="version"></A>
145<HR SIZE="6">
146<A NAME="SEC2"></A>
147<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
148<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> &lt; </A>]</TD>
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150<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
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152<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
153<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#SEC1">Top</A>]</TD>
154<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
155<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
156<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
157</TR></TABLE>
158<H2> 1.1 Version of library </H2>
159<!--docid::SEC2::-->
98<P> 160<P>
161
99There are four different versions of the math library routines: IEEE, 162There are four different versions of the math library routines: IEEE,
100POSIX, X/Open, or SVID. The version may be selected at runtime by 163POSIX, X/Open, or SVID. The version may be selected at runtime by
101setting the global variable <CODE>_LIB_VERSION</CODE>, defined in 164setting the global variable <CODE>_LIB_VERSION</CODE>, defined in
@@ -103,412 +166,395 @@ setting the global variable <CODE>_LIB_VERSION</CODE>, defined in
103in <TT>`math.h'</TT>: <CODE>_IEEE_</CODE>, <CODE>_POSIX_</CODE>, <CODE>_XOPEN_</CODE>, or 166in <TT>`math.h'</TT>: <CODE>_IEEE_</CODE>, <CODE>_POSIX_</CODE>, <CODE>_XOPEN_</CODE>, or
104<CODE>_SVID_</CODE>. The <CODE>_LIB_VERSION</CODE> variable is not specific to any 167<CODE>_SVID_</CODE>. The <CODE>_LIB_VERSION</CODE> variable is not specific to any
105thread, and changing it will affect all threads. 168thread, and changing it will affect all threads.
169</P><P>
106 170
107
108<P>
109The versions of the library differ only in how errors are handled. 171The versions of the library differ only in how errors are handled.
172</P><P>
110 173
111
112<P>
113In IEEE mode, the <CODE>matherr</CODE> function is never called, no warning 174In IEEE mode, the <CODE>matherr</CODE> function is never called, no warning
114messages are printed, and <CODE>errno</CODE> is never set. 175messages are printed, and <CODE>errno</CODE> is never set.
176</P><P>
115 177
116
117<P>
118In POSIX mode, <CODE>errno</CODE> is set correctly, but the <CODE>matherr</CODE> 178In POSIX mode, <CODE>errno</CODE> is set correctly, but the <CODE>matherr</CODE>
119function is never called and no warning messages are printed. 179function is never called and no warning messages are printed.
180</P><P>
120 181
121
122<P>
123In X/Open mode, <CODE>errno</CODE> is set correctly, and <CODE>matherr</CODE> is 182In X/Open mode, <CODE>errno</CODE> is set correctly, and <CODE>matherr</CODE> is
124called, but warning message are not printed. 183called, but warning message are not printed.
184</P><P>
125 185
126
127<P>
128In SVID mode, functions which overflow return 3.40282346638528860e+38, 186In SVID mode, functions which overflow return 3.40282346638528860e+38,
129the maximum single precision floating point value, rather than infinity. 187the maximum single precision floating point value, rather than infinity.
130Also, <CODE>errno</CODE> is set correctly, <CODE>matherr</CODE> is called, and, if 188Also, <CODE>errno</CODE> is set correctly, <CODE>matherr</CODE> is called, and, if
131<CODE>matherr</CODE> returns 0, warning messages are printed for some errors. 189<CODE>matherr</CODE> returns 0, warning messages are printed for some errors.
132For example, by default <SAMP>`log(-1.0)'</SAMP> writes this message on standard 190For example, by default <SAMP>`log(-1.0)'</SAMP> writes this message on standard
133error output: 191error output:
192</P><P>
134 193
194<TABLE><tr><td>&nbsp;</td><td class=example><pre>log: DOMAIN error
195</pre></td></tr></table></P><P>
135 196
136
137<PRE>
138log: DOMAIN error
139</PRE>
140
141<P>
142The library is set to X/Open mode by default. 197The library is set to X/Open mode by default.
143 198</P><P>
144 199
145 200<A NAME="acos"></A>
146 201<HR SIZE="6">
147<H2><A NAME="SEC3" HREF="libm_toc.html#TOC3"><CODE>acos</CODE>, <CODE>acosf</CODE>---arc cosine</A></H2> 202<A NAME="SEC3"></A>
148<P> 203<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
149<A NAME="IDX5"></A> 204<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC2"> &lt; </A>]</TD>
150<A NAME="IDX6"></A> 205<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC4"> &gt; </A>]</TD>
206<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
207<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
208<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
209<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#SEC1">Top</A>]</TD>
210<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
211<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
212<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
213</TR></TABLE>
214<H2> 1.2 <CODE>acos</CODE>, <CODE>acosf</CODE>---arc cosine </H2>
215<!--docid::SEC3::-->
151<STRONG>Synopsis</STRONG> 216<STRONG>Synopsis</STRONG>
152 217<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
153<PRE>
154#include &#60;math.h&#62;
155double acos(double <VAR>x</VAR>); 218double acos(double <VAR>x</VAR>);
156float acosf(float <VAR>x</VAR>); 219float acosf(float <VAR>x</VAR>);
157 220
158</PRE> 221</pre></td></tr></table><STRONG>Description</STRONG><BR>
159
160<P> 222<P>
161<STRONG>Description</STRONG><BR>
162
163 223
164<P>
165<CODE>acos</CODE> computes the inverse cosine (arc cosine) of the input value. 224<CODE>acos</CODE> computes the inverse cosine (arc cosine) of the input value.
166Arguments to <CODE>acos</CODE> must be in the range -1 to 1. 225Arguments to <CODE>acos</CODE> must be in the range -1 to 1.
226</P><P>
167 227
168
169<P>
170<CODE>acosf</CODE> is identical to <CODE>acos</CODE>, except that it performs 228<CODE>acosf</CODE> is identical to <CODE>acos</CODE>, except that it performs
171its calculations on <CODE>floats</CODE>. 229its calculations on <CODE>floats</CODE>.
230</P><P>
172 231
173
174<P>
175<BR> 232<BR>
176<STRONG>Returns</STRONG><BR> 233<STRONG>Returns</STRONG><BR>
234</P><P>
177 235
178
179<P>
180If <VAR>x</VAR> is not between -1 and 1, the returned value is NaN 236If <VAR>x</VAR> is not between -1 and 1, the returned value is NaN
181(not a number) the global variable <CODE>errno</CODE> is set to <CODE>EDOM</CODE>, and a 237(not a number) the global variable <CODE>errno</CODE> is set to <CODE>EDOM</CODE>, and a
182<CODE>DOMAIN error</CODE> message is sent as standard error output. 238<CODE>DOMAIN error</CODE> message is sent as standard error output.
239</P><P>
183 240
184
185<P>
186You can modify error handling for these functions using <CODE>matherr</CODE>. 241You can modify error handling for these functions using <CODE>matherr</CODE>.
187 242</P><P>
188 243
189<P> 244<BR>
190<BR> 245</P><P>
191 246
192 247<A NAME="acosh"></A>
193 248<HR SIZE="6">
194 249<A NAME="SEC4"></A>
195<H2><A NAME="SEC4" HREF="libm_toc.html#TOC4"><CODE>acosh</CODE>, <CODE>acoshf</CODE>---inverse hyperbolic cosine</A></H2> 250<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
196<P> 251<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC3"> &lt; </A>]</TD>
197<A NAME="IDX7"></A> 252<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC5"> &gt; </A>]</TD>
198<A NAME="IDX8"></A> 253<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
254<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
255<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
256<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#SEC1">Top</A>]</TD>
257<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
258<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
259<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
260</TR></TABLE>
261<H2> 1.3 <CODE>acosh</CODE>, <CODE>acoshf</CODE>---inverse hyperbolic cosine </H2>
262<!--docid::SEC4::-->
199<STRONG>Synopsis</STRONG> 263<STRONG>Synopsis</STRONG>
200 264<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
201<PRE>
202#include &#60;math.h&#62;
203double acosh(double <VAR>x</VAR>); 265double acosh(double <VAR>x</VAR>);
204float acoshf(float <VAR>x</VAR>); 266float acoshf(float <VAR>x</VAR>);
205 267
206</PRE> 268</pre></td></tr></table><STRONG>Description</STRONG><BR>
207
208<P>
209<STRONG>Description</STRONG><BR>
210<CODE>acosh</CODE> calculates the inverse hyperbolic cosine of <VAR>x</VAR>. 269<CODE>acosh</CODE> calculates the inverse hyperbolic cosine of <VAR>x</VAR>.
211<CODE>acosh</CODE> is defined as 270<CODE>acosh</CODE> is defined as
212
213
214<P> 271<P>
215<VAR>x</VAR> must be a number greater than or equal to 1.
216 272
273<VAR>x</VAR> must be a number greater than or equal to 1.
274</P><P>
217 275
218<P>
219<CODE>acoshf</CODE> is identical, other than taking and returning floats. 276<CODE>acoshf</CODE> is identical, other than taking and returning floats.
277</P><P>
220 278
221
222<P>
223<BR> 279<BR>
224<STRONG>Returns</STRONG><BR> 280<STRONG>Returns</STRONG><BR>
225<CODE>acosh</CODE> and <CODE>acoshf</CODE> return the calculated value. If <VAR>x</VAR> 281<CODE>acosh</CODE> and <CODE>acoshf</CODE> return the calculated value. If <VAR>x</VAR>
226less than 1, the return value is NaN and <CODE>errno</CODE> is set to <CODE>EDOM</CODE>. 282less than 1, the return value is NaN and <CODE>errno</CODE> is set to <CODE>EDOM</CODE>.
283</P><P>
227 284
228
229<P>
230You can change the error-handling behavior with the non-ANSI 285You can change the error-handling behavior with the non-ANSI
231<CODE>matherr</CODE> function. 286<CODE>matherr</CODE> function.
287</P><P>
232 288
233
234<P>
235<BR> 289<BR>
236<STRONG>Portability</STRONG><BR> 290<STRONG>Portability</STRONG><BR>
237Neither <CODE>acosh</CODE> nor <CODE>acoshf</CODE> are ANSI C. They are not recommended 291Neither <CODE>acosh</CODE> nor <CODE>acoshf</CODE> are ANSI C. They are not recommended
238for portable programs. 292for portable programs.
239 293</P><P>
240 294
241<P> 295<BR>
242<BR> 296</P><P>
243 297
244 298<A NAME="asin"></A>
245 299<HR SIZE="6">
246 300<A NAME="SEC5"></A>
247<H2><A NAME="SEC5" HREF="libm_toc.html#TOC5"><CODE>asin</CODE>, <CODE>asinf</CODE>---arc sine</A></H2> 301<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
248<P> 302<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC4"> &lt; </A>]</TD>
249<A NAME="IDX9"></A> 303<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC6"> &gt; </A>]</TD>
250<A NAME="IDX10"></A> 304<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
305<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
306<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
307<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#SEC1">Top</A>]</TD>
308<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
309<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
310<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
311</TR></TABLE>
312<H2> 1.4 <CODE>asin</CODE>, <CODE>asinf</CODE>---arc sine </H2>
313<!--docid::SEC5::-->
251<STRONG>Synopsis</STRONG> 314<STRONG>Synopsis</STRONG>
252 315<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
253<PRE>
254#include &#60;math.h&#62;
255double asin(double <VAR>x</VAR>); 316double asin(double <VAR>x</VAR>);
256float asinf(float <VAR>x</VAR>); 317float asinf(float <VAR>x</VAR>);
257 318
258</PRE> 319</pre></td></tr></table><STRONG>Description</STRONG><BR>
259
260<P> 320<P>
261<STRONG>Description</STRONG><BR>
262
263 321
264<P>
265<CODE>asin</CODE> computes the inverse sine (arc sine) of the argument <VAR>x</VAR>. 322<CODE>asin</CODE> computes the inverse sine (arc sine) of the argument <VAR>x</VAR>.
266Arguments to <CODE>asin</CODE> must be in the range -1 to 1. 323Arguments to <CODE>asin</CODE> must be in the range -1 to 1.
324</P><P>
267 325
268
269<P>
270<CODE>asinf</CODE> is identical to <CODE>asin</CODE>, other than taking and 326<CODE>asinf</CODE> is identical to <CODE>asin</CODE>, other than taking and
271returning floats. 327returning floats.
328</P><P>
272 329
273
274<P>
275You can modify error handling for these routines using <CODE>matherr</CODE>. 330You can modify error handling for these routines using <CODE>matherr</CODE>.
331</P><P>
276 332
277
278<P>
279<BR> 333<BR>
280<STRONG>Returns</STRONG><BR> 334<STRONG>Returns</STRONG><BR>
335</P><P>
281 336
282
283<P>
284If <VAR>x</VAR> is not in the range -1 to 1, <CODE>asin</CODE> and <CODE>asinf</CODE> 337If <VAR>x</VAR> is not in the range -1 to 1, <CODE>asin</CODE> and <CODE>asinf</CODE>
285return NaN (not a number), set the global variable <CODE>errno</CODE> to 338return NaN (not a number), set the global variable <CODE>errno</CODE> to
286<CODE>EDOM</CODE>, and issue a <CODE>DOMAIN error</CODE> message. 339<CODE>EDOM</CODE>, and issue a <CODE>DOMAIN error</CODE> message.
340</P><P>
287 341
288
289<P>
290You can change this error treatment using <CODE>matherr</CODE>. 342You can change this error treatment using <CODE>matherr</CODE>.
291 343</P><P>
292 344
293<P> 345<BR>
294<BR> 346</P><P>
295 347
296 348<A NAME="asinh"></A>
297 349<HR SIZE="6">
298 350<A NAME="SEC6"></A>
299<H2><A NAME="SEC6" HREF="libm_toc.html#TOC6"><CODE>asinh</CODE>, <CODE>asinhf</CODE>---inverse hyperbolic sine</A></H2> 351<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
300<P> 352<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC5"> &lt; </A>]</TD>
301<A NAME="IDX11"></A> 353<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC7"> &gt; </A>]</TD>
302<A NAME="IDX12"></A> 354<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
355<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
356<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
357<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#SEC1">Top</A>]</TD>
358<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
359<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
360<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
361</TR></TABLE>
362<H2> 1.5 <CODE>asinh</CODE>, <CODE>asinhf</CODE>---inverse hyperbolic sine </H2>
363<!--docid::SEC6::-->
303<STRONG>Synopsis</STRONG> 364<STRONG>Synopsis</STRONG>
304 365<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
305<PRE>
306#include &#60;math.h&#62;
307double asinh(double <VAR>x</VAR>); 366double asinh(double <VAR>x</VAR>);
308float asinhf(float <VAR>x</VAR>); 367float asinhf(float <VAR>x</VAR>);
309 368
310</PRE> 369</pre></td></tr></table><STRONG>Description</STRONG><BR>
311
312<P>
313<STRONG>Description</STRONG><BR>
314<CODE>asinh</CODE> calculates the inverse hyperbolic sine of <VAR>x</VAR>. 370<CODE>asinh</CODE> calculates the inverse hyperbolic sine of <VAR>x</VAR>.
315<CODE>asinh</CODE> is defined as 371<CODE>asinh</CODE> is defined as
316
317
318<P> 372<P>
319<CODE>asinhf</CODE> is identical, other than taking and returning floats.
320 373
374<CODE>asinhf</CODE> is identical, other than taking and returning floats.
375</P><P>
321 376
322<P>
323<BR> 377<BR>
324<STRONG>Returns</STRONG><BR> 378<STRONG>Returns</STRONG><BR>
325<CODE>asinh</CODE> and <CODE>asinhf</CODE> return the calculated value. 379<CODE>asinh</CODE> and <CODE>asinhf</CODE> return the calculated value.
380</P><P>
326 381
327
328<P>
329<BR> 382<BR>
330<STRONG>Portability</STRONG><BR> 383<STRONG>Portability</STRONG><BR>
331Neither <CODE>asinh</CODE> nor <CODE>asinhf</CODE> are ANSI C. 384Neither <CODE>asinh</CODE> nor <CODE>asinhf</CODE> are ANSI C.
332 385</P><P>
333 386
334<P> 387<BR>
335<BR> 388</P><P>
336 389
337 390<A NAME="atan"></A>
338 391<HR SIZE="6">
339 392<A NAME="SEC7"></A>
340<H2><A NAME="SEC7" HREF="libm_toc.html#TOC7"><CODE>atan</CODE>, <CODE>atanf</CODE>---arc tangent</A></H2> 393<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
341<P> 394<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC6"> &lt; </A>]</TD>
342<A NAME="IDX13"></A> 395<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC8"> &gt; </A>]</TD>
343<A NAME="IDX14"></A> 396<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
397<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
398<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
399<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#SEC1">Top</A>]</TD>
400<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
401<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
402<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
403</TR></TABLE>
404<H2> 1.6 <CODE>atan</CODE>, <CODE>atanf</CODE>---arc tangent </H2>
405<!--docid::SEC7::-->
344<STRONG>Synopsis</STRONG> 406<STRONG>Synopsis</STRONG>
345 407<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
346<PRE>
347#include &#60;math.h&#62;
348double atan(double <VAR>x</VAR>); 408double atan(double <VAR>x</VAR>);
349float atanf(float <VAR>x</VAR>); 409float atanf(float <VAR>x</VAR>);
350 410
351</PRE> 411</pre></td></tr></table><STRONG>Description</STRONG><BR>
352
353<P> 412<P>
354<STRONG>Description</STRONG><BR>
355
356 413
357<P>
358<CODE>atan</CODE> computes the inverse tangent (arc tangent) of the input value. 414<CODE>atan</CODE> computes the inverse tangent (arc tangent) of the input value.
415</P><P>
359 416
360
361<P>
362<CODE>atanf</CODE> is identical to <CODE>atan</CODE>, save that it operates on <CODE>floats</CODE>. 417<CODE>atanf</CODE> is identical to <CODE>atan</CODE>, save that it operates on <CODE>floats</CODE>.
418</P><P>
363 419
364
365<P>
366<BR> 420<BR>
367<STRONG>Returns</STRONG><BR> 421<STRONG>Returns</STRONG><BR>
422</P><P>
368 423
369
370<P>
371<BR> 424<BR>
372<STRONG>Portability</STRONG><BR> 425<STRONG>Portability</STRONG><BR>
373<CODE>atan</CODE> is ANSI C. <CODE>atanf</CODE> is an extension. 426<CODE>atan</CODE> is ANSI C. <CODE>atanf</CODE> is an extension.
374 427</P><P>
375 428
376<P> 429<BR>
377<BR> 430</P><P>
378 431
379 432<A NAME="atan2"></A>
380 433<HR SIZE="6">
381 434<A NAME="SEC8"></A>
382<H2><A NAME="SEC8" HREF="libm_toc.html#TOC8"><CODE>atan2</CODE>, <CODE>atan2f</CODE>---arc tangent of y/x</A></H2> 435<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
383<P> 436<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC7"> &lt; </A>]</TD>
384<A NAME="IDX15"></A> 437<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC9"> &gt; </A>]</TD>
385<A NAME="IDX16"></A> 438<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
439<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
440<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
441<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#SEC1">Top</A>]</TD>
442<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
443<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
444<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
445</TR></TABLE>
446<H2> 1.7 <CODE>atan2</CODE>, <CODE>atan2f</CODE>---arc tangent of y/x </H2>
447<!--docid::SEC8::-->
386<STRONG>Synopsis</STRONG> 448<STRONG>Synopsis</STRONG>
387 449<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
388<PRE>
389#include &#60;math.h&#62;
390double atan2(double <VAR>y</VAR>,double <VAR>x</VAR>); 450double atan2(double <VAR>y</VAR>,double <VAR>x</VAR>);
391float atan2f(float <VAR>y</VAR>,float <VAR>x</VAR>); 451float atan2f(float <VAR>y</VAR>,float <VAR>x</VAR>);
392 452
393</PRE> 453</pre></td></tr></table><STRONG>Description</STRONG><BR>
394
395<P> 454<P>
396<STRONG>Description</STRONG><BR>
397
398 455
399<P>
400<CODE>atan2</CODE> computes the inverse tangent (arc tangent) of <VAR>y</VAR>/<VAR>x</VAR>. 456<CODE>atan2</CODE> computes the inverse tangent (arc tangent) of <VAR>y</VAR>/<VAR>x</VAR>.
401<CODE>atan2</CODE> produces the correct result even for angles near 457<CODE>atan2</CODE> produces the correct result even for angles near
402(that is, when <VAR>x</VAR> is near 0). 458(that is, when <VAR>x</VAR> is near 0).
459</P><P>
403 460
404
405<P>
406<CODE>atan2f</CODE> is identical to <CODE>atan2</CODE>, save that it takes and returns 461<CODE>atan2f</CODE> is identical to <CODE>atan2</CODE>, save that it takes and returns
407<CODE>float</CODE>. 462<CODE>float</CODE>.
463</P><P>
408 464
409
410<P>
411<BR> 465<BR>
412<STRONG>Returns</STRONG><BR> 466<STRONG>Returns</STRONG><BR>
413<CODE>atan2</CODE> and <CODE>atan2f</CODE> return a value in radians, in the range of 467<CODE>atan2</CODE> and <CODE>atan2f</CODE> return a value in radians, in the range of
468</P><P>
414 469
415
416<P>
417If both <VAR>x</VAR> and <VAR>y</VAR> are 0.0, <CODE>atan2</CODE> causes a <CODE>DOMAIN</CODE> error. 470If both <VAR>x</VAR> and <VAR>y</VAR> are 0.0, <CODE>atan2</CODE> causes a <CODE>DOMAIN</CODE> error.
471</P><P>
418 472
419
420<P>
421You can modify error handling for these functions using <CODE>matherr</CODE>. 473You can modify error handling for these functions using <CODE>matherr</CODE>.
474</P><P>
422 475
423
424<P>
425<BR> 476<BR>
426<STRONG>Portability</STRONG><BR> 477<STRONG>Portability</STRONG><BR>
427<CODE>atan2</CODE> is ANSI C. <CODE>atan2f</CODE> is an extension. 478<CODE>atan2</CODE> is ANSI C. <CODE>atan2f</CODE> is an extension.
428 479</P><P>
429 480
430<P> 481<BR>
431<BR> 482</P><P>
432 483
433 484<A NAME="atanh"></A>
434 485<HR SIZE="6">
435 486<A NAME="SEC9"></A>
436<H2><A NAME="SEC9" HREF="libm_toc.html#TOC9"><CODE>atanh</CODE>, <CODE>atanhf</CODE>---inverse hyperbolic tangent</A></H2> 487<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
437<P> 488<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC8"> &lt; </A>]</TD>
438<A NAME="IDX17"></A> 489<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC10"> &gt; </A>]</TD>
439<A NAME="IDX18"></A> 490<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
491<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
492<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
493<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#SEC1">Top</A>]</TD>
494<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
495<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
496<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
497</TR></TABLE>
498<H2> 1.8 <CODE>atanh</CODE>, <CODE>atanhf</CODE>---inverse hyperbolic tangent </H2>
499<!--docid::SEC9::-->
440<STRONG>Synopsis</STRONG> 500<STRONG>Synopsis</STRONG>
441 501<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
442<PRE>
443#include &#60;math.h&#62;
444double atanh(double <VAR>x</VAR>); 502double atanh(double <VAR>x</VAR>);
445float atanhf(float <VAR>x</VAR>); 503float atanhf(float <VAR>x</VAR>);
446 504
447</PRE> 505</pre></td></tr></table><STRONG>Description</STRONG><BR>
448
449<P>
450<STRONG>Description</STRONG><BR>
451<CODE>atanh</CODE> calculates the inverse hyperbolic tangent of <VAR>x</VAR>. 506<CODE>atanh</CODE> calculates the inverse hyperbolic tangent of <VAR>x</VAR>.
452
453
454<P> 507<P>
508
455<CODE>atanhf</CODE> is identical, other than taking and returning 509<CODE>atanhf</CODE> is identical, other than taking and returning
456<CODE>float</CODE> values. 510<CODE>float</CODE> values.
511</P><P>
457 512
458
459<P>
460<BR> 513<BR>
461<STRONG>Returns</STRONG><BR> 514<STRONG>Returns</STRONG><BR>
462<CODE>atanh</CODE> and <CODE>atanhf</CODE> return the calculated value. 515<CODE>atanh</CODE> and <CODE>atanhf</CODE> return the calculated value.
516</P><P>
463 517
464
465<P>
466If 518If
467is greater than 1, the global <CODE>errno</CODE> is set to <CODE>EDOM</CODE> and 519is greater than 1, the global <CODE>errno</CODE> is set to <CODE>EDOM</CODE> and
468the result is a NaN. A <CODE>DOMAIN error</CODE> is reported. 520the result is a NaN. A <CODE>DOMAIN error</CODE> is reported.
521</P><P>
469 522
470
471<P>
472If 523If
473is 1, the global <CODE>errno</CODE> is set to <CODE>EDOM</CODE>; and the result is 524is 1, the global <CODE>errno</CODE> is set to <CODE>EDOM</CODE>; and the result is
474infinity with the same sign as <CODE>x</CODE>. A <CODE>SING error</CODE> is reported. 525infinity with the same sign as <CODE>x</CODE>. A <CODE>SING error</CODE> is reported.
526</P><P>
475 527
476
477<P>
478You can modify the error handling for these routines using 528You can modify the error handling for these routines using
479<CODE>matherr</CODE>. 529<CODE>matherr</CODE>.
530</P><P>
480 531
481
482<P>
483<BR> 532<BR>
484<STRONG>Portability</STRONG><BR> 533<STRONG>Portability</STRONG><BR>
485Neither <CODE>atanh</CODE> nor <CODE>atanhf</CODE> are ANSI C. 534Neither <CODE>atanh</CODE> nor <CODE>atanhf</CODE> are ANSI C.
486 535</P><P>
487 536
488<P> 537<BR>
489<BR> 538</P><P>
490 539
491 540<A NAME="jN"></A>
492 541<HR SIZE="6">
493 542<A NAME="SEC10"></A>
494<H2><A NAME="SEC10" HREF="libm_toc.html#TOC10"><CODE>jN</CODE>,<CODE>jNf</CODE>,<CODE>yN</CODE>,<CODE>yNf</CODE>---Bessel functions</A></H2> 543<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
495<P> 544<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC9"> &lt; </A>]</TD>
496<A NAME="IDX19"></A> 545<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC11"> &gt; </A>]</TD>
497<A NAME="IDX20"></A> 546<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
498<A NAME="IDX21"></A> 547<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
499<A NAME="IDX22"></A> 548<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
500<A NAME="IDX23"></A> 549<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#SEC1">Top</A>]</TD>
501<A NAME="IDX24"></A> 550<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
502<A NAME="IDX25"></A> 551<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
503<A NAME="IDX26"></A> 552<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
504<A NAME="IDX27"></A> 553</TR></TABLE>
505<A NAME="IDX28"></A> 554<H2> 1.9 <CODE>jN</CODE>,<CODE>jNf</CODE>,<CODE>yN</CODE>,<CODE>yNf</CODE>---Bessel functions </H2>
506<A NAME="IDX29"></A> 555<!--docid::SEC10::-->
507<A NAME="IDX30"></A>
508<STRONG>Synopsis</STRONG> 556<STRONG>Synopsis</STRONG>
509 557<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
510<PRE>
511#include &#60;math.h&#62;
512double j0(double <VAR>x</VAR>); 558double j0(double <VAR>x</VAR>);
513float j0f(float <VAR>x</VAR>); 559float j0f(float <VAR>x</VAR>);
514double j1(double <VAR>x</VAR>); 560double j1(double <VAR>x</VAR>);
@@ -522,395 +568,391 @@ float y1f(float <VAR>x</VAR>);
522double yn(int <VAR>n</VAR>, double <VAR>x</VAR>); 568double yn(int <VAR>n</VAR>, double <VAR>x</VAR>);
523float ynf(int <VAR>n</VAR>, float <VAR>x</VAR>); 569float ynf(int <VAR>n</VAR>, float <VAR>x</VAR>);
524 570
525</PRE> 571</pre></td></tr></table><STRONG>Description</STRONG><BR>
526
527<P>
528<STRONG>Description</STRONG><BR>
529The Bessel functions are a family of functions that solve the 572The Bessel functions are a family of functions that solve the
530differential equation 573differential equation
531These functions have many applications in engineering and physics. 574These functions have many applications in engineering and physics.
532
533
534<P> 575<P>
576
535<CODE>jn</CODE> calculates the Bessel function of the first kind of order 577<CODE>jn</CODE> calculates the Bessel function of the first kind of order
536<VAR>n</VAR>. <CODE>j0</CODE> and <CODE>j1</CODE> are special cases for order 0 and order 578<VAR>n</VAR>. <CODE>j0</CODE> and <CODE>j1</CODE> are special cases for order 0 and order
5371 respectively. 5791 respectively.
580</P><P>
538 581
539
540<P>
541Similarly, <CODE>yn</CODE> calculates the Bessel function of the second kind of 582Similarly, <CODE>yn</CODE> calculates the Bessel function of the second kind of
542order <VAR>n</VAR>, and <CODE>y0</CODE> and <CODE>y1</CODE> are special cases for order 0 and 583order <VAR>n</VAR>, and <CODE>y0</CODE> and <CODE>y1</CODE> are special cases for order 0 and
5431. 5841.
585</P><P>
544 586
545
546<P>
547<CODE>jnf</CODE>, <CODE>j0f</CODE>, <CODE>j1f</CODE>, <CODE>ynf</CODE>, <CODE>y0f</CODE>, and <CODE>y1f</CODE> perform the 587<CODE>jnf</CODE>, <CODE>j0f</CODE>, <CODE>j1f</CODE>, <CODE>ynf</CODE>, <CODE>y0f</CODE>, and <CODE>y1f</CODE> perform the
548same calculations, but on <CODE>float</CODE> rather than <CODE>double</CODE> values. 588same calculations, but on <CODE>float</CODE> rather than <CODE>double</CODE> values.
589</P><P>
549 590
550
551<P>
552<BR> 591<BR>
553<STRONG>Returns</STRONG><BR> 592<STRONG>Returns</STRONG><BR>
554The value of each Bessel function at <VAR>x</VAR> is returned. 593The value of each Bessel function at <VAR>x</VAR> is returned.
594</P><P>
555 595
556
557<P>
558<BR> 596<BR>
559<STRONG>Portability</STRONG><BR> 597<STRONG>Portability</STRONG><BR>
560None of the Bessel functions are in ANSI C. 598None of the Bessel functions are in ANSI C.
561 599</P><P>
562 600
563<P> 601<BR>
564<BR> 602</P><P>
565 603
566 604<A NAME="cosh"></A>
567 605<HR SIZE="6">
568 606<A NAME="SEC11"></A>
569<H2><A NAME="SEC11" HREF="libm_toc.html#TOC11"><CODE>cosh</CODE>, <CODE>coshf</CODE>---hyperbolic cosine</A></H2> 607<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
570<P> 608<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC10"> &lt; </A>]</TD>
609<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC12"> &gt; </A>]</TD>
610<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
611<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
612<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
613<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#SEC1">Top</A>]</TD>
614<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
615<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
616<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
617</TR></TABLE>
618<H2> 1.10 <CODE>cosh</CODE>, <CODE>coshf</CODE>---hyperbolic cosine </H2>
619<!--docid::SEC11::-->
571<STRONG>Synopsis</STRONG> 620<STRONG>Synopsis</STRONG>
572 621<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
573<PRE>
574#include &#60;math.h&#62;
575double cosh(double <VAR>x</VAR>); 622double cosh(double <VAR>x</VAR>);
576float coshf(float <VAR>x</VAR>) 623float coshf(float <VAR>x</VAR>)
577 624
578</PRE> 625</pre></td></tr></table><STRONG>Description</STRONG><BR>
579
580<P> 626<P>
581<STRONG>Description</STRONG><BR>
582 627
583
584<P>
585<CODE>cosh</CODE> computes the hyperbolic cosine of the argument <VAR>x</VAR>. 628<CODE>cosh</CODE> computes the hyperbolic cosine of the argument <VAR>x</VAR>.
586<CODE>cosh(<VAR>x</VAR>)</CODE> is defined as 629<CODE>cosh(<VAR>x</VAR>)</CODE> is defined as
630</P><P>
587 631
588
589<P>
590Angles are specified in radians. 632Angles are specified in radians.
591<CODE>coshf</CODE> is identical, save that it takes and returns <CODE>float</CODE>. 633<CODE>coshf</CODE> is identical, save that it takes and returns <CODE>float</CODE>.
634</P><P>
592 635
593
594<P>
595<BR> 636<BR>
596<STRONG>Returns</STRONG><BR> 637<STRONG>Returns</STRONG><BR>
597The computed value is returned. When the correct value would create 638The computed value is returned. When the correct value would create
598an overflow, <CODE>cosh</CODE> returns the value <CODE>HUGE_VAL</CODE> with the 639an overflow, <CODE>cosh</CODE> returns the value <CODE>HUGE_VAL</CODE> with the
599appropriate sign, and the global value <CODE>errno</CODE> is set to <CODE>ERANGE</CODE>. 640appropriate sign, and the global value <CODE>errno</CODE> is set to <CODE>ERANGE</CODE>.
641</P><P>
600 642
601
602<P>
603You can modify error handling for these functions using the 643You can modify error handling for these functions using the
604function <CODE>matherr</CODE>. 644function <CODE>matherr</CODE>.
645</P><P>
605 646
606
607<P>
608<BR> 647<BR>
609<STRONG>Portability</STRONG><BR> 648<STRONG>Portability</STRONG><BR>
610<CODE>cosh</CODE> is ANSI. 649<CODE>cosh</CODE> is ANSI.
611<CODE>coshf</CODE> is an extension. 650<CODE>coshf</CODE> is an extension.
612 651</P><P>
613 652
614<P> 653<BR>
615<BR> 654</P><P>
616 655
617 656<A NAME="erf"></A>
618 657<HR SIZE="6">
619 658<A NAME="SEC12"></A>
620<H2><A NAME="SEC12" HREF="libm_toc.html#TOC12"><CODE>erf</CODE>, <CODE>erff</CODE>, <CODE>erfc</CODE>, <CODE>erfcf</CODE>---error function</A></H2> 659<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
621<P> 660<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC11"> &lt; </A>]</TD>
622<A NAME="IDX31"></A> 661<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC13"> &gt; </A>]</TD>
623<A NAME="IDX32"></A> 662<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
624<A NAME="IDX33"></A> 663<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
625<A NAME="IDX34"></A> 664<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
665<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#SEC1">Top</A>]</TD>
666<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
667<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
668<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
669</TR></TABLE>
670<H2> 1.11 <CODE>erf</CODE>, <CODE>erff</CODE>, <CODE>erfc</CODE>, <CODE>erfcf</CODE>---error function </H2>
671<!--docid::SEC12::-->
626<STRONG>Synopsis</STRONG> 672<STRONG>Synopsis</STRONG>
627 673<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
628<PRE>
629#include &#60;math.h&#62;
630double erf(double <VAR>x</VAR>); 674double erf(double <VAR>x</VAR>);
631float erff(float <VAR>x</VAR>); 675float erff(float <VAR>x</VAR>);
632double erfc(double <VAR>x</VAR>); 676double erfc(double <VAR>x</VAR>);
633float erfcf(float <VAR>x</VAR>); 677float erfcf(float <VAR>x</VAR>);
634</PRE> 678</pre></td></tr></table><STRONG>Description</STRONG><BR>
635
636<P>
637<STRONG>Description</STRONG><BR>
638<CODE>erf</CODE> calculates an approximation to the "error function", 679<CODE>erf</CODE> calculates an approximation to the "error function",
639which estimates the probability that an observation will fall within 680which estimates the probability that an observation will fall within
640<VAR>x</VAR> standard deviations of the mean (assuming a normal 681<VAR>x</VAR> standard deviations of the mean (assuming a normal
641distribution). 682distribution).
642
643
644<P> 683<P>
684
645<CODE>erfc</CODE> calculates the complementary probability; that is, 685<CODE>erfc</CODE> calculates the complementary probability; that is,
646<CODE>erfc(<VAR>x</VAR>)</CODE> is <CODE>1 - erf(<VAR>x</VAR>)</CODE>. <CODE>erfc</CODE> is computed directly, 686<CODE>erfc(<VAR>x</VAR>)</CODE> is <CODE>1 - erf(<VAR>x</VAR>)</CODE>. <CODE>erfc</CODE> is computed directly,
647so that you can use it to avoid the loss of precision that would 687so that you can use it to avoid the loss of precision that would
648result from subtracting large probabilities (on large <VAR>x</VAR>) from 1. 688result from subtracting large probabilities (on large <VAR>x</VAR>) from 1.
689</P><P>
649 690
650
651<P>
652<CODE>erff</CODE> and <CODE>erfcf</CODE> differ from <CODE>erf</CODE> and <CODE>erfc</CODE> only in the 691<CODE>erff</CODE> and <CODE>erfcf</CODE> differ from <CODE>erf</CODE> and <CODE>erfc</CODE> only in the
653argument and result types. 692argument and result types.
693</P><P>
654 694
655
656<P>
657<BR> 695<BR>
658<STRONG>Returns</STRONG><BR> 696<STRONG>Returns</STRONG><BR>
659For positive arguments, <CODE>erf</CODE> and all its variants return a 697For positive arguments, <CODE>erf</CODE> and all its variants return a
660probability--a number between 0 and 1. 698probability--a number between 0 and 1.
699</P><P>
661 700
662
663<P>
664<BR> 701<BR>
665<STRONG>Portability</STRONG><BR> 702<STRONG>Portability</STRONG><BR>
666None of the variants of <CODE>erf</CODE> are ANSI C. 703None of the variants of <CODE>erf</CODE> are ANSI C.
667 704</P><P>
668 705
669<P> 706<BR>
670<BR> 707</P><P>
671 708
672 709<A NAME="exp"></A>
673 710<HR SIZE="6">
674 711<A NAME="SEC13"></A>
675<H2><A NAME="SEC13" HREF="libm_toc.html#TOC13"><CODE>exp</CODE>, <CODE>expf</CODE>---exponential</A></H2> 712<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
676<P> 713<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC12"> &lt; </A>]</TD>
677<A NAME="IDX35"></A> 714<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC14"> &gt; </A>]</TD>
678<A NAME="IDX36"></A> 715<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
716<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
717<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
718<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#SEC1">Top</A>]</TD>
719<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
720<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
721<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
722</TR></TABLE>
723<H2> 1.12 <CODE>exp</CODE>, <CODE>expf</CODE>---exponential </H2>
724<!--docid::SEC13::-->
679<STRONG>Synopsis</STRONG> 725<STRONG>Synopsis</STRONG>
680 726<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
681<PRE>
682#include &#60;math.h&#62;
683double exp(double <VAR>x</VAR>); 727double exp(double <VAR>x</VAR>);
684float expf(float <VAR>x</VAR>); 728float expf(float <VAR>x</VAR>);
685 729
686</PRE> 730</pre></td></tr></table><STRONG>Description</STRONG><BR>
687
688<P>
689<STRONG>Description</STRONG><BR>
690<CODE>exp</CODE> and <CODE>expf</CODE> calculate the exponential of <VAR>x</VAR>, that is, 731<CODE>exp</CODE> and <CODE>expf</CODE> calculate the exponential of <VAR>x</VAR>, that is,
691is the base of the natural system of logarithms, approximately 2.71828). 732is the base of the natural system of logarithms, approximately 2.71828).
692
693
694<P> 733<P>
734
695You can use the (non-ANSI) function <CODE>matherr</CODE> to specify 735You can use the (non-ANSI) function <CODE>matherr</CODE> to specify
696error handling for these functions. 736error handling for these functions.
737</P><P>
697 738
698
699<P>
700<BR> 739<BR>
701<STRONG>Returns</STRONG><BR> 740<STRONG>Returns</STRONG><BR>
702On success, <CODE>exp</CODE> and <CODE>expf</CODE> return the calculated value. 741On success, <CODE>exp</CODE> and <CODE>expf</CODE> return the calculated value.
703If the result underflows, the returned value is <CODE>0</CODE>. If the 742If the result underflows, the returned value is <CODE>0</CODE>. If the
704result overflows, the returned value is <CODE>HUGE_VAL</CODE>. In 743result overflows, the returned value is <CODE>HUGE_VAL</CODE>. In
705either case, <CODE>errno</CODE> is set to <CODE>ERANGE</CODE>. 744either case, <CODE>errno</CODE> is set to <CODE>ERANGE</CODE>.
745</P><P>
706 746
707
708<P>
709<BR> 747<BR>
710<STRONG>Portability</STRONG><BR> 748<STRONG>Portability</STRONG><BR>
711<CODE>exp</CODE> is ANSI C. <CODE>expf</CODE> is an extension. 749<CODE>exp</CODE> is ANSI C. <CODE>expf</CODE> is an extension.
712 750</P><P>
713 751
714<P> 752<BR>
715<BR> 753</P><P>
716 754
717 755<A NAME="fabs"></A>
718 756<HR SIZE="6">
719 757<A NAME="SEC14"></A>
720<H2><A NAME="SEC14" HREF="libm_toc.html#TOC14"><CODE>fabs</CODE>, <CODE>fabsf</CODE>---absolute value (magnitude)</A></H2> 758<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
721<P> 759<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC13"> &lt; </A>]</TD>
722<A NAME="IDX37"></A> 760<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC15"> &gt; </A>]</TD>
723<A NAME="IDX38"></A> 761<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
762<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
763<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
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765<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
766<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
767<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
768</TR></TABLE>
769<H2> 1.13 <CODE>fabs</CODE>, <CODE>fabsf</CODE>---absolute value (magnitude) </H2>
770<!--docid::SEC14::-->
724<STRONG>Synopsis</STRONG> 771<STRONG>Synopsis</STRONG>
725 772<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
726<PRE>
727#include &#60;math.h&#62;
728double fabs(double <VAR>x</VAR>); 773double fabs(double <VAR>x</VAR>);
729float fabsf(float <VAR>x</VAR>); 774float fabsf(float <VAR>x</VAR>);
730 775
731</PRE> 776</pre></td></tr></table><STRONG>Description</STRONG><BR>
732
733<P>
734<STRONG>Description</STRONG><BR>
735<CODE>fabs</CODE> and <CODE>fabsf</CODE> calculate 777<CODE>fabs</CODE> and <CODE>fabsf</CODE> calculate
736the absolute value (magnitude) of the argument <VAR>x</VAR>, by direct 778the absolute value (magnitude) of the argument <VAR>x</VAR>, by direct
737manipulation of the bit representation of <VAR>x</VAR>. 779manipulation of the bit representation of <VAR>x</VAR>.
738
739
740<P> 780<P>
781
741<BR> 782<BR>
742<STRONG>Returns</STRONG><BR> 783<STRONG>Returns</STRONG><BR>
743The calculated value is returned. No errors are detected. 784The calculated value is returned. No errors are detected.
785</P><P>
744 786
745
746<P>
747<BR> 787<BR>
748<STRONG>Portability</STRONG><BR> 788<STRONG>Portability</STRONG><BR>
749<CODE>fabs</CODE> is ANSI. 789<CODE>fabs</CODE> is ANSI.
750<CODE>fabsf</CODE> is an extension. 790<CODE>fabsf</CODE> is an extension.
751 791</P><P>
752 792
753<P> 793<BR>
754<BR> 794</P><P>
755 795
756 796<A NAME="floor"></A>
757 797<HR SIZE="6">
758 798<A NAME="SEC15"></A>
759<H2><A NAME="SEC15" HREF="libm_toc.html#TOC15"><CODE>floor</CODE>, <CODE>floorf</CODE>, <CODE>ceil</CODE>, <CODE>ceilf</CODE>---floor and ceiling</A></H2> 799<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
760<P> 800<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC14"> &lt; </A>]</TD>
761<A NAME="IDX39"></A> 801<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC16"> &gt; </A>]</TD>
762<A NAME="IDX40"></A> 802<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
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805<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#SEC1">Top</A>]</TD>
806<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
807<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
808<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
809</TR></TABLE>
810<H2> 1.14 <CODE>floor</CODE>, <CODE>floorf</CODE>, <CODE>ceil</CODE>, <CODE>ceilf</CODE>---floor and ceiling </H2>
811<!--docid::SEC15::-->
765<STRONG>Synopsis</STRONG> 812<STRONG>Synopsis</STRONG>
766 813<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
767<PRE>
768#include &#60;math.h&#62;
769double floor(double <VAR>x</VAR>); 814double floor(double <VAR>x</VAR>);
770float floorf(float <VAR>x</VAR>); 815float floorf(float <VAR>x</VAR>);
771double ceil(double <VAR>x</VAR>); 816double ceil(double <VAR>x</VAR>);
772float ceilf(float <VAR>x</VAR>); 817float ceilf(float <VAR>x</VAR>);
773 818
774</PRE> 819</pre></td></tr></table><STRONG>Description</STRONG><BR>
775
776<P>
777<STRONG>Description</STRONG><BR>
778<CODE>floor</CODE> and <CODE>floorf</CODE> find 820<CODE>floor</CODE> and <CODE>floorf</CODE> find
779the nearest integer less than or equal to <VAR>x</VAR>. 821the nearest integer less than or equal to <VAR>x</VAR>.
780<CODE>ceil</CODE> and <CODE>ceilf</CODE> find 822<CODE>ceil</CODE> and <CODE>ceilf</CODE> find
781the nearest integer greater than or equal to <VAR>x</VAR>. 823the nearest integer greater than or equal to <VAR>x</VAR>.
782
783
784<P> 824<P>
825
785<BR> 826<BR>
786<STRONG>Returns</STRONG><BR> 827<STRONG>Returns</STRONG><BR>
787<CODE>floor</CODE> and <CODE>ceil</CODE> return the integer result as a double. 828<CODE>floor</CODE> and <CODE>ceil</CODE> return the integer result as a double.
788<CODE>floorf</CODE> and <CODE>ceilf</CODE> return the integer result as a float. 829<CODE>floorf</CODE> and <CODE>ceilf</CODE> return the integer result as a float.
830</P><P>
789 831
790
791<P>
792<BR> 832<BR>
793<STRONG>Portability</STRONG><BR> 833<STRONG>Portability</STRONG><BR>
794<CODE>floor</CODE> and <CODE>ceil</CODE> are ANSI. 834<CODE>floor</CODE> and <CODE>ceil</CODE> are ANSI.
795<CODE>floorf</CODE> and <CODE>ceilf</CODE> are extensions. 835<CODE>floorf</CODE> and <CODE>ceilf</CODE> are extensions.
796 836</P><P>
797 837
798<P> 838<BR>
799<BR> 839</P><P>
800 840
801 841<A NAME="fmod"></A>
802 842<HR SIZE="6">
803 843<A NAME="SEC16"></A>
804<H2><A NAME="SEC16" HREF="libm_toc.html#TOC16"><CODE>fmod</CODE>, <CODE>fmodf</CODE>---floating-point remainder (modulo)</A></H2> 844<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
805<P> 845<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC15"> &lt; </A>]</TD>
806<A NAME="IDX43"></A> 846<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC17"> &gt; </A>]</TD>
807<A NAME="IDX44"></A> 847<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
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850<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#SEC1">Top</A>]</TD>
851<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
852<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
853<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
854</TR></TABLE>
855<H2> 1.15 <CODE>fmod</CODE>, <CODE>fmodf</CODE>---floating-point remainder (modulo) </H2>
856<!--docid::SEC16::-->
808<STRONG>Synopsis</STRONG> 857<STRONG>Synopsis</STRONG>
809 858<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
810<PRE>
811#include &#60;math.h&#62;
812double fmod(double <VAR>x</VAR>, double <VAR>y</VAR>) 859double fmod(double <VAR>x</VAR>, double <VAR>y</VAR>)
813float fmodf(float <VAR>x</VAR>, float <VAR>y</VAR>) 860float fmodf(float <VAR>x</VAR>, float <VAR>y</VAR>)
814 861
815</PRE> 862</pre></td></tr></table><STRONG>Description</STRONG><BR>
816
817<P>
818<STRONG>Description</STRONG><BR>
819The <CODE>fmod</CODE> and <CODE>fmodf</CODE> functions compute the floating-point 863The <CODE>fmod</CODE> and <CODE>fmodf</CODE> functions compute the floating-point
820remainder of <VAR>x</VAR>/<VAR>y</VAR> (<VAR>x</VAR> modulo <VAR>y</VAR>). 864remainder of <VAR>x</VAR>/<VAR>y</VAR> (<VAR>x</VAR> modulo <VAR>y</VAR>).
821
822
823<P> 865<P>
866
824<BR> 867<BR>
825<STRONG>Returns</STRONG><BR> 868<STRONG>Returns</STRONG><BR>
826The <CODE>fmod</CODE> function returns the value 869The <CODE>fmod</CODE> function returns the value
827for the largest integer <VAR>i</VAR> such that, if <VAR>y</VAR> is nonzero, the 870for the largest integer <VAR>i</VAR> such that, if <VAR>y</VAR> is nonzero, the
828result has the same sign as <VAR>x</VAR> and magnitude less than the 871result has the same sign as <VAR>x</VAR> and magnitude less than the
829magnitude of <VAR>y</VAR>. 872magnitude of <VAR>y</VAR>.
873</P><P>
830 874
831
832<P>
833<CODE>fmod(<VAR>x</VAR>,0)</CODE> returns NaN, and sets <CODE>errno</CODE> to <CODE>EDOM</CODE>. 875<CODE>fmod(<VAR>x</VAR>,0)</CODE> returns NaN, and sets <CODE>errno</CODE> to <CODE>EDOM</CODE>.
876</P><P>
834 877
835
836<P>
837You can modify error treatment for these functions using <CODE>matherr</CODE>. 878You can modify error treatment for these functions using <CODE>matherr</CODE>.
879</P><P>
838 880
839
840<P>
841<BR> 881<BR>
842<STRONG>Portability</STRONG><BR> 882<STRONG>Portability</STRONG><BR>
843<CODE>fmod</CODE> is ANSI C. <CODE>fmodf</CODE> is an extension. 883<CODE>fmod</CODE> is ANSI C. <CODE>fmodf</CODE> is an extension.
844 884</P><P>
845 885
846<P> 886<BR>
847<BR> 887</P><P>
848 888
849 889<A NAME="frexp"></A>
850 890<HR SIZE="6">
851 891<A NAME="SEC17"></A>
852<H2><A NAME="SEC17" HREF="libm_toc.html#TOC17"><CODE>frexp</CODE>, <CODE>frexpf</CODE>---split floating-point number</A></H2> 892<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
853<P> 893<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC16"> &lt; </A>]</TD>
854<A NAME="IDX45"></A> 894<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC18"> &gt; </A>]</TD>
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899<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
900<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
901<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
902</TR></TABLE>
903<H2> 1.16 <CODE>frexp</CODE>, <CODE>frexpf</CODE>---split floating-point number </H2>
904<!--docid::SEC17::-->
856<STRONG>Synopsis</STRONG> 905<STRONG>Synopsis</STRONG>
857 906<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
858<PRE>
859#include &#60;math.h&#62;
860double frexp(double <VAR>val</VAR>, int *<VAR>exp</VAR>); 907double frexp(double <VAR>val</VAR>, int *<VAR>exp</VAR>);
861float frexpf(float <VAR>val</VAR>, int *<VAR>exp</VAR>); 908float frexpf(float <VAR>val</VAR>, int *<VAR>exp</VAR>);
862 909
863</PRE> 910</pre></td></tr></table><STRONG>Description</STRONG><BR>
864
865<P>
866<STRONG>Description</STRONG><BR>
867All non zero, normal numbers can be described as <VAR>m</VAR> * 2**<VAR>p</VAR>. 911All non zero, normal numbers can be described as <VAR>m</VAR> * 2**<VAR>p</VAR>.
868<CODE>frexp</CODE> represents the double <VAR>val</VAR> as a mantissa <VAR>m</VAR> 912<CODE>frexp</CODE> represents the double <VAR>val</VAR> as a mantissa <VAR>m</VAR>
869and a power of two <VAR>p</VAR>. The resulting mantissa will always 913and a power of two <VAR>p</VAR>. The resulting mantissa will always
870be greater than or equal to <CODE>0.5</CODE>, and less than <CODE>1.0</CODE> (as 914be greater than or equal to <CODE>0.5</CODE>, and less than <CODE>1.0</CODE> (as
871long as <VAR>val</VAR> is nonzero). The power of two will be stored 915long as <VAR>val</VAR> is nonzero). The power of two will be stored
872in <CODE>*</CODE><VAR>exp</VAR>. 916in <CODE>*</CODE><VAR>exp</VAR>.
873
874
875<P> 917<P>
918
876<CODE>frexpf</CODE> is identical, other than taking and returning 919<CODE>frexpf</CODE> is identical, other than taking and returning
877floats rather than doubles. 920floats rather than doubles.
921</P><P>
878 922
879
880<P>
881<BR> 923<BR>
882<STRONG>Returns</STRONG><BR> 924<STRONG>Returns</STRONG><BR>
883<CODE>frexp</CODE> returns the mantissa <VAR>m</VAR>. If <VAR>val</VAR> is <CODE>0</CODE>, infinity, 925<CODE>frexp</CODE> returns the mantissa <VAR>m</VAR>. If <VAR>val</VAR> is <CODE>0</CODE>, infinity,
884or Nan, <CODE>frexp</CODE> will set <CODE>*</CODE><VAR>exp</VAR> to <CODE>0</CODE> and return <VAR>val</VAR>. 926or Nan, <CODE>frexp</CODE> will set <CODE>*</CODE><VAR>exp</VAR> to <CODE>0</CODE> and return <VAR>val</VAR>.
927</P><P>
885 928
886
887<P>
888<BR> 929<BR>
889<STRONG>Portability</STRONG><BR> 930<STRONG>Portability</STRONG><BR>
890<CODE>frexp</CODE> is ANSI. 931<CODE>frexp</CODE> is ANSI.
891<CODE>frexpf</CODE> is an extension. 932<CODE>frexpf</CODE> is an extension.
892 933</P><P>
893 934
894<P> 935<BR>
895<BR> 936</P><P>
896 937
897 938<A NAME="gamma"></A>
898 939<HR SIZE="6">
899 940<A NAME="SEC18"></A>
900<H2><A NAME="SEC18" HREF="libm_toc.html#TOC18"><CODE>gamma</CODE>, <CODE>gammaf</CODE>, <CODE>lgamma</CODE>, <CODE>lgammaf</CODE>, <CODE>gamma_r</CODE>,</A></H2> 941<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
901<P> 942<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC17"> &lt; </A>]</TD>
902<A NAME="IDX47"></A> 943<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC19"> &gt; </A>]</TD>
903<A NAME="IDX48"></A> 944<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
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905<A NAME="IDX50"></A> 946<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
906<A NAME="IDX51"></A> 947<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#SEC1">Top</A>]</TD>
907<A NAME="IDX52"></A> 948<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
908<A NAME="IDX53"></A> 949<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
909<A NAME="IDX54"></A> 950<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
951</TR></TABLE>
952<H2> 1.17 <CODE>gamma</CODE>, <CODE>gammaf</CODE>, <CODE>lgamma</CODE>, <CODE>lgammaf</CODE>, <CODE>gamma_r</CODE>, </H2>
953<!--docid::SEC18::-->
910<STRONG>Synopsis</STRONG> 954<STRONG>Synopsis</STRONG>
911 955<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
912<PRE>
913#include &#60;math.h&#62;
914double gamma(double <VAR>x</VAR>); 956double gamma(double <VAR>x</VAR>);
915float gammaf(float <VAR>x</VAR>); 957float gammaf(float <VAR>x</VAR>);
916double lgamma(double <VAR>x</VAR>); 958double lgamma(double <VAR>x</VAR>);
@@ -920,10 +962,7 @@ float gammaf_r(float <VAR>x</VAR>, int *<VAR>signgamp</VAR>);
920double lgamma_r(double <VAR>x</VAR>, int *<VAR>signgamp</VAR>); 962double lgamma_r(double <VAR>x</VAR>, int *<VAR>signgamp</VAR>);
921float lgammaf_r(float <VAR>x</VAR>, int *<VAR>signgamp</VAR>); 963float lgammaf_r(float <VAR>x</VAR>, int *<VAR>signgamp</VAR>);
922 964
923</PRE> 965</pre></td></tr></table><STRONG>Description</STRONG><BR>
924
925<P>
926<STRONG>Description</STRONG><BR>
927<CODE>gamma</CODE> calculates 966<CODE>gamma</CODE> calculates
928the natural logarithm of the gamma function of <VAR>x</VAR>. The gamma function 967the natural logarithm of the gamma function of <VAR>x</VAR>. The gamma function
929(<CODE>exp(gamma(<VAR>x</VAR>))</CODE>) is a generalization of factorial, and retains 968(<CODE>exp(gamma(<VAR>x</VAR>))</CODE>) is a generalization of factorial, and retains
@@ -931,26 +970,22 @@ the property that
931Accordingly, the results of the gamma function itself grow very 970Accordingly, the results of the gamma function itself grow very
932quickly. <CODE>gamma</CODE> is defined as 971quickly. <CODE>gamma</CODE> is defined as
933to extend the useful range of results representable. 972to extend the useful range of results representable.
934
935
936<P> 973<P>
974
937The sign of the result is returned in the global variable <CODE>signgam</CODE>, 975The sign of the result is returned in the global variable <CODE>signgam</CODE>,
938which is declared in math.h. 976which is declared in math.h.
977</P><P>
939 978
940
941<P>
942<CODE>gammaf</CODE> performs the same calculation as <CODE>gamma</CODE>, but uses and 979<CODE>gammaf</CODE> performs the same calculation as <CODE>gamma</CODE>, but uses and
943returns <CODE>float</CODE> values. 980returns <CODE>float</CODE> values.
981</P><P>
944 982
945
946<P>
947<CODE>lgamma</CODE> and <CODE>lgammaf</CODE> are alternate names for <CODE>gamma</CODE> and 983<CODE>lgamma</CODE> and <CODE>lgammaf</CODE> are alternate names for <CODE>gamma</CODE> and
948<CODE>gammaf</CODE>. The use of <CODE>lgamma</CODE> instead of <CODE>gamma</CODE> is a reminder 984<CODE>gammaf</CODE>. The use of <CODE>lgamma</CODE> instead of <CODE>gamma</CODE> is a reminder
949that these functions compute the log of the gamma function, rather 985that these functions compute the log of the gamma function, rather
950than the gamma function itself. 986than the gamma function itself.
987</P><P>
951 988
952
953<P>
954The functions <CODE>gamma_r</CODE>, <CODE>gammaf_r</CODE>, <CODE>lgamma_r</CODE>, and 989The functions <CODE>gamma_r</CODE>, <CODE>gammaf_r</CODE>, <CODE>lgamma_r</CODE>, and
955<CODE>lgammaf_r</CODE> are just like <CODE>gamma</CODE>, <CODE>gammaf</CODE>, <CODE>lgamma</CODE>, and 990<CODE>lgammaf_r</CODE> are just like <CODE>gamma</CODE>, <CODE>gammaf</CODE>, <CODE>lgamma</CODE>, and
956<CODE>lgammaf</CODE>, respectively, but take an additional argument. This 991<CODE>lgammaf</CODE>, respectively, but take an additional argument. This
@@ -959,87 +994,89 @@ argument is used to return the sign of the result, and the global
959variable <CODE>signgam</CODE> is not used. These functions may be used for 994variable <CODE>signgam</CODE> is not used. These functions may be used for
960reentrant calls (but they will still set the global variable <CODE>errno</CODE> 995reentrant calls (but they will still set the global variable <CODE>errno</CODE>
961if an error occurs). 996if an error occurs).
997</P><P>
962 998
963
964<P>
965<BR> 999<BR>
966<STRONG>Returns</STRONG><BR> 1000<STRONG>Returns</STRONG><BR>
967Normally, the computed result is returned. 1001Normally, the computed result is returned.
1002</P><P>
968 1003
969
970<P>
971When <VAR>x</VAR> is a nonpositive integer, <CODE>gamma</CODE> returns <CODE>HUGE_VAL</CODE> 1004When <VAR>x</VAR> is a nonpositive integer, <CODE>gamma</CODE> returns <CODE>HUGE_VAL</CODE>
972and <CODE>errno</CODE> is set to <CODE>EDOM</CODE>. If the result overflows, <CODE>gamma</CODE> 1005and <CODE>errno</CODE> is set to <CODE>EDOM</CODE>. If the result overflows, <CODE>gamma</CODE>
973returns <CODE>HUGE_VAL</CODE> and <CODE>errno</CODE> is set to <CODE>ERANGE</CODE>. 1006returns <CODE>HUGE_VAL</CODE> and <CODE>errno</CODE> is set to <CODE>ERANGE</CODE>.
1007</P><P>
974 1008
975
976<P>
977You can modify this error treatment using <CODE>matherr</CODE>. 1009You can modify this error treatment using <CODE>matherr</CODE>.
1010</P><P>
978 1011
979
980<P>
981<BR> 1012<BR>
982<STRONG>Portability</STRONG><BR> 1013<STRONG>Portability</STRONG><BR>
983Neither <CODE>gamma</CODE> nor <CODE>gammaf</CODE> is ANSI C. 1014Neither <CODE>gamma</CODE> nor <CODE>gammaf</CODE> is ANSI C.
984<BR> 1015<BR>
985 1016</P><P>
986 1017
987 1018<A NAME="hypot"></A>
988 1019<HR SIZE="6">
989<H2><A NAME="SEC19" HREF="libm_toc.html#TOC19"><CODE>hypot</CODE>, <CODE>hypotf</CODE>---distance from origin</A></H2> 1020<A NAME="SEC19"></A>
990<P> 1021<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
991<A NAME="IDX55"></A> 1022<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC18"> &lt; </A>]</TD>
992<A NAME="IDX56"></A> 1023<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC20"> &gt; </A>]</TD>
1024<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
1025<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
1026<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
1027<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#SEC1">Top</A>]</TD>
1028<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
1029<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
1030<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
1031</TR></TABLE>
1032<H2> 1.18 <CODE>hypot</CODE>, <CODE>hypotf</CODE>---distance from origin </H2>
1033<!--docid::SEC19::-->
993<STRONG>Synopsis</STRONG> 1034<STRONG>Synopsis</STRONG>
994 1035<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
995<PRE>
996#include &#60;math.h&#62;
997double hypot(double <VAR>x</VAR>, double <VAR>y</VAR>); 1036double hypot(double <VAR>x</VAR>, double <VAR>y</VAR>);
998float hypotf(float <VAR>x</VAR>, float <VAR>y</VAR>); 1037float hypotf(float <VAR>x</VAR>, float <VAR>y</VAR>);
999 1038
1000</PRE> 1039</pre></td></tr></table><STRONG>Description</STRONG><BR>
1001
1002<P>
1003<STRONG>Description</STRONG><BR>
1004<CODE>hypot</CODE> calculates the Euclidean distance 1040<CODE>hypot</CODE> calculates the Euclidean distance
1005between the origin (0,0) and a point represented by the 1041between the origin (0,0) and a point represented by the
1006Cartesian coordinates (<VAR>x</VAR>,<VAR>y</VAR>). <CODE>hypotf</CODE> differs only 1042Cartesian coordinates (<VAR>x</VAR>,<VAR>y</VAR>). <CODE>hypotf</CODE> differs only
1007in the type of its arguments and result. 1043in the type of its arguments and result.
1008
1009
1010<P> 1044<P>
1045
1011<BR> 1046<BR>
1012<STRONG>Returns</STRONG><BR> 1047<STRONG>Returns</STRONG><BR>
1013Normally, the distance value is returned. On overflow, 1048Normally, the distance value is returned. On overflow,
1014<CODE>hypot</CODE> returns <CODE>HUGE_VAL</CODE> and sets <CODE>errno</CODE> to 1049<CODE>hypot</CODE> returns <CODE>HUGE_VAL</CODE> and sets <CODE>errno</CODE> to
1015<CODE>ERANGE</CODE>. 1050<CODE>ERANGE</CODE>.
1051</P><P>
1016 1052
1017
1018<P>
1019You can change the error treatment with <CODE>matherr</CODE>. 1053You can change the error treatment with <CODE>matherr</CODE>.
1054</P><P>
1020 1055
1021
1022<P>
1023<BR> 1056<BR>
1024<STRONG>Portability</STRONG><BR> 1057<STRONG>Portability</STRONG><BR>
1025<CODE>hypot</CODE> and <CODE>hypotf</CODE> are not ANSI C. 1058<CODE>hypot</CODE> and <CODE>hypotf</CODE> are not ANSI C.
1026<BR> 1059<BR>
1027 1060</P><P>
1028 1061
1029 1062<A NAME="isnan"></A>
1030 1063<HR SIZE="6">
1031<H2><A NAME="SEC20" HREF="libm_toc.html#TOC20"><CODE>isnan</CODE>,<CODE>isnanf</CODE>,<CODE>isinf</CODE>,<CODE>isinff</CODE>,<CODE>finite</CODE>,<CODE>finitef</CODE>---test for exceptional numbers</A></H2> 1064<A NAME="SEC20"></A>
1032<P> 1065<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
1033<A NAME="IDX57"></A> 1066<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC19"> &lt; </A>]</TD>
1034<A NAME="IDX58"></A> 1067<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC21"> &gt; </A>]</TD>
1035<A NAME="IDX59"></A> 1068<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
1036<A NAME="IDX60"></A> 1069<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
1037<A NAME="IDX61"></A> 1070<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
1038<A NAME="IDX62"></A> 1071<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#SEC1">Top</A>]</TD>
1072<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
1073<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
1074<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
1075</TR></TABLE>
1076<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>
1077<!--docid::SEC20::-->
1039<STRONG>Synopsis</STRONG> 1078<STRONG>Synopsis</STRONG>
1040 1079<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;ieeefp.h&#62;
1041<PRE>
1042#include &#60;ieeefp.h&#62;
1043int isnan(double <VAR>arg</VAR>); 1080int isnan(double <VAR>arg</VAR>);
1044int isinf(double <VAR>arg</VAR>); 1081int isinf(double <VAR>arg</VAR>);
1045int finite(double <VAR>arg</VAR>); 1082int finite(double <VAR>arg</VAR>);
@@ -1047,121 +1084,116 @@ int isnanf(float <VAR>arg</VAR>);
1047int isinff(float <VAR>arg</VAR>); 1084int isinff(float <VAR>arg</VAR>);
1048int finitef(float <VAR>arg</VAR>); 1085int finitef(float <VAR>arg</VAR>);
1049 1086
1050</PRE> 1087</pre></td></tr></table><STRONG>Description</STRONG><BR>
1051
1052<P>
1053<STRONG>Description</STRONG><BR>
1054These functions provide information on the floating point 1088These functions provide information on the floating point
1055argument supplied. 1089argument supplied.
1056
1057
1058<P> 1090<P>
1091
1059There are five major number formats - 1092There are five major number formats -
1060<DL COMPACT> 1093<DL COMPACT>
1061 1094
1062<DT><CODE>zero</CODE> 1095<DT><CODE>zero</CODE>
1063<DD> 1096<DD>a number which contains all zero bits.
1064a number which contains all zero bits.
1065<DT><CODE>subnormal</CODE> 1097<DT><CODE>subnormal</CODE>
1066<DD> 1098<DD>Is used to represent number with a zero exponent, but a non zero fraction.
1067Is used to represent number with a zero exponent, but a non zero fraction.
1068<DT><CODE>normal</CODE> 1099<DT><CODE>normal</CODE>
1069<DD> 1100<DD>A number with an exponent, and a fraction
1070A number with an exponent, and a fraction
1071<DT><CODE>infinity</CODE> 1101<DT><CODE>infinity</CODE>
1072<DD> 1102<DD>A number with an all 1's exponent and a zero fraction.
1073A number with an all 1's exponent and a zero fraction.
1074<DT><CODE>NAN</CODE> 1103<DT><CODE>NAN</CODE>
1075<DD> 1104<DD>A number with an all 1's exponent and a non zero fraction.
1076A number with an all 1's exponent and a non zero fraction. 1105<P>
1077 1106
1078</DL> 1107</DL>
1079
1080<P> 1108<P>
1109
1081<CODE>isnan</CODE> returns 1 if the argument is a nan. <CODE>isinf</CODE> 1110<CODE>isnan</CODE> returns 1 if the argument is a nan. <CODE>isinf</CODE>
1082returns 1 if the argument is infinity. <CODE>finite</CODE> returns 1 if the 1111returns 1 if the argument is infinity. <CODE>finite</CODE> returns 1 if the
1083argument is zero, subnormal or normal. 1112argument is zero, subnormal or normal.
1084The <CODE>isnanf</CODE>, <CODE>isinff</CODE> and <CODE>finitef</CODE> perform the same 1113The <CODE>isnanf</CODE>, <CODE>isinff</CODE> and <CODE>finitef</CODE> perform the same
1085operations as their <CODE>isnan</CODE>, <CODE>isinf</CODE> and <CODE>finite</CODE> 1114operations as their <CODE>isnan</CODE>, <CODE>isinf</CODE> and <CODE>finite</CODE>
1086counterparts, but on single precision floating point numbers. 1115counterparts, but on single precision floating point numbers.
1087 1116</P><P>
1088 1117
1089<P> 1118<BR>
1090<BR> 1119</P><P>
1091 1120
1092 1121<A NAME="ldexp"></A>
1093 1122<HR SIZE="6">
1094 1123<A NAME="SEC21"></A>
1095<H2><A NAME="SEC21" HREF="libm_toc.html#TOC21"><CODE>ldexp</CODE>, <CODE>ldexpf</CODE>---load exponent</A></H2> 1124<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
1096<P> 1125<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC20"> &lt; </A>]</TD>
1097<A NAME="IDX63"></A> 1126<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC22"> &gt; </A>]</TD>
1098<A NAME="IDX64"></A> 1127<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
1128<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
1129<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
1130<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#SEC1">Top</A>]</TD>
1131<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
1132<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
1133<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
1134</TR></TABLE>
1135<H2> 1.20 <CODE>ldexp</CODE>, <CODE>ldexpf</CODE>---load exponent </H2>
1136<!--docid::SEC21::-->
1099<STRONG>Synopsis</STRONG> 1137<STRONG>Synopsis</STRONG>
1100 1138<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1101<PRE>
1102#include &#60;math.h&#62;
1103double ldexp(double <VAR>val</VAR>, int <VAR>exp</VAR>); 1139double ldexp(double <VAR>val</VAR>, int <VAR>exp</VAR>);
1104float ldexpf(float <VAR>val</VAR>, int <VAR>exp</VAR>); 1140float ldexpf(float <VAR>val</VAR>, int <VAR>exp</VAR>);
1105 1141
1106</PRE> 1142</pre></td></tr></table><STRONG>Description</STRONG><BR>
1107
1108<P>
1109<STRONG>Description</STRONG><BR>
1110<CODE>ldexp</CODE> calculates the value 1143<CODE>ldexp</CODE> calculates the value
1111<CODE>ldexpf</CODE> is identical, save that it takes and returns <CODE>float</CODE> 1144<CODE>ldexpf</CODE> is identical, save that it takes and returns <CODE>float</CODE>
1112rather than <CODE>double</CODE> values. 1145rather than <CODE>double</CODE> values.
1113
1114
1115<P> 1146<P>
1147
1116<BR> 1148<BR>
1117<STRONG>Returns</STRONG><BR> 1149<STRONG>Returns</STRONG><BR>
1118<CODE>ldexp</CODE> returns the calculated value. 1150<CODE>ldexp</CODE> returns the calculated value.
1151</P><P>
1119 1152
1120
1121<P>
1122Underflow and overflow both set <CODE>errno</CODE> to <CODE>ERANGE</CODE>. 1153Underflow and overflow both set <CODE>errno</CODE> to <CODE>ERANGE</CODE>.
1123On underflow, <CODE>ldexp</CODE> and <CODE>ldexpf</CODE> return 0.0. 1154On underflow, <CODE>ldexp</CODE> and <CODE>ldexpf</CODE> return 0.0.
1124On overflow, <CODE>ldexp</CODE> returns plus or minus <CODE>HUGE_VAL</CODE>. 1155On overflow, <CODE>ldexp</CODE> returns plus or minus <CODE>HUGE_VAL</CODE>.
1156</P><P>
1125 1157
1126
1127<P>
1128<BR> 1158<BR>
1129<STRONG>Portability</STRONG><BR> 1159<STRONG>Portability</STRONG><BR>
1130<CODE>ldexp</CODE> is ANSI, <CODE>ldexpf</CODE> is an extension. 1160<CODE>ldexp</CODE> is ANSI, <CODE>ldexpf</CODE> is an extension.
1131 1161</P><P>
1132 1162
1133<P> 1163<BR>
1134<BR> 1164</P><P>
1135 1165
1136 1166<A NAME="log"></A>
1137 1167<HR SIZE="6">
1138 1168<A NAME="SEC22"></A>
1139<H2><A NAME="SEC22" HREF="libm_toc.html#TOC22"><CODE>log</CODE>, <CODE>logf</CODE>---natural logarithms</A></H2> 1169<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
1140<P> 1170<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC21"> &lt; </A>]</TD>
1141<A NAME="IDX65"></A> 1171<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC23"> &gt; </A>]</TD>
1142<A NAME="IDX66"></A> 1172<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
1173<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
1174<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
1175<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#SEC1">Top</A>]</TD>
1176<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
1177<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
1178<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
1179</TR></TABLE>
1180<H2> 1.21 <CODE>log</CODE>, <CODE>logf</CODE>---natural logarithms </H2>
1181<!--docid::SEC22::-->
1143<STRONG>Synopsis</STRONG> 1182<STRONG>Synopsis</STRONG>
1144 1183<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1145<PRE>
1146#include &#60;math.h&#62;
1147double log(double <VAR>x</VAR>); 1184double log(double <VAR>x</VAR>);
1148float logf(float <VAR>x</VAR>); 1185float logf(float <VAR>x</VAR>);
1149 1186
1150</PRE> 1187</pre></td></tr></table><STRONG>Description</STRONG><BR>
1151
1152<P>
1153<STRONG>Description</STRONG><BR>
1154Return the natural logarithm of <VAR>x</VAR>, that is, its logarithm base e 1188Return the natural logarithm of <VAR>x</VAR>, that is, its logarithm base e
1155(where e is the base of the natural system of logarithms, 2.71828...). 1189(where e is the base of the natural system of logarithms, 2.71828<small>...</small>).
1156<CODE>log</CODE> and <CODE>logf</CODE> are identical save for the return and argument types. 1190<CODE>log</CODE> and <CODE>logf</CODE> are identical save for the return and argument types.
1157
1158
1159<P> 1191<P>
1192
1160You can use the (non-ANSI) function <CODE>matherr</CODE> to specify error 1193You can use the (non-ANSI) function <CODE>matherr</CODE> to specify error
1161handling for these functions. 1194handling for these functions.
1195</P><P>
1162 1196
1163
1164<P>
1165<BR> 1197<BR>
1166<STRONG>Returns</STRONG><BR> 1198<STRONG>Returns</STRONG><BR>
1167Normally, returns the calculated value. When <VAR>x</VAR> is zero, the 1199Normally, returns the calculated value. When <VAR>x</VAR> is zero, the
@@ -1169,753 +1201,761 @@ returned value is <CODE>-HUGE_VAL</CODE> and <CODE>errno</CODE> is set to <CODE>
1169When <VAR>x</VAR> is negative, the returned value is <CODE>-HUGE_VAL</CODE> and 1201When <VAR>x</VAR> is negative, the returned value is <CODE>-HUGE_VAL</CODE> and
1170<CODE>errno</CODE> is set to <CODE>EDOM</CODE>. You can control the error behavior via 1202<CODE>errno</CODE> is set to <CODE>EDOM</CODE>. You can control the error behavior via
1171<CODE>matherr</CODE>. 1203<CODE>matherr</CODE>.
1204</P><P>
1172 1205
1173
1174<P>
1175<BR> 1206<BR>
1176<STRONG>Portability</STRONG><BR> 1207<STRONG>Portability</STRONG><BR>
1177<CODE>log</CODE> is ANSI, <CODE>logf</CODE> is an extension. 1208<CODE>log</CODE> is ANSI, <CODE>logf</CODE> is an extension.
1178 1209</P><P>
1179 1210
1180<P> 1211<BR>
1181<BR> 1212</P><P>
1182 1213
1183 1214<A NAME="log10"></A>
1184 1215<HR SIZE="6">
1185 1216<A NAME="SEC23"></A>
1186<H2><A NAME="SEC23" HREF="libm_toc.html#TOC23"><CODE>log10</CODE>, <CODE>log10f</CODE>---base 10 logarithms</A></H2> 1217<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
1187<P> 1218<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC22"> &lt; </A>]</TD>
1188<A NAME="IDX67"></A> 1219<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC24"> &gt; </A>]</TD>
1189<A NAME="IDX68"></A> 1220<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
1221<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
1222<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
1223<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#SEC1">Top</A>]</TD>
1224<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
1225<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
1226<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
1227</TR></TABLE>
1228<H2> 1.22 <CODE>log10</CODE>, <CODE>log10f</CODE>---base 10 logarithms </H2>
1229<!--docid::SEC23::-->
1190<STRONG>Synopsis</STRONG> 1230<STRONG>Synopsis</STRONG>
1191 1231<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1192<PRE>
1193#include &#60;math.h&#62;
1194double log10(double <VAR>x</VAR>); 1232double log10(double <VAR>x</VAR>);
1195float log10f(float <VAR>x</VAR>); 1233float log10f(float <VAR>x</VAR>);
1196 1234
1197</PRE> 1235</pre></td></tr></table><STRONG>Description</STRONG><BR>
1198
1199<P>
1200<STRONG>Description</STRONG><BR>
1201<CODE>log10</CODE> returns the base 10 logarithm of <VAR>x</VAR>. 1236<CODE>log10</CODE> returns the base 10 logarithm of <VAR>x</VAR>.
1202It is implemented as <CODE>log(<VAR>x</VAR>) / log(10)</CODE>. 1237It is implemented as <CODE>log(<VAR>x</VAR>) / log(10)</CODE>.
1203
1204
1205<P> 1238<P>
1206<CODE>log10f</CODE> is identical, save that it takes and returns <CODE>float</CODE> values.
1207 1239
1240<CODE>log10f</CODE> is identical, save that it takes and returns <CODE>float</CODE> values.
1241</P><P>
1208 1242
1209<P>
1210<BR> 1243<BR>
1211<STRONG>Returns</STRONG><BR> 1244<STRONG>Returns</STRONG><BR>
1212<CODE>log10</CODE> and <CODE>log10f</CODE> return the calculated value. 1245<CODE>log10</CODE> and <CODE>log10f</CODE> return the calculated value.
1246</P><P>
1213 1247
1214
1215<P>
1216See the description of <CODE>log</CODE> for information on errors. 1248See the description of <CODE>log</CODE> for information on errors.
1249</P><P>
1217 1250
1218
1219<P>
1220<BR> 1251<BR>
1221<STRONG>Portability</STRONG><BR> 1252<STRONG>Portability</STRONG><BR>
1222<CODE>log10</CODE> is ANSI C. <CODE>log10f</CODE> is an extension. 1253<CODE>log10</CODE> is ANSI C. <CODE>log10f</CODE> is an extension.
1223 1254</P><P>
1224 1255
1225<P> 1256<BR>
1226<BR> 1257</P><P>
1227 1258
1228 1259<A NAME="pow"></A>
1229 1260<HR SIZE="6">
1230 1261<A NAME="SEC24"></A>
1231<H2><A NAME="SEC24" HREF="libm_toc.html#TOC24"><CODE>pow</CODE>, <CODE>powf</CODE>---x to the power y</A></H2> 1262<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
1232<P> 1263<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC23"> &lt; </A>]</TD>
1233<A NAME="IDX69"></A> 1264<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC25"> &gt; </A>]</TD>
1234<A NAME="IDX70"></A> 1265<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
1266<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
1267<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
1268<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#SEC1">Top</A>]</TD>
1269<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
1270<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
1271<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
1272</TR></TABLE>
1273<H2> 1.23 <CODE>pow</CODE>, <CODE>powf</CODE>---x to the power y </H2>
1274<!--docid::SEC24::-->
1235<STRONG>Synopsis</STRONG> 1275<STRONG>Synopsis</STRONG>
1236 1276<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1237<PRE>
1238#include &#60;math.h&#62;
1239double pow(double <VAR>x</VAR>, double <VAR>y</VAR>); 1277double pow(double <VAR>x</VAR>, double <VAR>y</VAR>);
1240float pow(float <VAR>x</VAR>, float <VAR>y</VAR>); 1278float pow(float <VAR>x</VAR>, float <VAR>y</VAR>);
1241 1279
1242</PRE> 1280</pre></td></tr></table><STRONG>Description</STRONG><BR>
1243
1244<P>
1245<STRONG>Description</STRONG><BR>
1246<CODE>pow</CODE> and <CODE>powf</CODE> calculate <VAR>x</VAR> raised to the exp1.0nt <VAR>y</VAR>. 1281<CODE>pow</CODE> and <CODE>powf</CODE> calculate <VAR>x</VAR> raised to the exp1.0nt <VAR>y</VAR>.
1247
1248
1249<P> 1282<P>
1283
1250<BR> 1284<BR>
1251<STRONG>Returns</STRONG><BR> 1285<STRONG>Returns</STRONG><BR>
1252On success, <CODE>pow</CODE> and <CODE>powf</CODE> return the value calculated. 1286On success, <CODE>pow</CODE> and <CODE>powf</CODE> return the value calculated.
1287</P><P>
1253 1288
1254
1255<P>
1256When the argument values would produce overflow, <CODE>pow</CODE> 1289When the argument values would produce overflow, <CODE>pow</CODE>
1257returns <CODE>HUGE_VAL</CODE> and set <CODE>errno</CODE> to <CODE>ERANGE</CODE>. If the 1290returns <CODE>HUGE_VAL</CODE> and set <CODE>errno</CODE> to <CODE>ERANGE</CODE>. If the
1258argument <VAR>x</VAR> passed to <CODE>pow</CODE> or <CODE>powf</CODE> is a negative 1291argument <VAR>x</VAR> passed to <CODE>pow</CODE> or <CODE>powf</CODE> is a negative
1259noninteger, and <VAR>y</VAR> is also not an integer, then <CODE>errno</CODE> 1292noninteger, and <VAR>y</VAR> is also not an integer, then <CODE>errno</CODE>
1260is set to <CODE>EDOM</CODE>. If <VAR>x</VAR> and <VAR>y</VAR> are both 0, then 1293is set to <CODE>EDOM</CODE>. If <VAR>x</VAR> and <VAR>y</VAR> are both 0, then
1261<CODE>pow</CODE> and <CODE>powf</CODE> return <CODE>1</CODE>. 1294<CODE>pow</CODE> and <CODE>powf</CODE> return <CODE>1</CODE>.
1295</P><P>
1262 1296
1263
1264<P>
1265You can modify error handling for these functions using <CODE>matherr</CODE>. 1297You can modify error handling for these functions using <CODE>matherr</CODE>.
1298</P><P>
1266 1299
1267
1268<P>
1269<BR> 1300<BR>
1270<STRONG>Portability</STRONG><BR> 1301<STRONG>Portability</STRONG><BR>
1271<CODE>pow</CODE> is ANSI C. <CODE>powf</CODE> is an extension. 1302<CODE>pow</CODE> is ANSI C. <CODE>powf</CODE> is an extension.
1272<BR> 1303<BR>
1273 1304</P><P>
1274 1305
1275 1306<A NAME="remainder"></A>
1276 1307<HR SIZE="6">
1277<H2><A NAME="SEC25" HREF="libm_toc.html#TOC25"><CODE>remainder</CODE>, <CODE>remainderf</CODE>---round and remainder</A></H2> 1308<A NAME="SEC25"></A>
1278<P> 1309<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
1279<A NAME="IDX71"></A> 1310<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC24"> &lt; </A>]</TD>
1280<A NAME="IDX72"></A> 1311<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC26"> &gt; </A>]</TD>
1312<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
1313<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
1314<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
1315<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#SEC1">Top</A>]</TD>
1316<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
1317<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
1318<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
1319</TR></TABLE>
1320<H2> 1.24 <CODE>remainder</CODE>, <CODE>remainderf</CODE>---round and remainder </H2>
1321<!--docid::SEC25::-->
1281<STRONG>Synopsis</STRONG> 1322<STRONG>Synopsis</STRONG>
1282 1323<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1283<PRE>
1284#include &#60;math.h&#62;
1285double remainder(double <VAR>x</VAR>, double <VAR>y</VAR>); 1324double remainder(double <VAR>x</VAR>, double <VAR>y</VAR>);
1286float remainderf(float <VAR>x</VAR>, float <VAR>y</VAR>); 1325float remainderf(float <VAR>x</VAR>, float <VAR>y</VAR>);
1287 1326
1288</PRE> 1327</pre></td></tr></table><STRONG>Description</STRONG><BR>
1289
1290<P>
1291<STRONG>Description</STRONG><BR>
1292<CODE>remainder</CODE> and <CODE>remainderf</CODE> find the remainder of 1328<CODE>remainder</CODE> and <CODE>remainderf</CODE> find the remainder of
1293<VAR>x</VAR>/<VAR>y</VAR>; this value is in the range -<VAR>y</VAR>/2 .. +<VAR>y</VAR>/2. 1329<VAR>x</VAR>/<VAR>y</VAR>; this value is in the range -<VAR>y</VAR>/2 .. +<VAR>y</VAR>/2.
1294
1295
1296<P> 1330<P>
1331
1297<BR> 1332<BR>
1298<STRONG>Returns</STRONG><BR> 1333<STRONG>Returns</STRONG><BR>
1299<CODE>remainder</CODE> returns the integer result as a double. 1334<CODE>remainder</CODE> returns the integer result as a double.
1335</P><P>
1300 1336
1301
1302<P>
1303<BR> 1337<BR>
1304<STRONG>Portability</STRONG><BR> 1338<STRONG>Portability</STRONG><BR>
1305<CODE>remainder</CODE> is a System V release 4. 1339<CODE>remainder</CODE> is a System V release 4.
1306<CODE>remainderf</CODE> is an extension. 1340<CODE>remainderf</CODE> is an extension.
1307 1341</P><P>
1308 1342
1309<P> 1343<BR>
1310<BR> 1344</P><P>
1311 1345
1312 1346<A NAME="sqrt"></A>
1313 1347<HR SIZE="6">
1314 1348<A NAME="SEC26"></A>
1315<H2><A NAME="SEC26" HREF="libm_toc.html#TOC26"><CODE>sqrt</CODE>, <CODE>sqrtf</CODE>---positive square root</A></H2> 1349<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
1316<P> 1350<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC25"> &lt; </A>]</TD>
1317<A NAME="IDX73"></A> 1351<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC27"> &gt; </A>]</TD>
1318<A NAME="IDX74"></A> 1352<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
1353<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
1354<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
1355<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#SEC1">Top</A>]</TD>
1356<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
1357<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
1358<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
1359</TR></TABLE>
1360<H2> 1.25 <CODE>sqrt</CODE>, <CODE>sqrtf</CODE>---positive square root </H2>
1361<!--docid::SEC26::-->
1319<STRONG>Synopsis</STRONG> 1362<STRONG>Synopsis</STRONG>
1320 1363<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1321<PRE>
1322#include &#60;math.h&#62;
1323double sqrt(double <VAR>x</VAR>); 1364double sqrt(double <VAR>x</VAR>);
1324float sqrtf(float <VAR>x</VAR>); 1365float sqrtf(float <VAR>x</VAR>);
1325 1366
1326</PRE> 1367</pre></td></tr></table><STRONG>Description</STRONG><BR>
1327
1328<P>
1329<STRONG>Description</STRONG><BR>
1330<CODE>sqrt</CODE> computes the positive square root of the argument. 1368<CODE>sqrt</CODE> computes the positive square root of the argument.
1331You can modify error handling for this function with 1369You can modify error handling for this function with
1332<CODE>matherr</CODE>. 1370<CODE>matherr</CODE>.
1333
1334
1335<P> 1371<P>
1372
1336<BR> 1373<BR>
1337<STRONG>Returns</STRONG><BR> 1374<STRONG>Returns</STRONG><BR>
1338On success, the square root is returned. If <VAR>x</VAR> is real and 1375On success, the square root is returned. If <VAR>x</VAR> is real and
1339positive, then the result is positive. If <VAR>x</VAR> is real and 1376positive, then the result is positive. If <VAR>x</VAR> is real and
1340negative, the global value <CODE>errno</CODE> is set to <CODE>EDOM</CODE> (domain error). 1377negative, the global value <CODE>errno</CODE> is set to <CODE>EDOM</CODE> (domain error).
1378</P><P>
1341 1379
1342
1343<P>
1344<BR> 1380<BR>
1345<STRONG>Portability</STRONG><BR> 1381<STRONG>Portability</STRONG><BR>
1346<CODE>sqrt</CODE> is ANSI C. <CODE>sqrtf</CODE> is an extension. 1382<CODE>sqrt</CODE> is ANSI C. <CODE>sqrtf</CODE> is an extension.
1347 1383</P><P>
1348 1384
1349<P> 1385<BR>
1350<BR> 1386</P><P>
1351 1387
1352 1388<A NAME="sin"></A>
1353 1389<HR SIZE="6">
1354 1390<A NAME="SEC27"></A>
1355<H2><A NAME="SEC27" HREF="libm_toc.html#TOC27"><CODE>sin</CODE>, <CODE>sinf</CODE>, <CODE>cos</CODE>, <CODE>cosf</CODE>---sine or cosine</A></H2> 1391<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
1356<P> 1392<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC26"> &lt; </A>]</TD>
1357<A NAME="IDX75"></A> 1393<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC28"> &gt; </A>]</TD>
1358<A NAME="IDX76"></A> 1394<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
1359<A NAME="IDX77"></A> 1395<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
1360<A NAME="IDX78"></A> 1396<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
1397<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#SEC1">Top</A>]</TD>
1398<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
1399<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
1400<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
1401</TR></TABLE>
1402<H2> 1.26 <CODE>sin</CODE>, <CODE>sinf</CODE>, <CODE>cos</CODE>, <CODE>cosf</CODE>---sine or cosine </H2>
1403<!--docid::SEC27::-->
1361<STRONG>Synopsis</STRONG> 1404<STRONG>Synopsis</STRONG>
1362 1405<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1363<PRE>
1364#include &#60;math.h&#62;
1365double sin(double <VAR>x</VAR>); 1406double sin(double <VAR>x</VAR>);
1366float sinf(float <VAR>x</VAR>); 1407float sinf(float <VAR>x</VAR>);
1367double cos(double <VAR>x</VAR>); 1408double cos(double <VAR>x</VAR>);
1368float cosf(float <VAR>x</VAR>); 1409float cosf(float <VAR>x</VAR>);
1369 1410
1370</PRE> 1411</pre></td></tr></table><STRONG>Description</STRONG><BR>
1371
1372<P>
1373<STRONG>Description</STRONG><BR>
1374<CODE>sin</CODE> and <CODE>cos</CODE> compute (respectively) the sine and cosine 1412<CODE>sin</CODE> and <CODE>cos</CODE> compute (respectively) the sine and cosine
1375of the argument <VAR>x</VAR>. Angles are specified in radians. 1413of the argument <VAR>x</VAR>. Angles are specified in radians.
1376
1377
1378<P> 1414<P>
1415
1379<CODE>sinf</CODE> and <CODE>cosf</CODE> are identical, save that they take and 1416<CODE>sinf</CODE> and <CODE>cosf</CODE> are identical, save that they take and
1380return <CODE>float</CODE> values. 1417return <CODE>float</CODE> values.
1418</P><P>
1381 1419
1382
1383<P>
1384<BR> 1420<BR>
1385<STRONG>Returns</STRONG><BR> 1421<STRONG>Returns</STRONG><BR>
1386The sine or cosine of <VAR>x</VAR> is returned. 1422The sine or cosine of <VAR>x</VAR> is returned.
1423</P><P>
1387 1424
1388
1389<P>
1390<BR> 1425<BR>
1391<STRONG>Portability</STRONG><BR> 1426<STRONG>Portability</STRONG><BR>
1392<CODE>sin</CODE> and <CODE>cos</CODE> are ANSI C. 1427<CODE>sin</CODE> and <CODE>cos</CODE> are ANSI C.
1393<CODE>sinf</CODE> and <CODE>cosf</CODE> are extensions. 1428<CODE>sinf</CODE> and <CODE>cosf</CODE> are extensions.
1394 1429</P><P>
1395 1430
1396<P> 1431<BR>
1397<BR> 1432</P><P>
1398 1433
1399 1434<A NAME="sinh"></A>
1400 1435<HR SIZE="6">
1401 1436<A NAME="SEC28"></A>
1402<H2><A NAME="SEC28" HREF="libm_toc.html#TOC28"><CODE>sinh</CODE>, <CODE>sinhf</CODE>---hyperbolic sine</A></H2> 1437<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
1403<P> 1438<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC27"> &lt; </A>]</TD>
1404<A NAME="IDX79"></A> 1439<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC29"> &gt; </A>]</TD>
1405<A NAME="IDX80"></A> 1440<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
1441<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
1442<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
1443<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#SEC1">Top</A>]</TD>
1444<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
1445<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
1446<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
1447</TR></TABLE>
1448<H2> 1.27 <CODE>sinh</CODE>, <CODE>sinhf</CODE>---hyperbolic sine </H2>
1449<!--docid::SEC28::-->
1406<STRONG>Synopsis</STRONG> 1450<STRONG>Synopsis</STRONG>
1407 1451<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1408<PRE>
1409#include &#60;math.h&#62;
1410double sinh(double <VAR>x</VAR>); 1452double sinh(double <VAR>x</VAR>);
1411float sinhf(float <VAR>x</VAR>); 1453float sinhf(float <VAR>x</VAR>);
1412 1454
1413</PRE> 1455</pre></td></tr></table><STRONG>Description</STRONG><BR>
1414
1415<P>
1416<STRONG>Description</STRONG><BR>
1417<CODE>sinh</CODE> computes the hyperbolic sine of the argument <VAR>x</VAR>. 1456<CODE>sinh</CODE> computes the hyperbolic sine of the argument <VAR>x</VAR>.
1418Angles are specified in radians. <CODE>sinh</CODE>(<VAR>x</VAR>) is defined as 1457Angles are specified in radians. <CODE>sinh</CODE>(<VAR>x</VAR>) is defined as
1419
1420
1421<P> 1458<P>
1422<CODE>sinhf</CODE> is identical, save that it takes and returns <CODE>float</CODE> values.
1423 1459
1460<CODE>sinhf</CODE> is identical, save that it takes and returns <CODE>float</CODE> values.
1461</P><P>
1424 1462
1425<P>
1426<BR> 1463<BR>
1427<STRONG>Returns</STRONG><BR> 1464<STRONG>Returns</STRONG><BR>
1428The hyperbolic sine of <VAR>x</VAR> is returned. 1465The hyperbolic sine of <VAR>x</VAR> is returned.
1466</P><P>
1429 1467
1430
1431<P>
1432When the correct result is too large to be representable (an 1468When the correct result is too large to be representable (an
1433overflow), <CODE>sinh</CODE> returns <CODE>HUGE_VAL</CODE> with the 1469overflow), <CODE>sinh</CODE> returns <CODE>HUGE_VAL</CODE> with the
1434appropriate sign, and sets the global value <CODE>errno</CODE> to 1470appropriate sign, and sets the global value <CODE>errno</CODE> to
1435<CODE>ERANGE</CODE>. 1471<CODE>ERANGE</CODE>.
1472</P><P>
1436 1473
1437
1438<P>
1439You can modify error handling for these functions with <CODE>matherr</CODE>. 1474You can modify error handling for these functions with <CODE>matherr</CODE>.
1475</P><P>
1440 1476
1441
1442<P>
1443<BR> 1477<BR>
1444<STRONG>Portability</STRONG><BR> 1478<STRONG>Portability</STRONG><BR>
1445<CODE>sinh</CODE> is ANSI C. 1479<CODE>sinh</CODE> is ANSI C.
1446<CODE>sinhf</CODE> is an extension. 1480<CODE>sinhf</CODE> is an extension.
1447 1481</P><P>
1448 1482
1449<P> 1483<BR>
1450<BR> 1484</P><P>
1451 1485
1452 1486<A NAME="tan"></A>
1453 1487<HR SIZE="6">
1454 1488<A NAME="SEC29"></A>
1455<H2><A NAME="SEC29" HREF="libm_toc.html#TOC29"><CODE>tan</CODE>, <CODE>tanf</CODE>---tangent</A></H2> 1489<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
1456<P> 1490<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC28"> &lt; </A>]</TD>
1457<A NAME="IDX81"></A> 1491<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC30"> &gt; </A>]</TD>
1458<A NAME="IDX82"></A> 1492<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
1493<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
1494<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
1495<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#SEC1">Top</A>]</TD>
1496<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
1497<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
1498<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
1499</TR></TABLE>
1500<H2> 1.28 <CODE>tan</CODE>, <CODE>tanf</CODE>---tangent </H2>
1501<!--docid::SEC29::-->
1459<STRONG>Synopsis</STRONG> 1502<STRONG>Synopsis</STRONG>
1460 1503<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1461<PRE>
1462#include &#60;math.h&#62;
1463double tan(double <VAR>x</VAR>); 1504double tan(double <VAR>x</VAR>);
1464float tanf(float <VAR>x</VAR>); 1505float tanf(float <VAR>x</VAR>);
1465 1506
1466</PRE> 1507</pre></td></tr></table><STRONG>Description</STRONG><BR>
1467
1468<P>
1469<STRONG>Description</STRONG><BR>
1470<CODE>tan</CODE> computes the tangent of the argument <VAR>x</VAR>. 1508<CODE>tan</CODE> computes the tangent of the argument <VAR>x</VAR>.
1471Angles are specified in radians. 1509Angles are specified in radians.
1472
1473
1474<P> 1510<P>
1475<CODE>tanf</CODE> is identical, save that it takes and returns <CODE>float</CODE> values.
1476 1511
1512<CODE>tanf</CODE> is identical, save that it takes and returns <CODE>float</CODE> values.
1513</P><P>
1477 1514
1478<P>
1479<BR> 1515<BR>
1480<STRONG>Returns</STRONG><BR> 1516<STRONG>Returns</STRONG><BR>
1481The tangent of <VAR>x</VAR> is returned. 1517The tangent of <VAR>x</VAR> is returned.
1518</P><P>
1482 1519
1483
1484<P>
1485<BR> 1520<BR>
1486<STRONG>Portability</STRONG><BR> 1521<STRONG>Portability</STRONG><BR>
1487<CODE>tan</CODE> is ANSI. <CODE>tanf</CODE> is an extension. 1522<CODE>tan</CODE> is ANSI. <CODE>tanf</CODE> is an extension.
1488 1523</P><P>
1489 1524
1490<P> 1525<BR>
1491<BR> 1526</P><P>
1492 1527
1493 1528<A NAME="tanh"></A>
1494 1529<HR SIZE="6">
1495 1530<A NAME="SEC30"></A>
1496<H2><A NAME="SEC30" HREF="libm_toc.html#TOC30"><CODE>tanh</CODE>, <CODE>tanhf</CODE>---hyperbolic tangent</A></H2> 1531<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
1497<P> 1532<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC29"> &lt; </A>]</TD>
1498<A NAME="IDX83"></A> 1533<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC31"> &gt; </A>]</TD>
1499<A NAME="IDX84"></A> 1534<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
1535<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
1536<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
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1538<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
1539<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
1540<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
1541</TR></TABLE>
1542<H2> 1.29 <CODE>tanh</CODE>, <CODE>tanhf</CODE>---hyperbolic tangent </H2>
1543<!--docid::SEC30::-->
1500<STRONG>Synopsis</STRONG> 1544<STRONG>Synopsis</STRONG>
1501 1545<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1502<PRE>
1503#include &#60;math.h&#62;
1504double tanh(double <VAR>x</VAR>); 1546double tanh(double <VAR>x</VAR>);
1505float tanhf(float <VAR>x</VAR>); 1547float tanhf(float <VAR>x</VAR>);
1506 1548
1507</PRE> 1549</pre></td></tr></table><STRONG>Description</STRONG><BR>
1508
1509<P> 1550<P>
1510<STRONG>Description</STRONG><BR>
1511
1512 1551
1513<P>
1514<CODE>tanh</CODE> computes the hyperbolic tangent of 1552<CODE>tanh</CODE> computes the hyperbolic tangent of
1515the argument <VAR>x</VAR>. Angles are specified in radians. 1553the argument <VAR>x</VAR>. Angles are specified in radians.
1554</P><P>
1516 1555
1517
1518<P>
1519<CODE>tanh(<VAR>x</VAR>)</CODE> is defined as 1556<CODE>tanh(<VAR>x</VAR>)</CODE> is defined as
1557<TABLE><tr><td>&nbsp;</td><td class=smallexample><FONT SIZE=-1><pre> sinh(<VAR>x</VAR>)/cosh(<VAR>x</VAR>)
1558</FONT></pre></td></tr></table><CODE>tanhf</CODE> is identical, save that it takes and returns <CODE>float</CODE> values.
1559</P><P>
1520 1560
1521<PRE>
1522 sinh(<VAR>x</VAR>)/cosh(<VAR>x</VAR>)
1523</PRE>
1524
1525<P>
1526<CODE>tanhf</CODE> is identical, save that it takes and returns <CODE>float</CODE> values.
1527
1528
1529<P>
1530<BR> 1561<BR>
1531<STRONG>Returns</STRONG><BR> 1562<STRONG>Returns</STRONG><BR>
1532The hyperbolic tangent of <VAR>x</VAR> is returned. 1563The hyperbolic tangent of <VAR>x</VAR> is returned.
1564</P><P>
1533 1565
1534
1535<P>
1536<BR> 1566<BR>
1537<STRONG>Portability</STRONG><BR> 1567<STRONG>Portability</STRONG><BR>
1538<CODE>tanh</CODE> is ANSI C. <CODE>tanhf</CODE> is an extension. 1568<CODE>tanh</CODE> is ANSI C. <CODE>tanhf</CODE> is an extension.
1539 1569</P><P>
1540 1570
1541<P> 1571<BR>
1542<BR> 1572<A NAME="cbrt"></A>
1543 1573<HR SIZE="6">
1544 1574<A NAME="SEC31"></A>
1545<H2><A NAME="SEC31" HREF="libm_toc.html#TOC31"><CODE>cbrt</CODE>, <CODE>cbrtf</CODE>---cube root</A></H2> 1575<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
1546<P> 1576<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC30"> &lt; </A>]</TD>
1547<A NAME="IDX85"></A> 1577<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC32"> &gt; </A>]</TD>
1548<A NAME="IDX86"></A> 1578<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
1579<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
1580<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
1581<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#SEC1">Top</A>]</TD>
1582<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
1583<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
1584<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
1585</TR></TABLE>
1586<H2> 1.30 <CODE>cbrt</CODE>, <CODE>cbrtf</CODE>---cube root </H2>
1587<!--docid::SEC31::-->
1549<STRONG>Synopsis</STRONG> 1588<STRONG>Synopsis</STRONG>
1550 1589<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1551<PRE>
1552#include &#60;math.h&#62;
1553double cbrt(double <VAR>x</VAR>); 1590double cbrt(double <VAR>x</VAR>);
1554float cbrtf(float <VAR>x</VAR>); 1591float cbrtf(float <VAR>x</VAR>);
1555 1592
1556</PRE> 1593</pre></td></tr></table><STRONG>Description</STRONG><BR>
1557
1558<P>
1559<STRONG>Description</STRONG><BR>
1560<CODE>cbrt</CODE> computes the cube root of the argument. 1594<CODE>cbrt</CODE> computes the cube root of the argument.
1561
1562
1563<P> 1595<P>
1596
1564<BR> 1597<BR>
1565<STRONG>Returns</STRONG><BR> 1598<STRONG>Returns</STRONG><BR>
1566The cube root is returned. 1599The cube root is returned.
1600</P><P>
1567 1601
1568
1569<P>
1570<BR> 1602<BR>
1571<STRONG>Portability</STRONG><BR> 1603<STRONG>Portability</STRONG><BR>
1572<CODE>cbrt</CODE> is in System V release 4. <CODE>cbrtf</CODE> is an extension. 1604<CODE>cbrt</CODE> is in System V release 4. <CODE>cbrtf</CODE> is an extension.
1573 1605</P><P>
1574 1606
1575<P> 1607<BR>
1576<BR> 1608<A NAME="copysign"></A>
1577 1609<HR SIZE="6">
1578 1610<A NAME="SEC32"></A>
1579<H2><A NAME="SEC32" HREF="libm_toc.html#TOC32"><CODE>copysign</CODE>, <CODE>copysignf</CODE>---sign of <VAR>y</VAR>, magnitude of <VAR>x</VAR></A></H2> 1611<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
1580<P> 1612<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC31"> &lt; </A>]</TD>
1581<A NAME="IDX87"></A> 1613<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC33"> &gt; </A>]</TD>
1582<A NAME="IDX88"></A> 1614<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
1615<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
1616<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
1617<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#SEC1">Top</A>]</TD>
1618<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
1619<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
1620<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
1621</TR></TABLE>
1622<H2> 1.31 <CODE>copysign</CODE>, <CODE>copysignf</CODE>---sign of <VAR>y</VAR>, magnitude of <VAR>x</VAR> </H2>
1623<!--docid::SEC32::-->
1583<STRONG>Synopsis</STRONG> 1624<STRONG>Synopsis</STRONG>
1584 1625<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1585<PRE>
1586#include &#60;math.h&#62;
1587double copysign (double <VAR>x</VAR>, double <VAR>y</VAR>); 1626double copysign (double <VAR>x</VAR>, double <VAR>y</VAR>);
1588float copysignf (float <VAR>x</VAR>, float <VAR>y</VAR>); 1627float copysignf (float <VAR>x</VAR>, float <VAR>y</VAR>);
1589 1628
1590</PRE> 1629</pre></td></tr></table><STRONG>Description</STRONG><BR>
1591
1592<P>
1593<STRONG>Description</STRONG><BR>
1594<CODE>copysign</CODE> constructs a number with the magnitude (absolute value) 1630<CODE>copysign</CODE> constructs a number with the magnitude (absolute value)
1595of its first argument, <VAR>x</VAR>, and the sign of its second argument, 1631of its first argument, <VAR>x</VAR>, and the sign of its second argument,
1596<VAR>y</VAR>. 1632<VAR>y</VAR>.
1597
1598
1599<P> 1633<P>
1634
1600<CODE>copysignf</CODE> does the same thing; the two functions differ only in 1635<CODE>copysignf</CODE> does the same thing; the two functions differ only in
1601the type of their arguments and result. 1636the type of their arguments and result.
1637</P><P>
1602 1638
1603
1604<P>
1605<BR> 1639<BR>
1606<STRONG>Returns</STRONG><BR> 1640<STRONG>Returns</STRONG><BR>
1607<CODE>copysign</CODE> returns a <CODE>double</CODE> with the magnitude of 1641<CODE>copysign</CODE> returns a <CODE>double</CODE> with the magnitude of
1608<VAR>x</VAR> and the sign of <VAR>y</VAR>. 1642<VAR>x</VAR> and the sign of <VAR>y</VAR>.
1609<CODE>copysignf</CODE> returns a <CODE>float</CODE> with the magnitude of 1643<CODE>copysignf</CODE> returns a <CODE>float</CODE> with the magnitude of
1610<VAR>x</VAR> and the sign of <VAR>y</VAR>. 1644<VAR>x</VAR> and the sign of <VAR>y</VAR>.
1645</P><P>
1611 1646
1612
1613<P>
1614<BR> 1647<BR>
1615<STRONG>Portability</STRONG><BR> 1648<STRONG>Portability</STRONG><BR>
1616<CODE>copysign</CODE> is not required by either ANSI C or the System V Interface 1649<CODE>copysign</CODE> is not required by either ANSI C or the System V Interface
1617Definition (Issue 2). 1650Definition (Issue 2).
1618 1651</P><P>
1619 1652
1620<P> 1653<BR>
1621<BR> 1654<A NAME="expm1"></A>
1622 1655<HR SIZE="6">
1623 1656<A NAME="SEC33"></A>
1624<H2><A NAME="SEC33" HREF="libm_toc.html#TOC33"><CODE>expm1</CODE>, <CODE>expm1f</CODE>---exponential minus 1</A></H2> 1657<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
1625<P> 1658<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC32"> &lt; </A>]</TD>
1626<A NAME="IDX89"></A> 1659<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC34"> &gt; </A>]</TD>
1627<A NAME="IDX90"></A> 1660<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
1661<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
1662<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
1663<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#SEC1">Top</A>]</TD>
1664<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
1665<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
1666<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
1667</TR></TABLE>
1668<H2> 1.32 <CODE>expm1</CODE>, <CODE>expm1f</CODE>---exponential minus 1 </H2>
1669<!--docid::SEC33::-->
1628<STRONG>Synopsis</STRONG> 1670<STRONG>Synopsis</STRONG>
1629 1671<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1630<PRE>
1631#include &#60;math.h&#62;
1632double expm1(double <VAR>x</VAR>); 1672double expm1(double <VAR>x</VAR>);
1633float expm1f(float <VAR>x</VAR>); 1673float expm1f(float <VAR>x</VAR>);
1634 1674
1635</PRE> 1675</pre></td></tr></table><STRONG>Description</STRONG><BR>
1636
1637<P>
1638<STRONG>Description</STRONG><BR>
1639<CODE>expm1</CODE> and <CODE>expm1f</CODE> calculate the exponential of <VAR>x</VAR> 1676<CODE>expm1</CODE> and <CODE>expm1f</CODE> calculate the exponential of <VAR>x</VAR>
1640and subtract 1, that is, 1677and subtract 1, that is,
1641is the base of the natural system of logarithms, approximately 1678is the base of the natural system of logarithms, approximately
16422.71828). The result is accurate even for small values of 16792.71828). The result is accurate even for small values of
1643<VAR>x</VAR>, where using <CODE>exp(<VAR>x</VAR>)-1</CODE> would lose many 1680<VAR>x</VAR>, where using <CODE>exp(<VAR>x</VAR>)-1</CODE> would lose many
1644significant digits. 1681significant digits.
1645
1646
1647<P> 1682<P>
1683
1648<BR> 1684<BR>
1649<STRONG>Returns</STRONG><BR> 1685<STRONG>Returns</STRONG><BR>
1650e raised to the power <VAR>x</VAR>, minus 1. 1686e raised to the power <VAR>x</VAR>, minus 1.
1687</P><P>
1651 1688
1652
1653<P>
1654<BR> 1689<BR>
1655<STRONG>Portability</STRONG><BR> 1690<STRONG>Portability</STRONG><BR>
1656Neither <CODE>expm1</CODE> nor <CODE>expm1f</CODE> is required by ANSI C or by 1691Neither <CODE>expm1</CODE> nor <CODE>expm1f</CODE> is required by ANSI C or by
1657the System V Interface Definition (Issue 2). 1692the System V Interface Definition (Issue 2).
1658 1693</P><P>
1659 1694
1660<P> 1695<BR>
1661<BR> 1696<A NAME="ilogb"></A>
1662 1697<HR SIZE="6">
1663 1698<A NAME="SEC34"></A>
1664<H2><A NAME="SEC34" HREF="libm_toc.html#TOC34"><CODE>ilogb</CODE>, <CODE>ilogbf</CODE>---get exponent of floating point number</A></H2> 1699<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
1665<P> 1700<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC33"> &lt; </A>]</TD>
1666<A NAME="IDX91"></A> 1701<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC35"> &gt; </A>]</TD>
1667<A NAME="IDX92"></A> 1702<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
1703<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
1704<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
1705<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#SEC1">Top</A>]</TD>
1706<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
1707<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
1708<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
1709</TR></TABLE>
1710<H2> 1.33 <CODE>ilogb</CODE>, <CODE>ilogbf</CODE>---get exponent of floating point number </H2>
1711<!--docid::SEC34::-->
1668<STRONG>Synopsis</STRONG> 1712<STRONG>Synopsis</STRONG>
1669 1713<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1670<PRE>
1671#include &#60;math.h&#62;
1672int ilogb(double <VAR>val</VAR>); 1714int ilogb(double <VAR>val</VAR>);
1673int ilogbf(float <VAR>val</VAR>); 1715int ilogbf(float <VAR>val</VAR>);
1674 1716
1675</PRE> 1717</pre></td></tr></table><STRONG>Description</STRONG><BR>
1676
1677<P> 1718<P>
1678<STRONG>Description</STRONG><BR>
1679
1680 1719
1681<P>
1682All non zero, normal numbers can be described as <VAR>m</VAR> * 1720All non zero, normal numbers can be described as <VAR>m</VAR> *
16832**<VAR>p</VAR>. <CODE>ilogb</CODE> and <CODE>ilogbf</CODE> examine the argument 17212**<VAR>p</VAR>. <CODE>ilogb</CODE> and <CODE>ilogbf</CODE> examine the argument
1684<VAR>val</VAR>, and return <VAR>p</VAR>. The functions <CODE>frexp</CODE> and 1722<VAR>val</VAR>, and return <VAR>p</VAR>. The functions <CODE>frexp</CODE> and
1685<CODE>frexpf</CODE> are similar to <CODE>ilogb</CODE> and <CODE>ilogbf</CODE>, but also 1723<CODE>frexpf</CODE> are similar to <CODE>ilogb</CODE> and <CODE>ilogbf</CODE>, but also
1686return <VAR>m</VAR>. 1724return <VAR>m</VAR>.
1725</P><P>
1687 1726
1688
1689<P>
1690<BR> 1727<BR>
1691<STRONG>Returns</STRONG><BR> 1728<STRONG>Returns</STRONG><BR>
1729</P><P>
1692 1730
1693
1694<P>
1695<CODE>ilogb</CODE> and <CODE>ilogbf</CODE> return the power of two used to form the 1731<CODE>ilogb</CODE> and <CODE>ilogbf</CODE> return the power of two used to form the
1696floating point argument. If <VAR>val</VAR> is <CODE>0</CODE>, they return <CODE>- 1732floating point argument. If <VAR>val</VAR> is <CODE>0</CODE>, they return <CODE>-
1697INT_MAX</CODE> (<CODE>INT_MAX</CODE> is defined in limits.h). If <VAR>val</VAR> is 1733INT_MAX</CODE> (<CODE>INT_MAX</CODE> is defined in limits.h). If <VAR>val</VAR> is
1698infinite, or NaN, they return <CODE>INT_MAX</CODE>. 1734infinite, or NaN, they return <CODE>INT_MAX</CODE>.
1735</P><P>
1699 1736
1700
1701<P>
1702<BR> 1737<BR>
1703<STRONG>Portability</STRONG><BR> 1738<STRONG>Portability</STRONG><BR>
1704Neither <CODE>ilogb</CODE> nor <CODE>ilogbf</CODE> is required by ANSI C or by 1739Neither <CODE>ilogb</CODE> nor <CODE>ilogbf</CODE> is required by ANSI C or by
1705the System V Interface Definition (Issue 2). 1740the System V Interface Definition (Issue 2).
1706<BR> 1741<BR>
1707 1742<A NAME="infinity"></A>
1708 1743<HR SIZE="6">
1709<H2><A NAME="SEC35" HREF="libm_toc.html#TOC35"><CODE>infinity</CODE>, <CODE>infinityf</CODE>---representation of infinity</A></H2> 1744<A NAME="SEC35"></A>
1710<P> 1745<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
1711<A NAME="IDX93"></A> 1746<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC34"> &lt; </A>]</TD>
1712<A NAME="IDX94"></A> 1747<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC36"> &gt; </A>]</TD>
1748<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
1749<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
1750<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
1751<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#SEC1">Top</A>]</TD>
1752<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
1753<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
1754<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
1755</TR></TABLE>
1756<H2> 1.34 <CODE>infinity</CODE>, <CODE>infinityf</CODE>---representation of infinity </H2>
1757<!--docid::SEC35::-->
1713<STRONG>Synopsis</STRONG> 1758<STRONG>Synopsis</STRONG>
1714 1759<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1715<PRE>
1716#include &#60;math.h&#62;
1717double infinity(void); 1760double infinity(void);
1718float infinityf(void); 1761float infinityf(void);
1719 1762
1720</PRE> 1763</pre></td></tr></table><STRONG>Description</STRONG><BR>
1721
1722<P>
1723<STRONG>Description</STRONG><BR>
1724<CODE>infinity</CODE> and <CODE>infinityf</CODE> return the special number IEEE 1764<CODE>infinity</CODE> and <CODE>infinityf</CODE> return the special number IEEE
1725infinity in double and single precision arithmetic 1765infinity in double and single precision arithmetic
1726respectivly. 1766respectivly.
1727
1728
1729<P> 1767<P>
1730<BR>
1731 1768
1732 1769<BR>
1733<H2><A NAME="SEC36" HREF="libm_toc.html#TOC36"><CODE>log1p</CODE>, <CODE>log1pf</CODE>---log of <CODE>1 + <VAR>x</VAR></CODE></A></H2> 1770<A NAME="log1p"></A>
1734<P> 1771<HR SIZE="6">
1735<A NAME="IDX95"></A> 1772<A NAME="SEC36"></A>
1736<A NAME="IDX96"></A> 1773<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
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1783</TR></TABLE>
1784<H2> 1.35 <CODE>log1p</CODE>, <CODE>log1pf</CODE>---log of <CODE>1 + <VAR>x</VAR></CODE> </H2>
1785<!--docid::SEC36::-->
1737<STRONG>Synopsis</STRONG> 1786<STRONG>Synopsis</STRONG>
1738 1787<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1739<PRE>
1740#include &#60;math.h&#62;
1741double log1p(double <VAR>x</VAR>); 1788double log1p(double <VAR>x</VAR>);
1742float log1pf(float <VAR>x</VAR>); 1789float log1pf(float <VAR>x</VAR>);
1743 1790
1744</PRE> 1791</pre></td></tr></table><STRONG>Description</STRONG><BR>
1745
1746<P>
1747<STRONG>Description</STRONG><BR>
1748<CODE>log1p</CODE> calculates 1792<CODE>log1p</CODE> calculates
1749the natural logarithm of <CODE>1+<VAR>x</VAR></CODE>. You can use <CODE>log1p</CODE> rather 1793the natural logarithm of <CODE>1+<VAR>x</VAR></CODE>. You can use <CODE>log1p</CODE> rather
1750than `<CODE>log(1+<VAR>x</VAR>)</CODE>' for greater precision when <VAR>x</VAR> is very 1794than `<CODE>log(1+<VAR>x</VAR>)</CODE>' for greater precision when <VAR>x</VAR> is very
1751small. 1795small.
1752
1753
1754<P> 1796<P>
1797
1755<CODE>log1pf</CODE> calculates the same thing, but accepts and returns 1798<CODE>log1pf</CODE> calculates the same thing, but accepts and returns
1756<CODE>float</CODE> values rather than <CODE>double</CODE>. 1799<CODE>float</CODE> values rather than <CODE>double</CODE>.
1800</P><P>
1757 1801
1758
1759<P>
1760<BR> 1802<BR>
1761<STRONG>Returns</STRONG><BR> 1803<STRONG>Returns</STRONG><BR>
1762<CODE>log1p</CODE> returns a <CODE>double</CODE>, the natural log of <CODE>1+<VAR>x</VAR></CODE>. 1804<CODE>log1p</CODE> returns a <CODE>double</CODE>, the natural log of <CODE>1+<VAR>x</VAR></CODE>.
1763<CODE>log1pf</CODE> returns a <CODE>float</CODE>, the natural log of <CODE>1+<VAR>x</VAR></CODE>. 1805<CODE>log1pf</CODE> returns a <CODE>float</CODE>, the natural log of <CODE>1+<VAR>x</VAR></CODE>.
1806</P><P>
1764 1807
1765
1766<P>
1767<BR> 1808<BR>
1768<STRONG>Portability</STRONG><BR> 1809<STRONG>Portability</STRONG><BR>
1769Neither <CODE>log1p</CODE> nor <CODE>log1pf</CODE> is required by ANSI C or by the System V 1810Neither <CODE>log1p</CODE> nor <CODE>log1pf</CODE> is required by ANSI C or by the System V
1770Interface Definition (Issue 2). 1811Interface Definition (Issue 2).
1771 1812</P><P>
1772 1813
1773<P> 1814<BR>
1774<BR> 1815<A NAME="matherr"></A>
1775 1816<HR SIZE="6">
1776 1817<A NAME="SEC37"></A>
1777<H2><A NAME="SEC37" HREF="libm_toc.html#TOC37"><CODE>matherr</CODE>---modifiable math error handler</A></H2> 1818<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
1778<P> 1819<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC36"> &lt; </A>]</TD>
1779<A NAME="IDX97"></A> 1820<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC38"> &gt; </A>]</TD>
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1825<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
1826<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
1827<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
1828</TR></TABLE>
1829<H2> 1.36 <CODE>matherr</CODE>---modifiable math error handler </H2>
1830<!--docid::SEC37::-->
1780<STRONG>Synopsis</STRONG> 1831<STRONG>Synopsis</STRONG>
1781 1832<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1782<PRE>
1783#include &#60;math.h&#62;
1784int matherr(struct exception *<VAR>e</VAR>); 1833int matherr(struct exception *<VAR>e</VAR>);
1785 1834
1786</PRE> 1835</pre></td></tr></table><STRONG>Description</STRONG><BR>
1787
1788<P>
1789<STRONG>Description</STRONG><BR>
1790<CODE>matherr</CODE> is called whenever a math library function generates an error. 1836<CODE>matherr</CODE> is called whenever a math library function generates an error.
1791You can replace <CODE>matherr</CODE> by your own subroutine to customize 1837You can replace <CODE>matherr</CODE> by your own subroutine to customize
1792error treatment. The customized <CODE>matherr</CODE> must return 0 if 1838error treatment. The customized <CODE>matherr</CODE> must return 0 if
1793it fails to resolve the error, and non-zero if the error is resolved. 1839it fails to resolve the error, and non-zero if the error is resolved.
1794
1795
1796<P> 1840<P>
1841
1797When <CODE>matherr</CODE> returns a nonzero value, no error message is printed 1842When <CODE>matherr</CODE> returns a nonzero value, no error message is printed
1798and the value of <CODE>errno</CODE> is not modified. You can accomplish either 1843and the value of <CODE>errno</CODE> is not modified. You can accomplish either
1799or both of these things in your own <CODE>matherr</CODE> using the information 1844or both of these things in your own <CODE>matherr</CODE> using the information
1800passed in the structure <CODE>*<VAR>e</VAR></CODE>. 1845passed in the structure <CODE>*<VAR>e</VAR></CODE>.
1846</P><P>
1801 1847
1802
1803<P>
1804This is the <CODE>exception</CODE> structure (defined in `<CODE>math.h</CODE>'): 1848This is the <CODE>exception</CODE> structure (defined in `<CODE>math.h</CODE>'):
1805 1849<TABLE><tr><td>&nbsp;</td><td class=smallexample><FONT SIZE=-1><pre> struct exception {
1806<PRE>
1807 struct exception {
1808 int type; 1850 int type;
1809 char *name; 1851 char *name;
1810 double arg1, arg2, retval; 1852 double arg1, arg2, retval;
1811 int err; 1853 int err;
1812 }; 1854 };
1813</PRE> 1855</FONT></pre></td></tr></table></P><P>
1814 1856
1815<P>
1816The members of the exception structure have the following meanings: 1857The members of the exception structure have the following meanings:
1817<DL COMPACT> 1858<DL COMPACT>
1818 1859
1819<DT><CODE>type</CODE> 1860<DT><CODE>type</CODE>
1820<DD> 1861<DD>The type of mathematical error that occured; macros encoding error
1821The type of mathematical error that occured; macros encoding error
1822types are also defined in `<CODE>math.h</CODE>'. 1862types are also defined in `<CODE>math.h</CODE>'.
1863<P>
1823 1864
1824<DT><CODE>name</CODE> 1865<DT><CODE>name</CODE>
1825<DD> 1866<DD>a pointer to a null-terminated string holding the
1826a pointer to a null-terminated string holding the
1827name of the math library function where the error occurred. 1867name of the math library function where the error occurred.
1868<P>
1828 1869
1829<DT><CODE>arg1, arg2</CODE> 1870<DT><CODE>arg1, arg2</CODE>
1830<DD> 1871<DD>The arguments which caused the error.
1831The arguments which caused the error. 1872<P>
1832 1873
1833<DT><CODE>retval</CODE> 1874<DT><CODE>retval</CODE>
1834<DD> 1875<DD>The error return value (what the calling function will return).
1835The error return value (what the calling function will return). 1876<P>
1836 1877
1837<DT><CODE>err</CODE> 1878<DT><CODE>err</CODE>
1838<DD> 1879<DD>If set to be non-zero, this is the new value assigned to <CODE>errno</CODE>.
1839If set to be non-zero, this is the new value assigned to <CODE>errno</CODE>.
1840</DL> 1880</DL>
1841
1842<P> 1881<P>
1882
1843The error types defined in `<CODE>math.h</CODE>' represent possible mathematical 1883The error types defined in `<CODE>math.h</CODE>' represent possible mathematical
1844errors as follows: 1884errors as follows:
1845 1885</P><P>
1846 1886
1847<DL COMPACT> 1887<DL COMPACT>
1848 1888
1849<DT><CODE>DOMAIN</CODE> 1889<DT><CODE>DOMAIN</CODE>
1850<DD> 1890<DD>An argument was not in the domain of the function; e.g. <CODE>log(-1.0)</CODE>.
1851An argument was not in the domain of the function; e.g. <CODE>log(-1.0)</CODE>. 1891<P>
1852 1892
1853<DT><CODE>SING</CODE> 1893<DT><CODE>SING</CODE>
1854<DD> 1894<DD>The requested calculation would result in a singularity; e.g. <CODE>pow(0.0,-2.0)</CODE>
1855The requested calculation would result in a singularity; e.g. <CODE>pow(0.0,-2.0)</CODE> 1895<P>
1856 1896
1857<DT><CODE>OVERFLOW</CODE> 1897<DT><CODE>OVERFLOW</CODE>
1858<DD> 1898<DD>A calculation would produce a result too large to represent; e.g.
1859A calculation would produce a result too large to represent; e.g.
1860<CODE>exp(1000.0)</CODE>. 1899<CODE>exp(1000.0)</CODE>.
1900<P>
1861 1901
1862<DT><CODE>UNDERFLOW</CODE> 1902<DT><CODE>UNDERFLOW</CODE>
1863<DD> 1903<DD>A calculation would produce a result too small to represent; e.g.
1864A calculation would produce a result too small to represent; e.g.
1865<CODE>exp(-1000.0)</CODE>. 1904<CODE>exp(-1000.0)</CODE>.
1905<P>
1866 1906
1867<DT><CODE>TLOSS</CODE> 1907<DT><CODE>TLOSS</CODE>
1868<DD> 1908<DD>Total loss of precision. The result would have no significant digits;
1869Total loss of precision. The result would have no significant digits;
1870e.g. <CODE>sin(10e70)</CODE>. 1909e.g. <CODE>sin(10e70)</CODE>.
1910<P>
1871 1911
1872<DT><CODE>PLOSS</CODE> 1912<DT><CODE>PLOSS</CODE>
1873<DD> 1913<DD>Partial loss of precision.
1874Partial loss of precision.
1875</DL> 1914</DL>
1876
1877<P> 1915<P>
1916
1878<BR> 1917<BR>
1879<STRONG>Returns</STRONG><BR> 1918<STRONG>Returns</STRONG><BR>
1880The library definition for <CODE>matherr</CODE> returns <CODE>0</CODE> in all cases. 1919The library definition for <CODE>matherr</CODE> returns <CODE>0</CODE> in all cases.
1920</P><P>
1881 1921
1882
1883<P>
1884You can change the calling function's result from a customized <CODE>matherr</CODE> 1922You can change the calling function's result from a customized <CODE>matherr</CODE>
1885by modifying <CODE>e-&#62;retval</CODE>, which propagates backs to the caller. 1923by modifying <CODE>e-&#62;retval</CODE>, which propagates backs to the caller.
1924</P><P>
1886 1925
1887
1888<P>
1889If <CODE>matherr</CODE> returns <CODE>0</CODE> (indicating that it was not able to resolve 1926If <CODE>matherr</CODE> returns <CODE>0</CODE> (indicating that it was not able to resolve
1890the error) the caller sets <CODE>errno</CODE> to an appropriate value, and prints 1927the error) the caller sets <CODE>errno</CODE> to an appropriate value, and prints
1891an error message. 1928an error message.
1929</P><P>
1892 1930
1893
1894<P>
1895<BR> 1931<BR>
1896<STRONG>Portability</STRONG><BR> 1932<STRONG>Portability</STRONG><BR>
1897<CODE>matherr</CODE> is not ANSI C. 1933<CODE>matherr</CODE> is not ANSI C.
1898 1934</P><P>
1899 1935
1900<P> 1936<BR>
1901<BR> 1937<A NAME="modf"></A>
1902 1938<HR SIZE="6">
1903 1939<A NAME="SEC38"></A>
1904<H2><A NAME="SEC38" HREF="libm_toc.html#TOC38"><CODE>modf</CODE>, <CODE>modff</CODE>---split fractional and integer parts</A></H2> 1940<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
1905<P> 1941<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC37"> &lt; </A>]</TD>
1906<A NAME="IDX98"></A> 1942<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC39"> &gt; </A>]</TD>
1907<A NAME="IDX99"></A> 1943<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
1944<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
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1946<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#SEC1">Top</A>]</TD>
1947<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
1948<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
1949<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
1950</TR></TABLE>
1951<H2> 1.37 <CODE>modf</CODE>, <CODE>modff</CODE>---split fractional and integer parts </H2>
1952<!--docid::SEC38::-->
1908<STRONG>Synopsis</STRONG> 1953<STRONG>Synopsis</STRONG>
1909 1954<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1910<PRE>
1911#include &#60;math.h&#62;
1912double modf(double <VAR>val</VAR>, double *<VAR>ipart</VAR>); 1955double modf(double <VAR>val</VAR>, double *<VAR>ipart</VAR>);
1913float modff(float <VAR>val</VAR>, float *<VAR>ipart</VAR>); 1956float modff(float <VAR>val</VAR>, float *<VAR>ipart</VAR>);
1914 1957
1915</PRE> 1958</pre></td></tr></table><STRONG>Description</STRONG><BR>
1916
1917<P>
1918<STRONG>Description</STRONG><BR>
1919<CODE>modf</CODE> splits the double <VAR>val</VAR> apart into an integer part 1959<CODE>modf</CODE> splits the double <VAR>val</VAR> apart into an integer part
1920and a fractional part, returning the fractional part and 1960and a fractional part, returning the fractional part and
1921storing the integer part in <CODE>*<VAR>ipart</VAR></CODE>. No rounding 1961storing the integer part in <CODE>*<VAR>ipart</VAR></CODE>. No rounding
@@ -1925,357 +1965,400 @@ is, if . <VAR>realpart</VAR> = modf(<VAR>val</VAR>, &#38;<VAR>intpart</VAR>); th
1925`<CODE><VAR>realpart</VAR>+<VAR>intpart</VAR></CODE>' is the same as <VAR>val</VAR>. 1965`<CODE><VAR>realpart</VAR>+<VAR>intpart</VAR></CODE>' is the same as <VAR>val</VAR>.
1926<CODE>modff</CODE> is identical, save that it takes and returns 1966<CODE>modff</CODE> is identical, save that it takes and returns
1927<CODE>float</CODE> rather than <CODE>double</CODE> values. 1967<CODE>float</CODE> rather than <CODE>double</CODE> values.
1928
1929
1930<P> 1968<P>
1969
1931<BR> 1970<BR>
1932<STRONG>Returns</STRONG><BR> 1971<STRONG>Returns</STRONG><BR>
1933The fractional part is returned. Each result has the same 1972The fractional part is returned. Each result has the same
1934sign as the supplied argument <VAR>val</VAR>. 1973sign as the supplied argument <VAR>val</VAR>.
1974</P><P>
1935 1975
1936
1937<P>
1938<BR> 1976<BR>
1939<STRONG>Portability</STRONG><BR> 1977<STRONG>Portability</STRONG><BR>
1940<CODE>modf</CODE> is ANSI C. <CODE>modff</CODE> is an extension. 1978<CODE>modf</CODE> is ANSI C. <CODE>modff</CODE> is an extension.
1941 1979</P><P>
1942 1980
1943<P> 1981<BR>
1944<BR> 1982<A NAME="nan"></A>
1945 1983<HR SIZE="6">
1946 1984<A NAME="SEC39"></A>
1947<H2><A NAME="SEC39" HREF="libm_toc.html#TOC39"><CODE>nan</CODE>, <CODE>nanf</CODE>---representation of infinity</A></H2> 1985<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
1948<P> 1986<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC38"> &lt; </A>]</TD>
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1950<A NAME="IDX101"></A> 1988<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
1989<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
1990<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
1991<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#SEC1">Top</A>]</TD>
1992<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
1993<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
1994<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
1995</TR></TABLE>
1996<H2> 1.38 <CODE>nan</CODE>, <CODE>nanf</CODE>---representation of infinity </H2>
1997<!--docid::SEC39::-->
1951<STRONG>Synopsis</STRONG> 1998<STRONG>Synopsis</STRONG>
1952 1999<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1953<PRE>
1954#include &#60;math.h&#62;
1955double nan(void); 2000double nan(void);
1956float nanf(void); 2001float nanf(void);
1957 2002
1958</PRE> 2003</pre></td></tr></table><STRONG>Description</STRONG><BR>
1959
1960<P>
1961<STRONG>Description</STRONG><BR>
1962<CODE>nan</CODE> and <CODE>nanf</CODE> return an IEEE NaN (Not a Number) in 2004<CODE>nan</CODE> and <CODE>nanf</CODE> return an IEEE NaN (Not a Number) in
1963double and single precision arithmetic respectivly. 2005double and single precision arithmetic respectivly.
1964
1965
1966<P> 2006<P>
1967<BR>
1968
1969 2007
1970<H2><A NAME="SEC40" HREF="libm_toc.html#TOC40"><CODE>nextafter</CODE>, <CODE>nextafterf</CODE>---get next number</A></H2> 2008<BR>
1971<P> 2009<A NAME="nextafter"></A>
1972<A NAME="IDX102"></A> 2010<HR SIZE="6">
1973<A NAME="IDX103"></A> 2011<A NAME="SEC40"></A>
2012<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
2013<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC39"> &lt; </A>]</TD>
2014<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC41"> &gt; </A>]</TD>
2015<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
2016<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
2017<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
2018<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#SEC1">Top</A>]</TD>
2019<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
2020<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
2021<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
2022</TR></TABLE>
2023<H2> 1.39 <CODE>nextafter</CODE>, <CODE>nextafterf</CODE>---get next number </H2>
2024<!--docid::SEC40::-->
1974<STRONG>Synopsis</STRONG> 2025<STRONG>Synopsis</STRONG>
1975 2026<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
1976<PRE>
1977#include &#60;math.h&#62;
1978double nextafter(double <VAR>val</VAR>, double <VAR>dir</VAR>); 2027double nextafter(double <VAR>val</VAR>, double <VAR>dir</VAR>);
1979float nextafterf(float <VAR>val</VAR>, float <VAR>dir</VAR>); 2028float nextafterf(float <VAR>val</VAR>, float <VAR>dir</VAR>);
1980 2029
1981</PRE> 2030</pre></td></tr></table><STRONG>Description</STRONG><BR>
1982
1983<P>
1984<STRONG>Description</STRONG><BR>
1985<CODE>nextafter</CODE> returns the double) precision floating point number 2031<CODE>nextafter</CODE> returns the double) precision floating point number
1986closest to <VAR>val</VAR> in the direction toward <VAR>dir</VAR>. <CODE>nextafterf</CODE> 2032closest to <VAR>val</VAR> in the direction toward <VAR>dir</VAR>. <CODE>nextafterf</CODE>
1987performs the same operation in single precision. For example, 2033performs the same operation in single precision. For example,
1988<CODE>nextafter(0.0,1.0)</CODE> returns the smallest positive number which is 2034<CODE>nextafter(0.0,1.0)</CODE> returns the smallest positive number which is
1989representable in double precision. 2035representable in double precision.
1990
1991
1992<P> 2036<P>
2037
1993<BR> 2038<BR>
1994<STRONG>Returns</STRONG><BR> 2039<STRONG>Returns</STRONG><BR>
1995Returns the next closest number to <VAR>val</VAR> in the direction toward 2040Returns the next closest number to <VAR>val</VAR> in the direction toward
1996<VAR>dir</VAR>. 2041<VAR>dir</VAR>.
2042</P><P>
1997 2043
1998
1999<P>
2000<BR> 2044<BR>
2001<STRONG>Portability</STRONG><BR> 2045<STRONG>Portability</STRONG><BR>
2002Neither <CODE>nextafter</CODE> nor <CODE>nextafterf</CODE> is required by ANSI C 2046Neither <CODE>nextafter</CODE> nor <CODE>nextafterf</CODE> is required by ANSI C
2003or by the System V Interface Definition (Issue 2). 2047or by the System V Interface Definition (Issue 2).
2004 2048</P><P>
2005 2049
2006<P> 2050<BR>
2007<BR> 2051<A NAME="scalbn"></A>
2008 2052<HR SIZE="6">
2009 2053<A NAME="SEC41"></A>
2010<H2><A NAME="SEC41" HREF="libm_toc.html#TOC41"><CODE>scalbn</CODE>, <CODE>scalbnf</CODE>---scale by integer</A></H2> 2054<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
2011<P> 2055<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC40"> &lt; </A>]</TD>
2012<A NAME="IDX104"></A> 2056<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &gt; </A>]</TD>
2013<A NAME="IDX105"></A> 2057<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
2058<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
2059<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
2060<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#SEC1">Top</A>]</TD>
2061<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
2062<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
2063<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
2064</TR></TABLE>
2065<H2> 1.40 <CODE>scalbn</CODE>, <CODE>scalbnf</CODE>---scale by integer </H2>
2066<!--docid::SEC41::-->
2014<STRONG>Synopsis</STRONG> 2067<STRONG>Synopsis</STRONG>
2015 2068<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;math.h&#62;
2016<PRE>
2017#include &#60;math.h&#62;
2018double scalbn(double <VAR>x</VAR>, int <VAR>y</VAR>); 2069double scalbn(double <VAR>x</VAR>, int <VAR>y</VAR>);
2019float scalbnf(float <VAR>x</VAR>, int <VAR>y</VAR>); 2070float scalbnf(float <VAR>x</VAR>, int <VAR>y</VAR>);
2020 2071
2021</PRE> 2072</pre></td></tr></table><STRONG>Description</STRONG><BR>
2022
2023<P>
2024<STRONG>Description</STRONG><BR>
2025<CODE>scalbn</CODE> and <CODE>scalbnf</CODE> scale <VAR>x</VAR> by <VAR>n</VAR>, returning <VAR>x</VAR> times 2073<CODE>scalbn</CODE> and <CODE>scalbnf</CODE> scale <VAR>x</VAR> by <VAR>n</VAR>, returning <VAR>x</VAR> times
20262 to the power <VAR>n</VAR>. The result is computed by manipulating the 20742 to the power <VAR>n</VAR>. The result is computed by manipulating the
2027exponent, rather than by actually performing an exponentiation or 2075exponent, rather than by actually performing an exponentiation or
2028multiplication. 2076multiplication.
2029
2030
2031<P> 2077<P>
2078
2032<BR> 2079<BR>
2033<STRONG>Returns</STRONG><BR> 2080<STRONG>Returns</STRONG><BR>
2034<VAR>x</VAR> times 2 to the power <VAR>n</VAR>. 2081<VAR>x</VAR> times 2 to the power <VAR>n</VAR>.
2082</P><P>
2035 2083
2036
2037<P>
2038<BR> 2084<BR>
2039<STRONG>Portability</STRONG><BR> 2085<STRONG>Portability</STRONG><BR>
2040Neither <CODE>scalbn</CODE> nor <CODE>scalbnf</CODE> is required by ANSI C or by the System V 2086Neither <CODE>scalbn</CODE> nor <CODE>scalbnf</CODE> is required by ANSI C or by the System V
2041Interface Definition (Issue 2). 2087Interface Definition (Issue 2).
2088</P><P>
2042 2089
2043
2044<P>
2045<BR> 2090<BR>
2091</P><P>
2046 2092
2047 2093<A NAME="Reentrancy"></A>
2048 2094<HR SIZE="6">
2049 2095<A NAME="SEC42"></A>
2050<H1><A NAME="SEC42" HREF="libm_toc.html#TOC42">Reentrancy Properties of <CODE>libm</CODE></A></H1> 2096<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
2051 2097<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC41"> &lt; </A>]</TD>
2098<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43"> &gt; </A>]</TD>
2099<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
2100<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
2101<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
2102<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#SEC1">Top</A>]</TD>
2103<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
2104<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
2105<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
2106</TR></TABLE>
2107<H1> 2. Reentrancy Properties of <CODE>libm</CODE> </H1>
2108<!--docid::SEC42::-->
2052<P> 2109<P>
2053<A NAME="IDX106"></A> 2110
2054<A NAME="IDX107"></A> 2111<A NAME="IDX5"></A>
2112<A NAME="IDX6"></A>
2055When a libm function detects an exceptional case, <CODE>errno</CODE> may be 2113When a libm function detects an exceptional case, <CODE>errno</CODE> may be
2056set, the <CODE>matherr</CODE> function may be called, and a error message 2114set, the <CODE>matherr</CODE> function may be called, and a error message
2057may be written to the standard error stream. This behavior may not 2115may be written to the standard error stream. This behavior may not
2058be reentrant. 2116be reentrant.
2117</P><P>
2059 2118
2060
2061<P>
2062With reentrant C libraries like the Red Hat newlib C library, <CODE>errno</CODE> is 2119With reentrant C libraries like the Red Hat newlib C library, <CODE>errno</CODE> is
2063a macro which expands to the per-thread error value. This makes it thread 2120a macro which expands to the per-thread error value. This makes it thread
2064safe. 2121safe.
2122</P><P>
2065 2123
2066
2067<P>
2068When the user provides his own <CODE>matherr</CODE> function it must be 2124When the user provides his own <CODE>matherr</CODE> function it must be
2069reentrant for the math library as a whole to be reentrant. 2125reentrant for the math library as a whole to be reentrant.
2126</P><P>
2070 2127
2071
2072<P>
2073In normal debugged programs, there are usually no math subroutine 2128In normal debugged programs, there are usually no math subroutine
2074errors--and therefore no assignments to <CODE>errno</CODE> and no <CODE>matherr</CODE> 2129errors--and therefore no assignments to <CODE>errno</CODE> and no <CODE>matherr</CODE>
2075calls; in that situation, the math functions behave reentrantly. 2130calls; in that situation, the math functions behave reentrantly.
2076 2131</P><P>
2077 2132
2078 2133<A NAME="Index"></A>
2079 2134<HR SIZE="6">
2080<H1><A NAME="SEC43" HREF="libm_toc.html#TOC43">Index</A></H1> 2135<A NAME="SEC43"></A>
2081<P> 2136<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0>
2082Jump to: 2137<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC42"> &lt; </A>]</TD>
2083<A HREF="#cindex_a">a</A> 2138<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt; ]</TD>
2084- 2139<TD VALIGN="MIDDLE" ALIGN="LEFT"> &nbsp; <TD VALIGN="MIDDLE" ALIGN="LEFT">[ &lt;&lt; ]</TD>
2085<A HREF="#cindex_c">c</A> 2140<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC1"> Up </A>]</TD>
2086- 2141<TD VALIGN="MIDDLE" ALIGN="LEFT">[ &gt;&gt; ]</TD>
2087<A HREF="#cindex_e">e</A> 2142<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#SEC1">Top</A>]</TD>
2088- 2143<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm_toc.html#SEC_Contents">Contents</A>]</TD>
2089<A HREF="#cindex_f">f</A> 2144<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC43">Index</A>]</TD>
2090- 2145<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="libm.html#SEC_About"> ? </A>]</TD>
2091<A HREF="#cindex_g">g</A> 2146</TR></TABLE>
2092- 2147<H1> Index </H1>
2093<A HREF="#cindex_h">h</A> 2148<!--docid::SEC43::-->
2094- 2149<table><tr><th valign=top>Jump to: &nbsp; </th><td><A HREF="libm.html#cp_A" style="text-decoration:none"><b>A</b></A>
2095<A HREF="#cindex_i">i</A> 2150 &nbsp;
2096- 2151<A HREF="libm.html#cp_C" style="text-decoration:none"><b>C</b></A>
2097<A HREF="#cindex_j">j</A> 2152 &nbsp;
2098- 2153<A HREF="libm.html#cp_E" style="text-decoration:none"><b>E</b></A>
2099<A HREF="#cindex_l">l</A> 2154 &nbsp;
2100- 2155<A HREF="libm.html#cp_F" style="text-decoration:none"><b>F</b></A>
2101<A HREF="#cindex_m">m</A> 2156 &nbsp;
2102- 2157<A HREF="libm.html#cp_G" style="text-decoration:none"><b>G</b></A>
2103<A HREF="#cindex_n">n</A> 2158 &nbsp;
2104- 2159<A HREF="libm.html#cp_H" style="text-decoration:none"><b>H</b></A>
2105<A HREF="#cindex_o">o</A> 2160 &nbsp;
2106- 2161<A HREF="libm.html#cp_I" style="text-decoration:none"><b>I</b></A>
2107<A HREF="#cindex_p">p</A> 2162 &nbsp;
2108- 2163<A HREF="libm.html#cp_J" style="text-decoration:none"><b>J</b></A>
2109<A HREF="#cindex_r">r</A> 2164 &nbsp;
2110- 2165<A HREF="libm.html#cp_L" style="text-decoration:none"><b>L</b></A>
2111<A HREF="#cindex_s">s</A> 2166 &nbsp;
2112- 2167<A HREF="libm.html#cp_M" style="text-decoration:none"><b>M</b></A>
2113<A HREF="#cindex_t">t</A> 2168 &nbsp;
2114- 2169<A HREF="libm.html#cp_N" style="text-decoration:none"><b>N</b></A>
2115<A HREF="#cindex_y">y</A> 2170 &nbsp;
2116<P> 2171<A HREF="libm.html#cp_O" style="text-decoration:none"><b>O</b></A>
2117<H2><A NAME="cindex_a">a</A></H2> 2172 &nbsp;
2118<DIR> 2173<A HREF="libm.html#cp_P" style="text-decoration:none"><b>P</b></A>
2119<LI><A HREF="libm.html#IDX5">acos</A> 2174 &nbsp;
2120<LI><A HREF="libm.html#IDX6">acosf</A> 2175<A HREF="libm.html#cp_R" style="text-decoration:none"><b>R</b></A>
2121<LI><A HREF="libm.html#IDX7">acosh</A> 2176 &nbsp;
2122<LI><A HREF="libm.html#IDX8">acoshf</A> 2177<A HREF="libm.html#cp_S" style="text-decoration:none"><b>S</b></A>
2123<LI><A HREF="libm.html#IDX9">asin</A> 2178 &nbsp;
2124<LI><A HREF="libm.html#IDX10">asinf</A> 2179<A HREF="libm.html#cp_T" style="text-decoration:none"><b>T</b></A>
2125<LI><A HREF="libm.html#IDX11">asinh</A> 2180 &nbsp;
2126<LI><A HREF="libm.html#IDX12">asinhf</A> 2181<A HREF="libm.html#cp_Y" style="text-decoration:none"><b>Y</b></A>
2127<LI><A HREF="libm.html#IDX13">atan</A> 2182 &nbsp;
2128<LI><A HREF="libm.html#IDX15">atan2</A> 2183</td></tr></table><br><P></P>
2129<LI><A HREF="libm.html#IDX16">atan2f</A> 2184<TABLE border=0>
2130<LI><A HREF="libm.html#IDX14">atanf</A> 2185<TR><TD></TD><TH ALIGN=LEFT>Index Entry</TH><TH ALIGN=LEFT> Section</TH></TR>
2131<LI><A HREF="libm.html#IDX17">atanh</A> 2186<TR><TD COLSPAN=3> <HR></TD></TR>
2132<LI><A HREF="libm.html#IDX18">atanhf</A> 2187<TR><TH><A NAME="cp_A"></A>A</TH><TD></TD><TD></TD></TR>
2133</DIR> 2188<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>
2134<H2><A NAME="cindex_c">c</A></H2> 2189<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>
2135<DIR> 2190<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>
2136<LI><A HREF="libm.html#IDX85">cbrt</A> 2191<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>
2137<LI><A HREF="libm.html#IDX86">cbrtf</A> 2192<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>
2138<LI><A HREF="libm.html#IDX41">ceil</A> 2193<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>
2139<LI><A HREF="libm.html#IDX42">ceilf</A> 2194<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>
2140<LI><A HREF="libm.html#IDX87">copysign</A> 2195<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>
2141<LI><A HREF="libm.html#IDX88">copysignf</A> 2196<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>
2142<LI><A HREF="libm.html#IDX77">cos</A> 2197<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>
2143<LI><A HREF="libm.html#IDX78">cosf</A> 2198<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>
2144</DIR> 2199<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>
2145<H2><A NAME="cindex_e">e</A></H2> 2200<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>
2146<DIR> 2201<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>
2147<LI><A HREF="libm.html#IDX31">erf</A> 2202<TR><TD COLSPAN=3> <HR></TD></TR>
2148<LI><A HREF="libm.html#IDX33">erfc</A> 2203<TR><TH><A NAME="cp_C"></A>C</TH><TD></TD><TD></TD></TR>
2149<LI><A HREF="libm.html#IDX34">erfcf</A> 2204<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>
2150<LI><A HREF="libm.html#IDX32">erff</A> 2205<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>
2151<LI><A HREF="libm.html#IDX35">exp</A> 2206<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>
2152<LI><A HREF="libm.html#IDX36">expf</A> 2207<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>
2153<LI><A HREF="libm.html#IDX89">expm1</A> 2208<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>
2154<LI><A HREF="libm.html#IDX90">expm1f</A> 2209<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>
2155</DIR> 2210<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>
2156<H2><A NAME="cindex_f">f</A></H2> 2211<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>
2157<DIR> 2212<TR><TD COLSPAN=3> <HR></TD></TR>
2158<LI><A HREF="libm.html#IDX37">fabs</A> 2213<TR><TH><A NAME="cp_E"></A>E</TH><TD></TD><TD></TD></TR>
2159<LI><A HREF="libm.html#IDX38">fabsf</A> 2214<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>
2160<LI><A HREF="libm.html#IDX59">finite</A> 2215<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>
2161<LI><A HREF="libm.html#IDX62">finitef</A> 2216<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>
2162<LI><A HREF="libm.html#IDX39">floor</A> 2217<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>
2163<LI><A HREF="libm.html#IDX40">floorf</A> 2218<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>
2164<LI><A HREF="libm.html#IDX43">fmod</A> 2219<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>
2165<LI><A HREF="libm.html#IDX44">fmodf</A> 2220<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>
2166<LI><A HREF="libm.html#IDX45">frexp</A> 2221<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>
2167<LI><A HREF="libm.html#IDX46">frexpf</A> 2222<TR><TD COLSPAN=3> <HR></TD></TR>
2168</DIR> 2223<TR><TH><A NAME="cp_F"></A>F</TH><TD></TD><TD></TD></TR>
2169<H2><A NAME="cindex_g">g</A></H2> 2224<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>
2170<DIR> 2225<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>
2171<LI><A HREF="libm.html#IDX47">gamma</A> 2226<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>
2172<LI><A HREF="libm.html#IDX51">gamma_r</A> 2227<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>
2173<LI><A HREF="libm.html#IDX48">gammaf</A> 2228<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>
2174<LI><A HREF="libm.html#IDX52">gammaf_r</A> 2229<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>
2175</DIR> 2230<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>
2176<H2><A NAME="cindex_h">h</A></H2> 2231<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>
2177<DIR> 2232<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>
2178<LI><A HREF="libm.html#IDX55">hypot</A> 2233<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>
2179<LI><A HREF="libm.html#IDX56">hypotf</A> 2234<TR><TD COLSPAN=3> <HR></TD></TR>
2180</DIR> 2235<TR><TH><A NAME="cp_G"></A>G</TH><TD></TD><TD></TD></TR>
2181<H2><A NAME="cindex_i">i</A></H2> 2236<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>
2182<DIR> 2237<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>
2183<LI><A HREF="libm.html#IDX91">ilogb</A> 2238<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>
2184<LI><A HREF="libm.html#IDX92">ilogbf</A> 2239<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>
2185<LI><A HREF="libm.html#IDX93">infinity</A> 2240<TR><TD COLSPAN=3> <HR></TD></TR>
2186<LI><A HREF="libm.html#IDX94">infinityf</A> 2241<TR><TH><A NAME="cp_H"></A>H</TH><TD></TD><TD></TD></TR>
2187<LI><A HREF="libm.html#IDX58">isinf</A> 2242<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>
2188<LI><A HREF="libm.html#IDX61">isinff</A> 2243<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>
2189<LI><A HREF="libm.html#IDX57">isnan</A> 2244<TR><TD COLSPAN=3> <HR></TD></TR>
2190<LI><A HREF="libm.html#IDX60">isnanf</A> 2245<TR><TH><A NAME="cp_I"></A>I</TH><TD></TD><TD></TD></TR>
2191</DIR> 2246<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>
2192<H2><A NAME="cindex_j">j</A></H2> 2247<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>
2193<DIR> 2248<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>
2194<LI><A HREF="libm.html#IDX19">j0</A> 2249<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>
2195<LI><A HREF="libm.html#IDX20">j0f</A> 2250<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>
2196<LI><A HREF="libm.html#IDX21">j1</A> 2251<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>
2197<LI><A HREF="libm.html#IDX22">j1f</A> 2252<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>
2198<LI><A HREF="libm.html#IDX23">jn</A> 2253<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>
2199<LI><A HREF="libm.html#IDX24">jnf</A> 2254<TR><TD COLSPAN=3> <HR></TD></TR>
2200</DIR> 2255<TR><TH><A NAME="cp_J"></A>J</TH><TD></TD><TD></TD></TR>
2201<H2><A NAME="cindex_l">l</A></H2> 2256<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>
2202<DIR> 2257<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>
2203<LI><A HREF="libm.html#IDX63">ldexp</A> 2258<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>
2204<LI><A HREF="libm.html#IDX64">ldexpf</A> 2259<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>
2205<LI><A HREF="libm.html#IDX49">lgamma</A> 2260<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>
2206<LI><A HREF="libm.html#IDX53">lgamma_r</A> 2261<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>
2207<LI><A HREF="libm.html#IDX50">lgammaf</A> 2262<TR><TD COLSPAN=3> <HR></TD></TR>
2208<LI><A HREF="libm.html#IDX54">lgammaf_r</A> 2263<TR><TH><A NAME="cp_L"></A>L</TH><TD></TD><TD></TD></TR>
2209<LI><A HREF="libm.html#IDX65">log</A> 2264<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>
2210<LI><A HREF="libm.html#IDX67">log10</A> 2265<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>
2211<LI><A HREF="libm.html#IDX68">log10f</A> 2266<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>
2212<LI><A HREF="libm.html#IDX95">log1p</A> 2267<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>
2213<LI><A HREF="libm.html#IDX96">log1pf</A> 2268<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>
2214<LI><A HREF="libm.html#IDX66">logf</A> 2269<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>
2215</DIR> 2270<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>
2216<H2><A NAME="cindex_m">m</A></H2> 2271<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>
2217<DIR> 2272<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>
2218<LI><A HREF="libm.html#IDX97">matherr</A> 2273<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>
2219<LI><A HREF="libm.html#IDX107"><CODE>matherr</CODE> and reentrancy</A> 2274<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>
2220<LI><A HREF="libm.html#IDX98">modf</A> 2275<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>
2221<LI><A HREF="libm.html#IDX99">modff</A> 2276<TR><TD COLSPAN=3> <HR></TD></TR>
2222</DIR> 2277<TR><TH><A NAME="cp_M"></A>M</TH><TD></TD><TD></TD></TR>
2223<H2><A NAME="cindex_n">n</A></H2> 2278<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>
2224<DIR> 2279<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>
2225<LI><A HREF="libm.html#IDX100">nan</A> 2280<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>
2226<LI><A HREF="libm.html#IDX101">nanf</A> 2281<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>
2227<LI><A HREF="libm.html#IDX102">nextafter</A> 2282<TR><TD COLSPAN=3> <HR></TD></TR>
2228<LI><A HREF="libm.html#IDX103">nextafterf</A> 2283<TR><TH><A NAME="cp_N"></A>N</TH><TD></TD><TD></TD></TR>
2229</DIR> 2284<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 infinity</A></TD></TR>
2230<H2><A NAME="cindex_o">o</A></H2> 2285<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 infinity</A></TD></TR>
2231<DIR> 2286<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>
2232<LI><A HREF="libm.html#IDX4">OS stubs</A> 2287<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>
2233</DIR> 2288<TR><TD COLSPAN=3> <HR></TD></TR>
2234<H2><A NAME="cindex_p">p</A></H2> 2289<TR><TH><A NAME="cp_O"></A>O</TH><TD></TD><TD></TD></TR>
2235<DIR> 2290<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>
2236<LI><A HREF="libm.html#IDX69">pow</A> 2291<TR><TD COLSPAN=3> <HR></TD></TR>
2237<LI><A HREF="libm.html#IDX70">powf</A> 2292<TR><TH><A NAME="cp_P"></A>P</TH><TD></TD><TD></TD></TR>
2238</DIR> 2293<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>
2239<H2><A NAME="cindex_r">r</A></H2> 2294<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>
2240<DIR> 2295<TR><TD COLSPAN=3> <HR></TD></TR>
2241<LI><A HREF="libm.html#IDX106">reentrancy</A> 2296<TR><TH><A NAME="cp_R"></A>R</TH><TD></TD><TD></TD></TR>
2242<LI><A HREF="libm.html#IDX71">remainder</A> 2297<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>
2243<LI><A HREF="libm.html#IDX72">remainderf</A> 2298<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>
2244</DIR> 2299<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>
2245<H2><A NAME="cindex_s">s</A></H2> 2300<TR><TD COLSPAN=3> <HR></TD></TR>
2246<DIR> 2301<TR><TH><A NAME="cp_S"></A>S</TH><TD></TD><TD></TD></TR>
2247<LI><A HREF="libm.html#IDX104">scalbn</A> 2302<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 integer</A></TD></TR>
2248<LI><A HREF="libm.html#IDX105">scalbnf</A> 2303<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 integer</A></TD></TR>
2249<LI><A HREF="libm.html#IDX75">sin</A> 2304<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>
2250<LI><A HREF="libm.html#IDX76">sinf</A> 2305<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>
2251<LI><A HREF="libm.html#IDX79">sinh</A> 2306<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>
2252<LI><A HREF="libm.html#IDX80">sinhf</A> 2307<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>
2253<LI><A HREF="libm.html#IDX73">sqrt</A> 2308<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>
2254<LI><A HREF="libm.html#IDX74">sqrtf</A> 2309<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>
2255<LI><A HREF="libm.html#IDX3">stubs</A> 2310<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>
2256<LI><A HREF="libm.html#IDX2">support subroutines</A> 2311<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>
2257<LI><A HREF="libm.html#IDX1">system calls</A> 2312<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>
2258</DIR> 2313<TR><TD COLSPAN=3> <HR></TD></TR>
2259<H2><A NAME="cindex_t">t</A></H2> 2314<TR><TH><A NAME="cp_T"></A>T</TH><TD></TD><TD></TD></TR>
2260<DIR> 2315<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>
2261<LI><A HREF="libm.html#IDX81">tan</A> 2316<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>
2262<LI><A HREF="libm.html#IDX82">tanf</A> 2317<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>
2263<LI><A HREF="libm.html#IDX83">tanh</A> 2318<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>
2264<LI><A HREF="libm.html#IDX84">tanhf</A> 2319<TR><TD COLSPAN=3> <HR></TD></TR>
2265</DIR> 2320<TR><TH><A NAME="cp_Y"></A>Y</TH><TD></TD><TD></TD></TR>
2266<H2><A NAME="cindex_y">y</A></H2> 2321<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>
2267<DIR> 2322<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>
2268<LI><A HREF="libm.html#IDX25">y0</A> 2323<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>
2269<LI><A HREF="libm.html#IDX26">y0f</A> 2324<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>
2270<LI><A HREF="libm.html#IDX27">y1</A> 2325<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>
2271<LI><A HREF="libm.html#IDX28">y1f</A> 2326<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>
2272<LI><A HREF="libm.html#IDX29">yn</A> 2327<TR><TD COLSPAN=3> <HR></TD></TR>
2273<LI><A HREF="libm.html#IDX30">ynf</A> 2328</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>
2274</DIR> 2329 &nbsp;
2275 2330<A HREF="libm.html#cp_C" style="text-decoration:none"><b>C</b></A>
2276 2331 &nbsp;
2277<P><HR><P> 2332<A HREF="libm.html#cp_E" style="text-decoration:none"><b>E</b></A>
2278This document was generated on 21 July 2002 using 2333 &nbsp;
2279<A HREF="http://wwwinfo.cern.ch/dis/texi2html/">texi2html</A>&nbsp;1.56k. 2334<A HREF="libm.html#cp_F" style="text-decoration:none"><b>F</b></A>
2280</BODY> 2335 &nbsp;
2281</HTML> 2336<A HREF="libm.html#cp_G" style="text-decoration:none"><b>G</b></A>
2337 &nbsp;
2338<A HREF="libm.html#cp_H" style="text-decoration:none"><b>H</b></A>
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2340<A HREF="libm.html#cp_I" style="text-decoration:none"><b>I</b></A>
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2342<A HREF="libm.html#cp_J" style="text-decoration:none"><b>J</b></A>
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2344<A HREF="libm.html#cp_L" style="text-decoration:none"><b>L</b></A>
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2346<A HREF="libm.html#cp_M" style="text-decoration:none"><b>M</b></A>
2347 &nbsp;
2348<A HREF="libm.html#cp_N" style="text-decoration:none"><b>N</b></A>
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2350<A HREF="libm.html#cp_O" style="text-decoration:none"><b>O</b></A>
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2352<A HREF="libm.html#cp_P" style="text-decoration:none"><b>P</b></A>
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2354<A HREF="libm.html#cp_R" style="text-decoration:none"><b>R</b></A>
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2356<A HREF="libm.html#cp_S" style="text-decoration:none"><b>S</b></A>
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2358<A HREF="libm.html#cp_T" style="text-decoration:none"><b>T</b></A>
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2360<A HREF="libm.html#cp_Y" style="text-decoration:none"><b>Y</b></A>
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