530 lines
20 KiB
HTML
530 lines
20 KiB
HTML
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
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<html>
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<head>
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<meta name="generator" content="HTML Tidy, see www.w3.org">
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<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
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<link type="text/css" rel="stylesheet" href="style.css"><!-- Generated by The Open Group's rhtm tool v1.2.1 -->
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<!-- Copyright (c) 2001 The Open Group, All Rights Reserved -->
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<title><math.h></title>
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</head>
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<body bgcolor="white">
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<script type="text/javascript" language="JavaScript" src="../jscript/codes.js">
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</script>
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<basefont size="3"> <a name="<math.h>"></a> <a name="tag_13_26"></a><!-- <math.h> -->
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<!--header start-->
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<center><font size="2">The Open Group Base Specifications Issue 6<br>
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IEEE Std 1003.1-2001<br>
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Copyright © 2001 The IEEE and The Open Group, All Rights reserved.</font></center>
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<!--header end-->
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<hr size="2" noshade>
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<h4><a name="tag_13_26_01"></a>NAME</h4>
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<blockquote>math.h - mathematical declarations</blockquote>
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<h4><a name="tag_13_26_02"></a>SYNOPSIS</h4>
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<blockquote class="synopsis">
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<p><tt>#include <math.h></tt></p>
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</blockquote>
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<h4><a name="tag_13_26_03"></a>DESCRIPTION</h4>
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<blockquote>
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<div class="box"><sup>[<a href="javascript:open_code('CX')">CX</a>]</sup> <img src="../images/opt-start.gif" alt="[Option Start]"
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border="0"> Some of the functionality described on this reference page extends the ISO C standard. Applications shall define
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the appropriate feature test macro (see the System Interfaces volume of IEEE Std 1003.1-2001, <a href=
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"../functions/xsh_chap02_02.html">Section 2.2, The Compilation Environment</a>) to enable the visibility of these symbols in this
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header. <img src="../images/opt-end.gif" alt="[Option End]" border="0"></div>
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<p>The <i><math.h></i> header shall include definitions for at least the following types:</p>
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<dl compact>
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<dt><b>float_t</b></dt>
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<dd>A real-floating type at least as wide as <b>float</b>.</dd>
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<dt><b>double_t</b></dt>
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<dd>A real-floating type at least as wide as <b>double</b>, and at least as wide as <b>float_t</b>.</dd>
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</dl>
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<p>If FLT_EVAL_METHOD equals 0, <b>float_t</b> and <b>double_t</b> shall be <b>float</b> and <b>double</b>, respectively; if
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FLT_EVAL_METHOD equals 1, they shall both be <b>double</b>; if FLT_EVAL_METHOD equals 2, they shall both be <b>long double</b>; for
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other values of FLT_EVAL_METHOD, they are otherwise implementation-defined.</p>
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<p>The <i><math.h></i> header shall define the following macros, where real-floating indicates that the argument shall be an
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expression of real-floating type:</p>
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<pre>
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<tt>int fpclassify(real-floating x);
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int isfinite(real-floating x);
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int isinf(real-floating x);
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int isnan(real-floating x);
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int isnormal(real-floating x);
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int signbit(real-floating x);
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int isgreater(real-floating x, real-floating y);
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int isgreaterequal(real-floating x, real-floating y);
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int isless(real-floating x, real-floating y);
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int islessequal(real-floating x, real-floating y);
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int islessgreater(real-floating x, real-floating y);
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int isunordered(real-floating x, real-floating y);
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</tt>
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</pre>
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<p>The <i><math.h></i> header shall provide for the following constants. The values are of type <b>double</b> and are
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accurate within the precision of the <b>double</b> type.</p>
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<dl compact>
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<dt>M_E</dt>
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<dd><sup>[<a href="javascript:open_code('XSI')">XSI</a>]</sup> <img src="../images/opt-start.gif" alt="[Option Start]" border="0">
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Value of <i>e</i></dd>
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<dt>M_LOG2E</dt>
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<dd>Value of log<small><sub>2</sub></small><i>e</i></dd>
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<dt>M_LOG10E</dt>
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<dd>Value of log<small><sub>10</sub></small><i>e</i></dd>
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<dt>M_LN2</dt>
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<dd>Value of log<small><sub>e</sub></small>2</dd>
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<dt>M_LN10</dt>
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<dd>Value of log<small><sub>e</sub></small>10</dd>
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<dt>M_PI</dt>
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<dd>Value of <sub><img src="../images/pi.gif"></sub></dd>
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<dt>M_PI_2</dt>
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<dd>Value of <sub><img src="../images/pi.gif"></sub>/2</dd>
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<dt>M_PI_4</dt>
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<dd>Value of <sub><img src="../images/pi.gif"></sub>/4</dd>
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<dt>M_1_PI</dt>
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<dd>Value of 1/<sub><img src="../images/pi.gif"></sub></dd>
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<dt>M_2_PI</dt>
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<dd>Value of 2/<sub><img src="../images/pi.gif"></sub></dd>
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<dt>M_2_SQRTPI</dt>
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<dd>Value of 2/ <sub><img src="../images/sqrt2.gif"><img src="../images/pi.gif"></sub></dd>
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<dt>M_SQRT2</dt>
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<dd>Value of <sub><img src="../images/sqrt2.gif"></sub>2</dd>
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<dt>M_SQRT1_2</dt>
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<dd>Value of 1/<sub><img src="../images/sqrt2.gif"></sub>2 <img src="../images/opt-end.gif" alt="[Option End]" border="0"></dd>
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</dl>
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<p>The header shall define the following symbolic constants:</p>
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<dl compact>
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<dt>MAXFLOAT</dt>
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<dd><sup>[<a href="javascript:open_code('XSI')">XSI</a>]</sup> <img src="../images/opt-start.gif" alt="[Option Start]" border="0">
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Value of maximum non-infinite single-precision floating-point number. <img src="../images/opt-end.gif" alt="[Option End]" border=
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"0"></dd>
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<dt>HUGE_VAL</dt>
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<dd>A positive <b>double</b> expression, not necessarily representable as a <b>float</b>. Used as an error value returned by the
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mathematics library. HUGE_VAL evaluates to +infinity on systems supporting IEEE Std 754-1985.</dd>
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<dt>HUGE_VALF</dt>
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<dd>A positive <b>float</b> constant expression. Used as an error value returned by the mathematics library. HUGE_VALF evaluates to
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+infinity on systems supporting IEEE Std 754-1985.</dd>
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<dt>HUGE_VALL</dt>
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<dd>A positive <b>long double</b> constant expression. Used as an error value returned by the mathematics library. HUGE_VALL
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evaluates to +infinity on systems supporting IEEE Std 754-1985.</dd>
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<dt>INFINITY</dt>
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<dd>A constant expression of type <b>float</b> representing positive or unsigned infinity, if available; else a positive constant
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of type <b>float</b> that overflows at translation time.</dd>
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<dt>NAN</dt>
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<dd>A constant expression of type <b>float</b> representing a quiet NaN. This symbolic constant is only defined if the
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implementation supports quiet NaNs for the <b>float</b> type.</dd>
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</dl>
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<p>The following macros shall be defined for number classification. They represent the mutually-exclusive kinds of floating-point
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values. They expand to integer constant expressions with distinct values. Additional implementation-defined floating-point
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classifications, with macro definitions beginning with FP_ and an uppercase letter, may also be specified by the
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implementation.</p>
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<blockquote>
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<pre>
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FP_INFINITE
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FP_NAN
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FP_NORMAL
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FP_SUBNORMAL
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FP_ZERO
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</pre>
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</blockquote>
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<p>The following optional macros indicate whether the <a href="../functions/fma.html"><i>fma</i>()</a> family of functions are fast
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compared with direct code:</p>
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<blockquote>
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<pre>
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FP_FAST_FMA
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FP_FAST_FMAF
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FP_FAST_FMAL
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</pre>
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</blockquote>
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<p>The FP_FAST_FMA macro shall be defined to indicate that the <a href="../functions/fma.html"><i>fma</i>()</a> function generally
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executes about as fast as, or faster than, a multiply and an add of <b>double</b> operands. The other macros have the equivalent
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meaning for the <b>float</b> and <b>long double</b> versions.</p>
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<p>The following macros shall expand to integer constant expressions whose values are returned by <i>ilogb</i>( <i>x</i>) if
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<i>x</i> is zero or NaN, respectively. The value of FP_ILOGB0 shall be either {INT_MIN} or - {INT_MAX}. The value of FP_ILOGBNAN
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shall be either {INT_MAX} or {INT_MIN}.</p>
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<blockquote>
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<pre>
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FP_ILOGB0
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FP_ILOGBNAN
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</pre>
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</blockquote>
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<p>The following macros shall expand to the integer constants 1 and 2, respectively;</p>
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<blockquote>
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<pre>
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MATH_ERRNO
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MATH_ERREXCEPT
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</pre>
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</blockquote>
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<p>The following macro shall expand to an expression that has type <b>int</b> and the value MATH_ERRNO, MATH_ERREXCEPT, or the
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bitwise-inclusive OR of both:</p>
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<blockquote>
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<pre>
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math_errhandling
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</pre>
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</blockquote>
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<p>The value of math_errhandling is constant for the duration of the program. It is unspecified whether math_errhandling is a macro
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or an identifier with external linkage. If a macro definition is suppressed or a program defines an identifier with the name
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math_errhandling , the behavior is undefined. If the expression (math_errhandling & MATH_ERREXCEPT) can be non-zero, the
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implementation shall define the macros FE_DIVBYZERO, FE_INVALID, and FE_OVERFLOW in <a href=
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"../basedefs/fenv.h.html"><i><fenv.h></i></a>.</p>
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<p>The following shall be declared as functions and may also be defined as macros. Function prototypes shall be provided.</p>
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<pre>
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<tt>double acos(double);
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float acosf(float);
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double acosh(double);
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float acoshf(float);
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long double acoshl(long double);
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long double acosl(long double);
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double asin(double);
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float asinf(float);
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double asinh(double);
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float asinhf(float);
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long double asinhl(long double);
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long double asinl(long double);
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double atan(double);
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double atan2(double, double);
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float atan2f(float, float);
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long double atan2l(long double, long double);
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float atanf(float);
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double atanh(double);
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float atanhf(float);
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long double atanhl(long double);
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long double atanl(long double);
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double cbrt(double);
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float cbrtf(float);
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long double cbrtl(long double);
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double ceil(double);
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float ceilf(float);
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long double ceill(long double);
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double copysign(double, double);
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float copysignf(float, float);
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long double copysignl(long double, long double);
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double cos(double);
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float cosf(float);
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double cosh(double);
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float coshf(float);
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long double coshl(long double);
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long double cosl(long double);
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double erf(double);
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double erfc(double);
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float erfcf(float);
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long double erfcl(long double);
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float erff(float);
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long double erfl(long double);
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double exp(double);
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double exp2(double);
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float exp2f(float);
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long double exp2l(long double);
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float expf(float);
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long double expl(long double);
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double expm1(double);
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float expm1f(float);
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long double expm1l(long double);
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double fabs(double);
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float fabsf(float);
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long double fabsl(long double);
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double fdim(double, double);
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float fdimf(float, float);
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long double fdiml(long double, long double);
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double floor(double);
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float floorf(float);
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long double floorl(long double);
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double fma(double, double, double);
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float fmaf(float, float, float);
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long double fmal(long double, long double, long double);
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double fmax(double, double);
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float fmaxf(float, float);
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long double fmaxl(long double, long double);
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double fmin(double, double);
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float fminf(float, float);
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long double fminl(long double, long double);
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double fmod(double, double);
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float fmodf(float, float);
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long double fmodl(long double, long double);
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double frexp(double, int *);
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float frexpf(float value, int *);
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long double frexpl(long double value, int *);
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double hypot(double, double);
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float hypotf(float, float);
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long double hypotl(long double, long double);
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int ilogb(double);
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int ilogbf(float);
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int ilogbl(long double);
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<sup>[<a href="javascript:open_code('XSI')">XSI</a>]</sup><img src="../images/opt-start.gif" alt="[Option Start]" border="0">
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double j0(double);
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double j1(double);
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double jn(int, double);
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<img src="../images/opt-end.gif" alt="[Option End]" border="0">
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double ldexp(double, int);
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float ldexpf(float, int);
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long double ldexpl(long double, int);
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double lgamma(double);
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float lgammaf(float);
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long double lgammal(long double);
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long long llrint(double);
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long long llrintf(float);
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long long llrintl(long double);
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long long llround(double);
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long long llroundf(float);
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long long llroundl(long double);
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double log(double);
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double log10(double);
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float log10f(float);
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long double log10l(long double);
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double log1p(double);
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float log1pf(float);
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long double log1pl(long double);
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double log2(double);
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float log2f(float);
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long double log2l(long double);
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double logb(double);
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float logbf(float);
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long double logbl(long double);
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float logf(float);
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long double logl(long double);
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long lrint(double);
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long lrintf(float);
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long lrintl(long double);
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long lround(double);
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long lroundf(float);
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long lroundl(long double);
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double modf(double, double *);
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float modff(float, float *);
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long double modfl(long double, long double *);
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double nan(const char *);
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float nanf(const char *);
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long double nanl(const char *);
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double nearbyint(double);
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float nearbyintf(float);
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long double nearbyintl(long double);
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double nextafter(double, double);
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float nextafterf(float, float);
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long double nextafterl(long double, long double);
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double nexttoward(double, long double);
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float nexttowardf(float, long double);
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long double nexttowardl(long double, long double);
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double pow(double, double);
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float powf(float, float);
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long double powl(long double, long double);
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double remainder(double, double);
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float remainderf(float, float);
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long double remainderl(long double, long double);
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double remquo(double, double, int *);
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float remquof(float, float, int *);
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long double remquol(long double, long double, int *);
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double rint(double);
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float rintf(float);
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long double rintl(long double);
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double round(double);
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float roundf(float);
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long double roundl(long double);
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<sup>[<a href="javascript:open_code('XSI')">XSI</a>]</sup><img src="../images/opt-start.gif" alt="[Option Start]" border="0">
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double scalb(double, double);
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<img src="../images/opt-end.gif" alt="[Option End]" border="0">
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double scalbln(double, long);
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float scalblnf(float, long);
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long double scalblnl(long double, long);
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double scalbn(double, int);
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float scalbnf(float, int);
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long double scalbnl(long double, int);
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double sin(double);
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float sinf(float);
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double sinh(double);
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float sinhf(float);
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long double sinhl(long double);
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long double sinl(long double);
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double sqrt(double);
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float sqrtf(float);
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long double sqrtl(long double);
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double tan(double);
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float tanf(float);
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double tanh(double);
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float tanhf(float);
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long double tanhl(long double);
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long double tanl(long double);
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double tgamma(double);
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float tgammaf(float);
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long double tgammal(long double);
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double trunc(double);
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float truncf(float);
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long double truncl(long double);
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<sup>[<a href="javascript:open_code('XSI')">XSI</a>]</sup><img src="../images/opt-start.gif" alt="[Option Start]" border="0">
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double y0(double);
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double y1(double);
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double yn(int, double);
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<img src="../images/opt-end.gif" alt="[Option End]" border="0">
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</tt>
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</pre>
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<p>The following external variable shall be defined:</p>
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<pre>
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<tt><sup>[<a href="javascript:open_code('XSI')">XSI</a>]</sup><img src="../images/opt-start.gif" alt="[Option Start]" border="0">
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extern int signgam;
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<img src="../images/opt-end.gif" alt="[Option End]" border="0">
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</tt>
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</pre>
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<p>The behavior of each of the functions defined in <i><math.h></i> is specified in the System Interfaces volume of
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IEEE Std 1003.1-2001 for all representable values of its input arguments, except where stated otherwise. Each function
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shall execute as if it were a single operation without generating any externally visible exceptional conditions.</p>
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</blockquote>
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<hr>
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<div class="box"><em>The following sections are informative.</em></div>
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<h4><a name="tag_13_26_04"></a>APPLICATION USAGE</h4>
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|
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<blockquote>
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<p>The FP_CONTRACT pragma can be used to allow (if the state is on) or disallow (if the state is off) the implementation to
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contract expressions. Each pragma can occur either outside external declarations or preceding all explicit declarations and
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statements inside a compound statement. When outside external declarations, the pragma takes effect from its occurrence until
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another FP_CONTRACT pragma is encountered, or until the end of the translation unit. When inside a compound statement, the pragma
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takes effect from its occurrence until another FP_CONTRACT pragma is encountered (including within a nested compound statement), or
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until the end of the compound statement; at the end of a compound statement the state for the pragma is restored to its condition
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just before the compound statement. If this pragma is used in any other context, the behavior is undefined. The default state (on
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or off) for the pragma is implementation-defined.</p>
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</blockquote>
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|
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<h4><a name="tag_13_26_05"></a>RATIONALE</h4>
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|
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|
<blockquote>
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|
<p>Before the ISO/IEC 9899:1999 standard, the math library was defined only for the floating type <b>double</b>. All the names
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|
formed by appending <tt>'f'</tt> or <tt>'l'</tt> to a name in <i><math.h></i> were reserved to allow for the definition of
|
|
<b>float</b> and <b>long double</b> libraries; and the ISO/IEC 9899:1999 standard provides for all three versions of math
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|
functions.</p>
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|
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|
<p>The functions <a href="../functions/ecvt.html"><i>ecvt</i>()</a>, <a href="../functions/fcvt.html"><i>fcvt</i>()</a>, and <a
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|
href="../functions/gcvt.html"><i>gcvt</i>()</a> have been dropped from the ISO C standard since their capability is available
|
|
through <a href="../functions/sprintf.html"><i>sprintf</i>()</a>. These are provided on XSI-conformant systems supporting the
|
|
Legacy Option Group.</p>
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</blockquote>
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|
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<h4><a name="tag_13_26_06"></a>FUTURE DIRECTIONS</h4>
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|
|
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<blockquote>
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|
<p>None.</p>
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|
</blockquote>
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|
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<h4><a name="tag_13_26_07"></a>SEE ALSO</h4>
|
|
|
|
<blockquote>
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|
<p><a href="stddef.h.html"><i><stddef.h></i></a> , <a href="sys/types.h.html"><i><sys/types.h></i></a> , the System
|
|
Interfaces volume of IEEE Std 1003.1-2001, <a href="../functions/acos.html"><i>acos</i>()</a>, <a href=
|
|
"../functions/acosh.html"><i>acosh</i>()</a>, <a href="../functions/asin.html"><i>asin</i>()</a>, <a href=
|
|
"../functions/atan.html"><i>atan</i>()</a>, <a href="../functions/atan2.html"><i>atan2</i>()</a>, <a href=
|
|
"../functions/cbrt.html"><i>cbrt</i>()</a>, <a href="../functions/ceil.html"><i>ceil</i>()</a>, <a href=
|
|
"../functions/cos.html"><i>cos</i>()</a>, <a href="../functions/cosh.html"><i>cosh</i>()</a>, <a href=
|
|
"../functions/erf.html"><i>erf</i>()</a>, <a href="../functions/exp.html"><i>exp</i>()</a>, <a href=
|
|
"../functions/expm1.html"><i>expm1</i>()</a>, <a href="../functions/fabs.html"><i>fabs</i>()</a>, <a href=
|
|
"../functions/floor.html"><i>floor</i>()</a>, <a href="../functions/fmod.html"><i>fmod</i>()</a>, <a href=
|
|
"../functions/frexp.html"><i>frexp</i>()</a>, <a href="../functions/hypot.html"><i>hypot</i>()</a>, <a href=
|
|
"../functions/ilogb.html"><i>ilogb</i>()</a>, <a href="../functions/isnan.html"><i>isnan</i>()</a>, <a href=
|
|
"../functions/j0.html"><i>j0</i>()</a>, <a href="../functions/ldexp.html"><i>ldexp</i>()</a>, <a href=
|
|
"../functions/lgamma.html"><i>lgamma</i>()</a>, <a href="../functions/log.html"><i>log</i>()</a>, <a href=
|
|
"../functions/log10.html"><i>log10</i>()</a>, <a href="../functions/log1p.html"><i>log1p</i>()</a>, <a href=
|
|
"../functions/logb.html"><i>logb</i>()</a>, <a href="../functions/modf.html"><i>modf</i>()</a>, <a href=
|
|
"../functions/nextafter.html"><i>nextafter</i>()</a>, <a href="../functions/pow.html"><i>pow</i>()</a>, <a href=
|
|
"../functions/remainder.html"><i>remainder</i>()</a>, <a href="../functions/rint.html"><i>rint</i>()</a>, <a href=
|
|
"../functions/scalb.html"><i>scalb</i>()</a>, <a href="../functions/sin.html"><i>sin</i>()</a>, <a href=
|
|
"../functions/sinh.html"><i>sinh</i>()</a>, <a href="../functions/sqrt.html"><i>sqrt</i>()</a>, <a href=
|
|
"../functions/tan.html"><i>tan</i>()</a>, <a href="../functions/tanh.html"><i>tanh</i>()</a>, <a href=
|
|
"../functions/y0.html"><i>y0</i>()</a></p>
|
|
</blockquote>
|
|
|
|
<h4><a name="tag_13_26_08"></a>CHANGE HISTORY</h4>
|
|
|
|
<blockquote>
|
|
<p>First released in Issue 1.</p>
|
|
</blockquote>
|
|
|
|
<h4><a name="tag_13_26_09"></a>Issue 6</h4>
|
|
|
|
<blockquote>
|
|
<p>This reference page is updated to align with the ISO/IEC 9899:1999 standard.<br>
|
|
</p>
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|
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|
</blockquote>
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|
|
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<div class="box"><em>End of informative text.</em></div>
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