<refentry id="glib-Numerical-Definitions">
<refmeta>
<refentrytitle>Numerical Definitions</refentrytitle>
<manvolnum>3</manvolnum>
<refmiscinfo>GLIB Library</refmiscinfo>
</refmeta>
<refnamediv>
<refname>Numerical Definitions</refname><refpurpose>mathematical constants, and floating point decomposition.</refpurpose>
</refnamediv>
<refsynopsisdiv><title>Synopsis</title>
<synopsis>
#include <glib.h>
#define <link linkend="G-IEEE754-FLOAT-BIAS-CAPS">G_IEEE754_FLOAT_BIAS</link>
#define <link linkend="G-IEEE754-DOUBLE-BIAS-CAPS">G_IEEE754_DOUBLE_BIAS</link>
union <link linkend="GFloatIEEE754">GFloatIEEE754</link>;
union <link linkend="GDoubleIEEE754">GDoubleIEEE754</link>;
#define <link linkend="G-E-CAPS">G_E</link>
#define <link linkend="G-LN2-CAPS">G_LN2</link>
#define <link linkend="G-LN10-CAPS">G_LN10</link>
#define <link linkend="G-PI-CAPS">G_PI</link>
#define <link linkend="G-PI-2-CAPS">G_PI_2</link>
#define <link linkend="G-PI-4-CAPS">G_PI_4</link>
#define <link linkend="G-SQRT2-CAPS">G_SQRT2</link>
#define <link linkend="G-LOG-2-BASE-10-CAPS">G_LOG_2_BASE_10</link>
</synopsis>
</refsynopsisdiv>
<refsect1>
<title>Description</title>
<para>
GLib offers mathematical constants such as <link linkend="G-PI-CAPS"><type>G_PI</type></link> for the value of pi;
many platforms have these in the C library, but some don't, the GLib
versions always exist.
</para>
<para>
The <link linkend="GFloatIEEE754"><type>GFloatIEEE754</type></link> and <link linkend="GDoubleIEEE754"><type>GDoubleIEEE754</type></link> unions are used to access the
sign, mantissa and exponent of IEEE floats and doubles. These
unions are defined as appropriate for a given platform.
IEEE floats and doubles are supported (used for
storage) by at least Intel, PPC and Sparc, for reference: <ulink url="http://cch.loria.fr/documentation/IEEE754/numerical_comp_guide/ncg_math.doc.html">http://cch.loria.fr/documentation/IEEE754/numerical_comp_guide/ncg_math.doc.html</ulink>
</para>
</refsect1>
<refsect1>
<title>Details</title>
<refsect2>
<title><anchor id="G-IEEE754-FLOAT-BIAS-CAPS"/>G_IEEE754_FLOAT_BIAS</title>
<indexterm><primary>G_IEEE754_FLOAT_BIAS</primary></indexterm><programlisting>#define G_IEEE754_FLOAT_BIAS (127)
</programlisting>
<para>
See <ulink url="http://cch.loria.fr/documentation/IEEE754/numerical_comp_guide/ncg_math.doc.html">http://cch.loria.fr/documentation/IEEE754/numerical_comp_guide/ncg_math.doc.html</ulink>
</para></refsect2>
<refsect2>
<title><anchor id="G-IEEE754-DOUBLE-BIAS-CAPS"/>G_IEEE754_DOUBLE_BIAS</title>
<indexterm><primary>G_IEEE754_DOUBLE_BIAS</primary></indexterm><programlisting>#define G_IEEE754_DOUBLE_BIAS (1023)
</programlisting>
<para>
See <ulink url="http://cch.loria.fr/documentation/IEEE754/numerical_comp_guide/ncg_math.doc.html">http://cch.loria.fr/documentation/IEEE754/numerical_comp_guide/ncg_math.doc.html</ulink>
</para></refsect2>
<refsect2>
<title><anchor id="GFloatIEEE754"/>union GFloatIEEE754</title>
<indexterm><primary>GFloatIEEE754</primary></indexterm><programlisting>union GFloatIEEE754
{
gfloat v_float;
struct {
guint mantissa : 23;
guint biased_exponent : 8;
guint sign : 1;
} mpn;
};
</programlisting>
<para>
The <link linkend="GFloatIEEE754"><type>GFloatIEEE754</type></link> and <link linkend="GDoubleIEEE754"><type>GDoubleIEEE754</type></link> unions are used to access the
sign, mantissa and exponent of IEEE floats and doubles. These
unions are defined as appropriate for a given platform.
IEEE floats and doubles are supported (used for
storage) by at least Intel, PPC and Sparc, for reference:
<ulink url="http://cch.loria.fr/documentation/IEEE754/numerical_comp_guide/ncg_math.doc.html">http://cch.loria.fr/documentation/IEEE754/numerical_comp_guide/ncg_math.doc.html</ulink>
</para></refsect2>
<refsect2>
<title><anchor id="GDoubleIEEE754"/>union GDoubleIEEE754</title>
<indexterm><primary>GDoubleIEEE754</primary></indexterm><programlisting>union GDoubleIEEE754
{
gdouble v_double;
struct {
guint mantissa_low : 32;
guint mantissa_high : 20;
guint biased_exponent : 11;
guint sign : 1;
} mpn;
};
</programlisting>
<para>
The <link linkend="GFloatIEEE754"><type>GFloatIEEE754</type></link> and <link linkend="GDoubleIEEE754"><type>GDoubleIEEE754</type></link> unions are used to access the
sign, mantissa and exponent of IEEE floats and doubles. These
unions are defined as appropriate for a given platform.
IEEE floats and doubles are supported (used for
storage) by at least Intel, PPC and Sparc, for reference:
<ulink url="http://cch.loria.fr/documentation/IEEE754/numerical_comp_guide/ncg_math.doc.html">http://cch.loria.fr/documentation/IEEE754/numerical_comp_guide/ncg_math.doc.html</ulink>
</para></refsect2>
<refsect2>
<title><anchor id="G-E-CAPS"/>G_E</title>
<indexterm><primary>G_E</primary></indexterm><programlisting>#define G_E 2.7182818284590452354E0
</programlisting>
<para>
The base of natural logarithms.
</para></refsect2>
<refsect2>
<title><anchor id="G-LN2-CAPS"/>G_LN2</title>
<indexterm><primary>G_LN2</primary></indexterm><programlisting>#define G_LN2 6.9314718055994530942E-1
</programlisting>
<para>
The natural logarithm of 2.
</para></refsect2>
<refsect2>
<title><anchor id="G-LN10-CAPS"/>G_LN10</title>
<indexterm><primary>G_LN10</primary></indexterm><programlisting>#define G_LN10 2.3025850929940456840E0
</programlisting>
<para>
The natural logarithm of 10.
</para></refsect2>
<refsect2>
<title><anchor id="G-PI-CAPS"/>G_PI</title>
<indexterm><primary>G_PI</primary></indexterm><programlisting>#define G_PI 3.14159265358979323846E0
</programlisting>
<para>
The value of pi (ratio of circle's circumference to its diameter).
</para></refsect2>
<refsect2>
<title><anchor id="G-PI-2-CAPS"/>G_PI_2</title>
<indexterm><primary>G_PI_2</primary></indexterm><programlisting>#define G_PI_2 1.57079632679489661923E0
</programlisting>
<para>
Pi divided by 2.
</para></refsect2>
<refsect2>
<title><anchor id="G-PI-4-CAPS"/>G_PI_4</title>
<indexterm><primary>G_PI_4</primary></indexterm><programlisting>#define G_PI_4 0.78539816339744830962E0
</programlisting>
<para>
Pi divided by 4.
</para></refsect2>
<refsect2>
<title><anchor id="G-SQRT2-CAPS"/>G_SQRT2</title>
<indexterm><primary>G_SQRT2</primary></indexterm><programlisting>#define G_SQRT2 1.4142135623730950488E0
</programlisting>
<para>
The square root of two.
</para></refsect2>
<refsect2>
<title><anchor id="G-LOG-2-BASE-10-CAPS"/>G_LOG_2_BASE_10</title>
<indexterm><primary>G_LOG_2_BASE_10</primary></indexterm><programlisting>#define G_LOG_2_BASE_10 (0.30102999566398119521)
</programlisting>
<para>
Used for fooling around with float formats, see
<ulink url="http://cch.loria.fr/documentation/IEEE754/numerical_comp_guide/ncg_math.doc.html">http://cch.loria.fr/documentation/IEEE754/numerical_comp_guide/ncg_math.doc.html</ulink>
</para></refsect2>
</refsect1>
<refsect1>
<title>See Also</title>
<para>
<ulink url="http://cch.loria.fr/documentation/IEEE754/numerical_comp_guide/ncg_math.doc.html">http://cch.loria.fr/documentation/IEEE754/numerical_comp_guide/ncg_math.doc.html</ulink>
</para>
</refsect1>
</refentry>