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<BLOCKQUOTE>
<H1><A NAME="NAME"><A NAME="1">NAME
</A></A></H1>
<P>
<B>cos</B> - returns cosine of scalars and vectors.
</P>
<H1><A NAME="SYNOPSIS"><A NAME="2">SYNOPSIS
</A></A></H1>
<PRE> float cos(float a);
float1 cos(float1 a);
float2 cos(float2 a);
float3 cos(float3 a);
float4 cos(float4 a);
half cos(half a);
half1 cos(half1 a);
half2 cos(half2 a);
half3 cos(half3 a);
half4 cos(half4 a);
fixed cos(fixed a);
fixed1 cos(fixed1 a);
fixed2 cos(fixed2 a);
fixed3 cos(fixed3 a);
fixed4 cos(fixed4 a);
</PRE>
<H1><A NAME="PARAMETERS"><A NAME="3">PARAMETERS
</A></A></H1>
<DL>
<DT><STRONG>a
</STRONG></DT>
<DD>
<P>
Vector or scalar of which to determine the cosine.
</P>
</DD></DL>
<H1><A NAME="DESCRIPTION"><A NAME="4">DESCRIPTION
</A></A></H1>
<P>
Returns the cosine of <I>a</I> in radians. The return value is in the range
[-1,+1].
</P>
<P>
For vectors, the returned vector contains the cosine of each
element of the input vector.
</P>
<H1><A NAME="REFERENCE_IMPLEMENTATION"><A NAME="5">REFERENCE IMPLEMENTATION
</A></A></H1>
<P>
<B>cos</B> is best implemented as a native cosine instruction, however <B>cos</B>
for a <B>float</B> scalar could be implemented by an approximation like this.
</P>
<PRE> cos(float a)
{
/* C simulation gives a max absolute error of less than 1.8e-7 */
const float4 c0 = float4( 0.0, 0.5,
1.0, 0.0 );
const float4 c1 = float4( 0.25, -9.0,
0.75, 0.159154943091 );
const float4 c2 = float4( 24.9808039603, -24.9808039603,
-60.1458091736, 60.1458091736 );
const float4 c3 = float4( 85.4537887573, -85.4537887573,
-64.9393539429, 64.9393539429 );
const float4 c4 = float4( 19.7392082214, -19.7392082214,
-1.0, 1.0 );
/* r0.x = cos(a) */
float3 r0, r1, r2;
r1.x = c1.w * a; // normalize input
r1.y = frac( r1.x ); // and extract fraction
r2.x = (float) ( r1.y < c1.x ); // range check: 0.0 to 0.25
r2.yz = (float2) ( r1.yy >= c1.yz ); // range check: 0.75 to 1.0
r2.y = dot( r2, c4.zwz ); // range check: 0.25 to 0.75
r0 = c0.xyz - r1.yyy; // range centering
r0 = r0 * r0;
r1 = c2.xyx * r0 + c2.zwz; // start power series
r1 = r1 * r0 + c3.xyx;
r1 = r1 * r0 + c3.zwz;
r1 = r1 * r0 + c4.xyx;
r1 = r1 * r0 + c4.zwz;
r0.x = dot( r1, -r2 ); // range extract
return r0.x;
</PRE>
<H1><A NAME="PROFILE_SUPPORT"><A NAME="6">PROFILE SUPPORT
</A></A></H1>
<P>
<B>cos</B> is fully supported in all profiles unless otherwise specified.
</P>
<P>
<B>cos</B> is supported via an approximation (shown above) in the
<A HREF="vs_1_1.html">vs_1_1</A>, <A HREF="vp20.html">vp20</A>, and <A HREF="arbvp1.html">arbvp1</A> profiles.
</P>
<P>
<B>cos</B> is unsupported in the <A HREF="fp20.html">fp20</A>, <A HREF="ps_1_1.html">ps_1_1</A>, <A HREF="ps_1_2.html">ps_1_2</A>, and <A HREF="ps_1_3.html">ps_1_3</A> profiles.
</P>
<H1><A NAME="SEE_ALSO"><A NAME="7">SEE ALSO
</A></A></H1>
<P>
<A HREF="acos.html"><I>acos</I></A>, <A HREF="dot.html"><I>dot</I></A>, <A HREF="frac.html"><I>frac</I></A>, <A HREF="sin.html"><I>sin</I></A>, <A HREF="sincos.html"><I>sincos</I></A>, <A HREF="tan.html"><I>tan</I></A>
</P>
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