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.rm #[ #] #H #V #F C
.IX Title "cos Cg"
.TH cos Cg "" "Cg Toolkit 1.5" "Cg Standard Library"
.UC
.SH "NAME"
\&\fBcos\fR \- returns cosine of scalars and vectors.
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 5
\&  float  cos( float  a );
\&  float1 cos( float1 a );
\&  float2 cos( float2 a );
\&  float3 cos( float3 a );
\&  float4 cos( float4 a );
.Ve
.Vb 5
\&  half   cos( half  a );
\&  half1  cos( half1 a );
\&  half2  cos( half2 a );
\&  half3  cos( half3 a );
\&  half4  cos( half4 a );
.Ve
.Vb 5
\&  fixed  cos( fixed  a );
\&  fixed1 cos( fixed1 a );
\&  fixed2 cos( fixed2 a );
\&  fixed3 cos( fixed3 a );
\&  fixed4 cos( fixed4 a );
.Ve
.SH "PARAMETERS"
.IX Header "PARAMETERS"
.Ip "a" 8
.IX Item "a"
Vector or scalar of which to determine the cosine.
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
Returns the cosine of \fIa\fR in radians. The return value is in the range
[\-1,+1].
.PP
For vectors, the returned vector contains the cosine of each
element of the input vector.
.SH "REFERENCE IMPLEMENTATION"
.IX Header "REFERENCE IMPLEMENTATION"
\&\fBcos\fR is best implemented as a native cosine instruction, however \fBcos\fR
for a \fBfloat\fR scalar could be implemented by an approximation like this.
.PP
.Vb 8
\&  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            );
.Ve
.Vb 2
\&    /* r0.x = cos(a) */
\&    float3 r0, r1, r2;
.Ve
.Vb 13
\&    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
.Ve
.Vb 1
\&    return r0.x;
.Ve
.SH "PROFILE SUPPORT"
.IX Header "PROFILE SUPPORT"
\&\fBcos\fR is fully supported in all profiles unless otherwise specified.
.PP
\&\fBcos\fR is supported via an approximation (shown above) in the
vs_1, vp20, and arbvp1 profiles.
.PP
\&\fBcos\fR is unsupported in the fp20 and ps_1 profiles.
.SH "SEE ALSO"
.IX Header "SEE ALSO"
the acos manpage,
the dot manpage,
the frac manpage,
the sin manpage,
the tan manpage
