NAME
    atan2 - returns arctangent of scalars and vectors.

SYNOPSIS
      float  atan2( float  y, float  x );
      float1 atan2( float1 y, float1 x );
      float2 atan2( float2 y, float2 x );
      float3 atan2( float3 y, float3 x );
      float4 atan2( float4 y, float4 x );
 
      half   atan2( half  y, half x );
      half1  atan2( half1 y, half x );
      half2  atan2( half2 y, half x );
      half3  atan2( half3 y, half x );
      half4  atan2( half4 y, half x );
 
      fixed  atan2( fixed  y, fixed x );
      fixed1 atan2( fixed1 y, fixed x );
      fixed2 atan2( fixed2 y, fixed x );
      fixed3 atan2( fixed3 y, fixed x );
      fixed4 atan2( fixed4 y, fixed x );

PARAMETERS
    y       Vector or scalar for numerator of ratio of which to determine
            the arctangent.

    x       Vector or scalar of denominator of ratio of which to determine
            the arctangent.

DESCRIPTION
    atan2 calculates the arctangent of y/x. atan2 is well defined for every
    point other than the origin, even if x equals 0 and y does not equal 0.

    For vectors, the returned vector contains the arctangent of each element
    of the input vector.

REFERENCE IMPLEMENTATION
    atan2 for a float2 scalar could be implemented as an approximation like
    this.

      float2 atan2(float2 y, float2 x)
      {
        float2 t0, t1, t2, t3, t4;
  
        t3 = abs(x);
        t1 = abs(y);
        t0 = max(t3, t1);
        t1 = min(t3, t1);
        t3 = float(1) / t0;
        t3 = t1 * t3;
    
        t4 = t3 * t3;
        t0 =         - float(0.013480470);
        t0 = t0 * t4 + float(0.057477314);
        t0 = t0 * t4 - float(0.121239071);
        t0 = t0 * t4 + float(0.195635925);
        t0 = t0 * t4 - float(0.332994597);
        t0 = t0 * t4 + float(0.999995630);
        t3 = t0 * t3;
    
        t3 = (abs(y) > abs(x)) ? float(1.570796327) - t3 : t3;
        t3 = (x < 0) ?  float(3.141592654) - t3 : t3;
        t3 = (y < 0) ? -t3 : t3;
    
        return t3;
      }    

PROFILE SUPPORT
    atan2 is supported in all profiles except fp20.

SEE ALSO
    the abs manpage, the acos manpage, the asin manpage, the atan manpage,
    the sqrt manpage, the tan manpage

