NAME

acos - returns arccosine of scalars and vectors.

SYNOPSIS

  float  acos( float  a );
  float1 acos( float2 a );
  float2 acos( float2 a );
  float3 acos( float3 a );
  float4 acos( float4 a );
 
  half   acos( half  a );
  half1  acos( half2 a );
  half2  acos( half2 a );
  half3  acos( half3 a );
  half4  acos( half4 a );
 
  fixed  acos( fixed  a );
  fixed1 acos( fixed2 a );
  fixed2 acos( fixed2 a );
  fixed3 acos( fixed3 a );
  fixed4 acos( fixed4 a );

PARAMETERS

a

Vector or scalar of which to determine the arccosine.

DESCRIPTION

Returns the arccosine of a in the range [0,pi], expecting a to be in the range [-1,+1].

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

REFERENCE IMPLEMENTATION

acos for a float scalar could be implemented like this.

  // Handbook of Mathematical Functions
  // M. Abramowitz and I.A. Stegun, Ed.

  // Absolute error <= 6.7e-5
  float acos(float x) {
    float negate = float(x < 0);
    x = abs(x);
    float ret = -0.0187293;
    ret = ret * x;
    ret = ret + 0.0742610;
    ret = ret * x;
    ret = ret - 0.2121144;
    ret = ret * x;
    ret = ret + 1.5707288;
    ret = ret * sqrt(1.0-x);
    ret = ret - 2 * negate * ret;
    return negate * 3.14159265358979 + ret;
  }

PROFILE SUPPORT

acos is supported in all profiles.

Support in the fp20 is limited.

SEE ALSO

abs, asin, cos, sqrt