Four-quadrant inverse tangent of fixed-point values
z = atan2(y,x)
z = atan2(y,x) returns the four-quadrant arctangent of fi input y/x using a table-lookup algorithm.
y and x can be real-valued, signed or unsigned scalars, vectors, matrices, or N-dimensional arrays containing fixed-point angle values in radians. The lengths of y and x must be the same. If they are not the same size, at least one input must be a scalar value. Valid data types of y and x are:
z is the four-quadrant arctangent of y/x. The numerictype of z depends on the signedness of y and x:
This arctangent calculation is accurate only to within the top 16 most-significant bits of the input.
Calculate the arctangent of unsigned and signed fixed-point input values. The first example uses unsigned, 16-bit word length values. The second example uses signed, 16-bit word length values.
y = fi(0.125,0,16); x = fi(0.5,0,16); z = atan2(y,x) z = 0.2450 DataTypeMode: Fixed-point: binary point scaling Signedness: Unsigned WordLength: 16 FractionLength: 15 y = fi(-0.1,1,16); x = fi(-0.9,1,16); z = atan2(y,x) z = -3.0309 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 16 FractionLength: 13
The four-quadrant arctangent is defined as follows, with respect to the atan function:
The atan2 function computes the four-quadrant arctangent of fixed-point inputs using an 8-bit lookup table as follows:
Divide the input absolute values to get an unsigned, fractional, fixed-point, 16-bit ratio between 0 and 1. The absolute values of y and x determine which value is the divisor.
The signs of the y and x inputs determine in what quadrant their ratio lies. The input with the larger absolute value is used as the denominator, thus producing a value between 0 and 1.
Compute the table index, based on the 16-bit, unsigned, stored integer value:
Use the 8 most-significant bits to obtain the first value from the table.
Use the next-greater table value as the second value.
Use the 8 least-significant bits to interpolate between the first and second values using nearest neighbor linear interpolation. This interpolation produces a value in the range [0, pi/4).
Perform octant correction on the resulting angle, based on the values of the original y and x inputs.
The atan2 function ignores and discards any fimath attached to the inputs. The output, z, is always associated with the default fimath.