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.

Input Arguments


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:

  • fi single

  • fi double

  • fi fixed-point with binary point scaling

  • fi scaled double with binary point scaling

Output Arguments


z is the four-quadrant arctangent of y/x. The numerictype of z depends on the signedness of y and x:

  • If either y or x is signed, z is a signed, fixed-point number in the range [–pi,pi]. It has a 16-bit word length and 13-bit fraction length (numerictype(1,16,13)).

  • If both y and x are unsigned, z is an unsigned, fixed-point number in the range [0,pi/2]. It has a 16-bit word length and 15-bit fraction length (numerictype(0,16,15)).

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 =

          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 =

          DataTypeMode: Fixed-point: binary point scaling
            Signedness: Signed
            WordLength: 16
        FractionLength: 13

More About

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Four-Quadrant Arctangent

The four-quadrant arctangent is defined as follows, with respect to the atan function:

atan2(y,x)={atan(yx)            x>0π+atan(yx)      y0,x<0π+atan(yx)    y<0,x<0π2                        y>0,x=0π2                      y<0,x=00                          y=0,x=0


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The atan2 function computes the four-quadrant arctangent of fixed-point inputs using an 8-bit lookup table as follows:

  1. 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.

  2. Compute the table index, based on the 16-bit, unsigned, stored integer value:

    1. Use the 8 most-significant bits to obtain the first value from the table.

    2. Use the next-greater table value as the second value.

  3. 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).

  4. Perform octant correction on the resulting angle, based on the values of the original y and x inputs.

fimath Propagation Rules

The atan2 function ignores and discards any fimath attached to the inputs. The output, z, is always associated with the default fimath.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Introduced in R2012a

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