Fast CORDIC algorithm with sine governed termination

A method for performing a two-dimensional rotation using a succession of CORDIC iterations, the method comprising:

• accessing a first point from a first memory location, wherein said first point specifies a location in a two-dimensional coordinate system;
• accessing a first angle value from a second memory location;
• applying the succession of CORDIC iterations to the first point and the first angle value in order to generate an output point and an output angle value, wherein each of said CORDIC iterations comprises a shift operation and an arithmetic operation;
• and
• operating on the output point and the output angle value in order to generate a rotated two-dimensional point, wherein said rotated two-dimensional point corresponds to a rotated image of the first point by an angle corresponding to the first angle value, wherein said operating comprises determining a cosine of said output angle value and multiplying said cosine by a first coordinate of said output point to generate a first product.

A system for performing a two dimensional rotation comprising:

• a succession of CORDIC stages, wherein a first CORDIC stage of said succession is configured to receive a two-dimensional input point and a rotation angle, wherein a last CORDIC stage of said succession is configured to generate an output point and an output angle;
• a completion unit coupled to the last CORDIC stage, wherein the completion unit is configured (a) to operate on the output point and output angle and (b) to generate a rotated two-dimensional point, wherein the rotated two-dimensional point comprises a rotated image of the two-dimensional input point by an angle corresponding to the rotation angle, wherein the completion unit comprises:
• a cosine unit coupled to receive the output angle from the last CORDIC stage, wherein said cosine unit is configured to compute a cosine value of the output angle;
• a first multiplication unit coupled to the cosine unit and further coupled to receive a first coordinate of said output point from the last CORDIC stage, wherein the first multiplication unit is configured to multiply the cosine value by the first coordinate to generate a first product.

A system for performing a function evaluation comprising:

• a succession of CORDIC stages, wherein a first CORDIC stage of said succession receives an input point and an input angle value, wherein a last CORDIC stage of said succession generates an output point and an output angle value;
• a completion unit coupled to the last CORDIC stage, and configured (a) to operate on the output point and output angle value, and (b) to generate a first resultant value which represents an evaluation of a first function, wherein the completion unit comprises:
• a cosine unit coupled to receive the output angle value from the last CORDIC stage, wherein the cosine unit is configured to compute a cosine of the output angle value;
• a first multiplication unit coupled to the cosine unit and further coupled to receive a first coordinate of the output point from the last CORDIC stage, wherein the first multiplication unit is configured to multiply the cosine by the first coordinate to generate a first product.