Synthesis of Arithmetic Circuits: FPGA, ASIC and Embedded Systems

14.5 SINE AND COSINE OPERATORS

This section presents an implementation for sine and cosine computation using CORDIC Algorithm 7.10 as described in Section 7.3.4. The circuit presented in Figure 14.19 is basically made up of three loop-circuits. The auxiliary sequence (upper loop) computes the successive values of the residual rotation angle a_i. A lookup table provides the successive values of tan⁻¹ 2⁻ⁱ to be added or subtracted from the current angle value a_i stored in register A: if a_i is negative, a_i+1 is computed as

Figure 14.19 CORDIC algorithm implementation for sine and cosine computation.

Otherwise, if a_i is positive,

The initial value a₀ is the argument angle a.

The main sequences, computing sin a (register Y) and cos a (register X) are built up according to the following rules:

If a_i is positive,

Otherwise, if a_i is negative,

As quoted in Section 7.3.4, the argument a can be ...