16-bit Cosine Function

COS_X calculates the cosine of an angle in radians. It has a fully pipelined architecture and uses fixed-point mathematics throughout. Input values are accepted as 16-bit unsigned values in the range 0 to π/2. Output values are 16-bit unsigned values in the range 0 to 1. For input values greater than π/2, the output clips to 0. Both input and output values are in [16 15] format with 1 integer bit and 15 fraction bits. As an example the input value 0xC000 would signify the value 1.5.

Internally, the function uses a 2^nd order polynomial of the form:

y = ax² + bx + c

The coefficients a, b and c dynamically change with respect to the input value in order to generate a more accurate approximation. The output result is accurate to within 0.0002.

Values are sampled on the rising clock-edge of clk when en is high. The function has a 3 clock-cycle latency.

• Synthesizable, technology independent VHDL Core
• Function y = cos(x)
• Input range 0 ≤ x ≤ π /2 (Quarter wave)
• Output range 0 ≤ y ≤ 1
• Based on a quadratic polynomial with dynamic coefficients
• Input values as 16-bit unsigned fractions
• Output values as 16-bit unsigned fractions in radians
• Accurate to within 0.0002
• High-speed fully pipelined architecture
• 3 clock-cycle latency

• Fixed-point mathematics
• Quadrature signal generation in digital communications
• Alternative to using a 65536 x 16-bit LUT (128kbytes)