355 CORDIC sin/cos generator :: Quicker, easier and cheaper to make your own chip!

How it works

This project computes the sine and cosine of an input angle using an iterative CORDIC (COordinate Rotation DIgital Computer) algorithm.

The angle is supplied as a 7-bit value on ui[6:0], where 0–127 maps linearly to 0°–360° (so each step is 360 / 128 ≈ 2.81°). Asserting start on ui[7] begins a computation.

Internally the design works in Q2.6 fixed-point (8-bit two's-complement, where 1.0 = 64 = 0x40):

Quadrant fold — the angle is reduced to the first quadrant (0°–90°), and per-quadrant sign flags are recorded so the result can be reflected back into the correct quadrant.
Rotation — a vector is pre-scaled by the CORDIC gain (1/K ≈ 0.607) and rotated through 8 fixed micro-rotations of arctan(2^-i), each taken from a small lookup table. A small FSM (IDLE → LOAD → 8× COMPUTE → DONE) sequences the iterations; each iteration drives a residual-angle accumulator toward zero while the vector's X and Y components converge to cos and sin.
Sign correction — the recorded quadrant flags are applied, producing the final signed sin and cos.

A result is ready roughly 11 clock cycles after start is asserted. start is a level: hold it high to recompute continuously, release it to freeze and hold the last result.

The outputs are 8-bit two's-complement Q2.6 values:

Raw (hex)	Decimal	Real value
`0x40`	+64	+1.0
`0x00`	0	0.0
`0xC0`	−64	−1.0

(Convert any output to its real value with raw / 64.)

sin appears on uo[7:0], cos on uio[7:0] (the bidirectional pins, configured as outputs).

How to test

Put a 7-bit angle on ui[6:0] (0–127 = 0°–360°).
Drive start (ui[7]) high to trigger a computation, then low to latch the result.
After ~11 clock cycles, read sin on uo[7:0] and cos on uio[7:0]. Interpret both as signed Q2.6 (value = raw / 64).

Example angles (input code → angle → expected outputs):

`ui[6:0]`	Angle	`sin` (uo)	`cos` (uio)
0	0°	`0x00` (0)	`0x40` (+1.0)
16	45°	`0x2E` (≈0.72)	`0x2C` (≈0.69)
32	90°	`0x41` (≈+1.0)	`0x01` (≈0)
64	180°	`0x00` (≈0)	`0xC0` (−1.0)
96	270°	`0xBF` (≈−1.0)	`0x01` (≈0)

Outputs are within ±a few LSB of the ideal due to the 8-iteration, 8-bit fixed-point approximation. The included cocotb test (test/test.py) sweeps all 128 angles and checks them bit-exactly against a golden CORDIC model.

External hardware

No external hardware is required to drive the design — the angle and start come from the demo board's input switches.

To view the outputs:

sin is on uo[7:0], which drives the demo board's 8 on-board LEDs directly.
cos is on uio[7:0] (the bidirectional/PMOD pins). To see it, attach an 8-bit LED PMOD (or any 8-LED breakout) to the uio header. This is optional — cos is still readable via the RP2040/test harness without it.

#	Input	Output	Bidirectional
0	angle[0]	sin[0]	cos[0]
1	angle[1]	sin[1]	cos[1]
2	angle[2]	sin[2]	cos[2]
3	angle[3]	sin[3]	cos[3]
4	angle[4]	sin[4]	cos[4]
5	angle[5]	sin[5]	cos[5]
6	angle[6]	sin[6]	cos[6]
7	start	sin[7]	cos[7]

355 CORDIC sin/cos generator