163 Asynchronous Multiplier
163 : Asynchronous Multiplier
- Author: Tommy Thorn
- Description: An asynchronous multiplier
- GitHub repository
- Clock: 50000000 Hz
How it works
This design emits a sequence of r = x^2+x, for x=0,1,2,... on the
outputs using the handshake protocol (tie ack to req to get free
running sequence). Well, in truth, we use 26-bits of internal
precision, but we only have 15-bits for outputs, we what is actually
emitted is r ^ (r >> 15).
The very naive algorithm (with the body unrolled once) is
x = 0
loop:
x = x + 1
a = b = c = x
while b != 0:
if (b & 1) == 1:
c += a
a *= 2
b /= 2
if (b & 1) == 1:
c += a
a *= 2
b /= 2
output (c)
which was hand translated (roughly following Introduction to Asynchronous Circuit Design ) into a token flow graph:
Note, I use a simpler, less expensive, construction for the conditional iteration as having independent control-flow for the trivial condition is overkill.
The graph was realized using four-phase bundled data. Alas, I'm still working on the timing analysis, so the inserted delays are (hopefully) way oversized.
How to test
The data is presented using the standard 4-phase (RTZ) protocol (idle, Req, Req+Ack, Ack, idle, ...). To get a continuous stream, simply tie ack to req. The values expected are 0, 2, 6, ..., x(x+1)
External hardware
A logic analyzer is convenient to pick up the values on the outputs, but default RP2040 works fine.
IO
| # | Input | Output | Bidirectional |
|---|---|---|---|
| 0 | ack | req | result_7 |
| 1 | result_0 | result_8 | |
| 2 | result_1 | result_9 | |
| 3 | result_2 | result_10 | |
| 4 | result_3 | result_11 | |
| 5 | result_4 | result_12 | |
| 6 | result_5 | result_13 | |
| 7 | result_6 | result_14 |