Taraṅga

The Signal Lab

Don't take the
paper's word for it.

These three instruments run the same LFSR semantics as the released RTL, live in your tab — no servers, nothing recorded. They are the paper's three central claims, made touchable: the one-gate multiply, the free dithering, and the graceful failure.

Instrument 1 · sc_mul.v — synthesized cell count: 1

Multiply with one gate.

Two values become pulse densities; one AND gate computes their product; a counter reads it back. Drag the sliders, reseed the streams, and watch 1/√L do its honest work.

Value A0.70
Value B0.45
Exact A×B
0.3150
One AND gate says
0.3125
|error| = 0.0025 at L=2,048 — precision improves as 1/√L, the honest price.
stream A — density 69%
stream B — density 45%
A ∧ B — THE ENTIRE MULTIPLIER
product stream — density 31.3%
Running estimate vs exact — convergence over 2,048 bits
RMS error vs stream length (16 fresh trials each)
L=16
0.169
L=64
0.070
L=256
0.024
L=1024
0.013
L=4096
0.007
Instrument 2 · the white-noise dithering theorem, live

Banding, dissolved by physics.

Drop the display to 3 bits and binary draws contour lines. The stochastic estimate at the same depth renders smooth — its quantization noise is provably white, which is exactly what display engineers pay extra hardware for.

Display depth3-bit · 8 levels
Stream length L256
6425610244096

Same gradient, same 3-bit display. Binary quantization draws contour lines — banding. The stochastic estimate's noise is spectrally white (proved in the paper), so the eye integrates it into a smooth ramp. The dithering hardware costs nothing: it is the arithmetic.

Binary — quantized to 3 bits
StochastiCore — same 3-bit display, L=256
Instrument 3 · the ~0.5% BER crossover, live

The wave bends. The integer shatters.

Inject bit errors into both representations of the same image. In binary, a flipped MSB is a half-scale explosion; in a stream, any flipped bit is worth 1/L. Find the crossover yourself — including the region below it where binary honestly wins.

Bit-error rate1.00%
0%0.5% crossover5%
Binary RMSE
0.0000
SC RMSE (L=256)
0.0000
Below the crossover (~0.5% BER): binary's exactness still beats SC's stream noise. Honest physics — slide right to see it invert.
Binary 8-bit under faults — salt-and-pepper catastrophe
StochastiCore under the same faults — graceful blur toward gray

Same gradient, same per-bit fault probability, fresh random pattern each run. The paper's site-resolved version (N=10,000, 95% CI) puts the compute-domain crossover at ~0.5% BER — matching the analytic 0.6%. Storage and control faults are a different story, and the paper says so.

Everything above is the browser miniature of the released design — the real thing is synthesizable Verilog that fits a $25–55 FPGA and drives a VGA monitor. Build it for $80–150 →