Zero Transcendentals — CRI Softmax & PwL Activations

The Sibacus datapath eliminates every transcendental function from the inference pipeline. exp(), erf(), sigmoid(), tanh(), and division are all replaced by shifts, adds, and comparisons — hardware that maps to any CMOS node.

exp() erf() sigmoid() tanh() ÷ division ✓ shifts + adds only
Pipeline Comparison — Traditional Softmax vs CRI
✗ Traditional Softmax
📥 Input scores x₁…xₙ Buffer
↓
📈 exp(xᵢ) for each score FP EXP UNIT
↓
∑ Σ exp(xᵢ) FP ADDER
↓
➗ exp(xᵢ) / Σ exp(xⱼ) FP DIVIDER
↓
📤 Probability outputs FP OUT
✓ CRI Softmax (Sibacus)
📥 Input scores x₁…xₙ Buffer
↓
⚖️ Comparator → max(x), min(x) CMP TREE
↓
🔄 g₀=(max−min)≫1, h₀=(max+min)≫1 SHIFT+ADD
↓
⏱️ q iterations: g≫1, h=(h+g)≫1 FSM LOOP
↓
📤 CRI softmax outputs INT OUT
Interactive CRI Recurrence — Step-by-Step Animation
4
Press ▶ Run to animate the CRI softmax recurrence
Input Attention Scores
Register g (half-range)
—
Register h (midpoint)
—
Barrel Shifter — Right Shift ≫1 (bits slide right, MSB fills 0)
Iteration Log
PwL Activation Unit — Piecewise-Linear GELU Approximation
True GELU
PwL (P=16)
Segment boundaries
Abs. Error

How PwL Works

The GELU curve is split into P = 16 linear segments. For each input x, a comparator selects the matching segment, then the output is computed as:

GELU(x) ≈ slope_r × x + offset_k

The key insight: each slope_r is constrained to be a power of two during training, so the multiplication becomes a single BSA shift.

Why No Lookup Table?

Unlike LUT-based approaches that store thousands of entries, PwL needs only 16 slope + 16 offset values — stored in tiny registers. The computation is a shift, an add, and a comparator. Nothing else.

Sample Segments

RangeSlopeShiftOffset
The Zero-Transcendental Datapath — Complete Sibacus PE
No exp. No erf. No sigmoid. No divider. No multiplier.

The entire Sibacus inference datapath is built from barrel shifters, integer adders, and comparators — primitive logic that maps cleanly to any CMOS process node. This is not a simplification. It's the complete datapath. CRI softmax and PwL activations together guarantee that no transcendental function evaluation hardware exists anywhere in the chip.

"The PwL activation unit and CRI softmax circuit together eliminate every transcendental function from the inference pipeline."