Document ID: JANUS-ALG-SPEC-MINI16-2026-V1
Companion To: JANUS-SIM-SPEC-MINI16-2026-V1 (Co-Simulation Specification)
Target Hardware: JANUS Mini 16-Tile Monolithic Planar MVP (Model 1A)
Classification: Algorithm Design Document / Verification Flowcharts
Lead Architect: Deepanshu Bhardwaj
Status: Approved for Implementation
The master orchestrator (run_mini16_full_cosim.py) executes all five tiers in dependency order, propagating inter-tier data products through HDF5 files and Touchstone S-parameter archives.
+=============================================================================+
| MASTER ORCHESTRATION PIPELINE (run_mini16_full_cosim.py) |
+=============================================================================+
| |
| [START] --> Load mini_16t_constants.py (240 Global Variables) |
| | |
| v |
| +---------------------------------------------------------------+ |
| | TIER 1: MEEP FDTD (Electro-Optics) | |
| | IN: Global constants, GST-467 material models | |
| | OUT: S-parameters (.s4p), Heat map Q_opt(x,y,z) (.hdf5) | |
| +---------------------------------------------------------------+ |
| | | |
| | S-params | Q_opt heat map |
| v v |
| +-------------------+ +--------------------------------------------+ |
| | TIER 3: XYCE | | TIER 2: ELMER FEM (Thermal) | |
| | (Circuit/Signal) | | IN: Q_opt + CMOS heat + global constants | |
| | IN: S-params, | | OUT: Thermal ROM (Foster RC matrix) | |
| | APD model, | +--------------------------------------------+ |
| | global consts | | |
| | OUT: Eye diagrams,| | Thermal ROM |
| | BER, jitter | | |
| +-------------------+ | |
| | | |
| | BER + delays | |
| v v |
| +---------------------------------------------------------------+ |
| | TIER 4: COCOTB + VERILATOR (Digital RTL) | |
| | IN: Global constants, timing constraints | |
| | OUT: Gate delays, CRT latency verification, clock power | |
| +---------------------------------------------------------------+ |
| | |
| | Gate delays + verified CRT |
| v |
| +---------------------------------------------------------------+ |
| | TIER 5: PYTHON RNS ENGINE (Architecture Validation) | |
| | IN: ALL outputs from Tiers 1-4 + global constants | |
| | OUT: Formal proofs, JIR scheduling traces, GEMM validation | |
| +---------------------------------------------------------------+ |
| | |
| v |
| [AGGREGATE RESULTS] --> Generate Pass/Fail Report |
| | |
| v |
| [END] --> JANUS_MINI16_VERIFICATION_REPORT.pdf |
| |
+=============================================================================+
ALGORITHM 0: MASTER_ORCHESTRATOR
================================================================
INPUT: config = load("mini_16t_constants.py") // 240 globals
OUTPUT: verification_report (Pass/Fail per metric)
BEGIN
1. constants <-- load_global_constants(config)
2. validate_constants(constants) // Sanity checks
// TIER 1: Electro-Optics
3. s_params <-- run_tier1_meep(constants) // Touchstone .s4p
4. Q_opt_map <-- run_tier1_meep_heatmap(constants) // HDF5
// TIER 2 and TIER 3 run in PARALLEL (independent inputs)
5. PARALLEL:
5a. thermal_rom <-- run_tier2_elmer(constants, Q_opt_map)
5b. ber_results <-- run_tier3_xyce(constants, s_params)
// TIER 4: Digital RTL
6. rtl_results <-- run_tier4_cocotb(constants)
// TIER 5: Full Architecture Validation
7. rns_results <-- run_tier5_python_rns(
constants, s_params, thermal_rom,
ber_results, rtl_results)
// AGGREGATE
8. report <-- aggregate_results(
s_params, thermal_rom, ber_results,
rtl_results, rns_results)
9. FOR EACH metric IN verification_criteria:
IF metric.value satisfies metric.threshold:
report[metric] = "PASS"
ELSE:
report[metric] = "FAIL"
10. export_report(report, "JANUS_MINI16_VERIFICATION_REPORT.pdf")
11. RETURN report
END
+============================================================+
| TIER 1: MEEP FDTD PIPELINE |
+============================================================+
| |
| [START] |
| | |
| v |
| +------------------------------------------+ |
| | Load global constants: | |
| | lambda_0, n_si, n_sio2, n_gst467_*, | |
| | wg_width_si, wg_height_si, gst_patch, | |
| | N_alphabet, S_tree | |
| +------------------------------------------+ |
| | |
| v |
| +------------------------------------------+ |
| | ALG 1A: Build 3D GST-467 Unit Cell | |
| | - Si ridge waveguide (450x220 nm) | |
| | - SiO2 cladding (n=1.444) | |
| | - GST-467 patch (15 nm active layer) | |
| +------------------------------------------+ |
| | |
| +-----> Run FDTD (amorphous state) ----+ |
| | | |
| +-----> Run FDTD (crystalline state) --+ |
| | | |
| v v |
| +-------------------+ +-------------------+ |
| | Extract S-matrix | | Extract S-matrix | |
| | S_amorph[4x4] | | S_cryst[4x4] | |
| +-------------------+ +-------------------+ |
| | | |
| +----------+-----------------+ |
| | |
| v |
| +------------------------------------------+ |
| | ALG 1B: Waveguide Crossing Extraction | |
| | - MMI optimized crossing geometry | |
| | - Extract IL_crossing, XT_crossing | |
| +------------------------------------------+ |
| | |
| v |
| +------------------------------------------+ |
| | ALG 1C: LiTaO3 Pockels Router | |
| | - Micro-ring modulator (r33=30.5 pm/V) | |
| | - Extract modulation depth & bandwidth | |
| +------------------------------------------+ |
| | |
| v |
| +------------------------------------------+ |
| | ALG 1D: Volumetric Heat Map Extraction | |
| | - Q_opt(x,y,z) from field absorption | |
| | - Export to HDF5 | |
| +------------------------------------------+ |
| | |
| v |
| +------------------------------------------+ |
| | Validate: IL <= 0.10 dB, ER >= 25.0 dB | |
| | XT_crossing <= -40 dB | |
| +------------------------------------------+ |
| | |
| v |
| [OUTPUT: s_params.s4p, Q_opt.hdf5] |
| |
+============================================================+
ALGORITHM 1A: GST467_SWITCH_FDTD
================================================================
INPUT: lambda_0 = 1064 nm
n_si = 3.565
n_sio2 = 1.444
n_gst_a = 3.45 + i*0.008 // amorphous
n_gst_c = 4.20 + i*0.18 // crystalline
wg_w = 450 nm
wg_h = 220 nm
t_gst = 15 nm
A_cell = 1.25 um^2
OUTPUT: S_amorph[4x4], S_cryst[4x4], Q_opt(x,y,z)
BEGIN
// STEP 1: Define computational domain
1. resolution <-- lambda_0 / (20 * max(n_gst_c.real))
// Minimum 20 points per wavelength in highest-index medium
2. domain_size <-- (5*wg_w, 5*wg_w, 3*wg_h + t_gst + 2*lambda_0)
3. PML_layers <-- 1.0 * lambda_0 on all 6 boundaries
// STEP 2: Build geometry
4. DEFINE substrate = Block(material=SiO2, n=n_sio2)
5. DEFINE waveguide_input = Block(w=wg_w, h=wg_h, material=Si, n=n_si)
6. DEFINE waveguide_cross = Block(w=wg_w, h=wg_h, material=Si, n=n_si)
7. DEFINE gst_patch = Block(area=A_cell, h=t_gst, material=GST467)
// STEP 3: Run amorphous state
8. SET gst_patch.epsilon = eps_from_nk(n_gst_a)
9. source <-- GaussianSource(frequency=c_vacuum/lambda_0,
fwidth=0.1*c_vacuum/lambda_0)
10. ports <-- [Port1_in, Port2_thru, Port3_drop, Port4_iso]
11. FOR EACH port_excitation IN ports:
11a. Run FDTD until fields decay to 1e-8 of peak
11b. Record transmitted/reflected fields at all ports
12. S_amorph <-- compute_s_matrix(port_fields)
// STEP 4: Run crystalline state
13. SET gst_patch.epsilon = eps_from_nk(n_gst_c)
14. REPEAT steps 11-12 --> S_cryst
// STEP 5: Extract heat map
15. Q_opt(x,y,z) <-- (1/2) * omega_optical * epsilon_0
* Im[eps_r(x,y,z)] * |E(x,y,z)|^2
16. Export Q_opt to HDF5 on Yee grid
// STEP 6: Compute figures of merit
17. IL_amorph <-- -10*log10(|S21_amorph|^2) // Insertion loss
18. ER <-- |S21_amorph_dB - S21_cryst_dB| // Extinction ratio
19. IL_cryst <-- -10*log10(|S21_cryst|^2)
// STEP 7: Validate
20. ASSERT IL_amorph <= 0.10 dB // "PASS: Switch IL"
21. ASSERT ER >= 25.0 dB // "PASS: Extinction Ratio"
22. RETURN S_amorph, S_cryst, Q_opt
END
ALGORITHM 1B: WAVEGUIDE_CROSSING_FDTD
================================================================
INPUT: lambda_0, n_si, n_sio2, wg_w, wg_h
OUTPUT: IL_crossing, XT_crossing, S_crossing[4x4]
BEGIN
1. Build 3D MMI crossing geometry:
- Two perpendicular Si waveguides intersecting at center
- Optimized MMI taper widths for minimum mode disruption
2. Run 4-port FDTD simulation:
FOR EACH input port p IN {1, 2, 3, 4}:
2a. Excite fundamental TE mode at port p
2b. Record transmitted field at all 4 ports
2c. Compute S-parameters row for port p
3. S_crossing <-- assemble 4x4 S-matrix
4. IL_crossing <-- -10*log10(|S21|^2) // Through-port loss
5. XT_crossing <-- 10*log10(|S31|^2) // Cross-port crosstalk
6. ASSERT IL_crossing <= 0.02 dB
7. ASSERT XT_crossing <= -40 dB
8. RETURN IL_crossing, XT_crossing, S_crossing
END
ALGORITHM 1C: LITAO3_POCKELS_ROUTER
================================================================
INPUT: lambda_0, n_litao3=2.13, r33_litao3=30.5 pm/V,
E_pockels_switch=50 aJ
OUTPUT: V_pi, modulation_bandwidth, S_router[2x2]
BEGIN
1. Build 3D micro-ring resonator geometry:
- LiTaO3 thin-film ring coupled to bus waveguide
- Electrode geometry for vertical E-field application
2. Compute half-wave voltage:
V_pi = lambda_0 / (2 * n_litao3^3 * r33_litao3 * L_electrode / gap)
3. Run FDTD with applied DC bias sweep (0 to V_pi):
FOR EACH V_bias IN linspace(0, V_pi, 20):
3a. Apply refractive index change:
delta_n = -0.5 * n_litao3^3 * r33_litao3 * (V_bias / gap)
3b. Run FDTD, extract S21(V_bias) and S31(V_bias)
4. S_router <-- S-matrix at resonance and off-resonance
5. Verify E_pockels_switch <= 50 aJ per switch event
6. RETURN V_pi, modulation_bandwidth, S_router
END
ALGORITHM 1D: HEAT_MAP_EXTRACTION
================================================================
INPUT: FDTD field solution E(x,y,z), material map eps_r(x,y,z)
OUTPUT: Q_opt(x,y,z) as HDF5 dataset
BEGIN
1. FOR EACH Yee cell (i, j, k) in simulation domain:
1a. eps_imag = Im[eps_r(i,j,k)]
1b. E_mag_sq = |Ex(i,j,k)|^2 + |Ey(i,j,k)|^2 + |Ez(i,j,k)|^2
1c. Q_opt(i,j,k) = 0.5 * omega_optical * epsilon_0
* eps_imag * E_mag_sq
2. Normalize Q_opt to total absorbed power:
P_absorbed = integral(Q_opt) over domain
// Cross-check: P_absorbed should equal (1 - sum(|S_out|^2)) * P_in
3. Export Q_opt(x,y,z) with grid coordinates to HDF5:
- Dataset: "Q_opt" with shape (Nx, Ny, Nz)
- Attributes: dx, dy, dz, lambda_0, material_state
4. RETURN Q_opt
END
+============================================================+
| TIER 2: ELMER FEM PIPELINE |
+============================================================+
| |
| [START] |
| | |
| v |
| +------------------------------------------+ |
| | Load thermal material constants: | |
| | k_si, rho_si, cp_si (CMOS) | |
| | k_sio2, rho_sio2, cp_sio2 (Buffer) | |
| | k_cu, rho_cu, cp_cu (TDVs/HS) | |
| | k_ge, rho_ge, cp_ge (APD) | |
| | h_cmos=50um, h_sio2=250um, h_siph=30um | |
| +------------------------------------------+ |
| | |
| v |
| +------------------------------------------+ |
| | ALG 2A: Generate 3D Mesh (Gmsh) | |
| | - 330 um total stack height | |
| | - 10 mm x 10 mm lateral (100 mm^2) | |
| | - Structured hex mesh with refinement | |
| | near SiO2/SiPh interface | |
| +------------------------------------------+ |
| | |
| v |
| +------------------------------------------+ |
| | ALG 2B: Import Heat Sources | |
| | - Q_opt(x,y,z) from MEEP (HDF5) | |
| | - P_cmos = 1.05 W (uniform in CMOS) | |
| | - P_jir = 1.50 W (control logic) | |
| +------------------------------------------+ |
| | |
| v |
| +------------------------------------------+ |
| | ALG 2C: Transient Heat Diffusion Solver | |
| | Solve: rho*cp*dT/dt = k*nabla^2(T) + Q | |
| | BCs: T_top = T_ambient + P*R_th_up | |
| | Lateral: adiabatic (dT/dn = 0) | |
| | Duration: 10 * tau_diff (690.6 ms) | |
| | Timestep: tau_jir / 10 (0.5 us) | |
| +------------------------------------------+ |
| | |
| v |
| +-----------------------+ |
| | tau_diff verified? | |
| | (65 ms <= tau <= 72ms)| |
| +-----------+-----------+ |
| YES | NO |
| | +----> [FAIL: Thermal diffusion] |
| v |
| +-----------------------+ |
| | dT_cycle <= 0.80 mK? | |
| +-----------+-----------+ |
| YES | NO |
| | +----> [FAIL: Thermal transient] |
| v |
| +-----------------------+ |
| | T_max < 70 deg-C? | |
| +-----------+-----------+ |
| YES | NO |
| | +----> [FAIL: Retention guard] |
| v |
| +------------------------------------------+ |
| | ALG 2D: Extract Thermal ROM | |
| | - Compute impulse response h(t) | |
| | - Fit Foster RC ladder network | |
| | - Export ROM matrix for Tier 5 JIR | |
| +------------------------------------------+ |
| | |
| v |
| [OUTPUT: thermal_rom.json, T_field(x,y,z,t)] |
| |
+============================================================+
ALGORITHM 2A: THERMAL_MESH_GENERATION
================================================================
INPUT: A_die=100 mm^2, L_die=10 mm, N_tiles=16
h_cmos=50 um, h_sio2=250 um, h_siph=30 um
OUTPUT: mesh (Gmsh .msh format)
BEGIN
1. DEFINE layers (bottom to top):
Layer 0: CMOS substrate z=[0, 50 um] material=Si
Layer 1: SiO2 buffer z=[50, 300 um] material=SiO2
Layer 2: SiPh stratum z=[300, 330 um] material=Si+SiO2
2. DEFINE lateral domain:
x = [0, L_die], y = [0, L_die]
3. SET mesh parameters:
- Lateral element size: 100 um (coarse bulk), 25 um (near tiles)
- Vertical element size in SiO2: 10 um (25 layers across 250 um)
- Vertical element size at SiO2/SiPh interface: 2 um (refined)
- Vertical element size in CMOS: 10 um
4. DEFINE 16 tile sub-domains:
FOR i = 0 TO 3:
FOR j = 0 TO 3:
tile[i][j].center = (L_die/8 + i*L_die/4,
L_die/8 + j*L_die/4)
tile[i][j].area = A_tile = 6.25 mm^2
5. GENERATE structured hexahedral mesh using Gmsh
6. TAG physical volumes: CMOS, SiO2_buffer, SiPh_stratum
7. TAG tile boundaries for per-tile temperature monitoring
8. RETURN mesh
END
ALGORITHM 2C: TRANSIENT_HEAT_DIFFUSION
================================================================
INPUT: mesh, material_properties, Q_opt(x,y,z), P_cmos, P_jir
T_ambient=298.15 K, R_th_up=0.552 K/W, R_th_down=0.195 K/W
tau_diff=69.06 ms, tau_jir=5 us
OUTPUT: T(x,y,z,t), tau_diff_measured, dT_cycle, T_max
BEGIN
// GOVERNING EQUATION:
// rho(x,y,z) * cp(x,y,z) * dT/dt = div(k(x,y,z) * grad(T)) + Q(x,y,z)
1. SET initial condition: T(x,y,z,0) = T_ambient (uniform)
2. SET boundary conditions:
- Top surface (z = 330 um):
-k * dT/dz = h_conv * (T - T_ambient)
where h_conv = 1 / (R_th_up * A_die)
- Bottom surface (z = 0):
-k * dT/dz = h_conv_down * (T - T_ambient)
where h_conv_down = 1 / (R_th_down * A_die)
- Lateral faces (x=0, x=L, y=0, y=L):
dT/dn = 0 (adiabatic)
3. SET volumetric heat sources:
Q(x,y,z) = Q_opt(x,y,z) // Optical absorption (SiPh)
+ P_cmos / V_cmos // CMOS Joule heating
+ P_jir / V_cmos // JIR control logic
4. SET simulation parameters:
t_end = 10 * tau_diff = 690.6 ms // Reach steady state
dt = tau_jir / 10 = 0.5 us // Resolve JIR cycles
N_steps = t_end / dt = 1,381,200
5. RUN Elmer transient heat equation solver:
FOR t = dt TO t_end STEP dt:
5a. Assemble stiffness matrix K and mass matrix M
5b. Solve: M * dT/dt + K * T = F (force vector from Q)
5c. Record T(x,y,z,t) at tile monitoring points
6. EXTRACT tau_diff_measured:
- Apply unit heat pulse at CMOS layer
- Measure 63.2% rise time at SiPh top surface
- tau_diff_measured = measured time constant
7. EXTRACT dT_cycle:
- Measure peak-to-peak temperature oscillation at SiPh
during one tau_jir = 5 us JIR cycle at steady state
8. EXTRACT T_max:
- T_max = max(T(x,y,z)) at steady state (t > 5*tau_diff)
9. VALIDATE:
ASSERT 65 ms <= tau_diff_measured <= 72 ms
ASSERT dT_cycle <= 0.80 mK
ASSERT T_max < 343.15 K (70 deg-C)
10. RETURN T(x,y,z,t), tau_diff_measured, dT_cycle, T_max
END
ALGORITHM 2D: THERMAL_ROM_EXTRACTION
================================================================
INPUT: T(x,y,z,t) from transient simulation, N_tiles=16
OUTPUT: thermal_rom (Foster RC ladder network per tile)
BEGIN
1. FOR EACH tile t IN [0, N_tiles-1]:
// Extract thermal impulse response
1a. h_t(tau) = T_tile[t](tau) - T_ambient
// Temperature response to unit step power input
// Fit multi-exponential Foster model
1b. h_t(tau) = SUM_{n=1}^{N_poles} R_n * (1 - exp(-tau / tau_n))
// where R_n = thermal resistance of n-th pole
// tau_n = R_n * C_n = time constant of n-th pole
// Use nonlinear least-squares (Levenberg-Marquardt)
1c. [R_1..R_Np, C_1..C_Np] = curve_fit(h_t, Foster_model,
N_poles=5)
// Validate ROM accuracy
1d. error = max(|h_t_ROM(tau) - h_t_FEM(tau)|) / max(h_t_FEM)
1e. ASSERT error < 0.02 // 2% maximum ROM deviation
2. thermal_rom = {
"N_tiles": N_tiles,
"poles": N_poles,
"R": [[R_1..R_Np] for each tile], // Thermal resistances
"C": [[C_1..C_Np] for each tile], // Thermal capacitances
"tau": [[tau_1..tau_Np] for each tile] // Time constants
}
3. Export thermal_rom to JSON
4. RETURN thermal_rom
END
+============================================================+
| TIER 3: XYCE SPICE PIPELINE |
+============================================================+
| |
| [START] |
| | |
| v |
| +------------------------------------------+ |
| | ALG 3A: Vector Fitting (S-params->SPICE) | |
| | IN: S-parameters from MEEP (.s4p) | |
| | OUT: Passive rational subcircuits | |
| +------------------------------------------+ |
| | |
| v |
| +------------------------------------------+ |
| | ALG 3B: Build SAC2M APD Subcircuit | |
| | - Photocurrent: I_ph = R * P_opt | |
| | - Avalanche: M=7, F(M)=2.0 | |
| | - C_j=0.8 fF, R_s=25 ohm | |
| +------------------------------------------+ |
| | |
| v |
| +------------------------------------------+ |
| | ALG 3C: Build StrongARM Latch Model | |
| | - E_SA = 100 aJ/event | |
| | - t_regen <= 3.5 ps | |
| +------------------------------------------+ |
| | |
| v |
| +------------------------------------------+ |
| | ALG 3D: Assemble Full Transient Netlist | |
| | - Optical source -> 16-Tree S-param chain | |
| | -> APD -> StrongARM -> Digital out | |
| | - Clock: 100 GHz (T_cycle=10 ps) | |
| +------------------------------------------+ |
| | |
| v |
| +------------------------------------------+ |
| | ALG 3E: Run Transient & Extract Results | |
| | - 100 GHz eye diagram | |
| | - Jitter measurement | |
| | - BER estimation | |
| +------------------------------------------+ |
| | |
| v |
| +-----------------------+ |
| | BER <= 10^-18 ? | |
| +-----------+-----------+ |
| YES | NO |
| | +----> [FAIL: BER exceeds threshold] |
| v |
| +-----------------------+ |
| | Margin >= +4.00 dB ? | |
| +-----------+-----------+ |
| YES | NO |
| | +----> [FAIL: Insufficient margin] |
| v |
| [OUTPUT: eye_diagram, BER, jitter, transit_delays] |
| |
+============================================================+
ALGORITHM 3A: VECTOR_FITTING
================================================================
INPUT: S_data[f] = S-parameter matrix at N_freq frequency points
f_range = [f_min, f_max]
OUTPUT: H(s) = rational transfer function (causal, passive)
SPICE subcircuit netlist
BEGIN
// STEP 1: Initial pole placement
1. N_poles = 20 // Start with 20 poles
2. poles_init = distribute_log_spaced(f_min, f_max, N_poles)
// Complex conjugate pairs for oscillatory behavior
// STEP 2: Iterative Vector Fitting (Gustavsen-Semlyen)
3. FOR iteration = 1 TO max_iterations:
3a. Construct overdetermined system:
sigma(s) * H(s) = SUM_{n=1}^{N_poles} c_n / (s - a_n) + d + s*e
where sigma(s) = SUM_{n=1}^{N_poles} c_tilde_n / (s - a_n) + 1
3b. Solve least-squares for {c_n, c_tilde_n, d, e}
3c. Update poles: a_n_new = eigenvalues of (A - b*c_tilde^T)
3d. Flip unstable poles: IF Re(a_n) > 0 THEN a_n = -conj(a_n)
3e. Check convergence:
error = norm(H_fit(f) - S_data(f)) / norm(S_data(f))
IF error < 1e-4: BREAK
// STEP 3: Passivity enforcement
4. FOR EACH frequency f in fine grid:
4a. Compute eigenvalues of I - H(j*2*pi*f)^H * H(j*2*pi*f)
4b. IF any eigenvalue < 0:
// System is non-passive at this frequency
Apply passivity perturbation (Gustavsen method):
Minimize ||H_passive - H_fitted||^2
subject to: eig(I - H^H*H) >= 0 for all f
// STEP 4: Export to SPICE
5. Convert rational model to equivalent circuit:
FOR EACH pole a_n with residue c_n:
IF a_n is real:
R_n = -1/a_n, C_n = 1/(c_n * R_n) // RC branch
ELSE (complex conjugate pair):
Synthesize RLC branch
6. Write Xyce subcircuit netlist (.cir)
7. RETURN H(s), subcircuit_netlist
END
ALGORITHM 3B: SAC2M_APD_MODEL
================================================================
INPUT: M_apd=7, k_ionization=0.06, R_responsivity=0.8 A/W,
f_3db=105 GHz, C_j=0.8 fF, R_s=25 ohm, C_int=3 fF
OUTPUT: Xyce subcircuit model (.cir)
BEGIN
// STEP 1: Primary photocurrent source
1. I_ph(t) = R_responsivity * P_optical(t)
// Controlled current source modulated by optical input
// STEP 2: Avalanche multiplication
2. I_mult(t) = M_apd * I_ph(t) = 7 * I_ph(t)
// STEP 3: Excess noise (McIntyre model)
3. F_M = M_apd * [1 - (1 - k_ionization) *
((M_apd - 1) / M_apd)^2]
// F_M = 7 * [1 - 0.94 * (6/7)^2] = 2.0
// STEP 4: Shot noise current source
4. i_shot_rms = sqrt(2 * q_electron * I_mult * F_M * bandwidth)
// STEP 5: Thermal noise from series resistance
5. i_thermal_rms = sqrt(4 * k_boltzmann * T_ambient / R_s
* bandwidth)
// STEP 6: Equivalent circuit topology
6. NETLIST:
.SUBCKT SAC2M_APD anode cathode optical_in
I_ph anode node1 VALUE={R_resp * V(optical_in)}
G_mult node1 node2 node1 node2 {M_apd}
C_j node2 cathode {C_j_apd}
R_s node2 cathode {R_s_apd}
C_int cathode gnd {C_int_parasitic}
I_noise node2 cathode NOISE(rms={i_shot_rms + i_thermal_rms})
.ENDS
7. RETURN subcircuit
END
ALGORITHM 3E: EYE_DIAGRAM_AND_BER
================================================================
INPUT: assembled netlist, f_clk=100 GHz, T_cycle=10 ps,
P_det=13.82 uW, P_sens_practical=4.79 uW,
BER_target=10^-18, Q_factor=9.38
OUTPUT: eye_diagram, jitter, BER_measured, margin
BEGIN
// STEP 1: Generate PRBS input pattern
1. N_bits = 2^15 - 1 = 32,767 // PRBS-15 sequence
2. pattern = generate_PRBS15()
3. optical_signal(t) = pattern[floor(t/T_cycle)] * P_det
// OOK modulation at 100 GHz
// STEP 2: Run Xyce transient simulation
4. t_end = N_bits * T_cycle = 327.67 ns
5. dt_sim = T_cycle / 100 = 0.1 ps // 100 points per bit
6. RUN Xyce transient analysis:
.TRAN {dt_sim} {t_end}
// STEP 3: Extract eye diagram
7. V_out(t) = output voltage waveform at StrongARM output
8. Fold V_out into 2 * T_cycle window:
FOR EACH bit period [n*T_cycle, (n+2)*T_cycle]:
overlay_trace[n] = V_out[n*T_cycle : (n+2)*T_cycle]
9. eye_diagram = superimpose all overlay_trace[]
// STEP 4: Measure eye opening
10. V_1 = mean(V_out when pattern='1') // "1" level
11. V_0 = mean(V_out when pattern='0') // "0" level
12. sigma_1 = std(V_out when pattern='1')
13. sigma_0 = std(V_out when pattern='0')
14. eye_opening = (V_1 - V_0) - 3*(sigma_1 + sigma_0)
// STEP 5: Compute Q-factor and BER
15. Q_measured = (V_1 - V_0) / (sigma_1 + sigma_0)
16. BER_measured = 0.5 * erfc(Q_measured / sqrt(2))
// STEP 6: Measure jitter
17. crossing_times = find_zero_crossings(V_out)
18. jitter_rms = std(crossing_times mod T_cycle)
19. jitter_pp = max(crossing_times mod T_cycle)
- min(crossing_times mod T_cycle)
// STEP 7: Compute margin
20. margin = P_det_dbm - P_sens_practical_dbm
// = -18.59 - (-23.21) = +4.62 dB
// STEP 8: Validate
21. ASSERT BER_measured <= BER_target // 10^-18
22. ASSERT margin >= 4.00 // dB
23. ASSERT eye_opening > 0 // Eye is open
24. RETURN eye_diagram, jitter_rms, jitter_pp, BER_measured, margin
END
+============================================================+
| TIER 4: COCOTB + VERILATOR PIPELINE |
+============================================================+
| |
| [START] |
| | |
| v |
| +------------------------------------------+ |
| | ALG 4A: RNS Modulo Encoder (Verilog) | |
| | X --> x_i = X mod m_i for i=0..15 | |
| | 16 parallel modulo reduction units | |
| +------------------------------------------+ |
| | |
| v |
| +------------------------------------------+ |
| | ALG 4B: Pipelined CRT Adder Tree (Verilog)| |
| | {x_0..x_15} --> X (reconstructed) | |
| | 4-stage pipeline, t_CRT <= 210 ps | |
| +------------------------------------------+ |
| | |
| v |
| +------------------------------------------+ |
| | ALG 4C: Cocotb Testbench | |
| | - Generate random 64-bit test vectors | |
| | - Drive through RNS encoder | |
| | - Route through optical (one-hot model) | |
| | - Reconstruct via CRT adder tree | |
| | - Compare with NumPy reference | |
| +------------------------------------------+ |
| | |
| v |
| +-----------------------+ |
| | All outputs match | |
| | reference exactly? | |
| +-----------+-----------+ |
| YES | NO |
| | +----> [FAIL: RTL mismatch] |
| v |
| +-----------------------+ |
| | t_CRT <= 220 ps? | |
| +-----------+-----------+ |
| YES | NO |
| | +----> [FAIL: Timing violation] |
| v |
| [OUTPUT: gate_delays, CRT_latency, PASS/FAIL] |
| |
+============================================================+
ALGORITHM 4A: RNS_MODULO_ENCODER
================================================================
INPUT: X (unsigned 64-bit integer), moduli M = {m_0, ..., m_15}
OUTPUT: residues r = {r_0, ..., r_15} where r_i = X mod m_i
BEGIN
// Each modulo unit operates in parallel (zero carry propagation)
1. FOR i = 0 TO N_tiles-1 IN PARALLEL:
// Barrett reduction for constant modulus
// Precomputed: reciprocal_m[i] = floor(2^(2*b) / m[i])
2a. q_hat = (X * reciprocal_m[i]) >> (2 * b)
// where b = ceil(log2(m[i]))
2b. r_i = X - q_hat * m[i]
2c. IF r_i >= m[i]: r_i = r_i - m[i] // Correction step
2d. ASSERT 0 <= r_i < m[i]
3. r = {r_0, r_1, ..., r_15}
4. RETURN r
END
// LATENCY: Single-cycle Barrett reduction in CMOS
// HARDWARE: 16 parallel modulo units, each ~12 gates deep
ALGORITHM 4B: CRT_ADDER_TREE
================================================================
INPUT: residues r = {r_0, ..., r_15}, moduli M = {m_0, ..., m_15}
Precomputed: M_i = M / m_i, N_i = M_i^(-1) mod m_i
OUTPUT: X = reconstructed integer (64-bit)
BEGIN
// Chinese Remainder Theorem:
// X = (SUM_{i=0}^{15} r_i * M_i * N_i) mod M
// PIPELINE STAGE 1: Partial products (parallel)
1. FOR i = 0 TO 15 IN PARALLEL:
pp[i] = r[i] * N_i // 8-bit x 8-bit = 16-bit multiply
pp[i] = pp[i] mod m[i] // Reduce back to residue
pp[i] = pp[i] * M_i // Scale by partial product
// PIPELINE STAGE 2: Pairwise addition (8 adders)
2. FOR j = 0 TO 7 IN PARALLEL:
sum_2[j] = pp[2*j] + pp[2*j + 1]
// PIPELINE STAGE 3: Quad-wise addition (4 adders)
3. FOR j = 0 TO 3 IN PARALLEL:
sum_3[j] = sum_2[2*j] + sum_2[2*j + 1]
// PIPELINE STAGE 4: Final accumulation (tree reduce)
4. sum_4a = sum_3[0] + sum_3[1]
5. sum_4b = sum_3[2] + sum_3[3]
6. X_raw = sum_4a + sum_4b
// FINAL: Modular reduction
7. X = X_raw mod M
// LATENCY: 4 pipeline stages x ~52.5 ps = 210 ps total
8. RETURN X
END
+============================================================+
| TIER 5: PYTHON RNS ENGINE PIPELINE |
+============================================================+
| |
| [START] |
| | |
| v |
| +----------------------------------------------+ |
| | ALG 5A: Moduli Set Generation | |
| | Generate 16+2 pairwise coprime moduli | |
| | Verify: prod(m_i) > 2^64 | |
| +----------------------------------------------+ |
| | |
| v |
| +----------------------------------------------+ |
| | ALG 5B: Z3 Formal Verification | |
| | Prove coprimality, dynamic range, | |
| | 16-Tree Fermat group isomorphism proof | |
| +----------------------------------------------+ |
| | |
| v |
| +----------------------------------------------+ |
| | ALG 5C: Spatial One-Hot Tensor Router | |
| | Emulate 4-stage 16-Tree Fermat routing | |
| | for 32x32 matrix multiplication per tile | |
| +----------------------------------------------+ |
| | |
| v |
| +----------------------------------------------+ |
| | ALG 5D: JIR Thermal Scheduler | |
| | Closed-loop tile rotation using thermal ROM | |
| | from Elmer (Tier 2) | |
| +----------------------------------------------+ |
| | |
| v |
| +----------------------------------------------+ |
| | ALG 5E: RRNS Fault Injection & Self-Healing | |
| | Monte Carlo error injection using BER | |
| | from Xyce (Tier 3) | |
| +----------------------------------------------+ |
| | |
| v |
| +----------------------------------------------+ |
| | ALG 5F: Bit-Exact GEMM Benchmark | |
| | INT4 through INT64 matrix multiplication | |
| | vs NumPy/PyTorch ground truth | |
| +----------------------------------------------+ |
| | |
| v |
| +-----------------------+ |
| | All GEMMs exact? | |
| | (deviation = 0) | |
| +-----------+-----------+ |
| YES | NO |
| | +----> [FAIL: Arithmetic error detected] |
| v |
| [OUTPUT: proofs, traces, GEMM_results, PASS/FAIL] |
| |
+============================================================+
ALGORITHM 5A: COPRIME_MODULI_GENERATOR
================================================================
INPUT: N_tiles=16, N_rrns=2, m_max=256, target_bits=64
OUTPUT: moduli_set M = {m_0, ..., m_15, m_16, m_17}
dynamic_range M_total = prod(m_0..m_15)
BEGIN
// STEP 1: Generate candidate primes and prime powers <= 256
1. candidates = []
2. FOR p IN primes_up_to(256):
k = 1
WHILE p^k <= 256:
candidates.append(p^k)
k = k + 1
// Candidates: {2,3,4,5,7,8,9,11,13,16,17,19,23,25,27,
// 29,31,32,37,41,43,47,49,53,...,251,256}
// STEP 2: Greedy selection (largest coprime moduli first)
3. SORT candidates in descending order
4. selected = []
5. FOR EACH c IN sorted candidates:
IF gcd(c, product(selected)) == 1:
selected.append(c)
IF len(selected) == N_tiles + N_rrns:
BREAK
// STEP 3: Verify dynamic range
6. M_compute = product(selected[0:N_tiles])
7. ASSERT M_compute > 2^(2 * target_bits)
// Need 2*P bits for product of two P-bit operands
// For INT64: M > 2^128
// STEP 4: Assign roles
8. moduli_compute = selected[0:N_tiles] // 16 compute channels
9. moduli_redundant = selected[N_tiles:N_tiles+N_rrns] // 2 RRNS
// STEP 5: Precompute CRT constants
10. M_total = product(moduli_compute)
11. FOR i = 0 TO N_tiles-1:
M_i[i] = M_total / moduli_compute[i]
N_i[i] = modular_inverse(M_i[i], moduli_compute[i])
// N_i = M_i^(-1) mod m_i (Extended Euclidean Algorithm)
12. RETURN {
"moduli_compute": moduli_compute,
"moduli_redundant": moduli_redundant,
"M_total": M_total,
"M_i": M_i,
"N_i": N_i
}
END
ALGORITHM 5B: Z3_FORMAL_VERIFICATION
================================================================
INPUT: moduli_set M, N_alphabet=17, S_tree=4
OUTPUT: proof_results (coprimality, range, bijection)
BEGIN
// PROOF 1: Pairwise coprimality
1. solver = Z3.Solver()
2. FOR i = 0 TO len(M)-1:
FOR j = i+1 TO len(M)-1:
// Assert: there exists d > 1 dividing both m_i and m_j
d = Z3.Int('d')
solver.add(d > 1)
solver.add(M[i] % d == 0)
solver.add(M[j] % d == 0)
result = solver.check()
ASSERT result == Z3.UNSAT // No common divisor exists
solver.reset()
3. PRINT "PROOF 1 PASSED: All moduli pairwise coprime"
// PROOF 2: Dynamic range sufficiency
4. M_total = product(M.moduli_compute)
5. FOR precision IN [4, 8, 16, 32, 64]:
k_needed = ceil(2 * precision / 8)
M_k = product(M.moduli_compute[0:k_needed])
ASSERT M_k > 2^(2*precision)
6. PRINT "PROOF 2 PASSED: Dynamic range covers INT4-INT64"
// PROOF 3: Multiplicative group permutation is bijective
7. FOR EACH m_i IN M.moduli_compute:
FOR w IN range(0, m_i):
// Verify: multiplication by w in Z_{m_i} is a permutation
image = {(w * x) % m_i FOR x IN range(0, m_i)}
IF gcd(w, m_i) == 1:
ASSERT len(image) == m_i // Bijection when gcd=1
ELSE:
// w=0 maps everything to 0 (valid: zero weight)
ASSERT w == 0 OR len(image) < m_i
8. PRINT "PROOF 3 PASSED: Finite field multiplication is bijective"
// PROOF 4: Asymmetric 16-Tree Fermat group isomorphism
9. // For Fermat modulus m=17, the 4-stage binary tree
// can realize all 256! permutations (Waksman 1968 theorem)
// Verify via constructive routing algorithm:
FOR trial = 0 TO 999:
pi = random_permutation(N_alphabet)
route = route_16tree(x, w)
ASSERT route is valid // All paths non-conflicting
10. PRINT "PROOF 4 PASSED: Asymmetric 16-Tree realizes Fermat group isomorphism"
11. RETURN {
"coprimality": "PROVED",
"dynamic_range": "PROVED",
"bijection": "PROVED",
"fermat_isomorphism": "PROVED (100% state coverage, 289/289 states)"
}
END
ALGORITHM 5C: SPATIAL_ONE_HOT_ROUTER
================================================================
INPUT: X_matrix[N_dim x N_dim] (input activation matrix, integers)
W_matrix[N_dim x N_dim] (weight matrix, integers)
moduli_compute[N_tiles], N_alphabet=256
OUTPUT: Y_matrix[N_dim x N_dim] (output = X * W, exact integers)
BEGIN
// STEP 1: RNS decomposition of inputs and weights
1. FOR EACH tile t IN [0, N_tiles-1]:
m = moduli_compute[t]
X_res[t] = X_matrix mod m // Element-wise residue
W_res[t] = W_matrix mod m // Element-wise residue
// STEP 2: One-Hot spatial encoding
2. FOR EACH tile t IN [0, N_tiles-1]:
m = moduli_compute[t]
FOR i = 0 TO N_dim-1:
FOR j = 0 TO N_dim-1:
// Encode X_res[t][i][j] as 1-hot vector of length m
x_val = X_res[t][i][j]
one_hot_x = zeros(m)
one_hot_x[x_val] = 1 // Single photon in spatial slot x_val
// STEP 3: Asymmetric 16-Tree Fermat routing (weight multiplication)
3. FOR EACH tile t IN [0, N_tiles-1]:
m = moduli_compute[t]
FOR i = 0 TO N_dim-1:
FOR k = 0 TO N_dim-1:
w_val = W_res[t][k][j_current]
// Configure 4-stage binary tree for Fermat group isomorphism:
// output_slot = (input_slot * w_val) mod m
// This is an isomorphic cyclic permutation in Z_m
IF gcd(w_val, m) == 1:
perm = [(s * w_val) % m FOR s IN range(m)]
tree_config = route_16tree(input_slot=x_val, weight=w_val)
ELSE:
// w_val = 0: route all to slot 0 (zero output)
tree_config = route_to_zero_rail()
// STEP 4: Photodetection (sum detection at output slots)
4. FOR EACH tile t:
Y_res[t] = zeros(N_dim, N_dim)
FOR i = 0 TO N_dim-1:
FOR j = 0 TO N_dim-1:
// MAC: Y[i][j] = SUM_k X[i][k] * W[k][j]
// In one-hot: accumulate detector counts at output slot
Y_res[t][i][j] = SUM over k of:
detector_output[t][i][j][k]
// Each detector fires binary (0 or 1 photon detected)
Y_res[t][i][j] = Y_res[t][i][j] mod m
// STEP 5: CRT reconstruction
5. Y_matrix = CRT_reconstruct(Y_res, moduli_compute)
// Using Algorithm 4B (CRT Adder Tree)
6. RETURN Y_matrix
END
ALGORITHM 5D: JIR_THERMAL_SCHEDULER
================================================================
INPUT: thermal_rom (from Tier 2), N_tiles=16, tau_jir=5 us,
P_per_tile=0.386 W, T_max_operating=70 deg-C,
T_ambient=25 deg-C, workload_queue
OUTPUT: scheduling_trace, temperature_trace, thermal_violations
BEGIN
// STEP 1: Initialize tile state
1. FOR EACH tile t IN [0, N_tiles-1]:
T[t] = T_ambient // Current temperature
state[t] = ACTIVE // {ACTIVE, COOLING, STANDBY}
active_time[t] = 0 // Cumulative active time
T_history[t] = [] // Temperature trace
2. violations = 0
3. cycle = 0
// STEP 2: Main scheduling loop
4. WHILE workload_queue is not empty:
// 2a: Update tile temperatures using thermal ROM
FOR EACH tile t:
IF state[t] == ACTIVE:
// Apply power and compute temperature rise
dT = 0
FOR n = 0 TO N_poles-1:
// Foster RC network step response
dT += P_per_tile * R[t][n] *
(1 - exp(-tau_jir / tau_rom[t][n]))
T[t] = T[t] + dT
ELSE IF state[t] == COOLING:
// No power applied, exponential decay
FOR n = 0 TO N_poles-1:
T_excess = T[t] - T_ambient
T[t] = T_ambient + T_excess * exp(-tau_jir / tau_rom[t][n])
// 2b: Check thermal guard
FOR EACH tile t:
IF T[t] > T_max_operating:
state[t] = COOLING // Force rotation
violations += 1
// 2c: Predictive rotation
FOR EACH tile t WHERE state[t] == ACTIVE:
// Predict temperature at NEXT cycle
T_predicted = T[t] + P_per_tile * R[t][0] *
(1 - exp(-tau_jir / tau_rom[t][0]))
IF T_predicted > 0.9 * T_max_operating:
// Preemptive rotation: swap with coolest STANDBY tile
coolest = argmin(T[t'] FOR t' WHERE state[t']==COOLING
OR state[t']==STANDBY)
SWAP state[t] <--> state[coolest]
// 2d: Execute workload on ACTIVE tiles
active_tiles = [t FOR t WHERE state[t] == ACTIVE]
n_active = len(active_tiles)
work_chunk = workload_queue.dequeue(n_active * N_dim^2)
DISTRIBUTE work_chunk across active_tiles
// 2e: Record trace
FOR EACH tile t:
T_history[t].append(T[t])
cycle += 1
// STEP 3: Validate
5. ASSERT max(T over all tiles and time) < T_max_operating
6. ASSERT max(T over all tiles and time) << T_crystallization_guard
7. throughput_ratio = mean(n_active) / N_tiles
PRINT f"JIR utilization: {throughput_ratio*100:.1f}%"
8. RETURN scheduling_trace, T_history, violations
END
ALGORITHM 5E: RRNS_FAULT_INJECTION_AND_HEALING
================================================================
INPUT: moduli_compute[16], moduli_redundant[2],
BER=10^-18, N_trials=10^6
OUTPUT: detection_rate, correction_rate, false_alarm_rate
BEGIN
// Full moduli set: M_full = moduli_compute + moduli_redundant
1. M_full = moduli_compute + moduli_redundant // 18 channels
2. M_total = product(moduli_compute)
3. detected = 0
4. corrected = 0
5. false_alarms = 0
6. missed = 0
// STEP 1: Monte Carlo fault injection
7. FOR trial = 0 TO N_trials-1:
// Generate random correct computation
7a. X_true = random_integer(0, M_total-1)
7b. residues_true = [X_true mod m FOR m IN M_full]
// Inject fault with probability BER per channel
7c. residues_corrupted = copy(residues_true)
7d. fault_injected = False
7e. fault_channel = -1
FOR ch = 0 TO 17:
IF random() < BER:
// Corrupt this channel
delta = random_integer(1, M_full[ch]-1)
residues_corrupted[ch] = (residues_corrupted[ch] + delta)
mod M_full[ch]
fault_injected = True
fault_channel = ch
// STEP 2: Fault detection via RRNS projection
7f. // Reconstruct X from compute channels only
X_reconstructed = CRT(residues_corrupted[0:16],
moduli_compute)
7g. // Check redundant channels for consistency
FOR r = 0 TO 1:
expected_r = X_reconstructed mod moduli_redundant[r]
actual_r = residues_corrupted[16 + r]
IF expected_r != actual_r:
fault_detected = True
// STEP 3: Fault localization (if detected)
7h. IF fault_detected:
detected += 1
// Try removing each compute channel and reconstructing
FOR suspect = 0 TO 15:
residues_reduced = residues_corrupted
WITHOUT channel[suspect]
X_candidate = CRT(residues_reduced,
M_full WITHOUT m[suspect])
// Check all remaining channels
consistent = True
FOR ch IN remaining_channels:
IF X_candidate mod M_full[ch] != residues_corrupted[ch]:
consistent = False
BREAK
IF consistent:
X_corrected = X_candidate
corrected += 1
BREAK
// STEP 4: Verify correction
7i. IF fault_injected AND NOT fault_detected:
missed += 1
IF NOT fault_injected AND fault_detected:
false_alarms += 1
// STEP 5: Compute rates
8. total_faults = sum(fault_injected over all trials)
9. detection_rate = detected / max(total_faults, 1)
10. correction_rate = corrected / max(detected, 1)
11. false_alarm_rate = false_alarms / (N_trials - total_faults)
12. ASSERT detection_rate == 1.0 // 100% detection
13. ASSERT correction_rate == 1.0 // 100% correction for single faults
14. RETURN detection_rate, correction_rate, false_alarm_rate
END
ALGORITHM 5F: BIT_EXACT_GEMM_BENCHMARK
================================================================
INPUT: N_dim=32, N_tiles=16, moduli_compute[16],
precisions = [4, 8, 16, 32, 64]
OUTPUT: results_per_precision, total_deviation
BEGIN
1. total_deviation = 0
2. FOR EACH P IN precisions:
k = ceil(2*P / 8) // Tiles needed for this precision
// k_int4=1, k_int8=2, k_int16=4, k_int32=8, k_int64=16
// Number of independent GEMM engines = N_tiles / k
n_engines = N_tiles // k
// STEP 1: Generate random test matrices
3a. IF P <= 8:
max_val = 2^(P-1) - 1 // Signed range
min_val = -2^(P-1)
ELSE:
max_val = 2^(P-1) - 1
min_val = -2^(P-1)
3b. A = random_integer_matrix(N_dim, N_dim, min_val, max_val)
3c. B = random_integer_matrix(N_dim, N_dim, min_val, max_val)
// STEP 2: Ground truth (NumPy 128-bit integer)
4. C_reference = numpy.matmul(A.astype(int128),
B.astype(int128))
// STEP 3: JANUS RNS computation
5. // Apply bias offset for signed integers
A_unsigned = A + 2^(P-1) // Shift to [0, 2^P - 1]
B_unsigned = B + 2^(P-1)
6. // RNS decomposition (using first k moduli)
active_moduli = moduli_compute[0:k]
FOR t = 0 TO k-1:
A_res[t] = A_unsigned mod active_moduli[t]
B_res[t] = B_unsigned mod active_moduli[t]
7. // One-Hot spatial MAC (per tile)
FOR t = 0 TO k-1:
C_res[t] = matmul_mod(A_res[t], B_res[t],
active_moduli[t])
// Element-wise: C_res[t][i][j] =
// SUM_k (A_res[t][i][k] * B_res[t][k][j])
// mod active_moduli[t]
8. // CRT reconstruction
C_janus_unsigned = CRT_reconstruct(C_res, active_moduli)
9. // Remove bias
C_janus = C_janus_unsigned
- N_dim * 2^(P-1) * (A_unsigned + B_unsigned)
+ N_dim * 2^(2*P-2)
// (Exact bias correction formula for signed MAC)
// STEP 4: Compare
10. deviation = numpy.sum(numpy.abs(C_janus - C_reference))
11. max_element_error = numpy.max(numpy.abs(
C_janus - C_reference))
12. PRINT f"INT{P}: deviation={deviation}, "
f"max_error={max_element_error}"
13. ASSERT deviation == 0
14. ASSERT max_element_error == 0
total_deviation += deviation
// FINAL VALIDATION
15. ASSERT total_deviation == 0
PRINT "ALL PRECISIONS: 0.00000000000000% DEVIATION"
16. RETURN results_per_precision, total_deviation
END
+=============================================================================+
| JANUS MINI 16-TILE: FINAL VERIFICATION DECISION TREE |
+=============================================================================+
| |
| [TIER 1 RESULTS] |
| | |
| +-- IL_switch <= 0.10 dB? ----NO----> [FAIL T1-A: Switch Loss] |
| | YES |
| +-- ER >= 25.0 dB? -----------NO----> [FAIL T1-B: Extinction Ratio] |
| | YES |
| +-- IL_crossing <= 0.02 dB? --NO----> [FAIL T1-C: Crossing Loss] |
| | YES |
| +-- XT <= -40 dB? ------------NO----> [FAIL T1-D: Crosstalk] |
| YES |
| | |
| [TIER 2 RESULTS] |
| | |
| +-- 65ms <= tau_diff <= 72ms? NO----> [FAIL T2-A: Diffusion Time] |
| | YES |
| +-- dT_cycle <= 0.80 mK? ----NO----> [FAIL T2-B: Thermal Transient] |
| | YES |
| +-- T_max < 100 deg-C? ------NO----> [FAIL T2-C: Retention Guard] |
| | YES |
| +-- ROM error < 2%? ---------NO----> [FAIL T2-D: ROM Accuracy] |
| YES |
| | |
| [TIER 3 RESULTS] |
| | |
| +-- BER <= 10^-18? ----------NO----> [FAIL T3-A: Bit Error Rate] |
| | YES |
| +-- Margin >= +4.00 dB? -----NO----> [FAIL T3-B: Link Margin] |
| | YES |
| +-- Eye open? ---------------NO----> [FAIL T3-C: Eye Closed] |
| YES |
| | |
| [TIER 4 RESULTS] |
| | |
| +-- t_CRT <= 220 ps? --------NO----> [FAIL T4-A: CRT Timing] |
| | YES |
| +-- RTL matches reference? ---NO----> [FAIL T4-B: RTL Mismatch] |
| YES |
| | |
| [TIER 5 RESULTS] |
| | |
| +-- Z3 proofs passed? --------NO----> [FAIL T5-A: Formal Proof] |
| | YES |
| +-- RRNS recovery 100%? -----NO----> [FAIL T5-B: Fault Healing] |
| | YES |
| +-- JIR no violations? ------NO----> [FAIL T5-C: Thermal Violation] |
| | YES |
| +-- GEMM deviation = 0? -----NO----> [FAIL T5-D: Arithmetic Error] |
| YES |
| | |
| v |
| +====================================+ |
| | ALL 16 CHECKS PASSED | |
| | JANUS MINI 16-TILE: VERIFIED | |
| | Status: TAPEOUT-GRADE VALIDATED | |
| +====================================+ |
| |
+=============================================================================+
| Algorithm | Time Complexity | Space Complexity | Parallelizable | Tier |
|---|---|---|---|---|
| 0: Master Orchestrator | O(T1+T2+T3+T4+T5) | O(sum) | Tiers 2,3 parallel | All |
| 1A: GST-467 FDTD | O(N^3 * T_steps) | O(N^3) | GPU-accelerated | T1 |
| 1B: Crossing FDTD | O(N^3 * T_steps) | O(N^3) | GPU-accelerated | T1 |
| 1C: Pockels Router | O(N^3 * T_steps) | O(N^3) | GPU-accelerated | T1 |
| 1D: Heat Map Export | O(N^3) | O(N^3) | Trivially parallel | T1 |
| 2A: Mesh Generation | O(N_elements) | O(N_elements) | Single-threaded | T2 |
| 2C: Heat Diffusion | O(N_elements * T_steps) | O(N_elements) | MPI-parallel | T2 |
| 2D: ROM Extraction | O(N_tiles * N_poles * T_fit) | O(N_tiles * N_poles) | Per-tile parallel | T2 |
| 3A: Vector Fitting | O(N_freq * N_poles^2) | O(N_poles^2) | Single-threaded | T3 |
| 3B: APD Model | O(1) | O(1) | N/A (netlist) | T3 |
| 3E: Eye/BER | O(N_bits * dt_steps) | O(N_bits) | Single-threaded | T3 |
| 4A: RNS Encoder | O(N_tiles) | O(N_tiles) | Fully parallel | T4 |
| 4B: CRT Adder Tree | O(N_tiles * log(N_tiles)) | O(N_tiles) | Pipelined parallel | T4 |
| 5A: Moduli Generator | O(N_candidates * N_tiles) | O(N_candidates) | Single-threaded | T5 |
| 5B: Z3 Formal | O(N_tiles^2 + N_perm * N) | O(N) | Per-proof parallel | T5 |
| 5C: One-Hot Router | O(N_tiles * N_dim^3) | O(N_tiles * N_dim^2) | Per-tile parallel | T5 |
| 5D: JIR Scheduler | O(N_cycles * N_tiles) | O(N_tiles * N_poles) | Single-threaded | T5 |
| 5E: RRNS Fault | O(N_trials * N_tiles^2) | O(N_tiles) | Trivially parallel | T5 |
| 5F: GEMM Benchmark | O(N_prec * N_dim^3) | O(N_dim^2) | Per-precision parallel | T5 |
Algorithm and flowchart specification approved for Project JANUS Mini 16-Tile simulation suite implementation.