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| equations-and-bounds |
Equations and Bounds |
established |
Derived from context files and official specifications |
[gb10-superchip memory-and-storage ai-workloads connectivity] |
[flops-fp4 memory-bandwidth model-memory-estimate nvlink-c2c-bandwidth storage-throughput] |
[tflops pflop bandwidth throughput fp4 fp8 fp16 fp32] |
[] |
[llm-memory-estimation.md] |
[Sustained vs. peak TFLOPS under real workloads Actual memory bandwidth under mixed CPU+GPU access patterns] |
Equations and Bounds
Reference for all quantitative specifications, formulas, and validation ranges for the Dell Pro Max GB10.
1. Compute Performance
Peak TFLOPS by Precision
| Precision |
Peak TFLOPS |
Source |
Notes |
| FP4 |
1,000 |
T0 Spec |
Headline figure, 1 PFLOP (w/ sparsity) |
| FP8 |
~500 |
T3 Infer |
Typical 2:1 ratio from FP4 |
| FP16 |
~250 |
T3 Infer |
Typical 4:1 ratio from FP4 |
| FP32 |
~125 |
T3 Infer |
Typical 8:1 ratio from FP4 |
| FP64 |
~0.675 |
T2 Bench |
HPL Linpack, Jeff Geerling |
Note: FP8/FP16/FP32 values are inferred from typical Blackwell architecture ratios. FP64 is benchmarked. FP4 headline includes sparsity.
GPU Cores
- CUDA cores: 6,144 (T0 Spec)
- Tensor Cores: 5th generation (count TBD)
- RT Cores: 4th generation (T0 Spec)
- Copy engines: 2 (T0 Spec)
- NVENC: 1 (T0 Spec)
- NVDEC: 1 (T0 Spec)
- CUDA compute capability: sm_121 (T1, build.nvidia.com/spark)
- CUDA toolkit: 13.0 / cu130 (T1, build.nvidia.com/spark)
2. Memory
Bandwidth
- Memory bandwidth: 273 GB/s (T0 Spec, LPDDR5X at 9,400 MT/s)
- NVLink-C2C bandwidth: 600 GB/s bidirectional (T0 Spec, CPU-GPU interconnect)
Configuration
- Interface: 256-bit, 16 channels LPDDR5X 8533 (T0 Spec, NVIDIA DGX Spark User Guide)
Capacity
- Total unified memory: 128 GB LPDDR5X (T0 Spec)
- Usable for models: ~109-115 GB (T3 Infer, after OS/framework/KV cache overhead)
3. Model Memory Estimation
Formula: Memory Required for Model Weights
Memory (GB) = Parameters (billions) × Bytes_per_parameter
| Precision |
Bytes/Param |
Formula |
| FP4 |
0.5 |
Params_B × 0.5 |
| FP8/INT8 |
1.0 |
Params_B × 1.0 |
| FP16 |
2.0 |
Params_B × 2.0 |
| FP32 |
4.0 |
Params_B × 4.0 |
Total Inference Memory (approximate)
Total Memory ≈ Model_Weights + KV_Cache + Activation_Memory + Framework_Overhead
Rule of thumb: budget 1.2-1.5x the raw model weight size for total inference memory.
Maximum Model Sizes (single unit, 128 GB)
| Precision |
Max Params (raw) |
Max Params (practical, ~110 GB usable) |
| FP4 |
256B |
~200B |
| FP8/INT8 |
128B |
~100B |
| FP16 |
64B |
~55B |
| FP32 |
32B |
~27B |
4. Networking Bounds
| Interface |
Spec Bandwidth |
Measured |
Direction |
| NVLink-C2C |
600 GB/s |
— |
Bidirectional |
| LPDDR5X memory |
273 GB/s |
— |
System memory |
| QSFP (per port) |
200 Gbps (25 GB/s) |
~106 Gbps single stream |
Network |
| QSFP (total) |
400 Gbps (50 GB/s) |
200+ Gbps RDMA |
2 ports combined |
| QSFP PCIe link |
x4 PCIe Gen 5 |
— |
Internal |
| 10 GbE Ethernet |
10 Gbps (1.25 GB/s) |
— |
Network |
| USB-C (per port) |
20 Gbps (2.5 GB/s) |
— |
I/O |
QSFP measured throughput from Jeff Geerling (T2 Benchmarked).
5. Power Bounds
| Parameter |
Dell Pro Max |
DGX Spark |
Source |
| PSU rating |
280W |
240W |
T0 Spec |
| GPU TDP |
140W |
140W |
T0 Spec |
| Idle draw |
~30W |
~40-45W |
T2 Bench |
| AI inference (LLM) |
60-90W |
60-90W |
T2 Bench |
| CPU-only load |
120-140W |
120-130W |
T2 Bench |
| CPU + GPU load |
~200W |
~200W |
T2 Bench |
6. Environmental Bounds
| Parameter |
Dell (T0 Owner's Manual) |
DGX Spark (T0 User Guide) |
| Operating temperature |
0°C to 35°C (32°F to 95°F) |
5°C to 30°C (41°F to 86°F) |
| Storage temperature |
-40°C to 65°C |
— |
| Operating humidity |
10% to 90% (non-condensing) |
10% to 90% (non-condensing) |
| Operating altitude |
-15.2 m to 3,048 m |
Up to 3,000 m |
| Operating vibration |
0.66 GRMS |
— |
| Operating shock |
110 G (2ms half-sine) |
— |
| Noise |
< 40 dB at 1-1.5m (T2 Bench) |
— |
7. Physical Bounds
| Parameter |
Value |
| Volume |
~1.15 L |
| Weight |
1.31 kg |
| Footprint |
150 × 150 mm |
| Height |
51 mm |
8. Validation Rules
When checking calculations:
- Model size estimates should not exceed 128 GB (single) or 256 GB (stacked)
- TFLOPS claims must specify precision — reject unqualified "1 PFLOP" statements
- Memory bandwidth (273 GB/s) is the system memory bus, NOT the NVLink-C2C (600 GB/s)
- Network bandwidth (QSFP) is in Gbps, not GB/s — divide by 8 for bytes
