MMM: Many-core Machine Model

• Many-core Machine Model (MMM) is an abstract framework that captures the key architectural, memory, and scheduling characteristics of many-core systems.
• MMM formalizes cost metrics—work, span, and parallelism overhead—to enable rigorous analysis and parameter tuning for efficient parallel algorithm design.
• Variants like the microthreaded Microgrid implement MMM concepts in hardware, achieving effective latency tolerance and measurable performance speedups.

A Many-core Machine Model (MMM) defines an abstract computational framework designed to capture the salient architectural, programmability, and cost characteristics of contemporary many-core systems, especially those featuring dozens to thousands of processing elements orchestrated to exploit both task and data parallelism. MMMs formalize notions of parallel computation, memory hierarchy, synchronization, and scheduling strategies, enabling rigorous analysis of parallel algorithms' efficiency and the principled minimization of parallelism overheads. Variants such as the microthreaded Microgrid instantiate MMM concepts in concrete hardware/ISA-level architectures, providing fine-grained parallel execution models coupled with latency-tolerant features and explicit resource control mechanisms (Uddin, 2013, Haque et al., 2014).

1. Fundamental Structure and Execution Semantics

The canonical MMM framework specifies an abstract machine comprising $P$ identical streaming multiprocessors (SMs), each integrating a collection of SIMD cores and fixed-sized low-latency local memory of $Z$ words. Cores within an SM execute "thread-blocks" in lock-step fashion, and global memory is modeled as unbounded but high-latency. The memory access policy distinguishes between low-latency, high-throughput local operations (arithmetic and local-memory accesses, 1 cycle each), and accesses between global and local memory (costing $U$ clock-cycles per word, $U > 1$). Global memory accesses follow a CREW discipline: concurrent reads per thread-block, exclusive (serialized) writes, and distinct thread-block accesses are serialized (Haque et al., 2014).

MMM programs have a two-level structure:

• At the coarse level, a fork-join DAG of kernels encodes inter-kernel dependencies.
• Each kernel implements an SIMD routine decomposed into thread-blocks, which cooperate only via local memory and communicate globally via high-latency memory transfers.

No implicit synchronization is assumed among blocks within the same kernel. At runtime, available thread-blocks are greedily assigned to SMs with scheduling order left unspecified to the programmer.

2. Cost Metrics and Analytical Model

An MMM introduces rigorous cost metrics grounded in classic work-span theory and extended to account for parallelism overhead. For a single thread-block $B$:

• $W(B)$: Total local operations by all threads (work).
• $S(B)$: Maximum local operations along any thread (span).
• $O(B) = (\alpha(B) + \beta(B))\cdot U$: Parallelism overhead, with $\alpha(B)$ and $\beta(B)$ as the maximal words read/written to global memory by any thread in $B$.

Aggregated metrics are defined across all thread-blocks $\mathcal{B}$:

• $W = \sum_{B\in \mathcal{B}} W(B)$ (total work),
• $S = \max_{\gamma} \sum_{B\in \gamma} S(B)$ (span over any path $\gamma$),
• $O = \sum_{B\in \mathcal{B}} O(B)$ (total overhead).

Key global parameters include $N = |\mathcal{B}|$ (number of blocks) and $L$ (critical path length in block-DAG, i.e., number of blocks on the longest chain).

The Graham–Brent theorem generalizes the classic parallel execution bound using these metrics:

$$T_P \leq (N/P + L) \cdot C, \quad C = \max_{B}(S(B) + O(B))$$

This bound reflects at most $\lceil N/P \rceil$ fully populated parallel execution steps and $L$ incomplete (serialized) steps, each incurring at most $C$ cycles (Haque et al., 2014).

3. Algorithmic Tuning and Parallel Overhead Minimization

Algorithm design under the MMM emphasizes aggressive parameter tuning to minimize overheads, given hardware constraints. The procedure is:

1. Identify a tunable parameter $s$ (e.g., threads/block, problem chunk size), constrained by local memory $Z$.
2. Express $W(s)$, $S(s)$, $O(s)$, $N(s)$, $L(s)$ as functions of $s$ and problem size $n$.
3. Formulate a parameterized bound $\widehat{T}(s) = (N(s)/P + L(s))\cdot C(s)$, $C(s) = \max_B[S(B) + O(B)]$.
4. Optimize $s$ within admissible bounds to minimize $\widehat{T}(s)$ (by solving $d\widehat{T}/ds=0$ or by asymptotic comparison).
5. Ensure $W(s) \approx \Theta(W(1))$, so overall work is not unduly increased even as overhead $O(s)$ is substantially reduced.

Empirical validation using algorithms such as univariate polynomial division, radix sort, polynomial multiplication, and Euclidean GCD demonstrates the MMM's value in guiding parameter selection (e.g., optimal $s \approx Z/7$ in polynomial division) and confirming that model-based optimization yields speedups (up to $2 \times$–$3 \times$) over naive implementations on real GPUs (Haque et al., 2014).

4. Microthreaded Architectures: The Microgrid Model

The Microgrid exemplifies a hardware/ISA-level MMM that implements microthreading—a hybrid von Neumann/dataflow execution model. Each microthread executes an in-order instruction stream; collections of microthreads are managed in families—ordered sets bound to contiguous blocks of cores ("places") parameterized by size, index, and resource windows. Hardware mechanisms institute creation, synchronization, and communication entirely in silicon—context-switches incur zero cycles, microthread creation incurs only a few cycles, and dataflow channels are modeled directly via special registers (I-structures).

Microgrid defines memory consistency via per-thread sequential consistency and per-family weak consistency. The join synchronization (e.g., via sl_sync instructions) becomes globally visible only after all concrete family writes are performed, ensuring predictable synchronization semantics (Uddin, 2013).

The Microgrid block-diagram includes a classic RISC pipeline, dynamic register allocation, per-thread and per-family state, a hardware scheduler, channel registers, and dual on-chip networks (delegation and distribution). These features enable fine-grained latency tolerance, rapid fork/join, explicit resource assignment, and analytical performance mapping.

5. Scalability, Scheduling, and Latency Tolerance

MMM accommodates explicit analytical modeling of speedup and resource usage. For $N$ microthreads on $c$ cores, total runtime decomposes into computation ($T_{\text{comp}}$), communication ($T_{\text{comm}}$), and synchronization ($T_{\text{sync}}$), yielding:

$$T_{\text{total}}(c) = T_{\text{comp}}/c + T_{\text{comm}}(c) + T_{\text{sync}}(c)$$

If $T_{\text{comm}}\propto \alpha\log c$ and $T_{\text{sync}}\propto \beta\cdot c$, the speedup and parallel efficiency follow:

$$S(c) = T_{\text{serial}} / T_{\text{total}}(c), \qquad E(c) = S(c)/c$$

With creation, context-switch, and family synchronization all quantified in cycles, the efficiency formula becomes:

$$E(c) \approx \frac{1}{1 + \frac{N\,\tau_{\text{create}}}{T_{\text{comp}}} + \frac{\tau_{\text{sync}}}{T_{\text{comp}}}}$$

Microgrid's hardware can hide memory/FPU latency by immediately scheduling ready microthreads in place of threads stalled on long-latency events, sustaining nearly one completed instruction per cycle at scale, subject to network contention and resource window sizes (Uddin, 2013).

6. Comparative Analysis and Research Context

The MMM framework distinguishes itself from earlier parallel machine models by explicitly incorporating both fork-join and SIMD parallelism, direct modeling of high-latency memory transfers, local memory constraints, and parameter-tunable algorithmic cost components. P-RISC, Multiscalar, and DDM-CMP represent early hybrid approaches but retain software control over thread management. Wavescalar explores a pure dataflow instruction set at hardware cost. Microgrid uniquely realizes full concurrency management—including fork/join, scheduling, synchronization—directly in hardware, using an abstract machine definition aligned with practical implementation (Uddin, 2013, Haque et al., 2014).

Experimentally, MMM-guided algorithmic tuning on contemporary GPUs and many-core CPUs confirms that selecting algorithmic parameters (e.g., chunk size, threads per block) to minimize derived overheads outperforms both naive and hand-tuned baselines. The model enables closed-form predictive analysis, and parameter settings are empirically validated, demonstrating speedups in key computational kernels such as sorting, polynomial arithmetic, and GCD computations.

---

Key References:

• "A Many-core Machine Model for Designing Algorithms with Minimum Parallelism Overheads" (Haque et al., 2014)
• "Microgrid - The microthreaded many-core architecture" (Uddin, 2013)