Sun–Ni Law

Estimate scaled parallel speedup when usable memory capacity bounds workload growth, with Amdahl and Gustafson recovered as special choices of an application-specific growth factor.

Version

v3 · 2026-09-06 · History

Domain-specific #

2896

Origin domain

parallel computing

Subdomain

performance modeling

Aliases

Sun and Ni's law, Sun-Ni's law, Memory-bounded speedup, Memory-bounded speedup model

Core Idea

The Sun–Ni law, originally called memory-bounded speedup, is a scaled parallel-performance model in which added processors bring added usable memory and that memory capacity limits how large a problem is selected. Sun and Ni introduced it beside fixed-size and fixed-time speedup: Amdahl asks how much faster a fixed workload runs, Gustafson scales workload to a fixed parallel time, and Sun–Ni scales workload to a memory-capacity bound.

For the simplified form, let p >= 1 be the processor or node count. Decompose a baseline workload into non-scaled sequential work W_s and parallelizable work W_p, and define.

Scope of Application

Parallel-algorithm scalability analysis. The law compares fixed-size, fixed-time, and memory-bounded interpretations of speedup for an algorithm. Its work–memory relation makes explicit which larger instance becomes feasible as aggregate capacity grows.

Algorithm–architecture co-design. Two algorithms with similar arithmetic complexity can have different replication, locality, or storage requirements. Their effective G(p) values reveal how much of nominal aggregate memory can support a larger job, providing a capacity-sensitive complement to timing alone.

Clarity

The first clarifying distinction is workload growth versus speedup. G(p) says how the parallelizable work changes under the memory bound. S_MB(p) says how quickly the resulting scaled job is solved relative to one processor. They are not the same number. In particular, G(p)>p can make memory-bounded speedup exceed Gustafson's endpoint while the ideal formula remains no greater than p when the sequential work is nonnegative.

Manages Complexity

Parallel scaling mixes at least four changes: processor count, memory capacity, problem size, and runtime. Fixed-size and fixed-time models each freeze one of those dimensions. Sun–Ni provides a third controlled comparison: let memory capacity select the enlarged problem, then compute the speedup for that same enlarged problem. This prevents a capacity-limited scientific workload from being judged solely by a fixed-job curve that no longer represents how the machine will be used.

Abstract Reasoning

Use this protocol:

1. Define the baseline problem and decompose its work into W_s and W_p. 2. Specify what one “processor” or node includes, especially its usable memory M. 3. Derive or measure the application relation W=g(M) for the selected problem family and storage layout. 4. Determine whether aggregate usable capacity is pM; if replication or reservation prevents this, derive G(p) directly.

Knowledge Transfer

Literal transfer occurs across parallel numerical kernels, memory-capacity planning, cache-tier analysis, and data-intensive architecture studies when the same roles remain: resources add usable capacity, capacity selects a scaled workload through g, the workload is decomposed, and speedup compares one versus p processors on that scaled job. The specific G(p) changes; the model grammar does not.

Transfer from a global-data algorithm to one with replication is a qualified variant, not a rename.

Relationships to Other Abstractions

Current abstraction Sun–Ni Law Domain-specific

Parents (2) — more general patterns this builds on

• Sun–Ni Law is a kind of Scalability Prime

  Scalability — strict subsumption. Sun–Ni is a specialized parallel-computing scalability model relating added resources, problem-size growth, and speedup.

• Sun–Ni Law presupposes Constraint Prime

  Constraint — strict presupposition. Memory capacity is the constitutive bound used to select the scaled workload.

Hierarchy paths (2) — routes to 2 parentless roots

• Sun–Ni Law → Scalability → Scale

Show alternative path (1)

Neighborhood in Abstraction Space

Sun–Ni Law sits in a sparse region of the domain-specific corpus (84^th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Unclustered & Miscellaneous (1565 abstractions)

Nearest neighbors

• Ninety-Ninety Rule — 0.82
• Requirements Churn — 0.81
• Memory Management — 0.80
• Amdahl's Law — 0.80
• Assembly Bonus Effect — 0.80

Computed from structural-signature embeddings · 2026-09-08