--- title: "Many Cores and the Limit on Speedup" description: "For a fixed workload with unchanged serial time, Amdahl's ideal model gives speedup 1 / (s + (1 - s) / N), where s is the serial fraction and N is the core count. For positive s, 1 / s is the limiting" canonical: https://lightmysky.com/learn/computing/many-cores-and-the-limit-on-speedup-mt_dy3-K9dV19 source: https://lightmysky.com/learn/computing/many-cores-and-the-limit-on-speedup-mt_dy3-K9dV19.md retrieved: 2026-11-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Many Cores and the Limit on Speedup For a fixed workload with unchanged serial time, Amdahl's ideal model gives speedup 1 / (s + (1 - s) / N), where s is the serial fraction and N is the core count. For positive s, 1 / s is the limiting bound. Coordination and resource contention can reduce gains. Subject: Computing · Area: Computer Systems · Ages 19 to 20 Page: https://lightmysky.com/learn/computing/many-cores-and-the-limit-on-speedup-mt_dy3-K9dV19 ## Ready when they can - Compute ideal finite-core speedup and the limiting bound for a fixed workload that is one tenth serial - Distinguish work that splits across cores from work that splits across data lanes - Explain why adding cores can make a program slower ## Lesson: Why ten cores do not always give tenfold speedup Pipelining overlaps stages inside a core; multiple cores can share a program's work. In Amdahl's model, the workload stays fixed and the serial part takes the same time. If its positive fraction is s, speedup approaches the bound 1 / s as core count grows. A serial tenth gives a tenfold bound, not tenfold speedup at every count. *(drawing: The serial part keeps its duration. Only the parallel part is divided among cores. Dividing both parts changes Amdahl's assumptions.)* **Example.** Normalize the one-core time to 1. For N cores, ideal time is s + (1 - s) / N; speedup is 1 divided by that time. This assumes equal sharing of the parallel part and no added overhead. With s = 0.25 and N = 3, time is 0.25 + 0.75 / 3 = 0.5, so speedup is 2. Multiple cores can execute different instruction streams. SIMD data lanes apply the same operation to several data elements together. Both can be used by one program: several cores might each perform SIMD additions. Lanes do not turn the serial part of a fixed workload into independent tasks. Actual time includes overhead that the ideal formula leaves out. Dividing work, coordinating results and waiting for shared resources all take time. A lock allows controlled access to a shared resource; workers may have to wait for it. If these costs exceed the time saved by parallel work, more cores can make the program slower. For a serial tenth on 100 cores, ideal time is 0.1 + 0.9 / 100 = 0.109. Speedup is 1 / 0.109, about 9.17. This is below ten because the parallel part still takes some time. Increasing N reduces that part, but leaves the serial 0.1 unchanged. **Recap.** For fixed work, unchanged serial time limits ideal speedup. Compute finite-core time before inverting it. Cores and SIMD lanes differ; overhead can erase the gain. *Original lesson, questions and flashcards written for this dataset.* ## Practice 8 questions on this page, each with its working shown. ## Needs first - [Pipelining and the Cost of a Hazard](https://lightmysky.com/learn/computing/pipelining-and-the-cost-of-a-hazard-mt_GI_fPY9d6s) ## Opens up - [What an Operating System Is: Privilege and System Calls](https://lightmysky.com/learn/computing/what-an-operating-system-is-privilege-and-system-calls-mt_0kMavEKxpX) - [Deep Learning: Convolution, Sequence and Scale](https://lightmysky.com/learn/computing/deep-learning-convolution-sequence-and-scale-mt_karzGN5JnI)