From a5faa6f49584aaac58258cd2bdd94389b33c9773 Mon Sep 17 00:00:00 2001 From: Johnny Kao <19386515+Johnny-Kao@users.noreply.github.com> Date: Wed, 7 Oct 2026 10:30:56 +0900 Subject: [PATCH 01/10] Add searchsorted performance blog post --- .../index.md | 225 ++++++++++++++++++ 1 file changed, 225 insertions(+) create mode 100644 content/posts/numpy/finding-another-layer-of-performance-in-np-searchsorted/index.md diff --git a/content/posts/numpy/finding-another-layer-of-performance-in-np-searchsorted/index.md b/content/posts/numpy/finding-another-layer-of-performance-in-np-searchsorted/index.md new file mode 100644 index 0000000..1cfdf54 --- /dev/null +++ b/content/posts/numpy/finding-another-layer-of-performance-in-np-searchsorted/index.md @@ -0,0 +1,225 @@ +--- +title: "Finding Another Layer of Performance in np.searchsorted" +date: 2026-10-07T09:11:00+09:00 +draft: true +description: "A performance investigation into reusing insertion-position locality in NumPy searchsorted, and why reducing work can complement CPU-friendly batched execution." +tags: ["numpy", "performance"] +displayInList: true +authors: ["Johnny Kao"] +--- + +I did not start from `np.searchsorted`. + +The idea came from a broader question I had been exploring in my own infrastructure work: + +> Has the system already paid for information that we are about to compute again? + +In my [CoreFoundry project](https://github.com/Johnny-Kao/CoreFoundry-Project), one recurring principle was simple: before adding more hardware or parallelism, first remove work that never needed to happen. + +That same question eventually led me to `np.searchsorted`. + +## Reusing information that already exists + +`np.searchsorted` finds insertion positions in a sorted array. + +Conceptually, every query can begin with the entire search space: + +```text +0 N +|-----------------------------------------------------| +``` + +But suppose several nearby queries produce insertion positions like: + +```text +500000 +500004 +500009 +500013 +500018 +``` + +After the first search, the next one is no longer starting with zero information. + +The previous insertion position is not only an output. When the workload has positional locality, it also contains information about where the next search is likely to land. + +```text +0 p N +|-------------------------|---------------------------| + [---- useful region ----] +``` + +That became the basic idea of the experiment: reuse information already produced by the search to reduce the amount of subsequent search work. + +There was one important constraint. + +Detecting locality should not require another full pass over the query array. An additional \(O(Q)\) scan just to decide whether an optimization should run could easily consume the performance benefit. + +Instead, the implementation uses intermediate position information already produced by the existing batched search. + +![Comparison between a full search range and a smaller useful search region around a previous insertion position.](search-space-reduction.png) + +*Figure 1. Positional locality can reduce the effective search space without adding a separate scan of the query array.* + +## Knowing when to use it + +The optimization itself was relatively simple. + +Deciding when to use it was harder. + +Compare these two workloads: + +```text +Strong locality + +100001 +100004 +100009 +100013 +100018 +``` + +and: + +```text +Random movement + +100001 +870003 +2401 +650002 +12000 +``` + +Both have previous insertion positions. + +Only the first has previous positions that provide useful information about the next search. + +So the problem became: + +> How much locality is enough to justify a different search path? + +I tested different selector configurations across multiple hardware profiles. + +One focused experiment compared **8, 16, and 32 observations** across four hardware profiles. + +The important result was simple: more observations were not consistently better. Some systems favored 16, while others favored 32. + +![Flow diagram showing the selector experiment progressing from 8, 16, and 32 observations to later convergence tests using only 16 and 32.](selector-convergence-flow.png) + +*Figure 2. The observation-count experiment narrowed the later search space: 8 was dropped, while 16 and 32 were carried forward for convergence testing.* + +Those later experiments produced another useful result: once the basic selector was already rejecting random workloads reliably, adding more decision rules did not help. More complicated policies mainly rejected useful local cases. + +At that point, the remaining problem was no longer classification. + +It was overhead. + +![Random-workload p95 candidate-to-baseline ratios for 8, 16, and 32 selector observations across four hardware profiles.](selector-observations.png) + +*Figure 3. Focused selector experiment at level 4. Lower is better; the best observation count varies by hardware profile, so increasing from 16 to 32 was not uniformly beneficial.* + +## What the benchmarks showed + +The final sign-off covered four logical resource profiles and 72 workload cases per profile, for 288 case/profile combinations. + +The matrix included: + +- `int32`, `int64`, and `float64` +- `side="left"` and `side="right"` +- dense and duplicate-heavy arrays +- strong-locality workloads +- random workloads +- reversal-heavy patterns +- cases above and below the activation threshold + +Across the final profiles, strong-locality workloads showed median speedups of roughly **5.3–5.8x**. + +| Runner | Strong-locality median | Active-random median | Worst active case | +| --- | ---: | ---: | ---: | +| AMD EPYC 7763 / 1 vCPU | 5.61x | 1.27x | 1.08x | +| Intel Xeon Platinum 8573C / 2 vCPU | 5.33x | 1.20x | 1.06x | +| AMD EPYC 7763 / 4 vCPU | 5.67x | 1.31x | 1.08x | +| AMD EPYC 9V45 / 4 vCPU | 5.78x | 1.23x | 1.04x | + +![Bar chart of final sign-off speedups across four hardware profiles, comparing strong-locality median, active-random median, and worst active case.](final-signoff-benchmark.png) + +*Figure 4. Final sign-off results. Strong-locality workloads gained more than 5x across all four profiles, while active random workloads and the worst active cases remained above baseline.* + +Earlier matrices showed the same pattern from another angle: + +- dense workloads at roughly `0.16-0.19x` baseline runtime +- duplicate-heavy workloads at roughly `0.13-0.15x` +- medium-locality workloads at roughly `0.38-0.47x` + +The important result was not simply the largest speedup. + +For a general-purpose numerical library, improving one workload while causing unpredictable regressions elsewhere is not a good trade. + +The more useful result was that the local path could produce large gains while unrelated workloads remained on, or close to, the existing execution path. + +## Why the threshold exists + +Initially, I expected locality alone to determine whether the optimization should run. + +The benchmarks showed otherwise. + +Even when locality exists, the workload has to be large enough to amortize the cost of observation, selection, branching, and path management. + +At smaller query counts, it is possible to remove search work while still increasing wall-clock time. + +This led to a separate activation gate. + +The implementation shown here uses + +\[ +Q \ge 2^{20} +\] + +as a conservative threshold. + +There is nothing mathematically special about \(2^{20}\). Earlier activation sweeps already showed why a portable gate needed to be conservative: three tested profiles could converge on a low activation candidate in that experimental setup, while the 1-vCPU / 2-GB profile failed the second-stage stability gate entirely. + +The exact crossover therefore depends on the machine and on the surrounding selector design. The final gate is intentionally more conservative than those early exploratory thresholds. + +This was a useful reminder: + +> A cheaper algorithmic path is not automatically a faster CPU path. + + + +## Then I found the earlier NumPy optimization + +Only after implementing and validating this work did I come across [NumPy PR #30517](https://github.com/numpy/numpy/pull/30517) and the Scientific Python article [Making `np.searchsorted` up to 25x Faster in NumPy 2.5](https://blog.scientific-python.org/numpy/searchsorted/). + +What was interesting was that the earlier work and this experiment were optimizing different layers of the same problem. + +![Diagram comparing earlier batched-search work, which improves how searches execute, with this experiment, which reduces how much search work is required.](two-layers-of-optimization.png) + +*Figure 5. The earlier batched-search work improves execution efficiency; this experiment reduces the amount of work. The two approaches are complementary and can stack.* + +The earlier work improves **how the searches execute**. This experiment focuses on **how much searching is necessary**. + +## A second layer of optimization + +This was the part of the experiment I found most useful beyond `searchsorted`. + +Performance work often begins with: + +> How can this computation execute faster? + +But there is another question worth asking: + +> Does all of this computation still need to happen? + +Modern CPUs can gain substantially from batching, overlapping independent work, and improving memory behavior. + +But after making execution more efficient, another opportunity may remain: use information the program has already produced to remove work entirely. + +In this case, insertion positions were not just outputs. + +They were structure. + +And reusing that structure exposed another layer of performance. + +A NumPy implementation of this experiment is currently under review in [PR #32895](https://github.com/numpy/numpy/pull/32895). The article is about the performance idea and the experiments behind it, rather than the outcome of that review. 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zZ!g^ON|6_;lAKoF+OqDZ!IfX89EMjp3jrdv7xCo`m{z&W^M{7;aCpPEhC4+kmlGzm z+J$=#aK?c_kDMKa4DZ|Epw2^*;tw2{?<$=NUwKKx8yL@ca8Y6|F11LR6RI3<2y_6} zMW+@?sTl&FyL$T>X)TjHY~%K>{O(|3w9hboTMKshEo$S3V90|VLgduYLVZI`hC`qa z?7V)fZpH#OKlsj~=iZr+;NniYUGJoWq3m-<>=xR=6>?c|NZjW zz0%RHyw#Qek$$|=PW|^s*eYK9=Y6fbIk5Ht21=lZ|NHgvBi~Ar``_0v{P7>y;(uR* u-|pYb`tM6@XA)i^i~jo>|4+Y-CDxfAqBSP}q;wMrr|h{4XVayw-u*u)A^VsB From e46c2be36e8791b8a4d2f4dd39af0d56e809d7ed Mon Sep 17 00:00:00 2001 From: Johnny Kao <19386515+Johnny-Kao@users.noreply.github.com> Date: Wed, 7 Oct 2026 10:44:47 +0900 Subject: [PATCH 05/10] Publish article on np.searchsorted performance optimization Updated the draft status to false and refined the descriptions and figures in the article about performance in np.searchsorted. --- .../index.md | 17 ++++++++++------- 1 file changed, 10 insertions(+), 7 deletions(-) diff --git a/content/posts/numpy/finding-another-layer-of-performance-in-np-searchsorted/index.md b/content/posts/numpy/finding-another-layer-of-performance-in-np-searchsorted/index.md index 1cfdf54..a0ff55c 100644 --- a/content/posts/numpy/finding-another-layer-of-performance-in-np-searchsorted/index.md +++ b/content/posts/numpy/finding-another-layer-of-performance-in-np-searchsorted/index.md @@ -1,7 +1,7 @@ --- title: "Finding Another Layer of Performance in np.searchsorted" date: 2026-10-07T09:11:00+09:00 -draft: true +draft: false description: "A performance investigation into reusing insertion-position locality in NumPy searchsorted, and why reducing work can complement CPU-friendly batched execution." tags: ["numpy", "performance"] displayInList: true @@ -170,23 +170,26 @@ At smaller query counts, it is possible to remove search work while still increa This led to a separate activation gate. -The implementation shown here uses +For the final validation, I used \[ Q \ge 2^{20} \] -as a conservative threshold. +as a conservative activation gate. There is nothing mathematically special about \(2^{20}\). Earlier activation sweeps already showed why a portable gate needed to be conservative: three tested profiles could converge on a low activation candidate in that experimental setup, while the 1-vCPU / 2-GB profile failed the second-stage stability gate entirely. -The exact crossover therefore depends on the machine and on the surrounding selector design. The final gate is intentionally more conservative than those early exploratory thresholds. +![Early activation-threshold sweep showing different random-workload p95 behavior across four hardware profiles.](early-activation-threshold-sweep.png) + +*Figure 5. Early activation sweeps were hardware-sensitive. Three profiles converged on low candidates in this experiment, while the 1-vCPU / 2-GB profile failed the second-stage stability gate. This exploratory sweep motivated a more conservative portable policy; it does not directly define the final \(2^{20}\) gate.* + +The exact crossover therefore depends on the machine and on the surrounding selector design. The final validation gate was intentionally more conservative than those early exploratory thresholds. This was a useful reminder: > A cheaper algorithmic path is not automatically a faster CPU path. - ## Then I found the earlier NumPy optimization @@ -196,7 +199,7 @@ What was interesting was that the earlier work and this experiment were optimizi ![Diagram comparing earlier batched-search work, which improves how searches execute, with this experiment, which reduces how much search work is required.](two-layers-of-optimization.png) -*Figure 5. The earlier batched-search work improves execution efficiency; this experiment reduces the amount of work. The two approaches are complementary and can stack.* +*Figure 6. The earlier batched-search work improves execution efficiency; this experiment reduces the amount of work. The two approaches are complementary and can stack.* The earlier work improves **how the searches execute**. This experiment focuses on **how much searching is necessary**. @@ -222,4 +225,4 @@ They were structure. And reusing that structure exposed another layer of performance. -A NumPy implementation of this experiment is currently under review in [PR #32895](https://github.com/numpy/numpy/pull/32895). The article is about the performance idea and the experiments behind it, rather than the outcome of that review. +A NumPy implementation of this experiment is currently under review in [PR #32895](https://github.com/numpy/numpy/pull/32895). The results discussed here describe the performance experiment itself rather than the outcome of that review. From 965a19dec6b9678b6a95f6a89224e9247283b786 Mon Sep 17 00:00:00 2001 From: "pre-commit-ci[bot]" <66853113+pre-commit-ci[bot]@users.noreply.github.com> Date: Wed, 7 Oct 2026 01:49:34 +0000 Subject: [PATCH 06/10] =?UTF-8?q?[pre-commit.ci=20=F0=9F=A4=96]=20Apply=20?= =?UTF-8?q?code=20format=20tools=20to=20PR?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../index.md | 25 +++++++++---------- 1 file changed, 12 insertions(+), 13 deletions(-) diff --git a/content/posts/numpy/finding-another-layer-of-performance-in-np-searchsorted/index.md b/content/posts/numpy/finding-another-layer-of-performance-in-np-searchsorted/index.md index a0ff55c..175381c 100644 --- a/content/posts/numpy/finding-another-layer-of-performance-in-np-searchsorted/index.md +++ b/content/posts/numpy/finding-another-layer-of-performance-in-np-searchsorted/index.md @@ -59,7 +59,7 @@ Instead, the implementation uses intermediate position information already produ ![Comparison between a full search range and a smaller useful search region around a previous insertion position.](search-space-reduction.png) -*Figure 1. Positional locality can reduce the effective search space without adding a separate scan of the query array.* +_Figure 1. Positional locality can reduce the effective search space without adding a separate scan of the query array._ ## Knowing when to use it @@ -107,7 +107,7 @@ The important result was simple: more observations were not consistently better. ![Flow diagram showing the selector experiment progressing from 8, 16, and 32 observations to later convergence tests using only 16 and 32.](selector-convergence-flow.png) -*Figure 2. The observation-count experiment narrowed the later search space: 8 was dropped, while 16 and 32 were carried forward for convergence testing.* +_Figure 2. The observation-count experiment narrowed the later search space: 8 was dropped, while 16 and 32 were carried forward for convergence testing._ Those later experiments produced another useful result: once the basic selector was already rejecting random workloads reliably, adding more decision rules did not help. More complicated policies mainly rejected useful local cases. @@ -117,7 +117,7 @@ It was overhead. ![Random-workload p95 candidate-to-baseline ratios for 8, 16, and 32 selector observations across four hardware profiles.](selector-observations.png) -*Figure 3. Focused selector experiment at level 4. Lower is better; the best observation count varies by hardware profile, so increasing from 16 to 32 was not uniformly beneficial.* +_Figure 3. Focused selector experiment at level 4. Lower is better; the best observation count varies by hardware profile, so increasing from 16 to 32 was not uniformly beneficial._ ## What the benchmarks showed @@ -135,16 +135,16 @@ The matrix included: Across the final profiles, strong-locality workloads showed median speedups of roughly **5.3–5.8x**. -| Runner | Strong-locality median | Active-random median | Worst active case | -| --- | ---: | ---: | ---: | -| AMD EPYC 7763 / 1 vCPU | 5.61x | 1.27x | 1.08x | -| Intel Xeon Platinum 8573C / 2 vCPU | 5.33x | 1.20x | 1.06x | -| AMD EPYC 7763 / 4 vCPU | 5.67x | 1.31x | 1.08x | -| AMD EPYC 9V45 / 4 vCPU | 5.78x | 1.23x | 1.04x | +| Runner | Strong-locality median | Active-random median | Worst active case | +| ---------------------------------- | ---------------------: | -------------------: | ----------------: | +| AMD EPYC 7763 / 1 vCPU | 5.61x | 1.27x | 1.08x | +| Intel Xeon Platinum 8573C / 2 vCPU | 5.33x | 1.20x | 1.06x | +| AMD EPYC 7763 / 4 vCPU | 5.67x | 1.31x | 1.08x | +| AMD EPYC 9V45 / 4 vCPU | 5.78x | 1.23x | 1.04x | ![Bar chart of final sign-off speedups across four hardware profiles, comparing strong-locality median, active-random median, and worst active case.](final-signoff-benchmark.png) -*Figure 4. Final sign-off results. Strong-locality workloads gained more than 5x across all four profiles, while active random workloads and the worst active cases remained above baseline.* +_Figure 4. Final sign-off results. Strong-locality workloads gained more than 5x across all four profiles, while active random workloads and the worst active cases remained above baseline._ Earlier matrices showed the same pattern from another angle: @@ -182,7 +182,7 @@ There is nothing mathematically special about \(2^{20}\). Earlier activation swe ![Early activation-threshold sweep showing different random-workload p95 behavior across four hardware profiles.](early-activation-threshold-sweep.png) -*Figure 5. Early activation sweeps were hardware-sensitive. Three profiles converged on low candidates in this experiment, while the 1-vCPU / 2-GB profile failed the second-stage stability gate. This exploratory sweep motivated a more conservative portable policy; it does not directly define the final \(2^{20}\) gate.* +_Figure 5. Early activation sweeps were hardware-sensitive. Three profiles converged on low candidates in this experiment, while the 1-vCPU / 2-GB profile failed the second-stage stability gate. This exploratory sweep motivated a more conservative portable policy; it does not directly define the final \(2^{20}\) gate._ The exact crossover therefore depends on the machine and on the surrounding selector design. The final validation gate was intentionally more conservative than those early exploratory thresholds. @@ -190,7 +190,6 @@ This was a useful reminder: > A cheaper algorithmic path is not automatically a faster CPU path. - ## Then I found the earlier NumPy optimization Only after implementing and validating this work did I come across [NumPy PR #30517](https://github.com/numpy/numpy/pull/30517) and the Scientific Python article [Making `np.searchsorted` up to 25x Faster in NumPy 2.5](https://blog.scientific-python.org/numpy/searchsorted/). @@ -199,7 +198,7 @@ What was interesting was that the earlier work and this experiment were optimizi ![Diagram comparing earlier batched-search work, which improves how searches execute, with this experiment, which reduces how much search work is required.](two-layers-of-optimization.png) -*Figure 6. The earlier batched-search work improves execution efficiency; this experiment reduces the amount of work. The two approaches are complementary and can stack.* +_Figure 6. The earlier batched-search work improves execution efficiency; this experiment reduces the amount of work. The two approaches are complementary and can stack._ The earlier work improves **how the searches execute**. This experiment focuses on **how much searching is necessary**. From 98821c3e8fd823d9ef6dee365ce6dcaf9e10c449 Mon Sep 17 00:00:00 2001 From: Johnny Kao <19386515+Johnny-Kao@users.noreply.github.com> Date: Wed, 7 Oct 2026 11:15:07 +0900 Subject: [PATCH 07/10] Fix math rendering in blog post --- .../index.md | 10 ++-------- 1 file changed, 2 insertions(+), 8 deletions(-) diff --git a/content/posts/numpy/finding-another-layer-of-performance-in-np-searchsorted/index.md b/content/posts/numpy/finding-another-layer-of-performance-in-np-searchsorted/index.md index 175381c..b4ffe09 100644 --- a/content/posts/numpy/finding-another-layer-of-performance-in-np-searchsorted/index.md +++ b/content/posts/numpy/finding-another-layer-of-performance-in-np-searchsorted/index.md @@ -170,15 +170,9 @@ At smaller query counts, it is possible to remove search work while still increa This led to a separate activation gate. -For the final validation, I used +For the final validation, I used $Q \ge 2^{20}$ as a conservative activation gate. -\[ -Q \ge 2^{20} -\] - -as a conservative activation gate. - -There is nothing mathematically special about \(2^{20}\). Earlier activation sweeps already showed why a portable gate needed to be conservative: three tested profiles could converge on a low activation candidate in that experimental setup, while the 1-vCPU / 2-GB profile failed the second-stage stability gate entirely. +There is nothing mathematically special about $2^{20}$. Earlier activation sweeps already showed why a portable gate needed to be conservative: three tested profiles could converge on a low activation candidate in that experimental setup, while the 1-vCPU / 2-GB profile failed the second-stage stability gate entirely. ![Early activation-threshold sweep showing different random-workload p95 behavior across four hardware profiles.](early-activation-threshold-sweep.png) From 55b191d654aeb532e8b34da5502bff54a0a5dd1b Mon Sep 17 00:00:00 2001 From: Johnny Kao <19386515+Johnny-Kao@users.noreply.github.com> Date: Wed, 7 Oct 2026 11:42:21 +0900 Subject: [PATCH 08/10] Enhance formatting for clarity in searchsorted article Updated formatting for emphasis and clarity in the article on optimizing np.searchsorted. --- .../index.md | 53 ++++++++++--------- 1 file changed, 27 insertions(+), 26 deletions(-) diff --git a/content/posts/numpy/finding-another-layer-of-performance-in-np-searchsorted/index.md b/content/posts/numpy/finding-another-layer-of-performance-in-np-searchsorted/index.md index b4ffe09..9a29b05 100644 --- a/content/posts/numpy/finding-another-layer-of-performance-in-np-searchsorted/index.md +++ b/content/posts/numpy/finding-another-layer-of-performance-in-np-searchsorted/index.md @@ -12,7 +12,7 @@ I did not start from `np.searchsorted`. The idea came from a broader question I had been exploring in my own infrastructure work: -> Has the system already paid for information that we are about to compute again? +**Has the system already paid for information that we are about to compute again?** In my [CoreFoundry project](https://github.com/Johnny-Kao/CoreFoundry-Project), one recurring principle was simple: before adding more hardware or parallelism, first remove work that never needed to happen. @@ -53,13 +53,13 @@ That became the basic idea of the experiment: reuse information already produced There was one important constraint. -Detecting locality should not require another full pass over the query array. An additional \(O(Q)\) scan just to decide whether an optimization should run could easily consume the performance benefit. +Detecting locality should not require another full pass over the query array. An additional $O(Q)$ scan just to decide whether an optimization should run could easily consume the performance benefit. Instead, the implementation uses intermediate position information already produced by the existing batched search. ![Comparison between a full search range and a smaller useful search region around a previous insertion position.](search-space-reduction.png) -_Figure 1. Positional locality can reduce the effective search space without adding a separate scan of the query array._ +*Figure 1. Positional locality can reduce the effective search space without adding a separate scan of the query array.* ## Knowing when to use it @@ -95,9 +95,7 @@ Both have previous insertion positions. Only the first has previous positions that provide useful information about the next search. -So the problem became: - -> How much locality is enough to justify a different search path? +So the problem became: **how much locality is enough to justify a different search path?** I tested different selector configurations across multiple hardware profiles. @@ -107,7 +105,7 @@ The important result was simple: more observations were not consistently better. ![Flow diagram showing the selector experiment progressing from 8, 16, and 32 observations to later convergence tests using only 16 and 32.](selector-convergence-flow.png) -_Figure 2. The observation-count experiment narrowed the later search space: 8 was dropped, while 16 and 32 were carried forward for convergence testing._ +*Figure 2. The observation-count experiment narrowed the later search space: 8 was dropped, while 16 and 32 were carried forward for convergence testing.* Those later experiments produced another useful result: once the basic selector was already rejecting random workloads reliably, adding more decision rules did not help. More complicated policies mainly rejected useful local cases. @@ -117,7 +115,7 @@ It was overhead. ![Random-workload p95 candidate-to-baseline ratios for 8, 16, and 32 selector observations across four hardware profiles.](selector-observations.png) -_Figure 3. Focused selector experiment at level 4. Lower is better; the best observation count varies by hardware profile, so increasing from 16 to 32 was not uniformly beneficial._ +*Figure 3. Focused selector experiment at level 4. Lower is better; the best observation count varies by hardware profile, so increasing from 16 to 32 was not uniformly beneficial.* ## What the benchmarks showed @@ -135,16 +133,16 @@ The matrix included: Across the final profiles, strong-locality workloads showed median speedups of roughly **5.3–5.8x**. -| Runner | Strong-locality median | Active-random median | Worst active case | -| ---------------------------------- | ---------------------: | -------------------: | ----------------: | -| AMD EPYC 7763 / 1 vCPU | 5.61x | 1.27x | 1.08x | -| Intel Xeon Platinum 8573C / 2 vCPU | 5.33x | 1.20x | 1.06x | -| AMD EPYC 7763 / 4 vCPU | 5.67x | 1.31x | 1.08x | -| AMD EPYC 9V45 / 4 vCPU | 5.78x | 1.23x | 1.04x | +| Runner | Strong-locality median | Active-random median | Worst active case | +| --- | ---: | ---: | ---: | +| AMD EPYC 7763 / 1 vCPU | 5.61x | 1.27x | 1.08x | +| Intel Xeon Platinum 8573C / 2 vCPU | 5.33x | 1.20x | 1.06x | +| AMD EPYC 7763 / 4 vCPU | 5.67x | 1.31x | 1.08x | +| AMD EPYC 9V45 / 4 vCPU | 5.78x | 1.23x | 1.04x | ![Bar chart of final sign-off speedups across four hardware profiles, comparing strong-locality median, active-random median, and worst active case.](final-signoff-benchmark.png) -_Figure 4. Final sign-off results. Strong-locality workloads gained more than 5x across all four profiles, while active random workloads and the worst active cases remained above baseline._ +*Figure 4. Final sign-off results. Strong-locality workloads gained more than 5x across all four profiles, while active random workloads and the worst active cases remained above baseline.* Earlier matrices showed the same pattern from another angle: @@ -170,19 +168,24 @@ At smaller query counts, it is possible to remove search work while still increa This led to a separate activation gate. -For the final validation, I used $Q \ge 2^{20}$ as a conservative activation gate. +For the final validation, I used + + +Q \ge 2^{20} + + +as a conservative activation gate. There is nothing mathematically special about $2^{20}$. Earlier activation sweeps already showed why a portable gate needed to be conservative: three tested profiles could converge on a low activation candidate in that experimental setup, while the 1-vCPU / 2-GB profile failed the second-stage stability gate entirely. ![Early activation-threshold sweep showing different random-workload p95 behavior across four hardware profiles.](early-activation-threshold-sweep.png) -_Figure 5. Early activation sweeps were hardware-sensitive. Three profiles converged on low candidates in this experiment, while the 1-vCPU / 2-GB profile failed the second-stage stability gate. This exploratory sweep motivated a more conservative portable policy; it does not directly define the final \(2^{20}\) gate._ +*Figure 5. Early activation sweeps were hardware-sensitive. Three profiles converged on low candidates in this experiment, while the 1-vCPU / 2-GB profile failed the second-stage stability gate. This exploratory sweep motivated a more conservative portable policy; it does not directly define the final $2^{20}$ gate.* The exact crossover therefore depends on the machine and on the surrounding selector design. The final validation gate was intentionally more conservative than those early exploratory thresholds. -This was a useful reminder: +A useful reminder from this experiment: **a cheaper algorithmic path is not automatically a faster CPU path.** -> A cheaper algorithmic path is not automatically a faster CPU path. ## Then I found the earlier NumPy optimization @@ -192,7 +195,7 @@ What was interesting was that the earlier work and this experiment were optimizi ![Diagram comparing earlier batched-search work, which improves how searches execute, with this experiment, which reduces how much search work is required.](two-layers-of-optimization.png) -_Figure 6. The earlier batched-search work improves execution efficiency; this experiment reduces the amount of work. The two approaches are complementary and can stack._ +*Figure 6. The earlier batched-search work improves execution efficiency; this experiment reduces the amount of work. The two approaches are complementary and can stack.* The earlier work improves **how the searches execute**. This experiment focuses on **how much searching is necessary**. @@ -200,13 +203,9 @@ The earlier work improves **how the searches execute**. This experiment focuses This was the part of the experiment I found most useful beyond `searchsorted`. -Performance work often begins with: - -> How can this computation execute faster? +Performance work often begins with: **How can this computation execute faster?** -But there is another question worth asking: - -> Does all of this computation still need to happen? +But there is another question worth asking: **Does all of this computation still need to happen?** Modern CPUs can gain substantially from batching, overlapping independent work, and improving memory behavior. @@ -219,3 +218,5 @@ They were structure. And reusing that structure exposed another layer of performance. A NumPy implementation of this experiment is currently under review in [PR #32895](https://github.com/numpy/numpy/pull/32895). The results discussed here describe the performance experiment itself rather than the outcome of that review. + +The code and related experiments are available through [my GitHub profile](https://github.com/Johnny-Kao). From c2c5296359041cbb291b77e378d1bf6065d65288 Mon Sep 17 00:00:00 2001 From: "pre-commit-ci[bot]" <66853113+pre-commit-ci[bot]@users.noreply.github.com> Date: Wed, 7 Oct 2026 02:44:36 +0000 Subject: [PATCH 09/10] =?UTF-8?q?[pre-commit.ci=20=F0=9F=A4=96]=20Apply=20?= =?UTF-8?q?code=20format=20tools=20to=20PR?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../index.md | 27 +++++++++---------- 1 file changed, 12 insertions(+), 15 deletions(-) diff --git a/content/posts/numpy/finding-another-layer-of-performance-in-np-searchsorted/index.md b/content/posts/numpy/finding-another-layer-of-performance-in-np-searchsorted/index.md index 9a29b05..d550557 100644 --- a/content/posts/numpy/finding-another-layer-of-performance-in-np-searchsorted/index.md +++ b/content/posts/numpy/finding-another-layer-of-performance-in-np-searchsorted/index.md @@ -59,7 +59,7 @@ Instead, the implementation uses intermediate position information already produ ![Comparison between a full search range and a smaller useful search region around a previous insertion position.](search-space-reduction.png) -*Figure 1. Positional locality can reduce the effective search space without adding a separate scan of the query array.* +_Figure 1. Positional locality can reduce the effective search space without adding a separate scan of the query array._ ## Knowing when to use it @@ -105,7 +105,7 @@ The important result was simple: more observations were not consistently better. ![Flow diagram showing the selector experiment progressing from 8, 16, and 32 observations to later convergence tests using only 16 and 32.](selector-convergence-flow.png) -*Figure 2. The observation-count experiment narrowed the later search space: 8 was dropped, while 16 and 32 were carried forward for convergence testing.* +_Figure 2. The observation-count experiment narrowed the later search space: 8 was dropped, while 16 and 32 were carried forward for convergence testing._ Those later experiments produced another useful result: once the basic selector was already rejecting random workloads reliably, adding more decision rules did not help. More complicated policies mainly rejected useful local cases. @@ -115,7 +115,7 @@ It was overhead. ![Random-workload p95 candidate-to-baseline ratios for 8, 16, and 32 selector observations across four hardware profiles.](selector-observations.png) -*Figure 3. Focused selector experiment at level 4. Lower is better; the best observation count varies by hardware profile, so increasing from 16 to 32 was not uniformly beneficial.* +_Figure 3. Focused selector experiment at level 4. Lower is better; the best observation count varies by hardware profile, so increasing from 16 to 32 was not uniformly beneficial._ ## What the benchmarks showed @@ -133,16 +133,16 @@ The matrix included: Across the final profiles, strong-locality workloads showed median speedups of roughly **5.3–5.8x**. -| Runner | Strong-locality median | Active-random median | Worst active case | -| --- | ---: | ---: | ---: | -| AMD EPYC 7763 / 1 vCPU | 5.61x | 1.27x | 1.08x | -| Intel Xeon Platinum 8573C / 2 vCPU | 5.33x | 1.20x | 1.06x | -| AMD EPYC 7763 / 4 vCPU | 5.67x | 1.31x | 1.08x | -| AMD EPYC 9V45 / 4 vCPU | 5.78x | 1.23x | 1.04x | +| Runner | Strong-locality median | Active-random median | Worst active case | +| ---------------------------------- | ---------------------: | -------------------: | ----------------: | +| AMD EPYC 7763 / 1 vCPU | 5.61x | 1.27x | 1.08x | +| Intel Xeon Platinum 8573C / 2 vCPU | 5.33x | 1.20x | 1.06x | +| AMD EPYC 7763 / 4 vCPU | 5.67x | 1.31x | 1.08x | +| AMD EPYC 9V45 / 4 vCPU | 5.78x | 1.23x | 1.04x | ![Bar chart of final sign-off speedups across four hardware profiles, comparing strong-locality median, active-random median, and worst active case.](final-signoff-benchmark.png) -*Figure 4. Final sign-off results. Strong-locality workloads gained more than 5x across all four profiles, while active random workloads and the worst active cases remained above baseline.* +_Figure 4. Final sign-off results. Strong-locality workloads gained more than 5x across all four profiles, while active random workloads and the worst active cases remained above baseline._ Earlier matrices showed the same pattern from another angle: @@ -170,23 +170,20 @@ This led to a separate activation gate. For the final validation, I used - Q \ge 2^{20} - as a conservative activation gate. There is nothing mathematically special about $2^{20}$. Earlier activation sweeps already showed why a portable gate needed to be conservative: three tested profiles could converge on a low activation candidate in that experimental setup, while the 1-vCPU / 2-GB profile failed the second-stage stability gate entirely. ![Early activation-threshold sweep showing different random-workload p95 behavior across four hardware profiles.](early-activation-threshold-sweep.png) -*Figure 5. Early activation sweeps were hardware-sensitive. Three profiles converged on low candidates in this experiment, while the 1-vCPU / 2-GB profile failed the second-stage stability gate. This exploratory sweep motivated a more conservative portable policy; it does not directly define the final $2^{20}$ gate.* +_Figure 5. Early activation sweeps were hardware-sensitive. Three profiles converged on low candidates in this experiment, while the 1-vCPU / 2-GB profile failed the second-stage stability gate. This exploratory sweep motivated a more conservative portable policy; it does not directly define the final $2^{20}$ gate._ The exact crossover therefore depends on the machine and on the surrounding selector design. The final validation gate was intentionally more conservative than those early exploratory thresholds. A useful reminder from this experiment: **a cheaper algorithmic path is not automatically a faster CPU path.** - ## Then I found the earlier NumPy optimization Only after implementing and validating this work did I come across [NumPy PR #30517](https://github.com/numpy/numpy/pull/30517) and the Scientific Python article [Making `np.searchsorted` up to 25x Faster in NumPy 2.5](https://blog.scientific-python.org/numpy/searchsorted/). @@ -195,7 +192,7 @@ What was interesting was that the earlier work and this experiment were optimizi ![Diagram comparing earlier batched-search work, which improves how searches execute, with this experiment, which reduces how much search work is required.](two-layers-of-optimization.png) -*Figure 6. The earlier batched-search work improves execution efficiency; this experiment reduces the amount of work. The two approaches are complementary and can stack.* +_Figure 6. The earlier batched-search work improves execution efficiency; this experiment reduces the amount of work. The two approaches are complementary and can stack._ The earlier work improves **how the searches execute**. This experiment focuses on **how much searching is necessary**. From dc611dabe289d4da328a8ef73e2f08466d8ca98a Mon Sep 17 00:00:00 2001 From: Johnny Kao <19386515+Johnny-Kao@users.noreply.github.com> Date: Wed, 7 Oct 2026 12:43:38 +0900 Subject: [PATCH 10/10] Update index.md --- .../index.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/content/posts/numpy/finding-another-layer-of-performance-in-np-searchsorted/index.md b/content/posts/numpy/finding-another-layer-of-performance-in-np-searchsorted/index.md index d550557..a2a1fa0 100644 --- a/content/posts/numpy/finding-another-layer-of-performance-in-np-searchsorted/index.md +++ b/content/posts/numpy/finding-another-layer-of-performance-in-np-searchsorted/index.md @@ -170,7 +170,7 @@ This led to a separate activation gate. For the final validation, I used -Q \ge 2^{20} +$Q \ge 2^{20}$ as a conservative activation gate.