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perf(analysis): IDW at a power of 2 weighs by squared distances, with no square root or power - #1520
Part of #1252 (IDW power-2 path, follow-up track).
What changes
At a power of 2, the default and the case GDAL is compared on, IDW now weighs each point by nearest² / d² from squared distances. It no longer takes a square root and a powf for every cell–point pair. Squaring keeps the distances' order, so the nearest points picked are the same. A cell on a point is found by d² < 1e-24 in place of d < 1e-12. Every other power runs as before.
The idea, squared distances at power 2, is the one GDAL's gdal_grid uses. I wrote the code from that idea and didn't follow GDAL's code.
The two distance loops are separate, one with the square root and one without. A branch inside the loop kept it from compiling tight, and the 12-nearest case ran 12% slower.
Measured (release, 40 threads available), 10,000 points onto 230 × 100 cells, the case in #1252:
On that benchmark, all 92,000 cells are the same as before to the bit, from every point and from the 12 nearest. That comparison ran on the code before the two loops were split; splitting them leaves the arithmetic unchanged.
The weights can differ from powf(2.0) in the last bit of an f64. The tie-breaking can differ too: where two squared distances round to the same distance, the truly nearer point is now kept. Either change could move a cell's f32 by a unit in the last place.
Tests
idw_at_power_two_is_the_general_paths_surface compares every cell, from every point and from the nearest 8, with the general path's weights (nearest/d).powf(2.0) made in the test. The general path can't be asked for at 2 itself. It also checks that a cell centred on a point takes the point's value.
idw_on_several_threads_is_idw_on_one now runs at powers 2 and 3, so both paths are checked bit for bit on 2, 7 and 16 threads against one.
cargo xtask ci checks fmt, clippy, tests and layers, and the wasm build passes. The only failures are the known box-only ones.
Summary by CodeRabbit
Improvements
Inverse-distance raster calculations with a power setting of 2 run faster while maintaining consistent results, including when cells are centered on data points or distances are tied.
No actionable comments were generated in the recent review.
Walkthrough
idw_on now uses squared distances when the power is 2 and ordinary distances for other powers. Tests compare power-2 results with a general-form reference and cover threading, neighbor selection, and exact-point output.
Changes: IDW power-2 calculation
Layer / File(s)
Summary
Distance and weight calculation crates/analysis/src/rasterops.rs
For power 2, idw_on uses squared distances and a corresponding exact-point threshold. Other powers use ordinary distances and power-based weights.
Power-2 result validation crates/analysis/src/rasterops.rs
Tests compare power-2 results with a square-root-distance reference for all-points and nearest-neighbor cases. The threading test checks powers 2 and 3. An exact-point case checks that the cell returns the point value.
opengeos/RustGIS#1252 — The issue tracks a squared-distance path for power-2 IDW, which this PR implements.
Suggested reviewers:giswqs
Merge Risk: Minimal · up to d627f
The identified concerns do not establish a remaining regression; the change is mergeable after normal checks.
Pre-merge checks: 5
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The title clearly identifies the power-2 IDW optimization.
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A rabbit checks the distances with care, Squared paths skip roots along the way. The nearest points still guide the weights, Tests check the ties and threads in play. Then one true point returns its value.
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crates/analysis/src/rasterops.rs
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The squared-domain threshold 1e-24 matches the old d < 1e-12 (line 557), so the exact-match rule is unchanged.
nearest²/d² equals (nearest/d)², so the weights are the same as the powf(2.0) path up to rounding. Squaring preserves order, so select_nth_unstable_by picks the same neighbours, apart from exact ties.
A zero distance never reaches the division, because the exact-match check catches anything below 1e-24 first.
Squared degree-scale distances can't overflow or underflow in f64.
Powers other than exactly 2.0, and NaN or infinite powers, take the unchanged general path. The power is still validated at line 549 before the branch.
Security: None found. The change adds no new input handling.
Performance: Nit, confidence low. The if squared branch remains inside the weight fold (line 610), per point and per cell. It is the same kind of in-loop branch the PR removes from the distance loop. It is loop-invariant, so the compiler will probably unswitch it, and the measured 12-nearest timing (0.82 s → 0.73 s) shows no regression. Splitting the fold the same way would be consistent, but the gain is probably small.
Quality:
Test name, idw_at_power_two_is_the_general_paths_surface (line 1823), overstates what it checks. It compares against a hand-written powf(2.0) reference inside the test, not the production general path. The check is still valid. Confidence: medium. This is a quality point, so per AGENTS.md it can wait for the release quality pass.
AGENTS.md: No violations found.
No unwrap, expect, or panic in non-test code. The new test uses unwrap_or_else(|e| panic!(..)), the same pattern the existing tests use.
No new strings, dependencies, or assets.
The PR body names the GDAL idea and states that the code was not copied, as the contributing rules require.
The lossy-looking differences (last-bit f32 changes and tie-breaking) are disclosed in the PR body. They are not data loss, so no notice is needed.
Not verified: cargo xtask ci and the wasm build. This review had no shell, so I could not run them.
Prior review threads: none on this PR, so nothing was left out as already raised. No inline comments were posted, because no finding is a bug or a crash path.
Change size
Compared with main, merge base 3225fd6 to PR head 20479af (whole PR, not just the latest push).
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Actionable comments posted: 1
Fix comments: Fix CodeRabbit comments on this PR
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Inline comments:
Review comments at @crates/analysis/src/rasterops.rs:
- Around line 1845-1855: Update the neighbor selection logic around `near` so a
tie at the eighth-neighbor boundary does not assume one specific point was
selected. Handle boundary ties separately and allow either tied neighbor’s valid
value, while preserving the existing inverse-distance calculation for non-tied
neighbors.
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crates/analysis/src/rasterops.rs
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Bugs: None found. I checked the changed idw_on logic and the new tests against the old code:
The squared-path exact-match threshold d² < 1e-24 is equivalent to the old d < 1e-12, and the non-squared path keeps 1e-12.
nearest² / d² equals (nearest / d)^2, and squaring preserves the nearest-point ordering.
The NaN, overflow and zero-distance behaviour is the same as before, and the non-2 powers take the unchanged path.
Confidence: high.
Security: None. The change is arithmetic on values already bounded by the existing size and work caps.
Performance: No problems. The squared path removes a sqrt and a powf per cell–point pair. One small inconsistency: the weight fold at crates/analysis/src/rasterops.rs:610 still branches on squared for every neighbour, although the PR's stated reason for splitting the distance loop was that branches inside loops hurt. Confidence: low, and the measured 12-nearest case still improved.
Quality (nits, left for the release quality pass per AGENTS.md; not posted inline):
At rasterops.rs:557, exact is in squared units on the squared path and in plain distance otherwise, and near holds squared distances on that path. A comment on the unit change would help. Confidence: medium.
The reference loop in idw_at_power_two_is_the_general_paths_surface hard-codes 100, 100 and 0.1 rather than deriving them from the extent. Confidence: medium.
The multi-thread test now runs four power/neighbour configurations instead of two, which adds debug-build test time. Confidence: low.
AGENTS.md: Compliant. There are no new unwrap, expect or panic calls in non-test code, and the test code follows the existing pattern. No data is dropped, so no notice is needed. The change is pure arithmetic, so wasm is unaffected. The GDAL idea is cited in a comment, and the PR body says the code was not followed.
Earlier concerns: One earlier thread was left alone. It was a CodeRabbit comment on the tied-boundary test at rasterops.rs:1855, which is resolved and outdated. The author answered it in d627f41 by accepting any tied neighbour, and I checked that the reference now does this.
Change size
Compared with main (merge base 3225fd6 to PR head d627f41), so this covers the whole PR, not only the latest push.
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Part of #1252 (IDW power-2 path, follow-up track).
What changes
At a power of 2, the default and the case GDAL is compared on, IDW now weighs each point by
nearest² / d²from squared distances. It no longer takes a square root and apowffor every cell–point pair. Squaring keeps the distances' order, so the nearest points picked are the same. A cell on a point is found byd² < 1e-24in place ofd < 1e-12. Every other power runs as before.The idea, squared distances at power 2, is the one GDAL's
gdal_griduses. I wrote the code from that idea and didn't follow GDAL's code.The two distance loops are separate, one with the square root and one without. A branch inside the loop kept it from compiling tight, and the 12-nearest case ran 12% slower.
Measured (release, 40 threads available), 10,000 points onto 230 × 100 cells, the case in #1252:
#1252 gives GDAL 0.19 s on one core.
Output
On that benchmark, all 92,000 cells are the same as before to the bit, from every point and from the 12 nearest. That comparison ran on the code before the two loops were split; splitting them leaves the arithmetic unchanged.
The weights can differ from
powf(2.0)in the last bit of an f64. The tie-breaking can differ too: where two squared distances round to the same distance, the truly nearer point is now kept. Either change could move a cell's f32 by a unit in the last place.Tests
idw_at_power_two_is_the_general_paths_surfacecompares every cell, from every point and from the nearest 8, with the general path's weights(nearest/d).powf(2.0)made in the test. The general path can't be asked for at 2 itself. It also checks that a cell centred on a point takes the point's value.idw_on_several_threads_is_idw_on_onenow runs at powers 2 and 3, so both paths are checked bit for bit on 2, 7 and 16 threads against one.cargo xtask cichecks fmt, clippy, tests and layers, and the wasm build passes. The only failures are the known box-only ones.Summary by CodeRabbit