Linus Baumberger
130 lines
5.2 KiB
Markdown
130 lines
5.2 KiB
Markdown
# Optimization: Branchless w() (negative result)
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- **Author**: Linus
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- **Predecessor**: variant_baseline.cpp
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- **File(s)**: variants/variant_branchless.cpp, variants/variant_branchless_sqrtfree.cpp
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- **Status**: probably: negative (slower)
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## What this changes
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Two attempts at making the field-of-view weight function `w()` branchless.
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**Attempt 1** (`variant_branchless.cpp`): replace the if/else in `w()` with an
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arithmetic blend `c_neg_times_dt + cond * (dt_neg - c_neg_times_dt)`, where
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`cond` is a 0.0/1.0 mask cast from a bool comparison. The `sqrt` inside
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`f.norm()` is kept.
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**Attempt 2** (`variant_branchless_sqrtfree.cpp`): on top of attempt 1, also
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eliminate the `sqrt` by squaring the comparison. Uses the fact that
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`cos_phi = cos(100 deg)` is negative, so `f.norm() * cos_phi <= 0`, meaning
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the condition is automatically true whenever `e.dot(f) >= 0`. For
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`e.dot(f) < 0`, both sides are non-positive so we can square them safely:
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`dot^2 <= f.dot(f) * cos_phi^2`. Needs the constant
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`cos_phi_sq = cos_phi * cos_phi` in `headers/constants.hpp`.
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Additionaly i split the mainloop into two loops, so we where able to remove the if-statement from the loop. Once again that didn't made a difference in the runtime analysis
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## Code (relevant snippet)
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Attempt 1 - arithmetic blend (still has sqrt):
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```cpp
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double w(Vector2d e, Vector2d f) {
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double dot = e.dot(f);
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double f_norm = f.norm();
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double cond = (double)(dot >= f_norm * cos_phi); // 1.0 or 0.0
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return c_neg_times_dt + cond * (dt_neg - c_neg_times_dt);
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}
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```
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Attempt 2 - blend + sqrt-free (squared comparison):
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```cpp
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double w(Vector2d e, Vector2d f) {
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double dot = e.x * f.x + e.y * f.y;
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double f_dot_f = f.x * f.x + f.y * f.y;
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// Bitwise | (not ||) keeps both sides evaluated -> no branch.
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double cond = (dot >= 0.0) | (dot * dot <= f_dot_f * cos_phi_sq);
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return c_neg_times_dt + cond * (dt_neg - c_neg_times_dt);
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}
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```
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## Benchmark
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Conditions: min of <N> runs, N_ITER=1000, -O3 -march=native -flto.
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A preliminary run on my laptop (Intel ULTRA 9 185H @ 2.2 GHz, WSL
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Ubuntu) showed both attempts about 8-13% slower than the baseline across
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N=50 to N=1000, with a roughly flat gap that did not scale with N.
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For the official numbers run on the testmachines
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### x86
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**Machine**:
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```
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<paste machine info here>
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```
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**Frequency**: <e.g., 2 GHz>
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Attempt 1 - branchless (arithmetic blend):
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| N | W(n) [Flops] | T(n) [Cycles] | Performance [Flops/Cycle] | Diff vs Baseline |
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| ---- | ------------ | ------------- | ------------------------- | ---------------- |
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| 50 | | | | |
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| 100 | | | | |
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| 200 | | | | |
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| 500 | | | | |
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| 1000 | | | | |
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Attempt 2 - branchless + sqrt-free:
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| N | W(n) [Flops] | T(n) [Cycles] | Performance [Flops/Cycle] | Diff vs Baseline |
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| ---- | ------------ | ------------- | ------------------------- | ---------------- |
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| 50 | | | | |
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| 100 | | | | |
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| 200 | | | | |
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| 500 | | | | |
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| 1000 | | | | |
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### ARM (Apple)
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**Machine**:
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```
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<paste machine info here>
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```
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**Frequency**: <e.g., 3.2 GHz>
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Attempt 1 - branchless (arithmetic blend):
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| N | W(n) [Flops] | T(n) [Cycles] | Performance [Flops/Cycle] | Diff vs Baseline |
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| ---- | ------------ | ------------- | ------------------------- | ---------------- |
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| 50 | | | | |
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| 100 | | | | |
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| 200 | | | | |
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| 500 | | | | |
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| 1000 | | | | |
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Attempt 2 - branchless + sqrt-free:
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| N | W(n) [Flops] | T(n) [Cycles] | Performance [Flops/Cycle] | Diff vs Baseline |
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| ---- | ------------ | ------------- | ------------------------- | ---------------- |
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| 50 | | | | |
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| 100 | | | | |
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| 200 | | | | |
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| 500 | | | | |
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| 1000 | | | | |
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## Analysis
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<Why it worked or did not. What surprised you. What bottleneck this hits
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or moves. Mention generated assembly or a profile if relevant.>
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## Takeaway
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<One short paragraph that could be lifted straight into the report.>
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