position: PSA: apply the double-angle sine formula #61
Conversation
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Apply the double-angle sine formula:
```
sin(2 * x) = 2 * sin(x) * cos(x)
```
The idea is:
* `sin(x)` and `sin(2 * x)` both appear as subexpressions within the
same expression
* computing `sin(x)` and `cos(x)` could conceivably be faster than
computing directly `sin(x)` and `sin(2 * x)`, because `sin(x)` and
`cos(x)` use the same polynomials in their implementations
* this relies on the compiler being smart enough
* this perhaps also relies on luck regarding things like inlining
heuristics
nsajko
commented
Jan 5, 2026
| (sin_Ω, cos_Ω) = sincos(Ω) | ||
| λₑ = L + p7 * sin(g) + p8 * sin(2 * g) + p9 + p10 * sin_Ω # Eq. 6 | ||
| (sin_g, cos_g) = sincos(g) | ||
| λₑ = L + p7 * sin_g + (p8 * 2) * (sin_g * cos_g) + p9 + p10 * sin_Ω # Eq. 6 |
Contributor
Author
There was a problem hiding this comment.
might also make sense to factor out sin_g:
Suggested change
| λₑ = L + p7 * sin_g + (p8 * 2) * (sin_g * cos_g) + p9 + p10 * sin_Ω # Eq. 6 | |
| λₑ = L + sin_g * (p7+ (p8 * 2) * cos_g) + p9 + p10 * sin_Ω # Eq. 6 |
Benchmark Results (Julia vlts)Time benchmarks
Memory benchmarks
|
Benchmark Results (Julia vpre)Time benchmarks
Memory benchmarks
|
Benchmark Results (Julia v1)Time benchmarks
Memory benchmarks
|
Codecov Report✅ All modified and coverable lines are covered by tests. Additional details and impacted files@@ Coverage Diff @@
## main #61 +/- ##
=========================================
Coverage 100.00% 100.00%
=========================================
Files 17 17
Lines 678 679 +1
=========================================
+ Hits 678 679 +1 ☔ View full report in Codecov by Sentry. 🚀 New features to boost your workflow:
|
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
1 participant
Add this suggestion to a batch that can be applied as a single commit.
This suggestion is invalid because no changes were made to the code.
Suggestions cannot be applied while the pull request is closed.
Suggestions cannot be applied while viewing a subset of changes.
Only one suggestion per line can be applied in a batch.
Add this suggestion to a batch that can be applied as a single commit.
Applying suggestions on deleted lines is not supported.
You must change the existing code in this line in order to create a valid suggestion.
Outdated suggestions cannot be applied.
This suggestion has been applied or marked resolved.
Suggestions cannot be applied from pending reviews.
Suggestions cannot be applied on multi-line comments.
Suggestions cannot be applied while the pull request is queued to merge.
Suggestion cannot be applied right now. Please check back later.
Apply the double-angle sine formula:
The idea is:
sin(x)andsin(2 * x)both appear as subexpressions within the same expressioncomputing
sin(x)andcos(x)could conceivably be faster than computing directlysin(x)andsin(2 * x), becausesin(::Float64)andcos(::Float64)use the same polynomials in their implementationsthis relies on the compiler being smart enough
this perhaps also relies on luck regarding things like inlining heuristics
Checklist