Branch on Bool alpha in diagonal matmul
#1256
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dkarrasch
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Apr 3, 2025
Codecov ReportAll modified and coverable lines are covered by tests ✅
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## master #1256 +/- ##
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- Coverage 92.03% 92.00% -0.04%
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Files 34 34
Lines 15459 15463 +4
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dkarrasch
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Apr 3, 2025
jishnub
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Apr 26, 2025
Similar to #1256, we may reduce branches in `@stable_muladdmul` for a non-zero `Bool` alpha in `Bidiagonal` matmul. The idea is that if `alpha::Bool` is non-zero, it must be `true`. We may therefore hardcode this value and reduce branches in `@stable_muladdmul`. In addition, if `beta` is unused in a method, we may hardcode `beta = false` as well, which further helps with compilation. ```julia julia> using LinearAlgebra julia> B = Bidiagonal(1:4, 1:3, :U); D = Diagonal(1:4); v = (1:4); ``` With this, ```julia julia> @time B * B; 0.406036 seconds (2.34 M allocations: 105.696 MiB, 4.31% gc time, 99.99% compilation time) # nightly 0.141480 seconds (588.18 k allocations: 26.049 MiB, 99.95% compilation time) # This PR ``` The rest are mainly reductions in allocation: ```julia julia> @time B * D; 0.141903 seconds (487.43 k allocations: 24.557 MiB, 99.96% compilation time) # nightly 0.147749 seconds (382.60 k allocations: 19.385 MiB, 99.96% compilation time) # this PR ``` ```julia julia> @time D * B; 0.136308 seconds (491.83 k allocations: 24.782 MiB, 99.95% compilation time) # nightly 0.136909 seconds (386.35 k allocations: 19.591 MiB, 99.94% compilation time) # this PR ``` ```julia julia> @time B * v; 0.087207 seconds (428.64 k allocations: 21.620 MiB, 99.93% compilation time) # master 0.089002 seconds (342.46 k allocations: 17.306 MiB, 99.92% compilation time) # this PR ``` This also improves performance for small `Bidiagonal` multiplication, as there are fewer operations to carry out. ```julia julia> n = 1; T = Bidiagonal(ones(n), ones(max(n-1,0)), :U); C = Matrix(T); julia> @Btime mul!($C, $T, $T); 33.360 ns (0 allocations: 0 bytes) # nightly 23.773 ns (0 allocations: 0 bytes) # this PR julia> n = 2; T = Bidiagonal(ones(n), ones(max(n-1,0)), :U); C = Matrix(T)); julia> @Btime mul!($C, $T, $T); 78.685 ns (0 allocations: 0 bytes) # nightly 31.388 ns (0 allocations: 0 bytes) # this PR julia> n = 3; T = Bidiagonal(ones(n), ones(max(n-1,0)), :U); C = Matrix(T); julia> @Btime mul!($C, $T, $T); 161.577 ns (0 allocations: 0 bytes) # nightly 41.256 ns (0 allocations: 0 bytes) # this PR ```
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The idea is that if
alphais known to be non-zero and aBool, it must betrue. We may therefore hardcode the value to reduce the branches in@stable_muladdmul.TTFX:
The TTFX in
D * Adoes not change by much, but the allocations go down.