Fast paths for ExactReal with BareInterval - #773
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Benchmark Results (Julia v1)Time benchmarks
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Can't all of this be captured by something in the vein of |
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Not quite; your approach saves a validation, but julia> iv1, iv2 = bareinterval(3, 3), bareinterval(3, 4)
([3.0, 3.0], [3.0, 4.0])
julia> @code_lowered iv1*iv2
CodeInfo(
1 ── %1 = IntervalArithmetic.isempty_interval
│ %2 = dynamic (%1)(x)
└─── goto #4 if not %2
2 ── %4 = x
└─── return %4
3 ── goto #4
4 ┄─ %7 = IntervalArithmetic.isempty_interval
│ %8 = dynamic (%7)(y)
└─── goto #7 if not %8
5 ── %10 = y
└─── return %10
6 ── goto #7
7 ┄─ %13 = IntervalArithmetic.isthinzero
│ %14 = dynamic (%13)(x)
└─── goto #10 if not %14
8 ── %16 = x
└─── return %16
9 ── goto #10
10 ┄ %19 = IntervalArithmetic.isthinzero
│ %20 = dynamic (%19)(y)
└─── goto #13 if not %20
11 ─ %22 = y
└─── return %22
12 ─ goto #13
13 ┄ %25 = IntervalArithmetic.:&
│ %26 = IntervalArithmetic.isbounded
│ %27 = dynamic (%26)(x)
│ %28 = IntervalArithmetic.isbounded
│ %29 = dynamic (%28)(y)
│ %30 = dynamic (%25)(%27, %29)
└─── goto #16 if not %30
14 ─ %32 = IntervalArithmetic._mult
│ %33 = IntervalArithmetic.:*
│ %34 = dynamic (%32)(%33, x, y)
└─── return %34
15 ─ goto #16
16 ┄ %37 = IntervalArithmetic._mult
│ %38 = IntervalArithmetic._unbounded_mul
│ %39 = dynamic (%37)(%38, x, y)
└─── return %39
)shows a lot of unnecessary work (it's not even showing the four-product min/max), given that a point only needs one signbit and two products. It cuts the time approximately in half, which is a game-changer for my application. To be clear, it's totally OK if you say "no," I don't want to push you into something you don't want. |
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I see. Oh no, I am not opposed in principle, but I always try to fix the root problems (otherwise we end up with too much band-aid...). |
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To clarify, you mean move those methods to |
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Indeed, sorry. Next to the fallback ones. |
An `ExactReal` is a point, so `+`, `-`, `*`, `/` and `\` against a `BareInterval` of the same number type apply the operation to the two endpoints directly, rather than promoting the point to a thin interval and running the interval-interval operator on it. Each method takes that route only where it is bitwise identical to the promotion, and delegates the rest: a non-finite point, whose thin interval is ill-formed; an unbounded interval under `*`, where `0 * Inf` is flavor dependent; and division by a zero point. Rounding still goes through `@round`, so the results are unchanged under every rounding mode. Mixed number types keep the promotion, which is where the point is rounded to the interval's number type. The type parameter is bounded by `NumTypes` so that these methods are more specific than the generic `ExactReal`/`BareInterval` methods, whose own parameters are bounded by `Real` and `NumTypes`; the tests assert that dispatch selects them. Point times interval costs 3.2 ns against the promotion route's 6.4-8.2 ns with rounding `:none`, and 6.7 ns against 9.1-10.2 ns with `:correct`. Assisted-by: Claude Opus 5 (claude-opus-5) <noreply@anthropic.com>
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Done |
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An
ExactRealis a point, so+,-,*,/and\against aBareIntervalof the same number type apply the operation to the two endpoints directly, rather than promoting the point to a thin interval and running the interval-interval operator on it.Each method takes that route only where it is bitwise identical to the promotion, and delegates the rest: a non-finite point, whose thin interval is ill-formed; an unbounded interval under
*, where0 * Infis flavor dependent; and division by a zero point. Rounding still goes through@round, so the results are unchanged under every rounding mode. Mixed number types keep the promotion, which is where the point is rounded to the interval's number type.The type parameter is bounded by
NumTypesso that these methods are more specific than the genericExactReal/BareIntervalmethods, whose own parameters are bounded byRealandNumTypes; the tests assert that dispatch selects them.Point times interval costs 3.2 ns against the promotion route's 6.4-8.2 ns with rounding
:none, and 6.7 ns against 9.1-10.2 ns with:correct.Assisted-by: Claude Opus 5 (claude-opus-5) noreply@anthropic.com