feature: Fractional Exponents #7

CrownedPhoenix · 2024-01-10T22:29:52Z

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NeedleInAJayStack

Excellent work!! I love this approach.

Just wondering - have we validated that exponents in a fractional form are sufficient? Like that defining units in a decimal-based format is not required/desired? Also worth noting (although it's probably completely irrelevant), is that integer fractions cannot represent all decimal values: https://en.wikipedia.org/wiki/Irrational_number

NeedleInAJayStack · 2024-01-11T02:04:02Z

Sources/Units/Unit/Fraction.swift

+
+    var positive: Bool {
+        switch (numerator, denominator) {
+            // 0/0 is not positive in this logic


Just as an aside, here's a fun math Wikipedia article on this particular fraction: https://en.wikipedia.org/wiki/Indeterminate_form#Indeterminate_form_0/0

NeedleInAJayStack · 2024-01-11T02:13:41Z

Sources/Units/Unit/Fraction.swift

+
+extension Fraction: Comparable {
+    public static func < (lhs: Fraction, rhs: Fraction) -> Bool {
+        return lhs.numerator < rhs.numerator


I don't think that this is correct - it should be:

Suggested change

return lhs.numerator < rhs.numerator

return lhs.asDouble < rhs.asDouble

You're right. I'll fix this. Instead of asDouble I'l just do the int math to create a common denominator and compare them that way.

Updated this logic.

NeedleInAJayStack · 2024-01-11T02:17:55Z

Sources/Units/Unit/Fraction.swift

+}
+
+extension SignedInteger {
+    func over<T: SignedInteger>(_ denominator: T) -> Fraction {


Were there type inference issues with using /, like 5.measured(in: .meter.pow(1/2))?

Yeah. That was what I originally tried.
It was ambiguous to the compiler whether 1 / 2 meant Int / Int or Fraction / Int or Fraction / Fraction etc because Fraction conforms to ExpressibleAsIntegerLiteral.

On that note, how do you feel about | as the operator? It wouldn't be ambiguous.

You could do 2|5 etc

I went ahead and did this - lmk if you like/dislike.

NeedleInAJayStack · 2024-01-11T02:20:47Z

Sources/Units/Unit/Fraction.swift

+        let gcd = Self.gcd(numerator, denominator)
+        self.numerator = numerator / gcd
+        self.denominator = denominator / gcd


Should this be public?

Yes. I guess the tests do a testable import so I didn't catch that.

I've made some more things public

NeedleInAJayStack · 2024-01-11T02:21:55Z

Sources/Units/Unit/Fraction.swift

@@ -0,0 +1,163 @@
+
+
+public struct Fraction: Hashable, Equatable, Sendable {


Could we provide documentation about this type? Specific areas that would be helpful to document after reading through:

init automatically reduces the input fraction

String representation uses |

Yes. Will do. I'll make a doc pass for everything I've added.

NeedleInAJayStack · 2024-01-11T02:23:09Z

Tests/UnitsTests/UnitTests.swift

@@ -7,6 +7,8 @@ final class UnitTests: XCTestCase {
        XCTAssertNotEqual(Unit.meter, Unit.foot)
        XCTAssertEqual(Unit.meter * Unit.second / Unit.second, Unit.meter)
        XCTAssertNotEqual(Unit.newton, Unit.kilogram * Unit.meter / Unit.second.pow(2))
+        XCTAssertNotEqual(Unit.meter.pow(1.over(2)), Unit.kilogram * Unit.meter / Unit.second.pow(2))
+        XCTAssertEqual(Unit.meter.pow(1.over(6)), Unit.meter.pow(1.over(2)).pow(1.over(3)) )


These tests are great, but could we also add specific tests for the Fraction functions?

Yeah. Just haven't yet cuz I didn't want to spend more time on it if it wasn't a productive direction to go. I'll make a more robust test suite for the Fraction.

I've added tests.

CrownedPhoenix · 2024-01-11T16:15:01Z

Just wondering - have we validated that exponents in a fractional form are sufficient? Like that defining units in a decimal-based format is not required/desired? Also worth noting (although it's probably completely irrelevant), is that integer fractions cannot represent all decimal values: https://en.wikipedia.org/wiki/Irrational_number

Fractional form is not sufficient. It's just a step in the right direction.
I think after this the next thing I'll work on is some sort of higher level type (maybe an enum) that subsumes both Fraction and Double. If the user enters a Double we assume they are both okay with double precision (as well as its limits) and that they have provided the exact value (at least to the desired significant figures) that they want used.

I haven't thought much about how we'll straddle the operation between ft^(2/5) * s^3.5 kinds of things. I suspect there's some tricky business around that and some decisions to be made.

NeedleInAJayStack · 2024-01-11T18:04:45Z

Fractional form is not sufficient. It's just a step in the right direction. I think after this the next thing I'll work on is some sort of higher level type (maybe an enum) that subsumes both Fraction and Double. If the user enters a Double we assume they are both okay with double precision (as well as its limits) and that they have provided the exact value (at least to the desired significant figures) that they want used.

I haven't thought much about how we'll straddle the operation between ft^(2/5) * s^3.5 kinds of things. I suspect there's some tricky business around that and some decisions to be made.

Oof, do you think we should continue down this direction then or just try and go toward a 'double'-ized exponent? I'd hate to introduce a Fraction concept if we were just going to subsume its functionality with a Double soon.

CrownedPhoenix · 2024-01-11T19:38:11Z

Fractional form is not sufficient. It's just a step in the right direction. I think after this the next thing I'll work on is some sort of higher level type (maybe an enum) that subsumes both Fraction and Double. If the user enters a Double we assume they are both okay with double precision (as well as its limits) and that they have provided the exact value (at least to the desired significant figures) that they want used.
I haven't thought much about how we'll straddle the operation between ft^(2/5) * s^3.5 kinds of things. I suspect there's some tricky business around that and some decisions to be made.

Oof, do you think we should continue down this direction then or just try and go toward a 'double'-ized exponent? I'd hate to introduce a Fraction concept if we were just going to subsume its functionality with a Double soon.

Sorry it won't be subsuming the functionality.
Brandon has said he needs support for both:

ft^(3/5)
m^1.5

The reason we need fraction parts is to preserve precision for as long as possible so we don't run into a case like m^1.0/m^0.9999... not cancelling right.

Can you think of any reason I wouldn't need to worry about that and could instead just convert all fractional exponents into Doubles and still get the right behavior during dimensional analysis?

The main use case is for intermediate units that when combined reduce into units that make sense.
So an equation might be composed of units that have no real world analogue but when combined cancel out with each other appropriately to create a "real" unit.

CrownedPhoenix marked this pull request as draft January 10, 2024 22:30

NeedleInAJayStack reviewed Jan 11, 2024

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CrownedPhoenix force-pushed the feature/fractional-exponents branch from bfa5aac to 53a7872 Compare January 11, 2024 17:59

feature: Fractional Exponents

03652e7

CrownedPhoenix force-pushed the feature/fractional-exponents branch from 53a7872 to 03652e7 Compare January 11, 2024 18:29

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feature: Fractional Exponents #7

feature: Fractional Exponents #7

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	return lhs.numerator < rhs.numerator
	return lhs.asDouble < rhs.asDouble

		@@ -0,0 +1,163 @@


		public struct Fraction: Hashable, Equatable, Sendable {

feature: Fractional Exponents #7

Are you sure you want to change the base?

feature: Fractional Exponents #7

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