Implement inverse trigonometric functions from ratio to angle.

[adamreichold]

Fixes #168

[adamreichold]

@iliekturtles I am somewhat at a loss as to the correct usage of the Convert trait, i.e. I get

error[E0271]: type mismatch resolving `<V as Conversion<V>>::T == <si::angle::radian as Conversion<V>>::T`
  --> src/si/ratio.rs:76:9
   |
37 | impl<U, V> Ratio<U, V>
   |         - this type parameter
...
76 |         Angle::new::<radian>(self.value.atanh())
   |         ^^^^^^^^^^^^^^^^^^^^ expected type parameter `V`, found struct `si::angle::radian`
   |
   = note: expected associated type `<V as Conversion<V>>::T`
              found associated type `<si::angle::radian as Conversion<V>>::T`

Could you give me a hint?

[iliekturtles]

Thanks for the PR! Sorry for my delay in responding, it has been a busy couple days. Let me know if you get any other compile errors once the fix I noted in the diff is applied.

[adamreichold]

@iliekturtles I wonder how to handle atan2. Personally, I only need it for Length values (to switch between coordinate systems), but strictly speaking it should apply to all pairs of quantities. Should I propose an implementation on si::Length or on the general Quantity?

[iliekturtles]

I think I'm inclined towards implementing for all quantities but I'm second guessing myself as I write this sentence. Do you have any examples where the function would be used on non-length quantities?

[adamreichold]

Do you have any examples where the function would be used on non-length quantities?

After some digging, I found a paper mentioning atan2 when computing magnetic field strengths (of rotationally symmetric sources) where the computation a field quantity expansion involves atan2.

I guess this is the basic example, any field which has a spherical or cylindrical symmetry might have modes which imply usage of atan2 but it is admittedly a bit fringe...

[Aehmlo]

An example of using the arctangent non-length quantities which immediately comes to mind for me is the phase delay in viscoelastic solids, which is something I could see myself wanting to work with in uom in the future. Additionally, in physics (particularly particle physics), there's often a desire to work in momentum space/other spaces rather than position space.

[adamreichold]

I think I'm inclined towards implementing for all quantities

An example of using the arctangent non-length quantities which immediately comes to mind

Amended the generic implementation on all si::Quantity values returning an si::Angle.

@iliekturtles Should be ready for review now.

[iliekturtles]

Changes look great! If you can amend the commit with tests similar to what is done for hypot in length.rs I'll merge!

uom/src/si/length.rs

Lines 85 to 102 in 4fceafc

	#[cfg(all(test, feature = "std"))]
	mod tests {
	storage_types! {
	types: Float;
	use si::quantities::*;
	use si::length::meter;
	use tests::Test;
	quickcheck! {
	#[allow(trivial_casts)]
	fn hypot(l: V, r: V) -> bool {
	Test::eq(&l.hypot(r),
	&Length::new::<meter>(l).hypot(Length::new::<meter>(r)).get::<meter>())
	}
	}
	}
	}

[adamreichold]

If you can amend the commit with tests

Added property-based tests for all new functions.

[iliekturtles]

Clippy doesn't like test_nan_or_eq's parameters. Since the function is only going to be called for floats the references can be dropped.

diff --git a/src/si/ratio.rs b/src/si/ratio.rs
index 8ceee33..4a3f853 100644
--- a/src/si/ratio.rs
+++ b/src/si/ratio.rs
@@ -161,33 +161,33 @@ mod tests {
             use si::quantities::*;
             use tests::Test;

-            fn test_nan_or_eq(yl: &V, yr: &V) -> bool {
-                (yl.is_nan() && yr.is_nan()) || Test::eq(yl, yr)
+            fn test_nan_or_eq(yl: V, yr: V) -> bool {
+                (yl.is_nan() && yr.is_nan()) || Test::eq(&yl, &yr)
             }

             quickcheck! {
                 fn acos(x: V) -> bool {
-                    test_nan_or_eq(&x.acos(), &Ratio::from(x).acos().get::<a::radian>())
+                    test_nan_or_eq(x.acos(), Ratio::from(x).acos().get::<a::radian>())
                 }

                 fn acosh(x: V) -> bool {
-                    test_nan_or_eq(&x.acosh(), &Ratio::from(x).acosh().get::<a::radian>())
+                    test_nan_or_eq(x.acosh(), Ratio::from(x).acosh().get::<a::radian>())
                 }

                 fn asin(x: V) -> bool {
-                    test_nan_or_eq(&x.asin(), &Ratio::from(x).asin().get::<a::radian>())
+                    test_nan_or_eq(x.asin(), Ratio::from(x).asin().get::<a::radian>())
                 }

                 fn asinh(x: V) -> bool {
-                    test_nan_or_eq(&x.asinh(), &Ratio::from(x).asinh().get::<a::radian>())
+                    test_nan_or_eq(x.asinh(), Ratio::from(x).asinh().get::<a::radian>())
                 }

                 fn atan(x: V) -> bool {
-                    test_nan_or_eq(&x.atan(), &Ratio::from(x).atan().get::<a::radian>())
+                    test_nan_or_eq(x.atan(), Ratio::from(x).atan().get::<a::radian>())
                 }

                 fn atanh(x: V) -> bool {
-                    test_nan_or_eq(&x.atanh(), &Ratio::from(x).atanh().get::<a::radian>())
+                    test_nan_or_eq(x.atanh(), Ratio::from(x).atanh().get::<a::radian>())
                 }
             }
         }