Algebra in core (#254)

* port Add to tl algebra

* port Sub to tl algebra

* port Mul to tl algebra

* Div with TruncatedDivision is failing

* / and tquot

* neg

* pow and tpow

* remove algebra.scala

* explicit truncating conversions

* populate some coulomb.ops.algebra instances

* refactor use of algebras

* scala.math.Ordering -> cats.kernel.Order

* refactor si, si.prefixes, mks, mksa to use export

* tweak directories

* refactor algebra to use export

* factor value-specific optimizations to separate import

* unit test optimized operations

build.sbt

@@ -35,6 +35,7 @@ lazy val core = crossProject(JVMPlatform, JSPlatform/*, NativePlatform*/)
   .in(file("core"))
   .settings(name := "coulomb-core")
   .settings(commonSettings :_*)
+  .settings(libraryDependencies += "org.typelevel" %%% "algebra" % "2.7.0")
 
 lazy val units = crossProject(JVMPlatform, JSPlatform/*, NativePlatform*/)
   .crossType(CrossType.Pure)

core/src/main/scala/coulomb/conversion/conversion.scala

@@ -22,6 +22,12 @@ import scala.annotation.implicitNotFound
 @implicitNotFound("No value conversion in scope for value types {VF} => {VT}")
 abstract class ValueConversion[VF, VT] extends (VF => VT)
 
+@implicitNotFound("No truncating value conversion in scope for value types {VF} => {VT}")
+abstract class TruncatingValueConversion[VF, VT] extends (VF => VT)
+
 /** Convert a value of type V from implied units UF to UT */
 @implicitNotFound("No unit conversion in scope for value type {V}, unit types {UF} => {UT}")
 abstract class UnitConversion[V, UF, UT] extends (V => V)
+
+@implicitNotFound("No truncating unit conversion in scope for value type {V}, unit types {UF} => {UT}")
+abstract class TruncatingUnitConversion[V, UF, UT] extends (V => V)

core/src/main/scala/coulomb/conversion/standard/standard.scala

@@ -16,7 +16,7 @@
 
 package coulomb.conversion.standard
 
-import coulomb.conversion.{ValueConversion, UnitConversion}
+import coulomb.conversion.*
 import coulomb.{coefficient, withUnit, Quantity}
 import coulomb.policy.{AllowTruncation, AllowImplicitConversions}
 
@@ -50,16 +50,16 @@ inline given ctx_VC_Long[VF](using num: Integral[VF]): ValueConversion[VF, Long]
     new ValueConversion[VF, Long]:
         def apply(v: VF): Long = num.toLong(v)
 
-inline given ctx_VC_Long_tr[VF](using num: Fractional[VF], at: AllowTruncation): ValueConversion[VF, Long] =
-    new ValueConversion[VF, Long]:
+inline given ctx_TVC_Long[VF](using num: Fractional[VF]): TruncatingValueConversion[VF, Long] =
+    new TruncatingValueConversion[VF, Long]:
         def apply(v: VF): Long = num.toLong(v)
 
 inline given ctx_VC_Int[VF](using num: Integral[VF]): ValueConversion[VF, Int] =
     new ValueConversion[VF, Int]:
         def apply(v: VF): Int = num.toInt(v)
 
-inline given ctx_VC_Int_tr[VF](using num: Fractional[VF], at: AllowTruncation): ValueConversion[VF, Int] =
-    new ValueConversion[VF, Int]:
+inline given ctx_TVC_Int_tr[VF](using num: Fractional[VF]): TruncatingValueConversion[VF, Int] =
+    new TruncatingValueConversion[VF, Int]:
         def apply(v: VF): Int = num.toInt(v)
 
 // unit conversions that discard fractional values can be imported from 
@@ -76,19 +76,17 @@ inline given ctx_UC_Float[UF, UT]:
     new UnitConversion[Float, UF, UT]:
         def apply(v: Float): Float = c * v
 
-inline given ctx_UC_Long[UF, UT](using AllowTruncation):
-        UnitConversion[Long, UF, UT] =
+inline given ctx_TUC_Long[UF, UT]: TruncatingUnitConversion[Long, UF, UT] =
     val nc = coulomb.conversion.infra.coefficientNumDouble[UF, UT]
     val dc = coulomb.conversion.infra.coefficientDenDouble[UF, UT]
     // using nc and dc is more efficient than using Rational directly in the conversion function
     // but still gives us 53 bits of integer precision for exact rational arithmetic, and also
     // graceful loss of precision if nc*v exceeds 53 bits
-    new UnitConversion[Long, UF, UT]:
+    new TruncatingUnitConversion[Long, UF, UT]:
         def apply(v: Long): Long = ((nc * v) / dc).toLong
 
-inline given ctx_UC_Int[UF, UT](using AllowTruncation):
-        UnitConversion[Int, UF, UT] =
+inline given ctx_TUC_Int[UF, UT]: TruncatingUnitConversion[Int, UF, UT] =
     val nc = coulomb.conversion.infra.coefficientNumDouble[UF, UT]
     val dc = coulomb.conversion.infra.coefficientDenDouble[UF, UT]
-    new UnitConversion[Int, UF, UT]:
+    new TruncatingUnitConversion[Int, UF, UT]:
         def apply(v: Int): Int = ((nc * v) / dc).toInt

core/src/main/scala/coulomb/infra/meta.scala

@@ -59,6 +59,24 @@ object meta:
             report.error(s"type expr ${typestr(TypeRepr.of[E])} is not a non-negative Int")
             '{ new coulomb.rational.typeexpr.NonNegInt[E] { val value = 0 } }
 
+    def teToPosInt[E](using Quotes, Type[E]): Expr[coulomb.rational.typeexpr.PosInt[E]] =
+        import quotes.reflect.*
+        val rationalTE(v) = TypeRepr.of[E]
+        if ((v.d == 1) && (v.n > 0) && (v.n.isValidInt)) then
+            '{ new coulomb.rational.typeexpr.PosInt[E] { val value = ${Expr(v.n.toInt)} } }
+        else
+            report.error(s"type expr ${typestr(TypeRepr.of[E])} is not a positive Int")
+            '{ new coulomb.rational.typeexpr.PosInt[E] { val value = 0 } }
+
+    def teToInt[E](using Quotes, Type[E]): Expr[coulomb.rational.typeexpr.AllInt[E]] =
+        import quotes.reflect.*
+        val rationalTE(v) = TypeRepr.of[E]
+        if ((v.d == 1) && (v.n.isValidInt)) then
+            '{ new coulomb.rational.typeexpr.AllInt[E] { val value = ${Expr(v.n.toInt)} } }
+        else
+            report.error(s"type expr ${typestr(TypeRepr.of[E])} is not an Int")
+            '{ new coulomb.rational.typeexpr.AllInt[E] { val value = 0 } }
+
     object rationalTE:
         def unapply(using Quotes)(tr: quotes.reflect.TypeRepr): Option[Rational] =
             import quotes.reflect.*

core/src/main/scala/coulomb/ops/algebra/algebra.scala

@@ -0,0 +1,35 @@
+/*
+ * Copyright 2022 Erik Erlandson
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package coulomb.ops.algebra
+
+import scala.annotation.implicitNotFound
+
+// there is no typelevel community typeclass that expresses the concept
+// "supports raising to fractional powers, without truncation"
+// The closest thing is spire NRoot, but it is also defined on truncating integer types,
+// so it is not helpful for distinguishing "pow" from "tpow", and in any case requires spire
+// https://github.com/typelevel/spire/issues/741
+
+@implicitNotFound("Fractional power not defined for value type ${V}")
+abstract class FractionalPower[V]:
+    /** returns v^e */
+    def pow(v: V, e: Double): V
+
+@implicitNotFound("Truncating power not defined for value type ${V}")
+abstract class TruncatingPower[V]:
+    /** returns v^e, truncated to integer value (toward zero) */
+    def tpow(v: V, e: Double): V 

core/src/main/scala/coulomb/ops/algebra/all.scala

@@ -0,0 +1,23 @@
+/*
+ * Copyright 2022 Erik Erlandson
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package coulomb.ops.algebra
+
+object all:
+    export coulomb.ops.algebra.int.{*,given}
+    export coulomb.ops.algebra.long.{*,given}
+    export coulomb.ops.algebra.float.{*,given}
+    export coulomb.ops.algebra.double.{*,given}

core/src/main/scala/coulomb/ops/algebra/double.scala

@@ -0,0 +1,37 @@
+/*
+ * Copyright 2022 Erik Erlandson
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package coulomb.ops.algebra
+
+import algebra.ring.TruncatedDivision
+
+object double:
+    given ctx_Double_is_FractionalPower: FractionalPower[Double] with
+        def pow(v: Double, e: Double): Double = math.pow(v, e)
+
+    given ctx_Double_is_TruncatingPower: TruncatingPower[Double] with
+        def tpow(v: Double, e: Double): Double = math.pow(v, e).toLong.toDouble
+
+    given ctx_Double_is_TruncatedDivision: TruncatedDivision[Double] with
+        def tquot(x: Double, y: Double): Double = (x / y).toLong.toDouble
+        // I don't care about these
+        def tmod(x: Double, y: Double): Double = ???
+        def fquot(x: Double, y: Double): Double = ???
+        def fmod(x: Double, y: Double): Double = ???
+        def abs(a: Double): Double = ???
+        def additiveCommutativeMonoid: algebra.ring.AdditiveCommutativeMonoid[Double] = ???
+        def order: cats.kernel.Order[Double] = ???
+        def signum(a: Double): Int = ???

core/src/main/scala/coulomb/ops/algebra/float.scala

@@ -0,0 +1,37 @@
+/*
+ * Copyright 2022 Erik Erlandson
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package coulomb.ops.algebra
+
+import algebra.ring.TruncatedDivision
+
+object float:
+    given ctx_Float_is_FractionalPower: FractionalPower[Float] with
+        def pow(v: Float, e: Double): Float = math.pow(v.toDouble, e).toFloat
+
+    given ctx_Float_is_TruncatingPower: TruncatingPower[Float] with
+        def tpow(v: Float, e: Double): Float = math.pow(v.toDouble, e).toLong.toFloat
+
+    given ctx_Float_is_TruncatedDivision: TruncatedDivision[Float] with
+        def tquot(x: Float, y: Float): Float = (x / y).toLong.toFloat
+        // I don't care about these
+        def tmod(x: Float, y: Float): Float = ???
+        def fquot(x: Float, y: Float): Float = ???
+        def fmod(x: Float, y: Float): Float = ???
+        def abs(a: Float): Float = ???
+        def additiveCommutativeMonoid: algebra.ring.AdditiveCommutativeMonoid[Float] = ???
+        def order: cats.kernel.Order[Float] = ???
+        def signum(a: Float): Int = ???

core/src/main/scala/coulomb/ops/algebra/int.scala

@@ -0,0 +1,35 @@
+/*
+ * Copyright 2022 Erik Erlandson
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package coulomb.ops.algebra
+
+import algebra.ring.TruncatedDivision
+
+object int:
+    given ctx_Int_is_TruncatingPower: TruncatingPower[Int] with
+        def tpow(v: Int, e: Double): Int = math.pow(v.toDouble, e).toInt
+
+    given ctx_Int_is_TruncatedDivision: TruncatedDivision[Int] with
+        def tquot(x: Int, y: Int): Int = x / y
+        // I don't care about these
+        def tmod(x: Int, y: Int): Int = ???
+        def fquot(x: Int, y: Int): Int = ???
+        def fmod(x: Int, y: Int): Int = ???
+        def abs(a: Int): Int = ???
+        def additiveCommutativeMonoid: algebra.ring.AdditiveCommutativeMonoid[Int] = ???
+        def order: cats.kernel.Order[Int] = ???
+        def signum(a: Int): Int = ???
+

core/src/main/scala/coulomb/ops/algebra/long.scala

@@ -0,0 +1,34 @@
+/*
+ * Copyright 2022 Erik Erlandson
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package coulomb.ops.algebra
+
+import algebra.ring.TruncatedDivision
+
+object long:
+    given ctx_Long_is_TruncatingPower: TruncatingPower[Long] with
+        def tpow(v: Long, e: Double): Long = math.pow(v.toDouble, e).toLong
+
+    given ctx_Long_is_TruncatedDivision: TruncatedDivision[Long] with
+        def tquot(x: Long, y: Long): Long = x / y
+        // I don't care about these
+        def tmod(x: Long, y: Long): Long = ???
+        def fquot(x: Long, y: Long): Long = ???
+        def fmod(x: Long, y: Long): Long = ???
+        def abs(a: Long): Long = ???
+        def additiveCommutativeMonoid: algebra.ring.AdditiveCommutativeMonoid[Long] = ???
+        def order: cats.kernel.Order[Long] = ???
+        def signum(a: Long): Int = ???

core/src/main/scala/coulomb/ops/ops.scala

@@ -20,6 +20,10 @@ import scala.annotation.implicitNotFound
 
 import coulomb.*
 
+@implicitNotFound("Negation not defined in scope for Quantity[${V}, ${U}]")
+abstract class Neg[V, U]:
+    def apply(v: V): V
+
 @implicitNotFound("Addition not defined in scope for Quantity[${VL}, ${UL}] and Quantity[${VR}, ${UR}]")
 abstract class Add[VL, UL, VR, UR]:
     type VO
@@ -44,16 +48,24 @@ abstract class Div[VL, UL, VR, UR]:
     type UO
     def apply(vl: VL, vr: VR): VO
 
-@implicitNotFound("Negation not defined in scope for Quantity[${V}, ${U}]")
-abstract class Neg[V, U]:
-    def apply(v: V): V
+@implicitNotFound("Truncating Division not defined in scope for Quantity[${VL}, ${UL}] and Quantity[${VR}, ${UR}]")
+abstract class TQuot[VL, UL, VR, UR]:
+    type VO
+    type UO
+    def apply(vl: VL, vr: VR): VO
 
 @implicitNotFound("Power not defined in scope for Quantity[${V}, ${U}] ^ ${P}")
 abstract class Pow[V, U, P]:
     type VO
     type UO
     def apply(v: V): VO
 
+@implicitNotFound("Truncating Power not defined in scope for Quantity[${V}, ${U}] ^ ${P}")
+abstract class TPow[V, U, P]:
+    type VO
+    type UO
+    def apply(v: V): VO
+
 @implicitNotFound("Ordering not defined in scope for Quantity[${VL}, ${UL}] and Quantity[${VR}, ${UR}]")
 abstract class Ord[VL, UL, VR, UR]:
     def apply(vl: VL, vr: VR): Int