Add angular unit radian (#49)

src/main/scala/libra/nonsi/package.scala

@@ -1,9 +1,14 @@
 package libra
 
-import ops.base.{Show, ConversionFactor}
-import spire._, spire.algebra._, spire.math._, spire.implicits._
+import libra.nonsi.Angle
+import libra.ops.quantity.ConvertTo
+import ops.base.{Conversion, ConversionFactor, Show}
+import spire._
+import spire.algebra._
+import spire.math._
+import spire.implicits._
 import singleton.ops._
-import libra.si.{Time, Second}
+import libra.si.{Second, Time}
 import shapeless._
 
 /* Non-SI units */
@@ -16,10 +21,12 @@ package object nonsi {
   trait Degree extends UnitOfMeasure[Angle]
   trait Arcminute extends UnitOfMeasure[Angle]
   trait Arcsecond extends UnitOfMeasure[Angle]
+  trait Radian extends UnitOfMeasure[Angle]
 
   implicit def degreeShow: Show[Degree] = Show[Degree]("degree")
   implicit def arcminuteShow: Show[Arcminute] = Show[Arcminute]("arcminute")
   implicit def arcsecondShow: Show[Arcsecond] = Show[Arcsecond]("arcsecond")
+  implicit def radian: Show[Radian] = Show[Radian]("rad")
 
   implicit def degreeArcminuteConversion[A](
       implicit c: ConvertableTo[A]
@@ -36,6 +43,25 @@ package object nonsi {
   ): ConversionFactor[A, Angle, Arcminute, Arcsecond] =
     new ConversionFactor(c.fromInt(60))
 
+  implicit def radianDegreeConversion[A](
+      implicit c: ConvertableTo[A]
+  ): ConversionFactor[A, Angle, Radian, Degree] =
+    new ConversionFactor(c.fromDouble(180 / pi))
+
+  implicit def radianArcminuteConversion[A](
+      implicit c: ConvertableTo[A],
+      multiplicative: MultiplicativeSemigroup[A]
+  ): ConversionFactor[A, Angle, Radian, Arcminute] =
+    degreeArcminuteConversion.compose(radianDegreeConversion)
+
+  implicit def radianArcsecondConversion[A](
+      implicit c: ConvertableTo[A],
+      multiplicative: MultiplicativeSemigroup[A]
+  ): ConversionFactor[A, Angle, Radian, Arcsecond] =
+    degreeArcsecondConversion.compose(radianDegreeConversion)
+
+
+
   type AngularVelocityQuantity[A, L <: UnitOfMeasure[Angle], T <: UnitOfMeasure[Time]] =
     Quantity[A, Term[Angle, L, Fraction[1, 1]] :: Term[Time, T, Fraction[-1, 1]] :: HNil]
 
@@ -46,5 +72,6 @@ package object nonsi {
     def degreessPerSecond: AngularVelocityQuantity[A, Degree, Second] = Quantity(a)
     def arcminutesPerSecond: AngularVelocityQuantity[A, Arcminute, Second] = Quantity(a)
     def arcsecondsPerSecond: AngularVelocityQuantity[A, Arcsecond, Second] = Quantity(a)
+    def radian: QuantityOf[A, Angle, Radian] = Quantity(a)
   }
 }

src/main/scala/libra/ops/base.scala

@@ -1,7 +1,10 @@
 package libra
 package ops
 
-import spire.algebra._, spire.implicits._
+import libra.UnitOfMeasure
+import spire.algebra._
+import spire.implicits._
+import spire.math.ConvertableFrom
 
 object base {
 
@@ -23,7 +26,11 @@ object base {
     * @tparam F the unit to convert from
     * @tparam T the unit to convert to
     */
-  case class ConversionFactor[A, D, F <: UnitOfMeasure[D], T <: UnitOfMeasure[D]](val value: A)
+  case class ConversionFactor[A, D, F <: UnitOfMeasure[D], T <: UnitOfMeasure[D]](val value: A) {
+    def compose[OtherF <: UnitOfMeasure[D]](otherConversionFactor: ConversionFactor[A, D, OtherF, F])
+                                           (implicit multiplicativeSemigroup: MultiplicativeSemigroup[A]): ConversionFactor[A, D, OtherF, T] =
+      new ConversionFactor(otherConversionFactor.value * value)
+  }
 
   /** Derived typeclass for the conversion factor from F to T
     *

src/test/scala/libra/NonSISpec.scala

@@ -1,7 +1,9 @@
 package libra
 
 import spire.implicits._
-import libra.nonsi._, libra.si._
+import spire.math._
+import libra.nonsi._
+import libra.si._
 
 import org.scalatest._
 
@@ -20,6 +22,10 @@ class NonSISpec extends WordSpec {
     "arcsecond value" in {
       assert(2.0.degree.to[Arcsecond].value === 7200.0)
     }
+
+    "radian value" in {
+      assert(180.0.degree.to[Radian].value === pi)
+    }
   }
 
   "arcminute" should {
@@ -76,6 +82,10 @@ class NonSISpec extends WordSpec {
     "arcsecond value" in {
       assert(2.0.arcminutesPerSecond.to[Arcsecond].value === 120.0)
     }
+
+    "radian value" in {
+      assert(10800.0.arcminutesPerSecond.to[Radian].value === pi)
+    }
   }
 
   "arcsecondsPerSecond" should {
@@ -90,5 +100,27 @@ class NonSISpec extends WordSpec {
     "arcminutesPerSecond value" in {
       assert(120.0.arcsecondsPerSecond.to[Arcminute].value === 2.0)
     }
+
+    "radian value" in {
+      assert(648000.0.arcsecondsPerSecond.to[Radian].value === pi)
+    }
+  }
+
+  "radians" should {
+    "show" in {
+      assert(2.radian.show === "2 rad [∠]")
+    }
+
+    "degree value" in {
+      assert(pi.radian.to[Degree].value === 180.0)
+    }
+
+    "arcminute value" in {
+      assert(pi.radian.to[Arcminute].value === 10800.0)
+    }
+
+    "arcsecond value" in {
+      assert(pi.radian.to[Arcsecond].value === 648000.0)
+    }
   }
 }