add par functions for Bitraverse

core/src/main/scala/cats/Parallel.scala

@@ -235,6 +235,52 @@ object Parallel extends ParallelArityFunctions2 {
     P.sequential(gtb)
   }
 
+  /**
+   * Like `Bitraverse[A].bitraverse`, but uses the applicative instance
+   * corresponding to the Parallel instance instead.
+   */
+  def parBitraverse[T[_, _]: Bitraverse, M[_], F[_], A, B, C, D](
+    tab: T[A, B]
+  )(f: A => M[C], g: B => M[D])(implicit P: Parallel[M, F]): M[T[C, D]] = {
+    val ftcd: F[T[C, D]] =
+      Bitraverse[T].bitraverse(tab)(f.andThen(P.parallel.apply), g.andThen(P.parallel.apply))(P.applicative)
+    P.sequential(ftcd)
+  }
+
+  /**
+   * Like `Bitraverse[A].bisequence`, but uses the applicative instance
+   * corresponding to the Parallel instance instead.
+   */
+  def parBisequence[T[_, _]: Bitraverse, M[_], F[_], A, B](
+    tmamb: T[M[A], M[B]]
+  )(implicit P: Parallel[M, F]): M[T[A, B]] = {
+    val ftab: F[T[A, B]] = Bitraverse[T].bitraverse(tmamb)(P.parallel.apply, P.parallel.apply)(P.applicative)
+    P.sequential(ftab)
+  }
+
+  /**
+   * Like `Bitraverse[A].leftTraverse`, but uses the applicative instance
+   * corresponding to the Parallel instance instead.
+   */
+  def parLeftTraverse[T[_, _]: Bitraverse, M[_], F[_], A, B, C](
+    tab: T[A, B]
+  )(f: A => M[C])(implicit P: Parallel[M, F]): M[T[C, B]] = {
+    val ftcb: F[T[C, B]] =
+      Bitraverse[T].bitraverse(tab)(f.andThen(P.parallel.apply), P.applicative.pure)(P.applicative)
+    P.sequential(ftcb)
+  }
+
+  /**
+   * Like `Bitraverse[A].leftSequence`, but uses the applicative instance
+   * corresponding to the Parallel instance instead.
+   */
+  def parLeftSequence[T[_, _]: Bitraverse, M[_], F[_], A, B](
+    tmab: T[M[A], B]
+  )(implicit P: Parallel[M, F]): M[T[A, B]] = {
+    val ftab: F[T[A, B]] = Bitraverse[T].bitraverse(tmab)(P.parallel.apply, P.applicative.pure)(P.applicative)
+    P.sequential(ftab)
+  }
+
   /**
    * Like `Applicative[F].ap`, but uses the applicative instance
    * corresponding to the Parallel instance instead.

core/src/main/scala/cats/syntax/all.scala

@@ -8,6 +8,7 @@ abstract class AllSyntaxBinCompat
     with AllSyntaxBinCompat2
     with AllSyntaxBinCompat3
     with AllSyntaxBinCompat4
+    with AllSyntaxBinCompat5
 
 trait AllSyntax
     extends AlternativeSyntax
@@ -87,3 +88,5 @@ trait AllSyntaxBinCompat4
     with ReducibleSyntaxBinCompat0
     with FoldableSyntaxBinCompat1
     with BitraverseSyntaxBinCompat0
+
+trait AllSyntaxBinCompat5 extends ParallelBitraverseSyntax

core/src/main/scala/cats/syntax/package.scala

@@ -39,7 +39,12 @@ package object syntax {
   object nested extends NestedSyntax
   object option extends OptionSyntax
   object order extends OrderSyntax
-  object parallel extends ParallelSyntax with ParallelTraverseSyntax with ParallelFlatSyntax with ParallelApplySyntax
+  object parallel
+      extends ParallelSyntax
+      with ParallelTraverseSyntax
+      with ParallelFlatSyntax
+      with ParallelApplySyntax
+      with ParallelBitraverseSyntax
   object partialOrder extends PartialOrderSyntax
   object profunctor extends ProfunctorSyntax
   object reducible extends ReducibleSyntax with ReducibleSyntaxBinCompat0

core/src/main/scala/cats/syntax/parallel.scala

@@ -1,6 +1,6 @@
 package cats.syntax
 
-import cats.{FlatMap, Foldable, Monad, Parallel, Traverse}
+import cats.{Bitraverse, FlatMap, Foldable, Monad, Parallel, Traverse}
 
 trait ParallelSyntax extends TupleParallelSyntax {
 
@@ -39,6 +39,28 @@ trait ParallelTraverseSyntax {
     new ParallelSequence_Ops[T, M, A](tma)
 }
 
+trait ParallelBitraverseSyntax {
+  implicit final def catsSyntaxParallelBitraverse[T[_, _]: Bitraverse, A, B](
+    tab: T[A, B]
+  ): ParallelBitraverseOps[T, A, B] =
+    new ParallelBitraverseOps[T, A, B](tab)
+
+  implicit final def catsSyntaxParallelBisequence[T[_, _]: Bitraverse, M[_], A, B](
+    tmamb: T[M[A], M[B]]
+  ): ParallelBisequenceOps[T, M, A, B] =
+    new ParallelBisequenceOps[T, M, A, B](tmamb)
+
+  implicit final def catsSyntaxParallelLeftTraverse[T[_, _]: Bitraverse, A, B](
+    tab: T[A, B]
+  ): ParallelLeftTraverseOps[T, A, B] =
+    new ParallelLeftTraverseOps[T, A, B](tab)
+
+  implicit final def catsSyntaxParallelLeftSequence[T[_, _]: Bitraverse, M[_], A, B](
+    tmab: T[M[A], B]
+  ): ParallelLeftSequenceOps[T, M, A, B] =
+    new ParallelLeftSequenceOps[T, M, A, B](tmab)
+}
+
 final class ParallelTraversableOps[T[_], A](private val ta: T[A]) extends AnyVal {
   def parTraverse[M[_]: Monad, F[_], B](f: A => M[B])(implicit T: Traverse[T], P: Parallel[M, F]): M[T[B]] =
     Parallel.parTraverse(ta)(f)
@@ -86,3 +108,24 @@ final class ParallelApplyOps[M[_], A, B](private val mab: M[A => B]) extends Any
   def <&>[F[_]](ma: M[A])(implicit P: Parallel[M, F]): M[B] =
     Parallel.parAp(mab)(ma)
 }
+
+final class ParallelBitraverseOps[T[_, _], A, B](private val tab: T[A, B]) extends AnyVal {
+  def parBitraverse[M[_], F[_], C, D](f: A => M[C], g: B => M[D])(implicit T: Bitraverse[T],
+                                                                  P: Parallel[M, F]): M[T[C, D]] =
+    Parallel.parBitraverse(tab)(f, g)
+}
+
+final class ParallelBisequenceOps[T[_, _], M[_], A, B](private val tmamb: T[M[A], M[B]]) extends AnyVal {
+  def parBisequence[F[_]](implicit T: Bitraverse[T], P: Parallel[M, F]): M[T[A, B]] =
+    Parallel.parBisequence(tmamb)
+}
+
+final class ParallelLeftTraverseOps[T[_, _], A, B](private val tab: T[A, B]) extends AnyVal {
+  def parLeftTraverse[M[_], F[_], C](f: A => M[C])(implicit T: Bitraverse[T], P: Parallel[M, F]): M[T[C, B]] =
+    Parallel.parLeftTraverse(tab)(f)
+}
+
+final class ParallelLeftSequenceOps[T[_, _], M[_], A, B](private val tmab: T[M[A], B]) extends AnyVal {
+  def parLeftSequence[F[_]](implicit T: Bitraverse[T], P: Parallel[M, F]): M[T[A, B]] =
+    Parallel.parLeftSequence(tmab)
+}

testkit/src/main/scala/cats/tests/CatsSuite.scala

@@ -47,6 +47,7 @@ trait CatsSuite
     with AllSyntaxBinCompat2
     with AllSyntaxBinCompat3
     with AllSyntaxBinCompat4
+    with AllSyntaxBinCompat5
     with StrictCatsEquality { self: FunSuiteLike =>
 
   implicit override val generatorDrivenConfig: PropertyCheckConfiguration =

tests/src/test/scala/cats/tests/ParallelSuite.scala

@@ -81,6 +81,18 @@ class ParallelSuite extends CatsSuite with ApplicativeErrorForEitherTest {
     }
   }
 
+  test("ParBitraverse identity should be equivalent to parBisequence") {
+    forAll { es: (Either[String, Int], Either[String, Long]) =>
+      es.parBitraverse(identity, identity) should ===(es.parBisequence)
+    }
+  }
+
+  test("ParLeftTraverse identity should be equivalent to parLeftSequence") {
+    forAll { es: (Either[String, Int], Either[String, Long]) =>
+      es.parLeftTraverse(identity) should ===(es.parLeftSequence)
+    }
+  }
+
   test("ParFlatTraverse should be equivalent to parTraverse map flatten") {
     forAll { es: List[Either[String, Int]] =>
       val f: Int => List[Int] = i => List(i, i + 1)

tests/src/test/scala/cats/tests/SyntaxSuite.scala

@@ -208,6 +208,20 @@ object SyntaxSuite
     (fa, fb, fc).parMapN(f)
   }
 
+  def testParallelBi[M[_], F[_], T[_, _]: Bitraverse, A, B, C, D](implicit P: Parallel[M, F]): Unit = {
+    val tab = mock[T[A, B]]
+    val f = mock[A => M[C]]
+    val g = mock[B => M[D]]
+    val mtcd = tab.parBitraverse(f, g)
+    val mtcb = tab.parLeftTraverse(f)
+
+    val tmamb = mock[T[M[A], M[B]]]
+    val mtab1 = tmamb.parBisequence
+
+    val tmab = mock[T[M[A], B]]
+    val mtab2 = tmab.parLeftSequence
+  }
+
   def testReducible[F[_]: Reducible, G[_]: Apply: SemigroupK, A: Semigroup, B, Z]: Unit = {
     val fa = mock[F[A]]
     val f1 = mock[(A, A) => A]