Packed vectors : use these whenever possible. The generic vector type is is represented at run-time by a linked list of boxed values. Packed types, however, store the vector components sequentially in memory. Vector operations can be defined using the generic types, and the compiler will inline and specialize these definitions for the packed types, avoiding any list cells or unnecessary heap allocations.

Packed vectors are related to their unpacked representations by way of an associated type. An instance of class PackedVec v declares that v has a packed representation, and the type of that is Packed v. The packed constructors are named VecNT where N is 2, 3 or 4 and T is I, F or D for Int, Float or Double. So the expression Vec3D x y z constructs a packed 3-vector of Doubles, the type of which is Packed (Vec3 Double). The constructor name is also a synonym for the packed type name, i.e., type Vec3D = Packed (Vec3 Double), so the packed type acts as if it had been declared data Vec3D = Vec3D x y z.

Storable, Num, Fractional, Fold, Map, and ZipWith instances are provided for packed vectors, so some operations do not require pack/unpack. For example, dot does not require pack/unpack because it is defined in terms of zipWith and fold. However transpose, det, gaussElim and most others are recursive, and so you'll still need to use pack/unpack with these. This goes for multmm as well because it uses transpose. Some functions, like multmv, do not need their arguments to be unpacked, but the result is a polymorphic vector (:.), so you will need to pack it again. I admit that this is awkward.

There are also instances for Take, Drop, Last, Head, Tail and Snoc. These come in handy for thinks like quaternions and homogenous coordinates.