Matrix data types and type inference

Quasar is an array language, this means that array types (vec, mat and cube) are primitive types and have built-in support (for example, this is in contrast with C/C++ where the user has to define it’s own matrix classes).

The reason for the built-in support is of course that this enables easier mapping of Quasar programs to different parallel devices (GPU, …). Moreover, the user is forced to use one representation for its data (rather than using different class libraries, where it is necessary to wrap one matrix class into another matrix class).

On the other hand, by default Quasar abstracts numeric values into one data type scalar. The type scalar just represents a scalar number, and whether this is a floating point number or a fix point number with 16/32/64-bit precision is actually implementation specific (note currently the Quasar runtime system only supports 32-bit and 64-bit floating point numbers).

Type parameters

For efficiency reasons, there is also support for integer data types int, int8, int16, int32, int64, uint8, uint16, uint32, uint64. (Please note that using 64-bit types can suffer from precision errors, because all the calculations are performed in scalar format). To support matrices built of these types, the array types vec, mat and cube are parametric, for example

• vec[int8] denotes a vector (1D array) of 8-bit signed integers
• cube[int] denotes a cube (3D array) of signed integers (note: by default, int is 32-bit).

To simplify the types (and to reduce key strokes while programming), there are a number of built-in type aliases:

type vec  : vec[scalar]      % real-valued vector
type cvec : vec[cscalar]    % complex-valued vector

type mat  : mat[scalar]      % real-valued vector
type cmat : mat[cscalar]    % complex-valued vector

type cube  : cube[scalar]    % real-valued vector
type ccube : cube[cscalar]  % complex-valued vector

Please note that these types are just aliases! For example, cube is just cube[scalar] and not cube[something else]:

a = cube[scalar](10)
assert(type(a, "cube"))    % Successful

b = cube[int](10)
assert(type(b, "cube"))    % Unsuccessful - compiler error

However, in case the intention is to check whether a or b is a 3D array regardless of the element type, the special ?? type can be used:

b = cube[int](10)
assert(type(b, "cube[??]"))   % Successful

Type inference

When the type is not specified (for example data that is read dynamically from a file, using the load("data.qd") function), the default data type is ‘??‘. This is a very generic type, every type comparison with ?? results in TRUE. For example:

assert(type(1i+1, '??'))
assert(type([1,2,3], '??'))

However, using variables of type ?? will prevent the compiler to optimize whole operations (for example, applying reductions or automatically generating kernel functions for for-loops). Therefore, it is generally a bad idea to have functions return variables of unspecified type ‘??‘ and correspondingly the compiler gives a warning message when this is the case.

Practically, the type inference starts from the matrix creation functions zeros, ones, imread, … that have a built-in mechanism for deciding the type of the result (based on the parameters of the function).

For example:

• A = zeros([1,1,4]) creates a vector of length 4 (vec)
• B = zeros([2,3]) creates a matrix of dimensions 2 x 3 (mat).
• C = imread("data.tif") creates a cube at all times.

Note that the type inference also works when a variable is passed to the matrix creation functions:

sz = [1,1,4]; A = zeros(sz)

In this case, the compiler knows that sz is a constant vector, it keeps track of the value and uses it for determining the type of zeros.

However: the compiler cannot do this when the variable sz is passed as argument of a function:

function A = create_data(sz)
    A = zeros(sz)
end

In this case, because the type of sz is unknown, the compiler cannot determine the type of A and will therefore use the default type ??. For convenience, the compiler then also generates a warning message “could not determine the type of output argument A”. The solution is then simply to specify the type of sz:

function A = create_data(sz : ivec2)
    A = zeros(sz)
end

This way, the compiler knows that sz is a vector of length 2, and can deduce the type of A, which is a matrix (mat).

Summary

The type system can be summarized as follows. There are 6 categories of types:

1. Primitive scalar types scalar, cscalar, int, int8, …
2. Matrix types vec, mat, cube

   with parametrized versions vec[??], mat[??], cube[??].

3. Classes: type R : class / type T : mutable class
4. Function types [?? -> ??], [(??,??)->(??,??)], …

   Device functions: [__device__ ?? -> ??] Kernel functions: [__kernel__ ?? -> ??]

5. Individual types type
6. Type classes: T : [scalar|mat|cube]

Finally, different types can be combined to define new types.

Exercise:

• Figure out what the following type means:

  type X : [vec[ [??->[int|mat|cube[??->??] ] | int -> ?? | __device__ mat->() ] | cscalar ]

  Just kidding;-)