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Metalibm Description Language

Metalibm Description Language (MDL) is the entry point for Metalibm. An implementation is built using MDL and static generation allowed by the Metalibm framework (e.g. generating table content using pythonsollya). The power of metalibm lies on mixing mathematical and code generation tools to generate an efficient implementation.

Basics MDL constructs

MDL is based on mix of control flow and dataflow nodes. Dataflow takes the form of operation expressions using nodes such as Addition, Multiplication, Variable, Constant. Control flow uses nodes such as ConditionBlock, SwitchBlock or Return.

Expression

MDL expressions are a composition of leaf nodes (Constant, Variable) and operation nodes (Addition, Multiplication, ...).

# a variable called x with undefined precision
x = Variable("x")
# Addition between x and the numerical value 3.
# Metalibm will promote 3 from numerical value to Constant node
y = Addition(x, 3)
# The previous expression can be written with implicit operations
z = x + 3

Control Flow

Control flow can be described in MDL using constructs such as ConditionBlock, Statement, Return.

Statement

ConditionBlock

if-then-else block can be described with ConditionBlock(, , ). The is optional.

# if (cond) then return a else return b
scheme = ConditionBlock(
    cond,
    Return(a),
    Return(b)
)

Variable and scope

MDL provides several variable construct. By default a variable is an input to the current scheme, it is considered alive everywhere (declared outside the scope of the scheme). A Variable node can be declared of var_type Variable.Local, it such a case its scope is reduced. If a variable first appears in an expression is scope is limited to the Statement surrounding the expression. If a variable first appears alone in a Statement is scope is the statement and every encapsulated sub-statement.

Tables

Attributes

Precision

MDL Nodes can be annotated with attributes which specifies their properties. For example you can specify the precision of a node by using precision attribute.

# a single precision variable called "t"
t = Variable("t", precision=ML_Binary32)

Basic MDL precisions include: ML_Binary32 (float), ML_Binary64 (double), ML_Int32 (int32_t), ML_UInt32 (uint32_t*), ML_UInt64, ML_Int64. MDL also contains compound precisions: ML_DoubleDouble, ML_TripleDouble and vector formats: v<i>float32 (vector of single precision elements), vfloat64 (vector of double precision elements), v<i>[u]int32, v<i>[u]int64, v<i>bool with <i> in 2, 3, 4, 8.

Tag

You can force the name of a node by using the tag attribute.

# An addition tagged "unique_sum", this name should appear in the generated code
unique_sum = Addition(t, x, tag="unique_sum")