reference.rst

Reference Guide

This guide defines all functionality exposed by loopy. If you would like a more gentle introduction, you may consider reading the example-based :ref:`tutorial` instead.

Domain Tree

Inames

Loops are (by default) entered exactly once. This is necessary to preserve dependency semantics--otherwise e.g. a fetch could happen inside one loop nest, and then the instruction using that fetch could be inside a wholly different loop nest.

Instructions

Expressions

Loopy's expressions are a slight superset of the expressions supported by :mod:`pymbolic`.

• if

• reductions

  • duplication of reduction inames

• complex-valued arithmetic
• tagging of array access and substitution rule use ("$")

Specifying Types

:mod:`loopy` uses the same type system as :mod:`numpy`. (See :class:`numpy.dtype`) It also uses :mod:`pyopencl` for a registry of user-defined types and their C equivalents. See :func:`pyopencl.tools.get_or_register_dtype` and related functions.

For a string representation of types, all numpy types (e.g. float32 etc.) are accepted, in addition to what is registered in :mod:`pyopencl`.

Iname Implementation Tags

Tag	Meaning
None | "for"	Sequential loop
"l.N"	Local (intra-group) axis N
"g.N"	Group-number axis N
"unr"	Unroll
"ilp" | "ilp.unr"	Unroll using instruction-level parallelism
"ilp.seq"	Realize parallel iname as innermost loop

(Throughout this table, N must be replaced by an actual number.)

"ILP" does three things:

• Restricts loops to be innermost
• Duplicates reduction storage for any reductions nested around ILP usage
• Causes a loop (unrolled or not) to be opened/generated for each involved instruction

Automatic Axis Assignment

Automatic local axes are chosen as follows:

1. For each instruction containing "l.auto" inames:

   1. Find the lowest-numbered unused axis. If none exists,

      use sequential unrolling instead.

   2. Find the iname that has the smallest stride in any global

      array access occurring in the instruction.

   3. Assign the low-stride iname to the available axis, splitting

      the iname if it is too long for the available axis size.

If you need different behavior, use :func:`tag_inames` and :func:`split_iname` to change the assignment of "l.auto" axes manually.

Creating Kernels

Arguments

Loop domains

TODO: Explain the domain tree

ISL syntax

The general syntax of an ISL set is the following:

{[VARIABLES]: CONDITIONS}

VARIABLES is a simple list of identifiers representing loop indices, or, as loopy calls them, inames. Example:

{[i, j, k]: CONDITIONS}

The following constructs are supported for CONDITIONS:

• Simple conditions: i <= 15, i>0
• Conjunctions: i > 0 and i <= 15
• Two-sided conditions: 0 < i <= 15 (equivalent to the previous example)
• Identical conditions on multiple variables: 0 < i,j <= 15
• Equality constraints: i = j*3 (Note: =, not ==.)
• Modulo: i mod 3 = 0
• Existential quantifiers: (exists l: i = 3*l) (equivalent to the previous example)

Examples of constructs that are not allowed:

• Multiplication by non-constants: j*k
• Disjunction: (i=1) or (i=5) (Note: This may be added in a future version of loopy. For now, loop domains have to be convex.)

Temporary Variables

Temporary variables model OpenCL's private and local address spaces. Both have the lifetime of a kernel invocation.

Instructions

Assignments

The general syntax of an instruction is a simple assignment:

LHS[i,j,k] = EXPRESSION

Several extensions of this syntax are defined, as discussed below. They may be combined freely.

You can also use an instruction to declare a new temporary variable. (See :ref:`temporaries`.) See :ref:`types` for what types are acceptable. If the LHS has a subscript, bounds on the indices are inferred (which must be constants at the time of kernel creation) and the declared temporary is created as an array. Instructions declaring temporaries have the following form:

<temp_var_type> LHS[i,j,k] = EXPRESSION

You can also create a temporary and ask loopy to determine its type automatically. This uses the following syntax:

<> LHS[i,j,k] = EXPRESSION

Lastly, each instruction may optionally have a number of attributes specified, using the following format:

LHS[i,j,k] = EXPRESSION {attr1,attr2=value1:value2}

These are usually key-value pairs. The following attributes are recognized:

• id=value sets the instruction's identifier to value. value must be unique within the kernel. This identifier is used to refer to the instruction after it has been created, such as from dep attributes (see below) or from :mod:`context matches <loopy.context_matching>`.

• id_prefix=value also sets the instruction's identifier, however uniqueness is ensured by loopy itself, by appending further components (often numbers) to the given id_prefix.

• inames=i:j:k forces the instruction to reside within the loops over :ref:`inames` i, j and k (and only those).

  Note

  The default for the inames that the instruction depends on is the inames used in the instruction itself plus the common subset of inames shared by writers of all variables read by the instruction.

  You can add a plus sign ("+") to the front of this option value to indicate that you would like the inames you specify here to be in addition to the ones found by the heuristic described above.

• dep=id1:id2 creates a dependency of this instruction on the instructions with identifiers id1 and id2. The meaning of this dependency is that the code generated for this instruction is required to appear textually after all of these dependees' generated code.

  Identifiers here are allowed to be wildcards as defined by the Python module :mod:`fnmatchcase`. This is helpful in conjunction with id_prefix.

  Note

  Since specifying all possible dependencies is cumbersome and error-prone, :mod:`loopy` employs a heuristic to automatically find dependencies. Specifically, :mod:`loopy` will automatically add a dependency to an instruction reading a variable if there is exactly one instruction writing that variable. ("Variable" here may mean either temporary variable or kernel argument.)

  If each variable in a kernel is only written once, then this heuristic should be able to compute all required dependencies.

  Conversely, if a variable is written by two different instructions, all ordering around that variable needs to be specified explicitly. It is recommended to use :func:`get_dot_dependency_graph` to visualize the dependency graph of possible orderings.

  You may use a leading asterisk ("*") to turn off the single-writer heuristic and indicate that the specified list of dependencies is exhaustive.

• priority=integer sets the instructions priority to the value integer. Instructions with higher priority will be scheduled sooner, if possible. Note that the scheduler may still schedule a lower-priority instruction ahead of a higher-priority one if loop orders or dependencies require it.

• if=variable1:variable2 Only execute this instruction if all condition variables (which must be scalar variables) evaluate to true (as defined by C).

Expression Syntax

TODO: Functions TODO: Reductions

C Block Instructions

Substitution Rules

Syntax of a substitution rule:

rule_name(arg1, arg2) := EXPRESSION

Kernels

Do not create :class:`LoopKernel` objects directly. Instead, use the following function, which is responsible for creating kernels:

Transforming Kernels

Matching contexts

Wrangling inames

Dealing with Parameters

Dealing with Substitution Rules

Caching, Precomputation and Prefetching

Influencing data access

Padding

Manipulating Instructions

Library interface

Argument types

Finishing up

Running

Automatic Testing

Troubleshooting

Printing :class:`LoopKernel` objects

If you're confused about things loopy is referring to in an error message or about the current state of the :class:`LoopKernel` you are transforming, the following always works:

print kernel

(And it yields a human-readable--albeit terse--representation of kernel.)

Options

Controlling caching