6.2. Numba Architecture

6.2.1. Introduction

Numba is a compiler for Python bytecode with optional type-specialization.

Suppose you type a function like this into the standard Python interpreter (henceforward referred to as “CPython”):

def add(a, b):
    return a + b

The interpreter will immediately parse the function and convert it into a bytecode representation that describes how the CPython interpreter should execute the function at a low level. For the example above, it looks something like this:

>>> import dis
>>> dis.dis(add)
2           0 LOAD_FAST                0 (a)
            3 LOAD_FAST                1 (b)
            6 BINARY_ADD
            7 RETURN_VALUE

CPython uses a stack-based interpreter (much like an HP calculator), so the code first pushes two local variables onto the stack. The BINARY_ADD opcode pops the top two arguments off the stack and makes a Python C API function call that is equivalent to calling a.__add__(b). The result is then pushed onto the top of the interpreter stack. Finally, the RETURN_VALUE opcode returns value on the top of the stack as the result of the function call.

Numba can take this bytecode and compile it to machine code that performs the same operations as the CPython interpreter, treating a and b as generic Python objects. The full semantics of Python are preserved, and the compiled function can be used with any kind of objects that have the add operator defined. When a Numba function is compiled this way, we say that it has been compiled in object mode, because the code still manipulates Python objects.

Numba code compiled in object mode is not much faster than executing the original Python function in the CPython interpreter. However, if we specialize the function to only run with certain data types, Numba can generate much shorter and more efficient code that manipulates the data natively without any calls into the Python C API. When code has been compiled for specific data types so that the function body no longer relies on the Python runtime, we say the function has been compiled in nopython mode. Numeric code compiled in nopython mode can be hundreds of times faster than the original Python.

6.2.2. Contexts

Numba is quite flexible, allowing it to generate code for different hardware architectures like CPUs and GPUs (just CUDA, for now). In order to support these different applications, Numba uses a typing context and a target context.

A typing context is used in the compiler frontend to perform type inference on values in the function. Similar typing contexts could be used for many architectures because for nearly all cases, typing inference is hardware-independent. However, Numba currently has a different typing context for each target.

A target context is used to generate the specific instruction sequence required to operate on the Numba types identified during type inference. Target contexts are architecture specific. For example, Numba has a “cpu” and a “gpu” context, and NumbaPro adds a “parallel” context which produces multithreaded CPU code.

6.2.3. Compiler Stages

The @jit decorator in Numba ultimately calls numba.compiler.compile_extra() which compiles the Python function in a multi-stage process, described below. Stage 1: Analyze Bytecode

At the start of compilation, the function bytecode is passed to an instance of the Numba interpreter (numba.interpreter). The interpreter object analyzes the bytecode to find the control flow graph (numba.controlflow). The control flow graph describes the ways that execution can move from one block to the next inside the function as a result of loops and branches.

The data flow analysis (numba.dataflow) takes the control flow graph and traces how values get pushed and popped off the Python interpreter stack for different code paths. This is important to understand the lifetimes of variables on the stack, which are needed in Stage 2.

If you set the environment variable NUMBA_DUMP_CFG to 1, Numba will dump the results of the control flow graph analysis to the screen. Our add() example is pretty boring, since there is only one statement block:

CFG adjacency lists:
{0: []}
CFG dominators:
{0: set([0])}
CFG post-dominators:
{0: set([0])}
CFG back edges: []
CFG loops:
CFG node-to-loops:
{0: []}

A function with more complex flow control will have a more interesting control flow graph. This function:

def doloops(n):
    acc = 0
    for i in range(n):
        acc += 1
        if n == 10:
    return acc

compiles to this bytecode:

 9           0 LOAD_CONST               1 (0)
             3 STORE_FAST               1 (acc)

10           6 SETUP_LOOP              46 (to 55)
             9 LOAD_GLOBAL              0 (range)
            12 LOAD_FAST                0 (n)
            15 CALL_FUNCTION            1
            18 GET_ITER
       >>   19 FOR_ITER                32 (to 54)
            22 STORE_FAST               2 (i)

11          25 LOAD_FAST                1 (acc)
            28 LOAD_CONST               2 (1)
            31 INPLACE_ADD
            32 STORE_FAST               1 (acc)

12          35 LOAD_FAST                0 (n)
            38 LOAD_CONST               3 (10)
            41 COMPARE_OP               2 (==)
            44 POP_JUMP_IF_FALSE       19

13          47 BREAK_LOOP
            48 JUMP_ABSOLUTE           19
            51 JUMP_ABSOLUTE           19
       >>   54 POP_BLOCK

14     >>   55 LOAD_FAST                1 (acc)
            58 RETURN_VALUE

The corresponding CFG for this bytecode is:

CFG adjacency lists:
{0: [6], 6: [19], 19: [54, 22], 22: [19, 47], 47: [55], 54: [55], 55: []}
CFG dominators:
{0: set([0]),
 6: set([0, 6]),
 19: set([0, 6, 19]),
 22: set([0, 6, 19, 22]),
 47: set([0, 6, 19, 22, 47]),
 54: set([0, 6, 19, 54]),
 55: set([0, 6, 19, 55])}
CFG post-dominators:
{0: set([0, 6, 19, 55]),
 6: set([6, 19, 55]),
 19: set([19, 55]),
 22: set([22, 55]),
 47: set([47, 55]),
 54: set([54, 55]),
 55: set([55])}
CFG back edges: [(22, 19)]
CFG loops:
{19: Loop(entries=set([6]), exits=set([54, 47]), header=19, body=set([19, 22]))}
CFG node-to-loops:
{0: [], 6: [], 19: [19], 22: [19], 47: [], 54: [], 55: []}

The numbers in the CFG refer to the bytecode offsets shown just to the left of the opcode names above. Stage 2: Generate the Numba IR

Once the control flow and data analyses are complete, the Numba interpreter can step through the bytecode and translate it into an Numba-internal intermediate representation. This translation process changes the function from a stack machine representation (used by the Python interpreter) to a register machine representation (used by LLVM).

Although the IR is stored in memory as a tree of objects, it can be serialized to a string for debugging. If you set the environment variable NUMBA_DUMP_IR equal to 1, the Numba IR will be dumped to the screen. For the add() function described above, the Numba IR looks like:

label 0:
    a = arg(0, name=a)                       ['a']
    b = arg(1, name=b)                       ['b']
    $0.3 = a + b                             ['$0.3', 'a', 'b']
    del b                                    []
    del a                                    []
    $0.4 = cast(value=$0.3)                  ['$0.3', '$0.4']
    del $0.3                                 []
    return $0.4                              ['$0.4']

The del instructions are produced by live variable analysis. Those instructions ensure references are not leaked in object mode, where each variable contains an owned reference to a PyObject. They are no-ops in nopython mode. Stage 3: Macro expansion

Now that the function has been translated into the Numba IR, macro expansion can be performed. Macro expansion converts specific attributes that are known to Numba into IR nodes representing function calls. This is initiated in the numba.compiler.translate_stage function, and is implemented in numba.macro.

Examples of attributes that are macro-expanded include the CUDA instrinsics for grid, block and thread dimensions and indices. For example, the assignment to tx in the following function:

def f(a):
    tx = cuda.threadIdx.x

has the following representation after translation to Numba IR:

$0.1 = global(cuda: <module 'numba.cuda' from '...'>) ['$0.1']
$0.2 = getattr(value=$0.1, attr=threadIdx) ['$0.1', '$0.2']
del $0.1                                 []
$0.3 = getattr(value=$0.2, attr=x)       ['$0.2', '$0.3']
del $0.2                                 []
tx = $0.3                                ['$0.3', 'tx']

After macro expansion, the $0.3 = getattr(value=$0.2, attr=x) IR node is translated into:

$0.3 = call tid.x(, )                    ['$0.3']

which represents an instance of the Intrinsic IR node for calling the tid.x intrinsic function. Stage 4: Infer Types

Now that the Numba IR has been generated and macro-expanded, type analysis can be performed. The types of the function arguments can be taken either from the explicit function signature given in the @jit decorator (such as @jit('float64(float64, float64)')), or they can be taken from the types of the actual function arguments if compilation is happening when the function is first called.

The type inference engine is found in numba.typeinfer. Its job is to assign a type to every intermediate variable in the Numba IR. The result of this pass can be seen by setting the NUMBA_DUMP_ANNOTATION environment variable to 1:

# File: archex.py
# --- LINE 4 ---


# --- LINE 5 ---

def add(a, b):

    # --- LINE 6 ---
    # label 0
    #   a = arg(0, name=a)  :: int64
    #   b = arg(1, name=b)  :: int64
    #   $0.3 = a + b  :: int64
    #   del b
    #   del a
    #   $0.4 = cast(value=$0.3)  :: int64
    #   del $0.3
    #   return $0.4

    return a + b

If type inference fails to find a consistent type assignment for all the intermediate variables, it will label every variable as type pyobject and fall back to object mode. Type inference can fail when unsupported Python types, language features, or functions are used in the function body. Stage 5: Rewrite Typed IR

Numba implements a user-extensible rewriting pass that reads and possibly rewrites Numba IR. This pass’s purpose is to perform any high-level optimizations that still require, or could at least benefit from, Numba IR type information.

One example of a problem domain that isn’t as easily optimized once lowered is the domain of multidimensional array operations. When Numba lowers an array operation, Numba treats the operation like a full ufunc kernel. During lowering a single array operation, Numba generates an inline broadcasting loop that creates a new result array. Then Numba generates an application loop that applies the operator over the array inputs. Recognizing and rewriting these loops once they are lowered into LLVM is hard, if not impossible.

An example pair of optimizations in the domain of array operators is loop fusion and shortcut deforestation. When the optimizer recognizes that the output of one array operator is being fed into another array operator, and only to that array operator, it can fuse the two loops into a single loop. The optimizer can further eliminate the temporary array allocated for the initial operation by directly feeding the result of the first operation into the second, skipping the store and load to the intermediate array. This elimination is known as shortcut deforestation. Numba currently uses the rewrite pass to implement these array optimizations. For more information, please consult the “Case study: Array Expressions” subsection, later in this document.

One can see the result of rewriting by setting the NUMBA_DUMP_IR environment variable to a non-zero value (such as 1). The following example shows the output of the rewrite pass as it recognizes an array expression consisting of a multiply and add, and outputs a fused kernel as a special operator, arrayexpr():

a0 = arg(0, name=a0)                     ['a0']
a1 = arg(1, name=a1)                     ['a1']
a2 = arg(2, name=a2)                     ['a2']
$0.3 = a0 * a1                           ['$0.3', 'a0', 'a1']
del a1                                   []
del a0                                   []
$0.5 = $0.3 + a2                         ['$0.3', '$0.5', 'a2']
del a2                                   []
del $0.3                                 []
$0.6 = cast(value=$0.5)                  ['$0.5', '$0.6']
del $0.5                                 []
return $0.6                              ['$0.6']
a0 = arg(0, name=a0)                     ['a0']
a1 = arg(1, name=a1)                     ['a1']
a2 = arg(2, name=a2)                     ['a2']
$0.5 = arrayexpr(ty=array(float64, 1d, C), expr=('+', [('*', [Var(a0, test.py (14)), Var(a1, test.py (14))]), Var(a2, test.py (14))])) ['$0.5', 'a0', 'a1', 'a2']
del a0                                   []
del a1                                   []
del a2                                   []
$0.6 = cast(value=$0.5)                  ['$0.5', '$0.6']
del $0.5                                 []
return $0.6                              ['$0.6']

Following this rewrite, Numba lowers the array expression into a new ufunc-like function that is inlined into a single loop that only allocates a single result array. Stage 6a: Generate No-Python LLVM IR

If type inference succeeds in finding a Numba type for every intermediate variable, then Numba can (potentially) generate specialized native code. This process is called lowering. The Numba IR tree is translated into LLVM IR by using helper classes from llvmlite. The machine-generated LLVM IR can seem unnecessarily verbose, but the LLVM toolchain is able to optimize it quite easily into compact, efficient code.

The basic lowering algorithm is generic, but the specifics of how particular Numba IR nodes are translated to LLVM instructions is handled by the target context selected for compilation. The default target context is the “cpu” context, defined in numba.targets.cpu.

The LLVM IR can be displayed by setting the NUMBA_DUMP_LLVM environment variable to 1. For the “cpu” context, our add() example would look like:

define i32 @"__main__.add$1.int64.int64"(i64* %"retptr",
                                         {i8*, i32}** %"excinfo",
                                         i8* %"env",
                                         i64 %"arg.a", i64 %"arg.b")
     %"a" = alloca i64
     %"b" = alloca i64
     %"$0.3" = alloca i64
     %"$0.4" = alloca i64
     br label %"B0"
     store i64 %"arg.a", i64* %"a"
     store i64 %"arg.b", i64* %"b"
     %".8" = load i64* %"a"
     %".9" = load i64* %"b"
     %".10" = add i64 %".8", %".9"
     store i64 %".10", i64* %"$0.3"
     %".12" = load i64* %"$0.3"
     store i64 %".12", i64* %"$0.4"
     %".14" = load i64* %"$0.4"
     store i64 %".14", i64* %"retptr"
     ret i32 0

The post-optimization LLVM IR can be output by setting NUMBA_DUMP_OPTIMIZED to 1. The optimizer shortens the code generated above quite significantly:

define i32 @"__main__.add$1.int64.int64"(i64* nocapture %retptr,
                                         { i8*, i32 }** nocapture readnone %excinfo,
                                         i8* nocapture readnone %env,
                                         i64 %arg.a, i64 %arg.b)
     %.10 = add i64 %arg.b, %arg.a
     store i64 %.10, i64* %retptr, align 8
     ret i32 0
} Stage 6b: Generate Object Mode LLVM IR

If type inference fails to find Numba types for all values inside a function, the function will be compiled in object mode. The generated LLVM will be significantly longer, as the compiled code will need to make calls to the Python C API to perform basically all operations. The optimized LLVM for our example add() function is:

@PyExc_SystemError = external global i8
@".const.Numba_internal_error:_object_mode_function_called_without_an_environment" = internal constant [73 x i8] c"Numba internal error: object mode function called without an environment\00"
@".const.name_'a'_is_not_defined" = internal constant [24 x i8] c"name 'a' is not defined\00"
@PyExc_NameError = external global i8
@".const.name_'b'_is_not_defined" = internal constant [24 x i8] c"name 'b' is not defined\00"

define i32 @"__main__.add$1.pyobject.pyobject"(i8** nocapture %retptr, { i8*, i32 }** nocapture readnone %excinfo, i8* readnone %env, i8* %arg.a, i8* %arg.b) {
  %.6 = icmp eq i8* %env, null
  br i1 %.6, label %entry.if, label %entry.endif, !prof !0

entry.if:                                         ; preds = %entry
  tail call void @PyErr_SetString(i8* @PyExc_SystemError, i8* getelementptr inbounds ([73 x i8]* @".const.Numba_internal_error:_object_mode_function_called_without_an_environment", i64 0, i64 0))
  ret i32 -1

entry.endif:                                      ; preds = %entry
  tail call void @Py_IncRef(i8* %arg.a)
  tail call void @Py_IncRef(i8* %arg.b)
  %.21 = icmp eq i8* %arg.a, null
  br i1 %.21, label %B0.if, label %B0.endif, !prof !0

B0.if:                                            ; preds = %entry.endif
  tail call void @PyErr_SetString(i8* @PyExc_NameError, i8* getelementptr inbounds ([24 x i8]* @".const.name_'a'_is_not_defined", i64 0, i64 0))
  tail call void @Py_DecRef(i8* null)
  tail call void @Py_DecRef(i8* %arg.b)
  ret i32 -1

B0.endif:                                         ; preds = %entry.endif
  %.30 = icmp eq i8* %arg.b, null
  br i1 %.30, label %B0.endif1, label %B0.endif1.1, !prof !0

B0.endif1:                                        ; preds = %B0.endif
  tail call void @PyErr_SetString(i8* @PyExc_NameError, i8* getelementptr inbounds ([24 x i8]* @".const.name_'b'_is_not_defined", i64 0, i64 0))
  tail call void @Py_DecRef(i8* %arg.a)
  tail call void @Py_DecRef(i8* null)
  ret i32 -1

B0.endif1.1:                                      ; preds = %B0.endif
  %.38 = tail call i8* @PyNumber_Add(i8* %arg.a, i8* %arg.b)
  %.39 = icmp eq i8* %.38, null
  br i1 %.39, label %B0.endif1.1.if, label %B0.endif1.1.endif, !prof !0

B0.endif1.1.if:                                   ; preds = %B0.endif1.1
  tail call void @Py_DecRef(i8* %arg.a)
  tail call void @Py_DecRef(i8* %arg.b)
  ret i32 -1

B0.endif1.1.endif:                                ; preds = %B0.endif1.1
  tail call void @Py_DecRef(i8* %arg.b)
  tail call void @Py_DecRef(i8* %arg.a)
  tail call void @Py_IncRef(i8* %.38)
  tail call void @Py_DecRef(i8* %.38)
  store i8* %.38, i8** %retptr, align 8
  ret i32 0

declare void @PyErr_SetString(i8*, i8*)

declare void @Py_IncRef(i8*)

declare void @Py_DecRef(i8*)

declare i8* @PyNumber_Add(i8*, i8*)

The careful reader might notice several unnecessary calls to Py_IncRef and Py_DecRef in the generated code. Currently Numba isn’t able to optimize those away.

Object mode compilation will also attempt to identify loops which can be extracted and statically-typed for “nopython” compilation. This process is called loop-lifting, and results in the creation of a hidden nopython mode function just containing the loop which is then called from the original function. Loop-lifting helps improve the performance of functions that need to access uncompilable code (such as I/O or plotting code) but still contain a time-intensive section of compilable code. Stage 7: Compile LLVM IR to Machine Code

In both “object mode” and “nopython mode”, the generated LLVM IR is compiled by the LLVM JIT compiler and the machine code is loaded into memory. A Python wrapper is also created (defined in numba.dispatcher.Overloaded) which can do the dynamic dispatch to the correct version of the compiled function if multiple type specializations were generated (for example, for both float32 and float64 versions of the same function).

The machine assembly code generated by LLVM can be dumped to the screen by setting the NUMBA_DUMP_ASSEMBLY environment variable to 1:

        .globl  __main__.add$1.int64.int64
        .align  16, 0x90
        .type   __main__.add$1.int64.int64,@function
        addq    %r8, %rcx
        movq    %rcx, (%rdi)
        xorl    %eax, %eax

The assembly output will also include the generated wrapper function that translates the Python arguments to native data types.