from __future__ import print_function
import numba
import numpy as np
import math
import llvm
import ctypes
print("numba version: %s \nNumPy version: %s\nllvm version: %s" % (numba.__version__,np.__version__, llvm.__version__))

numba version: 0.12.0
NumPy version: 1.7.1
llvm version: 0.12.1

# Numba and types¶

## Introduction¶

Numba translates Python code into fast executing native code. In order to generate fast native code, many dynamic features of Python need to be translated into static equivalents. This includes dynamic typing as well as polymorphism. The approach taken in numba is using type inference to generate type information for the code, so that it is possible to translate into native code. If all the values in a numba compiled function can be translated into native types, the resulting code will be competitive with that generated with a low level language.

The objective of type inference is assigning a type to every single value in the function. The type of a value can either be:

• Implicit, in the case of providing an object that will provide its type. This happens, for example, in literals.
• Explicit, in the case of the programmer explicitly writing the type of a given value. This happens, for example, when a signature is given to numba.jit. That signature explicitly types the arguments.
• Inferred, when the type is deduced from an operation and the types of the its operands. For example, inferring that the type of a + b, when a and b are of type int is going to be an int

Type inference is the process by which all the types that are neither implicit nor explicit are deduced.

## Type inference by example¶

Let’s take a very simple sample function to illustrate these concepts:

def sample_func(n):
tmp = n + 4;
return tmp + 3j;


When translating to native code it is needed to provide type information for every value involved in the sample function. This will include:

• The literals 4 and 3j. These two have an implicit type.
• The argument n. In the function, as is, it is yet untyped.
• Some intermediate values, like tmp and the return value. Their type is not known yet.

### Finding out the types of values¶

You can use the function numba.typeof to find out the numba type associated to a value.

print(numba.typeof.__doc__)

Get the type of a variable or value.

Used outside of Numba code, infers the type for the object.

Bear in mind that, when used from the Python interpreter, numba.typeof will return the numba type associated to the object passed as parameter. For example, let’s try using it on the literals found in our sample function:

numba.typeof(4)

int32

numba.typeof(3j)

complex128


Also note that the types of the results are numba types:

type(numba.typeof(4))

numba.types.Integer


As a note, when used inside numba compiled code, numba.typeof will return the type as inferred during type inference. This may be a more general type than the one which would be returned when evaluating using the Python interpreter.

### Type inference in numba.jit¶

Let’s illustrate how type inference works with numba.jit. In order to illustrate this, we will use the inspect_types method of a compiled function and prints information about the types being used while compiling. This will be the different native types when the function has been compiled successfully in nopython mode. If object mode has been used we will get plenty of pyobjects.

Note that inspect_types is new to numba 0.12. Note also that the behavior of object mode has changed quite a bit as well in this release.

def jit_sample_1(n):
tmp = n + 4;
return tmp + 3j;

numba.jit('c16(f8)', nopython=True)(jit_sample_1).inspect_types()

jit_sample_1 (float64,) -> complex128
--------------------------------------------------------------------------------
# --- LINE 1 ---

def jit_sample_1(n):

# --- LINE 2 ---
# label 0
#   $0.1 = const(<type 'int'>, 4) :: int32 #$0.2 = n + $0.1 :: float64 # tmp =$0.2  :: float64

tmp = n + 4;

# --- LINE 3 ---
#   $0.3 = const(<type 'complex'>, 3j) :: complex128 #$0.4 = tmp + $0.3 :: complex128 # return$0.4

return tmp + 3j;

================================================================================

The source code of the original function should be shown with lines annotated with the values involved in that lines with its type annotated following a couple of double periods. The form will look like “value = expression :: type”.

In this case, the resulting function will get a float64 argument and return a complex128. The literal 4 will be of type int32 ($0.1), while the result of adding the argument (n) to that literal will be a float64 ($0.2). The variable in the source code named tmp will be just float64 (assigned from $0.2). In the same way we can trace the next expression and see how tmp+3j results in a complex128 value that will be used as return value. The values named _$0.*_ are intermmediate values for the expression, and do not have a named counterpart in the source code.

If we were in object mode we would get something quite different. In order to illustrate, let’s add the forceobj keyword to numba.jit. This will force numba to use object mode when compiling. Usually you don’t want to use forceobj as object mode is slower than nopython mode:

numba.jit('c16(f8)', forceobj=True)(jit_sample_1).inspect_types()

jit_sample_1 (pyobject,) -> pyobject
--------------------------------------------------------------------------------
# --- LINE 1 ---

def jit_sample_1(n):

# --- LINE 2 ---
# label 0
#   $0.1 = const(<type 'int'>, 4) :: pyobject # tmp = n +$0.1  :: pyobject

tmp = n + 4;

# --- LINE 3 ---
#   $0.3 = const(<type 'complex'>, 3j) :: pyobject #$0.4 = tmp + $0.3 :: pyobject # return$0.4

return tmp + 3j;

================================================================================

As can be seen, everything is now a pyobject. That means that the operations will be executed by the Python runtime in the generated code.

Going back to the nopython mode, we can see how changing the input types will produced a different annotation for the code (and result in different code generation):

numba.jit('c16(i1)')(jit_sample_1).inspect_types()

jit_sample_1 (int8,) -> complex128
--------------------------------------------------------------------------------
# --- LINE 1 ---

def jit_sample_1(n):

# --- LINE 2 ---
# label 0
#   $0.1 = const(<type 'int'>, 4) :: int32 #$0.2 = n + $0.1 :: int64 # tmp =$0.2  :: int64

tmp = n + 4;

# --- LINE 3 ---
#   $0.3 = const(<type 'complex'>, 3j) :: complex128 #$0.4 = tmp + $0.3 :: complex128 # return$0.4

return tmp + 3j;

================================================================================

In this case, the input is an int8, but tmp ends being and int64 as it is added to an int32. Note that integer overflow of int64 is not handled by numba. In case of overflow the int64 will wrap around in the same way that it would happen in C.

### Providing hints to the type inferrer¶

In most cases, the type inferrer will provide a type for your code. However, sometimes you may want a given intermediate value to use a specific type. This can be achieved by using the locals keyword in numba.jit. In locals a dictionary can be passed that maps the name of different local variables to a numba type. The compiler will assign that type to that variable.

Let’s make a version of out function where we force tmp to be a float:

numba.jit('c16(i1)', locals={'tmp': numba.float64})(jit_sample_1).inspect_types()

jit_sample_1 (int8,) -> complex128
--------------------------------------------------------------------------------
# --- LINE 1 ---

def jit_sample_1(n):

# --- LINE 2 ---
# label 0
#   $0.1 = const(<type 'int'>, 4) :: int32 #$0.2 = n + $0.1 :: int64 # tmp =$0.2  :: float64

tmp = n + 4;

# --- LINE 3 ---
#   $0.3 = const(<type 'complex'>, 3j) :: complex128 #$0.4 = tmp + $0.3 :: complex128 # return$0.4

return tmp + 3j;

================================================================================

Note that as of numba 0.12, any type inference or type hints are ignored if object mode ends being generated, as everything gets treated as an object using the python runtime. This behavior may change in future versions.

numba.jit('c16(i1)', forceobj=True, locals={ 'tmp': numba.float64 })(jit_sample_1).inspect_types()

jit_sample_1 (pyobject,) -> pyobject
--------------------------------------------------------------------------------
# --- LINE 1 ---

def jit_sample_1(n):

# --- LINE 2 ---
# label 0
#   $0.1 = const(<type 'int'>, 4) :: pyobject # tmp = n +$0.1  :: pyobject

tmp = n + 4;

# --- LINE 3 ---
#   $0.3 = const(<type 'complex'>, 3j) :: pyobject #$0.4 = tmp + $0.3 :: pyobject # return$0.4

return tmp + 3j;

================================================================================

### Importance of type inference¶

It must be emphasized how important it is type inference in numba. A function where type inference is unable to provide a specific type for a value (that is, any type other than the generic pyobject). Any function that has a value fallback to pyobject will force the numba compiler to use the object mode. Object mode is way less efficient thant the nopython.

It is possible to know if a numba compiled function has fallen back to object mode by calling inspect_types on it. If there are values typed as pyobject that means that the object mode was used to compile it.

## Supported types in numba¶

Numba supports many different types. It also supports some composite types as well as structures. Starting with numba 0.12 there is a namespace for types (numba.types). The numba namespace also imports these types.

In this section you can find a set of basic types you can use in numba. Many of the types have a “short name” matching their equivalent NumPy dtype. The list is not exahustive.

### Integral types¶

type

numba type

short name

python equivalent

boolean

numba.types.bool__

b1

bool

signed integer

numba.types.int__

int

signed integer (8 bit)

numba.types.int8

i1

signed integer (16 bit)

numba.types.int16

i2

signed integer (32 bit)

numba.types.int32

i4

signed integer (64 bit)

numba.types.int64

i8

unsigned integer

numba.types.uint

unsigned integer (16 bit)

numba.types.uint16

u2

unsigned integer (32 bit)

numba.types.uint32

u4

unsigned integer (64 bit)

numba.types.uint64

u8

### Floating point types¶

type

numba type

short name

python equivalent

single precision floating point (32 bit)

numba.float32

f4

double precision floating point (64 bit)

numba.float64

f8

float

single precision complex (2 x 32 bit)

numba.complex64

c8

double precison complex (2 x 64 bit)

numba.complex128

c16

complex

### Array types¶

Array types are supported. An array type is built from a base type, a number of dimensions and potentially a layout specification. Some examples follow:

A one-dimensional array of float32

numba.types.float32[:]

array(float32, 1d, A)
numba.typeof(np.zeros((12,2), dtype=np.float32)[:,0]) # slicing out the inner dimension to avoid defaulting to C array order in the result

array(float32, 1d, A)

A two dimensional array of integers

numba.types.int_[:,:]

array(uint32, 2d, A)
numba.typeof(np.zeros((12,2,2), dtype='i')[:,0]) # slicing out the inner dimension to avoid defaulting to C array order in the result

array(int32, 2d, A)

A two dimensional array of type ‘c8’ (complex64) in C array order

numba.types.c8[:,::1]

array(complex64, 2d, C)
numba.typeof(np.zeros((12,12), dtype='c8', order='C'))

array(complex64, 2d, C)

A two dimensional array of type uint16 in FORTRAN array order

numba.types.uint16[::1,:]

array(uint16, 2d, F)
numba.typeof(np.zeros((12,12), dtype='u2', order='F'))

array(uint16, 2d, F)

Notice that the arity of the dimensions is not part of the types, only the number of dimensions. In that sense, an array with a shape (4,4) has the same numba type as another array with a shape (10, 12)

numba.typeof(np.zeros((4,4))) == numba.typeof(np.zeros((10,12)))

True


### Some extra types¶

A type signature for a function (also known as a function prototype) that returns a float64, taking a two dimensional float64 array as first argument and a float64 argument

numba.types.float64(numba.types.float64[:,:], numba.types.float64)

float64(array(float64, 2d, A), float64)

As can be seen the signature is just a type specification. In many places that a function signature is expected a string can be used instead. That string is in fact evaluated inside the numba.types namespace in order to build the actual type. This allows specifying the types in a compact way (as there is no need to fully qualify the base types) without polluting the active namespace (as it would happen by adding a __from numba.types import *__.

In numba 0.12 this is performed by the numba.sigutils.parse_signature function. Note that this function is likely to change or move in next versions, as it is just an implementation detail, but it can be used to show how the string version matches the other one, while keeping the syn

numba.sigutils.parse_signature('float64(float64[:,:], float64)')

float64(array(float64, 2d, A), float64)

A generic Python object

numba.types.pyobject

pyobject


## Notes about changes in this tutorial¶

In numba 0.12 there have been internal changes that have made material previously found in this tutorial obsolete.

• Some of the types previously supported in the numba type system have been dropped to be handled as pyobjects.
• The numba command line tool is no longer supported, but its functionality to get insights on how type inference works is now present in the form of the inspect_types method in the generated jitted function. This method is used in this tutorials to illustrate type inference.
• In 0.12 the object mode of numba has been greatly modified. Before it was using a mix of Python run-time and native code. In 0.12 object mode forces all values into pyobjects. As conversion to a string forces numba into object mode, the approach used in the previous version of this tutorial to print from inside the compiled function is no longer useful, as it will not print the staticly inferred types.

A sample of the this last point follows:

def old_style_sample(n):
print('arg n: '+ str(numba.typeof(n)))
print('literal 4: ' + str(numba.typeof(4)))
tmp = n + 4;
print('tmp: '+ str(numba.typeof(tmp)))
print('literal 3j:' + str(numba.typeof(3j)))
return tmp + 3j;

old_style_sample_jit = numba.jit('void(i1)')(old_style_sample)

numba.typeof(old_style_sample(42))

arg n: int32
literal 4: int32
tmp: int32
literal 3j:complex128
complex128

numba.typeof(old_style_sample_jit(42))

arg n: int32
literal 4: int32
tmp: int32
literal 3j:complex128
complex128


As can be seen, in both cases, Python and numba.jit, the results are the same. This is because numba.typeof is being evaluated with using the Python run-time.

If we use the inspect_types method on the jitted version, we will see that everything is in fact a pyobject

old_style_sample_jit.inspect_types()

old_style_sample (pyobject,) -> pyobject
--------------------------------------------------------------------------------
# --- LINE 1 ---

def old_style_sample(n):

# --- LINE 2 ---
# label 0
#   $0.1 = global(print: <built-in function print>) :: pyobject #$0.2 = const(<type 'str'>, arg n: )  :: pyobject
#   $0.3 = global(str: <type 'str'>) :: pyobject #$0.4 = global(numba: <module 'numba' from '/Users/jayvius/Projects/numba/numba/__init__.pyc'>)  :: pyobject
#   $0.5 = getattr(attr=typeof, value=$0.4)  :: pyobject
#   $0.6 = call$0.5(n, )  :: pyobject
#   $0.7 = call$0.3($0.6, ) :: pyobject #$0.8 = $0.2 +$0.7  :: pyobject
#   $0.9 = call$0.1($0.8, ) :: pyobject print('arg n: '+ str(numba.typeof(n))) # --- LINE 3 --- #$0.10 = global(print: <built-in function print>)  :: pyobject
#   $0.11 = const(<type 'str'>, literal 4: ) :: pyobject #$0.12 = global(str: <type 'str'>)  :: pyobject
#   $0.13 = global(numba: <module 'numba' from '/Users/jayvius/Projects/numba/numba/__init__.pyc'>) :: pyobject #$0.14 = getattr(attr=typeof, value=$0.13) :: pyobject #$0.15 = const(<type 'int'>, 4)  :: pyobject
#   $0.16 = call$0.14($0.15, ) :: pyobject #$0.17 = call $0.12($0.16, )  :: pyobject
#   $0.18 =$0.11 + $0.17 :: pyobject #$0.19 = call $0.10($0.18, )  :: pyobject

print('literal 4: ' + str(numba.typeof(4)))

# --- LINE 4 ---
#   $0.20 = const(<type 'int'>, 4) :: pyobject # tmp = n +$0.20  :: pyobject

tmp = n + 4;

# --- LINE 5 ---
#   $0.22 = global(print: <built-in function print>) :: pyobject #$0.23 = const(<type 'str'>, tmp: )  :: pyobject
#   $0.24 = global(str: <type 'str'>) :: pyobject #$0.25 = global(numba: <module 'numba' from '/Users/jayvius/Projects/numba/numba/__init__.pyc'>)  :: pyobject
#   $0.26 = getattr(attr=typeof, value=$0.25)  :: pyobject
#   $0.27 = call$0.26(tmp, )  :: pyobject
#   $0.28 = call$0.24($0.27, ) :: pyobject #$0.29 = $0.23 +$0.28  :: pyobject
#   $0.30 = call$0.22($0.29, ) :: pyobject print('tmp: '+ str(numba.typeof(tmp))) # --- LINE 6 --- #$0.31 = global(print: <built-in function print>)  :: pyobject
#   $0.32 = const(<type 'str'>, literal 3j:) :: pyobject #$0.33 = global(str: <type 'str'>)  :: pyobject
#   $0.34 = global(numba: <module 'numba' from '/Users/jayvius/Projects/numba/numba/__init__.pyc'>) :: pyobject #$0.35 = getattr(attr=typeof, value=$0.34) :: pyobject #$0.36 = const(<type 'complex'>, 3j)  :: pyobject
#   $0.37 = call$0.35($0.36, ) :: pyobject #$0.38 = call $0.33($0.37, )  :: pyobject
#   $0.39 =$0.32 + $0.38 :: pyobject #$0.40 = call $0.31($0.39, )  :: pyobject

print('literal 3j:' + str(numba.typeof(3j)))

# --- LINE 7 ---
#   $0.41 = const(<type 'complex'>, 3j) :: pyobject #$0.42 = tmp + $0.41 :: pyobject # return$0.42

return tmp + 3j;

================================================================================

Even more illustrating would be if locals was used to type an intermediate value:

old_style_sample_jit_2 = numba.jit('void(i1)', locals={'tmp': numba.float32})(old_style_sample)

numba.typeof(old_style_sample_jit_2(42))

arg n: int32
literal 4: int32
tmp: int32
literal 3j:complex128
complex128


The result seems to imply that tmp appears as an int32, but in fact is a pyobject and the whole function is being evaluated using the python run-time. So it is actually showing evaluating typeof at the runtime on the run-time value of tmp, which happens to be a Python int, translated into an int32 by numba.typeof. This can also be seen in the dump caused by the call to inspect_types.