Python is a fantastic glue language but with Numba it can also be a high-performance language. Numba compiles a subset of Python to low-level machine code and makes it easy to take NumPy-based data and transform it extremely quickly.
in Biomedical Engineering • MS/BS degrees in Elec. Comp. Engineering • Creator of SciPy (1998-2001) • Professor at BYU (2001-2007) • Author of NumPy (2005-2012) • Started Numba (2012) • Founding Chair of Numfocus / PyData • Current Python Software Foundation Director
about 97% of the time: premature optimization is the root of all evil. Yet we should not pass up our opportunities in that critical 3%" - Donald E. Knuth
Free and Open Source, Permissive License • Broad and friendly community • Over 36,000 packages on PyPI • Commercial Support • Many conferences (PyData, SciPy, PyCon...) • Executable pseudo-code • Can understand and edit code a year later • Fun to develop • Use of Indentation IPython • Interactive prompt on steroids (Notebook) • Allows less working memory • Allows failing quickly for exploration • List comprehensions • Iterator protocol and generators • Meta-programming • Introspection • (JIT Compiler and Concurrency) • Internet (FTP, HTTP, SMTP, XMLRPC) • Compression and Databases • Logging, unit-tests • Glue for other languages • Distribution has much, much more....
is developer time (both to create and to maintain) • Code that respects developer time is: - Easy to read - Easy to understand - Easy to modify • But execution speed does matter at times: Then what do you do?
the most important things you can do are: 1. Use proﬁling to understand where your program spends time. (Most of your code is irrelevant with respect to time spent. Only worry about the parts that matter.) I like the line-proﬁler kernprof.py binstar search -t conda line_proﬁler 2. Leverage NumPy-stack when working with data. 3. Use Numba to optimize hot-spots 4. Occasionally use Cython (especially for libraries).
together with array-level operations (e.g. NumPy or Pandas) (column-oriented is a subset of array-oriented) • Don’t use a lot of little small objects Object Attr1 Attr2 Attr3 Object Attr1 Attr2 Attr3 Object Attr1 Attr2 Attr3 Object Attr1 Attr2 Attr3 Object Attr1 Attr2 Attr3 Object Attr1 Attr2 Attr3 Attr1 Attr2 Attr3 Object1 Object2 Object3 Object4 Object5 Object6
arrays with your data (remember Pandas uses NumPy under-the-covers, so this applies to Pandas). Numba makes it easy to write simple functions that are fast that work with that data. • Numba is an open source Just-In-Time compiler for Python functions. • From the types of the function arguments, Numba can often generate a specialized, fast, machine code implementation at runtime. • Designed to work best with numerical code and NumPy arrays. • Uses the LLVM library as the compiler backend.
X (10.7 and later), and Linux - 32 and 64-bit x86 CPUs and NVIDIA GPUs - Python 2 and 3 - NumPy versions 1.6 through 1.9 • It does not require a C/C++ compiler on the user’s system. • Requires less than 70 MB to install. • Does not replace the standard Python interpreter (it’s just another module — all of your existing Python libraries are still available)
information (fastest to call at run-time) • without arguments --- detects input types, infers output, generates code if needed, and dispatches (a little more run- time call overhead) #@jit('void(double[:,:], double, double)') #@jit def numba_update(u, dx2, dy2): nx, ny = u.shape for i in xrange(1,nx-1): for j in xrange(1, ny-1): u[i,j] = ((u[i+1,j] + u[i-1,j]) * dy2 + (u[i,j+1] + u[i,j-1]) * dx2) / (2*(dx2+dy2)) # un-comment one of the ‘jit’ lines
image.shape m, n = filt.shape for i in range(m//2, M-m//2): for j in range(n//2, N-n//2): result = 0.0 for k in range(m): for l in range(n): result += image[i+k-m//2,j+l-n//2]*filt[k, l] output[i,j] = result ~800x speed-up
element-by-element over entire arrays Write kernels in Python! from numba import vectorize from math import sin @vectorize([‘f8(f8)’, ‘f4(f4)’]) def sinc(x): if x==0.0: return 1.0 else: return sin(x*pi)/(pi*x)
core of NumPy’s calculation element-by-element infrastructure • It’s how +,-,*,/, **, sin, cos, etc. work • It is not how linear-algebra calcs work (typically) — though see generalized ufuncs for a way.
the ﬁrst libraries I wrote • extended “umath” module by adding new “universal functions” to compute many scientiﬁc functions by wrapping C and Fortran libs. • Bessel functions are solutions to a differential equation: x 2 d 2 y dx 2 + x dy dx + ( x 2 ↵ 2) y = 0 y = J↵ ( x ) Jn (x) = 1 ⇡ Z ⇡ 0 cos (n⌧ x sin (⌧)) d⌧
10000 loops, best of 3: 75 us per loop In [7]: from scipy.special import j0 In [8]: %timeit j0(x) 10000 loops, best of 3: 75.3 us per loop But! Now code is in Python and can be experimented with more easily (and moved to the GPU / accelerator more easily)!
or efﬁcient array expression or ufunc. Use Numba to work with array elements directly. • Example: Suppose you have a boolean grid and you want to ﬁnd the maximum number neighbors a cell has in the grid: 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 3 2 1 2 2 1 1 2 1 2 2 2 2 2 1 1 1 1 1 1 1 1
purely as array operations (and even if you do, it is likely unreadable to non-NumPy experts). • Numba let’s you write out the loops, but avoid the penalty for having to loop over individual elements in 169x faster!
levels of optimization when compiling a function: - “object mode”: supports nearly all of Python, but generally cannot speed up code by a large factor (exception: see next slide) - “nopython mode”: supports a subset of Python, but runs at C/C++/FORTRAN speeds
loops and compile them in nopython mode. • Works great for functions that are bookended by uncompilable code, but have a compilable core loop. • All happens automatically.
else, while, for, range • NumPy arrays, int, ﬂoat, complex, booleans, and tuples • Almost all arithmetic, logical, and bitwise operators as well as functions from the math and numpy modules • Nearly all NumPy dtypes: int, ﬂoat, complex, datetime64, timedelta64 • Array element access (read and write) • Array reduction functions: sum, prod, max, min, etc • Calling other nopython mode compiled functions • Calling ctypes or cfﬁ-wrapped external functions
= cuda.shared.array(shape=(tpb, tpb), dtype=f4) sB = cuda.shared.array(shape=(tpb, tpb), dtype=f4) tx = cuda.threadIdx.x ty = cuda.threadIdx.y bx = cuda.blockIdx.x by = cuda.blockIdx.y bw = cuda.blockDim.x bh = cuda.blockDim.y x = tx + bx * bw y = ty + by * bh acc = 0. for i in range(bpg): if x < n and y < n: sA[ty, tx] = A[y, tx + i * tpb] sB[ty, tx] = B[ty + i * tpb, x] cuda.syncthreads() if x < n and y < n: for j in range(tpb): acc += sA[ty, j] * sB[j, tx] cuda.syncthreads() if x < n and y < n: C[y, x] = acc bpg = 50 tpb = 32 n = bpg * tpb A = np.array(np.random.random((n, n)), dtype=np.float32) B = np.array(np.random.random((n, n)), dtype=np.float32) C = np.empty_like(A) stream = cuda.stream() with stream.auto_synchronize(): dA = cuda.to_device(A, stream) dB = cuda.to_device(B, stream) dC = cuda.to_device(C, stream) cu_square_matrix_mul[(bpg, bpg), (tpb, tpb), stream](dA, dB, dC) dC.to_host(stream)
input. - Great for inserting a user-provided math expression into a larger algorithm, while still achieving C speeds. • Optimization (least squares, etc) libraries that can recompile themselves to inline a speciﬁc objective function right into the algorithm • Multithreaded calculation without having to worry about the global interpreter lock (GIL).
f4, f4, uint32, uint32, uint32)' @vectorize([sig], target='gpu') def mandel(tid, min_x, max_x, min_y, max_y, width, height, iters): pixel_size_x = (max_x - min_x) / width pixel_size_y = (max_y - min_y) / height x = tid % width y = tid / width real = min_x + x * pixel_size_x imag = min_y + y * pixel_size_y c = complex(real, imag) z = 0.0j for i in range(iters): z = z * z + c if (z.real * z.real + z.imag * z.imag) >= 4: return i return 255 Kind Time Speed-up Python 263.6 1.0x CPU 2.639 100x GPU 0.1676 1573x Tesla S2050
• Achieve the same speeds as compiled languages for numerical and array-processing code. • Can be used to create advanced workﬂows where user input drives compilation at runtime. • NumbaPro is part of Anaconda Accelerate and adds more features. • Numba is open source, available at: http://numba.pydata.org/ • Or: conda install numba