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1

Dynamic languages for interactive math…

The two-language approach: High-level dynamic language for productivity, + low-level language (C, Fortran, Cython, …) for performance-critical code. = Huge jump in complexity, loss of generality.

2

Just vectorize your code?

= rely on mature external libraries,

• perating on large blocks of data,

for performance-critical code

Good advice! But…

• Someone has to write those libraries.
• Eventually that person will be you.

— some problems are impossible or just very awkward to vectorize.

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7

Special Functions in Julia

Special functions s(x): classic case that cannot be vectorized well … switch between various polynomials depending on x

Many of Julia’s special functions come from the usual C/Fortran libraries, but some are written in pure Julia code.

Pure Julia erfinv(x) [ = erf–1(x) ] 3–4× faster than Matlab’s and 2–3× faster than SciPy’s (Fortran Cephes). Pure Julia polygamma(m, z) [ = (m+1)th derivative of the ln Γ function ] ~ 2× faster than SciPy’s (C/Fortran) for real z … and unlike SciPy’s, same code supports complex argument z

Julia code can actually be faster than typical “optimized” C/Fortran code, by using techniques [metaprogramming/codegen generation] that are hard in a low-level language.

8

Why can Julia be fast?

First need to understand: Why is Python slow? goto Jupyter/IJulia notebooks from 18.S096.

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MIT OpenCourseWare https://ocw.mit.edu

6.172 Performance Engineering of Software Systems

Fall 2018 For information about citing these materials or our Terms of Use, visit: https://ocw.mit.edu/terms.

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