12 Output the median after the samples are collected3ChatGPT 4ChatGPT 5Median #include #include #include auto median(std::vector& v) { std::ranges::sort(v); v[medianIndex]; } 6Evolution of a Median Algorithm Pete Isensee Engineering Director 7Goal 8 template constexpr auto median(Range&& rg) { // TODO // O(N) Projection = std::identity> constexpr auto median( ExecPolicy&& execPolicy, Range&& rg, Comparison comp = {}, Projection proj = {}) { // TODO }Median auto median(std::vector& v) { std::ranges::sort(v);

SIMD-style thinking to tackle some interesting problems • Intra-register sorting • Fast linear median-of-seven filter • Fast small-kernel convolution • Faster (?) UTF-8 to UTF-32 conversion (with vals5Copyright © 2020 Bob Steagall Fast Linear Median Filter 57 CppCon 2020 - Adventures in SIMD ThinkingCopyright © 2020 Bob Steagall K E W B C O M P U T I N G Fast Median Filter? • If we can sort two lanes of a fast median-of-seven linear filter • median: a value separating the higher half from the lower half of a data sample • If I have an array a of seven integers, and they are sorted, the median is a[3]

first > __stl_threshold) { RandomAccessIterator cut = __unguarded_partition (first, last, T(__median(*first, *(first + (last - first)/2), *(last - 1), first > __stl_threshold) { RandomAccessIterator cut = __unguarded_partition (first, last, T(__median(*first, *(first + (last - first)/2), *(last - 1), { quick sort loop(first cut comp); 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 (first, last, T(__median(*first, *(first + (last - first)/2), *(last - 1), template

ops with level parameter passed (GH545) • Ported skiplist data structure to C to speed up rolling_median by about 5-10x in most typical use cases (GH374) 8 Chapter 1. What’s New pandas: powerful Python Out[236]: -0.28367872471747613 In [237]: s[:3] Out[237]: a -0.284 b -1.537 c 0.163 In [238]: s[s > s.median()] Out[238]: a -0.284 c 0.163 In [239]: s[[4, 3, 1]] Out[239]: e -1.703 d -0.648 b -1.537 In non-null observations sum Sum of values mean Mean of values mad Mean absolute deviation median Arithmetic median of values min Minimum max Maximum abs Absolute Value prod Product of values std Unbiased

ops with level parameter passed (GH545) • Ported skiplist data structure to C to speed up rolling_median by about 5-10x in most typical use cases (GH374) 1.4 v.0.6.1 (December 13, 2011) 1.4.1 New features Out[236]: -0.28367872471747613 In [237]: s[:3] Out[237]: a -0.284 b -1.537 c 0.163 In [238]: s[s > s.median()] Out[238]: a -0.284 c 0.163 In [239]: s[[4, 3, 1]] Out[239]: e -1.703 d -0.648 b -1.537 In non-null observations sum Sum of values mean Mean of values mad Mean absolute deviation median Arithmetic median of values min Minimum max Maximum abs Absolute Value prod Product of values std Unbiased

ops with level parameter passed (GH545) • Ported skiplist data structure to C to speed up rolling_median by about 5-10x in most typical use cases (GH374) 1.5 v.0.6.1 (December 13, 2011) 1.5.1 New features Out[236]: -0.28367872471747613 In [237]: s[:3] Out[237]: a -0.284 b -1.537 c 0.163 In [238]: s[s > s.median()] Out[238]: a -0.284 c 0.163 In [239]: s[[4, 3, 1]] Out[239]: e -1.703 d -0.648 b -1.537 In non-null observations sum Sum of values mean Mean of values mad Mean absolute deviation median Arithmetic median of values min Minimum max Maximum abs Absolute Value prod Product of values std Unbiased

improvements • Improved implementation of rolling min and max (thanks to Bottleneck !) • Add accelerated ’median’ GroupBy option (GH1358) • Significantly improve the performance of parsing ISO8601-format date ops with level parameter passed (GH545) • Ported skiplist data structure to C to speed up rolling_median by about 5-10x in most typical use cases (GH374) 1.15 v.0.6.1 (December 13, 2011) 1.15.1 New features 3443118127316671 In [13]: s[:3] Out[13]: a -1.344 b 0.845 c 1.076 dtype: float64 In [14]: s[s > s.median()] Out[14]: c 1.076 e 1.644 dtype: float64 In [15]: s[[4, 3, 1]] Out[15]: e 1.644 d -0.109 b

improvements • Improved implementation of rolling min and max (thanks to Bottleneck !) • Add accelerated ’median’ GroupBy option (GH1358) • Significantly improve the performance of parsing ISO8601-format date ops with level parameter passed (GH545) • Ported skiplist data structure to C to speed up rolling_median by about 5-10x in most typical use cases (GH374) 1.16 v.0.6.1 (December 13, 2011) 1.16.1 New features 87590640278094278 In [13]: s[:3] Out[13]: a 0.876 b -2.211 c 0.974 dtype: float64 In [14]: s[s > s.median()] Out[14]: a 0.876 c 0.974 dtype: float64 In [15]: s[[4, 3, 1]] Out[15]: e -0.410 d -2.007

improvements • Improved implementation of rolling min and max (thanks to Bottleneck !) • Add accelerated ’median’ GroupBy option (GH1358) • Significantly improve the performance of parsing ISO8601-format date ops with level parameter passed (GH545) • Ported skiplist data structure to C to speed up rolling_median by about 5-10x in most typical use cases (GH374) 1.13 v.0.6.1 (December 13, 2011) 1.13.1 New features -1.3443118127316671 In [13]: s[:3] a -1.344 b 0.845 c 1.076 dtype: float64 In [14]: s[s > s.median()] c 1.076 e 1.644 dtype: float64 In [15]: s[[4, 3, 1]] e 1.644 d -0.109 b 0.845 dtype: float64

Optimizing Dynamically-Typed Object- Oriented Languages With Polymorphic Inline Caches PICs achieve a median speedup of 11%. As an important side effect, PICs collect type information by recording all of generate better code when recompiling a method. An experimental version of such a system achieves a median speedup of 27% for our set of SELF programs, reducing the number of non-inlined message sends by Optimizing Dynamically-Typed Object- Oriented Languages With Polymorphic Inline Caches PICs achieve a median speedup of 11%. As an important side effect, PICs collect type information by recording all of