double y0, double timestep) { auto k1 = fun(time, y0); auto k2 = fun(time + timestep * 0.5, y0 + k1 * timestep * 0.5); auto k3 = fun(time + timestep * 0.5, y0 + k2 * * timestep * 0.5); auto k4 = fun(time + timestep, y0 + k3 * timestep); return (y0 + (k1 + 2 * k2 + 2 * k3 + k4) * timestep / 6); } double stateOut = common::math::runge_kutta4(derivFun 1, 6> y0, double timestep) { auto k1 = fun(time, y0); auto k2 = fun(time + timestep * 0.5, y0 + k1 * timestep * 0.5); auto k3 = fun(time + timestep * 0.5, y0 + k2 *

parameter Does not throw exceptions when called If k1 == k2 ➡ hash()(k1) == hash()(k2) If k1 != k2 ➡ the probability that hash()(k1) == hash()(k2) 
 should be very small, approaching std::string lastName; int age; // ... std::size_t hash_code() const { std::size_t k1 = std::hash{}(firstName); std::size_t k2 = std::hash{}(lastName); std::size_t k1 = std::hash{}(firstName); std::size_t k2 = std::hash{}(lastName); std::size_t k3 = std::hash{}(age); } }; 🤔 return hash_combine(k1, k2, k3);

- Adventures in SIMD Thinking 5 S = s0 s1 s2 s3 s4 s5 s6 ... K = k0 k1 k2 r0 = ... r1 = s0k0 + s1k1 + s2k2 r2 = s1k0 + s2k1 + s3k2 r3 = s2k0 s5 s6 ... k0 k1 k2 r2 = s0 s1 s2 s3 s4 s5 s6 ... k0 k1 k2 r3 = s0 s1 s2 s3 s4 s5 s6 ... k0 k1 k2 r4 = s0 s1 s2 s3 s4 s5 s6 ... k0 k1 k2 r5 = s0 s1 s2 s3 s4 s5 s6 ... k0 k1 k2 Convolution CppCon 2020 - Adventures in SIMD Thinking 6Copyright © 2020

= [&]( const value_type a, const value_type sign) { const value_type k1 = da_dt(a, sign ); const value_type a1 = a + dt / two ∗ k1; const value_type k2 = da_dt(a1 , sign ); const value_type a2 = a + const value_type a3 = a + dt ∗ k3; const value_type k4 = da_dt(a3 , sign ); return a + dt / six ∗ (k1 + k2 + k2 + k3 + k3 + k4); }; CppCon - Vincent Reverdy - September 20th, 2024 - Aurora, Colorado Runge-Kutta of order 4 (RK4) Equations k1 = f(tn, yn) k2 = f � tn + h 2 , yn + h k1 2 � k3 = f � tn + h 2 , yn + h k2 2 � k4 = f(tn + h, yn + hk3) yn+1 = yn + h 6 (k1 + 2k2 + 2k3 + k4) tn+1 = tn +

copyIdx copyDone size slots newTable K1 V1 K2 V2 K3 V3 K4 V4 Table pairs CHM copyIdx copyDone size slots newTable K1 V1 K2 V2 K3 V3 K4 V4 K5 V5 K6 V6 K7 V7 K8 V8 K1 V1 K2 V2 1.dat 2.dat 3.dat Table copyIdx copyDone size slots newTable K1 V1 K2 V2 K3 V3 K4 V4 Table pairs CHM copyIdx copyDone size slots newTable K1 V1 K2 V2 K3 V3 K4 V4 K5 V5 K6 V6 K7 V7 K8 V8 K1 V1 K2 V2 1.dat 2.dat 3.dat Table copyIdx copyDone size slots newTable K1 V1 K2 V2 K3 V3 K4 V4 Table pairs CHM copyIdx copyDone size slots newTable K1 V1 K2 V2 K3 V3 K4 V4 K5 V5 K6 V6 K7 V7 K8 V8 K1 V1 K2 V2 1.dat 2.dat 3.dat Table

factor counts In Big O, we care about asymptotic analysis, when n → ∞ Thus, for example: t(n) = k1∙ n ∙ log(n) + k2 ∙ n ∈ O(n ∙ log(n)) 19 Algorithmic Complexity @ CppCon 2021 Only the dominating factor counts In Big O, we care about asymptotic analysis, when n → ∞ Thus, for example: t(n) = k1∙ n ∙ log(n) + k2 ∙ n ∈ O(n ∙ log(n)) 20Algorithmic Complexity @ CppCon 2021 Only the dominating factor counts In Big O, we care about asymptotic analysis, when n → ∞ Thus, for example: t(n) = k1∙ n ∙ log(n) + k2 ∙ n ∈ O(n ∙ log(n)) 21 Algorithmic Complexity @ CppCon 2021 Not in this talk.

reserved. So, there are seven ways to declare/initialize an int, right? [N. Josuttis] • int k0; • int k1 = 42; • int k2( 42 ); • int k3 = int( ); • int k4{ 42 }; • int k5{ }; • int k6 = { 42 }; • int

更好地处理频繁的重排序操作。如下面的例程所示，这使得它更适 用于实现各种 LRU 缓存。 • 对于OrderedDict ，相等操作检查匹配顺序。 常规的dict 可以使用 p == q and all(k1 == k2 for k1, k2 in zip(p, q)) 进行模拟 顺序相等性测试。 • OrderedDict 类的 popitem() 方法有不同的签名。它接受一个可选参数来指定弹出哪个元素。 常规的dict . >>> k1, k2 = T(), T() >>> d = weakref.WeakKeyDictionary() >>> d[k1] = 1 # d = {k1: 1} >>> d[k2] = 2 # d = {k1: 2} >>> del k1 # d = {} 一种变通做法是在重新赋值之前先移除键: >>> class T(str): pass ... >>> k1, k2 = T() T(), T() >>> d = weakref.WeakKeyDictionary() >>> d[k1] = 1 # d = {k1: 1} >>> del d[k1] >>> d[k2] = 2 # d = {k2: 2} >>> del k1 # d = {k2: 2} 在 3.9 版更改: 增加了对 | 和 |= 运算符的支持，相关说明见 PEP 584。 WeakKeyDictionary

更好地处理频繁的重排序操作。如下面的例程所示，这使得它更适用于 实现各种 LRU 缓存。 • 对于OrderedDict ，相等操作检查匹配顺序。 常规的dict 可以使用 p == q and all(k1 == k2 for k1, k2 in zip(p, q)) 进行模拟顺 序相等性测试。 • OrderedDict 类的 popitem() 方法有不同的签名。它接受一个可选参数来指定弹出哪个元素。 常规的dict . >>> k1, k2 = T(), T() >>> d = weakref.WeakKeyDictionary() >>> d[k1] = 1 # d = {k1: 1} >>> d[k2] = 2 # d = {k1: 2} >>> del k1 # d = {} 一种变通做法是在重新赋值之前先移除键: >>> class T(str): pass ... >>> k1, k2 = T() T(), T() >>> d = weakref.WeakKeyDictionary() >>> d[k1] = 1 # d = {k1: 1} >>> del d[k1] >>> d[k2] = 2 # d = {k2: 2} >>> del k1 # d = {k2: 2} 在 3.9 版更改: 增加了对 | 和 |= 运算符的支持，相关说明见 PEP 584。 WeakKeyDictionary

更好地处理频繁的重排序操作。如下面的例程所示，这使得它更适用 于实现各种 LRU 缓存。 • 对于OrderedDict ，相等操作检查匹配顺序。 常规的dict 可以使用 p == q and all(k1 == k2 for k1, k2 in zip(p, q)) 进行模拟顺序相 等性测试。 • OrderedDict 类的 popitem() 方法有不同的签名。它接受一个可选参数来指定弹出哪个元素。 常规的dict 的对应条目: >>> class T(str): pass ... >>> k1, k2 = T(), T() >>> d = weakref.WeakKeyDictionary() >>> d[k1] = 1 # d = {k1: 1} >>> d[k2] = 2 # d = {k1: 2} >>> del k1 # d = {} 一种变通做法是在重新赋值之前先移除键: 270 Chapter >>> class T(str): pass ... >>> k1, k2 = T(), T() >>> d = weakref.WeakKeyDictionary() >>> d[k1] = 1 # d = {k1: 1} >>> del d[k1] >>> d[k2] = 2 # d = {k2: 2} >>> del k1 # d = {k2: 2} 在 3.9 版本发生变更: 增加了对