const auto [ a, b ] = split_bits( ab ); const auto [ c, d ] = split_bits( cd ); auto x = a; auto y = b;a b a d a c a f a e b 1 b 0 b 3 b 2 b 5 b 4 b 7 b 6 b 9 b 8 b b b a b d b c b auto y = b;a b a d a c a f a e b 1 b 0 b 3 b 2 b 5 b 4 b 7 b 6 b 9 b 8 b b b a b d b c b f b e c 1 c 0 c 3 c 2 c 5 c 4 c 7 c 6 c 9 c 8 c b c a c d c c while ( y != y y.max_value ) ++y; while ( y != y.max_value ) ++y; const auto [ a, b ] = split_bits( ab ); const auto [ c, d ] = split_bits( cd ); auto x = a; auto y = b;a b a d a c a f a e b 1 b 0 b 3 b 2

beta, A.get_data(), inc_x_y, A.get_data(), inc_x_y); } # include void armpl_sgerb(....){ sgerb_(&m, &n, &alpha, x.get_data(), &inc_x_y, y.get_data(), &inc_x_y, &beta, A.get_data(), &m); beta, A.get_data(), inc_x_y, A.get_data(), inc_x_y); } # include void armpl_sgerb(....){ sgerb_(&m, &n, &alpha, x.get_data(), &inc_x_y, y.get_data(), &inc_x_y, &beta, A.get_data(), &m); cblas_sger(CblasColMajor, x.m, y.n, alpha, x.get_data(), 1, y.get_data(), 1, A.get_data(), R.m); cblas_saxpy(m * n, beta, A.get_data(), inc_x_y, A.get_data(), inc_x_y); } TA Simple Computation 1

Programming Models Outlook Summary Arithmetic & math 1 void f(std::simd x, 2 std::simd y) { 3 x += y; // x.size() additions 4 x = sqrt(x); // x.size() square roots 5 ... // etc. all operators += += += += += += += += += += += += += += += += += += += += += += += x0 x1 x2 x3 += += += += y0 y1 y2 y3 Matthias Kretz CppCon ’23 17 GSI Helmholtz Center for Heavy Ion ResearchMotivation std::simd std::simd y) { 2 if (x < y) { x = y; } // nonono, you don’t write ’if (truefalsetruetrue)’ either 3 x = simd_select(x < y, y, x); // x = y but only for the elements where x < y 4 if (all_of(x < y)) {..

float* x, float* y) { for (int i = 0; i < n; i++) y[i] = x[i] + y[i]; } TEST_CASE("cppcon-0", "[CUDA]") { int N = 1 << 20; float* x = new float[N]; float* y = new float[N]; for (int i = 0; i < N; i++) { x[i] = 1.0f; y[i] = 2.0f; } add_cpu(N, x, y); delete[] x; delete[] y; } An Even Easier Introduction to CUDA 4 |TEST_CASE("cppcon-1" 1 << 20; float* x; float* y; cudaMallocManaged(&x, N*sizeof(float)); cudaMallocManaged(&y, N*sizeof(float)); // … cudaFree(x); cudaFree(y); } An Even Easier Introduction to

branching 61 uint32_t fn(uint32_t x, uint32_t y, size_t cond) { if (cond == 27) return (x << 4) + y; else return (x >> 1) - y; } uint32_t res = fn1(x, y, 42); cmp rdx, 27 jne L_0F mov eax, edi shl branching 62 uint32_t fn(uint32_t x, uint32_t y, size_t cond) { if (cond == 27) return (x << 4) + y; else return (x >> 1) - y; } uint32_t res = fn1(x, y, 42); cmp rdx, 27 jne L_0F mov eax, edi shl branching 63 uint32_t fn(uint32_t x, uint32_t y, size_t cond) { if (cond == 27) return (x << 4) + y; else return (x >> 1) - y; } uint32_t res = fn1(x, y, 42); cmp rdx, 27 jne L_0F mov eax, edi shl

{P}C{Q} If precondition P is met, executing C establishes postcondition Q {x > 0, x < INT_MAX} y = x + 1 {y > 1}© 2023 Adobe. All Rights Reserved. Hoare Logic | Preconditions and Postconditions 9 Tony {P}C{Q} If precondition P is met, executing C establishes postcondition Q {x > 0, x < INT_MAX} y = x + 1 {y > 1}© 2023 Adobe. All Rights Reserved. Hoare Logic | Preconditions and Postconditions 9 Tony {P}C{Q} If precondition P is met, executing C establishes postcondition Q {x > 0, x < INT_MAX} y = x + 1 {y > 1}© 2023 Adobe. All Rights Reserved. Hoare Logic | Preconditions and Postconditions 9 Tony

constexpr rk4(T t, T y, auto dy_dt , T dt) { // Step 1 const T t1 = t; const T y1 = y; const T k1 = dy_dt(t1 , y1); // Step 2 const value_type t2 = t + dt / 2; const value_type y2 = y + dt / 2 ∗ k1; const dy_dt(t2 , y2); // Step 3 const value_type t3 = t + dt / 2; const value_type y3 = y + dt / 2 ∗ k2; const value_type k3 = dy_dt(t3 , y3); // Step 4 const value_type t4 = t + dt; const value_type y4 = y + dt dt ∗ k3; const value_type k4 = dy_dt(t3 , y3); // Result return y + dt / 6 ∗ (k1 + 2 ∗ k2 + 2 ∗ k3 + k4); }; Sequentiality Every intermediate step k depends on the previous one! CppCon - Vincent

instance = new PlottingSingleton; return instance; } void plot(double x, double y) { // ... } protected: PlottingSingleton(); private: inline static PlottingSingleton* static PlottingSingleton instance {}; return instance; } void plot(double x, double y) { // ... } private: PlottingSingleton(); }; Original Code – Design Patterns } private: Singleton(); }; class Plotting { public: void plot(double x, double y) { // ... } }; using PlottingSingleton = Singleton; Original Code – Singleton

{ q.w() } -> std::same_as; { q.x() } -> std::same_as; { q.y() } -> std::same_as; { q.z() } -> std::same_as; };Supporting S; private: Scalar w_, x_, y_, z_; // ... Constructors // ... Accessors }“Standard” Quaternion Type: Constructors Quat() = default; Quat(Scalar w, Scalar x, Scalar y, Scalar z) noexcept(std::is : w_(w), x_(x), y_(y), z_(z) {} Quat(Scalar && w, Scalar && x, Scalar && y, Scalar && z) noexcept(std::is_nothrow_move_constructible_v) : w_(move(w)), x_(move(x)), y_(move(y)), z_(move(z)) {}

implicit) void add_array(double* x, double* y, double* z, int size) { for (int i = 0; i < size; ++i) z[i] = x[i] + y[i]; } void add_array(double* x, double* y, double* z, int size) { for (int i = 0; 0; i < size; i += simd_size) simd_value(z[i]) = simd_value(x[i]) simd_op(+) simd_value(y[i]); }▪ Requirement to fundamentally re-engineer CFD software for extreme-scale parallel computing platforms was simd_value(x[i]) simd_op(+) simd_value(y[i]); simd_type operator+(simd_type x, simd_type y) { return simd_add(x, y); }Vectorzation: The loop body No vector type information in x, y, z or i →Explicit load and