| //===----------------------------------------------------------------------===// |
| // |
| // The LLVM Compiler Infrastructure |
| // |
| // This file is dual licensed under the MIT and the University of Illinois Open |
| // Source Licenses. See LICENSE.TXT for details. |
| // |
| //===----------------------------------------------------------------------===// |
| |
| // <random> |
| |
| // template<class RealType = double> |
| // class piecewise_linear_distribution |
| |
| // template<class _URNG> result_type operator()(_URNG& g); |
| |
| #include <iostream> |
| |
| #include <random> |
| #include <vector> |
| #include <iterator> |
| #include <numeric> |
| #include <cassert> |
| |
| template <class T> |
| inline |
| T |
| sqr(T x) |
| { |
| return x*x; |
| } |
| |
| double |
| f(double x, double a, double m, double b, double c) |
| { |
| return a + m*(sqr(x) - sqr(b))/2 + c*(x-b); |
| } |
| |
| int main() |
| { |
| { |
| typedef std::piecewise_linear_distribution<> D; |
| typedef D::param_type P; |
| typedef std::mt19937_64 G; |
| G g; |
| double b[] = {10, 14, 16, 17}; |
| double p[] = {0, 1, 1, 0}; |
| const size_t Np = sizeof(p) / sizeof(p[0]) - 1; |
| D d(b, b+Np+1, p); |
| const int N = 1000000; |
| std::vector<D::result_type> u; |
| for (int i = 0; i < N; ++i) |
| { |
| D::result_type v = d(g); |
| assert(d.min() <= v && v < d.max()); |
| u.push_back(v); |
| } |
| std::sort(u.begin(), u.end()); |
| int kp = -1; |
| double a; |
| double m; |
| double bk; |
| double c; |
| std::vector<double> areas(Np); |
| double S = 0; |
| for (int i = 0; i < areas.size(); ++i) |
| { |
| areas[i] = (p[i]+p[i+1])*(b[i+1]-b[i])/2; |
| S += areas[i]; |
| } |
| for (int i = 0; i < areas.size(); ++i) |
| areas[i] /= S; |
| for (int i = 0; i < Np+1; ++i) |
| p[i] /= S; |
| for (int i = 0; i < N; ++i) |
| { |
| int k = std::lower_bound(b, b+Np+1, u[i]) - b - 1; |
| if (k != kp) |
| { |
| a = 0; |
| for (int j = 0; j < k; ++j) |
| a += areas[j]; |
| m = (p[k+1] - p[k]) / (b[k+1] - b[k]); |
| bk = b[k]; |
| c = (b[k+1]*p[k] - b[k]*p[k+1]) / (b[k+1] - b[k]); |
| kp = k; |
| } |
| assert(std::abs(f(u[i], a, m, bk, c) - double(i)/N) < .001); |
| } |
| } |
| { |
| typedef std::piecewise_linear_distribution<> D; |
| typedef D::param_type P; |
| typedef std::mt19937_64 G; |
| G g; |
| double b[] = {10, 14, 16, 17}; |
| double p[] = {0, 0, 1, 0}; |
| const size_t Np = sizeof(p) / sizeof(p[0]) - 1; |
| D d(b, b+Np+1, p); |
| const int N = 1000000; |
| std::vector<D::result_type> u; |
| for (int i = 0; i < N; ++i) |
| { |
| D::result_type v = d(g); |
| assert(d.min() <= v && v < d.max()); |
| u.push_back(v); |
| } |
| std::sort(u.begin(), u.end()); |
| int kp = -1; |
| double a; |
| double m; |
| double bk; |
| double c; |
| std::vector<double> areas(Np); |
| double S = 0; |
| for (int i = 0; i < areas.size(); ++i) |
| { |
| areas[i] = (p[i]+p[i+1])*(b[i+1]-b[i])/2; |
| S += areas[i]; |
| } |
| for (int i = 0; i < areas.size(); ++i) |
| areas[i] /= S; |
| for (int i = 0; i < Np+1; ++i) |
| p[i] /= S; |
| for (int i = 0; i < N; ++i) |
| { |
| int k = std::lower_bound(b, b+Np+1, u[i]) - b - 1; |
| if (k != kp) |
| { |
| a = 0; |
| for (int j = 0; j < k; ++j) |
| a += areas[j]; |
| m = (p[k+1] - p[k]) / (b[k+1] - b[k]); |
| bk = b[k]; |
| c = (b[k+1]*p[k] - b[k]*p[k+1]) / (b[k+1] - b[k]); |
| kp = k; |
| } |
| assert(std::abs(f(u[i], a, m, bk, c) - double(i)/N) < .001); |
| } |
| } |
| { |
| typedef std::piecewise_linear_distribution<> D; |
| typedef D::param_type P; |
| typedef std::mt19937_64 G; |
| G g; |
| double b[] = {10, 14, 16, 17}; |
| double p[] = {1, 0, 0, 0}; |
| const size_t Np = sizeof(p) / sizeof(p[0]) - 1; |
| D d(b, b+Np+1, p); |
| const int N = 1000000; |
| std::vector<D::result_type> u; |
| for (int i = 0; i < N; ++i) |
| { |
| D::result_type v = d(g); |
| assert(d.min() <= v && v < d.max()); |
| u.push_back(v); |
| } |
| std::sort(u.begin(), u.end()); |
| int kp = -1; |
| double a; |
| double m; |
| double bk; |
| double c; |
| std::vector<double> areas(Np); |
| double S = 0; |
| for (int i = 0; i < areas.size(); ++i) |
| { |
| areas[i] = (p[i]+p[i+1])*(b[i+1]-b[i])/2; |
| S += areas[i]; |
| } |
| for (int i = 0; i < areas.size(); ++i) |
| areas[i] /= S; |
| for (int i = 0; i < Np+1; ++i) |
| p[i] /= S; |
| for (int i = 0; i < N; ++i) |
| { |
| int k = std::lower_bound(b, b+Np+1, u[i]) - b - 1; |
| if (k != kp) |
| { |
| a = 0; |
| for (int j = 0; j < k; ++j) |
| a += areas[j]; |
| m = (p[k+1] - p[k]) / (b[k+1] - b[k]); |
| bk = b[k]; |
| c = (b[k+1]*p[k] - b[k]*p[k+1]) / (b[k+1] - b[k]); |
| kp = k; |
| } |
| assert(std::abs(f(u[i], a, m, bk, c) - double(i)/N) < .001); |
| } |
| } |
| { |
| typedef std::piecewise_linear_distribution<> D; |
| typedef D::param_type P; |
| typedef std::mt19937_64 G; |
| G g; |
| double b[] = {10, 14, 16}; |
| double p[] = {0, 1, 0}; |
| const size_t Np = sizeof(p) / sizeof(p[0]) - 1; |
| D d(b, b+Np+1, p); |
| const int N = 1000000; |
| std::vector<D::result_type> u; |
| for (int i = 0; i < N; ++i) |
| { |
| D::result_type v = d(g); |
| assert(d.min() <= v && v < d.max()); |
| u.push_back(v); |
| } |
| std::sort(u.begin(), u.end()); |
| int kp = -1; |
| double a; |
| double m; |
| double bk; |
| double c; |
| std::vector<double> areas(Np); |
| double S = 0; |
| for (int i = 0; i < areas.size(); ++i) |
| { |
| areas[i] = (p[i]+p[i+1])*(b[i+1]-b[i])/2; |
| S += areas[i]; |
| } |
| for (int i = 0; i < areas.size(); ++i) |
| areas[i] /= S; |
| for (int i = 0; i < Np+1; ++i) |
| p[i] /= S; |
| for (int i = 0; i < N; ++i) |
| { |
| int k = std::lower_bound(b, b+Np+1, u[i]) - b - 1; |
| if (k != kp) |
| { |
| a = 0; |
| for (int j = 0; j < k; ++j) |
| a += areas[j]; |
| m = (p[k+1] - p[k]) / (b[k+1] - b[k]); |
| bk = b[k]; |
| c = (b[k+1]*p[k] - b[k]*p[k+1]) / (b[k+1] - b[k]); |
| kp = k; |
| } |
| assert(std::abs(f(u[i], a, m, bk, c) - double(i)/N) < .001); |
| } |
| } |
| { |
| typedef std::piecewise_linear_distribution<> D; |
| typedef D::param_type P; |
| typedef std::mt19937_64 G; |
| G g; |
| double b[] = {10, 14}; |
| double p[] = {1, 1}; |
| const size_t Np = sizeof(p) / sizeof(p[0]) - 1; |
| D d(b, b+Np+1, p); |
| const int N = 1000000; |
| std::vector<D::result_type> u; |
| for (int i = 0; i < N; ++i) |
| { |
| D::result_type v = d(g); |
| assert(d.min() <= v && v < d.max()); |
| u.push_back(v); |
| } |
| std::sort(u.begin(), u.end()); |
| int kp = -1; |
| double a; |
| double m; |
| double bk; |
| double c; |
| std::vector<double> areas(Np); |
| double S = 0; |
| for (int i = 0; i < areas.size(); ++i) |
| { |
| areas[i] = (p[i]+p[i+1])*(b[i+1]-b[i])/2; |
| S += areas[i]; |
| } |
| for (int i = 0; i < areas.size(); ++i) |
| areas[i] /= S; |
| for (int i = 0; i < Np+1; ++i) |
| p[i] /= S; |
| for (int i = 0; i < N; ++i) |
| { |
| int k = std::lower_bound(b, b+Np+1, u[i]) - b - 1; |
| if (k != kp) |
| { |
| a = 0; |
| for (int j = 0; j < k; ++j) |
| a += areas[j]; |
| m = (p[k+1] - p[k]) / (b[k+1] - b[k]); |
| bk = b[k]; |
| c = (b[k+1]*p[k] - b[k]*p[k+1]) / (b[k+1] - b[k]); |
| kp = k; |
| } |
| assert(std::abs(f(u[i], a, m, bk, c) - double(i)/N) < .001); |
| } |
| } |
| { |
| typedef std::piecewise_linear_distribution<> D; |
| typedef D::param_type P; |
| typedef std::mt19937_64 G; |
| G g; |
| double b[] = {10, 14, 16, 17}; |
| double p[] = {25, 62.5, 12.5, 0}; |
| const size_t Np = sizeof(p) / sizeof(p[0]) - 1; |
| D d(b, b+Np+1, p); |
| const int N = 1000000; |
| std::vector<D::result_type> u; |
| for (int i = 0; i < N; ++i) |
| { |
| D::result_type v = d(g); |
| assert(d.min() <= v && v < d.max()); |
| u.push_back(v); |
| } |
| std::sort(u.begin(), u.end()); |
| int kp = -1; |
| double a; |
| double m; |
| double bk; |
| double c; |
| std::vector<double> areas(Np); |
| double S = 0; |
| for (int i = 0; i < areas.size(); ++i) |
| { |
| areas[i] = (p[i]+p[i+1])*(b[i+1]-b[i])/2; |
| S += areas[i]; |
| } |
| for (int i = 0; i < areas.size(); ++i) |
| areas[i] /= S; |
| for (int i = 0; i < Np+1; ++i) |
| p[i] /= S; |
| for (int i = 0; i < N; ++i) |
| { |
| int k = std::lower_bound(b, b+Np+1, u[i]) - b - 1; |
| if (k != kp) |
| { |
| a = 0; |
| for (int j = 0; j < k; ++j) |
| a += areas[j]; |
| m = (p[k+1] - p[k]) / (b[k+1] - b[k]); |
| bk = b[k]; |
| c = (b[k+1]*p[k] - b[k]*p[k+1]) / (b[k+1] - b[k]); |
| kp = k; |
| } |
| assert(std::abs(f(u[i], a, m, bk, c) - double(i)/N) < .001); |
| } |
| } |
| } |