update ceph source to reef 18.1.2

[ceph.git] / ceph / src / boost / libs / math / test / quartic_roots_test.cpp

diff --git a/ceph/src/boost/libs/math/test/quartic_roots_test.cpp b/ceph/src/boost/libs/math/test/quartic_roots_test.cpp
new file mode 100644 (file)
index 0000000..60f9825
--- /dev/null
+++ b/ceph/src/boost/libs/math/test/quartic_roots_test.cpp
@@ -0,0 +1,136 @@
+/*
+ * Copyright Nick Thompson, 2021
+ * Use, modification and distribution are subject to the
+ * Boost Software License, Version 1.0. (See accompanying file
+ * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include "math_unit_test.hpp"
+#include <random>
+#include <boost/math/tools/quartic_roots.hpp>
+#ifdef BOOST_HAS_FLOAT128
+#include <boost/multiprecision/float128.hpp>
+using boost::multiprecision::float128;
+#endif
+
+using boost::math::tools::quartic_roots;
+using std::cbrt;
+using std::sqrt;
+
+template<class Real>
+void test_zero_coefficients()
+{
+    Real a = 0;
+    Real b = 0;
+    Real c = 0;
+    Real d = 0;
+    Real e = 0;
+    auto roots = quartic_roots(a,b,c,d,e);
+    CHECK_EQUAL(roots[0], Real(0));
+    CHECK_EQUAL(roots[1], Real(0));
+    CHECK_EQUAL(roots[2], Real(0));
+    CHECK_EQUAL(roots[3], Real(0));
+
+    b = 1;
+    e = 1;
+    // x^3 + 1 = 0:
+    roots = quartic_roots(a,b,c,d,e);
+    CHECK_EQUAL(roots[0], Real(-1));
+    CHECK_NAN(roots[1]);
+    CHECK_NAN(roots[2]);
+    CHECK_NAN(roots[3]);
+    e = -1;
+    // x^3 - 1 = 0:
+    roots = quartic_roots(a,b,c,d,e);
+    CHECK_EQUAL(roots[0], Real(1));
+    CHECK_NAN(roots[1]);
+    CHECK_NAN(roots[2]);
+    CHECK_NAN(roots[3]);
+
+    e = -2;
+    // x^3 - 2 = 0
+    roots = quartic_roots(a,b,c,d,e);
+    CHECK_ULP_CLOSE(roots[0], cbrt(Real(2)), 2);
+    CHECK_NAN(roots[1]);
+    CHECK_NAN(roots[2]);
+    CHECK_NAN(roots[3]);
+
+    // x^4 -1 = 0
+    // x = \pm 1:
+    roots = quartic_roots<Real>(1, 0, 0, 0, -1);
+    CHECK_ULP_CLOSE(Real(-1), roots[0], 3);
+    CHECK_ULP_CLOSE(Real(1), roots[1], 3);
+    CHECK_NAN(roots[2]);
+    CHECK_NAN(roots[3]);
+
+    // x^4 - 2 = 0 \implies x = \pm sqrt(sqrt(2))
+    roots = quartic_roots<Real>(1,0,0,0,-2);
+    CHECK_ULP_CLOSE(-sqrt(sqrt(Real(2))), roots[0], 3);
+    CHECK_ULP_CLOSE(sqrt(sqrt(Real(2))), roots[1], 3);
+    CHECK_NAN(roots[2]);
+    CHECK_NAN(roots[3]);
+
+    
+    // x(x-1)(x-2)(x-3) = x^4 - 6x^3 + 11x^2 - 6x
+    roots = quartic_roots(Real(1), Real(-6), Real(11), Real(-6), Real(0));
+    CHECK_ULP_CLOSE(roots[0], Real(0), 2);
+    CHECK_ULP_CLOSE(roots[1], Real(1), 2);
+    CHECK_ULP_CLOSE(roots[2], Real(2), 2);
+    CHECK_ULP_CLOSE(roots[3], Real(3), 2);
+
+     // (x-1)(x-2)(x-3)(x-4) = x^4 - 10x^3 + 35x^2 - (2*3*4 + 1*3*4 + 1*2*4 + 1*2*3)x + 1*2*3*4  
+    roots = quartic_roots<Real>(1, -10, 35, -24 - 12 - 8 - 6, 1*2*3*4);
+    CHECK_ULP_CLOSE(Real(1), roots[0], 2);
+    CHECK_ULP_CLOSE(Real(2), roots[1], 2);
+    CHECK_ULP_CLOSE(Real(3), roots[2], 2);
+    CHECK_ULP_CLOSE(Real(4), roots[3], 2);
+    
+    // Double root:
+    // (x+1)^2(x-2)(x-3) = x^4 - 3x^3 -3x^2 + 7x + 6
+    // Note: This test is unstable wrt to perturbations!
+    roots = quartic_roots(Real(1), Real(-3), Real(-3), Real(7), Real(6));
+    CHECK_ULP_CLOSE(Real(-1), roots[0], 2);
+    CHECK_ULP_CLOSE(Real(-1), roots[1], 2);
+    CHECK_ULP_CLOSE(Real(2), roots[2], 2);
+    CHECK_ULP_CLOSE(Real(3), roots[3], 2);
+
+     
+    std::uniform_real_distribution<Real> dis(-2,2);
+    std::mt19937 gen(12343);
+    // Expected roots
+    std::array<Real, 4> r;
+    int trials = 10;
+    for (int i = 0; i < trials; ++i) {
+        // Mathematica:
+        // Expand[(x - r0)*(x - r1)*(x - r2)*(x-r3)]
+        // r0 r1 r2 r3 - (r0 r1 r2 + r0 r1 r3 + r0 r2 r3 + r1r2r3)x
+        // + (r0 r1 + r0 r2 + r0 r3 + r1 r2 + r1r3 + r2 r3)x^2 - (r0 + r1 + r2 + r3) x^3 + x^4
+        for (auto & root : r) {
+            root = static_cast<Real>(dis(gen));
+        }
+        std::sort(r.begin(), r.end());
+        Real a = 1;
+        Real b = -(r[0] + r[1] + r[2] + r[3]);
+        Real c = r[0]*r[1] + r[0]*r[2] + r[0]*r[3] + r[1]*r[2] + r[1]*r[3] + r[2]*r[3];
+        Real d = -(r[0]*r[1]*r[2] + r[0]*r[1]*r[3] + r[0]*r[2]*r[3] + r[1]*r[2]*r[3]);
+        Real e = r[0]*r[1]*r[2]*r[3];
+
+        auto roots = quartic_roots(a, b, c, d, e);
+        // I could check the condition number here, but this is fine right?
+        CHECK_ULP_CLOSE(r[0], roots[0], 160);
+        CHECK_ULP_CLOSE(r[1], roots[1], 260);
+        CHECK_ULP_CLOSE(r[2], roots[2], 160);
+        CHECK_ULP_CLOSE(r[3], roots[3], 160);
+    }
+}
+
+
+int main()
+{
+    test_zero_coefficients<float>();
+    test_zero_coefficients<double>();
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+    test_zero_coefficients<long double>();
+#endif
+    return boost::math::test::report_errors();
+}