structured tests; fixed implementation

Author: Paul

libcxx/test/std/numerics/c.math/legendre.pass.cpp

@@ -18,94 +18,162 @@
 // template <class Integer>
 // double         legendre(unsigned n, Integer x);
 
+#include <array>
 #include <cassert>
 #include <cmath>
 #include <limits>
 
+#include "type_algorithms.h"
+
+inline constexpr unsigned g_max_n = 128;
+
 template <class T>
-void testLegendreNaNPropagation() {
-  const unsigned MaxN = 127;
-  const T x           = std::numeric_limits<T>::quiet_NaN();
-  for (unsigned n = 0; n <= MaxN; ++n) {
-    assert(std::isnan(std::legendre(n, x)));
-  }
+std::array<T, 7> sample_points() {
+  return {-1.0, -0.5, -0.1, 0.0, 0.1, 0.5, 1.0};
 }
 
-template <class T>
-void testLegendreNotNaN(const T x) {
-  assert(!std::isnan(x));
-  const unsigned MaxN = 127;
-  for (unsigned n = 0; n <= MaxN; ++n) {
-    assert(!std::isnan(std::legendre(n, x)));
+template <class Real>
+class CompareFloatingValues {
+private:
+  Real tol;
+
+public:
+  CompareFloatingValues() {
+    if (std::is_same_v<Real, float>)
+      tol = 1e-6f;
+    else if (std::is_same_v<Real, double>)
+      tol = 1e-9;
+    else
+      tol = 1e-12l;
   }
-}
 
-template <class T>
-void testLegendreThrows(const T x) {
-#ifndef _LIBCPP_NO_EXCEPTIONS
-  const unsigned MaxN = 127;
-  for (unsigned n = 0; n <= MaxN; ++n) {
-    bool Throws = false;
-    try {
-      std::legendre(n, x);
-    } catch (const std::domain_error&) {
-      Throws = true;
-    }
-    assert(Throws);
+  bool operator()(Real result, Real expected) const {
+    if (std::isinf(expected) && std::isinf(result))
+      return result == expected;
+
+    if (std::isnan(expected) || std::isnan(result))
+      return false;
+
+    return std::abs(result - expected) < (tol + std::abs(expected) * tol);
+  }
+};
+
+template <class Real>
+void test() {
+  { // checks if NaNs are reported correctly (i.e. output == input for input == NaN)
+    using nl = std::numeric_limits<Real>;
+    for (Real NaN : {nl::quiet_NaN(), nl::signaling_NaN()})
+      for (unsigned n = 0; n < g_max_n; ++n)
+        assert(std::isnan(std::legendre(n, NaN)));
   }
+
+  { // simple sample points for n=0..127 should not produce NaNs.
+    for (Real x : sample_points<Real>())
+      for (unsigned n = 0; n < g_max_n; ++n)
+        assert(!std::isnan(std::legendre(n, x)));
+  }
+
+  { // For x with abs(x) > 1 an domain_error exception should be thrown.
+#ifndef _LIBCPP_NO_EXCEPTIONS
+    for (double absX : {2.0, 7.77, 42.42, std::numeric_limits<double>::infinity()})
+      for (Real x : {-absX, absX})
+        for (unsigned n = 0; n < g_max_n; ++n) {
+          bool throws = false;
+          try {
+            std::legendre(n, x);
+          } catch (const std::domain_error&) {
+            throws = true;
+          }
+          assert(throws);
+        }
 #endif // _LIBCPP_NO_EXCEPTIONS
-}
+  }
 
-template <class T>
-void testLegendreAnalytic(const T x, const T AbsTolerance, const T RelTolerance) {
-  assert(!std::isnan(x));
-  const auto compareFloatingPoint = [AbsTolerance, RelTolerance](const T Result, const T ExpectedResult) {
-    if (std::isinf(ExpectedResult) && std::isinf(Result))
-      return true;
+  { // check against analytic polynoms for order n=0..6
+    for (Real x : sample_points<Real>()) {
+      const auto l0 = [](Real) -> Real { return 1; };
+      const auto l1 = [](Real y) -> Real { return y; };
+      const auto l2 = [](Real y) -> Real { return (3 * y * y - 1) / 2; };
+      const auto l3 = [](Real y) -> Real { return (5 * y * y - 3) * y / 2; };
+      const auto l4 = [](Real y) -> Real { return (35 * std::pow(y, 4) - 30 * y * y + 3) / 8; };
+      const auto l5 = [](Real y) -> Real { return (63 * std::pow(y, 4) - 70 * y * y + 15) * y / 8; };
+      const auto l6 = [](Real y) -> Real {
+        return (231 * std::pow(y, 6) - 315 * std::pow(y, 4) + 105 * y * y - 5) / 16;
+      };
+
+      const CompareFloatingValues<Real> compare;
+      assert(compare(std::legendre(0, x), l0(x)));
+      assert(compare(std::legendre(1, x), l1(x)));
+      assert(compare(std::legendre(2, x), l2(x)));
+      assert(compare(std::legendre(3, x), l3(x)));
+      assert(compare(std::legendre(4, x), l4(x)));
+      assert(compare(std::legendre(5, x), l5(x)));
+      assert(compare(std::legendre(6, x), l6(x)));
+    }
+  }
 
-    if (std::isnan(ExpectedResult) || std::isnan(Result))
-      return false;
+  { // checks std::legendref for bitwise equality with std::legendre(unsigned, float)
+    if constexpr (std::is_same_v<Real, float>)
+      for (unsigned n = 0; n < g_max_n; ++n)
+        for (float x : sample_points<float>())
+          assert(std::legendre(n, x) == std::legendref(n, x));
+  }
 
-    const T Tolerance = AbsTolerance + std::abs(ExpectedResult) * RelTolerance;
-    return std::abs(Result - ExpectedResult) < Tolerance;
-  };
-
-  const auto l0 = [](T) { return T(1); };
-  const auto l1 = [](T y) { return y; };
-  const auto l2 = [](T y) { return (T(3) * y * y - T(1)) / T(2); };
-  const auto l3 = [](T y) { return (T(5) * y * y - T(3)) * y / T(2); };
-  const auto l4 = [](T y) { return (T(35) * y * y * y * y - T(30) * y * y + T(3)) / T(8); };
-  const auto l5 = [](T y) { return (T(63) * y * y * y * y - T(70) * y * y + T(15)) * y / T(8); };
-  const auto l6 = [](T y) {
-    const T y2 = y * y;
-    return (T(231) * y2 * y2 * y2 - T(315) * y2 * y2 + T(105) * y2 - T(5)) / T(16);
-  };
-
-  assert(compareFloatingPoint(std::legendre(0, x), l0(x)));
-  assert(compareFloatingPoint(std::legendre(1, x), l1(x)));
-  assert(compareFloatingPoint(std::legendre(2, x), l2(x)));
-  assert(compareFloatingPoint(std::legendre(3, x), l3(x)));
-  assert(compareFloatingPoint(std::legendre(4, x), l4(x)));
-  assert(compareFloatingPoint(std::legendre(5, x), l5(x)));
-  assert(compareFloatingPoint(std::legendre(6, x), l6(x)));
-}
+  { // checks std::legendrel for bitwise equality with std::legendre(unsigned, long double)
+    if constexpr (std::is_same_v<Real, long double>)
+      for (unsigned n = 0; n < g_max_n; ++n)
+        for (long double x : sample_points<long double>()) {
+          assert(std::legendre(n, x) == std::legendrel(n, x));
+          assert(std::legendre(n, x) == std::legendrel(n, x));
+        }
+  }
 
-template <class T>
-void testLegendre(const T AbsTolerance, const T RelTolerance) {
-  testLegendreNaNPropagation<T>();
-  testLegendreThrows<T>(T(-5));
-  testLegendreThrows<T>(T(5));
+  { // evaluation at x=1: P_n(1) = 1
+    const CompareFloatingValues<Real> compare;
+    for (unsigned n = 0; n < g_max_n; ++n)
+      assert(compare(std::legendre(n, Real{1}), 1));
+  }
 
-  const T Samples[] = {T(-1.0), T(-0.5), T(-0.1), T(0.0), T(0.1), T(0.5), T(1.0)};
+  { // evaluation at x=-1: P_n(-1) = (-1)^n
+    const CompareFloatingValues<Real> compare;
+    for (unsigned n = 0; n < g_max_n; ++n)
+      assert(compare(std::legendre(n, Real{-1}), std::pow(-1, n)));
+  }
 
-  for (T x : Samples) {
-    testLegendreNotNaN(x);
-    testLegendreAnalytic(x, AbsTolerance, RelTolerance);
+  { // evaluation at x=0:
+    //    P_{2n  }(0) = (-1)^n (2n-1)!! / (2n)!!
+    //    P_{2n+1}(0) = 0
+    const CompareFloatingValues<Real> compare;
+    Real doubleFactorials{1};
+    for (unsigned n = 0; n < g_max_n; ++n) {
+      if (n & 1) // odd
+        doubleFactorials *= n;
+      else if (n != 0) // even and not zero
+        doubleFactorials /= n;
+
+      assert(compare(std::legendre(n, Real{0}), (n & 1) ? Real{0} : std::pow(-1, n / 2) * doubleFactorials));
+    }
   }
 }
 
+struct TestFloat {
+  template <class Real>
+  void operator()() {
+    test<Real>();
+  }
+};
+
+struct TestInt {
+  template <class Integer>
+  void operator()() {
+    // checks that std::legendre(unsigned, Integer) actually wraps std::legendre(unsigned, double)
+    for (unsigned n = 0; n < g_max_n; ++n)
+      for (Integer x : {-1, 0, 1})
+        assert(std::legendre(n, x) == std::legendre(n, static_cast<double>(x)));
+  }
+};
+
 int main() {
-  testLegendre<float>(1e-6f, 1e-6f);
-  testLegendre<double>(1e-9, 1e-9);
-  testLegendre<long double>(1e-12, 1e-12);
+  types::for_each(types::floating_point_types(), TestFloat());
+  types::for_each(types::type_list<short, int, long, long long>(), TestInt());
 }