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+// Licensed to the .NET Foundation under one or more agreements.
+// The .NET Foundation licenses this file to you under the MIT license.
+// See the LICENSE file in the project root for more information.
+
+/*=====================================================================
+**
+** Source: test1.c
+**
+** Purpose: Tests that atan2 returns correct values for a subset of values.
+** Tests with positive and negative values of x and y to ensure
+** atan2 is returning results from the correct quadrant.
+**
+**===================================================================*/
+
+#include <palsuite.h>
+
+// binary64 (double) has a machine epsilon of 2^-52 (approx. 2.22e-16). However, this
+// is slightly too accurate when writing tests meant to run against libm implementations
+// for various platforms. 2^-50 (approx. 8.88e-16) seems to be as accurate as we can get.
+//
+// The tests themselves will take PAL_EPSILON and adjust it according to the expected result
+// so that the delta used for comparison will compare the most significant digits and ignore
+// any digits that are outside the double precision range (15-17 digits).
+
+// For example, a test with an expect result in the format of 0.xxxxxxxxxxxxxxxxx will use
+// PAL_EPSILON for the variance, while an expected result in the format of 0.0xxxxxxxxxxxxxxxxx
+// will use PAL_EPSILON / 10 and and expected result in the format of x.xxxxxxxxxxxxxxxx will
+// use PAL_EPSILON * 10.
+#define PAL_EPSILON 8.8817841970012523e-16
+
+#define PAL_NAN sqrt(-1.0)
+#define PAL_POSINF -log(0.0)
+#define PAL_NEGINF log(0.0)
+
+/**
+ * Helper test structure
+ */
+struct test
+{
+ double x; /* first component of the value to test the function with */
+ double y; /* second component of the value to test the function with */
+ double expected; /* expected result */
+ double variance; /* maximum delta between the expected and actual result */
+};
+
+/**
+ * validate
+ *
+ * test validation function
+ */
+void __cdecl validate(double x, double y, double expected, double variance)
+{
+ double result = pow(x, y);
+
+ /*
+ * The test is valid when the difference between result
+ * and expected is less than or equal to variance
+ */
+ double delta = fabs(result - expected);
+
+ if (delta > variance)
+ {
+ Fail("pow(%g, %g) returned %20.17g when it should have returned %20.17g",
+ x, y, result, expected);
+ }
+}
+
+/**
+ * validate
+ *
+ * test validation function for values returning NaN
+ */
+void __cdecl validate_isnan(double x, double y)
+{
+ double result = pow(x, y);
+
+ if (!_isnan(result))
+ {
+ Fail("pow(%g, %g) returned %20.17g when it should have returned %20.17g",
+ x, y, result, PAL_NAN);
+ }
+}
+
+/**
+ * main
+ *
+ * executable entry point
+ */
+int __cdecl main(int argc, char **argv)
+{
+ struct test tests[] =
+ {
+ /* x y expected variance */
+ { PAL_NEGINF, PAL_NEGINF, 0, PAL_EPSILON },
+ { PAL_NEGINF, PAL_POSINF, PAL_POSINF, 0 },
+
+ { -10, PAL_NEGINF, 0, PAL_EPSILON },
+ { -10, -1, -0.1, PAL_EPSILON },
+ { -10, 0, 1, PAL_EPSILON * 10 },
+ { -10, 1, -10, PAL_EPSILON * 100 },
+ { -10, PAL_POSINF, PAL_POSINF, 0 },
+
+ { -2.7182818284590452, PAL_NEGINF, 0, PAL_EPSILON }, // x: -(e)
+ { -2.7182818284590452, -1, -0.36787944117144232, PAL_EPSILON }, // x: -(e)
+ { -2.7182818284590452, 0, 1, PAL_EPSILON * 10 }, // x: -(e)
+ { -2.7182818284590452, 1, -2.7182818284590452, PAL_EPSILON * 10 }, // x: -(e) expected: e
+ { -2.7182818284590452, PAL_POSINF, PAL_POSINF, 0 }, // x: -(e)
+
+ { -0.0, PAL_NEGINF, PAL_POSINF, 0 },
+ { -0.0, -1, PAL_NEGINF, 0 },
+ { -0.0, -0.0, 1, PAL_EPSILON * 10 },
+ { -0.0, 0, 1, PAL_EPSILON * 10 },
+ { -0.0, 1, -0.0, PAL_EPSILON },
+ { -0.0, PAL_POSINF, 0, PAL_EPSILON },
+
+ { 0.0, PAL_NEGINF, PAL_POSINF, 0 },
+ { 0.0, -1, PAL_POSINF, 0 },
+ { 0, -0.0, 1, PAL_EPSILON * 10 },
+ { 0, 0, 1, PAL_EPSILON * 10 },
+ { 0.0, 1, 0, PAL_EPSILON },
+ { 0.0, PAL_POSINF, 0, PAL_EPSILON },
+
+ { 1, PAL_NEGINF, 1, PAL_EPSILON * 10 },
+ { 1, PAL_POSINF, 1, PAL_EPSILON * 10 },
+
+ { 2.7182818284590452, PAL_NEGINF, 0, PAL_EPSILON },
+ { 2.7182818284590452, -3.1415926535897932, 0.043213918263772250, PAL_EPSILON / 10 }, // x: e y: -(pi)
+ { 2.7182818284590452, -2.7182818284590452, 0.065988035845312537, PAL_EPSILON / 10 }, // x: e y: -(e)
+ { 2.7182818284590452, -2.3025850929940457, 0.1, PAL_EPSILON }, // x: e y: -(ln(10))
+ { 2.7182818284590452, -1.5707963267948966, 0.20787957635076191, PAL_EPSILON }, // x: e y: -(pi / 2)
+ { 2.7182818284590452, -1.4426950408889634, 0.23629008834452270, PAL_EPSILON }, // x: e y: -(log2(e))
+ { 2.7182818284590452, -1.4142135623730950, 0.24311673443421421, PAL_EPSILON }, // x: e y: -(sqrt(2))
+ { 2.7182818284590452, -1.1283791670955126, 0.32355726390307110, PAL_EPSILON }, // x: e y: -(2 / sqrt(pi))
+ { 2.7182818284590452, -1, 0.36787944117144232, PAL_EPSILON }, // x: e y: -(1)
+ { 2.7182818284590452, -0.78539816339744831, 0.45593812776599624, PAL_EPSILON }, // x: e y: -(pi / 4)
+ { 2.7182818284590452, -0.70710678118654752, 0.49306869139523979, PAL_EPSILON }, // x: e y: -(1 / sqrt(2))
+ { 2.7182818284590452, -0.69314718055994531, 0.5, PAL_EPSILON }, // x: e y: -(ln(2))
+ { 2.7182818284590452, -0.63661977236758134, 0.52907780826773535, PAL_EPSILON }, // x: e y: -(2 / pi)
+ { 2.7182818284590452, -0.43429448190325183, 0.64772148514180065, PAL_EPSILON }, // x: e y: -(log10(e))
+ { 2.7182818284590452, -0.31830988618379067, 0.72737734929521647, PAL_EPSILON }, // x: e y: -(1 / pi)
+ { 2.7182818284590452, 0, 1, PAL_EPSILON * 10 }, // x: e
+ { 2.7182818284590452, 0.31830988618379067, 1.3748022274393586, PAL_EPSILON * 10 }, // x: e y: 1 / pi
+ { 2.7182818284590452, 0.43429448190325183, 1.5438734439711811, PAL_EPSILON * 10 }, // x: e y: log10(e)
+ { 2.7182818284590452, 0.63661977236758134, 1.8900811645722220, PAL_EPSILON * 10 }, // x: e y: 2 / pi
+ { 2.7182818284590452, 0.69314718055994531, 2, PAL_EPSILON * 10 }, // x: e y: ln(2)
+ { 2.7182818284590452, 0.70710678118654752, 2.0281149816474725, PAL_EPSILON * 10 }, // x: e y: 1 / sqrt(2)
+ { 2.7182818284590452, 0.78539816339744831, 2.1932800507380155, PAL_EPSILON * 10 }, // x: e y: pi / 4
+ { 2.7182818284590452, 1, 2.7182818284590452, PAL_EPSILON * 10 }, // x: e expected: e
+ { 2.7182818284590452, 1.1283791670955126, 3.0906430223107976, PAL_EPSILON * 10 }, // x: e y: 2 / sqrt(pi)
+ { 2.7182818284590452, 1.4142135623730950, 4.1132503787829275, PAL_EPSILON * 10 }, // x: e y: sqrt(2)
+ { 2.7182818284590452, 1.4426950408889634, 4.2320861065570819, PAL_EPSILON * 10 }, // x: e y: log2(e)
+ { 2.7182818284590452, 1.5707963267948966, 4.8104773809653517, PAL_EPSILON * 10 }, // x: e y: pi / 2
+ { 2.7182818284590452, 2.3025850929940457, 10, PAL_EPSILON * 100 }, // x: e y: ln(10)
+ { 2.7182818284590452, 2.7182818284590452, 15.154262241479264, PAL_EPSILON * 100 }, // x: e y: e
+ { 2.7182818284590452, 3.1415926535897932, 23.140692632779269, PAL_EPSILON * 100 }, // x: e y: pi
+ { 2.7182818284590452, PAL_POSINF, PAL_POSINF, 0 }, // x: e
+
+ { 10, PAL_NEGINF, 0, 0 },
+ { 10, -3.1415926535897932, 0.00072178415907472774, PAL_EPSILON / 1000 }, // y: -(pi)
+ { 10, -2.7182818284590452, 0.0019130141022243176, PAL_EPSILON / 100 }, // y: -(e)
+ { 10, -2.3025850929940457, 0.0049821282964407206, PAL_EPSILON / 100 }, // y: -(ln(10))
+ { 10, -1.5707963267948966, 0.026866041001136132, PAL_EPSILON / 10 }, // y: -(pi / 2)
+ { 10, -1.4426950408889634, 0.036083192820787210, PAL_EPSILON / 10 }, // y: -(log2(e))
+ { 10, -1.4142135623730950, 0.038528884700322026, PAL_EPSILON / 10 }, // y: -(sqrt(2))
+ { 10, -1.1283791670955126, 0.074408205860642723, PAL_EPSILON / 10 }, // y: -(2 / sqrt(pi))
+ { 10, -1, 0.1, PAL_EPSILON }, // y: -(1)
+ { 10, -0.78539816339744831, 0.16390863613957665, PAL_EPSILON }, // y: -(pi / 4)
+ { 10, -0.70710678118654752, 0.19628775993505562, PAL_EPSILON }, // y: -(1 / sqrt(2))
+ { 10, -0.69314718055994531, 0.20269956628651730, PAL_EPSILON }, // y: -(ln(2))
+ { 10, -0.63661977236758134, 0.23087676451600055, PAL_EPSILON }, // y: -(2 / pi)
+ { 10, -0.43429448190325183, 0.36787944117144232, PAL_EPSILON }, // y: -(log10(e))
+ { 10, -0.31830988618379067, 0.48049637305186868, PAL_EPSILON }, // y: -(1 / pi)
+ { 10, 0, 1, PAL_EPSILON * 10 },
+ { 10, 0.31830988618379067, 2.0811811619898573, PAL_EPSILON * 10 }, // y: 1 / pi
+ { 10, 0.43429448190325183, 2.7182818284590452, PAL_EPSILON * 10 }, // y: log10(e) expected: e
+ { 10, 0.63661977236758134, 4.3313150290214525, PAL_EPSILON * 10 }, // y: 2 / pi
+ { 10, 0.69314718055994531, 4.9334096679145963, PAL_EPSILON * 10 }, // y: ln(2)
+ { 10, 0.70710678118654752, 5.0945611704512962, PAL_EPSILON * 10 }, // y: 1 / sqrt(2)
+ { 10, 0.78539816339744831, 6.1009598002416937, PAL_EPSILON * 10 }, // y: pi / 4
+ { 10, 1, 10, PAL_EPSILON * 100 },
+ { 10, 1.1283791670955126, 13.439377934644400, PAL_EPSILON * 100 }, // y: 2 / sqrt(pi)
+ { 10, 1.4142135623730950, 25.954553519470081, PAL_EPSILON * 100 }, // y: sqrt(2)
+ { 10, 1.4426950408889634, 27.713733786437790, PAL_EPSILON * 100 }, // y: log2(e)
+ { 10, 1.5707963267948966, 37.221710484165167, PAL_EPSILON * 100 }, // y: pi / 2
+ { 10, 2.3025850929940457, 200.71743249053009, PAL_EPSILON * 1000 }, // y: ln(10)
+ { 10, 2.7182818284590452, 522.73529967043665, PAL_EPSILON * 1000 }, // y: e
+ { 10, 3.1415926535897932, 1385.4557313670111, PAL_EPSILON * 10000 }, // y: pi
+ { 10, PAL_POSINF, PAL_POSINF, 0 },
+
+ { PAL_POSINF, PAL_NEGINF, 0, PAL_EPSILON },
+ { PAL_POSINF, PAL_POSINF, PAL_POSINF, 0 },
+ };
+
+ if (PAL_Initialize(argc, argv) != 0)
+ {
+ return FAIL;
+ }
+
+ for (int i = 0; i < (sizeof(tests) / sizeof(struct test)); i++)
+ {
+ validate(tests[i].x, tests[i].y, tests[i].expected, tests[i].variance);
+ }
+
+ validate_isnan(-10, -1.5707963267948966); // y: -(pi / 2)
+ validate_isnan(-10, -0.78539816339744828); // y: -(pi / 4)
+ validate_isnan(-10, 0.78539816339744828); // y: pi / 4
+ validate_isnan(-10, 1.5707963267948966); // y: pi / 2
+
+ validate_isnan(-2.7182818284590452, -1.5707963267948966); // x: -(e) y: -(pi / 2)
+ validate_isnan(-2.7182818284590452, -0.78539816339744828); // x: -(e) y: -(pi / 4)
+ validate_isnan(-2.7182818284590452, 0.78539816339744828); // x: -(e) y: pi / 4
+ validate_isnan(-2.7182818284590452, 1.5707963267948966); // x: -(e) y: pi / 2
+
+ validate_isnan(-1, PAL_NEGINF);
+ validate_isnan(-1, PAL_POSINF);
+
+ validate_isnan(PAL_NAN, -0.0);
+ validate_isnan(PAL_NAN, 0);
+
+ validate_isnan(PAL_NEGINF, PAL_NAN);
+ validate_isnan(PAL_NAN, PAL_NEGINF);
+
+ validate_isnan(PAL_POSINF, PAL_NAN);
+ validate_isnan(PAL_NAN, PAL_POSINF);
+
+ validate_isnan(PAL_NAN, PAL_NAN);
+
+ PAL_Terminate();
+ return PASS;
+}