Add documentation to dart:math pow function.

tests/lib/math/double_pow_test.dart

+// Copyright (c) 2011, the Dart project authors.  Please see the AUTHORS file
+// for details. All rights reserved. Use of this source code is governed by a
+// BSD-style license that can be found in the LICENSE file.
+
+library math_test;
+import "package:expect/expect.dart";
+import 'dart:math';
+
+void checkVeryClose(double a, double b) {
+  // We find a ulp (unit in the last place) by shifting the original number
+  // to the right. This only works if we are not too close to infinity or if
+  // we work with denormals.
+  // We special case or 0.0, but not for infinity.
+  if (a == 0.0) {
+    final minimalDouble = 4.9406564584124654e-324;
+    Expect.equals(true, b.abs() <= minimalDouble);
+    return;
+  }
+  if (b == 0.0) {
+    // No need to look if they are close. Otherwise the check for 'a' above
+    // whould have triggered.
+    Expect.equals(a, b);
+  }
+  final double shiftRightBy52 = 2.220446049250313080847263336181640625e-16;
+  final double shiftedA = (a * shiftRightBy52).abs();
+  // Compared to 'a', 'shiftedA' is now ~1-2 ulp.
+
+  final double limitLow = a - shiftedA;
+  final double limitHigh = a + shiftedA;
+  Expect.equals(false, a == limitLow);
+  Expect.equals(false, a == limitHigh);
+  Expect.equals(true, limitLow <= b);
+  Expect.equals(true, b <= limitHigh);
+}
+
+const NaN = double.NAN;
+const Infinity = double.INFINITY;
+
+var samples = [
+  NaN,
+  -Infinity,
+  -3.0,  // Odd integer
+  -2.0,  // Even integer
+  -1.5,  // Non-integer, magnitude > 1
+  -1.0,  // Unit
+  -0.5,  // Non-integer, magnitude < 1.
+  -0.0,
+  0.5,  // Non-integer, magnitude < 1.
+  1.0,  // Unit
+  1.5,  // Non-integer, magnitude > 1
+  2.0,  // Even integer
+  3.0,  // Odd integer
+  Infinity
+];
+
+main() {
+  // Tests of pow(x, y):
+  for (var d in samples) {
+    // if `y` is zero (0.0 or -0.0), the result is always 1.0.
+    Expect.identical(1.0, pow(d, 0.0), "$d");
+    Expect.identical(1.0, pow(d, -0.0), "$d");
+  }
+  for (var d in samples) {
+    // if `x` is 1.0, the result is always 1.0.
+    Expect.identical(1.0, pow(1.0, d), "$d");
+  }
+  for (var d in samples) {
+    // otherwise, if either `x` or `y` is NaN then the result is NaN.
+    if (d != 0.0) Expect.identical(NaN, pow(NaN, d), "$d");
+    if (d != 1.0) Expect.identical(NaN, pow(d, NaN), "$d");
+  }
+
+  for (var d in samples) {
+    // if `x` is a finite and strictly negative and `y` is a finite non-integer,
+    // the result is NaN.
+    if (d < 0 && !d.isInfinite) {
+      Expect.identical(NaN, pow(d, 0.5), "$d");
+      Expect.identical(NaN, pow(d, -0.5), "$d");
+      Expect.identical(NaN, pow(d, 1.5), "$d");
+      Expect.identical(NaN, pow(d, -1.5), "$d");
+    }
+  }
+
+  for (var d in samples) {
+    if (d < 0) {
+      // if `x` is Infinity and `y` is strictly negative, the result is 0.0.
+      Expect.identical(0.0, pow(Infinity, d), "$d");
+    }
+    if (d > 0) {
+      // if `x` is Infinity and `y` is strictly positive, the result is Infinity.
+      Expect.identical(Infinity, pow(Infinity, d), "$d");
+    }
+  }
+
+  for (var d in samples) {
+    if (d < 0) {
+      // if `x` is 0.0 and `y` is strictly negative, the result is Infinity.
+      Expect.identical(Infinity, pow(0.0, d), "$d");
+    }
+    if (d > 0) {
+      // if `x` is 0.0 and `y` is strictly positive, the result is 0.0.
+      Expect.identical(0.0, pow(0.0, d), "$d");
+    }
+  }
+
+  for (var d in samples) {
+    if (!d.isInfinite && !d.isNaN) {
+      var dint = d.toInt();
+      if (d == dint && dint.isOdd) {
+        // if `x` is -Infinity or -0.0 and `y` is an odd integer, then the
+        // result is`-pow(-x ,y)`.
+        Expect.identical(-pow(Infinity, d), pow(-Infinity, d));
+        Expect.identical(-pow(0.0, d), pow(-0.0, d));
+        continue;
+      }
+    }
+    // if `x` is -Infinity or -0.0 and `y` is not an odd integer, then the
+    // result is the same as `pow(-x , y)`.
+    Expect.identical(pow(Infinity, d), pow(-Infinity, d));
+    Expect.identical(pow(0.0, d), pow(-0.0, d));
+  }
+
+  for (var d in samples) {
+
+    if (d.abs() < 1) {
+      // if `y` is Infinity and the absolute value of `x` is less than 1, the
+      // result is 0.0.
+      Expect.identical(0.0, pow(d, Infinity));
+    } else if (d.abs() > 1) {
+      // if `y` is Infinity and the absolute value of `x` is greater than 1,
+      // the result is Infinity.
+      Expect.identical(Infinity, pow(d, Infinity));
+    } else if (d == -1) {
+      // if `y` is Infinity and `x` is -1, the result is 1.0.
+      Expect.identical(1.0, pow(d, Infinity));
+    }
+    // if `y` is -Infinity, the result is `1/pow(x, Infinity)`.
+    Expect.identical(1/pow(d, Infinity), pow(d, -Infinity));
+  }
+
+  // Some non-exceptional values.
+  checkVeryClose(16.0, pow(4.0, 2.0));
+  checkVeryClose(SQRT2, pow(2.0, 0.5));
+  checkVeryClose(SQRT1_2, pow(0.5, 0.5));
+  // Denormal result.
+  Expect.identical(5e-324, pow(2.0, -1074.0));
+  // Overflow.
+  Expect.identical(Infinity, pow(10.0, 309.0));
+  // Underflow.
+  Expect.identical(0.0, pow(10.0, -325.0));
+
+  // Conversion to double.
+
+  // The second argument is an odd integer as int, but not when converted
+  // to double.
+  Expect.identical(Infinity, pow(-0.0, -9223372036854775809));
+}
+