content: // Copyright (c) 2012, 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.
  
  /**
   * Mathematical constants and functions, plus a random number generator.
   */
  library dart.math;
  
  part "jenkins_smi_hash.dart";
  part "point.dart";
  part "random.dart";
  part "rectangle.dart";
  
  /**
   * Base of the natural logarithms.
   *
   * Typically written as "e".
   */
  const double E = 2.718281828459045;
  
  /**
   * Natural logarithm of 10.
   */
  const double LN10 =  2.302585092994046;
  
  /**
   * Natural logarithm of 2.
   */
  const double LN2 =  0.6931471805599453;
  
  /**
   * Base-2 logarithm of [E].
   */
  const double LOG2E = 1.4426950408889634;
  
  /**
   * Base-10 logarithm of [E].
   */
  const double LOG10E = 0.4342944819032518;
  
  /**
   * The PI constant.
   */
  const double PI = 3.1415926535897932;
  
  /**
   * Square root of 1/2.
   */
  const double SQRT1_2 = 0.7071067811865476;
  
  /**
   * Square root of 2.
   */
  const double SQRT2 = 1.4142135623730951;
  
  /**
    * Returns the lesser of two numbers.
    *
    * Returns NaN if either argument is NaN.
    * The lesser of [:-0.0:] and [:0.0:] is [:-0.0:].
    * If the arguments are otherwise equal (including int and doubles with the
    * same mathematical value) then it is unspecified which of the two arguments
    * is returned.
    */
  num min(num a, num b) {
    // These partially redundant type checks improve code quality for dart2js.
    // Most of the improvement is at call sites from the inferred non-null num
    // return type.
    if (a is! num) throw new ArgumentError(a);
    if (b is! num) throw new ArgumentError(b);
  
    if (a > b) return b;
    if (a < b) return a;
    if (b is double) {
      // Special case for NaN and -0.0. If one argument is NaN return NaN.
      // [min] must also distinguish between -0.0 and 0.0.
      if (a is double) {
        if (a == 0.0) {
          // a is either 0.0 or -0.0. b is either 0.0, -0.0 or NaN.
          // The following returns -0.0 if either a or b is -0.0, and it
          // returns NaN if b is NaN.
          return (a + b) * a * b;
        }
      }
      // Check for NaN and b == -0.0.
      if (a == 0 && b.isNegative || b.isNaN) return b;
      return a;
    }
    return a;
  }
  
  /**
    * Returns the larger of two numbers.
    *
    * Returns NaN if either argument is NaN.
    * The larger of [:-0.0:] and [:0.0:] is [:0.0:]. If the arguments are
    * otherwise equal (including int and doubles with the same mathematical value)
    * then it is unspecified which of the two arguments is returned.
    */
  num max(num a, num b) {
    // These partially redundant type checks improve code quality for dart2js.
    // Most of the improvement is at call sites from the inferred non-null num
    // return type.
    if (a is! num) throw new ArgumentError(a);
    if (b is! num) throw new ArgumentError(b);
  
    if (a > b) return a;
    if (a < b) return b;
    if (b is double) {
      // Special case for NaN and -0.0. If one argument is NaN return NaN.
      // [max] must also distinguish between -0.0 and 0.0.
      if (a is double) {
        if (a == 0.0) {
          // a is either 0.0 or -0.0. b is either 0.0, -0.0, or NaN.
          // The following returns 0.0 if either a or b is 0.0, and it
          // returns NaN if b is NaN.
          return a + b;
        }
      }
      // Check for NaN.
      if (b.isNaN) return b;
      return a;
    }
    // max(-0.0, 0) must return 0.
    if (b == 0 && a.isNegative) return b;
    return a;
  }
  
  /**
   * A variant of [atan].
   *
   * Converts both arguments to doubles.
   *
   * Returns the angle between the positive x-axis and the vector ([b],[a]).
   * The result, in radians, is in the range -PI..PI.
   *
   * If [b] is positive, this is the same as [:atan(b/a):].
   *
   * The result is negative when [a] is negative (including when [a] is the
   * double -0.0).
   *
   * If [a] is equal to zero, the vector ([b],[a]) is considered parallel to
   * the x-axis, even if [b] is also equal to zero. The sign of [b] determines
   * the direction of the vector along the x-axis.
   *
   * Returns NaN if either argument is NaN.
   */
  external double atan2(num a, num b);
  
  /**
   * Returns [x] to the power of [exponent].
   *
   * If [x] is an [int] and [exponent] is a non-negative [int], the result is
   * an [int], otherwise both arguments are converted to doubles first, and the
   * result is a [double].
   *
   * For integers, the power is always equal to the mathematical result of `x` to
   * the power `exponent`, only limited by the available memory.
   *
   * For doubles, `pow(x, y)` handles edge cases as follows:
   *
   * - if `y` is zero (0.0 or -0.0), the result is always 1.0.
   * - if `x` is 1.0, the result is always 1.0.
   * - otherwise, if either `x` or `y` is NaN then the result is NaN.
   * - if `x` is negative (but not -0.0) and `y` is a finite non-integer, the
   *   result is NaN.
   * - if `x` is Infinity and `y` is negative, the result is 0.0.
   * - if `x` is Infinity and `y` is positive, the result is Infinity.
   * - if `x` is 0.0 and `y` is negative, the result is Infinity.
   * - if `x` is 0.0 and `y` is positive, the result is 0.0.
   * - if `x` is -Infinity or -0.0 and `y` is an odd integer, then the result is
   *   `-pow(-x ,y)`.
   * - if `x` is -Infinity or -0.0 and `y` is not an odd integer, then the result
   *   is the same as `pow(-x , y)`.
   * - if `y` is Infinity and the absolute value of `x` is less than 1, the
   *   result is 0.0.
   * - if `y` is Infinity and `x` is -1, the result is 1.0.
   * - if `y` is Infinity and the absolute value of `x` is greater than 1,
   *   the result is Infinity.
   * - if `y` is -Infinity, the result is `1/pow(x, Infinity)`.
   *
   * This corresponds to the `pow` function defined in the IEEE Standard 754-2008.
   *
   * Notice that an [int] result cannot overflow, but a [double] result might
   * be [double.INFINITY].
   */
  external num pow(num x, num exponent);
  
  /**
   * Converts [x] to a double and returns the sine of the value.
   *
   * If [x] is not a finite number, the result is NaN.
   */
  external double sin(num x);
  
  /**
   * Converts [x] to a double and returns the cosine of the value.
   *
   * If [x] is not a finite number, the result is NaN.
   */
  external double cos(num x);
  
  /**
   * Converts [x] to a double and returns the tangent of the value.
   *
   * The tangent function is equivalent to [:sin(x)/cos(x):] and may be
   * infinite (positive or negative) when [:cos(x):] is equal to zero.
   * If [x] is not a finite number, the result is NaN.
   */
  external double tan(num x);
  
  /**
   * Converts [x] to a double and returns the arc cosine of the value.
   *
   * Returns a value in the range -PI..PI, or NaN if [x] is outside
   * the range -1..1.
   */
  external double acos(num x);
  
  /**
   * Converts [x] to a double and returns the arc sine of the value.
   * Returns a value in the range -PI..PI, or  NaN if [x] is outside
   * the range -1..1.
   */
  external double asin(num x);
  
  /**
   * Converts [x] to a dobule and returns the arc tangent of the vlaue.
   * Returns a value in the range -PI/2..PI/2, or NaN if [x] is NaN.
   */
  external double atan(num x);
  
  /**
   * Converts [x] to a double and returns the positive square root of the value.
   *
   * Returns -0.0 if [x] is -0.0, and NaN if [x] is otherwise negative or NaN.
   */
  external double sqrt(num x);
  
  /**
   * Converts [x] to a double and returns the natural exponent, [E],
   * to the power [x].
   * Returns NaN if [x] is NaN.
   */
  external double exp(num x);
  
  /**
   * Converts [x] to a double and returns the natural logarithm of the value.
   * Returns negative infinity if [x] is equal to zero.
   * Returns NaN if [x] is NaN or less than zero.
   */
  external double log(num x);
  