vipunen/patched_sdk/lib/math/math.dart

// 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.
 * 
 * To use this library in your code:
 * 
 *     import 'dart:math';
 */
library dart.math;
import "dart:typed_data";

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.
  */
T min<T extends num>(T a, T 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.
  */
T max<T extends num>(T a, T 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.
 */
double atan2(num a, num b) => _atan2(a.toDouble(), b.toDouble());

/**
 * 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].
 */
num pow(num x, num exponent) {
  if ((x is int) && (exponent is int) && (exponent >= 0)) {
    return _intPow(x, exponent);
  }
  return _doublePow(x.toDouble(), exponent.toDouble());
}

/**
 * Converts [x] to a double and returns the sine of the value.
 *
 * If [x] is not a finite number, the result is NaN.
 */
double sin(num x) => _sin(x.toDouble());

/**
 * Converts [x] to a double and returns the cosine of the value.
 *
 * If [x] is not a finite number, the result is NaN.
 */
double cos(num x) => _cos(x.toDouble());

/**
 * 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.
 */
double tan(num x) => _tan(x.toDouble());

/**
 * Converts [x] to a double and returns the arc cosine of the value.
 *
 * Returns a value in the range 0..PI, or NaN if [x] is outside
 * the range -1..1.
 */
double acos(num x) => _acos(x.toDouble());

/**
 * Converts [x] to a double and returns the arc sine of the value.
 *
 * Returns a value in the range -PI/2..PI/2, or NaN if [x] is outside
 * the range -1..1.
 */
double asin(num x) => _asin(x.toDouble());

/**
 * Converts [x] to a double and returns the arc tangent of the value.
 *
 * Returns a value in the range -PI/2..PI/2, or NaN if [x] is NaN.
 */
double atan(num x) => _atan(x.toDouble());

/**
 * 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.
 */
double sqrt(num x) => _sqrt(x.toDouble());

/**
 * Converts [x] to a double and returns the natural exponent, [E],
 * to the power [x].
 *
 * Returns NaN if [x] is NaN.
 */
double exp(num x) => _exp(x.toDouble());

/**
 * 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.
 */
double log(num x) => _log(x.toDouble());

double _doublePow(double base, double exponent) {
  if (exponent == 0.0) {
    return 1.0; // ECMA-262 15.8.2.13
  }
  // Speed up simple cases.
  if (exponent == 1.0) return base;
  if (exponent == 2.0) return base * base;
  if (exponent == 3.0) return base * base * base;

  if (base == 1.0) return 1.0;

  if (base.isNaN || exponent.isNaN) {
    return double.NAN;
  }
  if ((base != -double.INFINITY) && (exponent == 0.5)) {
    if (base == 0.0) {
      return 0.0;
    }
    return sqrt(base);
  }
  return _pow(base.toDouble(), exponent.toDouble());
}
double _pow(double base, double exponent) native "Math_doublePow";
int _intPow(int base, int exponent) {
  // Exponentiation by squaring.
  int result = 1;
  while (exponent != 0) {
    if ((exponent & 1) == 1) {
      result *= base;
    }
    exponent >>= 1;
    // Skip unnecessary operation (can overflow to Mint or Bigint).
    if (exponent != 0) {
      base *= base;
    }
  }
  return result;
}
double _atan2(double a, double b) native "Math_atan2";
double _sin(double x) native "Math_sin";
double _cos(double x) native "Math_cos";
double _tan(double x) native "Math_tan";
double _acos(double x) native "Math_acos";
double _asin(double x) native "Math_asin";
double _atan(double x) native "Math_atan";
double _sqrt(double x) native "Math_sqrt";
double _exp(double x) native "Math_exp";
double _log(double x) native "Math_log";
class _Random implements Random {
  // Internal state of the random number generator.
  final Uint32List _state;
  static const _kSTATE_LO = 0;
  static const _kSTATE_HI = 1; // Unused in Dart code.

  _Random._withState(this._state);

  // The algorithm used here is Multiply with Carry (MWC) with a Base b = 2^32.
  // http://en.wikipedia.org/wiki/Multiply-with-carry
  // The constant A is selected from "Numerical Recipes 3rd Edition" p.348 B1.

  // Implements:
  //   var state =
  //       ((_A * (_state[_kSTATE_LO])) + _state[_kSTATE_HI]) & ((1 << 64) - 1);
  //   _state[_kSTATE_LO] = state & ((1 << 32) - 1);
  //   _state[_kSTATE_HI] = state >> 32;
  // This is a native to prevent 64-bit operations in Dart, which
  // fail with --throw_on_javascript_int_overflow.
  // TODO(regis): Implement in Dart and remove Random_nextState in math.cc.
  void _nextState() native "Random_nextState";

  int nextInt(int max) {
    const limit = 0x3FFFFFFF;
    if ((max <= 0) || ((max > limit) && (max > _POW2_32))) {
      throw new RangeError.range(
          max, 1, _POW2_32, "max", "Must be positive and <= 2^32");
    }
    if ((max & -max) == max) {
      // Fast case for powers of two.
      _nextState();
      return _state[_kSTATE_LO] & (max - 1);
    }

    int rnd32;
    int result;
    do {
      _nextState();
      rnd32 = _state[_kSTATE_LO];
      result = rnd32 % max;
    } while ((rnd32 - result + max) > _POW2_32);
    return result;
  }

  double nextDouble() {
    return ((nextInt(1 << 26) * _POW2_27_D) + nextInt(1 << 27)) / _POW2_53_D;
  }

  bool nextBool() {
    return nextInt(2) == 0;
  }

  // Constants used by the algorithm.
  static const _POW2_32 = 1 << 32;
  static const _POW2_53_D = 1.0 * (1 << 53);
  static const _POW2_27_D = 1.0 * (1 << 27);

  static const _A = 0xffffda61;

  // Use a singleton Random object to get a new seed if no seed was passed.
  static var _prng = new _Random._withState(_initialSeed());

  // This is a native to prevent 64-bit operations in Dart, which
  // fail with --throw_on_javascript_int_overflow.
  // TODO(regis): Implement here in Dart and remove native in math.cc.
  static Uint32List _setupSeed(int seed) native "Random_setupSeed";
  // Get a seed from the VM's random number provider.
  static Uint32List _initialSeed() native "Random_initialSeed";

  static int _nextSeed() {
    // Trigger the PRNG once to change the internal state.
    _prng._nextState();
    return _prng._state[_kSTATE_LO];
  }
}
class _SecureRandom implements Random {
  _SecureRandom() {
    // Throw early in constructor if entropy source is not hooked up.
    _getBytes(1);
  }

  // Return count bytes of entropy as a positive integer; count <= 8.
  static int _getBytes(int count) native "SecureRandom_getBytes";

  int nextInt(int max) {
    RangeError.checkValueInInterval(
        max, 1, _POW2_32, "max", "Must be positive and <= 2^32");
    final byteCount = ((max - 1).bitLength + 7) >> 3;
    if (byteCount == 0) {
      return 0; // Not random if max == 1.
    }
    var rnd;
    var result;
    do {
      rnd = _getBytes(byteCount);
      result = rnd % max;
    } while ((rnd - result + max) > (1 << (byteCount << 3)));
    return result;
  }

  double nextDouble() {
    return (_getBytes(7) >> 3) / _POW2_53_D;
  }

  bool nextBool() {
    return _getBytes(1).isEven;
  }

  // Constants used by the algorithm.
  static const _POW2_32 = 1 << 32;
  static const _POW2_53_D = 1.0 * (1 << 53);
}