/*
  * Copyright (c) 2006-2007 Erin Catto 
* This software is provided 'as-is', without any express or implied
* warranty.  In no event will the authors be held liable for any damages
* arising from the use of this software.
* Permission is granted to anyone to use this software for any purpose,
* including commercial applications, and to alter it and redistribute it
* freely, subject to the following restrictions:
* 1. The origin of this software must not be misrepresented; you must not
* claim that you wrote the original software. If you use this software
* in a product, an acknowledgment in the product documentation would be
* appreciated but is not required.
* 2. Altered source versions must be plainly marked, and must not be
* misrepresented the original software.
* 3. This notice may not be removed or altered from any source distribution.
*/

var b2Math = Class.create();
b2Math.prototype = {

        /*static public function b2InvSqrt(x)
        {
                float32 xhalf = 0.5f * x;
                int32 i = *(int32*)&x;
                i = 0x5f3759df - (i >> 1);
                x = *(float32*)&i;
                x = x * (1.5f - xhalf * x * x);
                return x;
        }*/

        // A * B

        // A^T * B

        // b2Math.b2Random number in range [-1,1]

        /*inline float32 b2Math.b2Random(float32 lo, float32 hi)
        {
                float32 r = (float32)rand();
                r /= RAND_MAX;
                r = (hi - lo) * r + lo;
                return r;
        }*/

        // "Next Largest Power of 2
        // Given a binary integer value x, the next largest power of 2 can be computed by a SWAR algorithm
        // that recursively "folds" the upper bits into the lower bits. This process yields a bit vector with
        // the same most significant 1, but all 1's below it. Adding 1 to that value yields the next
        // largest power of 2. For a 32-bit value:"

        // Temp vector functions to reduce calls to 'new'
        /*static public var tempVec = new b2Vec2();

        static public var tempAABB = new b2AABB();	*/

        initialize: function() {}}
b2Math.b2IsValid = function(x)
        {
                return isFinite(x);
        };
b2Math.b2Dot = function(a, b)
        {
                return a.x * b.x + a.y * b.y;
        };
b2Math.b2CrossVV = function(a, b)
        {
                return a.x * b.y - a.y * b.x;
        };
b2Math.b2CrossVF = function(a, s)
        {
                var v = new b2Vec2(s * a.y, -s * a.x);
                return v;
        };
b2Math.b2CrossFV = function(s, a)
        {
                var v = new b2Vec2(-s * a.y, s * a.x);
                return v;
        };
b2Math.b2MulMV = function(A, v)
        {
                var u = new b2Vec2(A.col1.x * v.x + A.col2.x * v.y, A.col1.y * v.x + A.col2.y * v.y);
                return u;
        };
b2Math.b2MulTMV = function(A, v)
        {
                var u = new b2Vec2(b2Math.b2Dot(v, A.col1), b2Math.b2Dot(v, A.col2));
                return u;
        };
b2Math.AddVV = function(a, b)
        {
                var v = new b2Vec2(a.x + b.x, a.y + b.y);
                return v;
        };
b2Math.SubtractVV = function(a, b)
        {
                var v = new b2Vec2(a.x - b.x, a.y - b.y);
                return v;
        };
b2Math.MulFV = function(s, a)
        {
                var v = new b2Vec2(s * a.x, s * a.y);
                return v;
        };
b2Math.AddMM = function(A, B)
        {
                var C = new b2Mat22(0, b2Math.AddVV(A.col1, B.col1), b2Math.AddVV(A.col2, B.col2));
                return C;
        };
b2Math.b2MulMM = function(A, B)
        {
                var C = new b2Mat22(0, b2Math.b2MulMV(A, B.col1), b2Math.b2MulMV(A, B.col2));
                return C;
        };
b2Math.b2MulTMM = function(A, B)
        {
                var c1 = new b2Vec2(b2Math.b2Dot(A.col1, B.col1), b2Math.b2Dot(A.col2, B.col1));
                var c2 = new b2Vec2(b2Math.b2Dot(A.col1, B.col2), b2Math.b2Dot(A.col2, B.col2));
                var C = new b2Mat22(0, c1, c2);
                return C;
        };
b2Math.b2Abs = function(a)
        {
                return a > 0.0 ? a : -a;
        };
b2Math.b2AbsV = function(a)
        {
                var b = new b2Vec2(b2Math.b2Abs(a.x), b2Math.b2Abs(a.y));
                return b;
        };
b2Math.b2AbsM = function(A)
        {
                var B = new b2Mat22(0, b2Math.b2AbsV(A.col1), b2Math.b2AbsV(A.col2));
                return B;
        };
b2Math.b2Min = function(a, b)
        {
                return a < b ? a : b;
        };
b2Math.b2MinV = function(a, b)
        {
                var c = new b2Vec2(b2Math.b2Min(a.x, b.x), b2Math.b2Min(a.y, b.y));
                return c;
        };
b2Math.b2Max = function(a, b)
        {
                return a > b ? a : b;
        };
b2Math.b2MaxV = function(a, b)
        {
                var c = new b2Vec2(b2Math.b2Max(a.x, b.x), b2Math.b2Max(a.y, b.y));
                return c;
        };
b2Math.b2Clamp = function(a, low, high)
        {
                return b2Math.b2Max(low, b2Math.b2Min(a, high));
        };
b2Math.b2ClampV = function(a, low, high)
        {
                return b2Math.b2MaxV(low, b2Math.b2MinV(a, high));
        };
b2Math.b2Swap = function(a, b)
        {
                var tmp = a[0];
                a[0] = b[0];
                b[0] = tmp;
        };
b2Math.b2Random = function()
        {
                return Math.random() * 2 - 1;
        };
b2Math.b2NextPowerOfTwo = function(x)
        {
                x |= (x >> 1) & 0x7FFFFFFF;
                x |= (x >> 2) & 0x3FFFFFFF;
                x |= (x >> 4) & 0x0FFFFFFF;
                x |= (x >> 8) & 0x00FFFFFF;
                x |= (x >> 16)& 0x0000FFFF;
                return x + 1;
        };
b2Math.b2IsPowerOfTwo = function(x)
        {
                var result = x > 0 && (x & (x - 1)) == 0;
                return result;
        };
b2Math.tempVec2 = new b2Vec2();
b2Math.tempVec3 = new b2Vec2();
b2Math.tempVec4 = new b2Vec2();
b2Math.tempVec5 = new b2Vec2();
b2Math.tempMat = new b2Mat22();



  *
  * This software is provided 'as-is', without any express or implied
  * warranty.  In no event will the authors be held liable for any damages
  * arising from the use of this software.
  * Permission is granted to anyone to use this software for any purpose,
  * including commercial applications, and to alter it and redistribute it
  * freely, subject to the following restrictions:
  * 1. The origin of this software must not be misrepresented; you must not
  * claim that you wrote the original software. If you use this software
  * in a product, an acknowledgment in the product documentation would be
  * appreciated but is not required.
  * 2. Altered source versions must be plainly marked, and must not be
  * misrepresented the original software.
  * 3. This notice may not be removed or altered from any source distribution.
  */
  
  var b2Math = Class.create();
  b2Math.prototype = {
  
          /*static public function b2InvSqrt(x)
          {
                  float32 xhalf = 0.5f * x;
                  int32 i = *(int32*)&x;
                  i = 0x5f3759df - (i >> 1);
                  x = *(float32*)&i;
                  x = x * (1.5f - xhalf * x * x);
                  return x;
          }*/
  
          // A * B
  
          // A^T * B
  
          // b2Math.b2Random number in range [-1,1]
  
          /*inline float32 b2Math.b2Random(float32 lo, float32 hi)
          {
                  float32 r = (float32)rand();
                  r /= RAND_MAX;
                  r = (hi - lo) * r + lo;
                  return r;
          }*/
  
          // "Next Largest Power of 2
          // Given a binary integer value x, the next largest power of 2 can be computed by a SWAR algorithm
          // that recursively "folds" the upper bits into the lower bits. This process yields a bit vector with
          // the same most significant 1, but all 1's below it. Adding 1 to that value yields the next
          // largest power of 2. For a 32-bit value:"
  
          // Temp vector functions to reduce calls to 'new'
          /*static public var tempVec = new b2Vec2();
  
          static public var tempAABB = new b2AABB();	*/
  
          initialize: function() {}}
  b2Math.b2IsValid = function(x)
          {
                  return isFinite(x);
          };
  b2Math.b2Dot = function(a, b)
          {
                  return a.x * b.x + a.y * b.y;
          };
  b2Math.b2CrossVV = function(a, b)
          {
                  return a.x * b.y - a.y * b.x;
          };
  b2Math.b2CrossVF = function(a, s)
          {
                  var v = new b2Vec2(s * a.y, -s * a.x);
                  return v;
          };
  b2Math.b2CrossFV = function(s, a)
          {
                  var v = new b2Vec2(-s * a.y, s * a.x);
                  return v;
          };
  b2Math.b2MulMV = function(A, v)
          {
                  var u = new b2Vec2(A.col1.x * v.x + A.col2.x * v.y, A.col1.y * v.x + A.col2.y * v.y);
                  return u;
          };
  b2Math.b2MulTMV = function(A, v)
          {
                  var u = new b2Vec2(b2Math.b2Dot(v, A.col1), b2Math.b2Dot(v, A.col2));
                  return u;
          };
  b2Math.AddVV = function(a, b)
          {
                  var v = new b2Vec2(a.x + b.x, a.y + b.y);
                  return v;
          };
  b2Math.SubtractVV = function(a, b)
          {
                  var v = new b2Vec2(a.x - b.x, a.y - b.y);
                  return v;
          };
  b2Math.MulFV = function(s, a)
          {
                  var v = new b2Vec2(s * a.x, s * a.y);
                  return v;
          };
  b2Math.AddMM = function(A, B)
          {
                  var C = new b2Mat22(0, b2Math.AddVV(A.col1, B.col1), b2Math.AddVV(A.col2, B.col2));
                  return C;
          };
  b2Math.b2MulMM = function(A, B)
          {
                  var C = new b2Mat22(0, b2Math.b2MulMV(A, B.col1), b2Math.b2MulMV(A, B.col2));
                  return C;
          };
  b2Math.b2MulTMM = function(A, B)
          {
                  var c1 = new b2Vec2(b2Math.b2Dot(A.col1, B.col1), b2Math.b2Dot(A.col2, B.col1));
                  var c2 = new b2Vec2(b2Math.b2Dot(A.col1, B.col2), b2Math.b2Dot(A.col2, B.col2));
                  var C = new b2Mat22(0, c1, c2);
                  return C;
          };
  b2Math.b2Abs = function(a)
          {
                  return a > 0.0 ? a : -a;
          };
  b2Math.b2AbsV = function(a)
          {
                  var b = new b2Vec2(b2Math.b2Abs(a.x), b2Math.b2Abs(a.y));
                  return b;
          };
  b2Math.b2AbsM = function(A)
          {
                  var B = new b2Mat22(0, b2Math.b2AbsV(A.col1), b2Math.b2AbsV(A.col2));
                  return B;
          };
  b2Math.b2Min = function(a, b)
          {
                  return a < b ? a : b;
          };
  b2Math.b2MinV = function(a, b)
          {
                  var c = new b2Vec2(b2Math.b2Min(a.x, b.x), b2Math.b2Min(a.y, b.y));
                  return c;
          };
  b2Math.b2Max = function(a, b)
          {
                  return a > b ? a : b;
          };
  b2Math.b2MaxV = function(a, b)
          {
                  var c = new b2Vec2(b2Math.b2Max(a.x, b.x), b2Math.b2Max(a.y, b.y));
                  return c;
          };
  b2Math.b2Clamp = function(a, low, high)
          {
                  return b2Math.b2Max(low, b2Math.b2Min(a, high));
          };
  b2Math.b2ClampV = function(a, low, high)
          {
                  return b2Math.b2MaxV(low, b2Math.b2MinV(a, high));
          };
  b2Math.b2Swap = function(a, b)
          {
                  var tmp = a[0];
                  a[0] = b[0];
                  b[0] = tmp;
          };
  b2Math.b2Random = function()
          {
                  return Math.random() * 2 - 1;
          };
  b2Math.b2NextPowerOfTwo = function(x)
          {
                  x |= (x >> 1) & 0x7FFFFFFF;
                  x |= (x >> 2) & 0x3FFFFFFF;
                  x |= (x >> 4) & 0x0FFFFFFF;
                  x |= (x >> 8) & 0x00FFFFFF;
                  x |= (x >> 16)& 0x0000FFFF;
                  return x + 1;
          };
  b2Math.b2IsPowerOfTwo = function(x)
          {
                  var result = x > 0 && (x & (x - 1)) == 0;
                  return result;
          };
  b2Math.tempVec2 = new b2Vec2();
  b2Math.tempVec3 = new b2Vec2();
  b2Math.tempVec4 = new b2Vec2();
  b2Math.tempVec5 = new b2Vec2();
  b2Math.tempMat = new b2Mat22();