text: ///////////////////////////////////////////////////////////////////////////////////////////////////
  // OpenGL Mathematics Copyright (c) 2005 - 2014 G-Truc Creation (www.g-truc.net)
  ///////////////////////////////////////////////////////////////////////////////////////////////////
  // Created : 2013-02-10
  // Updated : 2013-02-11
  // Licence : This source is under MIT licence
  // File    : test/gtc/gtc_dual_quaternion.cpp
  ///////////////////////////////////////////////////////////////////////////////////////////////////
  
  #define GLM_FORCE_RADIANS
  #include <glm/gtx/dual_quaternion.hpp>
  #include <glm/gtc/matrix_transform.hpp>
  #include <glm/gtc/epsilon.hpp>
  #include <glm/gtx/euler_angles.hpp>
  #include <glm/vector_relational.hpp>
  
  #include <iostream>
  
  int myrand()
  {
  	static int holdrand = 1;
  	return (((holdrand = holdrand * 214013L + 2531011L) >> 16) & 0x7fff);
  }
  
  float myfrand() // returns values from -1 to 1 inclusive
  {
  	return float(double(myrand()) / double( 0x7ffff )) * 2.0f - 1.0f;
  }
  
  int test_dquat_type()
  {
  	glm::dvec3 vA;
  	glm::dquat dqA,dqB;
  	glm::ddualquat C(dqA,dqB);
  	glm::ddualquat B(dqA);
  	glm::ddualquat D(dqA,vA);
  	return 0;
  }
  
  int test_scalars() {
      float const Epsilon = 0.0001f;
  
      int Error(0);
  
      glm::quat src_q1 = glm::quat(1.0f,2.0f,3.0f,4.0f);
      glm::quat src_q2 = glm::quat(5.0f,6.0f,7.0f,8.0f);
      glm::dualquat src1(src_q1,src_q2);
  
      {
          glm::dualquat dst1 = src1 * 2.0f;
          glm::dualquat dst2 = 2.0f * src1;
          glm::dualquat dst3 = src1;
          dst3 *= 2.0f;
          glm::dualquat dstCmp(src_q1 * 2.0f,src_q2 * 2.0f);
          Error += glm::all(glm::epsilonEqual(dst1.real,dstCmp.real, Epsilon)) && glm::all(glm::epsilonEqual(dst1.dual,dstCmp.dual, Epsilon)) ? 0 : 1;
          Error += glm::all(glm::epsilonEqual(dst2.real,dstCmp.real, Epsilon)) && glm::all(glm::epsilonEqual(dst2.dual,dstCmp.dual, Epsilon)) ? 0 : 1;
          Error += glm::all(glm::epsilonEqual(dst3.real,dstCmp.real, Epsilon)) && glm::all(glm::epsilonEqual(dst3.dual,dstCmp.dual, Epsilon)) ? 0 : 1;
      }
  
      {
          glm::dualquat dst1 = src1 / 2.0f;
          glm::dualquat dst2 = src1;
          dst2 /= 2.0f;
          glm::dualquat dstCmp(src_q1 / 2.0f,src_q2 / 2.0f);
          Error += glm::all(glm::epsilonEqual(dst1.real,dstCmp.real, Epsilon)) && glm::all(glm::epsilonEqual(dst1.dual,dstCmp.dual, Epsilon)) ? 0 : 1;
          Error += glm::all(glm::epsilonEqual(dst2.real,dstCmp.real, Epsilon)) && glm::all(glm::epsilonEqual(dst2.dual,dstCmp.dual, Epsilon)) ? 0 : 1;
      }
      return Error;
  }
  
  int test_inverse() 
  {
      int Error(0);
  
      float const Epsilon = 0.0001f;
  
      glm::dualquat dqid;
      glm::mat4x4 mid(1.0f);
  
      for (int j = 0; j < 100; ++j)
  	{
          glm::mat4x4 rot = glm::yawPitchRoll(myfrand() * 360.0f, myfrand() * 360.0f, myfrand() * 360.0f);
          glm::vec3 vt = glm::vec3(myfrand() * 10.0f, myfrand() * 10.0f, myfrand() * 10.0f);
  
          glm::mat4x4 m = glm::translate(mid, vt) * rot;
  
          glm::quat qr = glm::quat_cast(m);
  
          glm::dualquat dq(qr);
          
          glm::dualquat invdq = glm::inverse(dq);
  
          glm::dualquat r1 = invdq * dq;
          glm::dualquat r2 = dq * invdq;
  
          Error += glm::all(glm::epsilonEqual(r1.real, dqid.real, Epsilon)) && glm::all(glm::epsilonEqual(r1.dual, dqid.dual, Epsilon)) ? 0 : 1;
          Error += glm::all(glm::epsilonEqual(r2.real, dqid.real, Epsilon)) && glm::all(glm::epsilonEqual(r2.dual, dqid.dual, Epsilon)) ? 0 : 1;
  
          // testing commutative property
          glm::dualquat r (   glm::quat( myfrand() * glm::pi<float>() * 2.0f, myfrand(), myfrand(), myfrand() ),
                              glm::vec3(myfrand() * 10.0f, myfrand() * 10.0f, myfrand() * 10.0f) );
          glm::dualquat riq = (r * invdq) * dq;
          glm::dualquat rqi = (r * dq) * invdq;
  
          Error += glm::all(glm::epsilonEqual(riq.real, rqi.real, Epsilon)) && glm::all(glm::epsilonEqual(riq.dual, rqi.dual, Epsilon)) ? 0 : 1;
      }
  
      return Error;
  }
  
  int test_mul() 
  {
      int Error(0);
  
      float const Epsilon = 0.0001f;
  
      glm::mat4x4 mid(1.0f);
  
      for (int j = 0; j < 100; ++j) {
          // generate random rotations and translations and compare transformed by matrix and dualquats random points 
          glm::vec3 vt1 = glm::vec3(myfrand() * 10.0f, myfrand() * 10.0f, myfrand() * 10.0f);
          glm::vec3 vt2 = glm::vec3(myfrand() * 10.0f, myfrand() * 10.0f, myfrand() * 10.0f);
  
          glm::mat4x4 rot1 = glm::yawPitchRoll(myfrand() * 360.0f, myfrand() * 360.0f, myfrand() * 360.0f);
          glm::mat4x4 rot2 = glm::yawPitchRoll(myfrand() * 360.0f, myfrand() * 360.0f, myfrand() * 360.0f);
          glm::mat4x4 m1 = glm::translate(mid, vt1) * rot1;
          glm::mat4x4 m2 = glm::translate(mid, vt2) * rot2;
          glm::mat4x4 m3 = m2 * m1;
          glm::mat4x4 m4 = m1 * m2;
  
          glm::quat qrot1 = glm::quat_cast(rot1);
          glm::quat qrot2 = glm::quat_cast(rot2);
  
          glm::dualquat dq1 = glm::dualquat(qrot1,vt1);
          glm::dualquat dq2 = glm::dualquat(qrot2,vt2);
          glm::dualquat dq3 = dq2 * dq1;
          glm::dualquat dq4 = dq1 * dq2;
  
          for (int i = 0; i < 100; ++i) {
              glm::vec4 src_pt = glm::vec4(myfrand() * 4.0f, myfrand() * 5.0f, myfrand() * 3.0f,1.0f);
              // test both multiplication orders        
              glm::vec4 dst_pt_m3  = m3 * src_pt; 
              glm::vec4 dst_pt_dq3 = dq3 * src_pt;
           
              glm::vec4 dst_pt_m3_i  = glm::inverse(m3) * src_pt;
              glm::vec4 dst_pt_dq3_i = src_pt * dq3;
  
              glm::vec4 dst_pt_m4  = m4 * src_pt;
              glm::vec4 dst_pt_dq4 = dq4 * src_pt;
  
              glm::vec4 dst_pt_m4_i  = glm::inverse(m4) * src_pt;
              glm::vec4 dst_pt_dq4_i = src_pt * dq4;
  
              Error += glm::all(glm::epsilonEqual(dst_pt_m3, dst_pt_dq3, Epsilon)) ? 0 : 1;
              Error += glm::all(glm::epsilonEqual(dst_pt_m4, dst_pt_dq4, Epsilon)) ? 0 : 1;
              Error += glm::all(glm::epsilonEqual(dst_pt_m3_i, dst_pt_dq3_i, Epsilon)) ? 0 : 1;
              Error += glm::all(glm::epsilonEqual(dst_pt_m4_i, dst_pt_dq4_i, Epsilon)) ? 0 : 1;
          }
      } 
  
      return Error;
  }
  
  int main()
  {
      int Error(0);
  
      Error += test_dquat_type();
      Error += test_scalars();
      Error += test_inverse();
      Error += test_mul();
  
      //std::cout << "Errors count: " << Error << std::endl;
      return Error;
  }
  