GluProject and gluUnProject code

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GLU - the OpenGL Utility library is an additional library that contains a handful of functions for additional tasks.
It is traditional and can be found in a lot of tutorials and examples.
The code here comes from glh library (OpenGL Helper Library), which is for Windows, LGPL license http://www.geocities.com/vmelkon/glhlibrary.html (offline)

GLU offers gluProject and gluUnProject which require doubles.
glhlib, in section Block 9 in the header file, offers double and float, and many versions of these functions such as
glhProjectd
glhProjectf
glhUnProjectd
glhUnProjectf
glhProjectf_2 (large processing, 3D)
glhProjectf_3 (large processing, 4D)
glhUnProjectf_2 (large processing, 3D)
glhUnProjectf_3 (large processing, 4D)
glhProjectf_SSE_Aligned_2
glhProjectf_SSE_Aligned_WarmCache_2
glhProjectf_SSE_Unaligned_2 (don't use this)
glhUnProjectf_SSE_Aligned_2
glhUnProjectf_SSE_Aligned_WarmCache_2
glhUnProjectf_SSE_Unaligned_2 (don't use this)

Here, we will only list the source code for glhProjectf and glhUnProjectf.

 int glhProjectf(float objx, float objy, float objz, float *modelview, float *projection, int *viewport, float *windowCoordinate)
 {
     //Transformation vectors
     float fTempo[8];
     //Modelview transform
     fTempo[0]=modelview[0]*objx+modelview[4]*objy+modelview[8]*objz+modelview[12];  //w is always 1
     fTempo[1]=modelview[1]*objx+modelview[5]*objy+modelview[9]*objz+modelview[13];
     fTempo[2]=modelview[2]*objx+modelview[6]*objy+modelview[10]*objz+modelview[14];
     fTempo[3]=modelview[3]*objx+modelview[7]*objy+modelview[11]*objz+modelview[15];
     //Projection transform, the final row of projection matrix is always [0 0 -1 0]
     //so we optimize for that.
     fTempo[4]=projection[0]*fTempo[0]+projection[4]*fTempo[1]+projection[8]*fTempo[2]+projection[12]*fTempo[3];
     fTempo[5]=projection[1]*fTempo[0]+projection[5]*fTempo[1]+projection[9]*fTempo[2]+projection[13]*fTempo[3];
     fTempo[6]=projection[2]*fTempo[0]+projection[6]*fTempo[1]+projection[10]*fTempo[2]+projection[14]*fTempo[3];
     fTempo[7]=-fTempo[2];
     //The result normalizes between -1 and 1
     if(fTempo[7]==0.0) //The w value
        return 0;
     fTempo[7]=1.0/fTempo[7];
     //Perspective division
     fTempo[4]*=fTempo[7];
     fTempo[5]*=fTempo[7];
     fTempo[6]*=fTempo[7];
     //Window coordinates
     //Map x, y to range 0-1
     windowCoordinate[0]=(fTempo[4]*0.5+0.5)*viewport[2]+viewport[0];
     windowCoordinate[1]=(fTempo[5]*0.5+0.5)*viewport[3]+viewport[1];
     //This is only correct when glDepthRange(0.0, 1.0)
     windowCoordinate[2]=(1.0+fTempo[6])*0.5;   //Between 0 and 1
     return 1;
 }
 int glhUnProjectf(float winx, float winy, float winz, float *modelview, float *projection, int *viewport, float *objectCoordinate)
 {
     //Transformation matrices
     float m[16], A[16];
     float in[4], out[4];
     //Calculation for inverting a matrix, compute projection x modelview
     //and store in A[16]
     MultiplyMatrices4by4OpenGL_FLOAT(A, projection, modelview);
     //Now compute the inverse of matrix A
     if(glhInvertMatrixf2(A, m)==0)
        return 0;
     //Transformation of normalized coordinates between -1 and 1
     in[0]=(winx-(float)viewport[0])/(float)viewport[2]*2.0-1.0;
     in[1]=(winy-(float)viewport[1])/(float)viewport[3]*2.0-1.0;
     in[2]=2.0*winz-1.0;
     in[3]=1.0;
     //Objects coordinates
     MultiplyMatrixByVector4by4OpenGL_FLOAT(out, m, in);
     if(out[3]==0.0)
        return 0;
     out[3]=1.0/out[3];
     objectCoordinate[0]=out[0]*out[3];
     objectCoordinate[1]=out[1]*out[3];
     objectCoordinate[2]=out[2]*out[3];
     return 1;
 }
 void MultiplyMatrices4by4OpenGL_FLOAT(float *result, float *matrix1, float *matrix2)
 {
   result[0]=matrix1[0]*matrix2[0]+
     matrix1[4]*matrix2[1]+
     matrix1[8]*matrix2[2]+
     matrix1[12]*matrix2[3];
   result[4]=matrix1[0]*matrix2[4]+
     matrix1[4]*matrix2[5]+
     matrix1[8]*matrix2[6]+
     matrix1[12]*matrix2[7];
   result[8]=matrix1[0]*matrix2[8]+
     matrix1[4]*matrix2[9]+
     matrix1[8]*matrix2[10]+
     matrix1[12]*matrix2[11];
   result[12]=matrix1[0]*matrix2[12]+
     matrix1[4]*matrix2[13]+
     matrix1[8]*matrix2[14]+
     matrix1[12]*matrix2[15];
   result[1]=matrix1[1]*matrix2[0]+
     matrix1[5]*matrix2[1]+
     matrix1[9]*matrix2[2]+
     matrix1[13]*matrix2[3];
   result[5]=matrix1[1]*matrix2[4]+
     matrix1[5]*matrix2[5]+
     matrix1[9]*matrix2[6]+
     matrix1[13]*matrix2[7];
   result[9]=matrix1[1]*matrix2[8]+
     matrix1[5]*matrix2[9]+
     matrix1[9]*matrix2[10]+
     matrix1[13]*matrix2[11];
   result[13]=matrix1[1]*matrix2[12]+
     matrix1[5]*matrix2[13]+
     matrix1[9]*matrix2[14]+
     matrix1[13]*matrix2[15];
   result[2]=matrix1[2]*matrix2[0]+
     matrix1[6]*matrix2[1]+
     matrix1[10]*matrix2[2]+
     matrix1[14]*matrix2[3];
   result[6]=matrix1[2]*matrix2[4]+
     matrix1[6]*matrix2[5]+
     matrix1[10]*matrix2[6]+
     matrix1[14]*matrix2[7];
   result[10]=matrix1[2]*matrix2[8]+
     matrix1[6]*matrix2[9]+
     matrix1[10]*matrix2[10]+
     matrix1[14]*matrix2[11];
   result[14]=matrix1[2]*matrix2[12]+
     matrix1[6]*matrix2[13]+
     matrix1[10]*matrix2[14]+
     matrix1[14]*matrix2[15];
   result[3]=matrix1[3]*matrix2[0]+
     matrix1[7]*matrix2[1]+
     matrix1[11]*matrix2[2]+
     matrix1[15]*matrix2[3];
   result[7]=matrix1[3]*matrix2[4]+
     matrix1[7]*matrix2[5]+
     matrix1[11]*matrix2[6]+
     matrix1[15]*matrix2[7];
   result[11]=matrix1[3]*matrix2[8]+
     matrix1[7]*matrix2[9]+
     matrix1[11]*matrix2[10]+
     matrix1[15]*matrix2[11];
   result[15]=matrix1[3]*matrix2[12]+
     matrix1[7]*matrix2[13]+
     matrix1[11]*matrix2[14]+
     matrix1[15]*matrix2[15];
 }
 define SWAP_ROWS_DOUBLE(a, b) { sreal2 *_tmp = a; (a)=(b); (b)=_tmp; }
 define SWAP_ROWS_FLOAT(a, b) { sreal *_tmp = a; (a)=(b); (b)=_tmp; }
 define MAT(m,r,c) (m)[(c)*4+(r)]
 //This code comes directly from GLU except that it is for float
 int glhInvertMatrixf2(float *m, float *out)
 {
  float wtmp[4][8];
  float m0, m1, m2, m3, s;
  float *r0, *r1, *r2, *r3;
  r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3];
  r0[0] = MAT(m, 0, 0), r0[1] = MAT(m, 0, 1),
     r0[2] = MAT(m, 0, 2), r0[3] = MAT(m, 0, 3),
     r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0,
     r1[0] = MAT(m, 1, 0), r1[1] = MAT(m, 1, 1),
     r1[2] = MAT(m, 1, 2), r1[3] = MAT(m, 1, 3),
     r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0,
     r2[0] = MAT(m, 2, 0), r2[1] = MAT(m, 2, 1),
     r2[2] = MAT(m, 2, 2), r2[3] = MAT(m, 2, 3),
     r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0,
     r3[0] = MAT(m, 3, 0), r3[1] = MAT(m, 3, 1),
     r3[2] = MAT(m, 3, 2), r3[3] = MAT(m, 3, 3),
     r3[7] = 1.0, r3[4] = r3[5] = r3[6] = 0.0;
  /* choose pivot - or die */
  if (fabsf(r3[0]) > fabsf(r2[0]))
     SWAP_ROWS_FLOAT(r3, r2);
  if (fabsf(r2[0]) > fabsf(r1[0]))
     SWAP_ROWS_FLOAT(r2, r1);
  if (fabsf(r1[0]) > fabsf(r0[0]))
     SWAP_ROWS_FLOAT(r1, r0);
  if (0.0 == r0[0])
     return 0;
  /* eliminate first variable     */
  m1 = r1[0] / r0[0];
  m2 = r2[0] / r0[0];
  m3 = r3[0] / r0[0];
  s = r0[1];
  r1[1] -= m1 * s;
  r2[1] -= m2 * s;
  r3[1] -= m3 * s;
  s = r0[2];
  r1[2] -= m1 * s;
  r2[2] -= m2 * s;
  r3[2] -= m3 * s;
  s = r0[3];
  r1[3] -= m1 * s;
  r2[3] -= m2 * s;
  r3[3] -= m3 * s;
  s = r0[4];
  if (s != 0.0) {
     r1[4] -= m1 * s;
     r2[4] -= m2 * s;
     r3[4] -= m3 * s;
  }
  s = r0[5];
  if (s != 0.0) {
     r1[5] -= m1 * s;
     r2[5] -= m2 * s;
     r3[5] -= m3 * s;
  }
  s = r0[6];
  if (s != 0.0) {
     r1[6] -= m1 * s;
     r2[6] -= m2 * s;
     r3[6] -= m3 * s;
  }
  s = r0[7];
  if (s != 0.0) {
     r1[7] -= m1 * s;
     r2[7] -= m2 * s;
     r3[7] -= m3 * s;
  }
  /* choose pivot - or die */
  if (fabsf(r3[1]) > fabsf(r2[1]))
     SWAP_ROWS_FLOAT(r3, r2);
  if (fabsf(r2[1]) > fabsf(r1[1]))
     SWAP_ROWS_FLOAT(r2, r1);
  if (0.0 == r1[1])
     return 0;
  /* eliminate second variable */
  m2 = r2[1] / r1[1];
  m3 = r3[1] / r1[1];
  r2[2] -= m2 * r1[2];
  r3[2] -= m3 * r1[2];
  r2[3] -= m2 * r1[3];
  r3[3] -= m3 * r1[3];
  s = r1[4];
  if (0.0 != s) {
     r2[4] -= m2 * s;
     r3[4] -= m3 * s;
  }
  s = r1[5];
  if (0.0 != s) {
     r2[5] -= m2 * s;
     r3[5] -= m3 * s;
  }
  s = r1[6];
  if (0.0 != s) {
     r2[6] -= m2 * s;
     r3[6] -= m3 * s;
  }
  s = r1[7];
  if (0.0 != s) {
     r2[7] -= m2 * s;
     r3[7] -= m3 * s;
  }
  /* choose pivot - or die */
  if (fabsf(r3[2]) > fabsf(r2[2]))
     SWAP_ROWS_FLOAT(r3, r2);
  if (0.0 == r2[2])
     return 0;
  /* eliminate third variable */
  m3 = r3[2] / r2[2];
  r3[3] -= m3 * r2[3], r3[4] -= m3 * r2[4],
     r3[5] -= m3 * r2[5], r3[6] -= m3 * r2[6], r3[7] -= m3 * r2[7];
  /* last check */
  if (0.0 == r3[3])
     return 0;
  s = 1.0 / r3[3];              /* now back substitute row 3 */
  r3[4] *= s;
  r3[5] *= s;
  r3[6] *= s;
  r3[7] *= s;
  m2 = r2[3];                   /* now back substitute row 2 */
  s = 1.0 / r2[2];
  r2[4] = s * (r2[4] - r3[4] * m2), r2[5] = s * (r2[5] - r3[5] * m2),
     r2[6] = s * (r2[6] - r3[6] * m2), r2[7] = s * (r2[7] - r3[7] * m2);
  m1 = r1[3];
  r1[4] -= r3[4] * m1, r1[5] -= r3[5] * m1,
     r1[6] -= r3[6] * m1, r1[7] -= r3[7] * m1;
  m0 = r0[3];
  r0[4] -= r3[4] * m0, r0[5] -= r3[5] * m0,
     r0[6] -= r3[6] * m0, r0[7] -= r3[7] * m0;
  m1 = r1[2];                   /* now back substitute row 1 */
  s = 1.0 / r1[1];
  r1[4] = s * (r1[4] - r2[4] * m1), r1[5] = s * (r1[5] - r2[5] * m1),
     r1[6] = s * (r1[6] - r2[6] * m1), r1[7] = s * (r1[7] - r2[7] * m1);
  m0 = r0[2];
  r0[4] -= r2[4] * m0, r0[5] -= r2[5] * m0,
     r0[6] -= r2[6] * m0, r0[7] -= r2[7] * m0;
  m0 = r0[1];                   /* now back substitute row 0 */
  s = 1.0 / r0[0];
  r0[4] = s * (r0[4] - r1[4] * m0), r0[5] = s * (r0[5] - r1[5] * m0),
     r0[6] = s * (r0[6] - r1[6] * m0), r0[7] = s * (r0[7] - r1[7] * m0);
  MAT(out, 0, 0) = r0[4];
  MAT(out, 0, 1) = r0[5], MAT(out, 0, 2) = r0[6];
  MAT(out, 0, 3) = r0[7], MAT(out, 1, 0) = r1[4];
  MAT(out, 1, 1) = r1[5], MAT(out, 1, 2) = r1[6];
  MAT(out, 1, 3) = r1[7], MAT(out, 2, 0) = r2[4];
  MAT(out, 2, 1) = r2[5], MAT(out, 2, 2) = r2[6];
  MAT(out, 2, 3) = r2[7], MAT(out, 3, 0) = r3[4];
  MAT(out, 3, 1) = r3[5], MAT(out, 3, 2) = r3[6];
  MAT(out, 3, 3) = r3[7];
  return 1;
 }