GluProject and gluUnProject code

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];
 }