added aligned memory allocations (Gareth Hughes)

[mesa.git] / src / mesa / main / matrix.c

/* $Id: matrix.c,v 1.18 2000/06/27 22:10:00 brianp Exp $ */

/*
 * Mesa 3-D graphics library
 * Version:  3.3
 * 
 * Copyright (C) 1999-2000  Brian Paul   All Rights Reserved.
 * 
 * Permission is hereby granted, free of charge, to any person obtaining a
 * copy of this software and associated documentation files (the "Software"),
 * to deal in the Software without restriction, including without limitation
 * the rights to use, copy, modify, merge, publish, distribute, sublicense,
 * and/or sell copies of the Software, and to permit persons to whom the
 * Software is furnished to do so, subject to the following conditions:
 * 
 * The above copyright notice and this permission notice shall be included
 * in all copies or substantial portions of the Software.
 * 
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
 * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL
 * BRIAN PAUL BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN
 * AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
 * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
 */


/*
 * Matrix operations
 *
 *
 * NOTES:
 * 1. 4x4 transformation matrices are stored in memory in column major order.
 * 2. Points/vertices are to be thought of as column vectors.
 * 3. Transformation of a point p by a matrix M is: p' = M * p
 *
 */


#ifdef PC_HEADER
#include "all.h"
#else
#include "glheader.h"
#include "buffers.h"
#include "context.h"
#include "enums.h"
#include "matrix.h"
#include "mem.h"
#include "mmath.h"
#include "types.h"
#endif


static const char *types[] = {
   "MATRIX_GENERAL",
   "MATRIX_IDENTITY",
   "MATRIX_3D_NO_ROT",
   "MATRIX_PERSPECTIVE",
   "MATRIX_2D",
   "MATRIX_2D_NO_ROT",
   "MATRIX_3D"
};
static void matmul4( GLfloat *product, const GLfloat *a, const GLfloat *b );


static GLfloat Identity[16] = {
   1.0, 0.0, 0.0, 0.0,
   0.0, 1.0, 0.0, 0.0,
   0.0, 0.0, 1.0, 0.0,
   0.0, 0.0, 0.0, 1.0
};


static void print_matrix_floats( const GLfloat m[16] )
{
   int i;
   for (i=0;i<4;i++) {
      fprintf(stderr,"\t%f %f %f %f\n", m[i], m[4+i], m[8+i], m[12+i] );
   }
}

void gl_print_matrix( const GLmatrix *m )
{
   fprintf(stderr, "Matrix type: %s, flags: %x\n", types[m->type], m->flags);
   print_matrix_floats(m->m);
#if 1
   fprintf(stderr, "Inverse: \n");
   if (m->inv) {
      GLfloat prod[16];
      print_matrix_floats(m->inv);
      matmul4(prod, m->m, m->inv);
      fprintf(stderr, "Mat * Inverse:\n");
      print_matrix_floats(prod);
  } else 
      fprintf(stderr, "  - not available\n");
#endif
}



/*
 * This matmul was contributed by Thomas Malik 
 *
 * Perform a 4x4 matrix multiplication  (product = a x b).
 * Input:  a, b - matrices to multiply
 * Output:  product - product of a and b
 * WARNING: (product != b) assumed
 * NOTE:    (product == a) allowed    
 *
 * KW: 4*16 = 64 muls
 */
#define A(row,col)  a[(col<<2)+row]
#define B(row,col)  b[(col<<2)+row]
#define P(row,col)  product[(col<<2)+row]

static void matmul4( GLfloat *product, const GLfloat *a, const GLfloat *b )
{
   GLint i;
   for (i = 0; i < 4; i++) {
      GLfloat ai0=A(i,0),  ai1=A(i,1),  ai2=A(i,2),  ai3=A(i,3);
      P(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0) + ai3 * B(3,0);
      P(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1) + ai3 * B(3,1);
      P(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2) + ai3 * B(3,2);
      P(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3 * B(3,3);
   }
}




/* Multiply two matrices known to occupy only the top three rows,
 * such as typical modelling matrices, and ortho matrices.
 *
 * KW: 3*9 = 27 muls
 */
static void matmul34( GLfloat *product, const GLfloat *a, const GLfloat *b )
{
   GLint i;
   for (i = 0; i < 3; i++) {
      GLfloat ai0=A(i,0),  ai1=A(i,1),  ai2=A(i,2),  ai3=A(i,3);
      P(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0);
      P(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1);
      P(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2);
      P(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3;
   }
   P(3,0) = 0;
   P(3,1) = 0;
   P(3,2) = 0;
   P(3,3) = 1;
}

static void matmul4fd( GLfloat *product, const GLfloat *a, const GLdouble *b )
{
   GLint i;
   for (i = 0; i < 4; i++) {
      GLfloat ai0=A(i,0),  ai1=A(i,1),  ai2=A(i,2),  ai3=A(i,3);
      P(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0) + ai3 * B(3,0);
      P(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1) + ai3 * B(3,1);
      P(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2) + ai3 * B(3,2);
      P(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3 * B(3,3);
   }
}

#undef A
#undef B
#undef P



#define SWAP_ROWS(a, b) { GLfloat *_tmp = a; (a)=(b); (b)=_tmp; }
#define MAT(m,r,c) (m)[(c)*4+(r)]

/*
 * Compute inverse of 4x4 transformation matrix.
 * Code contributed by Jacques Leroy jle@star.be
 * Return GL_TRUE for success, GL_FALSE for failure (singular matrix)
 */
static GLboolean invert_matrix_general( GLmatrix *mat )
{
   const GLfloat *m = mat->m;
   GLfloat *out = mat->inv;
   GLfloat wtmp[4][8];
   GLfloat m0, m1, m2, m3, s;
   GLfloat *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 (fabs(r3[0])>fabs(r2[0])) SWAP_ROWS(r3, r2);
   if (fabs(r2[0])>fabs(r1[0])) SWAP_ROWS(r2, r1);
   if (fabs(r1[0])>fabs(r0[0])) SWAP_ROWS(r1, r0);
   if (0.0 == r0[0])  return GL_FALSE;
  
   /* 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 (fabs(r3[1])>fabs(r2[1])) SWAP_ROWS(r3, r2);
   if (fabs(r2[1])>fabs(r1[1])) SWAP_ROWS(r2, r1);
   if (0.0 == r1[1])  return GL_FALSE;
  
   /* 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 (fabs(r3[2])>fabs(r2[2])) SWAP_ROWS(r3, r2);
   if (0.0 == r2[2])  return GL_FALSE;
  
   /* 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 GL_FALSE;
  
   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 GL_TRUE;
}
#undef SWAP_ROWS

/* Adapted from graphics gems II.
 */  
static GLboolean invert_matrix_3d_general( GLmatrix *mat )
{
   const GLfloat *in = mat->m;
   GLfloat *out = mat->inv;
   GLfloat pos, neg, t;
   GLfloat det;

   /* Calculate the determinant of upper left 3x3 submatrix and
    * determine if the matrix is singular. 
    */
   pos = neg = 0.0;
   t =  MAT(in,0,0) * MAT(in,1,1) * MAT(in,2,2);
   if (t >= 0.0) pos += t; else neg += t;

   t =  MAT(in,1,0) * MAT(in,2,1) * MAT(in,0,2);
   if (t >= 0.0) pos += t; else neg += t;

   t =  MAT(in,2,0) * MAT(in,0,1) * MAT(in,1,2);
   if (t >= 0.0) pos += t; else neg += t;

   t = -MAT(in,2,0) * MAT(in,1,1) * MAT(in,0,2);
   if (t >= 0.0) pos += t; else neg += t;

   t = -MAT(in,1,0) * MAT(in,0,1) * MAT(in,2,2);
   if (t >= 0.0) pos += t; else neg += t;

   t = -MAT(in,0,0) * MAT(in,2,1) * MAT(in,1,2);
   if (t >= 0.0) pos += t; else neg += t;

   det = pos + neg;

   if (det*det < 1e-25) 
      return GL_FALSE;
   
   det = 1.0 / det;
   MAT(out,0,0) = (  (MAT(in,1,1)*MAT(in,2,2) - MAT(in,2,1)*MAT(in,1,2) )*det);
   MAT(out,0,1) = (- (MAT(in,0,1)*MAT(in,2,2) - MAT(in,2,1)*MAT(in,0,2) )*det);
   MAT(out,0,2) = (  (MAT(in,0,1)*MAT(in,1,2) - MAT(in,1,1)*MAT(in,0,2) )*det);
   MAT(out,1,0) = (- (MAT(in,1,0)*MAT(in,2,2) - MAT(in,2,0)*MAT(in,1,2) )*det);
   MAT(out,1,1) = (  (MAT(in,0,0)*MAT(in,2,2) - MAT(in,2,0)*MAT(in,0,2) )*det);
   MAT(out,1,2) = (- (MAT(in,0,0)*MAT(in,1,2) - MAT(in,1,0)*MAT(in,0,2) )*det);
   MAT(out,2,0) = (  (MAT(in,1,0)*MAT(in,2,1) - MAT(in,2,0)*MAT(in,1,1) )*det);
   MAT(out,2,1) = (- (MAT(in,0,0)*MAT(in,2,1) - MAT(in,2,0)*MAT(in,0,1) )*det);
   MAT(out,2,2) = (  (MAT(in,0,0)*MAT(in,1,1) - MAT(in,1,0)*MAT(in,0,1) )*det);

   /* Do the translation part */
   MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0) +
                     MAT(in,1,3) * MAT(out,0,1) +
                     MAT(in,2,3) * MAT(out,0,2) );
   MAT(out,1,3) = - (MAT(in,0,3) * MAT(out,1,0) +
                     MAT(in,1,3) * MAT(out,1,1) +
                     MAT(in,2,3) * MAT(out,1,2) );
   MAT(out,2,3) = - (MAT(in,0,3) * MAT(out,2,0) +
                     MAT(in,1,3) * MAT(out,2,1) +
                     MAT(in,2,3) * MAT(out,2,2) );
    
   return GL_TRUE;
}


static GLboolean invert_matrix_3d( GLmatrix *mat )
{
   const GLfloat *in = mat->m;
   GLfloat *out = mat->inv;

   if (!TEST_MAT_FLAGS(mat, MAT_FLAGS_ANGLE_PRESERVING))
   {
      return invert_matrix_3d_general( mat );
   }
   
   if (mat->flags & MAT_FLAG_UNIFORM_SCALE)
   {
      GLfloat  scale = (MAT(in,0,0) * MAT(in,0,0) +
                        MAT(in,0,1) * MAT(in,0,1) +
                        MAT(in,0,2) * MAT(in,0,2));

      if (scale == 0.0) 
         return GL_FALSE;

      scale = 1.0 / scale;

      /* Transpose and scale the 3 by 3 upper-left submatrix. */
      MAT(out,0,0) = scale * MAT(in,0,0);
      MAT(out,1,0) = scale * MAT(in,0,1);
      MAT(out,2,0) = scale * MAT(in,0,2);
      MAT(out,0,1) = scale * MAT(in,1,0);
      MAT(out,1,1) = scale * MAT(in,1,1);
      MAT(out,2,1) = scale * MAT(in,1,2);
      MAT(out,0,2) = scale * MAT(in,2,0);
      MAT(out,1,2) = scale * MAT(in,2,1);
      MAT(out,2,2) = scale * MAT(in,2,2);
   }
   else if (mat->flags & MAT_FLAG_ROTATION)
   {
      /* Transpose the 3 by 3 upper-left submatrix. */
      MAT(out,0,0) = MAT(in,0,0);
      MAT(out,1,0) = MAT(in,0,1);
      MAT(out,2,0) = MAT(in,0,2);
      MAT(out,0,1) = MAT(in,1,0);
      MAT(out,1,1) = MAT(in,1,1);
      MAT(out,2,1) = MAT(in,1,2);
      MAT(out,0,2) = MAT(in,2,0);
      MAT(out,1,2) = MAT(in,2,1);
      MAT(out,2,2) = MAT(in,2,2);
   }
   else /* pure translation */
   {
      MEMCPY( out, Identity, sizeof(Identity) );
      MAT(out,0,3) = - MAT(in,0,3);
      MAT(out,1,3) = - MAT(in,1,3);
      MAT(out,2,3) = - MAT(in,2,3);
      return GL_TRUE;
   }
    
   if (mat->flags & MAT_FLAG_TRANSLATION)
   {
      /* Do the translation part */
      MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0) +
                        MAT(in,1,3) * MAT(out,0,1) +
                        MAT(in,2,3) * MAT(out,0,2) );
      MAT(out,1,3) = - (MAT(in,0,3) * MAT(out,1,0) +
                        MAT(in,1,3) * MAT(out,1,1) +
                        MAT(in,2,3) * MAT(out,1,2) );
      MAT(out,2,3) = - (MAT(in,0,3) * MAT(out,2,0) +
                        MAT(in,1,3) * MAT(out,2,1) +
                        MAT(in,2,3) * MAT(out,2,2) );
   }
   else 
   {
      MAT(out,0,3) = MAT(out,1,3) = MAT(out,2,3) = 0.0;
   }
    
   return GL_TRUE;
}

  

static GLboolean invert_matrix_identity( GLmatrix *mat )
{
   MEMCPY( mat->inv, Identity, sizeof(Identity) );
   return GL_TRUE;
}


static GLboolean invert_matrix_3d_no_rot( GLmatrix *mat )
{
   const GLfloat *in = mat->m;
   GLfloat *out = mat->inv;

   if (MAT(in,0,0) == 0 || MAT(in,1,1) == 0 || MAT(in,2,2) == 0 )       
      return GL_FALSE;
  
   MEMCPY( out, Identity, 16 * sizeof(GLfloat) );
   MAT(out,0,0) = 1.0 / MAT(in,0,0);
   MAT(out,1,1) = 1.0 / MAT(in,1,1);
   MAT(out,2,2) = 1.0 / MAT(in,2,2);

   if (mat->flags & MAT_FLAG_TRANSLATION)
   {
      MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0));
      MAT(out,1,3) = - (MAT(in,1,3) * MAT(out,1,1));
      MAT(out,2,3) = - (MAT(in,2,3) * MAT(out,2,2));
   }

   return GL_TRUE;
}


static GLboolean invert_matrix_2d_no_rot( GLmatrix *mat )
{
   const GLfloat *in = mat->m;
   GLfloat *out = mat->inv;

   if (MAT(in,0,0) == 0 || MAT(in,1,1) == 0)       
      return GL_FALSE;
  
   MEMCPY( out, Identity, 16 * sizeof(GLfloat) );
   MAT(out,0,0) = 1.0 / MAT(in,0,0);
   MAT(out,1,1) = 1.0 / MAT(in,1,1);

   if (mat->flags & MAT_FLAG_TRANSLATION)
   {
      MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0));
      MAT(out,1,3) = - (MAT(in,1,3) * MAT(out,1,1));
   }

   return GL_TRUE;
}


static GLboolean invert_matrix_perspective( GLmatrix *mat )
{
   const GLfloat *in = mat->m;
   GLfloat *out = mat->inv;

   if (MAT(in,2,3) == 0)
      return GL_FALSE;

   MEMCPY( out, Identity, 16 * sizeof(GLfloat) );

   MAT(out,0,0) = 1.0 / MAT(in,0,0);
   MAT(out,1,1) = 1.0 / MAT(in,1,1);

   MAT(out,0,3) = MAT(in,0,2);
   MAT(out,1,3) = MAT(in,1,2);

   MAT(out,2,2) = 0;
   MAT(out,2,3) = -1;

   MAT(out,3,2) = 1.0 / MAT(in,2,3);
   MAT(out,3,3) = MAT(in,2,2) * MAT(out,3,2);

   return GL_TRUE;
}


typedef GLboolean (*inv_mat_func)( GLmatrix *mat );

static inv_mat_func inv_mat_tab[7] = {
   invert_matrix_general,
   invert_matrix_identity,
   invert_matrix_3d_no_rot,
   invert_matrix_perspective,
   invert_matrix_3d,            /* lazy! */
   invert_matrix_2d_no_rot,
   invert_matrix_3d
};


GLboolean gl_matrix_invert( GLmatrix *mat )
{
   if (inv_mat_tab[mat->type](mat)) {
#if 0
      GLmatrix m; m.inv = 0; m.type = 0; m.flags = 0;
      matmul4( m.m, mat->m, mat->inv );
      printf("inverted matrix of type %s:\n", types[mat->type]);
      gl_print_matrix( mat );
      gl_print_matrix( &m );
#endif
      return GL_TRUE;
   } else {
      MEMCPY( mat->inv, Identity, sizeof(Identity) );
      return GL_FALSE;
   }  
}



void gl_matrix_transposef( GLfloat to[16], const GLfloat from[16] )
{
   to[0] = from[0];
   to[1] = from[4];
   to[2] = from[8];
   to[3] = from[12];
   to[4] = from[1];
   to[5] = from[5];
   to[6] = from[9];
   to[7] = from[13];
   to[8] = from[2];
   to[9] = from[6];
   to[10] = from[10];
   to[11] = from[14];
   to[12] = from[3];
   to[13] = from[7];
   to[14] = from[11];
   to[15] = from[15];
}



void gl_matrix_transposed( GLdouble to[16], const GLdouble from[16] )
{
   to[0] = from[0];
   to[1] = from[4];
   to[2] = from[8];
   to[3] = from[12];
   to[4] = from[1];
   to[5] = from[5];
   to[6] = from[9];
   to[7] = from[13];
   to[8] = from[2];
   to[9] = from[6];
   to[10] = from[10];
   to[11] = from[14];
   to[12] = from[3];
   to[13] = from[7];
   to[14] = from[11];
   to[15] = from[15];
}



/*
 * Generate a 4x4 transformation matrix from glRotate parameters.
 */
void gl_rotation_matrix( GLfloat angle, GLfloat x, GLfloat y, GLfloat z,
                         GLfloat m[] )
{
   /* This function contributed by Erich Boleyn (erich@uruk.org) */
   GLfloat mag, s, c;
   GLfloat xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c;

   s = sin( angle * DEG2RAD );
   c = cos( angle * DEG2RAD );

   mag = GL_SQRT( x*x + y*y + z*z );

   if (mag == 0.0) {
      /* generate an identity matrix and return */
      MEMCPY(m, Identity, sizeof(GLfloat)*16);
      return;
   }

   x /= mag;
   y /= mag;
   z /= mag;

#define M(row,col)  m[col*4+row]

   /*
    *     Arbitrary axis rotation matrix.
    *
    *  This is composed of 5 matrices, Rz, Ry, T, Ry', Rz', multiplied
    *  like so:  Rz * Ry * T * Ry' * Rz'.  T is the final rotation
    *  (which is about the X-axis), and the two composite transforms
    *  Ry' * Rz' and Rz * Ry are (respectively) the rotations necessary
    *  from the arbitrary axis to the X-axis then back.  They are
    *  all elementary rotations.
    *
    *  Rz' is a rotation about the Z-axis, to bring the axis vector
    *  into the x-z plane.  Then Ry' is applied, rotating about the
    *  Y-axis to bring the axis vector parallel with the X-axis.  The
    *  rotation about the X-axis is then performed.  Ry and Rz are
    *  simply the respective inverse transforms to bring the arbitrary
    *  axis back to it's original orientation.  The first transforms
    *  Rz' and Ry' are considered inverses, since the data from the
    *  arbitrary axis gives you info on how to get to it, not how
    *  to get away from it, and an inverse must be applied.
    *
    *  The basic calculation used is to recognize that the arbitrary
    *  axis vector (x, y, z), since it is of unit length, actually
    *  represents the sines and cosines of the angles to rotate the
    *  X-axis to the same orientation, with theta being the angle about
    *  Z and phi the angle about Y (in the order described above)
    *  as follows:
    *
    *  cos ( theta ) = x / sqrt ( 1 - z^2 )
    *  sin ( theta ) = y / sqrt ( 1 - z^2 )
    *
    *  cos ( phi ) = sqrt ( 1 - z^2 )
    *  sin ( phi ) = z
    *
    *  Note that cos ( phi ) can further be inserted to the above
    *  formulas:
    *
    *  cos ( theta ) = x / cos ( phi )
    *  sin ( theta ) = y / sin ( phi )
    *
    *  ...etc.  Because of those relations and the standard trigonometric
    *  relations, it is pssible to reduce the transforms down to what
    *  is used below.  It may be that any primary axis chosen will give the
    *  same results (modulo a sign convention) using thie method.
    *
    *  Particularly nice is to notice that all divisions that might
    *  have caused trouble when parallel to certain planes or
    *  axis go away with care paid to reducing the expressions.
    *  After checking, it does perform correctly under all cases, since
    *  in all the cases of division where the denominator would have
    *  been zero, the numerator would have been zero as well, giving
    *  the expected result.
    */

   xx = x * x;
   yy = y * y;
   zz = z * z;
   xy = x * y;
   yz = y * z;
   zx = z * x;
   xs = x * s;
   ys = y * s;
   zs = z * s;
   one_c = 1.0F - c;

   M(0,0) = (one_c * xx) + c;
   M(0,1) = (one_c * xy) - zs;
   M(0,2) = (one_c * zx) + ys;
   M(0,3) = 0.0F;

   M(1,0) = (one_c * xy) + zs;
   M(1,1) = (one_c * yy) + c;
   M(1,2) = (one_c * yz) - xs;
   M(1,3) = 0.0F;

   M(2,0) = (one_c * zx) - ys;
   M(2,1) = (one_c * yz) + xs;
   M(2,2) = (one_c * zz) + c;
   M(2,3) = 0.0F;

   M(3,0) = 0.0F;
   M(3,1) = 0.0F;
   M(3,2) = 0.0F;
   M(3,3) = 1.0F;

#undef M
}

#define ZERO(x) (1<<x)
#define ONE(x)  (1<<(x+16))

#define MASK_NO_TRX      (ZERO(12) | ZERO(13) | ZERO(14))
#define MASK_NO_2D_SCALE ( ONE(0)  | ONE(5))

#define MASK_IDENTITY    ( ONE(0)  | ZERO(4)  | ZERO(8)  | ZERO(12) |\
                          ZERO(1)  |  ONE(5)  | ZERO(9)  | ZERO(13) |\
                          ZERO(2)  | ZERO(6)  |  ONE(10) | ZERO(14) |\
                          ZERO(3)  | ZERO(7)  | ZERO(11) |  ONE(15) )

#define MASK_2D_NO_ROT   (           ZERO(4)  | ZERO(8)  |           \
                          ZERO(1)  |            ZERO(9)  |           \
                          ZERO(2)  | ZERO(6)  |  ONE(10) | ZERO(14) |\
                          ZERO(3)  | ZERO(7)  | ZERO(11) |  ONE(15) )

#define MASK_2D          (                      ZERO(8)  |           \
                                                ZERO(9)  |           \
                          ZERO(2)  | ZERO(6)  |  ONE(10) | ZERO(14) |\
                          ZERO(3)  | ZERO(7)  | ZERO(11) |  ONE(15) )


#define MASK_3D_NO_ROT   (           ZERO(4)  | ZERO(8)  |           \
                          ZERO(1)  |            ZERO(9)  |           \
                          ZERO(2)  | ZERO(6)  |                      \
                          ZERO(3)  | ZERO(7)  | ZERO(11) |  ONE(15) )

#define MASK_3D          (                                           \
                                                                     \
                                                                     \
                          ZERO(3)  | ZERO(7)  | ZERO(11) |  ONE(15) )


#define MASK_PERSPECTIVE (           ZERO(4)  |            ZERO(12) |\
                          ZERO(1)  |                       ZERO(13) |\
                          ZERO(2)  | ZERO(6)  |                      \
                          ZERO(3)  | ZERO(7)  |            ZERO(15) )

#define SQ(x) ((x)*(x))
  
/* Determine type and flags from scratch.  This is expensive enough to
 * only want to do it once.
 */
static void analyze_from_scratch( GLmatrix *mat )
{
   const GLfloat *m = mat->m;
   GLuint mask = 0;
   GLuint i;

   for (i = 0 ; i < 16 ; i++) 
   {
      if (m[i] == 0.0) mask |= (1<<i);
   }
   
   if (m[0] == 1.0F) mask |= (1<<16);
   if (m[5] == 1.0F) mask |= (1<<21);
   if (m[10] == 1.0F) mask |= (1<<26);
   if (m[15] == 1.0F) mask |= (1<<31);

   mat->flags &= ~MAT_FLAGS_GEOMETRY;

   /* Check for translation - no-one really cares 
    */
   if ((mask & MASK_NO_TRX) != MASK_NO_TRX) 
      mat->flags |= MAT_FLAG_TRANSLATION;      

   /* Do the real work
    */
   if (mask == MASK_IDENTITY) {
      mat->type = MATRIX_IDENTITY;
   }
   else if ((mask & MASK_2D_NO_ROT) == MASK_2D_NO_ROT)  
   {
      mat->type = MATRIX_2D_NO_ROT;
      
      if ((mask & MASK_NO_2D_SCALE) != MASK_NO_2D_SCALE)
         mat->flags = MAT_FLAG_GENERAL_SCALE;
   }
   else if ((mask & MASK_2D) == MASK_2D)  
   {
      GLfloat mm = DOT2(m, m);
      GLfloat m4m4 = DOT2(m+4,m+4);
      GLfloat mm4 = DOT2(m,m+4);

      mat->type = MATRIX_2D;

      /* Check for scale */
      if (SQ(mm-1) > SQ(1e-6) ||
          SQ(m4m4-1) > SQ(1e-6)) 
         mat->flags |= MAT_FLAG_GENERAL_SCALE;

      /* Check for rotation */
      if (SQ(mm4) > SQ(1e-6))
         mat->flags |= MAT_FLAG_GENERAL_3D;
      else
         mat->flags |= MAT_FLAG_ROTATION;

   }
   else if ((mask & MASK_3D_NO_ROT) == MASK_3D_NO_ROT)
   {
      mat->type = MATRIX_3D_NO_ROT;

      /* Check for scale */
      if (SQ(m[0]-m[5]) < SQ(1e-6) && 
          SQ(m[0]-m[10]) < SQ(1e-6)) {
         if (SQ(m[0]-1.0) > SQ(1e-6))
            mat->flags |= MAT_FLAG_UNIFORM_SCALE;
      } else
         mat->flags |= MAT_FLAG_GENERAL_SCALE;
   }
   else if ((mask & MASK_3D) == MASK_3D)
   {
      GLfloat c1 = DOT3(m,m);
      GLfloat c2 = DOT3(m+4,m+4);
      GLfloat c3 = DOT3(m+8,m+8);
      GLfloat d1 = DOT3(m, m+4);
      GLfloat cp[3];

      mat->type = MATRIX_3D;

      /* Check for scale */
      if (SQ(c1-c2) < SQ(1e-6) && SQ(c1-c3) < SQ(1e-6)) {
         if (SQ(c1-1.0) > SQ(1e-6))
            mat->flags |= MAT_FLAG_UNIFORM_SCALE;
         /* else no scale at all */
      } else 
         mat->flags |= MAT_FLAG_GENERAL_SCALE;

      /* Check for rotation */
      if (SQ(d1) < SQ(1e-6)) {
         CROSS3( cp, m, m+4 );
         SUB_3V( cp, cp, (m+8) );
         if (LEN_SQUARED_3FV(cp) < SQ(1e-6)) 
            mat->flags |= MAT_FLAG_ROTATION;
         else
            mat->flags |= MAT_FLAG_GENERAL_3D;
      }
      else
         mat->flags |= MAT_FLAG_GENERAL_3D; /* shear, etc */
   }
   else if ((mask & MASK_PERSPECTIVE) == MASK_PERSPECTIVE && m[11]==-1.0F) 
   {
      mat->type = MATRIX_PERSPECTIVE;
      mat->flags |= MAT_FLAG_GENERAL;
   }
   else {
      mat->type = MATRIX_GENERAL;
      mat->flags |= MAT_FLAG_GENERAL;
   }
}


/* Analyse a matrix given that its flags are accurate - this is the
 * more common operation, hopefully. 
 */
static void analyze_from_flags( GLmatrix *mat )
{
   const GLfloat *m = mat->m;

   if (TEST_MAT_FLAGS(mat, 0)) {
      mat->type = MATRIX_IDENTITY;
   }
   else if (TEST_MAT_FLAGS(mat, (MAT_FLAG_TRANSLATION |
                                 MAT_FLAG_UNIFORM_SCALE |
                                 MAT_FLAG_GENERAL_SCALE)))
   {
      if ( m[10]==1.0F && m[14]==0.0F ) {
         mat->type = MATRIX_2D_NO_ROT;
      }
      else {
         mat->type = MATRIX_3D_NO_ROT;
      }
   }
   else if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D)) {
      if (                                 m[ 8]==0.0F               
            &&                             m[ 9]==0.0F
            && m[2]==0.0F && m[6]==0.0F && m[10]==1.0F && m[14]==0.0F)
      {
         mat->type = MATRIX_2D;
      }
      else 
      {
         mat->type = MATRIX_3D;
      }
   }
   else if (                 m[4]==0.0F                 && m[12]==0.0F
            && m[1]==0.0F                               && m[13]==0.0F
            && m[2]==0.0F && m[6]==0.0F
            && m[3]==0.0F && m[7]==0.0F && m[11]==-1.0F && m[15]==0.0F) 
   {
      mat->type = MATRIX_PERSPECTIVE;
   }
   else {
      mat->type = MATRIX_GENERAL;
   }

}


void gl_matrix_analyze( GLmatrix *mat ) 
{
   if (mat->flags & MAT_DIRTY_TYPE) {
      if (mat->flags & MAT_DIRTY_FLAGS) 
         analyze_from_scratch( mat );
      else
         analyze_from_flags( mat );
   }

   if (mat->inv && (mat->flags & MAT_DIRTY_INVERSE)) {
      gl_matrix_invert( mat );
   }

   mat->flags &= ~(MAT_DIRTY_FLAGS|
                   MAT_DIRTY_TYPE|
                   MAT_DIRTY_INVERSE);
}


#define GET_ACTIVE_MATRIX(ctx, mat, flags, where)                       \
do {                                                                    \
   ASSERT_OUTSIDE_BEGIN_END_AND_FLUSH(ctx, where);                      \
   if (MESA_VERBOSE&VERBOSE_API) fprintf(stderr, "%s\n", where);        \
   switch (ctx->Transform.MatrixMode) {                                 \
      case GL_MODELVIEW:                                                \
         mat = &ctx->ModelView;                                         \
         flags |= NEW_MODELVIEW;                                        \
         break;                                                         \
      case GL_PROJECTION:                                               \
         mat = &ctx->ProjectionMatrix;                                  \
         flags |= NEW_PROJECTION;                                       \
         break;                                                         \
      case GL_TEXTURE:                                                  \
         mat = &ctx->TextureMatrix[ctx->Texture.CurrentTransformUnit];  \
         flags |= NEW_TEXTURE_MATRIX;                                   \
         break;                                                         \
      case GL_COLOR:                                                    \
         mat = &ctx->ColorMatrix;                                       \
         flags |= NEW_COLOR_MATRIX;                                     \
         break;                                                         \
      default:                                                          \
         gl_problem(ctx, where);                                        \
   }                                                                    \
} while (0)


void
_mesa_Frustum( GLdouble left, GLdouble right,
               GLdouble bottom, GLdouble top,
               GLdouble nearval, GLdouble farval )
{
   GET_CURRENT_CONTEXT(ctx);
   GLfloat x, y, a, b, c, d;
   GLfloat m[16];
   GLmatrix *mat = 0;

   GET_ACTIVE_MATRIX( ctx,  mat, ctx->NewState, "glFrustrum" );

   if ((nearval<=0.0 || farval<=0.0) || (nearval == farval) || (left == right) || (top == bottom)) {
      gl_error( ctx,  GL_INVALID_VALUE, "glFrustum(near or far)" );
      return;
   }

   x = (2.0*nearval) / (right-left);
   y = (2.0*nearval) / (top-bottom);
   a = (right+left) / (right-left);
   b = (top+bottom) / (top-bottom);
   c = -(farval+nearval) / ( farval-nearval);
   d = -(2.0*farval*nearval) / (farval-nearval);  /* error? */

#define M(row,col)  m[col*4+row]
   M(0,0) = x;     M(0,1) = 0.0F;  M(0,2) = a;      M(0,3) = 0.0F;
   M(1,0) = 0.0F;  M(1,1) = y;     M(1,2) = b;      M(1,3) = 0.0F;
   M(2,0) = 0.0F;  M(2,1) = 0.0F;  M(2,2) = c;      M(2,3) = d;
   M(3,0) = 0.0F;  M(3,1) = 0.0F;  M(3,2) = -1.0F;  M(3,3) = 0.0F;
#undef M


   gl_mat_mul_floats( mat, m, MAT_FLAG_PERSPECTIVE );


   if (ctx->Transform.MatrixMode == GL_PROJECTION)
   {
      /* Need to keep a stack of near/far values in case the user push/pops
       * the projection matrix stack so that we can call Driver.NearFar()
       * after a pop.
       */
      ctx->NearFarStack[ctx->ProjectionStackDepth][0] = nearval;
      ctx->NearFarStack[ctx->ProjectionStackDepth][1] = farval;
      
      if (ctx->Driver.NearFar) {
         (*ctx->Driver.NearFar)( ctx, nearval, farval );
      }
   }
}


void
_mesa_Ortho( GLdouble left, GLdouble right,
             GLdouble bottom, GLdouble top,
             GLdouble nearval, GLdouble farval )
{
   GET_CURRENT_CONTEXT(ctx);
   GLfloat x, y, z;
   GLfloat tx, ty, tz;
   GLfloat m[16];
   GLmatrix *mat = 0;

   GET_ACTIVE_MATRIX( ctx,  mat, ctx->NewState, "glOrtho" );
   
   if ((left == right) || (bottom == top) || (nearval == farval)) {
      gl_error( ctx,  GL_INVALID_VALUE, "gl_Ortho((l = r) or (b = top) or (n=f)" );
      return;
   }

   x = 2.0 / (right-left);
   y = 2.0 / (top-bottom);
   z = -2.0 / (farval-nearval);
   tx = -(right+left) / (right-left);
   ty = -(top+bottom) / (top-bottom);
   tz = -(farval+nearval) / (farval-nearval);

#define M(row,col)  m[col*4+row]
   M(0,0) = x;     M(0,1) = 0.0F;  M(0,2) = 0.0F;  M(0,3) = tx;
   M(1,0) = 0.0F;  M(1,1) = y;     M(1,2) = 0.0F;  M(1,3) = ty;
   M(2,0) = 0.0F;  M(2,1) = 0.0F;  M(2,2) = z;     M(2,3) = tz;
   M(3,0) = 0.0F;  M(3,1) = 0.0F;  M(3,2) = 0.0F;  M(3,3) = 1.0F;
#undef M

   gl_mat_mul_floats( mat, m, (MAT_FLAG_GENERAL_SCALE|MAT_FLAG_TRANSLATION));

   if (ctx->Driver.NearFar) {
      (*ctx->Driver.NearFar)( ctx, nearval, farval );
   }
}


void
_mesa_MatrixMode( GLenum mode )
{
   GET_CURRENT_CONTEXT(ctx);
   ASSERT_OUTSIDE_BEGIN_END_AND_FLUSH(ctx, "glMatrixMode");
   switch (mode) {
      case GL_MODELVIEW:
      case GL_PROJECTION:
      case GL_TEXTURE:
      case GL_COLOR:
         ctx->Transform.MatrixMode = mode;
         break;
      default:
         gl_error( ctx,  GL_INVALID_ENUM, "glMatrixMode" );
   }
}



void
_mesa_PushMatrix( void )
{
   GET_CURRENT_CONTEXT(ctx);
   ASSERT_OUTSIDE_BEGIN_END_AND_FLUSH(ctx, "glPushMatrix");

   if (MESA_VERBOSE&VERBOSE_API)
      fprintf(stderr, "glPushMatrix %s\n", 
              gl_lookup_enum_by_nr(ctx->Transform.MatrixMode));

   switch (ctx->Transform.MatrixMode) {
      case GL_MODELVIEW:
         if (ctx->ModelViewStackDepth >= MAX_MODELVIEW_STACK_DEPTH - 1) {
            gl_error( ctx,  GL_STACK_OVERFLOW, "glPushMatrix");
            return;
         }
         gl_matrix_copy( &ctx->ModelViewStack[ctx->ModelViewStackDepth++],
                         &ctx->ModelView );
         break;
      case GL_PROJECTION:
         if (ctx->ProjectionStackDepth >= MAX_PROJECTION_STACK_DEPTH - 1) {
            gl_error( ctx,  GL_STACK_OVERFLOW, "glPushMatrix");
            return;
         }
         gl_matrix_copy( &ctx->ProjectionStack[ctx->ProjectionStackDepth++],
                         &ctx->ProjectionMatrix );

         /* Save near and far projection values */
         ctx->NearFarStack[ctx->ProjectionStackDepth][0]
            = ctx->NearFarStack[ctx->ProjectionStackDepth-1][0];
         ctx->NearFarStack[ctx->ProjectionStackDepth][1]
            = ctx->NearFarStack[ctx->ProjectionStackDepth-1][1];
         break;
      case GL_TEXTURE:
         {
            GLuint t = ctx->Texture.CurrentTransformUnit;
            if (ctx->TextureStackDepth[t] >= MAX_TEXTURE_STACK_DEPTH - 1) {
               gl_error( ctx,  GL_STACK_OVERFLOW, "glPushMatrix");
               return;
            }
            gl_matrix_copy( &ctx->TextureStack[t][ctx->TextureStackDepth[t]++],
                            &ctx->TextureMatrix[t] );
         }
         break;
      case GL_COLOR:
         if (ctx->ColorStackDepth >= MAX_COLOR_STACK_DEPTH - 1) {
            gl_error( ctx,  GL_STACK_OVERFLOW, "glPushMatrix");
            return;
         }
         gl_matrix_copy( &ctx->ColorStack[ctx->ColorStackDepth++],
                         &ctx->ColorMatrix );
         break;
      default:
         gl_problem(ctx, "Bad matrix mode in gl_PushMatrix");
   }
}



void
_mesa_PopMatrix( void )
{
   GET_CURRENT_CONTEXT(ctx);
   ASSERT_OUTSIDE_BEGIN_END_AND_FLUSH(ctx, "glPopMatrix");

   if (MESA_VERBOSE&VERBOSE_API)
      fprintf(stderr, "glPopMatrix %s\n", 
              gl_lookup_enum_by_nr(ctx->Transform.MatrixMode));

   switch (ctx->Transform.MatrixMode) {
      case GL_MODELVIEW:
         if (ctx->ModelViewStackDepth==0) {
            gl_error( ctx,  GL_STACK_UNDERFLOW, "glPopMatrix");
            return;
         }
         gl_matrix_copy( &ctx->ModelView,
                         &ctx->ModelViewStack[--ctx->ModelViewStackDepth] );
         ctx->NewState |= NEW_MODELVIEW;
         break;
      case GL_PROJECTION:
         if (ctx->ProjectionStackDepth==0) {
            gl_error( ctx,  GL_STACK_UNDERFLOW, "glPopMatrix");
            return;
         }

         gl_matrix_copy( &ctx->ProjectionMatrix,
                         &ctx->ProjectionStack[--ctx->ProjectionStackDepth] );
         ctx->NewState |= NEW_PROJECTION;

         /* Device driver near/far values */
         {
            GLfloat nearVal = ctx->NearFarStack[ctx->ProjectionStackDepth][0];
            GLfloat farVal  = ctx->NearFarStack[ctx->ProjectionStackDepth][1];
            if (ctx->Driver.NearFar) {
               (*ctx->Driver.NearFar)( ctx, nearVal, farVal );
            }
         }
         break;
      case GL_TEXTURE:
         {
            GLuint t = ctx->Texture.CurrentTransformUnit;
            if (ctx->TextureStackDepth[t]==0) {
               gl_error( ctx,  GL_STACK_UNDERFLOW, "glPopMatrix");
               return;
            }
            gl_matrix_copy(&ctx->TextureMatrix[t],
                           &ctx->TextureStack[t][--ctx->TextureStackDepth[t]]);
         }
         break;
      case GL_COLOR:
         if (ctx->ColorStackDepth==0) {
            gl_error( ctx,  GL_STACK_UNDERFLOW, "glPopMatrix");
            return;
         }
         gl_matrix_copy(&ctx->ColorMatrix,
                        &ctx->ColorStack[--ctx->ColorStackDepth]);
         break;
      default:
         gl_problem(ctx, "Bad matrix mode in gl_PopMatrix");
   }
}



void
_mesa_LoadIdentity( void )
{
   GET_CURRENT_CONTEXT(ctx);
   GLmatrix *mat = 0;
   GET_ACTIVE_MATRIX(ctx, mat, ctx->NewState, "glLoadIdentity");

   MEMCPY( mat->m, Identity, 16*sizeof(GLfloat) );

   if (mat->inv)
      MEMCPY( mat->inv, Identity, 16*sizeof(GLfloat) );

   mat->type = MATRIX_IDENTITY;
   
   /* Have to set this to dirty to make sure we recalculate the
    * combined matrix later.  The update_matrix in this case is a
    * shortcircuit anyway...
    */
   mat->flags = MAT_DIRTY_DEPENDENTS;   
}


void
_mesa_LoadMatrixf( const GLfloat *m )
{
   GET_CURRENT_CONTEXT(ctx);
   GLmatrix *mat = 0;
   GET_ACTIVE_MATRIX(ctx, mat, ctx->NewState, "glLoadMatrix");

   MEMCPY( mat->m, m, 16*sizeof(GLfloat) );
   mat->flags = (MAT_FLAG_GENERAL | MAT_DIRTY_ALL_OVER);

   if (ctx->Transform.MatrixMode == GL_PROJECTION) {

#define M(row,col)  m[col*4+row]
      GLfloat c = M(2,2);
      GLfloat d = M(2,3);
#undef M
      GLfloat n = (c ==  1.0 ? 0.0 : d / (c - 1.0));
      GLfloat f = (c == -1.0 ? 1.0 : d / (c + 1.0));

      /* Need to keep a stack of near/far values in case the user
       * push/pops the projection matrix stack so that we can call
       * Driver.NearFar() after a pop.
       */
      ctx->NearFarStack[ctx->ProjectionStackDepth][0] = n;
      ctx->NearFarStack[ctx->ProjectionStackDepth][1] = f;

      if (ctx->Driver.NearFar) {
         (*ctx->Driver.NearFar)( ctx, n, f );
      }
   }
}


void
_mesa_LoadMatrixd( const GLdouble *m )
{
   GLfloat f[16];
   GLint i;
   for (i = 0; i < 16; i++)
      f[i] = m[i];
   _mesa_LoadMatrixf(f);
}



/*
 * Multiply the active matrix by an arbitary matrix.
 */
void
_mesa_MultMatrixf( const GLfloat *m )
{
   GET_CURRENT_CONTEXT(ctx);
   GLmatrix *mat = 0;
   GET_ACTIVE_MATRIX( ctx,  mat, ctx->NewState, "glMultMatrix" );
   matmul4( mat->m, mat->m, m );
   mat->flags = (MAT_FLAG_GENERAL | MAT_DIRTY_ALL_OVER);
}


/*
 * Multiply the active matrix by an arbitary matrix.  
 */
void
_mesa_MultMatrixd( const GLdouble *m )
{
   GET_CURRENT_CONTEXT(ctx);
   GLmatrix *mat = 0;
   GET_ACTIVE_MATRIX( ctx,  mat, ctx->NewState, "glMultMatrix" );
   matmul4fd( mat->m, mat->m, m );
   mat->flags = (MAT_FLAG_GENERAL | MAT_DIRTY_ALL_OVER);
}




/*
 * Multiply a matrix by an array of floats with known properties.
 */
void gl_mat_mul_floats( GLmatrix *mat, const GLfloat *m, GLuint flags )
{
   mat->flags |= (flags |
                  MAT_DIRTY_TYPE | 
                  MAT_DIRTY_INVERSE | 
                  MAT_DIRTY_DEPENDENTS);

   if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D))
      matmul34( mat->m, mat->m, m );
   else 
      matmul4( mat->m, mat->m, m );      

}

/*
 * Multiply a matrix by an array of floats with known properties.
 */
void gl_mat_mul_mat( GLmatrix *mat, const GLmatrix *m )
{
   mat->flags |= (m->flags |
                  MAT_DIRTY_TYPE | 
                  MAT_DIRTY_INVERSE | 
                  MAT_DIRTY_DEPENDENTS);

   if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D))
      matmul34( mat->m, mat->m, m->m );
   else 
      matmul4( mat->m, mat->m, m->m );      
}



/*
 * Execute a glRotate call
 */
void
_mesa_Rotatef( GLfloat angle, GLfloat x, GLfloat y, GLfloat z )
{
   GET_CURRENT_CONTEXT(ctx);
   GLfloat m[16];
   if (angle != 0.0F) {
      GLmatrix *mat = 0;
      GET_ACTIVE_MATRIX( ctx,  mat, ctx->NewState, "glRotate" );

      gl_rotation_matrix( angle, x, y, z, m );
      gl_mat_mul_floats( mat, m, MAT_FLAG_ROTATION );
   }
}

void
_mesa_Rotated( GLdouble angle, GLdouble x, GLdouble y, GLdouble z )
{
   _mesa_Rotatef(angle, x, y, z);
}


/*
 * Execute a glScale call
 */
void
_mesa_Scalef( GLfloat x, GLfloat y, GLfloat z )
{
   GET_CURRENT_CONTEXT(ctx);
   GLmatrix *mat = 0;
   GLfloat *m;
   GET_ACTIVE_MATRIX(ctx, mat, ctx->NewState, "glScale");

   m = mat->m;
   m[0] *= x;   m[4] *= y;   m[8]  *= z;
   m[1] *= x;   m[5] *= y;   m[9]  *= z;
   m[2] *= x;   m[6] *= y;   m[10] *= z;
   m[3] *= x;   m[7] *= y;   m[11] *= z;

   if (fabs(x - y) < 1e-8 && fabs(x - z) < 1e-8)
      mat->flags |= MAT_FLAG_UNIFORM_SCALE;
   else
      mat->flags |= MAT_FLAG_GENERAL_SCALE;

   mat->flags |= (MAT_DIRTY_TYPE | 
                  MAT_DIRTY_INVERSE | 
                  MAT_DIRTY_DEPENDENTS);
}


void
_mesa_Scaled( GLdouble x, GLdouble y, GLdouble z )
{
   _mesa_Scalef(x, y, z);
}


/*
 * Execute a glTranslate call
 */
void
_mesa_Translatef( GLfloat x, GLfloat y, GLfloat z )
{
   GET_CURRENT_CONTEXT(ctx);
   GLmatrix *mat = 0;
   GLfloat *m;
   GET_ACTIVE_MATRIX(ctx, mat, ctx->NewState, "glTranslate");
   m = mat->m;
   m[12] = m[0] * x + m[4] * y + m[8]  * z + m[12];
   m[13] = m[1] * x + m[5] * y + m[9]  * z + m[13];
   m[14] = m[2] * x + m[6] * y + m[10] * z + m[14];
   m[15] = m[3] * x + m[7] * y + m[11] * z + m[15];

   mat->flags |= (MAT_FLAG_TRANSLATION | 
                  MAT_DIRTY_TYPE | 
                  MAT_DIRTY_INVERSE | 
                  MAT_DIRTY_DEPENDENTS);
}


void
_mesa_Translated( GLdouble x, GLdouble y, GLdouble z )
{
   _mesa_Translatef(x, y, z);
}



void
_mesa_LoadTransposeMatrixfARB( const GLfloat *m )
{
   GLfloat tm[16];
   gl_matrix_transposef(tm, m);
   _mesa_LoadMatrixf(tm);
}


void
_mesa_LoadTransposeMatrixdARB( const GLdouble *m )
{
   GLdouble tm[16];
   gl_matrix_transposed(tm, m);
   _mesa_LoadMatrixd(tm);
}


void
_mesa_MultTransposeMatrixfARB( const GLfloat *m )
{
   GLfloat tm[16];
   gl_matrix_transposef(tm, m);
   _mesa_MultMatrixf(tm);
}


void
_mesa_MultTransposeMatrixdARB( const GLdouble *m )
{
   GLdouble tm[16];
   gl_matrix_transposed(tm, m);
   _mesa_MultMatrixd(tm);
}


/*
 * Called via glViewport or display list execution.
 */
void
_mesa_Viewport( GLint x, GLint y, GLsizei width, GLsizei height )
{
   GET_CURRENT_CONTEXT(ctx);
   gl_Viewport(ctx, x, y, width, height);
}



/*
 * Define a new viewport and reallocate auxillary buffers if the size of
 * the window (color buffer) has changed.
 *
 * XXX This is directly called by device drivers, BUT this function
 * may be renamed _mesa_Viewport (without ctx arg) in the future so
 * use of _mesa_Viewport is encouraged.
 */
void
gl_Viewport( GLcontext *ctx, GLint x, GLint y, GLsizei width, GLsizei height )
{
   ASSERT_OUTSIDE_BEGIN_END_AND_FLUSH(ctx, "glViewport");

   if (width<0 || height<0) {
      gl_error( ctx,  GL_INVALID_VALUE, "glViewport" );
      return;
   }

   if (MESA_VERBOSE & VERBOSE_API)
      fprintf(stderr, "glViewport %d %d %d %d\n", x, y, width, height);
   
   /* clamp width, and height to implementation dependent range */
   width  = CLAMP( width,  1, MAX_WIDTH );
   height = CLAMP( height, 1, MAX_HEIGHT );

   /* Save viewport */
   ctx->Viewport.X = x;
   ctx->Viewport.Width = width;
   ctx->Viewport.Y = y;
   ctx->Viewport.Height = height;

   /* compute scale and bias values */
   ctx->Viewport.WindowMap.m[MAT_SX] = (GLfloat) width / 2.0F;
   ctx->Viewport.WindowMap.m[MAT_TX] = ctx->Viewport.WindowMap.m[MAT_SX] + x;
   ctx->Viewport.WindowMap.m[MAT_SY] = (GLfloat) height / 2.0F;
   ctx->Viewport.WindowMap.m[MAT_TY] = ctx->Viewport.WindowMap.m[MAT_SY] + y;
   ctx->Viewport.WindowMap.m[MAT_SZ] = 0.5 * ctx->Visual->DepthMaxF;
   ctx->Viewport.WindowMap.m[MAT_TZ] = 0.5 * ctx->Visual->DepthMaxF;

   ctx->Viewport.WindowMap.flags = MAT_FLAG_GENERAL_SCALE|MAT_FLAG_TRANSLATION;
   ctx->Viewport.WindowMap.type = MATRIX_3D_NO_ROT;

   ctx->ModelProjectWinMatrixUptodate = GL_FALSE;
   ctx->NewState |= NEW_VIEWPORT;

   /* Check if window/buffer has been resized and if so, reallocate the
    * ancillary buffers.
    */
   _mesa_ResizeBuffersMESA();


   ctx->RasterMask &= ~WINCLIP_BIT;

   if (   ctx->Viewport.X<0
       || ctx->Viewport.X + ctx->Viewport.Width > ctx->DrawBuffer->Width
       || ctx->Viewport.Y<0
       || ctx->Viewport.Y + ctx->Viewport.Height > ctx->DrawBuffer->Height) {
      ctx->RasterMask |= WINCLIP_BIT;
   }


   if (ctx->Driver.Viewport) {
      (*ctx->Driver.Viewport)( ctx, x, y, width, height );
   }
}



void
_mesa_DepthRange( GLclampd nearval, GLclampd farval )
{
   /*
    * nearval - specifies mapping of the near clipping plane to window
    *   coordinates, default is 0
    * farval - specifies mapping of the far clipping plane to window
    *   coordinates, default is 1
    *
    * After clipping and div by w, z coords are in -1.0 to 1.0,
    * corresponding to near and far clipping planes.  glDepthRange
    * specifies a linear mapping of the normalized z coords in
    * this range to window z coords.
    */
   GLfloat n, f;
   GET_CURRENT_CONTEXT(ctx);
   ASSERT_OUTSIDE_BEGIN_END_AND_FLUSH(ctx, "glDepthRange");

   if (MESA_VERBOSE&VERBOSE_API)
      fprintf(stderr, "glDepthRange %f %f\n", nearval, farval); 

   n = (GLfloat) CLAMP( nearval, 0.0, 1.0 );
   f = (GLfloat) CLAMP( farval, 0.0, 1.0 );

   ctx->Viewport.Near = n;
   ctx->Viewport.Far = f;
   ctx->Viewport.WindowMap.m[MAT_SZ] = ctx->Visual->DepthMaxF * ((f - n) / 2.0);
   ctx->Viewport.WindowMap.m[MAT_TZ] = ctx->Visual->DepthMaxF * ((f - n) / 2.0 + n);

   ctx->ModelProjectWinMatrixUptodate = GL_FALSE;

   if (ctx->Driver.DepthRange) {
      (*ctx->Driver.DepthRange)( ctx, nearval, farval );
   }
}


void gl_calculate_model_project_matrix( GLcontext *ctx )
{
   gl_matrix_mul( &ctx->ModelProjectMatrix,
                  &ctx->ProjectionMatrix,
                  &ctx->ModelView );

   gl_matrix_analyze( &ctx->ModelProjectMatrix );
}


void gl_matrix_ctr( GLmatrix *m )
{
   if ( m->m == 0 ) {
      m->m = (GLfloat *) ALIGN_MALLOC( 16 * sizeof(GLfloat), 16 );
   }
   MEMCPY( m->m, Identity, sizeof(Identity) );
   m->inv = 0;
   m->type = MATRIX_IDENTITY;
   m->flags = MAT_DIRTY_DEPENDENTS;
}

void gl_matrix_dtr( GLmatrix *m )
{
   if ( m->m != 0 ) {
      ALIGN_FREE( m->m );
      m->m = 0;
   }
   if ( m->inv != 0 ) {
      ALIGN_FREE( m->inv );
      m->inv = 0;
   }
}

#if 0
void gl_matrix_set_identity( GLmatrix *m )
{
   MEMCPY( m->m, Identity, sizeof(Identity) );
   m->type = MATRIX_IDENTITY;
   m->flags = MAT_DIRTY_DEPENDENTS;
}
#endif

void gl_matrix_alloc_inv( GLmatrix *m )
{
   if ( m->inv == 0 ) {
      m->inv = (GLfloat *) ALIGN_MALLOC( 16 * sizeof(GLfloat), 16 );
      MEMCPY( m->inv, Identity, 16 * sizeof(GLfloat) );
   }
}

void gl_matrix_copy( GLmatrix *to, const GLmatrix *from )
{
   MEMCPY( to->m, from->m, sizeof(Identity) );
   to->flags = from->flags | MAT_DIRTY_DEPENDENTS;
   to->type = from->type;

   if (to->inv != 0) {
      if (from->inv == 0) {
         gl_matrix_invert( to );
      } else {
         MEMCPY(to->inv, from->inv, sizeof(GLfloat)*16);
      }
   }
}

void gl_matrix_mul( GLmatrix *dest, const GLmatrix *a, const GLmatrix *b )
{
   dest->flags = (a->flags |
                  b->flags |
                  MAT_DIRTY_TYPE | 
                  MAT_DIRTY_INVERSE | 
                  MAT_DIRTY_DEPENDENTS);

   if (TEST_MAT_FLAGS(dest, MAT_FLAGS_3D))
      matmul34( dest->m, a->m, b->m );
   else 
      matmul4( dest->m, a->m, b->m );
}