Move the transform and lighting code to two new directories

	math:  Provides basic matrix and vector functionality that
               might be useful to multiple software t&l
	       implementations, and is used by core mesa to
	       manage the Model, Project, etc matrices.

	tnl:   The real transform & lighting code from core mesa,
	       including everything from glVertex3f through vertex
	       buffer handling, transformation, clipping, lighting
	       and handoff to a driver for rasterization.

The interfaces of these can be further tightened up, but the basic
splitting up of state and code move is done.

1 files changed, 1113 insertions, 0 deletions

diff --git a/src/mesa/math/m_matrix.c b/src/mesa/math/m_matrix.c
new file mode 100644
index 0000000000..ae55c946d9
--- /dev/null
+++ b/src/mesa/math/m_matrix.c
@@ -0,0 +1,1113 @@
+/* $Id: m_matrix.c,v 1.1 2000/11/16 21:05:41 keithw Exp $ */
+
+/*
+ * Mesa 3-D graphics library
+ * Version:  3.5
+ * 
+ * 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
+ */
+
+
+#include "glheader.h"
+#include "macros.h"
+#include "mem.h"
+#include "mmath.h"
+
+#include "m_matrix.h"
+
+
+static const char *types[] = {
+   "MATRIX_GENERAL",
+   "MATRIX_IDENTITY",
+   "MATRIX_3D_NO_ROT",
+   "MATRIX_PERSPECTIVE",
+   "MATRIX_2D",
+   "MATRIX_2D_NO_ROT",
+   "MATRIX_3D"
+};
+
+
+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
+};
+
+
+
+
+/*
+ * 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++) {
+      const 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 model matrices, and ortho matrices.  
+ */
+static void matmul34( GLfloat *product, const GLfloat *a, const GLfloat *b )
+{
+   GLint i;
+   for (i = 0; i < 3; i++) {
+      const 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;
+}
+
+
+#undef A
+#undef B
+#undef P
+
+
+/*
+ * Multiply a matrix by an array of floats with known properties.
+ */
+static void matrix_multf( GLmatrix *mat, const GLfloat *m, GLuint flags )
+{
+   mat->flags |= (flags | MAT_DIRTY_TYPE | MAT_DIRTY_INVERSE);
+
+   if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D))
+      matmul34( mat->m, mat->m, m );
+   else 
+      matmul4( mat->m, mat->m, m ); 
+}
+
+
+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 
+_math_matrix_print( const GLmatrix *m )
+{
+   fprintf(stderr, "Matrix type: %s, flags: %x\n", types[m->type], m->flags);
+   print_matrix_floats(m->m);
+   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");
+   }
+}
+
+
+
+
+#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
+};
+
+
+static GLboolean matrix_invert( GLmatrix *mat )
+{
+   if (inv_mat_tab[mat->type](mat)) {
+      mat->flags &= ~MAT_FLAG_SINGULAR;
+      return GL_TRUE;
+   } else {
+      mat->flags |= MAT_FLAG_SINGULAR;
+      MEMCPY( mat->inv, Identity, sizeof(Identity) );
+      return GL_FALSE;
+   }  
+}
+
+
+
+
+
+
+/*
+ * Generate a 4x4 transformation matrix from glRotate parameters, and
+ * postmultiply the input matrix by it.
+ */
+void 
+_math_matrix_rotate( GLmatrix *mat, 
+		     GLfloat angle, GLfloat x, GLfloat y, GLfloat z )
+{
+   /* 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;
+   GLfloat m[16];
+   
+   s = sin( angle * DEG2RAD );
+   c = cos( angle * DEG2RAD );
+
+   mag = GL_SQRT( x*x + y*y + z*z );
+
+   if (mag <= 1.0e-4) {
+      /* 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
+
+   matrix_multf( mat, m, MAT_FLAG_ROTATION );
+}
+
+
+void
+_math_matrix_frustrum( GLmatrix *mat, 
+		       GLfloat left, GLfloat right,
+		       GLfloat bottom, GLfloat top, 
+		       GLfloat nearval, GLfloat farval )
+{
+   GLfloat x, y, a, b, c, d;
+   GLfloat m[16];
+
+   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
+
+   matrix_multf( mat, m, MAT_FLAG_PERSPECTIVE );
+}
+
+void
+_math_matrix_ortho( GLmatrix *mat, 	
+		    GLfloat left, GLfloat right,
+		    GLfloat bottom, GLfloat top, 
+		    GLfloat nearval, GLfloat farval )
+{
+   GLfloat x, y, z;
+   GLfloat tx, ty, tz;
+   GLfloat m[16];
+
+   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
+
+   matrix_multf( mat, m, (MAT_FLAG_GENERAL_SCALE|MAT_FLAG_TRANSLATION));
+}
+
+
+#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 
+_math_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)) {
+      matrix_invert( mat );
+   }
+
+   mat->flags &= ~(MAT_DIRTY_FLAGS|
+		   MAT_DIRTY_TYPE|
+		   MAT_DIRTY_INVERSE);
+}
+
+
+void 
+_math_matrix_copy( GLmatrix *to, const GLmatrix *from )
+{
+   MEMCPY( to->m, from->m, sizeof(Identity) );
+   to->flags = from->flags;
+   to->type = from->type;
+
+   if (to->inv != 0) {
+      if (from->inv == 0) {
+	 matrix_invert( to );
+      }
+      else {
+	 MEMCPY(to->inv, from->inv, sizeof(GLfloat)*16);
+      }
+   }
+}
+
+
+void 
+_math_matrix_scale( GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z )
+{
+   GLfloat *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);
+}
+
+
+void 
+_math_matrix_translate( GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z )
+{
+   GLfloat *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);
+}
+
+
+void 
+_math_matrix_loadf( GLmatrix *mat, const GLfloat *m )
+{
+   MEMCPY( mat->m, m, 16*sizeof(GLfloat) );
+   mat->flags = (MAT_FLAG_GENERAL | MAT_DIRTY);
+}
+
+void 
+_math_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 = 0;
+}
+
+void 
+_math_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;
+   }
+}
+
+
+void 
+_math_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 
+_math_matrix_mul_matrix( GLmatrix *dest, const GLmatrix *a, const GLmatrix *b )
+{
+   dest->flags = (a->flags |
+		  b->flags |
+		  MAT_DIRTY_TYPE | 
+		  MAT_DIRTY_INVERSE);
+
+   if (TEST_MAT_FLAGS(dest, MAT_FLAGS_3D))
+      matmul34( dest->m, a->m, b->m );
+   else 
+      matmul4( dest->m, a->m, b->m );
+}
+
+
+void 
+_math_matrix_mul_floats( GLmatrix *dest, const GLfloat *m )
+{
+   dest->flags |= (MAT_FLAG_GENERAL |
+		   MAT_DIRTY_TYPE | 
+		   MAT_DIRTY_INVERSE);
+
+   matmul4( dest->m, dest->m, m );   
+}
+
+void 
+_math_matrix_set_identity( GLmatrix *mat )
+{
+   MEMCPY( mat->m, Identity, 16*sizeof(GLfloat) );
+
+   if (mat->inv)
+      MEMCPY( mat->inv, Identity, 16*sizeof(GLfloat) );
+
+   mat->type = MATRIX_IDENTITY;
+   mat->flags &= ~(MAT_DIRTY_FLAGS|
+		   MAT_DIRTY_TYPE|
+		   MAT_DIRTY_INVERSE);
+}
+
+
+
+void 
+_math_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 
+_math_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];
+}
+
+void 
+_math_transposefd( GLfloat 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];
+}