xserver and mesa git update 28-12-2010

1 files changed, 1641 insertions, 1642 deletions

diff --git a/mesalib/src/mesa/math/m_matrix.c b/mesalib/src/mesa/math/m_matrix.c
index 048b231c4..83eb787c7 100644
--- a/mesalib/src/mesa/math/m_matrix.c
+++ b/mesalib/src/mesa/math/m_matrix.c
@@ -1,1642 +1,1641 @@
-/*
- * Mesa 3-D graphics library
- * Version:  6.3
- *
- * Copyright (C) 1999-2005  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.
- */
-
-
-/**
- * \file m_matrix.c
- * Matrix operations.
- *
- * \note
- * -# 4x4 transformation matrices are stored in memory in column major order.
- * -# Points/vertices are to be thought of as column vectors.
- * -# Transformation of a point p by a matrix M is: p' = M * p
- */
-
-
-#include "main/glheader.h"
-#include "main/imports.h"
-#include "main/macros.h"
-#include "main/imports.h"
-
-#include "m_matrix.h"
-
-
-/**
- * \defgroup MatFlags MAT_FLAG_XXX-flags
- *
- * Bitmasks to indicate different kinds of 4x4 matrices in GLmatrix::flags
- * It would be nice to make all these flags private to m_matrix.c
- */
-/*@{*/
-#define MAT_FLAG_IDENTITY       0     /**< is an identity matrix flag.
-                                       *   (Not actually used - the identity
-                                       *   matrix is identified by the absense
-                                       *   of all other flags.)
-                                       */
-#define MAT_FLAG_GENERAL        0x1   /**< is a general matrix flag */
-#define MAT_FLAG_ROTATION       0x2   /**< is a rotation matrix flag */
-#define MAT_FLAG_TRANSLATION    0x4   /**< is a translation matrix flag */
-#define MAT_FLAG_UNIFORM_SCALE  0x8   /**< is an uniform scaling matrix flag */
-#define MAT_FLAG_GENERAL_SCALE  0x10  /**< is a general scaling matrix flag */
-#define MAT_FLAG_GENERAL_3D     0x20  /**< general 3D matrix flag */
-#define MAT_FLAG_PERSPECTIVE    0x40  /**< is a perspective proj matrix flag */
-#define MAT_FLAG_SINGULAR       0x80  /**< is a singular matrix flag */
-#define MAT_DIRTY_TYPE          0x100  /**< matrix type is dirty */
-#define MAT_DIRTY_FLAGS         0x200  /**< matrix flags are dirty */
-#define MAT_DIRTY_INVERSE       0x400  /**< matrix inverse is dirty */
-
-/** angle preserving matrix flags mask */
-#define MAT_FLAGS_ANGLE_PRESERVING (MAT_FLAG_ROTATION | \
-				    MAT_FLAG_TRANSLATION | \
-				    MAT_FLAG_UNIFORM_SCALE)
-
-/** geometry related matrix flags mask */
-#define MAT_FLAGS_GEOMETRY (MAT_FLAG_GENERAL | \
-			    MAT_FLAG_ROTATION | \
-			    MAT_FLAG_TRANSLATION | \
-			    MAT_FLAG_UNIFORM_SCALE | \
-			    MAT_FLAG_GENERAL_SCALE | \
-			    MAT_FLAG_GENERAL_3D | \
-			    MAT_FLAG_PERSPECTIVE | \
-	                    MAT_FLAG_SINGULAR)
-
-/** length preserving matrix flags mask */
-#define MAT_FLAGS_LENGTH_PRESERVING (MAT_FLAG_ROTATION | \
-				     MAT_FLAG_TRANSLATION)
-
-
-/** 3D (non-perspective) matrix flags mask */
-#define MAT_FLAGS_3D (MAT_FLAG_ROTATION | \
-		      MAT_FLAG_TRANSLATION | \
-		      MAT_FLAG_UNIFORM_SCALE | \
-		      MAT_FLAG_GENERAL_SCALE | \
-		      MAT_FLAG_GENERAL_3D)
-
-/** dirty matrix flags mask */
-#define MAT_DIRTY          (MAT_DIRTY_TYPE | \
-			    MAT_DIRTY_FLAGS | \
-			    MAT_DIRTY_INVERSE)
-
-/*@}*/
-
-
-/** 
- * Test geometry related matrix flags.
- * 
- * \param mat a pointer to a GLmatrix structure.
- * \param a flags mask.
- *
- * \returns non-zero if all geometry related matrix flags are contained within
- * the mask, or zero otherwise.
- */ 
-#define TEST_MAT_FLAGS(mat, a)  \
-    ((MAT_FLAGS_GEOMETRY & (~(a)) & ((mat)->flags) ) == 0)
-
-
-
-/**
- * Names of the corresponding GLmatrixtype values.
- */
-static const char *types[] = {
-   "MATRIX_GENERAL",
-   "MATRIX_IDENTITY",
-   "MATRIX_3D_NO_ROT",
-   "MATRIX_PERSPECTIVE",
-   "MATRIX_2D",
-   "MATRIX_2D_NO_ROT",
-   "MATRIX_3D"
-};
-
-
-/**
- * Identity matrix.
- */
-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
-};
-
-
-
-/**********************************************************************/
-/** \name Matrix multiplication */
-/*@{*/
-
-#define A(row,col)  a[(col<<2)+row]
-#define B(row,col)  b[(col<<2)+row]
-#define P(row,col)  product[(col<<2)+row]
-
-/**
- * Perform a full 4x4 matrix multiplication.
- *
- * \param a matrix.
- * \param b matrix.
- * \param product will receive the product of \p a and \p b.
- *
- * \warning Is assumed that \p product != \p b. \p product == \p a is allowed.
- *
- * \note KW: 4*16 = 64 multiplications
- * 
- * \author This \c matmul was contributed by Thomas Malik
- */
-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 orthogonal matrices.
- *
- * \param a matrix.
- * \param b matrix.
- * \param product will receive the product of \p a and \p b.
- */
-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.
- *
- * \param mat pointer to a GLmatrix structure containing the left multiplication
- * matrix, and that will receive the product result.
- * \param m right multiplication matrix array.
- * \param flags flags of the matrix \p m.
- * 
- * Joins both flags and marks the type and inverse as dirty.  Calls matmul34()
- * if both matrices are 3D, or matmul4() otherwise.
- */
-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 );
-}
-
-/**
- * Matrix multiplication.
- *
- * \param dest destination matrix.
- * \param a left matrix.
- * \param b right matrix.
- * 
- * Joins both flags and marks the type and inverse as dirty.  Calls matmul34()
- * if both matrices are 3D, or matmul4() otherwise.
- */
-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 );
-}
-
-/**
- * Matrix multiplication.
- *
- * \param dest left and destination matrix.
- * \param m right matrix array.
- * 
- * Marks the matrix flags with general flag, and type and inverse dirty flags.
- * Calls matmul4() for the multiplication.
- */
-void
-_math_matrix_mul_floats( GLmatrix *dest, const GLfloat *m )
-{
-   dest->flags |= (MAT_FLAG_GENERAL |
-		   MAT_DIRTY_TYPE |
-		   MAT_DIRTY_INVERSE |
-                   MAT_DIRTY_FLAGS);
-
-   matmul4( dest->m, dest->m, m );
-}
-
-/*@}*/
-
-
-/**********************************************************************/
-/** \name Matrix output */
-/*@{*/
-
-/**
- * Print a matrix array.
- *
- * \param m matrix array.
- *
- * Called by _math_matrix_print() to print a matrix or its inverse.
- */
-static void print_matrix_floats( const GLfloat m[16] )
-{
-   int i;
-   for (i=0;i<4;i++) {
-      _mesa_debug(NULL,"\t%f %f %f %f\n", m[i], m[4+i], m[8+i], m[12+i] );
-   }
-}
-
-/**
- * Dumps the contents of a GLmatrix structure.
- * 
- * \param m pointer to the GLmatrix structure.
- */
-void
-_math_matrix_print( const GLmatrix *m )
-{
-   _mesa_debug(NULL, "Matrix type: %s, flags: %x\n", types[m->type], m->flags);
-   print_matrix_floats(m->m);
-   _mesa_debug(NULL, "Inverse: \n");
-   if (m->inv) {
-      GLfloat prod[16];
-      print_matrix_floats(m->inv);
-      matmul4(prod, m->m, m->inv);
-      _mesa_debug(NULL, "Mat * Inverse:\n");
-      print_matrix_floats(prod);
-   }
-   else {
-      _mesa_debug(NULL, "  - not available\n");
-   }
-}
-
-/*@}*/
-
-
-/**
- * References an element of 4x4 matrix.
- *
- * \param m matrix array.
- * \param c column of the desired element.
- * \param r row of the desired element.
- * 
- * \return value of the desired element.
- *
- * Calculate the linear storage index of the element and references it. 
- */
-#define MAT(m,r,c) (m)[(c)*4+(r)]
-
-
-/**********************************************************************/
-/** \name Matrix inversion */
-/*@{*/
-
-/**
- * Swaps the values of two floating pointer variables.
- *
- * Used by invert_matrix_general() to swap the row pointers.
- */
-#define SWAP_ROWS(a, b) { GLfloat *_tmp = a; (a)=(b); (b)=_tmp; }
-
-/**
- * Compute inverse of 4x4 transformation matrix.
- * 
- * \param mat pointer to a GLmatrix structure. The matrix inverse will be
- * stored in the GLmatrix::inv attribute.
- * 
- * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
- * 
- * \author
- * Code contributed by Jacques Leroy jle@star.be
- *
- * Calculates the inverse matrix by performing the gaussian matrix reduction
- * with partial pivoting followed by back/substitution with the loops manually
- * unrolled.
- */
-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 (FABSF(r3[0])>FABSF(r2[0])) SWAP_ROWS(r3, r2);
-   if (FABSF(r2[0])>FABSF(r1[0])) SWAP_ROWS(r2, r1);
-   if (FABSF(r1[0])>FABSF(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 (FABSF(r3[1])>FABSF(r2[1])) SWAP_ROWS(r3, r2);
-   if (FABSF(r2[1])>FABSF(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 (FABSF(r3[2])>FABSF(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 = 1.0F/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  = 1.0F/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  = 1.0F/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  = 1.0F/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
-
-/**
- * Compute inverse of a general 3d transformation matrix.
- * 
- * \param mat pointer to a GLmatrix structure. The matrix inverse will be
- * stored in the GLmatrix::inv attribute.
- * 
- * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
- *
- * \author Adapted from graphics gems II.
- *
- * Calculates the inverse of the upper left by first calculating its
- * determinant and multiplying it to the symmetric adjust matrix of each
- * element. Finally deals with the translation part by transforming the
- * original translation vector using by the calculated submatrix inverse.
- */
-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 = 1.0F / 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;
-}
-
-/**
- * Compute inverse of a 3d transformation matrix.
- * 
- * \param mat pointer to a GLmatrix structure. The matrix inverse will be
- * stored in the GLmatrix::inv attribute.
- * 
- * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
- *
- * If the matrix is not an angle preserving matrix then calls
- * invert_matrix_3d_general for the actual calculation. Otherwise calculates
- * the inverse matrix analyzing and inverting each of the scaling, rotation and
- * translation parts.
- */
-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 = 1.0F / 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;
-}
-
-/**
- * Compute inverse of an identity transformation matrix.
- * 
- * \param mat pointer to a GLmatrix structure. The matrix inverse will be
- * stored in the GLmatrix::inv attribute.
- * 
- * \return always GL_TRUE.
- *
- * Simply copies Identity into GLmatrix::inv.
- */
-static GLboolean invert_matrix_identity( GLmatrix *mat )
-{
-   memcpy( mat->inv, Identity, sizeof(Identity) );
-   return GL_TRUE;
-}
-
-/**
- * Compute inverse of a no-rotation 3d transformation matrix.
- * 
- * \param mat pointer to a GLmatrix structure. The matrix inverse will be
- * stored in the GLmatrix::inv attribute.
- * 
- * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
- *
- * Calculates the 
- */
-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) = 1.0F / MAT(in,0,0);
-   MAT(out,1,1) = 1.0F / MAT(in,1,1);
-   MAT(out,2,2) = 1.0F / 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;
-}
-
-/**
- * Compute inverse of a no-rotation 2d transformation matrix.
- * 
- * \param mat pointer to a GLmatrix structure. The matrix inverse will be
- * stored in the GLmatrix::inv attribute.
- * 
- * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
- *
- * Calculates the inverse matrix by applying the inverse scaling and
- * translation to the identity matrix.
- */
-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) = 1.0F / MAT(in,0,0);
-   MAT(out,1,1) = 1.0F / 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;
-}
-
-#if 0
-/* broken */
-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) = 1.0F / MAT(in,0,0);
-   MAT(out,1,1) = 1.0F / 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) = 1.0F / MAT(in,2,3);
-   MAT(out,3,3) = MAT(in,2,2) * MAT(out,3,2);
-
-   return GL_TRUE;
-}
-#endif
-
-/**
- * Matrix inversion function pointer type.
- */
-typedef GLboolean (*inv_mat_func)( GLmatrix *mat );
-
-/**
- * Table of the matrix inversion functions according to the matrix type.
- */
-static inv_mat_func inv_mat_tab[7] = {
-   invert_matrix_general,
-   invert_matrix_identity,
-   invert_matrix_3d_no_rot,
-#if 0
-   /* Don't use this function for now - it fails when the projection matrix
-    * is premultiplied by a translation (ala Chromium's tilesort SPU).
-    */
-   invert_matrix_perspective,
-#else
-   invert_matrix_general,
-#endif
-   invert_matrix_3d,		/* lazy! */
-   invert_matrix_2d_no_rot,
-   invert_matrix_3d
-};
-
-/**
- * Compute inverse of a transformation matrix.
- * 
- * \param mat pointer to a GLmatrix structure. The matrix inverse will be
- * stored in the GLmatrix::inv attribute.
- * 
- * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
- *
- * Calls the matrix inversion function in inv_mat_tab corresponding to the
- * given matrix type.  In case of failure, updates the MAT_FLAG_SINGULAR flag,
- * and copies the identity matrix into GLmatrix::inv.
- */
-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;
-   }
-}
-
-/*@}*/
-
-
-/**********************************************************************/
-/** \name Matrix generation */
-/*@{*/
-
-/**
- * Generate a 4x4 transformation matrix from glRotate parameters, and
- * post-multiply the input matrix by it.
- *
- * \author
- * This function was contributed by Erich Boleyn (erich@uruk.org).
- * Optimizations contributed by Rudolf Opalla (rudi@khm.de).
- */
-void
-_math_matrix_rotate( GLmatrix *mat,
-		     GLfloat angle, GLfloat x, GLfloat y, GLfloat z )
-{
-   GLfloat xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c, s, c;
-   GLfloat m[16];
-   GLboolean optimized;
-
-   s = (GLfloat) sin( angle * DEG2RAD );
-   c = (GLfloat) cos( angle * DEG2RAD );
-
-   memcpy(m, Identity, sizeof(GLfloat)*16);
-   optimized = GL_FALSE;
-
-#define M(row,col)  m[col*4+row]
-
-   if (x == 0.0F) {
-      if (y == 0.0F) {
-         if (z != 0.0F) {
-            optimized = GL_TRUE;
-            /* rotate only around z-axis */
-            M(0,0) = c;
-            M(1,1) = c;
-            if (z < 0.0F) {
-               M(0,1) = s;
-               M(1,0) = -s;
-            }
-            else {
-               M(0,1) = -s;
-               M(1,0) = s;
-            }
-         }
-      }
-      else if (z == 0.0F) {
-         optimized = GL_TRUE;
-         /* rotate only around y-axis */
-         M(0,0) = c;
-         M(2,2) = c;
-         if (y < 0.0F) {
-            M(0,2) = -s;
-            M(2,0) = s;
-         }
-         else {
-            M(0,2) = s;
-            M(2,0) = -s;
-         }
-      }
-   }
-   else if (y == 0.0F) {
-      if (z == 0.0F) {
-         optimized = GL_TRUE;
-         /* rotate only around x-axis */
-         M(1,1) = c;
-         M(2,2) = c;
-         if (x < 0.0F) {
-            M(1,2) = s;
-            M(2,1) = -s;
-         }
-         else {
-            M(1,2) = -s;
-            M(2,1) = s;
-         }
-      }
-   }
-
-   if (!optimized) {
-      const GLfloat mag = SQRTF(x * x + y * y + z * z);
-
-      if (mag <= 1.0e-4) {
-         /* no rotation, leave mat as-is */
-         return;
-      }
-
-      x /= mag;
-      y /= mag;
-      z /= mag;
-
-
-      /*
-       *     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 its 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;
-
-      /* We already hold the identity-matrix so we can skip some statements */
-      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 );
-}
-
-/**
- * Apply a perspective projection matrix.
- *
- * \param mat matrix to apply the projection.
- * \param left left clipping plane coordinate.
- * \param right right clipping plane coordinate.
- * \param bottom bottom clipping plane coordinate.
- * \param top top clipping plane coordinate.
- * \param nearval distance to the near clipping plane.
- * \param farval distance to the far clipping plane.
- *
- * Creates the projection matrix and multiplies it with \p mat, marking the
- * MAT_FLAG_PERSPECTIVE flag.
- */
-void
-_math_matrix_frustum( 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 = (2.0F*nearval) / (right-left);
-   y = (2.0F*nearval) / (top-bottom);
-   a = (right+left) / (right-left);
-   b = (top+bottom) / (top-bottom);
-   c = -(farval+nearval) / ( farval-nearval);
-   d = -(2.0F*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 );
-}
-
-/**
- * Apply an orthographic projection matrix.
- *
- * \param mat matrix to apply the projection.
- * \param left left clipping plane coordinate.
- * \param right right clipping plane coordinate.
- * \param bottom bottom clipping plane coordinate.
- * \param top top clipping plane coordinate.
- * \param nearval distance to the near clipping plane.
- * \param farval distance to the far clipping plane.
- *
- * Creates the projection matrix and multiplies it with \p mat, marking the
- * MAT_FLAG_GENERAL_SCALE and MAT_FLAG_TRANSLATION flags.
- */
-void
-_math_matrix_ortho( GLmatrix *mat,
-		    GLfloat left, GLfloat right,
-		    GLfloat bottom, GLfloat top,
-		    GLfloat nearval, GLfloat farval )
-{
-   GLfloat m[16];
-
-#define M(row,col)  m[col*4+row]
-   M(0,0) = 2.0F / (right-left);
-   M(0,1) = 0.0F;
-   M(0,2) = 0.0F;
-   M(0,3) = -(right+left) / (right-left);
-
-   M(1,0) = 0.0F;
-   M(1,1) = 2.0F / (top-bottom);
-   M(1,2) = 0.0F;
-   M(1,3) = -(top+bottom) / (top-bottom);
-
-   M(2,0) = 0.0F;
-   M(2,1) = 0.0F;
-   M(2,2) = -2.0F / (farval-nearval);
-   M(2,3) = -(farval+nearval) / (farval-nearval);
-
-   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));
-}
-
-/**
- * Multiply a matrix with a general scaling matrix.
- *
- * \param mat matrix.
- * \param x x axis scale factor.
- * \param y y axis scale factor.
- * \param z z axis scale factor.
- *
- * Multiplies in-place the elements of \p mat by the scale factors. Checks if
- * the scales factors are roughly the same, marking the MAT_FLAG_UNIFORM_SCALE
- * flag, or MAT_FLAG_GENERAL_SCALE. Marks the MAT_DIRTY_TYPE and
- * MAT_DIRTY_INVERSE dirty flags.
- */
-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 (FABSF(x - y) < 1e-8 && FABSF(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);
-}
-
-/**
- * Multiply a matrix with a translation matrix.
- *
- * \param mat matrix.
- * \param x translation vector x coordinate.
- * \param y translation vector y coordinate.
- * \param z translation vector z coordinate.
- *
- * Adds the translation coordinates to the elements of \p mat in-place.  Marks
- * the MAT_FLAG_TRANSLATION flag, and the MAT_DIRTY_TYPE and MAT_DIRTY_INVERSE
- * dirty flags.
- */
-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);
-}
-
-
-/**
- * Set matrix to do viewport and depthrange mapping.
- * Transforms Normalized Device Coords to window/Z values.
- */
-void
-_math_matrix_viewport(GLmatrix *m, GLint x, GLint y, GLint width, GLint height,
-                      GLfloat zNear, GLfloat zFar, GLfloat depthMax)
-{
-   m->m[MAT_SX] = (GLfloat) width / 2.0F;
-   m->m[MAT_TX] = m->m[MAT_SX] + x;
-   m->m[MAT_SY] = (GLfloat) height / 2.0F;
-   m->m[MAT_TY] = m->m[MAT_SY] + y;
-   m->m[MAT_SZ] = depthMax * ((zFar - zNear) / 2.0F);
-   m->m[MAT_TZ] = depthMax * ((zFar - zNear) / 2.0F + zNear);
-   m->flags = MAT_FLAG_GENERAL_SCALE | MAT_FLAG_TRANSLATION;
-   m->type = MATRIX_3D_NO_ROT;
-}
-
-
-/**
- * Set a matrix to the identity matrix.
- *
- * \param mat matrix.
- *
- * Copies ::Identity into \p GLmatrix::m, and into GLmatrix::inv if not NULL.
- * Sets the matrix type to identity, and clear the dirty flags.
- */
-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);
-}
-
-/*@}*/
-
-
-/**********************************************************************/
-/** \name Matrix analysis */
-/*@{*/
-
-#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.  
- *
- * \param mat matrix.
- * 
- * This is expensive enough to only want to do it once.
- */
-static void analyse_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 == (GLuint) MASK_IDENTITY) {
-      mat->type = MATRIX_IDENTITY;
-   }
-   else if ((mask & MASK_2D_NO_ROT) == (GLuint) 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) == (GLuint) 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) == (GLuint) 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) == (GLuint) 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;
-   }
-}
-
-/**
- * Analyze a matrix given that its flags are accurate.
- * 
- * This is the more common operation, hopefully.
- */
-static void analyse_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;
-   }
-}
-
-/**
- * Analyze and update a matrix.
- *
- * \param mat matrix.
- *
- * If the matrix type is dirty then calls either analyse_from_scratch() or
- * analyse_from_flags() to determine its type, according to whether the flags
- * are dirty or not, respectively. If the matrix has an inverse and it's dirty
- * then calls matrix_invert(). Finally clears the dirty flags.
- */
-void
-_math_matrix_analyse( GLmatrix *mat )
-{
-   if (mat->flags & MAT_DIRTY_TYPE) {
-      if (mat->flags & MAT_DIRTY_FLAGS)
-	 analyse_from_scratch( mat );
-      else
-	 analyse_from_flags( mat );
-   }
-
-   if (mat->inv && (mat->flags & MAT_DIRTY_INVERSE)) {
-      matrix_invert( mat );
-      mat->flags &= ~MAT_DIRTY_INVERSE;
-   }
-
-   mat->flags &= ~(MAT_DIRTY_FLAGS | MAT_DIRTY_TYPE);
-}
-
-/*@}*/
-
-
-/**
- * Test if the given matrix preserves vector lengths.
- */
-GLboolean
-_math_matrix_is_length_preserving( const GLmatrix *m )
-{
-   return TEST_MAT_FLAGS( m, MAT_FLAGS_LENGTH_PRESERVING);
-}
-
-
-/**
- * Test if the given matrix does any rotation.
- * (or perhaps if the upper-left 3x3 is non-identity)
- */
-GLboolean
-_math_matrix_has_rotation( const GLmatrix *m )
-{
-   if (m->flags & (MAT_FLAG_GENERAL |
-                   MAT_FLAG_ROTATION |
-                   MAT_FLAG_GENERAL_3D |
-                   MAT_FLAG_PERSPECTIVE))
-      return GL_TRUE;
-   else
-      return GL_FALSE;
-}
-
-
-GLboolean
-_math_matrix_is_general_scale( const GLmatrix *m )
-{
-   return (m->flags & MAT_FLAG_GENERAL_SCALE) ? GL_TRUE : GL_FALSE;
-}
-
-
-GLboolean
-_math_matrix_is_dirty( const GLmatrix *m )
-{
-   return (m->flags & MAT_DIRTY) ? GL_TRUE : GL_FALSE;
-}
-
-
-/**********************************************************************/
-/** \name Matrix setup */
-/*@{*/
-
-/**
- * Copy a matrix.
- *
- * \param to destination matrix.
- * \param from source matrix.
- *
- * Copies all fields in GLmatrix, creating an inverse array if necessary.
- */
-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);
-      }
-   }
-}
-
-/**
- * Loads a matrix array into GLmatrix.
- * 
- * \param m matrix array.
- * \param mat matrix.
- *
- * Copies \p m into GLmatrix::m and marks the MAT_FLAG_GENERAL and MAT_DIRTY
- * flags.
- */
-void
-_math_matrix_loadf( GLmatrix *mat, const GLfloat *m )
-{
-   memcpy( mat->m, m, 16*sizeof(GLfloat) );
-   mat->flags = (MAT_FLAG_GENERAL | MAT_DIRTY);
-}
-
-/**
- * Matrix constructor.
- *
- * \param m matrix.
- *
- * Initialize the GLmatrix fields.
- */
-void
-_math_matrix_ctr( GLmatrix *m )
-{
-   m->m = (GLfloat *) _mesa_align_malloc( 16 * sizeof(GLfloat), 16 );
-   if (m->m)
-      memcpy( m->m, Identity, sizeof(Identity) );
-   m->inv = NULL;
-   m->type = MATRIX_IDENTITY;
-   m->flags = 0;
-}
-
-/**
- * Matrix destructor.
- *
- * \param m matrix.
- *
- * Frees the data in a GLmatrix.
- */
-void
-_math_matrix_dtr( GLmatrix *m )
-{
-   if (m->m) {
-      _mesa_align_free( m->m );
-      m->m = NULL;
-   }
-   if (m->inv) {
-      _mesa_align_free( m->inv );
-      m->inv = NULL;
-   }
-}
-
-/**
- * Allocate a matrix inverse.
- *
- * \param m matrix.
- *
- * Allocates the matrix inverse, GLmatrix::inv, and sets it to Identity.
- */
-void
-_math_matrix_alloc_inv( GLmatrix *m )
-{
-   if (!m->inv) {
-      m->inv = (GLfloat *) _mesa_align_malloc( 16 * sizeof(GLfloat), 16 );
-      if (m->inv)
-         memcpy( m->inv, Identity, 16 * sizeof(GLfloat) );
-   }
-}
-
-/*@}*/
-
-
-/**********************************************************************/
-/** \name Matrix transpose */
-/*@{*/
-
-/**
- * Transpose a GLfloat matrix.
- *
- * \param to destination array.
- * \param from source array.
- */
-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];
-}
-
-/**
- * Transpose a GLdouble matrix.
- *
- * \param to destination array.
- * \param from source array.
- */
-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];
-}
-
-/**
- * Transpose a GLdouble matrix and convert to GLfloat.
- *
- * \param to destination array.
- * \param from source array.
- */
-void
-_math_transposefd( GLfloat to[16], const GLdouble from[16] )
-{
-   to[0] = (GLfloat) from[0];
-   to[1] = (GLfloat) from[4];
-   to[2] = (GLfloat) from[8];
-   to[3] = (GLfloat) from[12];
-   to[4] = (GLfloat) from[1];
-   to[5] = (GLfloat) from[5];
-   to[6] = (GLfloat) from[9];
-   to[7] = (GLfloat) from[13];
-   to[8] = (GLfloat) from[2];
-   to[9] = (GLfloat) from[6];
-   to[10] = (GLfloat) from[10];
-   to[11] = (GLfloat) from[14];
-   to[12] = (GLfloat) from[3];
-   to[13] = (GLfloat) from[7];
-   to[14] = (GLfloat) from[11];
-   to[15] = (GLfloat) from[15];
-}
-
-/*@}*/
-
-
-/**
- * Transform a 4-element row vector (1x4 matrix) by a 4x4 matrix.  This
- * function is used for transforming clipping plane equations and spotlight
- * directions.
- * Mathematically,  u = v * m.
- * Input:  v - input vector
- *         m - transformation matrix
- * Output:  u - transformed vector
- */
-void
-_mesa_transform_vector( GLfloat u[4], const GLfloat v[4], const GLfloat m[16] )
-{
-   const GLfloat v0 = v[0], v1 = v[1], v2 = v[2], v3 = v[3];
-#define M(row,col)  m[row + col*4]
-   u[0] = v0 * M(0,0) + v1 * M(1,0) + v2 * M(2,0) + v3 * M(3,0);
-   u[1] = v0 * M(0,1) + v1 * M(1,1) + v2 * M(2,1) + v3 * M(3,1);
-   u[2] = v0 * M(0,2) + v1 * M(1,2) + v2 * M(2,2) + v3 * M(3,2);
-   u[3] = v0 * M(0,3) + v1 * M(1,3) + v2 * M(2,3) + v3 * M(3,3);
-#undef M
-}
+/*

+ * Mesa 3-D graphics library

+ * Version:  6.3

+ *

+ * Copyright (C) 1999-2005  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.

+ */

+

+

+/**

+ * \file m_matrix.c

+ * Matrix operations.

+ *

+ * \note

+ * -# 4x4 transformation matrices are stored in memory in column major order.

+ * -# Points/vertices are to be thought of as column vectors.

+ * -# Transformation of a point p by a matrix M is: p' = M * p

+ */

+

+

+#include "main/glheader.h"

+#include "main/imports.h"

+#include "main/macros.h"

+

+#include "m_matrix.h"

+

+

+/**

+ * \defgroup MatFlags MAT_FLAG_XXX-flags

+ *

+ * Bitmasks to indicate different kinds of 4x4 matrices in GLmatrix::flags

+ * It would be nice to make all these flags private to m_matrix.c

+ */

+/*@{*/

+#define MAT_FLAG_IDENTITY       0     /**< is an identity matrix flag.

+                                       *   (Not actually used - the identity

+                                       *   matrix is identified by the absense

+                                       *   of all other flags.)

+                                       */

+#define MAT_FLAG_GENERAL        0x1   /**< is a general matrix flag */

+#define MAT_FLAG_ROTATION       0x2   /**< is a rotation matrix flag */

+#define MAT_FLAG_TRANSLATION    0x4   /**< is a translation matrix flag */

+#define MAT_FLAG_UNIFORM_SCALE  0x8   /**< is an uniform scaling matrix flag */

+#define MAT_FLAG_GENERAL_SCALE  0x10  /**< is a general scaling matrix flag */

+#define MAT_FLAG_GENERAL_3D     0x20  /**< general 3D matrix flag */

+#define MAT_FLAG_PERSPECTIVE    0x40  /**< is a perspective proj matrix flag */

+#define MAT_FLAG_SINGULAR       0x80  /**< is a singular matrix flag */

+#define MAT_DIRTY_TYPE          0x100  /**< matrix type is dirty */

+#define MAT_DIRTY_FLAGS         0x200  /**< matrix flags are dirty */

+#define MAT_DIRTY_INVERSE       0x400  /**< matrix inverse is dirty */

+

+/** angle preserving matrix flags mask */

+#define MAT_FLAGS_ANGLE_PRESERVING (MAT_FLAG_ROTATION | \

+				    MAT_FLAG_TRANSLATION | \

+				    MAT_FLAG_UNIFORM_SCALE)

+

+/** geometry related matrix flags mask */

+#define MAT_FLAGS_GEOMETRY (MAT_FLAG_GENERAL | \

+			    MAT_FLAG_ROTATION | \

+			    MAT_FLAG_TRANSLATION | \

+			    MAT_FLAG_UNIFORM_SCALE | \

+			    MAT_FLAG_GENERAL_SCALE | \

+			    MAT_FLAG_GENERAL_3D | \

+			    MAT_FLAG_PERSPECTIVE | \

+	                    MAT_FLAG_SINGULAR)

+

+/** length preserving matrix flags mask */

+#define MAT_FLAGS_LENGTH_PRESERVING (MAT_FLAG_ROTATION | \

+				     MAT_FLAG_TRANSLATION)

+

+

+/** 3D (non-perspective) matrix flags mask */

+#define MAT_FLAGS_3D (MAT_FLAG_ROTATION | \

+		      MAT_FLAG_TRANSLATION | \

+		      MAT_FLAG_UNIFORM_SCALE | \

+		      MAT_FLAG_GENERAL_SCALE | \

+		      MAT_FLAG_GENERAL_3D)

+

+/** dirty matrix flags mask */

+#define MAT_DIRTY          (MAT_DIRTY_TYPE | \

+			    MAT_DIRTY_FLAGS | \

+			    MAT_DIRTY_INVERSE)

+

+/*@}*/

+

+

+/** 

+ * Test geometry related matrix flags.

+ * 

+ * \param mat a pointer to a GLmatrix structure.

+ * \param a flags mask.

+ *

+ * \returns non-zero if all geometry related matrix flags are contained within

+ * the mask, or zero otherwise.

+ */ 

+#define TEST_MAT_FLAGS(mat, a)  \

+    ((MAT_FLAGS_GEOMETRY & (~(a)) & ((mat)->flags) ) == 0)

+

+

+

+/**

+ * Names of the corresponding GLmatrixtype values.

+ */

+static const char *types[] = {

+   "MATRIX_GENERAL",

+   "MATRIX_IDENTITY",

+   "MATRIX_3D_NO_ROT",

+   "MATRIX_PERSPECTIVE",

+   "MATRIX_2D",

+   "MATRIX_2D_NO_ROT",

+   "MATRIX_3D"

+};

+

+

+/**

+ * Identity matrix.

+ */

+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

+};

+

+

+

+/**********************************************************************/

+/** \name Matrix multiplication */

+/*@{*/

+

+#define A(row,col)  a[(col<<2)+row]

+#define B(row,col)  b[(col<<2)+row]

+#define P(row,col)  product[(col<<2)+row]

+

+/**

+ * Perform a full 4x4 matrix multiplication.

+ *

+ * \param a matrix.

+ * \param b matrix.

+ * \param product will receive the product of \p a and \p b.

+ *

+ * \warning Is assumed that \p product != \p b. \p product == \p a is allowed.

+ *

+ * \note KW: 4*16 = 64 multiplications

+ * 

+ * \author This \c matmul was contributed by Thomas Malik

+ */

+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 orthogonal matrices.

+ *

+ * \param a matrix.

+ * \param b matrix.

+ * \param product will receive the product of \p a and \p b.

+ */

+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.

+ *

+ * \param mat pointer to a GLmatrix structure containing the left multiplication

+ * matrix, and that will receive the product result.

+ * \param m right multiplication matrix array.

+ * \param flags flags of the matrix \p m.

+ * 

+ * Joins both flags and marks the type and inverse as dirty.  Calls matmul34()

+ * if both matrices are 3D, or matmul4() otherwise.

+ */

+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 );

+}

+

+/**

+ * Matrix multiplication.

+ *

+ * \param dest destination matrix.

+ * \param a left matrix.

+ * \param b right matrix.

+ * 

+ * Joins both flags and marks the type and inverse as dirty.  Calls matmul34()

+ * if both matrices are 3D, or matmul4() otherwise.

+ */

+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 );

+}

+

+/**

+ * Matrix multiplication.

+ *

+ * \param dest left and destination matrix.

+ * \param m right matrix array.

+ * 

+ * Marks the matrix flags with general flag, and type and inverse dirty flags.

+ * Calls matmul4() for the multiplication.

+ */

+void

+_math_matrix_mul_floats( GLmatrix *dest, const GLfloat *m )

+{

+   dest->flags |= (MAT_FLAG_GENERAL |

+		   MAT_DIRTY_TYPE |

+		   MAT_DIRTY_INVERSE |

+                   MAT_DIRTY_FLAGS);

+

+   matmul4( dest->m, dest->m, m );

+}

+

+/*@}*/

+

+

+/**********************************************************************/

+/** \name Matrix output */

+/*@{*/

+

+/**

+ * Print a matrix array.

+ *

+ * \param m matrix array.

+ *

+ * Called by _math_matrix_print() to print a matrix or its inverse.

+ */

+static void print_matrix_floats( const GLfloat m[16] )

+{

+   int i;

+   for (i=0;i<4;i++) {

+      _mesa_debug(NULL,"\t%f %f %f %f\n", m[i], m[4+i], m[8+i], m[12+i] );

+   }

+}

+

+/**

+ * Dumps the contents of a GLmatrix structure.

+ * 

+ * \param m pointer to the GLmatrix structure.

+ */

+void

+_math_matrix_print( const GLmatrix *m )

+{

+   _mesa_debug(NULL, "Matrix type: %s, flags: %x\n", types[m->type], m->flags);

+   print_matrix_floats(m->m);

+   _mesa_debug(NULL, "Inverse: \n");

+   if (m->inv) {

+      GLfloat prod[16];

+      print_matrix_floats(m->inv);

+      matmul4(prod, m->m, m->inv);

+      _mesa_debug(NULL, "Mat * Inverse:\n");

+      print_matrix_floats(prod);

+   }

+   else {

+      _mesa_debug(NULL, "  - not available\n");

+   }

+}

+

+/*@}*/

+

+

+/**

+ * References an element of 4x4 matrix.

+ *

+ * \param m matrix array.

+ * \param c column of the desired element.

+ * \param r row of the desired element.

+ * 

+ * \return value of the desired element.

+ *

+ * Calculate the linear storage index of the element and references it. 

+ */

+#define MAT(m,r,c) (m)[(c)*4+(r)]

+

+

+/**********************************************************************/

+/** \name Matrix inversion */

+/*@{*/

+

+/**

+ * Swaps the values of two floating pointer variables.

+ *

+ * Used by invert_matrix_general() to swap the row pointers.

+ */

+#define SWAP_ROWS(a, b) { GLfloat *_tmp = a; (a)=(b); (b)=_tmp; }

+

+/**

+ * Compute inverse of 4x4 transformation matrix.

+ * 

+ * \param mat pointer to a GLmatrix structure. The matrix inverse will be

+ * stored in the GLmatrix::inv attribute.

+ * 

+ * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).

+ * 

+ * \author

+ * Code contributed by Jacques Leroy jle@star.be

+ *

+ * Calculates the inverse matrix by performing the gaussian matrix reduction

+ * with partial pivoting followed by back/substitution with the loops manually

+ * unrolled.

+ */

+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 (FABSF(r3[0])>FABSF(r2[0])) SWAP_ROWS(r3, r2);

+   if (FABSF(r2[0])>FABSF(r1[0])) SWAP_ROWS(r2, r1);

+   if (FABSF(r1[0])>FABSF(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 (FABSF(r3[1])>FABSF(r2[1])) SWAP_ROWS(r3, r2);

+   if (FABSF(r2[1])>FABSF(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 (FABSF(r3[2])>FABSF(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 = 1.0F/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  = 1.0F/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  = 1.0F/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  = 1.0F/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

+

+/**

+ * Compute inverse of a general 3d transformation matrix.

+ * 

+ * \param mat pointer to a GLmatrix structure. The matrix inverse will be

+ * stored in the GLmatrix::inv attribute.

+ * 

+ * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).

+ *

+ * \author Adapted from graphics gems II.

+ *

+ * Calculates the inverse of the upper left by first calculating its

+ * determinant and multiplying it to the symmetric adjust matrix of each

+ * element. Finally deals with the translation part by transforming the

+ * original translation vector using by the calculated submatrix inverse.

+ */

+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 = 1.0F / 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;

+}

+

+/**

+ * Compute inverse of a 3d transformation matrix.

+ * 

+ * \param mat pointer to a GLmatrix structure. The matrix inverse will be

+ * stored in the GLmatrix::inv attribute.

+ * 

+ * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).

+ *

+ * If the matrix is not an angle preserving matrix then calls

+ * invert_matrix_3d_general for the actual calculation. Otherwise calculates

+ * the inverse matrix analyzing and inverting each of the scaling, rotation and

+ * translation parts.

+ */

+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 = 1.0F / 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;

+}

+

+/**

+ * Compute inverse of an identity transformation matrix.

+ * 

+ * \param mat pointer to a GLmatrix structure. The matrix inverse will be

+ * stored in the GLmatrix::inv attribute.

+ * 

+ * \return always GL_TRUE.

+ *

+ * Simply copies Identity into GLmatrix::inv.

+ */

+static GLboolean invert_matrix_identity( GLmatrix *mat )

+{

+   memcpy( mat->inv, Identity, sizeof(Identity) );

+   return GL_TRUE;

+}

+

+/**

+ * Compute inverse of a no-rotation 3d transformation matrix.

+ * 

+ * \param mat pointer to a GLmatrix structure. The matrix inverse will be

+ * stored in the GLmatrix::inv attribute.

+ * 

+ * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).

+ *

+ * Calculates the 

+ */

+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) = 1.0F / MAT(in,0,0);

+   MAT(out,1,1) = 1.0F / MAT(in,1,1);

+   MAT(out,2,2) = 1.0F / 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;

+}

+

+/**

+ * Compute inverse of a no-rotation 2d transformation matrix.

+ * 

+ * \param mat pointer to a GLmatrix structure. The matrix inverse will be

+ * stored in the GLmatrix::inv attribute.

+ * 

+ * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).

+ *

+ * Calculates the inverse matrix by applying the inverse scaling and

+ * translation to the identity matrix.

+ */

+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) = 1.0F / MAT(in,0,0);

+   MAT(out,1,1) = 1.0F / 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;

+}

+

+#if 0

+/* broken */

+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) = 1.0F / MAT(in,0,0);

+   MAT(out,1,1) = 1.0F / 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) = 1.0F / MAT(in,2,3);

+   MAT(out,3,3) = MAT(in,2,2) * MAT(out,3,2);

+

+   return GL_TRUE;

+}

+#endif

+

+/**

+ * Matrix inversion function pointer type.

+ */

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

+

+/**

+ * Table of the matrix inversion functions according to the matrix type.

+ */

+static inv_mat_func inv_mat_tab[7] = {

+   invert_matrix_general,

+   invert_matrix_identity,

+   invert_matrix_3d_no_rot,

+#if 0

+   /* Don't use this function for now - it fails when the projection matrix

+    * is premultiplied by a translation (ala Chromium's tilesort SPU).

+    */

+   invert_matrix_perspective,

+#else

+   invert_matrix_general,

+#endif

+   invert_matrix_3d,		/* lazy! */

+   invert_matrix_2d_no_rot,

+   invert_matrix_3d

+};

+

+/**

+ * Compute inverse of a transformation matrix.

+ * 

+ * \param mat pointer to a GLmatrix structure. The matrix inverse will be

+ * stored in the GLmatrix::inv attribute.

+ * 

+ * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).

+ *

+ * Calls the matrix inversion function in inv_mat_tab corresponding to the

+ * given matrix type.  In case of failure, updates the MAT_FLAG_SINGULAR flag,

+ * and copies the identity matrix into GLmatrix::inv.

+ */

+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;

+   }

+}

+

+/*@}*/

+

+

+/**********************************************************************/

+/** \name Matrix generation */

+/*@{*/

+

+/**

+ * Generate a 4x4 transformation matrix from glRotate parameters, and

+ * post-multiply the input matrix by it.

+ *

+ * \author

+ * This function was contributed by Erich Boleyn (erich@uruk.org).

+ * Optimizations contributed by Rudolf Opalla (rudi@khm.de).

+ */

+void

+_math_matrix_rotate( GLmatrix *mat,

+		     GLfloat angle, GLfloat x, GLfloat y, GLfloat z )

+{

+   GLfloat xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c, s, c;

+   GLfloat m[16];

+   GLboolean optimized;

+

+   s = (GLfloat) sin( angle * DEG2RAD );

+   c = (GLfloat) cos( angle * DEG2RAD );

+

+   memcpy(m, Identity, sizeof(GLfloat)*16);

+   optimized = GL_FALSE;

+

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

+

+   if (x == 0.0F) {

+      if (y == 0.0F) {

+         if (z != 0.0F) {

+            optimized = GL_TRUE;

+            /* rotate only around z-axis */

+            M(0,0) = c;

+            M(1,1) = c;

+            if (z < 0.0F) {

+               M(0,1) = s;

+               M(1,0) = -s;

+            }

+            else {

+               M(0,1) = -s;

+               M(1,0) = s;

+            }

+         }

+      }

+      else if (z == 0.0F) {

+         optimized = GL_TRUE;

+         /* rotate only around y-axis */

+         M(0,0) = c;

+         M(2,2) = c;

+         if (y < 0.0F) {

+            M(0,2) = -s;

+            M(2,0) = s;

+         }

+         else {

+            M(0,2) = s;

+            M(2,0) = -s;

+         }

+      }

+   }

+   else if (y == 0.0F) {

+      if (z == 0.0F) {

+         optimized = GL_TRUE;

+         /* rotate only around x-axis */

+         M(1,1) = c;

+         M(2,2) = c;

+         if (x < 0.0F) {

+            M(1,2) = s;

+            M(2,1) = -s;

+         }

+         else {

+            M(1,2) = -s;

+            M(2,1) = s;

+         }

+      }

+   }

+

+   if (!optimized) {

+      const GLfloat mag = SQRTF(x * x + y * y + z * z);

+

+      if (mag <= 1.0e-4) {

+         /* no rotation, leave mat as-is */

+         return;

+      }

+

+      x /= mag;

+      y /= mag;

+      z /= mag;

+

+

+      /*

+       *     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 its 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;

+

+      /* We already hold the identity-matrix so we can skip some statements */

+      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 );

+}

+

+/**

+ * Apply a perspective projection matrix.

+ *

+ * \param mat matrix to apply the projection.

+ * \param left left clipping plane coordinate.

+ * \param right right clipping plane coordinate.

+ * \param bottom bottom clipping plane coordinate.

+ * \param top top clipping plane coordinate.

+ * \param nearval distance to the near clipping plane.

+ * \param farval distance to the far clipping plane.

+ *

+ * Creates the projection matrix and multiplies it with \p mat, marking the

+ * MAT_FLAG_PERSPECTIVE flag.

+ */

+void

+_math_matrix_frustum( 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 = (2.0F*nearval) / (right-left);

+   y = (2.0F*nearval) / (top-bottom);

+   a = (right+left) / (right-left);

+   b = (top+bottom) / (top-bottom);

+   c = -(farval+nearval) / ( farval-nearval);

+   d = -(2.0F*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 );

+}

+

+/**

+ * Apply an orthographic projection matrix.

+ *

+ * \param mat matrix to apply the projection.

+ * \param left left clipping plane coordinate.

+ * \param right right clipping plane coordinate.

+ * \param bottom bottom clipping plane coordinate.

+ * \param top top clipping plane coordinate.

+ * \param nearval distance to the near clipping plane.

+ * \param farval distance to the far clipping plane.

+ *

+ * Creates the projection matrix and multiplies it with \p mat, marking the

+ * MAT_FLAG_GENERAL_SCALE and MAT_FLAG_TRANSLATION flags.

+ */

+void

+_math_matrix_ortho( GLmatrix *mat,

+		    GLfloat left, GLfloat right,

+		    GLfloat bottom, GLfloat top,

+		    GLfloat nearval, GLfloat farval )

+{

+   GLfloat m[16];

+

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

+   M(0,0) = 2.0F / (right-left);

+   M(0,1) = 0.0F;

+   M(0,2) = 0.0F;

+   M(0,3) = -(right+left) / (right-left);

+

+   M(1,0) = 0.0F;

+   M(1,1) = 2.0F / (top-bottom);

+   M(1,2) = 0.0F;

+   M(1,3) = -(top+bottom) / (top-bottom);

+

+   M(2,0) = 0.0F;

+   M(2,1) = 0.0F;

+   M(2,2) = -2.0F / (farval-nearval);

+   M(2,3) = -(farval+nearval) / (farval-nearval);

+

+   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));

+}

+

+/**

+ * Multiply a matrix with a general scaling matrix.

+ *

+ * \param mat matrix.

+ * \param x x axis scale factor.

+ * \param y y axis scale factor.

+ * \param z z axis scale factor.

+ *

+ * Multiplies in-place the elements of \p mat by the scale factors. Checks if

+ * the scales factors are roughly the same, marking the MAT_FLAG_UNIFORM_SCALE

+ * flag, or MAT_FLAG_GENERAL_SCALE. Marks the MAT_DIRTY_TYPE and

+ * MAT_DIRTY_INVERSE dirty flags.

+ */

+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 (FABSF(x - y) < 1e-8 && FABSF(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);

+}

+

+/**

+ * Multiply a matrix with a translation matrix.

+ *

+ * \param mat matrix.

+ * \param x translation vector x coordinate.

+ * \param y translation vector y coordinate.

+ * \param z translation vector z coordinate.

+ *

+ * Adds the translation coordinates to the elements of \p mat in-place.  Marks

+ * the MAT_FLAG_TRANSLATION flag, and the MAT_DIRTY_TYPE and MAT_DIRTY_INVERSE

+ * dirty flags.

+ */

+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);

+}

+

+

+/**

+ * Set matrix to do viewport and depthrange mapping.

+ * Transforms Normalized Device Coords to window/Z values.

+ */

+void

+_math_matrix_viewport(GLmatrix *m, GLint x, GLint y, GLint width, GLint height,

+                      GLfloat zNear, GLfloat zFar, GLfloat depthMax)

+{

+   m->m[MAT_SX] = (GLfloat) width / 2.0F;

+   m->m[MAT_TX] = m->m[MAT_SX] + x;

+   m->m[MAT_SY] = (GLfloat) height / 2.0F;

+   m->m[MAT_TY] = m->m[MAT_SY] + y;

+   m->m[MAT_SZ] = depthMax * ((zFar - zNear) / 2.0F);

+   m->m[MAT_TZ] = depthMax * ((zFar - zNear) / 2.0F + zNear);

+   m->flags = MAT_FLAG_GENERAL_SCALE | MAT_FLAG_TRANSLATION;

+   m->type = MATRIX_3D_NO_ROT;

+}

+

+

+/**

+ * Set a matrix to the identity matrix.

+ *

+ * \param mat matrix.

+ *

+ * Copies ::Identity into \p GLmatrix::m, and into GLmatrix::inv if not NULL.

+ * Sets the matrix type to identity, and clear the dirty flags.

+ */

+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);

+}

+

+/*@}*/

+

+

+/**********************************************************************/

+/** \name Matrix analysis */

+/*@{*/

+

+#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.  

+ *

+ * \param mat matrix.

+ * 

+ * This is expensive enough to only want to do it once.

+ */

+static void analyse_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 == (GLuint) MASK_IDENTITY) {

+      mat->type = MATRIX_IDENTITY;

+   }

+   else if ((mask & MASK_2D_NO_ROT) == (GLuint) 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) == (GLuint) 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) == (GLuint) 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) == (GLuint) 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;

+   }

+}

+

+/**

+ * Analyze a matrix given that its flags are accurate.

+ * 

+ * This is the more common operation, hopefully.

+ */

+static void analyse_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;

+   }

+}

+

+/**

+ * Analyze and update a matrix.

+ *

+ * \param mat matrix.

+ *

+ * If the matrix type is dirty then calls either analyse_from_scratch() or

+ * analyse_from_flags() to determine its type, according to whether the flags

+ * are dirty or not, respectively. If the matrix has an inverse and it's dirty

+ * then calls matrix_invert(). Finally clears the dirty flags.

+ */

+void

+_math_matrix_analyse( GLmatrix *mat )

+{

+   if (mat->flags & MAT_DIRTY_TYPE) {

+      if (mat->flags & MAT_DIRTY_FLAGS)

+	 analyse_from_scratch( mat );

+      else

+	 analyse_from_flags( mat );

+   }

+

+   if (mat->inv && (mat->flags & MAT_DIRTY_INVERSE)) {

+      matrix_invert( mat );

+      mat->flags &= ~MAT_DIRTY_INVERSE;

+   }

+

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

+}

+

+/*@}*/

+

+

+/**

+ * Test if the given matrix preserves vector lengths.

+ */

+GLboolean

+_math_matrix_is_length_preserving( const GLmatrix *m )

+{

+   return TEST_MAT_FLAGS( m, MAT_FLAGS_LENGTH_PRESERVING);

+}

+

+

+/**

+ * Test if the given matrix does any rotation.

+ * (or perhaps if the upper-left 3x3 is non-identity)

+ */

+GLboolean

+_math_matrix_has_rotation( const GLmatrix *m )

+{

+   if (m->flags & (MAT_FLAG_GENERAL |

+                   MAT_FLAG_ROTATION |

+                   MAT_FLAG_GENERAL_3D |

+                   MAT_FLAG_PERSPECTIVE))

+      return GL_TRUE;

+   else

+      return GL_FALSE;

+}

+

+

+GLboolean

+_math_matrix_is_general_scale( const GLmatrix *m )

+{

+   return (m->flags & MAT_FLAG_GENERAL_SCALE) ? GL_TRUE : GL_FALSE;

+}

+

+

+GLboolean

+_math_matrix_is_dirty( const GLmatrix *m )

+{

+   return (m->flags & MAT_DIRTY) ? GL_TRUE : GL_FALSE;

+}

+

+

+/**********************************************************************/

+/** \name Matrix setup */

+/*@{*/

+

+/**

+ * Copy a matrix.

+ *

+ * \param to destination matrix.

+ * \param from source matrix.

+ *

+ * Copies all fields in GLmatrix, creating an inverse array if necessary.

+ */

+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);

+      }

+   }

+}

+

+/**

+ * Loads a matrix array into GLmatrix.

+ * 

+ * \param m matrix array.

+ * \param mat matrix.

+ *

+ * Copies \p m into GLmatrix::m and marks the MAT_FLAG_GENERAL and MAT_DIRTY

+ * flags.

+ */

+void

+_math_matrix_loadf( GLmatrix *mat, const GLfloat *m )

+{

+   memcpy( mat->m, m, 16*sizeof(GLfloat) );

+   mat->flags = (MAT_FLAG_GENERAL | MAT_DIRTY);

+}

+

+/**

+ * Matrix constructor.

+ *

+ * \param m matrix.

+ *

+ * Initialize the GLmatrix fields.

+ */

+void

+_math_matrix_ctr( GLmatrix *m )

+{

+   m->m = (GLfloat *) _mesa_align_malloc( 16 * sizeof(GLfloat), 16 );

+   if (m->m)

+      memcpy( m->m, Identity, sizeof(Identity) );

+   m->inv = NULL;

+   m->type = MATRIX_IDENTITY;

+   m->flags = 0;

+}

+

+/**

+ * Matrix destructor.

+ *

+ * \param m matrix.

+ *

+ * Frees the data in a GLmatrix.

+ */

+void

+_math_matrix_dtr( GLmatrix *m )

+{

+   if (m->m) {

+      _mesa_align_free( m->m );

+      m->m = NULL;

+   }

+   if (m->inv) {

+      _mesa_align_free( m->inv );

+      m->inv = NULL;

+   }

+}

+

+/**

+ * Allocate a matrix inverse.

+ *

+ * \param m matrix.

+ *

+ * Allocates the matrix inverse, GLmatrix::inv, and sets it to Identity.

+ */

+void

+_math_matrix_alloc_inv( GLmatrix *m )

+{

+   if (!m->inv) {

+      m->inv = (GLfloat *) _mesa_align_malloc( 16 * sizeof(GLfloat), 16 );

+      if (m->inv)

+         memcpy( m->inv, Identity, 16 * sizeof(GLfloat) );

+   }

+}

+

+/*@}*/

+

+

+/**********************************************************************/

+/** \name Matrix transpose */

+/*@{*/

+

+/**

+ * Transpose a GLfloat matrix.

+ *

+ * \param to destination array.

+ * \param from source array.

+ */

+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];

+}

+

+/**

+ * Transpose a GLdouble matrix.

+ *

+ * \param to destination array.

+ * \param from source array.

+ */

+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];

+}

+

+/**

+ * Transpose a GLdouble matrix and convert to GLfloat.

+ *

+ * \param to destination array.

+ * \param from source array.

+ */

+void

+_math_transposefd( GLfloat to[16], const GLdouble from[16] )

+{

+   to[0] = (GLfloat) from[0];

+   to[1] = (GLfloat) from[4];

+   to[2] = (GLfloat) from[8];

+   to[3] = (GLfloat) from[12];

+   to[4] = (GLfloat) from[1];

+   to[5] = (GLfloat) from[5];

+   to[6] = (GLfloat) from[9];

+   to[7] = (GLfloat) from[13];

+   to[8] = (GLfloat) from[2];

+   to[9] = (GLfloat) from[6];

+   to[10] = (GLfloat) from[10];

+   to[11] = (GLfloat) from[14];

+   to[12] = (GLfloat) from[3];

+   to[13] = (GLfloat) from[7];

+   to[14] = (GLfloat) from[11];

+   to[15] = (GLfloat) from[15];

+}

+

+/*@}*/

+

+

+/**

+ * Transform a 4-element row vector (1x4 matrix) by a 4x4 matrix.  This

+ * function is used for transforming clipping plane equations and spotlight

+ * directions.

+ * Mathematically,  u = v * m.

+ * Input:  v - input vector

+ *         m - transformation matrix

+ * Output:  u - transformed vector

+ */

+void

+_mesa_transform_vector( GLfloat u[4], const GLfloat v[4], const GLfloat m[16] )

+{

+   const GLfloat v0 = v[0], v1 = v[1], v2 = v[2], v3 = v[3];

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

+   u[0] = v0 * M(0,0) + v1 * M(1,0) + v2 * M(2,0) + v3 * M(3,0);

+   u[1] = v0 * M(0,1) + v1 * M(1,1) + v2 * M(2,1) + v3 * M(3,1);

+   u[2] = v0 * M(0,2) + v1 * M(1,2) + v2 * M(2,2) + v3 * M(3,2);

+   u[3] = v0 * M(0,3) + v1 * M(1,3) + v2 * M(2,3) + v3 * M(3,3);

+#undef M

+}