Name

    EXT_vertex_shader

Name Strings

    GL_EXT_vertex_shader

Contact

    Dave Gosselin, ATI Research (gosselin 'at' ati.com) and
    Evan Hart, ATI Research (ehart 'at' ati.com)

Version

    Date: 8/20/2001
    Revision: 1.00

Number

    248

Dependencies

    This spec is written against the 1.2.1 version of the GL spec.

    ARB_imaging affects the definition of this spec.

Overview

    EXT_vertex_shader adds a flexible way to change the per-vertex
    processing in the GL pipeline. It provides a method to replace
    the fixed vertex/normal transform and lighting with a user
    specified means of generating processed vertices, texture
    coordinates, color, and secondary color, along with a primitive's
    associated state.

Issues

    How should the user be told that their shader doesn't fit and/or
    won't run well with the hardware? Some kind of GetError() value or
    a return value from EndShader()?

        This is accomplished using GetIntegerv, GetFloatv, and
        GetDoubleV to return a maximum value for Instructions,
        constants, and volatiles as well as returned the numbers 
        of these resources consumed by the current shader.
    
    Is lighting or texture coordinate generation performed when a user
    defined vertex shader is enabled.

        No. The shader writer is responsible for generating any
        texture coordinates and color values.

    Should we have separate per-vertex calls for SetDataEXT?

        Yes. Changed to SetVariant and SetShaderState.

    Should SwizzleEXT and WriteMaskEXT be an op-code or possibly
    combined into a new API call that takes enums?

        No, they are different enough to have their own entry point.

    Does there need to be a call to get the size of a potentially
    optimized shader, potentially using some kind of proxy
    mechanism?

        The implementation dependent state values seem to provide
        enough info.

    Should more GL state be available for use by the shader (e.g.
    enable/disable states for lights)?

        No, enough flexibility is already provided.

    Should we give the opcode enumerants data type names or leave them
    generic?

        This presents an interesting question in that the 
        trade off is a more simple, concise interface for more
        difficult validation on the part of the implementation.

    How should client-defined clip planes be handled?

        Client clip-planes should be applied in the output coordinate
        frame. When a vertex shader is invoked, the eye-space
        clipping planes are transformed by the current projection
        matrix and are applied after the primitive is assembled from
        the transformed vertices. 

  What are better names for GenData/SetData?
  
     These are misleading, and they should be changed. The primary
     hurdle is devising a better set of names.
     
     RESOLVED: New names implemented
     
  Should the *Transform* calls be replaced with a different moniker?
  
     Possibly, the term transform is somewhat narrow for the
     functionality. The term shader has been suggested. It seems
     like a good choice as it fits with the RenderMan style
     terminology already in use.

     RESOLVED: Shader will be used.
     
  How should RasterPos be affected by this extension?
  
     It is probably confusing to have RasterPos affected by
     this extension, so it should be disallowed.
     
  How should the arrays/indexing be handled?
  
     The index operation should be more strictly defined
     to only operate on contiguous name sets allocated by a
     single GenSymbols call. Alternatively, it may be useful to
     enforce that data to be used as arrays be given a special
     designation. 

  Should color-index mode be included?

     No, all computations are supported for RGB only.



New Procedure and Functions

    void BeginVertexShaderEXT( void )
    void EndVertexShaderEXT( void )
    void BindVertexShaderEXT( GLuint id )
    uint GenVertexShadersEXT( GLuint range )
    void DeleteVertexShaderEXT( GLuint id )
    void ShaderOp1EXT( enum op, uint res, uint arg1 )
    void ShaderOp2EXT( enum op, uint res, uint arg1, uint arg2 )
    void ShaderOp3EXT( enum op, uint res, uint arg1, uint arg2, uint arg3 )
    void SwizzleEXT( uint res, uint in, enum outX, enum outY, enum outZ, 
                     enum outW )
    void WriteMaskEXT( uint res, uint in, enum outX, enum outY, enum outZ
                       enum outW )
    void InsertComponentEXT( uint res, uint src, uint num )
    void ExtractComponentEXT( uint res, uint src, uint num )
    uint GenSymbolsEXT( enum datatype, enum storagetype, enum range,
                     uint components ) 
    void SetInvariantEXT( uint id, enum type, void *addr )
    void SetLocalConstantEXT( uint id, enum type, void *addr )
    void Variant{bsifd ubusui}vEXT( uint id, T *addr )
    void VariantPointerEXT( uint id, enum type, uint stride, void *addr )
    void EnableVariantClientStateEXT( uint id)
    void DisableVariantClientStateEXT( uint id)
    uint BindLightParameterEXT( enum light, enum value)
    uint BindMaterialParameterEXT( enum face, enum value)
    uint BindTexGenParameterEXT( enum unit, enum coord, enum value)
    uint BindTextureUnitParameterEXT( enum unit, enum value)
    uint BindParameterEXT( enum value)
    boolean IsVariantEnabledEXT( uint id, enum cap);
    void GetVariantBooleanvEXT( uint id, enum value, boolean *data);
    void GetVariantIntegervEXT( uint id, enum value, int *data);
    void GetVariantFloatvEXT( uint id, enum value, float *data);
    void GetVariantPointervEXT( uint id, enum value, void **data);
    void GetInvariantBooleanvEXT( uint id, enum value, boolean *data);
    void GetInvariantIntegervEXT( uint id, enum value, int *data);
    void GetInvariantFloatvEXT( uint id, enum value, float *data);
    void GetLocalConstantBooleanvEXT( uint id, enum value, boolean *data);
    void GetLocalConstantIntegervEXT( uint id, enum value, int *data);
    void GetLocalConstantFloatvEXT( uint id, enum value, float *data);

New Tokens

    Accepted by the <cap> parameter of Enable, Disable, and IsEnabled,
    and by the <pname> parameter of GetBooleanv, GetIntegerv, GetFloatv,
    and GetDoublev:

      VERTEX_SHADER_EXT                   0x8780

    Accepted by the <value> parameter of GetVariantBooleanv, GetVariantIntegerv,
    and GetVariantFloatv:

      VARIANT_VALUE_EXT                   0x87E4
      VARIANT_DATATYPE_EXT                0x87E5
      VARIANT_ARRAY_STRIDE_EXT            0x87E6
      VARIANT_ARRAY_TYPE_EXT              0x87E7

    Accepted by the <cap> parameter of IsVariantEnabled:

      VARIANT_ARRAY_EXT                   0x87E8

    Accepted by the <pname> parameter of GetVariantPointerv:

      VARIANT_ARRAY_POINTER_EXT           0x87E9

    Accepted by the <value> parameter of GetInvariantBooleanv,
    GetInvariantIntegerv, and GetInvariantFloatv:

      INVARIANT_VALUE_EXT                 0x87EA
      INVARIANT_DATATYPE_EXT              0x87EB

    Accepted by the <value> parameter of GetLocalConstantBooleanv,
    GetLocalConstantIntegerv, and GetLocalConstantFloatv:

      LOCAL_CONSTANT_VALUE_EXT            0x87EC
      LOCAL_CONSTANT_DATATYPE_EXT         0x87ED

    Accepted by the <op> parameter of ShaderOp[1..3]EXT:

      OP_INDEX_EXT                        0x8782
      OP_NEGATE_EXT                       0x8783
      OP_DOT3_EXT                         0x8784
      OP_DOT4_EXT                         0x8785
      OP_MUL_EXT                          0x8786
      OP_ADD_EXT                          0x8787
      OP_MADD_EXT                         0x8788
      OP_FRAC_EXT                         0x8789
      OP_MAX_EXT                          0x878A
      OP_MIN_EXT                          0x878B
      OP_SET_GE_EXT                       0x878C
      OP_SET_LT_EXT                       0x878D
      OP_CLAMP_EXT                        0x878E
      OP_FLOOR_EXT                        0x878F
      OP_ROUND_EXT                        0x8790
      OP_EXP_BASE_2_EXT                   0x8791
      OP_LOG_BASE_2_EXT                   0x8792
      OP_POWER_EXT                        0x8793
      OP_RECIP_EXT                        0x8794
      OP_RECIP_SQRT_EXT                   0x8795
      OP_SUB_EXT                          0x8796
      OP_CROSS_PRODUCT_EXT                0x8797
      OP_MULTIPLY_MATRIX_EXT              0x8798
      OP_MOV_EXT                          0x8799

    Accepted by the <res> parameter of ShaderOp[1..3]EXT, the <res>
    parameter of WriteMaskEXT, or the <res> parameter of SwizzleEXT:

      OUTPUT_VERTEX_EXT                   0x879A
      OUTPUT_COLOR0_EXT                   0x879B
      OUTPUT_COLOR1_EXT                   0x879C
      OUTPUT_TEXTURE_COORD0_EXT           0x879D
      OUTPUT_TEXTURE_COORD1_EXT           0x879E
      OUTPUT_TEXTURE_COORD2_EXT           0x879F
      OUTPUT_TEXTURE_COORD3_EXT           0x87A0
      OUTPUT_TEXTURE_COORD4_EXT           0x87A1
      OUTPUT_TEXTURE_COORD5_EXT           0x87A2
      OUTPUT_TEXTURE_COORD6_EXT           0x87A3
      OUTPUT_TEXTURE_COORD7_EXT           0x87A4
      OUTPUT_TEXTURE_COORD8_EXT           0x87A5
      OUTPUT_TEXTURE_COORD9_EXT           0x87A6
      OUTPUT_TEXTURE_COORD10_EXT          0x87A7
      OUTPUT_TEXTURE_COORD11_EXT          0x87A8
      OUTPUT_TEXTURE_COORD12_EXT          0x87A9
      OUTPUT_TEXTURE_COORD13_EXT          0x87AA
      OUTPUT_TEXTURE_COORD14_EXT          0x87AB
      OUTPUT_TEXTURE_COORD15_EXT          0x87AC
      OUTPUT_TEXTURE_COORD16_EXT          0x87AD
      OUTPUT_TEXTURE_COORD17_EXT          0x87AE
      OUTPUT_TEXTURE_COORD18_EXT          0x87AF
      OUTPUT_TEXTURE_COORD19_EXT          0x87B0
      OUTPUT_TEXTURE_COORD20_EXT          0x87B1
      OUTPUT_TEXTURE_COORD21_EXT          0x87B2
      OUTPUT_TEXTURE_COORD22_EXT          0x87B3
      OUTPUT_TEXTURE_COORD23_EXT          0x87B4
      OUTPUT_TEXTURE_COORD24_EXT          0x87B5
      OUTPUT_TEXTURE_COORD25_EXT          0x87B6
      OUTPUT_TEXTURE_COORD26_EXT          0x87B7
      OUTPUT_TEXTURE_COORD27_EXT          0x87B8
      OUTPUT_TEXTURE_COORD28_EXT          0x87B9
      OUTPUT_TEXTURE_COORD29_EXT          0x87BA
      OUTPUT_TEXTURE_COORD30_EXT          0x87BB
      OUTPUT_TEXTURE_COORD31_EXT          0x87BC
      OUTPUT_FOG_EXT                      0x87BD

    Accepted by the <datatype> parameter of GenSymbolsEXT:

      SCALAR_EXT                          0x87BE
      VECTOR_EXT                          0x87BF
      MATRIX_EXT                          0x87C0

    Accepted by the <storagetype> parameter of GenSymbolsEXT:

      VARIANT_EXT                         0x87C1
      INVARIANT_EXT                       0x87C2
      LOCAL_CONSTANT_EXT                  0x87C3
      LOCAL_EXT                           0x87C4

    Accepted by the <pname> parameters of GetIntegerv, GetFloatv, and
    GetDoublev:

      MAX_VERTEX_SHADER_INSTRUCTIONS_EXT              0x87C5
      MAX_VERTEX_SHADER_VARIANTS_EXT                  0x87C6
      MAX_VERTEX_SHADER_INVARIANTS_EXT                0x87C7
      MAX_VERTEX_SHADER_LOCAL_CONSTANTS_EXT           0x87C8
      MAX_VERTEX_SHADER_LOCALS_EXT                    0x87C9
      MAX_OPTIMIZED_VERTEX_SHADER_INSTRUCTIONS_EXT    0x87CA
      MAX_OPTIMIZED_VERTEX_SHADER_VARIANTS_EXT        0x87CB
      MAX_OPTIMIZED_VERTEX_SHADER_LOCAL_CONSTANTS_EXT 0x87CC
      MAX_OPTIMIZED_VERTEX_SHADER_INARIANTS_EXT       0x87CD
      MAX_OPTIMIZED_VERTEX_SHADER_LOCALS_EXT          0x87CE
      VERTEX_SHADER_INSTRUCTIONS_EXT                  0x87CF
      VERTEX_SHADER_VARIANTS_EXT                      0x87D0
      VERTEX_SHADER_INVARIANTS_EXT                    0x87D1
      VERTEX_SHADER_LOCAL_CONSTANTS_EXT               0x87D2
      VERTEX_SHADER_LOCALS_EXT                        0x87D3
      VERTEX_SHADER_BINDING_EXT                       0x8781

    Accepted by the <pname> parameters of GetBooleanv:

      VERTEX_SHADER_OPTIMIZED_EXT                     0x87D4

    Accepted by the <out[XYZW]> parameters of SwizzleEXT:

      X_EXT                               0x87D5
      Y_EXT                               0x87D6
      Z_EXT                               0x87D7
      W_EXT                               0x87D8
      NEGATIVE_X_EXT                      0x87D9
      NEGATIVE_Y_EXT                      0x87DA
      NEGATIVE_Z_EXT                      0x87DB
      NEGATIVE_W_EXT                      0x87DC
      ZERO_EXT                            0x87dd
      ONE_EXT                             0x87de
      NEGATIVE_ONE_EXT                    0x87DF

    Accepted by the <range> parameter of GenSymbolsEXT: 

      NORMALIZED_RANGE_EXT                    0x87E0
      FULL_RANGE_EXT                          0x87E1

    Accepted by the <value> parameter of BindParameterEXT:

      CURRENT_VERTEX_EXT                  0x87E2
      MVP_MATRIX_EXT                      0x87E3

      
   
Additions to Chapter 2 of the OpenGL 1.2.1 Specification (Operation)

  - (2.6, p. 12) First paragraph changed to:
    "In the GL, most geometric objects are drawn by enclosing a series
    of coordinate sets that specify vertices and optionally normals,
    texture coordinates, colors, and user defined data between
    Begin/End pairs. There are ten geometric objects that are drawn
    this way: points, line segments, line segment loops, separated
    line segments, polygons, triangle strips, triangle fans, separated
    triangles, quadrilateral strips, and separated quadrilaterals."

  - (2.6, p. 13) Fourth paragraph changed to:
    "The current values are part of GL state. Vertices and normals are
    transformed, colors may be affected or replaced by lighting, and
    texture coordinates are transformed and possibly affected by a
    texture coordinate generation function. Alternatively the
    vertices, normals, texture coordinates, and colors may be
    transformed or replaced by a vertex shader program. In either case
    the processing indicated for each current value is applied for
    each vertex that is sent to the GL."

  - (2.6, p. 14)
    Should replace figure 2.2 with something showing the switch
    between built in vertex/normal transformation and lighting and the
    vertex shader program. 

  - (2.6.3, p. 19) First paragraph changed to:
    "The only GL commands that are allowed within any Begin/End pairs
    are the commands for specifying vertex coordinates, vertex color,
    normal coordinates, and texture coordinates (Vertex, Color, Index,
    Normal, TexCoord), the ArrayElement command (see section 2.8), the
    EvalCoord and EvalPoint commands (see section 5.1), commands for
    specifying lighting material parameters (Material commands; see
    section 2.13.2), display list invocation commands (CallList and
    CallLists; see section 5.4), the EdgeFlag command, and the
    VariantEXT command (see section 2.14). Executing any other GL
    command between the execution of Begin and the corresponding
    execution of End results in the error INVALID_OPERATION. Executing
    Begin after Begin has already been executed but before an End is
    executed generates the INVALID_OPERATION error, as does executing
    End without a previous corresponding Begin.

  - (2.8, p. 23) Added after the second paragraph:
    "In addition to the pre-defined GL vertex components, variants
    can be supplied via the vertex array mechanism. Variant arrays are
    specified by the call:

      void VariantPointerEXT( uint id, enum type, uint stride, void *addr )

    The type and stride parameters hold the same meaning as all other
    array calls. The size parameter is missing as in NormalPointer,
    and the size is fixed at 4. The id parameter specifies which
    variant this array is to be used with. Finally, variant arrays
    are enabled and disabled by calls to:

       void EnableVariantClientStateEXT( uint id)
       void DisableVariantClientStateEXT( uint id)

    The id parameter contains the id of the variant array to enable
    or disable. 
    
  - (2.10, p. 28) First Paragraph changed to:
    "Vertices, normals, and texture coordinates are transformed before
    their coordinates are used to produce an image in the
    framebuffer. This transformation can be accomplished with either 
    the OpenGL Per-Vertex operations or replaced by a vertex shader.
    We begin with a description of how vertex coordinates are
    transformed via the OpenGL Per-Vertex operations and how this
    transformation is controlled. The specification of a vertex shader
    is described in section 2.14." 

  - (2.10, p. 28) Second Paragraph changed to:
    "Figure 2.6 diagrams the sequence of transformations that are
    applied to vertices in OpenGL vertex processing. The vertex
    coordinates that are presented to the GL are termed object
    coordinates. The model-view matrix is applied to these coordinates
    to yield eye coordinates. Then another matrix, called the
    projection matrix, is applied to eye coordinates to yield clip
    coordinates. A perspective division is carried out on clip
    coordinates to yield normalized device coordinates. A final
    viewport transformation is applied to convert these coordinates
    into window coordinates." 

  - (2.10.2, p. 33) Eighth Paragraph changed to:
    "There is another 4 x 4 matrix that is applied to texture
    coordinates by the OpenGL per-vertex operations. This matrix
    is applied as 
         | m1 m5 m9  m13 | |s|
         | m2 m6 m10 m14 | |t|,
         | m3 m7 m11 m15 | |r|
         | m4 m8 m12 m16 | |q|
    where the left matrix is the current texture matrix. The matrix is
    applied to the coordinates resulting from texture coordinate
    generation (which may simply be the current texture coordinates),
    and the resulting transformed coordinates become the texture
    coordinates associated with a vertex. Setting the matrix mode to
    TEXTURE causes the already described matrix operations to apply to
    the texture matrix."

  - (2.11, p. 39) Added after the first paragraph"
    "When the user defined shader is eanbeld as described in section
    2.14, the ability to clip in eye-space is removed as eye-space is
    now undefined. Instead, client defined clip planes are applied in
    clip-space. The algorithm is identical, except the half-space is
    now defined as:

                                (x_clip)
        (p'1 p'2 p'3 p'4) P_inv (y_clip) >= 0
                                (z_clip)
                                (w_clip)

    Where P is the projection matrix and x_clip, y_clip, z_clip, and
    w_clip are the clip space vertex coordinates. When P is singular,
    the result of clipping is undefined. 

  - (2.12, p. 41) Added after the third paragraph:
    "The raster position is not affected by the current vertex shader
    program, instead they are always processed by the OpenGL vertex
    processing."

  - (2.13, p. 43) Second paragraph:
    "Next, lighting, if enabled (and vertex shaders are disabled),
    produces either a color index or primary and secondary colors.
    If lighting is disabled, the current color index or color is used
    in further processing (the current color is the primary color, and
    the secondary color is (0; 0; 0; 0)). After lighting or vertex
    shading, RGBA colors are clamped to the range [0; 1]. A color
    index is converted to fixed-point and then its integer portion is
    masked (see section 2.13.6). After clamping or masking, a
    primitive may be flatshaded, indicating that all vertices of the
    primitive are to have the same color. Finally, if a primitive is
    clipped, then colors (and texture coordinates) must be computed
    at the vertices introduced or modified by clipping." 

  - (2.13.1, p. 44) First paragraph:
    "GL lighting computes colors for each vertex sent to the GL. This
    is accomplished by applying an equation defined by a
    client-specified lighting model to a collection of parameters that
    can include the vertex coordinates, the coordinates of one or more
    light sources, the current normal, and parameters defining the
    characteristics of the light sources and a current material. The
    following discussion assumes that the GL is in RGBA mode. (Color
    index lighting is described in section 2.13.5.) Lighting may be in
    one of two states: 
       1. Lighting Off. In this state, the current color is assigned
                        to the vertex primary color. The secondary
                        color is (0; 0; 0; 0). Lighting is off if
                        vertex shaders are enabled."
       2. Lighting On. In this state, the vertex primary and secondary
                       colors are computed from the current lighting
                       parameters. Lighting is turned on or off using
                       the generic Enable or Disable commands with the
                       symbolic value LIGHTING." 

  - (2.13.8, p. 55) First paragraph:
    "After lighting or vertex shading, clamping or masking and possible
    flatshading, colors are clipped. Those colors associated with a
    vertex that lies within the clip volume are unaffected by clipping.
    If a primitive is clipped, however, the colors assigned to vertices
    produced by clipping are clipped colors."

  - (new section 2.14) Vertex Shaders and Coloring
    "The alternative to OpenGL per-vertex operations is defining a
    vertex shader. This vertex shader replaces the GL per-vertex
    processing by specifying the operations to perform on the
    incoming vertex and associated data. A vertex shader is defined
    between a BeginVertexShaderEXT and EndVertexShaderEXT block. These
    commands are defined as follows:  

        void BeginVertexShaderEXT( void );
        void EndVertexShaderEXT( void );

    The only GL operations allowed between BeginShader and
    EndShader are ShaderOp[1..3]EXT, GenSymbolsEXT, SetLocalConstantEXT,
    SwizzleEXT, WriteMaskEXT, InsertComponentEXT, and
    ExtractComponentEXT. Calling BeginVertexShader with a prior call to
    BeginVertexShader and no matching prior call to EndVertexShader
    results in the error INVALID_OPERATION. Likewise, calling
    EndVertexShader without a matching prior call to BeginVertexShader
    results in the error INVALID_OPERATION.
        In addition to a default vertex shader program, named vertex
    shaders can be created. The namespace for vertex shaders is
    unsigned integers with zero reserved by the GL. A vertetx shader is
    created by binding an unused name using: 

        void BindVertexShaderEXT( uint id );

    where id is the unused name. Once a vertex shader program has been
    created it can be rebound as the active vertex shader program by
    calling BindVertexShaderEXT. Calling BindShaderEXT with an argument
    of zero binds the default vertex shader program. A vertex shader
    program can be deleted, freeing the name, by calling
        
        void DeleteVertexShaderEXT( uint id );

    where id is the name to be deleted. Unique names can be generated
    using:

        uint GenShadersEXT( uint range );

    where range is the number of contiguous ids that should be
    created. It returns an integer n such that range contiguous empty
    shader ids, with values n, n+1, ..., n+range -1, are created.
    If range is 0, if there is no group of range contiguous names
    available, or if any error is generated, no vertex shader names
    are generated, and 0 is returned. The currently bound vertex
    shader can be determined by querying VERTEX_SHADER_BINDING_EXT.
        There are four kinds of data available from within a vertex 
    shader program: invariant data, local constant data, local data,
    and variant data. Invariant data is data that can only be set
    outside of a vertex shader program definition, it is set before a
    shader is executed and does not change during vertex shader program
    execution.  Local constant data is data that is local to the vertex
    shader program, it is set once during the context of the vertex
    shader program definition and does not change either before or
    during execution of the vertex shader program.  Local data is data
    that is local to the vertex shader program which can both be read
    from and written to during the execution of the vertex shader
    program but not prior to execution. The contents of local data are
    undefined until the data is written to, and values do not persist
    between executions of the vertex shader program. Variant data is
    data which is specified per vertex, it can only be read from during
    execution of the vertex shader program.
        The GenSymbolsEXT, SetInvariantEXT, SetLocalConstantEXT,
    SetVariantEXT, VariantPointerEXT, commands are used to stage
    these various kinds of data for use in the vertex shader program.
    This staging takes place in two parts. The first part involves
    defining a name and giving it a data type and storage class.
    This is done by calling 

        uint GenSymbolsEXT( enum datatype, enum storagetype, enum range,
                         uint components );

    where datatype can be one of SCALAR_EXT, VECTOR_EXT, MATRIX_EXT,
    and storagetype can be one of VARIANT_EXT, INVARIANT_EXT,
    LOCAL_CONSTANT_EXT, LOCAL_EXT, range can be NORMALIZED_RANGE_EXT
    or FULL_RANGE_EXT, and components determines how many names should
    be generated. It returns an integer that is the first
    name in a contiguous block of names of size components. The three
    datatypes available determine the size of the storage at each
    name: Scalars being one element, vectors being 4 elements, and
    matrices being 16 elements. These are all treated as decimals in
    the computations performed by ShaderOp[1..3]EXT. The storagetype
    determines where and how often a particular named piece of data
    may be set (using SetInvariantEXT, SetLocalConstantEXT, VariantEXT, or
    VariantPointerEXT). If this data is not set before being
    used the values used are undetermined and may result in
    unpredictable values being used in the calculation. The range
    determines the mapping of the data. When specifying input data
    with a storagetype of FULL_RANGE_EXT,  the data is allowed to
    occupy the full range of the  system's floating point values.
    When specifying  input data with a storagetype of
    NORMALIZED_RANGE_EXT, integer values are mapped according to
    table 2.6 and floating point values are clamped to -1 to 1.
    When a result outside the range -1 to 1 is written to a local
    with its storagetype set to NORMALIZED_RANGE_EXT, the results
    are undefined.
        Assigning values to the names generated is the second part of
    the staging process and is accomplished by calling

        void SetInvariantEXT( uint id, enum type, void *addr );
        void SetLocalConstantEXT( uint id, enum type, void *addr );
        void Variant{bsifd ubusui}vEXT( uint id, T *addr );
        void VariantPointerEXT( uint id, enum type, uint stride,
                                       void *addr );
    
    where id is a name returned by GenSymbolsEXT, and type is DOUBLE,
    FLOAT, BYTE, UNSIGNED_BYTE, SHORT, UNSIGNED_SHORT, INT, or
    UNSIGNED_INT, and addr is a pointer to
    the value to be assigned to the name. 
        SetInvariantEXT is used to set a single scalar, vector,
    or matrix value. It may be used outside of the vertex shader
    program to set invariant data. SetLocalConstantEXT may be used
    inside the vertex shader program to set local constants. Local
    constants may only be set once during the definition of a
    vertex shader program. Attempts to set a local constant more than
    once in a vertex shader program will fail and create the error
    ILLEGAL_OPERATION. VariantEXT data is used within a Begin, End
    pair to set per-vertex data. Alternatively a complete set of
    variant data may specified using arrays by using VariantPointerEXT.


        The operations to be performed on the vertex, normal, color,
    GL state data, and the staged data in the shader are defined by
    making a sequence of one or more calls (between BeginShader and
    EndShader) to one or more of the following:

        void ShaderOp1EXT( enum op, uint res, uint arg1 );
        void ShaderOp2EXT( enum op, uint res, uint arg1, uint arg2 );
        void ShaderOp3EXT( enum op, uint res, uint arg1, uint arg2, 
                              uint arg3);

    where op is one of the constants described below, and res is one
    of OUTPUT_VERTEX_EXT, OUTPUT_COLOR#_EXT, OUTPUT_TEXTURE_COORD#_EXT,
    OUTPUT_FOG_EXT, or a data id defined by GenSymbolsEXT (with it's
    storage type set as LOCAL_EXT), and arg[1..3] is a data id defined
    by GenSymbolsEXT.

        It should be noted that the OUTPUT_xxx_EXT identifiers are
    special and can only be written. The values propagated forward
    from the vertex shader program are the last values written to
    these identifiers. Partial writes to these identifiers can be
    accomplished by using WriteMaskEXT.
    
        To facilitate the use of GL state values in a vertex shader
    program, a parameter binding mechanism is provided. Items such as
    material properties, light positions, and matrices are bound to
    ids. The functions for binding these parameters mirror the
    functions for retrieving state values from GL. The bind functions
    return an id that can be used as an arg to ShaderOpnEXT. The data
    type and storage type of the id match the semantics of the GL state
    and are provided below. The ids returned from the bind calls may
    not be used with any of the set data calls. Below are the bind
    functions and tables of their associated states:

    Light Parameters:

        uint BindLightParameterEXT( enum light, enum value)

    Value                    Data Type   Storage Type
    ---------------------    ---------   ------------
    AMBIENT                  VECTOR      INVARIANT
    DIFFUSE                  VECTOR      INVARIANT
    SPECULAR                 VECTOR      INVARIANT
    POSITION                 VECTOR      INVARIANT
    CONSTANT_ATTENUATION     SCALAR      INVARIANT
    LINEAR_ATTENUATION       SCALAR      INVARIANT
    QUADRATIC_ATTENUATION    SCALAR      INVARIANT
    SPOT_DIRECTION           VECTOR      INVARIANT
    SPOT_EXPONENT            SCALAR      INVARIANT
    SPOT_CUTOFF              SCALAR      INVARIANT

    Material Parameters:

        uint BindMaterialParameterEXT( enum face, enum value)

    Value                    Data Type   Storage Type
    ---------------------    ---------   ------------
    AMBIENT                  VECTOR      VARIANT
    DIFFUSE                  VECTOR      VARIANT
    SPECULAR                 VECTOR      VARIANT
    EMISSION                 VECTOR      VARIANT
    SHININESS                SCALAR      VARIANT
    

    TexGen Parameters:

        uint BindTexGenParameterEXT( enum unit, enum coord, enum value)

    Value                    Data Type   Storage Type
    ---------------------    ---------   ------------
    EYE_PLANE                VECTOR      INVARIANT
    OBJECT_PLANE             VECTOR      INVARIANT

    Texture Unit Parameters

        uint BindTextureUnitParameterEXT( enum unit, enum value)

    Value                    Data Type   Storage Type
    ---------------------    ---------   ------------
    CURRENT_TEXTURE_COORDS   VECTOR      VARIANT
    TEXTURE_MATRIX           MATRIX      INVARIANT


    Standard Parameters:

        uint BindParameterEXT( enum value)

    Value                    Data Type   Storage Type
    ---------------------    ---------   ------------
    CURRENT_VERTEX_EXT       VECTOR      VARIANT
    CURRENT_NORMAL           VECTOR      VARIANT
    CURRENT_COLOR            VECTOR      VARIANT
    MODELVIEW_MATRIX         MATRIX      INVARIANT
    PROJECTION_MATRIX        MATRIX      INVARIANT
    MVP_MATRIX_EXT           MATRIX      INVARIANT
    COLOR_MATRIX             MATRIX      INVARIANT  ** Only supported under imaging subset
    CLIP_PLANEi              VECTOR      INVARIANT
    FOG_COLOR                VECTOR      INVARIANT
    FOG_DENSITY              SCALAR      INVARIANT
    FOG_START                SCALAR      INVARIANT
    FOG_END                  SCALAR      INVARIANT
    LIGHT_MODEL_AMBIENT      VECTOR      INVARIANT



    For matrices only the top value of the matrix stack may be
    accessed.
        Binding of the token MVP_MATRIX_EXT provides access to a
    matrix containing the concatenation of the MODELVIEW and
    PROJECTION matrices. Binding the token CURRENT_VERTEX_EXT
    provides access to the coordinates of the vertex being processed.
    A special case of the bindings is CURRENT_NORMAL as it only a
    3-tuple natively. In this case, it is expanded as a homogeneous
    vector with the fourth component set to 0. 
        Each operation is accepted by a particular
    ShaderOp[1..3]EXT based on the number of arguments it 
    accepts and it's results are based on the type of arguments (as
    bound by GenSymbolsEXT) it receives. This is described in the
    following table. S denotes a scalar, V denotes a vector, M denotes
    a matrix, [] denotes a particular element of the input or
    output, a1 denotes arg1, a2 denotes arg2, a3 denotes arg3, a4
    denotes arg4, r denotes the result, combinations of input and
    output not shown produce ILLEGAL_OPERATION.


    Table of operations


Operation            Number of Inputs  res  args  Output
------------------- ------------------ ---- ----- -----------------
OP_INDEX_EXT       2                  S   S,S      special see below
                                      V   S,V
                                      M   S,M      
                                         
OP_NEGATE_EXT      1                  S   S        r = -a1
                                      V   S        r[0] = -a1
                                                   r[1] = -a1
                                                   r[2] = -a1
                                                   r[3] = -a1
                                      V   V        r[0] = -a1[0]
                                                   r[1] = -a1[1]
                                                   r[2] = -a1[2]
                                                   r[3] = -a1[3]
                                                      
OP_DOT3_EXT        2                  S   V,V      r    = a1[0] * a2[0] +
                                                          a1[1] * a2[1] +
                                                          a1[2] * a2[2]
                                      V   V,V      r[0] = a1[0] * a2[0] +
                                                          a1[1] * a2[1] +
                                                          a1[2] * a2[2]
                                                   r[1] = a1[0] * a2[0] +
                                                          a1[1] * a2[1] +
                                                          a1[2] * a2[2]
                                                   r[2] = a1[0] * a2[0] +
                                                          a1[1] * a2[1] +
                                                          a1[2] * a2[2]
                                                   r[3] = unchanged
                                                      
OP_DOT4_EXT        2                  S   V,V      r    = a1[0] * a2[0] +
                                                          a1[1] * a2[1] +
                                                          a1[2] * a2[2] +
                                                          a1[3] * a2[3]
                                      V   V,V      r[0] = a1[0] * a2[0] +
                                                          a1[1] * a2[1] +
                                                          a1[2] * a2[2] +
                                                          a1[3] * a2[3]
                                                   r[1] = a1[0] * a2[0] +
                                                          a1[1] * a2[1] +
                                                          a1[2] * a2[2] +
                                                          a1[3] * a2[3]
                                                   r[2] = a1[0] * a2[0] +
                                                          a1[1] * a2[1] +
                                                          a1[2] * a2[2] +
                                                          a1[3] * a2[3]
                                                   r[3] = a1[0] * a2[0] +
                                                          a1[1] * a2[1] +
                                                          a1[2] * a2[2] +
                                                          a1[3] * a2[3]
                                                             
OP_MUL_EXT         2                  S   S,S      r = a1 * a2
                                      V   S,S      r[0] = r[1] = r[2] = r[3] = a1 * a2
                                                   r[1] = a1 * a2
                                                   r[2] = a1 * a2
                                                   r[3] = a1 * a2
                                      V   S,V      r[0] = a1 * a2[0]
                                                   r[1] = a1 * a2[1]
                                                   r[2] = a1 * a2[2]
                                                   r[3] = a1 * a2[3]
                                      V   V,S      r[0] = a1[0] * a2
                                                   r[1] = a1[1] * a2
                                                   r[2] = a1[2] * a2
                                                   r[3] = a1[3] * a2
                                      V   V,V      r[0] = a1[0] * a2[0]
                                                   r[1] = a1[1] * a2[1]
                                                   r[2] = a1[2] * a2[2]
                                                   r[3] = a1[3] * a2[3]
                                                      
OP_MOV_EXT         1                  S   S        r = a1 
                                      V   S        r[0] = a1
                                                   r[1] = a1
                                                  r[2] = a1
                                                   r[3] = a1
                                      V   V        r[0] = a1[0]
                                                   r[1] = a1[1]
                                                   r[2] = a1[2]
                                                   r[3] = a1[3]
                                                      
OP_ADD_EXT         2                  S   S,S      r = a1 + a2
                                      V   S,S      r[0] = a1 + a2
                                                   r[1] = a1 + a2
                                                   r[2] = a1 + a2
                                                   r[3] = a1 + a2
                                      V   S,V      r[0] = a1 + a2[0]
                                                   r[1] = a1 + a2[1]
                                                   r[2] = a1 + a2[2]
                                                   r[3] = a1 + a2[3]
                                      V   V,S      r[0] = a1[0] + a2
                                                   r[1] = a1[1] + a2
                                                   r[2] = a1[2] + a2
                                                   r[3] = a1[3] + a2
                                      V   V,V      r[0] = a1[0] + a2[0]
                                                   r[1] = a1[1] + a2[1]
                                                   r[2] = a1[2] + a2[2]
                                                   r[3] = a1[3] + a2[3]
                                                      
OP_MADD_EXT        3                  S   S,S,S    r = a1 * a2 + a3
                                      V   S,S,S    r[0] = a1 * a2 + a3
                                                   r[1] = a1 * a2 + a3
                                                   r[2] = a1 * a2 + a3
                                                   r[3] = a1 * a2 + a3
                                      V   S,V,V    r[0] = a1 * a2[0] +a3[0]
                                                   r[1] = a1 * a2[1] +a3[1]
                                                   r[2] = a1 * a2[2] +a3[2]
                                                   r[3] = a1 * a2[3] +a3[3]
                                      V   V,S,V    r[0] = a1[0] * a2 +a3[0]
                                                   r[1] = a1[1] * a2 +a3[1]
                                                   r[2] = a1[2] * a2 +a3[2]
                                                   r[3] = a1[3] * a2 +a3[3]
                                      V   S,S,V    r[0] = a1 * a2 +a3[0]
                                                   r[1] = a1 * a2 +a3[1]
                                                   r[2] = a1 * a2 +a3[2]
                                                   r[3] = a1 * a2 +a3[3]
                                      V   V,V,S    r[0] = a1[0] * a2[0] +a3
                                                   r[1] = a1[1] * a2[1] +a3
                                                   r[2] = a1[2] * a2[2] +a3
                                                   r[3] = a1[3] * a2[3] +a3
                                      V   V,S,S    r[0] = a1[0] * a2 +a3
                                                   r[1] = a1[1] * a2 +a3
                                                   r[2] = a1[2] * a2 +a3
                                                   r[3] = a1[3] * a2 +a3
                                      V   S,V,S    r[0] = a1 * a2[0] +a3
                                                   r[1] = a1 * a2[1] +a3
                                                   r[2] = a1 * a2[2] +a3
                                                   r[3] = a1 * a2[3] +a3
                                      V   V,V,V    r[0] = a1[0] * a2[0] +a3[0]
                                                   r[1] = a1[1] * a2[1] +a3[1]
                                                   r[2] = a1[2] * a2[2] +a3[2]
                                                   r[3] = a1[3] * a2[3] +a3[3]
                                                      
OP_FRAC_EXT        1                  S   S        r = a1 - FLOOR(a1)
                                      V   S        r[0] = a1 - FLOOR(a1)
                                                   r[1] = a1 - FLOOR(a1)
                                                   r[2] = a1 - FLOOR(a1)
                                                   r[3] = a1 - FLOOR(a1)
                                      V   V        r[0] = a1[0] - FLOOR(a1[0])
                                                   r[1] = a1[1] - FLOOR(a1[1])
                                                   r[2] = a1[2] - FLOOR(a1[2])
                                                   r[3] = a1[3] - FLOOR(a1[3])
                                                      
OP_MAX_EXT         2                  S   S,S      r = MAX(a1, a2)
                                      V   S,S      r[0] = MAX(a1, a2)
                                                   r[1] = MAX(a1, a2)
                                                   r[2] = MAX(a1, a2)
                                                   r[3] = MAX(a1, a2)
                                      V   S,V      r[0] = MAX(a1, a2[0])
                                                   r[1] = MAX(a1, a2[1])
                                                   r[2] = MAX(a1, a2[2])
                                                   r[3] = MAX(a1, a2[3])
                                      V   V,S      r[0] = MAX(a1[0], a2)
                                                   r[1] = MAX(a1[1], a2)
                                                   r[2] = MAX(a1[2], a2)
                                                   r[3] = MAX(a1[3], a2)
                                      V   V,V      r[0] = MAX(a1[0], a2[0])
                                                   r[1] = MAX(a1[1], a2[1])
                                                   r[2] = MAX(a1[2], a2[2])
                                                   r[3] = MAX(a1[3], a2[3])
                                                      
OP_MIN_EXT         2                  S   S,S      r = MIN(a1, a2)
                                      V   S,S      r[0] = MIN(a1, a2)
                                                   r[1] = MIN(a1, a2)
                                                   r[2] = MIN(a1, a2)
                                                   r[3] = MIN(a1, a2)
                                      V   S,V      r[0] = MIN(a1, a2[0])
                                                   r[1] = MIN(a1, a2[1])
                                                   r[2] = MIN(a1, a2[2])
                                                   r[3] = MIN(a1, a2[3])
                                      V   V,S      r[0] = MIN(a1[0], a2)
                                                   r[1] = MIN(a1[1], a2)
                                                   r[2] = MIN(a1[2], a2)
                                                   r[3] = MIN(a1[3], a2)
                                      V   V,V      r[0] = MIN(a1[0], a2[0])
                                                   r[1] = MIN(a1[1], a2[1])
                                                   r[2] = MIN(a1[2], a2[2])
                                                   r[3] = MIN(a1[3], a2[3])
                                                     
OP_SET_GE_EXT      2                  S   S,S      r = (a1 >= a2) ? 1 : 0
                                      V   S,S      r[0] = (a1 >= a2) ? 1 : 0
                                                   r[1] = (a1 >= a2) ? 1 : 0
                                                   r[2] = (a1 >= a2) ? 1 : 0
                                                   r[3] = (a1 >= a2) ? 1 : 0
                                      V   S,V      r[0] = (a1 >= a2[0]) ?1 : 0
                                                   r[1] = (a1 >= a2[1]) ? 1: 0
                                                   r[2] = (a1 >= a2[2]) ? 1: 0
                                                   r[3] = (a1 >= a2[3]) ? 1: 0
                                      V   V,S      r[0] = (a1[0] >= a2) ? 1: 0
                                                   r[1] = (a1[1] >= a2) ? 1: 0
                                                   r[2] = (a1[2] >= a2) ? 1: 0
                                                   r[3] = (a1[3] >= a2) ? 1: 0
                                      V   V,V      r[0] =(a1[0]>=a2[0]) ?1 : 0
                                                   r[1] =(a1[1]>=a2[1]) ?1 : 0
                                                   r[2] =(a1[2]>=a2[2]) ?1 : 0
                                                   r[3] =(a1[3]>=a2[3]) ?1 : 0
                                                      
OP_SET_LT_EXT      2                  S   S,S      r = (a1 < a2) ? 1 : 0
                                      V   S,S      r[0] = (a1 < a2) ? 1 : 0
                                                   r[1] = (a1 < a2) ? 1 : 0
                                                   r[2] = (a1 < a2) ? 1 : 0
                                                   r[3] = (a1 < a2) ? 1 : 0
                                      V   S,V      r[0] = (a1 < a2[0]) ? 1 : 0
                                                   r[1] = (a1 < a2[1]) ? 1 : 0
                                                   r[2] = (a1 < a2[2]) ? 1 : 0
                                                   r[3] = (a1 < a2[3]) ? 1 : 0
                                      V   V,S      r[0] = (a1[0] < a2) ? 1 : 0
                                                   r[1] = (a1[1] < a2) ? 1 : 0
                                                   r[2] = (a1[2] < a2) ? 1 : 0
                                                   r[3] = (a1[3] < a2) ? 1 : 0
                                      V   V,V      r[0] =(a1[0]< a2[0]) ?1 : 0
                                                   r[1] =(a1[1]< a2[1]) ?1 : 0
                                                   r[2] =(a1[2]< a2[2]) ?1 : 0
                                                   r[3] =(a1[3]< a2[3]) ?1 : 0 


OP_CLAMP_EXT       3                  S   S,S,S    r = ( a1 <= a2) ? a2 :
                                                          ( (a1>=a3) ? a3 :
                                                            (a1 ))
                                      V   S,S,S    r[0]= ( a1 <= a2) ? a2 :
                                                          ( (a1>=a3) ? a3 :
                                                            (a1 ))
                                                   r[1]= ( a1 <= a2) ? a2 :
                                                          ( (a1>=a3) ? a3 :
                                                            (a1 ))
                                                   r[2]= ( a1 <= a2) ? a2 :
                                                          ( (a1>=a3) ? a3 :
                                                            (a1 ))
                                                   r[3]= ( a1 <= a2) ? a2 :
                                                          ( (a1>=a3) ? a3 :
                                                            (a1 ))
                                      V   V,S,S    r[0]= ( a1[0] <= a2) ? a2 :
                                                          ( (a1[0]>=a3) ? a3 :
                                                            (a1[0] ))
                                                   r[1]= ( a1[1] <= a2) ? a2 :
                                                          ( (a1[1]>=a3) ? a3 :
                                                            (a1[1] ))
                                                   r[2]= ( a1[2] <= a2) ? a2 :
                                                           ( (a1[2]>=a3) ? a3 :
                                                            (a1[2] ))
                                                   r[3]= ( a1[3] <= a2) ? a2 :
                                                          ( (a1[3]>=a3) ? a3 :
                                                            (a1[3] ))
                                      V   V,V,S    r[0]= ( a1[0] <= a2[0]) ? a2[0] :
                                                          ( (a1[0]>=a3) ? a3 :
                                                            (a1[0] ))
                                                   r[1]= ( a1[1] <= a2[1]) ? a2[1] :
                                                          ( (a1[1]>=a3) ? a3 :
                                                            (a1[1] ))
                                                   r[2]= ( a1[2] <= a2[2]) ? a2[2] :
                                                           ( (a1[2]>=a3) ? a3 :
                                                            (a1[2] ))
                                                   r[3]= ( a1[3] <= a2[3]) ? a2[3] :
                                                          ( (a1[3]>=a3) ? a3 :
                                                            (a1[3] ))
                                      V   V,S,V    r[0]= ( a1[0] <= a2) ? a2 :
                                                          ( (a1[0]>=a3[0]) ? a3[0] :
                                                            (a1[0] ))
                                                   r[1]= ( a1[1] <= a2) ? a2 :
                                                          ( (a1[1]>=a3[1]) ? a3[1] :
                                                            (a1[1] ))
                                                   r[2]= ( a1[2] <= a2) ? a2 :
                                                           ( (a1[2]>=a3[2]) ? a3[2] :
                                                            (a1[2] ))
                                                   r[3]= ( a1[3] <= a2) ? a2 :
                                                          ( (a1[3]>=a3[3]) ? a3[3] :
                                                            (a1[3] ))
                                      V   V,V,V    r[0]= ( a1[0] <= a2[0]) ? a2[0] :
                                                          ( (a1[0]>=a3[0]) ? a3[0] :
                                                            (a1[0] ))
                                                   r[1]= ( a1[1] <= a2[1]) ? a2[1] :
                                                          ( (a1[1]>=a3[1]) ? a3[1] :
                                                            (a1[1] ))
                                                   r[2]= ( a1[2] <= a2[2]) ? a2[2] :
                                                           ( (a1[2]>=a3[2]) ? a3[2] :
                                                            (a1[2] ))
                                                   r[3]= ( a1[3] <= a2[3]) ? a2[3] :
                                                          ( (a1[3]>=a3[3]) ? a3[3] :
                                                            (a1[3] ))
                                                               
OP_FLOOR_EXT       1                  S   S        r = FLOOR(a1)
                                      V   S        r[0] = FLOOR(a1)
                                                   r[1] = FLOOR(a1)
                                                   r[2] = FLOOR(a1)
                                                   r[3] = FLOOR(a1)
                                      V   V        r[0] = FLOOR(a1[0])
                                                   r[1] = FLOOR(a1[1])
                                                   r[2] = FLOOR(a1[2])
                                                   r[3] = FLOOR(a1[3])
                                                      
OP_ROUND_EXT       1                  S   S        r = FLOOR(a1 + 0.5)
                                      V   S        r[0] = FLOOR(a1 + 0.5)
                                                   r[1] = FLOOR(a1 + 0.5)
                                                   r[2] = FLOOR(a1 + 0.5)
                                                   r[3] = FLOOR(a1 + 0.5)
                                      V   V        r[0] = FLOOR(a1[0] + 0.5)
                                                   r[1] = FLOOR(a1[1] + 0.5)
                                                   r[2] = FLOOR(a1[2] + 0.5)
                                                   r[3] = FLOOR(a1[3] + 0.5)
                                                      
OP_EXP_BASE_2_EXT  1                  S   S        r = 2 ^ a1
                                                      
OP_LOG_BASE_2_EXT  1                  S    S        r = (a1==0) ? MINUS_INF :
                                                         LOG2(a1)
                                                      r is undefined if a1 < 0

OP_POWER_EXT       2                  S   S,S      r = a1 ^ a2
                                                      r is undefined if a1 < 0
                                                       and -1 < a2 < 1
                                                      
OP_RECIP_EXT       1                  S   S        r = (a1==0) ? INF :
                                                        1.0 / a1
                                                      
OP_RECIP_SQRT_EXT    1                S   S        r = (a1==0) ? INF :
                                                        1.0 / SQRT(a1)
                                                      r is undefined if a1 < 0
                                                      
OP_SUB_EXT           2                S   S,S      r = a1 - a2
                                      V   S,S      r[0] = a1 - a2
                                                   r[1] = a1 - a2
                                                   r[2] = a1 - a2
                                                   r[3] = a1 - a2
                                      V   S,V      r[0] = a1 - a2[0]
                                                   r[1] = a1 - a2[1]
                                                   r[2] = a1 - a2[1]
                                                   r[3] = a1 - a2[3]
                                      V   V,S      r[0] = a1[0] - a2
                                                   r[1] = a1[1] - a2
                                                   r[2] = a1[2] - a2
                                                   r[3] = a1[3] - a2
                                      V   V,V      r[0] = a1[0] - a2[0]
                                                   r[1] = a1[1] - a2[1]
                                                   r[2] = a1[2] - a2[2]
                                                   r[3] = a1[3] - a2[3]
                                                      
OP_CROSS_PRODUCT_EXT   2              V   V,V      r[0] = a1[1] * a2[2] -
                                                          a2[1] * a1[2]
                                                   r[1] = a1[2] * a2[0] -
                                                          a2[2] * a1[0]
                                                   r[2] = a1[0] * a2[1] -
                                                          a2[0] * a1[1]
                                                   r[3] = 1
                                                      
OP_MULTIPLY_MATRIX_EXT 2              V   M,V      r[0] = a2[0] * a1[0] +
                                                          a2[1] * a1[4] +
                                                          a2[2] * a1[8] +
                                                          a2[3] * a1[12]
                                                   r[1] = a2[0] * a1[1] +
                                                          a2[1] * a1[5] +
                                                          a2[2] * a1[9] +
                                                          a2[3] * a1[13]
                                                   r[2] = a2[0] * a1[2] +
                                                          a2[1] * a1[6] +
                                                          a2[2] * a1[10] +
                                                          a2[3] * a1[14]
                                                   r[3] = a2[0] * a1[3] +
                                                          a2[1] * a1[7] +
                                                          a2[2] * a1[11] +
                                                          a2[3] * a1[15]
                                      


 
        A special operation is OP_INDEX_EXT. It is special in that it
    indexes a contiguous block of ids generated by a single call to
    GenSymbolsEXT. The value placed in res is the data item
    represented by:
    
       arg2 + int( value(arg1) )

   This allows data to be indexed on a per-vertex basis. The results
   are undefined if the offset is outside the range of the ids
   returned by the single call to GenSymbolsEXT.
        Additionally vector data can be rearranged by using the
    following call:

        void SwizzleEXT( uint res, uint in, enum outX, enum outY, enum outZ
                         enum outW )

    where in can be any vector value (VARIANT_EXT,
    GLOBAL_CONSTANT_EXT, LOCAL_CONSTANT_EXT, or LOCAL_EXT), and outX,
    outY, outZ, and outW may be one of X_EXT, Y_EXT, Z_EXT, W_EXT,
    NEGATIVE_X_EXT, NEGATIVE_Y_EXT, NEGATIVE_Z_EXT, NEGATIVE_W_EXT,
    ZERO_EXT, ONE_EXT, and NEGATIVE_ONE_EXT, and res is one of
    OUTPUT_VERTEX_EXT, OUTPUT_COLOR#_EXT, OUTPUT_TEXTURE_COORD#_EXT,
    or a data id defined by GenSymbolsEXT (with it's storage type
    set as LOCAL_EXT). The out[XYZW] parameters specify what value
    should be placed in the res vector.
        Vector data can also be masked by using the following call:

        void WriteMaskEXT( unint res, uint in, enum outX, enum outY, 
                           enum outZ, enum outW )

    where in is a vector value out[XYZW] are either GL_TRUE or
    GL_FALSE, and res is one of OUTPUT_VERTEX_EXT, OUTPUT_COLOR#_EXT,
    OUTPUT_TEXTURE_COORD#_EXT, or a data id defined by GenSymbolsEXT
    (with it's storage type set as LOCAL_EXT). For each output
    component marked TRUE, the source is copied into the destination,
    and for all components marked FALSE, the destination component
    is unchanged.
        Individual components of vector and matrix data can be
    accessed and modified by the following operations:

        void InsertComponentEXT( uint res, uint src, uint num )
        void ExtractComponentEXT( uint res, uint src, uint num )

    InsertComponentEXT allows a scalar within a vector or a vector
    within a matrix to be replaced. If src is a scalar, then res must
    be a vector, and if src is a vector, res must be a matrix. The
    num parameter controls which scalar or vector will be replaced.
    The mappings are as follows:
    
        Num    Type   Operation
        ------ ----   -------------------
        0        S    res[0] = src
        0        V    res[0] = src[0]
                      res[4] = src[1]
                      res[8] = src[2]
                      res[12] = src[3]

        1        S    res[1] = src
        1        V    res[1] = src[0]
                      res[5] = src[1]
                      res[9] = src[2]
                      res[13] = src[3]

        2        S    res[2] = src
        2        V    res[2] = src[0]
                      res[6] = src[1]
                      res[10] = src[2]
                      res[14] = src[3]

        3        S    res[3] = src
        3        V    res[3] = src[0]
                      res[7] = src[1]
                      res[11] = src[2]
                      res[15] = src[3]

    If the num parameter is greater than 3, the error INVALID_VALUE is
    generated. The opposite capability is provided by
    ExtractComponentEXT. Its arguments are either a matrix src and a
    vector res, or a vector src and a scalar res. Other combinations
    result in the error ILLEGAL_OPERATION. As with InsertComponentEXT,
    values for num greater than 3 generate the error INVALID_VALUE.

        There are four resources consumed when loading a vertex shader
    program: instruction storage, variant storage, constant storage,
    and local storage. The maximum values for these resources in a
    software implementation may be queried by calling GetIntegerv,
    GetFloatv, and GetDoublev with MAX_VERTEX_SHADER_INSTRUCTIONS_EXT,
    MAX_VERTEX_SHADER_VARIANTS_EXT, MAX_VERTEX_SHADER_INVARIANTS_EXT,
	MAX_VERTEX_SHADER_LOCAL_CONSTANTS_EXT, and
	MAX_VERTEX_SHADER_LOCALS_EXT respectively. Since a software
    implementation may co-exist with a hardware implementation with
    stricter resource limitations the resources available for a
    hardware implementation may be queried separately using
    MAX_OPTIMIZED_VERTEX_SHADER_INSTRUCTIONS_EXT,
    MAX_OPTIMIZED_VERTEX_SHADER_VARIANTS_EXT,
	MAX_OPTIMIZED_VERTEX_SHADER_INVARIANTS_EXT,
    MAX_OPTIMIZED_VERTEX_SHADER_LOCAL_CONSTANTS_EXT, and
    MAX_OPTIMIZED_VERTEX_SHADER_LOCALS_EXT. In implementations that
    operate purely in SW or purely in HW, these numbers may be
    identical to the max values. The number of these resources
    consumed by the current vertex shader program may be queried by
    calling GetIntegerv, GetFloatv, and GetDoublev with
    VERTEX_SHADER_INSTRUCTIONS_EXT, VERTEX_SHADER_VARIANTS_EXT,
    VERTEX_SHADER_LOCAL_CONSTANTS_EXT, VERTEX_SHADER_INVARIANTS_EXT,
	and VERTEX_SHADER_LOCALS_EXT.
        Additionally, an implementation reports where a vertex shader
    program falls within all the optimized limits by a query of 
    VERTEX_SHADER_OPTIMIZED_EXT. This boolean value will be true
    if the vertex shader program consumes less than the maximum
    optimizable resources in all catagories. This value is provided
    as a convenient shortcut for a common operation.
        Should a vertex shader program not fit within the
    implementation defined limits, then the program is considered
    undefined. When a vertex is submitted to an undefined program
    vertex shaders are implicitly disabled and GL per-vertex
    processing applies.
        The methods employed for counting operations and data
    usage are not intended to be identical from implementation to
    implementation. Instead, the reported totals should be based
    on micro-ops. The micro-ops represent the cost of the operation
    or data-type for the particular implementation. As a result,
    certain operations may take zero or multiple micro-ops. The
    only requirement is that micro-ops always be reported in a
    consistent manner, even if the vertex shader programs can be
    potentially implemented by different hardware."


Additions to Chapter 3 of the OpenGL 1.2.1 Specification (Rasterization):

    None

Additions to Chapter 4:

    None

Additions to Chapter 5:

    None

Additions to Chapter 6:

  - (New section after 6.1.11) User specified vertex processing queries
    "The commands

      boolean IsVariantEnabledEXT( uint id, enum cap);
      void GetVariantBooleanvEXT( uint id, enum value, boolean *data);
      void GetVariantIntegervEXT( uint id, enum value, int *data);
      void GetVariantFloatvEXT( uint id, enum value, float *data);
      void GetVariantPointervEXT( uint id, enum value, void **data);
      void GetInvariantBooleanvEXT( uint id, enum value, boolean *data);
      void GetInvariantIntegervEXT( uint id, enum value, int *data);
      void GetInvariantFloatvEXT( uint id, enum value, float *data);
      void GetLocalConstantBooleanvEXT( uint id, enum value, boolean *data);
      void GetLocalConstantIntegervEXT( uint id, enum value, int *data);
      void GetLocalConstantFloatvEXT( uint id, enum value, float *data);

    are used to retrieve state relating to symbols used in vertex
    shader programs. They take the id of the symbol for which
    information is being queried. If the symbol is invalid in the
    present shader or the storage type is inconsistent with the
    called function the error INVALID_VALUE is generated. All
    values returned are in the context of the presently bound vertex
    shader."

Additions to the GLX Specification

    Unknown

GLX Protocol

    Unknown

Errors

INVALID_VALUE is generated if the <num> parameter to InsertComponentEXT or
ExtractComponentEXT is grater than 3.

ILLEGAL_OPERATION is generated if the <src> parameter to InsertComponentsEXT
is of type VECTOR_EXT and the <res> parameter is not of type MATRIX_EXT. 

ILLEGAL_OPERATION is generated if the <src> parameter to InsertComponentsEXT
is of type SCALAR_EXT and the <res> parameter is not of type VECTOR_EXT. 

ILLEGAL_OPERATION is generated if the <src> parameter to ExtractComponentsEXT
is of type VECTOR_EXT and the <res> parameter is not of type SCALAR_EXT. 

ILLEGAL_OPERATION is generated if the <src> parameter to ExtractComponentsEXT
is of type MATRIX_EXT and the <res> parameter is not of type VECTOR_EXT. 

ILLEGAL_OPERATION is generated if the SetLocalConstantEXT is used multiple
times on a single symbol in the context of defining a shader.

ILLEGAL_OPERATION is generated if the arguments provided to ShaderOpEXT are
inconsistent with the table of operations. An example would be specifying
a SCALAR_EXT result to the addition of 2 vectors.

ILLEGAL_OPERATION is generated if the datatype of the <res> or <in>
parameters to WriteMaskEXT or SwizzleEXT is not VECTOR_EXT.

ILLEGAL_OPERATION is generated if if the <res> parameter of ShaderOPEXT,
SwizzleEXT, or WriteMaskEXT does is not a local or output storage type.

New State

Added after Table 6.27 Vertex Shader State:

    Get Value                         Get Command        Type      Initial Value     Attribute
    ----------------------------      -------------      -------   ---------------   --------------
    VERTEX_SHADER_INSTRUCTIONS_EXT    GetIntegerv         Z+           0                 -
    VERTEX_SHADER_VARIANTS_EXT        GetIntegerv         Z+           0                 -
    VERTEX_SHADER_INVARIANTS_EXT      GetIntegerv         Z+           0                 -
	VERTEX_SHADER_LOCAL_CONSTANTS_EXT GetIntegerv         Z+           0                 -
    VERTEX_SHADER_LOCALS_EXT          GetIntegerv         Z+           0                 -
    VERTEX_SHADER_OPTIMIZED_EXT       GetBooleanv         Z+          False              -
    VERTEX_SHADER_EXT                 IsEnabled           B           False              -
    VERTEX_SHADER_BINDING_EXT         GetIntegerv         Z+           0                 -

Added new Table Vertex Shader symbol state:

    Get Value                        Get Command             Type      Initial Value     Attribute
    ----------------------------     -------------           -------   ---------------   --------------
    VARIANT_VALUE_EXT                GetVariantFloatv         n * R      Undefined            -
    VARIANT_DATATYPE_EXT             GetVariantIntegerv       Z          Undefined            -
    VARIANT_ARRAY_STRIDE_EXT         GetVariantIntegerv       Z          0                    -
    VARIANT_ARRAY_TYPE_EXT           GetVariantIntegerv       Z8         FLOAT                -
    VARIANT_ARRAY_POINTER_EXT        GetVariantPointerv       Y          0                    -
    VARIANT_ARRAY_EXT                IsEnabled                B          FALSE                -
    INVARIANT_VALUE_EXT              GetInvariantFloatv       n * R      Undefined            -
    INVARIANT_DATATYPE_EXT           GetInvariantIntegerv     Z          Undefined            -
    LOCAL_CONSTANT_VALUE_EXT         GetLocalConstantFloatv   n * R      Undefined            -
    LOCAL_CONSTANT_DATATYPE_EXT      GetLocalConstantIntegerv n * R      Undefined            -


New Implementation Dependent State

    Get Value                                       Get Command        Type      Minimum Value   
    ---------------------------------------         -------------      -------   --------------- 
    MAX_VERTEX_SHADER_INSTRUCTIONS_EXT              GetIntegerv         Z+         32
    MAX_VERTEX_SHADER_VARIANTS_EXT                  GetIntegerv         Z+          4
    MAX_VERTEX_SHADER_INVARIANTS_EXT                GetIntegerv         Z+         16
    MAX_VERTEX_SHADER_LOCAL_CONSTANTS_EXT           GetIntegerv         Z+          8
    MAX_VERTEX_SHADER_LOCALS_EXT                    GetIntegerv         Z+          4
    MAX_OPTIMIZED_VERTEX_SHADER_INSTRUCTIONS_EXT    GetIntegerv         Z+         32
    MAX_OPTIMIZED_VERTEX_SHADER_VARIANTS_EXT        GetIntegerv         Z+          4
    MAX_OPTIMIZED_VERTEX_SHADER_INVARIANTS_EXT      GetIntegerv         Z+         16
    MAX_OPTIMIZED_VERTEX_SHADER_LOCAL_CONSTANTS_EXT GetIntegerv         Z+          8
    MAX_OPTIMIZED_VERTEX_SHADER_LOCALS_EXT          GetIntegerv         Z+          4

