Name

    NV_vertex_program2

Name Strings

    GL_NV_vertex_program2

Contact

    Pat Brown, NVIDIA Corporation (pbrown 'at' nvidia.com)
    Mark Kilgard, NVIDIA Corporation (mjk 'at' nvidia.com)

Notice

    Copyright NVIDIA Corporation, 2000-2002.

IP Status

    NVIDIA Proprietary.

Status

    Implemented in CineFX (NV30) Emulation driver, August 2002.
    Shipping in Release 40 NVIDIA driver for CineFX hardware, January 2003.

Version

    Last Modified Date:  05/16/2004
    NVIDIA Revision:     32

Number

    287

Dependencies

    Written based on the wording of the OpenGL 1.3 Specification and requires
    OpenGL 1.3.

    Written based on the wording of the NV_vertex_program extension
    specification, version 1.0.

    NV_vertex_program is required.

Overview

    This extension further enhances the concept of vertex programmability
    introduced by the NV_vertex_program extension, and extended by
    NV_vertex_program1_1.  These extensions create a separate vertex program
    mode where the configurable vertex transformation operations in unextended
    OpenGL are replaced by a user-defined program.

    This extension introduces the VP2 execution environment, which extends the
    VP1 execution environment introduced in NV_vertex_program.  The VP2
    environment provides several language features not present in previous
    vertex programming execution environments:

      * Branch instructions allow a program to jump to another instruction
        specified in the program.

      * Branching support allows for up to four levels of subroutine
        calls/returns.

      * A four-component condition code register allows an application to
        compute a component-wise write mask at run time and apply that mask to
        register writes.  

      * Conditional branches are supported, where the condition code register
        is used to determine if a branch should be taken.

      * Programmable user clipping is supported support (via the CLP0-CLP5
        clip distance registers).  Primitives are clipped to the area where
        the interpolated clip distances are greater than or equal to zero.

      * Instructions can perform a component-wise absolute value operation on
        any operand load.

    The VP2 execution environment provides a number of new instructions, and
    extends the semantics of several instructions already defined in
    NV_vertex_program.

      * ARR:  Operates like ARL, except that float-to-int conversion is done
        by rounding.  Equivalent results could be achieved (less efficiently)
        in NV_vertex program using an ADD/ARL sequence and a program parameter
        holding the value 0.5.

      * BRA, CAL, RET:  Branch, subroutine call, and subroutine return
        instructions.

      * COS, SIN:  Adds support for high-precision sine and cosine
        computations.

      * FLR, FRC:  Adds support for computing the floor and fractional portion
        of floating-point vector components.  Equivalent results could be
        achieved (less efficiently) in NV_vertex_program using the EXP
        instruction to compute the fractional portion of one component at a
        time.

      * EX2, LG2:  Adds support for high-precision exponentiation and
        logarithm computations.

      * ARA:  Adds pairs of components of an address register; useful for
        looping and other operations.

      * SEQ, SFL, SGT, SLE, SNE, STR:  Add six new "set on" instructions,
        similar to the SLT and SGE instructions defined in NV_vertex_program.
        Equivalent results could be achieved (less efficiently) in
        NV_vertex_program with multiple SLT, SGE, and arithmetic instructions.

      * SSG:  Adds a new "set sign" operation, which produces a vector holding
        negative one for negative components, zero for components with a value
        of zero, and positive one for positive components.  Equivalent results
        could be achieved (less efficiently) in NV_vertex_program with
        multiple SLT, SGE, and arithmetic instructions.

      * The ARL instruction is extended to operate on four components instead
        of a single component.

      * All instructions that produce integer or floating-point result vectors
        have variants that update the condition code register based on the
        result vector.

    This extension also raises some of the resource limitations in the
    NV_vertex_program extension.

      * 256 program parameter registers (versus 96 in NV_vertex_program).

      * 16 temporary registers (versus 12 in NV_vertex_program).

      * Two four-component integer address registers (versus one
        single-component register in NV_vertex_program).

      * 256 total vertex program instructions (versus 128 in
        NV_vertex_program).
      
      * Including loops, programs can execute up to 64K instructions.


Issues

    This extension builds upon the NV_vertex_program extension.  Should this
    specification contain selected edits to the NV_vertex_program
    specification or should the specs be unified?

      RESOLVED:  Since NV_vertex_program and NV_vertex_program2 programs share
      many features, the main section of this specification is unified and
      describes both types of programs.  Other sections containing
      NV_vertex_program features that are unchanged by this extension will not
      be edited.

    How can a program use condition codes to avoid extra computations?

      Consider the example of evaluating the OpenGL lighting model for a
      given light.  If the diffuse dot product is negative (roughly 1/2 the
      time for random geometry), the only contribution to the light is
      ambient.  In this case, condition codes and branching can skip over a
      number of unneeded instructions.
      
          # R0 holds accumulated light color
          # R2 holds normal
          # R3 holds computed light vector
          # R4 holds computed half vector
          # c[0] holds ambient light/material product
          # c[1] holds diffuse light/material product
          # c[2].xyz holds specular light/material product
          # c[2].w   holds specular exponent
          DP3C R1.x, R2, R3;            # diffuse dot product
          ADD  R0, R0, c[0];            # accumulate ambient
          BRA  pointsAway (LT.x)        # skip rest if diffuse dot < 0
          MOV  R1.w, c[2].w;
          DP3  R1.y, R2, R4;            # specular dot product
          LIT  R1, R1;                  # compute expontiated specular
          MAD  R4, c[1], R0.y;          # accumulate diffuse
          MAD  R4, c[2], R0.z;          # accumulate specular
        pointsAway:
          ...                           # continue execution

    How can a program use subroutines?

      With subroutines, a program can encapsulate a small piece of
      functionality into a subroutine and call it multiple times, as in CPU
      code.  Applications will need to identify the registers used to pass
      data to and from the subroutine.  

      Subroutines could be used for applications like evaluating lighting
      equations for a single light.  With conditional branching and
      subroutines, a variable number of lights (which could even vary
      per-vertex) can be easily supported.
    
        accumulate:
          # R0 holds the accumulated result
          # R1 holds the value to add
          ADD R0, R1;
          RET;

          # Compute floor(A)*B by repeated addition using a subroutine.  Yes,
          # this is a stupid example. 
          #
          # c[0] holds (A,B,0,1).
          # R0 holds the accumulated result
          # R1 holds B, the value to accumulate.
          # R2 holds the number of iterations remaining.
          MOV R0, c[0].z;               # start with zero
          MOV R1, c[0].y;
          FLRC R2.x, c[0].x;
          BRA done (LE.x);
        top:
          CAL accumulate;
          ADDC R2.x, R2.x, -c[0].w;     # decrement count
          BRA top (GT.x);
        done:
          ...

    How can conventional OpenGL clip planes be supported in vertex programs?

      The clip distance in the OpenGL specification can be evaluated with a
      simple DP4 instruction that writes to one of the six clip distance
      registers.  Primitives will automatically be clipped to the half-space
      where o[CLPx] >= 0, which matches the definition in the spec.

          # R0 holds eye coordinates
          # c[0] holds eye-space clip plane coefficients
          DP4 o[CLP0].x, R0, c[0];

      Note that the clip plane or clip distance volume corresponding to the
      o[CLPn] register used must be enabled, or no clipping will be performed.

      The clip distance registers allow for clip distance volumes to be
      computed more-or-less arbitrarily.  To approximate clipping to a sphere
      of radius <n>, the following code can be used.

          # R0 holds eye coordinates
          # c[0].xyz holds sphere center
          # c[0].w holds the square of the sphere radius
          SUB R1.xyz, R0, c[0];            # distance vector
          DP3 R1.w, R1, R1;                # compute distance squared
          SUB o[CLP0].x, c[0].w, R1.w;     # compute r^2 - d^2

      Since the clip distance is interpolated linearly over a primitive, the
      clip distance evaluated at a point will represent a piecewise-linear
      approximation of the true distance.  The approximation will become
      increasingly more accurate as the primitive is tesselated more finely.

    How can looping be achieved in vertex programs?

      Simple loops can be achieved using a general purpose floating-point
      register component as a counter.  The following code calls a function
      named "function" <n> times, where <n> is specified in a program
      parameter register component.

          # c[0].x holds the number of iterations to execute.
          # c[1].x holds the constant 1.0.
          MOVC R15.x, c[0].x;
        startLoop:
          CAL  function (GT.x);             # if (counter > 0) function();
          SUBC R15.x, R15.x, c[1].x;        # counter = counter - 1;
          BRA  startLoop (GT.x);            # if (counter > 0) goto start;
        endLoop:
          ...

      More complex loops (where a separate index may be needed for indexed
      addressing into the program parameter array) can be achieved using the
      ARA instruction, which will add the x/z and y/w components of an address
      register.

          # c[0].x holds the number of iterations to execute
          # c[0].y holds the initial index value
          # c[0].z holds the constant -1.0 (used for the iteration count)
          # c[0].w holds the index step value
          ARLC A1, c[0];
        startLoop:
          CAL  function (GT.x);             # if (counter > 0) function();
                                            # Note: A1.y can be used for
                                            # indexing in function().
          ARAC A1.xy, A1;                   # counter = counter - 1;
                                            # index += loopStep;
          BRA  startLoop (GT.x);            # if (counter > 0) goto start;
        endLoop:
          ...
          
    Should this specification add support for vertex state programs beyond the
    VP1 execution environment?

      No.  Vertex state programs are a little-used feature of
      NV_vertex_program and don't perform particularly well.  They are still
      supported for compatibility with the original NV_vertex_program spec,
      but they will not be extended to support new features.

    How are NaN's be handled in the "set on" instructions (SEQ, SGE, SGT, SLE,
    SLT, SNE)?  What about MIN, MAX?  SSG?  When doing condition code tests?

      Any of these instructions involving a NaN operand will produce a NaN
      result.  This behavior differs from the NV_fragment_program extension.
      There, SEQ, SGE, SGT, SLE, and SLT will produce 0.0 if either operand is
      a NaN, and SNE will produce 1.0 if either operand is a NaN.

      For condition code updates, NaN values will result in "UN" condition
      codes.  All conditionals using a "UN" condition code, except "TR" and
      "NE" will evaluate to false.  This behavior is identical to the
      functionality in NV_fragment_program.

    How can the various features of this extension be used to provide skinning
    functionality similar to that in ARB_vertex_blend and ARB_matrix_palette?
    And how can that functionality be extended?

      Assume an implementation that allows application of up to 8 matrices at
      once.  Further assume that v[12].xyzw and v[13].xyzw hold the set of 8
      weights, and v[14].xyzw and v[15].xyzw hold the set of 8 matrix indices.
      Furthermore, assume that the palette of matrices are stored/tracked at
      c[0], c[4], c[8], and so on.  As an additional optimization, an
      application can specify that fewer than 8 matrices should be applied by
      storing a negative palette index immediately after the last index is
      applied.

      Skinning support in this example can be provided by the following code:

          ARLC A0, v[14];                 # load 4 palette indices at once
          DP4 R1.x, c[A0.x+0], v[0];      # 1st matrix transform
          DP4 R1.y, c[A0.x+1], v[0];
          DP4 R1.z, c[A0.x+2], v[0];
          DP4 R1.w, c[A0.x+3], v[0];
          MUL R0, R1, v[12].x;            # accumulate weighted sum in R0
          BRA end (LT.y);                 # stop on a negative matrix index
          DP4 R1.x, c[A0.y+0], v[0];      # 2nd matrix transform
          DP4 R1.y, c[A0.y+1], v[0];
          DP4 R1.z, c[A0.y+2], v[0];
          DP4 R1.w, c[A0.y+3], v[0];
          MAD R0, R1, v[12].y, R0;        # accumulate weighted sum in R0
          BRA end (LT.z);                 # stop on a negative matrix index

          ...                             # 3rd and 4th matrix transform

          ARLC A0, v[15];                 # load next four palette indices
          BRA end (LT.x);
          DP4 R1.x, c[A0.x+0], v[0];      # 5th matrix transform
          DP4 R1.y, c[A0.x+1], v[0];
          DP4 R1.z, c[A0.x+2], v[0];
          DP4 R1.w, c[A0.x+3], v[0];
          MAD R0, R1, v[13].x, R0;        # accumulate weighted sum in R0
          BRA end (LT.y);                 # stop on a negative matrix index

          ...                             # 6th, 7th, and 8th matrix transform
        
        end:
          ...                             # any additional instructions

      The amount of code used by this example could further be reduced using a
      subroutine performing four transformations at a time:

          ARLC A0, v[14];  # load first four indices
          CAL  skin4;      # do first four transformations
          BRA  end (LT);   # end if any of the first 4 indices was < 0
          ARLC A0, v[15];  # load second four indices
          CAL  skin4;      # do second four transformations
        end:
          ...              # any additional instructions

    Why does the RCC instruction exist?

      RESOLVED:  To perform numeric operations that will avoid overflow and
      underflow issues.

    Should the specification provide more examples?

      RESOLVED:  It would be nice.


New Procedures and Functions

    None.


New Tokens

    None.


Additions to Chapter 2 of the OpenGL 1.3 Specification (OpenGL Operation)

    Modify Section 2.11, Clipping (p. 39)

    (modify last paragraph, p. 39) When the GL is not in vertex program mode

    (section 2.14), this view volume may be further restricted by as many as n
    client-defined clip planes to generate the clip volume. ...

    (add before next-to-last paragraph, p. 40) When the GL is in vertex
    program mode, the view volume may be restricted to the individual clip
    distance volumes derived from the per-vertex clip distances (o[CLP0] -
    o[CLP5]).  Clip distance volumes are applied if and only if per-vertex
    clip distances are not supported in the vertex program execution
    environment.  A point P belonging to the primitive under consideration is
    in the clip distance volume numbered n if and only if

      c_n(P) >= 0,

    where c_n(P) is the interpolated value of the clip distance CLPn at the
    point P.  For point primitives, c_n(P) is simply the clip distance for the
    vertex in question.  For line and triangle primitives, per-vertex clip
    distances are interpolated using a weighted mean, with weights derived
    according to the algorithms described in sections 3.4 and 3.5.

    (modify next-to-last paragraph, p.40) Client-defined clip planes or clip
    distance volumes are enabled with the generic Enable command and disabled
    with the Disable command. The value of the argument to either command is
    CLIP PLANEi where i is an integer between 0 and n; specifying a value of i
    enables or disables the plane equation with index i. The constants obey
    CLIP PLANEi = CLIP PLANE0 + i.


    Add Section 2.14,  Vertex Programs (p. 57).  This section supersedes the
    similar section added in the NV_vertex_program extension and extended in
    the NV_vertex_program1_1 extension.

    The conventional GL vertex transformation model described in sections 2.10
    through 2.13 is a configurable, but essentially hard-wired, sequence of
    per-vertex computations based on a canonical set of per-vertex parameters
    and vertex transformation related state such as transformation matrices,
    lighting parameters, and texture coordinate generation parameters.

    The general success and utility of the conventional GL vertex
    transformation model reflects its basic correspondence to the typical
    vertex transformation requirements of 3D applications.

    However when the conventional GL vertex transformation model is not
    sufficient, the vertex program mode provides a substantially more flexible
    model for vertex transformation.  The vertex program mode permits
    applications to define their own vertex programs.


    Section 2.14.1, Vertex Program Execution Environment

    The vertex program execution environment is an operational model that
    defines how a program is executed.  The execution environment includes a
    set of instructions, a set of registers, and semantic rules defining how
    operations are performed.  There are three vertex program execution
    environments, VP1, VP1.1, and VP2.  The environment names are taken from
    the mandatory program prefix strings found at the beginning of all vertex
    programs.  The VP1.1 execution environment is a minor addition to the VP1
    execution environment, so references to the VP1 execution environment
    below apply to both VP1 and VP1.1 execution environments except where
    otherwise noted.

    The vertex program instruction set consists primarily of floating-point
    4-component vector operations operating on per-vertex attributes and
    program parameters.  Vertex programs execute on a per-vertex basis and
    operate on each vertex completely independently from the processing of
    other vertices.  Vertex programs execute without data hazards so results
    computed in one operation can be used immediately afterwards.  Vertex
    programs produce a set of vertex result vectors that becomes the set of
    transformed vertex parameters used by primitive assembly.

    In the VP1 environment, vertex programs execute a finite fixed sequence of
    instructions with no branching or looping.  In the VP2 environment, vertex
    programs support conditional and unconditional branches and four levels of
    subroutine calls.

    The vertex program register set consists of six types of registers
    described in the following sections.


    Section 2.14.1.1, Vertex Attribute Registers

    The Vertex Attribute Registers are sixteen 4-component vector
    floating-point registers containing the current vertex's per-vertex
    attributes.  These registers are numbered 0 through 15.  These registers
    are private to each vertex program invocation and are initialized at each
    vertex program invocation by the current vertex attribute state specified
    with VertexAttribNV commands.  These registers are read-only during vertex
    program execution.  The VertexAttribNV commands used to update the vertex
    attribute registers can be issued both outside and inside of Begin/End
    pairs.  Vertex program execution is provoked by updating vertex attribute
    zero.  Updating vertex attribute zero outside of a Begin/End pair is
    ignored without generating any error (identical to the Vertex command
    operation).

    The commands

      void VertexAttrib{1234}{sfd}NV(uint index, T coords);
      void VertexAttrib{1234}{sfd}vNV(uint index, T coords);
      void VertexAttrib4ubNV(uint index, T coords);
      void VertexAttrib4ubvNV(uint index, T coords);

    specify the particular current vertex attribute indicated by index.
    The coordinates for each vertex attribute are named x, y, z, and w.
    The VertexAttrib1NV family of commands sets the x coordinate to the
    provided single argument while setting y and z to 0 and w to 1.
    Similarly, VertexAttrib2NV sets x and y to the specified values,
    z to 0 and w to 1; VertexAttrib3NV sets x, y, and z, with w set
    to 1, and VertexAttrib4NV sets all four coordinates.  The error
    INVALID_VALUE is generated if index is greater than 15.

    No conversions are applied to the vertex attributes specified as
    type short, float, or double.  However, vertex attributes specified
    as type ubyte are converted as described by Table 2.6.

    The commands

      void VertexAttribs{1234}{sfd}vNV(uint index, sizei n, T coords[]);
      void VertexAttribs4ubvNV(uint index, sizei n, GLubyte coords[]);

    specify a contiguous set of n vertex attributes.  The effect of

      VertexAttribs{1234}{sfd}vNV(index, n, coords)

    is the same (assuming no errors) as the command sequence

      #define NUM k  /* where k is 1, 2, 3, or 4 components */
      int i;
      for (i=n-1; i>=0; i--) {
        VertexAttrib{NUM}{sfd}vNV(i+index, &coords[i*NUM]);
      }

    VertexAttribs4ubvNV behaves similarly.

    The VertexAttribNV calls equivalent to VertexAttribsNV are issued in
    reverse order so that vertex program execution is provoked when index
    is zero only after all the other vertex attributes have first been
    specified.

    The set and operation of vertex attribute registers are identical for both
    VP1 and VP2 execution environment.


    Section 2.14.1.2, Program Parameter Registers

    The Program Parameter Registers are a set of 4-component floating-point
    vector registers containing the vertex program parameters.  In the VP1
    execution environment, there are 96 registers, numbered 0 through 95.  In
    the VP2 execution environment, there are 256 registers, numbered 0 through
    255.  This relatively large set of registers is intended to hold
    parameters such as matrices, lighting parameters, and constants required
    by vertex programs.  Vertex program parameter registers can be updated in
    one of two ways:  by the ProgramParameterNV commands outside of a
    Begin/End pair or by a vertex state program executed outside of a
    Begin/End pair (vertex state programs are discussed in section 2.14.3).

    The commands
     
      void ProgramParameter4fNV(enum target, uint index,
                                float x, float y, float z, float w)
      void ProgramParameter4dNV(enum target, uint index,
                                double x, double y, double z, double w)

    specify the particular program parameter indicated by index.
    The coordinates values x, y, z, and w are assigned to the respective
    components of the particular program parameter.  target must be
    VERTEX_PROGRAM_NV.

    The commands

      void ProgramParameter4dvNV(enum target, uint index, double *params);
      void ProgramParameter4fvNV(enum target, uint index, float *params);

    operate identically to ProgramParameter4fNV and ProgramParameter4dNV
    respectively except that the program parameters are passed as an
    array of four components.

    The error INVALID_VALUE is generated if the specified index is greater
    than or equal to the number of program parameters in the execution
    environment (96 for VP1, 256 for VP2).

    The commands

      void ProgramParameters4dvNV(enum target, uint index,
                                  uint num, double *params);
      void ProgramParameters4fvNV(enum target, uint index,
                                  uint num, float *params);

    specify a contiguous set of num program parameters.  The effect is
    the same (assuming no errors) as

      for (i=index; i<index+num; i++) {
        ProgramParameter4{fd}vNV(target, i, &params[i*4]);
      }

    The error INVALID_VALUE is generated if sum of <index> and <num> is
    greater than the number of program parameters in the execution environment
    (96 for VP1, 256 for VP2).

    The program parameter registers are shared to all vertex program
    invocations within a rendering context.  ProgramParameterNV command
    updates and vertex state program executions are serialized with respect to
    vertex program invocations and other vertex state program executions.

    Writes to the program parameter registers during vertex state program
    execution can be maskable on a per-component basis.

    The initial value of all 96 (VP1) or 256 (VP2) program parameter registers
    is (0,0,0,0).


    Section 2.14.1.3, Address Registers

    The Address Registers are 4-component vector registers with signed 10-bit
    integer components.  In the VP1 execution environment, there is only a
    single address register (A0) and only the x component of the register is
    accessible.  In the VP2 execution environment, there are two address
    registers (A0 and A1), of which all four components are accessible.  The
    address registers are private to each vertex program invocation and are
    initialized to (0,0,0,0) at every vertex program invocation.  These
    registers can be written during vertex program execution (but not read)
    and their values can be used for as a relative offset for reading vertex
    program parameter registers.  Only the vertex program parameter registers
    can be read using relative addressing (writes using relative addressing
    are not supported).

    See the discussion of relative addressing of program parameters in section
    2.14.2.1 and the discussion of the ARL instruction in section 2.14.3.4.


    Section 2.14.1.4, Temporary Registers

    The Temporary Registers are 4-component floating-point vector registers
    used to hold temporary results during vertex program execution.  In the
    VP1 execution environment, there are 12 temporary registers, numbered 0
    through 11.  In the VP2 execution environment, there are 16 temporary
    registers, numbered 0 through 15.  These registers are private to each
    vertex program invocation and initialized to (0,0,0,0) at every vertex
    program invocation.  These registers can be read and written during vertex
    program execution.  Writes to these registers can be maskable on a
    per-component basis.

    In the VP2 execution environment, there is one additional temporary
    pseudo-register, "CC".  CC is treated as unnumbered, write-only temporary
    register, whose sole purpose is to allow instructions to modify the
    condition code register (section 2.14.1.6) without overwriting the
    contents of any temporary register.


    Section 2.14.1.5, Vertex Result Registers

    The Vertex Result Registers are 4-component floating-point vector
    registers used to write the results of a vertex program.  There are 15
    result registers in the VP1 execution environment, and 21 in the VP2
    execution environment.  Each register value is initialized to (0,0,0,1) at
    the invocation of each vertex program.  Writes to the vertex result
    registers can be maskable on a per-component basis.  These registers are
    named in Table X.1 and further discussed below.


    Vertex Result                                      Component
    Register Name   Description                        Interpretation
    --------------  ---------------------------------  --------------
     HPOS            Homogeneous clip space position    (x,y,z,w)
     COL0            Primary color (front-facing)       (r,g,b,a)
     COL1            Secondary color (front-facing)     (r,g,b,a)
     BFC0            Back-facing primary color          (r,g,b,a)
     BFC1            Back-facing secondary color        (r,g,b,a)
     FOGC            Fog coordinate                     (f,*,*,*)
     PSIZ            Point size                         (p,*,*,*)
     TEX0            Texture coordinate set 0           (s,t,r,q)
     TEX1            Texture coordinate set 1           (s,t,r,q)
     TEX2            Texture coordinate set 2           (s,t,r,q)
     TEX3            Texture coordinate set 3           (s,t,r,q)
     TEX4            Texture coordinate set 4           (s,t,r,q)
     TEX5            Texture coordinate set 5           (s,t,r,q)
     TEX6            Texture coordinate set 6           (s,t,r,q)
     TEX7            Texture coordinate set 7           (s,t,r,q)
     CLP0(*)         Clip distance 0                    (d,*,*,*)
     CLP1(*)         Clip distance 1                    (d,*,*,*)
     CLP2(*)         Clip distance 2                    (d,*,*,*)
     CLP3(*)         Clip distance 3                    (d,*,*,*)
     CLP4(*)         Clip distance 4                    (d,*,*,*)
     CLP5(*)         Clip distance 5                    (d,*,*,*)

    Table X.1:  Vertex Result Registers.  (*) Registers CLP0 through CLP5, are
    available only in the VP2 execution environment.

    HPOS is the transformed vertex's homogeneous clip space position.  The
    vertex's homogeneous clip space position is converted to normalized device
    coordinates and transformed to window coordinates as described at the end
    of section 2.10 and in section 2.11.  Further processing (subsequent to
    vertex program termination) is responsible for clipping primitives
    assembled from vertex program-generated vertices as described in section
    2.10 but all client-defined clip planes are treated as if they are
    disabled when vertex program mode is enabled.

    Four distinct color results can be generated for each vertex.  COL0 is the
    transformed vertex's front-facing primary color.  COL1 is the transformed
    vertex's front-facing secondary color.  BFC0 is the transformed vertex's
    back-facing primary color.  BFC1 is the transformed vertex's back-facing
    secondary color.

    Primitive coloring may operate in two-sided color mode.  This behavior is
    enabled and disabled by calling Enable or Disable with the symbolic value
    VERTEX_PROGRAM_TWO_SIDE_NV.  The selection between the back-facing colors
    and the front-facing colors depends on the primitive of which the vertex
    is a part.  If the primitive is a point or a line segment, the
    front-facing colors are always selected.  If the primitive is a polygon
    and two-sided color mode is disabled, the front-facing colors are
    selected.  If it is a polygon and two-sided color mode is enabled, then
    the selection is based on the sign of the (clipped or unclipped) polygon's
    signed area computed in window coordinates.  This facingness determination
    is identical to the two-sided lighting facingness determination described
    in section 2.13.1.

    The selected primary and secondary colors for each primitive are clamped
    to the range [0,1] and then interpolated across the assembled primitive
    during rasterization with at least 8-bit accuracy for each color
    component.

    FOGC is the transformed vertex's fog coordinate.  The register's first
    floating-point component is interpolated across the assembled primitive
    during rasterization and used as the fog distance to compute per-fragment
    the fog factor when fog is enabled.  However, if both fog and vertex
    program mode are enabled, but the FOGC vertex result register is not
    written, the fog factor is overridden to 1.0.  The register's other three
    components are ignored.

    Point size determination may operate in program-specified point size mode.
    This behavior is enabled and disabled by calling Enable or Disable with
    the symbolic value VERTEX_PROGRAM_POINT_SIZE_NV.  If the vertex is for a
    point primitive and the mode is enabled and the PSIZ vertex result is
    written, the point primitive's size is determined by the clamped x
    component of the PSIZ register.  Otherwise (because vertex program mode is
    disabled, program-specified point size mode is disabled, or because the
    vertex program did not write PSIZ), the point primitive's size is
    determined by the point size state (the state specified using the
    PointSize command).

    The PSIZ register's x component is clamped to the range zero through
    either the hi value of ALIASED_POINT_SIZE_RANGE if point smoothing is
    disabled or the hi value of the SMOOTH_POINT_SIZE_RANGE if point smoothing
    is enabled.  The register's other three components are ignored.

    If the vertex is not for a point primitive, the value of the PSIZ vertex
    result register is ignored.

    TEX0 through TEX7 are the transformed vertex's texture coordinate sets for
    texture units 0 through 7.  These floating-point coordinates are
    interpolated across the assembled primitive during rasterization and used
    for accessing textures.  If the number of texture units supported is less
    than eight, the values of vertex result registers that do not correspond
    to existent texture units are ignored.

    CLP0 through CLP5, available only in the VP2 execution environment, are
    the transformed vertex's clip distances.  These floating-point coordinates
    are used by post-vertex program clipping process (see section 2.11).


    Section 2.14.1.6,  The Condition Code Register

    The VP2 execution environment provides a single four-component vector
    called the condition code register.  Each component of this register is
    one of four enumerated values:  GT (greater than), EQ (equal), LT (less
    than), or UN (unordered).  The condition code register can be used to mask
    writes to registers and to evaluate conditional branches.

    Most vertex program instructions can optionally update the condition code
    register.  When a vertex program instruction updates the condition code
    register, a condition code component is set to LT if the corresponding
    component of the result is less than zero, EQ if it is equal to zero, GT
    if it is greater than zero, and UN if it is NaN (not a number).

    The condition code register is initialized to a vector of EQ values each
    time a vertex program executes.

    There is no condition code register available in the VP1 execution
    environment.


    Section 2.14.1.7,  Semantic Meaning for Vertex Attributes and Program
                       Parameters 

    One important distinction between the conventional GL vertex
    transformation mode and the vertex program mode is that per-vertex
    parameters and other state parameters in vertex program mode do not have
    dedicated semantic interpretations the way that they do with the
    conventional GL vertex transformation mode.

    For example, in the conventional GL vertex transformation mode, the Normal
    command specifies a per-vertex normal.  The semantic that the Normal
    command supplies a normal for lighting is established because that is how
    the per-vertex attribute supplied by the Normal command is used by the
    conventional GL vertex transformation mode.  Similarly, other state
    parameters such as a light source position have semantic interpretations
    based on how the conventional GL vertex transformation model uses each
    particular parameter.

    In contrast, vertex attributes and program parameters for vertex programs
    have no pre-defined semantic meanings.  The meaning of a vertex attribute
    or program parameter in vertex program mode is defined by how the vertex
    attribute or program parameter is used by the current vertex program to
    compute and write values to the Vertex Result Registers.  This is the
    reason that per-vertex attributes and program parameters for vertex
    programs are numbered instead of named.

    For convenience however, the existing per-vertex parameters for the
    conventional GL vertex transformation mode (vertices, normals,
    colors, fog coordinates, vertex weights, and texture coordinates) are
    aliased to numbered vertex attributes.  This aliasing is specified in
    Table X.2.  The table includes how the various conventional components
    map to the 4-component vertex attribute components.

Vertex
Attribute  Conventional                                           Conventional
Register   Per-vertex        Conventional                         Component
Number     Parameter         Per-vertex Parameter Command         Mapping
---------  ---------------   -----------------------------------  ------------
 0         vertex position   Vertex                               x,y,z,w
 1         vertex weights    VertexWeightEXT                      w,0,0,1
 2         normal            Normal                               x,y,z,1
 3         primary color     Color                                r,g,b,a
 4         secondary color   SecondaryColorEXT                    r,g,b,1
 5         fog coordinate    FogCoordEXT                          fc,0,0,1
 6         -                 -                                    -
 7         -                 -                                    -
 8         texture coord 0   MultiTexCoord(GL_TEXTURE0_ARB, ...)  s,t,r,q
 9         texture coord 1   MultiTexCoord(GL_TEXTURE1_ARB, ...)  s,t,r,q
 10        texture coord 2   MultiTexCoord(GL_TEXTURE2_ARB, ...)  s,t,r,q
 11        texture coord 3   MultiTexCoord(GL_TEXTURE3_ARB, ...)  s,t,r,q
 12        texture coord 4   MultiTexCoord(GL_TEXTURE4_ARB, ...)  s,t,r,q
 13        texture coord 5   MultiTexCoord(GL_TEXTURE5_ARB, ...)  s,t,r,q
 14        texture coord 6   MultiTexCoord(GL_TEXTURE6_ARB, ...)  s,t,r,q
 15        texture coord 7   MultiTexCoord(GL_TEXTURE7_ARB, ...)  s,t,r,q

Table X.2:  Aliasing of vertex attributes with conventional per-vertex
parameters.

    Only vertex attribute zero is treated specially because it is
    the attribute that provokes the execution of the vertex program;
    this is the attribute that aliases to the Vertex command's vertex
    coordinates.

    The result of a vertex program is the set of post-transformation
    vertex parameters written to the Vertex Result Registers.
    All vertex programs must write a homogeneous clip space position, but
    the other Vertex Result Registers can be optionally written.

    Clipping and culling are not the responsibility of vertex programs because
    these operations assume the assembly of multiple vertices into a
    primitive.  View frustum clipping is performed subsequent to vertex
    program execution.  Clip planes are not supported in the VP1 execution
    environment.  Clip planes are supported indirectly via the clip distance
    (o[CLPx]) registers in the VP2 execution environment.


    Section 2.14.1.8,  Vertex Program Specification

    Vertex programs are specified as an array of ubytes.  The array is a
    string of ASCII characters encoding the program.

    The command

      LoadProgramNV(enum target, uint id, sizei len,
                    const ubyte *program);

    loads a vertex program when the target parameter is VERTEX_PROGRAM_NV.
    Multiple programs can be loaded with different names.  id names the
    program to load.  The name space for programs is the positive integers
    (zero is reserved).  The error INVALID_VALUE occurs if a program is loaded
    with an id of zero.  The error INVALID_OPERATION is generated if a program
    is loaded for an id that is currently loaded with a program of a different
    program target.  Managing the program name space and binding to vertex
    programs is discussed later in section 2.14.1.8.

    program is a pointer to an array of ubytes that represents the program
    being loaded.  The length of the array is indicated by len.

    A second program target type known as vertex state programs is discussed
    in 2.14.4.

    At program load time, the program is parsed into a set of tokens possibly
    separated by white space.  Spaces, tabs, newlines, carriage returns, and
    comments are considered whitespace.  Comments begin with the character "#"
    and are terminated by a newline, a carriage return, or the end of the
    program array.

    The Backus-Naur Form (BNF) grammar below specifies the syntactically valid
    sequences for several types of vertex programs.  The set of valid tokens
    can be inferred from the grammar.  The token "" represents an empty string
    and is used to indicate optional rules.  A program is invalid if it
    contains any undefined tokens or characters.

    The grammar provides for three different vertex program types,
    corresponding to the three vertex program execution environments.  VP1,
    VP1.1, and VP2 programs match the grammar rules <vp1-program>,
    <vp11-program>, and <vp2-program>, respectively.  Some grammar rules
    correspond to features or instruction forms available only in certain
    execution environments.  Rules beginning with the prefix "vp1-" are
    available only to VP1 and VP1.1 programs.  Rules beginning with the
    prefixes "vp11-" and "vp2-" are available only to VP1.1 and VP2 programs,
    respectively.


    <program>              ::= <vp1-program>
                             | <vp11-program>
                             | <vp2-program>

    <vp1-program>          ::= "!!VP1.0" <programBody> "END"

    <vp11-program>         ::= "!!VP1.1" <programBody> "END"

    <vp2-program>          ::= "!!VP2.0" <programBody> "END"

    <programBody>          ::= <optionSequence> <programText>

    <optionSequence>       ::= <option> <optionSequence>
                             | ""

    <option>               ::= "OPTION" <vp11-option> ";"
                             | "OPTION" <vp2-option> ";"

    <vp11-option>          ::= "NV_position_invariant"

    <vp2-option>           ::= "NV_position_invariant"

    <programText>          ::= <programTextItem> <programText>
                             | ""

    <programTextItem>      ::= <instruction> ";"
                             | <vp2-instructionLabel>

    <instruction>          ::= <ARL-instruction>
                             | <VECTORop-instruction>
                             | <SCALARop-instruction>
                             | <BINop-instruction>
                             | <TRIop-instruction>
                             | <vp2-BRA-instruction>
                             | <vp2-RET-instruction>
                             | <vp2-ARA-instruction>

    <ARL-instruction>      ::= <vp1-ARL-instruction>
                             | <vp2-ARL-instruction>

    <vp1-ARL-instruction>  ::= "ARL" <maskedAddrReg> "," <scalarSrc>

    <vp2-ARL-instruction>  ::= <vp2-ARLop> <maskedAddrReg> "," <vectorSrc>

    <vp2-ARLop>            ::= "ARL" | "ARLC"
                             | "ARR" | "ARRC"

    <VECTORop-instruction> ::= <VECTORop> <maskedDstReg> "," <vectorSrc>

    <VECTORop>             ::= "LIT"
                             | "MOV"
                             | <vp11-VECTORop>
                             | <vp2-VECTORop>

    <vp11-VECTORop>        ::= "ABS"

    <vp2-VECTORop>         ::=         "ABSC"
                             | "FLR" | "FLRC"
                             | "FRC" | "FRCC"
                             |         "LITC"
                             |         "MOVC"
                             | "SSG" | "SSGC"

    <SCALARop-instruction> ::= <SCALARop> <maskedDstReg> "," <scalarSrc>

    <SCALARop>             ::= "EXP"
                             | "LOG"
                             | "RCP"
                             | "RSQ"
                             | <vp11-SCALARop>
                             | <vp2-SCALARop>

    <vp11-SCALARop>        ::= "RCC"

    <vp2-SCALARop>         ::= "COS"  | "COSC"
                             | "EX2"  | "EX2C"
                             | "LG2"  | "LG2C"
                             |          "EXPC"
                             |          "LOGC"
                             |          "RCCC"
                             |          "RCPC"
                             |          "RSQC"
                             | "SIN"  | "SINC"

    <BINop-instruction>    ::= <BINop> <maskedDstReg> "," <vectorSrc> ","
                               <vectorSrc>

    <BINop>                ::= "ADD"
                             | "DP3"
                             | "DP4"
                             | "DST"
                             | "MAX"
                             | "MIN"
                             | "MUL"
                             | "SGE"
                             | "SLT"
                             | <vp11-BINop>
                             | <vp2-BINop>

    <vp11-BINop>           ::= "DPH"
                             | "SUB"

    <vp2-BINop>            ::=         "ADDC"
                             |         "DP3C"
                             |         "DP4C"
                             |         "DPHC"
                             |         "DSTC"
                             |         "MAXC"
                             |         "MINC"
                             |         "MULC"
                             | "SEQ" | "SEQC"
                             | "SFL" | "SFLC"
                             |         "SGEC"
                             | "SGT" | "SGTC"
                             |         "SLTC"
                             | "SLE" | "SLEC"
                             | "SNE" | "SNEC"
                             | "STR" | "STRC"
                             |         "SUBC"

    <TRIop-instruction>    ::= <TRIop> <maskedDstReg> "," <vectorSrc> "," 
                               <vectorSrc> "," <vectorSrc>

    <TRIop>                ::= "MAD"
                             | <vp2-TRIop>

    <vp2-TRIop>            ::= "MADC"

    <vp2-BRA-instruction>  ::= <vp2-BRANCHop> <vp2-branchLabel>
                                 <vp2-branchCondition>

    <vp2-BRANCHop>         ::= "BRA"
                             | "CAL"

    <vp2-RET-instruction>  ::= "RET" <vp2-branchCondition>

    <vp2-ARA-instruction>  ::= <vp2-ARAop> <maskedAddrReg> "," <addrRegister>

    <vp2-ARAop>            ::= "ARA" | "ARAC"

    <scalarSrc>            ::= <baseScalarSrc>
                             | <vp2-absScalarSrc>

    <vp2-absScalarSrc>     ::= <optionalSign> "|" <baseScalarSrc> "|"

    <baseScalarSrc>        ::= <optionalSign> <srcRegister> <scalarSuffix>

    <vectorSrc>            ::= <baseVectorSrc>
                             | <vp2-absVectorSrc>

    <vp2-absVectorSrc>     ::= <optionalSign> "|" <baseVectorSrc> "|"

    <baseVectorSrc>        ::= <optionalSign> <srcRegister> <swizzleSuffix>

    <srcRegister>          ::= <vtxAttribRegister>
                             | <progParamRegister>
                             | <tempRegister>

    <maskedDstReg>         ::= <dstRegister> <optionalWriteMask> 
                                   <optionalCCMask> 

    <dstRegister>          ::= <vtxResultRegister>
                             | <tempRegister>
                             | <vp2-nullRegister>

    <vp2-nullRegister>     ::= "CC"

    <vp2-branchCondition>  ::= <optionalCCMask>

    <vtxAttribRegister>    ::= "v" "[" vtxAttribRegNum "]"

    <vtxAttribRegNum>      ::= decimal integer from 0 to 15 inclusive
                             | "OPOS"
                             | "WGHT"
                             | "NRML"
                             | "COL0"
                             | "COL1"
                             | "FOGC"
                             | "TEX0"
                             | "TEX1"
                             | "TEX2"
                             | "TEX3"
                             | "TEX4"
                             | "TEX5"
                             | "TEX6"
                             | "TEX7"

    <progParamRegister>    ::= <absProgParamReg>
                             | <relProgParamReg>

    <absProgParamReg>      ::= "c" "[" <progParamRegNum> "]"

    <progParamRegNum>      ::= <vp1-progParamRegNum>
                             | <vp2-progParamRegNum>

    <vp1-progParamRegNum>  ::= decimal integer from 0 to 95 inclusive

    <vp2-progParamRegNum>  ::= decimal integer from 0 to 255 inclusive

    <relProgParamReg>      ::= "c" "[" <scalarAddr> <relProgParamOffset> "]"

    <relProgParamOffset>   ::= ""
                             | "+" <progParamPosOffset>
                             | "-" <progParamNegOffset>

    <progParamPosOffset>   ::= <vp1-progParamPosOff>
                             | <vp2-progParamPosOff>

    <vp1-progParamPosOff>  ::= decimal integer from 0 to 63 inclusive

    <vp2-progParamPosOff>  ::= decimal integer from 0 to 255 inclusive

    <progParamNegOffset>   ::= <vp1-progParamNegOff>
                             | <vp2-progParamNegOff>

    <vp1-progParamNegOff>  ::= decimal integer from 0 to 64 inclusive

    <vp2-progParamNegOff>  ::= decimal integer from 0 to 256 inclusive

    <tempRegister>         ::= "R0"  | "R1"  | "R2"  | "R3"
                             | "R4"  | "R5"  | "R6"  | "R7"
                             | "R8"  | "R9"  | "R10" | "R11"

    <vp2-tempRegister>     ::= "R12" | "R13" | "R14" | "R15" 

    <vtxResultRegister>    ::= "o" "[" <vtxResultRegName> "]"

    <vtxResultRegName>     ::= "HPOS"
                             | "COL0"
                             | "COL1"
                             | "BFC0"
                             | "BFC1"
                             | "FOGC"
                             | "PSIZ"
                             | "TEX0"
                             | "TEX1"
                             | "TEX2"
                             | "TEX3"
                             | "TEX4"
                             | "TEX5"
                             | "TEX6"
                             | "TEX7"
                             | <vp2-resultRegName>

    <vp2-resultRegName>    ::= "CLP0"
                             | "CLP1"
                             | "CLP2"
                             | "CLP3"
                             | "CLP4"
                             | "CLP5"

    <scalarAddr>           ::= <addrRegister> "." <addrRegisterComp>

    <maskedAddrReg>        ::= <addrRegister> <addrWriteMask>

    <addrRegister>         ::= "A0"
                             | <vp2-addrRegister>

    <vp2-addrRegister>     ::= "A1"

    <addrRegisterComp>     ::= "x"
                             | <vp2-addrRegisterComp>

    <vp2-addrRegisterComp> ::= "y"
                             | "z"
                             | "w"

    <addrWriteMask>        ::= "." "x"
                             | <vp2-addrWriteMask>

    <vp2-addrWriteMask>     ::= ""
                             | "."     "y"
                             | "." "x" "y"
                             | "."         "z"
                             | "." "x"     "z"
                             | "."     "y" "z"
                             | "." "x" "y" "z"
                             | "."             "w"
                             | "." "x"         "w"
                             | "."     "y"     "w"
                             | "." "x" "y"     "w"
                             | "."         "z" "w"
                             | "." "x"     "z" "w"
                             | "."     "y" "z" "w"
                             | "." "x" "y" "z" "w"

    
    <optionalSign>         ::= ""
                             | "-" 
                             | <vp2-optionalSign>

    <vp2-optionalSign>     ::= "+"

    <vp2-instructionLabel> ::= <vp2-branchLabel> ":"

    <vp2-branchLabel>      ::= <identifier>

    <optionalWriteMask>    ::= ""
                             | "." "x"
                             | "."     "y"
                             | "." "x" "y"
                             | "."         "z"
                             | "." "x"     "z"
                             | "."     "y" "z"
                             | "." "x" "y" "z"
                             | "."             "w"
                             | "." "x"         "w"
                             | "."     "y"     "w"
                             | "." "x" "y"     "w"
                             | "."         "z" "w"
                             | "." "x"     "z" "w"
                             | "."     "y" "z" "w"
                             | "." "x" "y" "z" "w"

    <optionalCCMask>       ::= ""
                             | <vp2-ccMask>

    <vp2-ccMask>           ::= "(" <vp2-ccMaskRule> <swizzleSuffix> ")"

    <vp2-ccMaskRule>       ::= "EQ" | "GE" | "GT" | "LE" | "LT" | "NE" 
                             | "TR" | "FL"

    <scalarSuffix>         ::= "." <component>

    <swizzleSuffix>        ::= ""
                             | "." <component>
                             | "." <component> <component>
                                   <component> <component>

    <component>            ::= "x" 
                             | "y" 
                             | "z" 
                             | "w"

    The <identifier> rule matches a sequence of one or more letters ("A"
    through "Z", "a" through "z", and "_") and digits ("0" through "9); the
    first character must be a letter.  The underscore ("_") counts as a
    letter.  Upper and lower case letters are different (names are
    case-sensitive).

    The <vertexAttribRegNum> rule matches both register numbers 0 through 15
    and a set of mnemonics that abbreviate the aliasing of conventional
    per-vertex parameters to vertex attribute register numbers.  Table X.3
    shows the mapping from mnemonic to vertex attribute register number and
    what the mnemonic abbreviates.

                   Vertex Attribute
        Mnemonic   Register Number     Meaning
        --------   ----------------    --------------------
         "OPOS"     0                  object position
         "WGHT"     1                  vertex weight
         "NRML"     2                  normal
         "COL0"     3                  primary color
         "COL1"     4                  secondary color
         "FOGC"     5                  fog coordinate
         "TEX0"     8                  texture coordinate 0
         "TEX1"     9                  texture coordinate 1
         "TEX2"     10                 texture coordinate 2
         "TEX3"     11                 texture coordinate 3
         "TEX4"     12                 texture coordinate 4
         "TEX5"     13                 texture coordinate 5
         "TEX6"     14                 texture coordinate 6
         "TEX7"     15                 texture coordinate 7

        Table X.3:  The mapping between vertex attribute register numbers,
        mnemonics, and meanings.

    A vertex program fails to load if it does not write at least one component
    of the HPOS register.

    A vertex program fails to load in the VP1 execution environment if it
    contains more than 128 instructions.  A vertex program fails to load in
    the VP2 execution environment if it contains more than 256 instructions.
    Each block of text matching the <instruction> rule counts as an
    instruction.

    A vertex program fails to load if any instruction sources more than one
    unique program parameter register.  An instruction can match the
    <progParamRegister> rule more than once only if all such matches are
    identical.

    A vertex program fails to load if any instruction sources more than one
    unique vertex attribute register.  An instruction can match the
    <vtxAttribRegister> rule more than once only if all such matches refer to
    the same register.

    The error INVALID_OPERATION is generated if a vertex program fails to load
    because it is not syntactically correct or for one of the semantic
    restrictions listed above.

    The error INVALID_OPERATION is generated if a program is loaded for id
    when id is currently loaded with a program of a different target.

    A successfully loaded vertex program is parsed into a sequence of
    instructions.  Each instruction is identified by its tokenized name.  The
    operation of these instructions when executed is defined in section
    2.14.1.10.

    A successfully loaded program replaces the program previously assigned to
    the name specified by id.  If the OUT_OF_MEMORY error is generated by
    LoadProgramNV, no change is made to the previous contents of the named
    program.

    Querying the value of PROGRAM_ERROR_POSITION_NV returns a ubyte offset
    into the last loaded program string indicating where the first error in
    the program.  If the program fails to load because of a semantic
    restriction that cannot be determined until the program is fully scanned,
    the error position will be len, the length of the program.  If the program
    loads successfully, the value of PROGRAM_ERROR_POSITION_NV is assigned the
    value negative one.


    Section 2.14.1.9,  Vertex Program Binding and Program Management

    The current vertex program is invoked whenever vertex attribute zero is
    updated (whether by a VertexAttributeNV or Vertex command).  The current
    vertex program is updated by

      BindProgramNV(enum target, uint id);

    where target must be VERTEX_PROGRAM_NV.  This binds the vertex program
    named by id as the current vertex program. The error INVALID_OPERATION
    is generated if id names a program that is not a vertex program
    (for example, if id names a vertex state program as described in
    section 2.14.4).  

    Binding to a nonexistent program id does not generate an error.
    In particular, binding to program id zero does not generate an error.
    However, because program zero cannot be loaded, program zero is
    always nonexistent.  If a program id is successfully loaded with a
    new vertex program and id is also the currently bound vertex program,
    the new program is considered the currently bound vertex program.

    The INVALID_OPERATION error is generated when both vertex program
    mode is enabled and Begin is called (or when a command that performs
    an implicit Begin is called) if the current vertex program is
    nonexistent or not valid.  A vertex program may not be valid for
    reasons explained in section 2.14.5.

    Programs are deleted by calling

      void DeleteProgramsNV(sizei n, const uint *ids);

    ids contains n names of programs to be deleted.  After a program
    is deleted, it becomes nonexistent, and its name is again unused.
    If a program that is currently bound is deleted, it is as though
    BindProgramNV has been executed with the same target as the deleted
    program and program zero.  Unused names in ids are silently ignored,
    as is the value zero.

    The command

      void GenProgramsNV(sizei n, uint *ids);

    returns n previously unused program names in ids.  These names
    are marked as used, for the purposes of GenProgramsNV only,
    but they become existent programs only when the are first loaded
    using LoadProgramNV.  The error INVALID_VALUE is generated if n
    is negative.

    An implementation may choose to establish a working set of programs on
    which binding and ExecuteProgramNV operations (execute programs are
    explained in section 2.14.4) are performed with higher performance.
    A program that is currently part of this working set is said to
    be resident.

    The command
      
      boolean AreProgramsResidentNV(sizei n, const uint *ids,
                                    boolean *residences);

    returns TRUE if all of the n programs named in ids are resident,
    or if the implementation does not distinguish a working set.  If at
    least one of the programs named in ids is not resident, then FALSE is
    returned, and the residence of each program is returned in residences.
    Otherwise the contents of residences are not changed.  If any of
    the names in ids are nonexistent or zero, FALSE is returned, the
    error INVALID_VALUE is generated, and the contents of residences
    are indeterminate.  The residence status of a single named program
    can also be queried by calling GetProgramivNV with id set to the
    name of the program and pname set to PROGRAM_RESIDENT_NV.

    AreProgramsResidentNV indicates only whether a program is
    currently resident, not whether it could not be made resident.
    An implementation may choose to make a program resident only on
    first use, for example.  The client may guide the GL implementation
    in determining which programs should be resident by requesting a
    set of programs to make resident.

    The command

      void RequestResidentProgramsNV(sizei n, const uint *ids);

    requests that the n programs named in ids should be made resident.
    While all the programs are not guaranteed to become resident,
    the implementation should make a best effort to make as many of
    the programs resident as possible.  As a result of making the
    requested programs resident, program names not among the requested
    programs may become non-resident.  Higher priority for residency
    should be given to programs listed earlier in the ids array.
    RequestResidentProgramsNV silently ignores attempts to make resident
    nonexistent program names or zero.  AreProgramsResidentNV can be
    called after RequestResidentProgramsNV to determine which programs
    actually became resident.


    Section 2.14.2,  Vertex Program Operation

    In the VP1 execution environment, there are twenty-one vertex program
    instructions.  Four instructions (ABS, DPH, RCC, and SUB) are available
    only in the VP1.1 execution environment.  The instructions and their
    respective input and output parameters are summarized in Table X.4.

      Instruction    Inputs  Output   Description
      -----------    ------  ------   --------------------------------
      ABS(*)         v       v        absolute value
      ADD            v,v     v        add
      ARL            v       as       address register load
      DP3            v,v     ssss     3-component dot product
      DP4            v,v     ssss     4-component dot product
      DPH(*)         v,v     ssss     homogeneous dot product
      DST            v,v     v        distance vector
      EXP            s       v        exponential base 2 (approximate)
      LIT            v       v        compute light coefficients
      LOG            s       v        logarithm base 2 (approximate)
      MAD            v,v,v   v        multiply and add
      MAX            v,v     v        maximum
      MIN            v,v     v        minimum
      MOV            v       v        move
      MUL            v,v     v        multiply
      RCC(*)         s       ssss     reciprocal (clamped)
      RCP            s       ssss     reciprocal
      RSQ            s       ssss     reciprocal square root
      SGE            v,v     v        set on greater than or equal
      SLT            v,v     v        set on less than
      SUB(*)         v,v     v        subtract

    Table X.4:  Summary of vertex program instructions in the VP1 execution
    environment.  "v" indicates a floating-point vector input or output, "s"
    indicates a floating-point scalar input, "ssss" indicates a scalar output
    replicated across a 4-component vector, "as" indicates a single component
    of an address register.


    In the VP2 execution environment, are thirty-nine vertex program
    instructions.  Vertex program instructions may have an optional suffix of
    "C" to allow an update of the condition code register (section 2.14.1.6).
    For example, there are two instructions to perform vector addition, "ADD"
    and "ADDC".  The vertex program instructions available in the VP2
    execution environment and their respective input and output parameters are
    summarized in Table X.5.

      Instruction    Inputs  Output   Description
      -----------    ------  ------   --------------------------------
      ABS[C]         v       v        absolute value
      ADD[C]         v,v     v        add
      ARA[C]         av      av       address register add
      ARL[C]         v       av       address register load
      ARR[C]         v       av       address register load (with round)
      BRA            as      none     branch
      CAL            as      none     subroutine call
      COS[C]         s       ssss     cosine
      DP3[C]         v,v     ssss     3-component dot product
      DP4[C]         v,v     ssss     4-component dot product
      DPH[C]         v,v     ssss     homogeneous dot product
      DST[C]         v,v     v        distance vector
      EX2[C]         s       ssss     exponential base 2
      EXP[C]         s       v        exponential base 2 (approximate)
      FLR[C]         v       v        floor
      FRC[C]         v       v        fraction
      LG2[C]         s       ssss     logarithm base 2
      LIT[C]         v       v        compute light coefficients
      LOG[C]         s       v        logarithm base 2 (approximate)
      MAD[C]         v,v,v   v        multiply and add
      MAX[C]         v,v     v        maximum
      MIN[C]         v,v     v        minimum
      MOV[C]         v       v        move
      MUL[C]         v,v     v        multiply
      RCC[C]         s       ssss     reciprocal (clamped)
      RCP[C]         s       ssss     reciprocal
      RET            none    none     subroutine call return
      RSQ[C]         s       ssss     reciprocal square root
      SEQ[C]         v,v     v        set on equal
      SFL[C]         v,v     v        set on false
      SGE[C]         v,v     v        set on greater than or equal
      SGT[C]         v,v     v        set on greater than
      SIN[C]         s       ssss     sine
      SLE[C]         v,v     v        set on less than or equal
      SLT[C]         v,v     v        set on less than
      SNE[C]         v,v     v        set on not equal
      SSG[C]         v       v        set sign
      STR[C]         v,v     v        set on true
      SUB[C]         v,v     v        subtract

    Table X.5:  Summary of vertex program instructions in the VP2 execution
    environment.  "v" indicates a floating-point vector input or output, "s"
    indicates a floating-point scalar input, "ssss" indicates a scalar output
    replicated across a 4-component vector, "av" indicates a full address
    register, "as" indicates a single component of an address register.


    Section 2.14.2.1,  Vertex Program Operands

    Most vertex program instructions operate on floating-point vectors,
    floating-point scalars, or integer scalars as, indicated in the grammar
    (see section 2.14.1.8) by the rules <vectorSrc>, <scalarSrc>, and
    <scalarAddr>, respectively.

    The basic set of floating-point scalar operands is defined by the grammar
    rule <baseScalarSrc>.  Scalar operands are single components of vertex
    attribute, program parameter, or temporary registers, as allowed by the
    <srcRegister> rule.  A vector component is selected by the <scalarSuffix>
    rule, where the characters "x", "y", "z", and "w" select the x, y, z, and
    w components, respectively, of the vector.

    The basic set of floating-point vector operands is defined by the grammar
    rule <baseVectorSrc>.  Vector operands can be obtained from vertex
    attribute, program parameter, or temporary registers as allowed by the
    <srcRegister> rule.

    Basic vector operands can be swizzled according to the <swizzleSuffix>
    rule.  In its most general form, the <swizzleSuffix> rule matches the
    pattern ".????" where each question mark is replaced with one of "x", "y",
    "z", or "w".  For such patterns, the x, y, z, and w components of the
    operand are taken from the vector components named by the first, second,
    third, and fourth character of the pattern, respectively.  For example, if
    the swizzle suffix is ".yzzx" and the specified source contains {2,8,9,0},
    the swizzled operand used by the instruction is {8,9,9,2}.  

    If the <swizzleSuffix> rule matches "", it is treated as though it were
    ".xyzw".  If the <swizzleSuffix> rule matches (ignoring whitespace) ".x",
    ".y", ".z", or ".w", these are treated the same as ".xxxx", ".yyyy",
    ".zzzz", and ".wwww" respectively.

    Floating-point scalar or vector operands can optionally be negated
    according to the <negate> rules in <baseScalarSrc> and <baseVectorSrc>.
    If the <negate> matches "-", each operand or operand component is negated.

    In the VP2 execution environment, a component-wise absolute value
    operation is performed on an operand if the <scalarSrc> or <vectorSrc>
    rules match <vp2-absScalarSrc> or <vp2-absVectorSrc>.  In this case, the
    absolute value of each component of the operand is taken.  In addition, if
    the <negate> rule in <vp2-absScalarSrc> or <vp2-absVectorSrc> matches "-",
    each component is subsequently negated.

    Integer scalar operands are single components of one of the address
    register vectors, as identified by the <addrRegister> rule.  A vector
    component is selected by the <scalarSuffix> rule in the same manner as
    floating-point scalar operands.  Negation and absolute value operations
    are not available for integer scalar operands.

    The following pseudo-code spells out the operand generation process.  In
    the pseudo-code, "float" and "int" are floating-point and integer scalar
    types, while "floatVec" and "intVec" are four-component vectors.  "source"
    is the register used for the operand, matching the <srcRegister> or
    <addrRegister> rules.  "absolute" is TRUE if the operand matches the
    <vp2-absScalarSrc> or <vp2-absVectorSrc> rules, and FALSE otherwise.
    "negateBase" is TRUE if the <negate> rule in <baseScalarSrc> or
    <baseVectorSrc> matches "-" and FALSE otherwise.  "negateAbs" is TRUE if
    the <negate> rule in <vp2-absScalarSrc> or <vp2-absVectorSrc> matches "-"
    and FALSE otherwise.  The ".c***", ".*c**", ".**c*", ".***c" modifiers
    refer to the x, y, z, and w components obtained by the swizzle operation.

      floatVec VectorLoad(floatVec source)
      {
          floatVec operand;

          operand.x = source.c***;
          operand.y = source.*c**;
          operand.z = source.**c*;
          operand.w = source.***c;
          if (negateBase) {
             operand.x = -operand.x;
             operand.y = -operand.y;
             operand.z = -operand.z;
             operand.w = -operand.w;
          }
          if (absolute) {
             operand.x = abs(operand.x);
             operand.y = abs(operand.y);
             operand.z = abs(operand.z);
             operand.w = abs(operand.w);
          }
          if (negateAbs) {
             operand.x = -operand.x;
             operand.y = -operand.y;
             operand.z = -operand.z;
             operand.w = -operand.w;
          }

          return operand;
      }

      float ScalarLoad(floatVec source) 
      {
          float operand;

          operand = source.c***;
          if (negateBase) {
            operand = -operand;
          }
          if (absolute) {
             operand = abs(operand);
          }
          if (negateAbs) {
            operand = -operand;
          }

          return operand;
      }

      intVec AddrVectorLoad(intVec addrReg)
      {
          intVec operand;

          operand.x = source.c***;
          operand.y = source.*c**;
          operand.z = source.**c*;
          operand.w = source.***c;

          return operand;
      }

      int AddrScalarLoad(intVec addrReg)
      {
          return source.c***;
      }

    If an operand is obtained from a program parameter register, by matching
    the <progParamRegister> rule, the register number can be obtained by
    absolute or relative addressing.  

    When absolute addressing is used, by matching the <absProgParamReg> rule,
    the program parameter register number is the number matching the
    <progParamRegNum>.

    When relative addressing is used, by matching the <relProgParamReg> rule,
    the program parameter register number is computed during program
    execution.  An index is computed by adding the integer scalar operand
    specified by the <scalarAddr> rule to the positive or negative offset
    specified by the <progParamOffset> rule.  If <progParamOffset> matches "",
    an offset of zero is used.

    The following pseudo-code spells out the process of loading a program
    parameter.  "addrReg" refers to the address register used for relative
    addressing, "absolute" is TRUE if the operand uses absolute addressing and
    FALSE otherwise.  "paramNumber" is the program parameter number for
    absolute addressing; "paramOffset" is the program parameter offset for
    relative addressing.  "paramRegiser" is an array holding the complete set
    of program parameter registers.

      floatVec ProgramParameterLoad(intVec addrReg)
      {
        int index;
        
        if (absolute) {
          index = paramNumber;
        } else {
          index = AddrScalarLoad(addrReg) + paramOffset
        }

        return paramRegister[index];
      }


    Section 2.14.2.2,  Vertex Program Destination Register Update

    Most vertex program instructions write a 4-component result vector to a
    single temporary, vertex result, or address register.  Writes to
    individual components of the destination register are controlled by
    individual component write masks specified as part of the instruction.  In
    the VP2 execution environment, writes are additionally controlled by the a
    condition code write mask, which is computed at run time.

    The component write mask is specified by the <optionalWriteMask> rule
    found in the <maskedDstReg> or <maskedAddrReg> rule.  If the optional mask
    is "", all components are enabled.  Otherwise, the optional mask names the
    individual components to enable.  The characters "x", "y", "z", and "w"
    match the x, y, z, and w components respectively.  For example, an
    optional mask of ".xzw" indicates that the x, z, and w components should
    be enabled for writing but the y component should not.  The grammar
    requires that the destination register mask components must be listed in
    "xyzw" order.

    In the VP2 execution environment, the condition code write mask is
    specified by the <optionalCCMask> rule found in the <maskedDstReg> and
    <maskedAddrReg> rules.  If the condition code mask matches "", all
    components are enabled.  Otherwise, the condition code register is loaded
    and swizzled according to the swizzle codes specified by <swizzleSuffix>.
    Each component of the swizzled condition code is tested according to the
    rule given by <ccMaskRule>.  <ccMaskRule> may have the values "EQ", "NE",
    "LT", "GE", LE", or "GT", which mean to enable writes if the corresponding
    condition code field evaluates to equal, not equal, less than, greater
    than or equal, less than or equal, or greater than, respectively.
    Comparisons involving condition codes of "UN" (unordered) evaluate to true
    for "NE" and false otherwise.  For example, if the condition code is
    (GT,LT,EQ,GT) and the condition code mask is "(NE.zyxw)", the swizzle
    operation will load (EQ,LT,GT,GT) and the mask will thus will enable
    writes on the y, z, and w components.  In addition, "TR" always enables
    writes and "FL" always disables writes, regardless of the condition code.

    Each component of the destination register is updated with the result of
    the vertex program instruction if and only if the component is enabled for
    writes by the component write mask, and the optional condition code mask
    (if applicable).  Otherwise, the component of the destination register
    remains unchanged.

    In the VP2 execution environment, a vertex program instruction can also
    optionally update the condition code register.  The condition code is
    updated if the condition code register update suffix "C" is present in the
    instruction.  The instruction "ADDC" will update the condition code; the
    otherwise equivalent instruction "ADD" will not.  If condition code
    updates are enabled, each component of the destination register enabled
    for writes is compared to zero.  The corresponding component of the
    condition code is set to "LT", "EQ", or "GT", if the written component is
    less than, equal to, or greater than zero, respectively.  Condition code
    components are set to "UN" if the written component is NaN.  Values of
    -0.0 and +0.0 both evaluate to "EQ".  If a component of the destination
    register is not enabled for writes, the corresponding condition code
    component is also unchanged.

    In the following example code,

        # R1=(-2, 0, 2, NaN)              R0                  CC
        MOVC R0, R1;               # ( -2,  0,   2, NaN) (LT,EQ,GT,UN)
        MOVC R0.xyz, R1.yzwx;      # (  0,  2, NaN, NaN) (EQ,GT,UN,UN)
        MOVC R0 (NE), R1.zywx;     # (  0,  0, NaN,  -2) (EQ,EQ,UN,LT)

    the first instruction writes (-2,0,2,NaN) to R0 and updates the condition
    code to (LT,EQ,GT,UN).  The second instruction, only the "x", "y", and "z"
    components of R0 and the condition code are updated, so R0 ends up with
    (0,2,NaN,NaN) and the condition code ends up with (EQ,GT,UN,UN).  In the
    third instruction, the condition code mask disables writes to the x
    component (its condition code field is "EQ"), so R0 ends up with
    (0,0,NaN,-2) and the condition code ends up with (EQ,EQ,UN,LT).

    The following pseudocode illustrates the process of writing a result
    vector to the destination register.  In the pseudocode, "instrmask" refers
    to the component write mask given by the <optionalWriteMask> rule.  In the
    VP1 execution environment, "ccMaskRule" is always "" and "updatecc" is
    always FALSE.  In the VP2 execution environment, "ccMaskRule" refers to
    the condition code mask rule given by <vp2-optionalCCMask> and "updatecc"
    is TRUE if and only if condition code updates are enabled.  "result",
    "destination", and "cc" refer to the result vector, the register selected
    by <dstRegister> and the condition code, respectively.  Condition codes do
    not exist in the VP1 execution environment.

      boolean TestCC(CondCode field) {
          switch (ccMaskRule) {
          case "EQ":  return (field == "EQ");
          case "NE":  return (field != "EQ");
          case "LT":  return (field == "LT");
          case "GE":  return (field == "GT" || field == "EQ");
          case "LE":  return (field == "LT" || field == "EQ");
          case "GT":  return (field == "GT");
          case "TR":  return TRUE;
          case "FL":  return FALSE;
          case "":    return TRUE;
          }
      }

      enum GenerateCC(float value) {
        if (value == NaN) {
          return UN;
        } else if (value < 0) {
          return LT;
        } else if (value == 0) {
          return EQ;
        } else {
          return GT;
        }
      }

      void UpdateDestination(floatVec destination, floatVec result)
      {
          floatVec merged;
          ccVec    mergedCC;

          // Merge the converted result into the destination register, under
          // control of the compile- and run-time write masks.
          merged = destination;
          mergedCC = cc;
          if (instrMask.x && TestCC(cc.c***)) {
              merged.x = result.x;
              if (updatecc) mergedCC.x = GenerateCC(result.x);
          }
          if (instrMask.y && TestCC(cc.*c**)) {
              merged.y = result.y;
              if (updatecc) mergedCC.y = GenerateCC(result.y);
          }
          if (instrMask.z && TestCC(cc.**c*)) {
              merged.z = result.z;
              if (updatecc) mergedCC.z = GenerateCC(result.z);
          }
          if (instrMask.w && TestCC(cc.***c)) {
              merged.w = result.w;
              if (updatecc) mergedCC.w = GenerateCC(result.w);
          }

          // Write out the new destination register and condition code.
          destination = merged;
          cc = mergedCC;
      }

    Section 2.14.2.3, Vertex Program Execution

    In the VP1 execution environment, vertex programs consist of a sequence of
    instructions without no support for branching.  Vertex programs begin by
    executing the first instruction in the program, and execute instructions
    in the order specified in the program until the last instruction is
    reached.

    VP2 vertex programs can contain one or more instruction labels, matching
    the grammar rule <vp2-instructionLabel>.  An instruction label can be
    referred to explicitly in branch (BRA) or subroutine call (CAL)
    instructions.  Instruction labels can be defined or used at any point in
    the body of a program, and can be used in instructions before being
    defined in the program string.

    VP2 vertex program branching instructions can be conditional.  The branch
    condition is specified by the <vp2-conditionMask> and may depend on the
    contents of the condition code register.  Branch conditions are evaluated
    by evaluating a condition code write mask in exactly the same manner as
    done for register writes (section 2.14.2.2).  If any of the four
    components of the condition code write mask are enabled, the branch is
    taken and execution continues with the instruction following the label
    specified in the instruction.  Otherwise, the instruction is ignored and
    vertex program execution continues with the next instruction.  In the
    following example code,

        MOVC CC, c[0];         # c[0]=(-2, 0, 2, NaN), CC gets (LT,EQ,GT,UN)
        BRA label1 (LT.xyzw);
        MOV R0,R1;             # not executed
      label1:
        BRA label2 (LT.wyzw);
        MOV R0,R2;             # executed
      label2:

    the first BRA instruction loads a condition code of (LT,EQ,GT,UN) while
    the second BRA instruction loads a condition code of (UN,EQ,GT,UN).  The
    first branch will be taken because the "x" component evaluates to LT; the
    second branch will not be taken because no component evaluates to LT.

    VP2 vertex programs can specify subroutine calls.  When a subroutine call
    (CAL) instruction is executed, a reference to the instruction immediately
    following the CAL instruction is pushed onto the call stack.  When a
    subroutine return (RET) instruction is executed, an instruction reference
    is popped off the call stack and program execution continues with the
    popped instruction.  A vertex program will terminate if a CAL instruction
    is executed with four entries already in the call stack or if a RET
    instruction is executed with an empty call stack.    

    If a VP2 vertex program has an instruction label "main", program execution
    begins with the instruction immediately following the instruction label.
    Otherwise, program execution begins with the first instruction of the
    program.  Instructions will be executed sequentially in the order
    specified in the program, although branch instructions will affect the
    instruction execution order, as described above.  A vertex program will
    terminate after executing a RET instruction with an empty call stack.  A
    vertex program will also terminate after executing the last instruction in
    the program, unless that instruction was a taken branch.

    A vertex program will fail to load if an instruction refers to a label
    that is not defined in the program string.

    A vertex program will terminate abnormally if a subroutine call
    instruction produces a call stack overflow.  Additionally, a vertex
    program will terminate abnormally after executing 65536 instructions to
    prevent hangs caused by infinite loops in the program.

    When a vertex program terminates, normally or abnormally, it will emit a
    vertex whose attributes are taken from the final values of the vertex
    result registers (section 2.14.1.5).


    Section 2.14.3,  Vertex Program Instruction Set

    The following sections describe the set of supported vertex program
    instructions.  Instructions available only in the VP1.1 or VP2 execution
    environment will be noted in the instruction description.  

    Each section will contain pseudocode describing the instruction.
    Instructions will have up to three operands, referred to as "op0", "op1",
    and "op2".  The operands are loaded using the mechanisms specified in
    section 2.14.2.1.  Most instructions will generate a result vector called
    "result".  The result vector is then written to the destination register
    specified in the instruction using the mechanisms specified in section
    2.14.2.2.

    Operands and results are represented as 32-bit single-precision
    floating-point numbers according to the IEEE 754 floating-point
    specification.  IEEE denorm encodings, used to represent numbers smaller
    than 2^-126, are not supported.  All such numbers are flushed to zero.
    There are three special encodings referred to in this section:  +INF means
    "positive infinity", -INF means "negative infinity", and NaN refers to
    "not a number".

    Arithmetic operations are typically carried out in single precision
    according to the rules specified in the IEEE 754 specification.  Any
    exceptions and special cases will be noted in the instruction description.


    Section 2.14.3.1,  ABS:  Absolute Value

    The ABS instruction performs a component-wise absolute value operation on
    the single operand to yield a result vector.

      tmp = VectorLoad(op0); 
      result.x = abs(tmp.x);
      result.y = abs(tmp.y);
      result.z = abs(tmp.z);
      result.w = abs(tmp.w);

    The following special-case rules apply to absolute value operation:

      1. abs(NaN) = NaN.
      2. abs(-INF) = abs(+INF) = +INF.
      3. abs(-0.0) = abs(+0.0) = +0.0.

    The ABS instruction is available only in the VP1.1 and VP2 execution
    environments.  

    In the VP1.0 execution environment, the same functionality can be achieved
    with "MAX result, src, -src".

    In the VP2 execution environment, the ABS instruction is effectively
    obsolete, since instructions can take the absolute value of each operand
    at no cost.


    Section 2.14.3.2,  ADD:  Add

    The ADD instruction performs a component-wise add of the two operands to
    yield a result vector.

      tmp0 = VectorLoad(op0);
      tmp1 = VectorLoad(op1);
      result.x = tmp0.x + tmp1.x;
      result.y = tmp0.y + tmp1.y;
      result.z = tmp0.z + tmp1.z;
      result.w = tmp0.w + tmp1.w;

    The following special-case rules apply to addition:

      1. "A+B" is always equivalent to "B+A".
      2. NaN + <x> = NaN, for all <x>.
      3. +INF + <x> = +INF, for all <x> except NaN and -INF.
      4. -INF + <x> = -INF, for all <x> except NaN and +INF.
      5. +INF + -INF = NaN.
      6. -0.0 + <x> = <x>, for all <x>.
      7. +0.0 + <x> = <x>, for all <x> except -0.0.


    Section 2.14.3.3,  ARA:  Address Register Add

    The ARA instruction adds two pairs of components of a vector address
    register operand to produce an integer result vector.  The "x" and "z"
    components of the result vector contain the sum of the "x" and "z"
    components of the operand; the "y" and "w" components of the result vector
    contain the sum of the "y" and "w" components of the operand.  Each
    component of the result vector is clamped to [-512, +511], the range of
    representable address register components.

      itmp = AddrVectorLoad(op0);
      iresult.x = itmp.x + itmp.z;
      iresult.y = itmp.y + itmp.w;
      iresult.z = itmp.x + itmp.z;
      iresult.w = itmp.y + itmp.w;
      if (iresult.x < -512) iresult.x = -512;
      if (iresult.x > 511)  iresult.x = 511;
      if (iresult.y < -512) iresult.y = -512;
      if (iresult.y > 511)  iresult.y = 511;
      if (iresult.z < -512) iresult.z = -512;
      if (iresult.z > 511)  iresult.z = 511;
      if (iresult.w < -512) iresult.w = -512;
      if (iresult.w > 511)  iresult.w = 511;

    Component swizzling is not supported when the operand is loaded.

    The ARA instruction is available only in the VP2 execution environment.


    Section 2.14.3.4,  ARL:  Address Register Load

    In the VP1 execution environment, the ARL instruction loads a single
    scalar operand and performs a floor operation to generate an integer
    scalar to be written to the address register.

      tmp = ScalarLoad(op0);
      iresult.x = floor(tmp);

    In the VP2 execution environment, the ARL instruction loads a single
    vector operand and performs a component-wise floor operation to generate
    an integer result vector.  Each component of the result vector is clamped
    to [-512, +511], the range of representable address register components.
    The ARL instruction applies all masking operations to address register
    writes as are described in section 2.14.2.2.

      tmp = VectorLoad(op0);
      iresult.x = floor(tmp.x);
      iresult.y = floor(tmp.y);
      iresult.z = floor(tmp.z);
      iresult.w = floor(tmp.w);
      if (iresult.x < -512) iresult.x = -512;
      if (iresult.x > 511)  iresult.x = 511;
      if (iresult.y < -512) iresult.y = -512;
      if (iresult.y > 511)  iresult.y = 511;
      if (iresult.z < -512) iresult.z = -512;
      if (iresult.z > 511)  iresult.z = 511;
      if (iresult.w < -512) iresult.w = -512;
      if (iresult.w > 511)  iresult.w = 511;

    The following special-case rules apply to floor computation:

      1. floor(NaN) = NaN.
      2. floor(<x>) = <x>, for -0.0, +0.0, -INF, and +INF.  In all cases, the
         sign of the result is equal to the sign of the operand.


    Section 2.14.3.5,  ARR:  Address Register Load (with round)

    The ARR instruction loads a single vector operand and performs a
    component-wise round operation to generate an integer result vector.  Each
    component of the result vector is clamped to [-512, +511], the range of
    representable address register components.  The ARR instruction applies
    all masking operations to address register writes as described in section
    2.14.2.2.

      tmp = VectorLoad(op0);
      iresult.x = round(tmp.x);
      iresult.y = round(tmp.y);
      iresult.z = round(tmp.z);
      iresult.w = round(tmp.w);
      if (iresult.x < -512) iresult.x = -512;
      if (iresult.x > 511)  iresult.x = 511;
      if (iresult.y < -512) iresult.y = -512;
      if (iresult.y > 511)  iresult.y = 511;
      if (iresult.z < -512) iresult.z = -512;
      if (iresult.z > 511)  iresult.z = 511;
      if (iresult.w < -512) iresult.w = -512;
      if (iresult.w > 511)  iresult.w = 511;

    The rounding function, round(x), returns the nearest integer to <x>.  If
    the fractional portion of <x> is 0.5, round(x) selects the nearest even
    integer.

    The ARR instruction is available only in the VP2 execution environment.


    Section 2.14.3.6,  BRA:  Branch

    The BRA instruction conditionally transfers control to the instruction
    following the label specified in the instruction.  The following
    pseudocode describes the operation of the instruction:

      if (TestCC(cc.c***) || TestCC(cc.*c**) || 
          TestCC(cc.**c*) || TestCC(cc.***c)) {
        // continue execution at instruction following <branchLabel>
      } else {
        // do nothing
      }

    In the pseudocode, <branchLabel> is the label specified in the instruction
    matching the <vp2-branchLabel> grammar rule.

    The BRA instruction is available only in the VP2 execution environment.


    Section 2.14.3.7,  CAL:  Subroutine Call

    The CAL instruction conditionally transfers control to the instruction
    following the label specified in the instruction.  It also pushes a
    reference to the instruction immediately following the CAL instruction
    onto the call stack, where execution will continue after executing the
    matching RET instruction.  The following pseudocode describes the
    operation of the instruction:

      if (TestCC(cc.c***) || TestCC(cc.*c**) || 
          TestCC(cc.**c*) || TestCC(cc.***c)) {
        if (callStackDepth >= 4) {
          // terminate vertex program
        } else {
          callStack[callStackDepth] = nextInstruction;
          callStackDepth++;
        }
        // continue execution at instruction following <branchLabel>
      } else {
        // do nothing
      }

    In the pseudocode, <branchLabel> is the label specified in the instruction
    matching the <vp2-branchLabel> grammar rule, <callStackDepth> is the
    current depth of the call stack, <callStack> is an array holding the call
    stack, and <nextInstruction> is a reference to the instruction immediately
    following the present one in the program string.
    
    The CAL instruction is available only in the VP2 execution environment.


    Section 2.14.3.8,  COS:  Cosine

    The COS instruction approximates the cosine of the angle specified by the
    scalar operand and replicates the approximation to all four components of
    the result vector.  The angle is specified in radians and does not have to
    be in the range [0,2*PI].

      tmp = ScalarLoad(op0);
      result.x = ApproxCosine(tmp);
      result.y = ApproxCosine(tmp);
      result.z = ApproxCosine(tmp);
      result.w = ApproxCosine(tmp);

    The approximation function ApproxCosine is accurate to at least 22 bits
    with an angle in the range [0,2*PI].

      | ApproxCosine(x) - cos(x) | < 1.0 / 2^22, if 0.0 <= x < 2.0 * PI.

    The error in the approximation will typically increase with the absolute
    value of the angle when the angle falls outside the range [0,2*PI].

    The following special-case rules apply to cosine approximation:

      1. ApproxCosine(NaN) = NaN.
      2. ApproxCosine(+/-INF) = NaN.
      3. ApproxCosine(+/-0.0) = +1.0.

    The COS instruction is available only in the VP2 execution environment.


    Section 2.14.3.9,  DP3:  3-component Dot Product

    The DP3 instruction computes a three component dot product of the two
    operands (using the x, y, and z components) and replicates the dot product
    to all four components of the result vector.

      tmp0 = VectorLoad(op0);
      tmp1 = VectorLoad(op1):
      result.x = (tmp0.x * tmp1.x) + (tmp0.y * tmp1.y) + 
                 (tmp0.z * tmp1.z);
      result.y = (tmp0.x * tmp1.x) + (tmp0.y * tmp1.y) + 
                 (tmp0.z * tmp1.z);
      result.z = (tmp0.x * tmp1.x) + (tmp0.y * tmp1.y) + 
                 (tmp0.z * tmp1.z);
      result.w = (tmp0.x * tmp1.x) + (tmp0.y * tmp1.y) + 
                 (tmp0.z * tmp1.z);


    Section 2.14.3.10,  DP4:  4-component Dot Product

    The DP4 instruction computes a four component dot product of the two
    operands and replicates the dot product to all four components of the
    result vector.

      tmp0 = VectorLoad(op0);
      tmp1 = VectorLoad(op1):
      result.x = (tmp0.x * tmp1.x) + (tmp0.y * tmp1.y) + 
                 (tmp0.z * tmp1.z) + (tmp0.w * tmp1.w);
      result.y = (tmp0.x * tmp1.x) + (tmp0.y * tmp1.y) + 
                 (tmp0.z * tmp1.z) + (tmp0.w * tmp1.w);
      result.z = (tmp0.x * tmp1.x) + (tmp0.y * tmp1.y) + 
                 (tmp0.z * tmp1.z) + (tmp0.w * tmp1.w);
      result.w = (tmp0.x * tmp1.x) + (tmp0.y * tmp1.y) + 
                 (tmp0.z * tmp1.z) + (tmp0.w * tmp1.w);


    Section 2.14.3.11,  DPH:  Homogeneous Dot Product

    The DPH instruction computes a four-component dot product of the two
    operands, except that the W component of the first operand is assumed to
    be 1.0.  The instruction replicates the dot product to all four components
    of the result vector.

      tmp0 = VectorLoad(op0);
      tmp1 = VectorLoad(op1):
      result.x = (tmp0.x * tmp1.x) + (tmp0.y * tmp1.y) + 
                 (tmp0.z * tmp1.z) + tmp1.w;
      result.y = (tmp0.x * tmp1.x) + (tmp0.y * tmp1.y) + 
                 (tmp0.z * tmp1.z) + tmp1.w;
      result.z = (tmp0.x * tmp1.x) + (tmp0.y * tmp1.y) + 
                 (tmp0.z * tmp1.z) + tmp1.w;
      result.w = (tmp0.x * tmp1.x) + (tmp0.y * tmp1.y) + 
                 (tmp0.z * tmp1.z) + tmp1.w;

    The DPH instruction is available only in the VP1.1 and VP2 execution
    environments.


    Section 2.14.3.12,  DST:  Distance Vector

    The DST instruction computes a distance vector from two specially-
    formatted operands.  The first operand should be of the form [NA, d^2,
    d^2, NA] and the second operand should be of the form [NA, 1/d, NA, 1/d],
    where NA values are not relevant to the calculation and d is a vector
    length.  If both vectors satisfy these conditions, the result vector will
    be of the form [1.0, d, d^2, 1/d].

    The exact behavior is specified in the following pseudo-code:

      tmp0 = VectorLoad(op0);
      tmp1 = VectorLoad(op1);
      result.x = 1.0;
      result.y = tmp0.y * tmp1.y;
      result.z = tmp0.z;
      result.w = tmp1.w;

    Given an arbitrary vector, d^2 can be obtained using the DP3 instruction
    (using the same vector for both operands) and 1/d can be obtained from d^2
    using the RSQ instruction.

    This distance vector is useful for per-vertex light attenuation
    calculations:  a DP3 operation using the distance vector and an
    attenuation constants vector as operands will yield the attenuation
    factor.


    Section 2.14.3.13,  EX2:  Exponential Base 2

    The EX2 instruction approximates 2 raised to the power of the scalar
    operand and replicates it to all four components of the result vector.

      tmp = ScalarLoad(op0);
      result.x = Approx2ToX(tmp);
      result.y = Approx2ToX(tmp);
      result.z = Approx2ToX(tmp);
      result.w = Approx2ToX(tmp);

    The approximation function is accurate to at least 22 bits:

      | Approx2ToX(x) - 2^x | < 1.0 / 2^22, if 0.0 <= x < 1.0,

    and, in general,
   
      | Approx2ToX(x) - 2^x | < (1.0 / 2^22) * (2^floor(x)).

    The following special-case rules apply to exponential approximation:

      1. Approx2ToX(NaN) = NaN.
      2. Approx2ToX(-INF) = +0.0.
      3. Approx2ToX(+INF) = +INF.
      4. Approx2ToX(+/-0.0) = +1.0.

    The EX2 instruction is available only in the VP2 execution environment.


    Section 2.14.3.14,  EXP:  Exponential Base 2 (approximate)

    The EXP instruction computes a rough approximation of 2 raised to the
    power of the scalar operand.  The approximation is returned in the "z"
    component of the result vector.  A vertex program can also use the "x" and
    "y" components of the result vector to generate a more accurate
    approximation by evaluating

        result.x * f(result.y),
    
    where f(x) is a user-defined function that approximates 2^x over the
    domain [0.0, 1.0).  The "w" component of the result vector is always 1.0.
    
    The exact behavior is specified in the following pseudo-code:

      tmp = ScalarLoad(op0);
      result.x = 2^floor(tmp);
      result.y = tmp - floor(tmp);
      result.z = RoughApprox2ToX(tmp);
      result.w = 1.0;

    The approximation function is accurate to at least 11 bits:

      | RoughApprox2ToX(x) - 2^x | < 1.0 / 2^11, if 0.0 <= x < 1.0,

    and, in general,
   
      | RoughApprox2ToX(x) - 2^x | < (1.0 / 2^11) * (2^floor(x)).

    The following special cases apply to the EXP instruction:

      1. RoughApprox2ToX(NaN) = NaN.
      2. RoughApprox2ToX(-INF) = +0.0.
      3. RoughApprox2ToX(+INF) = +INF.
      4. RoughApprox2ToX(+/-0.0) = +1.0.

    The EXP instruction is present for compatibility with the original
    NV_vertex_program instruction set; it is recommended that applications
    using NV_vertex_program2 use the EX2 instruction instead.


    Section 2.14.3.15,  FLR:  Floor

    The FLR instruction performs a component-wise floor operation on the
    operand to generate a result vector.  The floor of a value is defined as
    the largest integer less than or equal to the value.  The floor of 2.3 is
    2.0; the floor of -3.6 is -4.0.

      tmp = VectorLoad(op0);
      result.x = floor(tmp.x);
      result.y = floor(tmp.y);
      result.z = floor(tmp.z);
      result.w = floor(tmp.w);

    The following special-case rules apply to floor computation:

      1. floor(NaN) = NaN.
      2. floor(<x>) = <x>, for -0.0, +0.0, -INF, and +INF.  In all cases, the
         sign of the result is equal to the sign of the operand.

    The FLR instruction is available only in the VP2 execution environment.


    Section 2.14.3.16,  FRC:  Fraction

    The FRC instruction extracts the fractional portion of each component of
    the operand to generate a result vector.  The fractional portion of a
    component is defined as the result after subtracting off the floor of the
    component (see FLR), and is always in the range [0.00, 1.00).

    For negative values, the fractional portion is NOT the number written to
    the right of the decimal point -- the fractional portion of -1.7 is not
    0.7 -- it is 0.3.  0.3 is produced by subtracting the floor of -1.7 (-2.0)
    from -1.7.

      tmp = VectorLoad(op0);
      result.x = tmp.x - floor(tmp.x);
      result.y = tmp.y - floor(tmp.y);
      result.z = tmp.z - floor(tmp.z);
      result.w = tmp.w - floor(tmp.w);

    The following special-case rules, which can be derived from the rules for
    FLR and ADD apply to fraction computation:

      1. fraction(NaN) = NaN.
      2. fraction(+/-INF) = NaN.
      3. fraction(+/-0.0) = +0.0.

    The FRC instruction is available only in the VP2 execution environment.


    Section 2.14.3.17,  LG2:  Logarithm Base 2

    The LG2 instruction approximates the base 2 logarithm of the scalar
    operand and replicates it to all four components of the result vector.

      tmp = ScalarLoad(op0);
      result.x = ApproxLog2(tmp);
      result.y = ApproxLog2(tmp);
      result.z = ApproxLog2(tmp);
      result.w = ApproxLog2(tmp);
   
    The approximation function is accurate to at least 22 bits:

      | ApproxLog2(x) - log_2(x) | < 1.0 / 2^22.

    Note that for large values of x, there are not enough bits in the
    floating-point storage format to represent a result that precisely.

    The following special-case rules apply to logarithm approximation:

      1. ApproxLog2(NaN) = NaN.
      2. ApproxLog2(+INF) = +INF.
      3. ApproxLog2(+/-0.0) = -INF.
      4. ApproxLog2(x) = NaN, -INF < x < -0.0.
      5. ApproxLog2(-INF) = NaN.

    The LG2 instruction is available only in the VP2 execution environment.


    Section 2.14.3.18,  LIT:  Compute Light Coefficients

    The LIT instruction accelerates per-vertex lighting by computing lighting
    coefficients for ambient, diffuse, and specular light contributions.  The
    "x" component of the operand is assumed to hold a diffuse dot product (n
    dot VP_pli, as in the vertex lighting equations in Section 2.13.1).  The
    "y" component of the operand is assumed to hold a specular dot product (n
    dot h_i).  The "w" component of the operand is assumed to hold the
    specular exponent of the material (s_rm), and is clamped to the range
    (-128, +128) exclusive.

    The "x" component of the result vector receives the value that should be
    multiplied by the ambient light/material product (always 1.0).  The "y"
    component of the result vector receives the value that should be
    multiplied by the diffuse light/material product (n dot VP_pli).  The "z"
    component of the result vector receives the value that should be
    multiplied by the specular light/material product (f_i * (n dot h_i) ^
    s_rm).  The "w" component of the result is the constant 1.0.

    Negative diffuse and specular dot products are clamped to 0.0, as is done
    in the standard per-vertex lighting operations.  In addition, if the
    diffuse dot product is zero or negative, the specular coefficient is
    forced to zero.

      tmp = VectorLoad(op0);
      if (t.x < 0) t.x = 0;
      if (t.y < 0) t.y = 0;
      if (t.w < -(128.0-epsilon)) t.w = -(128.0-epsilon);
      else if (t.w > 128-epsilon) t.w = 128-epsilon;
      result.x = 1.0;
      result.y = t.x;
      result.z = (t.x > 0) ? RoughApproxPower(t.y, t.w) : 0.0;
      result.w = 1.0;

    The exponentiation approximation function is defined in terms of the base
    2 exponentiation and logarithm approximation operations in the EXP and LOG
    instructions, including errors and the processing of any special cases.
    In particular,

      RoughApproxPower(a,b) = RoughApproxExp2(b * RoughApproxLog2(a)).

    The following special-case rules, which can be derived from the rules in
    the LOG, MUL, and EXP instructions, apply to exponentiation:

      1. RoughApproxPower(NaN, <x>) = NaN,
      2. RoughApproxPower(<x>, <y>) = NaN, if x <= -0.0,
      3. RoughApproxPower(+/-0.0, <x>) = +0.0, if x > +0.0, or
                                         +INF, if x < -0.0,
      4. RoughApproxPower(+1.0, <x>) = +1.0, if x is not NaN,
      5. RoughApproxPower(+INF, <x>) = +INF, if x > +0.0, or
                                       +0.0, if x < -0.0,
      6. RoughApproxPower(<x>, +/-0.0) = +1.0, if x >= -0.0
      7. RoughApproxPower(<x>, +INF) = +0.0, if -0.0 <= x < +1.0,
                                       +INF, if x > +1.0,
      8. RoughApproxPower(<x>, +INF) = +INF, if -0.0 <= x < +1.0,
                                       +0.0, if x > +1.0,
      9. RoughApproxPower(<x>, +1.0) = <x>, if x >= +0.0, and
      10. RoughApproxPower(<x>, NaN) = NaN.


    Section 2.14.3.19,  LOG:  Logarithm Base 2 (Approximate)

    The LOG instruction computes a rough approximation of the base 2 logarithm
    of the absolute value of the scalar operand.  The approximation is
    returned in the "z" component of the result vector.  A vertex program can
    also use the "x" and "y" components of the result vector to generate a
    more accurate approximation by evaluating

        result.x + f(result.y),
    
    where f(x) is a user-defined function that approximates 2^x over the
    domain [1.0, 2.0).  The "w" component of the result vector is always 1.0.

    The exact behavior is specified in the following pseudo-code:

      tmp = fabs(ScalarLoad(op0));
      result.x = floor(log2(tmp));
      result.y = tmp / (2^floor(log2(tmp)));
      result.z = RoughApproxLog2(tmp);
      result.w = 1.0;
   
    The approximation function is accurate to at least 11 bits:

      | RoughApproxLog2(x) - log_2(x) | < 1.0 / 2^11.

    The following special-case rules apply to the LOG instruction:

      1. RoughApproxLog2(NaN) = NaN.
      2. RoughApproxLog2(+INF) = +INF.
      3. RoughApproxLog2(+0.0) = -INF.

    The LOG instruction is present for compatibility with the original
    NV_vertex_program instruction set; it is recommended that applications
    using NV_vertex_program2 use the LG2 instruction instead.


    Section 2.14.3.20,  MAD:  Multiply And Add

    The MAD instruction performs a component-wise multiply of the first two
    operands, and then does a component-wise add of the product to the third
    operand to yield a result vector.

      tmp0 = VectorLoad(op0);
      tmp1 = VectorLoad(op1);
      tmp2 = VectorLoad(op2);
      result.x = tmp0.x * tmp1.x + tmp2.x;
      result.y = tmp0.y * tmp1.y + tmp2.y;
      result.z = tmp0.z * tmp1.z + tmp2.z;
      result.w = tmp0.w * tmp1.w + tmp2.w;

    All special case rules applicable to the ADD and MUL instructions apply to
    the individual components of the MAD operation as well.


    Section 2.14.3.21,  MAX:  Maximum

    The MAX instruction computes component-wise maximums of the values in the
    two operands to yield a result vector.

      tmp0 = VectorLoad(op0);
      tmp1 = VectorLoad(op1);
      result.x = max(tmp0.x, tmp1.x);
      result.y = max(tmp0.y, tmp1.y);
      result.z = max(tmp0.z, tmp1.z);
      result.w = max(tmp0.w, tmp1.w);

    The following special cases apply to the maximum operation:

      1. max(A,B) is always equivalent to max(B,A).
      2. max(NaN, <x>) == NaN, for all <x>.


    Section 2.14.3.22,  MIN:  Minimum

    The MIN instruction computes component-wise minimums of the values in the
    two operands to yield a result vector.

      tmp0 = VectorLoad(op0);
      tmp1 = VectorLoad(op1);
      result.x = min(tmp0.x, tmp1.x);
      result.y = min(tmp0.y, tmp1.y);
      result.z = min(tmp0.z, tmp1.z);
      result.w = min(tmp0.w, tmp1.w);

    The following special cases apply to the minimum operation:

      1. min(A,B) is always equivalent to min(B,A).
      2. min(NaN, <x>) == NaN, for all <x>.


    Section 2.14.3.23,  MOV:  Move

    The MOV instruction copies the value of the operand to yield a result
    vector.

      result = VectorLoad(op0);


    Section 2.14.3.24,  MUL:  Multiply

    The MUL instruction performs a component-wise multiply of the two operands
    to yield a result vector.

      tmp0 = VectorLoad(op0);
      tmp1 = VectorLoad(op1);
      result.x = tmp0.x * tmp1.x;
      result.y = tmp0.y * tmp1.y;
      result.z = tmp0.z * tmp1.z;
      result.w = tmp0.w * tmp1.w;

    The following special-case rules apply to multiplication:

      1. "A*B" is always equivalent to "B*A".
      2. NaN * <x> = NaN, for all <x>.
      3. +/-0.0 * +/-INF = NaN.
      4. +/-0.0 * <x> = +/-0.0, for all <x> except -INF, +INF, and NaN.  The
         sign of the result is positive if the signs of the two operands match
         and negative otherwise.
      5. +/-INF * <x> = +/-INF, for all <x> except -0.0, +0.0, and NaN.  The 
         sign of the result is positive if the signs of the two operands match
         and negative otherwise.
      6. +1.0 * <x> = <x>, for all <x>.


    Section 2.14.3.25,  RCC:  Reciprocal (Clamped)

    The RCC instruction approximates the reciprocal of the scalar operand,
    clamps the result to one of two ranges, and replicates the clamped result
    to all four components of the result vector.

    If the approximate reciprocal is greater than 0.0, the result is clamped
    to the range [2^-64, 2^+64].  If the approximate reciprocal is not greater
    than zero, the result is clamped to the range [-2^+64, -2^-64].

      tmp = ScalarLoad(op0);
      result.x = ClampApproxReciprocal(tmp);
      result.y = ClampApproxReciprocal(tmp);
      result.z = ClampApproxReciprocal(tmp);
      result.w = ClampApproxReciprocal(tmp);

    The approximation function is accurate to at least 22 bits:

      | ClampApproxReciprocal(x) - (1/x) | < 1.0 / 2^22, if 1.0 <= x < 2.0.

    The following special-case rules apply to reciprocation:

      1. ClampApproxReciprocal(NaN) = NaN.
      2. ClampApproxReciprocal(+INF) = +2^-64.
      3. ClampApproxReciprocal(-INF) = -2^-64.
      4. ClampApproxReciprocal(+0.0) = +2^64.
      5. ClampApproxReciprocal(-0.0) = -2^64.
      6. ClampApproxReciprocal(x) = +2^-64, if -2^64 < x < +INF.
      7. ClampApproxReciprocal(x) = -2^-64, if -INF < x < -2^-64.
      8. ClampApproxReciprocal(x) = +2^64, if +0.0 < x < +2^-64.
      9. ClampApproxReciprocal(x) = -2^64, if -2^-64 < x < -0.0.

    The RCC instruction is available only in the VP1.1 and VP2 execution
    environments.


    Section 2.14.3.26,  RCP:  Reciprocal

    The RCP instruction approximates the reciprocal of the scalar operand and
    replicates it to all four components of the result vector.

      tmp = ScalarLoad(op0);
      result.x = ApproxReciprocal(tmp);
      result.y = ApproxReciprocal(tmp);
      result.z = ApproxReciprocal(tmp);
      result.w = ApproxReciprocal(tmp);

    The approximation function is accurate to at least 22 bits:

      | ApproxReciprocal(x) - (1/x) | < 1.0 / 2^22, if 1.0 <= x < 2.0.

    The following special-case rules apply to reciprocation:

      1. ApproxReciprocal(NaN) = NaN.
      2. ApproxReciprocal(+INF) = +0.0.
      3. ApproxReciprocal(-INF) = -0.0.
      4. ApproxReciprocal(+0.0) = +INF.
      5. ApproxReciprocal(-0.0) = -INF.


    Section 2.14.3.27,  RET:  Subroutine Call Return

    The RET instruction conditionally returns from a subroutine initiated by a
    CAL instruction by popping an instruction reference off the top of the
    call stack and transferring control to the referenced instruction.  The
    following pseudocode describes the operation of the instruction:

      if (TestCC(cc.c***) || TestCC(cc.*c**) || 
          TestCC(cc.**c*) || TestCC(cc.***c)) {
        if (callStackDepth <= 0) {
          // terminate vertex program
        } else {
          callStackDepth--;
          instruction = callStack[callStackDepth];
        }

        // continue execution at <instruction>
      } else {
        // do nothing
      }

    In the pseudocode, <callStackDepth> is the depth of the call stack,
    <callStack> is an array holding the call stack, and <instruction> is a
    reference to an instruction previously pushed onto the call stack.
    
    The RET instruction is available only in the VP2 execution environment.


    Section 2.14.3.28,  RSQ:  Reciprocal Square Root

    The RSQ instruction approximates the reciprocal of the square root of the
    scalar operand and replicates it to all four components of the result
    vector.

      tmp = ScalarLoad(op0);
      result.x = ApproxRSQRT(tmp);
      result.y = ApproxRSQRT(tmp);
      result.z = ApproxRSQRT(tmp);
      result.w = ApproxRSQRT(tmp);

    The approximation function is accurate to at least 22 bits:

      | ApproxRSQRT(x) - (1/x) | < 1.0 / 2^22, if 1.0 <= x < 4.0.

    The following special-case rules apply to reciprocal square roots:

      1. ApproxRSQRT(NaN) = NaN.
      2. ApproxRSQRT(+INF) = +0.0.
      3. ApproxRSQRT(-INF) = NaN.
      4. ApproxRSQRT(+0.0) = +INF.
      5. ApproxRSQRT(-0.0) = -INF.
      6. ApproxRSQRT(x) = NaN, if -INF < x < -0.0.


    Section 2.14.3.29,  SEQ:  Set on Equal

    The SEQ instruction performs a component-wise comparison of the two
    operands.  Each component of the result vector is 1.0 if the corresponding
    component of the first operand is equal to that of the second, and 0.0
    otherwise.

      tmp0 = VectorLoad(op0);
      tmp1 = VectorLoad(op1);
      result.x = (tmp0.x == tmp1.x) ? 1.0 : 0.0;
      result.y = (tmp0.y == tmp1.y) ? 1.0 : 0.0;
      result.z = (tmp0.z == tmp1.z) ? 1.0 : 0.0;
      result.w = (tmp0.w == tmp1.w) ? 1.0 : 0.0;
      if (tmp0.x is NaN or tmp1.x is NaN) result.x = NaN;
      if (tmp0.y is NaN or tmp1.y is NaN) result.y = NaN;
      if (tmp0.z is NaN or tmp1.z is NaN) result.z = NaN;
      if (tmp0.w is NaN or tmp1.w is NaN) result.w = NaN;

    The following special-case rules apply to SEQ:

      1. (<x> == <y>) and (<y> == <x>) always produce the same result.
      1. (NaN == <x>) is FALSE for all <x>, including NaN.
      2. (+INF == +INF) and (-INF == -INF) are TRUE.
      3. (-0.0 == +0.0) and (+0.0 == -0.0) are TRUE.

    The SEQ instruction is available only in the VP2 execution environment.


    Section 2.14.3.30,  SFL:  Set on False

    The SFL instruction is a degenerate case of the other "Set on"
    instructions that sets all components of the result vector to
    0.0.

      result.x = 0.0;
      result.y = 0.0;
      result.z = 0.0;
      result.w = 0.0;

    The SFL instruction is available only in the VP2 execution environment.


    Section 2.14.3.31,  SGE:  Set on Greater Than or Equal

    The SGE instruction performs a component-wise comparison of the two
    operands.  Each component of the result vector is 1.0 if the corresponding
    component of the first operands is greater than or equal that of the
    second, and 0.0 otherwise.

      tmp0 = VectorLoad(op0);
      tmp1 = VectorLoad(op1);
      result.x = (tmp0.x >= tmp1.x) ? 1.0 : 0.0;
      result.y = (tmp0.y >= tmp1.y) ? 1.0 : 0.0;
      result.z = (tmp0.z >= tmp1.z) ? 1.0 : 0.0;
      result.w = (tmp0.w >= tmp1.w) ? 1.0 : 0.0;
      if (tmp0.x is NaN or tmp1.x is NaN) result.x = NaN;
      if (tmp0.y is NaN or tmp1.y is NaN) result.y = NaN;
      if (tmp0.z is NaN or tmp1.z is NaN) result.z = NaN;
      if (tmp0.w is NaN or tmp1.w is NaN) result.w = NaN;

    The following special-case rules apply to SGE:

      1. (NaN >= <x>) and (<x> >= NaN) are FALSE for all <x>.
      2. (+INF >= +INF) and (-INF >= -INF) are TRUE.
      3. (-0.0 >= +0.0) and (+0.0 >= -0.0) are TRUE.


    Section 2.14.3.32,  SGT:  Set on Greater Than

    The SGT instruction performs a component-wise comparison of the two
    operands.  Each component of the result vector is 1.0 if the corresponding
    component of the first operands is greater than that of the second, and
    0.0 otherwise.

      tmp0 = VectorLoad(op0);
      tmp1 = VectorLoad(op1);
      result.x = (tmp0.x > tmp1.x) ? 1.0 : 0.0;
      result.y = (tmp0.y > tmp1.y) ? 1.0 : 0.0;
      result.z = (tmp0.z > tmp1.z) ? 1.0 : 0.0;
      result.w = (tmp0.w > tmp1.w) ? 1.0 : 0.0;
      if (tmp0.x is NaN or tmp1.x is NaN) result.x = NaN;
      if (tmp0.y is NaN or tmp1.y is NaN) result.y = NaN;
      if (tmp0.z is NaN or tmp1.z is NaN) result.z = NaN;
      if (tmp0.w is NaN or tmp1.w is NaN) result.w = NaN;

    The following special-case rules apply to SGT:

      1. (NaN > <x>) and (<x> > NaN) are FALSE for all <x>.
      2. (-0.0 > +0.0) and (+0.0 > -0.0) are FALSE.

    The SGT instruction is available only in the VP2 execution environment.


    Section 2.14.3.33,  SIN:  Sine

    The SIN instruction approximates the sine of the angle specified by the
    scalar operand and replicates it to all four components of the result
    vector.  The angle is specified in radians and does not have to be in the
    range [0,2*PI].

      tmp = ScalarLoad(op0);
      result.x = ApproxSine(tmp);
      result.y = ApproxSine(tmp);
      result.z = ApproxSine(tmp);
      result.w = ApproxSine(tmp);

    The approximation function is accurate to at least 22 bits with an angle
    in the range [0,2*PI].

      | ApproxSine(x) - sin(x) | < 1.0 / 2^22, if 0.0 <= x < 2.0 * PI.

    The error in the approximation will typically increase with the absolute
    value of the angle when the angle falls outside the range [0,2*PI].

    The following special-case rules apply to cosine approximation:

      1. ApproxSine(NaN) = NaN.
      2. ApproxSine(+/-INF) = NaN.
      3. ApproxSine(+/-0.0) = +/-0.0.  The sign of the result is equal to the
         sign of the single operand.

    The SIN instruction is available only in the VP2 execution environment.


    Section 2.14.3.34,  SLE:  Set on Less Than or Equal

    The SLE instruction performs a component-wise comparison of the two
    operands.  Each component of the result vector is 1.0 if the corresponding
    component of the first operand is less than or equal to that of the
    second, and 0.0 otherwise.

      tmp0 = VectorLoad(op0);
      tmp1 = VectorLoad(op1);
      result.x = (tmp0.x <= tmp1.x) ? 1.0 : 0.0;
      result.y = (tmp0.y <= tmp1.y) ? 1.0 : 0.0;
      result.z = (tmp0.z <= tmp1.z) ? 1.0 : 0.0;
      result.w = (tmp0.w <= tmp1.w) ? 1.0 : 0.0;
      if (tmp0.x is NaN or tmp1.x is NaN) result.x = NaN;
      if (tmp0.y is NaN or tmp1.y is NaN) result.y = NaN;
      if (tmp0.z is NaN or tmp1.z is NaN) result.z = NaN;
      if (tmp0.w is NaN or tmp1.w is NaN) result.w = NaN;

    The following special-case rules apply to SLE:

      1. (NaN <= <x>) and (<x> <= NaN) are FALSE for all <x>.
      2. (+INF <= +INF) and (-INF <= -INF) are TRUE.
      3. (-0.0 <= +0.0) and (+0.0 <= -0.0) are TRUE.

    The SLE instruction is available only in the VP2 execution environment.


    Section 2.14.3.35,  SLT:  Set on Less Than

    The SLT instruction performs a component-wise comparison of the two
    operands.  Each component of the result vector is 1.0 if the corresponding
    component of the first operand is less than that of the second, and 0.0
    otherwise.

      tmp0 = VectorLoad(op0);
      tmp1 = VectorLoad(op1);
      result.x = (tmp0.x < tmp1.x) ? 1.0 : 0.0;
      result.y = (tmp0.y < tmp1.y) ? 1.0 : 0.0;
      result.z = (tmp0.z < tmp1.z) ? 1.0 : 0.0;
      result.w = (tmp0.w < tmp1.w) ? 1.0 : 0.0;
      if (tmp0.x is NaN or tmp1.x is NaN) result.x = NaN;
      if (tmp0.y is NaN or tmp1.y is NaN) result.y = NaN;
      if (tmp0.z is NaN or tmp1.z is NaN) result.z = NaN;
      if (tmp0.w is NaN or tmp1.w is NaN) result.w = NaN;

    The following special-case rules apply to SLT:

      1. (NaN < <x>) and (<x> < NaN) are FALSE for all <x>.
      2. (-0.0 < +0.0) and (+0.0 < -0.0) are FALSE.


    Section 2.14.3.36,  SNE:  Set on Not Equal

    The SNE instruction performs a component-wise comparison of the two
    operands.  Each component of the result vector is 1.0 if the corresponding
    component of the first operand is not equal to that of the second, and 0.0
    otherwise.

      tmp0 = VectorLoad(op0);
      tmp1 = VectorLoad(op1);
      result.x = (tmp0.x != tmp1.x) ? 1.0 : 0.0;
      result.y = (tmp0.y != tmp1.y) ? 1.0 : 0.0;
      result.z = (tmp0.z != tmp1.z) ? 1.0 : 0.0;
      result.w = (tmp0.w != tmp1.w) ? 1.0 : 0.0;
      if (tmp0.x is NaN or tmp1.x is NaN) result.x = NaN;
      if (tmp0.y is NaN or tmp1.y is NaN) result.y = NaN;
      if (tmp0.z is NaN or tmp1.z is NaN) result.z = NaN;
      if (tmp0.w is NaN or tmp1.w is NaN) result.w = NaN;

    The following special-case rules apply to SNE:

      1. (<x> != <y>) and (<y> != <x>) always produce the same result.
      2. (NaN != <x>) is TRUE for all <x>, including NaN.
      3. (+INF != +INF) and (-INF != -INF) are FALSE.
      4. (-0.0 != +0.0) and (+0.0 != -0.0) are TRUE.

    The SNE instruction is available only in the VP2 execution environment.


    Section 2.14.3.37,  SSG:  Set Sign

    The SSG instruction generates a result vector containing the signs of each
    component of the single operand.  Each component of the result vector is
    1.0 if the corresponding component of the operand is greater than zero,
    0.0 if the corresponding component of the operand is equal to zero, and
    -1.0 if the corresponding component of the operand is less than zero.

      tmp = VectorLoad(op0);
      result.x = SetSign(tmp.x);
      result.y = SetSign(tmp.y);
      result.z = SetSign(tmp.z);
      result.w = SetSign(tmp.w);

    The following special-case rules apply to SSG:

      1. SetSign(NaN) = NaN.
      2. SetSign(-0.0) = SetSign(+0.0) = 0.0.
      3. SetSign(-INF) = -1.0.
      4. SetSign(+INF) = +1.0.
      5. SetSign(x) = -1.0, if -INF < x < -0.0.
      6. SetSign(x) = +1.0, if +0.0 < x < +INF.

    The SSG instruction is available only in the VP2 execution environment.


    Section 2.14.3.38,  STR:  Set on True

    The STR instruction is a degenerate case of the other "Set on"
    instructions that sets all components of the result vector to 1.0.

      result.x = 1.0;
      result.y = 1.0;
      result.z = 1.0;
      result.w = 1.0;

    The STR instruction is available only in the VP2 execution environment.


    Section 2.14.3.39,  SUB:  Subtract

    The SUB instruction performs a component-wise subtraction of the second
    operand from the first to yield a result vector.

      tmp0 = VectorLoad(op0);
      tmp1 = VectorLoad(op1);
      result.x = tmp0.x - tmp1.x;
      result.y = tmp0.y - tmp1.y;
      result.z = tmp0.z - tmp1.z;
      result.w = tmp0.w - tmp1.w;

    The SUB instruction is completely equivalent to an identical ADD
    instruction in which the negate operator on the second operand is
    reversed:

      1. "SUB R0, R1, R2" is equivalent to "ADD R0, R1, -R2".
      2. "SUB R0, R1, -R2" is equivalent to "ADD R0, R1, R2".
      3. "SUB R0, R1, |R2|" is equivalent to "ADD R0, R1, -|R2|".
      4. "SUB R0, R1, -|R2|" is equivalent to "ADD R0, R1, |R2|".

    The SUB instruction is available only in the VP1.1 and VP2 execution
    environments.


    2.14.4  Vertex Arrays for Vertex Attributes

    Data for vertex attributes in vertex program mode may be specified
    using vertex array commands.  The client may specify and enable any
    of sixteen vertex attribute arrays.

    The vertex attribute arrays are ignored when vertex program mode
    is disabled.  When vertex program mode is enabled, vertex attribute
    arrays are used.

    The command

      void VertexAttribPointerNV(uint index, int size, enum type,
                                 sizei stride, const void *pointer);

    describes the locations and organizations of the sixteen vertex
    attribute arrays.  index specifies the particular vertex attribute
    to be described.  size indicates the number of values per vertex
    that are stored in the array; size must be one of 1, 2, 3, or 4.
    type specifies the data type of the values stored in the array.
    type must be one of SHORT, FLOAT, DOUBLE, or UNSIGNED_BYTE and these
    values correspond to the array types short, int, float, double, and
    ubyte respectively.  The INVALID_OPERATION error is generated if
    type is UNSIGNED_BYTE and size is not 4.  The INVALID_VALUE error
    is generated if index is greater than 15.  The INVALID_VALUE error
    is generated if stride is negative.

    The one, two, three, or four values in an array that correspond to a
    single vertex attribute comprise an array element.  The values within
    each array element at stored sequentially in memory.  If the stride
    is specified as zero, then array elements are stored sequentially
    as well.  Otherwise points to the ith and (i+1)st elements of an array
    differ by stride basic machine units (typically unsigned bytes),
    the pointer to the (i+1)st element being greater.  pointer specifies
    the location in memory of the first value of the first element of
    the array being specified.

    Vertex attribute arrays are enabled with the EnableClientState command
    and disabled with the DisableClientState command.  The value of the
    argument to either command is VERTEX_ATTRIB_ARRAYi_NV where i is an
    integer between 0 and 15; specifying a value of i enables or
    disables the vertex attribute array with index i.  The constants
    obey VERTEX_ATTRIB_ARRAYi_NV = VERTEX_ATTRIB_ARRAY0_NV + i.

    When vertex program mode is enabled, the ArrayElement command operates
    as described in this section in contrast to the behavior described
    in section 2.8.  Likewise, any vertex array transfer commands that
    are defined in terms of ArrayElement (DrawArrays, DrawElements, and
    DrawRangeElements) assume the operation of ArrayElement described
    in this section when vertex program mode is enabled.

    When vertex program mode is enabled, the ArrayElement command
    transfers the ith element of particular enabled vertex arrays as
    described below.  For each enabled vertex attribute array, it is
    as though the corresponding command from section 2.14.1.1 were
    called with a pointer to element i.  For each vertex attribute,
    the corresponding command is VertexAttrib[size][type]v, where size
    is one of [1,2,3,4], and type is one of [s,f,d,ub], corresponding
    to the array types short, int, float, double, and ubyte respectively.

    However, if a given vertex attribute array is disabled, but its
    corresponding aliased conventional per-vertex parameter's vertex
    array (as described in section 2.14.1.6) is enabled, then it is
    as though the corresponding command from section 2.7 or section
    2.6.2 were called with a pointer to element i.  In this case, the
    corresponding command is determined as described in section 2.8's
    description of ArrayElement.

    If the vertex attribute array 0 is enabled, it is as though
    VertexAttrib[size][type]v(0, ...) is executed last, after the
    executions of other corresponding commands.  If the vertex attribute
    array 0 is disabled but the vertex array is enabled, it is as though
    Vertex[size][type]v is executed last, after the executions of other
    corresponding commands.

    2.14.5  Vertex State Programs

    Vertex state programs share the same instruction set as and a similar
    execution model to vertex programs.  While vertex programs are executed
    implicitly when a vertex transformation is provoked, vertex state programs
    are executed explicitly, independently of any vertices.  Vertex state
    programs can write program parameter registers, but may not write vertex
    result registers.  Vertex state programs have not been extended beyond the
    the VP1.0 execution environment, and are offered solely for compatibility
    with that execution environment.

    The purpose of a vertex state program is to update program parameter
    registers by means of an application-defined program.  Typically, an
    application will load a set of program parameters and then execute a
    vertex state program that reads and updates the program parameter
    registers.  For example, a vertex state program might normalize a set of
    unnormalized vectors previously loaded as program parameters.  The
    expectation is that subsequently executed vertex programs would use the
    normalized program parameters.

    Vertex state programs are loaded with the same LoadProgramNV command (see
    section 2.14.1.8) used to load vertex programs except that the target must
    be VERTEX_STATE_PROGRAM_NV when loading a vertex state program.

    Vertex state programs must conform to a more limited grammar than the
    grammar for vertex programs.  The vertex state program grammar for
    syntactically valid sequences is the same as the grammar defined in
    section 2.14.1.8 with the following modified rules:

    <program>              ::= <vp1-program>

    <vp1-program>          ::= "!!VSP1.0" <programBody> "END"

    <dstReg>               ::= <absProgParamReg>
                             | <temporaryReg>

    <vertexAttribReg>      ::= "v" "[" "0" "]"

    A vertex state program fails to load if it does not write at least
    one program parameter register.

    A vertex state program fails to load if it contains more than 128
    instructions.

    A vertex state program fails to load if any instruction sources more
    than one unique program parameter register.

    A vertex state program fails to load if any instruction sources
    more than one unique vertex attribute register (this is necessarily
    true because only vertex attribute 0 is available in vertex state
    programs).

    The error INVALID_OPERATION is generated if a vertex state program
    fails to load because it is not syntactically correct or for one
    of the other reasons listed above.

    A successfully loaded vertex state program is parsed into a sequence
    of instructions.  Each instruction is identified by its tokenized
    name.  The operation of these instructions when executed is defined
    in section 2.14.1.10.

    Executing vertex state programs is legal only outside a Begin/End
    pair.  A vertex state program may not read any vertex attribute
    register other than register zero.  A vertex state program may not
    write any vertex result register.

    The command

      ExecuteProgramNV(enum target, uint id, const float *params);

    executes the vertex state program named by id.  The target must be
    VERTEX_STATE_PROGRAM_NV and the id must be the name of program loaded
    with a target type of VERTEX_STATE_PROGRAM_NV.  params points to
    an array of four floating-point values that are loaded into vertex
    attribute register zero (the only vertex attribute readable from a
    vertex state program).

    The INVALID_OPERATION error is generated if the named program is
    nonexistent, is invalid, or the program is not a vertex state
    program.  A vertex state program may not be valid for reasons
    explained in section 2.14.5.


    2.14.6,  Program Options

    In the VP1.1 and VP2.0 execution environment, vertex programs may specify
    one or more program options that modify the execution environment,
    according to the <option> grammar rule.  The set of options available to
    the program is described below.

    Section 2.14.6.1, Position-Invariant Vertex Program Option

    If <vp11-option> or <vp2-option> matches "NV_position_invariant", the
    vertex program is presumed to be position-invariant.  By default, vertex
    programs are not position-invariant.  Even if programs emulate the
    conventional OpenGL transformation model, they may still not produce the
    exact same transform results, due to rounding errors or different
    operation orders.  Such programs may not work well for multi-pass
    rendering algorithms where the second and subsequent passes use an EQUAL
    depth test.

    Position-invariant vertex programs do not compute a final vertex position;
    instead, the GL computes vertex coordinates as described in section 2.10.
    This computation should produce exactly the same results as the
    conventional OpenGL transformation model, assuming vertex weighting and
    vertex blending are disabled.

    A vertex program that specifies the position-invariant option will fail to
    load if it writes to the HPOS result register.

    Additionally, in the VP1.1 execution environment, position-invariant
    programs can not use relative addressing for program parameters.  Any
    position-invariant VP1.1 program matches the grammar rule
    <relProgParamReg>, will fail to load.  No such restriction exists for
    VP2.0 programs.

    For position-invariant programs, the limit on the number of instructions
    allowed in a program is reduced by four:  position-invariant VP1.1 and
    VP2.0 programs may have no more than 124 or 252 instructions,
    respectively.


    2.14.7  Tracking Matrices 

    As a convenience to applications, standard GL matrix state can be
    tracked into program parameter vectors.  This permits vertex programs
    to access matrices specified through GL matrix commands.

    In addition to GL's conventional matrices, several additional matrices
    are available for tracking.  These matrices have names of the form
    MATRIXi_NV where i is between zero and n-1 where n is the value
    of the MAX_TRACK_MATRICES_NV implementation dependent constant.
    The MATRIXi_NV constants obey MATRIXi_NV = MATRIX0_NV + i.  The value
    of MAX_TRACK_MATRICES_NV must be at least eight.  The maximum
    stack depth for tracking matrices is defined by the
    MAX_TRACK_MATRIX_STACK_DEPTH_NV and must be at least 1.

    The command

      TrackMatrixNV(enum target, uint address, enum matrix, enum transform);

    tracks a given transformed version of a particular matrix into
    a contiguous sequence of four vertex program parameter registers
    beginning at address.  target must be VERTEX_PROGRAM_NV (though
    tracked matrices apply to vertex state programs as well because both
    vertex state programs and vertex programs shared the same program
    parameter registers).  matrix must be one of NONE, MODELVIEW,
    PROJECTION, TEXTURE, TEXTUREi_ARB (where i is between 0 and n-1
    where n is the number of texture units supported), COLOR (if
    the ARB_imaging subset is supported), MODELVIEW_PROJECTION_NV,
    or MATRIXi_NV.  transform must be one of IDENTITY_NV, INVERSE_NV,
    TRANSPOSE_NV, or INVERSE_TRANSPOSE_NV.  The INVALID_VALUE error is
    generated if address is not a multiple of four.

    The MODELVIEW_PROJECTION_NV matrix represents the concatenation of
    the current modelview and projection matrices.  If M is the current
    modelview matrix and P is the current projection matrix, then the
    MODELVIEW_PROJECTION_NV matrix is C and computed as

        C = P M

    Matrix tracking for the specified program parameter register and the
    next consecutive three registers is disabled when NONE is supplied
    for matrix.  When tracking is disabled the previously tracked program
    parameter registers retain the state of their last tracked values.
    Otherwise, the specified transformed version of matrix is tracked into
    the specified program parameter register and the next three registers.
    Whenever the matrix changes, the transformed version of the matrix
    is updated in the specified range of program parameter registers.
    If TEXTURE is specified for matrix, the texture matrix for the current
    active texture unit is tracked.  If TEXTUREi_ARB is specified for
    matrix, the <i>th texture matrix is tracked.

    Matrices are tracked row-wise meaning that the top row of the
    transformed matrix is loaded into the program parameter address,
    the second from the top row of the transformed matrix is loaded into
    the program parameter address+1, the third from the top row of the
    transformed matrix is loaded into the program parameter address+2,
    and the bottom row of the transformed matrix is loaded into the
    program parameter address+3.  The transformed matrix may be identical
    to the specified matrix, the inverse of the specified matrix, the
    transpose of the specified matrix, or the inverse transpose of the
    specified matrix, depending on the value of transform.

    When matrix tracking is enabled for a particular program parameter
    register sequence, updates to the program parameter using
    ProgramParameterNV commands, a vertex program, or a vertex state
    program are not possible.  The INVALID_OPERATION error is generated
    if a ProgramParameterNV command is used to update a program parameter
    register currently tracking a matrix.

    The INVALID_OPERATION error is generated by ExecuteProgramNV when
    the vertex state program requested for execution writes to a program
    parameter register that is currently tracking a matrix because the
    program is considered invalid.

    2.14.8  Required Vertex Program State 

    The state required for vertex programs consists of:

      a bit indicating whether or not program mode is enabled;

      a bit indicating whether or not two-sided color mode is enabled;

      a bit indicating whether or not program-specified point size mode
      is enabled;

      256 4-component floating-point program parameter registers;

      16 4-component vertex attribute registers (though this state is
      aliased with the current normal, primary color, secondary color,
      fog coordinate, weights, and texture coordinate sets);

      24 sets of matrix tracking state for each set of four sequential
      program parameter registers, consisting of a n-valued integer
      indicated the tracked matrix or GL_NONE (where n is 5 + the number
      of texture units supported + the number of tracking matrices
      supported) and a four-valued integer indicating the transformation
      of the tracked matrix;

      an unsigned integer naming the currently bound vertex program

      and the state must be maintained to indicate which integers
      are currently in use as program names.

   Each existent program object consists of a target, a boolean indicating
   whether the program is resident, an array of type ubyte containing the
   program string, and the length of the program string array.  Initially,
   no program objects exist.

   Program mode, two-sided color mode, and program-specified point size
   mode are all initially disabled.

   The initial state of all 256 program parameter registers is (0,0,0,0).

   The initial state of the 16 vertex attribute registers is (0,0,0,1)
   except in cases where a vertex attribute register aliases to a
   conventional GL transform mode vertex parameter in which case
   the initial state is the initial state of the respective aliased
   conventional vertex parameter.

   The initial state of the 24 sets of matrix tracking state is NONE
   for the tracked matrix and IDENTITY_NV for the transformation of the
   tracked matrix.

   The initial currently bound program is zero.

   The client state required to implement the 16 vertex attribute
   arrays consists of 16 boolean values, 16 memory pointers, 16 integer
   stride values, 16 symbolic constants representing array types,
   and 16 integers representing values per element.  Initially, the
   boolean values are each disabled, the memory pointers are each null,
   the strides are each zero, the array types are each FLOAT, and the
   integers representing values per element are each four."


Additions to Chapter 3 of the OpenGL 1.3 Specification (Rasterization)

    None.

Additions to Chapter 4 of the OpenGL 1.3 Specification (Per-Fragment
Operations and the Frame Buffer)

    None.

Additions to Chapter 5 of the OpenGL 1.3 Specification (Special Functions)

    None.

Additions to Chapter 6 of the OpenGL 1.3 Specification (State and
State Requests)

    None.

Additions to Appendix A of the OpenGL 1.3 Specification (Invariance)

    None.

Additions to the AGL/GLX/WGL Specifications

    None.

GLX Protocol

    All relevant protocol is defined in the NV_vertex_program extension.

Errors

    This list includes the errors specified in the NV_vertex_program
    extension, modified as appropriate.

    The error INVALID_VALUE is generated if VertexAttribNV is called where
    index is greater than 15.

    The error INVALID_VALUE is generated if any ProgramParameterNV has an
    index is greater than 255 (was 95 in NV_vertex_program).

    The error INVALID_VALUE is generated if VertexAttribPointerNV is called
    where index is greater than 15.

    The error INVALID_VALUE is generated if VertexAttribPointerNV is called
    where size is not one of 1, 2, 3, or 4.

    The error INVALID_VALUE is generated if VertexAttribPointerNV is called
    where stride is negative.

    The error INVALID_OPERATION is generated if VertexAttribPointerNV is
    called where type is UNSIGNED_BYTE and size is not 4.

    The error INVALID_VALUE is generated if LoadProgramNV is used to load a
    program with an id of zero.

    The error INVALID_OPERATION is generated if LoadProgramNV is used to load
    an id that is currently loaded with a program of a different program
    target.

    The error INVALID_OPERATION is generated if the program passed to
    LoadProgramNV fails to load because it is not syntactically correct based
    on the specified target.  The value of PROGRAM_ERROR_POSITION_NV is still
    updated when this error is generated.

    The error INVALID_OPERATION is generated if LoadProgramNV has a target of
    VERTEX_PROGRAM_NV and the specified program fails to load because it does
    not write the HPOS register at least once.  The value of
    PROGRAM_ERROR_POSITION_NV is still updated when this error is generated.

    The error INVALID_OPERATION is generated if LoadProgramNV has a target of
    VERTEX_STATE_PROGRAM_NV and the specified program fails to load because it
    does not write at least one program parameter register.  The value of
    PROGRAM_ERROR_POSITION_NV is still updated when this error is generated.

    The error INVALID_OPERATION is generated if the vertex program or vertex
    state program passed to LoadProgramNV fails to load because it contains
    more than 128 instructions (VP1 programs) or 256 instructions (VP2
    programs).  The value of PROGRAM_ERROR_POSITION_NV is still updated when
    this error is generated.

    The error INVALID_OPERATION is generated if a program is loaded with
    LoadProgramNV for id when id is currently loaded with a program of a
    different target.

    The error INVALID_OPERATION is generated if BindProgramNV attempts to bind
    to a program name that is not a vertex program (for example, if the
    program is a vertex state program).

    The error INVALID_VALUE is generated if GenProgramsNV is called where n is
    negative.

    The error INVALID_VALUE is generated if AreProgramsResidentNV is called
    and any of the queried programs are zero or do not exist.

    The error INVALID_OPERATION is generated if ExecuteProgramNV executes a
    program that does not exist.

    The error INVALID_OPERATION is generated if ExecuteProgramNV executes a
    program that is not a vertex state program.

    The error INVALID_OPERATION is generated if Begin, RasterPos, or a command
    that performs an explicit Begin is called when vertex program mode is
    enabled and the currently bound vertex program writes program parameters
    that are currently being tracked.

    The error INVALID_OPERATION is generated if ExecuteProgramNV is called and
    the vertex state program to execute writes program parameters that are
    currently being tracked.

    The error INVALID_VALUE is generated if TrackMatrixNV has a target of
    VERTEX_PROGRAM_NV and attempts to track an address is not a multiple of
    four.

    The error INVALID_VALUE is generated if GetProgramParameterNV is called to
    query an index greater than 255 (was 95 in NV_vertex_program).

    The error INVALID_VALUE is generated if GetVertexAttribNV is called to
    query an <index> greater than 15, or if <index> is zero and <pname> is
    CURRENT_ATTRIB_NV.

    The error INVALID_VALUE is generated if GetVertexAttribPointervNV is
    called to query an index greater than 15.

    The error INVALID_OPERATION is generated if GetProgramivNV is called and
    the program named id does not exist.

    The error INVALID_OPERATION is generated if GetProgramStringNV is called
    and the program named <program> does not exist.

    The error INVALID_VALUE is generated if GetTrackMatrixivNV is called with
    an <address> that is not divisible by four or greater than or equal to 256
    (was 96 in NV_vertex_program).

    The error INVALID_VALUE is generated if AreProgramsResidentNV,
    DeleteProgramsNV, GenProgramsNV, or RequestResidentProgramsNV are called
    where <n> is negative.

    The error INVALID_VALUE is generated if LoadProgramNV is called where
    <len> is negative.

    The error INVALID_VALUE is generated if ProgramParameters4dvNV or
    ProgramParameters4fvNV are called where <count> is negative.

    The error INVALID_VALUE is generated if VertexAttribs{1,2,3,4}{d,f,s}vNV
    is called where <count> is negative.

    The error INVALID_ENUM is generated if BindProgramNV,
    GetProgramParameterfvNV, GetProgramParameterdvNV, GetTrackMatrixivNV,
    ProgramParameter4fNV, ProgramParameter4dNV, ProgramParameter4fvNV,
    ProgramParameter4dvNV, ProgramParameters4fvNV, ProgramParameters4dvNV,
    or TrackMatrixNV are called where <target> is not VERTEX_PROGRAM_NV.

    The error INVALID_ENUM is generated if LoadProgramNV or
    ExecuteProgramNV are called where <target> is not either
    VERTEX_PROGRAM_NV or VERTEX_STATE_PROGRAM_NV.

New State

(Modify Table X.5, New State Introduced by NV_vertex_program from the
 NV_vertex_program specification.)

Get Value             Type    Get Command              Initial Value  Description         Sec       Attribute
--------------------- ------  -----------------------  -------------  ------------------  --------  ------------
PROGRAM_PARAMETER_NV  256xR4  GetProgramParameterNV    (0,0,0,0)      program parameters  2.14.1.2  -


(Modify Table X.7.  Vertex Program Per-vertex Execution State.  "VP1" and
"VP2" refer to the VP1 and VP2 execution environments, respectively.)

Get Value    Type    Get Command   Initial Value  Description              Sec       Attribute
---------    ------  -----------   -------------  -----------------------  --------  ---------
-            12xR4   -             (0,0,0,0)      VP1 temporary registers  2.14.1.4  -
-            16xR4   -             (0,0,0,0)      VP2 temporary registers  2.14.1.4  -
-            15xR4   -             (0,0,0,1)      vertex result registers  2.14.1.4  -
             Z4      -             (0,0,0,0)      VP1 address register     2.14.1.3  -
             2xZ4    -             (0,0,0,0)      VP2 address registers    2.14.1.3  -


Revision History

    Rev.  Date      Author   Changes
    ----  --------  -------  --------------------------------------------
    32    05/16/04  pbrown   Documented that it's not possible to results from
                             LG2 that are any more precise than what is
                             available in the fp32 storage format.

    31    08/17/03  pbrown   Added several overlooked opcodes (RCC, SUB, SIN)
                             to the grammar.  They are documented in the spec
                             body, however.

    30    02/28/03  pbrown   Fixed incorrect condition code example.

    29    12/08/02  pbrown   Fixed minor bug where "ABS" and "DPH" were listed
                             twice in the grammar. 
    
    28    10/29/02  pbrown   Remove support for indirect branching.  Added
                             missing o[CLPx] outputs to the grammar.  Minor
                             typo fixes.

    25    07/19/02  pbrown   Fixed several miscellaneous errors in the spec.

    24    06/28/02  pbrown   Fixed several erroneous resource limitations.

    23    06/07/02  pbrown   Removed stray and erroneous abs() from the
                             documentation of the LG2 instruction.

    22    06/06/02  pbrown   Added missing items from NV_vertex_program1_1, in
                             particular, program options.  Documented the
                             VP2.0 position-invariant programs have no
                             restrictions on indirect addressing.  

    21    06/19/02  pbrown   Cleaned up miscellaneous errors and issues
                             in the spec.

    20    05/17/02  pbrown   Documented LOG instruction as taking the 
                             absolute value of the operand, as in VP1.0.  
                             Fixed special-case rules for MUL.  Added clamps
                             to special-case clamping rules for RCC.

    18    05/09/02  pbrown   Clarified the handling of NaN/UN in certain
                             instructions and conditional operations.

    17    04/26/02  pbrown   Fix incorrectly specified algorithm for computing
                             the y result in the LOG instruction.

    16    04/21/02  pbrown   Added example for "paletted skinning".
                             Documented size limitation (10 bits) on the
                             address register and ARA, ARL, and ARR
                             instructions.  The limits needs to be exposed
                             because of the ARA instruction.  Cleaned up
                             documentation on absolute value on input
                             operations.  Added examples for masked writes and
                             CC updates, and for branching.  Fixed
                             out-of-range indexed branch language and
                             pseudocode to clamp to the actual table size
                             (rather than the theoretical maximum).
                             Documented ABS as semi-deprecated in VP2.  Fixed
                             special cases for MIN, MAX, SEQ, SGE, SGT, SLE,
                             SLT, and SNE.  Fix completely botched description
                             of RET.
 
    15    04/05/02  pbrown   Updated introduction to indicate that
                             ARL/ARR/ARA all can update condition code.
                             Minor fixes and optimizations to the looping
                             examples.  Add missing "set on" opcodes to the
                             grammar.  Fixed spec to clamp branch table
                             indices to [0,15].  Added a couple caveats to
                             the "ABS" pseudo-instruction.   Documented
                             "ARR" as using IEEE round to nearest even
                             mode.  Documented special cases for "SSG".
