Name

    ARB_derivative_control

Name Strings

    GL_ARB_derivative_control

Contact

    John Kessenich (cepheus 'at' frii.com)

Contributors

    Bill Licea-Kane, Qualcomm
        
Notice

    Copyright (c) 2014 The Khronos Group Inc. Copyright terms at
        http://www.khronos.org/registry/speccopyright.html

Specification Update Policy

    Khronos-approved extension specifications are updated in response to
    issues and bugs prioritized by the Khronos OpenGL Working Group. For
    extensions which have been promoted to a core Specification, fixes will
    first appear in the latest version of that core Specification, and will
    eventually be backported to the extension document. This policy is
    described in more detail at
        https://www.khronos.org/registry/OpenGL/docs/update_policy.php

Status

    Complete. 
    Approved by the ARB on June 26, 2014.
    Ratified by the Khronos Board of Promoters on August 7, 2014.

Version

    Last Modified Date: 7-Aug-2014
    Revision: 3

Number

    ARB Extension #163

Dependencies

    This extension is written against the GLSL 4.40 Specification.

    OpenGL 4.0 and GLSL 4.00 or later are required.

Overview

    This extension provides control over the spacial granularity at which the
    underlying implementation computes derivatives.  

    For example, for the coarse-granularity derivative, a single x derivative
    could be computed for each 2x2 group of pixels, using that same derivative
    value for all 4 pixels.  For the fine-granularity derivative, two
    derivatives could be computed for each 2x2 group of pixels; one for the top
    row and one for the bottom row.  Implementations vary somewhat on how this
    is done.

    To select the coarse derivative, use:

        dFdxCoarse(p)
        dFdyCoarse(p)
        fwidthCoarse(p)

    To select the fine derivative, use:

        dFdxFine(p)
        dFdyFine(p)
        fwidthFine(p)

    To select which ever is "better" (based on performance, API hints, or other
    factors), use:

        dFdx(p)
        dFdy(p)
        fwidth(p)

    This last set is the set of previously existing built-ins for derivatives,
    and continues to work in a backward compatible way.

IP Status

    No known IP claims.

New Procedures and Functions

    None.

New Tokens

    None.

Modifications to the OpenGL Specification

    None.

Additions to the OpenGL Shading Language

    Including the following line in a shader can be used to control the
    language features described in this extension:

        #extension GL_ARB_derivative_control : <behavior>

    where <behavior> is as specified in section 3.3.

    New preprocessor #defines are added to the OpenGL Shading Language:

        #define GL_ARB_derivative_control 1

Section 4.3.3 Constant Expressions

    Update the following sentence:
    
    "The following built-in functions must return 0 when evaluated with an
    argument that is a constant expression.

        dFdx
        dFdy
        fwidth
        dFdxCoarse
        dFdyCoarse
        fwidthCoarse
        dFdxFine
        dFdyFine
        fwidthFine"

Section 8.13.1 Derivative Functions

    After "dFdy is approximated similarly, with y replacing x.", add the
    following:

    "With multi-sample rasterization, for any given fragment or sample, 
    either neighboring fragments or samples may be considered.

    "It is typical to consider a 2x2 square of fragments or samples, and 
    compute independent dFdxFine per row and independent dFdyFine per column, 
    while computing only a single dFdxCoarse and a single dFdyCoarse for the
    entire 2x2 square.Thus, all second-order coarse derivatives, e.g., 
    dFdxCoarse(dFdxCoarse(x)), may be 0, even for non-linear arguments. 
    However, second-order fine derivatives, e.g., dFdxFine(dFdxFine(x)) 
    will properly reflect the difference between the independent fine 
    derivatives computed within the 2x2 square."

    Remove the following paragraphs:

    "A GL implementation may use the above or other methods to perform the 
    calculation, subject to the following conditions:

    "The method may use piecewise linear approximations. Such linear 
    approximations imply that higher order derivatives, dFdx(dFdx(x)) and 
    above, are undefined.

    "The method may assume that the function evaluated is continuous. Therefore
    derivatives within nonuniform control flow are undefined."

    Change the last paragraph before the table to say

    "In some implementations, varying degrees of derivative accuracy for dFdx 
    and dFdy may be obtained by providing GL hints (section 21.4 "Hints" of the
    OpenGL Graphics System Specification), allowing a user to make an image 
    quality versus speed trade off.These hints have no effect on dFdxCoarse, 
    dFdyCoarse, dFdxFineand dFdyFine."

    Add the following built-in functions to the table:
        
        genType dFdxFine(genType p)

    "Returns the partial derivative of p with respect to the window x
    coordinate.  Will use local differencing based on the value of p for the
    current fragment and its immediate neighbor(s)."

        genType dFdyFine(genType p)

    "Returns the partial derivative of p with respect to the window y 
    coordinate.  Will use local differencing based on the value of p for the
    current fragment and its immediate neighbor(s)."

        genType fwidthFine(genType p)

    "Return abs(dFdxFine(p)) + abs(dFdyFine(p))."

        genType dFdxCoarse(genType p)

    "Returns the partial derivative of p with respect to the window x
    coordinate.  Will use local differencing based on the value of p for the
    current fragment's neighbors, and will possibly, but not necessarily,
    include the value of p for the current fragment.  That is, over a 
    given area, the implementation can compute x derivatives in fewer 
    unique locations than would be allowed for dFdxFine(p)."

        genType dFdyCoarse(genType p)

    "Returns the partial derivative of p with respect to the window y
    coordinate.  Will use local differencing based on the value of p for the
    current fragment's neighbors, and will possibly, but not necessarily,
    include the value of p for the current fragment.  That is, over a
    given area, the implementation can compute y derivatives in fewer
    unique locations than would be allowed for dFdyFine(p)."

        genType fwidthCoarse(genType p)

    "Returns abs(dFdxCoarse(p)) + abs(dFdyCoarse(p))."

    Change the existing descriptions to the following:

        genType dFdx(genType p)

    "Returns either dFdxFine(p) or dFdxCoarse(p), based on implementation
    choice, presumably whichever is the faster, or by whichever is selected
    in the API through quality-versus-speed hints."

        genType dFdy(genType p)

    "Returns either dFdyFine(p) or dFdyCoarse(p), based on implementation
    choice, presumably whichever is the faster, or by whichever is selected
    in the API through quality-versus-speed hints."

    Doing the above change would remove:

    [Old Language to remove...]
    "These two functions are commonly used to estimate the 
    filter width used to anti-alias procedural textures. We
    are assuming that the expression is being evaluated in 
    parallel on a SIMD array so that at any given point in 
    time the value of the function is known at the grid points 
    represented by the SIMD array. Local differencing 
    between SIMD array elements can therefore be used to 
    derive dFdx, dFdy, etc."

        getType fwidth(getType p)

    "Returns abs(dFdx(p)) + abs(dFdy(p))."

Additions to the AGL/EGL/GLX/WGL Specifications

    None.

GLX Protocol

    None.

Errors

    No new API errors.

New State

    None.

New Implementation Dependent State

    None.

Conformance Tests

    TBD

Issues

    1.  Allow support on pre-4.0 versions?

        Resolution:  No, require 4.0.

    2.  Define higher-order derivatives?  Currently we say they are undefined,
        but don't see why they can't say more (like coarse is 0, and fine might
        be something you'd expect).

           dFdxFine(dFdyFine(a))      should work
           dFdxCoarse(dFdyCoarse(a))  should work or be 0

        Generally, the descriptive part of the derivative section may need
        slight tweaking, based on the decisions made.

        Resolution:  Yes, be more specific about how higher-order derivitives
        behave.  See the changes to the descriptive part of section 8.13.1.

Revision History

    Revision 1, 17-Apr-2014 (JohnK)
      - Create first version.
    Revision 2, 12-May-2014 (JohnK)
      - Write overview section
    Revision 3, 7-Aug-2014 (JohnK)
      - Match the core specification WRT to Bill's input derivatives, etc.
      - Add Bill as a contributor.
      - Close the issues.