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Introduction

The realm of shader programming today is dominated by GLSL, but the road to where we are was long and loopy.

Shader programs came about as a natural evolution of texture combination, another form of programmability found as late as the Wii (2006). However, texture combination on OpenGL is inherently more limited, from lack of features that cannot be worked around e.g. texture coordinate displacement, whilst extensions such as NV_texture_shader were never pulled in. At a point, texture combination was left behind.

In 2001 EXT_vertex_shader and ATI_fragment_shader were released, allowing the user to insert shader operations one by one with functions such as glShaderOp...EXT and glColorFragmentOp...ATI. Mesa supports the latter, yet not the former — seemingly inconsistent, when you consider the usual stance on such issues.

The two had little time in the sun, as the Architecture Review Board slammed down ARB_vertex_program and ARB_fragment_program, sealing the paradigm from then on: send all instructions at once in a textual form. This marked the beginning of what is termed ARB assembly.

This article is thanks to my dissatisfaction with introductory ARB assembly literature. Writing this required filling in many blanks, so I can't guarantee correctness. Always read the specs!

Integration

Unlike GLSL, where vertex and fragment shaders are separately compiled then linked together, ARB shaders are actually separate programs coming in separate extensions: ARB_vertex_program and ARB_fragment_program. It is possible for an OpenGL implementation to provide both, one or neither. Additionally, it is possible — and has happened — that an implementation supports one in hardware, and simulates another in software.

Like a GLSL shader, an ARB program replaces its corresponding part of the fixed-function pipeline. Thus replacing, say, the vertex program, means you lose the built-in Gouraud shading that may be available in silicon, and you will have to implement it manually.

ARB programs are easier to set up than GLSL programs, as practically everything needed is in the following:

GLuint program;

glGenProgramsARB(1, &program);
glBindProgramARB(GL_VERTEX_PROGRAM_ARB, program);

glProgramStringARB(GL_VERTEX_PROGRAM_ARB, GL_PROGRAM_FORMAT_ASCII_ARB, strlen(source), source);

if(glGetError() == GL_INVALID_OPERATION) {
	puts("Error during program compilation:");
	puts(glGetString(GL_PROGRAM_ERROR_STRING_ARB));
}

// Actually use for rendering
glEnable(GL_VERTEX_PROGRAM_ARB);

For fragment programs replace GL_VERTEX_PROGRAM_ARB with GL_FRAGMENT_PROGRAM_ARB.

Parameters are similar to GLSL uniforms except they are always 4-component vectors and lack textual names. They are passed using the glProgramEnvParameter...ARB and glProgramLocalParameter...ARB set of functions.

Environment parameters are shared by all programs of the same kind and local parameters aren't.

// Set 42nd environment parameter for all vertex programs.
glProgramEnvParameter4fARB(GL_VERTEX_PROGRAM_ARB, 42, 0.32550048828125, 0.255126953125, 0.29421997070312, 0.32421875);

// Set 3rd local parameter for the bound fragment program.
glProgramLocalParameter4fvARB(GL_FRAGMENT_PROGRAM_ARB, 3, (float[4]) {1, 2, 3, 4});

Matrix state is passed as built-in parameters, including their inverses, transpositions and inverse transpositions (see Appendix B).

Vertex attributes may be passed through the usual glColor..., glTexCoord... or gl...Pointer sets, but generic attributes like in GLSL are supported (glVertexAttrib...ARB, glVertexAttribPointerARB, glEnableVertexAttribArrayARB, etc.)

The Language

Despite common notions on assembly programming, ARB assembly is meant to be usable as a source language, as in written by humans. No graphics accelerator interprets ARB assembly itself as no binary form was ever standardized.

The language features only 4-component vectors as variables, and each variable is of one of six types:

• PARAM: used to name constants or program parameters
• ATTRIB: used for aliasing vertex attributes
• ADDRESS: for array indexing, this is the only integer vector, and only the first component is accessible (vertex program only)
• TEMP: used for intermediate computation (i.e. temporary expressions)
• ALIAS: provides another name to a variable
• OUTPUT: used for aliasing return variables, passed to the next stages

ATTRIB and OUTPUT are in reality aliases too, and are only for readability. Defining custom inputs and outputs is impossible. Passing information between vertex and fragment programs must be done through existing channels, e.g. the texture coordinate array.

By convention variable declarations except for TEMPs should be between the header and the instructions, though they are allowed to be anywhere according to parsing rules.

The following are the simplest useful vertex and fragment programs:

!!ARBvp1.0

# This is a comment.

# This is an attribute alias.
ATTRIB theColor = vertex.color;

# Multiply by the model-view-projection matrix to get the vertex NDCs.
# ARB assembly does not support matrix multiplication, thus 4 dot products.
DP4 result.position.x, state.matrix.mvp.row[0], vertex.position;
DP4 result.position.y, state.matrix.mvp.row[1], vertex.position;
DP4 result.position.z, state.matrix.mvp.row[2], vertex.position;
DP4 result.position.w, state.matrix.mvp.row[3], vertex.position;

# Copy the color and texture coordinate attributes directly.
MOV result.color, theColor;
MOV result.texcoord[0], vertex.texcoord;

END

!!ARBfp1.0

# This is a comment.

OUTPUT col = result.color;

# Directly copy interpolated color.
MOV col, fragment.color;

END

A program begins with either the !!ARBvp1.0 header for a vertex program, or !!ARBfp1.0 for a fragment program, designating the version.

Instructions are of the destination-source order, and feature something rarely seen in Assembly languages: source modifiers. In fact, each source operand may have an optional - sign attached to negate the value. ARB assembly also features swizzling in source operands.

If a scalar is passed as a vector operand, that scalar is replicated across all four components of the input vector (e.g. foo.x becomes foo.xxxx.) Likewise, if an instruction returns a scalar, it replicates said value to all components of the destination.

Destinations support syntax similar to swizzling, but they are not the same, but act as a write-mask! This is a common gotcha for those coming from GLSL-like languages. A destination such as a.xyw merely leaves the z component intact, whereas a.xwy is invalid, because the components are out of order.

Using a constant vector or scalar (immediate in Assembly speak) is defined as actually creating a nameless PARAM variable, and duplicate PARAMs are coalesced if they are deemed close enough.

Example usage of constants:

PARAM a = {1, 2, 3, 4};
PARAM b[] = { {0, 1, 0.0, 1.0}, {0, 5.2, 0, 3} };
PARAM c[3] = { {0, 0, 0, 0}, program.env[0], {123, 555, 3e5, 11} };
PARAM d[] = { program.local[0..5] };

TEMP e;
ADD e, 0, 5;
ADD e, e, {1, 2, 3, 4};

# The following actually adds 1 to the x and y components of e.
SUB e.xy, e, -{0, 0, 0, 1}.w;

MUL e, e, d[0];

Onto the meat and potatoes, here is the common instruction list:

The following have non-intuitive use cases:

SWZ d, s, i, i, i, i

# Let foo = (0.0, 1.0, 2.0, 3.0).

TEMP bar;
SWZ bar, foo, 1, -z, +y, -0;

# Now bar = (1.0, -2.0, 1.0, -0.0).

Exclusive features

Vertex programs and fragment programs each have exclusive instructions, an artifact of the limited shading model available at its development. It's well known that texture sampling used to be unavailable for vertex programs, but there's more to it.

I'd like the reader to keep in mind this excerpt from ARB_fragment_program:

The differences between the ARB_vertex_program instruction set and the ARB_fragment_program instruction set are minimal.

Indexing in vertex programs

ARB_vertex_program supports a primitive relative addressing with one index and one constant base.

Addressing supports ADDRESS variables for indices only, for which ARL must be used.

As an example:

PARAM array[3] = { {0.2, 0.3, 0.4, 1.0}, program.env[0..1] };

ADDRESS bar;

ARL bar, vertex.attrib[2].x;
MOV result.color, array[bar.x + 1];

Writing bar.x is necessary for forward compatibility.

The extension defines an ADDRESS variable as supporting values between -64 and 63 inclusive.

Partial-precision exp and log in vertex programs

EXP and LOG perform less accurate but faster versions of EX2 and LG2, and return results in the z component. Additionally, both return 1 in w, and return values in x and y that may be combined to refine the approximation.

Specifically, EXP returns 2^⌊α⌋ in x and α-⌊α⌋ in y, and the refinement is x + f(y), where f(y) itself approximates 2^y in the domain [0.0; 1.0).

Similarly, LOG returns ⌊log₂(α)⌋ in x and α·2^{-⌊log₂(α)⌋} in y, and the refinement is x + f(y), where f(y) itself approximates 2^y in the domain [1.0; 2.0).

It is possible for an implementation to perform the same result underneath as for EX2 and LG2.

Appendix C contains examples of refinement, though I cannot think of a practical case. I also couldn't find any use of these instructions anywhere. In an Nvidia patent from 2002, it is stated that EX2 and LG2 shouldn't be used, so these instructions are strange to say the least.

Position-invariant vertex programs

Perhaps your vertex program does nothing special to the position, compared to the fixed-function pipeline. In this case you can defer all vertex transformation to OpenGL by writing the following line before any statements.

OPTION ARB_position_invariant;

Upon use result.position becomes inaccessible, and there is a potential speedup depending on the hardware.

Trigonometry in fragment programs

Oh, you thought.

Vertex programs were originally forced to compute sin and cos manually, and one implementation each is included in Appendix C.

For fragment programs, there's SIN, COS with a full-range domain, and the return value in all components.

SCS computes both as long as the angle is within [-π; +π], placing the cosine in x, the sine in y, and leaving z and w undefined.

TEMP a;

SIN a, 3.1415926.x;
COS a, a.x;

SCS a, a.x;

# a.x is the cosine
# a.y is the sine
# a.z and a.w are undefined

In Appendix C is an example of reducing the angle to the range [-π; +π].

Texture instructions in fragment programs

TEX, TXP and TXB perform sampling, given texture coordinates, the unit to sample from and the target of the unit, whether 1D, 2D, 3D, CUBE or RECT.

TEX performs vanilla sampling. TXP interprets the texture coordinates as homogenous, and divides x, y and z values by w prior to sampling. TXB biases the LoD prior to sampling using w, with weighting equal to that of GL_TEXTURE_LOD_BIAS.

TEMP col;
TEX col, fragment.texcoord[0], texture[0], 2D;

Sampling an incomplete texture will give (0.0, 0.0, 0.0, 1.0).

There's an important caveat to make note of. Each sampling with a computed coordinate needs for that computation to first occur. Such sequences are limited in number, and they are called "texture indirections". Texture samplings that do not depend on each other can be parallelized, and so belong to the same texture indirection. Going over the limit, even without exceeding the instruction limit, will cause either an error or a switch to software rendering.

Despite this, the ARB decided with a very liberal definition of a texture indirection. One occurs, when:

• the coordinate is a TEMP that has been written to after the previous texture indirection, or
• the result is a TEMP that has been used after the previous texture indirection

The first texture indirection is the beginning of the program, therefore a program always has at least one texture indirection, even if there are no texture instructions. Passing a PARAM or a fragment attribute such as fragment.texcoord is not a texture indirection.

While hardware may analyze the source to minimize false indirections, it's not forced to.

Because of this, make sure to group as many TEX instructions together as possible. Another trick is to never reuse TEMP variables, although too many TEMPs are known to slow down things on relevant Nvidia hardware.

Discarding in fragment programs

KIL is a conditional version of the modern discard statement. Given an input vector, it discards the fragment if and only if any component of the input is negative.

KIL is a texture instruction, making it count towards the texture indirection limit!

Linear interpolation in fragment programs

LRP performs component-wise linear interpolation of the second and third inputs, using the first as the blend factor.

TEMP t;
LRP t, {0.5, 0, 1, 0.6666666}, {1, 2, 3, 0}, {3, 3, 2, 3};
# Now t is {2, 2, 2, 2}

RGBA components in fragment programs

Fragment programs are allowed to use the r, g, b, a symbols to specify vector components.

Saturation arithmetic in fragment programs

Any instruction in a fragment program, be it texture, arithmetic or even MOV and CMP, may be suffixed with _SAT causing each destination component to be clamped between 0 and 1.

TEMP t;
ADD_SAT t, 0, 5;
# Now t is {1, 1, 1, 1}

Paragon of Virtue, Nvidia

Now I know you're thinking just as me: "Wow, this is the greatest thing since sliced apples, and I'd love to delve even deeper." Well, Nvidia took it upon themselves to continue and update ARB assembly specifications to this day, right to the geometry shaders, compute shaders and even tessellation shaders, extending it with every modern feature there is.

In reality, this is because ARB assembly is used within Nvidia's shader infrastructure, but I'm not complaining. That and no other vendor really supports any of these. As for me, this is really the only thing that would push me to get an external card. Folk wisdom states: only Nvidia has the cool extensions. Having these at my disposal allows me to actually test my software's compatibility range.

If I ever make a next part, I shall detail the additions and the timeline of their introduction.

Conclusion

If you look around or ask any questions for this piece of tech, you're often met with resistance. Such people deem ARB assembly "useless", but only really because they were told to think so. Technology can't just "lose" its use, but that doesn't stop people from screaming it over and over.

Funnily enough, we've come back around to the portable assembly concept with SPIR-V, which allows its modules to specify required "capabilities". Each defined instruction must state the capability it depends on, right down to the most basic things taken for granted today, such as dynamic addressing. This suggests SPIR-V was built also with limited hardware in mind, but how in practice it works — or could work — I cannot say, as I am not sure of its coverage in the area. We'll see; after all, there's too much hardware for it to go anywhere.

I leave the grueling details last for those who intend to actually make use of this information.

Appendix C: Snippets

Some of the following snippets were borrowed from Matthias Wloka.

Divide a.x by b.x

TEMP t;
RCP t.x, b.x;
MUL t.x, t.x, a.x;

Square root of a.x

TEMP t;
RSQ t, a.x;
MUL t, t, a.x;

Clamping to [0; 1]

PARAM p = {0, 1};
MAX a, a, p.x;
MIN a, a, p.y;

Linear interpolation in vertex programs

TEMP t;
ADD t, b, -a;
MAD t, weight, t, a;

Reduce a to [-π; +π]

PARAM p = {0.1591549430919, 6.2831853071796, 3.1415926535898, 0.5};
TEMP t;
MAD t, a, p.x, p.w;
FRC t, t;
MAD t, t, p.y, -p.z;

High precision sine of a.x into t2

PARAM p0 = {0.25, -9, 0.75, 0.1591549430919};
PARAM p1 = {24.9808039603, -24.9808039603, -60.1458091736, 60.1458091736};
PARAM p2 = {85.4537887573, -85.4537887573, -64.9393539429, 64.9393539429};
PARAM p3 = {19.7392082214, -19.7392082214, -1, 1};
TEMP t0;
TEMP t1;
TEMP t2;
MAD t0, a.x, p0.w, p0.x;
FRC t0, t0;
SLT t1.x, t0, p0;
SGE t1.yz, t0, p0;
DP3 t1.y, t1, p3.zwzw;
ADD t2.xyz, -t0.y, {0, 0.5, 1, 0};
MUL t2, t2, t2;
MAD t0, p1.xyxy, t2, p1.zwzw;
MAD t0, t0, t2, p2.xyxy;
MAD t0, t0, t2, p2.zwzw;
MAD t0, t0, t2, p3.xyxy;
MAD t0, t0, t2, p3.zwzw;
DP3 t2, t0, t1;

High precision cosine of a.x into t2

PARAM p0 = {0.25, -9, 0.75, 0.1591549430919};
PARAM p1 = {24.9808039603, -24.9808039603, -60.1458091736, 60.1458091736};
PARAM p2 = {85.4537887573, -85.4537887573, -64.9393539429, 64.9393539429};
PARAM p3 = {19.7392082214, -19.7392082214, -1, 1};
TEMP t0;
TEMP t1;
TEMP t2;
MUL t0, a.x, p0.w;
FRC t0, t0;
SLT t1.x, t0, p0;
SGE t1.yz, t0, p0;
DP3 t1.y, t1, p3.zwzw;
ADD t2.xyz, -t0.y, {0, 0.5, 1, 0};
MUL t2, t2, t2;
MAD t0, p1.xyxy, t2, p1.zwzw;
MAD t0, t0, t2, p2.xyxy;
MAD t0, t0, t2, p2.zwzw;
MAD t0, t0, t2, p3.xyxy;
MAD t0, t0, t2, p3.zwzw;
DP3 t2, t0, t1;

Example EXP refinement

PARAM p0 = {9.61597636e-03, -1.32823968e-03, 1.47491097e-04, -1.08635004e-05};
PARAM p1 = {1.00000000e+00, -6.93147182e-01, 2.40226462e-01, -5.55036440e-02};
TEMP t;
EXP t, a.x;
MAD t.w, p0.w, t.y, p0.z;
MAD t.w, t.w, t.y, p0.y;
MAD t.w, t.w, t.y, p0.x;
MAD t.w, t.w, t.y, p1.w;
MAD t.w, t.w, t.y, p1.z;
MAD t.w, t.w, t.y, p1.y;
MAD t.w, t.w, t.y, p1.x;
RCP t.w, t.w;
MUL t, t.w, t.x;

Example LOG refinement

PARAM p0 = {2.41873696e-01, -1.37531206e-01, 5.20646796e-02, -9.31049418e-03};
PARAM p1 = {1.44268966e+00, -7.21165776e-01, 4.78684813e-01, -3.47305417e-01};
TEMP t;
LOG t, a.x;
ADD t.y, t.y, -1;
MAD t.w, p0.w, t.y, p0.z;
MAD t.w, t.w, t.y, p0.y;
MAD t.w, t.w, t.y, p0.x;
MAD t.w, t.w, t.y, p1.w;
MAD t.w, t.w, t.y, p1.z;
MAD t.w, t.w, t.y, p1.y;
MAD t.w, t.w, t.y, p1.x;
MAD t, t.w, t.y, t.x;