// 
// TODO:
// - implement texture1D, texture2D, texture3D, textureCube,
// - implement shadow1D, shadow2D,
// - implement dFdx, dFdy,
// 

// 
// From Shader Spec, ver. 1.051
// 
// The output of the fragment shader goes on to be processed by the fixed function operations at
// the back end of the OpenGL pipeline. Fragment shaders interface with the back end of the OpenGL
// pipeline using the built-in variables gl_FragColor and gl_FragDepth, or by executing the discard
// keyword.
// 
// These variables may be written more than once within a fragment shader. If so, the last value
// assigned is the one used in the subsequent fixed function pipeline. The values written to these
// variables may be read back after writing them. Reading from these variables before writing them
// results in an undefined value. The fixed functionality computed depth for a fragment may be
// obtained by reading gl_FragCoord.z, described below.
// 
// Writing to gl_FragColor specifies the fragment color that will be used by the subsequent fixed
// functionality pipeline. If subsequent fixed functionality consumes fragment color and an
// execution of a fragment shader does not write a value to gl_FragColor then the fragment color
// consumed is undefined.
// 
// If the frame buffer is configured as a color index buffer then behavior is undefined when using
// a fragment shader.
// 
// Writing to gl_FragDepth will establish the depth value for the fragment being processed. If
// depth buffering is enabled, and a shader does not write gl_FragDepth, then the fixed function
// value for depth will be used as the fragment’s depth value. If a shader statically assigns
// a value to gl_FragDepth, and there is an execution path through the shader that does not set
// gl_FragDepth, then the value of the fragment’s depth may be undefined for some executions of
// the shader. That is, if a shader statically writes gl_FragDepth, then it is responsible for
// always writing it. There is also no guarantee that a shader can compute the same depth value
// as the fixed function value; an implementation will provide invariant results within shaders
// computing depth with the same source-level expression, but invariance is not provided between
// shaders and fixed functionality.
// 
// Writes to gl_FragColor and gl_FragDepth need not be clamped within a shader. The fixed
// functionality pipeline following the fragment shader will clamp these values.
// 
// If a shader executes the discard keyword, the fragment is discarded, and the values of
// gl_FragDepth and gl_FragColor become irrelevant.
// 
// The variable gl_FragCoord is available as a read-only variable from within fragment shaders
// and it holds the window relative coordinates x, y, z, and 1/w values for the fragment. This
// value is the result of the fixed functionality that interpolates primitives after vertex
// processing to generate fragments. The z component is the depth value that would be used for
// the fragment’s depth if a shader contained no writes to gl_FragDepth. This is useful for
// invariance if a shader conditionally computes gl_FragDepth but otherwise wants the fixed
// functionality fragment depth.
// 
// The fragment shader has access to the read-only built-in variable gl_FrontFacing whose value
// is true if the fragment belongs to a front-facing primitive. One use of this is to emulate
// two-sided lighting by selecting one of two colors calculated by the vertex shader.
// 
// The built-in variables that are accessible from a fragment shader are intrinsically given types
// as follows:
// 

vec4 gl_FragCoord;
bool gl_FrontFacing;
vec4 gl_FragColor;
float gl_FragDepth;

// 
// However, they do not behave like variables with no qualifier; their behavior is as described
// above. These built-in variables have global scope.
// 

// 
// Unlike user-defined varying variables, the built-in varying variables don’t have a strict
// one-to-one correspondence between the vertex language and the fragment language. Two sets are
// provided, one for each language. Their relationship is described below.
// 
// The following varying variables are available to read from in a fragment shader. The gl_Color
// and gl_SecondaryColor names are the same names as attributes passed to the vertex shader.
// However, there is no name conflict, because attributes are visible only in vertex shaders
// and the following are only visible in a fragment shader.
// 

varying vec4 gl_Color;
varying vec4 gl_SecondaryColor;
varying vec4 gl_TexCoord[];                             // at most will be gl_MaxTextureCoordsARB
varying float gl_FogFragCoord;

// 
// The values in gl_Color and gl_SecondaryColor will be derived automatically by the system from
// gl_FrontColor, gl_BackColor, gl_FrontSecondaryColor, and gl_BackSecondaryColor based on which
// face is visible. If fixed functionality is used for vertex processing, then gl_FogFragCoord will
// either be the z-coordinate of the fragment in eye space, or the interpolation of the fog
// coordinate, as described in section 3.10 of the OpenGL 1.4 Specification. The gl_TexCoord[]
// values are the interpolated gl_TexCoord[] values from a vertex shader or the texture coordinates
// of any fixed pipeline based vertex functionality.
// 
// Indices to the fragment shader gl_TexCoord array are as described above in the vertex shader
// text.
// 

// 
// The OpenGL Shading Language defines an assortment of built-in convenience functions for scalar
// and vector operations. Many of these built-in functions can be used in more than one type
// of shader, but some are intended to provide a direct mapping to hardware and so are available
// only for a specific type of shader.
// 
// The built-in functions basically fall into three categories:
// 
// • They expose some necessary hardware functionality in a convenient way such as accessing
//   a texture map. There is no way in the language for these functions to be emulated by a shader.
// 
// • They represent a trivial operation (clamp, mix, etc.) that is very simple for the user
//   to write, but they are very common and may have direct hardware support. It is a very hard
//   problem for the compiler to map expressions to complex assembler instructions.
// 
// • They represent an operation graphics hardware is likely to accelerate at some point. The
//   trigonometry functions fall into this category.
// 
// Many of the functions are similar to the same named ones in common C libraries, but they support
// vector input as well as the more traditional scalar input.
// 
// Applications should be encouraged to use the built-in functions rather than do the equivalent
// computations in their own shader code since the built-in functions are assumed to be optimal
// (e.g., perhaps supported directly in hardware).
// 
// User code can replace built-in functions with their own if they choose, by simply re-declaring
// and defining the same name and argument list.
// 

// 
// Texture Lookup Functions
// 
// Texture lookup functions are available to both vertex and fragment shaders. However, level
// of detail is not computed by fixed functionality for vertex shaders, so there are some
// differences in operation between vertex and fragment texture lookups. The functions in the table
// below provide access to textures through samplers, as set up through the OpenGL API. Texture
// properties such as size, pixel format, number of dimensions, filtering method, number of mip-map
// levels, depth comparison, and so on are also defined by OpenGL API calls. Such properties are
// taken into account as the texture is accessed via the built-in functions defined below.
// 
// If a non-shadow texture call is made to a sampler whose texture has depth comparisons enabled,
// then results are undefined. If a shadow texture call is made to a sampler whose texture does not
// have depth comparisions enabled, the results are also undefined.
// 
// In all functions below, the bias parameter is optional for fragment shaders. The bias parameter
// is not accepted in a vertex shader. For a fragment shader, if bias is present, it is added to
// the calculated level of detail prior to performing the texture access operation. If the bias
// parameter is not provided, then the implementation automatically selects level of detail:
// For a texture that is not mip-mapped, the texture is used directly. If it is mip-mapped and
// running in a fragment shader, the LOD computed by the implementation is used to do the texture
// lookup. If it is mip-mapped and running on the vertex shader, then the base texture is used.
// 
// The built-ins suffixed with “Lod” are allowed only in a vertex shader. For the “Lod” functions,
// lod is directly used as the level of detail.
// 

// 
// Use the texture coordinate coord to do a texture lookup in the 1D texture currently bound
// to sampler. For the projective (“Proj”) versions, the texture coordinate coord.s is divided by
// the last component of coord.
// 
// XXX
vec4 texture1D (sampler1D sampler, float coord, float bias) {
    return vec4 (0.0);
}
vec4 texture1DProj (sampler1D sampler, vec2 coord, float bias) {
    return texture1D (sampler, coord.s / coord.t, bias);
}
vec4 texture1DProj (sampler1D sampler, vec4 coord, float bias) {
    return texture1D (sampler, coord.s / coord.q, bias);
}

// 
// Use the texture coordinate coord to do a texture lookup in the 2D texture currently bound
// to sampler. For the projective (“Proj”) versions, the texture coordinate (coord.s, coord.t) is
// divided by the last component of coord. The third component of coord is ignored for the vec4
// coord variant.
// 
// XXX
vec4 texture2D (sampler2D sampler, vec2 coord, float bias) {
    return vec4 (0.0);
}
vec4 texture2DProj (sampler2D sampler, vec3 coord, float bias) {
    return texture2D (sampler, vec2 (coord.s / coord.p, coord.t / coord.p), bias);
}
vec4 texture2DProj (sampler2D sampler, vec4 coord, float bias) {
    return texture2D (sampler, vec2 (coord.s / coord.q, coord.s / coord.q), bias);
}

// 
// Use the texture coordinate coord to do a texture lookup in the 3D texture currently bound
// to sampler. For the projective (“Proj”) versions, the texture coordinate is divided by coord.q.
// 
// XXX
vec4 texture3D (sampler3D sampler, vec3 coord, float bias) {
    return vec4 (0.0);
}   
vec4 texture3DProj (sampler3D sampler, vec4 coord, float bias) {
    return texture3DProj (sampler, vec3 (coord.s / coord.q, coord.t / coord.q, coord.p / coord.q),
        bias);
}

// 
// Use the texture coordinate coord to do a texture lookup in the cube map texture currently bound
// to sampler. The direction of coord is used to select which face to do a 2-dimensional texture
// lookup in, as described in section 3.8.6 in version 1.4 of the OpenGL specification.
// 
// XXX
vec4 textureCube (samplerCube sampler, vec3 coord, float bias) {
    return vec4 (0.0);
}

// 
// Use texture coordinate coord to do a depth comparison lookup on the depth texture bound
// to sampler, as described in section 3.8.14 of version 1.4 of the OpenGL specification. The 3rd
// component of coord (coord.p) is used as the R value. The texture bound to sampler must be a
// depth texture, or results are undefined. For the projective (“Proj”) version of each built-in,
// the texture coordinate is divide by coord.q, giving a depth value R of coord.p/coord.q. The
// second component of coord is ignored for the “1D” variants.
// 
// XXX
vec4 shadow1D (sampler1DShadow sampler, vec3 coord, float bias) {
    return vec4 (0.0);
}
// XXX
vec4 shadow2D (sampler2DShadow sampler, vec3 coord, float bias) {
    return vec4 (0.0);
}
vec4 shadow1DProj (sampler1DShadow sampler, vec4 coord, float bias) {
    return shadow1D (sampler, vec3 (coord.s / coord.q, 0.0, coord.p / coord.q), bias);
}
vec4 shadow2DProj (sampler2DShadow sampler, vec4 coord, float bias) {
    return shadow2D (sampler, vec3 (coord.s / coord.q, coord.t / coord.q, coord.p / coord.q), bias);
}

// 
// Fragment processing functions are only available in shaders intended for use on the fragment
// processor. Derivatives may be computationally expensive and/or numerically unstable. Therefore,
// an OpenGL implementation may approximate the true derivatives by using a fast but not entirely
// accurate derivative computation.
// 
// The expected behavior of a derivative is specified using forward/backward differencing.
// 
// Forward differencing:
// 
// F(x+dx) - F(x) ~ dFdx(x) * dx            1a
// dFdx(x) ~ (F(x+dx) - F(x)) / dx          1b
// 
// Backward differencing:
// 
// F(x-dx) - F(x) ~ -dFdx(x) * dx           2a
// dFdx(x) ~ (F(x) - F(x-dx)) / dx          2b
// 
// With single-sample rasterization, dx <= 1.0 in equations 1b and 2b. For multi-sample
// rasterization, dx < 2.0 in equations 1b and 2b.
// 
// dFdy is approximated similarly, with y replacing x.
// 
// A GL implementation may use the above or other methods to perform the calculation, subject
// to the following conditions:
// 
// 1) The method may use piecewise linear approximations. Such linear approximations imply that
//    higher order derivatives, dFdx(dFdx(x)) and above, are undefined.
// 
// 2) The method may assume that the function evaluated is continuous. Therefore derivatives within
//    the body of a non-uniform conditional are undefined.
// 
// 3) The method may differ per fragment, subject to the constraint that the method may vary by
//    window coordinates, not screen coordinates. The invariance requirement described in section
//    3.1 of the OpenGL 1.4 specification is relaxed for derivative calculations, because
//    the method may be a function of fragment location.
// 
// Other properties that are desirable, but not required, are:
// 
// 4) Functions should be evaluated within the interior of a primitive (interpolated, not
//    extrapolated).
// 
// 5) Functions for dFdx should be evaluated while holding y constant. Functions for dFdy should
//    be evaluated while holding x constant. However, mixed higher order derivatives, like
//    dFdx(dFdy(y)) and dFdy(dFdx(x)) are undefined.
// 
// In some implementations, varying degrees of derivative accuracy may be obtained by providing
// GL hints (section 5.6 of the OpenGL 1.4 specification), allowing a user to make an image
// quality versus speed tradeoff.
// 

// 
// Returns the derivative in x using local differencing for the input argument p.
// 
// XXX
float dFdx (float p) {
    return 0.0;
}
// XXX
vec2 dFdx (vec2 p) {
    return vec2 (0.0);
}
// XXX
vec3 dFdx (vec3 p) {
    return vec3 (0.0);
}
// XXX
vec4 dFdx (vec4 p) {
    return vec4 (0.0);
}

// 
// Returns the derivative in y using local differencing for the input argument p.
// 
// 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.
// 
// XXX
float dFdy (float p) {
    return 0.0;
}
// XXX
vec2 dFdy (vec2 p) {
    return vec2 (0.0);
}
// XXX
vec3 dFdy (vec3 p) {
    return vec3 (0.0);
}
// XXX
vec4 dFdy (vec4 p) {
    return vec4 (0.0);
}

// 
// Returns the sum of the absolute derivative in x and y using local differencing for the input
// argument p, i.e.:
// 
// return = abs (dFdx (p)) + abs (dFdy (p));
// 

float fwidth (float p) {
    return abs (dFdx (p)) + abs (dFdy (p));
}
vec2 fwidth (vec2 p) {
    return abs (dFdx (p)) + abs (dFdy (p));
}
vec3 fwidth (vec3 p) {
    return abs (dFdx (p)) + abs (dFdy (p));
}
vec4 fwidth (vec4 p) {
    return abs (dFdx (p)) + abs (dFdy (p));
}