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+
+// 
+// TODO:
+// - implement sin, asin, acos, atan, pow, log2, floor, ceil,
+// - implement texture1D, texture2D, texture3D, textureCube,
+// - implement shadow1D, shadow2D,
+// - implement noise1, noise2, noise3, noise4,
+// 
+
+// 
+// From Shader Spec, ver. 1.10, rev. 59
+// 
+// The following built-in constants are provided to vertex and fragment shaders.
+// 
+
+// 
+// Implementation dependent constants. The example values below
+// are the minimum values allowed for these maximums.
+// 
+
+const int gl_MaxLights = 8;                             // GL 1.0
+const int gl_MaxClipPlanes = 6;                         // GL 1.0
+const int gl_MaxTextureUnits = 2;                       // GL 1.3
+const int gl_MaxTextureCoords = 2;                      // ARB_fragment_program
+const int gl_MaxVertexAttribs = 16;                     // ARB_vertex_shader
+const int gl_MaxVertexUniformComponents = 512;          // ARB_vertex_shader
+const int gl_MaxVaryingFloats = 32;                     // ARB_vertex_shader
+const int gl_MaxVertexTextureImageUnits = 0;            // ARB_vertex_shader
+const int gl_MaxCombinedTextureImageUnits = 2;          // ARB_vertex_shader
+const int gl_MaxTextureImageUnits = 2;                  // ARB_fragment_shader
+const int gl_MaxFragmentUniformComponents = 64;         // ARB_fragment_shader
+const int gl_MaxDrawBuffers = 1;                        // proposed ARB_draw_buffers
+
+// 
+// As an aid to accessing OpenGL processing state, the following uniform variables are built into
+// the OpenGL Shading Language. All page numbers and notations are references to the 1.4
+// specification.
+// 
+
+// 
+// Matrix state. p. 31, 32, 37, 39, 40.
+// 
+
+uniform mat4 gl_ModelViewMatrix;
+uniform mat4 gl_ProjectionMatrix;
+uniform mat4 gl_ModelViewProjectionMatrix;
+uniform mat4 gl_TextureMatrix[gl_MaxTextureCoords];
+
+//
+// Derived matrix state that provides inverse and transposed versions
+// of the matrices above. Poorly conditioned matrices may result
+// in unpredictable values in their inverse forms.
+//
+uniform mat3 gl_NormalMatrix; // transpose of the inverse of the
+                              // upper leftmost 3x3 of gl_ModelViewMatrix
+
+uniform mat4 gl_ModelViewMatrixInverse;
+uniform mat4 gl_ProjectionMatrixInverse;
+uniform mat4 gl_ModelViewProjectionMatrixInverse;
+uniform mat4 gl_TextureMatrixInverse[gl_MaxTextureCoords];
+
+uniform mat4 gl_ModelViewMatrixTranspose;
+uniform mat4 gl_ProjectionMatrixTranspose;
+uniform mat4 gl_ModelViewProjectionMatrixTranspose;
+uniform mat4 gl_TextureMatrixTranspose[gl_MaxTextureCoords];
+
+uniform mat4 gl_ModelViewMatrixInverseTranspose;
+uniform mat4 gl_ProjectionMatrixInverseTranspose;
+uniform mat4 gl_ModelViewProjectionMatrixInverseTranspose;
+uniform mat4 gl_TextureMatrixInverseTranspose[gl_MaxTextureCoords];
+
+// 
+// Normal scaling p. 39.
+// 
+
+uniform float gl_NormalScale;
+
+// 
+// Depth range in window coordinates, p. 33
+// 
+
+struct gl_DepthRangeParameters {
+    float near;                                         // n
+    float far;                                          // f
+    float diff;                                         // f - n
+};
+
+uniform gl_DepthRangeParameters gl_DepthRange;
+
+// 
+// Clip planes p. 42.
+// 
+
+uniform vec4 gl_ClipPlane[gl_MaxClipPlanes];
+
+// 
+// Point Size, p. 66, 67.
+// 
+
+struct gl_PointParameters {
+    float size;
+    float sizeMin;
+    float sizeMax;
+    float fadeThresholdSize;
+    float distanceConstantAttenuation;
+    float distanceLinearAttenuation;
+    float distanceQuadraticAttenuation;
+};
+
+uniform gl_PointParameters gl_Point;
+
+// 
+// Material State p. 50, 55.
+// 
+
+struct gl_MaterialParameters {
+    vec4 emission;                                      // Ecm
+    vec4 ambient;                                       // Acm
+    vec4 diffuse;                                       // Dcm
+    vec4 specular;                                      // Scm
+    float shininess;                                    // Srm
+};
+
+uniform gl_MaterialParameters gl_FrontMaterial;
+uniform gl_MaterialParameters gl_BackMaterial;
+
+// 
+// Light State p 50, 53, 55.
+// 
+
+struct gl_LightSourceParameters {
+    vec4 ambient;                                       // Acli
+    vec4 diffuse;                                       // Dcli
+    vec4 specular;                                      // Scli
+    vec4 position;                                      // Ppli
+    vec4 halfVector;                                    // Derived: Hi
+    vec3 spotDirection;                                 // Sdli
+    float spotExponent;                                 // Srli
+    float spotCutoff;                                   // Crli
+                                                        // (range: [0.0,90.0], 180.0)
+    float spotCosCutoff;                                // Derived: cos(Crli)
+                                                        // (range: [1.0,0.0],-1.0)
+    float constantAttenuation;                          // K0
+    float linearAttenuation;                            // K1
+    float quadraticAttenuation;                         // K2
+};
+
+uniform gl_LightSourceParameters gl_LightSource[gl_MaxLights];
+
+struct gl_LightModelParameters {
+    vec4 ambient;                                       // Acs
+};
+
+uniform gl_LightModelParameters gl_LightModel;
+
+// 
+// Derived state from products of light and material.
+// 
+
+struct gl_LightModelProducts {
+    vec4 sceneColor;                                    // Derived. Ecm + Acm * Acs
+};
+
+uniform gl_LightModelProducts gl_FrontLightModelProduct;
+uniform gl_LightModelProducts gl_BackLightModelProduct;
+
+struct gl_LightProducts {
+    vec4 ambient;                                       // Acm * Acli
+    vec4 diffuse;                                       // Dcm * Dcli
+    vec4 specular;                                      // Scm * Scli
+};
+
+uniform gl_LightProducts gl_FrontLightProduct[gl_MaxLights];
+uniform gl_LightProducts gl_BackLightProduct[gl_MaxLights];
+
+// 
+// Texture Environment and Generation, p. 152, p. 40-42.
+// 
+
+uniform vec4 gl_TextureEnvColor[gl_MaxTextureImageUnits];
+uniform vec4 gl_EyePlaneS[gl_MaxTextureCoords];
+uniform vec4 gl_EyePlaneT[gl_MaxTextureCoords];
+uniform vec4 gl_EyePlaneR[gl_MaxTextureCoords];
+uniform vec4 gl_EyePlaneQ[gl_MaxTextureCoords];
+uniform vec4 gl_ObjectPlaneS[gl_MaxTextureCoords];
+uniform vec4 gl_ObjectPlaneT[gl_MaxTextureCoords];
+uniform vec4 gl_ObjectPlaneR[gl_MaxTextureCoords];
+uniform vec4 gl_ObjectPlaneQ[gl_MaxTextureCoords];
+
+// 
+// Fog p. 161
+// 
+
+struct gl_FogParameters {
+    vec4 color;
+    float density;
+    float start;
+    float end;
+    float scale;    // Derived:    1.0 / (end - start)
+};
+
+uniform gl_FogParameters gl_Fog;
+
+// 
+// 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.
+// 
+
+// 
+// 8.1 Angle and Trigonometry Functions
+// 
+// Function parameters specified as angle are assumed to be in units of radians. In no case will
+// any of these functions result in a divide by zero error. If the divisor of a ratio is 0, then
+// results will be undefined.
+// 
+// These all operate component-wise. The description is per component.
+// 
+
+// 
+// Converts degrees to radians and returns the result, i.e., result = PI*deg/180.
+// 
+
+float radians (float deg) {
+    return 3.141593 * deg / 180.0;
+}
+vec2 radians (vec2 deg) {
+    return vec2 (radians (deg.x), radians (deg.y));
+}
+vec3 radians (vec3 deg) {
+    return vec3 (radians (deg.x), radians (deg.y), radians (deg.z));
+}
+vec4 radians (vec4 deg) {
+    return vec4 (radians (deg.x), radians (deg.y), radians (deg.z), radians (deg.w));
+}
+
+// 
+// Converts radians to degrees and returns the result, i.e., result = 180*rad/PI.
+// 
+
+float degrees (float rad) {
+    return 180.0 * rad / 3.141593;
+}
+vec2 degrees (vec2 rad) {
+    return vec2 (degrees (rad.x), degrees (rad.y));
+}
+vec3 degrees (vec3 rad) {
+    return vec3 (degrees (rad.x), degrees (rad.y), degrees (rad.z));
+}
+vec4 degrees (vec4 rad) {
+    return vec4 (degrees (rad.x), degrees (rad.y), degrees (rad.z), degrees (rad.w));
+}
+
+// 
+// The standard trigonometric sine function.
+// 
+// XXX
+float sin (float angle) {
+    return 0.0;
+}
+vec2 sin (vec2 angle) {
+    return vec2 (sin (angle.x), sin (angle.y));
+}
+vec3 sin (vec3 angle) {
+    return vec3 (sin (angle.x), sin (angle.y), sin (angle.z));
+}
+vec4 sin (vec4 angle) {
+    return vec4 (sin (angle.x), sin (angle.y), sin (angle.z), sin (angle.w));
+}
+
+// 
+// The standard trigonometric cosine function.
+// 
+
+float cos (float angle) {
+    return sin (angle + 1.5708);
+}
+vec2 cos (vec2 angle) {
+    return vec2 (cos (angle.x), cos (angle.y));
+}
+vec3 cos (vec3 angle) {
+    return vec3 (cos (angle.x), cos (angle.y), cos (angle.z));
+}
+vec4 cos (vec4 angle) {
+    return vec4 (cos (angle.x), cos (angle.y), cos (angle.z), cos (angle.w));
+}
+
+// 
+// The standard trigonometric tangent.
+// 
+
+float tan (float angle) {
+    return sin (angle) / cos (angle);
+}
+vec2 tan (vec2 angle) {
+    return vec2 (tan (angle.x), tan (angle.y));
+}
+vec3 tan (vec3 angle) {
+    return vec3 (tan (angle.x), tan (angle.y), tan (angle.z));
+}
+vec4 tan (vec4 angle) {
+    return vec4 (tan (angle.x), tan (angle.y), tan (angle.z), tan (angle.w));
+}
+
+// 
+// Arc sine. Returns an angle whose sine is x. The range of values returned by this function is
+// [–PI/2, PI/2]. Results are undefined if |x| > 1.
+// 
+// XXX
+float asin (float x) {
+    return 0.0;
+}
+vec2 asin (vec2 x) {
+    return vec2 (asin (x.x), asin (x.y));
+}
+vec3 asin (vec3 x) {
+    return vec3 (asin (x.x), asin (x.y), asin (x.z));
+}
+vec4 asin (vec4 x) {
+    return vec4 (asin (x.x), asin (x.y), asin (x.z), asin (x.w));
+}
+
+// 
+// Arc cosine. Returns an angle whose cosine is x. The range of values returned by this function is
+// [0, PI]. Results are undefined if |x| > 1.
+// 
+// XXX
+float acos (float x) {
+    return 0.0;
+}
+vec2 acos (vec2 x) {
+    return vec2 (acos (x.x), acos (x.y));
+}
+vec3 acos (vec3 x) {
+    return vec3 (acos (x.x), acos (x.y), acos (x.z));
+}
+vec4 acos (vec4 x) {
+    return vec4 (acos (x.x), acos (x.y), acos (x.z), acos (x.w));
+}
+
+// 
+// Arc tangent. Returns an angle whose tangent is y/x. The signs of x and y are used to determine
+// what quadrant the angle is in. The range of values returned by this function is [–PI, PI].
+// Results are undefined if x and y are both 0.
+// 
+// XXX
+float atan (float x, float y) {
+    return 0.0;
+}
+vec2 atan (vec2 x, vec2 y) {
+    return vec2 (atan (x.x, y.x), atan (x.y, y.y));
+}
+vec3 atan (vec3 x, vec3 y) {
+    return vec3 (atan (x.x, y.x), atan (x.y, y.y), atan (x.z, y.z));
+}
+vec4 atan (vec4 x, vec4 y) {
+    return vec4 (atan (x.x, y.x), atan (x.y, y.y), atan (x.z, y.z), atan (x.w, y.w));
+}
+
+// 
+// Arc tangent. Returns an angle whose tangent is y_over_x. The range of values returned by this
+// function is [–PI/2, PI/2].
+// 
+// XXX
+float atan (float y_over_x) {
+    return 0.0;
+}
+vec2 atan (vec2 y_over_x) {
+    return vec2 (atan (y_over_x.x), atan (y_over_x.y));
+}
+vec3 atan (vec3 y_over_x) {
+    return vec3 (atan (y_over_x.x), atan (y_over_x.y), atan (y_over_x.z));
+}
+vec4 atan (vec4 y_over_x) {
+    return vec4 (atan (y_over_x.x), atan (y_over_x.y), atan (y_over_x.z), atan (y_over_x.w));
+}
+
+// 
+// 8.2 Exponential Functions
+// 
+// These all operate component-wise. The description is per component.
+// 
+
+// 
+// Returns x raised to the y power, i.e., x^y.
+// Results are undefined if x < 0.
+// Results are undefined if x = 0 and y <= 0.
+// 
+// XXX
+float pow (float x, float y) {
+    return 0.0;
+}
+vec2 pow (vec2 x, vec2 y) {
+    return vec2 (pow (x.x, y.x), pow (x.y, y.y));
+}
+vec3 pow (vec3 x, vec3 y) {
+    return vec3 (pow (x.x, y.x), pow (x.y, y.y), pow (x.z, y.z));
+}
+vec4 pow (vec4 x, vec4 y) {
+    return vec4 (pow (x.x, y.x), pow (x.y, y.y), pow (x.z, y.z), pow (x.w, y.w));
+}
+
+// 
+// Returns the natural exponentiation of x, i.e., e^x.
+// 
+
+float exp (float x) {
+    return pow (2.71828183, x);
+}
+vec2 exp (vec2 x) {
+    return vec2 (exp (x.x), exp (x.y));
+}
+vec3 exp (vec3 x) {
+    return vec3 (exp (x.x), exp (x.y), exp (x.z));
+}
+vec4 exp (vec4 x) {
+    return vec4 (exp (x.x), exp (x.y), exp (x.z), exp (x.w));
+}
+
+// 
+// Returns the natural logarithm of x, i.e., returns the value y which satisfies the equation
+// x = e^y.
+// Results are undefined if x <= 0.
+// 
+
+float log (float x) {
+    return log2 (x) / log2 (2.71828183);
+}
+vec2 log (vec2 x) {
+    return vec2 (log (x.x), log (x.y));
+}
+vec3 log (vec3 x) {
+    return vec3 (log (x.x), log (x.y), log (x.z));
+}
+vec4 log (vec4 x) {
+    return vec4 (log (x.x), log (x.y), log (x.z), log (x.w));
+}
+
+// 
+// Returns 2 raised to the x power, i.e., 2^x
+// 
+
+float exp2 (float x) {
+    return pow (2.0, x);
+}
+vec2 exp2 (vec2 x) {
+    return vec2 (exp2 (x.x), exp2 (x.y));
+}
+vec3 exp2 (vec3 x) {
+    return vec3 (exp2 (x.x), exp2 (x.y), exp2 (x.z));
+}
+vec4 exp2 (vec4 x) {
+    return vec4 (exp2 (x.x), exp2 (x.y), exp2 (x.z), exp2 (x.w));
+}
+
+// 
+// Returns the base 2 logarithm of x, i.e., returns the value y which satisfies the equation
+// x = 2^y.
+// Results are undefined if x <= 0.
+// 
+// XXX
+float log2 (float x) {
+    return 0.0;
+}
+vec2 log2 (vec2 x) {
+    return vec2 (log2 (x.x), log2 (x.y));
+}
+vec3 log2 (vec3 x) {
+    return vec3 (log2 (x.x), log2 (x.y), log2 (x.z));
+}
+vec4 log2 (vec4 x) {
+    return vec4 (log2 (x.x), log2 (x.y), log2 (x.z), log2 (x.w));
+}
+
+// 
+// Returns the positive square root of x.
+// Results are undefined if x < 0.
+// 
+
+float sqrt (float x) {
+    return pow (x, 0.5);
+}
+vec2 sqrt (vec2 x) {
+    return vec2 (sqrt (x.x), sqrt (x.y));
+}
+vec3 sqrt (vec3 x) {
+    return vec3 (sqrt (x.x), sqrt (x.y), sqrt (x.z));
+}
+vec4 sqrt (vec4 x) {
+    return vec4 (sqrt (x.x), sqrt (x.y), sqrt (x.z), sqrt (x.w));
+}
+
+// 
+// Returns the reciprocal of the positive square root of x.
+// Results are undefined if x <= 0.
+// 
+
+float inversesqrt (float x) {
+    return 1.0 / sqrt (x);
+}
+vec2 inversesqrt (vec2 x) {
+    return vec2 (inversesqrt (x.x), inversesqrt (x.y));
+}
+vec3 inversesqrt (vec3 x) {
+    return vec3 (inversesqrt (x.x), inversesqrt (x.y), inversesqrt (x.z));
+}
+vec4 inversesqrt (vec4 x) {
+    return vec4 (inversesqrt (x.x), inversesqrt (x.y), inversesqrt (x.z), inversesqrt (x.w));
+}
+
+// 
+// 8.3 Common Functions
+// 
+// These all operate component-wise. The description is per component.
+// 
+
+// 
+// Returns x if x >= 0, otherwise it returns –x
+// 
+
+float abs (float x) {
+    return x >= 0.0 ? x : -x;
+}
+vec2 abs (vec2 x) {
+    return vec2 (abs (x.x), abs (x.y));
+}
+vec3 abs (vec3 x) {
+    return vec3 (abs (x.x), abs (x.y), abs (x.z));
+}
+vec4 abs (vec4 x) {
+    return vec4 (abs (x.x), abs (x.y), abs (x.z), abs (x.w));
+}
+
+// 
+// Returns 1.0 if x > 0, 0.0 if x = 0, or –1.0 if x < 0
+// 
+
+float sign (float x) {
+    return x > 0.0 ? 1.0 : x < 0.0 ? -1.0 : 0.0;
+}
+vec2 sign (vec2 x) {
+    return vec2 (sign (x.x), sign (x.y));
+}
+vec3 sign (vec3 x) {
+    return vec3 (sign (x.x), sign (x.y), sign (x.z));
+}
+vec4 sign (vec4 x) {
+    return vec4 (sign (x.x), sign (x.y), sign (x.z), sign (x.w));
+}
+
+// 
+// Returns a value equal to the nearest integer that is less than or equal to x
+// 
+// XXX
+float floor (float x) {
+    return 0.0;
+}
+vec2 floor (vec2 x) {
+    return vec2 (floor (x.x), floor (x.y));
+}
+vec3 floor (vec3 x) {
+    return vec3 (floor (x.x), floor (x.y), floor (x.z));
+}
+vec4 floor (vec4 x) {
+    return vec4 (floor (x.x), floor (x.y), floor (x.z), floor (x.w));
+}
+
+// 
+// Returns a value equal to the nearest integer that is greater than or equal to x
+// 
+// XXX
+float ceil (float x) {
+    return 0.0;
+}
+vec2 ceil (vec2 x) {
+    return vec2 (ceil (x.x), ceil (x.y));
+}
+vec3 ceil (vec3 x) {
+    return vec3 (ceil (x.x), ceil (x.y), ceil (x.z));
+}
+vec4 ceil (vec4 x) {
+    return vec4 (ceil (x.x), ceil (x.y), ceil (x.z), ceil (x.w));
+}
+
+// 
+// Returns x – floor (x)
+// 
+
+float fract (float x) {
+    return x - floor (x);
+}
+vec2 fract (vec2 x) {
+    return vec2 (fract (x.x), fract (x.y));
+}
+vec3 fract (vec3 x) {
+    return vec3 (fract (x.x), fract (x.y), fract (x.z));
+}
+vec4 fract (vec4 x) {
+    return vec4 (fract (x.x), fract (x.y), fract (x.z), fract (x.w));
+}
+
+// 
+// Modulus. Returns x – y * floor (x/y)
+// 
+
+float mod (float x, float y) {
+    return x - y * floor (x / y);
+}
+vec2 mod (vec2 x, float y) {
+    return vec2 (mod (x.x, y), mod (x.y, y));
+}
+vec3 mod (vec3 x, float y) {
+    return vec3 (mod (x.x, y), mod (x.y, y), mod (x.z, y));
+}
+vec4 mod (vec4 x, float y) {
+    return vec4 (mod (x.x, y), mod (x.y, y), mod (x.z, y), mod (x.w, y));
+}
+vec2 mod (vec2 x, vec2 y) {
+    return vec2 (mod (x.x, y.x), mod (x.y, y.y));
+}
+vec3 mod (vec3 x, vec3 y) {
+    return vec3 (mod (x.x, y.x), mod (x.y, y.y), mod (x.z, y.z));
+}
+vec4 mod (vec4 x, vec4 y) {
+    return vec4 (mod (x.x, y.x), mod (x.y, y.y), mod (x.z, y.z), mod (x.w, y.w));
+}
+
+// 
+// Returns y if y < x, otherwise it returns x
+// 
+
+float min (float x, float y) {
+    return y < x ? y : x;
+}
+vec2 min (vec2 x, float y) {
+    return vec2 (min (x.x, y), min (x.y, y));
+}
+vec3 min (vec3 x, float y) {
+    return vec3 (min (x.x, y), min (x.y, y), min (x.z, y));
+}
+vec4 min (vec4 x, float y) {
+    return vec4 (min (x.x, y), min (x.y, y), min (x.z, y), min (x.w, y));
+}
+vec2 min (vec2 x, vec2 y) {
+    return vec2 (min (x.x, y.x), min (x.y, y.y));
+}
+vec3 min (vec3 x, vec3 y) {
+    return vec3 (min (x.x, y.x), min (x.y, y.y), min (x.z, y.z));
+}
+vec4 min (vec4 x, vec4 y) {
+    return vec4 (min (x.x, y.x), min (x.y, y.y), min (x.z, y.z), min (x.w, y.w));
+}
+
+// 
+// Returns y if x < y, otherwise it returns x
+// 
+
+float max (float x, float y) {
+    return min (y, x);
+}
+vec2 max (vec2 x, float y) {
+    return vec2 (max (x.x, y), max (x.y, y));
+}
+vec3 max (vec3 x, float y) {
+    return vec3 (max (x.x, y), max (x.y, y), max (x.z, y));
+}
+vec4 max (vec4 x, float y) {
+    return vec4 (max (x.x, y), max (x.y, y), max (x.z, y), max (x.w, y));
+}
+vec2 max (vec2 x, vec2 y) {
+    return vec2 (max (x.x, y.x), max (x.y, y.y));
+}
+vec3 max (vec3 x, vec3 y) {
+    return vec3 (max (x.x, y.x), max (x.y, y.y), max (x.z, y.z));
+}
+vec4 max (vec4 x, vec4 y) {
+    return vec4 (max (x.x, y.x), max (x.y, y.y), max (x.z, y.z), max (x.w, y.w));
+}
+
+// 
+// Returns min (max (x, minVal), maxVal)
+// 
+// Note that colors and depths written by fragment shaders will be clamped by the implementation
+// after the fragment shader runs.
+// 
+
+float clamp (float x, float minVal, float maxVal) {
+    return min (max (x, minVal), maxVal);
+}
+vec2 clamp (vec2 x, float minVal, float maxVal) {
+    return vec2 (clamp (x.x, minVal, maxVal), clamp (x.y, minVal, maxVal));
+}
+vec3 clamp (vec3 x, float minVal, float maxVal) {
+    return vec3 (clamp (x.x, minVal, maxVal), clamp (x.y, minVal, maxVal),
+        clamp (x.z, minVal, maxVal));
+}
+vec4 clamp (vec4 x, float minVal, float maxVal) {
+    return vec4 (clamp (x.x, minVal, maxVal), clamp (x.y, minVal, maxVal),
+        clamp (x.z, minVal, maxVal), clamp (x.w, minVal, maxVal));
+}
+vec2 clamp (vec2 x, vec2 minVal, vec2 maxVal) {
+    return vec2 (clamp (x.x, minVal.x, maxVal.x), clamp (x.y, minVal.y, maxVal.y));
+}
+vec3 clamp (vec3 x, vec3 minVal, vec3 maxVal) {
+    return vec3 (clamp (x.x, minVal.x, maxVal.x), clamp (x.y, minVal.y, maxVal.y),
+        clamp (x.z, minVal.z, maxVal.z));
+}
+vec4 clamp (vec4 x, vec4 minVal, vec4 maxVal) {
+    return vec4 (clamp (x.x, minVal.x, maxVal.y), clamp (x.y, minVal.y, maxVal.y),
+        clamp (x.z, minVal.z, maxVal.z), clamp (x.w, minVal.w, maxVal.w));
+}
+
+// 
+// Returns x * (1 – a) + y * a, i.e., the linear blend of x and y
+// 
+
+float mix (float x, float y, float a) {
+    return x * (1.0 - a) + y * a;
+}
+vec2 mix (vec2 x, vec2 y, float a) {
+    return vec2 (mix (x.x, y.x, a), mix (x.y, y.y, a));
+}
+vec3 mix (vec3 x, vec3 y, float a) {
+    return vec3 (mix (x.x, y.x, a), mix (x.y, y.y, a), mix (x.z, y.z, a));
+}
+vec4 mix (vec4 x, vec4 y, float a) {
+    return vec4 (mix (x.x, y.x, a), mix (x.y, y.y, a), mix (x.z, y.z, a), mix (x.w, y.w, a));
+}
+vec2 mix (vec2 x, vec2 y, vec2 a) {
+    return vec2 (mix (x.x, y.x, a.x), mix (x.y, y.y, a.y));
+}
+vec3 mix (vec3 x, vec3 y, vec3 a) {
+    return vec3 (mix (x.x, y.x, a.x), mix (x.y, y.y, a.y), mix (x.z, y.z, a.z));
+}
+vec4 mix (vec4 x, vec4 y, vec4 a) {
+    return vec4 (mix (x.x, y.x, a.x), mix (x.y, y.y, a.y), mix (x.z, y.z, a.z),
+        mix (x.w, y.w, a.w));
+}
+
+// 
+// Returns 0.0 if x < edge, otherwise it returns 1.0
+// 
+
+float step (float edge, float x) {
+    return x < edge ? 0.0 : 1.0;
+}
+vec2 step (float edge, vec2 x) {
+    return vec2 (step (edge, x.x), step (edge, x.y));
+}
+vec3 step (float edge, vec3 x) {
+    return vec3 (step (edge, x.x), step (edge, x.y), step (edge, x.z));
+}
+vec4 step (float edge, vec4 x) {
+    return vec4 (step (edge, x.x), step (edge, x.y), step (edge, x.z), step (edge, x.w));
+}
+vec2 step (vec2 edge, vec2 x) {
+    return vec2 (step (edge.x, x.x), step (edge.y, x.y));
+}
+vec3 step (vec3 edge, vec3 x) {
+    return vec3 (step (edge.x, x.x), step (edge.y, x.y), step (edge.z, x.z));
+}
+vec4 step (vec4 edge, vec4 x) {
+    return vec4 (step (edge.x, x.x), step (edge.y, x.y), step (edge.z, x.z), step (edge.w, x.w));
+}
+
+// 
+// Returns 0.0 if x <= edge0 and 1.0 if x >= edge1 and performs smooth Hermite interpolation
+// between 0 and 1 when edge0 < x < edge1. This is useful in cases where you would want a threshold
+// function with a smooth transition. This is equivalent to:
+// <type> t;
+// t = clamp ((x – edge0) / (edge1 – edge0), 0, 1);
+// return t * t * (3 – 2 * t);
+// 
+
+float smoothstep (float edge0, float edge1, float x) {
+    const float t = clamp ((x - edge0) / (edge1 - edge0), 0.0, 1.0);
+    return t * t * (3.0 - 2.0 * t);
+}
+vec2 smoothstep (float edge0, float edge1, vec2 x) {
+    return vec2 (smoothstep (edge0, edge1, x.x), smoothstep (edge0, edge1, x.y));
+}
+vec3 smoothstep (float edge0, float edge1, vec3 x) {
+    return vec3 (smoothstep (edge0, edge1, x.x), smoothstep (edge0, edge1, x.y),
+        smoothstep (edge0, edge1, x.z));
+}
+vec4 smoothstep (float edge0, float edge1, vec4 x) {
+    return vec4 (smoothstep (edge0, edge1, x.x), smoothstep (edge0, edge1, x.y),
+        smoothstep (edge0, edge1, x.z), smoothstep (edge0, edge1, x.w));
+}
+vec2 smoothstep (vec2 edge0, vec2 edge1, vec2 x) {
+    return vec2 (smoothstep (edge0.x, edge1.x, x.x), smoothstep (edge0.y, edge1.y, x.y));
+}
+vec3 smoothstep (vec3 edge0, vec3 edge1, vec3 x) {
+    return vec3 (smoothstep (edge0.x, edge1.x, x.x), smoothstep (edge0.y, edge1.y, x.y),
+        smoothstep (edge0.z, edge1.z, x.z));
+}
+vec4 smoothstep (vec4 edge0, vec4 edge1, vec4 x) {
+    return vec4 (smoothstep (edge0.x, edge1.x, x.x), smoothstep (edge0.y, edge1.y, x.y),
+        smoothstep (edge0.z, edge1.z, x.z), smoothstep (edge0.w, edge1.w, x.w));
+}
+
+// 
+// 8.4 Geometric Functions
+// 
+// These operate on vectors as vectors, not component-wise.
+// 
+
+// 
+// Returns the dot product of x and y, i.e., result = x[0] * y[0] + x[1] * y[1] + ...
+// 
+
+float dot (float x, float y) {
+    return x * y;
+}
+float dot (vec2 x, vec2 y) {
+    return dot (x.x, y.x) + dot (x.y, y.y);
+}
+float dot (vec3 x, vec3 y) {
+    return dot (x.x, y.x) + dot (x.y, y.y) + dot (x.z, y.z);
+}
+float dot (vec4 x, vec4 y) {
+    return dot (x.x, y.x) + dot (x.y, y.y) + dot (x.z, y.z) + dot (x.w, y.w);
+}
+
+// 
+// Returns the length of vector x, i.e., sqrt (x[0] * x[0] + x[1] * x[1] + ...)
+// 
+
+float length (float x) {
+    return sqrt (dot (x, x));
+}
+float length (vec2 x) {
+    return sqrt (dot (x, x));
+}
+float length (vec3 x) {
+    return sqrt (dot (x, x));
+}
+float length (vec4 x) {
+    return sqrt (dot (x, x));
+}
+
+// 
+// Returns the distance between p0 and p1, i.e. length (p0 – p1)
+// 
+
+float distance (float x, float y) {
+    return length (x - y);
+}
+float distance (vec2 x, vec2 y) {
+    return length (x - y);
+}
+float distance (vec3 x, vec3 y) {
+    return length (x - y);
+}
+float distance (vec4 x, vec4 y) {
+    return length (x - y);
+}
+
+// 
+// Returns the cross product of x and y, i.e.
+// result.0 = x[1] * y[2] - y[1] * x[2]
+// result.1 = x[2] * y[0] - y[2] * x[0]
+// result.2 = x[0] * y[1] - y[0] * x[1]
+// 
+
+vec3 cross (vec3 x, vec3 y) {
+    return vec3 (x.y * y.z - y.y * x.z, x.z * y.x - y.z * x.x, x.x * y.y - y.x * x.y);
+}
+
+// 
+// Returns a vector in the same direction as x but with a length of 1.
+// 
+
+float normalize (float x) {
+    return 1.0;
+}
+vec2 normalize (vec2 x) {
+    return x / length (x);
+}
+vec3 normalize (vec3 x) {
+    return x / length (x);
+}
+vec4 normalize (vec4 x) {
+    return x / length (x);
+}
+
+// 
+// If dot (Nref, I) < 0 return N otherwise return –N
+// 
+
+float faceforward (float N, float I, float Nref) {
+    return dot (Nref, I) < 0.0 ? N : -N;
+}
+vec2 faceforward (vec2 N, vec2 I, vec2 Nref) {
+    return dot (Nref, I) < 0.0 ? N : -N;
+}
+vec3 faceforward (vec3 N, vec3 I, vec3 Nref) {
+    return dot (Nref, I) < 0.0 ? N : -N;
+}
+vec4 faceforward (vec4 N, vec4 I, vec4 Nref) {
+    return dot (Nref, I) < 0.0 ? N : -N;
+}
+
+// 
+// For the incident vector I and surface orientation N, returns the reflection direction:
+// result = I - 2 * dot (N, I) * N
+// N must already be normalized in order to achieve the desired result.
+
+float reflect (float I, float N) {
+    return I - 2.0 * dot (N, I) * N;
+}
+vec2 reflect (vec2 I, vec2 N) {
+    return I - 2.0 * dot (N, I) * N;
+}
+vec3 reflect (vec3 I, vec3 N) {
+    return I - 2.0 * dot (N, I) * N;
+}
+vec4 reflect (vec4 I, vec4 N) {
+    return I - 2.0 * dot (N, I) * N;
+}
+
+//
+// For the incident vector I and surface normal N, and the ratio of inidices of refraction eta,
+// return the refraction vector. The returned result is computed by
+//
+// k = 1.0 - eta * eta * (1.0 - dot (N, I) * dot (N, I))
+// if (k < 0.0)
+//   result = genType (0.0)
+// else
+//   result = eta * I - (eta * dot (N, I) + sqrt (k)) * N
+//
+// The input parameters for the incident vector I and the surface normal N must already be
+// normalized to get the desired results.
+//
+
+float refract (float I, float N, float eta) {
+    const float k = 1.0 - eta * eta * (1.0 - dot (N, I) * dot (N, I));
+    if (k < 0.0)
+        return 0.0;
+    return eta * I - (eta * dot (N, I) + sqrt (k)) * N;
+}
+vec2 refract (vec2 I, vec2 N, float eta) {
+    const float k = 1.0 - eta * eta * (1.0 - dot (N, I) * dot (N, I));
+    if (k < 0.0)
+        return vec2 (0.0);
+    return eta * I - (eta * dot (N, I) + sqrt (k)) * N;
+}
+vec3 refract (vec3 I, vec3 N, float eta) {
+    const float k = 1.0 - eta * eta * (1.0 - dot (N, I) * dot (N, I));
+    if (k < 0.0)
+        return vec3 (0.0);
+    return eta * I - (eta * dot (N, I) + sqrt (k)) * N;
+}
+vec4 refract (vec4 I, vec4 N, float eta) {
+    const float k = 1.0 - eta * eta * (1.0 - dot (N, I) * dot (N, I));
+    if (k < 0.0)
+        return vec4 (0.0);
+    return eta * I - (eta * dot (N, I) + sqrt (k)) * N;
+}
+
+// 
+// 8.5 Matrix Functions
+// 
+
+// 
+// Multiply matrix x by matrix y component-wise, i.e., result[i][j] is the scalar product
+// of x[i][j] and y[i][j].
+// Note: to get linear algebraic matrix multiplication, use the multiply operator (*).
+// 
+
+mat2 matrixCompMult (mat2 x, mat2 y) {
+    return mat2 (
+        x[0].x * y[0].x, x[0].y * y[0].y,
+        x[1].x * y[1].x, x[1].y * y[1].y
+    );
+}
+mat3 matrixCompMult (mat3 x, mat3 y) {
+    return mat4 (
+        x[0].x * y[0].x, x[0].y * y[0].y, x[0].z * y[0].z,
+        x[1].x * y[1].x, x[1].y * y[1].y, x[1].z * y[1].z,
+        x[2].x * y[2].x, x[2].y * y[2].y, x[2].z * y[2].z
+    );
+}
+mat4 matrixCompMult (mat4 x, mat4 y) {
+    return mat4 (
+        x[0].x * y[0].x, x[0].y * y[0].y, x[0].z * y[0].z + x[0].w * y[0].w,
+        x[1].x * y[1].x, x[1].y * y[1].y, x[1].z * y[1].z + x[1].w * y[1].w,
+        x[2].x * y[2].x, x[2].y * y[2].y, x[2].z * y[2].z + x[2].w * y[2].w,
+        x[3].x * y[3].x, x[3].y * y[3].y, x[3].z * y[3].z + x[3].w * y[3].w
+    );
+}
+
+// 
+// 8.6 Vector Relational Functions
+// 
+// Relational and equality operators (<, <=, >, >=, ==, !=) are defined (or reserved) to produce
+// scalar Boolean results.
+// 
+
+// 
+// Returns the component-wise compare of x < y.
+// 
+
+bvec2 lessThan (vec2 x, vec2 y) {
+    return bvec2 (x.x < y.x, x.y < y.y);
+}
+bvec3 lessThan (vec3 x, vec3 y) {
+    return bvec3 (x.x < y.x, x.y < y.y, x.z < y.z);
+}
+bvec4 lessThan (vec4 x, vec4 y) {
+    return bvec4 (x.x < y.x, x.y < y.y, x.z < y.z, x.w < y.w);
+}
+bvec2 lessThan (ivec2 x, ivec2 y) {
+    return bvec2 (x.x < y.x, x.y < y.y);
+}
+bvec3 lessThan (ivec3 x, ivec3 y) {
+    return bvec3 (x.x < y.x, x.y < y.y, x.z < y.z);
+}
+bvec4 lessThan (ivec4 x, ivec4 y) {
+    return bvec4 (x.x < y.x, x.y < y.y, x.z < y.z, x.w < y.w);
+}
+
+// 
+// Returns the component-wise compare of x <= y.
+// 
+
+bvec2 lessThanEqual (vec2 x, vec2 y) {
+    return bvec2 (x.x <= y.x, x.y <= y.y);
+}
+bvec3 lessThanEqual (vec3 x, vec3 y) {
+    return bvec3 (x.x <= y.x, x.y <= y.y, x.z <= y.z);
+}
+bvec4 lessThanEqual (vec4 x, vec4 y) {
+    return bvec4 (x.x <= y.x, x.y <= y.y, x.z <= y.z, x.w <= y.w);
+}
+bvec2 lessThanEqual (ivec2 x, ivec2 y) {
+    return bvec2 (x.x <= y.x, x.y <= y.y);
+}
+bvec3 lessThanEqual (ivec3 x, ivec3 y) {
+    return bvec3 (x.x <= y.x, x.y <= y.y, x.z <= y.z);
+}
+bvec4 lessThanEqual (ivec4 x, ivec4 y) {
+    return bvec4 (x.x <= y.x, x.y <= y.y, x.z <= y.z, x.w <= y.w);
+}
+
+// 
+// Returns the component-wise compare of x > y.
+// 
+
+bvec2 greaterThan (vec2 x, vec2 y) {
+    return bvec2 (x.x > y.x, x.y > y.y);
+}
+bvec3 greaterThan (vec3 x, vec3 y) {
+    return bvec3 (x.x > y.x, x.y > y.y, x.z > y.z);
+}
+bvec4 greaterThan (vec4 x, vec4 y) {
+    return bvec4 (x.x > y.x, x.y > y.y, x.z > y.z, x.w > y.w);
+}
+bvec2 greaterThan (ivec2 x, ivec2 y) {
+    return bvec2 (x.x > y.x, x.y > y.y);
+}
+bvec3 greaterThan (ivec3 x, ivec3 y) {
+    return bvec3 (x.x > y.x, x.y > y.y, x.z > y.z);
+}
+bvec4 greaterThan (ivec4 x, ivec4 y) {
+    return bvec4 (x.x > y.x, x.y > y.y, x.z > y.z, x.w > y.w);
+}
+
+// 
+// Returns the component-wise compare of x >= y.
+// 
+
+bvec2 greaterThanEqual (vec2 x, vec2 y) {
+    return bvec2 (x.x >= y.x, x.y >= y.y);
+}
+bvec3 greaterThanEqual (vec3 x, vec3 y) {
+    return bvec3 (x.x >= y.x, x.y >= y.y, x.z >= y.z);
+}
+bvec4 greaterThanEqual (vec4 x, vec4 y) {
+    return bvec4 (x.x >= y.x, x.y >= y.y, x.z >= y.z, x.w >= y.w);
+}
+bvec2 greaterThanEqual (ivec2 x, ivec2 y) {
+    return bvec2 (x.x >= y.x, x.y >= y.y);
+}
+bvec3 greaterThanEqual (ivec3 x, ivec3 y) {
+    return bvec3 (x.x >= y.x, x.y >= y.y, x.z >= y.z);
+}
+bvec4 greaterThanEqual (ivec4 x, ivec4 y) {
+    return bvec4 (x.x >= y.x, x.y >= y.y, x.z >= y.z, x.w >= y.w);
+}
+
+// 
+// Returns the component-wise compare of x == y.
+// 
+
+bvec2 equal (vec2 x, vec2 y) {
+    return bvec2 (x.x == y.x, x.y == y.y);
+}
+bvec3 equal (vec3 x, vec3 y) {
+    return bvec3 (x.x == y.x, x.y == y.y, x.z == y.z);
+}
+bvec4 equal (vec4 x, vec4 y) {
+    return bvec4 (x.x == y.x, x.y == y.y, x.z == y.z, x.w == y.w);
+}
+bvec2 equal (ivec2 x, ivec2 y) {
+    return bvec2 (x.x == y.x, x.y == y.y);
+}
+bvec3 equal (ivec3 x, ivec3 y) {
+    return bvec3 (x.x == y.x, x.y == y.y, x.z == y.z);
+}
+bvec4 equal (ivec4 x, ivec4 y) {
+    return bvec4 (x.x == y.x, x.y == y.y, x.z == y.z, x.w == y.w);
+}
+
+// 
+// Returns the component-wise compare of x != y.
+// 
+
+bvec2 notEqual (vec2 x, vec2 y) {
+    return bvec2 (x.x != y.x, x.y != y.y);
+}
+bvec3 notEqual (vec3 x, vec3 y) {
+    return bvec3 (x.x != y.x, x.y != y.y, x.z != y.z);
+}
+bvec4 notEqual (vec4 x, vec4 y) {
+    return (bvec4 (x.x != y.x, x.y != y.y, x.z != y.z, x.w != y.w);
+}
+bvec2 notEqual (ivec2 x, ivec2 y) {
+    return (bvec2 (x.x != y.x, x.y != y.y);
+}
+bvec3 notEqual (ivec3 x, ivec3 y) {
+    return (bvec3 (x.x != y.x, x.y != y.y, x.z != y.z);
+}
+bvec4 notEqual (ivec4 x, ivec4 y) {
+    return (bvec4 (x.x != y.x, x.y != y.y, x.z != y.z, x.w != y.w);
+}
+
+// 
+// Returns true if any component of x is true.
+// 
+
+bool any (bvec2 x) {
+    return x.x || x.y;
+}
+bool any (bvec3 x) {
+    return x.x || x.y || x.z;
+}
+bool any (bvec4 x) {
+    return x.x || x.y || x.z || x.w;
+}
+
+// 
+// Returns true only if all components of x are true.
+// 
+
+bool all (bvec2 x) {
+    return x.x && x.y;
+}
+bool all (bvec3 x) {
+    return x.x && x.y && x.z;
+}
+bool all (bvec4 x) {
+    return x.x && x.y && x.z && x.w;
+}
+
+// 
+// Returns the component-wise logical complement of x.
+// 
+
+bvec2 not (bvec2 x) {
+    return bvec2 (!x.x, !x.y);
+}
+bvec3 not (bvec3 x) {
+    return bvec3 (!x.x, !x.y, !x.z);
+}
+bvec4 not (bvec4 x) {
+    return bvec4 (!x.x, !x.y, !x.z, !x.w);
+}
+
+// 
+// 8.7 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 that represents a depth texture with depth
+// comparisons turned on, then results are undefined. If a shadow texture call is made to a sampler
+// that represents a depth texture with depth comparisions turned off, the results are undefined.
+// If a shadow texture call is made to a sampler that does not represent a depth texture, then
+// results are 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) {
+    return vec4 (0.0);
+}
+vec4 texture1DProj (sampler1D sampler, vec2 coord) {
+    return texture1D (sampler, coord.s / coord.t);
+}
+vec4 texture1DProj (sampler1D sampler, vec4 coord) {
+    return texture1D (sampler, coord.s / coord.q);
+}
+
+// 
+// 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) {
+    return vec4 (0.0);
+}
+vec4 texture2DProj (sampler2D sampler, vec3 coord) {
+    return texture2D (sampler, vec2 (coord.s / coord.p, coord.t / coord.p));
+}
+vec4 texture2DProj (sampler2D sampler, vec4 coord) {
+    return texture2D (sampler, vec2 (coord.s / coord.q, coord.t / coord.q));
+}
+
+// 
+// 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) {
+    return vec4 (0.0);
+}
+vec4 texture3DProj (sampler3D sampler, vec4 coord) {
+    return texture3D (sampler, vec3 (coord.s / coord.q, coord.t / coord.q, coord.p / coord.q));
+}
+
+// 
+// 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) {
+    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) {
+    return vec4 (0.0);
+}
+// XXX
+vec4 shadow2D (sampler2DShadow sampler, vec3 coord) {
+    return vec4 (0.0);
+}
+vec4 shadow1DProj (sampler1DShadow sampler, vec4 coord) {
+    return shadow1D (sampler, vec3 (coord.s / coord.q, 0.0, coord.p / coord.q));
+}
+vec4 shadow2DProj (sampler2DShadow sampler, vec4 coord) {
+    return shadow2D (sampler, vec3 (coord.s / coord.q, coord.t / coord.q, coord.p / coord.q));
+}
+
+// 
+// 8.9 Noise Functions
+// 
+// Noise functions are available to both fragment and vertex shaders. They are stochastic functions
+// that can be used to increase visual complexity. Values returned by the following noise functions
+// give the appearance of randomness, but are not truly random. The noise functions below are
+// defined to have the following characteristics:
+// 
+// - The return value(s) are always in the range [-1,1], and cover at least the range [-0.6, 0.6],
+//   with a gaussian-like distribution.
+// • The return value(s) have an overall average of 0.0
+// • They are repeatable, in that a particular input value will always produce the same return value
+// • They are statistically invariant under rotation (i.e., no matter how the domain is rotated, it
+//   has the same statistical character)
+// • They have a statistical invariance under translation (i.e., no matter how the domain is
+//   translated, it has the same statistical character)
+// • They typically give different results under translation.
+// - The spatial frequency is narrowly concentrated, centered somewhere between 0.5 to 1.0.
+// 
+
+// 
+// Returns a 1D noise value based on the input value x.
+// 
+// XXX
+float noise1 (float x) {
+    return 0.0;
+}
+// XXX
+float noise1 (vec2 x) {
+    return 0.0;
+}
+// XXX
+float noise1 (vec3 x) {
+    return 0.0;
+}
+// XXX
+float noise1 (vec4 x) {
+    return 0.0;
+}
+
+// 
+// Returns a 2D noise value based on the input value x.
+// 
+// XXX
+vec2 noise2 (float x) {
+    return vec2 (0.0);
+}
+// XXX
+vec2 noise2 (vec2 x) {
+    return vec2 (0.0);
+}
+// XXX
+vec2 noise2 (vec3 x) {
+    return vec2 (0.0);
+}
+// XXX
+vec2 noise2 (vec4 x) {
+    return vec2 (0.0);
+}
+
+// 
+// Returns a 3D noise value based on the input value x.
+// 
+// XXX
+vec3 noise3 (float x) {
+    return vec3 (0.0);
+}
+// XXX
+vec3 noise3 (vec2 x) {
+    return vec3 (0.0);
+}
+// XXX
+vec3 noise3 (vec3 x) {
+    return vec3 (0.0);
+}
+// XXX
+vec3 noise3 (vec4 x) {
+    return vec3 (0.0);
+}
+
+// 
+// Returns a 4D noise value based on the input value x.
+// 
+// XXX
+vec4 noise4 (float x) {
+    return vec4 (0.0);
+}
+// XXX
+vec4 noise4 (vec2 x) {
+    return vec4 (0.0);
+}
+// XXX
+vec4 noise4 (vec3 x) {
+    return vec4 (0.0);
+}
+// XXX
+vec4 noise4 (vec4 x) {
+    return vec4 (0.0);
+}
+