Convert floating-point numbers to decimal digits in GLSL - algorithm

Question

As others have discussed, GLSL lacks any kind of printf debugging.
But sometimes I really want to examine numeric values while debugging my shaders.
I've been trying to create a visual debugging tool.
I found that it's possible to render an arbitrary series of digits fairly easily in a shader, if you work with a sampler2D in which the digits 0123456789 have been rendered in monospace. Basically, you just juggle your x coordinate.
Now, to use this to examine a floating-point number, I need an algorithm for converting a float to a sequence of decimal digits, such as you might find in any printf implementation.
Unfortunately, as far as I understand the topic, these algorithms seem to need to represent the
floating-point number in a higher-precision format, and I don't see how this is going to be
possible in GLSL where I seem to have only 32-bit floats available.
For this reason, I think this question is not a duplicate of any general "how does printf work" question, but rather specifically about how such algorithms can be made to work under the constraints of GLSL. I've seen this question and answer, but have no idea what's going on there.
The algorithms I've tried aren't very good.
My first try, marked Version A (commented out) seemed pretty bad:
to take three random examples, RenderDecimal(1.0) rendered as 1.099999702, RenderDecimal(2.5) gave me
2.599999246 and RenderDecimal(2.6) came out as 2.699999280.
My second try, marked Version B, seemed
slightly better: 1.0 and 2.6 both come out fine, but RenderDecimal(2.5) still mismatches an apparent
rounding-up of the 5 with the fact that the residual is 0.099.... The result appears as 2.599000022.
My minimal/complete/verifiable example, below, starts with some shortish GLSL 1.20 code, and then
I happen to have chosen Python 2.x for the rest, just to get the shaders compiled and the textures loaded and rendered. It requires the pygame, NumPy, PyOpenGL and PIL third-party packages. Note that the Python is really just boilerplate and could be trivially (though tediously) re-written in C or anything else. Only the GLSL code at the top is critical for this question, and for this reason I don't think the python or python 2.x tags would be helpful.
It requires the following image to be saved as digits.png:
vertexShaderSource = """\
varying vec2 vFragCoordinate;
void main(void)
{
vFragCoordinate = gl_Vertex.xy;
gl_Position = gl_ModelViewProjectionMatrix * gl_Vertex;
}
"""
fragmentShaderSource = """\
varying vec2 vFragCoordinate;
uniform vec2 uTextureSize;
uniform sampler2D uTextureSlotNumber;
float OrderOfMagnitude( float x )
{
return x == 0.0 ? 0.0 : floor( log( abs( x ) ) / log( 10.0 ) );
}
void RenderDecimal( float value )
{
// Assume that the texture to which uTextureSlotNumber refers contains
// a rendering of the digits '0123456789' packed together, such that
const vec2 startOfDigitsInTexture = vec2( 0, 0 ); // the lower-left corner of the first digit starts here and
const vec2 sizeOfDigit = vec2( 100, 125 ); // each digit spans this many pixels
const float nSpaces = 10.0; // assume we have this many digits' worth of space to render in
value = abs( value );
vec2 pos = vFragCoordinate - startOfDigitsInTexture;
float dpstart = max( 0.0, OrderOfMagnitude( value ) );
float decimal_position = dpstart - floor( pos.x / sizeOfDigit.x );
float remainder = mod( pos.x, sizeOfDigit.x );
if( pos.x >= 0 && pos.x < sizeOfDigit.x * nSpaces && pos.y >= 0 && pos.y < sizeOfDigit.y )
{
float digit_value;
// Version B
float dp, running_value = value;
for( dp = dpstart; dp >= decimal_position; dp -= 1.0 )
{
float base = pow( 10.0, dp );
digit_value = mod( floor( running_value / base ), 10.0 );
running_value -= digit_value * base;
}
// Version A
//digit_value = mod( floor( value * pow( 10.0, -decimal_position ) ), 10.0 );
vec2 textureSourcePosition = vec2( startOfDigitsInTexture.x + remainder + digit_value * sizeOfDigit.x, startOfDigitsInTexture.y + pos.y );
gl_FragColor = texture2D( uTextureSlotNumber, textureSourcePosition / uTextureSize );
}
// Render the decimal point
if( ( decimal_position == -1.0 && remainder / sizeOfDigit.x < 0.1 && abs( pos.y ) / sizeOfDigit.y < 0.1 ) ||
( decimal_position == 0.0 && remainder / sizeOfDigit.x > 0.9 && abs( pos.y ) / sizeOfDigit.y < 0.1 ) )
{
gl_FragColor = texture2D( uTextureSlotNumber, ( startOfDigitsInTexture + sizeOfDigit * vec2( 1.5, 0.5 ) ) / uTextureSize );
}
}
void main(void)
{
gl_FragColor = texture2D( uTextureSlotNumber, vFragCoordinate / uTextureSize );
RenderDecimal( 2.5 ); // for current demonstration purposes, just a constant
}
"""
# Python (PyOpenGL) code to demonstrate the above
# (Note: the same OpenGL calls could be made from any language)
import os, sys, time
import OpenGL
from OpenGL.GL import *
from OpenGL.GLU import *
import pygame, pygame.locals # just for getting a canvas to draw on
try: from PIL import Image # PIL.Image module for loading image from disk
except ImportError: import Image # old PIL didn't package its submodules on the path
import numpy # for manipulating pixel values on the Python side
def CompileShader( type, source ):
shader = glCreateShader( type )
glShaderSource( shader, source )
glCompileShader( shader )
result = glGetShaderiv( shader, GL_COMPILE_STATUS )
if result != 1:
raise Exception( "Shader compilation failed:\n" + glGetShaderInfoLog( shader ) )
return shader
class World:
def __init__( self, width, height ):
self.window = pygame.display.set_mode( ( width, height ), pygame.OPENGL | pygame.DOUBLEBUF )
# compile shaders
vertexShader = CompileShader( GL_VERTEX_SHADER, vertexShaderSource )
fragmentShader = CompileShader( GL_FRAGMENT_SHADER, fragmentShaderSource )
# build shader program
self.program = glCreateProgram()
glAttachShader( self.program, vertexShader )
glAttachShader( self.program, fragmentShader )
glLinkProgram( self.program )
# try to activate/enable shader program, handling errors wisely
try:
glUseProgram( self.program )
except OpenGL.error.GLError:
print( glGetProgramInfoLog( self.program ) )
raise
# enable alpha blending
glTexEnvf( GL_TEXTURE_ENV, GL_TEXTURE_ENV_MODE, GL_MODULATE )
glEnable( GL_DEPTH_TEST )
glEnable( GL_BLEND )
glBlendEquation( GL_FUNC_ADD )
glBlendFunc( GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA )
# set projection and background color
gluOrtho2D( 0, width, 0, height )
glClearColor( 0.0, 0.0, 0.0, 1.0 )
self.uTextureSlotNumber_addr = glGetUniformLocation( self.program, 'uTextureSlotNumber' )
self.uTextureSize_addr = glGetUniformLocation( self.program, 'uTextureSize' )
def RenderFrame( self, *textures ):
glClear( GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT )
for t in textures: t.Draw( world=self )
pygame.display.flip()
def Close( self ):
pygame.display.quit()
def Capture( self ):
w, h = self.window.get_size()
rawRGB = glReadPixels( 0, 0, w, h, GL_RGB, GL_UNSIGNED_BYTE )
return Image.frombuffer( 'RGB', ( w, h ), rawRGB, 'raw', 'RGB', 0, 1 ).transpose( Image.FLIP_TOP_BOTTOM )
class Texture:
def __init__( self, source, slot=0, position=(0,0,0) ):
# wrangle array
source = numpy.array( source )
if source.dtype.type not in [ numpy.float32, numpy.float64 ]: source = source.astype( float ) / 255.0
while source.ndim < 3: source = numpy.expand_dims( source, -1 )
if source.shape[ 2 ] == 1: source = source[ :, :, [ 0, 0, 0 ] ] # LUMINANCE -> RGB
if source.shape[ 2 ] == 2: source = source[ :, :, [ 0, 0, 0, 1 ] ] # LUMINANCE_ALPHA -> RGBA
if source.shape[ 2 ] == 3: source = source[ :, :, [ 0, 1, 2, 2 ] ]; source[ :, :, 3 ] = 1.0 # RGB -> RGBA
# now it can be transferred as GL_RGBA and GL_FLOAT
# housekeeping
self.textureSize = [ source.shape[ 1 ], source.shape[ 0 ] ]
self.textureSlotNumber = slot
self.textureSlotCode = getattr( OpenGL.GL, 'GL_TEXTURE%d' % slot )
self.listNumber = slot + 1
self.position = list( position )
# transfer texture content
glActiveTexture( self.textureSlotCode )
self.textureID = glGenTextures( 1 )
glBindTexture( GL_TEXTURE_2D, self.textureID )
glEnable( GL_TEXTURE_2D )
glTexImage2D( GL_TEXTURE_2D, 0, GL_RGBA32F, self.textureSize[ 0 ], self.textureSize[ 1 ], 0, GL_RGBA, GL_FLOAT, source[ ::-1 ] )
glTexParameterf( GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_NEAREST )
glTexParameterf( GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_NEAREST )
# define surface
w, h = self.textureSize
glNewList( self.listNumber, GL_COMPILE )
glBegin( GL_QUADS )
glColor3f( 1, 1, 1 )
glNormal3f( 0, 0, 1 )
glVertex3f( 0, h, 0 )
glVertex3f( w, h, 0 )
glVertex3f( w, 0, 0 )
glVertex3f( 0, 0, 0 )
glEnd()
glEndList()
def Draw( self, world ):
glPushMatrix()
glTranslate( *self.position )
glUniform1i( world.uTextureSlotNumber_addr, self.textureSlotNumber )
glUniform2f( world.uTextureSize_addr, *self.textureSize )
glCallList( self.listNumber )
glPopMatrix()
world = World( 1000, 800 )
digits = Texture( Image.open( 'digits.png' ) )
done = False
while not done:
world.RenderFrame( digits )
for event in pygame.event.get():
# Press 'q' to quit or 's' to save a timestamped snapshot
if event.type == pygame.locals.QUIT: done = True
elif event.type == pygame.locals.KEYUP and event.key in [ ord( 'q' ), 27 ]: done = True
elif event.type == pygame.locals.KEYUP and event.key in [ ord( 's' ) ]:
world.Capture().save( time.strftime( 'snapshot-%Y%m%d-%H%M%S.png' ) )
world.Close()

Answer 1

+1 for interesting problem. Was curious so I tried to code this. I need the use of arrays so I chose #version 420 core. My app is rendering single quad covering screen with coordinates <-1,+1>. I am using whole ASCII 8x8 pixel 32x8 characters font texture I created some years ago:
The vertex is simple:
//---------------------------------------------------------------------------
// Vertex
//---------------------------------------------------------------------------
#version 420 core
//---------------------------------------------------------------------------
layout(location=0) in vec4 vertex;
out vec2 pos; // screen position <-1,+1>
void main()
{
pos=vertex.xy;
gl_Position=vertex;
}
//---------------------------------------------------------------------------
Fragment is a bit more complicated:
//---------------------------------------------------------------------------
// Fragment
//---------------------------------------------------------------------------
#version 420 core
//---------------------------------------------------------------------------
in vec2 pos; // screen position <-1,+1>
out vec4 gl_FragColor; // fragment output color
uniform sampler2D txr_font; // ASCII 32x8 characters font texture unit
uniform float fxs,fys; // font/screen resolution ratio
//---------------------------------------------------------------------------
const int _txtsiz=32; // text buffer size
int txt[_txtsiz],txtsiz; // text buffer and its actual size
vec4 col; // color interface for txt_print()
//---------------------------------------------------------------------------
void txt_decimal(float x) // print float x into txt
{
int i,j,c; // l is size of string
float y,a;
const float base=10;
// handle sign
if (x<0.0) { txt[txtsiz]='-'; txtsiz++; x=-x; }
else { txt[txtsiz]='+'; txtsiz++; }
// divide to int(x).fract(y) parts of number
y=x; x=floor(x); y-=x;
// handle integer part
i=txtsiz; // start of integer part
for (;txtsiz<_txtsiz;)
{
a=x;
x=floor(x/base);
a-=base*x;
txt[txtsiz]=int(a)+'0'; txtsiz++;
if (x<=0.0) break;
}
j=txtsiz-1; // end of integer part
for (;i<j;i++,j--) // reverse integer digits
{
c=txt[i]; txt[i]=txt[j]; txt[j]=c;
}
// handle fractional part
for (txt[txtsiz]='.',txtsiz++;txtsiz<_txtsiz;)
{
y*=base;
a=floor(y);
y-=a;
txt[txtsiz]=int(a)+'0'; txtsiz++;
if (y<=0.0) break;
}
txt[txtsiz]=0; // string terminator
}
//---------------------------------------------------------------------------
void txt_print(float x0,float y0) // print txt at x0,y0 [chars]
{
int i;
float x,y;
// fragment position [chars] relative to x0,y0
x=0.5*(1.0+pos.x)/fxs; x-=x0;
y=0.5*(1.0-pos.y)/fys; y-=y0;
// inside bbox?
if ((x<0.0)||(x>float(txtsiz))||(y<0.0)||(y>1.0)) return;
// get font texture position for target ASCII
i=int(x); // char index in txt
x-=float(i);
i=txt[i];
x+=float(int(i&31));
y+=float(int(i>>5));
x/=32.0; y/=8.0; // offset in char texture
col=texture2D(txr_font,vec2(x,y));
}
//---------------------------------------------------------------------------
void main()
{
col=vec4(0.0,1.0,0.0,1.0); // background color
txtsiz=0;
txt[txtsiz]='F'; txtsiz++;
txt[txtsiz]='l'; txtsiz++;
txt[txtsiz]='o'; txtsiz++;
txt[txtsiz]='a'; txtsiz++;
txt[txtsiz]='t'; txtsiz++;
txt[txtsiz]=':'; txtsiz++;
txt[txtsiz]=' '; txtsiz++;
txt_decimal(12.345);
txt_print(1.0,1.0);
gl_FragColor=col;
}
//---------------------------------------------------------------------------
Here my CPU side uniforms:
glUniform1i(glGetUniformLocation(prog_id,"txr_font"),0);
glUniform1f(glGetUniformLocation(prog_id,"fxs"),(8.0)/float(xs));
glUniform1f(glGetUniformLocation(prog_id,"fys"),(8.0)/float(ys));
where xs,ys is my screen resolution. Font is 8x8 in unit 0
Here output for the test fragment code:
If your floating point accuracy is decreased due to HW implementation then you should consider printing in hex where no accuracy loss is present (using binary access). That could be converted to decadic base on integers later ...
see:
string hex2dec conversion on integer math
[Edit2] old style GLSL shaders
I tried to port to old style GLSL and suddenly it works (before it would not compile with arrays present but when I think of it I was trying char[] which was the real reason).
//---------------------------------------------------------------------------
// Vertex
//---------------------------------------------------------------------------
varying vec2 pos; // screen position <-1,+1>
void main()
{
pos=gl_Vertex.xy;
gl_Position=gl_Vertex;
}
//---------------------------------------------------------------------------
//---------------------------------------------------------------------------
// Fragment
//---------------------------------------------------------------------------
varying vec2 pos; // screen position <-1,+1>
uniform sampler2D txr_font; // ASCII 32x8 characters font texture unit
uniform float fxs,fys; // font/screen resolution ratio
//---------------------------------------------------------------------------
const int _txtsiz=32; // text buffer size
int txt[_txtsiz],txtsiz; // text buffer and its actual size
vec4 col; // color interface for txt_print()
//---------------------------------------------------------------------------
void txt_decimal(float x) // print float x into txt
{
int i,j,c; // l is size of string
float y,a;
const float base=10.0;
// handle sign
if (x<0.0) { txt[txtsiz]='-'; txtsiz++; x=-x; }
else { txt[txtsiz]='+'; txtsiz++; }
// divide to int(x).fract(y) parts of number
y=x; x=floor(x); y-=x;
// handle integer part
i=txtsiz; // start of integer part
for (;txtsiz<_txtsiz;)
{
a=x;
x=floor(x/base);
a-=base*x;
txt[txtsiz]=int(a)+'0'; txtsiz++;
if (x<=0.0) break;
}
j=txtsiz-1; // end of integer part
for (;i<j;i++,j--) // reverse integer digits
{
c=txt[i]; txt[i]=txt[j]; txt[j]=c;
}
// handle fractional part
for (txt[txtsiz]='.',txtsiz++;txtsiz<_txtsiz;)
{
y*=base;
a=floor(y);
y-=a;
txt[txtsiz]=int(a)+'0'; txtsiz++;
if (y<=0.0) break;
}
txt[txtsiz]=0; // string terminator
}
//---------------------------------------------------------------------------
void txt_print(float x0,float y0) // print txt at x0,y0 [chars]
{
int i;
float x,y;
// fragment position [chars] relative to x0,y0
x=0.5*(1.0+pos.x)/fxs; x-=x0;
y=0.5*(1.0-pos.y)/fys; y-=y0;
// inside bbox?
if ((x<0.0)||(x>float(txtsiz))||(y<0.0)||(y>1.0)) return;
// get font texture position for target ASCII
i=int(x); // char index in txt
x-=float(i);
i=txt[i];
x+=float(int(i-((i/32)*32)));
y+=float(int(i/32));
x/=32.0; y/=8.0; // offset in char texture
col=texture2D(txr_font,vec2(x,y));
}
//---------------------------------------------------------------------------
void main()
{
col=vec4(0.0,1.0,0.0,1.0); // background color
txtsiz=0;
txt[txtsiz]='F'; txtsiz++;
txt[txtsiz]='l'; txtsiz++;
txt[txtsiz]='o'; txtsiz++;
txt[txtsiz]='a'; txtsiz++;
txt[txtsiz]='t'; txtsiz++;
txt[txtsiz]=':'; txtsiz++;
txt[txtsiz]=' '; txtsiz++;
txt_decimal(12.345);
txt_print(1.0,1.0);
gl_FragColor=col;
}
//---------------------------------------------------------------------------

Answer 2

First of all I want to mention that the amazing solution of Spektre is almost perfect and even more a general solution for text output. I gave his answer an upvote.
As an alternative, I present a minimally invasive solution, and improve the code of the question.
I do not want to conceal the fact that I have studied the solution of Spektre and integrated into my solution.
// Assume that the texture to which uTextureSlotNumber refers contains
// a rendering of the digits '0123456789' packed together, such that
const vec2 startOfDigitsInTexture = vec2( 100, 125 ); // the lower-left corner of the first digit starts here and
const vec2 sizeOfDigit = vec2( 0.1, 0.2 ); // each digit spans this many pixels
const float nSpaces = 10.0; // assume we have this many digits' worth of space to render in
void RenderDigit( int strPos, int digit, vec2 pos )
{
float testStrPos = pos.x / sizeOfDigit.x;
if ( testStrPos >= float(strPos) && testStrPos < float(strPos+1) )
{
float start = sizeOfDigit.x * float(digit);
vec2 textureSourcePosition = vec2( startOfDigitsInTexture.x + start + mod( pos.x, sizeOfDigit.x ), startOfDigitsInTexture.y + pos.y );
gl_FragColor = texture2D( uTextureSlotNumber, textureSourcePosition / uTextureSize );
}
}
The function ValueToDigits interprets a floating point number an fills up an array with the digits.
Each number in the array is in (0, 9).
const int MAX_DIGITS = 32;
int digits[MAX_DIGITS];
int noOfDigits = 0;
int posOfComma = 0;
void Reverse( int start, int end )
{
for ( ; start < end; ++ start, -- end )
{
int digit = digits[start];
digits[start] = digits[end];
digits[end] = digit;
}
}
void ValueToDigits( float value )
{
const float base = 10.0;
int start = noOfDigits;
value = abs( value );
float frac = value; value = floor(value); frac -= value;
// integral digits
for ( ; value > 0.0 && noOfDigits < MAX_DIGITS; ++ noOfDigits )
{
float newValue = floor( value / base );
digits[noOfDigits] = int( value - base * newValue );
value = newValue;
}
Reverse( start, noOfDigits-1 );
posOfComma = noOfDigits;
// fractional digits
for ( ; frac > 0.0 && noOfDigits < MAX_DIGITS; ++ noOfDigits )
{
frac *= base;
float digit = floor( frac );
frac -= digit;
digits[noOfDigits] = int( digit );
}
}
Call ValueToDigits in your original function and find the digit and textur coordinates for the current fragment.
void RenderDecimal( float value )
{
// fill the array of digits with the floating point value
ValueToDigits( value );
// Render the digits
vec2 pos = vFragCoordinate.xy - startOfDigitsInTexture;
if( pos.x >= 0 && pos.x < sizeOfDigit.x * nSpaces && pos.y >= 0 && pos.y < sizeOfDigit.y )
{
// render the digits
for ( int strPos = 0; strPos < noOfDigits; ++ strPos )
RenderDigit( strPos, digits[strPos], pos );
}
// Render the decimal point
float testStrPos = pos.x / sizeOfDigit.x;
float remainder = mod( pos.x, sizeOfDigit.x );
if( ( testStrPos >= float(posOfComma) && testStrPos < float(posOfComma+1) && remainder / sizeOfDigit.x < 0.1 && abs( pos.y ) / sizeOfDigit.y < 0.1 ) ||
( testStrPos >= float(posOfComma-1) && testStrPos < float(posOfComma) && remainder / sizeOfDigit.x > 0.9 && abs( pos.y ) / sizeOfDigit.y < 0.1 ) )
{
gl_FragColor = texture2D( uTextureSlotNumber, ( startOfDigitsInTexture + sizeOfDigit * vec2( 1.5, 0.5 ) ) / uTextureSize );
}
}

Answer 3

Here's my updated fragment shader, which can be dropped into the listing in my original question. It implements the decimal-digit-finding algorithm Spektre proposed, in a way that is even compatible with the legacy GLSL 1.20 dialect I'm using. Without that constraint, Spektre's solution is, of course, much more elegant and powerful.
varying vec2 vFragCoordinate;
uniform vec2 uTextureSize;
uniform sampler2D uTextureSlotNumber;
float Digit( float x, int position, float base )
{
int i;
float digit;
if( position < 0 )
{
x = fract( x );
for( i = -1; i >= position; i-- )
{
if( x <= 0.0 ) { digit = 0.0; break; }
x *= base;
digit = floor( x );
x -= digit;
}
}
else
{
x = floor( x );
float prevx;
for( i = 0; i <= position; i++ )
{
if( x <= 0.0 ) { digit = 0.0; break; }
prevx = x;
x = floor( x / base );
digit = prevx - base * x;
}
}
return digit;
}
float OrderOfMagnitude( float x )
{
return x == 0.0 ? 0.0 : floor( log( abs( x ) ) / log( 10.0 ) );
}
void RenderDecimal( float value )
{
// Assume that the texture to which uTextureSlotNumber refers contains
// a rendering of the digits '0123456789' packed together, such that
const vec2 startOfDigitsInTexture = vec2( 0, 0 ); // the lower-left corner of the first digit starts here and
const vec2 sizeOfDigit = vec2( 100, 125 ); // each digit spans this many pixels
const float nSpaces = 10.0; // assume we have this many digits' worth of space to render in
value = abs( value );
vec2 pos = vFragCoordinate - startOfDigitsInTexture;
float dpstart = max( 0.0, OrderOfMagnitude( value ) );
int decimal_position = int( dpstart - floor( pos.x / sizeOfDigit.x ) );
float remainder = mod( pos.x, sizeOfDigit.x );
if( pos.x >= 0.0 && pos.x < sizeOfDigit.x * nSpaces && pos.y >= 0.0 && pos.y < sizeOfDigit.y )
{
float digit_value = Digit( value, decimal_position, 10.0 );
vec2 textureSourcePosition = vec2( startOfDigitsInTexture.x + remainder + digit_value * sizeOfDigit.x, startOfDigitsInTexture.y + pos.y );
gl_FragColor = texture2D( uTextureSlotNumber, textureSourcePosition / uTextureSize );
}
// Render the decimal point
if( ( decimal_position == -1 && remainder / sizeOfDigit.x < 0.1 && abs( pos.y ) / sizeOfDigit.y < 0.1 ) ||
( decimal_position == 0 && remainder / sizeOfDigit.x > 0.9 && abs( pos.y ) / sizeOfDigit.y < 0.1 ) )
{
gl_FragColor = texture2D( uTextureSlotNumber, ( startOfDigitsInTexture + sizeOfDigit * vec2( 1.5, 0.5 ) ) / uTextureSize );
}
}
void main(void)
{
gl_FragColor = texture2D( uTextureSlotNumber, vFragCoordinate / uTextureSize );
RenderDecimal( 2.5 ); // for current demonstration purposes, just a constant
}