Get accurate integer modulo in WebGL shader

Question

I want to get an accurate modulo of x and y in a WebGL fragment shader. x and y are integers.

Graphing mod(x,y), we get the following:

The actual code used to generate the red-and-black rectangle is:

gl_FragColor = vec4(mod(
  float(int(v_texCoord[0]*15.))/15.,
  float(int(v_texCoord[1]*15.))/15.
), 0, 0, 1);

Where v_texCoord is a vec2 ranging from 0,0 at the top-left to 1,1 at the bottom-right. Precision is set to mediump for both float and int.

Reading the chart, we see that although mod(6,6) is correctly 0, mod(7,7) is actually 7! How do I fix this?

I tried to implement my own mod() function. However, it has the same errors, and produces the same graph.

int func_mod(int x, int y) {
    return int(float(x)-float(y)*floor(float(x)/float(y)));
}

In Javascript, where I can debug it, the function works perfectly. I then tried an iterative approach, because I was worried I was going insane and I didn't trust the floating-point division anyway.

int iter_mod(int x, int y) {
    x = int(abs(float(x))); y = int(abs(float(y)));
    for(int i=0; i>-1; i++) {
        if(x < y) break;
        x = x - y;
    }
    return x;
}

This worked, but I can't graph it because it crashes linux with an error in ring 0 when I try. It works fine for the spritesheet calculations I need it for, but I really feel it's an incorrect solution.

(Update: It works perfectly on my phone. It's not my code in error now, it's just my problem…)

Answer 1

Here is a GLSL function that calculates MOD accurately with (float) parameters that should be integers:

/**
 * Returns accurate MOD when arguments are approximate integers.
 */
float modI(float a,float b) {
    float m=a-floor((a+0.5)/b)*b;
    return floor(m+0.5);
}

Please note, if a<0 and b>0 then the return value will be >=0, unlike other languages' % operator.

Answer 2

You're not modding 7 by 7 you're modding 7/15ths by 7/15ths

Try

gl_FragColor = vec4(mod(
  floor(v_texCoord[0] * 15.),
  floor(v_texCoord[1] * 15.)
) / 15., 0, 0, 1);

You can see the 2 versions running here

function render(num) {
  var gl = document.getElementById("c" + num).getContext("webgl");
  var programInfo = twgl.createProgramInfo(gl, ["vs", "fs"]);

  var arrays = {
    position: [-1, -1, 0, 1, -1, 0, -1, 1, 0, -1, 1, 0, 1, -1, 0, 1, 1, 0],
  };
  var bufferInfo = twgl.createBufferInfoFromArrays(gl, arrays);

  var uniforms = {
    resolution: [gl.canvas.width, gl.canvas.height],
    intMod: num == 1,
  };

  gl.useProgram(programInfo.program);
  twgl.setBuffersAndAttributes(gl, programInfo, bufferInfo);
  twgl.setUniforms(programInfo, uniforms);
  twgl.drawBufferInfo(gl, bufferInfo);
}

render(0)
render(1);

canvas { margin: 1em; height: 100px; width: 150px; }
div { display: inline-block; }
pre { text-align: center; }

<script src="https://twgljs.org/dist/3.x/twgl.min.js"></script>
  <script id="vs" type="notjs">
attribute vec4 position;

void main() {
  gl_Position = position;
}
  </script>
  <script id="fs" type="notjs">
precision mediump float;

uniform vec2 resolution;
uniform bool intMod;

void main() {
  vec2 v_texCoord = gl_FragCoord.xy / resolution.xy;

  if (!intMod) {
  
    gl_FragColor = vec4(mod(
      float(int(v_texCoord[0]*15.))/15.,
      float(int(v_texCoord[1]*15.))/15.
    ), 0, 0, 1);

  } else {

    gl_FragColor = vec4(mod(
      floor(v_texCoord[0]*15.),
      floor(v_texCoord[1]*15.)
    )/15., 0, 0, 1);
    
  }
  
}
  </script>
<div><canvas id="c0"></canvas><pre>mod with fractions</pre></div>
<div><canvas id="c1"></canvas><pre>mod with ints</pre></div>

You should also note that mod by 0 is undefined meaning you'll get different results on different GPUs

Answer 3

Note that since webGL2, we now have int operations so this problem is now trivially solve by x % y .