How is it possible to implement Perlin noise in glsl?

I would like to implement Perlin noise in glsl. I've found a lot of examples, but they are not written in shaders or are not well documented, and I am not able to undestand how the permutation or gradient selection works without lookup tables.

One of the examples is this: WebGL noise

I can recognise some similar function calls, but I do not really see how it solves the permutation and gradient selection, and why was it implemented this way. There are some unknown constants in the equations aswell.

---

My question in not specifically about the linked code, but about how to implement Perlin noise in a shader. But for the completeness, I include the code aswell:

// Classic Perlin noise
float cnoise(vec2 P)
{
  vec4 Pi = floor(P.xyxy) + vec4(0.0, 0.0, 1.0, 1.0);
  vec4 Pf = fract(P.xyxy) - vec4(0.0, 0.0, 1.0, 1.0);
  Pi = mod289(Pi); // To avoid truncation effects in permutation
  vec4 ix = Pi.xzxz;
  vec4 iy = Pi.yyww;
  vec4 fx = Pf.xzxz;
  vec4 fy = Pf.yyww;

  vec4 i = permute(permute(ix) + iy);

  vec4 gx = fract(i * (1.0 / 41.0)) * 2.0 - 1.0 ;
  vec4 gy = abs(gx) - 0.5 ;
  vec4 tx = floor(gx + 0.5);
  gx = gx - tx;

  vec2 g00 = vec2(gx.x,gy.x);
  vec2 g10 = vec2(gx.y,gy.y);
  vec2 g01 = vec2(gx.z,gy.z);
  vec2 g11 = vec2(gx.w,gy.w);

  vec4 norm = taylorInvSqrt(vec4(dot(g00, g00), dot(g01, g01), dot(g10, g10), dot(g11, g11)));
  g00 *= norm.x;  
  g01 *= norm.y;  
  g10 *= norm.z;  
  g11 *= norm.w;  

  float n00 = dot(g00, vec2(fx.x, fy.x));
  float n10 = dot(g10, vec2(fx.y, fy.y));
  float n01 = dot(g01, vec2(fx.z, fy.z));
  float n11 = dot(g11, vec2(fx.w, fy.w));

  vec2 fade_xy = fade(Pf.xy);
  vec2 n_x = mix(vec2(n00, n01), vec2(n10, n11), fade_xy.x);
  float n_xy = mix(n_x.x, n_x.y, fade_xy.y);
  return 2.3 * n_xy;
}