float length_(vec2 v)
{
  float n = dot(v, v);
  n = 1.0 / sqrt(n);
  n = 1.0 / n;
  return n;
}

float pow_(float x, float n)
{
  x = log2(x);
  x = x * n;
  x = exp2(x);
  return x;
}

float sin_(float x)
{
  x = x * 0.159154936671257019043 + 0.5; // 48
  x = fract(x); // nop
  x = sin((x - 0.5) * 6.28318548202514648438); // presubtract
  return x;
}

float cos_(float x)
{
  x = x * 0.159154936671257019043 + 0.5; // 48
  x = fract(x); // nop
  x = cos((x - 0.5) * 6.28318548202514648438); // presubtract
  return x;
}

vec3 palette(float d) {
  vec3 v = d + vec3(0.25, 0.40625, 0.5625); // 40 45 49
  v = v * 6.28318548202514648438; // (2 * pi * (1 / (2 * pi))) == 1
  v = cos_(v);
  v = vec3(0.5, 0.5, 0.5) * v + vec3(0.5, 0.5, 0.5); // 48
  return v;
}