How to access automatic mipmap level in GLSL fragment shader texture?

How do I determine what mipmap level was used when sampling a texture in a GLSL fragment shader?

I understand that I can manually sample a particular mipmap level of a texture using the textureLod(...) method:

uniform sampler2D myTexture;

void main()
{
    float mipmapLevel = 1;
    vec2 textureCoord = vec2(0.5, 0.5);
    gl_FragColor = textureLod(myTexture, textureCoord, mipmapLevel);
}

Or I could allow the mipmap level to be selected automatically using texture(...) like

uniform sampler2D myTexture;

void main()
{
    vec2 textureCoord = vec2(0.5, 0.5);
    gl_FragColor = texture(myTexture, textureCoord);
}

I prefer the latter, because I trust the driver's judgment about appropriate mipmap level more than I do my own.

But I'd like to know what mipmap level was used in the automatic sampling process, to help me rationally sample nearby pixels. Is there a way in GLSL to access the information about what mipmap level was used for an automatic texture sample?

Below are three distinct approaches to this problem, depending on which OpenGL features are available to you:

1. As pointed out by Andon M. Coleman in the comments, the solution in OpenGL version 4.00 and above is simple; just use the textureQueryLod function:

   #version 400
   
   uniform sampler2D myTexture;
   in vec2 textureCoord; // in normalized units
   out vec4 fragColor;
   
   void main()
   {
       float mipmapLevel = textureQueryLod(myTexture, textureCoord).x;
       fragColor = textureLod(myTexture, textureCoord, mipmapLevel);
   }
   

2. In earlier versions of OpenGL (2.0+?), you might be able to load an extension, to similar effect. This approach worked for my case. NOTE: the method call is capitalized differently in the extension, vs. the built-in (queryTextureLod vs queryTextureLOD).

   #version 330
   
   #extension GL_ARB_texture_query_lod : enable
   
   uniform sampler2D myTexture;
   in vec2 textureCoord; // in normalized units
   out vec4 fragColor;
   
   void main()
   {
       float mipmapLevel = 3; // default in case extension is unavailable...
   #ifdef GL_ARB_texture_query_lod
       mipmapLevel = textureQueryLOD(myTexture, textureCoord).x; // NOTE CAPITALIZATION
   #endif
       fragColor = textureLod(myTexture, textureCoord, mipmapLevel);
   }
   

3. If loading the extension does not work, you could estimate the automatic level of detail using the approach contributed by genpfault:

   #version 330
   
   uniform sampler2D myTexture;
   in vec2 textureCoord; // in normalized units
   out vec4 fragColor;
   
   // Does not take into account GL_TEXTURE_MIN_LOD/GL_TEXTURE_MAX_LOD/GL_TEXTURE_LOD_BIAS,
   // nor implementation-specific flexibility allowed by OpenGL spec
   float mip_map_level(in vec2 texture_coordinate) // in texel units
   {
       vec2  dx_vtc        = dFdx(texture_coordinate);
       vec2  dy_vtc        = dFdy(texture_coordinate);
       float delta_max_sqr = max(dot(dx_vtc, dx_vtc), dot(dy_vtc, dy_vtc));
       float mml = 0.5 * log2(delta_max_sqr);
       return max( 0, mml ); // Thanks @Nims
   }
   
   void main()
   {
       // convert normalized texture coordinates to texel units before calling mip_map_level
       float mipmapLevel = mip_map_level(textureCoord * textureSize(myTexture, 0));
       fragColor = textureLod(myTexture, textureCoord, mipmapLevel);
   }
   

In any case, for my particular application, I ended up just computing the mipmap level on the host side, and passing it to the shader, because the automatic level-of-detail turned out to be not exactly what I needed.