vo_opengl: add new HDR tone mapping algorithm

I call it `mobius` because apparently the form f(x) = (cx+a)/(dx+b) is
called a Möbius transform, which is the algorithm this is based on. In
the extremes it becomes `reinhard` (param=0.0 and `clip` (param=1.0),
smoothly transitioning between the two depending on the parameter.

This is a useful tone mapping algorithm since the tunable mobius
transform allows the user to decide the trade-off between color accuracy
and detail preservation on a continuous scale. The default of 0.3 is
already far more accurate than `reinhard` while also being reasonably
good at preserving highlights, without suffering from the overall
brightness drop and color distortion of `hable`.

For these reasons, make this the new default. Also expand and improve
the documentation for these tone mapping functions.

DOCS/man/options.rst

@@ -4645,13 +4645,27 @@ The following video options are currently all specific to ``--vo=opengl`` and
     display. Valid values are:
 
     clip
-        Hard-clip any out-of-range values.
+        Hard-clip any out-of-range values. Use this when you care about
+        perfect color accuracy for in-range values at the cost of completely
+        distorting out-of-range values. Not generally recommended.
+    mobius
+        Generalization of Reinhard to a Möbius transform with linear section.
+        Smoothly maps out-of-range values while retaining contrast and colors
+        for in-range material as much as possible. Use this when you care about
+        color accuracy more than detail preservation. This is somewhere in
+        between ``clip`` and ``reinhard``, depending on the value of
+        ``--tone-mapping-param``. (default)
     reinhard
         Reinhard tone mapping algorithm. Very simple continuous curve.
-        Preserves dynamic range and peak but uses nonlinear contrast.
+        Preserves overall image brightness but uses nonlinear contrast, which
+        results in flattening of details and degradation in color accuracy.
     hable
-        Similar to ``reinhard`` but preserves dark contrast better (slightly
-        sigmoidal). Developed by John Hable for use in video games. (default)
+        Similar to ``reinhard`` but preserves both dark and bright details
+        better (slightly sigmoidal), at the cost of slightly darkening
+        everything. Developed by John Hable for use in video games. Use this
+        when you care about detail preservation more than color/brightness
+        accuracy. This is roughly equivalent to
+        ``--hdr-tone-mapping=reinhard --tone-mapping-param=0.24``.
     gamma
         Fits a logarithmic transfer between the tone curves.
     linear
@@ -4662,6 +4676,12 @@ The following video options are currently all specific to ``--vo=opengl`` and
     Set tone mapping parameters. Ignored if the tone mapping algorithm is not
     tunable. This affects the following tone mapping algorithms:
 
+    mobius
+        Specifies the transition point from linear to mobius transform. Every
+        value below this point is guaranteed to be mapped 1:1. The higher the
+        value, the more accurate the result will be, at the cost of losing
+        bright details. Defaults to 0.3, which due to the steep initial slope
+        still preserves in-range colors fairly accurately.
     reinhard
         Specifies the local contrast coefficient at the display peak. Defaults
         to 0.5, which means that in-gamut values will be about half as bright

video/out/opengl/video.c

@@ -328,6 +328,7 @@ const struct m_sub_options gl_video_conf = {
         OPT_INTRANGE("target-brightness", target_brightness, 0, 1, 100000),
         OPT_CHOICE("hdr-tone-mapping", hdr_tone_mapping, 0,
                    ({"clip",     TONE_MAPPING_CLIP},
+                    {"mobius",   TONE_MAPPING_MOBIUS},
                     {"reinhard", TONE_MAPPING_REINHARD},
                     {"hable",    TONE_MAPPING_HABLE},
                     {"gamma",    TONE_MAPPING_GAMMA},

video/out/opengl/video.h

@@ -91,6 +91,7 @@ enum blend_subs_mode {
 
 enum tone_mapping {
     TONE_MAPPING_CLIP,
+    TONE_MAPPING_MOBIUS,
     TONE_MAPPING_REINHARD,
     TONE_MAPPING_HABLE,
     TONE_MAPPING_GAMMA,

video/out/opengl/video_shaders.c

@@ -377,6 +377,21 @@ static void pass_tone_map(struct gl_shader_cache *sc, float ref_peak,
         GLSL(color.rgb = clamp(color.rgb, 0.0, 1.0);)
         break;
 
+    case TONE_MAPPING_MOBIUS: {
+        float j = isnan(param) ? 0.3 : param;
+        // solve for M(j) = j; M(ref_peak) = 1.0; M'(j) = 1.0
+        // where M(x) = scale * (x+a)/(x+b)
+        float a = -j*j * (ref_peak - 1) / (j*j - 2*j + ref_peak),
+              b = (j*j - 2*j*ref_peak + ref_peak) / (ref_peak - 1);
+
+        GLSLF("color.rgb = mix(vec3(%f) * (color.rgb + vec3(%f))\n"
+              "                         / (color.rgb + vec3(%f)),\n"
+              "                color.rgb,\n"
+              "                lessThanEqual(color.rgb, vec3(%f)));\n",
+              (b*b + 2*b*j + j*j) / (b - a), a, b, j);
+        break;
+    }
+
     case TONE_MAPPING_REINHARD: {
         float contrast = isnan(param) ? 0.5 : param,
               offset = (1.0 - contrast) / contrast;