Solve maximum representable value.

Author: KelSolaar

notebooks/gamut_mapping_compression_functions_01.ipynb

@@ -43,7 +43,7 @@
       "*                [Clang 11.0.0 (clang-1100.0.33.16)]                          *\n",
       "*                                                                             *\n",
       "*   colour-science.org :                                                      *\n",
-      "*       colour : v0.3.15-132-g8ed24e8e                                        *\n",
+      "*       colour : v0.3.15-141-g3bebd7e9                                        *\n",
       "*                                                                             *\n",
       "*   Runtime :                                                                 *\n",
       "*       imageio : 2.8.0                                                       *\n",
@@ -128,7 +128,7 @@
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "2b308d2eb0af46088af0942ed25426fc",
+       "model_id": "0682438225404555bcfc31ffbf717986",
        "version_major": 2,
        "version_minor": 0
       },
@@ -197,7 +197,7 @@
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "444b6201127a401283c81573e1c28c86",
+       "model_id": "5026406f51784d0887ab0f01eeec1781",
        "version_major": 2,
        "version_minor": 0
       },
@@ -210,7 +210,7 @@
     }
    ],
    "source": [
-    "X, A, I = 1.2, 0.8, 1\n",
+    "X, A, I = 65504, 0.8, 1\n",
     "\n",
     "figure, axes = colour.plotting.plot_multi_functions(\n",
     "    {\n",
@@ -221,6 +221,7 @@
     "    },\n",
     "    **{\n",
     "        'standalone': False,\n",
+    "        'bounding_box': [0, 2, 0, 2],\n",
     "        'samples':\n",
     "        np.linspace(0, 2, 1000),\n",
     "        'plot_kwargs': [\n",
@@ -236,6 +237,117 @@
     "\n",
     "axes.scatter(X, I, c='b', s=50, zorder=4);"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[1, 1.0009766, 1.0019531, 1.0029297, 1.0039062, 1.0048828, 1.0058594, 1.0068359, 1.0078125, 1.0087891]\n"
+     ]
+    }
+   ],
+   "source": [
+    "HFD = [1]\n",
+    "\n",
+    "while True:\n",
+    "    HFD.append(np.nextafter(HFD[-1], +np.inf, dtype=np.float16))\n",
+    "    if HFD[-1] > 65504:\n",
+    "        break\n",
+    "\n",
+    "print(HFD[:10])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[ Threshold 0.0 ]\n",
+      "tanh 6.58594\n",
+      "atan 7376.0\n",
+      "simple 23168.0\n",
+      "\n",
+      "\n",
+      "[ Threshold 0.1 ]\n",
+      "tanh 6.02734\n",
+      "atan 6636.0\n",
+      "simple 14744.0\n",
+      "\n",
+      "\n",
+      "[ Threshold 0.2 ]\n",
+      "tanh 5.46875\n",
+      "atan 5900.0\n",
+      "simple 13104.0\n",
+      "\n",
+      "\n",
+      "[ Threshold 0.3 ]\n",
+      "tanh 4.91016\n",
+      "atan 3650.0\n",
+      "simple 8108.0\n",
+      "\n",
+      "\n",
+      "[ Threshold 0.4 ]\n",
+      "tanh 4.35156\n",
+      "atan 3130.0\n",
+      "simple 6952.0\n",
+      "\n",
+      "\n",
+      "[ Threshold 0.5 ]\n",
+      "tanh 3.61914\n",
+      "atan 1844.0\n",
+      "simple 5792.0\n",
+      "\n",
+      "\n",
+      "[ Threshold 0.6 ]\n",
+      "tanh 3.0957\n",
+      "atan 1476.0\n",
+      "simple 3278.0\n",
+      "\n",
+      "\n",
+      "[ Threshold 0.7 ]\n",
+      "tanh 2.57227\n",
+      "atan 783.0\n",
+      "simple 1738.0\n",
+      "\n",
+      "\n",
+      "[ Threshold 0.8 ]\n",
+      "tanh 1.97852\n",
+      "atan 369.5\n",
+      "simple 820.0\n",
+      "\n",
+      "\n",
+      "[ Threshold 0.9 ]\n",
+      "tanh 1.48926\n",
+      "atan 93.0625\n",
+      "simple 205.625\n",
+      "\n",
+      "\n",
+      "[ Threshold 1.0 ]\n",
+      "tanh 1\n",
+      "atan 1\n",
+      "simple 1\n",
+      "\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "for t in np.linspace(0, 1, 11):\n",
+    "    print(f'[ Threshold {np.around(t, 1)} ]')\n",
+    "    for func in (tanh_compression_function, atan_compression_function, simple_compression_function):\n",
+    "        print(func.__name__.split('_')[0],\n",
+    "              HFD[np.argmax((func(HFD[:-1], t, 1 - t) - func(HFD[1:], t, 1 - t)).astype(np.float16))])\n",
+    "    print('\\n')"
+   ]
   }
  ],
  "metadata": {