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:Assume moon light is RGB(5:5:8) (from 255 max), room light [at 2 meters distance from lamp on white paper] is RGB(55:50:40), sun light is RGB(230:225:210) on white paper. Then after algorithm moon light will become RGB(<math>2^{\ln(5)} : 2^{\ln(5)}: 2^{\ln(8)}</math>)=RGB(3.05:3.05:4.23) and this need multiply by 5.47, so moon light will become RGB(3.05:3.05:4.23) *5.47=(17:17:23) (moon light [if you don't playing videogames at night] is exception and night lights you must simulate with changing ambient lighting, over wise if you change <math>\ln()</math> to <math>\log_{10}()</math>, then you will get too bright shadows from flashlight; or you can peak moon light stronger than it is, like RGB(15:15:15) and you will get RGB(36:36:36) and I guaranty it will not have impact on shadows from flashlight). After applying algorithm, room lamp light on white paper from 2 meters distance will become RGB(<math>2^{\ln(55)} : 2^{\ln(50)}: 2^{\ln(40)}</math>)=RGB(16.08:15.05:12.9) and this need multiply by 5.47, so will become RGB(16.08:15.05:12.9) *5.4759=(88:82:71) (room light perhaps better should be choosen little bit stronger like RGB(100:100:100), which after algorithm will become RGB(133:133:133)). Sun light on white paper without specularity will become RGB(<math>2^{\ln(230)} : 2^{\ln(225)}: 2^{\ln(210)}</math>)=RGB(43.35:42.7:40.7) and by multiplying with 5.475876 we get RGB(237:234:223). For stronger HDR, instead rising <math>2^{\ln()}</math> we can choose <math>1.5^{\ln()}</math> and decrease ambiant light (this is light under shadow; means how bright is shadow; this is how bright object under shadow of sun light or flash light or lamp). So this algorithm weak light alone makes strong and weak light added to strong light makes overall lighting without noticeable difference. If you don't plan using any lights in videogame, but only Sun light, then you don't need this algorithm. Roughly can say, that in this algorithm need all lights sum passed through this algorithm multiply with diffuse [lighting] and with texture colors, but texture must be multiplied with ambient lighting first, which should made texture brightest colors about 10-50 and diffuse lighting from 0 to 1 multiplied after making texture brightest values 255 to 10-50; so it means, that in the end of algorithm need everything (final color(s) result) divide by 10-50. But actually ambient lighting is just another light without intensity fallow, so better first to multiply each light with diffuse [lighting] (N*L), which can be from 0 to 1 depending on angle between surface and light, and add all lights. Ambient lighting usually don't need to multiply with diffuse, because sky shining from all sides. Ambient lighting must be about from 10 to 100 depending on how strong HDR you want to make (<math>1.5^{\ln()}</math> or <math>2^{\ln()}</math>; ambient 10-20 if 1.5). So then all lights including ambient lighting added, then we pass through algorithm <math>2^{\ln(ambient+diffuse*light1+diffuse*light2+diffuse*light3)}</math>; then what we get, we multiply with texture colors, which can be from 0 to 1. And if texture with lighting need to clamp to 0-1 values then need divide by 255.
:Kinda official or faster way to made similar thing is <math>(ambient+diffuse*light1+diffuse*light2+diffuse*light3)*2/(1+(ambient+diffuse*light1+diffuse*light2+diffuse*light3))</math>, but all lights must be from 0 to 1 and better each light not exceed 0.8 (especially not sun light). For stronger HDR formula become this <math>texture*(ambient+diffuse*light1+diffuse*light2+diffuse*light3)*4/(1+3*(ambient+diffuse*light1+diffuse*light2+diffuse*light3))</math>, which increasing very weak light almost 4 times and strong lights intensity almost don't changing. But official formula multiplying texture first and I suggest don't do it, because dark and not so dark colors will be not such colorful and become more gray. So texture must be multiplied after algorithm and not by all lights sum like this <math>(ambient+diffuse*light1+diffuse*light2+diffuse*light3)*4/(1+3*texture*(ambient+diffuse*light1+diffuse*light2+diffuse*light3))</math>.
:So why in general <math>texture*(5.4759*2^{\ln(255*(ambient+diffuse*light1+diffuse*light2+diffuse*light3))})/255</math> formula better than this <math>texture*(ambient+diffuse*light1+diffuse*light2+diffuse*light3)*2/(1+(ambient+diffuse*light1+diffuse*light2+diffuse*light3))</math> ? Answer is that there almost no difference. In first formula weak light would loose color like from RGB(192:128:64) to RGB(209:158:98), and in second formula light also will lose color but little bit differently like from RGB(192:128:64) to RGB(219:170:102). For weak colours difference bigger: first algorithm RGB(20:10:5) converts to RGB(43.7:27: <math>5.4759\cdot 2^{\ln(5)}</math>)=RGB(43.7:10: <math>5.4759\cdot 2^{1.6094}</math>) =RGB(43.7:27: <math>5.4759\cdot 3.05133</math>)=RGB(43.7:27:16.7)=RGB(44:27:17); second algorithm RGB(20:10:5) converts to RGB(255*0.145:255*0.07547: <math>255\cdot 2\cdot (5/255)/(1+(5/255))</math>)=RGB(37:19.2: <math>255\cdot 2\cdot 0.0196/(1+0.0196)</math>)=RGB(37:19.2: <math>255\cdot 0.
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