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Use albedo-scaling correction for "multiscattering" GGX closures

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This commit is contained in:
Lukas Stockner
2022-07-04 23:31:47 +02:00
parent 0b89f591b4
commit 690f7c1831
4 changed files with 733 additions and 0 deletions
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22
intern/cycles/kernel/closure/bsdf_microfacet.h
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@@ -67,6 +67,25 @@ ccl_device_forceinline void bsdf_microfacet_fresnel_color(ccl_private const Shad
bsdf->sample_weight *= average(bsdf->extra->fresnel_color);
}
ccl_device_inline float3 microfacet_ggx_albedo_scaling(ccl_private const MicrofacetBsdf *bsdf,
ccl_private const ShaderData *sd,
const float3 Fss)
{
float mu = dot(sd->I, bsdf->N);
float rough = sqrtf(sqrtf(bsdf->alpha_x * bsdf->alpha_y));
float E = microfacet_ggx_E(mu, rough);
float E_avg = microfacet_ggx_E_avg(rough);
/* Fms here is based on the appendix of
* https://blog.selfshadow.com/publications/s2017-shading-course/imageworks/s2017_pbs_imageworks_slides_v2.pdf,
* with one Fss cancelled out since this is just a multiplier on top of
* the single-scattering BSDF, which already contains one bounce of Fresnel. */
float3 Fms = Fss * E_avg / (one_float3() - Fss * (1.0f - E_avg));
return one_float3() + Fms * ((1.0f - E) / E);
/* TODO: Ensure that increase in weight does not mess up glossy color, albedo etc. passes */
}
ccl_device int bsdf_microfacet_ggx_setup(ccl_private MicrofacetBsdf *bsdf)
{
bsdf->extra = NULL;
@@ -91,6 +110,7 @@ ccl_device int bsdf_microfacet_multi_ggx_setup(ccl_private MicrofacetBsdf *bsdf,
ccl_private const ShaderData *sd,
const float3 color)
{
bsdf->weight *= microfacet_ggx_albedo_scaling(bsdf, sd, saturate(color));
return bsdf_microfacet_ggx_setup(bsdf);
}
@@ -112,6 +132,8 @@ ccl_device int bsdf_microfacet_ggx_fresnel_setup(ccl_private MicrofacetBsdf *bsd
ccl_device int bsdf_microfacet_multi_ggx_fresnel_setup(ccl_private MicrofacetBsdf *bsdf,
ccl_private const ShaderData *sd)
{
float3 Fss = schlick_fresnel_Fss(bsdf->extra->cspec0);
bsdf->weight *= microfacet_ggx_albedo_scaling(bsdf, sd, Fss);
return bsdf_microfacet_ggx_fresnel_setup(bsdf, sd);
}

23
intern/cycles/kernel/closure/bsdf_microfacet_glass.h
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@@ -5,6 +5,24 @@
CCL_NAMESPACE_BEGIN
ccl_device_inline float3 microfacet_ggx_glass_albedo_scaling(
ccl_private const ShaderData *sd, ccl_private const MicrofacetBsdf *bsdf, const float3 Fss)
{
float mu = dot(sd->I, bsdf->N);
float rough = sqrtf(sqrtf(bsdf->alpha_x * bsdf->alpha_y));
float E = microfacet_ggx_glass_E(mu, rough, bsdf->ior);
/* Close enough for glass, coloring here is unphysical anyways and it's unclear how to
* approximate it better. */
float3 Fms = Fss;
return one_float3() + Fms * ((1.0f - E) / E);
/* TODO: Ensure that increase in weight does not mess up glossy color, albedo etc. passes */
}
/* Currently no non-albedo-scaled version is implemented, could easily be added
* but would still break compatibility with the old glass due to the microfacet Fresnel. */
ccl_device int bsdf_microfacet_multi_ggx_glass_setup(ccl_private MicrofacetBsdf *bsdf,
ccl_private const ShaderData *sd,
const float3 color)
@@ -16,6 +34,8 @@ ccl_device int bsdf_microfacet_multi_ggx_glass_setup(ccl_private MicrofacetBsdf
bsdf->type = CLOSURE_BSDF_MICROFACET_MULTI_GGX_GLASS_ID;
bsdf->weight *= microfacet_ggx_glass_albedo_scaling(sd, bsdf, saturate(color));
return SD_BSDF | SD_BSDF_HAS_EVAL | SD_BSDF_NEEDS_LCG;
}
@@ -31,6 +51,9 @@ ccl_device int bsdf_microfacet_multi_ggx_glass_fresnel_setup(ccl_private Microfa
bsdf_microfacet_fresnel_color(sd, bsdf);
float3 Fss = schlick_fresnel_Fss(bsdf->extra->cspec0);
bsdf->weight *= microfacet_ggx_glass_albedo_scaling(sd, bsdf, Fss);
return SD_BSDF | SD_BSDF_HAS_EVAL | SD_BSDF_NEEDS_LCG;
}

66
intern/cycles/kernel/closure/bsdf_microfacet_util.h
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@@ -76,4 +76,70 @@ ccl_device_forceinline float3 microfacet_ggx_sample_vndf(
return normalize(make_float3(alpha_x * Mh.x, alpha_y * Mh.y, max(0.0f, Mh.z)));
}
/* Albedo correction.
* TODO: Use proper lookup table code for this data. */
ccl_device_forceinline float microfacet_ggx_glass_E(float mu, float rough, float ior)
{
bool inv_table = (ior < 1.0f);
if (inv_table) {
ior = 1.0f / ior;
}
rough = saturatef(1 - rough) * 16.0f;
mu = saturatef(mu) * 16.0f;
ior = saturatef(sqrtf(0.5f * (ior - 1.0f))) * 16.0f;
int rough_i = min(15, (int)rough);
int rough_i1 = min(15, rough_i + 1);
int mu_i = min(15, (int)mu);
int mu_i1 = min(15, mu_i + 1);
int ior_i = min(15, (int)ior);
int ior_i1 = min(15, ior_i + 1);
rough -= rough_i;
mu -= mu_i;
ior -= ior_i;
auto &table = inv_table ? table_ggx_glass_inv_E : table_ggx_glass_E;
float a = lerp(table[ior_i][rough_i][mu_i], table[ior_i][rough_i][mu_i1], mu);
float b = lerp(table[ior_i][rough_i1][mu_i], table[ior_i][rough_i1][mu_i1], mu);
float c = lerp(table[ior_i1][rough_i][mu_i], table[ior_i1][rough_i][mu_i1], mu);
float d = lerp(table[ior_i1][rough_i1][mu_i], table[ior_i1][rough_i1][mu_i1], mu);
return lerp(lerp(a, b, rough), lerp(c, d, rough), ior);
}
ccl_device_forceinline float microfacet_ggx_E(float mu, float rough)
{
rough = saturatef(1 - rough) * 32.0f;
mu = saturatef(mu) * 32.0f;
int rough_i = min(31, (int)rough);
int rough_i1 = min(31, rough_i + 1);
int mu_i = min(31, (int)mu);
int mu_i1 = min(31, mu_i + 1);
rough -= rough_i;
mu -= mu_i;
float a = lerp(table_ggx_E[rough_i][mu_i], table_ggx_E[rough_i][mu_i1], mu);
float b = lerp(table_ggx_E[rough_i1][mu_i], table_ggx_E[rough_i1][mu_i1], mu);
return lerp(a, b, rough);
}
ccl_device_forceinline float microfacet_ggx_E_avg(float rough)
{
rough = saturatef(1 - rough) * 32.0f;
int rough_i = min(31, (int)rough);
int rough_i1 = min(31, rough_i + 1);
rough -= rough_i;
return lerp(table_ggx_E_avg[rough_i], table_ggx_E_avg[rough_i1], rough);
}
ccl_device_inline float3 schlick_fresnel_Fss(float3 F0)
{
return (one_float3() + 20.0f * saturate(F0)) * (1.0f / 21.0f);
}
CCL_NAMESPACE_END

622
intern/cycles/kernel/tables.h
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@@ -63,4 +63,626 @@ ccl_inline_constant float cie_colour_match[][3] = {
{0.0001f, 0.0000f, 0.0000f}, {0.0001f, 0.0000f, 0.0000f}, {0.0000f, 0.0000f, 0.0000f}
};
static const float table_ggx_E[32][32] = {
{0.938993f, 0.858736f, 0.800571f, 0.753374f, 0.713238f, 0.678442f, 0.647723f, 0.620302f, 0.595405f, 0.573038f, 0.552392f, 0.533285f, 0.515945f, 0.499677f, 0.484473f, 0.470426f, 0.457164f, 0.444816f, 0.433116f, 0.422004f, 0.411722f, 0.401847f, 0.392444f, 0.383611f, 0.375193f, 0.367147f, 0.359387f, 0.352163f, 0.345223f, 0.338525f, 0.332036f, 0.325866f},
{0.942738f, 0.866279f, 0.811134f, 0.766195f, 0.727883f, 0.694788f, 0.665388f, 0.639283f, 0.615624f, 0.594017f, 0.574515f, 0.556419f, 0.539656f, 0.524166f, 0.509889f, 0.496369f, 0.483729f, 0.471968f, 0.460875f, 0.450365f, 0.440542f, 0.431178f, 0.422252f, 0.41389f, 0.405924f, 0.398354f, 0.391047f, 0.384224f, 0.377665f, 0.371384f, 0.365363f, 0.359468f},
{0.946178f, 0.873743f, 0.821452f, 0.778574f, 0.742257f, 0.710809f, 0.682893f, 0.657944f, 0.635623f, 0.615179f, 0.596415f, 0.579404f, 0.56365f, 0.548923f, 0.535197f, 0.522582f, 0.510837f, 0.499666f, 0.489196f, 0.479435f, 0.470211f, 0.461503f, 0.4532f, 0.445456f, 0.438062f, 0.431058f, 0.424383f, 0.418092f, 0.412088f, 0.406399f, 0.40087f, 0.39569f},
{0.949756f, 0.881149f, 0.831485f, 0.790608f, 0.756361f, 0.726391f, 0.7001f, 0.676466f, 0.655176f, 0.636031f, 0.618395f, 0.602169f, 0.587374f, 0.573694f, 0.560934f, 0.549078f, 0.537966f, 0.52764f, 0.518107f, 0.509184f, 0.500732f, 0.492642f, 0.485138f, 0.478096f, 0.471514f, 0.465218f, 0.459228f, 0.453642f, 0.448353f, 0.443399f, 0.438603f, 0.434138f},
{0.953417f, 0.888246f, 0.840978f, 0.802406f, 0.770036f, 0.741652f, 0.716727f, 0.694556f, 0.674474f, 0.656312f, 0.639932f, 0.624841f, 0.610947f, 0.598109f, 0.586429f, 0.575584f, 0.565512f, 0.556085f, 0.547336f, 0.539137f, 0.531419f, 0.524487f, 0.517923f, 0.511844f, 0.506034f, 0.500635f, 0.495476f, 0.49075f, 0.486239f, 0.482136f, 0.478268f, 0.474605f},
{0.956708f, 0.895075f, 0.849858f, 0.813821f, 0.783021f, 0.756452f, 0.732847f, 0.711996f, 0.6933f, 0.67629f, 0.660854f, 0.646985f, 0.634265f, 0.622532f, 0.61175f, 0.601824f, 0.592715f, 0.584454f, 0.576767f, 0.569631f, 0.563046f, 0.556973f, 0.551345f, 0.546069f, 0.541248f, 0.536783f, 0.532655f, 0.528942f, 0.525551f, 0.52244f, 0.519561f, 0.516886f},
{0.959787f, 0.901339f, 0.858526f, 0.824767f, 0.795491f, 0.770587f, 0.748376f, 0.728728f, 0.71134f, 0.695646f, 0.681395f, 0.6685f, 0.656868f, 0.646354f, 0.636793f, 0.628025f, 0.620035f, 0.612715f, 0.606052f, 0.599955f, 0.594453f, 0.589562f, 0.585089f, 0.581059f, 0.577338f, 0.574072f, 0.5711f, 0.568439f, 0.566075f, 0.563943f, 0.562054f, 0.560442f},
{0.962795f, 0.906868f, 0.866905f, 0.835062f, 0.807402f, 0.783716f, 0.763213f, 0.744831f, 0.728521f, 0.714133f, 0.701219f, 0.689528f, 0.679048f, 0.669662f, 0.661165f, 0.653617f, 0.646934f, 0.640853f, 0.635463f, 0.630651f, 0.626301f, 0.622531f, 0.619196f, 0.616271f, 0.613734f, 0.611499f, 0.609711f, 0.608151f, 0.606875f, 0.605871f, 0.605133f, 0.604569f},
{0.965348f, 0.911877f, 0.87486f, 0.844371f, 0.818636f, 0.796204f, 0.77703f, 0.760093f, 0.745008f, 0.731726f, 0.719978f, 0.709726f, 0.700525f, 0.692423f, 0.68525f, 0.678907f, 0.673372f, 0.668563f, 0.664407f, 0.660819f, 0.657808f, 0.655239f, 0.653235f, 0.651498f, 0.65022f, 0.649273f, 0.648646f, 0.648209f, 0.648093f, 0.648143f, 0.648444f, 0.648997f},
{0.967272f, 0.916721f, 0.882236f, 0.852898f, 0.829009f, 0.807843f, 0.789712f, 0.774205f, 0.76051f, 0.748502f, 0.738002f, 0.728893f, 0.721084f, 0.714364f, 0.708633f, 0.703726f, 0.699584f, 0.696126f, 0.693243f, 0.691071f, 0.689301f, 0.688063f, 0.687214f, 0.686732f, 0.686602f, 0.686769f, 0.68723f, 0.687961f, 0.688866f, 0.689989f, 0.691226f, 0.692645f},
{0.968586f, 0.921257f, 0.88888f, 0.860793f, 0.838269f, 0.81852f, 0.80152f, 0.787156f, 0.77494f, 0.764349f, 0.755223f, 0.747519f, 0.741015f, 0.735657f, 0.731289f, 0.727743f, 0.725038f, 0.722978f, 0.721559f, 0.720651f, 0.720252f, 0.720234f, 0.720618f, 0.721337f, 0.722343f, 0.723618f, 0.725022f, 0.726747f, 0.728463f, 0.730413f, 0.732549f, 0.734727f},
{0.96923f, 0.925381f, 0.894794f, 0.867815f, 0.846234f, 0.828091f, 0.812338f, 0.799121f, 0.788072f, 0.779052f, 0.77153f, 0.765368f, 0.760397f, 0.756556f, 0.753644f, 0.751631f, 0.750357f, 0.749694f, 0.749655f, 0.750052f, 0.75089f, 0.7521f, 0.75363f, 0.755437f, 0.757483f, 0.759655f, 0.762073f, 0.764543f, 0.767111f, 0.769751f, 0.772424f, 0.775168f},
{0.969888f, 0.929051f, 0.899625f, 0.873925f, 0.853099f, 0.8364f, 0.822071f, 0.810155f, 0.800452f, 0.792754f, 0.786807f, 0.782287f, 0.779027f, 0.776843f, 0.775539f, 0.775069f, 0.775222f, 0.775969f, 0.777249f, 0.778874f, 0.78081f, 0.783044f, 0.785524f, 0.78813f, 0.790932f, 0.793787f, 0.79679f, 0.799823f, 0.802886f, 0.806013f, 0.809039f, 0.812126f},
{0.970458f, 0.93208f, 0.903415f, 0.878958f, 0.858946f, 0.843321f, 0.830534f, 0.82017f, 0.812067f, 0.806002f, 0.801686f, 0.798794f, 0.797162f, 0.796612f, 0.796887f, 0.797904f, 0.799518f, 0.801557f, 0.804076f, 0.806862f, 0.809902f, 0.813101f, 0.816464f, 0.819846f, 0.823393f, 0.826865f, 0.830303f, 0.833696f, 0.837071f, 0.840289f, 0.843405f, 0.846271f},
{0.97093f, 0.934339f, 0.906008f, 0.882733f, 0.863623f, 0.849053f, 0.837939f, 0.829376f, 0.823131f, 0.818944f, 0.816482f, 0.815457f, 0.815624f, 0.816719f, 0.818588f, 0.8211f, 0.824063f, 0.827308f, 0.830801f, 0.83448f, 0.838211f, 0.841892f, 0.845532f, 0.849179f, 0.852736f, 0.856301f, 0.859794f, 0.863242f, 0.866589f, 0.869835f, 0.872989f, 0.87607f},
{0.97133f, 0.935814f, 0.907571f, 0.885251f, 0.867183f, 0.853836f, 0.844417f, 0.837916f, 0.833826f, 0.831748f, 0.83136f, 0.832276f, 0.834192f, 0.836898f, 0.840127f, 0.843696f, 0.847553f, 0.851545f, 0.855775f, 0.85999f, 0.864261f, 0.868476f, 0.872636f, 0.876703f, 0.880618f, 0.884471f, 0.888169f, 0.891631f, 0.894991f, 0.898211f, 0.90118f, 0.903876f},
{0.971498f, 0.936194f, 0.907977f, 0.886424f, 0.869635f, 0.857961f, 0.850455f, 0.846173f, 0.844434f, 0.844569f, 0.846203f, 0.84897f, 0.852535f, 0.856708f, 0.861232f, 0.866047f, 0.870964f, 0.875868f, 0.880772f, 0.885482f, 0.890095f, 0.894455f, 0.89851f, 0.902212f, 0.905444f, 0.908352f, 0.911154f, 0.91382f, 0.916322f, 0.918733f, 0.921009f, 0.923178f},
{0.971515f, 0.935335f, 0.907242f, 0.886387f, 0.871259f, 0.861767f, 0.856719f, 0.855001f, 0.855742f, 0.858309f, 0.862141f, 0.866832f, 0.872116f, 0.877706f, 0.883307f, 0.888897f, 0.894213f, 0.899182f, 0.903721f, 0.907694f, 0.911501f, 0.915135f, 0.9186f, 0.921904f, 0.92507f, 0.927995f, 0.93078f, 0.933424f, 0.935897f, 0.938226f, 0.940385f, 0.942486f},
{0.971233f, 0.933273f, 0.90534f, 0.885326f, 0.872522f, 0.865959f, 0.863968f, 0.865225f, 0.868804f, 0.873881f, 0.879788f, 0.886066f, 0.892447f, 0.898536f, 0.904109f, 0.909139f, 0.914005f, 0.918666f, 0.923149f, 0.927344f, 0.93132f, 0.935081f, 0.938582f, 0.941808f, 0.944912f, 0.947718f, 0.950344f, 0.952816f, 0.95506f, 0.957285f, 0.959182f, 0.961045f},
{0.970675f, 0.929771f, 0.902079f, 0.883688f, 0.874158f, 0.871353f, 0.873055f, 0.877692f, 0.883998f, 0.891128f, 0.898349f, 0.90501f, 0.911219f, 0.917302f, 0.923128f, 0.928714f, 0.933918f, 0.93875f, 0.943234f, 0.947359f, 0.951162f, 0.954644f, 0.957807f, 0.960532f, 0.963028f, 0.96502f, 0.966619f, 0.967709f, 0.968388f, 0.968743f, 0.968939f, 0.969107f},
{0.969797f, 0.924729f, 0.89772f, 0.882373f, 0.877356f, 0.879119f, 0.884863f, 0.892627f, 0.900849f, 0.908641f, 0.916223f, 0.923627f, 0.930675f, 0.937267f, 0.943249f, 0.948668f, 0.953548f, 0.957771f, 0.961262f, 0.963879f, 0.965795f, 0.967087f, 0.967986f, 0.968618f, 0.969112f, 0.969598f, 0.97003f, 0.970412f, 0.970806f, 0.971111f, 0.971429f, 0.971676f},
{0.968571f, 0.918364f, 0.892897f, 0.882602f, 0.883448f, 0.890303f, 0.899597f, 0.908982f, 0.91838f, 0.92749f, 0.936094f, 0.943872f, 0.950714f, 0.956491f, 0.96096f, 0.964088f, 0.966142f, 0.967554f, 0.968578f, 0.969451f, 0.970231f, 0.970983f, 0.971692f, 0.972324f, 0.972884f, 0.973405f, 0.973905f, 0.974357f, 0.974748f, 0.975061f, 0.975408f, 0.975663f},
{0.965173f, 0.910926f, 0.889046f, 0.886257f, 0.893902f, 0.905002f, 0.916487f, 0.928009f, 0.93872f, 0.948183f, 0.95588f, 0.961395f, 0.964914f, 0.967118f, 0.968655f, 0.969977f, 0.97117f, 0.9723f, 0.973341f, 0.97427f, 0.975106f, 0.975873f, 0.976565f, 0.977188f, 0.977768f, 0.978231f, 0.978716f, 0.979142f, 0.97947f, 0.979811f, 0.980083f, 0.980371f},
{0.958495f, 0.903049f, 0.888471f, 0.895308f, 0.908717f, 0.923329f, 0.937428f, 0.949533f, 0.95859f, 0.964045f, 0.967168f, 0.96929f, 0.971163f, 0.97285f, 0.974399f, 0.97577f, 0.976987f, 0.978069f, 0.979037f, 0.97987f, 0.980611f, 0.9813f, 0.981886f, 0.982413f, 0.982955f, 0.983354f, 0.983723f, 0.984063f, 0.984398f, 0.984652f, 0.984856f, 0.985063f},
{0.948964f, 0.895629f, 0.894262f, 0.910481f, 0.929203f, 0.946257f, 0.958732f, 0.965248f, 0.968749f, 0.971476f, 0.973909f, 0.976056f, 0.977916f, 0.979486f, 0.980913f, 0.982035f, 0.983087f, 0.983982f, 0.984791f, 0.985417f, 0.986015f, 0.98649f, 0.987023f, 0.987391f, 0.98782f, 0.988115f, 0.988375f, 0.988643f, 0.988798f, 0.989001f, 0.98932f, 0.989353f},
{0.937118f, 0.893165f, 0.908694f, 0.93326f, 0.954062f, 0.964852f, 0.969648f, 0.973401f, 0.976567f, 0.979253f, 0.981432f, 0.983268f, 0.984715f, 0.985961f, 0.98706f, 0.987867f, 0.988676f, 0.989308f, 0.989769f, 0.990333f, 0.990721f, 0.991062f, 0.991439f, 0.9917f, 0.991872f, 0.992123f, 0.992216f, 0.99251f, 0.992717f, 0.992757f, 0.9929f, 0.993009f},
{0.924708f, 0.901613f, 0.933658f, 0.959845f, 0.969049f, 0.974478f, 0.978882f, 0.982268f, 0.984778f, 0.986833f, 0.988426f, 0.989638f, 0.990686f, 0.991441f, 0.99211f, 0.992683f, 0.993142f, 0.993536f, 0.993918f, 0.994134f, 0.994405f, 0.994602f, 0.994731f, 0.994885f, 0.995065f, 0.995196f, 0.995408f, 0.995475f, 0.995622f, 0.995727f, 0.995661f, 0.995728f},
{0.915237f, 0.924971f, 0.962986f, 0.973159f, 0.979981f, 0.984688f, 0.987889f, 0.989996f, 0.991679f, 0.992878f, 0.993788f, 0.994514f, 0.994998f, 0.995501f, 0.995976f, 0.996148f, 0.996387f, 0.996635f, 0.996847f, 0.996874f, 0.997059f, 0.997253f, 0.997307f, 0.997327f, 0.99745f, 0.9975f, 0.997533f, 0.997708f, 0.997762f, 0.997759f, 0.997849f, 0.997848f},
{0.916255f, 0.96181f, 0.977531f, 0.985756f, 0.990294f, 0.992823f, 0.994433f, 0.99559f, 0.996311f, 0.996834f, 0.997191f, 0.997456f, 0.997787f, 0.997998f, 0.998229f, 0.998384f, 0.998457f, 0.998433f, 0.998494f, 0.998608f, 0.998846f, 0.998789f, 0.998969f, 0.998877f, 0.999104f, 0.999046f, 0.99894f, 0.998958f, 0.998896f, 0.999038f, 0.99902f, 0.999228f},
{0.938232f, 0.980496f, 0.99117f, 0.995037f, 0.996819f, 0.997623f, 0.998332f, 0.99847f, 0.998858f, 0.999061f, 0.99919f, 0.999076f, 0.999342f, 0.999446f, 0.999543f, 0.99948f, 0.999434f, 0.999576f, 0.999513f, 0.999568f, 0.999704f, 0.999605f, 0.999723f, 0.999585f, 0.999633f, 0.999681f, 0.999639f, 0.999761f, 0.999682f, 0.999801f, 0.999803f, 0.999778f},
{0.969782f, 0.995572f, 0.998327f, 0.999031f, 0.999409f, 0.999456f, 0.999751f, 0.999859f, 0.999893f, 0.999819f, 0.999782f, 0.999831f, 0.999837f, 0.999896f, 0.999957f, 0.999955f, 0.999955f, 0.999942f, 0.999964f, 0.999976f, 0.999957f, 0.999954f, 0.999962f, 0.999964f, 0.999982f, 0.999974f, 0.999968f, 0.999979f, 0.999807f, 0.999926f, 0.999962f, 0.99998f},
{0.989677f, 0.999757f, 0.999788f, 0.999983f, 0.999994f, 0.999992f, 0.999994f, 0.999994f, 0.999999f, 0.999993f, 1.0f, 1.0f, 1.0f, 1.0f, 0.999998f, 0.999998f, 1.0f, 1.0f, 1.0f, 1.0f, 0.999996f, 0.999996f, 1.0f, 1.0f, 1.0f, 1.0f, 1.0f, 1.0f, 1.0f, 1.0f, 1.0f, 1.0f}
};
static const float table_ggx_E_avg[32] = {
0.422975f, 0.451614f, 0.481159f, 0.511595f, 0.543123f, 0.575053f, 0.60744f, 0.640006f, 0.672404f, 0.704199f, 0.735225f, 0.765683f, 0.794568f, 0.821832f, 0.847303f, 0.871297f, 0.892859f, 0.912368f, 0.929627f, 0.944333f, 0.957303f, 0.968517f, 0.976663f, 0.98424f, 0.989949f, 0.993637f, 0.996464f, 0.99818f, 0.999062f, 1.00023f, 1.00014f, 1.00005f
};
static const float table_ggx_glass_E[16][16][16] = {
{
{0.546145f, 0.554928f, 0.585355f, 0.617174f, 0.649281f, 0.681332f, 0.713313f, 0.744976f, 0.776317f, 0.807153f, 0.837756f, 0.867865f, 0.897538f, 0.926556f, 0.955152f, 0.983269f},
{0.551645f, 0.562942f, 0.597396f, 0.633016f, 0.668497f, 0.703397f, 0.737332f, 0.77021f, 0.801938f, 0.832256f, 0.861463f, 0.889042f, 0.915358f, 0.940463f, 0.964068f, 0.986394f},
{0.558163f, 0.572828f, 0.611968f, 0.651944f, 0.691117f, 0.728661f, 0.764305f, 0.797737f, 0.828922f, 0.857906f, 0.88465f, 0.909353f, 0.932072f, 0.952713f, 0.971759f, 0.989101f},
{0.565942f, 0.584818f, 0.629791f, 0.67474f, 0.717467f, 0.757342f, 0.793846f, 0.826921f, 0.856543f, 0.883185f, 0.906937f, 0.928087f, 0.946762f, 0.963324f, 0.978089f, 0.991121f},
{0.575588f, 0.600003f, 0.651733f, 0.701856f, 0.748046f, 0.789334f, 0.825551f, 0.857055f, 0.884071f, 0.907377f, 0.927335f, 0.944636f, 0.959475f, 0.972171f, 0.983223f, 0.992751f},
{0.587534f, 0.619243f, 0.678746f, 0.734276f, 0.782725f, 0.823985f, 0.858453f, 0.886872f, 0.910116f, 0.929464f, 0.945487f, 0.958873f, 0.970007f, 0.979376f, 0.987371f, 0.994102f},
{0.602621f, 0.644047f, 0.712131f, 0.771979f, 0.821102f, 0.860106f, 0.890869f, 0.914867f, 0.933558f, 0.948679f, 0.960717f, 0.97046f, 0.978469f, 0.985064f, 0.990606f, 0.995082f},
{0.622241f, 0.675982f, 0.752631f, 0.814525f, 0.861237f, 0.89565f, 0.920899f, 0.939713f, 0.953529f, 0.964417f, 0.972942f, 0.979727f, 0.98495f, 0.989355f, 0.992982f, 0.99591f},
{0.647882f, 0.717283f, 0.800443f, 0.860146f, 0.900533f, 0.928044f, 0.946791f, 0.960059f, 0.969236f, 0.976488f, 0.981957f, 0.986275f, 0.989738f, 0.992396f, 0.99457f, 0.996447f},
{0.68242f, 0.76935f, 0.853133f, 0.904615f, 0.935514f, 0.954804f, 0.967174f, 0.975482f, 0.980791f, 0.985194f, 0.988401f, 0.990902f, 0.992909f, 0.994567f, 0.995782f, 0.996746f},
{0.729096f, 0.830817f, 0.905183f, 0.943073f, 0.963073f, 0.974575f, 0.981729f, 0.986219f, 0.988659f, 0.990971f, 0.992639f, 0.993905f, 0.995049f, 0.995809f, 0.996428f, 0.996998f},
{0.789156f, 0.895256f, 0.948956f, 0.971336f, 0.981801f, 0.987517f, 0.990816f, 0.99266f, 0.993256f, 0.994337f, 0.995166f, 0.995713f, 0.99628f, 0.99667f, 0.996902f, 0.997157f},
{0.859066f, 0.949326f, 0.978616f, 0.988459f, 0.99247f, 0.99464f, 0.995801f, 0.99628f, 0.995737f, 0.996129f, 0.996486f, 0.996763f, 0.996855f, 0.997043f, 0.997051f, 0.997208f},
{0.923198f, 0.983437f, 0.99374f, 0.996554f, 0.997289f, 0.997815f, 0.998037f, 0.997932f, 0.996729f, 0.99701f, 0.997112f, 0.997122f, 0.997151f, 0.997181f, 0.99723f, 0.997244f},
{0.967523f, 0.997301f, 0.998877f, 0.999232f, 0.998936f, 0.99887f, 0.998817f, 0.998544f, 0.997149f, 0.99719f, 0.997292f, 0.997176f, 0.997165f, 0.997177f, 0.997329f, 0.99722f},
{0.993657f, 0.999821f, 0.999725f, 0.999639f, 0.999132f, 0.998963f, 0.998883f, 0.998629f, 0.997223f, 0.997127f, 0.997255f, 0.997299f, 0.997234f, 0.997171f, 0.997179f, 0.997287f}
},
{
{0.631613f, 0.585535f, 0.60389f, 0.63012f, 0.658841f, 0.688715f, 0.719004f, 0.749476f, 0.779917f, 0.810074f, 0.839943f, 0.869533f, 0.898583f, 0.927148f, 0.955291f, 0.982522f},
{0.643297f, 0.597422f, 0.618572f, 0.647969f, 0.679661f, 0.71191f, 0.743979f, 0.775505f, 0.806121f, 0.835601f, 0.863966f, 0.891141f, 0.917079f, 0.941526f, 0.9647f, 0.98657f},
{0.656436f, 0.611642f, 0.636216f, 0.668916f, 0.703763f, 0.738348f, 0.771739f, 0.803497f, 0.8336f, 0.861669f, 0.887586f, 0.911674f, 0.933799f, 0.954275f, 0.97294f, 0.989745f},
{0.671787f, 0.628907f, 0.657412f, 0.69396f, 0.731665f, 0.767909f, 0.801987f, 0.83317f, 0.861465f, 0.887144f, 0.910067f, 0.930601f, 0.948912f, 0.965124f, 0.979652f, 0.992398f},
{0.689418f, 0.649953f, 0.683015f, 0.723425f, 0.763416f, 0.800574f, 0.833967f, 0.863372f, 0.889006f, 0.911341f, 0.930665f, 0.947338f, 0.961831f, 0.974299f, 0.985131f, 0.994478f},
{0.710308f, 0.675785f, 0.713876f, 0.757741f, 0.79883f, 0.835433f, 0.866612f, 0.892936f, 0.914899f, 0.933343f, 0.948684f, 0.961643f, 0.972544f, 0.981751f, 0.989502f, 0.996116f},
{0.734531f, 0.707423f, 0.750347f, 0.796438f, 0.836942f, 0.870809f, 0.898257f, 0.920374f, 0.938042f, 0.952242f, 0.963848f, 0.973335f, 0.981043f, 0.987507f, 0.992916f, 0.99742f},
{0.763463f, 0.745538f, 0.792477f, 0.83811f, 0.875748f, 0.904854f, 0.927199f, 0.944194f, 0.957484f, 0.967775f, 0.975886f, 0.982365f, 0.987617f, 0.991907f, 0.995436f, 0.998383f},
{0.797243f, 0.790409f, 0.838764f, 0.880622f, 0.912262f, 0.935119f, 0.951644f, 0.96379f, 0.972864f, 0.979631f, 0.984944f, 0.989097f, 0.992341f, 0.995011f, 0.997214f, 0.998982f},
{0.835707f, 0.839576f, 0.884783f, 0.919588f, 0.943649f, 0.959666f, 0.970729f, 0.978468f, 0.984043f, 0.98819f, 0.991292f, 0.993741f, 0.995631f, 0.99718f, 0.998433f, 0.9994f},
{0.87631f, 0.887301f, 0.926002f, 0.951959f, 0.967963f, 0.977871f, 0.984215f, 0.988547f, 0.991591f, 0.993787f, 0.995463f, 0.996735f, 0.997747f, 0.998521f, 0.999191f, 0.999696f},
{0.911712f, 0.927518f, 0.958425f, 0.975578f, 0.984504f, 0.989532f, 0.992666f, 0.994708f, 0.996143f, 0.997182f, 0.997949f, 0.998526f, 0.998986f, 0.999337f, 0.999623f, 0.999866f},
{0.933586f, 0.957793f, 0.981399f, 0.990218f, 0.994028f, 0.996008f, 0.997254f, 0.998024f, 0.998572f, 0.998947f, 0.999234f, 0.999449f, 0.999618f, 0.999754f, 0.999868f, 0.999953f},
{0.943785f, 0.982754f, 0.994593f, 0.997301f, 0.998376f, 0.998932f, 0.999247f, 0.999475f, 0.999609f, 0.999713f, 0.999788f, 0.999845f, 0.999898f, 0.999926f, 0.999963f, 0.999987f},
{0.963548f, 0.997089f, 0.999224f, 0.999595f, 0.999763f, 0.999841f, 0.99989f, 0.999923f, 0.999943f, 0.999958f, 0.99997f, 0.999978f, 0.999985f, 0.99999f, 0.999994f, 0.999997f},
{0.992398f, 0.999883f, 0.999938f, 0.99995f, 0.99995f, 0.999961f, 0.999968f, 0.999957f, 0.999972f, 0.999978f, 0.999969f, 0.999965f, 0.999976f, 0.999972f, 0.999972f, 0.999975f}
},
{
{0.7033f, 0.624366f, 0.628578f, 0.647018f, 0.670764f, 0.697179f, 0.724674f, 0.752952f, 0.781676f, 0.810399f, 0.838951f, 0.867394f, 0.895481f, 0.923f, 0.950124f, 0.975904f},
{0.71783f, 0.640314f, 0.646483f, 0.667403f, 0.693574f, 0.721948f, 0.750909f, 0.779952f, 0.808798f, 0.836672f, 0.863665f, 0.889655f, 0.914717f, 0.938198f, 0.960705f, 0.981332f},
{0.73379f, 0.658809f, 0.667588f, 0.691082f, 0.719766f, 0.749734f, 0.779826f, 0.808921f, 0.83682f, 0.863278f, 0.887645f, 0.910721f, 0.932106f, 0.951828f, 0.969822f, 0.985843f},
{0.751787f, 0.680693f, 0.692507f, 0.718771f, 0.749456f, 0.780616f, 0.810739f, 0.838952f, 0.864925f, 0.888953f, 0.910546f, 0.929958f, 0.947602f, 0.963301f, 0.977202f, 0.989426f},
{0.771632f, 0.706199f, 0.721422f, 0.750329f, 0.782343f, 0.813589f, 0.842857f, 0.869098f, 0.892508f, 0.913093f, 0.931231f, 0.947079f, 0.960913f, 0.972917f, 0.983348f, 0.992309f},
{0.794009f, 0.736069f, 0.754824f, 0.785859f, 0.817909f, 0.848151f, 0.874727f, 0.898082f, 0.917887f, 0.934733f, 0.949146f, 0.9615f, 0.971885f, 0.980801f, 0.988265f, 0.994553f},
{0.81858f, 0.770343f, 0.792317f, 0.823838f, 0.854519f, 0.882076f, 0.905208f, 0.924371f, 0.940351f, 0.953406f, 0.964235f, 0.973197f, 0.980488f, 0.986779f, 0.992066f, 0.996382f},
{0.84565f, 0.808161f, 0.832237f, 0.862468f, 0.890477f, 0.91359f, 0.93242f, 0.947124f, 0.959126f, 0.96853f, 0.976047f, 0.982215f, 0.987344f, 0.991477f, 0.994879f, 0.997734f},
{0.874026f, 0.847531f, 0.872048f, 0.89919f, 0.922681f, 0.940799f, 0.954911f, 0.96549f, 0.973778f, 0.980043f, 0.985121f, 0.988998f, 0.992127f, 0.994722f, 0.996887f, 0.998578f},
{0.901745f, 0.88446f, 0.90746f, 0.930681f, 0.949353f, 0.962582f, 0.972388f, 0.979433f, 0.984484f, 0.988402f, 0.991401f, 0.993684f, 0.995532f, 0.997017f, 0.998276f, 0.999172f},
{0.92477f, 0.913415f, 0.936122f, 0.956473f, 0.970167f, 0.979084f, 0.985043f, 0.989036f, 0.99183f, 0.993909f, 0.995522f, 0.996708f, 0.997708f, 0.998436f, 0.999098f, 0.999583f},
{0.937524f, 0.934214f, 0.959427f, 0.976221f, 0.985122f, 0.990088f, 0.993034f, 0.994956f, 0.996266f, 0.997246f, 0.997978f, 0.998526f, 0.998961f, 0.999307f, 0.999597f, 0.999814f},
{0.938082f, 0.95327f, 0.979643f, 0.99008f, 0.994165f, 0.996258f, 0.997424f, 0.998121f, 0.99862f, 0.998978f, 0.999263f, 0.999442f, 0.999613f, 0.999743f, 0.999853f, 0.999932f},
{0.937776f, 0.978551f, 0.993783f, 0.997285f, 0.998457f, 0.998989f, 0.999303f, 0.999512f, 0.999633f, 0.999719f, 0.999798f, 0.999849f, 0.999891f, 0.999916f, 0.999962f, 0.999985f},
{0.959602f, 0.996313f, 0.999131f, 0.999611f, 0.999778f, 0.999847f, 0.9999f, 0.999932f, 0.999941f, 0.999959f, 0.999973f, 0.999979f, 0.999985f, 0.999988f, 0.999993f, 0.999997f},
{0.992047f, 0.999866f, 0.999938f, 0.999952f, 0.99995f, 0.999963f, 0.999969f, 0.999957f, 0.999972f, 0.999977f, 0.999969f, 0.999965f, 0.999976f, 0.999972f, 0.999972f, 0.999975f}
},
{
{0.755135f, 0.661173f, 0.653773f, 0.664733f, 0.683312f, 0.705748f, 0.730117f, 0.755903f, 0.782496f, 0.809353f, 0.836357f, 0.863372f, 0.889953f, 0.916305f, 0.942201f, 0.966181f},
{0.770474f, 0.680031f, 0.674374f, 0.68761f, 0.708103f, 0.732226f, 0.757874f, 0.784137f, 0.810612f, 0.836641f, 0.862026f, 0.886647f, 0.910527f, 0.932779f, 0.954265f, 0.973625f},
{0.787016f, 0.701255f, 0.698294f, 0.713503f, 0.736268f, 0.761355f, 0.787675f, 0.813929f, 0.839407f, 0.863906f, 0.886723f, 0.90856f, 0.928769f, 0.94772f, 0.964805f, 0.979988f},
{0.805089f, 0.725584f, 0.725517f, 0.743068f, 0.767051f, 0.79318f, 0.819282f, 0.84439f, 0.867851f, 0.890054f, 0.910067f, 0.928265f, 0.945076f, 0.960184f, 0.973426f, 0.984878f},
{0.824429f, 0.75299f, 0.756091f, 0.775729f, 0.800469f, 0.826213f, 0.851312f, 0.874399f, 0.895384f, 0.914253f, 0.931078f, 0.945795f, 0.95901f, 0.970548f, 0.980428f, 0.989062f},
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{0.957907f, 0.925126f, 0.931868f, 0.947943f, 0.962145f, 0.972694f, 0.980115f, 0.984894f, 0.988325f, 0.990804f, 0.992483f, 0.993697f, 0.994771f, 0.995353f, 0.996007f, 0.996485f},
{0.947059f, 0.923637f, 0.945659f, 0.966036f, 0.978634f, 0.986174f, 0.990319f, 0.993109f, 0.99469f, 0.995891f, 0.996685f, 0.997324f, 0.997742f, 0.998093f, 0.998319f, 0.99846f},
{0.932316f, 0.937019f, 0.968993f, 0.98433f, 0.991339f, 0.994711f, 0.996512f, 0.997512f, 0.998152f, 0.998564f, 0.998851f, 0.999032f, 0.999202f, 0.999314f, 0.999398f, 0.999459f},
{0.927979f, 0.969703f, 0.989979f, 0.995709f, 0.997768f, 0.998636f, 0.999094f, 0.999377f, 0.999553f, 0.999636f, 0.999704f, 0.999729f, 0.999786f, 0.999821f, 0.999844f, 0.999872f},
{0.955042f, 0.994732f, 0.998592f, 0.999391f, 0.999705f, 0.999812f, 0.999893f, 0.999918f, 0.999934f, 0.99995f, 0.999956f, 0.999966f, 0.999973f, 0.999969f, 0.999977f, 0.999983f},
{0.991714f, 0.999817f, 0.999923f, 0.999947f, 0.999951f, 0.999962f, 0.999969f, 0.999956f, 0.999973f, 0.999978f, 0.999969f, 0.999966f, 0.999976f, 0.999972f, 0.999971f, 0.999974f}
},
{
{0.890624f, 0.794913f, 0.751595f, 0.728315f, 0.716165f, 0.711259f, 0.710489f, 0.713487f, 0.719264f, 0.72661f, 0.735377f, 0.745399f, 0.755902f, 0.767561f, 0.779444f, 0.791432f},
{0.902561f, 0.817053f, 0.779069f, 0.759979f, 0.750559f, 0.747973f, 0.749392f, 0.753796f, 0.760216f, 0.768113f, 0.776937f, 0.786565f, 0.797039f, 0.80733f, 0.817108f, 0.826796f},
{0.914196f, 0.839209f, 0.806955f, 0.791422f, 0.785544f, 0.784497f, 0.787997f, 0.793195f, 0.800421f, 0.808331f, 0.816868f, 0.826063f, 0.83466f, 0.843702f, 0.852359f, 0.860494f},
{0.925655f, 0.860665f, 0.83391f, 0.822388f, 0.818834f, 0.820022f, 0.824499f, 0.830276f, 0.837635f, 0.845529f, 0.853455f, 0.861507f, 0.869202f, 0.877202f, 0.884398f, 0.891023f},
{0.936108f, 0.881133f, 0.85936f, 0.850771f, 0.849623f, 0.852478f, 0.857742f, 0.864299f, 0.870899f, 0.878544f, 0.8859f, 0.893041f, 0.900033f, 0.906907f, 0.91244f, 0.917751f},
{0.945738f, 0.899317f, 0.881803f, 0.876366f, 0.876596f, 0.880928f, 0.886643f, 0.893232f, 0.90038f, 0.907277f, 0.913822f, 0.920371f, 0.926364f, 0.931915f, 0.936756f, 0.94087f},
{0.953892f, 0.914299f, 0.900195f, 0.897005f, 0.89897f, 0.904506f, 0.910921f, 0.918114f, 0.92501f, 0.931694f, 0.937925f, 0.943503f, 0.94808f, 0.952466f, 0.956531f, 0.959867f},
{0.960106f, 0.924951f, 0.913294f, 0.912564f, 0.917012f, 0.923719f, 0.931536f, 0.93876f, 0.94542f, 0.951927f, 0.957144f, 0.961631f, 0.965882f, 0.969256f, 0.972213f, 0.974584f},
{0.963489f, 0.930305f, 0.92158f, 0.924196f, 0.931797f, 0.940695f, 0.949222f, 0.956532f, 0.963004f, 0.968356f, 0.972664f, 0.976165f, 0.979009f, 0.981425f, 0.983548f, 0.985218f},
{0.963473f, 0.92992f, 0.926131f, 0.93442f, 0.946014f, 0.956334f, 0.965333f, 0.972178f, 0.977249f, 0.981065f, 0.984335f, 0.986485f, 0.9884f, 0.98998f, 0.991134f, 0.991982f},
{0.958326f, 0.925614f, 0.93211f, 0.947913f, 0.961902f, 0.972276f, 0.979642f, 0.984396f, 0.987816f, 0.990302f, 0.992003f, 0.993238f, 0.99431f, 0.994931f, 0.995598f, 0.996026f},
{0.947422f, 0.924138f, 0.945912f, 0.966055f, 0.978472f, 0.985964f, 0.990089f, 0.992852f, 0.99445f, 0.995661f, 0.9965f, 0.997122f, 0.99754f, 0.997916f, 0.998136f, 0.998282f},
{0.932675f, 0.937446f, 0.969148f, 0.984324f, 0.9913f, 0.994631f, 0.996427f, 0.997433f, 0.998081f, 0.998488f, 0.998776f, 0.998951f, 0.99912f, 0.999257f, 0.999339f, 0.9994f},
{0.928284f, 0.969893f, 0.990039f, 0.995709f, 0.997756f, 0.998618f, 0.999072f, 0.999362f, 0.999535f, 0.999619f, 0.999689f, 0.999712f, 0.999778f, 0.999807f, 0.99983f, 0.999854f},
{0.955178f, 0.994767f, 0.998607f, 0.999394f, 0.9997f, 0.999809f, 0.999889f, 0.999916f, 0.999933f, 0.999949f, 0.999952f, 0.999963f, 0.999969f, 0.999967f, 0.999977f, 0.999982f},
{0.991724f, 0.999818f, 0.999923f, 0.999947f, 0.999951f, 0.999962f, 0.999969f, 0.999955f, 0.999973f, 0.999978f, 0.999969f, 0.999966f, 0.999976f, 0.999971f, 0.999971f, 0.999974f}
},
{
{0.893434f, 0.797814f, 0.752922f, 0.727812f, 0.713735f, 0.706931f, 0.704372f, 0.705642f, 0.709603f, 0.715397f, 0.722403f, 0.731039f, 0.739981f, 0.750329f, 0.761289f, 0.772331f},
{0.905203f, 0.819884f, 0.780557f, 0.759869f, 0.748764f, 0.74445f, 0.744254f, 0.74695f, 0.751782f, 0.758117f, 0.765638f, 0.773848f, 0.783125f, 0.79231f, 0.801129f, 0.810013f},
{0.916605f, 0.841987f, 0.808558f, 0.791604f, 0.78415f, 0.781576f, 0.783488f, 0.787291f, 0.793066f, 0.79974f, 0.807069f, 0.815146f, 0.822749f, 0.830759f, 0.838712f, 0.846306f},
{0.927836f, 0.863206f, 0.835518f, 0.822659f, 0.817761f, 0.81748f, 0.820596f, 0.825366f, 0.831471f, 0.838282f, 0.845202f, 0.852335f, 0.859172f, 0.866653f, 0.873016f, 0.879285f},
{0.938008f, 0.883324f, 0.860708f, 0.850965f, 0.848699f, 0.850403f, 0.854568f, 0.86014f, 0.865852f, 0.872584f, 0.879233f, 0.885634f, 0.892101f, 0.898517f, 0.90361f, 0.908631f},
{0.947304f, 0.901111f, 0.882892f, 0.876543f, 0.875772f, 0.879161f, 0.883957f, 0.889877f, 0.896303f, 0.902553f, 0.908637f, 0.91475f, 0.920323f, 0.925431f, 0.930243f, 0.934371f},
{0.955132f, 0.915713f, 0.900974f, 0.896986f, 0.898208f, 0.903074f, 0.908749f, 0.915397f, 0.921827f, 0.928078f, 0.934038f, 0.939215f, 0.94377f, 0.947926f, 0.951965f, 0.955321f},
{0.961061f, 0.925986f, 0.913823f, 0.912456f, 0.916355f, 0.9225f, 0.929826f, 0.936681f, 0.943031f, 0.94939f, 0.954417f, 0.958823f, 0.962909f, 0.96627f, 0.969289f, 0.971649f},
{0.964207f, 0.931075f, 0.921945f, 0.924141f, 0.931276f, 0.939751f, 0.947996f, 0.955015f, 0.961373f, 0.96664f, 0.970834f, 0.974377f, 0.977259f, 0.979673f, 0.981779f, 0.983545f},
{0.963978f, 0.930519f, 0.926508f, 0.934408f, 0.945704f, 0.955672f, 0.964484f, 0.971222f, 0.976174f, 0.980013f, 0.983308f, 0.985497f, 0.987412f, 0.989029f, 0.99017f, 0.991111f},
{0.958762f, 0.926217f, 0.932511f, 0.94797f, 0.961684f, 0.971881f, 0.979163f, 0.983856f, 0.987279f, 0.989795f, 0.991492f, 0.992756f, 0.993819f, 0.994449f, 0.99516f, 0.995594f},
{0.947832f, 0.924771f, 0.946249f, 0.966141f, 0.978386f, 0.985761f, 0.989856f, 0.992601f, 0.994222f, 0.995427f, 0.996276f, 0.996921f, 0.997338f, 0.997714f, 0.997952f, 0.998097f},
{0.933114f, 0.93796f, 0.969371f, 0.984371f, 0.991257f, 0.994548f, 0.996345f, 0.997353f, 0.997996f, 0.998405f, 0.998696f, 0.998877f, 0.999051f, 0.999192f, 0.999279f, 0.999336f},
{0.928676f, 0.970165f, 0.990118f, 0.995726f, 0.997746f, 0.998599f, 0.99905f, 0.999336f, 0.999517f, 0.999599f, 0.999669f, 0.999686f, 0.999762f, 0.999791f, 0.999811f, 0.999834f},
{0.955348f, 0.994803f, 0.998615f, 0.999396f, 0.999697f, 0.999803f, 0.999889f, 0.999915f, 0.999931f, 0.999947f, 0.999949f, 0.999962f, 0.999966f, 0.999967f, 0.99997f, 0.999978f},
{0.991734f, 0.999819f, 0.999923f, 0.999947f, 0.999951f, 0.999962f, 0.999969f, 0.999955f, 0.999973f, 0.999978f, 0.999969f, 0.999966f, 0.999976f, 0.999971f, 0.999971f, 0.999974f}
},
{
{0.895766f, 0.800041f, 0.753664f, 0.726898f, 0.711004f, 0.702437f, 0.698171f, 0.697751f, 0.70003f, 0.704347f, 0.7097f, 0.716982f, 0.724742f, 0.733595f, 0.743427f, 0.753685f},
{0.907349f, 0.822096f, 0.781567f, 0.75938f, 0.746575f, 0.74062f, 0.738894f, 0.73996f, 0.743312f, 0.748194f, 0.754427f, 0.761379f, 0.769242f, 0.777495f, 0.785436f, 0.793383f},
{0.918598f, 0.844123f, 0.809641f, 0.791319f, 0.7824f, 0.77837f, 0.778798f, 0.781282f, 0.785739f, 0.791183f, 0.797331f, 0.804284f, 0.810899f, 0.817841f, 0.825218f, 0.832207f},
{0.929631f, 0.865211f, 0.836575f, 0.822486f, 0.816343f, 0.814767f, 0.816643f, 0.820147f, 0.825207f, 0.831048f, 0.837014f, 0.843117f, 0.849265f, 0.855874f, 0.861713f, 0.86756f},
{0.939552f, 0.885097f, 0.861661f, 0.850918f, 0.847426f, 0.848121f, 0.851277f, 0.855917f, 0.860636f, 0.86656f, 0.872519f, 0.878149f, 0.884097f, 0.890198f, 0.894954f, 0.899522f},
{0.948613f, 0.902507f, 0.883647f, 0.876371f, 0.874718f, 0.877191f, 0.881224f, 0.886323f, 0.892109f, 0.897762f, 0.90331f, 0.90898f, 0.914114f, 0.919126f, 0.923574f, 0.927664f},
{0.956161f, 0.916811f, 0.901554f, 0.89681f, 0.897271f, 0.901427f, 0.906562f, 0.91262f, 0.918545f, 0.924355f, 0.929955f, 0.935019f, 0.939407f, 0.943388f, 0.947411f, 0.950763f},
{0.961875f, 0.926812f, 0.914214f, 0.912295f, 0.915596f, 0.921195f, 0.928058f, 0.93455f, 0.940557f, 0.946781f, 0.951559f, 0.955916f, 0.959969f, 0.963305f, 0.966318f, 0.96869f},
{0.964815f, 0.931745f, 0.922315f, 0.924067f, 0.930668f, 0.938737f, 0.946705f, 0.953519f, 0.959637f, 0.964868f, 0.969074f, 0.972498f, 0.975442f, 0.977914f, 0.980016f, 0.981782f},
{0.964467f, 0.931144f, 0.926877f, 0.934474f, 0.945292f, 0.955041f, 0.963646f, 0.970267f, 0.975109f, 0.978975f, 0.982244f, 0.984445f, 0.9864f, 0.988078f, 0.989237f, 0.990188f},
{0.959202f, 0.926855f, 0.932978f, 0.948112f, 0.961503f, 0.97153f, 0.978656f, 0.983336f, 0.986739f, 0.989265f, 0.990959f, 0.992223f, 0.993323f, 0.993972f, 0.994708f, 0.995183f},
{0.948301f, 0.925526f, 0.946736f, 0.966259f, 0.978299f, 0.985574f, 0.989635f, 0.992358f, 0.993987f, 0.995201f, 0.996059f, 0.996718f, 0.997147f, 0.997501f, 0.997776f, 0.997928f},
{0.933641f, 0.938601f, 0.969659f, 0.984442f, 0.991226f, 0.994473f, 0.996258f, 0.997281f, 0.997916f, 0.998332f, 0.998633f, 0.998808f, 0.998971f, 0.999132f, 0.999212f, 0.999281f},
{0.929114f, 0.970469f, 0.990208f, 0.995737f, 0.997744f, 0.99858f, 0.999031f, 0.999318f, 0.999502f, 0.99958f, 0.999644f, 0.999669f, 0.999741f, 0.999768f, 0.999797f, 0.999821f},
{0.955539f, 0.994859f, 0.998629f, 0.999398f, 0.999695f, 0.999801f, 0.999885f, 0.999914f, 0.999925f, 0.999945f, 0.999946f, 0.999959f, 0.999961f, 0.999964f, 0.999968f, 0.999974f},
{0.991748f, 0.99982f, 0.999924f, 0.999947f, 0.999951f, 0.999962f, 0.999969f, 0.999955f, 0.999973f, 0.999978f, 0.999969f, 0.999965f, 0.999976f, 0.999971f, 0.999971f, 0.999972f}
}
};
static const float table_ggx_glass_inv_E[16][16][16] = {
{
{0.467207f, 0.538927f, 0.574659f, 0.608772f, 0.642304f, 0.675257f, 0.707957f, 0.740158f, 0.771917f, 0.803155f, 0.83407f, 0.864431f, 0.894363f, 0.923674f, 0.952321f, 0.980283f},
{0.464609f, 0.544532f, 0.584937f, 0.623371f, 0.660449f, 0.696496f, 0.731308f, 0.764927f, 0.797233f, 0.82808f, 0.85774f, 0.885719f, 0.912446f, 0.937796f, 0.96165f, 0.984053f},
{0.461956f, 0.551493f, 0.597421f, 0.640579f, 0.681798f, 0.720813f, 0.757636f, 0.792069f, 0.824053f, 0.85368f, 0.881081f, 0.906327f, 0.929485f, 0.950494f, 0.969874f, 0.987302f},
{0.45894f, 0.559813f, 0.612552f, 0.661377f, 0.706645f, 0.748464f, 0.786586f, 0.820906f, 0.851626f, 0.879155f, 0.903579f, 0.925338f, 0.944554f, 0.961512f, 0.976562f, 0.989744f},
{0.456133f, 0.570329f, 0.631129f, 0.685976f, 0.73567f, 0.779491f, 0.817903f, 0.850987f, 0.879359f, 0.903643f, 0.924492f, 0.942345f, 0.957678f, 0.970785f, 0.982122f, 0.991754f},
{0.453071f, 0.583454f, 0.65385f, 0.715586f, 0.768731f, 0.813542f, 0.850635f, 0.881055f, 0.905815f, 0.926283f, 0.943045f, 0.957066f, 0.968633f, 0.9783f, 0.986587f, 0.993419f},
{0.451459f, 0.600348f, 0.681926f, 0.750265f, 0.805757f, 0.84933f, 0.883432f, 0.909636f, 0.929928f, 0.946092f, 0.958852f, 0.969084f, 0.977468f, 0.984297f, 0.990051f, 0.994624f},
{0.451195f, 0.62222f, 0.716361f, 0.789977f, 0.845362f, 0.885478f, 0.914407f, 0.935464f, 0.950656f, 0.962478f, 0.971595f, 0.978785f, 0.984267f, 0.988836f, 0.992629f, 0.995593f},
{0.454655f, 0.650514f, 0.757753f, 0.833856f, 0.8855f, 0.91928f, 0.941692f, 0.956897f, 0.967189f, 0.975121f, 0.981058f, 0.985686f, 0.9893f, 0.992086f, 0.99434f, 0.996262f},
{0.466375f, 0.687794f, 0.805606f, 0.879126f, 0.922795f, 0.948203f, 0.963606f, 0.97338f, 0.979543f, 0.984405f, 0.98786f, 0.990528f, 0.992651f, 0.994388f, 0.995646f, 0.996643f},
{0.494072f, 0.736034f, 0.857614f, 0.922007f, 0.954045f, 0.970447f, 0.979529f, 0.985027f, 0.987903f, 0.990558f, 0.992345f, 0.993723f, 0.994905f, 0.995714f, 0.996365f, 0.996948f},
{0.54918f, 0.796767f, 0.91f, 0.957384f, 0.976739f, 0.985349f, 0.989745f, 0.992093f, 0.99292f, 0.994137f, 0.995029f, 0.995624f, 0.996217f, 0.996624f, 0.996871f, 0.997133f},
{0.643871f, 0.870216f, 0.955899f, 0.981825f, 0.990287f, 0.993789f, 0.995402f, 0.996054f, 0.995607f, 0.99605f, 0.996438f, 0.996734f, 0.996834f, 0.997026f, 0.997038f, 0.997198f},
{0.77505f, 0.944715f, 0.986041f, 0.994556f, 0.996691f, 0.99757f, 0.997928f, 0.997881f, 0.996692f, 0.996987f, 0.997098f, 0.997113f, 0.997145f, 0.997175f, 0.997226f, 0.997242f},
{0.910815f, 0.989663f, 0.997687f, 0.998948f, 0.99884f, 0.998825f, 0.998798f, 0.998538f, 0.997143f, 0.997186f, 0.997289f, 0.997175f, 0.997165f, 0.997177f, 0.997328f, 0.99722f},
{0.988773f, 0.999559f, 0.999684f, 0.999632f, 0.999128f, 0.998962f, 0.998883f, 0.998629f, 0.997223f, 0.997127f, 0.997255f, 0.997299f, 0.997234f, 0.997171f, 0.997179f, 0.997287f}
},
{
{0.331776f, 0.492473f, 0.54275f, 0.58052f, 0.615581f, 0.650102f, 0.683863f, 0.717645f, 0.750486f, 0.782911f, 0.814667f, 0.845786f, 0.876317f, 0.905953f, 0.934498f, 0.958563f},
{0.322602f, 0.492259f, 0.548848f, 0.591202f, 0.629944f, 0.667743f, 0.704394f, 0.740062f, 0.774339f, 0.807034f, 0.838191f, 0.867899f, 0.895982f, 0.922349f, 0.947096f, 0.967158f},
{0.313884f, 0.492341f, 0.556257f, 0.603478f, 0.646619f, 0.687837f, 0.727374f, 0.764869f, 0.799831f, 0.832292f, 0.862188f, 0.889588f, 0.914668f, 0.937611f, 0.958241f, 0.974788f},
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},
{
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}
};
/* clang-format on */