WIP: Vulkan: Workbench #107886

Closed
Jeroen Bakker wants to merge 88 commits from Jeroen-Bakker:vulkan-draw-manager-workbench into main

When changing the target branch, be careful to rebase the branch in your fork to match. See documentation.
24 changed files with 1294 additions and 1826 deletions
Showing only changes of commit a44d153c6a - Show all commits

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@ -496,6 +496,7 @@ option(WITH_CYCLES_DEBUG "Build Cycles with options useful for debug
option(WITH_CYCLES_STANDALONE "Build Cycles standalone application" OFF)
option(WITH_CYCLES_STANDALONE_GUI "Build Cycles standalone with GUI" OFF)
option(WITH_CYCLES_PRECOMPUTE "Build Cycles data precomputation tool" OFF)
option(WITH_CYCLES_HYDRA_RENDER_DELEGATE "Build Cycles Hydra render delegate" OFF)
@ -507,6 +508,7 @@ mark_as_advanced(WITH_CYCLES_KERNEL_ASAN)
mark_as_advanced(WITH_CYCLES_LOGGING)
mark_as_advanced(WITH_CYCLES_DEBUG_NAN)
mark_as_advanced(WITH_CYCLES_NATIVE_ONLY)
mark_as_advanced(WITH_CYCLES_PRECOMPUTE)
# NVIDIA CUDA & OptiX
if(NOT APPLE)

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@ -119,3 +119,22 @@ if(WITH_CYCLES_STANDALONE)
$<TARGET_FILE:cycles>
DESTINATION ${CMAKE_INSTALL_PREFIX})
endif()
if(WITH_CYCLES_PRECOMPUTE)
set(SRC
cycles_precompute.cpp
)
add_executable(cycles_precompute ${SRC} ${INC} ${INC_SYS})
unset(SRC)
target_link_libraries(cycles_precompute PRIVATE ${LIB})
if(UNIX AND NOT APPLE)
set_target_properties(cycles_precompute PROPERTIES INSTALL_RPATH $ORIGIN/lib)
endif()
install(PROGRAMS
$<TARGET_FILE:cycles_precompute>
DESTINATION ${CMAKE_INSTALL_PREFIX})
endif()

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@ -0,0 +1,192 @@
#include "util/math.h"
#include "util/string.h"
#include "util/system.h"
#include "util/array.h"
#include "util/hash.h"
#include "util/task.h"
#include "kernel/device/cpu/compat.h"
#include "kernel/device/cpu/globals.h"
#include "kernel/sample/lcg.h"
#include "kernel/sample/mapping.h"
#include "kernel/closure/bsdf_microfacet.h"
#include <iostream>
CCL_NAMESPACE_BEGIN
static float precompute_ggx_E(float rough, float mu, float3 rand)
{
MicrofacetBsdf bsdf;
bsdf.weight = one_float3();
bsdf.sample_weight = 1.0f;
bsdf.N = make_float3(0.0f, 0.0f, 1.0f);
bsdf.alpha_x = bsdf.alpha_y = sqr(rough);
bsdf.ior = 1.0f;
bsdf.T = make_float3(1.0f, 0.0f, 0.0f);
bsdf_microfacet_ggx_setup(&bsdf);
float3 omega_in;
Spectrum eval;
float pdf = 0.0f, sampled_eta;
float2 sampled_roughness;
bsdf_microfacet_ggx_sample((ShaderClosure *)&bsdf,
0,
make_float3(0.0f, 0.0f, 1.0f),
make_float3(sqrtf(1.0f - sqr(mu)), 0.0f, mu),
rand,
&eval,
&omega_in,
&pdf,
&sampled_roughness,
&sampled_eta);
if (pdf != 0.0f) {
return average(eval) / pdf;
}
return 0.0f;
}
static float precompute_ggx_glass_E(float rough, float mu, float eta, float3 rand)
{
MicrofacetBsdf bsdf;
bsdf.weight = one_float3();
bsdf.sample_weight = 1.0f;
bsdf.N = make_float3(0.0f, 0.0f, 1.0f);
bsdf.alpha_x = bsdf.alpha_y = sqr(rough);
bsdf.ior = eta;
bsdf.T = make_float3(1.0f, 0.0f, 0.0f);
bsdf_microfacet_ggx_glass_setup(&bsdf);
float3 omega_in;
Spectrum eval;
float pdf = 0.0f, sampled_eta;
float2 sampled_roughness;
bsdf_microfacet_ggx_sample((ShaderClosure *)&bsdf,
0,
make_float3(0.0f, 0.0f, 1.0f),
make_float3(sqrtf(1.0f - sqr(mu)), 0.0f, mu),
rand,
&eval,
&omega_in,
&pdf,
&sampled_roughness,
&sampled_eta);
if (pdf != 0.0f) {
return average(eval) / pdf;
}
return 0.0f;
}
struct PrecomputeTerm {
int samples;
int nx, ny, nz;
std::function<float(float, float, float, float3)> evaluation;
};
static bool cycles_precompute(std::string name)
{
std::map<string, PrecomputeTerm> precompute_terms;
precompute_terms["ggx_E"] = {
1 << 23, 32, 32, 1, [](float rough, float mu, float ior, float3 rand) {
return precompute_ggx_E(rough, mu, rand);
}};
precompute_terms["ggx_Eavg"] = {
1 << 26, 32, 1, 1, [](float rough, float mu, float ior, float3 rand) {
return 2.0f * mu * precompute_ggx_E(rough, mu, rand);
}};
precompute_terms["ggx_glass_E"] = {
1 << 23, 16, 16, 16, [](float rough, float mu, float ior, float3 rand) {
return precompute_ggx_glass_E(rough, mu, ior, rand);
}};
precompute_terms["ggx_glass_Eavg"] = {
1 << 26, 16, 1, 16, [](float rough, float mu, float ior, float3 rand) {
return 2.0f * mu * precompute_ggx_glass_E(rough, mu, ior, rand);
}};
precompute_terms["ggx_glass_inv_E"] = {
1 << 23, 16, 16, 16, [](float rough, float mu, float ior, float3 rand) {
return precompute_ggx_glass_E(rough, mu, 1.0f / ior, rand);
}};
precompute_terms["ggx_glass_inv_Eavg"] = {
1 << 26, 16, 1, 16, [](float rough, float mu, float ior, float3 rand) {
return 2.0f * mu * precompute_ggx_glass_E(rough, mu, 1.0f / ior, rand);
}};
if (precompute_terms.count(name) == 0) {
return false;
}
const PrecomputeTerm &term = precompute_terms[name];
const int samples = term.samples;
const int nz = term.nz, ny = term.ny, nx = term.nx;
std::cout << "static const float table_" << name << "[" << nz * ny * nx << "] = {" << std::endl;
for (int z = 0; z < nz; z++) {
array<float> data(nx * ny);
parallel_for(0, nx * ny, [&](int64_t i) {
int y = i / nx, x = i % nx;
uint seed = hash_uint2(x, y);
double sum = 0.0;
for (int sample = 0; sample < samples; sample++) {
float4 rand = sobol_burley_sample_4D(sample, 0, seed, 0xffffffff);
float rough = (nx == 1) ? 0.0f : clamp(float(x) / float(nx - 1), 1e-4f, 1.0f);
float mu = (ny == 1) ? rand.w : clamp(float(y) / float(ny - 1), 1e-4f, 1.0f);
float ior = (nz == 1) ? 0.0f : clamp(float(z) / float(nz - 1), 1e-4f, 0.99f);
/* This parametrization ensures that the entire [1..inf] range of IORs is covered
* and that most precision is allocated to the common areas (1-2). */
ior = ior_from_F0(sqr(sqr(ior)));
float value = term.evaluation(rough, mu, ior, float4_to_float3(rand));
if (isnan(value)) {
value = 0.0f;
}
sum += (double)value;
}
data[y * nx + x] = saturatef(float(sum / double(samples)));
});
/* Print data formatted as C++ array */
for (int y = 0; y < ny; y++) {
std::cout << " ";
for (int x = 0; x < nx; x++) {
std::cout << std::to_string(data[y * nx + x]);
if (x + 1 < nx) {
/* Next number will follow in same line */
std::cout << "f, ";
}
else if (y + 1 < ny || z + 1 < nz) {
/* Next number will follow in next line */
std::cout << "f,";
}
else {
/* No next number */
std::cout << "f";
}
}
std::cout << std::endl;
}
/* If the array is three-dimensional, put an empty line between each slice. */
if (ny > 1 && z + 1 < nz) {
std::cout << std::endl;
}
}
std::cout << "};" << std::endl;
return true;
}
CCL_NAMESPACE_END
int main(int argc, const char **argv)
{
if (argc < 2) {
return 1;
}
return ccl::cycles_precompute(argv[1]) ? 0 : 1;
}

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@ -123,8 +123,6 @@ set(SRC_KERNEL_CLOSURE_HEADERS
closure/bsdf_diffuse.h
closure/bsdf_diffuse_ramp.h
closure/bsdf_microfacet.h
closure/bsdf_microfacet_multi.h
closure/bsdf_microfacet_multi_impl.h
closure/bsdf_oren_nayar.h
closure/bsdf_phong_ramp.h
closure/bsdf_toon.h

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@ -10,7 +10,6 @@
#include "kernel/closure/bsdf_phong_ramp.h"
#include "kernel/closure/bsdf_diffuse_ramp.h"
#include "kernel/closure/bsdf_microfacet.h"
#include "kernel/closure/bsdf_microfacet_multi.h"
#include "kernel/closure/bsdf_transparent.h"
#include "kernel/closure/bsdf_ashikhmin_shirley.h"
#include "kernel/closure/bsdf_toon.h"
@ -170,34 +169,6 @@ ccl_device_inline int bsdf_sample(KernelGlobals kg,
label = bsdf_microfacet_ggx_sample(
sc, path_flag, Ng, sd->wi, rand, eval, wo, pdf, sampled_roughness, eta);
break;
case CLOSURE_BSDF_MICROFACET_MULTI_GGX_ID:
label = bsdf_microfacet_multi_ggx_sample(kg,
sc,
Ng,
sd->wi,
rand.x,
rand.y,
eval,
wo,
pdf,
&sd->lcg_state,
sampled_roughness,
eta);
break;
case CLOSURE_BSDF_MICROFACET_MULTI_GGX_GLASS_ID:
label = bsdf_microfacet_multi_ggx_glass_sample(kg,
sc,
Ng,
sd->wi,
rand.x,
rand.y,
eval,
wo,
pdf,
&sd->lcg_state,
sampled_roughness,
eta);
break;
case CLOSURE_BSDF_MICROFACET_BECKMANN_ID:
case CLOSURE_BSDF_MICROFACET_BECKMANN_REFRACTION_ID:
case CLOSURE_BSDF_MICROFACET_BECKMANN_GLASS_ID:
@ -339,13 +310,6 @@ ccl_device_inline void bsdf_roughness_eta(const KernelGlobals kg,
*eta = CLOSURE_IS_REFRACTIVE(bsdf->type) ? 1.0f / bsdf->ior : bsdf->ior;
break;
}
case CLOSURE_BSDF_MICROFACET_MULTI_GGX_ID:
case CLOSURE_BSDF_MICROFACET_MULTI_GGX_GLASS_ID: {
ccl_private const MicrofacetBsdf *bsdf = (ccl_private const MicrofacetBsdf *)sc;
*roughness = make_float2(bsdf->alpha_x, bsdf->alpha_y);
*eta = bsdf->ior;
break;
}
case CLOSURE_BSDF_ASHIKHMIN_SHIRLEY_ID: {
ccl_private const MicrofacetBsdf *bsdf = (ccl_private const MicrofacetBsdf *)sc;
*roughness = make_float2(bsdf->alpha_x, bsdf->alpha_y);
@ -433,13 +397,11 @@ ccl_device_inline int bsdf_label(const KernelGlobals kg,
case CLOSURE_BSDF_SHARP_GLASS_ID:
case CLOSURE_BSDF_MICROFACET_GGX_ID:
case CLOSURE_BSDF_MICROFACET_GGX_CLEARCOAT_ID:
case CLOSURE_BSDF_MICROFACET_MULTI_GGX_ID:
case CLOSURE_BSDF_MICROFACET_BECKMANN_ID:
case CLOSURE_BSDF_MICROFACET_GGX_REFRACTION_ID:
case CLOSURE_BSDF_MICROFACET_BECKMANN_REFRACTION_ID:
case CLOSURE_BSDF_MICROFACET_GGX_GLASS_ID:
case CLOSURE_BSDF_MICROFACET_BECKMANN_GLASS_ID:
case CLOSURE_BSDF_MICROFACET_MULTI_GGX_GLASS_ID: {
case CLOSURE_BSDF_MICROFACET_BECKMANN_GLASS_ID: {
ccl_private const MicrofacetBsdf *bsdf = (ccl_private const MicrofacetBsdf *)sc;
label = ((bsdf_is_transmission(sc, wo)) ? LABEL_TRANSMIT : LABEL_REFLECT) |
((bsdf->alpha_x * bsdf->alpha_y <= 1e-7f) ? LABEL_SINGULAR : LABEL_GLOSSY);
@ -542,12 +504,6 @@ ccl_device_inline
case CLOSURE_BSDF_MICROFACET_GGX_GLASS_ID:
eval = bsdf_microfacet_ggx_eval(sc, sd->N, sd->wi, wo, pdf);
break;
case CLOSURE_BSDF_MICROFACET_MULTI_GGX_ID:
eval = bsdf_microfacet_multi_ggx_eval(sc, sd->N, sd->wi, wo, pdf, &sd->lcg_state);
break;
case CLOSURE_BSDF_MICROFACET_MULTI_GGX_GLASS_ID:
eval = bsdf_microfacet_multi_ggx_glass_eval(sc, sd->wi, wo, pdf, &sd->lcg_state);
break;
case CLOSURE_BSDF_MICROFACET_BECKMANN_ID:
case CLOSURE_BSDF_MICROFACET_BECKMANN_REFRACTION_ID:
case CLOSURE_BSDF_MICROFACET_BECKMANN_GLASS_ID:
@ -613,14 +569,11 @@ ccl_device void bsdf_blur(KernelGlobals kg, ccl_private ShaderClosure *sc, float
/* TODO: do we want to blur volume closures? */
#if defined(__SVM__) || defined(__OSL__)
switch (sc->type) {
case CLOSURE_BSDF_MICROFACET_MULTI_GGX_ID:
case CLOSURE_BSDF_MICROFACET_MULTI_GGX_GLASS_ID:
bsdf_microfacet_multi_ggx_blur(sc, roughness);
break;
case CLOSURE_BSDF_MICROFACET_GGX_ID:
case CLOSURE_BSDF_MICROFACET_GGX_CLEARCOAT_ID:
case CLOSURE_BSDF_MICROFACET_GGX_REFRACTION_ID:
case CLOSURE_BSDF_MICROFACET_GGX_GLASS_ID:
/* TODO: Recompute energy preservation after blur? */
bsdf_microfacet_ggx_blur(sc, roughness);
break;
case CLOSURE_BSDF_MICROFACET_BECKMANN_ID:

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@ -28,19 +28,8 @@ enum MicrofacetFresnel {
DIELECTRIC_TINT, /* used by the OSL MaterialX closures */
CONDUCTOR,
GENERALIZED_SCHLICK,
CONSTANT, /* only needed by MultiGGX */
PRINCIPLED_V1,
};
typedef struct FresnelPrincipledV1 {
Spectrum color; /* only needed by MultiGGX */
Spectrum cspec0;
} FresnelPrincipledV1;
typedef struct FresnelConstant {
Spectrum color;
} FresnelConstant;
typedef struct FresnelDielectricTint {
Spectrum reflection_tint;
Spectrum transmission_tint;
@ -53,7 +42,9 @@ typedef struct FresnelConductor {
typedef struct FresnelGeneralizedSchlick {
Spectrum reflection_tint;
Spectrum transmission_tint;
/* Reflectivity at perpendicular (F0) and glancing (F90) angles. */
Spectrum f0, f90;
/* Negative exponent signals a special case where the real Fresnel is remapped to F0...F90. */
float exponent;
} FresnelGeneralizedSchlick;
@ -61,8 +52,18 @@ typedef struct MicrofacetBsdf {
SHADER_CLOSURE_BASE;
float alpha_x, alpha_y, ior;
/* Used to account for missing energy due to the single-scattering microfacet model.
* This could be included in bsdf->weight as well, but there it would mess up the color
* channels.
* Note that this is currently only used by GGX. */
float energy_scale;
/* Fresnel model to apply, as well as the extra data for it.
* For NONE and DIELECTRIC, no extra storage is needed, so the pointer is NULL for them. */
int fresnel_type;
ccl_private void *fresnel;
float3 T;
} MicrofacetBsdf;
@ -218,12 +219,7 @@ ccl_device_forceinline Spectrum microfacet_fresnel(ccl_private const MicrofacetB
const float3 H,
const bool refraction)
{
if (bsdf->fresnel_type == MicrofacetFresnel::PRINCIPLED_V1) {
kernel_assert(!refraction);
ccl_private FresnelPrincipledV1 *fresnel = (ccl_private FresnelPrincipledV1 *)bsdf->fresnel;
return interpolate_fresnel_color(wi, H, bsdf->ior, fresnel->cspec0);
}
else if (bsdf->fresnel_type == MicrofacetFresnel::DIELECTRIC) {
if (bsdf->fresnel_type == MicrofacetFresnel::DIELECTRIC) {
const float F = fresnel_dielectric_cos(dot(wi, H), bsdf->ior);
return make_spectrum(refraction ? 1.0f - F : F);
}
@ -241,18 +237,29 @@ ccl_device_forceinline Spectrum microfacet_fresnel(ccl_private const MicrofacetB
else if (bsdf->fresnel_type == MicrofacetFresnel::GENERALIZED_SCHLICK) {
ccl_private FresnelGeneralizedSchlick *fresnel = (ccl_private FresnelGeneralizedSchlick *)
bsdf->fresnel;
float cosI = dot(wi, H);
if (bsdf->ior < 1.0f) {
/* When going from a higher to a lower IOR, we must use the transmitted angle. */
float sinT2 = (1.0f - sqr(cosI)) / sqr(bsdf->ior);
if (sinT2 >= 1.0f) {
/* Total internal reflection */
return refraction ? zero_spectrum() : fresnel->reflection_tint;
}
cosI = safe_sqrtf(1.0f - sinT2);
float s;
if (fresnel->exponent < 0.0f) {
/* Special case: Use real Fresnel curve to determine the interpolation between F0 and F90.
* Used by Principled v1. */
const float F_real = fresnel_dielectric_cos(dot(wi, H), bsdf->ior);
const float F0_real = F0_from_ior(bsdf->ior);
s = inverse_lerp(F0_real, 1.0f, F_real);
}
else {
/* Regular case: Generalized Schlick term. */
float cosI = dot(wi, H);
if (bsdf->ior < 1.0f) {
/* When going from a higher to a lower IOR, we must use the transmitted angle. */
const float sinT2 = (1.0f - sqr(cosI)) / sqr(bsdf->ior);
if (sinT2 >= 1.0f) {
/* Total internal reflection */
return refraction ? zero_spectrum() : fresnel->reflection_tint;
}
cosI = safe_sqrtf(1.0f - sinT2);
}
/* TODO(lukas): Is a special case for exponent==5 worth it? */
s = powf(1.0f - cosI, fresnel->exponent);
}
/* TODO(lukas): Is a special case for exponent==5 worth it? */
const float s = powf(1.0f - cosI, fresnel->exponent);
const Spectrum F = mix(fresnel->f0, fresnel->f90, s);
if (refraction) {
return (one_spectrum() - F) * fresnel->transmission_tint;
@ -261,23 +268,75 @@ ccl_device_forceinline Spectrum microfacet_fresnel(ccl_private const MicrofacetB
return F * fresnel->reflection_tint;
}
}
else if (bsdf->fresnel_type == MicrofacetFresnel::CONSTANT) {
/* CONSTANT is only used my MultiGGX, which doesn't call this function.
* Therefore, this case only happens when determining the albedo of a MultiGGX closure.
* In that case, return 1.0 since the constant color is already baked into the weight. */
return one_spectrum();
}
else {
return one_spectrum();
}
}
ccl_device_inline void microfacet_ggx_preserve_energy(KernelGlobals kg,
ccl_private MicrofacetBsdf *bsdf,
ccl_private const ShaderData *sd,
const Spectrum Fss)
{
const float mu = dot(sd->wi, bsdf->N);
const float rough = sqrtf(sqrtf(bsdf->alpha_x * bsdf->alpha_y));
float E, E_avg;
if (bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_ID) {
E = lookup_table_read_2D(kg, rough, mu, kernel_data.tables.ggx_E, 32, 32);
E_avg = lookup_table_read(kg, rough, kernel_data.tables.ggx_Eavg, 32);
}
else if (bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_GLASS_ID) {
int ofs = kernel_data.tables.ggx_glass_E;
int avg_ofs = kernel_data.tables.ggx_glass_Eavg;
float ior = bsdf->ior;
if (ior < 1.0f) {
ior = 1.0f / ior;
ofs = kernel_data.tables.ggx_glass_inv_E;
avg_ofs = kernel_data.tables.ggx_glass_inv_Eavg;
}
/* TODO: Bias mu towards more precision for low values. */
float z = sqrtf(fabsf((ior - 1.0f) / (ior + 1.0f)));
E = lookup_table_read_3D(kg, rough, mu, z, ofs, 16, 16, 16);
E_avg = lookup_table_read_2D(kg, rough, z, avg_ofs, 16, 16);
}
else {
kernel_assert(false);
E = 1.0f;
E_avg = 1.0f;
}
const float missing_factor = ((1.0f - E) / E);
bsdf->energy_scale = 1.0f + missing_factor;
/* Check if we need to account for extra darkening/saturation due to multi-bounce Fresnel. */
if (Fss != one_spectrum()) {
/* Fms here is based on the appendix of "Revisiting Physically Based Shading at Imageworks"
* by Christopher Kulla and Alejandro Conty,
* 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. */
const Spectrum Fms = Fss * E_avg / (one_spectrum() - Fss * (1.0f - E_avg));
/* Since we already include the energy compensation in bsdf->energy_scale,
* this term is what's needed to make the full BSDF * weight * energy_scale
* computation work out to the correct value. */
const Spectrum darkening = (one_spectrum() + Fms * missing_factor) / bsdf->energy_scale;
bsdf->weight *= darkening;
bsdf->sample_weight *= average(darkening);
}
}
/* This function estimates the albedo of the BSDF (NOT including the bsdf->weight) as caused by
* the applied Fresnel model for the given view direction.
* The base microfacet model is assumed to have an albedo of 1, but e.g. a reflection-only
* closure with Fresnel applied can end up having a very low overall albedo.
* The base microfacet model is assumed to have an albedo of 1 (we have the energy preservation
* code for that), but e.g. a reflection-only closure with Fresnel applied can end up having
* a very low overall albedo.
* This is used to adjust the sample weight, as well as for the Diff/Gloss/Trans Color pass
* and the Denoising Albedo pass. */
* and the Denoising Albedo pass.
*
* NOTE: This code assumes the microfacet surface is fairly smooth. For very high roughness,
* the results are much more uniform across the surface.
* For better results, we'd be blending between this and Fss based on roughness, but that
* would involve storing or recomputing Fss, which is probably not worth it. */
ccl_device Spectrum bsdf_microfacet_estimate_fresnel(ccl_private const ShaderData *sd,
ccl_private const MicrofacetBsdf *bsdf)
{
@ -658,45 +717,105 @@ ccl_device int bsdf_microfacet_sample(ccl_private const ShaderClosure *sc,
/* Fresnel term setup functions. These get called after the distribution-specific setup functions
* like bsdf_microfacet_ggx_setup. */
ccl_device void bsdf_microfacet_setup_fresnel_principledv1(
ccl_private MicrofacetBsdf *bsdf,
ccl_private const ShaderData *sd,
ccl_private FresnelPrincipledV1 *fresnel)
{
fresnel->cspec0 = saturate(fresnel->cspec0);
bsdf->fresnel_type = MicrofacetFresnel::PRINCIPLED_V1;
bsdf->fresnel = fresnel;
bsdf->sample_weight *= average(bsdf_microfacet_estimate_fresnel(sd, bsdf));
}
ccl_device void bsdf_microfacet_setup_fresnel_conductor(ccl_private MicrofacetBsdf *bsdf,
ccl_device void bsdf_microfacet_setup_fresnel_conductor(KernelGlobals kg,
ccl_private MicrofacetBsdf *bsdf,
ccl_private const ShaderData *sd,
ccl_private FresnelConductor *fresnel)
ccl_private FresnelConductor *fresnel,
const bool preserve_energy)
{
bsdf->fresnel_type = MicrofacetFresnel::CONDUCTOR;
bsdf->fresnel = fresnel;
bsdf->sample_weight *= average(bsdf_microfacet_estimate_fresnel(sd, bsdf));
if (preserve_energy) {
/* In order to estimate Fss of the conductor, we fit the F82-tint model to it based on the
* value at 0° and ~82° and then use the analytic expression for its Fss. */
Spectrum F0 = fresnel_conductor(1.0f, fresnel->n, fresnel->k);
Spectrum F82 = fresnel_conductor(1.0f / 7.0f, fresnel->n, fresnel->k);
/* 0.46266436f is (1 - 1/7)^5, 17.651384f is 1/(1/7 * (1 - 1/7)^6) */
Spectrum B = (mix(F0, one_spectrum(), 0.46266436f) - F82) * 17.651384f;
Spectrum Fss = saturate(mix(F0, one_spectrum(), 1.0f / 21.0f) - B * (1.0f / 126.0f));
microfacet_ggx_preserve_energy(kg, bsdf, sd, Fss);
}
}
ccl_device void bsdf_microfacet_setup_fresnel_dielectric_tint(
KernelGlobals kg,
ccl_private MicrofacetBsdf *bsdf,
ccl_private const ShaderData *sd,
ccl_private FresnelDielectricTint *fresnel)
ccl_private FresnelDielectricTint *fresnel,
const bool preserve_energy)
{
bsdf->fresnel_type = MicrofacetFresnel::DIELECTRIC_TINT;
bsdf->fresnel = fresnel;
bsdf->sample_weight *= average(bsdf_microfacet_estimate_fresnel(sd, bsdf));
if (preserve_energy) {
/* Assume that the transmissive tint makes up most of the overall color. */
microfacet_ggx_preserve_energy(kg, bsdf, sd, fresnel->transmission_tint);
}
}
ccl_device void bsdf_microfacet_setup_fresnel_generalized_schlick(
KernelGlobals kg,
ccl_private MicrofacetBsdf *bsdf,
ccl_private const ShaderData *sd,
ccl_private FresnelGeneralizedSchlick *fresnel)
ccl_private FresnelGeneralizedSchlick *fresnel,
const bool preserve_energy)
{
bsdf->fresnel_type = MicrofacetFresnel::GENERALIZED_SCHLICK;
bsdf->fresnel = fresnel;
bsdf->sample_weight *= average(bsdf_microfacet_estimate_fresnel(sd, bsdf));
if (preserve_energy) {
Spectrum Fss = one_spectrum();
/* Multi-bounce Fresnel is only supported for reflective lobes here. */
if (is_zero(fresnel->transmission_tint)) {
float s;
if (fresnel->exponent < 0.0f) {
const float eta = bsdf->ior;
const float real_F0 = F0_from_ior(bsdf->ior);
/* Numerical fit for the integral of 2*cosI * F(cosI, eta) over 0...1 with F being
* the real dielectric Fresnel. From "Revisiting Physically Based Shading at Imageworks"
* by Christopher Kulla and Alejandro Conty. */
float real_Fss;
if (eta < 1.0f) {
real_Fss = 0.997118f + eta * (0.1014f - eta * (0.965241f + eta * 0.130607f));
}
else {
real_Fss = (eta - 1.0f) / (4.08567f + 1.00071f * eta);
}
s = saturatef(inverse_lerp(real_F0, 1.0f, real_Fss));
}
else {
/* Integral of 2*cosI * (1 - cosI)^exponent over 0...1*/
s = 2.0f / ((fresnel->exponent + 3.0f) * fresnel->exponent + 2.0f);
}
/* Due to the linearity of the generalized model, this ends up working. */
Fss = fresnel->reflection_tint * mix(fresnel->f0, fresnel->f90, s);
}
else {
/* For transmissive BSDFs, assume that the transmissive tint makes up most of the overall
* color. */
Fss = fresnel->transmission_tint;
}
microfacet_ggx_preserve_energy(kg, bsdf, sd, Fss);
}
}
ccl_device void bsdf_microfacet_setup_fresnel_constant(KernelGlobals kg,
ccl_private MicrofacetBsdf *bsdf,
ccl_private const ShaderData *sd,
const Spectrum color)
{
/* Constant Fresnel is a special case - the color is already baked into the closure's
* weight, so we just need to perform the energy preservation. */
kernel_assert(bsdf->fresnel_type == MicrofacetFresnel::NONE ||
bsdf->fresnel_type == MicrofacetFresnel::DIELECTRIC);
microfacet_ggx_preserve_energy(kg, bsdf, sd, color);
}
/* GGX microfacet with Smith shadow-masking from:
@ -718,6 +837,7 @@ ccl_device int bsdf_microfacet_ggx_setup(ccl_private MicrofacetBsdf *bsdf)
bsdf->alpha_y = saturatef(bsdf->alpha_y);
bsdf->fresnel_type = MicrofacetFresnel::NONE;
bsdf->energy_scale = 1.0f;
bsdf->type = CLOSURE_BSDF_MICROFACET_GGX_ID;
return SD_BSDF | SD_BSDF_HAS_EVAL;
@ -730,6 +850,7 @@ ccl_device int bsdf_microfacet_ggx_clearcoat_setup(ccl_private MicrofacetBsdf *b
bsdf->alpha_y = bsdf->alpha_x;
bsdf->fresnel_type = MicrofacetFresnel::DIELECTRIC;
bsdf->energy_scale = 1.0f;
bsdf->type = CLOSURE_BSDF_MICROFACET_GGX_CLEARCOAT_ID;
bsdf->sample_weight *= average(bsdf_microfacet_estimate_fresnel(sd, bsdf));
@ -742,6 +863,7 @@ ccl_device int bsdf_microfacet_ggx_refraction_setup(ccl_private MicrofacetBsdf *
bsdf->alpha_y = bsdf->alpha_x;
bsdf->fresnel_type = MicrofacetFresnel::NONE;
bsdf->energy_scale = 1.0f;
bsdf->type = CLOSURE_BSDF_MICROFACET_GGX_REFRACTION_ID;
return SD_BSDF | SD_BSDF_HAS_EVAL | SD_BSDF_HAS_TRANSMISSION;
@ -753,6 +875,7 @@ ccl_device int bsdf_microfacet_ggx_glass_setup(ccl_private MicrofacetBsdf *bsdf)
bsdf->alpha_y = bsdf->alpha_x;
bsdf->fresnel_type = MicrofacetFresnel::DIELECTRIC;
bsdf->energy_scale = 1.0f;
bsdf->type = CLOSURE_BSDF_MICROFACET_GGX_GLASS_ID;
return SD_BSDF | SD_BSDF_HAS_EVAL | SD_BSDF_HAS_TRANSMISSION;
@ -772,7 +895,8 @@ ccl_device Spectrum bsdf_microfacet_ggx_eval(ccl_private const ShaderClosure *sc
const float3 wo,
ccl_private float *pdf)
{
return bsdf_microfacet_eval<MicrofacetType::GGX>(sc, Ng, wi, wo, pdf);
ccl_private const MicrofacetBsdf *bsdf = (ccl_private const MicrofacetBsdf *)sc;
return bsdf->energy_scale * bsdf_microfacet_eval<MicrofacetType::GGX>(sc, Ng, wi, wo, pdf);
}
ccl_device int bsdf_microfacet_ggx_sample(ccl_private const ShaderClosure *sc,
@ -786,8 +910,11 @@ ccl_device int bsdf_microfacet_ggx_sample(ccl_private const ShaderClosure *sc,
ccl_private float2 *sampled_roughness,
ccl_private float *eta)
{
return bsdf_microfacet_sample<MicrofacetType::GGX>(
int label = bsdf_microfacet_sample<MicrofacetType::GGX>(
sc, path_flag, Ng, wi, rand, eval, wo, pdf, sampled_roughness, eta);
*eval *= ((ccl_private const MicrofacetBsdf *)sc)->energy_scale;
return label;
}
/* Beckmann microfacet with Smith shadow-masking from:

View File

@ -1,759 +0,0 @@
/* SPDX-License-Identifier: Apache-2.0
* Copyright 2011-2022 Blender Foundation */
#pragma once
#include "kernel/sample/lcg.h"
#include "kernel/sample/mapping.h"
CCL_NAMESPACE_BEGIN
/* Most of the code is based on the supplemental implementations from
* https://eheitzresearch.wordpress.com/240-2/. */
/* === GGX Microfacet distribution functions === */
/* Isotropic GGX microfacet distribution */
ccl_device_forceinline float D_ggx(float3 wm, float alpha)
{
wm.z *= wm.z;
alpha *= alpha;
float tmp = (1.0f - wm.z) + alpha * wm.z;
return alpha / max(M_PI_F * tmp * tmp, 1e-7f);
}
/* Anisotropic GGX microfacet distribution */
ccl_device_forceinline float D_ggx_aniso(const float3 wm, const float2 alpha)
{
float slope_x = -wm.x / alpha.x;
float slope_y = -wm.y / alpha.y;
float tmp = wm.z * wm.z + slope_x * slope_x + slope_y * slope_y;
return 1.0f / max(M_PI_F * tmp * tmp * alpha.x * alpha.y, 1e-7f);
}
/* Sample slope distribution (based on page 14 of the supplemental implementation). */
ccl_device_forceinline float2 mf_sampleP22_11(const float cosI,
const float randx,
const float randy)
{
if (cosI > 0.9999f || fabsf(cosI) < 1e-6f) {
const float r = sqrtf(randx / max(1.0f - randx, 1e-7f));
const float phi = M_2PI_F * randy;
return make_float2(r * cosf(phi), r * sinf(phi));
}
const float sinI = sin_from_cos(cosI);
const float tanI = sinI / cosI;
const float projA = 0.5f * (cosI + 1.0f);
if (projA < 0.0001f)
return make_float2(0.0f, 0.0f);
const float A = 2.0f * randx * projA / cosI - 1.0f;
float tmp = A * A - 1.0f;
if (fabsf(tmp) < 1e-7f)
return make_float2(0.0f, 0.0f);
tmp = 1.0f / tmp;
const float D = safe_sqrtf(tanI * tanI * tmp * tmp - (A * A - tanI * tanI) * tmp);
const float slopeX2 = tanI * tmp + D;
const float slopeX = (A < 0.0f || slopeX2 > 1.0f / tanI) ? (tanI * tmp - D) : slopeX2;
float U2;
if (randy >= 0.5f)
U2 = 2.0f * (randy - 0.5f);
else
U2 = 2.0f * (0.5f - randy);
const float z = (U2 * (U2 * (U2 * 0.27385f - 0.73369f) + 0.46341f)) /
(U2 * (U2 * (U2 * 0.093073f + 0.309420f) - 1.0f) + 0.597999f);
const float slopeY = z * sqrtf(1.0f + slopeX * slopeX);
if (randy >= 0.5f)
return make_float2(slopeX, slopeY);
else
return make_float2(slopeX, -slopeY);
}
/* Visible normal sampling for the GGX distribution
* (based on page 7 of the supplemental implementation). */
ccl_device_forceinline float3 mf_sample_vndf(const float3 wi,
const float2 alpha,
const float randx,
const float randy)
{
const float3 wi_11 = normalize(make_float3(alpha.x * wi.x, alpha.y * wi.y, wi.z));
const float2 slope_11 = mf_sampleP22_11(wi_11.z, randx, randy);
const float3 cossin_phi = safe_normalize(make_float3(wi_11.x, wi_11.y, 0.0f));
const float slope_x = alpha.x * (cossin_phi.x * slope_11.x - cossin_phi.y * slope_11.y);
const float slope_y = alpha.y * (cossin_phi.y * slope_11.x + cossin_phi.x * slope_11.y);
kernel_assert(isfinite(slope_x));
return normalize(make_float3(-slope_x, -slope_y, 1.0f));
}
/* === Phase functions: Glossy and Glass === */
/* Phase function for reflective materials. */
ccl_device_forceinline float3 mf_sample_phase_glossy(const float3 wi,
ccl_private Spectrum *weight,
const float3 wm)
{
return -wi + 2.0f * wm * dot(wi, wm);
}
ccl_device_forceinline Spectrum mf_eval_phase_glossy(const float3 w,
const float lambda,
const float3 wo,
const float2 alpha)
{
if (w.z > 0.9999f)
return zero_spectrum();
const float3 wh = normalize(wo - w);
if (wh.z < 0.0f)
return zero_spectrum();
float pArea = (w.z < -0.9999f) ? 1.0f : lambda * w.z;
const float dotW_WH = dot(-w, wh);
if (dotW_WH < 0.0f)
return zero_spectrum();
float phase = max(0.0f, dotW_WH) * 0.25f / max(pArea * dotW_WH, 1e-7f);
if (alpha.x == alpha.y)
phase *= D_ggx(wh, alpha.x);
else
phase *= D_ggx_aniso(wh, alpha);
return make_spectrum(phase);
}
/* Phase function for dielectric transmissive materials, including both reflection and refraction
* according to the dielectric fresnel term. */
ccl_device_forceinline float3 mf_sample_phase_glass(const float3 wi,
const float eta,
const float3 wm,
const float randV,
ccl_private bool *outside)
{
float cosI = dot(wi, wm);
float f = fresnel_dielectric_cos(cosI, eta);
if (randV < f) {
*outside = true;
return -wi + 2.0f * wm * cosI;
}
*outside = false;
float inv_eta = 1.0f / eta;
float cosT = -safe_sqrtf(1.0f - (1.0f - cosI * cosI) * inv_eta * inv_eta);
return normalize(wm * (cosI * inv_eta + cosT) - wi * inv_eta);
}
ccl_device_forceinline Spectrum mf_eval_phase_glass(const float3 w,
const float lambda,
const float3 wo,
const bool wo_outside,
const float2 alpha,
const float eta)
{
if (w.z > 0.9999f)
return zero_spectrum();
float pArea = (w.z < -0.9999f) ? 1.0f : lambda * w.z;
float v;
if (wo_outside) {
const float3 wh = normalize(wo - w);
if (wh.z < 0.0f)
return zero_spectrum();
const float dotW_WH = dot(-w, wh);
v = fresnel_dielectric_cos(dotW_WH, eta) * max(0.0f, dotW_WH) * D_ggx(wh, alpha.x) * 0.25f /
(pArea * dotW_WH);
}
else {
float3 wh = normalize(wo * eta - w);
if (wh.z < 0.0f)
wh = -wh;
const float dotW_WH = dot(-w, wh), dotWO_WH = dot(wo, wh);
if (dotW_WH < 0.0f)
return zero_spectrum();
float temp = dotW_WH + eta * dotWO_WH;
v = (1.0f - fresnel_dielectric_cos(dotW_WH, eta)) * max(0.0f, dotW_WH) * max(0.0f, -dotWO_WH) *
D_ggx(wh, alpha.x) / (pArea * temp * temp);
}
return make_spectrum(v);
}
/* === Utility functions for the random walks === */
/* Smith Lambda function for GGX (based on page 12 of the supplemental implementation). */
ccl_device_forceinline float mf_lambda(const float3 w, const float2 alpha)
{
if (w.z > 0.9999f)
return 0.0f;
else if (w.z < -0.9999f)
return -0.9999f;
const float inv_wz2 = 1.0f / max(w.z * w.z, 1e-7f);
const float2 wa = make_float2(w.x, w.y) * alpha;
float v = sqrtf(1.0f + dot(wa, wa) * inv_wz2);
if (w.z <= 0.0f)
v = -v;
return 0.5f * (v - 1.0f);
}
/* Height distribution CDF (based on page 4 of the supplemental implementation). */
ccl_device_forceinline float mf_invC1(const float h)
{
return 2.0f * saturatef(h) - 1.0f;
}
ccl_device_forceinline float mf_C1(const float h)
{
return saturatef(0.5f * (h + 1.0f));
}
/* Masking function (based on page 16 of the supplemental implementation). */
ccl_device_forceinline float mf_G1(const float3 w, const float C1, const float lambda)
{
if (w.z > 0.9999f)
return 1.0f;
if (w.z < 1e-5f)
return 0.0f;
return powf(C1, lambda);
}
/* Sampling from the visible height distribution (based on page 17 of the supplemental
* implementation). */
ccl_device_forceinline bool mf_sample_height(const float3 w,
ccl_private float *h,
ccl_private float *C1,
ccl_private float *G1,
ccl_private float *lambda,
const float U)
{
if (w.z > 0.9999f)
return false;
if (w.z < -0.9999f) {
*C1 *= U;
*h = mf_invC1(*C1);
*G1 = mf_G1(w, *C1, *lambda);
}
else if (fabsf(w.z) >= 0.0001f) {
if (U > 1.0f - *G1)
return false;
if (*lambda >= 0.0f) {
*C1 = 1.0f;
}
else {
*C1 *= powf(1.0f - U, -1.0f / *lambda);
}
*h = mf_invC1(*C1);
*G1 = mf_G1(w, *C1, *lambda);
}
return true;
}
/* === PDF approximations for the different phase functions. ===
* As explained in bsdf_microfacet_multi_impl.h, using approximations with MIS still produces an
* unbiased result. */
/* Approximation for the albedo of the single-scattering GGX distribution,
* the missing energy is then approximated as a diffuse reflection for the PDF. */
ccl_device_forceinline float mf_ggx_albedo(float r)
{
float albedo = 0.806495f * expf(-1.98712f * r * r) + 0.199531f;
albedo -= ((((((1.76741f * r - 8.43891f) * r + 15.784f) * r - 14.398f) * r + 6.45221f) * r -
1.19722f) *
r +
0.027803f) *
r +
0.00568739f;
return saturatef(albedo);
}
ccl_device_inline float mf_ggx_transmission_albedo(float a, float ior)
{
if (ior < 1.0f) {
ior = 1.0f / ior;
}
a = saturatef(a);
ior = clamp(ior, 1.0f, 3.0f);
float I_1 = 0.0476898f * expf(-0.978352f * (ior - 0.65657f) * (ior - 0.65657f)) -
0.033756f * ior + 0.993261f;
float R_1 = (((0.116991f * a - 0.270369f) * a + 0.0501366f) * a - 0.00411511f) * a + 1.00008f;
float I_2 = (((-2.08704f * ior + 26.3298f) * ior - 127.906f) * ior + 292.958f) * ior - 287.946f +
199.803f / (ior * ior) - 101.668f / (ior * ior * ior);
float R_2 = ((((5.3725f * a - 24.9307f) * a + 22.7437f) * a - 3.40751f) * a + 0.0986325f) * a +
0.00493504f;
return saturatef(1.0f + I_2 * R_2 * 0.0019127f - (1.0f - I_1) * (1.0f - R_1) * 9.3205f);
}
ccl_device_forceinline float mf_ggx_pdf(const float3 wi, const float3 wo, const float alpha)
{
float D = D_ggx(normalize(wi + wo), alpha);
float lambda = mf_lambda(wi, make_float2(alpha, alpha));
float singlescatter = 0.25f * D / max((1.0f + lambda) * wi.z, 1e-7f);
float multiscatter = wo.z * M_1_PI_F;
float albedo = mf_ggx_albedo(alpha);
return albedo * singlescatter + (1.0f - albedo) * multiscatter;
}
ccl_device_forceinline float mf_ggx_aniso_pdf(const float3 wi, const float3 wo, const float2 alpha)
{
float D = D_ggx_aniso(normalize(wi + wo), alpha);
float lambda = mf_lambda(wi, alpha);
float singlescatter = 0.25f * D / max((1.0f + lambda) * wi.z, 1e-7f);
float multiscatter = wo.z * M_1_PI_F;
float albedo = mf_ggx_albedo(sqrtf(alpha.x * alpha.y));
return albedo * singlescatter + (1.0f - albedo) * multiscatter;
}
ccl_device_forceinline float mf_glass_pdf(const float3 wi,
const float3 wo,
const float alpha,
const float eta)
{
bool reflective = (wi.z * wo.z > 0.0f);
float wh_len;
float3 wh = normalize_len(wi + (reflective ? wo : (wo * eta)), &wh_len);
if (wh.z < 0.0f)
wh = -wh;
float3 r_wi = (wi.z < 0.0f) ? -wi : wi;
float lambda = mf_lambda(r_wi, make_float2(alpha, alpha));
float D = D_ggx(wh, alpha);
float fresnel = fresnel_dielectric_cos(dot(r_wi, wh), eta);
float multiscatter = fabsf(wo.z * M_1_PI_F);
if (reflective) {
float singlescatter = 0.25f * D / max((1.0f + lambda) * r_wi.z, 1e-7f);
float albedo = mf_ggx_albedo(alpha);
return fresnel * (albedo * singlescatter + (1.0f - albedo) * multiscatter);
}
else {
float singlescatter = fabsf(dot(r_wi, wh) * dot(wo, wh) * D * eta * eta /
max((1.0f + lambda) * r_wi.z * wh_len * wh_len, 1e-7f));
float albedo = mf_ggx_transmission_albedo(alpha, eta);
return (1.0f - fresnel) * (albedo * singlescatter + (1.0f - albedo) * multiscatter);
}
}
/* === Actual random walk implementations === */
/* One version of mf_eval and mf_sample per phase function. */
#define MF_NAME_JOIN(x, y) x##_##y
#define MF_NAME_EVAL(x, y) MF_NAME_JOIN(x, y)
#define MF_FUNCTION_FULL_NAME(prefix) MF_NAME_EVAL(prefix, MF_PHASE_FUNCTION)
#define MF_PHASE_FUNCTION glass
#define MF_MULTI_GLASS
#include "kernel/closure/bsdf_microfacet_multi_impl.h"
#define MF_PHASE_FUNCTION glossy
#define MF_MULTI_GLOSSY
#include "kernel/closure/bsdf_microfacet_multi_impl.h"
ccl_device void bsdf_microfacet_multi_ggx_blur(ccl_private ShaderClosure *sc, float roughness)
{
ccl_private MicrofacetBsdf *bsdf = (ccl_private MicrofacetBsdf *)sc;
bsdf->alpha_x = fmaxf(roughness, bsdf->alpha_x);
bsdf->alpha_y = fmaxf(roughness, bsdf->alpha_y);
}
/* === Closure implementations === */
/* Multi-scattering GGX Glossy closure */
ccl_device int bsdf_microfacet_multi_ggx_common_setup(ccl_private MicrofacetBsdf *bsdf)
{
bsdf->alpha_x = clamp(bsdf->alpha_x, 1e-4f, 1.0f);
bsdf->alpha_y = clamp(bsdf->alpha_y, 1e-4f, 1.0f);
return SD_BSDF | SD_BSDF_HAS_EVAL | SD_BSDF_NEEDS_LCG;
}
ccl_device int bsdf_microfacet_multi_ggx_setup(ccl_private MicrofacetBsdf *bsdf)
{
if (is_zero(bsdf->T))
bsdf->T = make_float3(1.0f, 0.0f, 0.0f);
ccl_private FresnelConstant *fresnel = (ccl_private FresnelConstant *)bsdf->fresnel;
fresnel->color = saturate(fresnel->color);
bsdf->fresnel_type = MicrofacetFresnel::CONSTANT;
bsdf->type = CLOSURE_BSDF_MICROFACET_MULTI_GGX_ID;
return bsdf_microfacet_multi_ggx_common_setup(bsdf);
}
ccl_device int bsdf_microfacet_multi_ggx_fresnel_setup(ccl_private MicrofacetBsdf *bsdf,
ccl_private const ShaderData *sd)
{
if (is_zero(bsdf->T))
bsdf->T = make_float3(1.0f, 0.0f, 0.0f);
ccl_private FresnelPrincipledV1 *fresnel = (ccl_private FresnelPrincipledV1 *)bsdf->fresnel;
fresnel->color = saturate(fresnel->color);
fresnel->cspec0 = saturate(fresnel->cspec0);
bsdf->fresnel_type = MicrofacetFresnel::PRINCIPLED_V1;
bsdf->type = CLOSURE_BSDF_MICROFACET_MULTI_GGX_ID;
bsdf->sample_weight *= average(bsdf_microfacet_estimate_fresnel(sd, bsdf));
return bsdf_microfacet_multi_ggx_common_setup(bsdf);
}
ccl_device int bsdf_microfacet_multi_ggx_refraction_setup(ccl_private MicrofacetBsdf *bsdf)
{
bsdf->alpha_y = bsdf->alpha_x;
ccl_private FresnelConstant *fresnel = (ccl_private FresnelConstant *)bsdf->fresnel;
fresnel->color = saturate(fresnel->color);
bsdf->fresnel_type = MicrofacetFresnel::CONSTANT;
bsdf->type = CLOSURE_BSDF_MICROFACET_MULTI_GGX_ID;
return bsdf_microfacet_multi_ggx_common_setup(bsdf);
}
ccl_device Spectrum bsdf_microfacet_multi_ggx_eval(ccl_private const ShaderClosure *sc,
const float3 Ng,
const float3 wi,
const float3 wo,
ccl_private float *pdf,
ccl_private uint *lcg_state)
{
ccl_private const MicrofacetBsdf *bsdf = (ccl_private const MicrofacetBsdf *)sc;
const float cosNgO = dot(Ng, wo);
if ((cosNgO < 0.0f) || bsdf->alpha_x * bsdf->alpha_y < 1e-7f) {
*pdf = 0.0f;
return zero_spectrum();
}
float3 X, Y, Z;
Z = bsdf->N;
/* Ensure that the both directions are on the outside w.r.t. the shading normal. */
if (dot(Z, wi) <= 0.0f || dot(Z, wo) <= 0.0f) {
*pdf = 0.0f;
return zero_spectrum();
}
Spectrum color, cspec0;
bool use_fresnel;
if (bsdf->fresnel_type == MicrofacetFresnel::PRINCIPLED_V1) {
ccl_private FresnelPrincipledV1 *fresnel = (ccl_private FresnelPrincipledV1 *)bsdf->fresnel;
use_fresnel = true;
color = fresnel->color;
cspec0 = fresnel->cspec0;
}
else {
kernel_assert(bsdf->fresnel_type == MicrofacetFresnel::CONSTANT);
ccl_private FresnelConstant *fresnel = (ccl_private FresnelConstant *)bsdf->fresnel;
use_fresnel = false;
color = fresnel->color;
cspec0 = zero_spectrum();
}
bool is_aniso = (bsdf->alpha_x != bsdf->alpha_y);
if (is_aniso)
make_orthonormals_tangent(Z, bsdf->T, &X, &Y);
else
make_orthonormals(Z, &X, &Y);
float3 local_I = make_float3(dot(wi, X), dot(wi, Y), dot(wi, Z));
float3 local_O = make_float3(dot(wo, X), dot(wo, Y), dot(wo, Z));
if (is_aniso)
*pdf = mf_ggx_aniso_pdf(local_I, local_O, make_float2(bsdf->alpha_x, bsdf->alpha_y));
else
*pdf = mf_ggx_pdf(local_I, local_O, bsdf->alpha_x);
if (*pdf <= 0.f) {
*pdf = 0.f;
return make_float3(0.f, 0.f, 0.f);
}
return mf_eval_glossy(local_I,
local_O,
true,
color,
bsdf->alpha_x,
bsdf->alpha_y,
lcg_state,
bsdf->ior,
use_fresnel,
cspec0);
}
ccl_device int bsdf_microfacet_multi_ggx_sample(KernelGlobals kg,
ccl_private const ShaderClosure *sc,
float3 Ng,
float3 wi,
float randu,
float randv,
ccl_private Spectrum *eval,
ccl_private float3 *wo,
ccl_private float *pdf,
ccl_private uint *lcg_state,
ccl_private float2 *sampled_roughness,
ccl_private float *eta)
{
ccl_private const MicrofacetBsdf *bsdf = (ccl_private const MicrofacetBsdf *)sc;
float3 X, Y, Z;
Z = bsdf->N;
/* Ensure that the view direction is on the outside w.r.t. the shading normal. */
if (dot(Z, wi) <= 0.0f) {
*pdf = 0.0f;
return LABEL_NONE;
}
/* Special case: Extremely low roughness.
* Don't bother with microfacets, just do specular reflection. */
if (bsdf->alpha_x * bsdf->alpha_y < 1e-7f) {
*wo = 2 * dot(Z, wi) * Z - wi;
if (dot(Ng, *wo) <= 0.0f) {
*pdf = 0.0f;
return LABEL_NONE;
}
*pdf = 1e6f;
*eval = make_spectrum(1e6f);
return LABEL_REFLECT | LABEL_SINGULAR;
}
Spectrum color, cspec0;
bool use_fresnel;
if (bsdf->fresnel_type == MicrofacetFresnel::PRINCIPLED_V1) {
ccl_private FresnelPrincipledV1 *fresnel = (ccl_private FresnelPrincipledV1 *)bsdf->fresnel;
use_fresnel = true;
color = fresnel->color;
cspec0 = fresnel->cspec0;
}
else {
kernel_assert(bsdf->fresnel_type == MicrofacetFresnel::CONSTANT);
ccl_private FresnelConstant *fresnel = (ccl_private FresnelConstant *)bsdf->fresnel;
use_fresnel = false;
color = fresnel->color;
cspec0 = zero_spectrum();
}
*eta = bsdf->ior;
*sampled_roughness = make_float2(bsdf->alpha_x, bsdf->alpha_y);
bool is_aniso = (bsdf->alpha_x != bsdf->alpha_y);
if (is_aniso)
make_orthonormals_tangent(Z, bsdf->T, &X, &Y);
else
make_orthonormals(Z, &X, &Y);
float3 local_I = make_float3(dot(wi, X), dot(wi, Y), dot(wi, Z));
float3 local_O;
*eval = mf_sample_glossy(local_I,
&local_O,
color,
bsdf->alpha_x,
bsdf->alpha_y,
lcg_state,
bsdf->ior,
use_fresnel,
cspec0);
*wo = X * local_O.x + Y * local_O.y + Z * local_O.z;
/* Ensure that the light direction is on the outside w.r.t. the geometry normal. */
if (dot(Ng, *wo) <= 0.0f) {
*pdf = 0.0f;
return LABEL_NONE;
}
if (is_aniso)
*pdf = mf_ggx_aniso_pdf(local_I, local_O, make_float2(bsdf->alpha_x, bsdf->alpha_y));
else
*pdf = mf_ggx_pdf(local_I, local_O, bsdf->alpha_x);
*pdf = fmaxf(0.f, *pdf);
*eval *= *pdf;
return LABEL_REFLECT | LABEL_GLOSSY;
}
/* Multi-scattering GGX Glass closure */
ccl_device int bsdf_microfacet_multi_ggx_glass_setup(ccl_private MicrofacetBsdf *bsdf)
{
bsdf->alpha_x = clamp(bsdf->alpha_x, 1e-4f, 1.0f);
bsdf->alpha_y = bsdf->alpha_x;
bsdf->ior = max(0.0f, bsdf->ior);
ccl_private FresnelConstant *fresnel = (ccl_private FresnelConstant *)bsdf->fresnel;
fresnel->color = saturate(fresnel->color);
bsdf->fresnel_type = MicrofacetFresnel::CONSTANT;
bsdf->type = CLOSURE_BSDF_MICROFACET_MULTI_GGX_GLASS_ID;
return SD_BSDF | SD_BSDF_HAS_EVAL | SD_BSDF_NEEDS_LCG | SD_BSDF_HAS_TRANSMISSION;
}
ccl_device int bsdf_microfacet_multi_ggx_glass_fresnel_setup(ccl_private MicrofacetBsdf *bsdf,
ccl_private const ShaderData *sd)
{
bsdf->alpha_x = clamp(bsdf->alpha_x, 1e-4f, 1.0f);
bsdf->alpha_y = bsdf->alpha_x;
bsdf->ior = max(0.0f, bsdf->ior);
ccl_private FresnelPrincipledV1 *fresnel = (ccl_private FresnelPrincipledV1 *)bsdf->fresnel;
fresnel->color = saturate(fresnel->color);
fresnel->cspec0 = saturate(fresnel->cspec0);
bsdf->fresnel_type = MicrofacetFresnel::PRINCIPLED_V1;
bsdf->type = CLOSURE_BSDF_MICROFACET_MULTI_GGX_GLASS_ID;
bsdf->sample_weight *= average(bsdf_microfacet_estimate_fresnel(sd, bsdf));
return SD_BSDF | SD_BSDF_HAS_EVAL | SD_BSDF_NEEDS_LCG;
}
ccl_device Spectrum bsdf_microfacet_multi_ggx_glass_eval(ccl_private const ShaderClosure *sc,
const float3 wi,
const float3 wo,
ccl_private float *pdf,
ccl_private uint *lcg_state)
{
ccl_private const MicrofacetBsdf *bsdf = (ccl_private const MicrofacetBsdf *)sc;
if (bsdf->alpha_x * bsdf->alpha_y < 1e-7f) {
*pdf = 0.0f;
return zero_spectrum();
}
float3 X, Y, Z;
Z = bsdf->N;
make_orthonormals(Z, &X, &Y);
float3 local_I = make_float3(dot(wi, X), dot(wi, Y), dot(wi, Z));
float3 local_O = make_float3(dot(wo, X), dot(wo, Y), dot(wo, Z));
const bool is_transmission = local_O.z < 0.0f;
Spectrum color, cspec0;
bool use_fresnel;
if (bsdf->fresnel_type == MicrofacetFresnel::PRINCIPLED_V1) {
ccl_private FresnelPrincipledV1 *fresnel = (ccl_private FresnelPrincipledV1 *)bsdf->fresnel;
use_fresnel = true;
color = fresnel->color;
cspec0 = is_transmission ? fresnel->color : fresnel->cspec0;
}
else {
kernel_assert(bsdf->fresnel_type == MicrofacetFresnel::CONSTANT);
ccl_private FresnelConstant *fresnel = (ccl_private FresnelConstant *)bsdf->fresnel;
use_fresnel = false;
color = fresnel->color;
cspec0 = zero_spectrum();
}
*pdf = mf_glass_pdf(local_I, local_O, bsdf->alpha_x, bsdf->ior);
kernel_assert(*pdf >= 0.f);
return mf_eval_glass(local_I,
local_O,
!is_transmission,
color,
bsdf->alpha_x,
bsdf->alpha_y,
lcg_state,
bsdf->ior,
!is_transmission && use_fresnel,
cspec0);
}
ccl_device int bsdf_microfacet_multi_ggx_glass_sample(KernelGlobals kg,
ccl_private const ShaderClosure *sc,
float3 Ng,
float3 wi,
float randu,
float randv,
ccl_private Spectrum *eval,
ccl_private float3 *wo,
ccl_private float *pdf,
ccl_private uint *lcg_state,
ccl_private float2 *sampled_roughness,
ccl_private float *eta)
{
ccl_private const MicrofacetBsdf *bsdf = (ccl_private const MicrofacetBsdf *)sc;
float3 X, Y, Z;
Z = bsdf->N;
*eta = bsdf->ior;
*sampled_roughness = make_float2(bsdf->alpha_x, bsdf->alpha_y);
if (bsdf->alpha_x * bsdf->alpha_y < 1e-7f) {
float3 T;
bool inside;
float fresnel = fresnel_dielectric(bsdf->ior, Z, wi, &T, &inside);
*pdf = 1e6f;
*eval = make_spectrum(1e6f);
if (randu < fresnel) {
*wo = 2 * dot(Z, wi) * Z - wi;
return LABEL_REFLECT | LABEL_SINGULAR;
}
else {
*wo = T;
return LABEL_TRANSMIT | LABEL_SINGULAR;
}
}
Spectrum color, cspec0;
bool use_fresnel;
if (bsdf->fresnel_type == MicrofacetFresnel::PRINCIPLED_V1) {
ccl_private FresnelPrincipledV1 *fresnel = (ccl_private FresnelPrincipledV1 *)bsdf->fresnel;
use_fresnel = true;
color = fresnel->color;
cspec0 = fresnel->cspec0;
}
else {
kernel_assert(bsdf->fresnel_type == MicrofacetFresnel::CONSTANT);
ccl_private FresnelConstant *fresnel = (ccl_private FresnelConstant *)bsdf->fresnel;
use_fresnel = false;
color = fresnel->color;
cspec0 = zero_spectrum();
}
make_orthonormals(Z, &X, &Y);
float3 local_I = make_float3(dot(wi, X), dot(wi, Y), dot(wi, Z));
float3 local_O;
*eval = mf_sample_glass(local_I,
&local_O,
color,
bsdf->alpha_x,
bsdf->alpha_y,
lcg_state,
bsdf->ior,
use_fresnel,
cspec0);
*pdf = mf_glass_pdf(local_I, local_O, bsdf->alpha_x, bsdf->ior);
kernel_assert(*pdf >= 0.f);
*eval *= *pdf;
*wo = X * local_O.x + Y * local_O.y + Z * local_O.z;
if (local_O.z * local_I.z > 0.0f) {
return LABEL_REFLECT | LABEL_GLOSSY;
}
else {
return LABEL_TRANSMIT | LABEL_GLOSSY;
}
}
CCL_NAMESPACE_END

View File

@ -1,250 +0,0 @@
/* SPDX-License-Identifier: Apache-2.0
* Copyright 2011-2022 Blender Foundation */
/* Evaluate the BSDF from wi to wo.
* Evaluation is split into the analytical single-scattering BSDF and the multi-scattering BSDF,
* which is evaluated stochastically through a random walk. At each bounce (except for the first
* one), the amount of reflection from here towards wo is evaluated before bouncing again.
*
* Because of the random walk, the evaluation is not deterministic, but its expected value is equal
* to the correct BSDF, which is enough for Monte-Carlo rendering. The PDF also can't be determined
* analytically, so the single-scattering PDF plus a diffuse term to account for the
* multi-scattered energy is used. In combination with MIS, that is enough to produce an unbiased
* result, although the balance heuristic isn't necessarily optimal anymore.
*/
ccl_device_forceinline Spectrum MF_FUNCTION_FULL_NAME(mf_eval)(float3 wi,
float3 wo,
const bool wo_outside,
const Spectrum color,
const float alpha_x,
const float alpha_y,
ccl_private uint *lcg_state,
const float eta,
bool use_fresnel,
const Spectrum cspec0)
{
/* Evaluating for a shallower incoming direction produces less noise, and the properties of the
* BSDF guarantee reciprocity. */
bool swapped = false;
#ifdef MF_MULTI_GLASS
if (wi.z * wo.z < 0.0f) {
/* Glass transmission is a special case and requires the directions to change hemisphere. */
if (-wo.z < wi.z) {
swapped = true;
float3 tmp = -wo;
wo = -wi;
wi = tmp;
}
}
else
#endif
if (wo.z < wi.z)
{
swapped = true;
float3 tmp = wo;
wo = wi;
wi = tmp;
}
if (wi.z < 1e-5f || (wo.z < 1e-5f && wo_outside) || (wo.z > -1e-5f && !wo_outside))
return zero_spectrum();
const float2 alpha = make_float2(alpha_x, alpha_y);
float lambda_r = mf_lambda(-wi, alpha);
float shadowing_lambda = mf_lambda(wo_outside ? wo : -wo, alpha);
/* Analytically compute single scattering for lower noise. */
Spectrum eval;
Spectrum throughput = one_spectrum();
const float3 wh = normalize(wi + wo);
#ifdef MF_MULTI_GLASS
eval = mf_eval_phase_glass(-wi, lambda_r, wo, wo_outside, alpha, eta);
if (wo_outside)
eval *= -lambda_r / (shadowing_lambda - lambda_r);
else
eval *= -lambda_r * beta(-lambda_r, shadowing_lambda + 1.0f);
#else /* MF_MULTI_GLOSSY */
const float G2 = 1.0f / (1.0f - (lambda_r + 1.0f) + shadowing_lambda);
float val = G2 * 0.25f / wi.z;
if (alpha.x == alpha.y)
val *= D_ggx(wh, alpha.x);
else
val *= D_ggx_aniso(wh, alpha);
eval = make_spectrum(val);
#endif
if (use_fresnel) {
throughput = interpolate_fresnel_color(wi, wh, eta, cspec0);
eval *= throughput;
}
float3 wr = -wi;
float hr = 1.0f;
float C1_r = 1.0f;
float G1_r = 0.0f;
bool outside = true;
for (int order = 0; order < 10; order++) {
/* Sample microfacet height. */
float height_rand = lcg_step_float(lcg_state);
if (!mf_sample_height(wr, &hr, &C1_r, &G1_r, &lambda_r, height_rand))
break;
/* Sample microfacet normal. */
float vndf_rand_y = lcg_step_float(lcg_state);
float vndf_rand_x = lcg_step_float(lcg_state);
float3 wm = mf_sample_vndf(-wr, alpha, vndf_rand_x, vndf_rand_y);
#ifdef MF_MULTI_GLASS
if (order == 0 && use_fresnel) {
/* Evaluate amount of scattering towards wo on this microfacet. */
Spectrum phase;
if (outside)
phase = mf_eval_phase_glass(wr, lambda_r, wo, wo_outside, alpha, eta);
else
phase = mf_eval_phase_glass(wr, lambda_r, -wo, !wo_outside, alpha, 1.0f / eta);
eval = throughput * phase *
mf_G1(wo_outside ? wo : -wo,
mf_C1((outside == wo_outside) ? hr : -hr),
shadowing_lambda);
}
#endif
if (order > 0) {
/* Evaluate amount of scattering towards wo on this microfacet. */
Spectrum phase;
#ifdef MF_MULTI_GLASS
if (outside)
phase = mf_eval_phase_glass(wr, lambda_r, wo, wo_outside, alpha, eta);
else
phase = mf_eval_phase_glass(wr, lambda_r, -wo, !wo_outside, alpha, 1.0f / eta);
#else /* MF_MULTI_GLOSSY */
phase = mf_eval_phase_glossy(wr, lambda_r, wo, alpha) * throughput;
#endif
eval += throughput * phase *
mf_G1(wo_outside ? wo : -wo,
mf_C1((outside == wo_outside) ? hr : -hr),
shadowing_lambda);
}
if (order + 1 < 10) {
/* Bounce from the microfacet. */
#ifdef MF_MULTI_GLASS
bool next_outside;
float3 wi_prev = -wr;
float phase_rand = lcg_step_float(lcg_state);
wr = mf_sample_phase_glass(-wr, outside ? eta : 1.0f / eta, wm, phase_rand, &next_outside);
if (!next_outside) {
outside = !outside;
wr = -wr;
hr = -hr;
}
if (use_fresnel && !next_outside) {
throughput *= color;
}
else if (use_fresnel && order > 0) {
throughput *= interpolate_fresnel_color(wi_prev, wm, eta, cspec0);
}
#else /* MF_MULTI_GLOSSY */
if (use_fresnel && order > 0) {
throughput *= interpolate_fresnel_color(-wr, wm, eta, cspec0);
}
wr = mf_sample_phase_glossy(-wr, &throughput, wm);
#endif
lambda_r = mf_lambda(wr, alpha);
if (!use_fresnel)
throughput *= color;
C1_r = mf_C1(hr);
G1_r = mf_G1(wr, C1_r, lambda_r);
}
}
if (swapped)
eval *= fabsf(wi.z / wo.z);
return eval;
}
/* Perform a random walk on the microsurface starting from wi, returning the direction in which the
* walk escaped the surface in wo. The function returns the throughput between wi and wo. Without
* reflection losses due to coloring or fresnel absorption in conductors, the sampling is optimal.
*/
ccl_device_forceinline Spectrum MF_FUNCTION_FULL_NAME(mf_sample)(float3 wi,
ccl_private float3 *wo,
const Spectrum color,
const float alpha_x,
const float alpha_y,
ccl_private uint *lcg_state,
const float eta,
bool use_fresnel,
const Spectrum cspec0)
{
const float2 alpha = make_float2(alpha_x, alpha_y);
Spectrum throughput = one_spectrum();
float3 wr = -wi;
float lambda_r = mf_lambda(wr, alpha);
float hr = 1.0f;
float C1_r = 1.0f;
float G1_r = 0.0f;
bool outside = true;
int order;
for (order = 0; order < 10; order++) {
/* Sample microfacet height. */
float height_rand = lcg_step_float(lcg_state);
if (!mf_sample_height(wr, &hr, &C1_r, &G1_r, &lambda_r, height_rand)) {
/* The random walk has left the surface. */
*wo = outside ? wr : -wr;
return throughput;
}
/* Sample microfacet normal. */
float vndf_rand_y = lcg_step_float(lcg_state);
float vndf_rand_x = lcg_step_float(lcg_state);
float3 wm = mf_sample_vndf(-wr, alpha, vndf_rand_x, vndf_rand_y);
/* First-bounce color is already accounted for in mix weight. */
if (!use_fresnel && order > 0)
throughput *= color;
/* Bounce from the microfacet. */
#ifdef MF_MULTI_GLASS
bool next_outside;
float3 wi_prev = -wr;
float phase_rand = lcg_step_float(lcg_state);
wr = mf_sample_phase_glass(-wr, outside ? eta : 1.0f / eta, wm, phase_rand, &next_outside);
if (!next_outside) {
hr = -hr;
wr = -wr;
outside = !outside;
}
if (use_fresnel) {
if (!next_outside) {
throughput *= color;
}
else {
throughput *= interpolate_fresnel_color(wi_prev, wm, eta, cspec0);
}
}
#else /* MF_MULTI_GLOSSY */
if (use_fresnel) {
throughput *= interpolate_fresnel_color(-wr, wm, eta, cspec0);
}
wr = mf_sample_phase_glossy(-wr, &throughput, wm);
#endif
/* Update random walk parameters. */
lambda_r = mf_lambda(wr, alpha);
G1_r = mf_G1(wr, C1_r, lambda_r);
}
*wo = make_float3(0.0f, 0.0f, 1.0f);
return zero_spectrum();
}
#undef MF_MULTI_GLASS
#undef MF_MULTI_GLOSSY
#undef MF_PHASE_FUNCTION

View File

@ -75,12 +75,17 @@ ccl_device Spectrum fresnel_conductor(float cosi, const Spectrum eta, const Spec
return (Rparl2 + Rperp2) * 0.5f;
}
ccl_device float ior_from_F0(Spectrum f0)
ccl_device float ior_from_F0(float f0)
{
const float sqrt_f0 = sqrtf(clamp(average(f0), 0.0f, 0.99f));
const float sqrt_f0 = sqrtf(clamp(f0, 0.0f, 0.99f));
return (1.0f + sqrt_f0) / (1.0f - sqrt_f0);
}
ccl_device float F0_from_ior(float ior)
{
return sqr((ior - 1.0f) / (ior + 1.0f));
}
ccl_device float schlick_fresnel(float u)
{
float m = clamp(1.0f - u, 0.0f, 1.0f);

View File

@ -14,7 +14,6 @@
#include "kernel/closure/bsdf_ashikhmin_velvet.h"
#include "kernel/closure/bsdf_diffuse.h"
#include "kernel/closure/bsdf_microfacet.h"
#include "kernel/closure/bsdf_microfacet_multi.h"
#include "kernel/closure/bsdf_oren_nayar.h"
#include "kernel/closure/bsdf_transparent.h"
#include "kernel/closure/bsdf_ashikhmin_shirley.h"
@ -209,27 +208,12 @@ ccl_device void osl_closure_dielectric_bsdf_setup(KernelGlobals kg,
bsdf->alpha_x = closure->alpha_x;
bsdf->alpha_y = closure->alpha_y;
bsdf->ior = closure->ior;
if (sd->flag & SD_BACKFACING) {
bsdf->ior = 1.0f / bsdf->ior;
}
bsdf->T = closure->T;
/* GGX */
if (closure->distribution == make_string("ggx", 11253504724482777663ull) ||
closure->distribution == make_string("default", 4430693559278735917ull))
{
if (has_reflection && has_transmission) {
sd->flag |= bsdf_microfacet_ggx_glass_setup(bsdf);
}
else if (has_transmission) {
sd->flag |= bsdf_microfacet_ggx_refraction_setup(bsdf);
}
else {
sd->flag |= bsdf_microfacet_ggx_setup(bsdf);
}
}
bool preserve_energy = false;
/* Beckmann */
else {
if (closure->distribution == make_string("beckmann", 14712237670914973463ull)) {
if (has_reflection && has_transmission) {
sd->flag |= bsdf_microfacet_beckmann_glass_setup(bsdf);
}
@ -240,10 +224,24 @@ ccl_device void osl_closure_dielectric_bsdf_setup(KernelGlobals kg,
sd->flag |= bsdf_microfacet_beckmann_setup(bsdf);
}
}
/* GGX (either single- or multiscattering) */
else {
if (has_reflection && has_transmission) {
sd->flag |= bsdf_microfacet_ggx_glass_setup(bsdf);
}
else if (has_transmission) {
sd->flag |= bsdf_microfacet_ggx_refraction_setup(bsdf);
}
else {
sd->flag |= bsdf_microfacet_ggx_setup(bsdf);
}
preserve_energy = (closure->distribution == make_string("multi_ggx", 16842698693386468366ull));
}
fresnel->reflection_tint = rgb_to_spectrum(closure->reflection_tint);
fresnel->transmission_tint = rgb_to_spectrum(closure->transmission_tint);
bsdf_microfacet_setup_fresnel_dielectric_tint(bsdf, sd, fresnel);
bsdf_microfacet_setup_fresnel_dielectric_tint(kg, bsdf, sd, fresnel, preserve_energy);
}
ccl_device void osl_closure_conductor_bsdf_setup(KernelGlobals kg,
@ -274,20 +272,21 @@ ccl_device void osl_closure_conductor_bsdf_setup(KernelGlobals kg,
bsdf->ior = 0.0f;
bsdf->T = closure->T;
/* GGX */
if (closure->distribution == make_string("ggx", 11253504724482777663ull) ||
closure->distribution == make_string("default", 4430693559278735917ull))
{
sd->flag |= bsdf_microfacet_ggx_setup(bsdf);
}
bool preserve_energy = false;
/* Beckmann */
else {
if (closure->distribution == make_string("beckmann", 14712237670914973463ull)) {
sd->flag |= bsdf_microfacet_beckmann_setup(bsdf);
}
/* GGX (either single- or multiscattering) */
else {
sd->flag |= bsdf_microfacet_ggx_setup(bsdf);
preserve_energy = (closure->distribution == make_string("multi_ggx", 16842698693386468366ull));
}
fresnel->n = rgb_to_spectrum(closure->ior);
fresnel->k = rgb_to_spectrum(closure->extinction);
bsdf_microfacet_setup_fresnel_conductor(bsdf, sd, fresnel);
bsdf_microfacet_setup_fresnel_conductor(kg, bsdf, sd, fresnel, preserve_energy);
}
ccl_device void osl_closure_generalized_schlick_bsdf_setup(
@ -319,28 +318,16 @@ ccl_device void osl_closure_generalized_schlick_bsdf_setup(
bsdf->N = ensure_valid_specular_reflection(sd->Ng, sd->wi, closure->N);
bsdf->alpha_x = closure->alpha_x;
bsdf->alpha_y = closure->alpha_y;
bsdf->ior = ior_from_F0(closure->f0);
bsdf->ior = ior_from_F0(average(closure->f0));
if (sd->flag & SD_BACKFACING) {
bsdf->ior = 1.0f / bsdf->ior;
}
bsdf->T = closure->T;
/* GGX */
if (closure->distribution == make_string("ggx", 11253504724482777663ull) ||
closure->distribution == make_string("default", 4430693559278735917ull))
{
if (has_reflection && has_transmission) {
sd->flag |= bsdf_microfacet_ggx_glass_setup(bsdf);
}
else if (has_transmission) {
sd->flag |= bsdf_microfacet_ggx_refraction_setup(bsdf);
}
else {
sd->flag |= bsdf_microfacet_ggx_setup(bsdf);
}
}
bool preserve_energy = false;
/* Beckmann */
else {
if (closure->distribution == make_string("beckmann", 14712237670914973463ull)) {
if (has_reflection && has_transmission) {
sd->flag |= bsdf_microfacet_beckmann_glass_setup(bsdf);
}
@ -351,13 +338,27 @@ ccl_device void osl_closure_generalized_schlick_bsdf_setup(
sd->flag |= bsdf_microfacet_beckmann_setup(bsdf);
}
}
/* GGX (either single- or multiscattering) */
else {
if (has_reflection && has_transmission) {
sd->flag |= bsdf_microfacet_ggx_glass_setup(bsdf);
}
else if (has_transmission) {
sd->flag |= bsdf_microfacet_ggx_refraction_setup(bsdf);
}
else {
sd->flag |= bsdf_microfacet_ggx_setup(bsdf);
}
preserve_energy = (closure->distribution == make_string("multi_ggx", 16842698693386468366ull));
}
fresnel->reflection_tint = rgb_to_spectrum(closure->reflection_tint);
fresnel->transmission_tint = rgb_to_spectrum(closure->transmission_tint);
fresnel->f0 = rgb_to_spectrum(closure->f0);
fresnel->f90 = rgb_to_spectrum(closure->f90);
fresnel->exponent = closure->exponent;
bsdf_microfacet_setup_fresnel_generalized_schlick(bsdf, sd, fresnel);
bsdf_microfacet_setup_fresnel_generalized_schlick(kg, bsdf, sd, fresnel, preserve_energy);
}
/* Standard microfacet closures */
@ -413,7 +414,7 @@ ccl_device void osl_closure_microfacet_setup(KernelGlobals kg,
else if (closure->distribution == make_string("ashikhmin_shirley", 11318482998918370922ull)) {
sd->flag |= bsdf_ashikhmin_shirley_setup(bsdf);
}
/* GGX */
/* GGX (either single- or multiscattering) */
else {
if (closure->refract == 1) {
sd->flag |= bsdf_microfacet_ggx_refraction_setup(bsdf);
@ -424,195 +425,15 @@ ccl_device void osl_closure_microfacet_setup(KernelGlobals kg,
else {
sd->flag |= bsdf_microfacet_ggx_setup(bsdf);
}
if (closure->distribution == make_string("multi_ggx", 16842698693386468366ull)) {
/* Since there's no dedicated color input, the weight is the best we got. */
bsdf_microfacet_setup_fresnel_constant(kg, bsdf, sd, rgb_to_spectrum(weight));
}
}
}
ccl_device void osl_closure_microfacet_ggx_setup(
KernelGlobals kg,
ccl_private ShaderData *sd,
uint32_t path_flag,
float3 weight,
ccl_private const MicrofacetGGXIsotropicClosure *closure)
{
if (osl_closure_skip(kg, sd, path_flag, LABEL_GLOSSY | LABEL_REFLECT)) {
return;
}
ccl_private MicrofacetBsdf *bsdf = (ccl_private MicrofacetBsdf *)bsdf_alloc(
sd, sizeof(MicrofacetBsdf), rgb_to_spectrum(weight));
if (!bsdf) {
return;
}
bsdf->N = ensure_valid_specular_reflection(sd->Ng, sd->wi, closure->N);
bsdf->alpha_x = bsdf->alpha_y = closure->alpha_x;
sd->flag |= bsdf_microfacet_ggx_setup(bsdf);
}
ccl_device void osl_closure_microfacet_ggx_aniso_setup(
KernelGlobals kg,
ccl_private ShaderData *sd,
uint32_t path_flag,
float3 weight,
ccl_private const MicrofacetGGXClosure *closure)
{
if (osl_closure_skip(kg, sd, path_flag, LABEL_GLOSSY | LABEL_REFLECT)) {
return;
}
ccl_private MicrofacetBsdf *bsdf = (ccl_private MicrofacetBsdf *)bsdf_alloc(
sd, sizeof(MicrofacetBsdf), rgb_to_spectrum(weight));
if (!bsdf) {
return;
}
bsdf->N = ensure_valid_specular_reflection(sd->Ng, sd->wi, closure->N);
bsdf->alpha_x = closure->alpha_x;
bsdf->alpha_y = closure->alpha_y;
bsdf->T = closure->T;
sd->flag |= bsdf_microfacet_ggx_setup(bsdf);
}
ccl_device void osl_closure_microfacet_ggx_refraction_setup(
KernelGlobals kg,
ccl_private ShaderData *sd,
uint32_t path_flag,
float3 weight,
ccl_private const MicrofacetGGXRefractionClosure *closure)
{
if (osl_closure_skip(kg, sd, path_flag, LABEL_GLOSSY | LABEL_TRANSMIT)) {
return;
}
ccl_private MicrofacetBsdf *bsdf = (ccl_private MicrofacetBsdf *)bsdf_alloc(
sd, sizeof(MicrofacetBsdf), rgb_to_spectrum(weight));
if (!bsdf) {
return;
}
bsdf->N = ensure_valid_specular_reflection(sd->Ng, sd->wi, closure->N);
bsdf->alpha_x = closure->alpha_x;
bsdf->ior = closure->ior;
sd->flag |= bsdf_microfacet_ggx_refraction_setup(bsdf);
}
/* GGX closures with Fresnel */
ccl_device void osl_closure_microfacet_ggx_fresnel_setup(
KernelGlobals kg,
ccl_private ShaderData *sd,
uint32_t path_flag,
float3 weight,
ccl_private const MicrofacetGGXFresnelClosure *closure)
{
if (osl_closure_skip(kg, sd, path_flag, LABEL_GLOSSY | LABEL_REFLECT)) {
return;
}
ccl_private MicrofacetBsdf *bsdf = (ccl_private MicrofacetBsdf *)bsdf_alloc(
sd, sizeof(MicrofacetBsdf), rgb_to_spectrum(weight));
if (!bsdf) {
return;
}
ccl_private FresnelPrincipledV1 *fresnel = (ccl_private FresnelPrincipledV1 *)
closure_alloc_extra(sd, sizeof(FresnelPrincipledV1));
if (!fresnel) {
return;
}
bsdf->N = ensure_valid_specular_reflection(sd->Ng, sd->wi, closure->N);
bsdf->alpha_x = closure->alpha_x;
bsdf->alpha_y = bsdf->alpha_x;
bsdf->ior = closure->ior;
bsdf->T = zero_float3();
sd->flag |= bsdf_microfacet_ggx_setup(bsdf);
fresnel->color = rgb_to_spectrum(closure->color);
fresnel->cspec0 = rgb_to_spectrum(closure->cspec0);
bsdf_microfacet_setup_fresnel_principledv1(bsdf, sd, fresnel);
}
ccl_device void osl_closure_microfacet_ggx_aniso_fresnel_setup(
KernelGlobals kg,
ccl_private ShaderData *sd,
uint32_t path_flag,
float3 weight,
ccl_private const MicrofacetGGXAnisoFresnelClosure *closure)
{
if (osl_closure_skip(kg, sd, path_flag, LABEL_GLOSSY | LABEL_REFLECT)) {
return;
}
ccl_private MicrofacetBsdf *bsdf = (ccl_private MicrofacetBsdf *)bsdf_alloc(
sd, sizeof(MicrofacetBsdf), rgb_to_spectrum(weight));
if (!bsdf) {
return;
}
ccl_private FresnelPrincipledV1 *fresnel = (ccl_private FresnelPrincipledV1 *)
closure_alloc_extra(sd, sizeof(FresnelPrincipledV1));
if (!fresnel) {
return;
}
bsdf->N = ensure_valid_specular_reflection(sd->Ng, sd->wi, closure->N);
bsdf->alpha_x = closure->alpha_x;
bsdf->alpha_y = closure->alpha_y;
bsdf->ior = closure->ior;
bsdf->T = closure->T;
sd->flag |= bsdf_microfacet_ggx_setup(bsdf);
fresnel->color = rgb_to_spectrum(closure->color);
fresnel->cspec0 = rgb_to_spectrum(closure->cspec0);
bsdf_microfacet_setup_fresnel_principledv1(bsdf, sd, fresnel);
}
/* Multi-scattering GGX closures */
ccl_device void osl_closure_microfacet_multi_ggx_setup(
KernelGlobals kg,
ccl_private ShaderData *sd,
uint32_t path_flag,
float3 weight,
ccl_private const MicrofacetMultiGGXClosure *closure)
{
/* Technically, the MultiGGX closure may also transmit. However,
* since this is set statically and only used for caustic flags, this
* is probably as good as it gets. */
if (osl_closure_skip(kg, sd, path_flag, LABEL_GLOSSY | LABEL_REFLECT)) {
return;
}
ccl_private MicrofacetBsdf *bsdf = (ccl_private MicrofacetBsdf *)bsdf_alloc(
sd, sizeof(MicrofacetBsdf), rgb_to_spectrum(weight));
if (!bsdf) {
return;
}
ccl_private FresnelConstant *fresnel = (ccl_private FresnelConstant *)closure_alloc_extra(
sd, sizeof(FresnelConstant));
if (!fresnel) {
return;
}
bsdf->N = ensure_valid_specular_reflection(sd->Ng, sd->wi, closure->N);
bsdf->alpha_x = closure->alpha_x;
bsdf->alpha_y = bsdf->alpha_x;
bsdf->ior = 1.0f;
bsdf->fresnel = fresnel;
fresnel->color = rgb_to_spectrum(closure->color);
bsdf->T = zero_float3();
sd->flag |= bsdf_microfacet_multi_ggx_setup(bsdf);
}
/* Special-purpose Microfacet closures */
ccl_device void osl_closure_microfacet_multi_ggx_glass_setup(
KernelGlobals kg,
@ -634,23 +455,15 @@ ccl_device void osl_closure_microfacet_multi_ggx_glass_setup(
return;
}
ccl_private FresnelConstant *fresnel = (ccl_private FresnelConstant *)closure_alloc_extra(
sd, sizeof(FresnelConstant));
if (!fresnel) {
return;
}
bsdf->N = ensure_valid_specular_reflection(sd->Ng, sd->wi, closure->N);
bsdf->alpha_x = closure->alpha_x;
bsdf->alpha_y = bsdf->alpha_x;
bsdf->ior = closure->ior;
bsdf->fresnel = fresnel;
fresnel->color = rgb_to_spectrum(closure->color);
bsdf->T = zero_float3();
sd->flag |= bsdf_microfacet_multi_ggx_glass_setup(bsdf);
sd->flag |= bsdf_microfacet_ggx_glass_setup(bsdf);
bsdf_microfacet_setup_fresnel_constant(kg, bsdf, sd, rgb_to_spectrum(closure->color));
}
ccl_device void osl_closure_microfacet_multi_ggx_aniso_setup(
@ -658,11 +471,8 @@ ccl_device void osl_closure_microfacet_multi_ggx_aniso_setup(
ccl_private ShaderData *sd,
uint32_t path_flag,
float3 weight,
ccl_private const MicrofacetMultiGGXAnisoClosure *closure)
ccl_private const MicrofacetMultiGGXClosure *closure)
{
/* Technically, the MultiGGX closure may also transmit. However,
* since this is set statically and only used for caustic flags, this
* is probably as good as it gets. */
if (osl_closure_skip(kg, sd, path_flag, LABEL_GLOSSY | LABEL_REFLECT)) {
return;
}
@ -673,37 +483,24 @@ ccl_device void osl_closure_microfacet_multi_ggx_aniso_setup(
return;
}
ccl_private FresnelConstant *fresnel = (ccl_private FresnelConstant *)closure_alloc_extra(
sd, sizeof(FresnelConstant));
if (!fresnel) {
return;
}
bsdf->N = ensure_valid_specular_reflection(sd->Ng, sd->wi, closure->N);
bsdf->alpha_x = closure->alpha_x;
bsdf->alpha_y = closure->alpha_y;
bsdf->ior = 1.0f;
bsdf->fresnel = fresnel;
fresnel->color = rgb_to_spectrum(closure->color);
bsdf->T = closure->T;
sd->flag |= bsdf_microfacet_multi_ggx_setup(bsdf);
sd->flag |= bsdf_microfacet_ggx_setup(bsdf);
bsdf_microfacet_setup_fresnel_constant(kg, bsdf, sd, rgb_to_spectrum(closure->color));
}
/* Multi-scattering GGX closures with Fresnel */
ccl_device void osl_closure_microfacet_multi_ggx_fresnel_setup(
ccl_device void osl_closure_microfacet_aniso_fresnel_setup(
KernelGlobals kg,
ccl_private ShaderData *sd,
uint32_t path_flag,
float3 weight,
ccl_private const MicrofacetMultiGGXFresnelClosure *closure)
ccl_private const MicrofacetAnisoFresnelClosure *closure)
{
/* Technically, the MultiGGX closure may also transmit. However,
* since this is set statically and only used for caustic flags, this
* is probably as good as it gets. */
if (osl_closure_skip(kg, sd, path_flag, LABEL_GLOSSY | LABEL_REFLECT)) {
return;
}
@ -714,88 +511,8 @@ ccl_device void osl_closure_microfacet_multi_ggx_fresnel_setup(
return;
}
ccl_private FresnelPrincipledV1 *fresnel = (ccl_private FresnelPrincipledV1 *)
closure_alloc_extra(sd, sizeof(FresnelPrincipledV1));
if (!fresnel) {
return;
}
bsdf->N = ensure_valid_specular_reflection(sd->Ng, sd->wi, closure->N);
bsdf->alpha_x = closure->alpha_x;
bsdf->alpha_y = bsdf->alpha_x;
bsdf->ior = closure->ior;
bsdf->fresnel = fresnel;
fresnel->color = rgb_to_spectrum(closure->color);
fresnel->cspec0 = rgb_to_spectrum(closure->cspec0);
bsdf->T = zero_float3();
sd->flag |= bsdf_microfacet_multi_ggx_fresnel_setup(bsdf, sd);
}
ccl_device void osl_closure_microfacet_multi_ggx_glass_fresnel_setup(
KernelGlobals kg,
ccl_private ShaderData *sd,
uint32_t path_flag,
float3 weight,
ccl_private const MicrofacetMultiGGXGlassFresnelClosure *closure)
{
/* Technically, the MultiGGX closure may also transmit. However,
* since this is set statically and only used for caustic flags, this
* is probably as good as it gets. */
if (osl_closure_skip(kg, sd, path_flag, LABEL_GLOSSY | LABEL_REFLECT)) {
return;
}
ccl_private MicrofacetBsdf *bsdf = (ccl_private MicrofacetBsdf *)bsdf_alloc(
sd, sizeof(MicrofacetBsdf), rgb_to_spectrum(weight));
if (!bsdf) {
return;
}
ccl_private FresnelPrincipledV1 *fresnel = (ccl_private FresnelPrincipledV1 *)
closure_alloc_extra(sd, sizeof(FresnelPrincipledV1));
if (!fresnel) {
return;
}
bsdf->N = ensure_valid_specular_reflection(sd->Ng, sd->wi, closure->N);
bsdf->alpha_x = closure->alpha_x;
bsdf->alpha_y = bsdf->alpha_x;
bsdf->ior = closure->ior;
bsdf->fresnel = fresnel;
fresnel->color = rgb_to_spectrum(closure->color);
fresnel->cspec0 = rgb_to_spectrum(closure->cspec0);
bsdf->T = zero_float3();
sd->flag |= bsdf_microfacet_multi_ggx_glass_fresnel_setup(bsdf, sd);
}
ccl_device void osl_closure_microfacet_multi_ggx_aniso_fresnel_setup(
KernelGlobals kg,
ccl_private ShaderData *sd,
uint32_t path_flag,
float3 weight,
ccl_private const MicrofacetMultiGGXAnisoFresnelClosure *closure)
{
/* Technically, the MultiGGX closure may also transmit. However,
* since this is set statically and only used for caustic flags, this
* is probably as good as it gets. */
if (osl_closure_skip(kg, sd, path_flag, LABEL_GLOSSY | LABEL_REFLECT)) {
return;
}
ccl_private MicrofacetBsdf *bsdf = (ccl_private MicrofacetBsdf *)bsdf_alloc(
sd, sizeof(MicrofacetBsdf), rgb_to_spectrum(weight));
if (!bsdf) {
return;
}
ccl_private FresnelPrincipledV1 *fresnel = (ccl_private FresnelPrincipledV1 *)
closure_alloc_extra(sd, sizeof(FresnelPrincipledV1));
ccl_private FresnelGeneralizedSchlick *fresnel = (ccl_private FresnelGeneralizedSchlick *)
closure_alloc_extra(sd, sizeof(FresnelGeneralizedSchlick));
if (!fresnel) {
return;
}
@ -804,91 +521,23 @@ ccl_device void osl_closure_microfacet_multi_ggx_aniso_fresnel_setup(
bsdf->alpha_x = closure->alpha_x;
bsdf->alpha_y = closure->alpha_y;
bsdf->ior = closure->ior;
bsdf->fresnel = fresnel;
fresnel->color = rgb_to_spectrum(closure->color);
fresnel->cspec0 = rgb_to_spectrum(closure->cspec0);
bsdf->T = closure->T;
sd->flag |= bsdf_microfacet_multi_ggx_fresnel_setup(bsdf, sd);
/* Only GGX (either single- or multiscattering) supported here */
sd->flag |= bsdf_microfacet_ggx_setup(bsdf);
const bool preserve_energy = (closure->distribution ==
make_string("multi_ggx", 16842698693386468366ull));
fresnel->reflection_tint = one_spectrum();
fresnel->transmission_tint = zero_spectrum();
fresnel->f0 = rgb_to_spectrum(closure->f0);
fresnel->f90 = rgb_to_spectrum(closure->f90);
fresnel->exponent = -1.0f;
bsdf_microfacet_setup_fresnel_generalized_schlick(kg, bsdf, sd, fresnel, preserve_energy);
}
/* Beckmann closures */
ccl_device void osl_closure_microfacet_beckmann_setup(
KernelGlobals kg,
ccl_private ShaderData *sd,
uint32_t path_flag,
float3 weight,
ccl_private const MicrofacetBeckmannIsotropicClosure *closure)
{
if (osl_closure_skip(kg, sd, path_flag, LABEL_GLOSSY | LABEL_REFLECT)) {
return;
}
ccl_private MicrofacetBsdf *bsdf = (ccl_private MicrofacetBsdf *)bsdf_alloc(
sd, sizeof(MicrofacetBsdf), rgb_to_spectrum(weight));
if (!bsdf) {
return;
}
bsdf->N = ensure_valid_specular_reflection(sd->Ng, sd->wi, closure->N);
bsdf->alpha_x = bsdf->alpha_y = closure->alpha_x;
sd->flag |= bsdf_microfacet_beckmann_setup(bsdf);
}
ccl_device void osl_closure_microfacet_beckmann_aniso_setup(
KernelGlobals kg,
ccl_private ShaderData *sd,
uint32_t path_flag,
float3 weight,
ccl_private const MicrofacetBeckmannClosure *closure)
{
if (osl_closure_skip(kg, sd, path_flag, LABEL_GLOSSY | LABEL_REFLECT)) {
return;
}
ccl_private MicrofacetBsdf *bsdf = (ccl_private MicrofacetBsdf *)bsdf_alloc(
sd, sizeof(MicrofacetBsdf), rgb_to_spectrum(weight));
if (!bsdf) {
return;
}
bsdf->N = ensure_valid_specular_reflection(sd->Ng, sd->wi, closure->N);
bsdf->alpha_x = closure->alpha_x;
bsdf->alpha_y = closure->alpha_y;
bsdf->T = closure->T;
sd->flag |= bsdf_microfacet_beckmann_setup(bsdf);
}
ccl_device void osl_closure_microfacet_beckmann_refraction_setup(
KernelGlobals kg,
ccl_private ShaderData *sd,
uint32_t path_flag,
float3 weight,
ccl_private const MicrofacetBeckmannRefractionClosure *closure)
{
if (osl_closure_skip(kg, sd, path_flag, LABEL_GLOSSY | LABEL_TRANSMIT)) {
return;
}
ccl_private MicrofacetBsdf *bsdf = (ccl_private MicrofacetBsdf *)bsdf_alloc(
sd, sizeof(MicrofacetBsdf), rgb_to_spectrum(weight));
if (!bsdf) {
return;
}
bsdf->N = ensure_valid_specular_reflection(sd->Ng, sd->wi, closure->N);
bsdf->alpha_x = closure->alpha_x;
bsdf->ior = closure->ior;
sd->flag |= bsdf_microfacet_beckmann_refraction_setup(bsdf);
}
/* Ashikhmin closures */
/* Ashikhmin Velvet */
ccl_device void osl_closure_ashikhmin_velvet_setup(
KernelGlobals kg,
@ -913,31 +562,6 @@ ccl_device void osl_closure_ashikhmin_velvet_setup(
sd->flag |= bsdf_ashikhmin_velvet_setup(bsdf);
}
ccl_device void osl_closure_ashikhmin_shirley_setup(
KernelGlobals kg,
ccl_private ShaderData *sd,
uint32_t path_flag,
float3 weight,
ccl_private const AshikhminShirleyClosure *closure)
{
if (osl_closure_skip(kg, sd, path_flag, LABEL_GLOSSY | LABEL_REFLECT)) {
return;
}
ccl_private MicrofacetBsdf *bsdf = (ccl_private MicrofacetBsdf *)bsdf_alloc(
sd, sizeof(MicrofacetBsdf), rgb_to_spectrum(weight));
if (!bsdf) {
return;
}
bsdf->N = ensure_valid_specular_reflection(sd->Ng, sd->wi, closure->N);
bsdf->alpha_x = closure->alpha_x;
bsdf->alpha_y = closure->alpha_y;
bsdf->T = closure->T;
sd->flag |= bsdf_ashikhmin_shirley_setup(bsdf);
}
ccl_device void osl_closure_diffuse_toon_setup(KernelGlobals kg,
ccl_private ShaderData *sd,
uint32_t path_flag,

View File

@ -83,30 +83,6 @@ OSL_CLOSURE_STRUCT_BEGIN(Microfacet, microfacet)
OSL_CLOSURE_STRUCT_MEMBER(Microfacet, INT, int, refract, NULL)
OSL_CLOSURE_STRUCT_END(Microfacet, microfacet)
OSL_CLOSURE_STRUCT_BEGIN(MicrofacetGGXIsotropic, microfacet_ggx)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetGGXIsotropic, VECTOR, packed_float3, N, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetGGXIsotropic, FLOAT, float, alpha_x, NULL)
OSL_CLOSURE_STRUCT_END(MicrofacetGGXIsotropic, microfacet_ggx)
OSL_CLOSURE_STRUCT_BEGIN(MicrofacetGGX, microfacet_ggx_aniso)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetGGX, VECTOR, packed_float3, N, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetGGX, VECTOR, packed_float3, T, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetGGX, FLOAT, float, alpha_x, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetGGX, FLOAT, float, alpha_y, NULL)
OSL_CLOSURE_STRUCT_END(MicrofacetGGX, microfacet_ggx_aniso)
OSL_CLOSURE_STRUCT_BEGIN(MicrofacetGGXRefraction, microfacet_ggx_refraction)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetGGXRefraction, VECTOR, packed_float3, N, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetGGXRefraction, FLOAT, float, alpha_x, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetGGXRefraction, FLOAT, float, ior, NULL)
OSL_CLOSURE_STRUCT_END(MicrofacetGGXRefraction, microfacet_ggx_refraction)
OSL_CLOSURE_STRUCT_BEGIN(MicrofacetMultiGGX, microfacet_multi_ggx)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGX, VECTOR, packed_float3, N, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGX, FLOAT, float, alpha_x, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGX, VECTOR, packed_float3, color, NULL)
OSL_CLOSURE_STRUCT_END(MicrofacetMultiGGX, microfacet_multi_ggx)
OSL_CLOSURE_STRUCT_BEGIN(MicrofacetMultiGGXGlass, microfacet_multi_ggx_glass)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGXGlass, VECTOR, packed_float3, N, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGXGlass, FLOAT, float, alpha_x, NULL)
@ -114,82 +90,24 @@ OSL_CLOSURE_STRUCT_BEGIN(MicrofacetMultiGGXGlass, microfacet_multi_ggx_glass)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGXGlass, VECTOR, packed_float3, color, NULL)
OSL_CLOSURE_STRUCT_END(MicrofacetMultiGGXGlass, microfacet_multi_ggx_glass)
OSL_CLOSURE_STRUCT_BEGIN(MicrofacetMultiGGXAniso, microfacet_multi_ggx_aniso)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGXAniso, VECTOR, packed_float3, N, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGXAniso, VECTOR, packed_float3, T, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGXAniso, FLOAT, float, alpha_x, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGXAniso, FLOAT, float, alpha_y, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGXAniso, VECTOR, packed_float3, color, NULL)
OSL_CLOSURE_STRUCT_END(MicrofacetMultiGGXAniso, microfacet_multi_ggx_aniso)
OSL_CLOSURE_STRUCT_BEGIN(MicrofacetMultiGGX, microfacet_multi_ggx_aniso)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGX, VECTOR, packed_float3, N, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGX, VECTOR, packed_float3, T, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGX, FLOAT, float, alpha_x, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGX, FLOAT, float, alpha_y, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGX, VECTOR, packed_float3, color, NULL)
OSL_CLOSURE_STRUCT_END(MicrofacetMultiGGX, microfacet_multi_ggx_aniso)
OSL_CLOSURE_STRUCT_BEGIN(MicrofacetGGXFresnel, microfacet_ggx_fresnel)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetGGXFresnel, VECTOR, packed_float3, N, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetGGXFresnel, FLOAT, float, alpha_x, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetGGXFresnel, FLOAT, float, ior, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetGGXFresnel, VECTOR, packed_float3, color, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetGGXFresnel, VECTOR, packed_float3, cspec0, NULL)
OSL_CLOSURE_STRUCT_END(MicrofacetGGXFresnel, microfacet_ggx_fresnel)
OSL_CLOSURE_STRUCT_BEGIN(MicrofacetGGXAnisoFresnel, microfacet_ggx_aniso_fresnel)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetGGXAnisoFresnel, VECTOR, packed_float3, N, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetGGXAnisoFresnel, VECTOR, packed_float3, T, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetGGXAnisoFresnel, FLOAT, float, alpha_x, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetGGXAnisoFresnel, FLOAT, float, alpha_y, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetGGXAnisoFresnel, FLOAT, float, ior, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetGGXAnisoFresnel, VECTOR, packed_float3, color, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetGGXAnisoFresnel, VECTOR, packed_float3, cspec0, NULL)
OSL_CLOSURE_STRUCT_END(MicrofacetGGXAnisoFresnel, microfacet_ggx_aniso_fresnel)
OSL_CLOSURE_STRUCT_BEGIN(MicrofacetMultiGGXFresnel, microfacet_multi_ggx_fresnel)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGXFresnel, VECTOR, packed_float3, N, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGXFresnel, FLOAT, float, alpha_x, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGXFresnel, FLOAT, float, ior, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGXFresnel, VECTOR, packed_float3, color, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGXFresnel, VECTOR, packed_float3, cspec0, NULL)
OSL_CLOSURE_STRUCT_END(MicrofacetMultiGGXFresnel, microfacet_multi_ggx_fresnel)
OSL_CLOSURE_STRUCT_BEGIN(MicrofacetMultiGGXGlassFresnel, microfacet_multi_ggx_glass_fresnel)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGXGlassFresnel, VECTOR, packed_float3, N, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGXGlassFresnel, FLOAT, float, alpha_x, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGXGlassFresnel, FLOAT, float, ior, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGXGlassFresnel, VECTOR, packed_float3, color, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGXGlassFresnel, VECTOR, packed_float3, cspec0, NULL)
OSL_CLOSURE_STRUCT_END(MicrofacetMultiGGXGlassFresnel, microfacet_multi_ggx_glass_fresnel)
OSL_CLOSURE_STRUCT_BEGIN(MicrofacetMultiGGXAnisoFresnel, microfacet_multi_ggx_aniso_fresnel)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGXAnisoFresnel, VECTOR, packed_float3, N, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGXAnisoFresnel, VECTOR, packed_float3, T, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGXAnisoFresnel, FLOAT, float, alpha_x, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGXAnisoFresnel, FLOAT, float, alpha_y, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGXAnisoFresnel, FLOAT, float, ior, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGXAnisoFresnel, VECTOR, packed_float3, color, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetMultiGGXAnisoFresnel, VECTOR, packed_float3, cspec0, NULL)
OSL_CLOSURE_STRUCT_END(MicrofacetMultiGGXAnisoFresnel, microfacet_multi_ggx_aniso_fresnel)
OSL_CLOSURE_STRUCT_BEGIN(MicrofacetBeckmannIsotropic, microfacet_beckmann)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetBeckmannIsotropic, VECTOR, packed_float3, N, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetBeckmannIsotropic, FLOAT, float, alpha_x, NULL)
OSL_CLOSURE_STRUCT_END(MicrofacetBeckmannIsotropic, microfacet_beckmann)
OSL_CLOSURE_STRUCT_BEGIN(MicrofacetBeckmann, microfacet_beckmann_aniso)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetBeckmann, VECTOR, packed_float3, N, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetBeckmann, VECTOR, packed_float3, T, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetBeckmann, FLOAT, float, alpha_x, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetBeckmann, FLOAT, float, alpha_y, NULL)
OSL_CLOSURE_STRUCT_END(MicrofacetBeckmann, microfacet_beckmann_aniso)
OSL_CLOSURE_STRUCT_BEGIN(MicrofacetBeckmannRefraction, microfacet_beckmann_refraction)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetBeckmannRefraction, VECTOR, packed_float3, N, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetBeckmannRefraction, FLOAT, float, alpha_x, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetBeckmannRefraction, FLOAT, float, ior, NULL)
OSL_CLOSURE_STRUCT_END(MicrofacetBeckmannRefraction, microfacet_beckmann_refraction)
OSL_CLOSURE_STRUCT_BEGIN(AshikhminShirley, ashikhmin_shirley)
OSL_CLOSURE_STRUCT_MEMBER(AshikhminShirley, VECTOR, packed_float3, N, NULL)
OSL_CLOSURE_STRUCT_MEMBER(AshikhminShirley, VECTOR, packed_float3, T, NULL)
OSL_CLOSURE_STRUCT_MEMBER(AshikhminShirley, FLOAT, float, alpha_x, NULL)
OSL_CLOSURE_STRUCT_MEMBER(AshikhminShirley, FLOAT, float, alpha_y, NULL)
OSL_CLOSURE_STRUCT_END(AshikhminShirley, ashikhmin_shirley)
OSL_CLOSURE_STRUCT_BEGIN(MicrofacetAnisoFresnel, microfacet_aniso_fresnel)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetAnisoFresnel, VECTOR, packed_float3, N, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetAnisoFresnel, VECTOR, packed_float3, T, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetAnisoFresnel, FLOAT, float, alpha_x, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetAnisoFresnel, FLOAT, float, alpha_y, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetAnisoFresnel, VECTOR, packed_float3, f0, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetAnisoFresnel, VECTOR, packed_float3, f90, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetAnisoFresnel, FLOAT, float, ior, NULL)
OSL_CLOSURE_STRUCT_MEMBER(MicrofacetAnisoFresnel, STRING, DeviceString, distribution, NULL)
OSL_CLOSURE_STRUCT_END(MicrofacetAnisoFresnel, microfacet_aniso_fresnel)
OSL_CLOSURE_STRUCT_BEGIN(AshikhminVelvet, ashikhmin_velvet)
OSL_CLOSURE_STRUCT_MEMBER(AshikhminVelvet, VECTOR, packed_float3, N, NULL)

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@ -36,3 +36,9 @@ color fresnel_conductor(float cosi, color eta, color k)
color Rperp2 = (tmp_f - (2.0 * eta * cosi) + cosi2) / (tmp_f + (2.0 * eta * cosi) + cosi2);
return (Rparl2 + Rperp2) * 0.5;
}
float F0_from_ior(float eta)
{
float f0 = (eta - 1.0) / (eta + 1.0);
return f0 * f0;
}

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@ -40,7 +40,7 @@ shader node_glossy_bsdf(color Color = 0.8,
}
if (distribution == "Multiscatter GGX")
BSDF = Color * microfacet_multi_ggx(Normal, roughness, Color);
BSDF = Color * microfacet_multi_ggx_aniso(Normal, T, roughness_u, roughness_v, Color);
else
BSDF = Color * microfacet(distribution, Normal, T, roughness_u, roughness_v, 0.0, 0);
}

View File

@ -4,7 +4,7 @@
#include "node_fresnel.h"
#include "stdcycles.h"
shader node_principled_bsdf(string distribution = "Multiscatter GGX",
shader node_principled_bsdf(string distribution = "multi_ggx",
string subsurface_method = "random_walk",
color BaseColor = color(0.8, 0.8, 0.8),
float Subsurface = 0.0,
@ -34,6 +34,7 @@ shader node_principled_bsdf(string distribution = "Multiscatter GGX",
float diffuse_weight = (1.0 - clamp(Metallic, 0.0, 1.0)) * (1.0 - clamp(Transmission, 0.0, 1.0));
float final_transmission = clamp(Transmission, 0.0, 1.0) * (1.0 - clamp(Metallic, 0.0, 1.0));
float specular_weight = (1.0 - final_transmission);
float r2 = Roughness * Roughness;
vector T = Tangent;
@ -65,52 +66,35 @@ shader node_principled_bsdf(string distribution = "Multiscatter GGX",
}
if (Sheen > 1e-5) {
color sheen_color = color(1.0, 1.0, 1.0) * (1.0 - SheenTint) + m_ctint * SheenTint;
color sheen_color = mix(color(1.0), m_ctint, SheenTint);
BSDF = BSDF + sheen_color * Sheen * principled_sheen(Normal);
BSDF += sheen_color * Sheen * principled_sheen(Normal);
}
BSDF = BSDF * diffuse_weight;
BSDF *= diffuse_weight;
}
if (specular_weight > 1e-5) {
float aspect = sqrt(1.0 - Anisotropic * 0.9);
float r2 = Roughness * Roughness;
float alpha_x = r2 / aspect;
float alpha_y = r2 * aspect;
color tmp_col = color(1.0, 1.0, 1.0) * (1.0 - SpecularTint) + m_ctint * SpecularTint;
color tmp_col = mix(color(1.0), m_ctint, SpecularTint);
color Cspec0 = (Specular * 0.08 * tmp_col) * (1.0 - Metallic) + BaseColor * Metallic;
if (distribution == "GGX" || Roughness <= 0.075) {
BSDF = BSDF + specular_weight *
microfacet_ggx_aniso_fresnel(Normal,
T,
alpha_x,
alpha_y,
(2.0 / (1.0 - sqrt(0.08 * Specular))) - 1.0,
BaseColor,
Cspec0);
}
else {
BSDF = BSDF + specular_weight * microfacet_multi_ggx_aniso_fresnel(
Normal,
T,
alpha_x,
alpha_y,
(2.0 / (1.0 - sqrt(0.08 * Specular))) - 1.0,
BaseColor,
Cspec0);
}
float eta = (2.0 / (1.0 - sqrt(0.08 * Specular))) - 1.0;
string spec_dist = (Roughness <= 0.075) ? "ggx" : distribution;
BSDF += specular_weight * microfacet_aniso_fresnel(
Normal, T, alpha_x, alpha_y, Cspec0, color(1.0), eta, spec_dist);
}
if (final_transmission > 1e-5) {
color Cspec0 = BaseColor * SpecularTint + color(1.0, 1.0, 1.0) * (1.0 - SpecularTint);
color Cspec0 = mix(color(1.0), BaseColor, SpecularTint);
float eta = backfacing() ? 1.0 / f : f;
if (distribution == "GGX" || Roughness <= 5e-2) {
if (distribution == "ggx" || Roughness <= 5e-2) {
float cosNI = dot(Normal, I);
float Fr = fresnel_dielectric_cos(cosNI, eta);
@ -119,26 +103,23 @@ shader node_principled_bsdf(string distribution = "Multiscatter GGX",
refl_roughness = 0.0;
float transmission_roughness = refl_roughness;
if (distribution == "GGX")
if (distribution == "ggx")
transmission_roughness = 1.0 - (1.0 - refl_roughness) * (1.0 - TransmissionRoughness);
BSDF = BSDF +
final_transmission *
(Fr * microfacet_ggx_fresnel(
Normal, refl_roughness * refl_roughness, eta, BaseColor, Cspec0) +
(1.0 - Fr) * BaseColor *
microfacet_ggx_refraction(
Normal, transmission_roughness * transmission_roughness, eta));
closure color refraction = microfacet(
"ggx", Normal, transmission_roughness * transmission_roughness, eta, 1);
closure color reflection = microfacet_aniso_fresnel(
Normal, T, r2, r2, Cspec0, color(1.0), eta, "ggx");
BSDF += final_transmission * mix(BaseColor * refraction, reflection, Fr);
}
else {
BSDF = BSDF +
final_transmission * microfacet_multi_ggx_glass_fresnel(
Normal, Roughness * Roughness, eta, BaseColor, Cspec0);
BSDF += final_transmission *
dielectric_bsdf(Normal, vector(0.0), Cspec0, BaseColor, r2, r2, eta, "multi_ggx");
}
}
if (Clearcoat > 1e-5) {
BSDF = BSDF + principled_clearcoat(
ClearcoatNormal, Clearcoat, ClearcoatRoughness * ClearcoatRoughness);
BSDF += principled_clearcoat(
ClearcoatNormal, Clearcoat, ClearcoatRoughness * ClearcoatRoughness);
}
}

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@ -20,31 +20,21 @@ closure color diffuse_ramp(normal N, color colors[8]) BUILTIN;
closure color phong_ramp(normal N, float exponent, color colors[8]) BUILTIN;
closure color diffuse_toon(normal N, float size, float smooth) BUILTIN;
closure color glossy_toon(normal N, float size, float smooth) BUILTIN;
closure color microfacet_ggx(normal N, float ag) BUILTIN;
closure color microfacet_ggx_aniso(normal N, vector T, float ax, float ay) BUILTIN;
closure color microfacet_ggx_refraction(normal N, float ag, float eta) BUILTIN;
closure color microfacet_multi_ggx(normal N, float ag, color C) BUILTIN;
closure color microfacet_multi_ggx_aniso(normal N, vector T, float ax, float ay, color C) BUILTIN;
closure color microfacet_multi_ggx_glass(normal N, float ag, float eta, color C) BUILTIN;
closure color microfacet_ggx_fresnel(normal N, float ag, float eta, color C, color Cspec0) BUILTIN;
closure color microfacet_ggx_aniso_fresnel(
normal N, vector T, float ax, float ay, float eta, color C, color Cspec0) BUILTIN;
closure color
microfacet_multi_ggx_fresnel(normal N, float ag, float eta, color C, color Cspec0) BUILTIN;
closure color microfacet_multi_ggx_aniso_fresnel(
normal N, vector T, float ax, float ay, float eta, color C, color Cspec0) BUILTIN;
closure color
microfacet_multi_ggx_glass_fresnel(normal N, float ag, float eta, color C, color Cspec0) BUILTIN;
closure color microfacet_beckmann(normal N, float ab) BUILTIN;
closure color microfacet_beckmann_aniso(normal N, vector T, float ax, float ay) BUILTIN;
closure color microfacet_beckmann_refraction(normal N, float ab, float eta) BUILTIN;
closure color ashikhmin_shirley(normal N, vector T, float ax, float ay) BUILTIN;
closure color ashikhmin_velvet(normal N, float sigma) BUILTIN;
closure color ambient_occlusion() BUILTIN;
closure color principled_diffuse(normal N, float roughness) BUILTIN;
closure color principled_sheen(normal N) BUILTIN;
closure color principled_clearcoat(normal N, float clearcoat, float clearcoat_roughness) BUILTIN;
/* Needed to pass along the color for multiscattering saturation adjustment,
* otherwise could be replaced by microfacet() */
closure color microfacet_multi_ggx_glass(normal N, float ag, float eta, color C) BUILTIN;
closure color microfacet_multi_ggx_aniso(normal N, vector T, float ax, float ay, color C) BUILTIN;
/* Needed to pass along the IOR for the Principled V1 Fresnel calculation,
* otherwise could be replaced by generalized_schlick_bsdf() */
closure color microfacet_aniso_fresnel(
normal N, vector T, float ax, float ay, color f0, color f90, float eta, string dist) BUILTIN;
// BSSRDF
closure color bssrdf(string method, normal N, vector radius, color albedo) BUILTIN;

View File

@ -261,9 +261,9 @@ ccl_device_noinline int svm_node_closure_bsdf(KernelGlobals kg,
ccl_private MicrofacetBsdf *bsdf = (ccl_private MicrofacetBsdf *)bsdf_alloc(
sd, sizeof(MicrofacetBsdf), spec_weight);
ccl_private FresnelPrincipledV1 *fresnel =
(bsdf != NULL) ? (ccl_private FresnelPrincipledV1 *)closure_alloc_extra(
sd, sizeof(FresnelPrincipledV1)) :
ccl_private FresnelGeneralizedSchlick *fresnel =
(bsdf != NULL) ? (ccl_private FresnelGeneralizedSchlick *)closure_alloc_extra(
sd, sizeof(FresnelGeneralizedSchlick)) :
NULL;
if (bsdf && fresnel) {
@ -283,22 +283,17 @@ ccl_device_noinline int svm_node_closure_bsdf(KernelGlobals kg,
one_float3(); // normalize lum. to isolate hue+sat
float3 tmp_col = make_float3(1.0f - specular_tint) + m_ctint * specular_tint;
fresnel->cspec0 = rgb_to_spectrum((specular * 0.08f * tmp_col) * (1.0f - metallic) +
base_color * metallic);
fresnel->color = rgb_to_spectrum(base_color);
fresnel->f0 = rgb_to_spectrum((specular * 0.08f * tmp_col) * (1.0f - metallic) +
base_color * metallic);
fresnel->f90 = one_spectrum();
fresnel->exponent = -1.0f;
fresnel->reflection_tint = one_spectrum();
fresnel->transmission_tint = zero_spectrum();
/* setup bsdf */
/* Use single-scatter GGX. */
if (distribution == CLOSURE_BSDF_MICROFACET_GGX_GLASS_ID || roughness <= 0.075f) {
sd->flag |= bsdf_microfacet_ggx_setup(bsdf);
bsdf_microfacet_setup_fresnel_principledv1(bsdf, sd, fresnel);
} /* Use multi-scatter GGX. */
else {
bsdf->fresnel = fresnel;
sd->flag |= bsdf_microfacet_multi_ggx_fresnel_setup(bsdf, sd);
}
sd->flag |= bsdf_microfacet_ggx_setup(bsdf);
const bool is_multiggx = (distribution == CLOSURE_BSDF_MICROFACET_MULTI_GGX_GLASS_ID);
bsdf_microfacet_setup_fresnel_generalized_schlick(kg, bsdf, sd, fresnel, is_multiggx);
}
}
#ifdef __CAUSTICS_TRICKS__
@ -313,7 +308,7 @@ ccl_device_noinline int svm_node_closure_bsdf(KernelGlobals kg,
#endif
if (final_transmission > CLOSURE_WEIGHT_CUTOFF) {
Spectrum glass_weight = weight * final_transmission;
float3 cspec0 = base_color * specular_tint + make_float3(1.0f - specular_tint);
Spectrum cspec0 = base_color * specular_tint + make_float3(1.0f - specular_tint);
/* Use single-scatter GGX. */
if (roughness <= 5e-2f || distribution == CLOSURE_BSDF_MICROFACET_GGX_GLASS_ID) {
@ -327,15 +322,14 @@ ccl_device_noinline int svm_node_closure_bsdf(KernelGlobals kg,
{
ccl_private MicrofacetBsdf *bsdf = (ccl_private MicrofacetBsdf *)bsdf_alloc(
sd, sizeof(MicrofacetBsdf), glass_weight * fresnel);
ccl_private FresnelPrincipledV1 *fresnel =
(bsdf != NULL) ? (ccl_private FresnelPrincipledV1 *)closure_alloc_extra(
sd, sizeof(FresnelPrincipledV1)) :
ccl_private FresnelGeneralizedSchlick *fresnel =
(bsdf != NULL) ? (ccl_private FresnelGeneralizedSchlick *)closure_alloc_extra(
sd, sizeof(FresnelGeneralizedSchlick)) :
NULL;
if (bsdf && fresnel) {
bsdf->N = valid_reflection_N;
bsdf->T = zero_float3();
bsdf->fresnel = fresnel;
bsdf->alpha_x = refl_roughness * refl_roughness;
bsdf->alpha_y = refl_roughness * refl_roughness;
@ -344,9 +338,13 @@ ccl_device_noinline int svm_node_closure_bsdf(KernelGlobals kg,
/* setup bsdf */
sd->flag |= bsdf_microfacet_ggx_setup(bsdf);
fresnel->color = rgb_to_spectrum(base_color);
fresnel->cspec0 = rgb_to_spectrum(cspec0);
bsdf_microfacet_setup_fresnel_principledv1(bsdf, sd, fresnel);
fresnel->f0 = cspec0;
fresnel->f90 = one_spectrum();
fresnel->exponent = -1.0f;
fresnel->reflection_tint = one_spectrum();
fresnel->transmission_tint = zero_spectrum();
bsdf_microfacet_setup_fresnel_generalized_schlick(kg, bsdf, sd, fresnel, false);
}
}
@ -364,7 +362,6 @@ ccl_device_noinline int svm_node_closure_bsdf(KernelGlobals kg,
if (bsdf) {
bsdf->N = valid_reflection_N;
bsdf->T = zero_float3();
bsdf->fresnel = NULL;
if (distribution == CLOSURE_BSDF_MICROFACET_GGX_GLASS_ID)
transmission_roughness = 1.0f - (1.0f - refl_roughness) *
@ -384,25 +381,28 @@ ccl_device_noinline int svm_node_closure_bsdf(KernelGlobals kg,
else {
ccl_private MicrofacetBsdf *bsdf = (ccl_private MicrofacetBsdf *)bsdf_alloc(
sd, sizeof(MicrofacetBsdf), glass_weight);
ccl_private FresnelPrincipledV1 *fresnel =
(bsdf != NULL) ? (ccl_private FresnelPrincipledV1 *)closure_alloc_extra(
sd, sizeof(FresnelPrincipledV1)) :
ccl_private FresnelGeneralizedSchlick *fresnel =
(bsdf != NULL) ? (ccl_private FresnelGeneralizedSchlick *)closure_alloc_extra(
sd, sizeof(FresnelGeneralizedSchlick)) :
NULL;
if (bsdf && fresnel) {
bsdf->N = valid_reflection_N;
bsdf->fresnel = fresnel;
bsdf->T = zero_float3();
bsdf->alpha_x = roughness * roughness;
bsdf->alpha_y = roughness * roughness;
bsdf->ior = ior;
fresnel->color = rgb_to_spectrum(base_color);
fresnel->cspec0 = rgb_to_spectrum(cspec0);
fresnel->f0 = make_spectrum(F0_from_ior(ior));
fresnel->f90 = one_spectrum();
fresnel->exponent = -1.0f;
fresnel->reflection_tint = cspec0;
fresnel->transmission_tint = base_color;
/* setup bsdf */
sd->flag |= bsdf_microfacet_multi_ggx_glass_fresnel_setup(bsdf, sd);
sd->flag |= bsdf_microfacet_ggx_glass_setup(bsdf);
bsdf_microfacet_setup_fresnel_generalized_schlick(kg, bsdf, sd, fresnel, true);
}
}
}
@ -492,7 +492,6 @@ ccl_device_noinline int svm_node_closure_bsdf(KernelGlobals kg,
bsdf->N = maybe_ensure_valid_specular_reflection(sd, N);
bsdf->ior = 1.0f;
bsdf->fresnel = NULL;
/* compute roughness */
float anisotropy = clamp(param2, -0.99f, 0.99f);
@ -525,20 +524,16 @@ ccl_device_noinline int svm_node_closure_bsdf(KernelGlobals kg,
sd->flag |= bsdf_reflection_setup(bsdf);
else if (type == CLOSURE_BSDF_MICROFACET_BECKMANN_ID)
sd->flag |= bsdf_microfacet_beckmann_setup(bsdf);
else if (type == CLOSURE_BSDF_MICROFACET_GGX_ID)
sd->flag |= bsdf_microfacet_ggx_setup(bsdf);
else if (type == CLOSURE_BSDF_MICROFACET_MULTI_GGX_ID) {
kernel_assert(stack_valid(data_node.w));
ccl_private FresnelConstant *fresnel = (ccl_private FresnelConstant *)closure_alloc_extra(
sd, sizeof(FresnelConstant));
if (fresnel) {
bsdf->fresnel = fresnel;
fresnel->color = rgb_to_spectrum(stack_load_float3(stack, data_node.w));
sd->flag |= bsdf_microfacet_multi_ggx_setup(bsdf);
}
else if (type == CLOSURE_BSDF_ASHIKHMIN_SHIRLEY_ID) {
sd->flag |= bsdf_ashikhmin_shirley_setup(bsdf);
}
else {
sd->flag |= bsdf_ashikhmin_shirley_setup(bsdf);
sd->flag |= bsdf_microfacet_ggx_setup(bsdf);
if (type == CLOSURE_BSDF_MICROFACET_MULTI_GGX_ID) {
kernel_assert(stack_valid(data_node.w));
const Spectrum color = rgb_to_spectrum(stack_load_float3(stack, data_node.w));
bsdf_microfacet_setup_fresnel_constant(kg, bsdf, sd, color);
}
}
break;
@ -557,7 +552,6 @@ ccl_device_noinline int svm_node_closure_bsdf(KernelGlobals kg,
if (bsdf) {
bsdf->N = maybe_ensure_valid_specular_reflection(sd, N);
bsdf->T = zero_float3();
bsdf->fresnel = NULL;
float eta = fmaxf(param2, 1e-5f);
eta = (sd->flag & SD_BACKFACING) ? 1.0f / eta : eta;
@ -587,7 +581,8 @@ ccl_device_noinline int svm_node_closure_bsdf(KernelGlobals kg,
}
case CLOSURE_BSDF_SHARP_GLASS_ID:
case CLOSURE_BSDF_MICROFACET_GGX_GLASS_ID:
case CLOSURE_BSDF_MICROFACET_BECKMANN_GLASS_ID: {
case CLOSURE_BSDF_MICROFACET_BECKMANN_GLASS_ID:
case CLOSURE_BSDF_MICROFACET_MULTI_GGX_GLASS_ID: {
#ifdef __CAUSTICS_TRICKS__
if (!kernel_data.integrator.caustics_reflective &&
!kernel_data.integrator.caustics_refractive && (path_flag & PATH_RAY_DIFFUSE))
@ -621,49 +616,19 @@ ccl_device_noinline int svm_node_closure_bsdf(KernelGlobals kg,
if (type == CLOSURE_BSDF_MICROFACET_BECKMANN_GLASS_ID)
sd->flag |= bsdf_microfacet_beckmann_glass_setup(bsdf);
else
else {
sd->flag |= bsdf_microfacet_ggx_glass_setup(bsdf);
if (type == CLOSURE_BSDF_MICROFACET_MULTI_GGX_GLASS_ID) {
kernel_assert(stack_valid(data_node.z));
const Spectrum color = rgb_to_spectrum(stack_load_float3(stack, data_node.z));
bsdf_microfacet_setup_fresnel_constant(kg, bsdf, sd, color);
}
}
}
}
break;
}
case CLOSURE_BSDF_MICROFACET_MULTI_GGX_GLASS_ID: {
#ifdef __CAUSTICS_TRICKS__
if (!kernel_data.integrator.caustics_reflective &&
!kernel_data.integrator.caustics_refractive && (path_flag & PATH_RAY_DIFFUSE))
break;
#endif
Spectrum weight = sd->svm_closure_weight * mix_weight;
ccl_private MicrofacetBsdf *bsdf = (ccl_private MicrofacetBsdf *)bsdf_alloc(
sd, sizeof(MicrofacetBsdf), weight);
if (!bsdf) {
break;
}
ccl_private FresnelConstant *fresnel = (ccl_private FresnelConstant *)closure_alloc_extra(
sd, sizeof(FresnelConstant));
if (!fresnel) {
break;
}
bsdf->N = maybe_ensure_valid_specular_reflection(sd, N);
bsdf->fresnel = fresnel;
bsdf->T = zero_float3();
float roughness = sqr(param1);
bsdf->alpha_x = roughness;
bsdf->alpha_y = roughness;
float eta = fmaxf(param2, 1e-5f);
bsdf->ior = (sd->flag & SD_BACKFACING) ? 1.0f / eta : eta;
kernel_assert(stack_valid(data_node.z));
fresnel->color = rgb_to_spectrum(stack_load_float3(stack, data_node.z));
/* setup bsdf */
sd->flag |= bsdf_microfacet_multi_ggx_glass_setup(bsdf);
break;
}
case CLOSURE_BSDF_ASHIKHMIN_VELVET_ID: {
Spectrum weight = sd->svm_closure_weight * mix_weight;
ccl_private VelvetBsdf *bsdf = (ccl_private VelvetBsdf *)bsdf_alloc(

View File

@ -423,7 +423,7 @@ typedef enum ClosureType {
CLOSURE_BSDF_MICROFACET_GGX_ID,
CLOSURE_BSDF_MICROFACET_GGX_CLEARCOAT_ID,
CLOSURE_BSDF_MICROFACET_BECKMANN_ID,
CLOSURE_BSDF_MICROFACET_MULTI_GGX_ID,
CLOSURE_BSDF_MICROFACET_MULTI_GGX_ID, /* virtual closure */
CLOSURE_BSDF_ASHIKHMIN_SHIRLEY_ID,
CLOSURE_BSDF_ASHIKHMIN_VELVET_ID,
CLOSURE_BSDF_PHONG_RAMP_ID,
@ -437,7 +437,7 @@ typedef enum ClosureType {
CLOSURE_BSDF_SHARP_GLASS_ID,
CLOSURE_BSDF_MICROFACET_BECKMANN_GLASS_ID,
CLOSURE_BSDF_MICROFACET_GGX_GLASS_ID,
CLOSURE_BSDF_MICROFACET_MULTI_GGX_GLASS_ID,
CLOSURE_BSDF_MICROFACET_MULTI_GGX_GLASS_ID, /* virtual closure */
CLOSURE_BSDF_HAIR_PRINCIPLED_ID,
CLOSURE_BSDF_HAIR_TRANSMISSION_ID,

View File

@ -1224,7 +1224,13 @@ typedef enum KernelBVHLayout {
typedef struct KernelTables {
int filter_table_offset;
int pad1, pad2, pad3;
int ggx_E;
int ggx_Eavg;
int ggx_glass_E;
int ggx_glass_Eavg;
int ggx_glass_inv_E;
int ggx_glass_inv_Eavg;
int pad1;
} KernelTables;
static_assert_align(KernelTables, 16);

View File

@ -40,4 +40,21 @@ ccl_device float lookup_table_read_2D(
return (1.0f - t) * data0 + t * data1;
}
ccl_device float lookup_table_read_3D(
KernelGlobals kg, float x, float y, float z, int offset, int xsize, int ysize, int zsize)
{
z = saturatef(z) * (zsize - 1);
int index = min(float_to_int(z), zsize - 1);
int nindex = min(index + 1, zsize - 1);
float t = z - index;
float data0 = lookup_table_read_2D(kg, x, y, offset + xsize * ysize * index, xsize, ysize);
if (t == 0.0f)
return data0;
float data1 = lookup_table_read_2D(kg, x, y, offset + xsize * ysize * nindex, xsize, ysize);
return (1.0f - t) * data0 + t * data1;
}
CCL_NAMESPACE_END

View File

@ -29,6 +29,8 @@
namespace OCIO = OCIO_NAMESPACE;
#endif
#include "scene/shader.tables"
CCL_NAMESPACE_BEGIN
thread_mutex ShaderManager::lookup_table_mutex;
@ -564,6 +566,15 @@ void ShaderManager::device_update_common(Device * /*device*/,
dscene->shaders.copy_to_device();
/* lookup tables */
KernelTables *ktables = &dscene->data.tables;
ktables->ggx_E = ensure_bsdf_table(dscene, scene, table_ggx_E);
ktables->ggx_Eavg = ensure_bsdf_table(dscene, scene, table_ggx_Eavg);
ktables->ggx_glass_E = ensure_bsdf_table(dscene, scene, table_ggx_glass_E);
ktables->ggx_glass_Eavg = ensure_bsdf_table(dscene, scene, table_ggx_glass_Eavg);
ktables->ggx_glass_inv_E = ensure_bsdf_table(dscene, scene, table_ggx_glass_inv_E);
ktables->ggx_glass_inv_Eavg = ensure_bsdf_table(dscene, scene, table_ggx_glass_inv_Eavg);
/* integrator */
KernelIntegrator *kintegrator = &dscene->data.integrator;
kintegrator->use_volumes = has_volumes;
@ -583,8 +594,13 @@ void ShaderManager::device_update_common(Device * /*device*/,
kfilm->is_rec709 = is_rec709;
}
void ShaderManager::device_free_common(Device * /*device*/, DeviceScene *dscene, Scene * /*scene*/)
void ShaderManager::device_free_common(Device * /*device*/, DeviceScene *dscene, Scene *scene)
{
for (auto &entry : bsdf_tables) {
scene->lookup_tables->remove_table(&entry.second);
}
bsdf_tables.clear();
dscene->shaders.free();
}
@ -889,4 +905,17 @@ void ShaderManager::init_xyz_transforms()
#endif
}
size_t ShaderManager::ensure_bsdf_table_impl(DeviceScene *dscene,
Scene *scene,
const float *table,
size_t n)
{
/* Since the BSDF tables are static arrays, we can use their address to identify them. */
if (!(bsdf_tables.count(table))) {
vector<float> entries(table, table + n);
bsdf_tables[table] = scene->lookup_tables->add_table(dscene, entries);
}
return bsdf_tables[table];
}
CCL_NAMESPACE_END

View File

@ -233,6 +233,15 @@ class ShaderManager {
static thread_mutex lookup_table_mutex;
unordered_map<const float *, size_t> bsdf_tables;
template<std::size_t n>
size_t ensure_bsdf_table(DeviceScene *dscene, Scene *scene, const float (&table)[n])
{
return ensure_bsdf_table_impl(dscene, scene, table, n);
}
size_t ensure_bsdf_table_impl(DeviceScene *dscene, Scene *scene, const float *table, size_t n);
uint get_graph_kernel_features(ShaderGraph *graph);
thread_spin_lock attribute_lock_;

View File

@ -0,0 +1,635 @@
/* SPDX-License-Identifier: Apache-2.0
* Copyright 2011-2022 Blender Foundation */
/* Note: this file has a non-standard extension so it is skipped by clang-format. */
CCL_NAMESPACE_BEGIN
/* Precomputed BSDF albedo tables for various microfacet distributions. */
static const float table_ggx_E[1024] = {
1.000000f, 0.980405f, 0.994967f, 0.997749f, 0.998725f, 0.999173f, 0.999411f, 0.999550f, 0.999634f, 0.999686f, 0.999716f, 0.999732f, 0.999738f, 0.999735f, 0.999726f, 0.999712f, 0.999693f, 0.999671f, 0.999645f, 0.999615f, 0.999583f, 0.999548f, 0.999511f, 0.999471f, 0.999429f, 0.999385f, 0.999338f, 0.999290f, 0.999240f, 0.999188f, 0.999134f, 0.999079f,
1.000000f, 0.999451f, 0.990086f, 0.954714f, 0.911203f, 0.891678f, 0.893893f, 0.905010f, 0.917411f, 0.928221f, 0.936755f, 0.943104f, 0.947567f, 0.950455f, 0.952036f, 0.952526f, 0.952096f, 0.950879f, 0.948983f, 0.946495f, 0.943484f, 0.940010f, 0.936122f, 0.931864f, 0.927272f, 0.922380f, 0.917217f, 0.911810f, 0.906184f, 0.900361f, 0.894361f, 0.888202f,
1.000000f, 0.999866f, 0.997676f, 0.987331f, 0.962386f, 0.929174f, 0.902886f, 0.890270f, 0.888687f, 0.893114f, 0.899716f, 0.906297f, 0.911810f, 0.915853f, 0.918345f, 0.919348f, 0.918982f, 0.917380f, 0.914671f, 0.910973f, 0.906393f, 0.901026f, 0.894957f, 0.888261f, 0.881006f, 0.873254f, 0.865061f, 0.856478f, 0.847553f, 0.838329f, 0.828845f, 0.819138f,
1.000000f, 0.999941f, 0.998997f, 0.994519f, 0.982075f, 0.959460f, 0.931758f, 0.907714f, 0.892271f, 0.885248f, 0.884058f, 0.885962f, 0.888923f, 0.891666f, 0.893488f, 0.894054f, 0.893246f, 0.891062f, 0.887565f, 0.882845f, 0.877003f, 0.870143f, 0.862365f, 0.853766f, 0.844436f, 0.834459f, 0.823915f, 0.812876f, 0.801410f, 0.789581f, 0.777445f, 0.765057f,
1.000000f, 0.999967f, 0.999442f, 0.996987f, 0.989925f, 0.975437f, 0.953654f, 0.929078f, 0.907414f, 0.891877f, 0.882635f, 0.878166f, 0.876572f, 0.876236f, 0.876004f, 0.875144f, 0.873238f, 0.870080f, 0.865601f, 0.859812f, 0.852774f, 0.844571f, 0.835302f, 0.825069f, 0.813976f, 0.802123f, 0.789609f, 0.776523f, 0.762954f, 0.748982f, 0.734682f, 0.720122f,
1.000000f, 0.999979f, 0.999644f, 0.998096f, 0.993618f, 0.983950f, 0.967765f, 0.946488f, 0.923989f, 0.904160f, 0.889039f, 0.878704f, 0.872099f, 0.867839f, 0.864665f, 0.861611f, 0.858015f, 0.853468f, 0.847745f, 0.840752f, 0.832480f, 0.822973f, 0.812312f, 0.800592f, 0.787922f, 0.774411f, 0.760171f, 0.745308f, 0.729926f, 0.714121f, 0.697985f, 0.681600f,
1.000000f, 0.999985f, 0.999752f, 0.998684f, 0.995603f, 0.988803f, 0.976727f, 0.959272f, 0.938451f, 0.917446f, 0.898932f, 0.884154f, 0.873043f, 0.864773f, 0.858278f, 0.852565f, 0.846845f, 0.840555f, 0.833331f, 0.824969f, 0.815378f, 0.804550f, 0.792533f, 0.779405f, 0.765271f, 0.750246f, 0.734447f, 0.717996f, 0.701008f, 0.683595f, 0.665862f, 0.647905f,
1.000000f, 0.999989f, 0.999816f, 0.999032f, 0.996781f, 0.991766f, 0.982561f, 0.968421f, 0.950089f, 0.929705f, 0.909775f, 0.892112f, 0.877428f, 0.865535f, 0.855737f, 0.847185f, 0.839084f, 0.830796f, 0.821858f, 0.811969f, 0.800961f, 0.788766f, 0.775391f, 0.760894f, 0.745367f, 0.728923f, 0.711685f, 0.693783f, 0.675344f, 0.656491f, 0.637343f, 0.618009f,
1.000000f, 0.999991f, 0.999858f, 0.999255f, 0.997533f, 0.993686f, 0.986490f, 0.974988f, 0.959173f, 0.940264f, 0.920251f, 0.901030f, 0.883794f, 0.868900f, 0.856078f, 0.844728f, 0.834154f, 0.823720f, 0.812914f, 0.801368f, 0.788846f, 0.775227f, 0.760476f, 0.744623f, 0.727744f, 0.709946f, 0.691355f, 0.672105f, 0.652332f, 0.632172f, 0.611753f, 0.591195f,
1.000000f, 0.999993f, 0.999886f, 0.999406f, 0.998040f, 0.994992f, 0.989227f, 0.979769f, 0.966203f, 0.949069f, 0.929766f, 0.909990f, 0.891126f, 0.873921f, 0.858498f, 0.844545f, 0.831539f, 0.818909f, 0.806146f, 0.792847f, 0.778733f, 0.763633f, 0.747476f, 0.730264f, 0.712056f, 0.692949f, 0.673066f, 0.652547f, 0.631533f, 0.610170f, 0.588596f, 0.566939f,
1.000000f, 0.999995f, 0.999906f, 0.999513f, 0.998399f, 0.995917f, 0.991195f, 0.983312f, 0.971656f, 0.956303f, 0.938125f, 0.918488f, 0.898757f, 0.879901f, 0.862353f, 0.846089f, 0.830787f, 0.815992f, 0.801242f, 0.786135f, 0.770368f, 0.753741f, 0.736147f, 0.717566f, 0.698037f, 0.677649f, 0.656520f, 0.634791f, 0.612611f, 0.590130f, 0.567495f, 0.544843f,
1.000000f, 0.999996f, 0.999921f, 0.999591f, 0.998661f, 0.996594f, 0.992650f, 0.985988f, 0.975917f, 0.962217f, 0.945336f, 0.926280f, 0.906266f, 0.886338f, 0.867144f, 0.848905f, 0.831508f, 0.814643f, 0.797929f, 0.780995f, 0.763540f, 0.745347f, 0.726289f, 0.706324f, 0.685477f, 0.663824f, 0.641483f, 0.618591f, 0.595303f, 0.571774f, 0.548156f, 0.524596f,
1.000000f, 0.999996f, 0.999933f, 0.999651f, 0.998859f, 0.997104f, 0.993752f, 0.988046f, 0.979280f, 0.967055f, 0.951498f, 0.933282f, 0.913407f, 0.892888f, 0.872490f, 0.852624f, 0.833371f, 0.814578f, 0.795964f, 0.777219f, 0.758062f, 0.738279f, 0.717734f, 0.696371f, 0.674202f, 0.651296f, 0.627765f, 0.603747f, 0.579398f, 0.554878f, 0.530346f, 0.505951f,
1.000000f, 0.999997f, 0.999941f, 0.999696f, 0.999012f, 0.997497f, 0.994604f, 0.989656f, 0.981964f, 0.971026f, 0.956742f, 0.939495f, 0.920052f, 0.899322f, 0.878109f, 0.856955f, 0.836102f, 0.815549f, 0.795133f, 0.774620f, 0.753771f, 0.732389f, 0.710341f, 0.687567f, 0.664071f, 0.639918f, 0.615213f, 0.590097f, 0.564725f, 0.539263f, 0.513871f, 0.488706f,
1.000000f, 0.999997f, 0.999949f, 0.999733f, 0.999132f, 0.997806f, 0.995276f, 0.990935f, 0.984129f, 0.974304f, 0.961200f, 0.944967f, 0.926144f, 0.905496f, 0.883799f, 0.861667f, 0.839472f, 0.817348f, 0.795251f, 0.773035f, 0.750522f, 0.727545f, 0.703988f, 0.679793f, 0.654965f, 0.629565f, 0.603699f, 0.577506f, 0.551143f, 0.524778f, 0.498576f, 0.472695f,
1.000000f, 0.999997f, 0.999954f, 0.999762f, 0.999228f, 0.998053f, 0.995814f, 0.991966f, 0.985893f, 0.977026f, 0.964995f, 0.949768f, 0.931677f, 0.911324f, 0.889415f, 0.866586f, 0.843295f, 0.819794f, 0.796153f, 0.772321f, 0.748187f, 0.723632f, 0.698566f, 0.672945f, 0.646780f, 0.620134f, 0.593114f, 0.565860f, 0.538532f, 0.511298f, 0.484328f, 0.457779f,
1.000000f, 0.999998f, 0.999959f, 0.999786f, 0.999307f, 0.998254f, 0.996252f, 0.992808f, 0.987348f, 0.979302f, 0.968235f, 0.953973f, 0.936669f, 0.916763f, 0.894859f, 0.871576f, 0.847421f, 0.822737f, 0.797698f, 0.772347f, 0.746651f, 0.720547f, 0.693982f, 0.666934f, 0.639428f, 0.611535f, 0.583366f, 0.555065f, 0.526792f, 0.498719f, 0.471015f, 0.443841f,
1.000000f, 0.999998f, 0.999962f, 0.999805f, 0.999371f, 0.998420f, 0.996612f, 0.993502f, 0.988557f, 0.981218f, 0.971011f, 0.957656f, 0.941156f, 0.921798f, 0.900070f, 0.876539f, 0.851730f, 0.826051f, 0.799763f, 0.773002f, 0.745814f, 0.718199f, 0.690150f, 0.661679f, 0.632832f, 0.603691f, 0.574377f, 0.545037f, 0.515837f, 0.486949f, 0.458544f, 0.430781f,
1.000000f, 0.999998f, 0.999966f, 0.999822f, 0.999425f, 0.998558f, 0.996912f, 0.994082f, 0.989572f, 0.982843f, 0.973398f, 0.960884f, 0.945180f, 0.926433f, 0.905008f, 0.881402f, 0.856128f, 0.829631f, 0.802244f, 0.774186f, 0.745583f, 0.716504f, 0.686997f, 0.657112f, 0.626924f, 0.596535f, 0.566077f, 0.535706f, 0.505592f, 0.475910f, 0.446831f, 0.418514f,
1.000000f, 0.999998f, 0.999968f, 0.999836f, 0.999471f, 0.998674f, 0.997165f, 0.994570f, 0.990430f, 0.984229f, 0.975460f, 0.963718f, 0.948785f, 0.930682f, 0.909656f, 0.886116f, 0.860541f, 0.833390f, 0.805050f, 0.775811f, 0.745878f, 0.715390f, 0.684454f, 0.653169f, 0.621644f, 0.590007f, 0.558407f, 0.527011f, 0.495995f, 0.465536f, 0.435808f, 0.406965f,
1.000000f, 0.999999f, 0.999970f, 0.999848f, 0.999509f, 0.998773f, 0.997379f, 0.994985f, 0.991163f, 0.985419f, 0.977249f, 0.966213f, 0.952014f, 0.934568f, 0.914006f, 0.890646f, 0.864912f, 0.837258f, 0.808105f, 0.777803f, 0.746627f, 0.714789f, 0.682460f, 0.649794f, 0.616939f, 0.584055f, 0.551314f, 0.518896f, 0.486987f, 0.455768f, 0.425410f, 0.396069f,
1.000000f, 0.999999f, 0.999973f, 0.999858f, 0.999542f, 0.998857f, 0.997562f, 0.995341f, 0.991792f, 0.986447f, 0.978809f, 0.968414f, 0.954908f, 0.938115f, 0.918063f, 0.894970f, 0.869199f, 0.841178f, 0.811344f, 0.780093f, 0.747765f, 0.714642f, 0.680962f, 0.646935f, 0.612760f, 0.578633f, 0.544751f, 0.511315f, 0.478520f, 0.446553f, 0.415586f, 0.385770f,
1.000000f, 0.999999f, 0.999974f, 0.999867f, 0.999571f, 0.998930f, 0.997720f, 0.995648f, 0.992336f, 0.987340f, 0.980174f, 0.970361f, 0.957504f, 0.941351f, 0.921833f, 0.899078f, 0.873371f, 0.845104f, 0.814712f, 0.782625f, 0.749237f, 0.714896f, 0.679909f, 0.644547f, 0.609064f, 0.573697f, 0.538677f, 0.504225f, 0.470550f, 0.437846f, 0.406286f, 0.376017f,
1.000000f, 0.999999f, 0.999976f, 0.999874f, 0.999596f, 0.998993f, 0.997858f, 0.995914f, 0.992810f, 0.988121f, 0.981374f, 0.972090f, 0.959837f, 0.944301f, 0.925331f, 0.902963f, 0.877406f, 0.848999f, 0.818163f, 0.785347f, 0.750991f, 0.715502f, 0.679256f, 0.642589f, 0.605812f, 0.569211f, 0.533054f, 0.497587f, 0.463038f, 0.429607f, 0.397469f, 0.366766f,
1.000000f, 0.999999f, 0.999977f, 0.999881f, 0.999618f, 0.999049f, 0.997978f, 0.996147f, 0.993224f, 0.988806f, 0.982434f, 0.973628f, 0.961935f, 0.946991f, 0.928572f, 0.906628f, 0.881288f, 0.852834f, 0.821659f, 0.788217f, 0.752981f, 0.716417f, 0.678962f, 0.641022f, 0.602968f, 0.565141f, 0.527849f, 0.491370f, 0.455949f, 0.421800f, 0.389096f, 0.357977f,
1.000000f, 0.999999f, 0.999978f, 0.999887f, 0.999637f, 0.999097f, 0.998083f, 0.996352f, 0.993588f, 0.989410f, 0.983373f, 0.975002f, 0.963827f, 0.949446f, 0.931571f, 0.910076f, 0.885009f, 0.856589f, 0.825169f, 0.791196f, 0.755170f, 0.717601f, 0.678991f, 0.639812f, 0.600501f, 0.561455f, 0.523031f, 0.485541f, 0.449253f, 0.414392f, 0.381135f, 0.349616f,
1.000000f, 0.999999f, 0.999979f, 0.999892f, 0.999655f, 0.999141f, 0.998177f, 0.996533f, 0.993910f, 0.989945f, 0.984209f, 0.976232f, 0.965536f, 0.951688f, 0.934346f, 0.913314f, 0.888564f, 0.860245f, 0.828665f, 0.794253f, 0.757521f, 0.719020f, 0.679309f, 0.638927f, 0.598380f, 0.558126f, 0.518574f, 0.480074f, 0.442922f, 0.407354f, 0.373554f, 0.341651f,
1.000000f, 0.999999f, 0.999980f, 0.999897f, 0.999669f, 0.999179f, 0.998260f, 0.996693f, 0.994197f, 0.990422f, 0.984956f, 0.977337f, 0.967083f, 0.953737f, 0.936913f, 0.916351f, 0.891951f, 0.863792f, 0.832128f, 0.797360f, 0.760004f, 0.720642f, 0.679885f, 0.638338f, 0.596578f, 0.555128f, 0.514452f, 0.474944f, 0.436929f, 0.400661f, 0.366328f, 0.334053f,
1.000000f, 0.999999f, 0.999981f, 0.999901f, 0.999683f, 0.999213f, 0.998334f, 0.996836f, 0.994452f, 0.990848f, 0.985625f, 0.978332f, 0.968486f, 0.955612f, 0.939288f, 0.919197f, 0.895172f, 0.867221f, 0.835539f, 0.800494f, 0.762592f, 0.722438f, 0.680691f, 0.638020f, 0.595071f, 0.552438f, 0.510643f, 0.470129f, 0.431253f, 0.394289f, 0.359430f, 0.326796f,
1.000000f, 0.999999f, 0.999982f, 0.999905f, 0.999695f, 0.999244f, 0.998400f, 0.996965f, 0.994681f, 0.991230f, 0.986227f, 0.979231f, 0.969761f, 0.957330f, 0.941486f, 0.921863f, 0.898229f, 0.870526f, 0.838887f, 0.803634f, 0.765260f, 0.724383f, 0.681702f, 0.637948f, 0.593837f, 0.550034f, 0.507126f, 0.465607f, 0.425873f, 0.388216f, 0.352839f, 0.319858f,
1.000000f, 0.999999f, 0.999982f, 0.999908f, 0.999706f, 0.999271f, 0.998459f, 0.997080f, 0.994886f, 0.991574f, 0.986770f, 0.980045f, 0.970922f, 0.958906f, 0.943521f, 0.924358f, 0.901128f, 0.873705f, 0.842159f, 0.806765f, 0.767988f, 0.726453f, 0.682895f, 0.638100f, 0.592854f, 0.547896f, 0.503881f, 0.461361f, 0.420769f, 0.382424f, 0.346535f, 0.313216f,
1.000000f, 0.999999f, 0.999983f, 0.999911f, 0.999716f, 0.999296f, 0.998513f, 0.997184f, 0.995072f, 0.991884f, 0.987261f, 0.980785f, 0.971982f, 0.960355f, 0.945407f, 0.926694f, 0.903873f, 0.876756f, 0.845349f, 0.809871f, 0.770757f, 0.728630f, 0.684249f, 0.638454f, 0.592102f, 0.546006f, 0.500893f, 0.457373f, 0.415925f, 0.376893f, 0.340499f, 0.306853f
};
static const float table_ggx_Eavg[32] = {
1.000000f, 0.999992f, 0.999897f, 0.999548f, 0.998729f, 0.997199f, 0.994703f, 0.990986f, 0.985805f, 0.978930f, 0.970160f, 0.959321f, 0.946279f, 0.930937f, 0.913247f, 0.893209f, 0.870874f, 0.846345f, 0.819774f, 0.791360f, 0.761345f, 0.730001f, 0.697631f, 0.664547f, 0.631068f, 0.597509f, 0.564165f, 0.531311f, 0.499191f, 0.468013f, 0.437950f, 0.409137f
};
static const float table_ggx_glass_E[4096] = {
0.999985f, 1.000000f, 0.999989f, 0.999990f, 1.000000f, 0.999999f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 0.995405f, 0.998159f, 0.997352f, 0.995556f, 0.993264f, 0.990673f, 0.987859f, 0.984857f, 0.981686f, 0.978366f, 0.974910f, 0.971336f, 0.967655f, 0.963881f, 0.960025f,
1.000000f, 0.999037f, 0.984373f, 0.951223f, 0.908812f, 0.850714f, 0.787824f, 0.732387f, 0.688038f, 0.653736f, 0.627288f, 0.606724f, 0.590534f, 0.577604f, 0.567136f, 0.558556f,
1.000000f, 0.999790f, 0.996491f, 0.983048f, 0.954803f, 0.911598f, 0.857483f, 0.801146f, 0.750002f, 0.707130f, 0.672506f, 0.644881f, 0.622845f, 0.605146f, 0.590797f, 0.579049f,
1.000000f, 0.999901f, 0.998395f, 0.991953f, 0.976043f, 0.947847f, 0.907820f, 0.860180f, 0.811070f, 0.765424f, 0.725673f, 0.692262f, 0.664642f, 0.641911f, 0.623184f, 0.607670f,
1.000000f, 0.999943f, 0.999081f, 0.995375f, 0.985803f, 0.967476f, 0.939094f, 0.901894f, 0.859442f, 0.816061f, 0.775183f, 0.738672f, 0.707095f, 0.680251f, 0.657599f, 0.638515f,
1.000000f, 0.999964f, 0.999418f, 0.997064f, 0.990881f, 0.978596f, 0.958507f, 0.930339f, 0.895632f, 0.857261f, 0.818368f, 0.781421f, 0.747848f, 0.718200f, 0.692449f, 0.670282f,
1.000000f, 0.999976f, 0.999609f, 0.998028f, 0.993836f, 0.985334f, 0.970961f, 0.949851f, 0.922317f, 0.889899f, 0.854891f, 0.819635f, 0.785941f, 0.754930f, 0.727098f, 0.702515f,
1.000000f, 0.999983f, 0.999729f, 0.998628f, 0.995695f, 0.989681f, 0.979281f, 0.963516f, 0.942069f, 0.915536f, 0.885302f, 0.853191f, 0.820962f, 0.790000f, 0.761205f, 0.735019f,
1.000000f, 0.999988f, 0.999807f, 0.999027f, 0.996943f, 0.992630f, 0.985061f, 0.973329f, 0.956860f, 0.935671f, 0.910431f, 0.882327f, 0.852785f, 0.823168f, 0.794564f, 0.767691f,
1.000000f, 0.999992f, 0.999862f, 0.999306f, 0.997815f, 0.994714f, 0.989218f, 0.980549f, 0.968095f, 0.951578f, 0.931158f, 0.907462f, 0.881472f, 0.854302f, 0.827016f, 0.800477f,
1.000000f, 0.999994f, 0.999903f, 0.999508f, 0.998451f, 0.996240f, 0.992293f, 0.985990f, 0.976770f, 0.964243f, 0.948276f, 0.929081f, 0.907187f, 0.883360f, 0.858467f, 0.833340f,
1.000000f, 0.999996f, 0.999933f, 0.999659f, 0.998925f, 0.997388f, 0.994627f, 0.990177f, 0.983575f, 0.974422f, 0.962463f, 0.947642f, 0.930135f, 0.910340f, 0.888830f, 0.866259f,
1.000000f, 0.999997f, 0.999956f, 0.999775f, 0.999292f, 0.998273f, 0.996437f, 0.993456f, 0.988984f, 0.982691f, 0.974287f, 0.963598f, 0.950566f, 0.935300f, 0.918059f, 0.899216f,
1.000000f, 0.999998f, 0.999974f, 0.999866f, 0.999577f, 0.998969f, 0.997868f, 0.996070f, 0.993349f, 0.989468f, 0.984197f, 0.977335f, 0.968739f, 0.958323f, 0.946109f, 0.932199f,
1.000000f, 0.999999f, 0.999988f, 0.999938f, 0.999806f, 0.999525f, 0.999015f, 0.998179f, 0.996906f, 0.995072f, 0.992543f, 0.989188f, 0.984877f, 0.979492f, 0.972944f, 0.965165f,
1.000000f, 1.000000f, 0.999999f, 0.999995f, 0.999985f, 0.999964f, 0.999925f, 0.999860f, 0.999762f, 0.999618f, 0.999419f, 0.999153f, 0.998802f, 0.998352f, 0.997801f, 0.997112f,
1.000000f, 0.995388f, 0.998717f, 0.998982f, 0.998625f, 0.997974f, 0.997140f, 0.996182f, 0.995130f, 0.993999f, 0.992798f, 0.991533f, 0.990206f, 0.988822f, 0.987383f, 0.985894f,
1.000000f, 0.998651f, 0.978192f, 0.943710f, 0.926163f, 0.904416f, 0.868343f, 0.824688f, 0.781400f, 0.742589f, 0.709377f, 0.681460f, 0.658110f, 0.638518f, 0.622000f, 0.607981f,
1.000000f, 0.999773f, 0.995969f, 0.981116f, 0.957538f, 0.930096f, 0.894925f, 0.851684f, 0.805599f, 0.761916f, 0.723411f, 0.690729f, 0.663465f, 0.640826f, 0.622007f, 0.606292f,
1.000000f, 0.999911f, 0.998475f, 0.992107f, 0.977460f, 0.954862f, 0.924548f, 0.886566f, 0.843561f, 0.799865f, 0.759023f, 0.722868f, 0.691844f, 0.665632f, 0.643614f, 0.625119f,
1.000000f, 0.999950f, 0.999175f, 0.995723f, 0.986844f, 0.970734f, 0.946942f, 0.915586f, 0.878129f, 0.837559f, 0.797224f, 0.759605f, 0.726013f, 0.696786f, 0.671701f, 0.650322f,
1.000000f, 0.999968f, 0.999475f, 0.997315f, 0.991570f, 0.980337f, 0.962445f, 0.937545f, 0.906282f, 0.870486f, 0.832776f, 0.795698f, 0.761069f, 0.729848f, 0.702311f, 0.678351f,
1.000000f, 0.999979f, 0.999643f, 0.998177f, 0.994255f, 0.986313f, 0.973041f, 0.953715f, 0.928347f, 0.897880f, 0.864109f, 0.829178f, 0.795033f, 0.763020f, 0.733880f, 0.707879f,
1.000000f, 0.999985f, 0.999746f, 0.998712f, 0.995937f, 0.990229f, 0.980411f, 0.965602f, 0.945430f, 0.920208f, 0.890979f, 0.859337f, 0.826964f, 0.795377f, 0.765624f, 0.738299f,
1.000000f, 0.999989f, 0.999817f, 0.999073f, 0.997075f, 0.992926f, 0.985659f, 0.974419f, 0.958652f, 0.938260f, 0.913723f, 0.886014f, 0.856456f, 0.826428f, 0.797093f, 0.769282f,
1.000000f, 0.999991f, 0.999868f, 0.999329f, 0.997882f, 0.994860f, 0.989503f, 0.981072f, 0.968962f, 0.952856f, 0.932834f, 0.909386f, 0.883374f, 0.855884f, 0.828001f, 0.800646f,
1.000000f, 0.999994f, 0.999905f, 0.999517f, 0.998476f, 0.996291f, 0.992395f, 0.986168f, 0.977075f, 0.964700f, 0.948872f, 0.929742f, 0.907742f, 0.883594f, 0.858150f, 0.832280f,
1.000000f, 0.999996f, 0.999933f, 0.999660f, 0.998926f, 0.997385f, 0.994618f, 0.990151f, 0.983532f, 0.974353f, 0.962345f, 0.947409f, 0.929670f, 0.909496f, 0.887408f, 0.864093f,
1.000000f, 0.999997f, 0.999955f, 0.999771f, 0.999277f, 0.998237f, 0.996357f, 0.993308f, 0.988723f, 0.982284f, 0.973688f, 0.962731f, 0.949336f, 0.933578f, 0.915681f, 0.896025f,
1.000000f, 0.999998f, 0.999973f, 0.999859f, 0.999554f, 0.998910f, 0.997742f, 0.995841f, 0.992953f, 0.988845f, 0.983268f, 0.976012f, 0.966908f, 0.955859f, 0.942858f, 0.927996f,
1.000000f, 0.999999f, 0.999986f, 0.999929f, 0.999774f, 0.999452f, 0.998859f, 0.997892f, 0.996414f, 0.994288f, 0.991361f, 0.987491f, 0.982523f, 0.976329f, 0.968792f, 0.959831f,
1.000000f, 1.000000f, 0.999997f, 0.999982f, 0.999942f, 0.999857f, 0.999704f, 0.999448f, 0.999060f, 0.998493f, 0.997714f, 0.996670f, 0.995320f, 0.993613f, 0.991499f, 0.988921f,
1.000000f, 0.995365f, 0.998801f, 0.999276f, 0.999227f, 0.998963f, 0.998568f, 0.998082f, 0.997529f, 0.996923f, 0.996273f, 0.995583f, 0.994856f, 0.994093f, 0.993298f, 0.992470f,
1.000000f, 0.998400f, 0.974244f, 0.935839f, 0.925457f, 0.920630f, 0.903983f, 0.875865f, 0.841964f, 0.807196f, 0.774375f, 0.744706f, 0.718426f, 0.695348f, 0.675129f, 0.657387f,
1.000000f, 0.999729f, 0.995093f, 0.977435f, 0.953654f, 0.934130f, 0.912830f, 0.883507f, 0.847141f, 0.808095f, 0.770242f, 0.735737f, 0.705344f, 0.679048f, 0.656456f, 0.637080f,
1.000000f, 0.999904f, 0.998303f, 0.991076f, 0.975623f, 0.955620f, 0.932714f, 0.904383f, 0.869703f, 0.831042f, 0.791868f, 0.754930f, 0.721663f, 0.692511f, 0.667329f, 0.645711f,
1.000000f, 0.999950f, 0.999166f, 0.995545f, 0.986347f, 0.971067f, 0.950765f, 0.925206f, 0.893847f, 0.857809f, 0.819700f, 0.782222f, 0.747305f, 0.715920f, 0.688322f, 0.664353f,
1.000000f, 0.999970f, 0.999497f, 0.997349f, 0.991580f, 0.980677f, 0.964385f, 0.942677f, 0.915420f, 0.883167f, 0.847684f, 0.811270f, 0.776018f, 0.743303f, 0.713816f, 0.687720f,
1.000000f, 0.999979f, 0.999662f, 0.998244f, 0.994377f, 0.986622f, 0.974078f, 0.956417f, 0.933464f, 0.905495f, 0.873578f, 0.839486f, 0.805137f, 0.772120f, 0.741468f, 0.713698f,
1.000000f, 0.999985f, 0.999760f, 0.998765f, 0.996051f, 0.990449f, 0.980961f, 0.966960f, 0.948125f, 0.924486f, 0.896610f, 0.865696f, 0.833324f, 0.801053f, 0.770094f, 0.741288f,
1.000000f, 0.999989f, 0.999825f, 0.999106f, 0.997145f, 0.993050f, 0.985914f, 0.975021f, 0.959903f, 0.940392f, 0.916674f, 0.889467f, 0.859911f, 0.829349f, 0.799017f, 0.769914f,
1.000000f, 0.999992f, 0.999871f, 0.999343f, 0.997913f, 0.994898f, 0.989563f, 0.981215f, 0.969336f, 0.953599f, 0.933946f, 0.910703f, 0.884586f, 0.856581f, 0.827793f, 0.799252f,
1.000000f, 0.999994f, 0.999905f, 0.999520f, 0.998473f, 0.996269f, 0.992322f, 0.986046f, 0.976919f, 0.964556f, 0.948744f, 0.929525f, 0.907225f, 0.882483f, 0.856137f, 0.829089f,
1.000000f, 0.999996f, 0.999932f, 0.999655f, 0.998905f, 0.997315f, 0.994456f, 0.989845f, 0.983045f, 0.973644f, 0.961379f, 0.946083f, 0.927839f, 0.906910f, 0.883827f, 0.859263f,
1.000000f, 0.999997f, 0.999953f, 0.999760f, 0.999238f, 0.998136f, 0.996141f, 0.992892f, 0.988035f, 0.981227f, 0.972155f, 0.960609f, 0.946489f, 0.929771f, 0.910717f, 0.889658f,
1.000000f, 0.999998f, 0.999970f, 0.999844f, 0.999505f, 0.998789f, 0.997485f, 0.995350f, 0.992123f, 0.987537f, 0.981342f, 0.973304f, 0.963244f, 0.951027f, 0.936610f, 0.920084f,
1.000000f, 0.999999f, 0.999983f, 0.999911f, 0.999717f, 0.999310f, 0.998567f, 0.997335f, 0.995468f, 0.992786f, 0.989111f, 0.984278f, 0.978116f, 0.970461f, 0.961172f, 0.950156f,
1.000000f, 1.000000f, 0.999992f, 0.999961f, 0.999873f, 0.999687f, 0.999348f, 0.998783f, 0.997916f, 0.996657f, 0.994936f, 0.992649f, 0.989728f, 0.986067f, 0.981571f, 0.976141f,
1.000000f, 0.995351f, 0.998825f, 0.999374f, 0.999438f, 0.999320f, 0.999098f, 0.998806f, 0.998460f, 0.998073f, 0.997651f, 0.997201f, 0.996723f, 0.996222f, 0.995696f, 0.995148f,
1.000000f, 0.998247f, 0.971853f, 0.930499f, 0.922466f, 0.925445f, 0.919781f, 0.902821f, 0.877948f, 0.849240f, 0.819764f, 0.791363f, 0.764922f, 0.740764f, 0.718887f, 0.699161f,
1.000000f, 0.999691f, 0.994374f, 0.974344f, 0.949194f, 0.933147f, 0.920047f, 0.900903f, 0.873664f, 0.840927f, 0.806286f, 0.772525f, 0.741186f, 0.712937f, 0.687847f, 0.665746f,
1.000000f, 0.999891f, 0.998077f, 0.989841f, 0.972944f, 0.953646f, 0.935232f, 0.914098f, 0.886967f, 0.854149f, 0.818325f, 0.782378f, 0.748372f, 0.717379f, 0.689780f, 0.665505f,
1.000000f, 0.999948f, 0.999095f, 0.995105f, 0.985120f, 0.969684f, 0.951429f, 0.930275f, 0.904363f, 0.873183f, 0.838235f, 0.801991f, 0.766711f, 0.733862f, 0.704162f, 0.677798f,
1.000000f, 0.999969f, 0.999481f, 0.997211f, 0.991093f, 0.979948f, 0.964446f, 0.945167f, 0.921457f, 0.892837f, 0.860035f, 0.824915f, 0.789586f, 0.755768f, 0.724509f, 0.696306f,
1.000000f, 0.999980f, 0.999662f, 0.998216f, 0.994213f, 0.986278f, 0.973997f, 0.957520f, 0.936668f, 0.911128f, 0.881257f, 0.848288f, 0.814019f, 0.780159f, 0.748034f, 0.718404f,
1.000000f, 0.999986f, 0.999763f, 0.998768f, 0.996003f, 0.990290f, 0.980821f, 0.967303f, 0.949566f, 0.927380f, 0.900854f, 0.870765f, 0.838439f, 0.805471f, 0.773240f, 0.742756f,
1.000000f, 0.999990f, 0.999828f, 0.999112f, 0.997132f, 0.992951f, 0.985733f, 0.974930f, 0.960250f, 0.941434f, 0.918449f, 0.891675f, 0.862029f, 0.830797f, 0.799266f, 0.768611f,
1.000000f, 0.999992f, 0.999874f, 0.999345f, 0.997890f, 0.994798f, 0.989332f, 0.980869f, 0.969008f, 0.953434f, 0.933980f, 0.910769f, 0.884320f, 0.855554f, 0.825575f, 0.795502f,
1.000000f, 0.999994f, 0.999906f, 0.999513f, 0.998440f, 0.996149f, 0.992040f, 0.985528f, 0.976163f, 0.963589f, 0.947551f, 0.927984f, 0.905085f, 0.879413f, 0.851774f, 0.823130f,
1.000000f, 0.999996f, 0.999930f, 0.999641f, 0.998853f, 0.997173f, 0.994130f, 0.989225f, 0.982030f, 0.972164f, 0.959346f, 0.943372f, 0.924226f, 0.902133f, 0.877591f, 0.851276f,
1.000000f, 0.999997f, 0.999949f, 0.999742f, 0.999176f, 0.997970f, 0.995769f, 0.992189f, 0.986844f, 0.979388f, 0.969535f, 0.957031f, 0.941711f, 0.923565f, 0.902781f, 0.879717f,
1.000000f, 0.999998f, 0.999966f, 0.999823f, 0.999435f, 0.998604f, 0.997084f, 0.994588f, 0.990810f, 0.985469f, 0.978302f, 0.969050f, 0.957516f, 0.943553f, 0.927085f, 0.908201f,
1.000000f, 0.999999f, 0.999977f, 0.999887f, 0.999639f, 0.999111f, 0.998133f, 0.996516f, 0.994047f, 0.990516f, 0.985714f, 0.979460f, 0.971538f, 0.961773f, 0.950012f, 0.936120f,
1.000000f, 0.999999f, 0.999987f, 0.999932f, 0.999781f, 0.999458f, 0.998865f, 0.997872f, 0.996341f, 0.994130f, 0.991100f, 0.987136f, 0.982102f, 0.975874f, 0.968306f, 0.959261f,
1.000000f, 0.995343f, 0.998834f, 0.999417f, 0.999534f, 0.999486f, 0.999351f, 0.999156f, 0.998917f, 0.998643f, 0.998341f, 0.998014f, 0.997667f, 0.997300f, 0.996916f, 0.996514f,
1.000000f, 0.998152f, 0.970350f, 0.926992f, 0.919810f, 0.926744f, 0.927339f, 0.917618f, 0.899592f, 0.876390f, 0.850767f, 0.824690f, 0.799364f, 0.775412f, 0.753093f, 0.732480f,
1.000000f, 0.999662f, 0.993854f, 0.972077f, 0.945526f, 0.931029f, 0.922665f, 0.910276f, 0.890044f, 0.863129f, 0.832392f, 0.800590f, 0.769662f, 0.740698f, 0.714184f, 0.690214f,
1.000000f, 0.999881f, 0.997877f, 0.988770f, 0.970473f, 0.951066f, 0.935189f, 0.918918f, 0.897606f, 0.870055f, 0.837934f, 0.803874f, 0.770140f, 0.738260f, 0.709006f, 0.682637f,
1.000000f, 0.999944f, 0.999017f, 0.994627f, 0.983760f, 0.967743f, 0.950500f, 0.932327f, 0.910645f, 0.883712f, 0.852009f, 0.817534f, 0.782559f, 0.748862f, 0.717541f, 0.689106f,
1.000000f, 0.999967f, 0.999451f, 0.997009f, 0.990405f, 0.978715f, 0.963443f, 0.945744f, 0.924775f, 0.899237f, 0.869030f, 0.835420f, 0.800394f, 0.765814f, 0.733053f, 0.702884f,
1.000000f, 0.999979f, 0.999652f, 0.998128f, 0.993877f, 0.985555f, 0.973154f, 0.957354f, 0.938058f, 0.914542f, 0.886497f, 0.854660f, 0.820578f, 0.786015f, 0.752477f, 0.720993f,
1.000000f, 0.999985f, 0.999760f, 0.998732f, 0.995835f, 0.989850f, 0.980146f, 0.966771f, 0.949739f, 0.928657f, 0.903252f, 0.873820f, 0.841491f, 0.807763f, 0.774164f, 0.741895f,
1.000000f, 0.999990f, 0.999826f, 0.999093f, 0.997027f, 0.992657f, 0.985168f, 0.974212f, 0.959656f, 0.941256f, 0.918706f, 0.892130f, 0.862190f, 0.830060f, 0.797147f, 0.764696f,
1.000000f, 0.999992f, 0.999870f, 0.999328f, 0.997815f, 0.994567f, 0.988825f, 0.980053f, 0.967938f, 0.952246f, 0.932681f, 0.909189f, 0.882118f, 0.852259f, 0.820769f, 0.788851f,
1.000000f, 0.999994f, 0.999903f, 0.999496f, 0.998369f, 0.995932f, 0.991547f, 0.984629f, 0.974796f, 0.961723f, 0.945138f, 0.924851f, 0.900967f, 0.873946f, 0.844593f, 0.813961f,
1.000000f, 0.999995f, 0.999928f, 0.999621f, 0.998775f, 0.996954f, 0.993626f, 0.988273f, 0.980454f, 0.969838f, 0.956104f, 0.939056f, 0.918565f, 0.894820f, 0.868295f, 0.839747f,
1.000000f, 0.999997f, 0.999945f, 0.999718f, 0.999092f, 0.997740f, 0.995253f, 0.991184f, 0.985131f, 0.976743f, 0.965717f, 0.951804f, 0.934809f, 0.914653f, 0.891571f, 0.865936f,
1.000000f, 0.999997f, 0.999960f, 0.999794f, 0.999339f, 0.998357f, 0.996540f, 0.993539f, 0.988990f, 0.982587f, 0.974059f, 0.963136f, 0.949594f, 0.933262f, 0.914088f, 0.892194f,
1.000000f, 0.999998f, 0.999971f, 0.999855f, 0.999537f, 0.998843f, 0.997560f, 0.995425f, 0.992140f, 0.987444f, 0.981109f, 0.972937f, 0.962686f, 0.950191f, 0.935263f, 0.917776f,
1.000000f, 0.999999f, 0.999980f, 0.999897f, 0.999669f, 0.999176f, 0.998257f, 0.996711f, 0.994312f, 0.990857f, 0.986147f, 0.980028f, 0.972349f, 0.962984f, 0.951747f, 0.938446f,
1.000000f, 0.995338f, 0.998838f, 0.999440f, 0.999586f, 0.999577f, 0.999490f, 0.999351f, 0.999175f, 0.998968f, 0.998736f, 0.998484f, 0.998214f, 0.997928f, 0.997626f, 0.997311f,
1.000000f, 0.998092f, 0.969422f, 0.924749f, 0.917886f, 0.926986f, 0.931290f, 0.926250f, 0.913085f, 0.894264f, 0.872124f, 0.848514f, 0.824720f, 0.801539f, 0.779408f, 0.758534f,
1.000000f, 0.999643f, 0.993497f, 0.970499f, 0.942854f, 0.929021f, 0.923442f, 0.915421f, 0.900249f, 0.878008f, 0.850911f, 0.821420f, 0.791524f, 0.762584f, 0.735343f, 0.710141f,
1.000000f, 0.999872f, 0.997720f, 0.987944f, 0.968504f, 0.948723f, 0.934249f, 0.921133f, 0.903975f, 0.880621f, 0.851861f, 0.819891f, 0.786954f, 0.754774f, 0.724418f, 0.696424f,
1.000000f, 0.999941f, 0.998942f, 0.994201f, 0.982545f, 0.965851f, 0.949003f, 0.932731f, 0.914054f, 0.890431f, 0.861560f, 0.828880f, 0.794502f, 0.760357f, 0.727794f, 0.697582f,
1.000000f, 0.999966f, 0.999415f, 0.996792f, 0.989702f, 0.977385f, 0.961984f, 0.945192f, 0.926129f, 0.902953f, 0.874868f, 0.842631f, 0.807991f, 0.772842f, 0.738772f, 0.706761f,
1.000000f, 0.999978f, 0.999635f, 0.998018f, 0.993472f, 0.984659f, 0.971907f, 0.956353f, 0.938049f, 0.915975f, 0.889331f, 0.858374f, 0.824386f, 0.789120f, 0.754188f, 0.720854f,
1.000000f, 0.999985f, 0.999751f, 0.998669f, 0.995592f, 0.989245f, 0.979123f, 0.965596f, 0.948856f, 0.928433f, 0.903711f, 0.874633f, 0.842050f, 0.807429f, 0.772336f, 0.738157f,
1.000000f, 0.999990f, 0.999820f, 0.999051f, 0.996866f, 0.992215f, 0.984304f, 0.972966f, 0.958226f, 0.939838f, 0.917349f, 0.890568f, 0.859995f, 0.826715f, 0.792153f, 0.757701f,
1.000000f, 0.999992f, 0.999867f, 0.999298f, 0.997691f, 0.994215f, 0.988063f, 0.978772f, 0.966154f, 0.949994f, 0.929930f, 0.905745f, 0.877620f, 0.846305f, 0.812937f, 0.778847f,
1.000000f, 0.999994f, 0.999899f, 0.999469f, 0.998258f, 0.995624f, 0.990838f, 0.983336f, 0.972760f, 0.958874f, 0.941336f, 0.919894f, 0.894559f, 0.865712f, 0.834213f, 0.801176f,
1.000000f, 0.999995f, 0.999922f, 0.999592f, 0.998670f, 0.996654f, 0.992943f, 0.986954f, 0.978268f, 0.966560f, 0.951539f, 0.932919f, 0.910556f, 0.884624f, 0.855596f, 0.824331f,
1.000000f, 0.999997f, 0.999939f, 0.999685f, 0.998980f, 0.997439f, 0.994566f, 0.989850f, 0.982832f, 0.973172f, 0.960564f, 0.944737f, 0.925481f, 0.902756f, 0.876764f, 0.848011f,
1.000000f, 0.999997f, 0.999953f, 0.999760f, 0.999222f, 0.998042f, 0.995847f, 0.992171f, 0.986606f, 0.978789f, 0.968444f, 0.955311f, 0.939175f, 0.919856f, 0.897362f, 0.871839f,
1.000000f, 0.999998f, 0.999965f, 0.999817f, 0.999412f, 0.998518f, 0.996844f, 0.994017f, 0.989671f, 0.983465f, 0.975149f, 0.964496f, 0.951323f, 0.935445f, 0.916701f, 0.895043f,
1.000000f, 0.999998f, 0.999973f, 0.999857f, 0.999535f, 0.998835f, 0.997511f, 0.995268f, 0.991772f, 0.986725f, 0.979890f, 0.971099f, 0.960227f, 0.947129f, 0.931637f, 0.913594f,
1.000000f, 0.995335f, 0.998841f, 0.999454f, 0.999617f, 0.999633f, 0.999575f, 0.999472f, 0.999335f, 0.999171f, 0.998985f, 0.998781f, 0.998561f, 0.998327f, 0.998080f, 0.997821f,
1.000000f, 0.998057f, 0.968893f, 0.923459f, 0.916722f, 0.927045f, 0.933608f, 0.931619f, 0.921879f, 0.906373f, 0.887096f, 0.865718f, 0.843494f, 0.821270f, 0.799603f, 0.778777f,
1.000000f, 0.999630f, 0.993270f, 0.969511f, 0.941118f, 0.927569f, 0.923625f, 0.918415f, 0.906730f, 0.888060f, 0.863984f, 0.836655f, 0.807988f, 0.779413f, 0.751852f, 0.725815f,
1.000000f, 0.999866f, 0.997609f, 0.987360f, 0.967111f, 0.946922f, 0.933184f, 0.922045f, 0.907742f, 0.887488f, 0.861456f, 0.831398f, 0.799368f, 0.767173f, 0.736051f, 0.706747f,
1.000000f, 0.999936f, 0.998884f, 0.993871f, 0.981590f, 0.964266f, 0.947497f, 0.932325f, 0.915646f, 0.894410f, 0.867724f, 0.836543f, 0.802774f, 0.768338f, 0.734726f, 0.702937f,
1.000000f, 0.999964f, 0.999381f, 0.996594f, 0.989068f, 0.976145f, 0.960438f, 0.944059f, 0.926151f, 0.904562f, 0.877990f, 0.846777f, 0.812393f, 0.776702f, 0.741371f, 0.707616f,
1.000000f, 0.999977f, 0.999616f, 0.997896f, 0.993058f, 0.983726f, 0.970492f, 0.954856f, 0.937005f, 0.915755f, 0.889934f, 0.859457f, 0.825319f, 0.789215f, 0.752845f, 0.717588f,
1.000000f, 0.999984f, 0.999738f, 0.998590f, 0.995306f, 0.988536f, 0.977873f, 0.963933f, 0.947112f, 0.926849f, 0.902275f, 0.873099f, 0.839926f, 0.804143f, 0.767380f, 0.731136f,
1.000000f, 0.999989f, 0.999812f, 0.998996f, 0.996656f, 0.991651f, 0.983203f, 0.971253f, 0.956000f, 0.937219f, 0.914295f, 0.886837f, 0.855208f, 0.820400f, 0.783895f, 0.747196f,
1.000000f, 0.999992f, 0.999859f, 0.999254f, 0.997520f, 0.993744f, 0.987064f, 0.977043f, 0.963617f, 0.946599f, 0.925582f, 0.900200f, 0.870532f, 0.837295f, 0.801669f, 0.765094f,
1.000000f, 0.999994f, 0.999891f, 0.999426f, 0.998108f, 0.995200f, 0.989896f, 0.981609f, 0.970024f, 0.954912f, 0.935970f, 0.912863f, 0.885512f, 0.854314f, 0.820197f, 0.784360f,
1.000000f, 0.999995f, 0.999914f, 0.999553f, 0.998523f, 0.996252f, 0.992040f, 0.985224f, 0.975379f, 0.962194f, 0.945386f, 0.924662f, 0.899836f, 0.871115f, 0.839063f, 0.804620f,
1.000000f, 0.999997f, 0.999931f, 0.999645f, 0.998833f, 0.997041f, 0.993672f, 0.988105f, 0.979841f, 0.968489f, 0.953793f, 0.935483f, 0.913352f, 0.887395f, 0.857937f, 0.825571f,
1.000000f, 0.999996f, 0.999946f, 0.999716f, 0.999075f, 0.997647f, 0.994947f, 0.990417f, 0.983533f, 0.973887f, 0.961201f, 0.945264f, 0.925853f, 0.902884f, 0.876431f, 0.846788f,
1.000000f, 0.999997f, 0.999957f, 0.999772f, 0.999256f, 0.998115f, 0.995939f, 0.992236f, 0.986522f, 0.978386f, 0.967529f, 0.953795f, 0.937007f, 0.917074f, 0.893916f, 0.867565f,
1.000000f, 0.999998f, 0.999963f, 0.999808f, 0.999376f, 0.998420f, 0.996599f, 0.993479f, 0.988597f, 0.981542f, 0.972038f, 0.959955f, 0.945226f, 0.927773f, 0.907511f, 0.884305f,
1.000000f, 0.995335f, 0.998844f, 0.999465f, 0.999639f, 0.999669f, 0.999632f, 0.999552f, 0.999442f, 0.999308f, 0.999153f, 0.998983f, 0.998797f, 0.998600f, 0.998390f, 0.998171f,
1.000000f, 0.998044f, 0.968696f, 0.922973f, 0.916296f, 0.927294f, 0.935224f, 0.935229f, 0.927867f, 0.914821f, 0.897813f, 0.878318f, 0.857513f, 0.836257f, 0.815119f, 0.794485f,
1.000000f, 0.999624f, 0.993156f, 0.969020f, 0.940235f, 0.926824f, 0.923789f, 0.920324f, 0.911013f, 0.894903f, 0.873185f, 0.847683f, 0.820176f, 0.792074f, 0.764380f, 0.737725f,
1.000000f, 0.999862f, 0.997543f, 0.987009f, 0.966250f, 0.945776f, 0.932390f, 0.922391f, 0.909912f, 0.891815f, 0.867819f, 0.839273f, 0.808062f, 0.775915f, 0.744179f, 0.713729f,
1.000000f, 0.999934f, 0.998840f, 0.993630f, 0.980895f, 0.963078f, 0.946202f, 0.931596f, 0.916075f, 0.896373f, 0.871175f, 0.841070f, 0.807718f, 0.772954f, 0.738364f, 0.705076f,
1.000000f, 0.999963f, 0.999351f, 0.996429f, 0.988543f, 0.975067f, 0.958965f, 0.942618f, 0.925261f, 0.904521f, 0.878830f, 0.848156f, 0.813742f, 0.777356f, 0.740733f, 0.705209f,
1.000000f, 0.999976f, 0.999593f, 0.997779f, 0.992648f, 0.982804f, 0.969002f, 0.953011f, 0.935135f, 0.914113f, 0.888522f, 0.857980f, 0.823355f, 0.786161f, 0.748188f, 0.710935f,
1.000000f, 0.999983f, 0.999725f, 0.998500f, 0.994983f, 0.987753f, 0.976443f, 0.961866f, 0.944536f, 0.923912f, 0.898955f, 0.869139f, 0.834944f, 0.797666f, 0.758979f, 0.720489f,
1.000000f, 0.999988f, 0.999800f, 0.998925f, 0.996398f, 0.990976f, 0.981847f, 0.969068f, 0.952950f, 0.933279f, 0.909384f, 0.880743f, 0.847536f, 0.810789f, 0.772008f, 0.732801f,
1.000000f, 0.999991f, 0.999848f, 0.999191f, 0.997295f, 0.993140f, 0.985784f, 0.974812f, 0.960228f, 0.941901f, 0.919390f, 0.892251f, 0.860487f, 0.824834f, 0.786546f, 0.747163f,
1.000000f, 0.999993f, 0.999881f, 0.999369f, 0.997902f, 0.994643f, 0.988678f, 0.979359f, 0.966399f, 0.949633f, 0.928731f, 0.903335f, 0.873372f, 0.839281f, 0.802053f, 0.763068f,
1.000000f, 0.999994f, 0.999905f, 0.999496f, 0.998329f, 0.995725f, 0.990852f, 0.982969f, 0.971599f, 0.956461f, 0.937293f, 0.913808f, 0.885894f, 0.853766f, 0.818146f, 0.780156f,
1.000000f, 0.999996f, 0.999921f, 0.999590f, 0.998646f, 0.996528f, 0.992521f, 0.985848f, 0.975946f, 0.962425f, 0.945039f, 0.923544f, 0.897845f, 0.868008f, 0.834488f, 0.798085f,
1.000000f, 0.999996f, 0.999934f, 0.999659f, 0.998882f, 0.997141f, 0.993801f, 0.988155f, 0.979569f, 0.967566f, 0.951911f, 0.932421f, 0.909015f, 0.881690f, 0.850699f, 0.816519f,
1.000000f, 0.999996f, 0.999945f, 0.999714f, 0.999066f, 0.997605f, 0.994799f, 0.989987f, 0.982516f, 0.971896f, 0.957849f, 0.940259f, 0.919094f, 0.894392f, 0.866221f, 0.834798f,
1.000000f, 0.999997f, 0.999952f, 0.999750f, 0.999181f, 0.997914f, 0.995465f, 0.991237f, 0.984588f, 0.974987f, 0.962151f, 0.946012f, 0.926653f, 0.904147f, 0.878556f, 0.849884f,
1.000000f, 0.995337f, 0.998849f, 0.999474f, 0.999655f, 0.999697f, 0.999673f, 0.999609f, 0.999518f, 0.999405f, 0.999274f, 0.999128f, 0.998968f, 0.998797f, 0.998615f, 0.998423f,
1.000000f, 0.998052f, 0.968822f, 0.923265f, 0.916662f, 0.927944f, 0.936637f, 0.937891f, 0.932151f, 0.920891f, 0.905625f, 0.887660f, 0.868061f, 0.847666f, 0.827052f, 0.806635f,
1.000000f, 0.999623f, 0.993153f, 0.969006f, 0.940211f, 0.926863f, 0.924254f, 0.921762f, 0.913922f, 0.899581f, 0.879602f, 0.855532f, 0.828968f, 0.801287f, 0.773504f, 0.746324f,
1.000000f, 0.999860f, 0.997516f, 0.986877f, 0.965924f, 0.945296f, 0.932018f, 0.922554f, 0.911097f, 0.894339f, 0.871706f, 0.844219f, 0.813562f, 0.781384f, 0.749046f, 0.717517f,
1.000000f, 0.999932f, 0.998811f, 0.993481f, 0.980459f, 0.962295f, 0.945210f, 0.930718f, 0.915703f, 0.896784f, 0.872406f, 0.842881f, 0.809626f, 0.774388f, 0.738759f, 0.703967f,
1.000000f, 0.999962f, 0.999327f, 0.996291f, 0.988107f, 0.974159f, 0.957580f, 0.940962f, 0.923592f, 0.903062f, 0.877585f, 0.846930f, 0.812107f, 0.774804f, 0.736746f, 0.699373f,
1.000000f, 0.999975f, 0.999571f, 0.997657f, 0.992255f, 0.981883f, 0.967421f, 0.950799f, 0.932444f, 0.911052f, 0.885074f, 0.853957f, 0.818370f, 0.779796f, 0.740007f, 0.700593f,
1.000000f, 0.999982f, 0.999706f, 0.998397f, 0.994632f, 0.986872f, 0.974779f, 0.959300f, 0.941070f, 0.919535f, 0.893583f, 0.862567f, 0.826849f, 0.787697f, 0.746802f, 0.705863f,
1.000000f, 0.999987f, 0.999782f, 0.998834f, 0.996072f, 0.990154f, 0.980185f, 0.966294f, 0.948893f, 0.927835f, 0.902369f, 0.871911f, 0.836607f, 0.797476f, 0.756062f, 0.714084f,
1.000000f, 0.999990f, 0.999833f, 0.999109f, 0.997003f, 0.992369f, 0.984152f, 0.971915f, 0.955755f, 0.935592f, 0.910961f, 0.881426f, 0.846974f, 0.808391f, 0.767037f, 0.724539f,
1.000000f, 0.999992f, 0.999867f, 0.999292f, 0.997631f, 0.993915f, 0.987083f, 0.976413f, 0.961637f, 0.942644f, 0.919132f, 0.890789f, 0.857552f, 0.819982f, 0.779213f, 0.736731f,
1.000000f, 0.999994f, 0.999891f, 0.999423f, 0.998071f, 0.995029f, 0.989302f, 0.980012f, 0.966642f, 0.948946f, 0.926737f, 0.899769f, 0.868025f, 0.831862f, 0.792195f, 0.750277f,
1.000000f, 0.999995f, 0.999908f, 0.999518f, 0.998395f, 0.995854f, 0.990995f, 0.982894f, 0.970873f, 0.954534f, 0.933692f, 0.908243f, 0.878166f, 0.843771f, 0.805670f, 0.764892f,
1.000000f, 0.999996f, 0.999922f, 0.999589f, 0.998635f, 0.996480f, 0.992312f, 0.985223f, 0.974419f, 0.959410f, 0.939975f, 0.916084f, 0.887813f, 0.855398f, 0.819314f, 0.780252f,
1.000000f, 0.999996f, 0.999932f, 0.999642f, 0.998819f, 0.996953f, 0.993329f, 0.987079f, 0.977358f, 0.963575f, 0.945473f, 0.923115f, 0.896667f, 0.866416f, 0.832654f, 0.795872f,
1.000000f, 0.999996f, 0.999938f, 0.999679f, 0.998940f, 0.997276f, 0.994034f, 0.988387f, 0.979485f, 0.966655f, 0.949608f, 0.928453f, 0.903518f, 0.875176f, 0.843709f, 0.809330f,
1.000000f, 0.995343f, 0.998855f, 0.999483f, 0.999669f, 0.999718f, 0.999704f, 0.999652f, 0.999575f, 0.999478f, 0.999364f, 0.999236f, 0.999096f, 0.998945f, 0.998784f, 0.998615f,
1.000000f, 0.998083f, 0.969303f, 0.924430f, 0.917931f, 0.929179f, 0.938138f, 0.940083f, 0.935376f, 0.925368f, 0.911393f, 0.894614f, 0.875999f, 0.856324f, 0.836157f, 0.815926f,
1.000000f, 0.999629f, 0.993257f, 0.969480f, 0.941061f, 0.927776f, 0.925202f, 0.923072f, 0.915997f, 0.902730f, 0.883901f, 0.860843f, 0.834978f, 0.807577f, 0.779658f, 0.751951f,
1.000000f, 0.999861f, 0.997527f, 0.986952f, 0.966093f, 0.945483f, 0.932121f, 0.922708f, 0.911589f, 0.895462f, 0.873549f, 0.846656f, 0.816239f, 0.783848f, 0.750829f, 0.718183f,
1.000000f, 0.999931f, 0.998797f, 0.993409f, 0.980244f, 0.961841f, 0.944467f, 0.929718f, 0.914624f, 0.895827f, 0.871621f, 0.842148f, 0.808628f, 0.772679f, 0.735883f, 0.699500f,
1.000000f, 0.999960f, 0.999304f, 0.996172f, 0.987729f, 0.973327f, 0.956177f, 0.938978f, 0.921091f, 0.900152f, 0.874277f, 0.843070f, 0.807425f, 0.768903f, 0.729218f, 0.689856f,
1.000000f, 0.999973f, 0.999548f, 0.997531f, 0.991825f, 0.980882f, 0.965598f, 0.948047f, 0.928751f, 0.906409f, 0.879409f, 0.847132f, 0.810118f, 0.769800f, 0.727940f, 0.686197f,
1.000000f, 0.999981f, 0.999682f, 0.998272f, 0.994204f, 0.985815f, 0.972740f, 0.956015f, 0.936399f, 0.913386f, 0.885808f, 0.852995f, 0.815241f, 0.773789f, 0.730378f, 0.686765f,
1.000000f, 0.999986f, 0.999761f, 0.998716f, 0.995668f, 0.989101f, 0.978044f, 0.962666f, 0.943491f, 0.920413f, 0.892719f, 0.859812f, 0.821845f, 0.779846f, 0.735462f, 0.690470f,
1.000000f, 0.999989f, 0.999813f, 0.998997f, 0.996616f, 0.991347f, 0.981992f, 0.968097f, 0.949806f, 0.927145f, 0.899708f, 0.867065f, 0.829307f, 0.787277f, 0.742452f, 0.696583f,
1.000000f, 0.999991f, 0.999849f, 0.999187f, 0.997264f, 0.992935f, 0.984960f, 0.972503f, 0.955315f, 0.933385f, 0.906506f, 0.874432f, 0.837230f, 0.795607f, 0.750846f, 0.704615f,
1.000000f, 0.999993f, 0.999872f, 0.999321f, 0.997721f, 0.994091f, 0.987221f, 0.976077f, 0.960090f, 0.939078f, 0.912949f, 0.881662f, 0.845301f, 0.804470f, 0.760276f, 0.714188f,
1.000000f, 0.999994f, 0.999890f, 0.999419f, 0.998059f, 0.994951f, 0.988977f, 0.978987f, 0.964177f, 0.944209f, 0.918995f, 0.888621f, 0.853316f, 0.813628f, 0.770455f, 0.725040f,
1.000000f, 0.999994f, 0.999903f, 0.999492f, 0.998310f, 0.995607f, 0.990346f, 0.981362f, 0.967689f, 0.948783f, 0.924566f, 0.895218f, 0.861122f, 0.822828f, 0.781114f, 0.736951f,
1.000000f, 0.999995f, 0.999914f, 0.999549f, 0.998501f, 0.996109f, 0.991426f, 0.983297f, 0.970650f, 0.952799f, 0.929588f, 0.901313f, 0.868512f, 0.831837f, 0.791942f, 0.749584f,
1.000000f, 0.999995f, 0.999921f, 0.999587f, 0.998635f, 0.996461f, 0.992195f, 0.984724f, 0.972915f, 0.955941f, 0.933578f, 0.906196f, 0.874554f, 0.839421f, 0.801478f, 0.761256f,
1.000000f, 0.995353f, 0.998865f, 0.999494f, 0.999683f, 0.999736f, 0.999729f, 0.999686f, 0.999620f, 0.999535f, 0.999435f, 0.999322f, 0.999197f, 0.999062f, 0.998918f, 0.998766f,
1.000000f, 0.998142f, 0.970240f, 0.926708f, 0.920346f, 0.931220f, 0.939975f, 0.942092f, 0.937929f, 0.928707f, 0.915627f, 0.899725f, 0.881865f, 0.862749f, 0.842926f, 0.822811f,
1.000000f, 0.999640f, 0.993481f, 0.970495f, 0.942871f, 0.929672f, 0.926767f, 0.924403f, 0.917472f, 0.904673f, 0.886466f, 0.863995f, 0.838527f, 0.811225f, 0.783058f, 0.754755f,
1.000000f, 0.999864f, 0.997569f, 0.987205f, 0.966716f, 0.946238f, 0.932608f, 0.922795f, 0.911423f, 0.895275f, 0.873498f, 0.846701f, 0.816172f, 0.783347f, 0.749489f, 0.715648f,
1.000000f, 0.999930f, 0.998788f, 0.993377f, 0.980152f, 0.961536f, 0.943727f, 0.928369f, 0.912666f, 0.893344f, 0.868722f, 0.838781f, 0.804584f, 0.767636f, 0.729484f, 0.691397f,
1.000000f, 0.999959f, 0.999279f, 0.996040f, 0.987304f, 0.972370f, 0.954439f, 0.936304f, 0.917405f, 0.895435f, 0.868538f, 0.836248f, 0.799330f, 0.759260f, 0.717727f, 0.676233f,
1.000000f, 0.999971f, 0.999519f, 0.997370f, 0.991285f, 0.979590f, 0.963201f, 0.944311f, 0.923528f, 0.899607f, 0.870990f, 0.836968f, 0.798051f, 0.755634f, 0.711449f, 0.667187f,
1.000000f, 0.999979f, 0.999652f, 0.998105f, 0.993635f, 0.984397f, 0.969980f, 0.951526f, 0.929938f, 0.904772f, 0.874915f, 0.839670f, 0.799368f, 0.755217f, 0.709017f, 0.662536f,
1.000000f, 0.999984f, 0.999732f, 0.998553f, 0.995112f, 0.987668f, 0.975125f, 0.957697f, 0.936069f, 0.910260f, 0.879610f, 0.843577f, 0.802361f, 0.757048f, 0.709369f, 0.661181f,
1.000000f, 0.999987f, 0.999785f, 0.998842f, 0.996080f, 0.989949f, 0.979048f, 0.962879f, 0.941712f, 0.915732f, 0.884654f, 0.848162f, 0.806442f, 0.760467f, 0.711831f, 0.662405f,
1.000000f, 0.999989f, 0.999821f, 0.999038f, 0.996754f, 0.991590f, 0.982053f, 0.967179f, 0.946783f, 0.920992f, 0.889804f, 0.853131f, 0.811229f, 0.764994f, 0.715888f, 0.665713f,
1.000000f, 0.999991f, 0.999847f, 0.999181f, 0.997236f, 0.992805f, 0.984396f, 0.970756f, 0.951286f, 0.925956f, 0.894889f, 0.858256f, 0.816447f, 0.770312f, 0.721200f, 0.670770f,
1.000000f, 0.999992f, 0.999864f, 0.999283f, 0.997594f, 0.993722f, 0.986241f, 0.973735f, 0.955274f, 0.930582f, 0.899822f, 0.863404f, 0.821902f, 0.776188f, 0.727504f, 0.677325f,
1.000000f, 0.999993f, 0.999880f, 0.999363f, 0.997868f, 0.994431f, 0.987713f, 0.976227f, 0.958784f, 0.934853f, 0.904567f, 0.868500f, 0.827467f, 0.782451f, 0.734612f, 0.685220f,
1.000000f, 0.999994f, 0.999891f, 0.999425f, 0.998078f, 0.994987f, 0.988897f, 0.978306f, 0.961859f, 0.938761f, 0.909049f, 0.873455f, 0.833026f, 0.788954f, 0.742359f, 0.694317f,
1.000000f, 0.999994f, 0.999899f, 0.999469f, 0.998230f, 0.995395f, 0.989794f, 0.979946f, 0.964372f, 0.942073f, 0.912956f, 0.877817f, 0.838022f, 0.794995f, 0.749934f, 0.703736f,
1.000000f, 0.995372f, 0.998882f, 0.999509f, 0.999698f, 0.999754f, 0.999751f, 0.999715f, 0.999657f, 0.999581f, 0.999491f, 0.999390f, 0.999278f, 0.999156f, 0.999026f, 0.998888f,
1.000000f, 0.998242f, 0.971833f, 0.930547f, 0.924331f, 0.934324f, 0.942304f, 0.944064f, 0.939950f, 0.931093f, 0.918552f, 0.903232f, 0.885894f, 0.867167f, 0.847559f, 0.827465f,
1.000000f, 0.999659f, 0.993827f, 0.972071f, 0.945685f, 0.932510f, 0.928824f, 0.925669f, 0.918261f, 0.905332f, 0.887252f, 0.864969f, 0.839592f, 0.812164f, 0.783606f, 0.754618f,
1.000000f, 0.999867f, 0.997633f, 0.987557f, 0.967567f, 0.947227f, 0.933086f, 0.922399f, 0.910177f, 0.893396f, 0.871192f, 0.844036f, 0.813046f, 0.779516f, 0.744671f, 0.709514f,
1.000000f, 0.999930f, 0.998771f, 0.993300f, 0.979919f, 0.960922f, 0.942369f, 0.925957f, 0.909076f, 0.888654f, 0.863025f, 0.832120f, 0.796861f, 0.758657f, 0.718960f, 0.679045f,
1.000000f, 0.999956f, 0.999239f, 0.995830f, 0.986625f, 0.970820f, 0.951661f, 0.932046f, 0.911534f, 0.887936f, 0.859439f, 0.825540f, 0.786932f, 0.745027f, 0.701449f, 0.657704f,
1.000000f, 0.999969f, 0.999473f, 0.997118f, 0.990453f, 0.977609f, 0.959545f, 0.938648f, 0.915693f, 0.889524f, 0.858630f, 0.822317f, 0.781060f, 0.736208f, 0.689492f, 0.642615f,
1.000000f, 0.999976f, 0.999606f, 0.997854f, 0.992781f, 0.982286f, 0.965882f, 0.944911f, 0.920520f, 0.892413f, 0.859550f, 0.821273f, 0.777916f, 0.730738f, 0.681511f, 0.632081f,
1.000000f, 0.999981f, 0.999687f, 0.998312f, 0.994284f, 0.985568f, 0.970883f, 0.950549f, 0.925506f, 0.896024f, 0.861574f, 0.821689f, 0.776670f, 0.727675f, 0.676486f, 0.625008f,
1.000000f, 0.999985f, 0.999743f, 0.998616f, 0.995303f, 0.987934f, 0.974828f, 0.955478f, 0.930373f, 0.899997f, 0.864294f, 0.823096f, 0.776766f, 0.726395f, 0.673719f, 0.620682f,
1.000000f, 0.999987f, 0.999781f, 0.998827f, 0.996025f, 0.989682f, 0.977961f, 0.959749f, 0.934996f, 0.904136f, 0.867474f, 0.825208f, 0.777828f, 0.726456f, 0.672745f, 0.618613f,
1.000000f, 0.999988f, 0.999810f, 0.998982f, 0.996552f, 0.991001f, 0.980464f, 0.963424f, 0.939294f, 0.908297f, 0.870947f, 0.827811f, 0.779621f, 0.727558f, 0.673225f, 0.618454f,
1.000000f, 0.999990f, 0.999830f, 0.999096f, 0.996952f, 0.992022f, 0.982488f, 0.966579f, 0.943252f, 0.912412f, 0.874629f, 0.830792f, 0.781979f, 0.729501f, 0.674937f, 0.619990f,
1.000000f, 0.999991f, 0.999846f, 0.999185f, 0.997261f, 0.992825f, 0.984141f, 0.969298f, 0.946884f, 0.916421f, 0.878440f, 0.834092f, 0.784810f, 0.732168f, 0.677746f, 0.623118f,
1.000000f, 0.999992f, 0.999858f, 0.999254f, 0.997503f, 0.993468f, 0.985501f, 0.971650f, 0.950197f, 0.920309f, 0.882351f, 0.837660f, 0.788084f, 0.735510f, 0.681629f, 0.627864f,
1.000000f, 0.999992f, 0.999868f, 0.999309f, 0.997692f, 0.993974f, 0.986604f, 0.973631f, 0.953141f, 0.923966f, 0.886221f, 0.841379f, 0.791669f, 0.739403f, 0.686462f, 0.634174f,
1.000000f, 0.995413f, 0.998913f, 0.999532f, 0.999717f, 0.999772f, 0.999771f, 0.999739f, 0.999687f, 0.999618f, 0.999537f, 0.999445f, 0.999344f, 0.999233f, 0.999114f, 0.998988f,
1.000000f, 0.998400f, 0.974429f, 0.936758f, 0.930501f, 0.938746f, 0.945098f, 0.945820f, 0.941234f, 0.932309f, 0.919951f, 0.904932f, 0.887890f, 0.869377f, 0.849842f, 0.829658f,
1.000000f, 0.999681f, 0.994258f, 0.974035f, 0.949106f, 0.935700f, 0.930671f, 0.926035f, 0.917515f, 0.903922f, 0.885496f, 0.863037f, 0.837465f, 0.809716f, 0.780605f, 0.750826f,
1.000000f, 0.999867f, 0.997657f, 0.987721f, 0.967895f, 0.947244f, 0.932082f, 0.919954f, 0.906332f, 0.888399f, 0.865291f, 0.837388f, 0.805642f, 0.771219f, 0.735246f, 0.698702f,
1.000000f, 0.999925f, 0.998707f, 0.992961f, 0.978875f, 0.958705f, 0.938638f, 0.920490f, 0.901846f, 0.879769f, 0.852684f, 0.820426f, 0.783826f, 0.744171f, 0.702835f, 0.661064f,
1.000000f, 0.999951f, 0.999157f, 0.995375f, 0.985160f, 0.967563f, 0.946128f, 0.924097f, 0.901206f, 0.875334f, 0.844707f, 0.808799f, 0.768233f, 0.724320f, 0.678633f, 0.632651f,
1.000000f, 0.999965f, 0.999391f, 0.996667f, 0.988943f, 0.974050f, 0.953115f, 0.929017f, 0.902852f, 0.873624f, 0.839810f, 0.800723f, 0.756819f, 0.709381f, 0.660104f, 0.610670f,
1.000000f, 0.999972f, 0.999530f, 0.997437f, 0.991362f, 0.978783f, 0.959185f, 0.934340f, 0.905871f, 0.873756f, 0.837055f, 0.795148f, 0.748369f, 0.697964f, 0.645713f, 0.593434f,
1.000000f, 0.999977f, 0.999618f, 0.997931f, 0.992983f, 0.982271f, 0.964282f, 0.939592f, 0.909677f, 0.875207f, 0.835895f, 0.791409f, 0.742095f, 0.689182f, 0.634462f, 0.579861f,
1.000000f, 0.999981f, 0.999679f, 0.998269f, 0.994120f, 0.984880f, 0.968507f, 0.944532f, 0.913892f, 0.877580f, 0.835951f, 0.789083f, 0.737498f, 0.682417f, 0.625664f, 0.569212f,
1.000000f, 0.999983f, 0.999722f, 0.998511f, 0.994947f, 0.986867f, 0.971985f, 0.949030f, 0.918252f, 0.880613f, 0.836955f, 0.787880f, 0.734206f, 0.677265f, 0.618859f, 0.560978f,
1.000000f, 0.999985f, 0.999755f, 0.998689f, 0.995564f, 0.988405f, 0.974849f, 0.953070f, 0.922585f, 0.884086f, 0.838719f, 0.787615f, 0.732013f, 0.673422f, 0.613712f, 0.554814f,
1.000000f, 0.999987f, 0.999780f, 0.998827f, 0.996034f, 0.989616f, 0.977223f, 0.956653f, 0.926786f, 0.887858f, 0.841111f, 0.788160f, 0.730739f, 0.670705f, 0.610002f, 0.550491f,
1.000000f, 0.999988f, 0.999799f, 0.998932f, 0.996407f, 0.990586f, 0.979197f, 0.959827f, 0.930789f, 0.891800f, 0.844011f, 0.789411f, 0.730324f, 0.669025f, 0.607615f, 0.547908f,
1.000000f, 0.999989f, 0.999814f, 0.999017f, 0.996706f, 0.991378f, 0.980863f, 0.962638f, 0.934581f, 0.895866f, 0.847385f, 0.791390f, 0.730794f, 0.668422f, 0.606630f, 0.547188f,
1.000000f, 0.999989f, 0.999827f, 0.999089f, 0.996952f, 0.992038f, 0.982292f, 0.965160f, 0.938212f, 0.900086f, 0.851302f, 0.794258f, 0.732412f, 0.669246f, 0.607505f, 0.548948f,
1.000000f, 0.995527f, 0.998988f, 0.999578f, 0.999746f, 0.999792f, 0.999788f, 0.999757f, 0.999709f, 0.999646f, 0.999572f, 0.999487f, 0.999393f, 0.999292f, 0.999182f, 0.999065f,
1.000000f, 0.998630f, 0.978259f, 0.945594f, 0.938363f, 0.943208f, 0.946704f, 0.945624f, 0.940084f, 0.930762f, 0.918345f, 0.903424f, 0.886518f, 0.868076f, 0.848494f, 0.828108f,
1.000000f, 0.999686f, 0.994379f, 0.974597f, 0.949667f, 0.934937f, 0.927853f, 0.921320f, 0.911428f, 0.896989f, 0.878093f, 0.855342f, 0.829503f, 0.801381f, 0.771709f, 0.741121f,
1.000000f, 0.999854f, 0.997413f, 0.986433f, 0.964455f, 0.941275f, 0.923775f, 0.909649f, 0.894422f, 0.875277f, 0.851284f, 0.822663f, 0.790233f, 0.755013f, 0.718042f, 0.680244f,
1.000000f, 0.999911f, 0.998460f, 0.991601f, 0.974763f, 0.950692f, 0.926863f, 0.905686f, 0.884687f, 0.860771f, 0.832199f, 0.798686f, 0.760917f, 0.720034f, 0.677317f, 0.633973f,
1.000000f, 0.999939f, 0.998951f, 0.994222f, 0.981435f, 0.959489f, 0.933079f, 0.906577f, 0.880075f, 0.851316f, 0.818348f, 0.780447f, 0.738092f, 0.692475f, 0.645047f, 0.597247f,
1.000000f, 0.999955f, 0.999220f, 0.995720f, 0.985790f, 0.966702f, 0.940181f, 0.910358f, 0.879136f, 0.845680f, 0.808362f, 0.766337f, 0.719885f, 0.670150f, 0.618757f, 0.567295f,
1.000000f, 0.999964f, 0.999386f, 0.996651f, 0.988710f, 0.972315f, 0.947035f, 0.915627f, 0.880780f, 0.842993f, 0.801433f, 0.755396f, 0.705118f, 0.651733f, 0.596910f, 0.542404f,
1.000000f, 0.999970f, 0.999497f, 0.997273f, 0.990734f, 0.976637f, 0.953160f, 0.921481f, 0.884126f, 0.842575f, 0.796931f, 0.746983f, 0.693063f, 0.636338f, 0.578514f, 0.521455f,
1.000000f, 0.999975f, 0.999573f, 0.997701f, 0.992188f, 0.979945f, 0.958416f, 0.927337f, 0.888509f, 0.843869f, 0.794433f, 0.740656f, 0.683196f, 0.623342f, 0.562868f, 0.503667f,
1.000000f, 0.999978f, 0.999630f, 0.998013f, 0.993256f, 0.982510f, 0.962846f, 0.932888f, 0.893436f, 0.846421f, 0.793557f, 0.736072f, 0.675142f, 0.612325f, 0.549463f, 0.488487f,
1.000000f, 0.999980f, 0.999672f, 0.998245f, 0.994061f, 0.984514f, 0.966548f, 0.937969f, 0.898572f, 0.849868f, 0.794002f, 0.732975f, 0.668639f, 0.602965f, 0.537948f, 0.475509f,
1.000000f, 0.999982f, 0.999704f, 0.998422f, 0.994681f, 0.986106f, 0.969639f, 0.942542f, 0.903685f, 0.853930f, 0.795521f, 0.731167f, 0.663513f, 0.595046f, 0.528062f, 0.464468f,
1.000000f, 0.999983f, 0.999729f, 0.998565f, 0.995174f, 0.987383f, 0.972219f, 0.946621f, 0.908635f, 0.858379f, 0.797926f, 0.730503f, 0.659617f, 0.588452f, 0.519655f, 0.455184f,
1.000000f, 0.999985f, 0.999750f, 0.998678f, 0.995570f, 0.988433f, 0.974409f, 0.950253f, 0.913383f, 0.863096f, 0.801085f, 0.730928f, 0.656937f, 0.583162f, 0.512731f, 0.447692f,
1.000000f, 0.999986f, 0.999768f, 0.998774f, 0.995908f, 0.989329f, 0.976331f, 0.953588f, 0.918034f, 0.868186f, 0.805172f, 0.732710f, 0.655891f, 0.579707f, 0.507923f, 0.442761f,
1.000000f, 0.996312f, 0.999240f, 0.999651f, 0.999760f, 0.999787f, 0.999779f, 0.999749f, 0.999703f, 0.999645f, 0.999575f, 0.999495f, 0.999407f, 0.999309f, 0.999204f, 0.999092f,
1.000000f, 0.998301f, 0.972928f, 0.931704f, 0.920748f, 0.925333f, 0.930051f, 0.930602f, 0.926625f, 0.918661f, 0.907363f, 0.893324f, 0.877064f, 0.859040f, 0.839650f, 0.819231f,
1.000000f, 0.999525f, 0.991428f, 0.961144f, 0.923725f, 0.903320f, 0.896105f, 0.891629f, 0.884225f, 0.872051f, 0.855024f, 0.833730f, 0.808951f, 0.781485f, 0.752085f, 0.721414f,
1.000000f, 0.999774f, 0.995997f, 0.978904f, 0.944981f, 0.910598f, 0.887366f, 0.871985f, 0.857707f, 0.840241f, 0.817970f, 0.790838f, 0.759542f, 0.725052f, 0.688400f, 0.650532f,
1.000000f, 0.999866f, 0.997668f, 0.987231f, 0.961720f, 0.926013f, 0.892610f, 0.866048f, 0.842981f, 0.818867f, 0.790927f, 0.758281f, 0.721314f, 0.681005f, 0.638561f, 0.595155f,
1.000000f, 0.999910f, 0.998450f, 0.991465f, 0.972609f, 0.940671f, 0.903484f, 0.868578f, 0.836857f, 0.805400f, 0.771279f, 0.733075f, 0.690796f, 0.645329f, 0.597985f, 0.550096f,
1.000000f, 0.999934f, 0.998877f, 0.993833f, 0.979565f, 0.952395f, 0.915451f, 0.875635f, 0.836658f, 0.797939f, 0.757376f, 0.713464f, 0.665999f, 0.615761f, 0.564091f, 0.512452f,
1.000000f, 0.999949f, 0.999134f, 0.995276f, 0.984114f, 0.961248f, 0.926533f, 0.884641f, 0.840287f, 0.794994f, 0.747999f, 0.698280f, 0.645647f, 0.590843f, 0.535249f, 0.480393f,
1.000000f, 0.999958f, 0.999301f, 0.996212f, 0.987189f, 0.967857f, 0.936066f, 0.894071f, 0.846193f, 0.795328f, 0.742217f, 0.686680f, 0.628856f, 0.569615f, 0.510364f, 0.452686f,
1.000000f, 0.999965f, 0.999416f, 0.996852f, 0.989347f, 0.972802f, 0.944007f, 0.903118f, 0.853287f, 0.797992f, 0.739251f, 0.678005f, 0.614995f, 0.551366f, 0.488656f, 0.428473f,
1.000000f, 0.999970f, 0.999498f, 0.997309f, 0.990906f, 0.976548f, 0.950521f, 0.911388f, 0.860855f, 0.802240f, 0.738510f, 0.671750f, 0.603568f, 0.535592f, 0.469551f, 0.407102f,
1.000000f, 0.999973f, 0.999559f, 0.997645f, 0.992065f, 0.979424f, 0.955846f, 0.918761f, 0.868427f, 0.807506f, 0.739482f, 0.667504f, 0.594210f, 0.521887f, 0.452611f, 0.388102f,
1.000000f, 0.999976f, 0.999605f, 0.997901f, 0.992948f, 0.981668f, 0.960198f, 0.925230f, 0.875721f, 0.813375f, 0.741762f, 0.664925f, 0.586603f, 0.509959f, 0.437510f, 0.371096f,
1.000000f, 0.999978f, 0.999641f, 0.998100f, 0.993634f, 0.983446f, 0.963777f, 0.930872f, 0.882581f, 0.819548f, 0.745028f, 0.663733f, 0.580515f, 0.499559f, 0.423985f, 0.355802f,
1.000000f, 0.999980f, 0.999669f, 0.998256f, 0.994180f, 0.984875f, 0.966740f, 0.935768f, 0.888948f, 0.825804f, 0.749026f, 0.663698f, 0.575750f, 0.490506f, 0.411849f, 0.342017f,
1.000000f, 0.999981f, 0.999693f, 0.998386f, 0.994628f, 0.986052f, 0.969236f, 0.940057f, 0.894841f, 0.832060f, 0.753620f, 0.664714f, 0.572245f, 0.482769f, 0.401059f, 0.329698f
};
static const float table_ggx_glass_Eavg[256] = {
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 0.999948f, 0.999526f, 0.998250f, 0.995368f, 0.990153f, 0.982226f, 0.971590f, 0.958500f, 0.943359f, 0.926629f, 0.908785f, 0.890266f, 0.871452f, 0.852674f, 0.834183f,
1.000000f, 0.999940f, 0.999462f, 0.998212f, 0.995774f, 0.991512f, 0.984795f, 0.975285f, 0.963001f, 0.948259f, 0.931521f, 0.913309f, 0.894118f, 0.874394f, 0.854521f, 0.834797f,
1.000000f, 0.999936f, 0.999404f, 0.998052f, 0.995642f, 0.991777f, 0.985879f, 0.977416f, 0.966120f, 0.952052f, 0.935530f, 0.917035f, 0.897098f, 0.876222f, 0.854858f, 0.833395f,
1.000000f, 0.999933f, 0.999357f, 0.997885f, 0.995352f, 0.991530f, 0.985983f, 0.978146f, 0.967570f, 0.954055f, 0.937708f, 0.918892f, 0.898089f, 0.875842f, 0.852684f, 0.829081f,
1.000000f, 0.999930f, 0.999320f, 0.997734f, 0.995026f, 0.991065f, 0.985531f, 0.977907f, 0.967633f, 0.954330f, 0.937894f, 0.918515f, 0.896607f, 0.872718f, 0.847450f, 0.821371f,
1.000000f, 0.999928f, 0.999290f, 0.997605f, 0.994707f, 0.990512f, 0.984770f, 0.977000f, 0.966604f, 0.953075f, 0.936122f, 0.915787f, 0.892406f, 0.866527f, 0.838798f, 0.809912f,
1.000000f, 0.999926f, 0.999266f, 0.997495f, 0.994409f, 0.989914f, 0.983790f, 0.975569f, 0.964631f, 0.950373f, 0.932381f, 0.910592f, 0.885253f, 0.856934f, 0.826371f, 0.794380f,
1.000000f, 0.999925f, 0.999248f, 0.997401f, 0.994124f, 0.989277f, 0.982606f, 0.973644f, 0.961719f, 0.946182f, 0.926552f, 0.902670f, 0.874805f, 0.843553f, 0.809751f, 0.774356f,
1.000000f, 0.999925f, 0.999234f, 0.997319f, 0.993845f, 0.988576f, 0.981182f, 0.971131f, 0.957731f, 0.940281f, 0.918293f, 0.891626f, 0.860559f, 0.825811f, 0.788362f, 0.749315f,
1.000000f, 0.999924f, 0.999223f, 0.997242f, 0.993540f, 0.987743f, 0.979384f, 0.967830f, 0.952347f, 0.932247f, 0.907072f, 0.876767f, 0.841769f, 0.802929f, 0.761410f, 0.718503f,
1.000000f, 0.999924f, 0.999213f, 0.997156f, 0.993169f, 0.986668f, 0.976990f, 0.963370f, 0.945041f, 0.921363f, 0.892008f, 0.857117f, 0.817340f, 0.773777f, 0.727800f, 0.680887f,
1.000000f, 0.999924f, 0.999202f, 0.997042f, 0.992642f, 0.985137f, 0.973602f, 0.957122f, 0.934914f, 0.906478f, 0.871730f, 0.831125f, 0.785646f, 0.736704f, 0.685926f, 0.634955f,
1.000000f, 0.999924f, 0.999184f, 0.996841f, 0.991769f, 0.982715f, 0.968441f, 0.947900f, 0.920380f, 0.885624f, 0.843955f, 0.796294f, 0.744081f, 0.689112f, 0.633285f, 0.578354f,
1.000000f, 0.999923f, 0.999128f, 0.996370f, 0.990004f, 0.978288f, 0.959700f, 0.933154f, 0.898161f, 0.854912f, 0.804326f, 0.747966f, 0.687872f, 0.626278f, 0.565335f, 0.506855f,
1.000000f, 0.999914f, 0.998848f, 0.994908f, 0.985894f, 0.969773f, 0.944970f, 0.910567f, 0.866457f, 0.813420f, 0.753069f, 0.687695f, 0.619929f, 0.552409f, 0.487430f, 0.426737f
};
static const float table_ggx_glass_inv_E[4096] = {
0.999985f, 1.000000f, 0.999989f, 0.999990f, 1.000000f, 0.999999f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 0.995082f, 0.997750f, 0.996814f, 0.994756f, 0.991983f, 0.988694f, 0.985008f, 0.980991f, 0.976680f, 0.972098f, 0.967263f, 0.962191f, 0.956897f, 0.951393f, 0.945694f,
1.000000f, 0.997327f, 0.950645f, 0.832222f, 0.702110f, 0.601791f, 0.544343f, 0.516691f, 0.504458f, 0.499346f, 0.497379f, 0.496755f, 0.496683f, 0.496802f, 0.496978f, 0.497139f,
1.000000f, 0.996432f, 0.971516f, 0.904908f, 0.818245f, 0.748255f, 0.698217f, 0.661132f, 0.632581f, 0.610204f, 0.592497f, 0.578360f, 0.566979f, 0.557720f, 0.550120f, 0.543824f,
1.000000f, 0.999653f, 0.994103f, 0.970001f, 0.920214f, 0.860776f, 0.807060f, 0.761582f, 0.722953f, 0.690200f, 0.662685f, 0.639760f, 0.620730f, 0.604930f, 0.591761f, 0.580730f,
1.000000f, 0.999842f, 0.997455f, 0.987479f, 0.964275f, 0.927927f, 0.884581f, 0.840264f, 0.798180f, 0.759801f, 0.725804f, 0.696324f, 0.671106f, 0.649700f, 0.631572f, 0.616216f,
1.000000f, 0.999929f, 0.998864f, 0.994331f, 0.982910f, 0.962055f, 0.932008f, 0.895627f, 0.856527f, 0.817676f, 0.781038f, 0.747745f, 0.718231f, 0.692480f, 0.670225f, 0.651075f,
1.000000f, 0.999961f, 0.999376f, 0.996863f, 0.990329f, 0.977586f, 0.957377f, 0.930096f, 0.897609f, 0.862462f, 0.826970f, 0.792904f, 0.761375f, 0.732918f, 0.707657f, 0.685460f,
1.000000f, 0.999976f, 0.999613f, 0.998053f, 0.993938f, 0.985660f, 0.971838f, 0.951879f, 0.926313f, 0.896583f, 0.864557f, 0.832070f, 0.800565f, 0.771014f, 0.743952f, 0.719567f,
1.000000f, 0.999984f, 0.999745f, 0.998715f, 0.995974f, 0.990366f, 0.980729f, 0.966212f, 0.946629f, 0.922522f, 0.895070f, 0.865716f, 0.835888f, 0.806747f, 0.779117f, 0.753489f,
1.000000f, 0.999989f, 0.999826f, 0.999123f, 0.997243f, 0.993362f, 0.986560f, 0.976040f, 0.961305f, 0.942373f, 0.919782f, 0.894446f, 0.867512f, 0.840089f, 0.813118f, 0.787284f,
1.000000f, 0.999993f, 0.999881f, 0.999395f, 0.998094f, 0.995389f, 0.990595f, 0.983039f, 0.972175f, 0.957736f, 0.939825f, 0.918897f, 0.895690f, 0.871077f, 0.845921f, 0.820980f,
1.000000f, 0.999995f, 0.999918f, 0.999585f, 0.998693f, 0.996832f, 0.993503f, 0.988186f, 0.980393f, 0.969766f, 0.956157f, 0.939679f, 0.920694f, 0.899742f, 0.877484f, 0.854586f,
1.000000f, 0.999997f, 0.999946f, 0.999726f, 0.999136f, 0.997899f, 0.995672f, 0.992082f, 0.986739f, 0.979309f, 0.969547f, 0.957358f, 0.942813f, 0.926153f, 0.907762f, 0.888097f,
1.000000f, 0.999998f, 0.999967f, 0.999832f, 0.999469f, 0.998707f, 0.997331f, 0.995094f, 0.991728f, 0.986971f, 0.980592f, 0.972409f, 0.962344f, 0.950403f, 0.936705f, 0.921469f,
1.000000f, 0.999999f, 0.999983f, 0.999915f, 0.999727f, 0.999335f, 0.998625f, 0.997464f, 0.995701f, 0.993179f, 0.989726f, 0.985207f, 0.979490f, 0.972486f, 0.964145f, 0.954484f,
1.000000f, 1.000000f, 0.999994f, 0.999967f, 0.999894f, 0.999741f, 0.999464f, 0.999009f, 0.998309f, 0.997296f, 0.995883f, 0.993986f, 0.991504f, 0.988339f, 0.984390f, 0.979542f,
1.000000f, 0.995236f, 0.998550f, 0.998801f, 0.998428f, 0.997742f, 0.996831f, 0.995743f, 0.994509f, 0.993153f, 0.991690f, 0.990130f, 0.988479f, 0.986742f, 0.984923f, 0.983024f,
1.000000f, 0.997491f, 0.958825f, 0.887405f, 0.836169f, 0.777014f, 0.700137f, 0.619723f, 0.550159f, 0.497933f, 0.462916f, 0.441865f, 0.430862f, 0.426506f, 0.426279f, 0.428417f,
1.000000f, 0.999387f, 0.987949f, 0.938920f, 0.854742f, 0.761659f, 0.675893f, 0.609056f, 0.563787f, 0.535678f, 0.518945f, 0.509098f, 0.503253f, 0.499699f, 0.497454f, 0.495959f,
1.000000f, 0.999697f, 0.992974f, 0.956997f, 0.880103f, 0.793559f, 0.724151f, 0.674443f, 0.639020f, 0.613009f, 0.593289f, 0.577939f, 0.565706f, 0.555794f, 0.547620f, 0.540809f,
1.000000f, 0.998971f, 0.990531f, 0.966765f, 0.920386f, 0.858725f, 0.798945f, 0.749892f, 0.711318f, 0.680491f, 0.655226f, 0.634142f, 0.616388f, 0.601357f, 0.588586f, 0.577688f,
1.000000f, 0.999848f, 0.997453f, 0.986597f, 0.958949f, 0.913663f, 0.861319f, 0.812788f, 0.771829f, 0.737675f, 0.708689f, 0.683692f, 0.661970f, 0.643061f, 0.626615f, 0.612317f,
1.000000f, 0.999918f, 0.998627f, 0.992720f, 0.976730f, 0.947034f, 0.906966f, 0.864277f, 0.824492f, 0.789204f, 0.758048f, 0.730349f, 0.705627f, 0.683579f, 0.663985f, 0.646642f,
1.000000f, 0.999947f, 0.999111f, 0.995378f, 0.985462f, 0.966521f, 0.938604f, 0.905036f, 0.869938f, 0.836001f, 0.804272f, 0.774971f, 0.748071f, 0.723512f, 0.701250f, 0.681195f,
1.000000f, 0.999965f, 0.999442f, 0.997183f, 0.991249f, 0.979598f, 0.961119f, 0.936455f, 0.907646f, 0.877051f, 0.846437f, 0.816822f, 0.788744f, 0.762490f, 0.738197f, 0.715942f,
1.000000f, 0.999979f, 0.999660f, 0.998288f, 0.994651f, 0.987309f, 0.975057f, 0.957452f, 0.935116f, 0.909384f, 0.881821f, 0.853716f, 0.826017f, 0.799342f, 0.774067f, 0.750429f,
1.000000f, 0.999987f, 0.999784f, 0.998907f, 0.996567f, 0.991766f, 0.983508f, 0.971084f, 0.954354f, 0.933827f, 0.910448f, 0.885334f, 0.859505f, 0.833742f, 0.808627f, 0.784554f,
1.000000f, 0.999992f, 0.999858f, 0.999280f, 0.997733f, 0.994535f, 0.988921f, 0.980212f, 0.967995f, 0.952272f, 0.933425f, 0.912153f, 0.889282f, 0.865590f, 0.841742f, 0.818257f,
1.000000f, 0.999995f, 0.999906f, 0.999523f, 0.998498f, 0.996361f, 0.992567f, 0.986552f, 0.977881f, 0.966282f, 0.951793f, 0.934713f, 0.915529f, 0.894853f, 0.873307f, 0.851407f,
1.000000f, 0.999996f, 0.999940f, 0.999690f, 0.999024f, 0.997628f, 0.995121f, 0.991104f, 0.985173f, 0.977015f, 0.966461f, 0.953524f, 0.938375f, 0.921364f, 0.902945f, 0.883553f,
1.000000f, 0.999998f, 0.999962f, 0.999809f, 0.999389f, 0.998514f, 0.996933f, 0.994364f, 0.990509f, 0.985082f, 0.977837f, 0.968625f, 0.957380f, 0.944176f, 0.929178f, 0.912684f,
1.000000f, 0.999999f, 0.999973f, 0.999862f, 0.999565f, 0.998939f, 0.997802f, 0.995933f, 0.993080f, 0.988962f, 0.983276f, 0.975719f, 0.965982f, 0.953785f, 0.938866f, 0.921038f,
1.000000f, 0.995264f, 0.998700f, 0.999181f, 0.999146f, 0.998899f, 0.998518f, 0.998034f, 0.997464f, 0.996820f, 0.996113f, 0.995349f, 0.994536f, 0.993675f, 0.992770f, 0.991822f,
1.000000f, 0.997506f, 0.959780f, 0.895886f, 0.867758f, 0.847192f, 0.811951f, 0.761560f, 0.702769f, 0.642860f, 0.587308f, 0.539284f, 0.500040f, 0.469478f, 0.446760f, 0.430697f,
1.000000f, 0.999403f, 0.988921f, 0.947698f, 0.887836f, 0.831693f, 0.772965f, 0.707226f, 0.641001f, 0.582776f, 0.537128f, 0.504336f, 0.482382f, 0.468571f, 0.460416f, 0.456006f,
1.000000f, 0.999734f, 0.994985f, 0.971627f, 0.918352f, 0.846555f, 0.770872f, 0.699786f, 0.639815f, 0.593898f, 0.561036f, 0.538362f, 0.522894f, 0.512265f, 0.504808f, 0.499436f,
1.000000f, 0.999845f, 0.996884f, 0.980556f, 0.935434f, 0.863605f, 0.786812f, 0.721647f, 0.671750f, 0.634636f, 0.606898f, 0.585793f, 0.569400f, 0.556404f, 0.545880f, 0.537246f,
1.000000f, 0.999883f, 0.997078f, 0.981152f, 0.942190f, 0.884389f, 0.821505f, 0.765319f, 0.719739f, 0.683723f, 0.655004f, 0.631650f, 0.612346f, 0.596152f, 0.582440f, 0.570744f,
1.000000f, 0.999708f, 0.995826f, 0.983677f, 0.958470f, 0.917402f, 0.865810f, 0.813738f, 0.767950f, 0.730061f, 0.698996f, 0.673189f, 0.651349f, 0.632596f, 0.616345f, 0.602177f,
1.000000f, 0.999917f, 0.998624f, 0.992763f, 0.976951f, 0.946967f, 0.904504f, 0.857014f, 0.811931f, 0.772830f, 0.739955f, 0.712217f, 0.688432f, 0.667676f, 0.649364f, 0.633098f,
1.000000f, 0.999950f, 0.999175f, 0.995639f, 0.985685f, 0.965189f, 0.932959f, 0.892918f, 0.851405f, 0.812999f, 0.779369f, 0.750289f, 0.724925f, 0.702481f, 0.682374f, 0.664235f,
1.000000f, 0.999965f, 0.999425f, 0.996976f, 0.990134f, 0.975876f, 0.952425f, 0.921070f, 0.885697f, 0.850344f, 0.817472f, 0.787847f, 0.761314f, 0.737404f, 0.715685f, 0.695837f,
1.000000f, 0.999974f, 0.999576f, 0.997806f, 0.992983f, 0.983078f, 0.966551f, 0.943335f, 0.915131f, 0.884541f, 0.853930f, 0.824734f, 0.797553f, 0.772445f, 0.749281f, 0.727863f,
1.000000f, 0.999983f, 0.999708f, 0.998519f, 0.995334f, 0.988826f, 0.977711f, 0.961295f, 0.939903f, 0.914764f, 0.887583f, 0.859907f, 0.832855f, 0.807035f, 0.782699f, 0.759885f,
1.000000f, 0.999988f, 0.999811f, 0.999042f, 0.996990f, 0.992740f, 0.985312f, 0.973911f, 0.958186f, 0.938466f, 0.915581f, 0.890711f, 0.864992f, 0.839356f, 0.814445f, 0.790603f,
1.000000f, 0.999993f, 0.999876f, 0.999372f, 0.998020f, 0.995197f, 0.990179f, 0.982272f, 0.970926f, 0.955919f, 0.937441f, 0.916057f, 0.892562f, 0.867872f, 0.842769f, 0.817881f,
1.000000f, 0.999995f, 0.999915f, 0.999566f, 0.998632f, 0.996669f, 0.993140f, 0.987456f, 0.979025f, 0.967403f, 0.952286f, 0.933661f, 0.911774f, 0.887060f, 0.860168f, 0.831767f,
1.000000f, 0.999996f, 0.999937f, 0.999677f, 0.998980f, 0.997510f, 0.994842f, 0.990476f, 0.983850f, 0.974367f, 0.961453f, 0.944585f, 0.923348f, 0.897484f, 0.866932f, 0.831849f,
1.000000f, 0.995274f, 0.998753f, 0.999314f, 0.999400f, 0.999312f, 0.999128f, 0.998872f, 0.998561f, 0.998199f, 0.997795f, 0.997353f, 0.996877f, 0.996371f, 0.995835f, 0.995272f,
1.000000f, 0.997511f, 0.960071f, 0.898620f, 0.878659f, 0.873821f, 0.860219f, 0.833543f, 0.796233f, 0.752198f, 0.705231f, 0.658472f, 0.614230f, 0.573972f, 0.538477f, 0.508025f,
1.000000f, 0.999405f, 0.989130f, 0.949830f, 0.897468f, 0.858122f, 0.823932f, 0.782744f, 0.732512f, 0.677594f, 0.623754f, 0.575427f, 0.534943f, 0.502899f, 0.478646f, 0.461005f,
1.000000f, 0.999738f, 0.995228f, 0.974062f, 0.929086f, 0.874707f, 0.820986f, 0.765529f, 0.707500f, 0.650969f, 0.600887f, 0.560050f, 0.528786f, 0.505868f, 0.489538f, 0.478098f,
1.000000f, 0.999852f, 0.997285f, 0.984298f, 0.949907f, 0.894687f, 0.830051f, 0.764655f, 0.703610f, 0.650720f, 0.607837f, 0.574686f, 0.549707f, 0.531052f, 0.517044f, 0.506390f,
1.000000f, 0.999903f, 0.998164f, 0.988845f, 0.961108f, 0.909217f, 0.842075f, 0.774576f, 0.716020f, 0.668788f, 0.631760f, 0.602815f, 0.580035f, 0.561884f, 0.547230f, 0.535234f,
1.000000f, 0.999929f, 0.998507f, 0.990285f, 0.965135f, 0.917992f, 0.857129f, 0.795963f, 0.742667f, 0.699055f, 0.663951f, 0.635517f, 0.612188f, 0.592805f, 0.576520f, 0.562709f,
1.000000f, 0.999930f, 0.997985f, 0.987991f, 0.965712f, 0.929365f, 0.880981f, 0.827897f, 0.777686f, 0.734212f, 0.698025f, 0.668119f, 0.643237f, 0.622258f, 0.604347f, 0.588895f,
1.000000f, 0.999892f, 0.998245f, 0.991593f, 0.976269f, 0.949053f, 0.909388f, 0.861824f, 0.813348f, 0.769138f, 0.731260f, 0.699559f, 0.673029f, 0.650560f, 0.631217f, 0.614335f,
1.000000f, 0.999951f, 0.999193f, 0.995758f, 0.986165f, 0.966390f, 0.934469f, 0.892812f, 0.847190f, 0.803233f, 0.764153f, 0.730780f, 0.702574f, 0.678537f, 0.657746f, 0.639441f,
1.000000f, 0.999967f, 0.999464f, 0.997169f, 0.990665f, 0.976632f, 0.952374f, 0.918124f, 0.877615f, 0.835913f, 0.796893f, 0.762354f, 0.732463f, 0.706676f, 0.684154f, 0.664217f,
1.000000f, 0.999976f, 0.999599f, 0.997898f, 0.993113f, 0.982787f, 0.964563f, 0.937646f, 0.903767f, 0.866396f, 0.829112f, 0.794260f, 0.762877f, 0.735004f, 0.710259f, 0.688126f,
1.000000f, 0.999981f, 0.999687f, 0.998378f, 0.994751f, 0.987065f, 0.973532f, 0.953125f, 0.926150f, 0.894376f, 0.860258f, 0.826066f, 0.793349f, 0.762938f, 0.735056f, 0.709572f,
1.000000f, 0.999985f, 0.999762f, 0.998782f, 0.996155f, 0.990674f, 0.981030f, 0.966111f, 0.945407f, 0.919258f, 0.888814f, 0.855632f, 0.821323f, 0.787139f, 0.753957f, 0.722283f,
1.000000f, 0.999990f, 0.999832f, 0.999154f, 0.997326f, 0.993492f, 0.986639f, 0.975713f, 0.959807f, 0.938406f, 0.911476f, 0.879541f, 0.843530f, 0.804526f, 0.763704f, 0.722042f,
1.000000f, 0.999993f, 0.999880f, 0.999393f, 0.998081f, 0.995315f, 0.990310f, 0.982153f, 0.969868f, 0.952528f, 0.929350f, 0.899824f, 0.863810f, 0.821621f, 0.773983f, 0.722012f,
1.000000f, 0.995279f, 0.998777f, 0.999375f, 0.999516f, 0.999502f, 0.999409f, 0.999263f, 0.999075f, 0.998852f, 0.998598f, 0.998317f, 0.998011f, 0.997682f, 0.997333f, 0.996965f,
1.000000f, 0.997512f, 0.960193f, 0.899810f, 0.883560f, 0.886229f, 0.883754f, 0.870744f, 0.848142f, 0.818228f, 0.783377f, 0.745763f, 0.707244f, 0.669288f, 0.632992f, 0.599103f,
1.000000f, 0.999406f, 0.989202f, 0.950635f, 0.901346f, 0.869619f, 0.848470f, 0.824120f, 0.791055f, 0.749978f, 0.704165f, 0.657309f, 0.612523f, 0.571935f, 0.536685f, 0.507097f,
1.000000f, 0.999738f, 0.995293f, 0.974815f, 0.932797f, 0.886032f, 0.845632f, 0.806855f, 0.763730f, 0.715650f, 0.665786f, 0.618169f, 0.575818f, 0.540180f, 0.511466f, 0.489052f,
1.000000f, 0.999852f, 0.997364f, 0.985187f, 0.954180f, 0.907250f, 0.855836f, 0.804425f, 0.752168f, 0.699650f, 0.649724f, 0.605354f, 0.568138f, 0.538243f, 0.514846f, 0.496802f,
1.000000f, 0.999904f, 0.998287f, 0.990135f, 0.966897f, 0.924434f, 0.868932f, 0.809150f, 0.750508f, 0.696302f, 0.648748f, 0.608872f, 0.576454f, 0.550541f, 0.529942f, 0.513537f,
1.000000f, 0.999932f, 0.998757f, 0.992664f, 0.974035f, 0.935966f, 0.880421f, 0.817418f, 0.756776f, 0.703644f, 0.659295f, 0.622981f, 0.593394f, 0.569220f, 0.549366f, 0.532937f,
1.000000f, 0.999948f, 0.998998f, 0.993796f, 0.977216f, 0.942154f, 0.889613f, 0.829330f, 0.771355f, 0.720748f, 0.678401f, 0.643376f, 0.614334f, 0.590114f, 0.569735f, 0.552482f,
1.000000f, 0.999956f, 0.999008f, 0.993380f, 0.976671f, 0.945269f, 0.900482f, 0.847803f, 0.794303f, 0.745187f, 0.702581f, 0.666575f, 0.636395f, 0.611019f, 0.589522f, 0.571144f,
1.000000f, 0.999642f, 0.997254f, 0.990779f, 0.977436f, 0.953828f, 0.918026f, 0.872140f, 0.821771f, 0.772688f, 0.728481f, 0.690385f, 0.658196f, 0.631079f, 0.608078f, 0.588383f,
1.000000f, 0.999950f, 0.999173f, 0.995700f, 0.986407f, 0.967945f, 0.938044f, 0.897296f, 0.849725f, 0.800827f, 0.754988f, 0.714460f, 0.679710f, 0.650226f, 0.625133f, 0.603566f,
1.000000f, 0.999969f, 0.999491f, 0.997328f, 0.991190f, 0.977844f, 0.954242f, 0.919490f, 0.876027f, 0.828587f, 0.781834f, 0.738874f, 0.700951f, 0.668123f, 0.639755f, 0.615082f,
1.000000f, 0.999977f, 0.999617f, 0.997990f, 0.993387f, 0.983289f, 0.964865f, 0.936338f, 0.898372f, 0.854074f, 0.807560f, 0.762265f, 0.720225f, 0.682178f, 0.648063f, 0.617433f,
1.000000f, 0.999981f, 0.999683f, 0.998357f, 0.994648f, 0.986594f, 0.971921f, 0.948760f, 0.916623f, 0.876794f, 0.831897f, 0.784881f, 0.738053f, 0.692914f, 0.650113f, 0.609792f,
1.000000f, 0.999984f, 0.999734f, 0.998629f, 0.995610f, 0.989205f, 0.977699f, 0.959459f, 0.933369f, 0.899232f, 0.857885f, 0.811010f, 0.760542f, 0.708378f, 0.655964f, 0.604417f,
1.000000f, 0.999988f, 0.999800f, 0.998989f, 0.996796f, 0.992182f, 0.983853f, 0.970359f, 0.950269f, 0.922385f, 0.886016f, 0.841174f, 0.788665f, 0.730019f, 0.667293f, 0.602764f,
1.000000f, 0.995281f, 0.998789f, 0.999407f, 0.999577f, 0.999602f, 0.999558f, 0.999470f, 0.999349f, 0.999201f, 0.999030f, 0.998838f, 0.998627f, 0.998399f, 0.998155f, 0.997896f,
1.000000f, 0.997513f, 0.960249f, 0.900406f, 0.886089f, 0.892774f, 0.896456f, 0.891395f, 0.877963f, 0.857758f, 0.832434f, 0.803495f, 0.772286f, 0.739949f, 0.707458f, 0.675561f,
1.000000f, 0.999407f, 0.989231f, 0.951000f, 0.903200f, 0.875363f, 0.861319f, 0.847061f, 0.825875f, 0.796742f, 0.761239f, 0.721786f, 0.680816f, 0.640463f, 0.602298f, 0.567378f,
1.000000f, 0.999738f, 0.995315f, 0.975112f, 0.934395f, 0.891271f, 0.858018f, 0.829830f, 0.799044f, 0.762384f, 0.720541f, 0.676210f, 0.632355f, 0.591401f, 0.554867f, 0.523436f,
1.000000f, 0.999852f, 0.997386f, 0.985489f, 0.955810f, 0.912598f, 0.868448f, 0.827505f, 0.786526f, 0.742772f, 0.696651f, 0.650629f, 0.607470f, 0.569086f, 0.536346f, 0.509224f,
1.000000f, 0.999904f, 0.998316f, 0.990504f, 0.968816f, 0.930527f, 0.882628f, 0.832611f, 0.782598f, 0.732654f, 0.683857f, 0.638184f, 0.597439f, 0.562499f, 0.533360f, 0.509454f,
1.000000f, 0.999932f, 0.998803f, 0.993191f, 0.976633f, 0.943607f, 0.895857f, 0.840574f, 0.783946f, 0.729575f, 0.679617f, 0.635398f, 0.597373f, 0.565310f, 0.538606f, 0.516438f,
1.000000f, 0.999948f, 0.999083f, 0.994709f, 0.981260f, 0.952269f, 0.906208f, 0.848944f, 0.789028f, 0.732726f, 0.682916f, 0.640159f, 0.603957f, 0.573434f, 0.547734f, 0.526040f,
1.000000f, 0.999958f, 0.999244f, 0.995504f, 0.983610f, 0.957032f, 0.913261f, 0.857335f, 0.798097f, 0.742316f, 0.693015f, 0.650643f, 0.614578f, 0.583949f, 0.557917f, 0.535717f,
1.000000f, 0.999965f, 0.999300f, 0.995552f, 0.983604f, 0.958348f, 0.918639f, 0.868000f, 0.812623f, 0.758282f, 0.708524f, 0.664736f, 0.626955f, 0.594631f, 0.567030f, 0.543396f,
1.000000f, 0.999961f, 0.998876f, 0.993452f, 0.981396f, 0.960356f, 0.927836f, 0.883938f, 0.832391f, 0.778550f, 0.726910f, 0.680091f, 0.638976f, 0.603454f, 0.572900f, 0.546588f,
1.000000f, 0.999948f, 0.999141f, 0.995636f, 0.986808f, 0.969928f, 0.942322f, 0.902955f, 0.853928f, 0.799818f, 0.745449f, 0.694280f, 0.648026f, 0.607120f, 0.571170f, 0.539507f,
1.000000f, 0.999971f, 0.999515f, 0.997458f, 0.991643f, 0.978974f, 0.956207f, 0.921417f, 0.875407f, 0.821675f, 0.764848f, 0.708938f, 0.656438f, 0.608371f, 0.564828f, 0.525338f,
1.000000f, 0.999977f, 0.999625f, 0.998046f, 0.993587f, 0.983730f, 0.965409f, 0.935992f, 0.894749f, 0.843544f, 0.786131f, 0.726560f, 0.667972f, 0.612238f, 0.560125f, 0.511730f,
1.000000f, 0.999981f, 0.999680f, 0.998335f, 0.994583f, 0.986395f, 0.971213f, 0.946522f, 0.910722f, 0.863973f, 0.808275f, 0.746767f, 0.682739f, 0.618900f, 0.557115f, 0.498536f,
1.000000f, 0.999981f, 0.999699f, 0.998465f, 0.995126f, 0.988082f, 0.975371f, 0.954899f, 0.924785f, 0.883853f, 0.832029f, 0.770609f, 0.702046f, 0.629568f, 0.556527f, 0.485918f,
1.000000f, 0.995282f, 0.998796f, 0.999425f, 0.999611f, 0.999659f, 0.999642f, 0.999587f, 0.999504f, 0.999400f, 0.999277f, 0.999137f, 0.998983f, 0.998814f, 0.998633f, 0.998441f,
1.000000f, 0.997513f, 0.960278f, 0.900724f, 0.887483f, 0.896459f, 0.903728f, 0.903412f, 0.895650f, 0.881748f, 0.863017f, 0.840610f, 0.815525f, 0.788635f, 0.760702f, 0.732374f,
1.000000f, 0.999406f, 0.989241f, 0.951173f, 0.904157f, 0.878444f, 0.868446f, 0.860220f, 0.846617f, 0.825875f, 0.798692f, 0.766633f, 0.731460f, 0.694854f, 0.658274f, 0.622879f,
1.000000f, 0.999737f, 0.995320f, 0.975238f, 0.935149f, 0.893906f, 0.864579f, 0.842702f, 0.820146f, 0.792448f, 0.758869f, 0.720774f, 0.680337f, 0.639759f, 0.600864f, 0.564924f,
1.000000f, 0.999851f, 0.997390f, 0.985602f, 0.956507f, 0.915093f, 0.874811f, 0.840192f, 0.807403f, 0.772125f, 0.732870f, 0.690663f, 0.647724f, 0.606303f, 0.568131f, 0.534194f,
1.000000f, 0.999903f, 0.998318f, 0.990625f, 0.969560f, 0.933162f, 0.889260f, 0.845564f, 0.803221f, 0.760306f, 0.715854f, 0.670786f, 0.627061f, 0.586488f, 0.550288f, 0.518905f,
1.000000f, 0.999931f, 0.998809f, 0.993343f, 0.977536f, 0.946684f, 0.903274f, 0.854232f, 0.804128f, 0.754285f, 0.705289f, 0.658308f, 0.614732f, 0.575639f, 0.541492f, 0.512202f,
1.000000f, 0.999948f, 0.999096f, 0.994935f, 0.982501f, 0.956236f, 0.914970f, 0.863407f, 0.807776f, 0.752439f, 0.699918f, 0.651662f, 0.608475f, 0.570547f, 0.537739f, 0.509589f,
1.000000f, 0.999958f, 0.999275f, 0.995902f, 0.985571f, 0.962583f, 0.923689f, 0.871527f, 0.812829f, 0.754063f, 0.699203f, 0.649900f, 0.606478f, 0.568627f, 0.535870f, 0.507601f,
1.000000f, 0.999965f, 0.999383f, 0.996447f, 0.987229f, 0.966133f, 0.929214f, 0.878067f, 0.819103f, 0.759216f, 0.702844f, 0.651887f, 0.606737f, 0.567112f, 0.532548f, 0.502454f,
1.000000f, 0.999969f, 0.999429f, 0.996540f, 0.987322f, 0.966773f, 0.932016f, 0.884166f, 0.827678f, 0.768075f, 0.709745f, 0.655332f, 0.605919f, 0.561753f, 0.522522f, 0.487763f,
1.000000f, 0.999968f, 0.999268f, 0.995284f, 0.984967f, 0.966145f, 0.936275f, 0.894014f, 0.841088f, 0.781733f, 0.720705f, 0.661589f, 0.606471f, 0.556170f, 0.510737f, 0.469825f,
1.000000f, 0.999951f, 0.999187f, 0.995914f, 0.987863f, 0.972540f, 0.946931f, 0.908810f, 0.858448f, 0.799008f, 0.735076f, 0.670924f, 0.609496f, 0.552335f, 0.499952f, 0.452233f,
1.000000f, 0.999973f, 0.999555f, 0.997668f, 0.992328f, 0.980601f, 0.959061f, 0.924916f, 0.877395f, 0.818463f, 0.752161f, 0.683031f, 0.614861f, 0.550061f, 0.489851f, 0.434654f,
1.000000f, 0.999978f, 0.999641f, 0.998129f, 0.993860f, 0.984408f, 0.966592f, 0.937159f, 0.894046f, 0.837539f, 0.770472f, 0.697165f, 0.622089f, 0.548834f, 0.479806f, 0.416360f,
1.000000f, 0.999980f, 0.999677f, 0.998316f, 0.994494f, 0.986091f, 0.970357f, 0.944295f, 0.905394f, 0.852501f, 0.786514f, 0.710447f, 0.628796f, 0.546440f, 0.467649f, 0.395427f,
1.000000f, 0.995283f, 0.998800f, 0.999435f, 0.999631f, 0.999691f, 0.999691f, 0.999655f, 0.999595f, 0.999516f, 0.999421f, 0.999313f, 0.999192f, 0.999059f, 0.998917f, 0.998764f,
1.000000f, 0.997512f, 0.960289f, 0.900893f, 0.888264f, 0.898575f, 0.907972f, 0.910513f, 0.906231f, 0.896299f, 0.881871f, 0.863923f, 0.843273f, 0.820621f, 0.796574f, 0.771649f,
1.000000f, 0.999405f, 0.989242f, 0.951252f, 0.904648f, 0.880121f, 0.872458f, 0.867827f, 0.858917f, 0.843645f, 0.822263f, 0.795882f, 0.765817f, 0.733393f, 0.699798f, 0.666063f,
1.000000f, 0.999737f, 0.995318f, 0.975282f, 0.935499f, 0.895244f, 0.868096f, 0.849903f, 0.832452f, 0.810814f, 0.783502f, 0.751086f, 0.715043f, 0.677112f, 0.638938f, 0.601879f,
1.000000f, 0.999851f, 0.997386f, 0.985632f, 0.956797f, 0.916269f, 0.878042f, 0.847041f, 0.819403f, 0.790195f, 0.756908f, 0.719491f, 0.679341f, 0.638364f, 0.598372f, 0.560777f,
1.000000f, 0.999902f, 0.998314f, 0.990652f, 0.969838f, 0.934317f, 0.892448f, 0.852349f, 0.815038f, 0.777756f, 0.738291f, 0.696378f, 0.653243f, 0.610715f, 0.570450f, 0.533612f,
1.000000f, 0.999931f, 0.998805f, 0.993377f, 0.977845f, 0.947940f, 0.906676f, 0.861280f, 0.815943f, 0.770863f, 0.725219f, 0.679104f, 0.633630f, 0.590317f, 0.550417f, 0.514624f,
1.000000f, 0.999947f, 0.999093f, 0.994984f, 0.982895f, 0.957752f, 0.918880f, 0.871041f, 0.819643f, 0.767602f, 0.716077f, 0.665972f, 0.618404f, 0.574405f, 0.534630f, 0.499381f,
1.000000f, 0.999957f, 0.999273f, 0.995983f, 0.986141f, 0.964597f, 0.928467f, 0.879916f, 0.824267f, 0.766440f, 0.709605f, 0.655628f, 0.605583f, 0.560068f, 0.519284f, 0.483185f,
1.000000f, 0.999964f, 0.999388f, 0.996606f, 0.988176f, 0.969082f, 0.935243f, 0.886835f, 0.828531f, 0.766332f, 0.704864f, 0.646706f, 0.592981f, 0.544086f, 0.499969f, 0.460436f,
1.000000f, 0.999969f, 0.999462f, 0.996977f, 0.989321f, 0.971637f, 0.939471f, 0.892050f, 0.833246f, 0.769016f, 0.704403f, 0.642408f, 0.584516f, 0.531265f, 0.482743f, 0.438826f,
1.000000f, 0.999972f, 0.999497f, 0.997057f, 0.989393f, 0.971996f, 0.941268f, 0.896395f, 0.839702f, 0.775622f, 0.708797f, 0.642841f, 0.580000f, 0.521463f, 0.467672f, 0.418720f,
1.000000f, 0.999972f, 0.999371f, 0.996026f, 0.987157f, 0.970597f, 0.943509f, 0.903421f, 0.850272f, 0.786874f, 0.717688f, 0.647101f, 0.578407f, 0.513634f, 0.453828f, 0.399366f,
1.000000f, 0.999962f, 0.999368f, 0.996733f, 0.989833f, 0.976117f, 0.952471f, 0.915908f, 0.865184f, 0.801869f, 0.729929f, 0.654168f, 0.578853f, 0.507031f, 0.440545f, 0.380228f,
1.000000f, 0.999976f, 0.999611f, 0.997961f, 0.993266f, 0.982780f, 0.962941f, 0.930172f, 0.882238f, 0.819483f, 0.745055f, 0.663908f, 0.581283f, 0.501532f, 0.427616f, 0.361193f,
1.000000f, 0.999980f, 0.999676f, 0.998309f, 0.994432f, 0.985758f, 0.969118f, 0.940802f, 0.897514f, 0.837756f, 0.762936f, 0.677418f, 0.587328f, 0.498831f, 0.416740f, 0.343944f,
1.000000f, 0.995284f, 0.998803f, 0.999441f, 0.999642f, 0.999710f, 0.999718f, 0.999694f, 0.999647f, 0.999582f, 0.999504f, 0.999414f, 0.999312f, 0.999201f, 0.999080f, 0.998951f,
1.000000f, 0.997512f, 0.960292f, 0.900975f, 0.888686f, 0.899761f, 0.910395f, 0.914614f, 0.912405f, 0.904872f, 0.893093f, 0.877966f, 0.860221f, 0.840462f, 0.819208f, 0.796894f,
1.000000f, 0.999405f, 0.989238f, 0.951276f, 0.904877f, 0.880987f, 0.874630f, 0.872074f, 0.865948f, 0.854019f, 0.836327f, 0.813747f, 0.787361f, 0.758246f, 0.727412f, 0.695734f,
1.000000f, 0.999737f, 0.995312f, 0.975285f, 0.935633f, 0.895869f, 0.869876f, 0.853742f, 0.839276f, 0.821353f, 0.798151f, 0.769798f, 0.737350f, 0.702173f, 0.665661f, 0.629043f,
1.000000f, 0.999850f, 0.997379f, 0.985625f, 0.956883f, 0.916759f, 0.879558f, 0.850506f, 0.825820f, 0.800359f, 0.771144f, 0.737499f, 0.700220f, 0.660799f, 0.620820f, 0.581736f,
1.000000f, 0.999902f, 0.998306f, 0.990638f, 0.969902f, 0.934739f, 0.893834f, 0.855594f, 0.821126f, 0.787404f, 0.751594f, 0.712639f, 0.671124f, 0.628474f, 0.586340f, 0.546124f,
1.000000f, 0.999930f, 0.998796f, 0.993357f, 0.977898f, 0.948353f, 0.908039f, 0.864468f, 0.821839f, 0.779918f, 0.737104f, 0.692614f, 0.646983f, 0.601522f, 0.557744f, 0.516844f,
1.000000f, 0.999946f, 0.999083f, 0.994962f, 0.982947f, 0.958178f, 0.920299f, 0.874253f, 0.825298f, 0.775678f, 0.725608f, 0.675136f, 0.624987f, 0.576365f, 0.530474f, 0.488210f,
1.000000f, 0.999956f, 0.999261f, 0.995963f, 0.986220f, 0.965139f, 0.930136f, 0.883416f, 0.829854f, 0.773384f, 0.716136f, 0.659351f, 0.604123f, 0.551503f, 0.502397f, 0.457343f,
1.000000f, 0.999963f, 0.999381f, 0.996624f, 0.988423f, 0.970106f, 0.937845f, 0.891629f, 0.835197f, 0.773425f, 0.710114f, 0.647711f, 0.587740f, 0.531184f, 0.478705f, 0.430616f,
1.000000f, 0.999968f, 0.999464f, 0.997068f, 0.989893f, 0.973513f, 0.943505f, 0.898286f, 0.840457f, 0.775113f, 0.707123f, 0.639883f, 0.575385f, 0.514719f, 0.458478f, 0.406970f,
1.000000f, 0.999971f, 0.999518f, 0.997342f, 0.990741f, 0.975475f, 0.947004f, 0.903070f, 0.845362f, 0.778426f, 0.707289f, 0.635853f, 0.566724f, 0.501440f, 0.440912f, 0.385604f,
1.000000f, 0.999974f, 0.999544f, 0.997381f, 0.990696f, 0.975518f, 0.948161f, 0.906540f, 0.851004f, 0.784431f, 0.711198f, 0.635679f, 0.561400f, 0.490787f, 0.425353f, 0.365921f,
1.000000f, 0.999971f, 0.999304f, 0.995978f, 0.988280f, 0.974075f, 0.950003f, 0.912685f, 0.860537f, 0.794859f, 0.719504f, 0.639410f, 0.559229f, 0.482529f, 0.411669f, 0.347942f,
1.000000f, 0.999974f, 0.999565f, 0.997708f, 0.992443f, 0.980948f, 0.959813f, 0.925528f, 0.875653f, 0.810248f, 0.732357f, 0.647157f, 0.560340f, 0.476823f, 0.400035f, 0.331897f,
1.000000f, 0.999980f, 0.999676f, 0.998305f, 0.994391f, 0.985550f, 0.968368f, 0.938734f, 0.892932f, 0.829321f, 0.749688f, 0.659212f, 0.564921f, 0.473581f, 0.390180f, 0.317446f,
1.000000f, 0.995284f, 0.998804f, 0.999444f, 0.999649f, 0.999720f, 0.999733f, 0.999714f, 0.999674f, 0.999618f, 0.999548f, 0.999468f, 0.999377f, 0.999277f, 0.999169f, 0.999053f,
1.000000f, 0.997511f, 0.960289f, 0.901005f, 0.888885f, 0.900363f, 0.911663f, 0.916803f, 0.915736f, 0.909530f, 0.899242f, 0.885721f, 0.869663f, 0.851634f, 0.832099f, 0.811466f,
1.000000f, 0.999404f, 0.989232f, 0.951270f, 0.904948f, 0.881357f, 0.875662f, 0.874199f, 0.869582f, 0.859498f, 0.843900f, 0.823539f, 0.799383f, 0.772396f, 0.743448f, 0.713338f,
1.000000f, 0.999736f, 0.995304f, 0.975264f, 0.935642f, 0.896072f, 0.870612f, 0.855492f, 0.842579f, 0.826666f, 0.805776f, 0.779833f, 0.749653f, 0.716403f, 0.681265f, 0.645355f,
1.000000f, 0.999849f, 0.997370f, 0.985595f, 0.956856f, 0.916856f, 0.880077f, 0.851914f, 0.828681f, 0.805175f, 0.778204f, 0.746802f, 0.711421f, 0.673228f, 0.633628f, 0.593933f,
1.000000f, 0.999901f, 0.998296f, 0.990603f, 0.969847f, 0.934766f, 0.894195f, 0.856719f, 0.823539f, 0.791566f, 0.757680f, 0.720436f, 0.679984f, 0.637406f, 0.594174f, 0.551717f,
1.000000f, 0.999929f, 0.998784f, 0.993309f, 0.977807f, 0.948280f, 0.908200f, 0.865216f, 0.823601f, 0.782972f, 0.741355f, 0.697452f, 0.651329f, 0.604006f, 0.556943f, 0.511515f,
1.000000f, 0.999945f, 0.999070f, 0.994912f, 0.982853f, 0.958118f, 0.920485f, 0.875042f, 0.827032f, 0.778447f, 0.728966f, 0.678055f, 0.625944f, 0.573684f, 0.522641f, 0.474050f,
1.000000f, 0.999956f, 0.999251f, 0.995932f, 0.986200f, 0.965274f, 0.930739f, 0.884939f, 0.832635f, 0.777366f, 0.720585f, 0.662901f, 0.605062f, 0.548168f, 0.493456f, 0.441994f,
1.000000f, 0.999962f, 0.999373f, 0.996618f, 0.988491f, 0.970487f, 0.938987f, 0.894031f, 0.839138f, 0.778529f, 0.715265f, 0.651254f, 0.587957f, 0.526632f, 0.468422f, 0.414199f,
1.000000f, 0.999968f, 0.999462f, 0.997093f, 0.990092f, 0.974273f, 0.945421f, 0.901867f, 0.845664f, 0.781073f, 0.712340f, 0.642651f, 0.574201f, 0.508557f, 0.446828f, 0.389860f,
1.000000f, 0.999971f, 0.999524f, 0.997429f, 0.991210f, 0.976951f, 0.950194f, 0.908174f, 0.851673f, 0.784555f, 0.711642f, 0.637052f, 0.563754f, 0.493742f, 0.428379f, 0.368565f,
1.000000f, 0.999975f, 0.999569f, 0.997647f, 0.991870f, 0.978507f, 0.953171f, 0.912734f, 0.857072f, 0.789157f, 0.713541f, 0.634828f, 0.556787f, 0.482180f, 0.412907f, 0.350140f,
1.000000f, 0.999977f, 0.999582f, 0.997604f, 0.991564f, 0.978111f, 0.953898f, 0.916014f, 0.863007f, 0.796031f, 0.718779f, 0.636196f, 0.553097f, 0.473399f, 0.399812f, 0.333928f,
1.000000f, 0.999955f, 0.999237f, 0.996489f, 0.990324f, 0.978430f, 0.957354f, 0.923234f, 0.873265f, 0.807238f, 0.728095f, 0.641110f, 0.552257f, 0.466791f, 0.388451f, 0.319337f,
1.000000f, 0.999980f, 0.999676f, 0.998299f, 0.994349f, 0.985351f, 0.967719f, 0.937130f, 0.889763f, 0.824107f, 0.742285f, 0.649870f, 0.554162f, 0.462036f, 0.378442f, 0.305989f,
1.000000f, 0.995284f, 0.998804f, 0.999446f, 0.999652f, 0.999725f, 0.999740f, 0.999724f, 0.999687f, 0.999634f, 0.999568f, 0.999492f, 0.999406f, 0.999311f, 0.999208f, 0.999098f,
1.000000f, 0.997511f, 0.960284f, 0.901003f, 0.888942f, 0.900590f, 0.912189f, 0.917748f, 0.917206f, 0.911615f, 0.902013f, 0.889241f, 0.873977f, 0.856768f, 0.838075f, 0.818279f,
1.000000f, 0.999403f, 0.989226f, 0.951247f, 0.904929f, 0.881422f, 0.875975f, 0.874958f, 0.870990f, 0.861727f, 0.847075f, 0.827739f, 0.804628f, 0.778648f, 0.750639f, 0.721328f,
1.000000f, 0.999735f, 0.995295f, 0.975231f, 0.935580f, 0.896025f, 0.870709f, 0.855938f, 0.843609f, 0.828504f, 0.808588f, 0.783681f, 0.754503f, 0.722104f, 0.687576f, 0.651942f,
1.000000f, 0.999848f, 0.997360f, 0.985556f, 0.956763f, 0.916724f, 0.879989f, 0.852036f, 0.829234f, 0.806371f, 0.780182f, 0.749567f, 0.714816f, 0.676938f, 0.637197f, 0.596804f,
1.000000f, 0.999900f, 0.998284f, 0.990550f, 0.969710f, 0.934519f, 0.893858f, 0.856387f, 0.823348f, 0.791625f, 0.757994f, 0.720839f, 0.680069f, 0.636588f, 0.591729f, 0.546835f,
1.000000f, 0.999928f, 0.998773f, 0.993263f, 0.977688f, 0.948075f, 0.907943f, 0.865013f, 0.823579f, 0.783224f, 0.741798f, 0.697762f, 0.650887f, 0.601974f, 0.552381f, 0.503517f,
1.000000f, 0.999945f, 0.999062f, 0.994881f, 0.982790f, 0.958040f, 0.920489f, 0.875301f, 0.827751f, 0.779733f, 0.730697f, 0.679770f, 0.626870f, 0.572826f, 0.518979f, 0.466743f,
1.000000f, 0.999955f, 0.999246f, 0.995916f, 0.986184f, 0.965323f, 0.931015f, 0.885691f, 0.834125f, 0.779686f, 0.723524f, 0.665834f, 0.607019f, 0.548073f, 0.490339f, 0.435150f,
1.000000f, 0.999962f, 0.999373f, 0.996619f, 0.988535f, 0.970697f, 0.939609f, 0.895401f, 0.841545f, 0.782010f, 0.719433f, 0.655283f, 0.590734f, 0.527088f, 0.465722f, 0.407904f,
1.000000f, 0.999968f, 0.999463f, 0.997115f, 0.990219f, 0.974709f, 0.946527f, 0.904071f, 0.849246f, 0.785904f, 0.717781f, 0.647661f, 0.577649f, 0.509486f, 0.444684f, 0.384456f,
1.000000f, 0.999971f, 0.999528f, 0.997475f, 0.991437f, 0.977692f, 0.951962f, 0.911448f, 0.856566f, 0.790615f, 0.717942f, 0.642489f, 0.567318f, 0.494773f, 0.426595f, 0.364046f,
1.000000f, 0.999975f, 0.999578f, 0.997733f, 0.992296f, 0.979810f, 0.955974f, 0.917293f, 0.863025f, 0.795639f, 0.719578f, 0.639531f, 0.559508f, 0.482585f, 0.410973f, 0.346112f,
1.000000f, 0.999977f, 0.999610f, 0.997884f, 0.992738f, 0.980875f, 0.958232f, 0.921269f, 0.868446f, 0.801055f, 0.722874f, 0.638931f, 0.554163f, 0.472686f, 0.397447f, 0.330196f,
1.000000f, 0.999978f, 0.999565f, 0.997403f, 0.991432f, 0.979516f, 0.958528f, 0.924585f, 0.874704f, 0.808512f, 0.728875f, 0.641091f, 0.551264f, 0.464814f, 0.385631f, 0.315904f,
1.000000f, 0.999980f, 0.999676f, 0.998292f, 0.994295f, 0.985125f, 0.967084f, 0.935829f, 0.887676f, 0.821316f, 0.739011f, 0.646348f, 0.550586f, 0.458535f, 0.375096f, 0.302843f,
1.000000f, 0.995284f, 0.998805f, 0.999446f, 0.999652f, 0.999726f, 0.999742f, 0.999726f, 0.999690f, 0.999638f, 0.999573f, 0.999497f, 0.999412f, 0.999319f, 0.999217f, 0.999109f,
1.000000f, 0.997511f, 0.960278f, 0.900983f, 0.888916f, 0.900587f, 0.912250f, 0.917908f, 0.917495f, 0.912056f, 0.902622f, 0.890032f, 0.874957f, 0.857948f, 0.839453f, 0.819858f,
1.000000f, 0.999403f, 0.989217f, 0.951216f, 0.904855f, 0.881312f, 0.875855f, 0.874881f, 0.871011f, 0.861890f, 0.847414f, 0.828269f, 0.805342f, 0.779535f, 0.751654f, 0.722409f,
1.000000f, 0.999735f, 0.995287f, 0.975194f, 0.935480f, 0.895835f, 0.870421f, 0.855571f, 0.843205f, 0.828107f, 0.808210f, 0.783319f, 0.754116f, 0.721610f, 0.686849f, 0.650834f,
1.000000f, 0.999848f, 0.997350f, 0.985508f, 0.956627f, 0.916439f, 0.879490f, 0.851287f, 0.828198f, 0.805024f, 0.778469f, 0.747390f, 0.712022f, 0.673310f, 0.632463f, 0.590663f,
1.000000f, 0.999900f, 0.998276f, 0.990513f, 0.969612f, 0.934314f, 0.893516f, 0.855889f, 0.822696f, 0.790800f, 0.756946f, 0.719429f, 0.678072f, 0.633700f, 0.587564f, 0.540993f,
1.000000f, 0.999928f, 0.998768f, 0.993241f, 0.977633f, 0.947976f, 0.907810f, 0.864886f, 0.823513f, 0.783251f, 0.741884f, 0.697761f, 0.650515f, 0.600848f, 0.550036f, 0.499480f,
1.000000f, 0.999945f, 0.999060f, 0.994873f, 0.982777f, 0.958041f, 0.920561f, 0.875536f, 0.828257f, 0.780592f, 0.731891f, 0.681116f, 0.628018f, 0.573302f, 0.518254f, 0.464324f,
1.000000f, 0.999955f, 0.999247f, 0.995921f, 0.986211f, 0.965426f, 0.931295f, 0.886306f, 0.835243f, 0.781429f, 0.725868f, 0.668540f, 0.609650f, 0.550059f, 0.491114f, 0.434261f,
1.000000f, 0.999962f, 0.999374f, 0.996629f, 0.988590f, 0.970879f, 0.940076f, 0.896375f, 0.843261f, 0.784609f, 0.722845f, 0.659190f, 0.594586f, 0.530250f, 0.467640f, 0.408199f,
1.000000f, 0.999968f, 0.999465f, 0.997128f, 0.990290f, 0.974955f, 0.947163f, 0.905388f, 0.851522f, 0.789266f, 0.722065f, 0.652422f, 0.582245f, 0.513266f, 0.447157f, 0.385363f,
1.000000f, 0.999972f, 0.999530f, 0.997493f, 0.991538f, 0.978036f, 0.952836f, 0.913211f, 0.859501f, 0.794737f, 0.722931f, 0.647753f, 0.572188f, 0.498666f, 0.429163f, 0.365186f,
1.000000f, 0.999975f, 0.999580f, 0.997764f, 0.992463f, 0.980361f, 0.957300f, 0.919782f, 0.866810f, 0.800499f, 0.724974f, 0.644830f, 0.564130f, 0.486139f, 0.413298f, 0.347228f,
1.000000f, 0.999977f, 0.999617f, 0.997960f, 0.993118f, 0.982006f, 0.960566f, 0.924916f, 0.873094f, 0.806184f, 0.727943f, 0.643492f, 0.557922f, 0.475485f, 0.399271f, 0.331161f,
1.000000f, 0.999979f, 0.999637f, 0.998017f, 0.993219f, 0.982367f, 0.961927f, 0.928184f, 0.878334f, 0.812034f, 0.732125f, 0.643915f, 0.553566f, 0.466563f, 0.386869f, 0.316698f,
1.000000f, 0.999980f, 0.999675f, 0.998280f, 0.994216f, 0.984850f, 0.966503f, 0.935014f, 0.886874f, 0.820774f, 0.738841f, 0.646535f, 0.551042f, 0.459158f, 0.375796f, 0.303554f,
1.000000f, 0.995284f, 0.998804f, 0.999446f, 0.999652f, 0.999725f, 0.999741f, 0.999725f, 0.999687f, 0.999635f, 0.999569f, 0.999493f, 0.999407f, 0.999312f, 0.999210f, 0.999100f,
1.000000f, 0.997510f, 0.960272f, 0.900957f, 0.888850f, 0.900465f, 0.912056f, 0.917636f, 0.917129f, 0.911583f, 0.902026f, 0.889301f, 0.874076f, 0.856904f, 0.838235f, 0.818452f,
1.000000f, 0.999403f, 0.989210f, 0.951184f, 0.904763f, 0.881115f, 0.875512f, 0.874354f, 0.870268f, 0.860899f, 0.846149f, 0.826693f, 0.803430f, 0.777250f, 0.748961f, 0.719274f,
1.000000f, 0.999734f, 0.995279f, 0.975155f, 0.935366f, 0.895578f, 0.869943f, 0.854786f, 0.842031f, 0.826459f, 0.806013f, 0.780495f, 0.750587f, 0.717288f, 0.681647f, 0.644646f,
1.000000f, 0.999848f, 0.997346f, 0.985485f, 0.956561f, 0.916289f, 0.879212f, 0.850822f, 0.827497f, 0.804019f, 0.777098f, 0.745565f, 0.709663f, 0.670316f, 0.628717f, 0.586038f,
1.000000f, 0.999900f, 0.998275f, 0.990505f, 0.969587f, 0.934262f, 0.893425f, 0.855747f, 0.822486f, 0.790499f, 0.756509f, 0.718790f, 0.677140f, 0.632349f, 0.585661f, 0.538386f,
1.000000f, 0.999928f, 0.998768f, 0.993243f, 0.977639f, 0.947997f, 0.907867f, 0.865006f, 0.823723f, 0.783570f, 0.742296f, 0.698204f, 0.650885f, 0.600994f, 0.549785f, 0.498656f,
1.000000f, 0.999945f, 0.999060f, 0.994877f, 0.982795f, 0.958102f, 0.920709f, 0.875837f, 0.828783f, 0.781397f, 0.732985f, 0.682444f, 0.629450f, 0.574646f, 0.519295f, 0.464849f,
1.000000f, 0.999955f, 0.999247f, 0.995925f, 0.986233f, 0.965502f, 0.931491f, 0.886717f, 0.835982f, 0.782584f, 0.727470f, 0.670523f, 0.611850f, 0.552237f, 0.493010f, 0.435639f,
1.000000f, 0.999962f, 0.999374f, 0.996634f, 0.988615f, 0.970969f, 0.940313f, 0.896884f, 0.844187f, 0.786070f, 0.724876f, 0.661700f, 0.597367f, 0.533012f, 0.470085f, 0.410101f,
1.000000f, 0.999968f, 0.999465f, 0.997134f, 0.990322f, 0.975066f, 0.947455f, 0.906016f, 0.852661f, 0.791049f, 0.724510f, 0.655390f, 0.585463f, 0.516409f, 0.449926f, 0.387555f,
1.000000f, 0.999971f, 0.999531f, 0.997501f, 0.991579f, 0.978183f, 0.953219f, 0.914022f, 0.860936f, 0.796914f, 0.725810f, 0.651119f, 0.575713f, 0.502010f, 0.432062f, 0.367489f,
1.000000f, 0.999975f, 0.999581f, 0.997776f, 0.992527f, 0.980582f, 0.957862f, 0.920918f, 0.868711f, 0.803199f, 0.728318f, 0.648503f, 0.567789f, 0.489490f, 0.416147f, 0.349507f,
1.000000f, 0.999977f, 0.999620f, 0.997986f, 0.993247f, 0.982427f, 0.961553f, 0.926709f, 0.875746f, 0.809518f, 0.731656f, 0.647247f, 0.561449f, 0.478611f, 0.401907f, 0.333308f,
1.000000f, 0.999979f, 0.999648f, 0.998134f, 0.993732f, 0.983669f, 0.964160f, 0.931158f, 0.881732f, 0.815571f, 0.735600f, 0.647188f, 0.556541f, 0.469195f, 0.389144f, 0.318641f,
1.000000f, 0.999980f, 0.999673f, 0.998257f, 0.994093f, 0.984576f, 0.966265f, 0.935152f, 0.887595f, 0.822055f, 0.740532f, 0.648457f, 0.553048f, 0.461141f, 0.377688f, 0.305312f,
1.000000f, 0.995284f, 0.998804f, 0.999445f, 0.999651f, 0.999724f, 0.999739f, 0.999722f, 0.999684f, 0.999630f, 0.999563f, 0.999485f, 0.999398f, 0.999302f, 0.999198f, 0.999086f,
1.000000f, 0.997510f, 0.960267f, 0.900933f, 0.888781f, 0.900318f, 0.911801f, 0.917239f, 0.916567f, 0.910833f, 0.901062f, 0.888105f, 0.872627f, 0.855182f, 0.836220f, 0.816125f,
1.000000f, 0.999402f, 0.989206f, 0.951160f, 0.904689f, 0.880944f, 0.875182f, 0.873804f, 0.869439f, 0.859739f, 0.844607f, 0.824729f, 0.801003f, 0.774321f, 0.745496f, 0.715236f,
1.000000f, 0.999734f, 0.995278f, 0.975147f, 0.935339f, 0.895510f, 0.869798f, 0.854523f, 0.841602f, 0.825821f, 0.805121f, 0.779311f, 0.749073f, 0.715413f, 0.679387f, 0.641971f,
1.000000f, 0.999848f, 0.997346f, 0.985485f, 0.956559f, 0.916282f, 0.879189f, 0.850766f, 0.827382f, 0.803814f, 0.776771f, 0.745088f, 0.708998f, 0.669438f, 0.627598f, 0.584655f,
1.000000f, 0.999900f, 0.998275f, 0.990506f, 0.969593f, 0.934278f, 0.893458f, 0.855801f, 0.822559f, 0.790580f, 0.756578f, 0.718819f, 0.677102f, 0.632212f, 0.585386f, 0.537943f,
1.000000f, 0.999928f, 0.998768f, 0.993244f, 0.977646f, 0.948020f, 0.907922f, 0.865112f, 0.823896f, 0.783820f, 0.742617f, 0.698579f, 0.651280f, 0.601369f, 0.550088f, 0.498847f,
1.000000f, 0.999945f, 0.999060f, 0.994879f, 0.982802f, 0.958127f, 0.920774f, 0.875972f, 0.829021f, 0.781764f, 0.733493f, 0.683077f, 0.630174f, 0.575404f, 0.520024f, 0.465484f,
1.000000f, 0.999955f, 0.999247f, 0.995927f, 0.986241f, 0.965530f, 0.931565f, 0.886875f, 0.836271f, 0.783048f, 0.728128f, 0.671370f, 0.612838f, 0.553298f, 0.494056f, 0.436595f,
1.000000f, 0.999962f, 0.999375f, 0.996635f, 0.988624f, 0.971000f, 0.940397f, 0.897068f, 0.844529f, 0.786627f, 0.725678f, 0.662737f, 0.598585f, 0.534315f, 0.471376f, 0.411283f,
1.000000f, 0.999968f, 0.999465f, 0.997136f, 0.990333f, 0.975103f, 0.947555f, 0.906236f, 0.853072f, 0.791717f, 0.725468f, 0.656617f, 0.586883f, 0.517912f, 0.451388f, 0.388886f,
1.000000f, 0.999972f, 0.999531f, 0.997504f, 0.991593f, 0.978230f, 0.953348f, 0.914303f, 0.861452f, 0.797735f, 0.726957f, 0.652547f, 0.577323f, 0.503668f, 0.433644f, 0.368907f,
1.000000f, 0.999975f, 0.999582f, 0.997780f, 0.992547f, 0.980652f, 0.958047f, 0.921309f, 0.869402f, 0.804249f, 0.729712f, 0.650157f, 0.569569f, 0.491256f, 0.417789f, 0.350958f,
1.000000f, 0.999977f, 0.999620f, 0.997993f, 0.993284f, 0.982553f, 0.961871f, 0.927340f, 0.876772f, 0.810939f, 0.733379f, 0.649135f, 0.563353f, 0.480418f, 0.403550f, 0.334740f,
1.000000f, 0.999979f, 0.999651f, 0.998159f, 0.993858f, 0.984047f, 0.964963f, 0.932452f, 0.883441f, 0.817541f, 0.737667f, 0.649219f, 0.558458f, 0.470943f, 0.390703f, 0.320005f,
1.000000f, 0.999980f, 0.999668f, 0.998199f, 0.993985f, 0.984715f, 0.966955f, 0.936405f, 0.889231f, 0.823875f, 0.742384f, 0.650248f, 0.554726f, 0.462681f, 0.379081f, 0.306563f,
1.000000f, 0.995284f, 0.998804f, 0.999445f, 0.999650f, 0.999723f, 0.999738f, 0.999720f, 0.999682f, 0.999627f, 0.999560f, 0.999482f, 0.999394f, 0.999297f, 0.999192f, 0.999079f,
1.000000f, 0.997510f, 0.960266f, 0.900925f, 0.888755f, 0.900262f, 0.911700f, 0.917082f, 0.916341f, 0.910526f, 0.900670f, 0.887614f, 0.872031f, 0.854471f, 0.835387f, 0.815164f,
1.000000f, 0.999402f, 0.989206f, 0.951159f, 0.904685f, 0.880930f, 0.875151f, 0.873744f, 0.869339f, 0.859591f, 0.844401f, 0.824460f, 0.800665f, 0.773907f, 0.745002f, 0.714660f,
1.000000f, 0.999734f, 0.995278f, 0.975148f, 0.935340f, 0.895509f, 0.869794f, 0.854510f, 0.841571f, 0.825764f, 0.805031f, 0.779183f, 0.748902f, 0.715194f, 0.679117f, 0.641650f,
1.000000f, 0.999848f, 0.997346f, 0.985485f, 0.956560f, 0.916285f, 0.879193f, 0.850771f, 0.827383f, 0.803807f, 0.776749f, 0.745046f, 0.708931f, 0.669342f, 0.627471f, 0.584496f,
1.000000f, 0.999900f, 0.998275f, 0.990507f, 0.969594f, 0.934282f, 0.893466f, 0.855814f, 0.822578f, 0.790603f, 0.756600f, 0.718837f, 0.677111f, 0.632207f, 0.585365f, 0.537902f,
1.000000f, 0.999928f, 0.998768f, 0.993244f, 0.977647f, 0.948023f, 0.907931f, 0.865129f, 0.823926f, 0.783862f, 0.742672f, 0.698642f, 0.651347f, 0.601434f, 0.550148f, 0.498895f,
1.000000f, 0.999945f, 0.999060f, 0.994879f, 0.982803f, 0.958131f, 0.920784f, 0.875992f, 0.829057f, 0.781821f, 0.733571f, 0.683176f, 0.630288f, 0.575529f, 0.520149f, 0.465605f,
1.000000f, 0.999955f, 0.999247f, 0.995927f, 0.986242f, 0.965534f, 0.931575f, 0.886898f, 0.836313f, 0.783116f, 0.728228f, 0.671499f, 0.612995f, 0.553471f, 0.494235f, 0.436771f,
1.000000f, 0.999962f, 0.999375f, 0.996636f, 0.988625f, 0.971005f, 0.940409f, 0.897095f, 0.844579f, 0.786709f, 0.725799f, 0.662898f, 0.598779f, 0.534532f, 0.471600f, 0.411502f,
1.000000f, 0.999968f, 0.999465f, 0.997137f, 0.990334f, 0.975108f, 0.947569f, 0.906268f, 0.853132f, 0.791816f, 0.725613f, 0.656809f, 0.587115f, 0.518167f, 0.451652f, 0.389139f,
1.000000f, 0.999972f, 0.999531f, 0.997504f, 0.991595f, 0.978237f, 0.953366f, 0.914343f, 0.861527f, 0.797858f, 0.727135f, 0.652779f, 0.577593f, 0.503960f, 0.433938f, 0.369185f,
1.000000f, 0.999975f, 0.999582f, 0.997781f, 0.992550f, 0.980661f, 0.958072f, 0.921364f, 0.869504f, 0.804411f, 0.729938f, 0.650437f, 0.569884f, 0.491585f, 0.418109f, 0.351255f,
1.000000f, 0.999977f, 0.999620f, 0.997994f, 0.993289f, 0.982570f, 0.961917f, 0.927431f, 0.876930f, 0.811170f, 0.733679f, 0.649480f, 0.563719f, 0.480779f, 0.403887f, 0.335045f,
1.000000f, 0.999979f, 0.999651f, 0.998163f, 0.993872f, 0.984095f, 0.965078f, 0.932660f, 0.883746f, 0.817923f, 0.738091f, 0.649655f, 0.558875f, 0.471330f, 0.391049f, 0.320309f,
1.000000f, 0.999980f, 0.999658f, 0.998277f, 0.994324f, 0.985318f, 0.967688f, 0.937159f, 0.889944f, 0.824522f, 0.742959f, 0.650753f, 0.555166f, 0.463063f, 0.379413f, 0.306851f
};
static const float table_ggx_glass_inv_Eavg[256] = {
1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f, 1.000000f,
1.000000f, 0.999883f, 0.998571f, 0.994611f, 0.987932f, 0.979340f, 0.969124f, 0.957150f, 0.943358f, 0.927910f, 0.911111f, 0.893347f, 0.875001f, 0.856410f, 0.837886f, 0.819667f,
1.000000f, 0.999879f, 0.998460f, 0.993636f, 0.983961f, 0.969802f, 0.952851f, 0.934658f, 0.915966f, 0.896938f, 0.877591f, 0.857980f, 0.838240f, 0.818537f, 0.799061f, 0.779987f,
1.000000f, 0.999877f, 0.998430f, 0.993345f, 0.982442f, 0.964923f, 0.941902f, 0.915671f, 0.888444f, 0.861595f, 0.835705f, 0.810866f, 0.787027f, 0.764116f, 0.742069f, 0.720883f,
1.000000f, 0.999876f, 0.998425f, 0.993276f, 0.981921f, 0.962787f, 0.936011f, 0.903450f, 0.867828f, 0.831654f, 0.796632f, 0.763575f, 0.732728f, 0.704029f, 0.677271f, 0.652272f,
1.000000f, 0.999877f, 0.998435f, 0.993313f, 0.981879f, 0.962128f, 0.933439f, 0.896895f, 0.854943f, 0.810510f, 0.766198f, 0.723791f, 0.684211f, 0.647805f, 0.614506f, 0.584089f,
1.000000f, 0.999877f, 0.998450f, 0.993399f, 0.982078f, 0.962279f, 0.932879f, 0.894276f, 0.848326f, 0.797836f, 0.745795f, 0.694724f, 0.646345f, 0.601608f, 0.560861f, 0.524053f,
1.000000f, 0.999878f, 0.998470f, 0.993509f, 0.982397f, 0.962854f, 0.933472f, 0.894132f, 0.846118f, 0.791843f, 0.734286f, 0.676340f, 0.620361f, 0.567934f, 0.519922f, 0.476637f,
1.000000f, 0.999879f, 0.998491f, 0.993625f, 0.982756f, 0.963613f, 0.934645f, 0.895397f, 0.846683f, 0.790470f, 0.729520f, 0.666816f, 0.605085f, 0.546425f, 0.492207f, 0.443121f,
1.000000f, 0.999880f, 0.998512f, 0.993737f, 0.983113f, 0.964411f, 0.936030f, 0.897312f, 0.848722f, 0.791863f, 0.729200f, 0.663653f, 0.598087f, 0.534951f, 0.475998f, 0.422303f,
1.000000f, 0.999881f, 0.998529f, 0.993838f, 0.983432f, 0.965152f, 0.937379f, 0.899354f, 0.851322f, 0.794586f, 0.731348f, 0.664390f, 0.596615f, 0.530632f, 0.468483f, 0.411497f,
1.000000f, 0.999882f, 0.998544f, 0.993921f, 0.983702f, 0.965776f, 0.938551f, 0.901202f, 0.853839f, 0.797572f, 0.734403f, 0.666974f, 0.598137f, 0.530590f, 0.466524f, 0.407467f,
1.000000f, 0.999883f, 0.998556f, 0.993986f, 0.983909f, 0.966256f, 0.939459f, 0.902655f, 0.855886f, 0.800135f, 0.737288f, 0.669858f, 0.600660f, 0.532400f, 0.467352f, 0.407150f,
1.000000f, 0.999883f, 0.998565f, 0.994033f, 0.984050f, 0.966579f, 0.940057f, 0.903620f, 0.857258f, 0.801907f, 0.739358f, 0.672075f, 0.602828f, 0.534326f, 0.468867f, 0.408146f,
1.000000f, 0.999883f, 0.998570f, 0.994058f, 0.984128f, 0.966748f, 0.940358f, 0.904091f, 0.857927f, 0.802767f, 0.740383f, 0.673205f, 0.603988f, 0.535434f, 0.469853f, 0.408957f,
1.000000f, 0.999883f, 0.998572f, 0.994065f, 0.984146f, 0.966784f, 0.940421f, 0.904186f, 0.858056f, 0.802932f, 0.740578f, 0.673420f, 0.604211f, 0.535654f, 0.470057f, 0.409136f
};
CCL_NAMESPACE_END

View File

@ -2350,7 +2350,7 @@ NODE_DEFINE(GlossyBsdfNode)
distribution_enum.insert("beckmann", CLOSURE_BSDF_MICROFACET_BECKMANN_ID);
distribution_enum.insert("ggx", CLOSURE_BSDF_MICROFACET_GGX_ID);
distribution_enum.insert("ashikhmin_shirley", CLOSURE_BSDF_ASHIKHMIN_SHIRLEY_ID);
distribution_enum.insert("Multiscatter GGX", CLOSURE_BSDF_MICROFACET_MULTI_GGX_ID);
distribution_enum.insert("multi_ggx", CLOSURE_BSDF_MICROFACET_MULTI_GGX_ID);
SOCKET_ENUM(distribution, "Distribution", distribution_enum, CLOSURE_BSDF_MICROFACET_GGX_ID);
SOCKET_IN_VECTOR(tangent, "Tangent", zero_float3(), SocketType::LINK_TANGENT);
@ -2444,6 +2444,7 @@ void GlossyBsdfNode::compile(SVMCompiler &compiler)
if (closure == CLOSURE_BSDF_REFLECTION_ID)
BsdfNode::compile(compiler, NULL, NULL);
/* TODO: Just use weight for legacy MultiGGX? Would also simplify OSL. */
else if (closure == CLOSURE_BSDF_MICROFACET_MULTI_GGX_ID)
BsdfNode::compile(
compiler, input("Roughness"), input("Anisotropy"), input("Rotation"), input("Color"));
@ -2471,7 +2472,7 @@ NODE_DEFINE(GlassBsdfNode)
distribution_enum.insert("sharp", CLOSURE_BSDF_SHARP_GLASS_ID);
distribution_enum.insert("beckmann", CLOSURE_BSDF_MICROFACET_BECKMANN_GLASS_ID);
distribution_enum.insert("ggx", CLOSURE_BSDF_MICROFACET_GGX_GLASS_ID);
distribution_enum.insert("Multiscatter GGX", CLOSURE_BSDF_MICROFACET_MULTI_GGX_GLASS_ID);
distribution_enum.insert("multi_ggx", CLOSURE_BSDF_MICROFACET_MULTI_GGX_GLASS_ID);
SOCKET_ENUM(
distribution, "Distribution", distribution_enum, CLOSURE_BSDF_MICROFACET_GGX_GLASS_ID);
SOCKET_IN_FLOAT(roughness, "Roughness", 0.0f);
@ -2749,8 +2750,8 @@ NODE_DEFINE(PrincipledBsdfNode)
NodeType *type = NodeType::add("principled_bsdf", create, NodeType::SHADER);
static NodeEnum distribution_enum;
distribution_enum.insert("GGX", CLOSURE_BSDF_MICROFACET_GGX_GLASS_ID);
distribution_enum.insert("Multiscatter GGX", CLOSURE_BSDF_MICROFACET_MULTI_GGX_GLASS_ID);
distribution_enum.insert("ggx", CLOSURE_BSDF_MICROFACET_GGX_GLASS_ID);
distribution_enum.insert("multi_ggx", CLOSURE_BSDF_MICROFACET_MULTI_GGX_GLASS_ID);
SOCKET_ENUM(
distribution, "Distribution", distribution_enum, CLOSURE_BSDF_MICROFACET_MULTI_GGX_GLASS_ID);

View File

@ -4752,8 +4752,8 @@ static const EnumPropertyItem node_glossy_items[] = {
"MULTI_GGX",
0,
"Multiscatter GGX",
"Slower than GGX but gives a more energy conserving results, which would otherwise be "
"visible as excessive darkening"},
"GGX with additional correction to account for multiple scattering, preserve energy and "
"prevent unexpected darkening at high roughness"},
{0, NULL, 0, NULL, NULL},
};
@ -4764,8 +4764,8 @@ static const EnumPropertyItem node_glass_items[] = {
"MULTI_GGX",
0,
"Multiscatter GGX",
"Slower than GGX but gives a more energy conserving results, which would otherwise be "
"visible as excessive darkening"},
"GGX with additional correction to account for multiple scattering, preserve energy and "
"prevent unexpected darkening at high roughness"},
{0, NULL, 0, NULL, NULL},
};