diff options
author | Clément Foucault <foucault.clem@gmail.com> | 2017-04-18 13:50:09 +0300 |
---|---|---|
committer | Clément Foucault <foucault.clem@gmail.com> | 2017-04-18 14:10:17 +0300 |
commit | edcf128ce279e1fa721a1ba16fc3a3dfeac4833b (patch) | |
tree | 4317cd33b39f63f90a26c33faf5790b965ebc3cd /source/blender/draw/engines | |
parent | f1fb605ec9ffd69b82652f3702de8b7ada570fd8 (diff) |
Eevee: Introduction of world preconvolved envmap.
For now only compute GGX convolution. The GGX LUT used for the split sum approximation (UE4) is merged with the LTX mag LUT that uses the same parameters (theta and roughness)
Diffstat (limited to 'source/blender/draw/engines')
16 files changed, 1828 insertions, 90 deletions
diff --git a/source/blender/draw/engines/eevee/eevee.c b/source/blender/draw/engines/eevee/eevee.c index e028249d2bb..f1eaead42c7 100644 --- a/source/blender/draw/engines/eevee/eevee.c +++ b/source/blender/draw/engines/eevee/eevee.c @@ -26,6 +26,8 @@ #include "DRW_render.h" #include "BLI_dynstr.h" +#include "BLI_rand.h" +#include "GPU_glew.h" #include "eevee.h" #include "eevee_private.h" @@ -39,29 +41,162 @@ static struct { struct GPUShader *depth_sh; struct GPUShader *tonemap; struct GPUShader *shadow_sh; + /* Temp : use world shader */ + struct GPUShader *probe_sh; + struct GPUShader *probe_filter_sh; + struct GPUTexture *ltc_mat; - struct GPUTexture *ltc_mag; + struct GPUTexture *brdf_lut; + struct GPUTexture *hammersley; + struct GPUTexture *jitter; float camera_pos[3]; } e_data = {NULL}; /* Engine data */ extern char datatoc_ltc_lib_glsl[]; +extern char datatoc_bsdf_lut_frag_glsl[]; extern char datatoc_bsdf_common_lib_glsl[]; extern char datatoc_bsdf_direct_lib_glsl[]; +extern char datatoc_bsdf_sampling_lib_glsl[]; extern char datatoc_lit_surface_frag_glsl[]; extern char datatoc_lit_surface_vert_glsl[]; extern char datatoc_tonemap_frag_glsl[]; extern char datatoc_shadow_frag_glsl[]; extern char datatoc_shadow_geom_glsl[]; extern char datatoc_shadow_vert_glsl[]; +extern char datatoc_probe_filter_frag_glsl[]; +extern char datatoc_probe_frag_glsl[]; +extern char datatoc_probe_geom_glsl[]; +extern char datatoc_probe_vert_glsl[]; + +/* Van der Corput sequence */ + /* From http://holger.dammertz.org/stuff/notes_HammersleyOnHemisphere.html */ +static float radical_inverse(int i) { + unsigned int bits = (unsigned int)i; + bits = (bits << 16u) | (bits >> 16u); + bits = ((bits & 0x55555555u) << 1u) | ((bits & 0xAAAAAAAAu) >> 1u); + bits = ((bits & 0x33333333u) << 2u) | ((bits & 0xCCCCCCCCu) >> 2u); + bits = ((bits & 0x0F0F0F0Fu) << 4u) | ((bits & 0xF0F0F0F0u) >> 4u); + bits = ((bits & 0x00FF00FFu) << 8u) | ((bits & 0xFF00FF00u) >> 8u); + return (float)bits * 2.3283064365386963e-10f; +} + +static struct GPUTexture *create_hammersley_sample_texture(int samples) +{ + struct GPUTexture *tex; + float (*texels)[2] = MEM_mallocN(sizeof(float[2]) * samples, "hammersley_tex"); + int i; + + for (i = 0; i < samples; i++) { + float phi = radical_inverse(i) * 2.0f * M_PI; + texels[i][0] = cos(phi); + texels[i][1] = sinf(phi); + } + + tex = DRW_texture_create_1D(samples, DRW_TEX_RG_16, DRW_TEX_WRAP, (float *)texels); + MEM_freeN(texels); + return tex; +} + +static struct GPUTexture *create_jitter_texture(int w, int h) +{ + struct GPUTexture *tex; + float (*texels)[2] = MEM_mallocN(sizeof(float[2]) * w * h, "jitter_tex"); + int i; + + /* TODO replace by something more evenly distributed like blue noise */ + for (i = 0; i < w * h; i++) { + texels[i][0] = 2.0f * BLI_frand() - 1.0f; + texels[i][1] = 2.0f * BLI_frand() - 1.0f; + normalize_v2(texels[i]); + } + + tex = DRW_texture_create_2D(w, h, DRW_TEX_RG_16, DRW_TEX_WRAP, (float *)texels); + MEM_freeN(texels); + return tex; +} + +static struct GPUTexture *create_ggx_lut_texture(int w, int h) +{ + struct GPUTexture *tex; +#if 0 /* Used only to generate the LUT values */ + struct GPUFrameBuffer *fb = NULL; + static float samples_ct = 8192.0f; + static float inv_samples_ct = 1.0f / 8192.0f; + + char *lib_str = NULL; + + DynStr *ds_vert = BLI_dynstr_new(); + BLI_dynstr_append(ds_vert, datatoc_bsdf_common_lib_glsl); + BLI_dynstr_append(ds_vert, datatoc_bsdf_sampling_lib_glsl); + lib_str = BLI_dynstr_get_cstring(ds_vert); + BLI_dynstr_free(ds_vert); + + struct GPUShader *sh = DRW_shader_create_with_lib(datatoc_probe_vert_glsl, datatoc_probe_geom_glsl, datatoc_bsdf_lut_frag_glsl, lib_str, + "#define HAMMERSLEY_SIZE 8192\n" + "#define BRDF_LUT_SIZE 64\n" + "#define NOISE_SIZE 64\n"); + + DRWPass *pass = DRW_pass_create("Probe Filtering", DRW_STATE_WRITE_COLOR); + DRWShadingGroup *grp = DRW_shgroup_create(sh, pass); + DRW_shgroup_uniform_float(grp, "sampleCount", &samples_ct, 1); + DRW_shgroup_uniform_float(grp, "invSampleCount", &inv_samples_ct, 1); + DRW_shgroup_uniform_texture(grp, "texHammersley", e_data.hammersley, 0); + DRW_shgroup_uniform_texture(grp, "texJitter", e_data.jitter, 1); + + struct Batch *geom = DRW_cache_fullscreen_quad_get(); + DRW_shgroup_call_add(grp, geom, NULL); + + float *texels = MEM_mallocN(sizeof(float[2]) * w * h, "lut"); + + tex = DRW_texture_create_2D(w, h, DRW_TEX_RG_16, DRW_TEX_FILTER, (float *)texels); + + DRWFboTexture tex_filter = {&tex, DRW_BUF_RG_16, DRW_TEX_FILTER}; + DRW_framebuffer_init(&fb, w, h, &tex_filter, 1); + + DRW_framebuffer_bind(fb); + DRW_draw_pass(pass); + + float *data = MEM_mallocN(sizeof(float[3]) * w * h, "lut"); + glReadBuffer(GL_COLOR_ATTACHMENT0); + glReadPixels(0, 0, w, h, GL_RGB, GL_FLOAT, data); + + printf("{"); + for (int i = 0; i < w*h * 3; i+=3) { + printf("%ff, %ff, ", data[i], data[i+1]); i+=3; + printf("%ff, %ff, ", data[i], data[i+1]); i+=3; + printf("%ff, %ff, ", data[i], data[i+1]); i+=3; + printf("%ff, %ff, \n", data[i], data[i+1]); + } + printf("}"); + + MEM_freeN(texels); + MEM_freeN(data); +#else + float (*texels)[3] = MEM_mallocN(sizeof(float[3]) * 64 * 64, "bsdf lut texels"); + + for (int i = 0; i < 64 * 64; i++) { + texels[i][0] = bsdf_split_sum_ggx[i*2 + 0]; + texels[i][1] = bsdf_split_sum_ggx[i*2 + 1]; + texels[i][2] = ltc_mag_ggx[i]; + } + + tex = DRW_texture_create_2D(64, 64, DRW_TEX_RGB_16, DRW_TEX_FILTER, (float *)texels); + MEM_freeN(texels); +#endif + + return tex; +} + /* *********** FUNCTIONS *********** */ -static void EEVEE_engine_init(void *vedata) +static void EEVEE_engine_init(void *ved) { - EEVEE_TextureList *txl = ((EEVEE_Data *)vedata)->txl; - EEVEE_FramebufferList *fbl = ((EEVEE_Data *)vedata)->fbl; - EEVEE_StorageList *stl = ((EEVEE_Data *)vedata)->stl; + EEVEE_Data *vedata = (EEVEE_Data *)ved; + EEVEE_TextureList *txl = vedata->txl; + EEVEE_FramebufferList *fbl = vedata->fbl; + EEVEE_StorageList *stl = vedata->stl; DRWFboTexture tex = {&txl->color, DRW_BUF_RGBA_16, DRW_TEX_FILTER}; @@ -98,6 +233,26 @@ static void EEVEE_engine_init(void *vedata) e_data.shadow_sh = DRW_shader_create(datatoc_shadow_vert_glsl, datatoc_shadow_geom_glsl, datatoc_shadow_frag_glsl, NULL); } + if (!e_data.probe_sh) { + e_data.probe_sh = DRW_shader_create(datatoc_probe_vert_glsl, datatoc_probe_geom_glsl, datatoc_probe_frag_glsl, NULL); + } + + if (!e_data.probe_filter_sh) { + char *lib_str = NULL; + + DynStr *ds_vert = BLI_dynstr_new(); + BLI_dynstr_append(ds_vert, datatoc_bsdf_common_lib_glsl); + BLI_dynstr_append(ds_vert, datatoc_bsdf_sampling_lib_glsl); + lib_str = BLI_dynstr_get_cstring(ds_vert); + BLI_dynstr_free(ds_vert); + + e_data.probe_filter_sh = DRW_shader_create_with_lib(datatoc_probe_vert_glsl, datatoc_probe_geom_glsl, datatoc_probe_filter_frag_glsl, lib_str, + "#define HAMMERSLEY_SIZE 8192\n" + "#define NOISE_SIZE 64\n"); + + MEM_freeN(lib_str); + } + if (!e_data.tonemap) { e_data.tonemap = DRW_shader_create_fullscreen(datatoc_tonemap_frag_glsl, NULL); } @@ -106,21 +261,40 @@ static void EEVEE_engine_init(void *vedata) e_data.ltc_mat = DRW_texture_create_2D(64, 64, DRW_TEX_RGBA_16, DRW_TEX_FILTER, ltc_mat_ggx); } - if (!e_data.ltc_mag) { - e_data.ltc_mag = DRW_texture_create_2D(64, 64, DRW_TEX_R_16, DRW_TEX_FILTER, ltc_mag_ggx); + if (!e_data.hammersley) { + e_data.hammersley = create_hammersley_sample_texture(8192); } - if (stl->lamps == NULL) { - EEVEE_lights_init(stl); + if (!e_data.jitter) { + e_data.jitter = create_jitter_texture(64, 64); + } + + if (!e_data.brdf_lut) { + e_data.brdf_lut = create_ggx_lut_texture(64, 64); } - // EEVEE_lights_update(stl); { float viewinvmat[4][4]; DRW_viewport_matrix_get(viewinvmat, DRW_MAT_VIEWINV); copy_v3_v3(e_data.camera_pos, viewinvmat[3]); } + + EEVEE_lights_init(stl); + + EEVEE_probes_init(vedata); + + // EEVEE_lights_update(stl); +} + +static DRWShadingGroup *eevee_cube_shgroup(struct GPUShader *sh, DRWPass *pass, struct Batch *geom) +{ + DRWShadingGroup *grp = DRW_shgroup_instance_create(sh, pass, geom); + + for (int i = 0; i < 6; ++i) + DRW_shgroup_dynamic_call_add(grp); + + return grp; } static void EEVEE_cache_init(void *vedata) @@ -135,7 +309,6 @@ static void EEVEE_cache_init(void *vedata) } { - /* Shadow Pass */ psl->shadow_pass = DRW_pass_create("Shadow Pass", DRW_STATE_WRITE_DEPTH | DRW_STATE_DEPTH_LESS); stl->g_data->shadow_shgrp = DRW_shgroup_create(e_data.shadow_sh, psl->shadow_pass); DRW_shgroup_uniform_mat4(stl->g_data->shadow_shgrp, "ShadowMatrix", (float *)stl->lamps->shadowmat); @@ -143,6 +316,31 @@ static void EEVEE_cache_init(void *vedata) } { + psl->probe_background = DRW_pass_create("Probe Background Pass", DRW_STATE_WRITE_DEPTH | DRW_STATE_WRITE_COLOR); + + struct Batch *geom = DRW_cache_fullscreen_quad_get(); + DRWShadingGroup *grp = eevee_cube_shgroup(e_data.probe_sh, psl->probe_background, geom); + DRW_shgroup_uniform_int(grp, "Layer", &stl->probes->layer, 1); + DRW_shgroup_uniform_buffer(grp, "probeLatLong", &stl->probes->backgroundtex, 0); + } + + { + psl->probe_prefilter = DRW_pass_create("Probe Filtering", DRW_STATE_WRITE_COLOR); + + struct Batch *geom = DRW_cache_fullscreen_quad_get(); + DRWShadingGroup *grp = eevee_cube_shgroup(e_data.probe_filter_sh, psl->probe_prefilter, geom); + DRW_shgroup_uniform_float(grp, "sampleCount", &stl->probes->samples_ct, 1); + DRW_shgroup_uniform_float(grp, "invSampleCount", &stl->probes->invsamples_ct, 1); + DRW_shgroup_uniform_float(grp, "roughnessSquared", &stl->probes->roughness, 1); + DRW_shgroup_uniform_float(grp, "lodFactor", &stl->probes->lodfactor, 1); + DRW_shgroup_uniform_float(grp, "lodMax", &stl->probes->lodmax, 1); + DRW_shgroup_uniform_int(grp, "Layer", &stl->probes->layer, 1); + DRW_shgroup_uniform_texture(grp, "texHammersley", e_data.hammersley, 0); + // DRW_shgroup_uniform_texture(grp, "texJitter", e_data.jitter, 1); + DRW_shgroup_uniform_texture(grp, "probeHdr", txl->probe_rt, 3); + } + + { psl->depth_pass = DRW_pass_create("Depth Pass", DRW_STATE_WRITE_DEPTH | DRW_STATE_DEPTH_LESS); stl->g_data->depth_shgrp = DRW_shgroup_create(e_data.depth_sh, psl->depth_pass); @@ -158,9 +356,11 @@ static void EEVEE_cache_init(void *vedata) DRW_shgroup_uniform_block(stl->g_data->default_lit_grp, "light_block", stl->light_ubo, 0); DRW_shgroup_uniform_block(stl->g_data->default_lit_grp, "shadow_block", stl->shadow_ubo, 1); DRW_shgroup_uniform_int(stl->g_data->default_lit_grp, "light_count", &stl->lamps->num_light, 1); + DRW_shgroup_uniform_float(stl->g_data->default_lit_grp, "lodMax", &stl->probes->lodmax, 1); DRW_shgroup_uniform_vec3(stl->g_data->default_lit_grp, "cameraPos", e_data.camera_pos, 1); DRW_shgroup_uniform_texture(stl->g_data->default_lit_grp, "ltcMat", e_data.ltc_mat, 0); - DRW_shgroup_uniform_texture(stl->g_data->default_lit_grp, "ltcMag", e_data.ltc_mag, 1); + DRW_shgroup_uniform_texture(stl->g_data->default_lit_grp, "brdfLut", e_data.brdf_lut, 1); + DRW_shgroup_uniform_texture(stl->g_data->default_lit_grp, "probeFiltered", txl->probe_pool, 2); /* NOTE : Adding Shadow Map textures uniform in EEVEE_cache_finish */ } @@ -208,8 +408,8 @@ static void EEVEE_cache_finish(void *vedata) EEVEE_lights_cache_finish(stl, txl, fbl); /* Shadows binding */ - DRW_shgroup_uniform_texture(stl->g_data->default_lit_grp, "shadowMaps", txl->shadow_depth_map_pool, 2); - DRW_shgroup_uniform_texture(stl->g_data->default_lit_grp, "shadowCubes", txl->shadow_depth_cube_pool, 3); + DRW_shgroup_uniform_texture(stl->g_data->default_lit_grp, "shadowMaps", txl->shadow_depth_map_pool, 4); + DRW_shgroup_uniform_texture(stl->g_data->default_lit_grp, "shadowCubes", txl->shadow_depth_cube_pool, 5); } static void EEVEE_draw_scene(void *vedata) @@ -221,6 +421,9 @@ static void EEVEE_draw_scene(void *vedata) DefaultFramebufferList *dfbl = DRW_viewport_framebuffer_list_get(); DefaultTextureList *dtxl = DRW_viewport_texture_list_get(); + /* Refresh Probes */ + EEVEE_refresh_probe((EEVEE_Data *)vedata); + /* Refresh shadows */ EEVEE_draw_shadows((EEVEE_Data *)vedata); @@ -250,9 +453,13 @@ static void EEVEE_engine_free(void) { DRW_SHADER_FREE_SAFE(e_data.default_lit); DRW_SHADER_FREE_SAFE(e_data.shadow_sh); + DRW_SHADER_FREE_SAFE(e_data.probe_sh); + DRW_SHADER_FREE_SAFE(e_data.probe_filter_sh); DRW_SHADER_FREE_SAFE(e_data.tonemap); DRW_TEXTURE_FREE_SAFE(e_data.ltc_mat); - DRW_TEXTURE_FREE_SAFE(e_data.ltc_mag); + DRW_TEXTURE_FREE_SAFE(e_data.brdf_lut); + DRW_TEXTURE_FREE_SAFE(e_data.hammersley); + DRW_TEXTURE_FREE_SAFE(e_data.jitter); } static void EEVEE_collection_settings_create(RenderEngine *UNUSED(engine), IDProperty *props) diff --git a/source/blender/draw/engines/eevee/eevee_lights.c b/source/blender/draw/engines/eevee/eevee_lights.c index 9c19020050d..12d8fc2db27 100644 --- a/source/blender/draw/engines/eevee/eevee_lights.c +++ b/source/blender/draw/engines/eevee/eevee_lights.c @@ -241,46 +241,6 @@ static void eevee_light_setup(Object *ob, EEVEE_LampsInfo *linfo, EEVEE_LampEngi evli->shadowid = -1.0f; } -static float texcomat[4][4] = { /* From NDC to TexCo */ - {0.5, 0.0, 0.0, 0.0}, - {0.0, 0.5, 0.0, 0.0}, - {0.0, 0.0, 0.5, 0.0}, - {0.5, 0.5, 0.5, 1.0} -}; - -static float cubefacemat[6][4][4] = { - /* Pos X */ - {{0.0, 0.0, -1.0, 0.0}, - {0.0, -1.0, 0.0, 0.0}, - {-1.0, 0.0, 0.0, 0.0}, - {0.0, 0.0, 0.0, 1.0}}, - /* Neg X */ - {{0.0, 0.0, 1.0, 0.0}, - {0.0, -1.0, 0.0, 0.0}, - {1.0, 0.0, 0.0, 0.0}, - {0.0, 0.0, 0.0, 1.0}}, - /* Pos Y */ - {{1.0, 0.0, 0.0, 0.0}, - {0.0, 0.0, 1.0, 0.0}, - {0.0, -1.0, 0.0, 0.0}, - {0.0, 0.0, 0.0, 1.0}}, - /* Neg Y */ - {{1.0, 0.0, 0.0, 0.0}, - {0.0, 0.0, -1.0, 0.0}, - {0.0, 1.0, 0.0, 0.0}, - {0.0, 0.0, 0.0, 1.0}}, - /* Pos Z */ - {{1.0, 0.0, 0.0, 0.0}, - {0.0, -1.0, 0.0, 0.0}, - {0.0, 0.0, -1.0, 0.0}, - {0.0, 0.0, 0.0, 1.0}}, - /* Neg Z */ - {{-1.0, 0.0, 0.0, 0.0}, - {0.0, -1.0, 0.0, 0.0}, - {0.0, 0.0, 1.0, 0.0}, - {0.0, 0.0, 0.0, 1.0}}, -}; - static void eevee_shadow_cube_setup(Object *ob, EEVEE_LampsInfo *linfo, EEVEE_LampEngineData *led) { float projmat[4][4]; diff --git a/source/blender/draw/engines/eevee/eevee_lut.h b/source/blender/draw/engines/eevee/eevee_lut.h index 4fdfb4c33e2..f2b53467708 100644 --- a/source/blender/draw/engines/eevee/eevee_lut.h +++ b/source/blender/draw/engines/eevee/eevee_lut.h @@ -2318,4 +2318,1030 @@ static float ltc_mag_ggx[64 * 64] = { 0.942877, }; +static float bsdf_split_sum_ggx[64 * 64 * 2] = { + 1.000000f, 0.000000f, 1.000000f, 0.000000f, 1.000000f, 0.000000f, 1.000000f, 0.000000f, + 1.000000f, 0.000000f, 1.000000f, 0.000000f, 0.999512f, 0.000000f, 0.999512f, 0.000000f, + 0.999512f, 0.000000f, 0.999023f, 0.000001f, 0.999023f, 0.000001f, 0.998535f, 0.000001f, + 0.998047f, 0.000001f, 0.997559f, 0.000002f, 0.997070f, 0.000003f, 0.996094f, 0.000004f, + 0.994629f, 0.000004f, 0.993652f, 0.000006f, 0.991699f, 0.000007f, 0.989746f, 0.000008f, + 0.987305f, 0.000010f, 0.984375f, 0.000012f, 0.980957f, 0.000013f, 0.977539f, 0.000016f, + 0.973145f, 0.000018f, 0.967773f, 0.000020f, 0.961914f, 0.000023f, 0.955566f, 0.000025f, + 0.947754f, 0.000028f, 0.939941f, 0.000031f, 0.930664f, 0.000033f, 0.920410f, 0.000036f, + 0.909180f, 0.000039f, 0.896973f, 0.000042f, 0.884277f, 0.000044f, 0.870117f, 0.000047f, + 0.854980f, 0.000049f, 0.838867f, 0.000051f, 0.821777f, 0.000053f, 0.803711f, 0.000055f, + 0.785156f, 0.000057f, 0.765625f, 0.000058f, 0.745605f, 0.000059f, 0.724609f, 0.000060f, + 0.703613f, 0.000061f, 0.681641f, 0.000061f, 0.659668f, 0.000061f, 0.637695f, 0.000061f, + 0.615234f, 0.000061f, 0.592773f, 0.000060f, 0.570801f, 0.000060f, 0.548340f, 0.000059f, + 0.526855f, 0.000058f, 0.504883f, 0.000057f, 0.483887f, 0.000055f, 0.462891f, 0.000054f, + 0.442627f, 0.000053f, 0.422607f, 0.000051f, 0.403320f, 0.000050f, 0.384766f, 0.000048f, + 0.366455f, 0.000046f, 0.348877f, 0.000045f, 0.332031f, 0.000043f, 0.315918f, 0.000041f, + 0.999512f, 0.000000f, 0.999512f, 0.000000f, 1.000000f, 0.000000f, 1.000000f, 0.000000f, + 0.999512f, 0.000000f, 1.000000f, 0.000000f, 0.999512f, 0.000000f, 0.999512f, 0.000000f, + 0.999512f, 0.000000f, 0.999023f, 0.000001f, 0.999023f, 0.000001f, 0.998535f, 0.000002f, + 0.998047f, 0.000003f, 0.997559f, 0.000004f, 0.997070f, 0.000005f, 0.996094f, 0.000006f, + 0.994629f, 0.000008f, 0.993164f, 0.000010f, 0.991699f, 0.000012f, 0.989746f, 0.000015f, + 0.987305f, 0.000018f, 0.984375f, 0.000020f, 0.980957f, 0.000024f, 0.977051f, 0.000027f, + 0.972168f, 0.000031f, 0.967285f, 0.000035f, 0.961426f, 0.000039f, 0.954590f, 0.000043f, + 0.947266f, 0.000048f, 0.938965f, 0.000052f, 0.929199f, 0.000057f, 0.919434f, 0.000061f, + 0.908203f, 0.000065f, 0.895996f, 0.000069f, 0.882812f, 0.000073f, 0.868652f, 0.000077f, + 0.853027f, 0.000080f, 0.837402f, 0.000083f, 0.820312f, 0.000086f, 0.802246f, 0.000088f, + 0.783691f, 0.000090f, 0.764160f, 0.000092f, 0.744141f, 0.000093f, 0.723633f, 0.000093f, + 0.702637f, 0.000094f, 0.681152f, 0.000094f, 0.659180f, 0.000093f, 0.637207f, 0.000093f, + 0.615234f, 0.000091f, 0.593262f, 0.000090f, 0.571289f, 0.000088f, 0.549316f, 0.000087f, + 0.527344f, 0.000085f, 0.505859f, 0.000082f, 0.485107f, 0.000080f, 0.464355f, 0.000078f, + 0.444336f, 0.000075f, 0.424561f, 0.000072f, 0.405273f, 0.000070f, 0.386719f, 0.000067f, + 0.368652f, 0.000065f, 0.351318f, 0.000062f, 0.334473f, 0.000059f, 0.318115f, 0.000057f, + 0.999512f, 0.000000f, 0.999512f, 0.000000f, 0.999512f, 0.000000f, 1.000000f, 0.000000f, + 0.999512f, 0.000000f, 0.999512f, 0.000000f, 0.999512f, 0.000001f, 0.999512f, 0.000001f, + 0.999512f, 0.000001f, 0.999512f, 0.000003f, 0.999023f, 0.000002f, 0.998535f, 0.000004f, + 0.998047f, 0.000005f, 0.997559f, 0.000007f, 0.997070f, 0.000009f, 0.996094f, 0.000011f, + 0.994629f, 0.000013f, 0.993164f, 0.000017f, 0.991211f, 0.000020f, 0.989258f, 0.000024f, + 0.986816f, 0.000028f, 0.983887f, 0.000033f, 0.980469f, 0.000038f, 0.976562f, 0.000043f, + 0.971680f, 0.000049f, 0.966797f, 0.000055f, 0.960449f, 0.000062f, 0.953613f, 0.000068f, + 0.946289f, 0.000075f, 0.937500f, 0.000081f, 0.928223f, 0.000088f, 0.917969f, 0.000094f, + 0.906738f, 0.000100f, 0.894531f, 0.000106f, 0.880859f, 0.000111f, 0.866699f, 0.000116f, + 0.851562f, 0.000120f, 0.835449f, 0.000124f, 0.818359f, 0.000127f, 0.800781f, 0.000130f, + 0.782227f, 0.000132f, 0.762695f, 0.000134f, 0.742676f, 0.000134f, 0.722656f, 0.000135f, + 0.701660f, 0.000134f, 0.680176f, 0.000133f, 0.658691f, 0.000132f, 0.636719f, 0.000130f, + 0.615234f, 0.000128f, 0.593262f, 0.000125f, 0.571289f, 0.000123f, 0.549805f, 0.000119f, + 0.528320f, 0.000116f, 0.507324f, 0.000112f, 0.486328f, 0.000109f, 0.466064f, 0.000105f, + 0.446045f, 0.000101f, 0.426514f, 0.000097f, 0.407471f, 0.000093f, 0.388916f, 0.000089f, + 0.370850f, 0.000085f, 0.353516f, 0.000082f, 0.336914f, 0.000078f, 0.320557f, 0.000074f, + 1.000000f, 0.000000f, 0.999512f, 0.000000f, 0.999512f, 0.000000f, 0.999512f, 0.000000f, + 1.000000f, 0.000000f, 1.000000f, 0.000001f, 0.999512f, 0.000001f, 0.999512f, 0.000002f, + 0.999512f, 0.000002f, 0.999023f, 0.000003f, 0.999023f, 0.000005f, 0.998535f, 0.000006f, + 0.998535f, 0.000008f, 0.997559f, 0.000011f, 0.997070f, 0.000014f, 0.996094f, 0.000017f, + 0.994629f, 0.000020f, 0.993164f, 0.000026f, 0.991211f, 0.000030f, 0.989258f, 0.000036f, + 0.986816f, 0.000043f, 0.983398f, 0.000050f, 0.979980f, 0.000058f, 0.976074f, 0.000066f, + 0.971191f, 0.000074f, 0.965820f, 0.000082f, 0.959961f, 0.000093f, 0.952637f, 0.000101f, + 0.945312f, 0.000111f, 0.936523f, 0.000120f, 0.927246f, 0.000129f, 0.916504f, 0.000137f, + 0.905273f, 0.000145f, 0.892578f, 0.000153f, 0.879395f, 0.000160f, 0.865234f, 0.000166f, + 0.850098f, 0.000171f, 0.833984f, 0.000176f, 0.816895f, 0.000179f, 0.799316f, 0.000182f, + 0.780762f, 0.000184f, 0.761230f, 0.000185f, 0.741699f, 0.000185f, 0.721191f, 0.000184f, + 0.700684f, 0.000183f, 0.679688f, 0.000181f, 0.658203f, 0.000178f, 0.636719f, 0.000175f, + 0.615234f, 0.000171f, 0.593262f, 0.000167f, 0.571777f, 0.000162f, 0.550293f, 0.000158f, + 0.529297f, 0.000152f, 0.508301f, 0.000147f, 0.487793f, 0.000142f, 0.467529f, 0.000136f, + 0.447754f, 0.000131f, 0.428223f, 0.000125f, 0.409424f, 0.000120f, 0.391113f, 0.000115f, + 0.373291f, 0.000109f, 0.355957f, 0.000104f, 0.339355f, 0.000099f, 0.323242f, 0.000094f, + 0.999512f, 0.000002f, 0.999512f, 0.000002f, 1.000000f, 0.000002f, 0.999512f, 0.000002f, + 1.000000f, 0.000002f, 0.999512f, 0.000002f, 0.999512f, 0.000002f, 0.999512f, 0.000003f, + 0.999512f, 0.000004f, 0.999512f, 0.000005f, 0.999023f, 0.000007f, 0.998535f, 0.000010f, + 0.998047f, 0.000012f, 0.997559f, 0.000017f, 0.996582f, 0.000020f, 0.995605f, 0.000025f, + 0.994629f, 0.000032f, 0.993164f, 0.000038f, 0.991211f, 0.000047f, 0.988770f, 0.000055f, + 0.986328f, 0.000063f, 0.983398f, 0.000074f, 0.979492f, 0.000085f, 0.975586f, 0.000095f, + 0.970703f, 0.000108f, 0.965332f, 0.000121f, 0.958984f, 0.000132f, 0.952148f, 0.000145f, + 0.944336f, 0.000157f, 0.935547f, 0.000170f, 0.925781f, 0.000181f, 0.915039f, 0.000192f, + 0.903809f, 0.000203f, 0.891113f, 0.000212f, 0.877930f, 0.000220f, 0.863281f, 0.000227f, + 0.848145f, 0.000234f, 0.832031f, 0.000239f, 0.814941f, 0.000242f, 0.797363f, 0.000245f, + 0.778809f, 0.000247f, 0.759766f, 0.000247f, 0.740234f, 0.000246f, 0.720215f, 0.000244f, + 0.699707f, 0.000241f, 0.678711f, 0.000237f, 0.657715f, 0.000233f, 0.636230f, 0.000228f, + 0.614746f, 0.000222f, 0.593750f, 0.000216f, 0.572266f, 0.000209f, 0.551270f, 0.000202f, + 0.530273f, 0.000195f, 0.509277f, 0.000187f, 0.489014f, 0.000180f, 0.468994f, 0.000172f, + 0.449463f, 0.000165f, 0.430176f, 0.000157f, 0.411377f, 0.000150f, 0.393311f, 0.000143f, + 0.375488f, 0.000136f, 0.358398f, 0.000129f, 0.341797f, 0.000123f, 0.325684f, 0.000116f, + 0.999512f, 0.000005f, 0.999512f, 0.000005f, 0.999512f, 0.000005f, 0.999512f, 0.000005f, + 0.999512f, 0.000005f, 0.999512f, 0.000005f, 0.999512f, 0.000006f, 0.999512f, 0.000007f, + 0.999512f, 0.000008f, 0.999512f, 0.000011f, 0.999023f, 0.000013f, 0.998535f, 0.000015f, + 0.998047f, 0.000019f, 0.997559f, 0.000026f, 0.996582f, 0.000033f, 0.995605f, 0.000040f, + 0.994141f, 0.000047f, 0.993164f, 0.000058f, 0.991211f, 0.000069f, 0.988770f, 0.000080f, + 0.985840f, 0.000093f, 0.982910f, 0.000106f, 0.979004f, 0.000121f, 0.975098f, 0.000137f, + 0.970215f, 0.000153f, 0.964355f, 0.000169f, 0.958008f, 0.000186f, 0.951172f, 0.000201f, + 0.943359f, 0.000218f, 0.934082f, 0.000233f, 0.924316f, 0.000248f, 0.914062f, 0.000262f, + 0.902344f, 0.000275f, 0.889648f, 0.000286f, 0.875977f, 0.000295f, 0.861816f, 0.000304f, + 0.846680f, 0.000311f, 0.830566f, 0.000316f, 0.813477f, 0.000319f, 0.795898f, 0.000321f, + 0.777344f, 0.000322f, 0.758301f, 0.000320f, 0.739258f, 0.000318f, 0.719238f, 0.000314f, + 0.698730f, 0.000309f, 0.678223f, 0.000303f, 0.657227f, 0.000296f, 0.636230f, 0.000288f, + 0.614746f, 0.000280f, 0.593750f, 0.000271f, 0.572754f, 0.000262f, 0.551758f, 0.000252f, + 0.531250f, 0.000243f, 0.510742f, 0.000233f, 0.490479f, 0.000223f, 0.470703f, 0.000213f, + 0.451172f, 0.000203f, 0.432129f, 0.000194f, 0.413574f, 0.000184f, 0.395508f, 0.000175f, + 0.377930f, 0.000166f, 0.360840f, 0.000157f, 0.344238f, 0.000149f, 0.328125f, 0.000141f, + 0.999512f, 0.000011f, 0.999512f, 0.000011f, 0.999512f, 0.000011f, 0.999512f, 0.000011f, + 0.999512f, 0.000011f, 0.999512f, 0.000012f, 0.999512f, 0.000014f, 0.999512f, 0.000015f, + 0.999512f, 0.000017f, 0.999023f, 0.000020f, 0.998535f, 0.000022f, 0.998535f, 0.000028f, + 0.998047f, 0.000034f, 0.997559f, 0.000042f, 0.996582f, 0.000050f, 0.995605f, 0.000060f, + 0.994141f, 0.000072f, 0.992676f, 0.000084f, 0.990723f, 0.000099f, 0.988281f, 0.000115f, + 0.985840f, 0.000133f, 0.982422f, 0.000150f, 0.978516f, 0.000171f, 0.974609f, 0.000191f, + 0.969238f, 0.000211f, 0.963867f, 0.000232f, 0.957520f, 0.000253f, 0.950195f, 0.000274f, + 0.941895f, 0.000294f, 0.933105f, 0.000314f, 0.922852f, 0.000332f, 0.912109f, 0.000348f, + 0.900879f, 0.000363f, 0.888184f, 0.000377f, 0.874512f, 0.000387f, 0.859863f, 0.000397f, + 0.844727f, 0.000404f, 0.828613f, 0.000408f, 0.811523f, 0.000411f, 0.793945f, 0.000412f, + 0.775879f, 0.000411f, 0.756836f, 0.000407f, 0.737793f, 0.000403f, 0.717773f, 0.000396f, + 0.697754f, 0.000389f, 0.677246f, 0.000380f, 0.656738f, 0.000370f, 0.635742f, 0.000359f, + 0.614746f, 0.000347f, 0.594238f, 0.000335f, 0.573242f, 0.000323f, 0.552734f, 0.000310f, + 0.532227f, 0.000297f, 0.511719f, 0.000284f, 0.491943f, 0.000272f, 0.472412f, 0.000259f, + 0.453125f, 0.000246f, 0.434082f, 0.000234f, 0.415771f, 0.000222f, 0.397705f, 0.000211f, + 0.380127f, 0.000199f, 0.363281f, 0.000189f, 0.346680f, 0.000178f, 0.330811f, 0.000168f, + 0.999512f, 0.000022f, 0.999512f, 0.000022f, 0.999512f, 0.000022f, 0.999512f, 0.000022f, + 0.999512f, 0.000023f, 0.999512f, 0.000025f, 0.999512f, 0.000024f, 0.999512f, 0.000028f, + 0.999023f, 0.000030f, 0.999023f, 0.000035f, 0.999023f, 0.000040f, 0.998535f, 0.000046f, + 0.998047f, 0.000056f, 0.997559f, 0.000063f, 0.996094f, 0.000077f, 0.995605f, 0.000089f, + 0.994141f, 0.000106f, 0.992188f, 0.000123f, 0.990234f, 0.000143f, 0.987793f, 0.000163f, + 0.985352f, 0.000185f, 0.981934f, 0.000211f, 0.978027f, 0.000236f, 0.973633f, 0.000261f, + 0.968750f, 0.000288f, 0.962891f, 0.000314f, 0.956055f, 0.000341f, 0.949219f, 0.000366f, + 0.940918f, 0.000391f, 0.931641f, 0.000414f, 0.921875f, 0.000436f, 0.910645f, 0.000455f, + 0.898926f, 0.000471f, 0.886230f, 0.000487f, 0.872559f, 0.000499f, 0.858398f, 0.000509f, + 0.842773f, 0.000515f, 0.826660f, 0.000518f, 0.810059f, 0.000520f, 0.792480f, 0.000519f, + 0.774414f, 0.000515f, 0.755371f, 0.000509f, 0.736328f, 0.000501f, 0.716797f, 0.000492f, + 0.696777f, 0.000480f, 0.676758f, 0.000468f, 0.656250f, 0.000454f, 0.635742f, 0.000439f, + 0.615234f, 0.000424f, 0.594238f, 0.000408f, 0.573730f, 0.000392f, 0.553223f, 0.000375f, + 0.533203f, 0.000359f, 0.513184f, 0.000342f, 0.493408f, 0.000326f, 0.474121f, 0.000310f, + 0.455078f, 0.000294f, 0.436279f, 0.000279f, 0.417969f, 0.000264f, 0.400146f, 0.000250f, + 0.382812f, 0.000237f, 0.365723f, 0.000223f, 0.349365f, 0.000211f, 0.333496f, 0.000199f, + 0.999512f, 0.000041f, 0.999512f, 0.000041f, 0.999512f, 0.000041f, 0.999512f, 0.000042f, + 0.999512f, 0.000042f, 0.999512f, 0.000044f, 0.999512f, 0.000046f, 0.999512f, 0.000049f, + 0.999512f, 0.000054f, 0.999512f, 0.000059f, 0.999023f, 0.000065f, 0.998535f, 0.000076f, + 0.998047f, 0.000087f, 0.997070f, 0.000098f, 0.996582f, 0.000117f, 0.995117f, 0.000135f, + 0.993652f, 0.000152f, 0.992188f, 0.000176f, 0.989746f, 0.000201f, 0.987793f, 0.000228f, + 0.984863f, 0.000256f, 0.981445f, 0.000286f, 0.977539f, 0.000318f, 0.973145f, 0.000352f, + 0.967773f, 0.000384f, 0.961914f, 0.000417f, 0.955566f, 0.000451f, 0.947754f, 0.000481f, + 0.939453f, 0.000510f, 0.930176f, 0.000537f, 0.919922f, 0.000563f, 0.909180f, 0.000585f, + 0.897461f, 0.000604f, 0.884766f, 0.000620f, 0.871094f, 0.000632f, 0.856445f, 0.000641f, + 0.841309f, 0.000647f, 0.825195f, 0.000648f, 0.808105f, 0.000648f, 0.790527f, 0.000643f, + 0.772949f, 0.000637f, 0.754395f, 0.000627f, 0.735352f, 0.000615f, 0.715820f, 0.000601f, + 0.695801f, 0.000585f, 0.675781f, 0.000568f, 0.655762f, 0.000550f, 0.635742f, 0.000530f, + 0.615234f, 0.000510f, 0.594727f, 0.000490f, 0.574707f, 0.000469f, 0.554199f, 0.000448f, + 0.534180f, 0.000428f, 0.514648f, 0.000407f, 0.495117f, 0.000387f, 0.475830f, 0.000367f, + 0.456787f, 0.000348f, 0.438232f, 0.000329f, 0.420166f, 0.000311f, 0.402344f, 0.000294f, + 0.385254f, 0.000277f, 0.368408f, 0.000262f, 0.352051f, 0.000246f, 0.336182f, 0.000232f, + 0.999512f, 0.000072f, 0.999512f, 0.000072f, 0.999512f, 0.000072f, 0.999512f, 0.000072f, + 0.999512f, 0.000073f, 0.999512f, 0.000076f, 0.999512f, 0.000078f, 0.999512f, 0.000082f, + 0.999023f, 0.000086f, 0.999023f, 0.000095f, 0.998535f, 0.000102f, 0.998047f, 0.000116f, + 0.998047f, 0.000131f, 0.997070f, 0.000147f, 0.996094f, 0.000167f, 0.995117f, 0.000195f, + 0.993652f, 0.000219f, 0.991699f, 0.000246f, 0.989746f, 0.000278f, 0.987305f, 0.000315f, + 0.984375f, 0.000350f, 0.980957f, 0.000385f, 0.976562f, 0.000427f, 0.972168f, 0.000467f, + 0.967285f, 0.000509f, 0.960938f, 0.000548f, 0.954102f, 0.000587f, 0.946777f, 0.000623f, + 0.937988f, 0.000657f, 0.928711f, 0.000690f, 0.918457f, 0.000718f, 0.907715f, 0.000741f, + 0.895508f, 0.000762f, 0.882812f, 0.000778f, 0.869141f, 0.000791f, 0.854492f, 0.000798f, + 0.839355f, 0.000802f, 0.823242f, 0.000801f, 0.806152f, 0.000796f, 0.789062f, 0.000788f, + 0.770996f, 0.000777f, 0.752930f, 0.000762f, 0.733887f, 0.000745f, 0.714844f, 0.000726f, + 0.695312f, 0.000704f, 0.675293f, 0.000682f, 0.655273f, 0.000658f, 0.635254f, 0.000633f, + 0.615234f, 0.000607f, 0.595215f, 0.000582f, 0.575195f, 0.000556f, 0.555176f, 0.000530f, + 0.535645f, 0.000504f, 0.515625f, 0.000479f, 0.496582f, 0.000455f, 0.477539f, 0.000431f, + 0.458984f, 0.000407f, 0.440430f, 0.000385f, 0.422363f, 0.000363f, 0.404785f, 0.000343f, + 0.387695f, 0.000323f, 0.370850f, 0.000304f, 0.354736f, 0.000286f, 0.338867f, 0.000268f, + 0.999512f, 0.000119f, 0.999512f, 0.000119f, 0.999512f, 0.000119f, 0.999512f, 0.000119f, + 0.999512f, 0.000121f, 0.999512f, 0.000122f, 0.999512f, 0.000128f, 0.999512f, 0.000131f, + 0.999512f, 0.000139f, 0.999023f, 0.000149f, 0.998535f, 0.000161f, 0.998047f, 0.000179f, + 0.998047f, 0.000194f, 0.997070f, 0.000220f, 0.996094f, 0.000247f, 0.994629f, 0.000275f, + 0.993652f, 0.000309f, 0.991699f, 0.000344f, 0.989746f, 0.000385f, 0.986816f, 0.000429f, + 0.983887f, 0.000471f, 0.980469f, 0.000519f, 0.976074f, 0.000565f, 0.971680f, 0.000614f, + 0.966309f, 0.000664f, 0.959961f, 0.000710f, 0.953125f, 0.000754f, 0.945312f, 0.000797f, + 0.936523f, 0.000837f, 0.927246f, 0.000873f, 0.916992f, 0.000902f, 0.905762f, 0.000929f, + 0.893555f, 0.000950f, 0.880859f, 0.000966f, 0.866699f, 0.000977f, 0.852539f, 0.000981f, + 0.836914f, 0.000981f, 0.821289f, 0.000977f, 0.804688f, 0.000968f, 0.787109f, 0.000955f, + 0.769531f, 0.000937f, 0.751465f, 0.000917f, 0.732422f, 0.000894f, 0.713379f, 0.000868f, + 0.694336f, 0.000840f, 0.674805f, 0.000811f, 0.655273f, 0.000780f, 0.635254f, 0.000749f, + 0.615723f, 0.000716f, 0.595703f, 0.000685f, 0.575684f, 0.000653f, 0.556152f, 0.000621f, + 0.536621f, 0.000590f, 0.517090f, 0.000559f, 0.498291f, 0.000530f, 0.479492f, 0.000501f, + 0.460938f, 0.000473f, 0.442627f, 0.000446f, 0.424805f, 0.000420f, 0.407227f, 0.000396f, + 0.390137f, 0.000373f, 0.373535f, 0.000350f, 0.357422f, 0.000329f, 0.341553f, 0.000309f, + 0.999512f, 0.000187f, 0.999512f, 0.000187f, 0.999512f, 0.000188f, 0.999512f, 0.000188f, + 0.999512f, 0.000190f, 0.999512f, 0.000194f, 0.999512f, 0.000201f, 0.999023f, 0.000204f, + 0.999023f, 0.000213f, 0.999023f, 0.000228f, 0.998535f, 0.000242f, 0.998535f, 0.000264f, + 0.997559f, 0.000285f, 0.997070f, 0.000311f, 0.996094f, 0.000351f, 0.995117f, 0.000386f, + 0.993164f, 0.000429f, 0.991211f, 0.000470f, 0.989258f, 0.000520f, 0.986328f, 0.000575f, + 0.983398f, 0.000628f, 0.979492f, 0.000683f, 0.975586f, 0.000741f, 0.970703f, 0.000801f, + 0.965332f, 0.000855f, 0.958984f, 0.000910f, 0.951660f, 0.000961f, 0.943848f, 0.001009f, + 0.935059f, 0.001053f, 0.925781f, 0.001090f, 0.915039f, 0.001123f, 0.903809f, 0.001152f, + 0.891602f, 0.001172f, 0.878906f, 0.001186f, 0.864746f, 0.001194f, 0.850586f, 0.001195f, + 0.835449f, 0.001191f, 0.819336f, 0.001181f, 0.802734f, 0.001164f, 0.785645f, 0.001144f, + 0.768066f, 0.001121f, 0.750000f, 0.001092f, 0.731445f, 0.001061f, 0.712402f, 0.001027f, + 0.693359f, 0.000992f, 0.674316f, 0.000955f, 0.654785f, 0.000916f, 0.635254f, 0.000877f, + 0.615723f, 0.000838f, 0.596191f, 0.000799f, 0.576660f, 0.000760f, 0.557129f, 0.000721f, + 0.538086f, 0.000684f, 0.518555f, 0.000648f, 0.500000f, 0.000612f, 0.481445f, 0.000578f, + 0.462891f, 0.000545f, 0.444824f, 0.000513f, 0.427246f, 0.000483f, 0.409912f, 0.000454f, + 0.392822f, 0.000427f, 0.376221f, 0.000401f, 0.360107f, 0.000376f, 0.344482f, 0.000353f, + 0.999512f, 0.000284f, 0.999512f, 0.000284f, 0.999512f, 0.000284f, 0.999512f, 0.000285f, + 0.999512f, 0.000287f, 0.999512f, 0.000292f, 0.999512f, 0.000296f, 0.999023f, 0.000307f, + 0.999023f, 0.000320f, 0.999023f, 0.000338f, 0.998535f, 0.000349f, 0.998047f, 0.000381f, + 0.997559f, 0.000407f, 0.996582f, 0.000447f, 0.995605f, 0.000480f, 0.994629f, 0.000531f, + 0.992676f, 0.000579f, 0.990723f, 0.000637f, 0.988770f, 0.000693f, 0.985840f, 0.000755f, + 0.982422f, 0.000824f, 0.979004f, 0.000889f, 0.975098f, 0.000958f, 0.969727f, 0.001024f, + 0.963867f, 0.001090f, 0.957520f, 0.001152f, 0.950684f, 0.001211f, 0.942383f, 0.001263f, + 0.933594f, 0.001309f, 0.923828f, 0.001353f, 0.913086f, 0.001387f, 0.901855f, 0.001413f, + 0.889648f, 0.001432f, 0.876465f, 0.001443f, 0.862793f, 0.001446f, 0.848145f, 0.001442f, + 0.833008f, 0.001431f, 0.817383f, 0.001413f, 0.800781f, 0.001390f, 0.783691f, 0.001362f, + 0.766113f, 0.001328f, 0.748535f, 0.001291f, 0.729980f, 0.001250f, 0.711426f, 0.001207f, + 0.692871f, 0.001163f, 0.673828f, 0.001116f, 0.654785f, 0.001068f, 0.635254f, 0.001020f, + 0.616211f, 0.000973f, 0.596680f, 0.000926f, 0.577637f, 0.000878f, 0.558105f, 0.000833f, + 0.539062f, 0.000788f, 0.520508f, 0.000745f, 0.501465f, 0.000702f, 0.483154f, 0.000663f, + 0.465088f, 0.000624f, 0.447266f, 0.000587f, 0.429443f, 0.000552f, 0.412354f, 0.000518f, + 0.395508f, 0.000486f, 0.378906f, 0.000456f, 0.363037f, 0.000427f, 0.347168f, 0.000400f, + 0.999512f, 0.000417f, 0.999512f, 0.000417f, 0.999512f, 0.000418f, 0.999512f, 0.000419f, + 0.999512f, 0.000422f, 0.999512f, 0.000425f, 0.999023f, 0.000434f, 0.999023f, 0.000447f, + 0.999023f, 0.000462f, 0.999023f, 0.000480f, 0.998047f, 0.000508f, 0.998047f, 0.000538f, + 0.997070f, 0.000576f, 0.996582f, 0.000621f, 0.995605f, 0.000669f, 0.993652f, 0.000721f, + 0.992188f, 0.000784f, 0.990723f, 0.000849f, 0.987793f, 0.000918f, 0.985840f, 0.000996f, + 0.982422f, 0.001071f, 0.978516f, 0.001148f, 0.973633f, 0.001225f, 0.968750f, 0.001304f, + 0.962891f, 0.001378f, 0.956543f, 0.001447f, 0.948730f, 0.001511f, 0.940918f, 0.001568f, + 0.931641f, 0.001617f, 0.921875f, 0.001660f, 0.911621f, 0.001697f, 0.899902f, 0.001719f, + 0.887695f, 0.001735f, 0.874512f, 0.001740f, 0.860840f, 0.001738f, 0.846191f, 0.001725f, + 0.831055f, 0.001706f, 0.815430f, 0.001679f, 0.798828f, 0.001646f, 0.782227f, 0.001607f, + 0.764648f, 0.001562f, 0.747070f, 0.001514f, 0.729004f, 0.001462f, 0.710449f, 0.001409f, + 0.691895f, 0.001352f, 0.673340f, 0.001295f, 0.654297f, 0.001237f, 0.635254f, 0.001179f, + 0.616211f, 0.001122f, 0.597168f, 0.001065f, 0.578125f, 0.001010f, 0.559570f, 0.000955f, + 0.540527f, 0.000902f, 0.521973f, 0.000852f, 0.503418f, 0.000803f, 0.485352f, 0.000755f, + 0.467285f, 0.000710f, 0.449463f, 0.000668f, 0.431885f, 0.000626f, 0.414795f, 0.000587f, + 0.398193f, 0.000551f, 0.381836f, 0.000516f, 0.365723f, 0.000483f, 0.350098f, 0.000452f, + 0.999023f, 0.000597f, 0.999023f, 0.000597f, 0.999023f, 0.000597f, 0.999023f, 0.000598f, + 0.999023f, 0.000602f, 0.999023f, 0.000610f, 0.999023f, 0.000618f, 0.999023f, 0.000632f, + 0.998535f, 0.000651f, 0.998535f, 0.000675f, 0.998047f, 0.000704f, 0.997559f, 0.000742f, + 0.997070f, 0.000787f, 0.996094f, 0.000843f, 0.995117f, 0.000902f, 0.993652f, 0.000966f, + 0.992188f, 0.001039f, 0.990234f, 0.001117f, 0.987793f, 0.001197f, 0.984863f, 0.001286f, + 0.981445f, 0.001372f, 0.977539f, 0.001464f, 0.972656f, 0.001553f, 0.967773f, 0.001639f, + 0.961914f, 0.001722f, 0.955078f, 0.001798f, 0.947754f, 0.001868f, 0.938965f, 0.001928f, + 0.930176f, 0.001982f, 0.920410f, 0.002026f, 0.909668f, 0.002056f, 0.897949f, 0.002075f, + 0.885254f, 0.002085f, 0.872559f, 0.002083f, 0.858398f, 0.002071f, 0.844238f, 0.002048f, + 0.828613f, 0.002018f, 0.812988f, 0.001980f, 0.796875f, 0.001934f, 0.780273f, 0.001883f, + 0.763184f, 0.001824f, 0.745605f, 0.001763f, 0.728027f, 0.001698f, 0.709473f, 0.001632f, + 0.691406f, 0.001563f, 0.672852f, 0.001494f, 0.654297f, 0.001422f, 0.635254f, 0.001355f, + 0.616699f, 0.001286f, 0.598145f, 0.001218f, 0.579102f, 0.001152f, 0.560547f, 0.001089f, + 0.541992f, 0.001027f, 0.523438f, 0.000968f, 0.505371f, 0.000911f, 0.487305f, 0.000857f, + 0.469482f, 0.000804f, 0.451904f, 0.000755f, 0.434570f, 0.000708f, 0.417480f, 0.000663f, + 0.400879f, 0.000621f, 0.384521f, 0.000581f, 0.368652f, 0.000544f, 0.353027f, 0.000508f, + 0.999023f, 0.000833f, 0.999023f, 0.000833f, 0.999023f, 0.000834f, 0.999023f, 0.000835f, + 0.999023f, 0.000840f, 0.999023f, 0.000845f, 0.998535f, 0.000861f, 0.998535f, 0.000875f, + 0.998535f, 0.000897f, 0.998047f, 0.000928f, 0.997559f, 0.000965f, 0.997070f, 0.001007f, + 0.996582f, 0.001061f, 0.995605f, 0.001128f, 0.994629f, 0.001195f, 0.993164f, 0.001276f, + 0.991699f, 0.001362f, 0.989258f, 0.001453f, 0.986816f, 0.001539f, 0.983887f, 0.001645f, + 0.980469f, 0.001747f, 0.976562f, 0.001849f, 0.971680f, 0.001945f, 0.966309f, 0.002045f, + 0.959961f, 0.002136f, 0.953613f, 0.002218f, 0.945801f, 0.002291f, 0.937500f, 0.002357f, + 0.928223f, 0.002407f, 0.917969f, 0.002447f, 0.907227f, 0.002472f, 0.895508f, 0.002487f, + 0.883301f, 0.002485f, 0.870117f, 0.002474f, 0.856445f, 0.002451f, 0.841797f, 0.002417f, + 0.826660f, 0.002373f, 0.811035f, 0.002317f, 0.794922f, 0.002258f, 0.778320f, 0.002190f, + 0.761230f, 0.002117f, 0.744141f, 0.002041f, 0.726562f, 0.001961f, 0.708496f, 0.001880f, + 0.690430f, 0.001796f, 0.672363f, 0.001713f, 0.654297f, 0.001630f, 0.635742f, 0.001547f, + 0.617188f, 0.001466f, 0.598633f, 0.001387f, 0.580078f, 0.001310f, 0.561523f, 0.001235f, + 0.543457f, 0.001164f, 0.524902f, 0.001095f, 0.507324f, 0.001029f, 0.489258f, 0.000967f, + 0.471680f, 0.000906f, 0.454346f, 0.000850f, 0.437012f, 0.000796f, 0.420166f, 0.000745f, + 0.403564f, 0.000698f, 0.387451f, 0.000652f, 0.371582f, 0.000609f, 0.356201f, 0.000569f, + 0.998535f, 0.001139f, 0.998535f, 0.001139f, 0.998535f, 0.001140f, 0.998535f, 0.001142f, + 0.998535f, 0.001147f, 0.998535f, 0.001159f, 0.998535f, 0.001168f, 0.998047f, 0.001190f, + 0.998047f, 0.001217f, 0.997559f, 0.001254f, 0.997559f, 0.001301f, 0.997070f, 0.001356f, + 0.996094f, 0.001416f, 0.995605f, 0.001493f, 0.994141f, 0.001574f, 0.992676f, 0.001663f, + 0.990723f, 0.001759f, 0.988770f, 0.001867f, 0.986328f, 0.001980f, 0.982910f, 0.002087f, + 0.979492f, 0.002199f, 0.975586f, 0.002319f, 0.970703f, 0.002422f, 0.965332f, 0.002531f, + 0.958496f, 0.002628f, 0.952148f, 0.002714f, 0.944336f, 0.002792f, 0.935547f, 0.002851f, + 0.926270f, 0.002903f, 0.916016f, 0.002935f, 0.904785f, 0.002954f, 0.893066f, 0.002956f, + 0.880859f, 0.002947f, 0.867676f, 0.002920f, 0.853516f, 0.002882f, 0.839355f, 0.002831f, + 0.824219f, 0.002769f, 0.809082f, 0.002699f, 0.792969f, 0.002619f, 0.776367f, 0.002533f, + 0.759766f, 0.002443f, 0.742676f, 0.002350f, 0.725586f, 0.002251f, 0.708008f, 0.002151f, + 0.689941f, 0.002052f, 0.671875f, 0.001953f, 0.653809f, 0.001854f, 0.635742f, 0.001758f, + 0.617676f, 0.001663f, 0.599121f, 0.001572f, 0.581055f, 0.001482f, 0.562988f, 0.001395f, + 0.544922f, 0.001313f, 0.526855f, 0.001234f, 0.508789f, 0.001158f, 0.491455f, 0.001086f, + 0.473877f, 0.001018f, 0.456787f, 0.000954f, 0.439697f, 0.000892f, 0.422852f, 0.000834f, + 0.406494f, 0.000780f, 0.390381f, 0.000729f, 0.374512f, 0.000680f, 0.359131f, 0.000635f, + 0.998047f, 0.001528f, 0.998047f, 0.001528f, 0.998047f, 0.001529f, 0.998047f, 0.001532f, + 0.998047f, 0.001539f, 0.998047f, 0.001546f, 0.998047f, 0.001562f, 0.998047f, 0.001589f, + 0.997559f, 0.001621f, 0.997559f, 0.001668f, 0.996582f, 0.001715f, 0.996582f, 0.001777f, + 0.995605f, 0.001859f, 0.994629f, 0.001939f, 0.993652f, 0.002035f, 0.992188f, 0.002140f, + 0.990234f, 0.002243f, 0.987793f, 0.002369f, 0.985352f, 0.002489f, 0.981934f, 0.002621f, + 0.978516f, 0.002750f, 0.974121f, 0.002876f, 0.969238f, 0.002991f, 0.963867f, 0.003105f, + 0.957031f, 0.003206f, 0.950195f, 0.003300f, 0.942383f, 0.003374f, 0.933594f, 0.003431f, + 0.923828f, 0.003473f, 0.913574f, 0.003498f, 0.902344f, 0.003506f, 0.890625f, 0.003494f, + 0.878418f, 0.003468f, 0.865234f, 0.003426f, 0.851074f, 0.003366f, 0.836914f, 0.003296f, + 0.822266f, 0.003216f, 0.806641f, 0.003122f, 0.791016f, 0.003023f, 0.774902f, 0.002916f, + 0.758301f, 0.002804f, 0.741211f, 0.002689f, 0.724121f, 0.002573f, 0.707031f, 0.002453f, + 0.689453f, 0.002335f, 0.671875f, 0.002216f, 0.653809f, 0.002102f, 0.636230f, 0.001987f, + 0.618164f, 0.001878f, 0.600098f, 0.001771f, 0.582031f, 0.001668f, 0.564453f, 0.001569f, + 0.546387f, 0.001475f, 0.528809f, 0.001384f, 0.511230f, 0.001297f, 0.493652f, 0.001217f, + 0.476318f, 0.001139f, 0.459229f, 0.001065f, 0.442383f, 0.000996f, 0.425781f, 0.000930f, + 0.409424f, 0.000869f, 0.393311f, 0.000811f, 0.377686f, 0.000757f, 0.362305f, 0.000707f, + 0.997559f, 0.002018f, 0.997559f, 0.002018f, 0.997559f, 0.002018f, 0.997559f, 0.002022f, + 0.997559f, 0.002028f, 0.997559f, 0.002045f, 0.997559f, 0.002066f, 0.997559f, 0.002092f, + 0.997559f, 0.002129f, 0.996582f, 0.002176f, 0.996094f, 0.002235f, 0.995605f, 0.002312f, + 0.995605f, 0.002407f, 0.993652f, 0.002491f, 0.992676f, 0.002605f, 0.991211f, 0.002729f, + 0.989258f, 0.002846f, 0.987305f, 0.002987f, 0.984375f, 0.003120f, 0.980957f, 0.003263f, + 0.977051f, 0.003403f, 0.972656f, 0.003542f, 0.967285f, 0.003666f, 0.961914f, 0.003782f, + 0.955566f, 0.003889f, 0.947754f, 0.003967f, 0.939941f, 0.004044f, 0.931152f, 0.004097f, + 0.921387f, 0.004131f, 0.911133f, 0.004139f, 0.899902f, 0.004131f, 0.888184f, 0.004108f, + 0.875488f, 0.004055f, 0.862305f, 0.003990f, 0.848633f, 0.003914f, 0.834473f, 0.003819f, + 0.819824f, 0.003712f, 0.804199f, 0.003593f, 0.788574f, 0.003469f, 0.772949f, 0.003338f, + 0.756348f, 0.003201f, 0.739746f, 0.003063f, 0.723145f, 0.002924f, 0.706055f, 0.002781f, + 0.688965f, 0.002644f, 0.671387f, 0.002506f, 0.653809f, 0.002371f, 0.636230f, 0.002239f, + 0.618652f, 0.002111f, 0.601074f, 0.001989f, 0.583496f, 0.001871f, 0.565430f, 0.001759f, + 0.547852f, 0.001650f, 0.530273f, 0.001547f, 0.513184f, 0.001449f, 0.495850f, 0.001356f, + 0.478760f, 0.001269f, 0.461670f, 0.001185f, 0.445068f, 0.001107f, 0.428467f, 0.001035f, + 0.412354f, 0.000965f, 0.396240f, 0.000901f, 0.380615f, 0.000840f, 0.365479f, 0.000783f, + 0.997070f, 0.002625f, 0.997070f, 0.002625f, 0.997070f, 0.002626f, 0.997070f, 0.002630f, + 0.997070f, 0.002640f, 0.997070f, 0.002659f, 0.997070f, 0.002676f, 0.996582f, 0.002708f, + 0.996582f, 0.002752f, 0.996094f, 0.002813f, 0.995605f, 0.002886f, 0.995117f, 0.002956f, + 0.994141f, 0.003071f, 0.992676f, 0.003172f, 0.991699f, 0.003292f, 0.990234f, 0.003433f, + 0.988281f, 0.003580f, 0.985840f, 0.003727f, 0.982910f, 0.003870f, 0.979492f, 0.004028f, + 0.975586f, 0.004177f, 0.971191f, 0.004322f, 0.966309f, 0.004456f, 0.959961f, 0.004570f, + 0.953125f, 0.004669f, 0.945801f, 0.004757f, 0.937500f, 0.004826f, 0.928711f, 0.004864f, + 0.918945f, 0.004883f, 0.908691f, 0.004875f, 0.897461f, 0.004845f, 0.885254f, 0.004795f, + 0.872559f, 0.004723f, 0.859863f, 0.004631f, 0.846191f, 0.004520f, 0.832031f, 0.004398f, + 0.817383f, 0.004261f, 0.802246f, 0.004116f, 0.786621f, 0.003963f, 0.770996f, 0.003805f, + 0.754883f, 0.003639f, 0.738770f, 0.003475f, 0.722168f, 0.003307f, 0.705078f, 0.003143f, + 0.688477f, 0.002981f, 0.671387f, 0.002821f, 0.653809f, 0.002665f, 0.636719f, 0.002512f, + 0.619141f, 0.002367f, 0.602051f, 0.002226f, 0.584473f, 0.002090f, 0.566895f, 0.001963f, + 0.549805f, 0.001840f, 0.532227f, 0.001722f, 0.515137f, 0.001613f, 0.498047f, 0.001508f, + 0.481201f, 0.001409f, 0.464355f, 0.001316f, 0.447754f, 0.001228f, 0.431396f, 0.001145f, + 0.415283f, 0.001069f, 0.399414f, 0.000997f, 0.383789f, 0.000929f, 0.368652f, 0.000865f, + 0.996582f, 0.003370f, 0.996582f, 0.003370f, 0.996582f, 0.003372f, 0.996582f, 0.003378f, + 0.996582f, 0.003389f, 0.996094f, 0.003410f, 0.996094f, 0.003435f, 0.996094f, 0.003471f, + 0.996094f, 0.003523f, 0.995117f, 0.003588f, 0.995117f, 0.003664f, 0.994141f, 0.003754f, + 0.993164f, 0.003864f, 0.992676f, 0.003990f, 0.990723f, 0.004128f, 0.989746f, 0.004288f, + 0.987793f, 0.004429f, 0.984375f, 0.004601f, 0.981445f, 0.004757f, 0.978027f, 0.004925f, + 0.974121f, 0.005089f, 0.969727f, 0.005241f, 0.964355f, 0.005375f, 0.958008f, 0.005486f, + 0.951172f, 0.005596f, 0.943848f, 0.005665f, 0.935547f, 0.005718f, 0.925781f, 0.005737f, + 0.916016f, 0.005733f, 0.905762f, 0.005707f, 0.894531f, 0.005650f, 0.882324f, 0.005569f, + 0.870117f, 0.005466f, 0.856934f, 0.005341f, 0.843262f, 0.005199f, 0.829102f, 0.005043f, + 0.814941f, 0.004871f, 0.799805f, 0.004692f, 0.784668f, 0.004505f, 0.769043f, 0.004314f, + 0.753418f, 0.004116f, 0.737305f, 0.003922f, 0.721191f, 0.003729f, 0.704590f, 0.003536f, + 0.687988f, 0.003347f, 0.670898f, 0.003162f, 0.654297f, 0.002983f, 0.637207f, 0.002810f, + 0.620117f, 0.002642f, 0.603027f, 0.002481f, 0.585938f, 0.002329f, 0.568359f, 0.002182f, + 0.551270f, 0.002045f, 0.534180f, 0.001913f, 0.517090f, 0.001788f, 0.500488f, 0.001671f, + 0.483643f, 0.001560f, 0.467041f, 0.001456f, 0.450684f, 0.001358f, 0.434326f, 0.001266f, + 0.418213f, 0.001181f, 0.402588f, 0.001101f, 0.386963f, 0.001025f, 0.371826f, 0.000954f, + 0.995605f, 0.004276f, 0.995605f, 0.004276f, 0.995605f, 0.004280f, 0.995605f, 0.004284f, + 0.995605f, 0.004299f, 0.995117f, 0.004318f, 0.995117f, 0.004349f, 0.995117f, 0.004383f, + 0.994629f, 0.004456f, 0.994629f, 0.004524f, 0.994141f, 0.004612f, 0.993164f, 0.004704f, + 0.992676f, 0.004848f, 0.991699f, 0.004974f, 0.990234f, 0.005142f, 0.987793f, 0.005291f, + 0.986328f, 0.005474f, 0.982910f, 0.005638f, 0.980469f, 0.005825f, 0.976562f, 0.005989f, + 0.972656f, 0.006157f, 0.967773f, 0.006313f, 0.961914f, 0.006443f, 0.955566f, 0.006554f, + 0.948730f, 0.006645f, 0.940918f, 0.006702f, 0.932617f, 0.006733f, 0.923340f, 0.006733f, + 0.913574f, 0.006699f, 0.902832f, 0.006645f, 0.891602f, 0.006550f, 0.879395f, 0.006435f, + 0.867188f, 0.006294f, 0.854004f, 0.006130f, 0.840332f, 0.005951f, 0.826660f, 0.005756f, + 0.812500f, 0.005543f, 0.797363f, 0.005325f, 0.782715f, 0.005100f, 0.767090f, 0.004871f, + 0.751465f, 0.004642f, 0.735840f, 0.004414f, 0.719727f, 0.004185f, 0.703613f, 0.003960f, + 0.687500f, 0.003744f, 0.670898f, 0.003531f, 0.654297f, 0.003326f, 0.637695f, 0.003128f, + 0.620605f, 0.002939f, 0.604004f, 0.002756f, 0.586914f, 0.002584f, 0.569824f, 0.002420f, + 0.553223f, 0.002264f, 0.536133f, 0.002117f, 0.519531f, 0.001978f, 0.502930f, 0.001847f, + 0.486328f, 0.001723f, 0.469727f, 0.001607f, 0.453369f, 0.001498f, 0.437256f, 0.001395f, + 0.421387f, 0.001300f, 0.405762f, 0.001211f, 0.390381f, 0.001127f, 0.375244f, 0.001050f, + 0.994141f, 0.005367f, 0.994141f, 0.005367f, 0.994141f, 0.005371f, 0.994141f, 0.005375f, + 0.994141f, 0.005394f, 0.994141f, 0.005413f, 0.994141f, 0.005447f, 0.994141f, 0.005508f, + 0.993652f, 0.005558f, 0.993652f, 0.005650f, 0.992676f, 0.005741f, 0.991699f, 0.005848f, + 0.991211f, 0.006004f, 0.990234f, 0.006149f, 0.988281f, 0.006317f, 0.986328f, 0.006504f, + 0.984863f, 0.006687f, 0.981934f, 0.006866f, 0.978516f, 0.007050f, 0.974609f, 0.007233f, + 0.970215f, 0.007393f, 0.965820f, 0.007553f, 0.959961f, 0.007675f, 0.953125f, 0.007774f, + 0.946289f, 0.007843f, 0.938477f, 0.007889f, 0.929688f, 0.007889f, 0.920410f, 0.007858f, + 0.910156f, 0.007793f, 0.899414f, 0.007694f, 0.888672f, 0.007565f, 0.876465f, 0.007401f, + 0.864258f, 0.007214f, 0.851074f, 0.007008f, 0.837402f, 0.006779f, 0.823730f, 0.006535f, + 0.809570f, 0.006279f, 0.794922f, 0.006023f, 0.780273f, 0.005753f, 0.765137f, 0.005482f, + 0.750000f, 0.005215f, 0.734375f, 0.004944f, 0.718750f, 0.004681f, 0.703125f, 0.004425f, + 0.687012f, 0.004173f, 0.670898f, 0.003929f, 0.654297f, 0.003700f, 0.638184f, 0.003473f, + 0.621582f, 0.003260f, 0.604980f, 0.003056f, 0.588379f, 0.002861f, 0.571777f, 0.002676f, + 0.555176f, 0.002502f, 0.538574f, 0.002337f, 0.521973f, 0.002180f, 0.505371f, 0.002035f, + 0.488770f, 0.001898f, 0.472656f, 0.001769f, 0.456299f, 0.001649f, 0.440430f, 0.001534f, + 0.424561f, 0.001430f, 0.408936f, 0.001329f, 0.393555f, 0.001238f, 0.378418f, 0.001151f, + 0.993164f, 0.006672f, 0.993164f, 0.006672f, 0.993164f, 0.006676f, 0.993164f, 0.006687f, + 0.993164f, 0.006699f, 0.993164f, 0.006721f, 0.992676f, 0.006760f, 0.992676f, 0.006821f, + 0.992188f, 0.006897f, 0.991699f, 0.006973f, 0.991211f, 0.007099f, 0.990234f, 0.007206f, + 0.990234f, 0.007366f, 0.988281f, 0.007519f, 0.986328f, 0.007706f, 0.984863f, 0.007912f, + 0.982422f, 0.008087f, 0.979980f, 0.008286f, 0.977051f, 0.008476f, 0.972656f, 0.008667f, + 0.968262f, 0.008827f, 0.962891f, 0.008980f, 0.957520f, 0.009079f, 0.951172f, 0.009171f, + 0.943848f, 0.009216f, 0.935547f, 0.009224f, 0.926758f, 0.009193f, 0.917480f, 0.009125f, + 0.906738f, 0.009010f, 0.895996f, 0.008865f, 0.885254f, 0.008682f, 0.873047f, 0.008469f, + 0.860840f, 0.008232f, 0.847656f, 0.007973f, 0.834473f, 0.007690f, 0.820801f, 0.007397f, + 0.807129f, 0.007092f, 0.792969f, 0.006783f, 0.778320f, 0.006462f, 0.763184f, 0.006145f, + 0.748535f, 0.005833f, 0.733398f, 0.005524f, 0.717773f, 0.005219f, 0.702148f, 0.004925f, + 0.686523f, 0.004639f, 0.670898f, 0.004364f, 0.654785f, 0.004097f, 0.638672f, 0.003847f, + 0.622559f, 0.003605f, 0.605957f, 0.003376f, 0.589844f, 0.003157f, 0.573242f, 0.002951f, + 0.556641f, 0.002756f, 0.540527f, 0.002573f, 0.523926f, 0.002399f, 0.507812f, 0.002237f, + 0.491455f, 0.002085f, 0.475342f, 0.001943f, 0.459229f, 0.001809f, 0.443359f, 0.001684f, + 0.427734f, 0.001567f, 0.412109f, 0.001457f, 0.396973f, 0.001356f, 0.382080f, 0.001261f, + 0.991699f, 0.008217f, 0.991699f, 0.008217f, 0.991699f, 0.008217f, 0.991699f, 0.008232f, + 0.991211f, 0.008240f, 0.991211f, 0.008270f, 0.991211f, 0.008324f, 0.991211f, 0.008377f, + 0.990723f, 0.008461f, 0.990234f, 0.008553f, 0.989746f, 0.008682f, 0.988770f, 0.008820f, + 0.987793f, 0.008972f, 0.986816f, 0.009163f, 0.985352f, 0.009338f, 0.982910f, 0.009567f, + 0.980957f, 0.009758f, 0.977539f, 0.009956f, 0.974609f, 0.010155f, 0.970215f, 0.010330f, + 0.965820f, 0.010483f, 0.960449f, 0.010597f, 0.954590f, 0.010696f, 0.947754f, 0.010750f, + 0.940430f, 0.010757f, 0.932129f, 0.010735f, 0.923340f, 0.010651f, 0.913574f, 0.010536f, + 0.903809f, 0.010376f, 0.892578f, 0.010162f, 0.881348f, 0.009926f, 0.869629f, 0.009651f, + 0.857422f, 0.009354f, 0.844727f, 0.009026f, 0.831543f, 0.008690f, 0.817871f, 0.008331f, + 0.804199f, 0.007973f, 0.790527f, 0.007603f, 0.775879f, 0.007233f, 0.761719f, 0.006866f, + 0.747070f, 0.006500f, 0.731934f, 0.006145f, 0.716797f, 0.005798f, 0.701660f, 0.005466f, + 0.686523f, 0.005138f, 0.670898f, 0.004829f, 0.655273f, 0.004532f, 0.639160f, 0.004246f, + 0.623535f, 0.003975f, 0.607422f, 0.003719f, 0.591309f, 0.003477f, 0.575195f, 0.003246f, + 0.558594f, 0.003029f, 0.542480f, 0.002827f, 0.526367f, 0.002634f, 0.510254f, 0.002455f, + 0.494141f, 0.002285f, 0.478271f, 0.002129f, 0.462402f, 0.001980f, 0.446533f, 0.001843f, + 0.430908f, 0.001715f, 0.415527f, 0.001594f, 0.400391f, 0.001483f, 0.385498f, 0.001378f, + 0.989746f, 0.010040f, 0.989746f, 0.010040f, 0.989746f, 0.010040f, 0.989746f, 0.010048f, + 0.989746f, 0.010071f, 0.989746f, 0.010094f, 0.989258f, 0.010147f, 0.989258f, 0.010223f, + 0.988770f, 0.010300f, 0.988770f, 0.010406f, 0.987793f, 0.010529f, 0.986816f, 0.010696f, + 0.986328f, 0.010857f, 0.984863f, 0.011055f, 0.982422f, 0.011238f, 0.981445f, 0.011467f, + 0.978516f, 0.011673f, 0.975098f, 0.011871f, 0.972168f, 0.012062f, 0.967285f, 0.012215f, + 0.962402f, 0.012352f, 0.957031f, 0.012459f, 0.951172f, 0.012535f, 0.944336f, 0.012535f, + 0.937012f, 0.012520f, 0.928711f, 0.012428f, 0.919922f, 0.012299f, 0.910156f, 0.012115f, + 0.899414f, 0.011879f, 0.889160f, 0.011612f, 0.877441f, 0.011299f, 0.865723f, 0.010956f, + 0.853516f, 0.010582f, 0.841309f, 0.010193f, 0.828125f, 0.009773f, 0.814941f, 0.009361f, + 0.801270f, 0.008926f, 0.787598f, 0.008499f, 0.773926f, 0.008064f, 0.759766f, 0.007641f, + 0.745117f, 0.007225f, 0.730469f, 0.006817f, 0.716309f, 0.006424f, 0.701172f, 0.006042f, + 0.686035f, 0.005676f, 0.670898f, 0.005329f, 0.655273f, 0.004993f, 0.640137f, 0.004673f, + 0.624512f, 0.004372f, 0.608398f, 0.004086f, 0.592773f, 0.003817f, 0.576660f, 0.003561f, + 0.561035f, 0.003323f, 0.544922f, 0.003098f, 0.528809f, 0.002884f, 0.512695f, 0.002686f, + 0.497070f, 0.002501f, 0.481201f, 0.002327f, 0.465332f, 0.002165f, 0.449707f, 0.002014f, + 0.434326f, 0.001873f, 0.418945f, 0.001740f, 0.403809f, 0.001617f, 0.388916f, 0.001504f, + 0.987793f, 0.012169f, 0.987793f, 0.012169f, 0.987793f, 0.012169f, 0.987793f, 0.012184f, + 0.987305f, 0.012207f, 0.987305f, 0.012245f, 0.987305f, 0.012291f, 0.986816f, 0.012360f, + 0.986816f, 0.012459f, 0.986328f, 0.012573f, 0.985840f, 0.012695f, 0.984863f, 0.012878f, + 0.983887f, 0.013046f, 0.982422f, 0.013237f, 0.980469f, 0.013466f, 0.979004f, 0.013680f, + 0.976074f, 0.013878f, 0.972656f, 0.014069f, 0.969238f, 0.014259f, 0.964355f, 0.014397f, + 0.959961f, 0.014488f, 0.954102f, 0.014580f, 0.947754f, 0.014595f, 0.940430f, 0.014557f, + 0.933105f, 0.014481f, 0.925293f, 0.014328f, 0.915527f, 0.014122f, 0.906250f, 0.013870f, + 0.895996f, 0.013565f, 0.885254f, 0.013206f, 0.873535f, 0.012817f, 0.862305f, 0.012383f, + 0.850098f, 0.011932f, 0.837891f, 0.011452f, 0.824707f, 0.010963f, 0.812012f, 0.010460f, + 0.798828f, 0.009964f, 0.785156f, 0.009460f, 0.771484f, 0.008965f, 0.757812f, 0.008484f, + 0.743652f, 0.008003f, 0.729492f, 0.007542f, 0.715332f, 0.007095f, 0.700684f, 0.006668f, + 0.686035f, 0.006256f, 0.670898f, 0.005863f, 0.655762f, 0.005489f, 0.640625f, 0.005135f, + 0.625488f, 0.004799f, 0.609863f, 0.004478f, 0.594238f, 0.004181f, 0.578613f, 0.003901f, + 0.562988f, 0.003635f, 0.547363f, 0.003386f, 0.531250f, 0.003153f, 0.515625f, 0.002935f, + 0.500000f, 0.002729f, 0.484131f, 0.002539f, 0.468506f, 0.002361f, 0.453125f, 0.002195f, + 0.437744f, 0.002041f, 0.422363f, 0.001897f, 0.407471f, 0.001763f, 0.392578f, 0.001637f, + 0.985352f, 0.014641f, 0.985352f, 0.014641f, 0.984863f, 0.014648f, 0.984863f, 0.014656f, + 0.984863f, 0.014679f, 0.984863f, 0.014717f, 0.984863f, 0.014771f, 0.984375f, 0.014839f, + 0.984375f, 0.014938f, 0.983398f, 0.015060f, 0.983398f, 0.015244f, 0.981934f, 0.015388f, + 0.980957f, 0.015587f, 0.979492f, 0.015778f, 0.977539f, 0.015976f, 0.975586f, 0.016190f, + 0.972656f, 0.016388f, 0.969727f, 0.016571f, 0.965820f, 0.016739f, 0.961426f, 0.016861f, + 0.956055f, 0.016922f, 0.950684f, 0.016953f, 0.943848f, 0.016922f, 0.937012f, 0.016815f, + 0.929199f, 0.016663f, 0.920410f, 0.016434f, 0.911621f, 0.016144f, 0.901855f, 0.015793f, + 0.891602f, 0.015411f, 0.880859f, 0.014954f, 0.869629f, 0.014473f, 0.857910f, 0.013947f, + 0.846191f, 0.013390f, 0.833984f, 0.012825f, 0.821289f, 0.012253f, 0.809082f, 0.011665f, + 0.795898f, 0.011086f, 0.782715f, 0.010506f, 0.769531f, 0.009933f, 0.755859f, 0.009377f, + 0.742188f, 0.008842f, 0.728516f, 0.008316f, 0.714355f, 0.007812f, 0.700195f, 0.007336f, + 0.685547f, 0.006874f, 0.670898f, 0.006435f, 0.656250f, 0.006020f, 0.641602f, 0.005623f, + 0.626465f, 0.005253f, 0.611328f, 0.004902f, 0.596191f, 0.004570f, 0.580566f, 0.004261f, + 0.564941f, 0.003967f, 0.549316f, 0.003695f, 0.533691f, 0.003437f, 0.518066f, 0.003199f, + 0.502930f, 0.002975f, 0.487305f, 0.002766f, 0.471680f, 0.002571f, 0.456299f, 0.002388f, + 0.441162f, 0.002220f, 0.426025f, 0.002062f, 0.411133f, 0.001916f, 0.396240f, 0.001781f, + 0.982422f, 0.017502f, 0.982422f, 0.017502f, 0.982422f, 0.017502f, 0.982422f, 0.017517f, + 0.981934f, 0.017532f, 0.981934f, 0.017593f, 0.981934f, 0.017639f, 0.981934f, 0.017731f, + 0.981445f, 0.017838f, 0.980957f, 0.017960f, 0.979980f, 0.018112f, 0.979004f, 0.018295f, + 0.978027f, 0.018478f, 0.975586f, 0.018677f, 0.974609f, 0.018860f, 0.972168f, 0.019073f, + 0.969238f, 0.019287f, 0.965820f, 0.019455f, 0.962402f, 0.019562f, 0.958008f, 0.019653f, + 0.952637f, 0.019653f, 0.946289f, 0.019623f, 0.939453f, 0.019516f, 0.932617f, 0.019348f, + 0.924316f, 0.019089f, 0.916016f, 0.018784f, 0.907227f, 0.018387f, 0.897461f, 0.017944f, + 0.887207f, 0.017426f, 0.876465f, 0.016861f, 0.865234f, 0.016266f, 0.854004f, 0.015640f, + 0.842285f, 0.014999f, 0.830078f, 0.014320f, 0.818359f, 0.013641f, 0.805664f, 0.012962f, + 0.792969f, 0.012291f, 0.780273f, 0.011627f, 0.767090f, 0.010979f, 0.753906f, 0.010345f, + 0.740723f, 0.009735f, 0.727539f, 0.009155f, 0.713867f, 0.008591f, 0.699707f, 0.008049f, + 0.685547f, 0.007534f, 0.671387f, 0.007050f, 0.656738f, 0.006588f, 0.642578f, 0.006149f, + 0.627441f, 0.005737f, 0.612793f, 0.005352f, 0.597656f, 0.004986f, 0.582520f, 0.004642f, + 0.567383f, 0.004322f, 0.551758f, 0.004021f, 0.536621f, 0.003744f, 0.520996f, 0.003481f, + 0.505859f, 0.003235f, 0.490479f, 0.003006f, 0.475098f, 0.002794f, 0.459717f, 0.002596f, + 0.444580f, 0.002411f, 0.429688f, 0.002241f, 0.414795f, 0.002081f, 0.400146f, 0.001933f, + 0.979004f, 0.020798f, 0.979004f, 0.020798f, 0.979004f, 0.020798f, 0.979004f, 0.020813f, + 0.979004f, 0.020844f, 0.978516f, 0.020874f, 0.978516f, 0.020935f, 0.978027f, 0.021027f, + 0.978027f, 0.021149f, 0.977539f, 0.021286f, 0.977051f, 0.021454f, 0.975586f, 0.021622f, + 0.974121f, 0.021820f, 0.972656f, 0.021988f, 0.970215f, 0.022186f, 0.968750f, 0.022385f, + 0.965820f, 0.022552f, 0.961914f, 0.022675f, 0.958008f, 0.022736f, 0.953613f, 0.022751f, + 0.948242f, 0.022736f, 0.942383f, 0.022614f, 0.935547f, 0.022415f, 0.927734f, 0.022156f, + 0.919922f, 0.021790f, 0.911621f, 0.021362f, 0.901855f, 0.020859f, 0.892090f, 0.020279f, + 0.882324f, 0.019638f, 0.872070f, 0.018951f, 0.860840f, 0.018234f, 0.849609f, 0.017487f, + 0.838379f, 0.016708f, 0.826172f, 0.015930f, 0.814453f, 0.015144f, 0.802246f, 0.014359f, + 0.790527f, 0.013588f, 0.777832f, 0.012833f, 0.765137f, 0.012100f, 0.752441f, 0.011383f, + 0.739258f, 0.010696f, 0.726074f, 0.010040f, 0.712891f, 0.009415f, 0.699219f, 0.008812f, + 0.685547f, 0.008240f, 0.671875f, 0.007698f, 0.657715f, 0.007191f, 0.643555f, 0.006710f, + 0.628906f, 0.006252f, 0.614258f, 0.005829f, 0.599609f, 0.005428f, 0.584473f, 0.005051f, + 0.569336f, 0.004704f, 0.554199f, 0.004372f, 0.539062f, 0.004063f, 0.523926f, 0.003780f, + 0.508789f, 0.003513f, 0.493652f, 0.003263f, 0.478271f, 0.003033f, 0.463135f, 0.002817f, + 0.448242f, 0.002615f, 0.433350f, 0.002430f, 0.418457f, 0.002256f, 0.403809f, 0.002094f, + 0.975098f, 0.024582f, 0.975098f, 0.024567f, 0.975098f, 0.024582f, 0.975098f, 0.024597f, + 0.975098f, 0.024628f, 0.975098f, 0.024658f, 0.975098f, 0.024734f, 0.974609f, 0.024826f, + 0.973633f, 0.024933f, 0.973633f, 0.025055f, 0.972656f, 0.025223f, 0.972168f, 0.025421f, + 0.970215f, 0.025589f, 0.968262f, 0.025742f, 0.966309f, 0.025925f, 0.964355f, 0.026108f, + 0.960938f, 0.026230f, 0.957520f, 0.026321f, 0.953613f, 0.026352f, 0.948242f, 0.026260f, + 0.943848f, 0.026154f, 0.937500f, 0.025970f, 0.930664f, 0.025650f, 0.922852f, 0.025253f, + 0.915039f, 0.024765f, 0.906738f, 0.024200f, 0.897461f, 0.023560f, 0.887207f, 0.022827f, + 0.877441f, 0.022064f, 0.866699f, 0.021225f, 0.855957f, 0.020370f, 0.845215f, 0.019470f, + 0.833984f, 0.018570f, 0.822266f, 0.017654f, 0.811035f, 0.016754f, 0.799316f, 0.015854f, + 0.787109f, 0.014984f, 0.775391f, 0.014122f, 0.763184f, 0.013298f, 0.750488f, 0.012489f, + 0.737793f, 0.011726f, 0.725098f, 0.010986f, 0.712402f, 0.010284f, 0.699219f, 0.009621f, + 0.685547f, 0.008987f, 0.671875f, 0.008392f, 0.658203f, 0.007828f, 0.644531f, 0.007305f, + 0.630371f, 0.006802f, 0.615723f, 0.006336f, 0.601562f, 0.005898f, 0.586914f, 0.005489f, + 0.571777f, 0.005104f, 0.557129f, 0.004745f, 0.541992f, 0.004414f, 0.526855f, 0.004101f, + 0.511719f, 0.003809f, 0.496826f, 0.003538f, 0.481689f, 0.003286f, 0.466797f, 0.003052f, + 0.451904f, 0.002832f, 0.437012f, 0.002630f, 0.422363f, 0.002441f, 0.407715f, 0.002268f, + 0.970703f, 0.028870f, 0.970703f, 0.028870f, 0.970703f, 0.028885f, 0.970703f, 0.028900f, + 0.970703f, 0.028915f, 0.970703f, 0.028961f, 0.970215f, 0.029022f, 0.970215f, 0.029114f, + 0.969727f, 0.029251f, 0.968750f, 0.029373f, 0.968262f, 0.029526f, 0.966797f, 0.029678f, + 0.966309f, 0.029877f, 0.964844f, 0.030045f, 0.962402f, 0.030167f, 0.959473f, 0.030304f, + 0.956543f, 0.030411f, 0.953125f, 0.030411f, 0.948242f, 0.030319f, 0.943359f, 0.030197f, + 0.938477f, 0.029968f, 0.931641f, 0.029648f, 0.924805f, 0.029221f, 0.917969f, 0.028687f, + 0.909180f, 0.028030f, 0.900879f, 0.027313f, 0.891602f, 0.026505f, 0.881836f, 0.025620f, + 0.871582f, 0.024673f, 0.861816f, 0.023697f, 0.851074f, 0.022659f, 0.840820f, 0.021622f, + 0.829590f, 0.020569f, 0.818359f, 0.019516f, 0.807129f, 0.018478f, 0.795898f, 0.017456f, + 0.784180f, 0.016464f, 0.772461f, 0.015503f, 0.760742f, 0.014572f, 0.748535f, 0.013672f, + 0.736816f, 0.012817f, 0.724121f, 0.012001f, 0.711914f, 0.011215f, 0.698730f, 0.010483f, + 0.686035f, 0.009789f, 0.672852f, 0.009132f, 0.659180f, 0.008514f, 0.645508f, 0.007935f, + 0.631836f, 0.007389f, 0.617676f, 0.006878f, 0.603516f, 0.006397f, 0.588867f, 0.005951f, + 0.574219f, 0.005531f, 0.559570f, 0.005142f, 0.544922f, 0.004776f, 0.529785f, 0.004436f, + 0.515137f, 0.004120f, 0.500000f, 0.003828f, 0.485352f, 0.003555f, 0.470215f, 0.003302f, + 0.455566f, 0.003065f, 0.440918f, 0.002844f, 0.426270f, 0.002642f, 0.411621f, 0.002451f, + 0.965820f, 0.033752f, 0.965820f, 0.033752f, 0.965820f, 0.033752f, 0.965820f, 0.033783f, + 0.965820f, 0.033783f, 0.965820f, 0.033875f, 0.965332f, 0.033905f, 0.965332f, 0.033997f, + 0.964844f, 0.034088f, 0.963867f, 0.034241f, 0.963379f, 0.034393f, 0.962402f, 0.034546f, + 0.960938f, 0.034698f, 0.958496f, 0.034851f, 0.957520f, 0.034973f, 0.954102f, 0.035034f, + 0.951172f, 0.035034f, 0.947754f, 0.034943f, 0.942871f, 0.034821f, 0.937988f, 0.034576f, + 0.932129f, 0.034180f, 0.926270f, 0.033722f, 0.918945f, 0.033142f, 0.911133f, 0.032410f, + 0.902832f, 0.031616f, 0.894531f, 0.030685f, 0.885254f, 0.029694f, 0.876465f, 0.028641f, + 0.866699f, 0.027512f, 0.856445f, 0.026337f, 0.846191f, 0.025146f, 0.835449f, 0.023926f, + 0.825195f, 0.022720f, 0.814453f, 0.021515f, 0.803711f, 0.020340f, 0.792480f, 0.019165f, + 0.781250f, 0.018051f, 0.770020f, 0.016968f, 0.758789f, 0.015915f, 0.747070f, 0.014931f, + 0.735352f, 0.013977f, 0.723145f, 0.013069f, 0.710938f, 0.012215f, 0.698730f, 0.011398f, + 0.686035f, 0.010635f, 0.673340f, 0.009918f, 0.660156f, 0.009239f, 0.646484f, 0.008598f, + 0.633301f, 0.008003f, 0.619141f, 0.007446f, 0.605469f, 0.006927f, 0.591309f, 0.006439f, + 0.576660f, 0.005985f, 0.562500f, 0.005562f, 0.547852f, 0.005165f, 0.533203f, 0.004795f, + 0.518066f, 0.004456f, 0.503418f, 0.004135f, 0.488770f, 0.003841f, 0.474121f, 0.003565f, + 0.459229f, 0.003311f, 0.444580f, 0.003073f, 0.430176f, 0.002853f, 0.415771f, 0.002647f, + 0.960449f, 0.039276f, 0.960449f, 0.039276f, 0.960449f, 0.039276f, 0.960449f, 0.039307f, + 0.960449f, 0.039337f, 0.959961f, 0.039368f, 0.959961f, 0.039429f, 0.959961f, 0.039520f, + 0.959473f, 0.039612f, 0.958984f, 0.039764f, 0.958008f, 0.039886f, 0.956543f, 0.040009f, + 0.955566f, 0.040131f, 0.953125f, 0.040253f, 0.951172f, 0.040314f, 0.948242f, 0.040283f, + 0.945801f, 0.040222f, 0.940918f, 0.040039f, 0.936523f, 0.039764f, 0.931152f, 0.039368f, + 0.926270f, 0.038879f, 0.919434f, 0.038208f, 0.913086f, 0.037445f, 0.905273f, 0.036530f, + 0.897461f, 0.035522f, 0.888184f, 0.034393f, 0.879395f, 0.033173f, 0.870117f, 0.031891f, + 0.860352f, 0.030563f, 0.850586f, 0.029190f, 0.840820f, 0.027802f, 0.830566f, 0.026398f, + 0.820312f, 0.025009f, 0.810059f, 0.023636f, 0.799805f, 0.022308f, 0.789062f, 0.020996f, + 0.778809f, 0.019730f, 0.767578f, 0.018524f, 0.756348f, 0.017365f, 0.745605f, 0.016251f, + 0.733887f, 0.015213f, 0.722656f, 0.014206f, 0.710938f, 0.013260f, 0.698730f, 0.012367f, + 0.686523f, 0.011536f, 0.673828f, 0.010742f, 0.661133f, 0.010002f, 0.647949f, 0.009308f, + 0.634766f, 0.008659f, 0.621094f, 0.008057f, 0.607422f, 0.007488f, 0.593262f, 0.006958f, + 0.579102f, 0.006466f, 0.564941f, 0.006004f, 0.550781f, 0.005577f, 0.536133f, 0.005177f, + 0.521484f, 0.004807f, 0.506836f, 0.004463f, 0.492432f, 0.004143f, 0.477783f, 0.003847f, + 0.463135f, 0.003571f, 0.448730f, 0.003315f, 0.434082f, 0.003077f, 0.419922f, 0.002857f, + 0.954102f, 0.045502f, 0.954102f, 0.045502f, 0.954102f, 0.045502f, 0.954102f, 0.045532f, + 0.954102f, 0.045563f, 0.954102f, 0.045593f, 0.953613f, 0.045654f, 0.953613f, 0.045715f, + 0.953125f, 0.045868f, 0.952148f, 0.045990f, 0.951660f, 0.046082f, 0.950195f, 0.046143f, + 0.948242f, 0.046265f, 0.946777f, 0.046265f, 0.943848f, 0.046265f, 0.941895f, 0.046204f, + 0.938477f, 0.046021f, 0.935059f, 0.045685f, 0.929199f, 0.045258f, 0.925293f, 0.044708f, + 0.919434f, 0.044006f, 0.912109f, 0.043121f, 0.905273f, 0.042145f, 0.897949f, 0.041016f, + 0.890137f, 0.039734f, 0.881348f, 0.038391f, 0.872559f, 0.036926f, 0.863770f, 0.035431f, + 0.854004f, 0.033813f, 0.844727f, 0.032227f, 0.835449f, 0.030640f, 0.825195f, 0.029037f, + 0.815430f, 0.027451f, 0.806152f, 0.025909f, 0.795898f, 0.024399f, 0.785645f, 0.022934f, + 0.775391f, 0.021530f, 0.765137f, 0.020187f, 0.754883f, 0.018890f, 0.743652f, 0.017670f, + 0.732910f, 0.016510f, 0.721680f, 0.015411f, 0.710449f, 0.014374f, 0.698730f, 0.013405f, + 0.686523f, 0.012482f, 0.674316f, 0.011620f, 0.662109f, 0.010811f, 0.649414f, 0.010063f, + 0.636230f, 0.009354f, 0.623047f, 0.008698f, 0.609375f, 0.008080f, 0.595703f, 0.007507f, + 0.582031f, 0.006973f, 0.567871f, 0.006477f, 0.553711f, 0.006016f, 0.539551f, 0.005585f, + 0.524902f, 0.005180f, 0.510254f, 0.004810f, 0.496094f, 0.004463f, 0.481689f, 0.004147f, + 0.467041f, 0.003847f, 0.452637f, 0.003571f, 0.438232f, 0.003315f, 0.424072f, 0.003077f, + 0.947266f, 0.052490f, 0.947266f, 0.052490f, 0.947266f, 0.052490f, 0.947266f, 0.052521f, + 0.947266f, 0.052551f, 0.946777f, 0.052582f, 0.946777f, 0.052612f, 0.946289f, 0.052734f, + 0.945801f, 0.052795f, 0.945312f, 0.052887f, 0.944336f, 0.052948f, 0.942871f, 0.053040f, + 0.941406f, 0.053009f, 0.939941f, 0.053009f, 0.937012f, 0.052917f, 0.934570f, 0.052704f, + 0.931641f, 0.052399f, 0.926758f, 0.051971f, 0.922852f, 0.051331f, 0.917480f, 0.050568f, + 0.911133f, 0.049622f, 0.904297f, 0.048523f, 0.898438f, 0.047272f, 0.890137f, 0.045868f, + 0.882812f, 0.044312f, 0.874512f, 0.042694f, 0.865723f, 0.040955f, 0.856934f, 0.039154f, + 0.847656f, 0.037354f, 0.838867f, 0.035522f, 0.829590f, 0.033661f, 0.820312f, 0.031830f, + 0.811035f, 0.030060f, 0.801270f, 0.028305f, 0.791992f, 0.026611f, 0.782227f, 0.024994f, + 0.772461f, 0.023422f, 0.762695f, 0.021927f, 0.752441f, 0.020508f, 0.742188f, 0.019165f, + 0.731445f, 0.017883f, 0.721191f, 0.016678f, 0.709961f, 0.015556f, 0.698730f, 0.014488f, + 0.687012f, 0.013489f, 0.675293f, 0.012550f, 0.663086f, 0.011673f, 0.650879f, 0.010849f, + 0.638184f, 0.010086f, 0.625000f, 0.009369f, 0.611816f, 0.008705f, 0.598145f, 0.008087f, + 0.584961f, 0.007511f, 0.570801f, 0.006977f, 0.556641f, 0.006474f, 0.542480f, 0.006012f, + 0.528320f, 0.005581f, 0.514160f, 0.005180f, 0.499756f, 0.004807f, 0.485596f, 0.004459f, + 0.471191f, 0.004139f, 0.456787f, 0.003843f, 0.442383f, 0.003569f, 0.428467f, 0.003313f, + 0.939453f, 0.060333f, 0.939453f, 0.060333f, 0.939453f, 0.060333f, 0.939453f, 0.060333f, + 0.939453f, 0.060394f, 0.938965f, 0.060394f, 0.938965f, 0.060455f, 0.938477f, 0.060516f, + 0.937988f, 0.060577f, 0.937500f, 0.060638f, 0.936035f, 0.060669f, 0.935547f, 0.060669f, + 0.933594f, 0.060608f, 0.931641f, 0.060516f, 0.929688f, 0.060272f, 0.927246f, 0.059967f, + 0.922363f, 0.059448f, 0.918945f, 0.058868f, 0.914062f, 0.057953f, 0.908691f, 0.056946f, + 0.902832f, 0.055786f, 0.897461f, 0.054382f, 0.890137f, 0.052826f, 0.882324f, 0.051117f, + 0.874023f, 0.049255f, 0.866211f, 0.047302f, 0.858398f, 0.045288f, 0.849609f, 0.043213f, + 0.840820f, 0.041107f, 0.832031f, 0.038971f, 0.823730f, 0.036896f, 0.814453f, 0.034821f, + 0.806152f, 0.032806f, 0.796875f, 0.030853f, 0.788086f, 0.028961f, 0.778809f, 0.027161f, + 0.769531f, 0.025421f, 0.760254f, 0.023788f, 0.750488f, 0.022217f, 0.740723f, 0.020737f, + 0.730957f, 0.019333f, 0.720703f, 0.018021f, 0.709961f, 0.016785f, 0.698730f, 0.015625f, + 0.687500f, 0.014549f, 0.676270f, 0.013535f, 0.664551f, 0.012573f, 0.652344f, 0.011688f, + 0.640137f, 0.010864f, 0.627441f, 0.010086f, 0.614258f, 0.009369f, 0.601074f, 0.008698f, + 0.587402f, 0.008080f, 0.573730f, 0.007500f, 0.560059f, 0.006962f, 0.545898f, 0.006462f, + 0.531738f, 0.006001f, 0.517578f, 0.005569f, 0.503418f, 0.005165f, 0.489502f, 0.004795f, + 0.475098f, 0.004452f, 0.460938f, 0.004131f, 0.446777f, 0.003838f, 0.432861f, 0.003563f, + 0.930664f, 0.069031f, 0.930664f, 0.069031f, 0.930664f, 0.069031f, 0.930664f, 0.069031f, + 0.930664f, 0.069092f, 0.930664f, 0.069092f, 0.930176f, 0.069214f, 0.929688f, 0.069153f, + 0.929199f, 0.069214f, 0.929199f, 0.069275f, 0.927246f, 0.069214f, 0.926758f, 0.069153f, + 0.925293f, 0.069031f, 0.923340f, 0.068787f, 0.920410f, 0.068420f, 0.917480f, 0.067932f, + 0.914551f, 0.067261f, 0.911133f, 0.066345f, 0.905273f, 0.065247f, 0.900391f, 0.063965f, + 0.894043f, 0.062469f, 0.888184f, 0.060699f, 0.880859f, 0.058807f, 0.873535f, 0.056763f, + 0.866211f, 0.054565f, 0.858887f, 0.052277f, 0.850586f, 0.049896f, 0.841797f, 0.047485f, + 0.833496f, 0.045105f, 0.825684f, 0.042664f, 0.817383f, 0.040283f, 0.809082f, 0.037964f, + 0.800781f, 0.035706f, 0.792480f, 0.033539f, 0.784180f, 0.031433f, 0.775391f, 0.029449f, + 0.766602f, 0.027542f, 0.757812f, 0.025726f, 0.748535f, 0.024017f, 0.739258f, 0.022400f, + 0.729980f, 0.020874f, 0.719727f, 0.019440f, 0.709961f, 0.018097f, 0.699219f, 0.016830f, + 0.688477f, 0.015656f, 0.677246f, 0.014557f, 0.665527f, 0.013527f, 0.653809f, 0.012573f, + 0.641602f, 0.011681f, 0.629395f, 0.010841f, 0.616699f, 0.010071f, 0.603516f, 0.009346f, + 0.590332f, 0.008682f, 0.577148f, 0.008057f, 0.563477f, 0.007481f, 0.549316f, 0.006943f, + 0.535645f, 0.006443f, 0.521484f, 0.005978f, 0.507324f, 0.005550f, 0.493408f, 0.005150f, + 0.479248f, 0.004780f, 0.465332f, 0.004436f, 0.451172f, 0.004124f, 0.437256f, 0.003828f, + 0.920898f, 0.078735f, 0.920898f, 0.078735f, 0.920898f, 0.078735f, 0.920898f, 0.078735f, + 0.920898f, 0.078796f, 0.920898f, 0.078796f, 0.920410f, 0.078796f, 0.919922f, 0.078857f, + 0.919922f, 0.078857f, 0.918945f, 0.078796f, 0.917480f, 0.078735f, 0.916992f, 0.078613f, + 0.915039f, 0.078308f, 0.913086f, 0.077942f, 0.910645f, 0.077454f, 0.908691f, 0.076660f, + 0.905273f, 0.075745f, 0.899902f, 0.074585f, 0.895996f, 0.073181f, 0.889648f, 0.071533f, + 0.883789f, 0.069641f, 0.877930f, 0.067566f, 0.872070f, 0.065247f, 0.864258f, 0.062805f, + 0.856934f, 0.060242f, 0.849121f, 0.057556f, 0.841797f, 0.054810f, 0.833984f, 0.052063f, + 0.827148f, 0.049316f, 0.818848f, 0.046570f, 0.811035f, 0.043915f, 0.803223f, 0.041290f, + 0.795898f, 0.038788f, 0.788086f, 0.036377f, 0.779785f, 0.034058f, 0.771973f, 0.031830f, + 0.763672f, 0.029755f, 0.755371f, 0.027771f, 0.747070f, 0.025894f, 0.738281f, 0.024139f, + 0.729004f, 0.022476f, 0.719238f, 0.020935f, 0.709473f, 0.019470f, 0.699707f, 0.018097f, + 0.688965f, 0.016830f, 0.678223f, 0.015640f, 0.666992f, 0.014534f, 0.655762f, 0.013496f, + 0.643555f, 0.012535f, 0.631348f, 0.011642f, 0.619141f, 0.010803f, 0.606445f, 0.010033f, + 0.593262f, 0.009308f, 0.580078f, 0.008644f, 0.566406f, 0.008018f, 0.553223f, 0.007446f, + 0.539062f, 0.006908f, 0.525391f, 0.006413f, 0.511230f, 0.005951f, 0.497559f, 0.005527f, + 0.483643f, 0.005131f, 0.469482f, 0.004765f, 0.455566f, 0.004421f, 0.441650f, 0.004108f, + 0.910156f, 0.089539f, 0.910156f, 0.089539f, 0.910156f, 0.089539f, 0.910156f, 0.089539f, + 0.910156f, 0.089539f, 0.909668f, 0.089539f, 0.909668f, 0.089539f, 0.909180f, 0.089539f, + 0.908691f, 0.089478f, 0.907715f, 0.089417f, 0.907227f, 0.089233f, 0.905762f, 0.088989f, + 0.904297f, 0.088562f, 0.902832f, 0.088013f, 0.900391f, 0.087280f, 0.896973f, 0.086243f, + 0.895020f, 0.085083f, 0.889160f, 0.083557f, 0.884766f, 0.081787f, 0.878906f, 0.079712f, + 0.874512f, 0.077393f, 0.867676f, 0.074951f, 0.860840f, 0.072205f, 0.854492f, 0.069275f, + 0.848145f, 0.066223f, 0.840820f, 0.063171f, 0.833008f, 0.060059f, 0.826172f, 0.056885f, + 0.819336f, 0.053741f, 0.812012f, 0.050690f, 0.804688f, 0.047699f, 0.797852f, 0.044800f, + 0.790527f, 0.042023f, 0.783691f, 0.039337f, 0.776367f, 0.036804f, 0.768555f, 0.034393f, + 0.761230f, 0.032074f, 0.753418f, 0.029922f, 0.745117f, 0.027893f, 0.736816f, 0.025970f, + 0.728516f, 0.024170f, 0.719238f, 0.022491f, 0.709961f, 0.020905f, 0.700195f, 0.019440f, + 0.689941f, 0.018066f, 0.679688f, 0.016785f, 0.668457f, 0.015587f, 0.657227f, 0.014473f, + 0.645996f, 0.013443f, 0.633789f, 0.012474f, 0.621582f, 0.011581f, 0.609375f, 0.010750f, + 0.596191f, 0.009972f, 0.583496f, 0.009262f, 0.569824f, 0.008591f, 0.556641f, 0.007973f, + 0.542969f, 0.007404f, 0.529297f, 0.006874f, 0.515625f, 0.006378f, 0.501465f, 0.005920f, + 0.487793f, 0.005501f, 0.474121f, 0.005108f, 0.460205f, 0.004742f, 0.446289f, 0.004406f, + 0.898438f, 0.101440f, 0.898438f, 0.101440f, 0.898438f, 0.101440f, 0.898438f, 0.101440f, + 0.897949f, 0.101440f, 0.897949f, 0.101440f, 0.897461f, 0.101440f, 0.896973f, 0.101379f, + 0.896973f, 0.101318f, 0.895996f, 0.101135f, 0.895508f, 0.100830f, 0.894043f, 0.100464f, + 0.893066f, 0.099854f, 0.890625f, 0.099121f, 0.888184f, 0.098083f, 0.885254f, 0.096802f, + 0.882324f, 0.095215f, 0.878418f, 0.093323f, 0.872559f, 0.091125f, 0.869629f, 0.088623f, + 0.862793f, 0.085815f, 0.855957f, 0.082764f, 0.850098f, 0.079590f, 0.844727f, 0.076172f, + 0.837402f, 0.072693f, 0.831055f, 0.069092f, 0.824219f, 0.065491f, 0.817871f, 0.061981f, + 0.811035f, 0.058472f, 0.804688f, 0.055023f, 0.797852f, 0.051697f, 0.791992f, 0.048492f, + 0.785645f, 0.045410f, 0.778809f, 0.042480f, 0.771973f, 0.039673f, 0.765625f, 0.037018f, + 0.758789f, 0.034515f, 0.750977f, 0.032166f, 0.743652f, 0.029968f, 0.735840f, 0.027878f, + 0.727539f, 0.025940f, 0.718750f, 0.024124f, 0.709961f, 0.022430f, 0.700684f, 0.020844f, + 0.690918f, 0.019363f, 0.680664f, 0.017975f, 0.670410f, 0.016693f, 0.659180f, 0.015495f, + 0.647949f, 0.014389f, 0.636230f, 0.013359f, 0.624512f, 0.012398f, 0.611816f, 0.011505f, + 0.599609f, 0.010681f, 0.586426f, 0.009911f, 0.573730f, 0.009201f, 0.560547f, 0.008537f, + 0.546875f, 0.007927f, 0.533203f, 0.007355f, 0.519531f, 0.006828f, 0.505859f, 0.006340f, + 0.492432f, 0.005890f, 0.478516f, 0.005470f, 0.464844f, 0.005077f, 0.450928f, 0.004719f, + 0.885254f, 0.114624f, 0.885254f, 0.114624f, 0.885254f, 0.114624f, 0.885254f, 0.114624f, + 0.884766f, 0.114624f, 0.884766f, 0.114563f, 0.884766f, 0.114502f, 0.884277f, 0.114380f, + 0.883789f, 0.114258f, 0.883301f, 0.114014f, 0.882324f, 0.113525f, 0.881348f, 0.112976f, + 0.879395f, 0.112183f, 0.877441f, 0.111145f, 0.875977f, 0.109802f, 0.872559f, 0.108215f, + 0.869141f, 0.106201f, 0.865723f, 0.103821f, 0.860352f, 0.101196f, 0.854492f, 0.098145f, + 0.850586f, 0.094849f, 0.845215f, 0.091187f, 0.838379f, 0.087463f, 0.833496f, 0.083496f, + 0.826660f, 0.079468f, 0.820801f, 0.075378f, 0.814453f, 0.071289f, 0.809082f, 0.067322f, + 0.803711f, 0.063354f, 0.797363f, 0.059540f, 0.791992f, 0.055878f, 0.786133f, 0.052338f, + 0.780762f, 0.048950f, 0.774414f, 0.045746f, 0.768555f, 0.042664f, 0.762207f, 0.039795f, + 0.755859f, 0.037079f, 0.749023f, 0.034546f, 0.741699f, 0.032135f, 0.734863f, 0.029892f, + 0.727051f, 0.027802f, 0.718750f, 0.025833f, 0.710449f, 0.024002f, 0.701172f, 0.022293f, + 0.691895f, 0.020706f, 0.682129f, 0.019226f, 0.671875f, 0.017853f, 0.661133f, 0.016571f, + 0.650391f, 0.015381f, 0.639160f, 0.014282f, 0.626953f, 0.013252f, 0.615234f, 0.012299f, + 0.602539f, 0.011414f, 0.590332f, 0.010597f, 0.577148f, 0.009834f, 0.563965f, 0.009132f, + 0.550781f, 0.008476f, 0.537598f, 0.007866f, 0.523926f, 0.007309f, 0.510254f, 0.006786f, + 0.496826f, 0.006306f, 0.483154f, 0.005856f, 0.469482f, 0.005440f, 0.455811f, 0.005054f, + 0.870605f, 0.129028f, 0.870605f, 0.129028f, 0.870605f, 0.129028f, 0.870605f, 0.129028f, + 0.870605f, 0.129028f, 0.870605f, 0.129028f, 0.870117f, 0.128906f, 0.870117f, 0.128784f, + 0.869629f, 0.128540f, 0.869141f, 0.128052f, 0.868164f, 0.127563f, 0.867188f, 0.126709f, + 0.865723f, 0.125732f, 0.863281f, 0.124329f, 0.862305f, 0.122742f, 0.858887f, 0.120544f, + 0.854980f, 0.118103f, 0.850098f, 0.115173f, 0.847168f, 0.111938f, 0.843750f, 0.108276f, + 0.836426f, 0.104309f, 0.832031f, 0.100159f, 0.827148f, 0.095764f, 0.821289f, 0.091187f, + 0.815918f, 0.086609f, 0.810547f, 0.081970f, 0.806152f, 0.077393f, 0.800781f, 0.072937f, + 0.795410f, 0.068542f, 0.790039f, 0.064270f, 0.785645f, 0.060242f, 0.780762f, 0.056335f, + 0.775391f, 0.052643f, 0.770020f, 0.049133f, 0.765137f, 0.045807f, 0.759766f, 0.042694f, + 0.753906f, 0.039734f, 0.747559f, 0.036987f, 0.740723f, 0.034393f, 0.733887f, 0.031982f, + 0.726562f, 0.029739f, 0.719238f, 0.027618f, 0.710449f, 0.025650f, 0.702148f, 0.023834f, + 0.692871f, 0.022125f, 0.683594f, 0.020538f, 0.673828f, 0.019058f, 0.663574f, 0.017685f, + 0.652832f, 0.016418f, 0.641602f, 0.015244f, 0.629883f, 0.014153f, 0.618164f, 0.013138f, + 0.605957f, 0.012192f, 0.593750f, 0.011314f, 0.581055f, 0.010506f, 0.567871f, 0.009750f, + 0.555176f, 0.009056f, 0.541504f, 0.008408f, 0.528320f, 0.007809f, 0.514648f, 0.007252f, + 0.501465f, 0.006741f, 0.487793f, 0.006260f, 0.474365f, 0.005817f, 0.460938f, 0.005409f, + 0.854492f, 0.145020f, 0.854492f, 0.145020f, 0.854492f, 0.145020f, 0.854492f, 0.145020f, + 0.854492f, 0.144897f, 0.854492f, 0.144897f, 0.854004f, 0.144653f, 0.854492f, 0.144531f, + 0.854004f, 0.144165f, 0.853027f, 0.143555f, 0.852051f, 0.142822f, 0.851074f, 0.141724f, + 0.850586f, 0.140503f, 0.848145f, 0.138672f, 0.846191f, 0.136475f, 0.843262f, 0.133911f, + 0.839844f, 0.130859f, 0.835449f, 0.127319f, 0.832031f, 0.123474f, 0.828613f, 0.119141f, + 0.823242f, 0.114502f, 0.819824f, 0.109558f, 0.813477f, 0.104431f, 0.809570f, 0.099304f, + 0.804199f, 0.094055f, 0.799316f, 0.088867f, 0.794922f, 0.083740f, 0.791992f, 0.078735f, + 0.786621f, 0.073914f, 0.783203f, 0.069214f, 0.779297f, 0.064758f, 0.774902f, 0.060516f, + 0.770508f, 0.056488f, 0.765625f, 0.052673f, 0.761230f, 0.049072f, 0.756348f, 0.045715f, + 0.750977f, 0.042511f, 0.745605f, 0.039551f, 0.739746f, 0.036774f, 0.733398f, 0.034180f, + 0.726562f, 0.031738f, 0.719238f, 0.029495f, 0.711426f, 0.027390f, 0.703125f, 0.025421f, + 0.694336f, 0.023605f, 0.685059f, 0.021912f, 0.675781f, 0.020340f, 0.665527f, 0.018875f, + 0.655273f, 0.017517f, 0.644043f, 0.016251f, 0.632812f, 0.015091f, 0.621582f, 0.014008f, + 0.609375f, 0.013000f, 0.597168f, 0.012070f, 0.584473f, 0.011200f, 0.571777f, 0.010406f, + 0.559082f, 0.009659f, 0.545898f, 0.008972f, 0.532715f, 0.008339f, 0.519531f, 0.007748f, + 0.505859f, 0.007198f, 0.492676f, 0.006691f, 0.479248f, 0.006218f, 0.465820f, 0.005783f, + 0.837402f, 0.162476f, 0.837402f, 0.162476f, 0.837402f, 0.162476f, 0.837402f, 0.162354f, + 0.837402f, 0.162354f, 0.836914f, 0.162231f, 0.836914f, 0.161987f, 0.836426f, 0.161743f, + 0.836426f, 0.161133f, 0.835449f, 0.160522f, 0.835449f, 0.159546f, 0.834473f, 0.158203f, + 0.833496f, 0.156372f, 0.831055f, 0.154175f, 0.830078f, 0.151489f, 0.826660f, 0.148315f, + 0.823242f, 0.144531f, 0.821289f, 0.140381f, 0.817383f, 0.135620f, 0.812012f, 0.130615f, + 0.810547f, 0.125122f, 0.805176f, 0.119507f, 0.800293f, 0.113647f, 0.797852f, 0.107788f, + 0.792480f, 0.101868f, 0.788574f, 0.096008f, 0.785156f, 0.090332f, 0.782715f, 0.084839f, + 0.779297f, 0.079468f, 0.774902f, 0.074341f, 0.772461f, 0.069458f, 0.769531f, 0.064819f, + 0.765137f, 0.060486f, 0.761719f, 0.056366f, 0.758301f, 0.052490f, 0.753418f, 0.048828f, + 0.749023f, 0.045410f, 0.743652f, 0.042206f, 0.738770f, 0.039215f, 0.732422f, 0.036438f, + 0.726074f, 0.033844f, 0.719238f, 0.031433f, 0.711914f, 0.029190f, 0.704102f, 0.027100f, + 0.695801f, 0.025146f, 0.687012f, 0.023346f, 0.677734f, 0.021667f, 0.667969f, 0.020111f, + 0.657715f, 0.018646f, 0.646973f, 0.017319f, 0.636230f, 0.016068f, 0.624512f, 0.014923f, + 0.612793f, 0.013855f, 0.601074f, 0.012863f, 0.588379f, 0.011948f, 0.576172f, 0.011093f, + 0.563477f, 0.010300f, 0.550293f, 0.009567f, 0.537109f, 0.008896f, 0.523926f, 0.008263f, + 0.510742f, 0.007687f, 0.497559f, 0.007145f, 0.484375f, 0.006645f, 0.470947f, 0.006180f, + 0.818359f, 0.181519f, 0.818359f, 0.181519f, 0.818359f, 0.181519f, 0.817871f, 0.181519f, + 0.817871f, 0.181396f, 0.817871f, 0.181274f, 0.817871f, 0.181030f, 0.817871f, 0.180542f, + 0.817871f, 0.179932f, 0.817383f, 0.178955f, 0.816406f, 0.177612f, 0.815918f, 0.175903f, + 0.814941f, 0.173584f, 0.812500f, 0.170898f, 0.811035f, 0.167603f, 0.808594f, 0.163696f, + 0.805664f, 0.159180f, 0.802246f, 0.154175f, 0.799805f, 0.148560f, 0.796875f, 0.142700f, + 0.792480f, 0.136353f, 0.789551f, 0.129883f, 0.787598f, 0.123230f, 0.782227f, 0.116577f, + 0.780273f, 0.109985f, 0.777344f, 0.103516f, 0.774414f, 0.097168f, 0.771973f, 0.091125f, + 0.770508f, 0.085205f, 0.767578f, 0.079651f, 0.765625f, 0.074341f, 0.763184f, 0.069336f, + 0.760254f, 0.064636f, 0.757812f, 0.060181f, 0.754395f, 0.056000f, 0.750977f, 0.052063f, + 0.747559f, 0.048431f, 0.742188f, 0.044983f, 0.737793f, 0.041779f, 0.732422f, 0.038818f, + 0.726074f, 0.036041f, 0.719727f, 0.033447f, 0.712891f, 0.031052f, 0.705566f, 0.028824f, + 0.697266f, 0.026749f, 0.688965f, 0.024826f, 0.679688f, 0.023041f, 0.670410f, 0.021393f, + 0.660645f, 0.019852f, 0.649902f, 0.018433f, 0.639160f, 0.017105f, 0.627930f, 0.015869f, + 0.616211f, 0.014748f, 0.604492f, 0.013687f, 0.592773f, 0.012718f, 0.580078f, 0.011818f, + 0.567871f, 0.010979f, 0.554688f, 0.010201f, 0.541992f, 0.009483f, 0.528809f, 0.008812f, + 0.515625f, 0.008194f, 0.502441f, 0.007626f, 0.489502f, 0.007088f, 0.476318f, 0.006599f, + 0.797363f, 0.202393f, 0.797363f, 0.202393f, 0.797363f, 0.202393f, 0.797363f, 0.202393f, + 0.797363f, 0.202148f, 0.797363f, 0.202026f, 0.797363f, 0.201660f, 0.797363f, 0.201050f, + 0.796875f, 0.200195f, 0.796875f, 0.198975f, 0.796387f, 0.197266f, 0.795898f, 0.195068f, + 0.794922f, 0.192261f, 0.792969f, 0.188843f, 0.792480f, 0.184937f, 0.789551f, 0.180298f, + 0.787598f, 0.174927f, 0.785645f, 0.168823f, 0.782715f, 0.162231f, 0.779297f, 0.155273f, + 0.775879f, 0.148071f, 0.775391f, 0.140747f, 0.772461f, 0.133179f, 0.770508f, 0.125732f, + 0.767578f, 0.118347f, 0.766113f, 0.111206f, 0.764648f, 0.104248f, 0.763184f, 0.097595f, + 0.762695f, 0.091187f, 0.761719f, 0.085144f, 0.759277f, 0.079407f, 0.758301f, 0.073975f, + 0.755859f, 0.068909f, 0.754395f, 0.064087f, 0.751465f, 0.059631f, 0.748535f, 0.055450f, + 0.745117f, 0.051514f, 0.741211f, 0.047852f, 0.737305f, 0.044434f, 0.731934f, 0.041260f, + 0.726562f, 0.038300f, 0.720215f, 0.035553f, 0.713867f, 0.032990f, 0.706543f, 0.030624f, + 0.699219f, 0.028427f, 0.690918f, 0.026382f, 0.682129f, 0.024475f, 0.672852f, 0.022720f, + 0.663086f, 0.021088f, 0.652832f, 0.019577f, 0.642578f, 0.018173f, 0.631348f, 0.016876f, + 0.620117f, 0.015671f, 0.608398f, 0.014565f, 0.596680f, 0.013535f, 0.584473f, 0.012573f, + 0.572266f, 0.011681f, 0.559570f, 0.010857f, 0.546875f, 0.010101f, 0.533691f, 0.009392f, + 0.520996f, 0.008736f, 0.507812f, 0.008125f, 0.494629f, 0.007565f, 0.481689f, 0.007042f, + 0.774414f, 0.225098f, 0.774414f, 0.225098f, 0.774414f, 0.225098f, 0.774414f, 0.225098f, + 0.774414f, 0.224854f, 0.774902f, 0.224609f, 0.774414f, 0.224121f, 0.774414f, 0.223389f, + 0.774414f, 0.222290f, 0.773926f, 0.220581f, 0.773926f, 0.218628f, 0.773926f, 0.215942f, + 0.773438f, 0.212524f, 0.772461f, 0.208374f, 0.771484f, 0.203491f, 0.770508f, 0.197754f, + 0.769043f, 0.191284f, 0.766113f, 0.184204f, 0.763672f, 0.176514f, 0.760742f, 0.168457f, + 0.760742f, 0.160278f, 0.757812f, 0.151855f, 0.757812f, 0.143433f, 0.756836f, 0.135132f, + 0.754395f, 0.126953f, 0.755371f, 0.119141f, 0.755371f, 0.111511f, 0.754395f, 0.104309f, + 0.753418f, 0.097351f, 0.754395f, 0.090820f, 0.753906f, 0.084595f, 0.752441f, 0.078796f, + 0.751465f, 0.073303f, 0.750000f, 0.068176f, 0.748535f, 0.063354f, 0.746094f, 0.058899f, + 0.743164f, 0.054718f, 0.740234f, 0.050812f, 0.736816f, 0.047150f, 0.731934f, 0.043793f, + 0.727051f, 0.040649f, 0.721191f, 0.037720f, 0.714844f, 0.035004f, 0.708008f, 0.032501f, + 0.700684f, 0.030167f, 0.692871f, 0.027985f, 0.684570f, 0.025986f, 0.675781f, 0.024124f, + 0.666016f, 0.022385f, 0.656250f, 0.020782f, 0.645996f, 0.019302f, 0.635254f, 0.017929f, + 0.624023f, 0.016647f, 0.612793f, 0.015480f, 0.601074f, 0.014381f, 0.588867f, 0.013367f, + 0.576660f, 0.012428f, 0.563965f, 0.011559f, 0.551270f, 0.010750f, 0.539062f, 0.010002f, + 0.525879f, 0.009308f, 0.513184f, 0.008659f, 0.500000f, 0.008064f, 0.487061f, 0.007511f, + 0.750000f, 0.249878f, 0.749512f, 0.249878f, 0.750000f, 0.249878f, 0.750000f, 0.249756f, + 0.750000f, 0.249512f, 0.750000f, 0.249146f, 0.750000f, 0.248413f, 0.750488f, 0.247559f, + 0.750488f, 0.246094f, 0.750488f, 0.244141f, 0.750488f, 0.241577f, 0.750488f, 0.238281f, + 0.748535f, 0.234009f, 0.749512f, 0.229004f, 0.749023f, 0.223022f, 0.747070f, 0.216309f, + 0.745117f, 0.208496f, 0.743164f, 0.200195f, 0.744629f, 0.191406f, 0.741211f, 0.182251f, + 0.741699f, 0.172852f, 0.740234f, 0.163330f, 0.742676f, 0.154053f, 0.741211f, 0.144775f, + 0.743652f, 0.135864f, 0.744629f, 0.127197f, 0.743164f, 0.118958f, 0.744629f, 0.111145f, + 0.745605f, 0.103638f, 0.746582f, 0.096558f, 0.748047f, 0.089966f, 0.747559f, 0.083679f, + 0.747559f, 0.077820f, 0.746582f, 0.072327f, 0.745605f, 0.067261f, 0.744629f, 0.062469f, + 0.742676f, 0.058014f, 0.739746f, 0.053864f, 0.735840f, 0.049988f, 0.731934f, 0.046417f, + 0.727539f, 0.043091f, 0.722168f, 0.039978f, 0.716309f, 0.037079f, 0.709473f, 0.034424f, + 0.702637f, 0.031952f, 0.695312f, 0.029663f, 0.687012f, 0.027542f, 0.678223f, 0.025558f, + 0.668945f, 0.023743f, 0.659180f, 0.022049f, 0.649414f, 0.020477f, 0.638672f, 0.019028f, + 0.627930f, 0.017670f, 0.616699f, 0.016434f, 0.604980f, 0.015274f, 0.593262f, 0.014198f, + 0.581055f, 0.013206f, 0.568848f, 0.012283f, 0.556641f, 0.011429f, 0.543945f, 0.010643f, + 0.531250f, 0.009903f, 0.518066f, 0.009224f, 0.505371f, 0.008591f, 0.492676f, 0.008003f, + 0.723145f, 0.276611f, 0.723145f, 0.276611f, 0.723145f, 0.276611f, 0.723145f, 0.276611f, + 0.723145f, 0.276123f, 0.723145f, 0.275635f, 0.723145f, 0.274902f, 0.723633f, 0.273682f, + 0.723633f, 0.271973f, 0.724121f, 0.269531f, 0.724609f, 0.266113f, 0.725098f, 0.262207f, + 0.725098f, 0.257080f, 0.724609f, 0.250732f, 0.722656f, 0.243652f, 0.725586f, 0.235474f, + 0.724121f, 0.226685f, 0.723145f, 0.216919f, 0.722656f, 0.206787f, 0.720703f, 0.196289f, + 0.723145f, 0.185791f, 0.723633f, 0.175171f, 0.724121f, 0.164795f, 0.728027f, 0.154663f, + 0.730469f, 0.144897f, 0.731934f, 0.135498f, 0.734863f, 0.126587f, 0.737305f, 0.118103f, + 0.739258f, 0.110107f, 0.739746f, 0.102478f, 0.741699f, 0.095398f, 0.743164f, 0.088745f, + 0.743652f, 0.082520f, 0.743652f, 0.076660f, 0.743652f, 0.071228f, 0.742676f, 0.066101f, + 0.741211f, 0.061401f, 0.739258f, 0.057007f, 0.735840f, 0.052887f, 0.732422f, 0.049103f, + 0.728516f, 0.045563f, 0.723145f, 0.042297f, 0.717773f, 0.039246f, 0.711914f, 0.036438f, + 0.704590f, 0.033813f, 0.697754f, 0.031403f, 0.689453f, 0.029160f, 0.681152f, 0.027069f, + 0.671875f, 0.025146f, 0.662598f, 0.023346f, 0.652832f, 0.021698f, 0.642578f, 0.020157f, + 0.631836f, 0.018738f, 0.621094f, 0.017426f, 0.609375f, 0.016205f, 0.597656f, 0.015076f, + 0.585938f, 0.014023f, 0.573730f, 0.013054f, 0.561523f, 0.012146f, 0.548828f, 0.011314f, + 0.536621f, 0.010536f, 0.523926f, 0.009811f, 0.511230f, 0.009148f, 0.498291f, 0.008530f, + 0.693848f, 0.305664f, 0.693848f, 0.305664f, 0.693848f, 0.305664f, 0.693848f, 0.305664f, + 0.693848f, 0.305176f, 0.694336f, 0.304443f, 0.694824f, 0.303467f, 0.695312f, 0.302002f, + 0.695312f, 0.299561f, 0.696289f, 0.296631f, 0.696777f, 0.292725f, 0.696777f, 0.287598f, + 0.697754f, 0.281250f, 0.698242f, 0.273926f, 0.698730f, 0.265137f, 0.697266f, 0.255615f, + 0.699707f, 0.245239f, 0.699707f, 0.234131f, 0.700195f, 0.222412f, 0.702637f, 0.210693f, + 0.705078f, 0.198853f, 0.708496f, 0.187134f, 0.708984f, 0.175781f, 0.715332f, 0.164673f, + 0.718750f, 0.154053f, 0.722168f, 0.143921f, 0.724121f, 0.134277f, 0.727539f, 0.125244f, + 0.731934f, 0.116638f, 0.733398f, 0.108582f, 0.736816f, 0.101013f, 0.738281f, 0.093872f, + 0.740234f, 0.087219f, 0.741699f, 0.081055f, 0.741211f, 0.075256f, 0.741211f, 0.069885f, + 0.740723f, 0.064880f, 0.738281f, 0.060211f, 0.736328f, 0.055908f, 0.732910f, 0.051849f, + 0.729004f, 0.048157f, 0.724609f, 0.044678f, 0.719727f, 0.041473f, 0.713379f, 0.038483f, + 0.707031f, 0.035736f, 0.699707f, 0.033173f, 0.692383f, 0.030823f, 0.684082f, 0.028625f, + 0.675293f, 0.026596f, 0.666016f, 0.024704f, 0.656738f, 0.022964f, 0.646484f, 0.021347f, + 0.636230f, 0.019852f, 0.625488f, 0.018463f, 0.614258f, 0.017181f, 0.602539f, 0.015976f, + 0.590820f, 0.014877f, 0.578613f, 0.013855f, 0.566895f, 0.012901f, 0.554688f, 0.012024f, + 0.541992f, 0.011200f, 0.529297f, 0.010437f, 0.516602f, 0.009735f, 0.503906f, 0.009079f, + 0.662598f, 0.337158f, 0.662598f, 0.337158f, 0.662598f, 0.337158f, 0.662598f, 0.336914f, + 0.662598f, 0.336670f, 0.663086f, 0.335938f, 0.663086f, 0.334473f, 0.664062f, 0.332520f, + 0.665039f, 0.329834f, 0.666016f, 0.325928f, 0.665527f, 0.320801f, 0.667969f, 0.314697f, + 0.667480f, 0.306885f, 0.669922f, 0.298096f, 0.669434f, 0.287842f, 0.671387f, 0.276367f, + 0.675781f, 0.264404f, 0.675781f, 0.251465f, 0.677734f, 0.238403f, 0.681152f, 0.225342f, + 0.686035f, 0.212036f, 0.690430f, 0.199219f, 0.694824f, 0.186768f, 0.700684f, 0.174805f, + 0.702637f, 0.163330f, 0.708008f, 0.152466f, 0.714844f, 0.142212f, 0.718750f, 0.132446f, + 0.724609f, 0.123291f, 0.728516f, 0.114685f, 0.731445f, 0.106628f, 0.734375f, 0.099121f, + 0.736816f, 0.092102f, 0.738770f, 0.085510f, 0.740723f, 0.079407f, 0.740234f, 0.073730f, + 0.739258f, 0.068420f, 0.738770f, 0.063538f, 0.736328f, 0.058960f, 0.734375f, 0.054718f, + 0.730469f, 0.050781f, 0.726562f, 0.047150f, 0.721191f, 0.043762f, 0.715332f, 0.040619f, + 0.709473f, 0.037720f, 0.702637f, 0.035034f, 0.695312f, 0.032532f, 0.687500f, 0.030243f, + 0.678711f, 0.028107f, 0.669922f, 0.026123f, 0.660645f, 0.024277f, 0.650391f, 0.022583f, + 0.640137f, 0.021011f, 0.629395f, 0.019547f, 0.618652f, 0.018188f, 0.607422f, 0.016937f, + 0.595703f, 0.015778f, 0.583984f, 0.014694f, 0.572266f, 0.013695f, 0.560059f, 0.012764f, + 0.547852f, 0.011902f, 0.535156f, 0.011101f, 0.522461f, 0.010353f, 0.510254f, 0.009666f, + 0.628418f, 0.371338f, 0.628418f, 0.371338f, 0.628418f, 0.371094f, 0.628418f, 0.371094f, + 0.628418f, 0.370361f, 0.629395f, 0.369385f, 0.629883f, 0.367920f, 0.630859f, 0.365234f, + 0.631836f, 0.361816f, 0.633301f, 0.357178f, 0.634766f, 0.350830f, 0.635742f, 0.343262f, + 0.638184f, 0.333984f, 0.640137f, 0.322998f, 0.641113f, 0.311035f, 0.645508f, 0.297852f, + 0.647949f, 0.283691f, 0.652344f, 0.269043f, 0.657227f, 0.254395f, 0.662598f, 0.239868f, + 0.669922f, 0.225464f, 0.673340f, 0.211426f, 0.680664f, 0.197876f, 0.685547f, 0.184937f, + 0.693359f, 0.172729f, 0.700684f, 0.161011f, 0.705566f, 0.150146f, 0.711426f, 0.139771f, + 0.718750f, 0.130005f, 0.722168f, 0.120911f, 0.727051f, 0.112427f, 0.732422f, 0.104431f, + 0.733887f, 0.097046f, 0.737305f, 0.090088f, 0.738770f, 0.083618f, 0.740234f, 0.077637f, + 0.739258f, 0.072083f, 0.738281f, 0.066895f, 0.736816f, 0.062073f, 0.734375f, 0.057648f, + 0.731934f, 0.053497f, 0.728027f, 0.049683f, 0.723145f, 0.046112f, 0.717773f, 0.042816f, + 0.712402f, 0.039764f, 0.705566f, 0.036957f, 0.698242f, 0.034332f, 0.690430f, 0.031891f, + 0.682617f, 0.029663f, 0.673340f, 0.027573f, 0.664551f, 0.025650f, 0.654785f, 0.023865f, + 0.644531f, 0.022202f, 0.634277f, 0.020676f, 0.623535f, 0.019257f, 0.612305f, 0.017929f, + 0.601074f, 0.016708f, 0.589355f, 0.015579f, 0.577637f, 0.014526f, 0.565430f, 0.013550f, + 0.553223f, 0.012642f, 0.541016f, 0.011787f, 0.528809f, 0.011009f, 0.516113f, 0.010277f, + 0.591309f, 0.407959f, 0.591797f, 0.407959f, 0.591797f, 0.407959f, 0.591797f, 0.407471f, + 0.592285f, 0.406982f, 0.592773f, 0.405762f, 0.593750f, 0.403564f, 0.594727f, 0.400391f, + 0.596680f, 0.396240f, 0.598145f, 0.390137f, 0.600098f, 0.382568f, 0.602539f, 0.373047f, + 0.604980f, 0.361816f, 0.606934f, 0.348877f, 0.611816f, 0.334473f, 0.616699f, 0.319336f, + 0.620605f, 0.302979f, 0.627930f, 0.286865f, 0.634277f, 0.270508f, 0.638672f, 0.254150f, + 0.647949f, 0.238525f, 0.654297f, 0.223389f, 0.663086f, 0.208862f, 0.673828f, 0.195068f, + 0.680176f, 0.182007f, 0.689941f, 0.169678f, 0.696289f, 0.157959f, 0.705078f, 0.147095f, + 0.713867f, 0.136841f, 0.719727f, 0.127197f, 0.724121f, 0.118225f, 0.729980f, 0.109863f, + 0.731934f, 0.101990f, 0.735840f, 0.094727f, 0.737305f, 0.087952f, 0.738770f, 0.081604f, + 0.740234f, 0.075745f, 0.739258f, 0.070312f, 0.738281f, 0.065247f, 0.735840f, 0.060608f, + 0.733398f, 0.056274f, 0.729492f, 0.052246f, 0.725098f, 0.048523f, 0.720703f, 0.045074f, + 0.714355f, 0.041870f, 0.708496f, 0.038910f, 0.701660f, 0.036163f, 0.693848f, 0.033630f, + 0.686035f, 0.031281f, 0.677734f, 0.029099f, 0.668457f, 0.027069f, 0.659180f, 0.025192f, + 0.648926f, 0.023453f, 0.639160f, 0.021851f, 0.628418f, 0.020355f, 0.617676f, 0.018967f, + 0.605957f, 0.017685f, 0.594727f, 0.016495f, 0.583008f, 0.015388f, 0.571289f, 0.014366f, + 0.559570f, 0.013412f, 0.546875f, 0.012520f, 0.534668f, 0.011696f, 0.522461f, 0.010925f, + 0.551758f, 0.447754f, 0.551758f, 0.447754f, 0.552246f, 0.447510f, 0.552246f, 0.447266f, + 0.552734f, 0.446289f, 0.553223f, 0.444580f, 0.555176f, 0.441895f, 0.556152f, 0.438232f, + 0.558594f, 0.432617f, 0.561035f, 0.425049f, 0.563477f, 0.415527f, 0.566406f, 0.404053f, + 0.570312f, 0.390381f, 0.575195f, 0.375000f, 0.578613f, 0.358154f, 0.584473f, 0.340332f, + 0.593750f, 0.322266f, 0.600098f, 0.303955f, 0.611328f, 0.286133f, 0.617676f, 0.268555f, + 0.629395f, 0.251709f, 0.640625f, 0.235352f, 0.649902f, 0.219849f, 0.661621f, 0.205078f, + 0.671387f, 0.191284f, 0.678711f, 0.178223f, 0.688965f, 0.166016f, 0.699707f, 0.154419f, + 0.707031f, 0.143555f, 0.714844f, 0.133545f, 0.719727f, 0.124084f, 0.726074f, 0.115295f, + 0.731445f, 0.107056f, 0.734863f, 0.099365f, 0.737305f, 0.092285f, 0.739258f, 0.085632f, + 0.740234f, 0.079529f, 0.739746f, 0.073792f, 0.739258f, 0.068542f, 0.737793f, 0.063599f, + 0.734863f, 0.059082f, 0.731934f, 0.054871f, 0.727539f, 0.050964f, 0.723633f, 0.047394f, + 0.717773f, 0.044006f, 0.711426f, 0.040924f, 0.705078f, 0.038055f, 0.697754f, 0.035400f, + 0.689941f, 0.032928f, 0.681641f, 0.030655f, 0.672852f, 0.028534f, 0.663574f, 0.026581f, + 0.653809f, 0.024750f, 0.644043f, 0.023071f, 0.633301f, 0.021515f, 0.622559f, 0.020050f, + 0.611328f, 0.018707f, 0.600098f, 0.017456f, 0.588867f, 0.016296f, 0.577148f, 0.015221f, + 0.565430f, 0.014221f, 0.553223f, 0.013290f, 0.541504f, 0.012421f, 0.528809f, 0.011620f, + 0.509277f, 0.490234f, 0.509277f, 0.490234f, 0.509277f, 0.489990f, 0.509766f, 0.489502f, + 0.510254f, 0.488525f, 0.511230f, 0.486328f, 0.512695f, 0.482910f, 0.514160f, 0.478027f, + 0.517578f, 0.470947f, 0.520996f, 0.461670f, 0.523926f, 0.449707f, 0.528809f, 0.435303f, + 0.534180f, 0.418945f, 0.540527f, 0.400635f, 0.548340f, 0.381348f, 0.554688f, 0.361328f, + 0.566895f, 0.340820f, 0.577637f, 0.320801f, 0.588867f, 0.301270f, 0.601074f, 0.282471f, + 0.610352f, 0.264404f, 0.624023f, 0.247070f, 0.637207f, 0.230591f, 0.649414f, 0.215210f, + 0.662109f, 0.200562f, 0.672852f, 0.186768f, 0.685547f, 0.173828f, 0.693359f, 0.161743f, + 0.702148f, 0.150391f, 0.711426f, 0.139771f, 0.720703f, 0.129883f, 0.726074f, 0.120667f, + 0.730469f, 0.112061f, 0.733887f, 0.104065f, 0.738281f, 0.096619f, 0.739258f, 0.089722f, + 0.740234f, 0.083252f, 0.741699f, 0.077332f, 0.740723f, 0.071777f, 0.739258f, 0.066711f, + 0.736816f, 0.061951f, 0.734375f, 0.057556f, 0.730469f, 0.053497f, 0.726074f, 0.049713f, + 0.720703f, 0.046234f, 0.714844f, 0.042999f, 0.708496f, 0.039978f, 0.701172f, 0.037231f, + 0.693848f, 0.034637f, 0.685547f, 0.032257f, 0.677246f, 0.030060f, 0.667969f, 0.028000f, + 0.658691f, 0.026108f, 0.648926f, 0.024338f, 0.638672f, 0.022705f, 0.627930f, 0.021194f, + 0.617188f, 0.019775f, 0.605957f, 0.018463f, 0.594727f, 0.017258f, 0.583008f, 0.016129f, + 0.571289f, 0.015076f, 0.559570f, 0.014099f, 0.547852f, 0.013191f, 0.535645f, 0.012337f, + 0.463623f, 0.536133f, 0.463623f, 0.536133f, 0.463867f, 0.535645f, 0.464111f, 0.535156f, + 0.465088f, 0.533691f, 0.466064f, 0.530762f, 0.468506f, 0.526367f, 0.471191f, 0.520020f, + 0.474609f, 0.511230f, 0.478516f, 0.499268f, 0.483643f, 0.484375f, 0.489990f, 0.466797f, + 0.495361f, 0.447266f, 0.502441f, 0.425537f, 0.515137f, 0.403564f, 0.526855f, 0.380859f, + 0.540039f, 0.358887f, 0.553711f, 0.336914f, 0.564453f, 0.315918f, 0.587891f, 0.295898f, + 0.600098f, 0.276611f, 0.610840f, 0.258545f, 0.624512f, 0.241211f, 0.641113f, 0.225098f, + 0.657715f, 0.209717f, 0.668457f, 0.195312f, 0.678223f, 0.181763f, 0.687988f, 0.169067f, + 0.701172f, 0.157104f, 0.707031f, 0.146118f, 0.715332f, 0.135620f, 0.723145f, 0.125977f, + 0.728516f, 0.117126f, 0.734375f, 0.108704f, 0.736328f, 0.100952f, 0.739746f, 0.093750f, + 0.741699f, 0.087036f, 0.742188f, 0.080872f, 0.741699f, 0.075134f, 0.741211f, 0.069763f, + 0.739258f, 0.064819f, 0.736816f, 0.060272f, 0.733398f, 0.056030f, 0.729004f, 0.052124f, + 0.724121f, 0.048492f, 0.718750f, 0.045105f, 0.712402f, 0.041992f, 0.705078f, 0.039093f, + 0.698242f, 0.036407f, 0.689941f, 0.033905f, 0.681641f, 0.031616f, 0.672852f, 0.029480f, + 0.663574f, 0.027512f, 0.653809f, 0.025665f, 0.644043f, 0.023956f, 0.633301f, 0.022369f, + 0.622559f, 0.020889f, 0.611816f, 0.019516f, 0.601074f, 0.018250f, 0.589355f, 0.017059f, + 0.578125f, 0.015961f, 0.565918f, 0.014946f, 0.554199f, 0.013992f, 0.542480f, 0.013107f, + 0.414551f, 0.584961f, 0.414551f, 0.584961f, 0.414795f, 0.584961f, 0.415039f, 0.583984f, + 0.416260f, 0.582031f, 0.418457f, 0.578613f, 0.420166f, 0.572754f, 0.424072f, 0.563965f, + 0.428467f, 0.552246f, 0.433838f, 0.537109f, 0.441162f, 0.518066f, 0.448730f, 0.497070f, + 0.458984f, 0.473633f, 0.467773f, 0.449219f, 0.480713f, 0.424072f, 0.497559f, 0.399414f, + 0.511719f, 0.375244f, 0.529297f, 0.352051f, 0.543945f, 0.329834f, 0.566895f, 0.308838f, + 0.581543f, 0.288574f, 0.598633f, 0.269531f, 0.619629f, 0.251465f, 0.635742f, 0.234497f, + 0.646973f, 0.218506f, 0.659668f, 0.203369f, 0.674805f, 0.189331f, 0.684570f, 0.176025f, + 0.695801f, 0.163696f, 0.707031f, 0.152222f, 0.718750f, 0.141357f, 0.723145f, 0.131348f, + 0.729004f, 0.122009f, 0.734375f, 0.113342f, 0.738281f, 0.105286f, 0.741211f, 0.097778f, + 0.743164f, 0.090820f, 0.744629f, 0.084412f, 0.744629f, 0.078430f, 0.743652f, 0.072876f, + 0.742676f, 0.067749f, 0.739746f, 0.062988f, 0.735840f, 0.058624f, 0.731934f, 0.054535f, + 0.727539f, 0.050751f, 0.721680f, 0.047241f, 0.715820f, 0.044006f, 0.709473f, 0.040985f, + 0.702148f, 0.038208f, 0.694824f, 0.035614f, 0.686523f, 0.033234f, 0.677734f, 0.031006f, + 0.668457f, 0.028946f, 0.659180f, 0.027023f, 0.649414f, 0.025238f, 0.639160f, 0.023590f, + 0.628906f, 0.022049f, 0.618164f, 0.020630f, 0.606934f, 0.019287f, 0.595703f, 0.018051f, + 0.584473f, 0.016907f, 0.572754f, 0.015839f, 0.561035f, 0.014839f, 0.549316f, 0.013908f, + 0.361816f, 0.637695f, 0.361816f, 0.637695f, 0.362061f, 0.637207f, 0.362793f, 0.636230f, + 0.364258f, 0.633301f, 0.366455f, 0.628906f, 0.369873f, 0.621094f, 0.374512f, 0.609375f, + 0.378906f, 0.593750f, 0.387451f, 0.573730f, 0.396484f, 0.550293f, 0.407471f, 0.524414f, + 0.419189f, 0.497314f, 0.433594f, 0.469971f, 0.453613f, 0.442627f, 0.473633f, 0.416016f, + 0.488037f, 0.390381f, 0.509277f, 0.365967f, 0.528809f, 0.343262f, 0.549805f, 0.320801f, + 0.574707f, 0.299805f, 0.590332f, 0.280029f, 0.609375f, 0.261475f, 0.631836f, 0.243774f, + 0.641602f, 0.227173f, 0.659668f, 0.211426f, 0.671387f, 0.196777f, 0.685059f, 0.183105f, + 0.698730f, 0.170166f, 0.705078f, 0.158203f, 0.715820f, 0.146973f, 0.723145f, 0.136597f, + 0.730469f, 0.126831f, 0.737793f, 0.117920f, 0.740723f, 0.109558f, 0.741699f, 0.101807f, + 0.745117f, 0.094604f, 0.747559f, 0.087891f, 0.747070f, 0.081726f, 0.747070f, 0.075989f, + 0.744141f, 0.070679f, 0.742676f, 0.065796f, 0.739258f, 0.061218f, 0.735840f, 0.056976f, + 0.730957f, 0.053070f, 0.725586f, 0.049438f, 0.719727f, 0.046082f, 0.713867f, 0.042938f, + 0.706543f, 0.040070f, 0.699219f, 0.037384f, 0.690918f, 0.034882f, 0.682617f, 0.032562f, + 0.673828f, 0.030426f, 0.664551f, 0.028442f, 0.654785f, 0.026581f, 0.645020f, 0.024857f, + 0.634766f, 0.023254f, 0.624023f, 0.021774f, 0.613281f, 0.020386f, 0.602051f, 0.019089f, + 0.590820f, 0.017899f, 0.579590f, 0.016769f, 0.567871f, 0.015732f, 0.556641f, 0.014755f, + 0.305420f, 0.694336f, 0.305420f, 0.694336f, 0.305664f, 0.693848f, 0.306641f, 0.691895f, + 0.308105f, 0.687988f, 0.311279f, 0.681152f, 0.316162f, 0.669922f, 0.321777f, 0.654297f, + 0.330078f, 0.632812f, 0.344238f, 0.606934f, 0.353027f, 0.578125f, 0.367432f, 0.547852f, + 0.385498f, 0.517578f, 0.405273f, 0.487793f, 0.422852f, 0.458496f, 0.448730f, 0.431152f, + 0.473633f, 0.404541f, 0.493896f, 0.379639f, 0.519531f, 0.355469f, 0.539551f, 0.332520f, + 0.563477f, 0.310791f, 0.583008f, 0.290283f, 0.604004f, 0.270752f, 0.626953f, 0.252686f, + 0.642090f, 0.235352f, 0.657715f, 0.218994f, 0.672852f, 0.203857f, 0.686523f, 0.189575f, + 0.699219f, 0.176270f, 0.707031f, 0.163818f, 0.717285f, 0.152344f, 0.723633f, 0.141602f, + 0.730469f, 0.131592f, 0.739258f, 0.122375f, 0.741699f, 0.113708f, 0.745605f, 0.105713f, + 0.747559f, 0.098267f, 0.748047f, 0.091370f, 0.749023f, 0.085022f, 0.748535f, 0.079102f, + 0.747070f, 0.073608f, 0.746582f, 0.068542f, 0.742188f, 0.063843f, 0.739258f, 0.059448f, + 0.734375f, 0.055420f, 0.730469f, 0.051666f, 0.724609f, 0.048187f, 0.717773f, 0.044952f, + 0.710938f, 0.041962f, 0.704102f, 0.039154f, 0.695801f, 0.036591f, 0.687988f, 0.034180f, + 0.679199f, 0.031952f, 0.670410f, 0.029892f, 0.660645f, 0.027969f, 0.650879f, 0.026184f, + 0.640625f, 0.024521f, 0.630371f, 0.022964f, 0.619629f, 0.021515f, 0.608887f, 0.020172f, + 0.598145f, 0.018921f, 0.586914f, 0.017761f, 0.575195f, 0.016663f, 0.563965f, 0.015656f, + 0.244995f, 0.754395f, 0.245117f, 0.754395f, 0.245483f, 0.753418f, 0.246704f, 0.750977f, + 0.249634f, 0.745117f, 0.253662f, 0.734863f, 0.260010f, 0.717773f, 0.268555f, 0.694336f, + 0.277344f, 0.665527f, 0.292480f, 0.632812f, 0.309814f, 0.599121f, 0.331787f, 0.565918f, + 0.352539f, 0.533203f, 0.376465f, 0.501953f, 0.405518f, 0.472412f, 0.433838f, 0.444336f, + 0.456787f, 0.417236f, 0.488281f, 0.391357f, 0.510254f, 0.366211f, 0.540039f, 0.343018f, + 0.564941f, 0.320557f, 0.579590f, 0.299561f, 0.606445f, 0.279541f, 0.627441f, 0.260498f, + 0.638184f, 0.242676f, 0.666504f, 0.226074f, 0.670898f, 0.210327f, 0.687988f, 0.195801f, + 0.700684f, 0.182129f, 0.706055f, 0.169312f, 0.718262f, 0.157471f, 0.727539f, 0.146362f, + 0.735840f, 0.136108f, 0.738770f, 0.126587f, 0.743164f, 0.117737f, 0.746582f, 0.109497f, + 0.751953f, 0.101868f, 0.751953f, 0.094788f, 0.753906f, 0.088257f, 0.752930f, 0.082153f, + 0.750977f, 0.076538f, 0.749512f, 0.071289f, 0.745605f, 0.066406f, 0.742188f, 0.061951f, + 0.738281f, 0.057770f, 0.734375f, 0.053894f, 0.729004f, 0.050293f, 0.722656f, 0.046967f, + 0.715332f, 0.043854f, 0.708496f, 0.040985f, 0.701172f, 0.038330f, 0.693359f, 0.035828f, + 0.684570f, 0.033539f, 0.676270f, 0.031403f, 0.666992f, 0.029404f, 0.657227f, 0.027542f, + 0.646973f, 0.025818f, 0.636719f, 0.024200f, 0.626465f, 0.022705f, 0.615723f, 0.021301f, + 0.604980f, 0.020004f, 0.593750f, 0.018784f, 0.582520f, 0.017654f, 0.571289f, 0.016586f, + 0.180542f, 0.818848f, 0.180664f, 0.818848f, 0.181274f, 0.817383f, 0.183350f, 0.812988f, + 0.187134f, 0.802734f, 0.193237f, 0.784180f, 0.201416f, 0.757324f, 0.214355f, 0.723145f, + 0.231445f, 0.685547f, 0.248901f, 0.648438f, 0.272217f, 0.611816f, 0.302979f, 0.577148f, + 0.329834f, 0.544922f, 0.364258f, 0.514160f, 0.394043f, 0.484619f, 0.425781f, 0.456055f, + 0.456543f, 0.428467f, 0.481934f, 0.402344f, 0.512207f, 0.376709f, 0.540039f, 0.352783f, + 0.566406f, 0.329346f, 0.579102f, 0.307617f, 0.607910f, 0.286865f, 0.627930f, 0.267822f, + 0.645996f, 0.249512f, 0.661621f, 0.232178f, 0.677734f, 0.216309f, 0.691406f, 0.201172f, + 0.702637f, 0.187256f, 0.711426f, 0.174194f, 0.721680f, 0.161987f, 0.730957f, 0.150879f, + 0.736328f, 0.140259f, 0.742188f, 0.130493f, 0.746582f, 0.121582f, 0.750488f, 0.113159f, + 0.751953f, 0.105347f, 0.752930f, 0.098083f, 0.756836f, 0.091370f, 0.755859f, 0.085144f, + 0.755371f, 0.079346f, 0.752441f, 0.073975f, 0.750488f, 0.069031f, 0.746582f, 0.064392f, + 0.743652f, 0.060120f, 0.737793f, 0.056152f, 0.733398f, 0.052460f, 0.727051f, 0.049011f, + 0.720215f, 0.045837f, 0.713867f, 0.042847f, 0.706543f, 0.040100f, 0.699219f, 0.037537f, + 0.690430f, 0.035156f, 0.682129f, 0.032928f, 0.672852f, 0.030884f, 0.663086f, 0.028961f, + 0.653809f, 0.027161f, 0.644043f, 0.025497f, 0.633301f, 0.023941f, 0.622559f, 0.022491f, + 0.612305f, 0.021133f, 0.601074f, 0.019867f, 0.590332f, 0.018692f, 0.579102f, 0.017578f, + 0.111816f, 0.888184f, 0.112000f, 0.887207f, 0.112976f, 0.883789f, 0.115845f, 0.873047f, + 0.122864f, 0.849609f, 0.133301f, 0.813477f, 0.147217f, 0.770996f, 0.167236f, 0.728027f, + 0.196411f, 0.688965f, 0.222290f, 0.653320f, 0.258057f, 0.619629f, 0.293457f, 0.587402f, + 0.328613f, 0.556152f, 0.361328f, 0.524902f, 0.392578f, 0.495850f, 0.430420f, 0.466064f, + 0.459961f, 0.437744f, 0.482422f, 0.410889f, 0.511230f, 0.385010f, 0.536621f, 0.359863f, + 0.568848f, 0.336182f, 0.592773f, 0.313721f, 0.614258f, 0.293213f, 0.626953f, 0.273193f, + 0.646484f, 0.254639f, 0.657227f, 0.237427f, 0.683105f, 0.221191f, 0.693359f, 0.205933f, + 0.698242f, 0.191772f, 0.709473f, 0.178589f, 0.724609f, 0.166260f, 0.733398f, 0.154907f, + 0.739746f, 0.144165f, 0.745605f, 0.134399f, 0.750977f, 0.125122f, 0.753906f, 0.116577f, + 0.754883f, 0.108704f, 0.758301f, 0.101257f, 0.759766f, 0.094482f, 0.757812f, 0.088074f, + 0.759766f, 0.082092f, 0.758301f, 0.076660f, 0.756348f, 0.071594f, 0.752441f, 0.066833f, + 0.748047f, 0.062469f, 0.741699f, 0.058380f, 0.736816f, 0.054596f, 0.732910f, 0.051086f, + 0.726074f, 0.047791f, 0.719727f, 0.044769f, 0.711914f, 0.041901f, 0.704590f, 0.039276f, + 0.696289f, 0.036804f, 0.688477f, 0.034546f, 0.678711f, 0.032410f, 0.669922f, 0.030411f, + 0.660156f, 0.028564f, 0.650391f, 0.026840f, 0.640625f, 0.025223f, 0.630371f, 0.023727f, + 0.619629f, 0.022324f, 0.608887f, 0.020996f, 0.597656f, 0.019775f, 0.586914f, 0.018631f, + 0.038452f, 0.960938f, 0.039124f, 0.957520f, 0.042480f, 0.933594f, 0.051575f, 0.879395f, + 0.069275f, 0.824219f, 0.091064f, 0.785156f, 0.126343f, 0.753906f, 0.154419f, 0.725586f, + 0.192139f, 0.695312f, 0.234375f, 0.663086f, 0.273438f, 0.630371f, 0.305908f, 0.597656f, + 0.338379f, 0.565430f, 0.379150f, 0.532227f, 0.413818f, 0.501465f, 0.444336f, 0.471191f, + 0.471436f, 0.442383f, 0.504395f, 0.414795f, 0.531250f, 0.388672f, 0.547363f, 0.364014f, + 0.579590f, 0.340088f, 0.603516f, 0.317627f, 0.622559f, 0.297119f, 0.635742f, 0.276855f, + 0.669434f, 0.258301f, 0.670410f, 0.241089f, 0.685547f, 0.224854f, 0.699219f, 0.209717f, + 0.712402f, 0.195190f, 0.720703f, 0.182373f, 0.729980f, 0.169678f, 0.746582f, 0.158325f, + 0.744629f, 0.147705f, 0.748535f, 0.137695f, 0.760254f, 0.128296f, 0.757812f, 0.119629f, + 0.761230f, 0.111755f, 0.762207f, 0.104248f, 0.764160f, 0.097290f, 0.763184f, 0.090881f, + 0.762207f, 0.084900f, 0.760742f, 0.079285f, 0.759766f, 0.074097f, 0.755859f, 0.069275f, + 0.752930f, 0.064758f, 0.747559f, 0.060669f, 0.742676f, 0.056793f, 0.737305f, 0.053131f, + 0.731445f, 0.049774f, 0.725586f, 0.046661f, 0.718262f, 0.043732f, 0.710449f, 0.041077f, + 0.702637f, 0.038544f, 0.694336f, 0.036163f, 0.685547f, 0.033966f, 0.676758f, 0.031921f, + 0.667480f, 0.030014f, 0.657715f, 0.028229f, 0.647461f, 0.026566f, 0.637207f, 0.025009f, + 0.626953f, 0.023544f, 0.616699f, 0.022186f, 0.605957f, 0.020920f, 0.594727f, 0.019730f +}; #endif /* __EEVEE_LUT_H__ */ diff --git a/source/blender/draw/engines/eevee/eevee_private.h b/source/blender/draw/engines/eevee/eevee_private.h index 59029b1f1af..c98e0b6529b 100644 --- a/source/blender/draw/engines/eevee/eevee_private.h +++ b/source/blender/draw/engines/eevee/eevee_private.h @@ -33,7 +33,14 @@ struct Object; #define MAX_CASCADE_NUM 4 typedef struct EEVEE_PassList { + /* Shadows */ struct DRWPass *shadow_pass; + + /* Probes */ + struct DRWPass *probe_background; + struct DRWPass *probe_prefilter; + struct DRWPass *probe_sh; + struct DRWPass *depth_pass; struct DRWPass *depth_pass_cull; struct DRWPass *pass; @@ -41,17 +48,29 @@ typedef struct EEVEE_PassList { } EEVEE_PassList; typedef struct EEVEE_FramebufferList { - struct GPUFrameBuffer *main; /* HDR */ + /* Shadows */ struct GPUFrameBuffer *shadow_cube_fb; struct GPUFrameBuffer *shadow_map_fb; struct GPUFrameBuffer *shadow_cascade_fb; + /* Probes */ + struct GPUFrameBuffer *probe_fb; + struct GPUFrameBuffer *probe_filter_fb; + struct GPUFrameBuffer *probe_sh_fb; + + struct GPUFrameBuffer *main; /* HDR */ } EEVEE_FramebufferList; typedef struct EEVEE_TextureList { - struct GPUTexture *color; /* R11_G11_B10 */ + /* Shadows */ struct GPUTexture *shadow_depth_cube_pool; struct GPUTexture *shadow_depth_map_pool; struct GPUTexture *shadow_depth_cascade_pool; + /* Probes */ + struct GPUTexture *probe_rt; /* R16_G16_B16 */ + struct GPUTexture *probe_depth_rt; + struct GPUTexture *probe_pool; /* R11_G11_B10 */ + + struct GPUTexture *color; /* R16_G16_B16 */ } EEVEE_TextureList; typedef struct EEVEE_StorageList { @@ -61,6 +80,9 @@ typedef struct EEVEE_StorageList { struct GPUUniformBuffer *light_ubo; struct GPUUniformBuffer *shadow_ubo; + /* Probes */ + struct EEVEE_ProbesInfo *probes; + struct g_data *g_data; } EEVEE_StorageList; @@ -111,6 +133,20 @@ typedef struct EEVEE_LampsInfo { struct EEVEE_ShadowMap shadow_map_data[MAX_SHADOW_MAP]; struct EEVEE_ShadowCascade shadow_cascade_data[MAX_SHADOW_CASCADE]; } EEVEE_LampsInfo; + +/* ************ PROBE DATA ************* */ +typedef struct EEVEE_ProbesInfo { + /* For rendering probes */ + float probemat[6][4][4]; + int layer; + float samples_ct; + float invsamples_ct; + float roughness; + float lodfactor; + float lodmax; + struct GPUTexture *backgroundtex; +} EEVEE_ProbesInfo; + /* *********************************** */ typedef struct EEVEE_Data { @@ -131,11 +167,7 @@ typedef struct g_data{ struct DRWShadingGroup *default_lit_grp; struct DRWShadingGroup *shadow_shgrp; struct DRWShadingGroup *depth_shgrp; - struct DRWShadingGroup *depth_shgrp_select; - struct DRWShadingGroup *depth_shgrp_active; struct DRWShadingGroup *depth_shgrp_cull; - struct DRWShadingGroup *depth_shgrp_cull_select; - struct DRWShadingGroup *depth_shgrp_cull_active; struct ListBase lamps; /* Lamps gathered during cache iteration */ } g_data; /* Transient data */ @@ -146,4 +178,54 @@ void EEVEE_lights_cache_init(EEVEE_StorageList *stl); void EEVEE_lights_cache_add(EEVEE_StorageList *stl, struct Object *ob); void EEVEE_lights_cache_finish(EEVEE_StorageList *stl, EEVEE_TextureList *txl, EEVEE_FramebufferList *fbl); void EEVEE_lights_update(EEVEE_StorageList *stl); -void EEVEE_draw_shadows(EEVEE_Data *vedata);
\ No newline at end of file +void EEVEE_draw_shadows(EEVEE_Data *vedata); + +/* eevee_probes.c */ +void EEVEE_probes_init(EEVEE_Data *vedata); +void EEVEE_probes_cache_init(EEVEE_Data *vedata); +void EEVEE_probes_cache_add(EEVEE_Data *vedata, Object *ob); +void EEVEE_probes_cache_finish(EEVEE_Data *vedata); +void EEVEE_probes_update(EEVEE_Data *vedata); +void EEVEE_refresh_probe(EEVEE_Data *vedata); + +/* Shadow Matrix */ +static const float texcomat[4][4] = { /* From NDC to TexCo */ + {0.5, 0.0, 0.0, 0.0}, + {0.0, 0.5, 0.0, 0.0}, + {0.0, 0.0, 0.5, 0.0}, + {0.5, 0.5, 0.5, 1.0} +}; + +/* Cubemap Matrices */ +static const float cubefacemat[6][4][4] = { + /* Pos X */ + {{0.0, 0.0, -1.0, 0.0}, + {0.0, -1.0, 0.0, 0.0}, + {-1.0, 0.0, 0.0, 0.0}, + {0.0, 0.0, 0.0, 1.0}}, + /* Neg X */ + {{0.0, 0.0, 1.0, 0.0}, + {0.0, -1.0, 0.0, 0.0}, + {1.0, 0.0, 0.0, 0.0}, + {0.0, 0.0, 0.0, 1.0}}, + /* Pos Y */ + {{1.0, 0.0, 0.0, 0.0}, + {0.0, 0.0, 1.0, 0.0}, + {0.0, -1.0, 0.0, 0.0}, + {0.0, 0.0, 0.0, 1.0}}, + /* Neg Y */ + {{1.0, 0.0, 0.0, 0.0}, + {0.0, 0.0, -1.0, 0.0}, + {0.0, 1.0, 0.0, 0.0}, + {0.0, 0.0, 0.0, 1.0}}, + /* Pos Z */ + {{1.0, 0.0, 0.0, 0.0}, + {0.0, -1.0, 0.0, 0.0}, + {0.0, 0.0, -1.0, 0.0}, + {0.0, 0.0, 0.0, 1.0}}, + /* Neg Z */ + {{-1.0, 0.0, 0.0, 0.0}, + {0.0, -1.0, 0.0, 0.0}, + {0.0, 0.0, 1.0, 0.0}, + {0.0, 0.0, 0.0, 1.0}}, +}; diff --git a/source/blender/draw/engines/eevee/eevee_probes.c b/source/blender/draw/engines/eevee/eevee_probes.c new file mode 100644 index 00000000000..78e1a0cf52f --- /dev/null +++ b/source/blender/draw/engines/eevee/eevee_probes.c @@ -0,0 +1,209 @@ +/* + * Copyright 2016, Blender Foundation. + * + * This program is free software; you can redistribute it and/or + * modify it under the terms of the GNU General Public License + * as published by the Free Software Foundation; either version 2 + * of the License, or (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program; if not, write to the Free Software Foundation, + * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. + * + * Contributor(s): Blender Institute + * + */ + +/** \file eevee_lights.c + * \ingroup DNA + */ + +#include "DNA_world_types.h" +#include "DNA_texture_types.h" +#include "DNA_image_types.h" + +#include "DRW_render.h" + +#include "eevee.h" +#include "eevee_private.h" +#include "GPU_texture.h" +#include "GPU_glew.h" + +typedef struct EEVEE_ProbeData { + short probe_id, shadow_id; +} EEVEE_ProbeData; + +/* TODO Option */ +#define PROBE_SIZE 512 + +/* *********** FUNCTIONS *********** */ + +void EEVEE_probes_init(EEVEE_Data *vedata) +{ + EEVEE_StorageList *stl = vedata->stl; + EEVEE_FramebufferList *fbl = vedata->fbl; + EEVEE_TextureList *txl = vedata->txl; + + if (!stl->probes) { + stl->probes = MEM_callocN(sizeof(EEVEE_ProbesInfo), "EEVEE_ProbesInfo"); + } + + if (!txl->probe_rt) { + float *test_tex; + const float face_col[6][4] = {{1.0f, 0.0f, 0.0f, 1.0f}, {0.0f, 1.0f, 0.0f, 1.0f}, {0.0f, 0.0f, 1.0f, 1.0f}, + {1.0f, 0.0f, 1.0f, 1.0f}, {1.0f, 1.0f, 0.0f, 1.0f}, {0.0f, 1.0f, 1.0f, 1.0f}}; + + test_tex = MEM_mallocN(sizeof(float) * 6 * PROBE_SIZE * PROBE_SIZE * 4, "test tex"); + + for (int i = 0; i < 6; ++i) { + for (int j = 0; j < PROBE_SIZE * PROBE_SIZE; ++j) { + copy_v4_v4(test_tex + i * PROBE_SIZE * PROBE_SIZE * 4 + j * 4, face_col[i]); + } + } + + txl->probe_rt = DRW_texture_create_cube(PROBE_SIZE, DRW_TEX_RGBA_16, DRW_TEX_FILTER | DRW_TEX_MIPMAP, (float *)test_tex); + txl->probe_depth_rt = DRW_texture_create_cube(PROBE_SIZE, DRW_TEX_DEPTH_24, DRW_TEX_FILTER, NULL); + + MEM_freeN(test_tex); + } + + DRWFboTexture tex_probe[2] = {{&txl->probe_depth_rt, DRW_BUF_DEPTH_24, DRW_TEX_FILTER}, + {&txl->probe_rt, DRW_BUF_RGBA_16, DRW_TEX_FILTER | DRW_TEX_MIPMAP}}; + + DRW_framebuffer_init(&fbl->probe_fb, PROBE_SIZE, PROBE_SIZE, tex_probe, 2); + + if (!txl->probe_pool) { + float *test_tex; + const float face_col[6][4] = {{1.0f, 0.0f, 0.0f, 1.0f}, {0.0f, 1.0f, 0.0f, 1.0f}, {0.0f, 0.0f, 1.0f, 1.0f}, + {1.0f, 0.0f, 1.0f, 1.0f}, {1.0f, 1.0f, 0.0f, 1.0f}, {0.0f, 1.0f, 1.0f, 1.0f}}; + + test_tex = MEM_mallocN(sizeof(float) * 6 * PROBE_SIZE * PROBE_SIZE * 4, "test tex"); + + for (int i = 0; i < 6; ++i) { + for (int j = 0; j < PROBE_SIZE * PROBE_SIZE; ++j) { + copy_v4_v4(test_tex + i * PROBE_SIZE * PROBE_SIZE * 4 + j * 4, face_col[i]); + } + } + + /* TODO array */ + txl->probe_pool = DRW_texture_create_cube(PROBE_SIZE, DRW_TEX_RGBA_16, DRW_TEX_FILTER | DRW_TEX_MIPMAP, (float *)test_tex); + MEM_freeN(test_tex); + } + + DRWFboTexture tex_filter = {&txl->probe_pool, DRW_BUF_RGBA_16, DRW_TEX_FILTER | DRW_TEX_MIPMAP}; + + DRW_framebuffer_init(&fbl->probe_filter_fb, PROBE_SIZE, PROBE_SIZE, &tex_filter, 1); +} + +void EEVEE_probes_cache_init(EEVEE_Data *UNUSED(vedata)) +{ + return; +} + +void EEVEE_probes_cache_add(EEVEE_Data *UNUSED(vedata), Object *UNUSED(ob)) +{ + return; +} + +void EEVEE_probes_cache_finish(EEVEE_Data *UNUSED(vedata)) +{ + return; +} + +void EEVEE_probes_update(EEVEE_Data *UNUSED(vedata)) +{ + return; +} + +void EEVEE_refresh_probe(EEVEE_Data *vedata) +{ + EEVEE_FramebufferList *fbl = vedata->fbl; + EEVEE_TextureList *txl = vedata->txl; + EEVEE_PassList *psl = vedata->psl; + EEVEE_StorageList *stl = vedata->stl; + EEVEE_ProbesInfo *pinfo = stl->probes; + + const bContext *C = DRW_get_context(); + Scene *scene = CTX_data_scene(C); + World *world = scene->world; + + float projmat[4][4]; + + /* 1 - Render to cubemap target using geometry shader. */ + /* We don't need to clear since we render the background. */ + pinfo->layer = 0; + perspective_m4(projmat, -0.1f, 0.1f, -0.1f, 0.1f, 0.1f, 100.0f); + for (int i = 0; i < 6; ++i) { + mul_m4_m4m4(pinfo->probemat[i], projmat, cubefacemat[i]); + } + + /* Debug Tex : Use World 1st Tex Slot */ + if (world && world->mtex[0]) { + MTex *mtex = world->mtex[0]; + if (mtex && mtex->tex) { + Tex *tex = mtex->tex; + if (tex->ima) { + pinfo->backgroundtex = GPU_texture_from_blender(tex->ima, &tex->iuser, GL_TEXTURE_2D, true, 0.0, 0); + + DRW_framebuffer_bind(fbl->probe_fb); + DRW_draw_pass(psl->probe_background); + } + } + } + + /* 2 - Let gpu create Mipmaps for Filtered Importance Sampling. */ + /* Bind next framebuffer to be able to write to probe_rt. */ + DRW_framebuffer_bind(fbl->probe_filter_fb); + DRW_texture_generate_mipmaps(txl->probe_rt); + + /* 3 - Render to probe array to the specified layer, do prefiltering. */ + /* Detach to rebind the right mipmap. */ + DRW_framebuffer_texture_detach(txl->probe_pool); + float mipsize = PROBE_SIZE * 2; + int miplevels = 1 + (int)floorf(log2f(PROBE_SIZE)); + for (int i = 0; i < miplevels - 2; i++) { + float bias = (i == 0) ? 0.0f : 1.0f; + + mipsize /= 2; + CLAMP_MIN(mipsize, 1); + + pinfo->layer = 0; + pinfo->roughness = (float)i / ((float)miplevels - 3.0f); + pinfo->roughness *= pinfo->roughness; /* Disney Roughness */ + pinfo->roughness *= pinfo->roughness; /* Distribute Roughness accros lod more evenly */ + CLAMP(pinfo->roughness, 1e-8f, 0.99999f); /* Avoid artifacts */ + +#if 1 /* Variable Sample count (fast) */ + switch (i) { + case 0: pinfo->samples_ct = 1.0f; break; + case 1: pinfo->samples_ct = 16.0f; break; + case 2: pinfo->samples_ct = 32.0f; break; + case 3: pinfo->samples_ct = 64.0f; break; + default: pinfo->samples_ct = 128.0f; break; + } +#else /* Constant Sample count (slow) */ + pinfo->samples_ct = 1024.0f; +#endif + + pinfo->invsamples_ct = 1.0f / pinfo->samples_ct; + pinfo->lodfactor = bias + 0.5f * log((float)(PROBE_SIZE * PROBE_SIZE) * pinfo->invsamples_ct) / log(2); + pinfo->lodmax = (float)miplevels - 3.0f; + + DRW_framebuffer_texture_attach(fbl->probe_filter_fb, txl->probe_pool, 0, i); + DRW_framebuffer_viewport_size(fbl->probe_filter_fb, mipsize, mipsize); + DRW_draw_pass(psl->probe_prefilter); + DRW_framebuffer_texture_detach(txl->probe_pool); + } + /* reattach to have a valid framebuffer. */ + DRW_framebuffer_texture_attach(fbl->probe_filter_fb, txl->probe_pool, 0, 0); + + /* 4 - Compute spherical harmonics */ + /* TODO */ + // DRW_framebuffer_bind(fbl->probe_sh_fb); + // DRW_draw_pass(psl->probe_sh); +} diff --git a/source/blender/draw/engines/eevee/shaders/bsdf_common_lib.glsl b/source/blender/draw/engines/eevee/shaders/bsdf_common_lib.glsl index ef684e3b970..96402f5ada2 100644 --- a/source/blender/draw/engines/eevee/shaders/bsdf_common_lib.glsl +++ b/source/blender/draw/engines/eevee/shaders/bsdf_common_lib.glsl @@ -1,5 +1,6 @@ #define M_PI 3.14159265358979323846 /* pi */ +#define M_PI_2 1.57079632679489661923 /* pi/2 */ #define M_1_PI 0.318309886183790671538 /* 1/pi */ #define M_1_2PI 0.159154943091895335768 /* 1/(2*pi) */ #define M_1_PI2 0.101321183642337771443 /* 1/(pi^2) */ @@ -52,6 +53,10 @@ struct ShadowMapData { #define sh_map_far near_far_bias.y #define sh_map_bias near_far_bias.z +#ifndef MAX_CASCADE_NUM +#define MAX_CASCADE_NUM 1 +#endif + struct ShadowCascadeData { mat4 shadowmat[MAX_CASCADE_NUM]; vec4 bias_count; @@ -98,26 +103,6 @@ float hypot(float x, float y) { return sqrt(x*x + y*y); } float inverse_distance(vec3 V) { return max( 1 / length(V), 1e-8); } -float linear_depth(float z, float zf, float zn) -{ - if (gl_ProjectionMatrix[3][3] == 0.0) { - return (zn * zf) / (z * (zn - zf) + zf); - } - else { - return (z * 2.0 - 1.0) * zf; - } -} - -float buffer_depth(float z, float zf, float zn) -{ - if (gl_ProjectionMatrix[3][3] == 0.0) { - return (zf * (zn - z)) / (z * (zn - zf)); - } - else { - return (z / (zf * 2.0)) + 0.5; - } -} - float line_plane_intersect_dist(vec3 lineorigin, vec3 linedirection, vec3 planeorigin, vec3 planenormal) { return dot(planenormal, planeorigin - lineorigin) / dot(planenormal, linedirection); @@ -149,6 +134,45 @@ vec3 line_aligned_plane_intersect(vec3 lineorigin, vec3 linedirection, vec3 plan return lineorigin + linedirection * dist; } +/* -- Tangent Space conversion -- */ +vec3 tangent_to_world(vec3 vector, vec3 N, vec3 T, vec3 B) +{ + return T * vector.x + B * vector.y + N * vector.z; +} + +vec3 world_to_tangent(vec3 vector, vec3 N, vec3 T, vec3 B) +{ + return vec3( dot(T, vector), dot(B, vector), dot(N, vector)); +} + +void make_orthonormal_basis(vec3 N, out vec3 T, out vec3 B) +{ + vec3 UpVector = abs(N.z) < 0.99999 ? vec3(0.0,0.0,1.0) : vec3(1.0,0.0,0.0); + T = normalize( cross(UpVector, N) ); + B = cross(N, T); +} + +/* ---- Opengl Depth conversion ---- */ +float linear_depth(float z, float zf, float zn) +{ + if (gl_ProjectionMatrix[3][3] == 0.0) { + return (zn * zf) / (z * (zn - zf) + zf); + } + else { + return (z * 2.0 - 1.0) * zf; + } +} + +float buffer_depth(float z, float zf, float zn) +{ + if (gl_ProjectionMatrix[3][3] == 0.0) { + return (zf * (zn - z)) / (z * (zn - zf)); + } + else { + return (z / (zf * 2.0)) + 0.5; + } +} + float rectangle_solid_angle(AreaData ad) { vec3 n0 = normalize(cross(ad.corner[0], ad.corner[1])); @@ -166,7 +190,9 @@ float rectangle_solid_angle(AreaData ad) vec3 get_specular_dominant_dir(vec3 N, vec3 R, float roughness) { - return normalize(mix(N, R, 1.0 - roughness * roughness)); + float smoothness = 1.0 - roughness; + float fac = smoothness * (sqrt(smoothness) + roughness); + return normalize(mix(N, R, fac)); } /* From UE4 paper */ diff --git a/source/blender/draw/engines/eevee/shaders/bsdf_direct_lib.glsl b/source/blender/draw/engines/eevee/shaders/bsdf_direct_lib.glsl index afa87dfb2c8..105b637c371 100644 --- a/source/blender/draw/engines/eevee/shaders/bsdf_direct_lib.glsl +++ b/source/blender/draw/engines/eevee/shaders/bsdf_direct_lib.glsl @@ -129,7 +129,7 @@ float direct_ggx_sphere(LightData ld, ShadingData sd, float roughness) bsdf *= 1.25331413731; #endif - bsdf *= texture(ltcMag, uv).r; /* Bsdf intensity */ + bsdf *= texture(brdfLut, uv).b; /* Bsdf intensity */ bsdf *= M_1_2PI * M_1_PI; #else float energy_conservation; @@ -150,7 +150,7 @@ float direct_ggx_rectangle(LightData ld, ShadingData sd, float roughness) mat3 ltcmat = ltc_matrix(uv); float bsdf = ltc_evaluate(sd.N, sd.V, ltcmat, sd.area_data.corner); - bsdf *= texture(ltcMag, uv).r; /* Bsdf intensity */ + bsdf *= texture(brdfLut, uv).b; /* Bsdf intensity */ bsdf *= M_1_2PI; #else float energy_conservation; diff --git a/source/blender/draw/engines/eevee/shaders/bsdf_lut_frag.glsl b/source/blender/draw/engines/eevee/shaders/bsdf_lut_frag.glsl new file mode 100644 index 00000000000..b8fac61519e --- /dev/null +++ b/source/blender/draw/engines/eevee/shaders/bsdf_lut_frag.glsl @@ -0,0 +1,46 @@ + +out vec4 FragColor; + +void main() { + vec3 N, T, B, V; + + float NV = ( 1.0 - (clamp(gl_FragCoord.y / BRDF_LUT_SIZE, 1e-4, 0.9999))); + float sqrtRoughness = clamp(gl_FragCoord.x / BRDF_LUT_SIZE, 1e-4, 0.9999); + float a = sqrtRoughness * sqrtRoughness; + float a2 = a * a; + + N = vec3(0.0, 0.0, 1.0); + T = vec3(1.0, 0.0, 0.0); + B = vec3(0.0, 1.0, 0.0); + V = vec3(sqrt(1.0 - NV * NV), 0.0, NV); + + setup_noise(); + + /* Integrating BRDF */ + float brdf_accum = 0.0; + float fresnel_accum = 0.0; + for (float i = 0; i < sampleCount; i++) { + vec3 H = sample_ggx(i, a2, N, T, B); /* Microfacet normal */ + vec3 L = -reflect(V, H); + float NL = L.z; + + if (NL > 0.0) { + float NH = max(H.z, 0.0); + float VH = max(dot(V, H), 0.0); + + float G1_v = G1_Smith_GGX(NV, a2); + float G1_l = G1_Smith_GGX(NL, a2); + float G_smith = 4.0 * NV * NL / (G1_v * G1_l); /* See G1_Smith_GGX for explanations. */ + + float brdf = (G_smith * VH) / (NH * NV); + float Fc = pow(1.0 - VH, 5.0); + + brdf_accum += (1.0 - Fc) * brdf; + fresnel_accum += Fc * brdf; + } + } + brdf_accum /= sampleCount; + fresnel_accum /= sampleCount; + + FragColor = vec4(brdf_accum, fresnel_accum, 0.0, 1.0); +}
\ No newline at end of file diff --git a/source/blender/draw/engines/eevee/shaders/bsdf_sampling_lib.glsl b/source/blender/draw/engines/eevee/shaders/bsdf_sampling_lib.glsl new file mode 100644 index 00000000000..da14a2dfee4 --- /dev/null +++ b/source/blender/draw/engines/eevee/shaders/bsdf_sampling_lib.glsl @@ -0,0 +1,54 @@ + +uniform sampler1D texHammersley; +uniform sampler2D texJitter; +uniform float sampleCount; +uniform float invSampleCount; + +vec2 jitternoise = vec2(0.0); + +void setup_noise(void) +{ + jitternoise = texture(texJitter, gl_FragCoord.xy / NOISE_SIZE, 0).rg; /* Global variable */ +} + +vec3 hammersley_3d(float i, float invsamplenbr) +{ + vec3 Xi; /* Theta, cos(Phi), sin(Phi) */ + + Xi.x = i * invsamplenbr; /* i/samples */ + Xi.x = fract(Xi.x + jitternoise.x); + + int u = int(mod(i + jitternoise.y * HAMMERSLEY_SIZE, HAMMERSLEY_SIZE)); + + Xi.yz = texelFetch(texHammersley, u, 0).rg; + + return Xi; +} + +vec3 hammersley_3d(float i) +{ + return hammersley_3d(i, invSampleCount); +} + +/* -------------- BSDFS -------------- */ + +float pdf_ggx_reflect(float NH, float a2) +{ + return NH * a2 / D_ggx_opti(NH, a2); +} + +vec3 sample_ggx(float nsample, float a2, vec3 N, vec3 T, vec3 B) +{ + vec3 Xi = hammersley_3d(nsample); + + /* Theta is the aperture angle of the cone */ + float z = sqrt( (1.0 - Xi.x) / ( 1.0 + a2 * Xi.x - Xi.x ) ); /* cos theta */ + float r = sqrt( 1.0 - z * z ); /* sin theta */ + float x = r * Xi.y; + float y = r * Xi.z; + + /* Microfacet Normal */ + vec3 Ht = vec3(x, y, z); + + return tangent_to_world(Ht, N, T, B); +} diff --git a/source/blender/draw/engines/eevee/shaders/lit_surface_frag.glsl b/source/blender/draw/engines/eevee/shaders/lit_surface_frag.glsl index 6c62e7c2e47..9bd8dba452d 100644 --- a/source/blender/draw/engines/eevee/shaders/lit_surface_frag.glsl +++ b/source/blender/draw/engines/eevee/shaders/lit_surface_frag.glsl @@ -3,6 +3,13 @@ uniform int light_count; uniform vec3 cameraPos; uniform vec3 eye; uniform mat4 ProjectionMatrix; + +uniform samplerCube probeFiltered; +uniform float lodMax; + +#ifndef USE_LTC +uniform sampler2D brdfLut; +#endif uniform sampler2DArrayShadow shadowCubes; uniform sampler2DArrayShadow shadowMaps; // uniform sampler2DArrayShadow shadowCascades; @@ -190,13 +197,16 @@ void main() sd.R = reflect(-sd.V, sd.N); /* hardcoded test vars */ - vec3 albedo = vec3(0.8); - vec3 specular = mix(vec3(0.03), vec3(1.0), pow(max(0.0, 1.0 - dot(sd.N, sd.V)), 5.0)); - float roughness = 0.1; + vec3 albedo = vec3(0.0); + vec3 f0 = mix(vec3(0.83, 0.5, 0.1), vec3(0.03, 0.03, 0.03), saturate(worldPosition.y/2)); + vec3 specular = mix(f0, vec3(1.0), pow(max(0.0, 1.0 - dot(sd.N, sd.V)), 5.0)); + float roughness = saturate(worldPosition.x/lodMax); sd.spec_dominant_dir = get_specular_dominant_dir(sd.N, sd.R, roughness); vec3 radiance = vec3(0.0); + + /* Analitic Lights */ for (int i = 0; i < MAX_LIGHT && i < light_count; ++i) { LightData ld = lights_data[i]; @@ -212,5 +222,11 @@ void main() radiance += vis * (albedo * diff + specular * spec) * ld.l_color; } + /* Envmaps */ + vec2 uv = ltc_coords(dot(sd.N, sd.V), sqrt(roughness)); + vec2 brdf_lut = texture(brdfLut, uv).rg; + vec3 Li = textureLod(probeFiltered, sd.spec_dominant_dir, roughness * lodMax).rgb; + radiance += Li * brdf_lut.y + f0 * Li * brdf_lut.x; + fragColor = vec4(radiance, 1.0); }
\ No newline at end of file diff --git a/source/blender/draw/engines/eevee/shaders/ltc_lib.glsl b/source/blender/draw/engines/eevee/shaders/ltc_lib.glsl index 131b0c2de78..279b18313e7 100644 --- a/source/blender/draw/engines/eevee/shaders/ltc_lib.glsl +++ b/source/blender/draw/engines/eevee/shaders/ltc_lib.glsl @@ -4,7 +4,7 @@ #define LTC_LUT_SIZE 64 uniform sampler2D ltcMat; -uniform sampler2D ltcMag; +uniform sampler2D brdfLut; /* from Real-Time Area Lighting: a Journey from Research to Production * Stephen Hill and Eric Heitz */ diff --git a/source/blender/draw/engines/eevee/shaders/probe_filter_frag.glsl b/source/blender/draw/engines/eevee/shaders/probe_filter_frag.glsl new file mode 100644 index 00000000000..553b0a0f27b --- /dev/null +++ b/source/blender/draw/engines/eevee/shaders/probe_filter_frag.glsl @@ -0,0 +1,49 @@ + +uniform samplerCube probeHdr; +uniform float roughnessSquared; +uniform float lodFactor; +uniform float lodMax; + +in vec3 worldPosition; + +out vec4 FragColor; + +void main() { + vec3 N, T, B, V; + + vec3 R = normalize(worldPosition); + + /* Isotropic assumption */ + N = V = R; + + make_orthonormal_basis(N, T, B); /* Generate tangent space */ + + /* Noise to dither the samples */ + /* Note : ghosting is better looking than noise. */ + // setup_noise(); + + /* Integrating Envmap */ + float weight = 0.0; + vec3 out_radiance = vec3(0.0); + for (float i = 0; i < sampleCount; i++) { + vec3 H = sample_ggx(i, roughnessSquared, N, T, B); /* Microfacet normal */ + vec3 L = -reflect(V, H); + float NL = dot(N, L); + + if (NL > 0.0) { + float NH = max(1e-8, dot(N, H)); /* cosTheta */ + + /* Coarse Approximation of the mapping distortion + * Unit Sphere -> Cubemap Face */ + const float dist = 4.0 * M_PI / 6.0; + float pdf = pdf_ggx_reflect(NH, roughnessSquared); + /* http://http.developer.nvidia.com/GPUGems3/gpugems3_ch20.html : Equation 13 */ + float lod = clamp(lodFactor - 0.5 * log2(pdf * dist), 0.0, lodMax) ; + + out_radiance += textureCubeLod(probeHdr, L, lod).rgb * NL; + weight += NL; + } + } + + FragColor = vec4(out_radiance / weight, 1.0); +}
\ No newline at end of file diff --git a/source/blender/draw/engines/eevee/shaders/probe_frag.glsl b/source/blender/draw/engines/eevee/shaders/probe_frag.glsl new file mode 100644 index 00000000000..1a2d2f48989 --- /dev/null +++ b/source/blender/draw/engines/eevee/shaders/probe_frag.glsl @@ -0,0 +1,26 @@ + +in vec3 worldPosition; + +uniform sampler2D probeLatLong; + +out vec4 FragColor; + +float hypot(float x, float y) { return sqrt(x*x + y*y); } + +void node_tex_environment_equirectangular(vec3 co, sampler2D ima, out vec4 color) +{ + vec3 nco = normalize(co); + float u = -atan(nco.y, nco.x) / (2.0 * 3.1415) + 0.5; + float v = atan(nco.z, hypot(nco.x, nco.y)) / 3.1415 + 0.5; + + color = texture2D(ima, vec2(u, v)); +} + +void main() { + vec3 L = normalize(worldPosition); + vec2 uvs = gl_FragCoord.xy / 256.0; + float dist = dot(L, vec3(0.0,1.0,0.0)); + dist = (dist > 0.99) ? 1e1 : 0.0; + FragColor = vec4(dist,dist,dist, 1.0); + node_tex_environment_equirectangular(L, probeLatLong, FragColor); +}
\ No newline at end of file diff --git a/source/blender/draw/engines/eevee/shaders/probe_geom.glsl b/source/blender/draw/engines/eevee/shaders/probe_geom.glsl new file mode 100644 index 00000000000..ad112977e9f --- /dev/null +++ b/source/blender/draw/engines/eevee/shaders/probe_geom.glsl @@ -0,0 +1,28 @@ + +layout(triangles) in; +layout(triangle_strip, max_vertices=3) out; + +uniform int Layer; + +in vec4 vPos[]; +in int face[]; + +out vec3 worldPosition; +out vec3 worldNormal; + +const vec3 maj_axes[6] = vec3[6](vec3(1.0, 0.0, 0.0), vec3(-1.0, 0.0, 0.0), vec3(0.0, 1.0, 0.0), vec3(0.0, -1.0, 0.0), vec3( 0.0, 0.0, 1.0), vec3( 0.0, 0.0, -1.0)); +const vec3 x_axis[6] = vec3[6](vec3(0.0, 0.0, -1.0), vec3( 0.0, 0.0, 1.0), vec3(1.0, 0.0, 0.0), vec3(1.0, 0.0, 0.0), vec3( 1.0, 0.0, 0.0), vec3(-1.0, 0.0, 0.0)); +const vec3 y_axis[6] = vec3[6](vec3(0.0, -1.0, 0.0), vec3( 0.0, -1.0, 0.0), vec3(0.0, 0.0, 1.0), vec3(0.0, 0.0, -1.0), vec3( 0.0, -1.0, 0.0), vec3( 0.0, -1.0, 0.0)); + +void main() { + int f = face[0]; + gl_Layer = Layer + f; + + for (int v = 0; v < 3; ++v) { + gl_Position = vPos[v]; + worldPosition = x_axis[f] * vPos[v].x + y_axis[f] * vPos[v].y + maj_axes[f]; + EmitVertex(); + } + + EndPrimitive(); +}
\ No newline at end of file diff --git a/source/blender/draw/engines/eevee/shaders/probe_vert.glsl b/source/blender/draw/engines/eevee/shaders/probe_vert.glsl new file mode 100644 index 00000000000..16b66a584a3 --- /dev/null +++ b/source/blender/draw/engines/eevee/shaders/probe_vert.glsl @@ -0,0 +1,10 @@ + +in vec3 pos; + +out vec4 vPos; +out int face; + +void main() { + vPos = vec4(pos, 1.0); + face = gl_InstanceID; +}
\ No newline at end of file diff --git a/source/blender/draw/engines/eevee/shaders/shadow_vert.glsl b/source/blender/draw/engines/eevee/shaders/shadow_vert.glsl index 1adf2ccfab9..c7f4d4ba777 100644 --- a/source/blender/draw/engines/eevee/shaders/shadow_vert.glsl +++ b/source/blender/draw/engines/eevee/shaders/shadow_vert.glsl @@ -1,5 +1,4 @@ -uniform mat4 ShadowMatrix; uniform mat4 ModelMatrix; in vec3 pos; |