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big royale cleanup

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hunterk 2016-08-26 11:28:24 -05:00
parent cc581b1418
commit 6035d32e17
35 changed files with 452 additions and 10749 deletions
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5
blurs/blur9fast-horizontal.slang
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@ -54,9 +54,8 @@ layout(std140, set = 0, binding = 0) uniform UBO
////////////////////////////////// INCLUDES ////////////////////////////////// ////////////////////////////////// INCLUDES //////////////////////////////////
// #included by vertex shader: // #included by vertex shader:
//#include "../include/gamma-management.h" #include "../include/gamma-management.h"
//#include "../include/blur-functions.h" #include "../include/blur-functions.h"
#include "../crt/shaders/crt-royale/src/includes.h"
#pragma stage vertex #pragma stage vertex
layout(location = 0) in vec4 Position; layout(location = 0) in vec4 Position;

5
blurs/blur9fast-vertical.slang
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@ -54,9 +54,8 @@ layout(std140, set = 0, binding = 0) uniform UBO
////////////////////////////////// INCLUDES ////////////////////////////////// ////////////////////////////////// INCLUDES //////////////////////////////////
// #included by vertex shader: // #included by vertex shader:
//#include "../include/gamma-management.h" #include "../include/gamma-management.h"
//#include "../include/blur-functions.h" #include "../include/blur-functions.h"
#include "../crt/shaders/crt-royale/src/includes.h"
#pragma stage vertex #pragma stage vertex
layout(location = 0) in vec4 Position; layout(location = 0) in vec4 Position;

92
crt/crt-royale-test.slangp
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@ -1,92 +0,0 @@
# IMPORTANT:
# Shader passes need to know details about the image in the mask_texture LUT
# files, so set the following constants in user-preset-constants.h accordingly:
# 1.) mask_triads_per_tile = (number of horizontal triads in mask texture LUT's)
# 2.) mask_texture_small_size = (texture size of mask*texture_small LUT's)
# 3.) mask_texture_large_size = (texture size of mask*texture_large LUT's)
# 4.) mask_grille_avg_color = (avg. brightness of mask_grille_texture* LUT's, in [0, 1])
# 5.) mask_slot_avg_color = (avg. brightness of mask_slot_texture* LUT's, in [0, 1])
# 6.) mask_shadow_avg_color = (avg. brightness of mask_shadow_texture* LUT's, in [0, 1])
# Shader passes also need to know certain scales set in this preset, but their
# compilation model doesn't currently allow the preset file to tell them. Make
# sure to set the following constants in user-preset-constants.h accordingly too:
# 1.) bloom_approx_scale_x = scale_x2
# 2.) mask_resize_viewport_scale = vec2(scale_x6, scale_y5)
# Finally, shader passes need to know the value of geom_max_aspect_ratio used to
# calculate scale_y5 (among other values):
# 1.) geom_max_aspect_ratio = (geom_max_aspect_ratio used to calculate scale_y5)
shaders = "1"//"12"
# Set an identifier, filename, and sampling traits for the phosphor mask texture.
# Load an aperture grille, slot mask, and an EDP shadow mask, and load a small
# non-mipmapped version and a large mipmapped version.
# TODO: Test masks in other directories.
textures = "mask_grille_texture_small;mask_grille_texture_large;mask_slot_texture_small;mask_slot_texture_large;mask_shadow_texture_small;mask_shadow_texture_large"
mask_grille_texture_small = "shaders/crt-royale/TileableLinearApertureGrille15Wide8And5d5SpacingResizeTo64.png"
mask_grille_texture_large = "shaders/crt-royale/TileableLinearApertureGrille15Wide8And5d5Spacing.png"
mask_slot_texture_small = "shaders/crt-royale/TileableLinearSlotMaskTall15Wide9And4d5Horizontal9d14VerticalSpacingResizeTo64.png"
mask_slot_texture_large = "shaders/crt-royale/TileableLinearSlotMaskTall15Wide9And4d5Horizontal9d14VerticalSpacing.png"
mask_shadow_texture_small = "shaders/crt-royale/TileableLinearShadowMaskEDPResizeTo64.png"
mask_shadow_texture_large = "shaders/crt-royale/TileableLinearShadowMaskEDP.png"
mask_grille_texture_small_wrap_mode = "repeat"
mask_grille_texture_large_wrap_mode = "repeat"
mask_slot_texture_small_wrap_mode = "repeat"
mask_slot_texture_large_wrap_mode = "repeat"
mask_shadow_texture_small_wrap_mode = "repeat"
mask_shadow_texture_large_wrap_mode = "repeat"
mask_grille_texture_small_linear = "true"
mask_grille_texture_large_linear = "true"
mask_slot_texture_small_linear = "true"
mask_slot_texture_large_linear = "true"
mask_shadow_texture_small_linear = "true"
mask_shadow_texture_large_linear = "true"
mask_grille_texture_small_mipmap = "false" # Mipmapping causes artifacts with manually resized masks without tex2Dlod
mask_grille_texture_large_mipmap = "true" # Essential for hardware-resized masks
mask_slot_texture_small_mipmap = "false" # Mipmapping causes artifacts with manually resized masks without tex2Dlod
mask_slot_texture_large_mipmap = "true" # Essential for hardware-resized masks
mask_shadow_texture_small_mipmap = "false" # Mipmapping causes artifacts with manually resized masks without tex2Dlod
mask_shadow_texture_large_mipmap = "true" # Essential for hardware-resized masks
# Pass5: Lanczos-resize the phosphor mask vertically. Set the absolute
# scale_x5 == mask_texture_small_size.x (see IMPORTANT above). Larger scales
# will blur, and smaller scales could get nasty. The vertical size must be
# based on the viewport size and calculated carefully to avoid artifacts later.
# First calculate the minimum number of mask tiles we need to draw.
# Since curvature is computed after the scanline masking pass:
# num_resized_mask_tiles = 2.0;
# If curvature were computed in the scanline masking pass (it's not):
# max_mask_texel_border = ~3.0 * (1/3.0 + 4.0*sqrt(2.0) + 0.5 + 1.0);
# max_mask_tile_border = max_mask_texel_border/
# (min_resized_phosphor_triad_size * mask_triads_per_tile);
# num_resized_mask_tiles = max(2.0, 1.0 + max_mask_tile_border * 2.0);
# At typical values (triad_size >= 2.0, mask_triads_per_tile == 8):
# num_resized_mask_tiles = ~3.8
# Triad sizes are given in horizontal terms, so we need geom_max_aspect_ratio
# to relate them to vertical resolution. The widest we expect is:
# geom_max_aspect_ratio = 4.0/3.0 # Note: Shader passes need to know this!
# The fewer triads we tile across the screen, the larger each triad will be as a
# fraction of the viewport size, and the larger scale_y5 must be to draw a full
# num_resized_mask_tiles. Therefore, we must decide the smallest number of
# triads we'll guarantee can be displayed on screen. We'll set this according
# to 3-pixel triads at 768p resolution (the lowest anyone's likely to use):
# min_allowed_viewport_triads = 768.0*geom_max_aspect_ratio / 3.0 = 341.333333
# Now calculate the viewport scale that ensures we can draw resized_mask_tiles:
# min_scale_x = resized_mask_tiles * mask_triads_per_tile /
# min_allowed_viewport_triads
# scale_y5 = geom_max_aspect_ratio * min_scale_x
# # Some code might depend on equal scales:
# scale_x6 = scale_y5
# Given our default geom_max_aspect_ratio and min_allowed_viewport_triads:
# scale_y5 = 4.0/3.0 * 2.0/(341.33333 / 8.0) = 0.0625
# IMPORTANT: The scales MUST be calculated in this way. If you wish to change
# geom_max_aspect_ratio, update that constant in user-preset-constants.h!
shader0 = "shaders/crt-royale/src/crt-royale-mask-resize-vertical.slang"
filter_linear0 = "true"
scale_type_x0 = "absolute"
scale_x0 = "64"
scale_type_y0 = "viewport"
scale_y0 = "0.0625" # Safe for >= 341.333 horizontal triads at viewport size
#srgb_framebuffer0 = "false" # mask_texture is already assumed linear

33
crt/shaders/crt-royale/src/bloom-functions.h
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@ -1,6 +1,39 @@
#ifndef BLOOM_FUNCTIONS_H #ifndef BLOOM_FUNCTIONS_H
#define BLOOM_FUNCTIONS_H #define BLOOM_FUNCTIONS_H
///////////////////////////// GPL LICENSE NOTICE /////////////////////////////
// crt-royale: A full-featured CRT shader, with cheese.
// Copyright (C) 2014 TroggleMonkey <trogglemonkey@gmx.com>
//
// 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 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., 59 Temple
// Place, Suite 330, Boston, MA 02111-1307 USA
///////////////////////////////// DESCRIPTION ////////////////////////////////
// These utility functions and constants help several passes determine the
// size and center texel weight of the phosphor bloom in a uniform manner.
////////////////////////////////// INCLUDES //////////////////////////////////
// We need to calculate the correct blur sigma using some .cgp constants:
#include "../user-settings.h"
#include "derived-settings-and-constants.h"
#include "../../../../include/blur-functions.h"
/////////////////////////////// BLOOM CONSTANTS ////////////////////////////// /////////////////////////////// BLOOM CONSTANTS //////////////////////////////
// Compute constants with manual inlines of the functions below: // Compute constants with manual inlines of the functions below:

1916
crt/shaders/crt-royale/src/blur-functions-old.h
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595
crt/shaders/crt-royale/src/blur-functions.h
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@ -1,595 +0,0 @@
#ifndef BLUR_FUNCTIONS_H
#define BLUR_FUNCTIONS_H
///////////////////////////////// MIT LICENSE ////////////////////////////////
// Copyright (C) 2014 TroggleMonkey
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to
// deal in the Software without restriction, including without limitation the
// rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
// sell copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
// IN THE SOFTWARE.
///////////////////////////////// DESCRIPTION ////////////////////////////////
// This file provides reusable one-pass and separable (two-pass) blurs.
// Requires: All blurs share these requirements (dxdy requirement is split):
// 1.) All requirements of gamma-management.h must be satisfied!
// 2.) filter_linearN must == "true" in your .cgp preset unless
// you're using tex2DblurNresize at 1x scale.
// 3.) mipmap_inputN must == "true" in your .cgp preset if
// IN.output_size < IN.video_size.
// 4.) IN.output_size == IN.video_size / pow(2, M), where M is some
// positive integer. tex2Dblur*resize can resize arbitrarily
// (and the blur will be done after resizing), but arbitrary
// resizes "fail" with other blurs due to the way they mix
// static weights with bilinear sample exploitation.
// 5.) In general, dxdy should contain the uv pixel spacing:
// dxdy = (IN.video_size/IN.output_size)/IN.texture_size
// 6.) For separable blurs (tex2DblurNresize and tex2DblurNfast),
// zero out the dxdy component in the unblurred dimension:
// dxdy = vec2(dxdy.x, 0.0) or vec2(0.0, dxdy.y)
// Many blurs share these requirements:
// 1.) One-pass blurs require scale_xN == scale_yN or scales > 1.0,
// or they will blur more in the lower-scaled dimension.
// 2.) One-pass shared sample blurs require ddx(), ddy(), and
// tex2Dlod() to be supported by the current Cg profile, and
// the drivers must support high-quality derivatives.
// 3.) One-pass shared sample blurs require:
// tex_uv.w == log2(IN.video_size/IN.output_size).y;
// Non-wrapper blurs share this requirement:
// 1.) sigma is the intended standard deviation of the blur
// Wrapper blurs share this requirement, which is automatically
// met (unless OVERRIDE_BLUR_STD_DEVS is #defined; see below):
// 1.) blurN_std_dev must be global static const float values
// specifying standard deviations for Nx blurs in units
// of destination pixels
// Optional: 1.) The including file (or an earlier included file) may
// optionally #define USE_BINOMIAL_BLUR_STD_DEVS to replace
// default standard deviations with those matching a binomial
// distribution. (See below for details/properties.)
// 2.) The including file (or an earlier included file) may
// optionally #define OVERRIDE_BLUR_STD_DEVS and override:
// static const float blur3_std_dev
// static const float blur4_std_dev
// static const float blur5_std_dev
// static const float blur6_std_dev
// static const float blur7_std_dev
// static const float blur8_std_dev
// static const float blur9_std_dev
// static const float blur10_std_dev
// static const float blur11_std_dev
// static const float blur12_std_dev
// static const float blur17_std_dev
// static const float blur25_std_dev
// static const float blur31_std_dev
// static const float blur43_std_dev
// 3.) The including file (or an earlier included file) may
// optionally #define OVERRIDE_ERROR_BLURRING and override:
// static const float error_blurring
// This tuning value helps mitigate weighting errors from one-
// pass shared-sample blurs sharing bilinear samples between
// fragments. Values closer to 0.0 have "correct" blurriness
// but allow more artifacts, and values closer to 1.0 blur away
// artifacts by sampling closer to halfway between texels.
// UPDATE 6/21/14: The above static constants may now be overridden
// by non-static uniform constants. This permits exposing blur
// standard deviations as runtime GUI shader parameters. However,
// using them keeps weights from being statically computed, and the
// speed hit depends on the blur: On my machine, uniforms kill over
// 53% of the framerate with tex2Dblur12x12shared, but they only
// drop the framerate by about 18% with tex2Dblur11fast.
// Quality and Performance Comparisons:
// For the purposes of the following discussion, "no sRGB" means
// GAMMA_ENCODE_EVERY_FBO is #defined, and "sRGB" means it isn't.
// 1.) tex2DblurNfast is always faster than tex2DblurNresize.
// 2.) tex2DblurNresize functions are the only ones that can arbitrarily resize
// well, because they're the only ones that don't exploit bilinear samples.
// This also means they're the only functions which can be truly gamma-
// correct without linear (or sRGB FBO) input, but only at 1x scale.
// 3.) One-pass shared sample blurs only have a speed advantage without sRGB.
// They also have some inaccuracies due to their shared-[bilinear-]sample
// design, which grow increasingly bothersome for smaller blurs and higher-
// frequency source images (relative to their resolution). I had high
// hopes for them, but their most realistic use case is limited to quickly
// reblurring an already blurred input at full resolution. Otherwise:
// a.) If you're blurring a low-resolution source, you want a better blur.
// b.) If you're blurring a lower mipmap, you want a better blur.
// c.) If you're blurring a high-resolution, high-frequency source, you
// want a better blur.
// 4.) The one-pass blurs without shared samples grow slower for larger blurs,
// but they're competitive with separable blurs at 5x5 and smaller, and
// even tex2Dblur7x7 isn't bad if you're wanting to conserve passes.
// Here are some framerates from a GeForce 8800GTS. The first pass resizes to
// viewport size (4x in this test) and linearizes for sRGB codepaths, and the
// remaining passes perform 6 full blurs. Mipmapped tests are performed at the
// same scale, so they just measure the cost of mipmapping each FBO (only every
// other FBO is mipmapped for separable blurs, to mimic realistic usage).
// Mipmap Neither sRGB+Mipmap sRGB Function
// 76.0 92.3 131.3 193.7 tex2Dblur3fast
// 63.2 74.4 122.4 175.5 tex2Dblur3resize
// 93.7 121.2 159.3 263.2 tex2Dblur3x3
// 59.7 68.7 115.4 162.1 tex2Dblur3x3resize
// 63.2 74.4 122.4 175.5 tex2Dblur5fast
// 49.3 54.8 100.0 132.7 tex2Dblur5resize
// 59.7 68.7 115.4 162.1 tex2Dblur5x5
// 64.9 77.2 99.1 137.2 tex2Dblur6x6shared
// 55.8 63.7 110.4 151.8 tex2Dblur7fast
// 39.8 43.9 83.9 105.8 tex2Dblur7resize
// 40.0 44.2 83.2 104.9 tex2Dblur7x7
// 56.4 65.5 71.9 87.9 tex2Dblur8x8shared
// 49.3 55.1 99.9 132.5 tex2Dblur9fast
// 33.3 36.2 72.4 88.0 tex2Dblur9resize
// 27.8 29.7 61.3 72.2 tex2Dblur9x9
// 37.2 41.1 52.6 60.2 tex2Dblur10x10shared
// 44.4 49.5 91.3 117.8 tex2Dblur11fast
// 28.8 30.8 63.6 75.4 tex2Dblur11resize
// 33.6 36.5 40.9 45.5 tex2Dblur12x12shared
// TODO: Fill in benchmarks for new untested blurs.
// tex2Dblur17fast
// tex2Dblur25fast
// tex2Dblur31fast
// tex2Dblur43fast
// tex2Dblur3x3resize
///////////////////////////// SETTINGS MANAGEMENT ////////////////////////////
// Set static standard deviations, but allow users to override them with their
// own constants (even non-static uniforms if they're okay with the speed hit):
#ifndef OVERRIDE_BLUR_STD_DEVS
// blurN_std_dev values are specified in terms of dxdy strides.
#ifdef USE_BINOMIAL_BLUR_STD_DEVS
// By request, we can define standard deviations corresponding to a
// binomial distribution with p = 0.5 (related to Pascal's triangle).
// This distribution works such that blurring multiple times should
// have the same result as a single larger blur. These values are
// larger than default for blurs up to 6x and smaller thereafter.
const float blur3_std_dev = 0.84931640625;
const float blur4_std_dev = 0.84931640625;
const float blur5_std_dev = 1.0595703125;
const float blur6_std_dev = 1.06591796875;
const float blur7_std_dev = 1.17041015625;
const float blur8_std_dev = 1.1720703125;
const float blur9_std_dev = 1.2259765625;
const float blur10_std_dev = 1.21982421875;
const float blur11_std_dev = 1.25361328125;
const float blur12_std_dev = 1.2423828125;
const float blur17_std_dev = 1.27783203125;
const float blur25_std_dev = 1.2810546875;
const float blur31_std_dev = 1.28125;
const float blur43_std_dev = 1.28125;
#else
// The defaults are the largest values that keep the largest unused
// blur term on each side <= 1.0/256.0. (We could get away with more
// or be more conservative, but this compromise is pretty reasonable.)
const float blur3_std_dev = 0.62666015625;
const float blur4_std_dev = 0.66171875;
const float blur5_std_dev = 0.9845703125;
const float blur6_std_dev = 1.02626953125;
const float blur7_std_dev = 1.36103515625;
const float blur8_std_dev = 1.4080078125;
const float blur9_std_dev = 1.7533203125;
const float blur10_std_dev = 1.80478515625;
const float blur11_std_dev = 2.15986328125;
const float blur12_std_dev = 2.215234375;
const float blur17_std_dev = 3.45535583496;
const float blur25_std_dev = 5.3409576416;
const float blur31_std_dev = 6.86488037109;
const float blur43_std_dev = 10.1852050781;
#endif // USE_BINOMIAL_BLUR_STD_DEVS
#endif // OVERRIDE_BLUR_STD_DEVS
#ifndef OVERRIDE_ERROR_BLURRING
// error_blurring should be in [0.0, 1.0]. Higher values reduce ringing
// in shared-sample blurs but increase blurring and feature shifting.
const float error_blurring = 0.5;
#endif
// Make a length squared helper macro (for usage with static constants):
#define LENGTH_SQ(vec) (dot(vec, vec))
/////////////////////////////////// HELPERS //////////////////////////////////
vec4 uv2_to_uv4(vec2 tex_uv)
{
// Make a vec2 uv offset safe for adding to vec4 tex2Dlod coords:
return vec4(tex_uv, 0.0, 0.0);
}
// Make a length squared helper macro (for usage with static constants):
#define LENGTH_SQ(vec) (dot(vec, vec))
float get_fast_gaussian_weight_sum_inv(const float sigma)
{
// We can use the Gaussian integral to calculate the asymptotic weight for
// the center pixel. Since the unnormalized center pixel weight is 1.0,
// the normalized weight is the same as the weight sum inverse. Given a
// large enough blur (9+), the asymptotic weight sum is close and faster:
// center_weight = 0.5 *
// (erf(0.5/(sigma*sqrt(2.0))) - erf(-0.5/(sigma*sqrt(2.0))))
// erf(-x) == -erf(x), so we get 0.5 * (2.0 * erf(blah blah)):
// However, we can get even faster results with curve-fitting. These are
// also closer than the asymptotic results, because they were constructed
// from 64 blurs sizes from [3, 131) and 255 equally-spaced sigmas from
// (0, blurN_std_dev), so the results for smaller sigmas are biased toward
// smaller blurs. The max error is 0.0031793913.
// Relative FPS: 134.3 with erf, 135.8 with curve-fitting.
//static const float temp = 0.5/sqrt(2.0);
//return erf(temp/sigma);
return min(exp(exp(0.348348412457428/
(sigma - 0.0860587260734721))), 0.399334576340352/sigma);
}
vec3 tex2Dblur17fast(const sampler2D tex, const vec2 tex_uv,
const vec2 dxdy, const float sigma)
{
// Requires: Same as tex2Dblur11()
// Returns: A 1D 17x Gaussian blurred texture lookup using 1 nearest
// neighbor and 8 linear taps. It may be mipmapped depending
// on settings and dxdy.
// First get the texel weights and normalization factor as above.
const float denom_inv = 0.5/(sigma*sigma);
const float w0 = 1.0;
const float w1 = exp(-1.0 * denom_inv);
const float w2 = exp(-4.0 * denom_inv);
const float w3 = exp(-9.0 * denom_inv);
const float w4 = exp(-16.0 * denom_inv);
const float w5 = exp(-25.0 * denom_inv);
const float w6 = exp(-36.0 * denom_inv);
const float w7 = exp(-49.0 * denom_inv);
const float w8 = exp(-64.0 * denom_inv);
//const float weight_sum_inv = 1.0 / (w0 + 2.0 * (
// w1 + w2 + w3 + w4 + w5 + w6 + w7 + w8));
const float weight_sum_inv = get_fast_gaussian_weight_sum_inv(sigma);
// Calculate combined weights and linear sample ratios between texel pairs.
const float w1_2 = w1 + w2;
const float w3_4 = w3 + w4;
const float w5_6 = w5 + w6;
const float w7_8 = w7 + w8;
const float w1_2_ratio = w2/w1_2;
const float w3_4_ratio = w4/w3_4;
const float w5_6_ratio = w6/w5_6;
const float w7_8_ratio = w8/w7_8;
// Statically normalize weights, sum weighted samples, and return:
vec3 sum = vec3(0.0);
sum += w7_8 * tex2D_linearize(tex, tex_uv - (7.0 + w7_8_ratio) * dxdy).rgb;
sum += w5_6 * tex2D_linearize(tex, tex_uv - (5.0 + w5_6_ratio) * dxdy).rgb;
sum += w3_4 * tex2D_linearize(tex, tex_uv - (3.0 + w3_4_ratio) * dxdy).rgb;
sum += w1_2 * tex2D_linearize(tex, tex_uv - (1.0 + w1_2_ratio) * dxdy).rgb;
sum += w0 * tex2D_linearize(tex, tex_uv).rgb;
sum += w1_2 * tex2D_linearize(tex, tex_uv + (1.0 + w1_2_ratio) * dxdy).rgb;
sum += w3_4 * tex2D_linearize(tex, tex_uv + (3.0 + w3_4_ratio) * dxdy).rgb;
sum += w5_6 * tex2D_linearize(tex, tex_uv + (5.0 + w5_6_ratio) * dxdy).rgb;
sum += w7_8 * tex2D_linearize(tex, tex_uv + (7.0 + w7_8_ratio) * dxdy).rgb;
return sum * weight_sum_inv;
}
vec3 tex2Dblur25fast(const sampler2D tex, const vec2 tex_uv,
const vec2 dxdy, const float sigma)
{
// Requires: Same as tex2Dblur11()
// Returns: A 1D 25x Gaussian blurred texture lookup using 1 nearest
// neighbor and 12 linear taps. It may be mipmapped depending
// on settings and dxdy.
// First get the texel weights and normalization factor as above.
const float denom_inv = 0.5/(sigma*sigma);
const float w0 = 1.0;
const float w1 = exp(-1.0 * denom_inv);
const float w2 = exp(-4.0 * denom_inv);
const float w3 = exp(-9.0 * denom_inv);
const float w4 = exp(-16.0 * denom_inv);
const float w5 = exp(-25.0 * denom_inv);
const float w6 = exp(-36.0 * denom_inv);
const float w7 = exp(-49.0 * denom_inv);
const float w8 = exp(-64.0 * denom_inv);
const float w9 = exp(-81.0 * denom_inv);
const float w10 = exp(-100.0 * denom_inv);
const float w11 = exp(-121.0 * denom_inv);
const float w12 = exp(-144.0 * denom_inv);
//const float weight_sum_inv = 1.0 / (w0 + 2.0 * (
// w1 + w2 + w3 + w4 + w5 + w6 + w7 + w8 + w9 + w10 + w11 + w12));
const float weight_sum_inv = get_fast_gaussian_weight_sum_inv(sigma);
// Calculate combined weights and linear sample ratios between texel pairs.
const float w1_2 = w1 + w2;
const float w3_4 = w3 + w4;
const float w5_6 = w5 + w6;
const float w7_8 = w7 + w8;
const float w9_10 = w9 + w10;
const float w11_12 = w11 + w12;
const float w1_2_ratio = w2/w1_2;
const float w3_4_ratio = w4/w3_4;
const float w5_6_ratio = w6/w5_6;
const float w7_8_ratio = w8/w7_8;
const float w9_10_ratio = w10/w9_10;
const float w11_12_ratio = w12/w11_12;
// Statically normalize weights, sum weighted samples, and return:
vec3 sum = vec3(0.0);
sum += w11_12 * tex2D_linearize(tex, tex_uv - (11.0 + w11_12_ratio) * dxdy).rgb;
sum += w9_10 * tex2D_linearize(tex, tex_uv - (9.0 + w9_10_ratio) * dxdy).rgb;
sum += w7_8 * tex2D_linearize(tex, tex_uv - (7.0 + w7_8_ratio) * dxdy).rgb;
sum += w5_6 * tex2D_linearize(tex, tex_uv - (5.0 + w5_6_ratio) * dxdy).rgb;
sum += w3_4 * tex2D_linearize(tex, tex_uv - (3.0 + w3_4_ratio) * dxdy).rgb;
sum += w1_2 * tex2D_linearize(tex, tex_uv - (1.0 + w1_2_ratio) * dxdy).rgb;
sum += w0 * tex2D_linearize(tex, tex_uv).rgb;
sum += w1_2 * tex2D_linearize(tex, tex_uv + (1.0 + w1_2_ratio) * dxdy).rgb;
sum += w3_4 * tex2D_linearize(tex, tex_uv + (3.0 + w3_4_ratio) * dxdy).rgb;
sum += w5_6 * tex2D_linearize(tex, tex_uv + (5.0 + w5_6_ratio) * dxdy).rgb;
sum += w7_8 * tex2D_linearize(tex, tex_uv + (7.0 + w7_8_ratio) * dxdy).rgb;
sum += w9_10 * tex2D_linearize(tex, tex_uv + (9.0 + w9_10_ratio) * dxdy).rgb;
sum += w11_12 * tex2D_linearize(tex, tex_uv + (11.0 + w11_12_ratio) * dxdy).rgb;
return sum * weight_sum_inv;
}
vec3 tex2Dblur31fast(const sampler2D tex, const vec2 tex_uv,
const vec2 dxdy, const float sigma)
{
// Requires: Same as tex2Dblur11()
// Returns: A 1D 31x Gaussian blurred texture lookup using 16 linear
// taps. It may be mipmapped depending on settings and dxdy.
// First get the texel weights and normalization factor as above.
const float denom_inv = 0.5/(sigma*sigma);
const float w0 = 1.0;
const float w1 = exp(-1.0 * denom_inv);
const float w2 = exp(-4.0 * denom_inv);
const float w3 = exp(-9.0 * denom_inv);
const float w4 = exp(-16.0 * denom_inv);
const float w5 = exp(-25.0 * denom_inv);
const float w6 = exp(-36.0 * denom_inv);
const float w7 = exp(-49.0 * denom_inv);
const float w8 = exp(-64.0 * denom_inv);
const float w9 = exp(-81.0 * denom_inv);
const float w10 = exp(-100.0 * denom_inv);
const float w11 = exp(-121.0 * denom_inv);
const float w12 = exp(-144.0 * denom_inv);
const float w13 = exp(-169.0 * denom_inv);
const float w14 = exp(-196.0 * denom_inv);
const float w15 = exp(-225.0 * denom_inv);
//const float weight_sum_inv = 1.0 /
// (w0 + 2.0 * (w1 + w2 + w3 + w4 + w5 + w6 + w7 + w8 +
// w9 + w10 + w11 + w12 + w13 + w14 + w15));
const float weight_sum_inv = get_fast_gaussian_weight_sum_inv(sigma);
// Calculate combined weights and linear sample ratios between texel pairs.
// The center texel (with weight w0) is used twice, so halve its weight.
const float w0_1 = w0 * 0.5 + w1;
const float w2_3 = w2 + w3;
const float w4_5 = w4 + w5;
const float w6_7 = w6 + w7;
const float w8_9 = w8 + w9;
const float w10_11 = w10 + w11;
const float w12_13 = w12 + w13;
const float w14_15 = w14 + w15;
const float w0_1_ratio = w1/w0_1;
const float w2_3_ratio = w3/w2_3;
const float w4_5_ratio = w5/w4_5;
const float w6_7_ratio = w7/w6_7;
const float w8_9_ratio = w9/w8_9;
const float w10_11_ratio = w11/w10_11;
const float w12_13_ratio = w13/w12_13;
const float w14_15_ratio = w15/w14_15;
// Statically normalize weights, sum weighted samples, and return:
vec3 sum = vec3(0.0);
sum += w14_15 * tex2D_linearize(tex, tex_uv - (14.0 + w14_15_ratio) * dxdy).rgb;
sum += w12_13 * tex2D_linearize(tex, tex_uv - (12.0 + w12_13_ratio) * dxdy).rgb;
sum += w10_11 * tex2D_linearize(tex, tex_uv - (10.0 + w10_11_ratio) * dxdy).rgb;
sum += w8_9 * tex2D_linearize(tex, tex_uv - (8.0 + w8_9_ratio) * dxdy).rgb;
sum += w6_7 * tex2D_linearize(tex, tex_uv - (6.0 + w6_7_ratio) * dxdy).rgb;
sum += w4_5 * tex2D_linearize(tex, tex_uv - (4.0 + w4_5_ratio) * dxdy).rgb;
sum += w2_3 * tex2D_linearize(tex, tex_uv - (2.0 + w2_3_ratio) * dxdy).rgb;
sum += w0_1 * tex2D_linearize(tex, tex_uv - w0_1_ratio * dxdy).rgb;
sum += w0_1 * tex2D_linearize(tex, tex_uv + w0_1_ratio * dxdy).rgb;
sum += w2_3 * tex2D_linearize(tex, tex_uv + (2.0 + w2_3_ratio) * dxdy).rgb;
sum += w4_5 * tex2D_linearize(tex, tex_uv + (4.0 + w4_5_ratio) * dxdy).rgb;
sum += w6_7 * tex2D_linearize(tex, tex_uv + (6.0 + w6_7_ratio) * dxdy).rgb;
sum += w8_9 * tex2D_linearize(tex, tex_uv + (8.0 + w8_9_ratio) * dxdy).rgb;
sum += w10_11 * tex2D_linearize(tex, tex_uv + (10.0 + w10_11_ratio) * dxdy).rgb;
sum += w12_13 * tex2D_linearize(tex, tex_uv + (12.0 + w12_13_ratio) * dxdy).rgb;
sum += w14_15 * tex2D_linearize(tex, tex_uv + (14.0 + w14_15_ratio) * dxdy).rgb;
return sum * weight_sum_inv;
}
vec3 tex2Dblur43fast(const sampler2D tex, const vec2 tex_uv,
const vec2 dxdy, const float sigma)
{
// Requires: Same as tex2Dblur11()
// Returns: A 1D 43x Gaussian blurred texture lookup using 22 linear
// taps. It may be mipmapped depending on settings and dxdy.
// First get the texel weights and normalization factor as above.
const float denom_inv = 0.5/(sigma*sigma);
const float w0 = 1.0;
const float w1 = exp(-1.0 * denom_inv);
const float w2 = exp(-4.0 * denom_inv);
const float w3 = exp(-9.0 * denom_inv);
const float w4 = exp(-16.0 * denom_inv);
const float w5 = exp(-25.0 * denom_inv);
const float w6 = exp(-36.0 * denom_inv);
const float w7 = exp(-49.0 * denom_inv);
const float w8 = exp(-64.0 * denom_inv);
const float w9 = exp(-81.0 * denom_inv);
const float w10 = exp(-100.0 * denom_inv);
const float w11 = exp(-121.0 * denom_inv);
const float w12 = exp(-144.0 * denom_inv);
const float w13 = exp(-169.0 * denom_inv);
const float w14 = exp(-196.0 * denom_inv);
const float w15 = exp(-225.0 * denom_inv);
const float w16 = exp(-256.0 * denom_inv);
const float w17 = exp(-289.0 * denom_inv);
const float w18 = exp(-324.0 * denom_inv);
const float w19 = exp(-361.0 * denom_inv);
const float w20 = exp(-400.0 * denom_inv);
const float w21 = exp(-441.0 * denom_inv);
//const float weight_sum_inv = 1.0 /
// (w0 + 2.0 * (w1 + w2 + w3 + w4 + w5 + w6 + w7 + w8 + w9 + w10 + w11 +
// w12 + w13 + w14 + w15 + w16 + w17 + w18 + w19 + w20 + w21));
const float weight_sum_inv = get_fast_gaussian_weight_sum_inv(sigma);
// Calculate combined weights and linear sample ratios between texel pairs.
// The center texel (with weight w0) is used twice, so halve its weight.
const float w0_1 = w0 * 0.5 + w1;
const float w2_3 = w2 + w3;
const float w4_5 = w4 + w5;
const float w6_7 = w6 + w7;
const float w8_9 = w8 + w9;
const float w10_11 = w10 + w11;
const float w12_13 = w12 + w13;
const float w14_15 = w14 + w15;
const float w16_17 = w16 + w17;
const float w18_19 = w18 + w19;
const float w20_21 = w20 + w21;
const float w0_1_ratio = w1/w0_1;
const float w2_3_ratio = w3/w2_3;
const float w4_5_ratio = w5/w4_5;
const float w6_7_ratio = w7/w6_7;
const float w8_9_ratio = w9/w8_9;
const float w10_11_ratio = w11/w10_11;
const float w12_13_ratio = w13/w12_13;
const float w14_15_ratio = w15/w14_15;
const float w16_17_ratio = w17/w16_17;
const float w18_19_ratio = w19/w18_19;
const float w20_21_ratio = w21/w20_21;
// Statically normalize weights, sum weighted samples, and return:
vec3 sum = vec3(0.0);
sum += w20_21 * tex2D_linearize(tex, tex_uv - (20.0 + w20_21_ratio) * dxdy).rgb;
sum += w18_19 * tex2D_linearize(tex, tex_uv - (18.0 + w18_19_ratio) * dxdy).rgb;
sum += w16_17 * tex2D_linearize(tex, tex_uv - (16.0 + w16_17_ratio) * dxdy).rgb;
sum += w14_15 * tex2D_linearize(tex, tex_uv - (14.0 + w14_15_ratio) * dxdy).rgb;
sum += w12_13 * tex2D_linearize(tex, tex_uv - (12.0 + w12_13_ratio) * dxdy).rgb;
sum += w10_11 * tex2D_linearize(tex, tex_uv - (10.0 + w10_11_ratio) * dxdy).rgb;
sum += w8_9 * tex2D_linearize(tex, tex_uv - (8.0 + w8_9_ratio) * dxdy).rgb;
sum += w6_7 * tex2D_linearize(tex, tex_uv - (6.0 + w6_7_ratio) * dxdy).rgb;
sum += w4_5 * tex2D_linearize(tex, tex_uv - (4.0 + w4_5_ratio) * dxdy).rgb;
sum += w2_3 * tex2D_linearize(tex, tex_uv - (2.0 + w2_3_ratio) * dxdy).rgb;
sum += w0_1 * tex2D_linearize(tex, tex_uv - w0_1_ratio * dxdy).rgb;
sum += w0_1 * tex2D_linearize(tex, tex_uv + w0_1_ratio * dxdy).rgb;
sum += w2_3 * tex2D_linearize(tex, tex_uv + (2.0 + w2_3_ratio) * dxdy).rgb;
sum += w4_5 * tex2D_linearize(tex, tex_uv + (4.0 + w4_5_ratio) * dxdy).rgb;
sum += w6_7 * tex2D_linearize(tex, tex_uv + (6.0 + w6_7_ratio) * dxdy).rgb;
sum += w8_9 * tex2D_linearize(tex, tex_uv + (8.0 + w8_9_ratio) * dxdy).rgb;
sum += w10_11 * tex2D_linearize(tex, tex_uv + (10.0 + w10_11_ratio) * dxdy).rgb;
sum += w12_13 * tex2D_linearize(tex, tex_uv + (12.0 + w12_13_ratio) * dxdy).rgb;
sum += w14_15 * tex2D_linearize(tex, tex_uv + (14.0 + w14_15_ratio) * dxdy).rgb;
sum += w16_17 * tex2D_linearize(tex, tex_uv + (16.0 + w16_17_ratio) * dxdy).rgb;
sum += w18_19 * tex2D_linearize(tex, tex_uv + (18.0 + w18_19_ratio) * dxdy).rgb;
sum += w20_21 * tex2D_linearize(tex, tex_uv + (20.0 + w20_21_ratio) * dxdy).rgb;
return sum * weight_sum_inv;
}
//////////////////// ARBITRARILY RESIZABLE ONE-PASS BLURS ////////////////////
vec3 tex2Dblur3x3resize(const sampler2D tex, const vec2 tex_uv,
const vec2 dxdy, const float sigma)
{
// Requires: Global requirements must be met (see file description).
// Returns: A 3x3 Gaussian blurred mipmapped texture lookup of the
// resized input.
// Description:
// This is the only arbitrarily resizable one-pass blur; tex2Dblur5x5resize
// would perform like tex2Dblur9x9, MUCH slower than tex2Dblur5resize.
const float denom_inv = 0.5/(sigma*sigma);
// Load each sample. We need all 3x3 samples. Quad-pixel communication
// won't help either: This should perform like tex2Dblur5x5, but sharing a
// 4x4 sample field would perform more like tex2Dblur8x8shared (worse).
const vec2 sample4_uv = tex_uv;
const vec2 dx = vec2(dxdy.x, 0.0);
const vec2 dy = vec2(0.0, dxdy.y);
const vec2 sample1_uv = sample4_uv - dy;
const vec2 sample7_uv = sample4_uv + dy;
const vec3 sample0 = tex2D_linearize(tex, sample1_uv - dx).rgb;
const vec3 sample1 = tex2D_linearize(tex, sample1_uv).rgb;
const vec3 sample2 = tex2D_linearize(tex, sample1_uv + dx).rgb;
const vec3 sample3 = tex2D_linearize(tex, sample4_uv - dx).rgb;
const vec3 sample4 = tex2D_linearize(tex, sample4_uv).rgb;
const vec3 sample5 = tex2D_linearize(tex, sample4_uv + dx).rgb;
const vec3 sample6 = tex2D_linearize(tex, sample7_uv - dx).rgb;
const vec3 sample7 = tex2D_linearize(tex, sample7_uv).rgb;
const vec3 sample8 = tex2D_linearize(tex, sample7_uv + dx).rgb;
// Statically compute Gaussian sample weights:
const float w4 = 1.0;
const float w1_3_5_7 = exp(-LENGTH_SQ(vec2(1.0, 0.0)) * denom_inv);
const float w0_2_6_8 = exp(-LENGTH_SQ(vec2(1.0, 1.0)) * denom_inv);
const float weight_sum_inv = 1.0/(w4 + 4.0 * (w1_3_5_7 + w0_2_6_8));
// Weight and sum the samples:
const vec3 sum = w4 * sample4 +
w1_3_5_7 * (sample1 + sample3 + sample5 + sample7) +
w0_2_6_8 * (sample0 + sample2 + sample6 + sample8);
return sum * weight_sum_inv;
}
// Resizable one-pass blurs:
vec3 tex2Dblur3x3resize(const sampler2D texture, const vec2 tex_uv,
const vec2 dxdy)
{
return tex2Dblur3x3resize(texture, tex_uv, dxdy, blur3_std_dev);
}
vec3 tex2Dblur9fast(const sampler2D tex, const vec2 tex_uv,
const vec2 dxdy, const float sigma)
{
// Requires: Same as tex2Dblur11()
// Returns: A 1D 9x Gaussian blurred texture lookup using 1 nearest
// neighbor and 4 linear taps. It may be mipmapped depending
// on settings and dxdy.
// First get the texel weights and normalization factor as above.
const float denom_inv = 0.5/(sigma*sigma);
const float w0 = 1.0;
const float w1 = exp(-1.0 * denom_inv);
const float w2 = exp(-4.0 * denom_inv);
const float w3 = exp(-9.0 * denom_inv);
const float w4 = exp(-16.0 * denom_inv);
const float weight_sum_inv = 1.0 / (w0 + 2.0 * (w1 + w2 + w3 + w4));
// Calculate combined weights and linear sample ratios between texel pairs.
const float w12 = w1 + w2;
const float w34 = w3 + w4;
const float w12_ratio = w2/w12;
const float w34_ratio = w4/w34;
// Statically normalize weights, sum weighted samples, and return:
vec3 sum = vec3(0.0);
sum += w34 * tex2D_linearize(tex, tex_uv - (3.0 + w34_ratio) * dxdy).rgb;
sum += w12 * tex2D_linearize(tex, tex_uv - (1.0 + w12_ratio) * dxdy).rgb;
sum += w0 * tex2D_linearize(tex, tex_uv).rgb;
sum += w12 * tex2D_linearize(tex, tex_uv + (1.0 + w12_ratio) * dxdy).rgb;
sum += w34 * tex2D_linearize(tex, tex_uv + (3.0 + w34_ratio) * dxdy).rgb;
return sum * weight_sum_inv;
}
vec3 tex2Dblur9fast(const sampler2D tex, const vec2 tex_uv,
const vec2 dxdy)
{
return tex2Dblur9fast(tex, tex_uv, dxdy, blur9_std_dev);
}
vec3 tex2Dblur17fast(const sampler2D texture, const vec2 tex_uv,
const vec2 dxdy)
{
return tex2Dblur17fast(texture, tex_uv, dxdy, blur17_std_dev);
}
vec3 tex2Dblur25fast(const sampler2D texture, const vec2 tex_uv,
const vec2 dxdy)
{
return tex2Dblur25fast(texture, tex_uv, dxdy, blur25_std_dev);
}
vec3 tex2Dblur43fast(const sampler2D texture, const vec2 tex_uv,
const vec2 dxdy)
{
return tex2Dblur43fast(texture, tex_uv, dxdy, blur43_std_dev);
}
vec3 tex2Dblur31fast(const sampler2D texture, const vec2 tex_uv,
const vec2 dxdy)
{
return tex2Dblur31fast(texture, tex_uv, dxdy, blur31_std_dev);
}
#endif // BLUR_FUNCTIONS_H

8
crt/shaders/crt-royale/src/crt-royale-bloom-approx.slang
View file

@ -32,7 +32,13 @@ layout(push_constant) uniform Push
////////////////////////////////// INCLUDES ////////////////////////////////// ////////////////////////////////// INCLUDES //////////////////////////////////
#include "includes.h" #include "../user-settings.h"
#include "derived-settings-and-constants.h"
#include "bind-shader-params.h"
#include "../../../../include/gamma-management.h"
#include "../../../../include/blur-functions.h"
#include "scanline-functions.h"
#include "bloom-functions.h"
/////////////////////////////////// HELPERS ////////////////////////////////// /////////////////////////////////// HELPERS //////////////////////////////////

4
crt/shaders/crt-royale/src/crt-royale-bloom-horizontal-reconstitute.slang
View file

@ -40,8 +40,8 @@ layout(push_constant) uniform Push
////////////////////////////////// INCLUDES ////////////////////////////////// ////////////////////////////////// INCLUDES //////////////////////////////////
//#include "../../../../include/gamma-management.h" #include "../../../../include/gamma-management.h"
//#include "bloom-functions.h" #include "bloom-functions.h"
#include "phosphor-mask-resizing.h" #include "phosphor-mask-resizing.h"
#include "scanline-functions.h" #include "scanline-functions.h"

5
crt/shaders/crt-royale/src/crt-royale-bloom-vertical.slang
View file

@ -38,10 +38,9 @@ layout(push_constant) uniform Push
////////////////////////////////// INCLUDES ////////////////////////////////// ////////////////////////////////// INCLUDES //////////////////////////////////
//#include "../../../../include/gamma-management.h" #include "../../../../include/gamma-management.h"
//#include "bloom-functions.h" #include "bloom-functions.h"
#include "phosphor-mask-resizing.h" #include "phosphor-mask-resizing.h"
#include "includes.h"
#pragma stage vertex #pragma stage vertex
layout(location = 0) in vec4 Position; layout(location = 0) in vec4 Position;

6
crt/shaders/crt-royale/src/crt-royale-brightpass.slang
View file

@ -40,12 +40,12 @@ layout(push_constant) uniform Push
////////////////////////////////// INCLUDES ////////////////////////////////// ////////////////////////////////// INCLUDES //////////////////////////////////
//#include "../../../../include/gamma-management.h" #include "../../../../include/gamma-management.h"
//#include "../../../../include/blur-functions.h" #include "../../../../include/blur-functions.h"
#include "phosphor-mask-resizing.h" #include "phosphor-mask-resizing.h"
#include "scanline-functions.h" #include "scanline-functions.h"
#include "bloom-functions.h" #include "bloom-functions.h"
#include "includes.h"
#pragma stage vertex #pragma stage vertex
layout(location = 0) in vec4 Position; layout(location = 0) in vec4 Position;

7
crt/shaders/crt-royale/src/crt-royale-first-pass-linearize-crt-gamma-bob-fields.slang
View file

@ -42,11 +42,12 @@ layout(std140, set = 0, binding = 0) uniform UBO
#define FIRST_PASS #define FIRST_PASS
#define SIMULATE_CRT_ON_LCD #define SIMULATE_CRT_ON_LCD
//#include "params.inc"
////////////////////////////////// INCLUDES ////////////////////////////////// ////////////////////////////////// INCLUDES //////////////////////////////////
#include "includes.h" #include "../user-settings.h"
#include "bind-shader-params.h"
#include "../../../../include/gamma-management.h"
#include "scanline-functions.h"
#pragma stage vertex #pragma stage vertex
layout(location = 0) in vec4 Position; layout(location = 0) in vec4 Position;

10
crt/shaders/crt-royale/src/crt-royale-geometry-aa-last-pass.slang
View file

@ -37,7 +37,7 @@ layout(push_constant) uniform Push
#include "derived-settings-and-constants.h" #include "derived-settings-and-constants.h"
#include "bind-shader-params.h" #include "bind-shader-params.h"
#ifndef RUNTIME_GEOMETRY_TILT #ifndef DONT_DEFINE //RUNTIME_GEOMETRY_TILT
// Create a local-to-global rotation matrix for the CRT's coordinate frame // Create a local-to-global rotation matrix for the CRT's coordinate frame
// and its global-to-local inverse. See the vertex shader for details. // and its global-to-local inverse. See the vertex shader for details.
// It's faster to compute these statically if possible. // It's faster to compute these statically if possible.
@ -97,7 +97,7 @@ void main()
const vec2 geom_overscan = get_geom_overscan_vector(); const vec2 geom_overscan = get_geom_overscan_vector();
geom_aspect_and_overscan = vec4(geom_aspect, geom_overscan); geom_aspect_and_overscan = vec4(geom_aspect, geom_overscan);
#ifdef RUNTIME_GEOMETRY_TILT #ifdef DONT_DEFINE //RUNTIME_GEOMETRY_TILT
// Create a local-to-global rotation matrix for the CRT's coordinate // Create a local-to-global rotation matrix for the CRT's coordinate
// frame and its global-to-local inverse. Rotate around the x axis // frame and its global-to-local inverse. Rotate around the x axis
// first (pitch) and then the y axis (yaw) with yucky Euler angles. // first (pitch) and then the y axis (yaw) with yucky Euler angles.
@ -238,5 +238,9 @@ void main()
color = tex2D_linearize(Source, tex_uv).rgb; color = tex2D_linearize(Source, tex_uv).rgb;
} }
FragColor = vec4(texture(Source, tex_uv).rgb, 1.0); // Dim borders and output the final result:
const float border_dim_factor = get_border_dim_factor(video_uv, geom_aspect);
const vec3 final_color = color * border_dim_factor;
FragColor = encode_output(vec4(final_color, 1.0));
} }

8
crt/shaders/crt-royale/src/crt-royale-mask-resize-horizontal.slang
View file

@ -71,17 +71,17 @@ void main()
// and the number of tiles that will fit in the FBO. // and the number of tiles that will fit in the FBO.
const vec2 output_tiles_this_pass = registers.OutputSize.xy / mask_resize_tile_size; const vec2 output_tiles_this_pass = registers.OutputSize.xy / mask_resize_tile_size;
const vec2 output_video_uv = tex_uv; const vec2 output_video_uv = tex_uv;
const vec2 tile_uv_wrap = output_video_uv * output_tiles_this_pass; tile_uv_wrap = output_video_uv * output_tiles_this_pass;
// Get the texel size of an input tile and related values: // Get the texel size of an input tile and related values:
const vec2 input_tile_size = vec2(min( const vec2 input_tile_size = vec2(min(
mask_resize_src_lut_size.x, registers.SourceSize.x), mask_resize_tile_size.y); mask_resize_src_lut_size.x, registers.SourceSize.x), mask_resize_tile_size.y);
const vec2 tile_size_uv = input_tile_size * registers.SourceSize.zw; tile_size_uv = input_tile_size * registers.SourceSize.zw;
const vec2 input_tiles_per_texture = registers.SourceSize.xy / input_tile_size; input_tiles_per_texture = registers.SourceSize.xy / input_tile_size;
// Derive [wrapped] texture uv coords from [wrapped] tile uv coords and // Derive [wrapped] texture uv coords from [wrapped] tile uv coords and
// the tile size in uv coords, and save frac() for the fragment shader. // the tile size in uv coords, and save frac() for the fragment shader.
const vec2 src_tex_uv_wrap = tile_uv_wrap * tile_size_uv; src_tex_uv_wrap = tile_uv_wrap * tile_size_uv;
resize_magnification_scale = mask_resize_tile_size / input_tile_size; resize_magnification_scale = mask_resize_tile_size / input_tile_size;
src_dxdy = vec2(registers.SourceSize.z, 0.0); src_dxdy = vec2(registers.SourceSize.z, 0.0);

6
crt/shaders/crt-royale/src/crt-royale-mask-resize-vertical.slang
View file

@ -31,9 +31,9 @@ layout(push_constant) uniform Push
///////////////////////////// SETTINGS MANAGEMENT //////////////////////////// ///////////////////////////// SETTINGS MANAGEMENT ////////////////////////////
//#include "../user-settings.h" #include "../user-settings.h"
//#include "derived-settings-and-constants.h" #include "derived-settings-and-constants.h"
//#include "bind-shader-params.h" #include "bind-shader-params.h"
////////////////////////////////// INCLUDES ////////////////////////////////// ////////////////////////////////// INCLUDES //////////////////////////////////

23
crt/shaders/crt-royale/src/crt-royale-scanlines-horizontal-apply-mask.slang
View file

@ -41,11 +41,11 @@ layout(push_constant) uniform Push
////////////////////////////////// INCLUDES ////////////////////////////////// ////////////////////////////////// INCLUDES //////////////////////////////////
//#include "scanline-functions.h" #include "scanline-functions.h"
#include "phosphor-mask-resizing.h" #include "phosphor-mask-resizing.h"
//#include "bloom-functions.h"//"bloom-functions.h" #include "bloom-functions.h"//"bloom-functions.h"
//#include "../../../../include/gamma-management.h" #include "../../../../include/gamma-management.h"
#include "includes.h"
/////////////////////////////////// HELPERS ////////////////////////////////// /////////////////////////////////// HELPERS //////////////////////////////////
vec4 tex2Dtiled_mask_linearize(const sampler2D tex, vec4 tex2Dtiled_mask_linearize(const sampler2D tex,
@ -88,11 +88,11 @@ void main()
video_uv = TexCoord; video_uv = TexCoord;
const vec2 scanline_texture_size_inv = const vec2 scanline_texture_size_inv =
registers.VERTICAL_SCANLINESSize.zw; registers.VERTICAL_SCANLINESSize.zw;
scanline_tex_uv = video_uv * registers.VERTICAL_SCANLINESSize.xy * scanline_tex_uv = video_uv;// * registers.VERTICAL_SCANLINESSize.xy *
scanline_texture_size_inv; scanline_texture_size_inv;
blur3x3_tex_uv = video_uv * registers.BLOOM_APPROXSize.xy * blur3x3_tex_uv = video_uv;// * registers.BLOOM_APPROXSize.xy *
registers.BLOOM_APPROXSize.zw; registers.BLOOM_APPROXSize.zw;
halation_tex_uv = video_uv * registers.HALATION_BLURSize.xy * halation_tex_uv = video_uv;// * registers.HALATION_BLURSize.xy *
registers.HALATION_BLURSize.zw; registers.HALATION_BLURSize.zw;
// Get a consistent name for the final mask texture size. Sample mode 0 // Get a consistent name for the final mask texture size. Sample mode 0
@ -109,10 +109,9 @@ void main()
#endif #endif
// Compute mask tile dimensions, starting points, etc.: // Compute mask tile dimensions, starting points, etc.:
vec2 mask_tiles_per_screen; mask_tile_start_uv_and_size = get_mask_sampling_parameters(
mask_tile_start_uv_and_size = vec4(get_mask_sampling_parameters(
mask_resize_texture_size, mask_resize_video_size, registers.OutputSize.xy, mask_resize_texture_size, mask_resize_video_size, registers.OutputSize.xy,
mask_tiles_per_screen)); //TODO/FIXME: is this right? I wrapped in a vec4 because that's what it needs to compile mask_tiles_per_screen);
} }
#pragma stage fragment #pragma stage fragment
@ -200,12 +199,12 @@ void main()
const vec3 halation_intensity_dim = const vec3 halation_intensity_dim =
vec3(dot(halation_color, vec3(auto_dim_factor/3.0))); vec3(dot(halation_color, vec3(auto_dim_factor/3.0)));
const vec3 electron_intensity_dim = mix(scanline_color_dim, const vec3 electron_intensity_dim = mix(scanline_color_dim,
halation_intensity_dim, halation_weight); halation_intensity_dim, params.halation_weight);
// Apply the phosphor mask: // Apply the phosphor mask:
const vec3 phosphor_emission_dim = electron_intensity_dim * const vec3 phosphor_emission_dim = electron_intensity_dim *
phosphor_mask_sample; phosphor_mask_sample;
#define PHOSPHOR_BLOOM_FAKE // TODO/FIXME: something seems wrong with the non-FAKE path
#ifdef PHOSPHOR_BLOOM_FAKE #ifdef PHOSPHOR_BLOOM_FAKE
// The BLOOM_APPROX pass approximates a blurred version of a masked // The BLOOM_APPROX pass approximates a blurred version of a masked
// and scanlined image. It's usually used to compute the brightpass, // and scanlined image. It's usually used to compute the brightpass,

6
crt/shaders/crt-royale/src/crt-royale-scanlines-vertical-interlacing.slang
View file

@ -31,7 +31,11 @@ layout(push_constant) uniform Push
////////////////////////////////// INCLUDES ////////////////////////////////// ////////////////////////////////// INCLUDES //////////////////////////////////
#include "includes.h" #include "../user-settings.h"
#include "derived-settings-and-constants.h"
#include "bind-shader-params.h"
#include "scanline-functions.h"
#include "../../../../include/gamma-management.h"
#pragma stage vertex #pragma stage vertex
layout(location = 0) in vec4 Position; layout(location = 0) in vec4 Position;

547
crt/shaders/crt-royale/src/gamma-management-old.h
View file

@ -1,547 +0,0 @@
#ifndef GAMMA_MANAGEMENT_H
#define GAMMA_MANAGEMENT_H
///////////////////////////////// MIT LICENSE ////////////////////////////////
// Copyright (C) 2014 TroggleMonkey
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to
// deal in the Software without restriction, including without limitation the
// rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
// sell copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
// IN THE SOFTWARE.
///////////////////////////////// DESCRIPTION ////////////////////////////////
// This file provides gamma-aware tex*D*() and encode_output() functions.
// Requires: Before #include-ing this file, the including file must #define
// the following macros when applicable and follow their rules:
// 1.) #define FIRST_PASS if this is the first pass.
// 2.) #define LAST_PASS if this is the last pass.
// 3.) If sRGB is available, set srgb_framebufferN = "true" for
// every pass except the last in your .cgp preset.
// 4.) If sRGB isn't available but you want gamma-correctness with
// no banding, #define GAMMA_ENCODE_EVERY_FBO each pass.
// 5.) #define SIMULATE_CRT_ON_LCD if desired (precedence over 5-7)
// 6.) #define SIMULATE_GBA_ON_LCD if desired (precedence over 6-7)
// 7.) #define SIMULATE_LCD_ON_CRT if desired (precedence over 7)
// 8.) #define SIMULATE_GBA_ON_CRT if desired (precedence over -)
// If an option in [5, 8] is #defined in the first or last pass, it
// should be #defined for both. It shouldn't make a difference
// whether it's #defined for intermediate passes or not.
// Optional: The including file (or an earlier included file) may optionally
// #define a number of macros indicating it will override certain
// macros and associated constants are as follows:
// static constants with either static or uniform constants. The
// 1.) OVERRIDE_STANDARD_GAMMA: The user must first define:
// static const float ntsc_gamma
// static const float pal_gamma
// static const float crt_reference_gamma_high
// static const float crt_reference_gamma_low
// static const float lcd_reference_gamma
// static const float crt_office_gamma
// static const float lcd_office_gamma
// 2.) OVERRIDE_DEVICE_GAMMA: The user must first define:
// static const float crt_gamma
// static const float gba_gamma
// static const float lcd_gamma
// 3.) OVERRIDE_FINAL_GAMMA: The user must first define:
// static const float input_gamma
// static const float intermediate_gamma
// static const float output_gamma
// (intermediate_gamma is for GAMMA_ENCODE_EVERY_FBO.)
// 4.) OVERRIDE_ALPHA_ASSUMPTIONS: The user must first define:
// static const bool assume_opaque_alpha
// The gamma constant overrides must be used in every pass or none,
// and OVERRIDE_FINAL_GAMMA bypasses all of the SIMULATE* macros.
// OVERRIDE_ALPHA_ASSUMPTIONS may be set on a per-pass basis.
// Usage: After setting macros appropriately, ignore gamma correction and
// replace all tex*D*() calls with equivalent gamma-aware
// tex*D*_linearize calls, except:
// 1.) When you read an LUT, use regular tex*D or a gamma-specified
// function, depending on its gamma encoding:
// tex*D*_linearize_gamma (takes a runtime gamma parameter)
// 2.) If you must read pass0's original input in a later pass, use
// tex2D_linearize_ntsc_gamma. If you want to read pass0's
// input with gamma-corrected bilinear filtering, consider
// creating a first linearizing pass and reading from the input
// of pass1 later.
// Then, return encode_output(color) from every fragment shader.
// Finally, use the global gamma_aware_bilinear boolean if you want
// to statically branch based on whether bilinear filtering is
// gamma-correct or not (e.g. for placing Gaussian blur samples).
//
// Detailed Policy:
// tex*D*_linearize() functions enforce a consistent gamma-management policy
// based on the FIRST_PASS and GAMMA_ENCODE_EVERY_FBO settings. They assume
// their input texture has the same encoding characteristics as the input for
// the current pass (which doesn't apply to the exceptions listed above).
// Similarly, encode_output() enforces a policy based on the LAST_PASS and
// GAMMA_ENCODE_EVERY_FBO settings. Together, they result in one of the
// following two pipelines.
// Typical pipeline with intermediate sRGB framebuffers:
// linear_color = pow(pass0_encoded_color, input_gamma);
// intermediate_output = linear_color; // Automatic sRGB encoding
// linear_color = intermediate_output; // Automatic sRGB decoding
// final_output = pow(intermediate_output, 1.0/output_gamma);
// Typical pipeline without intermediate sRGB framebuffers:
// linear_color = pow(pass0_encoded_color, input_gamma);
// intermediate_output = pow(linear_color, 1.0/intermediate_gamma);
// linear_color = pow(intermediate_output, intermediate_gamma);
// final_output = pow(intermediate_output, 1.0/output_gamma);
// Using GAMMA_ENCODE_EVERY_FBO is much slower, but it's provided as a way to
// easily get gamma-correctness without banding on devices where sRGB isn't
// supported.
//
// Use This Header to Maximize Code Reuse:
// The purpose of this header is to provide a consistent interface for texture
// reads and output gamma-encoding that localizes and abstracts away all the
// annoying details. This greatly reduces the amount of code in each shader
// pass that depends on the pass number in the .cgp preset or whether sRGB
// FBO's are being used: You can trivially change the gamma behavior of your
// whole pass by commenting or uncommenting 1-3 #defines. To reuse the same
// code in your first, Nth, and last passes, you can even put it all in another
// header file and #include it from skeleton .cg files that #define the
// appropriate pass-specific settings.
//
// Rationale for Using Three Macros:
// This file uses GAMMA_ENCODE_EVERY_FBO instead of an opposite macro like
// SRGB_PIPELINE to ensure sRGB is assumed by default, which hopefully imposes
// a lower maintenance burden on each pass. At first glance it seems we could
// accomplish everything with two macros: GAMMA_CORRECT_IN / GAMMA_CORRECT_OUT.
// This works for simple use cases where input_gamma == output_gamma, but it
// breaks down for more complex scenarios like CRT simulation, where the pass
// number determines the gamma encoding of the input and output.
/////////////////////////////// BASE CONSTANTS ///////////////////////////////
// Set standard gamma constants, but allow users to override them:
#ifndef OVERRIDE_STANDARD_GAMMA
// Standard encoding gammas:
const float ntsc_gamma = 2.2; // Best to use NTSC for PAL too?
const float pal_gamma = 2.8; // Never actually 2.8 in practice
// Typical device decoding gammas (only use for emulating devices):
// CRT/LCD reference gammas are higher than NTSC and Rec.709 video standard
// gammas: The standards purposely undercorrected for an analog CRT's
// assumed 2.5 reference display gamma to maintain contrast in assumed
// [dark] viewing conditions: http://www.poynton.com/PDFs/GammaFAQ.pdf
// These unstated assumptions about display gamma and perceptual rendering
// intent caused a lot of confusion, and more modern CRT's seemed to target
// NTSC 2.2 gamma with circuitry. LCD displays seem to have followed suit
// (they struggle near black with 2.5 gamma anyway), especially PC/laptop
// displays designed to view sRGB in bright environments. (Standards are
// also in flux again with BT.1886, but it's underspecified for displays.)
const float crt_reference_gamma_high = 2.5; // In (2.35, 2.55)
const float crt_reference_gamma_low = 2.35; // In (2.35, 2.55)
const float lcd_reference_gamma = 2.5; // To match CRT
const float crt_office_gamma = 2.2; // Circuitry-adjusted for NTSC
const float lcd_office_gamma = 2.2; // Approximates sRGB
#endif // OVERRIDE_STANDARD_GAMMA
// Assuming alpha == 1.0 might make it easier for users to avoid some bugs,
// but only if they're aware of it.
#ifndef OVERRIDE_ALPHA_ASSUMPTIONS
const bool assume_opaque_alpha = false;
#endif
/////////////////////// DERIVED CONSTANTS AS FUNCTIONS ///////////////////////
// gamma-management.h should be compatible with overriding gamma values with
// runtime user parameters, but we can only define other global constants in
// terms of static constants, not uniform user parameters. To get around this
// limitation, we need to define derived constants using functions.
// Set device gamma constants, but allow users to override them:
#ifdef OVERRIDE_DEVICE_GAMMA
// The user promises to globally define the appropriate constants:
float get_crt_gamma() { return crt_gamma; }
float get_gba_gamma() { return gba_gamma; }
float get_lcd_gamma() { return lcd_gamma; }
#else
float get_crt_gamma() { return crt_reference_gamma_high; }
float get_gba_gamma() { return 3.5; } // Game Boy Advance; in (3.0, 4.0)
float get_lcd_gamma() { return lcd_office_gamma; }
#endif // OVERRIDE_DEVICE_GAMMA
// Set decoding/encoding gammas for the first/lass passes, but allow overrides:
#ifdef OVERRIDE_FINAL_GAMMA
// The user promises to globally define the appropriate constants:
float get_intermediate_gamma() { return intermediate_gamma; }
float get_input_gamma() { return input_gamma; }
float get_output_gamma() { return output_gamma; }
#else
// If we gamma-correct every pass, always use ntsc_gamma between passes to
// ensure middle passes don't need to care if anything is being simulated:
float get_intermediate_gamma() { return ntsc_gamma; }
#ifdef SIMULATE_CRT_ON_LCD
float get_input_gamma() { return get_crt_gamma(); }
float get_output_gamma() { return get_lcd_gamma(); }
#else
#ifdef SIMULATE_GBA_ON_LCD
float get_input_gamma() { return get_gba_gamma(); }
float get_output_gamma() { return get_lcd_gamma(); }
#else
#ifdef SIMULATE_LCD_ON_CRT
float get_input_gamma() { return get_lcd_gamma(); }
float get_output_gamma() { return get_crt_gamma(); }
#else
#ifdef SIMULATE_GBA_ON_CRT
float get_input_gamma() { return get_gba_gamma(); }
float get_output_gamma() { return get_crt_gamma(); }
#else // Don't simulate anything:
float get_input_gamma() { return ntsc_gamma; }
float get_output_gamma() { return ntsc_gamma; }
#endif // SIMULATE_GBA_ON_CRT
#endif // SIMULATE_LCD_ON_CRT
#endif // SIMULATE_GBA_ON_LCD
#endif // SIMULATE_CRT_ON_LCD
#endif // OVERRIDE_FINAL_GAMMA
// Set decoding/encoding gammas for the current pass. Use static constants for
// linearize_input and gamma_encode_output, because they aren't derived, and
// they let the compiler do dead-code elimination.
#ifndef GAMMA_ENCODE_EVERY_FBO
#ifdef FIRST_PASS
const bool linearize_input = true;
float get_pass_input_gamma() { return get_input_gamma(); }
#else
const bool linearize_input = false;
float get_pass_input_gamma() { return 1.0; }
#endif
#ifdef LAST_PASS
const bool gamma_encode_output = true;
float get_pass_output_gamma() { return get_output_gamma(); }
#else
const bool gamma_encode_output = false;
float get_pass_output_gamma() { return 1.0; }
#endif
#else
const bool linearize_input = true;
const bool gamma_encode_output = true;
#ifdef FIRST_PASS
float get_pass_input_gamma() { return get_input_gamma(); }
#else
float get_pass_input_gamma() { return get_intermediate_gamma(); }
#endif
#ifdef LAST_PASS
float get_pass_output_gamma() { return get_output_gamma(); }
#else
float get_pass_output_gamma() { return get_intermediate_gamma(); }
#endif
#endif
// Users might want to know if bilinear filtering will be gamma-correct:
const bool gamma_aware_bilinear = !linearize_input;
////////////////////// COLOR ENCODING/DECODING FUNCTIONS /////////////////////
vec4 encode_output(const vec4 color)
{
if(gamma_encode_output)
{
if(assume_opaque_alpha)
{
return vec4(pow(color.rgb, vec3(1.0/get_pass_output_gamma())), 1.0);
}
else
{
return vec4(pow(color.rgb, vec3(1.0/get_pass_output_gamma())), color.a);
}
}
else
{
return color;
}
}
vec4 decode_input(const vec4 color)
{
if(linearize_input)
{
if(assume_opaque_alpha)
{
return vec4(pow(color.rgb, vec3(get_pass_input_gamma())), 1.0);
}
else
{
return vec4(pow(color.rgb, vec3(get_pass_input_gamma())), color.a);
}
}
else
{
return color;
}
}
vec4 decode_gamma_input(const vec4 color, const vec3 gamma)
{
if(assume_opaque_alpha)
{
return vec4(pow(color.rgb, vec3(gamma)), 1.0);
}
else
{
return vec4(pow(color.rgb, vec3(gamma)), color.a);
}
}
/////////////////////////// TEXTURE LOOKUP WRAPPERS //////////////////////////
// "SMART" LINEARIZING TEXTURE LOOKUP FUNCTIONS:
// Provide a wide array of linearizing texture lookup wrapper functions. The
// Cg shader spec Retroarch uses only allows for 2D textures, but 1D and 3D
// lookups are provided for completeness in case that changes someday. Nobody
// is likely to use the *fetch and *proj functions, but they're included just
// in case. The only tex*D texture sampling functions omitted are:
// - tex*Dcmpbias
// - tex*Dcmplod
// - tex*DARRAY*
// - tex*DMS*
// - Variants returning integers
// Standard line length restrictions are ignored below for vertical brevity.
/*
// tex1D:
vec4 tex1D_linearize(const sampler1D texture, const float tex_coords)
{ return decode_input(tex1D(texture, tex_coords)); }
vec4 tex1D_linearize(const sampler1D texture, const vec2 tex_coords)
{ return decode_input(tex1D(texture, tex_coords)); }
vec4 tex1D_linearize(const sampler1D texture, const float tex_coords, const int texel_off)
{ return decode_input(tex1D(texture, tex_coords, texel_off)); }
vec4 tex1D_linearize(const sampler1D texture, const vec2 tex_coords, const int texel_off)
{ return decode_input(tex1D(texture, tex_coords, texel_off)); }
vec4 tex1D_linearize(const sampler1D texture, const float tex_coords, const float dx, const float dy)
{ return decode_input(tex1D(texture, tex_coords, dx, dy)); }
vec4 tex1D_linearize(const sampler1D texture, const vec2 tex_coords, const float dx, const float dy)
{ return decode_input(tex1D(texture, tex_coords, dx, dy)); }
vec4 tex1D_linearize(const sampler1D texture, const float tex_coords, const float dx, const float dy, const int texel_off)
{ return decode_input(tex1D(texture, tex_coords, dx, dy, texel_off)); }
vec4 tex1D_linearize(const sampler1D texture, const vec2 tex_coords, const float dx, const float dy, const int texel_off)
{ return decode_input(tex1D(texture, tex_coords, dx, dy, texel_off)); }
// tex1Dbias:
vec4 tex1Dbias_linearize(const sampler1D texture, const vec4 tex_coords)
{ return decode_input(tex1Dbias(texture, tex_coords)); }
vec4 tex1Dbias_linearize(const sampler1D texture, const vec4 tex_coords, const int texel_off)
{ return decode_input(tex1Dbias(texture, tex_coords, texel_off)); }
// tex1Dfetch:
vec4 tex1Dfetch_linearize(const sampler1D texture, const int4 tex_coords)
{ return decode_input(tex1Dfetch(texture, tex_coords)); }
vec4 tex1Dfetch_linearize(const sampler1D texture, const int4 tex_coords, const int texel_off)
{ return decode_input(tex1Dfetch(texture, tex_coords, texel_off)); }
// tex1Dlod:
vec4 tex1Dlod_linearize(const sampler1D texture, const vec4 tex_coords)
{ return decode_input(tex1Dlod(texture, tex_coords)); }
vec4 tex1Dlod_linearize(const sampler1D texture, const vec4 tex_coords, const int texel_off)
{ return decode_input(tex1Dlod(texture, tex_coords, texel_off)); }
// tex1Dproj:
vec4 tex1Dproj_linearize(const sampler1D texture, const vec2 tex_coords)
{ return decode_input(tex1Dproj(texture, tex_coords)); }
vec4 tex1Dproj_linearize(const sampler1D texture, const vec3 tex_coords)
{ return decode_input(tex1Dproj(texture, tex_coords)); }
vec4 tex1Dproj_linearize(const sampler1D texture, const vec2 tex_coords, const int texel_off)
{ return decode_input(tex1Dproj(texture, tex_coords, texel_off)); }
vec4 tex1Dproj_linearize(const sampler1D texture, const vec3 tex_coords, const int texel_off)
{ return decode_input(tex1Dproj(texture, tex_coords, texel_off)); }
*/
// tex2D:
vec4 tex2D_linearize(const sampler2D tex, const vec2 tex_coords)
{ return decode_input(vec4(texture(tex, tex_coords))); }
vec4 tex2D_linearize(const sampler2D tex, const vec3 tex_coords)
{ return decode_input(vec4(texture(tex, tex_coords))); }
vec4 tex2D_linearize(const sampler2D tex, const vec2 tex_coords, const int texel_off)
{ return decode_input(vec4(texture(tex, tex_coords, texel_off))); }
vec4 tex2D_linearize(const sampler2D tex, const vec3 tex_coords, const int texel_off)
{ return decode_input(vec4(texture(tex, tex_coords, texel_off))); }
vec4 tex2D_linearize(const sampler2D tex, const vec2 tex_coords, const vec2 dx, const vec2 dy)
{ return decode_input(vec4(texture(tex, tex_coords, dx, dy))); }
vec4 tex2D_linearize(const sampler2D tex, const vec3 tex_coords, const vec2 dx, const vec2 dy)
{ return decode_input(vec4(texture(tex, tex_coords, dx, dy))); }
vec4 tex2D_linearize(const sampler2D tex, const vec2 tex_coords, const vec2 dx, const vec2 dy, const int texel_off)
{ return decode_input(vec4(texture(tex, tex_coords, dx, dy, texel_off))); }
vec4 tex2D_linearize(const sampler2D tex, const vec3 tex_coords, const vec2 dx, const vec2 dy, const int texel_off)
{ return decode_input(vec4(texture(tex, tex_coords, dx, dy, texel_off))); }
// tex2Dbias:
vec4 tex2Dbias_linearize(const sampler2D tex, const vec4 tex_coords)
{ return decode_input(vec4(tex2Dbias(tex, tex_coords))); }
vec4 tex2Dbias_linearize(const sampler2D tex, const vec4 tex_coords, const int texel_off)
{ return decode_input(vec4(tex2Dbias(tex, tex_coords, texel_off))); }
// tex2Dfetch:
vec4 tex2Dfetch_linearize(const sampler2D tex, const ivec4 tex_coords)
{ return decode_input(vec4(texture2Dfetch(tex, tex_coords))); }
vec4 tex2Dfetch_linearize(const sampler2D tex, const ivec4 tex_coords, const int texel_off)
{ return decode_input(vec4(texture2Dfetch(tex, tex_coords, texel_off))); }
// tex2Dlod:
vec4 tex2Dlod_linearize(const sampler2D tex, const vec4 tex_coords)
{ return decode_input(vec4(texture2Dlod(tex, tex_coords))); }
vec4 tex2Dlod_linearize(const sampler2D tex, const vec4 tex_coords, const int texel_off)
{ return decode_input(vec4(texture2Dlod(tex, tex_coords, texel_off))); }
// tex2Dproj:
vec4 tex2Dproj_linearize(const sampler2D tex, const vec3 tex_coords)
{ return decode_input(vec4(tex2Dproj(tex, tex_coords))); }
vec4 tex2Dproj_linearize(const sampler2D tex, const vec4 tex_coords)
{ return decode_input(vec4(tex2Dproj(tex, tex_coords))); }
vec4 tex2Dproj_linearize(const sampler2D tex, const vec3 tex_coords, const int texel_off)
{ return decode_input(vec4(tex2Dproj(tex, tex_coords, texel_off))); }
vec4 tex2Dproj_linearize(const sampler2D tex, const vec4 tex_coords, const int texel_off)
{ return decode_input(vec4(tex2Dproj(tex, tex_coords, texel_off))); }
/*
// tex3D:
vec4 tex3D_linearize(const sampler3D texture, const vec3 tex_coords)
{ return decode_input(tex3D(texture, tex_coords)); }
vec4 tex3D_linearize(const sampler3D texture, const vec3 tex_coords, const int texel_off)
{ return decode_input(tex3D(texture, tex_coords, texel_off)); }
vec4 tex3D_linearize(const sampler3D texture, const vec3 tex_coords, const vec3 dx, const vec3 dy)
{ return decode_input(tex3D(texture, tex_coords, dx, dy)); }
vec4 tex3D_linearize(const sampler3D texture, const vec3 tex_coords, const vec3 dx, const vec3 dy, const int texel_off)
{ return decode_input(tex3D(texture, tex_coords, dx, dy, texel_off)); }
// tex3Dbias:
vec4 tex3Dbias_linearize(const sampler3D texture, const vec4 tex_coords)
{ return decode_input(tex3Dbias(texture, tex_coords)); }
vec4 tex3Dbias_linearize(const sampler3D texture, const vec4 tex_coords, const int texel_off)
{ return decode_input(tex3Dbias(texture, tex_coords, texel_off)); }
// tex3Dfetch:
vec4 tex3Dfetch_linearize(const sampler3D texture, const int4 tex_coords)
{ return decode_input(tex3Dfetch(texture, tex_coords)); }
vec4 tex3Dfetch_linearize(const sampler3D texture, const int4 tex_coords, const int texel_off)
{ return decode_input(tex3Dfetch(texture, tex_coords, texel_off)); }
// tex3Dlod:
vec4 tex3Dlod_linearize(const sampler3D texture, const vec4 tex_coords)
{ return decode_input(tex3Dlod(texture, tex_coords)); }
vec4 tex3Dlod_linearize(const sampler3D texture, const vec4 tex_coords, const int texel_off)
{ return decode_input(tex3Dlod(texture, tex_coords, texel_off)); }
// tex3Dproj:
vec4 tex3Dproj_linearize(const sampler3D texture, const vec4 tex_coords)
{ return decode_input(tex3Dproj(texture, tex_coords)); }
vec4 tex3Dproj_linearize(const sampler3D texture, const vec4 tex_coords, const int texel_off)
{ return decode_input(tex3Dproj(texture, tex_coords, texel_off)); }
*/
// NONSTANDARD "SMART" LINEARIZING TEXTURE LOOKUP FUNCTIONS:
// This narrow selection of nonstandard tex2D* functions can be useful:
// tex2Dlod0: Automatically fill in the tex2D LOD parameter for mip level 0.
vec4 tex2Dlod0_linearize(const sampler2D texture, const vec2 tex_coords)
{ return decode_input(vec4(texture2Dlod(texture, vec4(tex_coords, 0.0, 0.0)))); }
vec4 tex2Dlod0_linearize(const sampler2D texture, const vec2 tex_coords, const int texel_off)
{ return decode_input(vec4(texture2Dlod(texture, vec4(tex_coords, 0.0, 0.0), texel_off))); }
// MANUALLY LINEARIZING TEXTURE LOOKUP FUNCTIONS:
// Provide a narrower selection of tex2D* wrapper functions that decode an
// input sample with a specified gamma value. These are useful for reading
// LUT's and for reading the input of pass0 in a later pass.
// tex2D:
vec4 tex2D_linearize_gamma(const sampler2D tex, const vec2 tex_coords, const vec3 gamma)
{ return decode_gamma_input(vec4(texture(tex, tex_coords), vec3(gamma))); }
vec4 tex2D_linearize_gamma(const sampler2D tex, const vec3 tex_coords, const vec3 gamma)
{ return decode_gamma_input(vec4(texture(tex, tex_coords), vec3(gamma))); }
vec4 tex2D_linearize_gamma(const sampler2D tex, const vec2 tex_coords, const int texel_off, const vec3 gamma)
{ return decode_gamma_input(vec4(texture(tex, tex_coords, texel_off), vec3(gamma))); }
vec4 tex2D_linearize_gamma(const sampler2D tex, const vec3 tex_coords, const int texel_off, const vec3 gamma)
{ return decode_gamma_input(vec4(texture(tex, tex_coords, texel_off), vec3(gamma))); }
vec4 tex2D_linearize_gamma(const sampler2D tex, const vec2 tex_coords, const vec2 dx, const vec2 dy, const vec3 gamma)
{ return decode_gamma_input(vec4(texture(tex, tex_coords, dx, dy), vec3(gamma))); }
vec4 tex2D_linearize_gamma(const sampler2D tex, const vec3 tex_coords, const vec2 dx, const vec2 dy, const vec3 gamma)
{ return decode_gamma_input(vec4(texture(tex, tex_coords, dx, dy), vec3(gamma))); }
vec4 tex2D_linearize_gamma(const sampler2D tex, const vec2 tex_coords, const vec2 dx, const vec2 dy, const int texel_off, const vec3 gamma)
{ return decode_gamma_input(vec4(texture(tex, tex_coords, dx, dy, texel_off), vec3(gamma))); }
vec4 tex2D_linearize_gamma(const sampler2D tex, const vec3 tex_coords, const vec2 dx, const vec2 dy, const int texel_off, const vec3 gamma)
{ return decode_gamma_input(vec4(texture(tex, tex_coords, dx, dy, texel_off), vec3(gamma))); }
// tex2Dbias:
vec4 tex2Dbias_linearize_gamma(const sampler2D tex, const vec4 tex_coords, const vec3 gamma)
{ return decode_gamma_input(vec4(tex2Dbias(tex, tex_coords), vec3(gamma))); }
vec4 tex2Dbias_linearize_gamma(const sampler2D tex, const vec4 tex_coords, const int texel_off, const vec3 gamma)
{ return decode_gamma_input(vec4(tex2Dbias(tex, tex_coords, texel_off), vec3(gamma))); }
// tex2Dfetch:
vec4 tex2Dfetch_linearize_gamma(const sampler2D tex, const int4 tex_coords, const vec3 gamma)
{ return decode_gamma_input(vec4(tex2Dfetch(tex, tex_coords), vec3(gamma))); }
vec4 tex2Dfetch_linearize_gamma(const sampler2D tex, const int4 tex_coords, const int texel_off, const vec3 gamma)
{ return decode_gamma_input(vec4(tex2Dfetch(tex, tex_coords, texel_off), vec3(gamma))); }
// tex2Dlod:
vec4 tex2Dlod_linearize_gamma(const sampler2D tex, const vec4 tex_coords, const vec3 gamma)
{ return decode_gamma_input(vec4(tex2Dlod(tex, tex_coords), vec3(gamma))); }
vec4 tex2Dlod_linearize_gamma(const sampler2D tex, const vec4 tex_coords, const int texel_off, const vec3 gamma)
{ return decode_gamma_input(vec4(tex2Dlod(tex, tex_coords, texel_off), vec3(gamma))); }
#endif // GAMMA_MANAGEMENT_H

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#ifndef GEOMETRY_FUNCTIONS_H
#define GEOMETRY_FUNCTIONS_H
///////////////////////////// GPL LICENSE NOTICE /////////////////////////////
// crt-royale: A full-featured CRT shader, with cheese.
// Copyright (C) 2014 TroggleMonkey <trogglemonkey@gmx.com>
//
// 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 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., 59 Temple
// Place, Suite 330, Boston, MA 02111-1307 USA
////////////////////////////////// INCLUDES //////////////////////////////////
#include "../user-settings.h"
#include "derived-settings-and-constants.h"
#include "bind-shader-params.h"
//////////////////////////// MACROS AND CONSTANTS ////////////////////////////
// Curvature-related constants:
#define MAX_POINT_CLOUD_SIZE 9
///////////////////////////// CURVATURE FUNCTIONS /////////////////////////////
vec2 quadratic_solve(const float a, const float b_over_2, const float c)
{
// Requires: 1.) a, b, and c are quadratic formula coefficients
// 2.) b_over_2 = b/2.0 (simplifies terms to factor 2 out)
// 3.) b_over_2 must be guaranteed < 0.0 (avoids a branch)
// Returns: Returns vec2(first_solution, discriminant), so the caller
// can choose how to handle the "no intersection" case. The
// Kahan or Citardauq formula is used for numerical robustness.
const float discriminant = b_over_2*b_over_2 - a*c;
const float solution0 = c/(-b_over_2 + sqrt(discriminant));
return vec2(solution0, discriminant);
}
vec2 intersect_sphere(const vec3 view_vec, const vec3 eye_pos_vec)
{
// Requires: 1.) view_vec and eye_pos_vec are 3D vectors in the sphere's
// local coordinate frame (eye_pos_vec is a position, i.e.
// a vector from the origin to the eye/camera)
// 2.) geom_radius is a global containing the sphere's radius
// Returns: Cast a ray of direction view_vec from eye_pos_vec at a
// sphere of radius geom_radius, and return the distance to
// the first intersection in units of length(view_vec).
// http://wiki.cgsociety.org/index.php/Ray_Sphere_Intersection
// Quadratic formula coefficients (b_over_2 is guaranteed negative):
const float a = dot(view_vec, view_vec);
const float b_over_2 = dot(view_vec, eye_pos_vec); // * 2.0 factored out
const float c = dot(eye_pos_vec, eye_pos_vec) - geom_radius*geom_radius;
return quadratic_solve(a, b_over_2, c);
}
vec2 intersect_cylinder(const vec3 view_vec, const vec3 eye_pos_vec)
{
// Requires: 1.) view_vec and eye_pos_vec are 3D vectors in the sphere's
// local coordinate frame (eye_pos_vec is a position, i.e.
// a vector from the origin to the eye/camera)
// 2.) geom_radius is a global containing the cylinder's radius
// Returns: Cast a ray of direction view_vec from eye_pos_vec at a
// cylinder of radius geom_radius, and return the distance to
// the first intersection in units of length(view_vec). The
// derivation of the coefficients is in Christer Ericson's
// Real-Time Collision Detection, p. 195-196, and this version
// uses LaGrange's identity to reduce operations.
// Arbitrary "cylinder top" reference point for an infinite cylinder:
const vec3 cylinder_top_vec = vec3(0.0, geom_radius, 0.0);
const vec3 cylinder_axis_vec = vec3(0.0, 1.0, 0.0);//vec3(0.0, 2.0*geom_radius, 0.0);
const vec3 top_to_eye_vec = eye_pos_vec - cylinder_top_vec;
const vec3 axis_x_view = cross(cylinder_axis_vec, view_vec);
const vec3 axis_x_top_to_eye = cross(cylinder_axis_vec, top_to_eye_vec);
// Quadratic formula coefficients (b_over_2 is guaranteed negative):
const float a = dot(axis_x_view, axis_x_view);
const float b_over_2 = dot(axis_x_top_to_eye, axis_x_view);
const float c = dot(axis_x_top_to_eye, axis_x_top_to_eye) -
geom_radius*geom_radius;//*dot(cylinder_axis_vec, cylinder_axis_vec);
return quadratic_solve(a, b_over_2, c);
}
vec2 cylinder_xyz_to_uv(const vec3 intersection_pos_local,
const vec2 geom_aspect)
{
// Requires: An xyz intersection position on a cylinder.
// Returns: video_uv coords mapped to range [-0.5, 0.5]
// Mapping: Define square_uv.x to be the signed arc length in xz-space,
// and define square_uv.y = -intersection_pos_local.y (+v = -y).
// Start with a numerically robust arc length calculation.
const float angle_from_image_center = atan(intersection_pos_local.z,
intersection_pos_local.x);
const float signed_arc_len = angle_from_image_center * geom_radius;
// Get a uv-mapping where [-0.5, 0.5] maps to a "square" area, then divide
// by the aspect ratio to stretch the mapping appropriately:
const vec2 square_uv = vec2(signed_arc_len, -intersection_pos_local.y);
const vec2 video_uv = square_uv / geom_aspect;
return video_uv;
}
vec3 cylinder_uv_to_xyz(const vec2 video_uv, const vec2 geom_aspect)
{
// Requires: video_uv coords mapped to range [-0.5, 0.5]
// Returns: An xyz intersection position on a cylinder. This is the
// inverse of cylinder_xyz_to_uv().
// Expand video_uv by the aspect ratio to get proportionate x/y lengths,
// then calculate an xyz position for the cylindrical mapping above.
const vec2 square_uv = video_uv * geom_aspect;
const float arc_len = square_uv.x;
const float angle_from_image_center = arc_len / geom_radius;
const float x_pos = sin(angle_from_image_center) * geom_radius;
const float z_pos = cos(angle_from_image_center) * geom_radius;
// Or: z = sqrt(geom_radius**2 - x**2)
// Or: z = geom_radius/sqrt(1.0 + tan(angle)**2), x = z * tan(angle)
const vec3 intersection_pos_local = vec3(x_pos, -square_uv.y, z_pos);
return intersection_pos_local;
}
vec2 sphere_xyz_to_uv(const vec3 intersection_pos_local,
const vec2 geom_aspect)
{
// Requires: An xyz intersection position on a sphere.
// Returns: video_uv coords mapped to range [-0.5, 0.5]
// Mapping: First define square_uv.x/square_uv.y ==
// intersection_pos_local.x/intersection_pos_local.y. Then,
// length(square_uv) is the arc length from the image center
// at (0.0, 0.0, geom_radius) along the tangent great circle.
// Credit for this mapping goes to cgwg: I never managed to
// understand his code, but he told me his mapping was based on
// great circle distances when I asked him about it, which
// informed this very similar (almost identical) mapping.
// Start with a numerically robust arc length calculation between the ray-
// sphere intersection point and the image center using a method posted by
// Roger Stafford on comp.soft-sys.matlab:
// https://groups.google.com/d/msg/comp.soft-sys.matlab/zNbUui3bjcA/c0HV_bHSx9cJ
const vec3 image_center_pos_local = vec3(0.0, 0.0, geom_radius);
const float cp_len =
length(cross(intersection_pos_local, image_center_pos_local));
const float dp = dot(intersection_pos_local, image_center_pos_local);
const float angle_from_image_center = atan(dp, cp_len);
const float arc_len = angle_from_image_center * geom_radius;
// Get a uv-mapping where [-0.5, 0.5] maps to a "square" area, then divide
// by the aspect ratio to stretch the mapping appropriately:
const vec2 square_uv_unit = normalize(vec2(intersection_pos_local.x,
-intersection_pos_local.y));
const vec2 square_uv = arc_len * square_uv_unit;
const vec2 video_uv = square_uv / geom_aspect;
return video_uv;
}
vec3 sphere_uv_to_xyz(const vec2 video_uv, const vec2 geom_aspect)
{
// Requires: video_uv coords mapped to range [-0.5, 0.5]
// Returns: An xyz intersection position on a sphere. This is the
// inverse of sphere_xyz_to_uv().
// Expand video_uv by the aspect ratio to get proportionate x/y lengths,
// then calculate an xyz position for the spherical mapping above.
const vec2 square_uv = video_uv * geom_aspect;
// Using length or sqrt here butchers the framerate on my 8800GTS if
// this function is called too many times, and so does taking the max
// component of square_uv/square_uv_unit (program length threshold?).
//float arc_len = length(square_uv);
const vec2 square_uv_unit = normalize(square_uv);
const float arc_len = square_uv.y/square_uv_unit.y;
const float angle_from_image_center = arc_len / geom_radius;
const float xy_dist_from_sphere_center =
sin(angle_from_image_center) * geom_radius;
//vec2 xy_pos = xy_dist_from_sphere_center * (square_uv/FIX_ZERO(arc_len));
const vec2 xy_pos = xy_dist_from_sphere_center * square_uv_unit;
const float z_pos = cos(angle_from_image_center) * geom_radius;
const vec3 intersection_pos_local = vec3(xy_pos.x, -xy_pos.y, z_pos);
return intersection_pos_local;
}
vec2 sphere_alt_xyz_to_uv(const vec3 intersection_pos_local,
const vec2 geom_aspect)
{
// Requires: An xyz intersection position on a cylinder.
// Returns: video_uv coords mapped to range [-0.5, 0.5]
// Mapping: Define square_uv.x to be the signed arc length in xz-space,
// and define square_uv.y == signed arc length in yz-space.
// See cylinder_xyz_to_uv() for implementation details (very similar).
const vec2 angle_from_image_center = atan((intersection_pos_local.zz),
vec2(intersection_pos_local.x, -intersection_pos_local.y));
const vec2 signed_arc_len = angle_from_image_center * geom_radius;
const vec2 video_uv = signed_arc_len / geom_aspect;
return video_uv;
}
vec3 sphere_alt_uv_to_xyz(const vec2 video_uv, const vec2 geom_aspect)
{
// Requires: video_uv coords mapped to range [-0.5, 0.5]
// Returns: An xyz intersection position on a sphere. This is the
// inverse of sphere_alt_xyz_to_uv().
// See cylinder_uv_to_xyz() for implementation details (very similar).
const vec2 square_uv = video_uv * geom_aspect;
const vec2 arc_len = square_uv;
const vec2 angle_from_image_center = arc_len / geom_radius;
const vec2 xy_pos = sin(angle_from_image_center) * geom_radius;
const float z_pos = sqrt(geom_radius*geom_radius - dot(xy_pos, xy_pos));
return vec3(xy_pos.x, -xy_pos.y, z_pos);
}
inline vec2 intersect(const vec3 view_vec_local, const vec3 eye_pos_local,
const float geom_mode)
{
return geom_mode < 2.5 ? intersect_sphere(view_vec_local, eye_pos_local) :
intersect_cylinder(view_vec_local, eye_pos_local);
}
inline vec2 xyz_to_uv(const vec3 intersection_pos_local,
const vec2 geom_aspect, const float geom_mode)
{
return geom_mode < 1.5 ?
sphere_xyz_to_uv(intersection_pos_local, geom_aspect) :
geom_mode < 2.5 ?
sphere_alt_xyz_to_uv(intersection_pos_local, geom_aspect) :
cylinder_xyz_to_uv(intersection_pos_local, geom_aspect);
}
inline vec3 uv_to_xyz(const vec2 uv, const vec2 geom_aspect,
const float geom_mode)
{
return geom_mode < 1.5 ? sphere_uv_to_xyz(uv, geom_aspect) :
geom_mode < 2.5 ? sphere_alt_uv_to_xyz(uv, geom_aspect) :
cylinder_uv_to_xyz(uv, geom_aspect);
}
vec2 view_vec_to_uv(const vec3 view_vec_local, const vec3 eye_pos_local,
const vec2 geom_aspect, const float geom_mode, out vec3 intersection_pos)
{
// Get the intersection point on the primitive, given an eye position
// and view vector already in its local coordinate frame:
const vec2 intersect_dist_and_discriminant = intersect(view_vec_local,
eye_pos_local, geom_mode);
const vec3 intersection_pos_local = eye_pos_local +
view_vec_local * intersect_dist_and_discriminant.x;
// Save the intersection position to an output parameter:
intersection_pos = intersection_pos_local;
// Transform into uv coords, but give out-of-range coords if the
// view ray doesn't intersect the primitive in the first place:
return intersect_dist_and_discriminant.y > 0.005 ?
xyz_to_uv(intersection_pos_local, geom_aspect, geom_mode) : vec2(1.0);
}
vec3 get_ideal_global_eye_pos_for_points(vec3 eye_pos,
const vec2 geom_aspect, const vec3 global_coords[MAX_POINT_CLOUD_SIZE],
const int num_points)
{
// Requires: Parameters:
// 1.) Starting eye_pos is a global 3D position at which the
// camera contains all points in global_coords[] in its FOV
// 2.) geom_aspect = get_aspect_vector(
// IN.output_size.x / IN.output_size.y);
// 3.) global_coords is a point cloud containing global xyz
// coords of extreme points on the simulated CRT screen.
// Globals:
// 1.) geom_view_dist must be > 0.0. It controls the "near
// plane" used to interpret flat_video_uv as a view
// vector, which controls the field of view (FOV).
// Eyespace coordinate frame: +x = right, +y = up, +z = back
// Returns: Return an eye position at which the point cloud spans as
// much of the screen as possible (given the FOV controlled by
// geom_view_dist) without being cropped or sheared.
// Algorithm:
// 1.) Move the eye laterally to a point which attempts to maximize the
// the amount we can move forward without clipping the CRT screen.
// 2.) Move forward by as much as possible without clipping the CRT.
// Get the allowed movement range by solving for the eye_pos offsets
// that result in each point being projected to a screen edge/corner in
// pseudo-normalized device coords (where xy ranges from [-0.5, 0.5]
// and z = eyespace z):
// pndc_coord = vec3(vec2(eyespace_xyz.x, -eyespace_xyz.y)*
// geom_view_dist / (geom_aspect * -eyespace_xyz.z), eyespace_xyz.z);
// Notes:
// The field of view is controlled by geom_view_dist's magnitude relative to
// the view vector's x and y components:
// view_vec.xy ranges from [-0.5, 0.5] * geom_aspect
// view_vec.z = -geom_view_dist
// But for the purposes of perspective divide, it should be considered:
// view_vec.xy ranges from [-0.5, 0.5] * geom_aspect / geom_view_dist
// view_vec.z = -1.0
const int max_centering_iters = 1; // Keep for easy testing.
for(int iter = 0; iter < max_centering_iters; iter++)
{
// 0.) Get the eyespace coordinates of our point cloud:
vec3 eyespace_coords[MAX_POINT_CLOUD_SIZE];
for(int i = 0; i < num_points; i++)
{
eyespace_coords[i] = global_coords[i] - eye_pos;
}
// 1a.)For each point, find out how far we can move eye_pos in each
// lateral direction without the point clipping the frustum.
// Eyespace +y = up, screenspace +y = down, so flip y after
// applying the eyespace offset (on the way to "clip space").
// Solve for two offsets per point based on:
// (eyespace_xyz.xy - offset_dr) * vec2(1.0, -1.0) *
// geom_view_dist / (geom_aspect * -eyespace_xyz.z) = vec2(-0.5)
// (eyespace_xyz.xy - offset_dr) * vec2(1.0, -1.0) *
// geom_view_dist / (geom_aspect * -eyespace_xyz.z) = vec2(0.5)
// offset_ul and offset_dr represent the farthest we can move the
// eye_pos up-left and down-right. Save the min of all offset_dr's
// and the max of all offset_ul's (since it's negative).
float abs_radius = abs(geom_radius); // In case anyone gets ideas. ;)
vec2 offset_dr_min = vec2(10.0 * abs_radius, 10.0 * abs_radius);
vec2 offset_ul_max = vec2(-10.0 * abs_radius, -10.0 * abs_radius);
for(int i = 0; i < num_points; i++)
{
const vec2 flipy = vec2(1.0, -1.0);
vec3 eyespace_xyz = eyespace_coords[i];
vec2 offset_dr = eyespace_xyz.xy - vec2(-0.5) *
(geom_aspect * -eyespace_xyz.z) / (geom_view_dist * flipy);
vec2 offset_ul = eyespace_xyz.xy - vec2(0.5) *
(geom_aspect * -eyespace_xyz.z) / (geom_view_dist * flipy);
offset_dr_min = min(offset_dr_min, offset_dr);
offset_ul_max = max(offset_ul_max, offset_ul);
}
// 1b.)Update eye_pos: Adding the average of offset_ul_max and
// offset_dr_min gives it equal leeway on the top vs. bottom
// and left vs. right. Recalculate eyespace_coords accordingly.
vec2 center_offset = 0.5 * (offset_ul_max + offset_dr_min);
eye_pos.xy += center_offset;
for(int i = 0; i < num_points; i++)
{
eyespace_coords[i] = global_coords[i] - eye_pos;
}
// 2a.)For each point, find out how far we can move eye_pos forward
// without the point clipping the frustum. Flip the y
// direction in advance (matters for a later step, not here).
// Solve for four offsets per point based on:
// eyespace_xyz_flipy.x * geom_view_dist /
// (geom_aspect.x * (offset_z - eyespace_xyz_flipy.z)) =-0.5
// eyespace_xyz_flipy.y * geom_view_dist /
// (geom_aspect.y * (offset_z - eyespace_xyz_flipy.z)) =-0.5
// eyespace_xyz_flipy.x * geom_view_dist /
// (geom_aspect.x * (offset_z - eyespace_xyz_flipy.z)) = 0.5
// eyespace_xyz_flipy.y * geom_view_dist /
// (geom_aspect.y * (offset_z - eyespace_xyz_flipy.z)) = 0.5
// We'll vectorize the actual computation. Take the maximum of
// these four for a single offset, and continue taking the max
// for every point (use max because offset.z is negative).
float offset_z_max = -10.0 * geom_radius * geom_view_dist;
for(int i = 0; i < num_points; i++)
{
vec3 eyespace_xyz_flipy = eyespace_coords[i] *
vec3(1.0, -1.0, 1.0);
vec4 offset_zzzz = eyespace_xyz_flipy.zzzz +
(eyespace_xyz_flipy.xyxy * geom_view_dist) /
(vec4(-0.5, -0.5, 0.5, 0.5) * vec4(geom_aspect, geom_aspect));
// Ignore offsets that push positive x/y values to opposite
// boundaries, and vice versa, and don't let the camera move
// past a point in the dead center of the screen:
offset_z_max = (eyespace_xyz_flipy.x < 0.0) ?
max(offset_z_max, offset_zzzz.x) : offset_z_max;
offset_z_max = (eyespace_xyz_flipy.y < 0.0) ?
max(offset_z_max, offset_zzzz.y) : offset_z_max;
offset_z_max = (eyespace_xyz_flipy.x > 0.0) ?
max(offset_z_max, offset_zzzz.z) : offset_z_max;
offset_z_max = (eyespace_xyz_flipy.y > 0.0) ?
max(offset_z_max, offset_zzzz.w) : offset_z_max;
offset_z_max = max(offset_z_max, eyespace_xyz_flipy.z);
}
// 2b.)Update eye_pos: Add the maximum (smallest negative) z offset.
eye_pos.z += offset_z_max;
}
return eye_pos;
}
vec3 get_ideal_global_eye_pos(const vec3x3 local_to_global,
const vec2 geom_aspect, const float geom_mode)
{
// Start with an initial eye_pos that includes the entire primitive
// (sphere or cylinder) in its field-of-view:
const vec3 high_view = vec3(0.0, geom_aspect.y, -geom_view_dist);
const vec3 low_view = high_view * vec3(1.0, -1.0, 1.0);
const float len_sq = dot(high_view, high_view);
const float fov = abs(acos(dot(high_view, low_view)/len_sq));
// Trigonometry/similar triangles say distance = geom_radius/sin(fov/2):
const float eye_z_spherical = geom_radius/sin(fov*0.5);
const vec3 eye_pos = geom_mode < 2.5 ?
vec3(0.0, 0.0, eye_z_spherical) :
vec3(0.0, 0.0, max(geom_view_dist, eye_z_spherical));
// Get global xyz coords of extreme sample points on the simulated CRT
// screen. Start with the center, edge centers, and corners of the
// video image. We can't ignore backfacing points: They're occluded
// by closer points on the primitive, but they may NOT be occluded by
// the convex hull of the remaining samples (i.e. the remaining convex
// hull might not envelope points that do occlude a back-facing point.)
const int num_points = MAX_POINT_CLOUD_SIZE;
vec3 global_coords[MAX_POINT_CLOUD_SIZE];
global_coords[0] = mul(local_to_global, uv_to_xyz(vec2(0.0, 0.0), geom_aspect, geom_mode));
global_coords[1] = mul(local_to_global, uv_to_xyz(vec2(0.0, -0.5), geom_aspect, geom_mode));
global_coords[2] = mul(local_to_global, uv_to_xyz(vec2(0.0, 0.5), geom_aspect, geom_mode));
global_coords[3] = mul(local_to_global, uv_to_xyz(vec2(-0.5, 0.0), geom_aspect, geom_mode));
global_coords[4] = mul(local_to_global, uv_to_xyz(vec2(0.5, 0.0), geom_aspect, geom_mode));
global_coords[5] = mul(local_to_global, uv_to_xyz(vec2(-0.5, -0.5), geom_aspect, geom_mode));
global_coords[6] = mul(local_to_global, uv_to_xyz(vec2(0.5, -0.5), geom_aspect, geom_mode));
global_coords[7] = mul(local_to_global, uv_to_xyz(vec2(-0.5, 0.5), geom_aspect, geom_mode));
global_coords[8] = mul(local_to_global, uv_to_xyz(vec2(0.5, 0.5), geom_aspect, geom_mode));
// Adding more inner image points could help in extreme cases, but too many
// points will kille the framerate. For safety, default to the initial
// eye_pos if any z coords are negative:
float num_negative_z_coords = 0.0;
for(int i = 0; i < num_points; i++)
{
num_negative_z_coords += float(global_coords[0].z < 0.0);
}
// Outsource the optimized eye_pos calculation:
return num_negative_z_coords > 0.5 ? eye_pos :
get_ideal_global_eye_pos_for_points(eye_pos, geom_aspect,
global_coords, num_points);
}
mat3x3 get_pixel_to_object_matrix(const mat3x3 global_to_local,
const vec3 eye_pos_local, const vec3 view_vec_global,
const vec3 intersection_pos_local, const vec3 normal,
const vec2 output_size_inv)
{
// Requires: See get_curved_video_uv_coords_and_tangent_matrix for
// descriptions of each parameter.
// Returns: Return a transformation matrix from 2D pixel-space vectors
// (where (+1.0, +1.0) is a vector to one pixel down-right,
// i.e. same directionality as uv texels) to 3D object-space
// vectors in the CRT's local coordinate frame (right-handed)
// ***which are tangent to the CRT surface at the intersection
// position.*** (Basically, we want to convert pixel-space
// vectors to 3D vectors along the CRT's surface, for later
// conversion to uv vectors.)
// Shorthand inputs:
const vec3 pos = intersection_pos_local;
const vec3 eye_pos = eye_pos_local;
// Get a piecewise-linear matrix transforming from "pixelspace" offset
// vectors (1.0 = one pixel) to object space vectors in the tangent
// plane (faster than finding 3 view-object intersections).
// 1.) Get the local view vecs for the pixels to the right and down:
const vec3 view_vec_right_global = view_vec_global +
vec3(output_size_inv.x, 0.0, 0.0);
const vec3 view_vec_down_global = view_vec_global +
vec3(0.0, -output_size_inv.y, 0.0);
const vec3 view_vec_right_local =
(view_vec_right_global * global_to_local);
const vec3 view_vec_down_local =
(view_vec_down_global * global_to_local);
// 2.) Using the true intersection point, intersect the neighboring
// view vectors with the tangent plane:
const vec3 intersection_vec_dot_normal = dot(pos - eye_pos, normal);
const vec3 right_pos = eye_pos + (intersection_vec_dot_normal /
dot(view_vec_right_local, normal))*view_vec_right_local;
const vec3 down_pos = eye_pos + (intersection_vec_dot_normal /
dot(view_vec_down_local, normal))*view_vec_down_local;
// 3.) Subtract the original intersection pos from its neighbors; the
// resulting vectors are object-space vectors tangent to the plane.
// These vectors are the object-space transformations of (1.0, 0.0)
// and (0.0, 1.0) pixel offsets, so they form the first two basis
// vectors of a pixelspace to object space transformation. This
// transformation is 2D to 3D, so use (0, 0, 0) for the third vector.
const vec3 object_right_vec = right_pos - pos;
const vec3 object_down_vec = down_pos - pos;
const vec3x3 pixel_to_object = vec3x3(
object_right_vec.x, object_down_vec.x, 0.0,
object_right_vec.y, object_down_vec.y, 0.0,
object_right_vec.z, object_down_vec.z, 0.0);
return pixel_to_object;
}
mat3x3 get_object_to_tangent_matrix(const vec3 intersection_pos_local,
const vec3 normal, const vec2 geom_aspect, const float geom_mode)
{
// Requires: See get_curved_video_uv_coords_and_tangent_matrix for
// descriptions of each parameter.
// Returns: Return a transformation matrix from 3D object-space vectors
// in the CRT's local coordinate frame (right-handed, +y = up)
// to 2D video_uv vectors (+v = down).
// Description:
// The TBN matrix formed by the [tangent, bitangent, normal] basis
// vectors transforms ordinary vectors from tangent->object space.
// The cotangent matrix formed by the [cotangent, cobitangent, normal]
// basis vectors transforms normal vectors (covectors) from
// tangent->object space. It's the inverse-transpose of the TBN matrix.
// We want the inverse of the TBN matrix (transpose of the cotangent
// matrix), which transforms ordinary vectors from object->tangent space.
// Start by calculating the relevant basis vectors in accordance with
// Christian Schüler's blog post "Followup: Normal Mapping Without
// Precomputed Tangents": http://www.thetenthplanet.de/archives/1180
// With our particular uv mapping, the scale of the u and v directions
// is determined entirely by the aspect ratio for cylindrical and ordinary
// spherical mappings, and so tangent and bitangent lengths are also
// determined by it (the alternate mapping is more complex). Therefore, we
// must ensure appropriate cotangent and cobitangent lengths as well.
// Base these off the uv<=>xyz mappings for each primitive.
const vec3 pos = intersection_pos_local;
const vec3 x_vec = vec3(1.0, 0.0, 0.0);
const vec3 y_vec = vec3(0.0, 1.0, 0.0);
// The tangent and bitangent vectors correspond with increasing u and v,
// respectively. Mathematically we'd base the cotangent/cobitangent on
// those, but we'll compute the cotangent/cobitangent directly when we can.
vec3 cotangent_unscaled, cobitangent_unscaled;
// geom_mode should be constant-folded without RUNTIME_GEOMETRY_MODE.
if(geom_mode < 1.5)
{
// Sphere:
// tangent = normalize(cross(normal, cross(x_vec, pos))) * geom_aspect.x
// bitangent = normalize(cross(cross(y_vec, pos), normal)) * geom_aspect.y
// inv_determinant = 1.0/length(cross(bitangent, tangent))
// cotangent = cross(normal, bitangent) * inv_determinant
// == normalize(cross(y_vec, pos)) * geom_aspect.y * inv_determinant
// cobitangent = cross(tangent, normal) * inv_determinant
// == normalize(cross(x_vec, pos)) * geom_aspect.x * inv_determinant
// Simplified (scale by inv_determinant below):
cotangent_unscaled = normalize(cross(y_vec, pos)) * geom_aspect.y;
cobitangent_unscaled = normalize(cross(x_vec, pos)) * geom_aspect.x;
}
else if(geom_mode < 2.5)
{
// Sphere, alternate mapping:
// This mapping works a bit like the cylindrical mapping in two
// directions, which makes the lengths and directions more complex.
// Unfortunately, I can't find much of a shortcut:
const vec3 tangent = normalize(
cross(y_vec, vec3(pos.x, 0.0, pos.z))) * geom_aspect.x;
const vec3 bitangent = normalize(
cross(x_vec, vec3(0.0, pos.yz))) * geom_aspect.y;
cotangent_unscaled = cross(normal, bitangent);
cobitangent_unscaled = cross(tangent, normal);
}
else
{
// Cylinder:
// tangent = normalize(cross(y_vec, normal)) * geom_aspect.x;
// bitangent = vec3(0.0, -geom_aspect.y, 0.0);
// inv_determinant = 1.0/length(cross(bitangent, tangent))
// cotangent = cross(normal, bitangent) * inv_determinant
// == normalize(cross(y_vec, pos)) * geom_aspect.y * inv_determinant
// cobitangent = cross(tangent, normal) * inv_determinant
// == vec3(0.0, -geom_aspect.x, 0.0) * inv_determinant
cotangent_unscaled = cross(y_vec, normal) * geom_aspect.y;
cobitangent_unscaled = vec3(0.0, -geom_aspect.x, 0.0);
}
const vec3 computed_normal =
cross(cobitangent_unscaled, cotangent_unscaled);
const float inv_determinant = rsqrt(dot(computed_normal, computed_normal));
const vec3 cotangent = cotangent_unscaled * inv_determinant;
const vec3 cobitangent = cobitangent_unscaled * inv_determinant;
// The [cotangent, cobitangent, normal] column vecs form the cotangent
// frame, i.e. the inverse-transpose TBN matrix. Get its transpose:
const mat3x3 object_to_tangent = mat3x3(cotangent, cobitangent, normal);
return object_to_tangent;
}
vec2 get_curved_video_uv_coords_and_tangent_matrix(
const vec2 flat_video_uv, const vec3 eye_pos_local,
const vec2 output_size_inv, const vec2 geom_aspect,
const float geom_mode, const mat3x3 global_to_local,
out mat2x2 pixel_to_tangent_video_uv)
{
// Requires: Parameters:
// 1.) flat_video_uv coords are in range [0.0, 1.0], where
// (0.0, 0.0) is the top-left corner of the screen and
// (1.0, 1.0) is the bottom-right corner.
// 2.) eye_pos_local is the 3D camera position in the simulated
// CRT's local coordinate frame. For best results, it must
// be computed based on the same geom_view_dist used here.
// 3.) output_size_inv = vec2(1.0)/IN.output_size
// 4.) geom_aspect = get_aspect_vector(
// IN.output_size.x / IN.output_size.y);
// 5.) geom_mode is a static or runtime mode setting:
// 0 = off, 1 = sphere, 2 = sphere alt., 3 = cylinder
// 6.) global_to_local is a 3x3 matrix transforming (ordinary)
// worldspace vectors to the CRT's local coordinate frame
// Globals:
// 1.) geom_view_dist must be > 0.0. It controls the "near
// plane" used to interpret flat_video_uv as a view
// vector, which controls the field of view (FOV).
// Returns: Return final uv coords in [0.0, 1.0], and return a pixel-
// space to video_uv tangent-space matrix in the out parameter.
// (This matrix assumes pixel-space +y = down, like +v = down.)
// We'll transform flat_video_uv into a view vector, project
// the view vector from the camera/eye, intersect with a sphere
// or cylinder representing the simulated CRT, and convert the
// intersection position into final uv coords and a local
// transformation matrix.
// First get the 3D view vector (geom_aspect and geom_view_dist are globals):
// 1.) Center uv around (0.0, 0.0) and make (-0.5, -0.5) and (0.5, 0.5)
// correspond to the top-left/bottom-right output screen corners.
// 2.) Multiply by geom_aspect to preemptively "undo" Retroarch's screen-
// space 2D aspect correction. We'll reapply it in uv-space.
// 3.) (x, y) = (u, -v), because +v is down in 2D screenspace, but +y
// is up in 3D worldspace (enforce a right-handed system).
// 4.) The view vector z controls the "near plane" distance and FOV.
// For the effect of "looking through a window" at a CRT, it should be
// set equal to the user's distance from their physical screen, in
// units of the viewport's physical diagonal size.
const vec2 view_uv = (flat_video_uv - vec2(0.5)) * geom_aspect;
const vec3 view_vec_global =
vec3(view_uv.x, -view_uv.y, -geom_view_dist);
// Transform the view vector into the CRT's local coordinate frame, convert
// to video_uv coords, and get the local 3D intersection position:
const vec3 view_vec_local = mul(global_to_local, view_vec_global);
vec3 pos;
const vec2 centered_uv = view_vec_to_uv(
view_vec_local, eye_pos_local, geom_aspect, geom_mode, pos);
const vec2 video_uv = centered_uv + vec2(0.5);
// Get a pixel-to-tangent-video-uv matrix. The caller could deal with
// all but one of these cases, but that would be more complicated.
#ifdef DRIVERS_ALLOW_DERIVATIVES
// Derivatives obtain a matrix very fast, but the direction of pixel-
// space +y seems to depend on the pass. Enforce the correct direction
// on a best-effort basis (but it shouldn't matter for antialiasing).
const vec2 duv_dx = ddx(video_uv);
const vec2 duv_dy = ddy(video_uv);
#ifdef LAST_PASS
pixel_to_tangent_video_uv = vec2x2(
duv_dx.x, duv_dy.x,
-duv_dx.y, -duv_dy.y);
#else
pixel_to_tangent_video_uv = vec2x2(
duv_dx.x, duv_dy.x,
duv_dx.y, duv_dy.y);
#endif
#else
// Manually define a transformation matrix. We'll assume pixel-space
// +y = down, just like +v = down.
if(geom_force_correct_tangent_matrix)
{
// Get the surface normal based on the local intersection position:
const vec3 normal_base = geom_mode < 2.5 ? pos :
vec3(pos.x, 0.0, pos.z);
const vec3 normal = normalize(normal_base);
// Get pixel-to-object and object-to-tangent matrices and combine
// them into a 2x2 pixel-to-tangent matrix for video_uv offsets:
const vec3x3 pixel_to_object = get_pixel_to_object_matrix(
global_to_local, eye_pos_local, view_vec_global, pos, normal,
output_size_inv);
const vec3x3 object_to_tangent = get_object_to_tangent_matrix(
pos, normal, geom_aspect, geom_mode);
const vec3x3 pixel_to_tangent3x3 =
mul(object_to_tangent, pixel_to_object);
pixel_to_tangent_video_uv = vec2x2(
pixel_to_tangent3x3._m00_m01_m10_m11);
}
else
{
// Ignore curvature, and just consider flat scaling. The
// difference is only apparent with strong curvature:
pixel_to_tangent_video_uv = vec2x2(
output_size_inv.x, 0.0, 0.0, output_size_inv.y);
}
#endif
return video_uv;
}
float get_border_dim_factor(const vec2 video_uv, const vec2 geom_aspect)
{
// COPYRIGHT NOTE FOR THIS FUNCTION:
// Copyright (C) 2010-2012 cgwg, 2014 TroggleMonkey
// This function uses an algorithm first coded in several of cgwg's GPL-
// licensed lines in crt-geom-curved.cg and its ancestors. The line
// between algorithm and code is nearly indistinguishable here, so it's
// unclear whether I could even release this project under a non-GPL
// license with this function included.
// Calculate border_dim_factor from the proximity to uv-space image
// borders; geom_aspect/border_size/border/darkness/border_compress are globals:
const vec2 edge_dists = min(video_uv, vec2(1.0) - video_uv) *
geom_aspect;
const vec2 border_penetration =
max(vec2(border_size) - edge_dists, vec2(0.0));
const float penetration_ratio = length(border_penetration)/border_size;
const float border_escape_ratio = max(1.0 - penetration_ratio, 0.0);
const float border_dim_factor =
pow(border_escape_ratio, border_darkness) * max(1.0, border_compress);
return min(border_dim_factor, 1.0);
}
#endif // GEOMETRY_FUNCTIONS_H

23
crt/shaders/crt-royale/src/geometry-functions.h
View file

@ -659,4 +659,27 @@ vec2 get_curved_video_uv_coords_and_tangent_matrix(
return video_uv; return video_uv;
} }
float get_border_dim_factor(const vec2 video_uv, const vec2 geom_aspect)
{
// COPYRIGHT NOTE FOR THIS FUNCTION:
// Copyright (C) 2010-2012 cgwg, 2014 TroggleMonkey
// This function uses an algorithm first coded in several of cgwg's GPL-
// licensed lines in crt-geom-curved.cg and its ancestors. The line
// between algorithm and code is nearly indistinguishable here, so it's
// unclear whether I could even release this project under a non-GPL
// license with this function included.
// Calculate border_dim_factor from the proximity to uv-space image
// borders; geom_aspect/border_size/border/darkness/border_compress are globals:
const vec2 edge_dists = min(video_uv, vec2(1.0) - video_uv) *
geom_aspect;
const vec2 border_penetration =
max(vec2(border_size) - edge_dists, vec2(0.0));
const float penetration_ratio = length(border_penetration)/border_size;
const float border_escape_ratio = max(1.0 - penetration_ratio, 0.0);
const float border_dim_factor =
pow(border_escape_ratio, border_darkness) * max(1.0, border_compress);
return min(border_dim_factor, 1.0);
}
#endif // GEOMETRY_FUNCTIONS_H #endif // GEOMETRY_FUNCTIONS_H

11
crt/shaders/crt-royale/src/includes.h
View file

@ -1,11 +0,0 @@
#define INCLUDES
#include "../user-settings.h"
#include "derived-settings-and-constants.h"
#include "special-functions.h" //#include "../../../../include/special-functions.h" <-move includes into crt-royale's src directory until it's actually working
#include "bind-shader-params.h"
#include "gamma-management.h" //#include "../../../../include/gamma-management.h" <-move includes into crt-royale's src directory until it's actually working
#include "blur-functions.h" //#include "../../../../include/blur-functions.h" <-move includes into crt-royale's src directory until it's actually working
#include "scanline-functions.h"
#include "bloom-functions.h"
//#include "phosphor-mask-resizing.h"

678
crt/shaders/crt-royale/src/phosphor-mask-resizing-old.h
View file

@ -1,678 +0,0 @@
#ifndef PHOSPHOR_MASK_RESIZING_H
#define PHOSPHOR_MASK_RESIZING_H
///////////////////////////// GPL LICENSE NOTICE /////////////////////////////
// crt-royale: A full-featured CRT shader, with cheese.
// Copyright (C) 2014 TroggleMonkey <trogglemonkey@gmx.com>
//
// 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 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., 59 Temple
// Place, Suite 330, Boston, MA 02111-1307 USA
////////////////////////////////// INCLUDES //////////////////////////////////
//#include "../user-settings.h"
//#include "derived-settings-and-constants.h"
#include "includes.h"
///////////////////////////// CODEPATH SELECTION /////////////////////////////
// Choose a looping strategy based on what's allowed:
// Dynamic loops not allowed: Use a flat static loop.
// Dynamic loops accomodated: Coarsely branch around static loops.
// Dynamic loops assumed allowed: Use a flat dynamic loop.
#ifndef DRIVERS_ALLOW_DYNAMIC_BRANCHES
#ifdef ACCOMODATE_POSSIBLE_DYNAMIC_LOOPS
#define BREAK_LOOPS_INTO_PIECES
#else
#define USE_SINGLE_STATIC_LOOP
#endif
#endif // No else needed: Dynamic loops assumed.
////////////////////////////////// CONSTANTS /////////////////////////////////
// The larger the resized tile, the fewer samples we'll need for downsizing.
// See if we can get a static min tile size > mask_min_allowed_tile_size:
const float mask_min_allowed_tile_size = ceil(
mask_min_allowed_triad_size * mask_triads_per_tile);
const float mask_min_expected_tile_size =
mask_min_allowed_tile_size;
// Limit the number of sinc resize taps by the maximum minification factor:
const float pi_over_lobes = pi/mask_sinc_lobes;
const float max_sinc_resize_samples_float = 2.0 * mask_sinc_lobes *
mask_resize_src_lut_size.x/mask_min_expected_tile_size;
// Vectorized loops sample in multiples of 4. Round up to be safe:
const float max_sinc_resize_samples_m4 = ceil(
max_sinc_resize_samples_float * 0.25) * 4.0;
///////////////////////// RESAMPLING FUNCTION HELPERS ////////////////////////
float get_dynamic_loop_size(const float magnification_scale)
{
// Requires: The following global constants must be defined:
// 1.) mask_sinc_lobes
// 2.) max_sinc_resize_samples_m4
// Returns: The minimum number of texture samples for a correct downsize
// at magnification_scale.
// We're downsizing, so the filter is sized across 2*lobes output pixels
// (not 2*lobes input texels). This impacts distance measurements and the
// minimum number of input samples needed.
const float min_samples_float = 2.0 * mask_sinc_lobes / magnification_scale;
const float min_samples_m4 = ceil(min_samples_float * 0.25) * 4.0;
#ifdef DRIVERS_ALLOW_DYNAMIC_BRANCHES
const float max_samples_m4 = max_sinc_resize_samples_m4;
#else // ifdef BREAK_LOOPS_INTO_PIECES
// Simulating loops with branches imposes a 128-sample limit.
const float max_samples_m4 = min(128.0, max_sinc_resize_samples_m4);
#endif
return min(min_samples_m4, max_samples_m4);
}
vec2 get_first_texel_tile_uv_and_dist(const vec2 tex_uv,
const vec2 texture_size, const float dr,
const float input_tiles_per_texture_r, const float samples,
const bool vertical)
{
// Requires: 1.) dr == du == 1.0/texture_size.x or
// dr == dv == 1.0/texture_size.y
// (whichever direction we're resampling in).
// It's a scalar to save register space.
// 2.) input_tiles_per_texture_r is the number of input tiles
// that can fit in the input texture in the direction we're
// resampling this pass.
// 3.) vertical indicates whether we're resampling vertically
// this pass (or horizontally).
// Returns: Pack and return the first sample's tile_uv coord in [0, 1]
// and its texel distance from the destination pixel, in the
// resized dimension only.
// We'll start with the topmost or leftmost sample and work down or right,
// so get the first sample location and distance. Modify both dimensions
// as if we're doing a one-pass 2D resize; we'll throw away the unneeded
// (and incorrect) dimension at the end.
const vec2 curr_texel = tex_uv * texture_size;
const vec2 prev_texel =
floor(curr_texel - vec2(under_half)) + vec2(0.5);
const vec2 first_texel = prev_texel - vec2(samples/2.0 - 1.0);
const vec2 first_texel_uv_wrap_2D = first_texel * dr;
const vec2 first_texel_dist_2D = curr_texel - first_texel;
// Convert from tex_uv to tile_uv coords so we can sub fracts for fmods.
const vec2 first_texel_tile_uv_wrap_2D =
first_texel_uv_wrap_2D * input_tiles_per_texture_r;
// Project wrapped coordinates to the [0, 1] range. We'll do this with all
// samples,but the first texel is special, since it might be negative.
const vec2 coord_negative =
vec2(first_texel_tile_uv_wrap_2D < vec2(0.0));
const vec2 first_texel_tile_uv_2D =
fract(first_texel_tile_uv_wrap_2D) + coord_negative;
// Pack the first texel's tile_uv coord and texel distance in 1D:
const vec2 tile_u_and_dist =
vec2(first_texel_tile_uv_2D.x, first_texel_dist_2D.x);
const vec2 tile_v_and_dist =
vec2(first_texel_tile_uv_2D.y, first_texel_dist_2D.y);
return vertical ? tile_v_and_dist : tile_u_and_dist;
//return mix(tile_u_and_dist, tile_v_and_dist, float(vertical));
}
vec4 tex2Dlod0try(const sampler2D tex, const vec2 tex_uv)
{
// Mipmapping and anisotropic filtering get confused by sinc-resampling.
// One [slow] workaround is to select the lowest mip level:
#ifdef ANISOTROPIC_RESAMPLING_COMPAT_TEX2DLOD
return tex2Dlod(tex, vec4(tex_uv, 0.0, 0.0));
#else
#ifdef ANISOTROPIC_RESAMPLING_COMPAT_TEX2DBIAS
return tex2Dbias(tex, vec4(tex_uv, 0.0, -16.0));
#else
return texture(tex, tex_uv);
#endif
#endif
}
////////////////////////////// LOOP BODY MACROS //////////////////////////////
// Using inline functions can exceed the temporary register limit, so we're
// stuck with #define macros (I'm TRULY sorry). They're declared here instead
// of above to be closer to the actual invocation sites. Steps:
// 1.) Get the exact texel location.
// 2.) Sample the phosphor mask (already assumed encoded in linear RGB).
// 3.) Get the distance from the current pixel and sinc weight:
// sinc(dist) = sin(pi * dist)/(pi * dist)
// We can also use the slower/smoother Lanczos instead:
// L(x) = sinc(dist) * sinc(dist / lobes)
// 4.) Accumulate the weight sum in weights, and accumulate the weighted texels
// in pixel_color (we'll normalize outside the loop at the end).
// We vectorize the loop to help reduce the Lanczos window's cost.
// The r coord is the coord in the dimension we're resizing along (u or v),
// and first_texel_tile_uv_rrrr is a vec4 of the first texel's u or v
// tile_uv coord in [0, 1]. tex_uv_r will contain the tile_uv u or v coord
// for four new texel samples.
#define CALCULATE_R_COORD_FOR_4_SAMPLES \
const vec4 true_i = vec4(i_base + i) + vec4(0.0, 1.0, 2.0, 3.0); \
const vec4 tile_uv_r = fract( \
first_texel_tile_uv_rrrr + true_i * tile_dr); \
const vec4 tex_uv_r = tile_uv_r * tile_size_uv_r;
#ifdef PHOSPHOR_MASK_RESIZE_LANCZOS_WINDOW
#define CALCULATE_SINC_RESAMPLE_WEIGHTS \
const vec4 pi_dist_over_lobes = pi_over_lobes * dist; \
const vec4 weights = min(sin(pi_dist) * sin(pi_dist_over_lobes) /\
(pi_dist*pi_dist_over_lobes), vec4(1.0));
#else
#define CALCULATE_SINC_RESAMPLE_WEIGHTS \
const vec4 weights = min(sin(pi_dist)/pi_dist, vec4(1.0));
#endif
#define UPDATE_COLOR_AND_WEIGHT_SUMS \
const vec4 dist = magnification_scale * \
abs(first_dist_unscaled - true_i); \
const vec4 pi_dist = pi * dist; \
CALCULATE_SINC_RESAMPLE_WEIGHTS; \
pixel_color += new_sample0 * weights.xxx; \
pixel_color += new_sample1 * weights.yyy; \
pixel_color += new_sample2 * weights.zzz; \
pixel_color += new_sample3 * weights.www; \
weight_sum += weights;
#define VERTICAL_SINC_RESAMPLE_LOOP_BODY \
CALCULATE_R_COORD_FOR_4_SAMPLES; \
const vec3 new_sample0 = tex2Dlod0try(texture, \
vec2(tex_uv.x, tex_uv_r.x)).rgb; \
const vec3 new_sample1 = tex2Dlod0try(texture, \
vec2(tex_uv.x, tex_uv_r.y)).rgb; \
const vec3 new_sample2 = tex2Dlod0try(texture, \
vec2(tex_uv.x, tex_uv_r.z)).rgb; \
const vec3 new_sample3 = tex2Dlod0try(texture, \
vec2(tex_uv.x, tex_uv_r.w)).rgb; \
UPDATE_COLOR_AND_WEIGHT_SUMS;
#define HORIZONTAL_SINC_RESAMPLE_LOOP_BODY \
CALCULATE_R_COORD_FOR_4_SAMPLES; \
const vec3 new_sample0 = tex2Dlod0try(texture, \
vec2(tex_uv_r.x, tex_uv.y)).rgb; \
const vec3 new_sample1 = tex2Dlod0try(texture, \
vec2(tex_uv_r.y, tex_uv.y)).rgb; \
const vec3 new_sample2 = tex2Dlod0try(texture, \
vec2(tex_uv_r.z, tex_uv.y)).rgb; \
const vec3 new_sample3 = tex2Dlod0try(texture, \
vec2(tex_uv_r.w, tex_uv.y)).rgb; \
UPDATE_COLOR_AND_WEIGHT_SUMS;
//////////////////////////// RESAMPLING FUNCTIONS ////////////////////////////
vec3 downsample_vertical_sinc_tiled(const sampler2D texture,
const vec2 tex_uv, const vec2 texture_size, const float dr,
const float magnification_scale, const float tile_size_uv_r)
{
// Requires: 1.) dr == du == 1.0/texture_size.x or
// dr == dv == 1.0/texture_size.y
// (whichever direction we're resampling in).
// It's a scalar to save register space.
// 2.) tile_size_uv_r is the number of texels an input tile
// takes up in the input texture, in the direction we're
// resampling this pass.
// 3.) magnification_scale must be <= 1.0.
// Returns: Return a [Lanczos] sinc-resampled pixel of a vertically
// downsized input tile embedded in an input texture. (The
// vertical version is special-cased though: It assumes the
// tile size equals the [static] texture size, since it's used
// on an LUT texture input containing one tile. For more
// generic use, eliminate the "static" in the parameters.)
// The "r" in "dr," "tile_size_uv_r," etc. refers to the dimension
// we're resizing along, e.g. "dy" in this case.
#ifdef USE_SINGLE_STATIC_LOOP
// A static loop can be faster, but it might blur too much from using
// more samples than it should.
const int samples = int(max_sinc_resize_samples_m4);
#else
const int samples = int(get_dynamic_loop_size(magnification_scale));
#endif
// Get the first sample location (scalar tile uv coord along the resized
// dimension) and distance from the output location (in texels):
const float input_tiles_per_texture_r = 1.0/tile_size_uv_r;
// true = vertical resize:
const vec2 first_texel_tile_r_and_dist = get_first_texel_tile_uv_and_dist(
tex_uv, texture_size, dr, input_tiles_per_texture_r, samples, true);
const vec4 first_texel_tile_uv_rrrr = first_texel_tile_r_and_dist.xxxx;
const vec4 first_dist_unscaled = first_texel_tile_r_and_dist.yyyy;
// Get the tile sample offset:
const float tile_dr = dr * input_tiles_per_texture_r;
// Sum up each weight and weighted sample color, varying the looping
// strategy based on our expected dynamic loop capabilities. See the
// loop body macros above.
int i_base = 0;
vec4 weight_sum = vec4(0.0);
vec3 pixel_color = vec3(0.0);
const int i_step = 4;
#ifdef BREAK_LOOPS_INTO_PIECES
if(samples - i_base >= 64)
{
for(int i = 0; i < 64; i += i_step)
{
VERTICAL_SINC_RESAMPLE_LOOP_BODY;
}
i_base += 64;
}
if(samples - i_base >= 32)
{
for(int i = 0; i < 32; i += i_step)
{
VERTICAL_SINC_RESAMPLE_LOOP_BODY;
}
i_base += 32;
}
if(samples - i_base >= 16)
{
for(int i = 0; i < 16; i += i_step)
{
VERTICAL_SINC_RESAMPLE_LOOP_BODY;
}
i_base += 16;
}
if(samples - i_base >= 8)
{
for(int i = 0; i < 8; i += i_step)
{
VERTICAL_SINC_RESAMPLE_LOOP_BODY;
}
i_base += 8;
}
if(samples - i_base >= 4)
{
for(int i = 0; i < 4; i += i_step)
{
VERTICAL_SINC_RESAMPLE_LOOP_BODY;
}
i_base += 4;
}
// Do another 4-sample block for a total of 128 max samples.
if(samples - i_base > 0)
{
for(int i = 0; i < 4; i += i_step)
{
VERTICAL_SINC_RESAMPLE_LOOP_BODY;
}
}
#else
for(int i = 0; i < samples; i += i_step)
{
VERTICAL_SINC_RESAMPLE_LOOP_BODY;
}
#endif
// Normalize so the weight_sum == 1.0, and return:
const vec2 weight_sum_reduce = weight_sum.xy + weight_sum.zw;
const vec3 scalar_weight_sum = vec3(weight_sum_reduce.x +
weight_sum_reduce.y);
return (pixel_color/scalar_weight_sum);
}
vec3 downsample_horizontal_sinc_tiled(const sampler2D texture,
const vec2 tex_uv, const vec2 texture_size, const float dr,
const float magnification_scale, const float tile_size_uv_r)
{
// Differences from downsample_horizontal_sinc_tiled:
// 1.) The dr and tile_size_uv_r parameters are not static consts.
// 2.) The "vertical" parameter to get_first_texel_tile_uv_and_dist is
// set to false instead of true.
// 3.) The horizontal version of the loop body is used.
// TODO: If we can get guaranteed compile-time dead code elimination,
// we can combine the vertical/horizontal downsampling functions by:
// 1.) Add an extra static const bool parameter called "vertical."
// 2.) Supply it with the result of get_first_texel_tile_uv_and_dist().
// 3.) Use a conditional assignment in the loop body macro. This is the
// tricky part: We DO NOT want to incur the extra conditional
// assignment in the inner loop at runtime!
// The "r" in "dr," "tile_size_uv_r," etc. refers to the dimension
// we're resizing along, e.g. "dx" in this case.
#ifdef USE_SINGLE_STATIC_LOOP
// If we have to load all samples, we might as well use them.
const int samples = int(max_sinc_resize_samples_m4);
#else
const int samples = int(get_dynamic_loop_size(magnification_scale));
#endif
// Get the first sample location (scalar tile uv coord along resized
// dimension) and distance from the output location (in texels):
const float input_tiles_per_texture_r = 1.0/tile_size_uv_r;
// false = horizontal resize:
const vec2 first_texel_tile_r_and_dist = get_first_texel_tile_uv_and_dist(
tex_uv, texture_size, dr, input_tiles_per_texture_r, samples, false);
const vec4 first_texel_tile_uv_rrrr = first_texel_tile_r_and_dist.xxxx;
const vec4 first_dist_unscaled = first_texel_tile_r_and_dist.yyyy;
// Get the tile sample offset:
const float tile_dr = dr * input_tiles_per_texture_r;
// Sum up each weight and weighted sample color, varying the looping
// strategy based on our expected dynamic loop capabilities. See the
// loop body macros above.
int i_base = 0;
vec4 weight_sum = vec4(0.0);
vec3 pixel_color = vec3(0.0);
const int i_step = 4;
#ifdef BREAK_LOOPS_INTO_PIECES
if(samples - i_base >= 64)
{
for(int i = 0; i < 64; i += i_step)
{
HORIZONTAL_SINC_RESAMPLE_LOOP_BODY;
}
i_base += 64;
}
if(samples - i_base >= 32)
{
for(int i = 0; i < 32; i += i_step)
{
HORIZONTAL_SINC_RESAMPLE_LOOP_BODY;
}
i_base += 32;
}
if(samples - i_base >= 16)
{
for(int i = 0; i < 16; i += i_step)
{
HORIZONTAL_SINC_RESAMPLE_LOOP_BODY;
}
i_base += 16;
}
if(samples - i_base >= 8)
{
for(int i = 0; i < 8; i += i_step)
{
HORIZONTAL_SINC_RESAMPLE_LOOP_BODY;
}
i_base += 8;
}
if(samples - i_base >= 4)
{
for(int i = 0; i < 4; i += i_step)
{
HORIZONTAL_SINC_RESAMPLE_LOOP_BODY;
}
i_base += 4;
}
// Do another 4-sample block for a total of 128 max samples.
if(samples - i_base > 0)
{
for(int i = 0; i < 4; i += i_step)
{
HORIZONTAL_SINC_RESAMPLE_LOOP_BODY;
}
}
#else
for(int i = 0; i < samples; i += i_step)
{
HORIZONTAL_SINC_RESAMPLE_LOOP_BODY;
}
#endif
// Normalize so the weight_sum == 1.0, and return:
const vec2 weight_sum_reduce = weight_sum.xy + weight_sum.zw;
const vec3 scalar_weight_sum = vec3(weight_sum_reduce.x +
weight_sum_reduce.y);
return (pixel_color/scalar_weight_sum);
}
//////////////////////////// TILE SIZE CALCULATION ///////////////////////////
vec2 get_resized_mask_tile_size(const vec2 estimated_viewport_size,
const vec2 estimated_mask_resize_output_size,
const bool solemnly_swear_same_inputs_for_every_pass)
{
// Requires: The following global constants must be defined according to
// certain constraints:
// 1.) mask_resize_num_triads: Must be high enough that our
// mask sampling method won't have artifacts later
// (long story; see derived-settings-and-constants.h)
// 2.) mask_resize_src_lut_size: Texel size of our mask LUT
// 3.) mask_triads_per_tile: Num horizontal triads in our LUT
// 4.) mask_min_allowed_triad_size: User setting (the more
// restrictive it is, the faster the resize will go)
// 5.) mask_min_allowed_tile_size_x < mask_resize_src_lut_size.x
// 6.) mask_triad_size_desired_{runtime, static}
// 7.) mask_num_triads_desired_{runtime, static}
// 8.) mask_specify_num_triads must be 0.0/1.0 (false/true)
// The function parameters must be defined as follows:
// 1.) estimated_viewport_size == (final viewport size);
// If mask_specify_num_triads is 1.0/true and the viewport
// estimate is wrong, the number of triads will differ from
// the user's preference by about the same factor.
// 2.) estimated_mask_resize_output_size: Must equal the
// output size of the MASK_RESIZE pass.
// Exception: The x component may be estimated garbage if
// and only if the caller throws away the x result.
// 3.) solemnly_swear_same_inputs_for_every_pass: Set to false,
// unless you can guarantee that every call across every
// pass will use the same sizes for the other parameters.
// When calling this across multiple passes, always use the
// same y viewport size/scale, and always use the same x
// viewport size/scale when using the x result.
// Returns: Return the final size of a manually resized mask tile, after
// constraining the desired size to avoid artifacts. Under
// unusual circumstances, tiles may become stretched vertically
// (see wall of text below).
// Stated tile properties must be correct:
const float tile_aspect_ratio_inv =
mask_resize_src_lut_size.y/mask_resize_src_lut_size.x;
const float tile_aspect_ratio = 1.0/tile_aspect_ratio_inv;
const vec2 tile_aspect = vec2(1.0, tile_aspect_ratio_inv);
// If mask_specify_num_triads is 1.0/true and estimated_viewport_size.x is
// wrong, the user preference will be misinterpreted:
const float desired_tile_size_x = mask_triads_per_tile * mix(
mask_triad_size_desired,
estimated_viewport_size.x / mask_num_triads_desired,
mask_specify_num_triads);
if(get_mask_sample_mode() > 0.5)
{
// We don't need constraints unless we're sampling MASK_RESIZE.
return desired_tile_size_x * tile_aspect;
}
// Make sure we're not upsizing:
const float temp_tile_size_x =
min(desired_tile_size_x, mask_resize_src_lut_size.x);
// Enforce min_tile_size and max_tile_size in both dimensions:
const vec2 temp_tile_size = temp_tile_size_x * tile_aspect;
const vec2 min_tile_size =
mask_min_allowed_tile_size * tile_aspect;
const vec2 max_tile_size =
estimated_mask_resize_output_size / mask_resize_num_tiles;
const vec2 clamped_tile_size =
clamp(temp_tile_size, min_tile_size, max_tile_size);
// Try to maintain tile_aspect_ratio. This is the tricky part:
// If we're currently resizing in the y dimension, the x components
// could be MEANINGLESS. (If estimated_mask_resize_output_size.x is
// bogus, then so is max_tile_size.x and clamped_tile_size.x.)
// We can't adjust the y size based on clamped_tile_size.x. If it
// clamps when it shouldn't, it won't clamp again when later passes
// call this function with the correct sizes, and the discrepancy will
// break the sampling coords in MASKED_SCANLINES. Instead, we'll limit
// the x size based on the y size, but not vice versa, unless the
// caller swears the parameters were the same (correct) in every pass.
// As a result, triads could appear vertically stretched if:
// a.) mask_resize_src_lut_size.x > mask_resize_src_lut_size.y: Wide
// LUT's might clamp x more than y (all provided LUT's are square)
// b.) true_viewport_size.x < true_viewport_size.y: The user is playing
// with a vertically oriented screen (not accounted for anyway)
// c.) mask_resize_viewport_scale.x < masked_resize_viewport_scale.y:
// Viewport scales are equal by default.
// If any of these are the case, you can fix the stretching by setting:
// mask_resize_viewport_scale.x = mask_resize_viewport_scale.y *
// (1.0 / min_expected_aspect_ratio) *
// (mask_resize_src_lut_size.x / mask_resize_src_lut_size.y)
const float x_tile_size_from_y =
clamped_tile_size.y * tile_aspect_ratio;
const float y_tile_size_from_x = mix(clamped_tile_size.y,
clamped_tile_size.x * tile_aspect_ratio_inv,
float(solemnly_swear_same_inputs_for_every_pass));
const vec2 reclamped_tile_size = vec2(
min(clamped_tile_size.x, x_tile_size_from_y),
min(clamped_tile_size.y, y_tile_size_from_x));
// We need integer tile sizes in both directions for tiled sampling to
// work correctly. Use floor (to make sure we don't round up), but be
// careful to avoid a rounding bug where floor decreases whole numbers:
const vec2 final_resized_tile_size =
floor(reclamped_tile_size + vec2(FIX_ZERO(0.0)));
return final_resized_tile_size;
}
///////////////////////// FINAL MASK SAMPLING HELPERS ////////////////////////
vec4 get_mask_sampling_parameters(const vec2 mask_resize_texture_size,
const vec2 mask_resize_video_size, const vec2 true_viewport_size,
out vec2 mask_tiles_per_screen)
{
// Requires: 1.) Requirements of get_resized_mask_tile_size() must be
// met, particularly regarding global constants.
// The function parameters must be defined as follows:
// 1.) mask_resize_texture_size == MASK_RESIZE.texture_size
// if get_mask_sample_mode() is 0 (otherwise anything)
// 2.) mask_resize_video_size == MASK_RESIZE.video_size
// if get_mask_sample_mode() is 0 (otherwise anything)
// 3.) true_viewport_size == IN.output_size for a pass set to
// 1.0 viewport scale (i.e. it must be correct)
// Returns: Return a vec4 containing:
// xy: tex_uv coords for the start of the mask tile
// zw: tex_uv size of the mask tile from start to end
// mask_tiles_per_screen is an out parameter containing the
// number of mask tiles that will fit on the screen.
// First get the final resized tile size. The viewport size and mask
// resize viewport scale must be correct, but don't solemnly swear they
// were correct in both mask resize passes unless you know it's true.
// (We can better ensure a correct tile aspect ratio if the parameters are
// guaranteed correct in all passes...but if we lie, we'll get inconsistent
// sizes across passes, resulting in broken texture coordinates.)
const float mask_sample_mode = get_mask_sample_mode();
const vec2 mask_resize_tile_size = get_resized_mask_tile_size(
true_viewport_size, mask_resize_video_size, false);
if(mask_sample_mode < 0.5)
{
// Sample MASK_RESIZE: The resized tile is a fracttion of the texture
// size and starts at a nonzero offset to allow for border texels:
const vec2 mask_tile_uv_size = mask_resize_tile_size /
mask_resize_texture_size;
const vec2 skipped_tiles = mask_start_texels/mask_resize_tile_size;
const vec2 mask_tile_start_uv = skipped_tiles * mask_tile_uv_size;
// mask_tiles_per_screen must be based on the *true* viewport size:
mask_tiles_per_screen = true_viewport_size / mask_resize_tile_size;
return vec4(mask_tile_start_uv, mask_tile_uv_size);
}
else
{
// If we're tiling at the original size (1:1 pixel:texel), redefine a
// "tile" to be the full texture containing many triads. Otherwise,
// we're hardware-resampling an LUT, and the texture truly contains a
// single unresized phosphor mask tile anyway.
const vec2 mask_tile_uv_size = vec2(1.0);
const vec2 mask_tile_start_uv = vec2(0.0);
if(mask_sample_mode > 1.5)
{
// Repeat the full LUT at a 1:1 pixel:texel ratio without resizing:
mask_tiles_per_screen = true_viewport_size/mask_texture_large_size;
}
else
{
// Hardware-resize the original LUT:
mask_tiles_per_screen = true_viewport_size / mask_resize_tile_size;
}
return vec4(mask_tile_start_uv, mask_tile_uv_size);
}
}
vec2 fix_tiling_discontinuities_normalized(const vec2 tile_uv,
vec2 duv_dx, vec2 duv_dy)
{
// Requires: 1.) duv_dx == ddx(tile_uv)
// 2.) duv_dy == ddy(tile_uv)
// 3.) tile_uv contains tile-relative uv coords in [0, 1],
// such that (0.5, 0.5) is the center of a tile, etc.
// ("Tile" can mean texture, the video embedded in the
// texture, or some other "tile" embedded in a texture.)
// Returns: Return new tile_uv coords that contain no discontinuities
// across a 2x2 pixel quad.
// Description:
// When uv coords wrap from 1.0 to 0.0, they create a discontinuity in the
// derivatives, which we assume happened if the absolute difference between
// any fragment in a 2x2 block is > ~half a tile. If the current block has
// a u or v discontinuity and the current fragment is in the first half of
// the tile along that axis (i.e. it wrapped from 1.0 to 0.0), add a tile
// to that coord to make the 2x2 block continuous. (It will now have a
// coord > 1.0 in the padding area beyond the tile.) This function takes
// derivatives as parameters so the caller can reuse them.
// In case we're using high-quality (nVidia-style) derivatives, ensure
// diagonically opposite fragments see each other for correctness:
duv_dx = abs(duv_dx) + abs(ddy(duv_dx));
duv_dy = abs(duv_dy) + abs(ddx(duv_dy));
const vec2 pixel_in_first_half_tile = vec2(tile_uv < vec2(0.5));
const vec2 jump_exists = vec2(duv_dx + duv_dy > vec2(0.5));
return tile_uv + jump_exists * pixel_in_first_half_tile;
}
vec2 convert_phosphor_tile_uv_wrap_to_tex_uv(const vec2 tile_uv_wrap,
const vec4 mask_tile_start_uv_and_size)
{
// Requires: 1.) tile_uv_wrap contains tile-relative uv coords, where the
// tile spans from [0, 1], such that (0.5, 0.5) is at the
// tile center. The input coords can range from [0, inf],
// and their fracttional parts map to a repeated tile.
// ("Tile" can mean texture, the video embedded in the
// texture, or some other "tile" embedded in a texture.)
// 2.) mask_tile_start_uv_and_size.xy contains tex_uv coords
// for the start of the embedded tile in the full texture.
// 3.) mask_tile_start_uv_and_size.zw contains the [fracttional]
// tex_uv size of the embedded tile in the full texture.
// Returns: Return tex_uv coords (used for texture sampling)
// corresponding to tile_uv_wrap.
if(get_mask_sample_mode() < 0.5)
{
// Manually repeat the resized mask tile to fill the screen:
// First get fracttional tile_uv coords. Using fract/fmod on coords
// confuses anisotropic filtering; fix it as user options dictate.
// derived-settings-and-constants.h disables incompatible options.
#ifdef ANISOTROPIC_TILING_COMPAT_TILE_FLAT_TWICE
vec2 tile_uv = fract(tile_uv_wrap * 0.5) * 2.0;
#else
vec2 tile_uv = fract(tile_uv_wrap);
#endif
#ifdef ANISOTROPIC_TILING_COMPAT_FIX_DISCONTINUITIES
const vec2 tile_uv_dx = ddx(tile_uv);
const vec2 tile_uv_dy = ddy(tile_uv);
tile_uv = fix_tiling_discontinuities_normalized(tile_uv,
tile_uv_dx, tile_uv_dy);
#endif
// The tile is embedded in a padded FBO, and it may start at a
// nonzero offset if border texels are used to avoid artifacts:
const vec2 mask_tex_uv = mask_tile_start_uv_and_size.xy +
tile_uv * mask_tile_start_uv_and_size.zw;
return mask_tex_uv;
}
else
{
// Sample from the input phosphor mask texture with hardware tiling.
// If we're tiling at the original size (mode 2), the "tile" is the
// whole texture, and it contains a large number of triads mapped with
// a 1:1 pixel:texel ratio. OTHERWISE, the texture contains a single
// unresized tile. tile_uv_wrap already has correct coords for both!
return tile_uv_wrap;
}
}
#endif // PHOSPHOR_MASK_RESIZING_H

5
crt/shaders/crt-royale/src/phosphor-mask-resizing.h
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@ -22,9 +22,8 @@
////////////////////////////////// INCLUDES ////////////////////////////////// ////////////////////////////////// INCLUDES //////////////////////////////////
//#include "../user-settings.h" #include "../user-settings.h"
//#include "derived-settings-and-constants.h" #include "derived-settings-and-constants.h"
#include "includes.h"
///////////////////////////// CODEPATH SELECTION ///////////////////////////// ///////////////////////////// CODEPATH SELECTION /////////////////////////////

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crt/shaders/crt-royale/src/quad-pixel-communication.h
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@ -1,243 +0,0 @@
#ifndef QUAD_PIXEL_COMMUNICATION_H
#define QUAD_PIXEL_COMMUNICATION_H
///////////////////////////////// MIT LICENSE ////////////////////////////////
// Copyright (C) 2014 TroggleMonkey*
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to
// deal in the Software without restriction, including without limitation the
// rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
// sell copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
// IN THE SOFTWARE.
///////////////////////////////// DISCLAIMER /////////////////////////////////
// *This code was inspired by "Shader Amortization using Pixel Quad Message
// Passing" by Eric Penner, published in GPU Pro 2, Chapter VI.2. My intent
// is not to plagiarize his fundamentally similar code and assert my own
// copyright, but the algorithmic helper functions require so little code that
// implementations can't vary by much except bugfixes and conventions. I just
// wanted to license my own particular code here to avoid ambiguity and make it
// clear that as far as I'm concerned, people can do as they please with it.
///////////////////////////////// DESCRIPTION ////////////////////////////////
// Given screen pixel numbers, derive a "quad vector" describing a fragment's
// position in its 2x2 pixel quad. Given that vector, obtain the values of any
// variable at neighboring fragments.
// Requires: Using this file in general requires:
// 1.) ddx() and ddy() are present in the current Cg profile.
// 2.) The GPU driver is using fine/high-quality derivatives.
// Functions will give incorrect results if this is not true,
// so a test function is included.
///////////////////// QUAD-PIXEL COMMUNICATION PRIMITIVES ////////////////////
vec4 get_quad_vector_naive(const vec4 output_pixel_num_wrt_uvxy)
{
// Requires: Two measures of the current fragment's output pixel number
// in the range ([0, IN.output_size.x), [0, IN.output_size.y)):
// 1.) output_pixel_num_wrt_uvxy.xy increase with uv coords.
// 2.) output_pixel_num_wrt_uvxy.zw increase with screen xy.
// Returns: Two measures of the fragment's position in its 2x2 quad:
// 1.) The .xy components are its 2x2 placement with respect to
// uv direction (the origin (0, 0) is at the top-left):
// top-left = (-1.0, -1.0) top-right = ( 1.0, -1.0)
// bottom-left = (-1.0, 1.0) bottom-right = ( 1.0, 1.0)
// You need this to arrange/weight shared texture samples.
// 2.) The .zw components are its 2x2 placement with respect to
// screen xy direction (IN.position); the origin varies.
// quad_gather needs this measure to work correctly.
// Note: quad_vector.zw = quad_vector.xy * vec2(
// ddx(output_pixel_num_wrt_uvxy.x),
// ddy(output_pixel_num_wrt_uvxy.y));
// Caveats: This function assumes the GPU driver always starts 2x2 pixel
// quads at even pixel numbers. This assumption can be wrong
// for odd output resolutions (nondeterministically so).
const vec4 pixel_odd = frac(output_pixel_num_wrt_uvxy * 0.5) * 2.0;
const vec4 quad_vector = pixel_odd * 2.0 - vec4(1.0);
return quad_vector;
}
vec4 get_quad_vector(const vec4 output_pixel_num_wrt_uvxy)
{
// Requires: Same as get_quad_vector_naive() (see that first).
// Returns: Same as get_quad_vector_naive() (see that first), but it's
// correct even if the 2x2 pixel quad starts at an odd pixel,
// which can occur at odd resolutions.
const vec4 quad_vector_guess =
get_quad_vector_naive(output_pixel_num_wrt_uvxy);
// If quad_vector_guess.zw doesn't increase with screen xy, we know
// the 2x2 pixel quad starts at an odd pixel:
const vec2 odd_start_mirror = 0.5 * vec2(ddx(quad_vector_guess.z),
ddy(quad_vector_guess.w));
return quad_vector_guess * odd_start_mirror.xyxy;
}
vec4 get_quad_vector(const vec2 output_pixel_num_wrt_uv)
{
// Requires: 1.) ddx() and ddy() are present in the current Cg profile.
// 2.) output_pixel_num_wrt_uv must increase with uv coords and
// measure the current fragment's output pixel number in:
// ([0, IN.output_size.x), [0, IN.output_size.y))
// Returns: Same as get_quad_vector_naive() (see that first), but it's
// correct even if the 2x2 pixel quad starts at an odd pixel,
// which can occur at odd resolutions.
// Caveats: This function requires less information than the version
// taking a vec4, but it's potentially slower.
// Do screen coords increase with or against uv? Get the direction
// with respect to (uv.x, uv.y) for (screen.x, screen.y) in {-1, 1}.
const vec2 screen_uv_mirror = vec2(ddx(output_pixel_num_wrt_uv.x),
ddy(output_pixel_num_wrt_uv.y));
const vec2 pixel_odd_wrt_uv = frac(output_pixel_num_wrt_uv * 0.5) * 2.0;
const vec2 quad_vector_uv_guess = (pixel_odd_wrt_uv - vec2(0.5)) * 2.0;
const vec2 quad_vector_screen_guess = quad_vector_uv_guess * screen_uv_mirror;
// If quad_vector_screen_guess doesn't increase with screen xy, we know
// the 2x2 pixel quad starts at an odd pixel:
const vec2 odd_start_mirror = 0.5 * vec2(ddx(quad_vector_screen_guess.x),
ddy(quad_vector_screen_guess.y));
const vec4 quad_vector_guess = vec4(
quad_vector_uv_guess, quad_vector_screen_guess);
return quad_vector_guess * odd_start_mirror.xyxy;
}
void quad_gather(const vec4 quad_vector, const vec4 curr,
out vec4 adjx, out vec4 adjy, out vec4 diag)
{
// Requires: 1.) ddx() and ddy() are present in the current Cg profile.
// 2.) The GPU driver is using fine/high-quality derivatives.
// 3.) quad_vector describes the current fragment's location in
// its 2x2 pixel quad using get_quad_vector()'s conventions.
// 4.) curr is any vector you wish to get neighboring values of.
// Returns: Values of an input vector (curr) at neighboring fragments
// adjacent x, adjacent y, and diagonal (via out parameters).
adjx = curr - ddx(curr) * quad_vector.z;
adjy = curr - ddy(curr) * quad_vector.w;
diag = adjx - ddy(adjx) * quad_vector.w;
}
void quad_gather(const vec4 quad_vector, const vec3 curr,
out vec3 adjx, out vec3 adjy, out vec3 diag)
{
// vec3 version
adjx = curr - ddx(curr) * quad_vector.z;
adjy = curr - ddy(curr) * quad_vector.w;
diag = adjx - ddy(adjx) * quad_vector.w;
}
void quad_gather(const vec4 quad_vector, const vec2 curr,
out vec2 adjx, out vec2 adjy, out vec2 diag)
{
// vec2 version
adjx = curr - ddx(curr) * quad_vector.z;
adjy = curr - ddy(curr) * quad_vector.w;
diag = adjx - ddy(adjx) * quad_vector.w;
}
vec4 quad_gather(const vec4 quad_vector, const float curr)
{
// Float version:
// Returns: return.x == current
// return.y == adjacent x
// return.z == adjacent y
// return.w == diagonal
vec4 all = vec4(curr);
all.y = all.x - ddx(all.x) * quad_vector.z;
all.zw = all.xy - ddy(all.xy) * quad_vector.w;
return all;
}
vec4 quad_gather_sum(const vec4 quad_vector, const vec4 curr)
{
// Requires: Same as quad_gather()
// Returns: Sum of an input vector (curr) at all fragments in a quad.
vec4 adjx, adjy, diag;
quad_gather(quad_vector, curr, adjx, adjy, diag);
return (curr + adjx + adjy + diag);
}
vec3 quad_gather_sum(const vec4 quad_vector, const vec3 curr)
{
// vec3 version:
vec3 adjx, adjy, diag;
quad_gather(quad_vector, curr, adjx, adjy, diag);
return (curr + adjx + adjy + diag);
}
vec2 quad_gather_sum(const vec4 quad_vector, const vec2 curr)
{
// vec2 version:
vec2 adjx, adjy, diag;
quad_gather(quad_vector, curr, adjx, adjy, diag);
return (curr + adjx + adjy + diag);
}
float quad_gather_sum(const vec4 quad_vector, const float curr)
{
// Float version:
const vec4 all_values = quad_gather(quad_vector, curr);
return (all_values.x + all_values.y + all_values.z + all_values.w);
}
bool fine_derivatives_working(const vec4 quad_vector, vec4 curr)
{
// Requires: 1.) ddx() and ddy() are present in the current Cg profile.
// 2.) quad_vector describes the current fragment's location in
// its 2x2 pixel quad using get_quad_vector()'s conventions.
// 3.) curr must be a test vector with non-constant derivatives
// (its value should change nonlinearly across fragments).
// Returns: true if fine/hybrid/high-quality derivatives are used, or
// false if coarse derivatives are used or inconclusive
// Usage: Test whether quad-pixel communication is working!
// Method: We can confirm fine derivatives are used if the following
// holds (ever, for any value at any fragment):
// (ddy(curr) != ddy(adjx)) or (ddx(curr) != ddx(adjy))
// The more values we test (e.g. test a vec4 two ways), the
// easier it is to demonstrate fine derivatives are working.
// TODO: Check for floating point exact comparison issues!
vec4 ddx_curr = ddx(curr);
vec4 ddy_curr = ddy(curr);
vec4 adjx = curr - ddx_curr * quad_vector.z;
vec4 adjy = curr - ddy_curr * quad_vector.w;
bool ddy_different = any(ddy_curr != ddy(adjx));
bool ddx_different = any(ddx_curr != ddx(adjy));
return any(bool2(ddy_different, ddx_different));
}
bool fine_derivatives_working_fast(const vec4 quad_vector, float curr)
{
// Requires: Same as fine_derivatives_working()
// Returns: Same as fine_derivatives_working()
// Usage: This is faster than fine_derivatives_working() but more
// likely to return false negatives, so it's less useful for
// offline testing/debugging. It's also useless as the basis
// for dynamic runtime branching as of May 2014: Derivatives
// (and quad-pixel communication) are currently disallowed in
// branches. However, future GPU's may allow you to use them
// in dynamic branches if you promise the branch condition
// evaluates the same for every fragment in the quad (and/or if
// the driver enforces that promise by making a single fragment
// control branch decisions). If that ever happens, this
// version may become a more economical choice.
float ddx_curr = ddx(curr);
float ddy_curr = ddy(curr);
float adjx = curr - ddx_curr * quad_vector.z;
return (ddy_curr != ddy(adjx));
}
#endif // QUAD_PIXEL_COMMUNICATION_H

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crt/shaders/crt-royale/src/scanline-functions-old.h
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#ifndef SCANLINE_FUNCTIONS_H
#define SCANLINE_FUNCTIONS_H
///////////////////////////// GPL LICENSE NOTICE /////////////////////////////
// crt-royale: A full-featured CRT shader, with cheese.
// Copyright (C) 2014 TroggleMonkey <trogglemonkey@gmx.com>
//
// 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 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., 59 Temple
// Place, Suite 330, Boston, MA 02111-1307 USA
////////////////////////////////// INCLUDES //////////////////////////////////
#include "../user-settings.h"
#include "derived-settings-and-constants.h"
#include "../../../../include/special-functions.h"
#include "../../../../include/gamma-management.h"
///////////////////////////// SCANLINE FUNCTIONS /////////////////////////////
/*
inline float3 get_gaussian_sigma(const float3 color, const float sigma_range)
{
// Requires: Globals:
// 1.) beam_min_sigma and beam_max_sigma are global floats
// containing the desired minimum and maximum beam standard
// deviations, for dim and bright colors respectively.
// 2.) beam_max_sigma must be > 0.0
// 3.) beam_min_sigma must be in (0.0, beam_max_sigma]
// 4.) beam_spot_power must be defined as a global float.
// Parameters:
// 1.) color is the underlying source color along a scanline
// 2.) sigma_range = beam_max_sigma - beam_min_sigma; we take
// sigma_range as a parameter to avoid repeated computation
// when beam_{min, max}_sigma are runtime shader parameters
// Optional: Users may set beam_spot_shape_function to 1 to define the
// inner f(color) subfunction (see below) as:
// f(color) = sqrt(1.0 - (color - 1.0)*(color - 1.0))
// Otherwise (technically, if beam_spot_shape_function < 0.5):
// f(color) = pow(color, beam_spot_power)
// Returns: The standard deviation of the Gaussian beam for "color:"
// sigma = beam_min_sigma + sigma_range * f(color)
// Details/Discussion:
// The beam's spot shape vaguely resembles an aspect-corrected f() in the
// range [0, 1] (not quite, but it's related). f(color) = color makes
// spots look like diamonds, and a spherical function or cube balances
// between variable width and a soft/realistic shape. A beam_spot_power
// > 1.0 can produce an ugly spot shape and more initial clipping, but the
// final shape also differs based on the horizontal resampling filter and
// the phosphor bloom. For instance, resampling horizontally in nonlinear
// light and/or with a sharp (e.g. Lanczos) filter will sharpen the spot
// shape, but a sixth root is still quite soft. A power function (default
// 1.0/3.0 beam_spot_power) is most flexible, but a fixed spherical curve
// has the highest variability without an awful spot shape.
//
// beam_min_sigma affects scanline sharpness/aliasing in dim areas, and its
// difference from beam_max_sigma affects beam width variability. It only
// affects clipping [for pure Gaussians] if beam_spot_power > 1.0 (which is
// a conservative estimate for a more complex constraint).
//
// beam_max_sigma affects clipping and increasing scanline width/softness
// as color increases. The wider this is, the more scanlines need to be
// evaluated to avoid distortion. For a pure Gaussian, the max_beam_sigma
// at which the first unused scanline always has a weight < 1.0/255.0 is:
// num scanlines = 2, max_beam_sigma = 0.2089; distortions begin ~0.34
// num scanlines = 3, max_beam_sigma = 0.3879; distortions begin ~0.52
// num scanlines = 4, max_beam_sigma = 0.5723; distortions begin ~0.70
// num scanlines = 5, max_beam_sigma = 0.7591; distortions begin ~0.89
// num scanlines = 6, max_beam_sigma = 0.9483; distortions begin ~1.08
// Generalized Gaussians permit more leeway here as steepness increases.
if(beam_spot_shape_function < 0.5)
{
// Use a power function:
return float3(beam_min_sigma) + sigma_range *
pow(color, beam_spot_power);
}
else
{
// Use a spherical function:
const float3 color_minus_1 = color - float3(1.0);
return float3(beam_min_sigma) + sigma_range *
sqrt(float3(1.0) - color_minus_1*color_minus_1);
}
}
inline float3 get_generalized_gaussian_beta(const float3 color,
const float shape_range)
{
// Requires: Globals:
// 1.) beam_min_shape and beam_max_shape are global floats
// containing the desired min/max generalized Gaussian
// beta parameters, for dim and bright colors respectively.
// 2.) beam_max_shape must be >= 2.0
// 3.) beam_min_shape must be in [2.0, beam_max_shape]
// 4.) beam_shape_power must be defined as a global float.
// Parameters:
// 1.) color is the underlying source color along a scanline
// 2.) shape_range = beam_max_shape - beam_min_shape; we take
// shape_range as a parameter to avoid repeated computation
// when beam_{min, max}_shape are runtime shader parameters
// Returns: The type-I generalized Gaussian "shape" parameter beta for
// the given color.
// Details/Discussion:
// Beta affects the scanline distribution as follows:
// a.) beta < 2.0 narrows the peak to a spike with a discontinuous slope
// b.) beta == 2.0 just degenerates to a Gaussian
// c.) beta > 2.0 flattens and widens the peak, then drops off more steeply
// than a Gaussian. Whereas high sigmas widen and soften peaks, high
// beta widen and sharpen peaks at the risk of aliasing.
// Unlike high beam_spot_powers, high beam_shape_powers actually soften shape
// transitions, whereas lower ones sharpen them (at the risk of aliasing).
return beam_min_shape + shape_range * pow(color, beam_shape_power);
}
float3 scanline_gaussian_integral_contrib(const float3 dist,
const float3 color, const float pixel_height, const float sigma_range)
{
// Requires: 1.) dist is the distance of the [potentially separate R/G/B]
// point(s) from a scanline in units of scanlines, where
// 1.0 means the sample point straddles the next scanline.
// 2.) color is the underlying source color along a scanline.
// 3.) pixel_height is the output pixel height in scanlines.
// 4.) Requirements of get_gaussian_sigma() must be met.
// Returns: Return a scanline's light output over a given pixel.
// Details:
// The CRT beam profile follows a roughly Gaussian distribution which is
// wider for bright colors than dark ones. The integral over the full
// range of a Gaussian function is always 1.0, so we can vary the beam
// with a standard deviation without affecting brightness. 'x' = distance:
// gaussian sample = 1/(sigma*sqrt(2*pi)) * e**(-(x**2)/(2*sigma**2))
// gaussian integral = 0.5 (1.0 + erf(x/(sigma * sqrt(2))))
// Use a numerical approximation of the "error function" (the Gaussian
// indefinite integral) to find the definite integral of the scanline's
// average brightness over a given pixel area. Even if curved coords were
// used in this pass, a flat scalar pixel height works almost as well as a
// pixel height computed from a full pixel-space to scanline-space matrix.
const float3 sigma = get_gaussian_sigma(color, sigma_range);
const float3 ph_offset = float3(pixel_height * 0.5);
const float3 denom_inv = 1.0/(sigma*sqrt(2.0));
const float3 integral_high = erf((dist + ph_offset)*denom_inv);
const float3 integral_low = erf((dist - ph_offset)*denom_inv);
return color * 0.5*(integral_high - integral_low)/pixel_height;
}
float3 scanline_generalized_gaussian_integral_contrib(const float3 dist,
const float3 color, const float pixel_height, const float sigma_range,
const float shape_range)
{
// Requires: 1.) Requirements of scanline_gaussian_integral_contrib()
// must be met.
// 2.) Requirements of get_gaussian_sigma() must be met.
// 3.) Requirements of get_generalized_gaussian_beta() must be
// met.
// Returns: Return a scanline's light output over a given pixel.
// A generalized Gaussian distribution allows the shape (beta) to vary
// as well as the width (alpha). "gamma" refers to the gamma function:
// generalized sample =
// beta/(2*alpha*gamma(1/beta)) * e**(-(|x|/alpha)**beta)
// ligamma(s, z) is the lower incomplete gamma function, for which we only
// implement two of four branches (because we keep 1/beta <= 0.5):
// generalized integral = 0.5 + 0.5* sign(x) *
// ligamma(1/beta, (|x|/alpha)**beta)/gamma(1/beta)
// See get_generalized_gaussian_beta() for a discussion of beta.
// We base alpha on the intended Gaussian sigma, but it only strictly
// models models standard deviation at beta == 2, because the standard
// deviation depends on both alpha and beta (keeping alpha independent is
// faster and preserves intuitive behavior and a full spectrum of results).
const float3 alpha = sqrt(2.0) * get_gaussian_sigma(color, sigma_range);
const float3 beta = get_generalized_gaussian_beta(color, shape_range);
const float3 alpha_inv = float3(1.0)/alpha;
const float3 s = float3(1.0)/beta;
const float3 ph_offset = float3(pixel_height * 0.5);
// Pass beta to gamma_impl to avoid repeated divides. Similarly pass
// beta (i.e. 1/s) and 1/gamma(s) to normalized_ligamma_impl.
const float3 gamma_s_inv = float3(1.0)/gamma_impl(s, beta);
const float3 dist1 = dist + ph_offset;
const float3 dist0 = dist - ph_offset;
const float3 integral_high = sign(dist1) * normalized_ligamma_impl(
s, pow(abs(dist1)*alpha_inv, beta), beta, gamma_s_inv);
const float3 integral_low = sign(dist0) * normalized_ligamma_impl(
s, pow(abs(dist0)*alpha_inv, beta), beta, gamma_s_inv);
return color * 0.5*(integral_high - integral_low)/pixel_height;
}
float3 scanline_gaussian_sampled_contrib(const float3 dist, const float3 color,
const float pixel_height, const float sigma_range)
{
// See scanline_gaussian integral_contrib() for detailed comments!
// gaussian sample = 1/(sigma*sqrt(2*pi)) * e**(-(x**2)/(2*sigma**2))
const float3 sigma = get_gaussian_sigma(color, sigma_range);
// Avoid repeated divides:
const float3 sigma_inv = float3(1.0)/sigma;
const float3 inner_denom_inv = 0.5 * sigma_inv * sigma_inv;
const float3 outer_denom_inv = sigma_inv/sqrt(2.0*pi);
if(beam_antialias_level > 0.5)
{
// Sample 1/3 pixel away in each direction as well:
const float3 sample_offset = float3(pixel_height/3.0);
const float3 dist2 = dist + sample_offset;
const float3 dist3 = abs(dist - sample_offset);
// Average three pure Gaussian samples:
const float3 scale = color/3.0 * outer_denom_inv;
const float3 weight1 = exp(-(dist*dist)*inner_denom_inv);
const float3 weight2 = exp(-(dist2*dist2)*inner_denom_inv);
const float3 weight3 = exp(-(dist3*dist3)*inner_denom_inv);
return scale * (weight1 + weight2 + weight3);
}
else
{
return color*exp(-(dist*dist)*inner_denom_inv)*outer_denom_inv;
}
}
float3 scanline_generalized_gaussian_sampled_contrib(const float3 dist,
const float3 color, const float pixel_height, const float sigma_range,
const float shape_range)
{
// See scanline_generalized_gaussian_integral_contrib() for details!
// generalized sample =
// beta/(2*alpha*gamma(1/beta)) * e**(-(|x|/alpha)**beta)
const float3 alpha = sqrt(2.0) * get_gaussian_sigma(color, sigma_range);
const float3 beta = get_generalized_gaussian_beta(color, shape_range);
// Avoid repeated divides:
const float3 alpha_inv = float3(1.0)/alpha;
const float3 beta_inv = float3(1.0)/beta;
const float3 scale = color * beta * 0.5 * alpha_inv /
gamma_impl(beta_inv, beta);
if(beam_antialias_level > 0.5)
{
// Sample 1/3 pixel closer to and farther from the scanline too.
const float3 sample_offset = float3(pixel_height/3.0);
const float3 dist2 = dist + sample_offset;
const float3 dist3 = abs(dist - sample_offset);
// Average three generalized Gaussian samples:
const float3 weight1 = exp(-pow(abs(dist*alpha_inv), beta));
const float3 weight2 = exp(-pow(abs(dist2*alpha_inv), beta));
const float3 weight3 = exp(-pow(abs(dist3*alpha_inv), beta));
return scale/3.0 * (weight1 + weight2 + weight3);
}
else
{
return scale * exp(-pow(abs(dist*alpha_inv), beta));
}
}
inline float3 scanline_contrib(float3 dist, float3 color,
float pixel_height, const float sigma_range, const float shape_range)
{
// Requires: 1.) Requirements of scanline_gaussian_integral_contrib()
// must be met.
// 2.) Requirements of get_gaussian_sigma() must be met.
// 3.) Requirements of get_generalized_gaussian_beta() must be
// met.
// Returns: Return a scanline's light output over a given pixel, using
// a generalized or pure Gaussian distribution and sampling or
// integrals as desired by user codepath choices.
if(beam_generalized_gaussian)
{
if(beam_antialias_level > 1.5)
{
return scanline_generalized_gaussian_integral_contrib(
dist, color, pixel_height, sigma_range, shape_range);
}
else
{
return scanline_generalized_gaussian_sampled_contrib(
dist, color, pixel_height, sigma_range, shape_range);
}
}
else
{
if(beam_antialias_level > 1.5)
{
return scanline_gaussian_integral_contrib(
dist, color, pixel_height, sigma_range);
}
else
{
return scanline_gaussian_sampled_contrib(
dist, color, pixel_height, sigma_range);
}
}
}
inline float3 get_raw_interpolated_color(const float3 color0,
const float3 color1, const float3 color2, const float3 color3,
const float4 weights)
{
// Use max to avoid bizarre artifacts from negative colors:
return max(mul(weights, float4x3(color0, color1, color2, color3)), 0.0);
}
float3 get_interpolated_linear_color(const float3 color0, const float3 color1,
const float3 color2, const float3 color3, const float4 weights)
{
// Requires: 1.) Requirements of include/gamma-management.h must be met:
// intermediate_gamma must be globally defined, and input
// colors are interpreted as linear RGB unless you #define
// GAMMA_ENCODE_EVERY_FBO (in which case they are
// interpreted as gamma-encoded with intermediate_gamma).
// 2.) color0-3 are colors sampled from a texture with tex2D().
// They are interpreted as defined in requirement 1.
// 3.) weights contains weights for each color, summing to 1.0.
// 4.) beam_horiz_linear_rgb_weight must be defined as a global
// float in [0.0, 1.0] describing how much blending should
// be done in linear RGB (rest is gamma-corrected RGB).
// 5.) RUNTIME_SCANLINES_HORIZ_FILTER_COLORSPACE must be #defined
// if beam_horiz_linear_rgb_weight is anything other than a
// static constant, or we may try branching at runtime
// without dynamic branches allowed (slow).
// Returns: Return an interpolated color lookup between the four input
// colors based on the weights in weights. The final color will
// be a linear RGB value, but the blending will be done as
// indicated above.
const float intermediate_gamma = get_intermediate_gamma();
// Branch if beam_horiz_linear_rgb_weight is static (for free) or if the
// profile allows dynamic branches (faster than computing extra pows):
#ifndef RUNTIME_SCANLINES_HORIZ_FILTER_COLORSPACE
#define SCANLINES_BRANCH_FOR_LINEAR_RGB_WEIGHT
#else
#ifdef DRIVERS_ALLOW_DYNAMIC_BRANCHES
#define SCANLINES_BRANCH_FOR_LINEAR_RGB_WEIGHT
#endif
#endif
#ifdef SCANLINES_BRANCH_FOR_LINEAR_RGB_WEIGHT
// beam_horiz_linear_rgb_weight is static, so we can branch:
#ifdef GAMMA_ENCODE_EVERY_FBO
const float3 gamma_mixed_color = pow(get_raw_interpolated_color(
color0, color1, color2, color3, weights), intermediate_gamma);
if(beam_horiz_linear_rgb_weight > 0.0)
{
const float3 linear_mixed_color = get_raw_interpolated_color(
pow(color0, intermediate_gamma),
pow(color1, intermediate_gamma),
pow(color2, intermediate_gamma),
pow(color3, intermediate_gamma),
weights);
return lerp(gamma_mixed_color, linear_mixed_color,
beam_horiz_linear_rgb_weight);
}
else
{
return gamma_mixed_color;
}
#else
const float3 linear_mixed_color = get_raw_interpolated_color(
color0, color1, color2, color3, weights);
if(beam_horiz_linear_rgb_weight < 1.0)
{
const float3 gamma_mixed_color = get_raw_interpolated_color(
pow(color0, 1.0/intermediate_gamma),
pow(color1, 1.0/intermediate_gamma),
pow(color2, 1.0/intermediate_gamma),
pow(color3, 1.0/intermediate_gamma),
weights);
return lerp(gamma_mixed_color, linear_mixed_color,
beam_horiz_linear_rgb_weight);
}
else
{
return linear_mixed_color;
}
#endif // GAMMA_ENCODE_EVERY_FBO
#else
#ifdef GAMMA_ENCODE_EVERY_FBO
// Inputs: color0-3 are colors in gamma-encoded RGB.
const float3 gamma_mixed_color = pow(get_raw_interpolated_color(
color0, color1, color2, color3, weights), intermediate_gamma);
const float3 linear_mixed_color = get_raw_interpolated_color(
pow(color0, intermediate_gamma),
pow(color1, intermediate_gamma),
pow(color2, intermediate_gamma),
pow(color3, intermediate_gamma),
weights);
return lerp(gamma_mixed_color, linear_mixed_color,
beam_horiz_linear_rgb_weight);
#else
// Inputs: color0-3 are colors in linear RGB.
const float3 linear_mixed_color = get_raw_interpolated_color(
color0, color1, color2, color3, weights);
const float3 gamma_mixed_color = get_raw_interpolated_color(
pow(color0, 1.0/intermediate_gamma),
pow(color1, 1.0/intermediate_gamma),
pow(color2, 1.0/intermediate_gamma),
pow(color3, 1.0/intermediate_gamma),
weights);
return lerp(gamma_mixed_color, linear_mixed_color,
beam_horiz_linear_rgb_weight);
#endif // GAMMA_ENCODE_EVERY_FBO
#endif // SCANLINES_BRANCH_FOR_LINEAR_RGB_WEIGHT
}
float3 get_scanline_color(const sampler2D texture, const float2 scanline_uv,
const float2 uv_step_x, const float4 weights)
{
// Requires: 1.) scanline_uv must be vertically snapped to the caller's
// desired line or scanline and horizontally snapped to the
// texel just left of the output pixel (color1)
// 2.) uv_step_x must contain the horizontal uv distance
// between texels.
// 3.) weights must contain interpolation filter weights for
// color0, color1, color2, and color3, where color1 is just
// left of the output pixel.
// Returns: Return a horizontally interpolated texture lookup using 2-4
// nearby texels, according to weights and the conventions of
// get_interpolated_linear_color().
// We can ignore the outside texture lookups for Quilez resampling.
const float3 color1 = tex2D(texture, scanline_uv).rgb;
const float3 color2 = tex2D(texture, scanline_uv + uv_step_x).rgb;
float3 color0 = float3(0.0);
float3 color3 = float3(0.0);
if(beam_horiz_filter > 0.5)
{
color0 = tex2D(texture, scanline_uv - uv_step_x).rgb;
color3 = tex2D(texture, scanline_uv + 2.0 * uv_step_x).rgb;
}
// Sample the texture as-is, whether it's linear or gamma-encoded:
// get_interpolated_linear_color() will handle the difference.
return get_interpolated_linear_color(color0, color1, color2, color3, weights);
}
float3 sample_single_scanline_horizontal(const sampler2D texture,
const float2 tex_uv, const float2 texture_size,
const float2 texture_size_inv)
{
// TODO: Add function requirements.
// Snap to the previous texel and get sample dists from 2/4 nearby texels:
const float2 curr_texel = tex_uv * texture_size;
// Use under_half to fix a rounding bug right around exact texel locations.
const float2 prev_texel =
floor(curr_texel - float2(under_half)) + float2(0.5);
const float2 prev_texel_hor = float2(prev_texel.x, curr_texel.y);
const float2 prev_texel_hor_uv = prev_texel_hor * texture_size_inv;
const float prev_dist = curr_texel.x - prev_texel_hor.x;
const float4 sample_dists = float4(1.0 + prev_dist, prev_dist,
1.0 - prev_dist, 2.0 - prev_dist);
// Get Quilez, Lanczos2, or Gaussian resize weights for 2/4 nearby texels:
float4 weights;
if(beam_horiz_filter < 0.5)
{
// Quilez:
const float x = sample_dists.y;
const float w2 = x*x*x*(x*(x*6.0 - 15.0) + 10.0);
weights = float4(0.0, 1.0 - w2, w2, 0.0);
}
else if(beam_horiz_filter < 1.5)
{
// Gaussian:
float inner_denom_inv = 1.0/(2.0*beam_horiz_sigma*beam_horiz_sigma);
weights = exp(-(sample_dists*sample_dists)*inner_denom_inv);
}
else
{
// Lanczos2:
const float4 pi_dists = FIX_ZERO(sample_dists * pi);
weights = 2.0 * sin(pi_dists) * sin(pi_dists * 0.5) /
(pi_dists * pi_dists);
}
// Ensure the weight sum == 1.0:
const float4 final_weights = weights/dot(weights, float4(1.0));
// Get the interpolated horizontal scanline color:
const float2 uv_step_x = float2(texture_size_inv.x, 0.0);
return get_scanline_color(
texture, prev_texel_hor_uv, uv_step_x, final_weights);
}
float3 sample_rgb_scanline_horizontal(const sampler2D texture,
const float2 tex_uv, const float2 texture_size,
const float2 texture_size_inv)
{
// TODO: Add function requirements.
// Rely on a helper to make convergence easier.
if(beam_misconvergence)
{
const float3 convergence_offsets_rgb =
get_convergence_offsets_x_vector();
const float3 offset_u_rgb =
convergence_offsets_rgb * texture_size_inv.xxx;
const float2 scanline_uv_r = tex_uv - float2(offset_u_rgb.r, 0.0);
const float2 scanline_uv_g = tex_uv - float2(offset_u_rgb.g, 0.0);
const float2 scanline_uv_b = tex_uv - float2(offset_u_rgb.b, 0.0);
const float3 sample_r = sample_single_scanline_horizontal(
texture, scanline_uv_r, texture_size, texture_size_inv);
const float3 sample_g = sample_single_scanline_horizontal(
texture, scanline_uv_g, texture_size, texture_size_inv);
const float3 sample_b = sample_single_scanline_horizontal(
texture, scanline_uv_b, texture_size, texture_size_inv);
return float3(sample_r.r, sample_g.g, sample_b.b);
}
else
{
return sample_single_scanline_horizontal(texture, tex_uv, texture_size,
texture_size_inv);
}
}
float2 get_last_scanline_uv(const float2 tex_uv, const float2 texture_size,
const float2 texture_size_inv, const float2 il_step_multiple,
const float frame_count, out float dist)
{
// Compute texture coords for the last/upper scanline, accounting for
// interlacing: With interlacing, only consider even/odd scanlines every
// other frame. Top-field first (TFF) order puts even scanlines on even
// frames, and BFF order puts them on odd frames. Texels are centered at:
// frac(tex_uv * texture_size) == x.5
// Caution: If these coordinates ever seem incorrect, first make sure it's
// not because anisotropic filtering is blurring across field boundaries.
// Note: TFF/BFF won't matter for sources that double-weave or similar.
const float field_offset = floor(il_step_multiple.y * 0.75) *
fmod(frame_count + float(interlace_bff), 2.0);
const float2 curr_texel = tex_uv * texture_size;
// Use under_half to fix a rounding bug right around exact texel locations.
const float2 prev_texel_num = floor(curr_texel - float2(under_half));
const float wrong_field = fmod(
prev_texel_num.y + field_offset, il_step_multiple.y);
const float2 scanline_texel_num = prev_texel_num - float2(0.0, wrong_field);
// Snap to the center of the previous scanline in the current field:
const float2 scanline_texel = scanline_texel_num + float2(0.5);
const float2 scanline_uv = scanline_texel * texture_size_inv;
// Save the sample's distance from the scanline, in units of scanlines:
dist = (curr_texel.y - scanline_texel.y)/il_step_multiple.y;
return scanline_uv;
}
*/
bool is_interlaced(float num_lines)
{
// Detect interlacing based on the number of lines in the source.
if(interlace_detect)
{
// NTSC: 525 lines, 262.5/field; 486 active (2 half-lines), 243/field
// NTSC Emulators: Typically 224 or 240 lines
// PAL: 625 lines, 312.5/field; 576 active (typical), 288/field
// PAL Emulators: ?
// ATSC: 720p, 1080i, 1080p
// Where do we place our cutoffs? Assumptions:
// 1.) We only need to care about active lines.
// 2.) Anything > 288 and <= 576 lines is probably interlaced.
// 3.) Anything > 576 lines is probably not interlaced...
// 4.) ...except 1080 lines, which is a crapshoot (user decision).
// 5.) Just in case the main program uses calculated video sizes,
// we should nudge the float thresholds a bit.
bool sd_interlace;
if (num_lines > 288.5 && num_lines < 576.5)
{sd_interlace = true;}
else
{sd_interlace = false;}
bool hd_interlace;
if (num_lines > 1079.5 && num_lines < 1080.5)
{hd_interlace = false;}
else
{hd_interlace = sd_interlace || hd_interlace;}
}
else
{
return false;
}
}
#endif // SCANLINE_FUNCTIONS_H

8
crt/shaders/crt-royale/src/scanline-functions.h
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@ -22,10 +22,10 @@
////////////////////////////////// INCLUDES ////////////////////////////////// ////////////////////////////////// INCLUDES //////////////////////////////////
//#include "../user-settings.h" #include "../user-settings.h"
//#include "derived-settings-and-constants.h" #include "derived-settings-and-constants.h"
//#include "../../../../include/special-functions.h" #include "../../../../include/special-functions.h"
//#include "../../../../include/gamma-management.h" #include "../../../../include/gamma-management.h"
///////////////////////////// SCANLINE FUNCTIONS ///////////////////////////// ///////////////////////////// SCANLINE FUNCTIONS /////////////////////////////

498
crt/shaders/crt-royale/src/special-functions-old.h
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@ -1,498 +0,0 @@
#ifndef SPECIAL_FUNCTIONS_H
#define SPECIAL_FUNCTIONS_H
///////////////////////////////// MIT LICENSE ////////////////////////////////
// Copyright (C) 2014 TroggleMonkey
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to
// deal in the Software without restriction, including without limitation the
// rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
// sell copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
// IN THE SOFTWARE.
///////////////////////////////// DESCRIPTION ////////////////////////////////
// This file implements the following mathematical special functions:
// 1.) erf() = 2/sqrt(pi) * indefinite_integral(e**(-x**2))
// 2.) gamma(s), a real-numbered extension of the integer factorial function
// It also implements normalized_ligamma(s, z), a normalized lower incomplete
// gamma function for s < 0.5 only. Both gamma() and normalized_ligamma() can
// be called with an _impl suffix to use an implementation version with a few
// extra precomputed parameters (which may be useful for the caller to reuse).
// See below for details.
//
// Design Rationale:
// Pretty much every line of code in this file is duplicated four times for
// different input types (vec4/vec3/vec2/float). This is unfortunate,
// but Cg doesn't allow function templates. Macros would be far less verbose,
// but they would make the code harder to document and read. I don't expect
// these functions will require a whole lot of maintenance changes unless
// someone ever has need for more robust incomplete gamma functions, so code
// duplication seems to be the lesser evil in this case.
/////////////////////////// GAUSSIAN ERROR FUNCTION //////////////////////////
vec4 erf6(vec4 x)
{
// Requires: x is the standard parameter to erf().
// Returns: Return an Abramowitz/Stegun approximation of erf(), where:
// erf(x) = 2/sqrt(pi) * integral(e**(-x**2))
// This approximation has a max absolute error of 2.5*10**-5
// with solid numerical robustness and efficiency. See:
// https://en.wikipedia.org/wiki/Error_function#Approximation_with_elementary_functions
const vec4 one = vec4(1.0);
const vec4 sign_x = sign(x);
const vec4 t = one/(one + 0.47047*abs(x));
const vec4 result = one - t*(0.3480242 + t*(-0.0958798 + t*0.7478556))*
exp(-(x*x));
return result * sign_x;
}
vec3 erf6(const vec3 x)
{
// vec3 version:
const vec3 one = vec3(1.0);
const vec3 sign_x = sign(x);
const vec3 t = one/(one + 0.47047*abs(x));
const vec3 result = one - t*(0.3480242 + t*(-0.0958798 + t*0.7478556))*
exp(-(x*x));
return result * sign_x;
}
vec2 erf6(const vec2 x)
{
// vec2 version:
const vec2 one = vec2(1.0);
const vec2 sign_x = sign(x);
const vec2 t = one/(one + 0.47047*abs(x));
const vec2 result = one - t*(0.3480242 + t*(-0.0958798 + t*0.7478556))*
exp(-(x*x));
return result * sign_x;
}
float erf6(const float x)
{
// Float version:
const float sign_x = sign(x);
const float t = 1.0/(1.0 + 0.47047*abs(x));
const float result = 1.0 - t*(0.3480242 + t*(-0.0958798 + t*0.7478556))*
exp(-(x*x));
return result * sign_x;
}
vec4 erft(const vec4 x)
{
// Requires: x is the standard parameter to erf().
// Returns: Approximate erf() with the hyperbolic tangent. The error is
// visually noticeable, but it's blazing fast and perceptually
// close...at least on ATI hardware. See:
// http://www.maplesoft.com/applications/view.aspx?SID=5525&view=html
// Warning: Only use this if your hardware drivers correctly implement
// tanh(): My nVidia 8800GTS returns garbage output.
return tanh(1.202760580 * x);
}
vec3 erft(const vec3 x)
{
// vec3 version:
return tanh(1.202760580 * x);
}
vec2 erft(const vec2 x)
{
// vec2 version:
return tanh(1.202760580 * x);
}
float erft(const float x)
{
// Float version:
return tanh(1.202760580 * x);
}
vec4 erf(const vec4 x)
{
// Requires: x is the standard parameter to erf().
// Returns: Some approximation of erf(x), depending on user settings.
#ifdef ERF_FAST_APPROXIMATION
return erft(x);
#else
return erf6(x);
#endif
}
vec3 erf(const vec3 x)
{
// vec3 version:
#ifdef ERF_FAST_APPROXIMATION
return erft(x);
#else
return erf6(x);
#endif
}
vec2 erf(const vec2 x)
{
// vec2 version:
#ifdef ERF_FAST_APPROXIMATION
return erft(x);
#else
return erf6(x);
#endif
}
float erf(const float x)
{
// Float version:
#ifdef ERF_FAST_APPROXIMATION
return erft(x);
#else
return erf6(x);
#endif
}
/////////////////////////// COMPLETE GAMMA FUNCTION //////////////////////////
vec4 gamma_impl(const vec4 s, const vec4 s_inv)
{
// Requires: 1.) s is the standard parameter to the gamma function, and
// it should lie in the [0, 36] range.
// 2.) s_inv = 1.0/s. This implementation function requires
// the caller to precompute this value, giving users the
// opportunity to reuse it.
// Returns: Return approximate gamma function (real-numbered factorial)
// output using the Lanczos approximation with two coefficients
// calculated using Paul Godfrey's method here:
// http://my.fit.edu/~gabdo/gamma.txt
// An optimal g value for s in [0, 36] is ~1.12906830989, with
// a maximum relative error of 0.000463 for 2**16 equally
// evals. We could use three coeffs (0.0000346 error) without
// hurting latency, but this allows more parallelism with
// outside instructions.
const vec4 g = vec4(1.12906830989);
const vec4 c0 = vec4(0.8109119309638332633713423362694399653724431);
const vec4 c1 = vec4(0.4808354605142681877121661197951496120000040);
const vec4 e = vec4(2.71828182845904523536028747135266249775724709);
const vec4 sph = s + vec4(0.5);
const vec4 lanczos_sum = c0 + c1/(s + vec4(1.0));
const vec4 base = (sph + g)/e; // or (s + g + vec4(0.5))/e
// gamma(s + 1) = base**sph * lanczos_sum; divide by s for gamma(s).
// This has less error for small s's than (s -= 1.0) at the beginning.
return (pow(base, sph) * lanczos_sum) * s_inv;
}
vec3 gamma_impl(const vec3 s, const vec3 s_inv)
{
// vec3 version:
const vec3 g = vec3(1.12906830989);
const vec3 c0 = vec3(0.8109119309638332633713423362694399653724431);
const vec3 c1 = vec3(0.4808354605142681877121661197951496120000040);
const vec3 e = vec3(2.71828182845904523536028747135266249775724709);
const vec3 sph = s + vec3(0.5);
const vec3 lanczos_sum = c0 + c1/(s + vec3(1.0));
const vec3 base = (sph + g)/e;
return (pow(base, sph) * lanczos_sum) * s_inv;
}
vec2 gamma_impl(const vec2 s, const vec2 s_inv)
{
// vec2 version:
const vec2 g = vec2(1.12906830989);
const vec2 c0 = vec2(0.8109119309638332633713423362694399653724431);
const vec2 c1 = vec2(0.4808354605142681877121661197951496120000040);
const vec2 e = vec2(2.71828182845904523536028747135266249775724709);
const vec2 sph = s + vec2(0.5);
const vec2 lanczos_sum = c0 + c1/(s + vec2(1.0));
const vec2 base = (sph + g)/e;
return (pow(base, sph) * lanczos_sum) * s_inv;
}
float gamma_impl(const float s, const float s_inv)
{
// Float version:
const float g = 1.12906830989;
const float c0 = 0.8109119309638332633713423362694399653724431;
const float c1 = 0.4808354605142681877121661197951496120000040;
const float e = 2.71828182845904523536028747135266249775724709;
const float sph = s + 0.5;
const float lanczos_sum = c0 + c1/(s + 1.0);
const float base = (sph + g)/e;
return (pow(base, sph) * lanczos_sum) * s_inv;
}
vec4 gamma(const vec4 s)
{
// Requires: s is the standard parameter to the gamma function, and it
// should lie in the [0, 36] range.
// Returns: Return approximate gamma function output with a maximum
// relative error of 0.000463. See gamma_impl for details.
return gamma_impl(s, vec4(1.0)/s);
}
vec3 gamma(const vec3 s)
{
// vec3 version:
return gamma_impl(s, vec3(1.0)/s);
}
vec2 gamma(const vec2 s)
{
// vec2 version:
return gamma_impl(s, vec2(1.0)/s);
}
float gamma(const float s)
{
// Float version:
return gamma_impl(s, 1.0/s);
}
//////////////// INCOMPLETE GAMMA FUNCTIONS (RESTRICTED INPUT) ///////////////
// Lower incomplete gamma function for small s and z (implementation):
vec4 ligamma_small_z_impl(const vec4 s, const vec4 z, const vec4 s_inv)
{
// Requires: 1.) s < ~0.5
// 2.) z <= ~0.775075
// 3.) s_inv = 1.0/s (precomputed for outside reuse)
// Returns: A series representation for the lower incomplete gamma
// function for small s and small z (4 terms).
// The actual "rolled up" summation looks like:
// last_sign = 1.0; last_pow = 1.0; last_factorial = 1.0;
// sum = last_sign * last_pow / ((s + k) * last_factorial)
// for(int i = 0; i < 4; ++i)
// {
// last_sign *= -1.0; last_pow *= z; last_factorial *= i;
// sum += last_sign * last_pow / ((s + k) * last_factorial);
// }
// Unrolled, constant-unfolded and arranged for madds and parallelism:
const vec4 scale = pow(z, s);
vec4 sum = s_inv; // Summation iteration 0 result
// Summation iterations 1, 2, and 3:
const vec4 z_sq = z*z;
const vec4 denom1 = s + vec4(1.0);
const vec4 denom2 = 2.0*s + vec4(4.0);
const vec4 denom3 = 6.0*s + vec4(18.0);
//vec4 denom4 = 24.0*s + vec4(96.0);
sum -= z/denom1;
sum += z_sq/denom2;
sum -= z * z_sq/denom3;
//sum += z_sq * z_sq / denom4;
// Scale and return:
return scale * sum;
}
vec3 ligamma_small_z_impl(const vec3 s, const vec3 z, const vec3 s_inv)
{
// vec3 version:
const vec3 scale = pow(z, s);
vec3 sum = s_inv;
const vec3 z_sq = z*z;
const vec3 denom1 = s + vec3(1.0);
const vec3 denom2 = 2.0*s + vec3(4.0);
const vec3 denom3 = 6.0*s + vec3(18.0);
sum -= z/denom1;
sum += z_sq/denom2;
sum -= z * z_sq/denom3;
return scale * sum;
}
vec2 ligamma_small_z_impl(const vec2 s, const vec2 z, const vec2 s_inv)
{
// vec2 version:
const vec2 scale = pow(z, s);
vec2 sum = s_inv;
const vec2 z_sq = z*z;
const vec2 denom1 = s + vec2(1.0);
const vec2 denom2 = 2.0*s + vec2(4.0);
const vec2 denom3 = 6.0*s + vec2(18.0);
sum -= z/denom1;
sum += z_sq/denom2;
sum -= z * z_sq/denom3;
return scale * sum;
}
float ligamma_small_z_impl(const float s, const float z, const float s_inv)
{
// Float version:
const float scale = pow(z, s);
float sum = s_inv;
const float z_sq = z*z;
const float denom1 = s + 1.0;
const float denom2 = 2.0*s + 4.0;
const float denom3 = 6.0*s + 18.0;
sum -= z/denom1;
sum += z_sq/denom2;
sum -= z * z_sq/denom3;
return scale * sum;
}
// Upper incomplete gamma function for small s and large z (implementation):
vec4 uigamma_large_z_impl(const vec4 s, const vec4 z)
{
// Requires: 1.) s < ~0.5
// 2.) z > ~0.775075
// Returns: Gauss's continued fraction representation for the upper
// incomplete gamma function (4 terms).
// The "rolled up" continued fraction looks like this. The denominator
// is truncated, and it's calculated "from the bottom up:"
// denom = vec4('inf');
// vec4 one = vec4(1.0);
// for(int i = 4; i > 0; --i)
// {
// denom = ((i * 2.0) - one) + z - s + (i * (s - i))/denom;
// }
// Unrolled and constant-unfolded for madds and parallelism:
const vec4 numerator = pow(z, s) * exp(-z);
vec4 denom = vec4(7.0) + z - s;
denom = vec4(5.0) + z - s + (3.0*s - vec4(9.0))/denom;
denom = vec4(3.0) + z - s + (2.0*s - vec4(4.0))/denom;
denom = vec4(1.0) + z - s + (s - vec4(1.0))/denom;
return numerator / denom;
}
vec3 uigamma_large_z_impl(const vec3 s, const vec3 z)
{
// vec3 version:
const vec3 numerator = pow(z, s) * exp(-z);
vec3 denom = vec3(7.0) + z - s;
denom = vec3(5.0) + z - s + (3.0*s - vec3(9.0))/denom;
denom = vec3(3.0) + z - s + (2.0*s - vec3(4.0))/denom;
denom = vec3(1.0) + z - s + (s - vec3(1.0))/denom;
return numerator / denom;
}
vec2 uigamma_large_z_impl(const vec2 s, const vec2 z)
{
// vec2 version:
const vec2 numerator = pow(z, s) * exp(-z);
vec2 denom = vec2(7.0) + z - s;
denom = vec2(5.0) + z - s + (3.0*s - vec2(9.0))/denom;
denom = vec2(3.0) + z - s + (2.0*s - vec2(4.0))/denom;
denom = vec2(1.0) + z - s + (s - vec2(1.0))/denom;
return numerator / denom;
}
float uigamma_large_z_impl(const float s, const float z)
{
// Float version:
const float numerator = pow(z, s) * exp(-z);
float denom = 7.0 + z - s;
denom = 5.0 + z - s + (3.0*s - 9.0)/denom;
denom = 3.0 + z - s + (2.0*s - 4.0)/denom;
denom = 1.0 + z - s + (s - 1.0)/denom;
return numerator / denom;
}
// Normalized lower incomplete gamma function for small s (implementation):
vec4 normalized_ligamma_impl(const vec4 s, const vec4 z,
const vec4 s_inv, const vec4 gamma_s_inv)
{
// Requires: 1.) s < ~0.5
// 2.) s_inv = 1/s (precomputed for outside reuse)
// 3.) gamma_s_inv = 1/gamma(s) (precomputed for outside reuse)
// Returns: Approximate the normalized lower incomplete gamma function
// for s < 0.5. Since we only care about s < 0.5, we only need
// to evaluate two branches (not four) based on z. Each branch
// uses four terms, with a max relative error of ~0.00182. The
// branch threshold and specifics were adapted for fewer terms
// from Gil/Segura/Temme's paper here:
// http://oai.cwi.nl/oai/asset/20433/20433B.pdf
// Evaluate both branches: Real branches test slower even when available.
const vec4 thresh = vec4(0.775075);
const bool4 z_is_large = z > thresh;
const vec4 large_z = vec4(1.0) - uigamma_large_z_impl(s, z) * gamma_s_inv;
const vec4 small_z = ligamma_small_z_impl(s, z, s_inv) * gamma_s_inv;
// Combine the results from both branches:
return large_z * vec4(z_is_large) + small_z * vec4(!z_is_large);
}
vec3 normalized_ligamma_impl(const vec3 s, const vec3 z,
const vec3 s_inv, const vec3 gamma_s_inv)
{
// vec3 version:
const vec3 thresh = vec3(0.775075);
const bool3 z_is_large = z > thresh;
const vec3 large_z = vec3(1.0) - uigamma_large_z_impl(s, z) * gamma_s_inv;
const vec3 small_z = ligamma_small_z_impl(s, z, s_inv) * gamma_s_inv;
return large_z * vec3(z_is_large) + small_z * vec3(!z_is_large);
}
vec2 normalized_ligamma_impl(const vec2 s, const vec2 z,
const vec2 s_inv, const vec2 gamma_s_inv)
{
// vec2 version:
const vec2 thresh = vec2(0.775075);
const bool2 z_is_large = z > thresh;
const vec2 large_z = vec2(1.0) - uigamma_large_z_impl(s, z) * gamma_s_inv;
const vec2 small_z = ligamma_small_z_impl(s, z, s_inv) * gamma_s_inv;
return large_z * vec2(z_is_large) + small_z * vec2(!z_is_large);
}
float normalized_ligamma_impl(const float s, const float z,
const float s_inv, const float gamma_s_inv)
{
// Float version:
const float thresh = 0.775075;
const bool z_is_large = z > thresh;
const float large_z = 1.0 - uigamma_large_z_impl(s, z) * gamma_s_inv;
const float small_z = ligamma_small_z_impl(s, z, s_inv) * gamma_s_inv;
return large_z * float(z_is_large) + small_z * float(!z_is_large);
}
// Normalized lower incomplete gamma function for small s:
vec4 normalized_ligamma(const vec4 s, const vec4 z)
{
// Requires: s < ~0.5
// Returns: Approximate the normalized lower incomplete gamma function
// for s < 0.5. See normalized_ligamma_impl() for details.
const vec4 s_inv = vec4(1.0)/s;
const vec4 gamma_s_inv = vec4(1.0)/gamma_impl(s, s_inv);
return normalized_ligamma_impl(s, z, s_inv, gamma_s_inv);
}
vec3 normalized_ligamma(const vec3 s, const vec3 z)
{
// vec3 version:
const vec3 s_inv = vec3(1.0)/s;
const vec3 gamma_s_inv = vec3(1.0)/gamma_impl(s, s_inv);
return normalized_ligamma_impl(s, z, s_inv, gamma_s_inv);
}
vec2 normalized_ligamma(const vec2 s, const vec2 z)
{
// vec2 version:
const vec2 s_inv = vec2(1.0)/s;
const vec2 gamma_s_inv = vec2(1.0)/gamma_impl(s, s_inv);
return normalized_ligamma_impl(s, z, s_inv, gamma_s_inv);
}
float normalized_ligamma(const float s, const float z)
{
// Float version:
const float s_inv = 1.0/s;
const float gamma_s_inv = 1.0/gamma_impl(s, s_inv);
return normalized_ligamma_impl(s, z, s_inv, gamma_s_inv);
}
#endif // SPECIAL_FUNCTIONS_H

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#ifndef SPECIAL_FUNCTIONS_H
#define SPECIAL_FUNCTIONS_H
///////////////////////////////// MIT LICENSE ////////////////////////////////
// Copyright (C) 2014 TroggleMonkey
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to
// deal in the Software without restriction, including without limitation the
// rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
// sell copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
// IN THE SOFTWARE.
///////////////////////////////// DESCRIPTION ////////////////////////////////
// This file implements the following mathematical special functions:
// 1.) erf() = 2/sqrt(pi) * indefinite_integral(e**(-x**2))
// 2.) gamma(s), a real-numbered extension of the integer factorial function
// It also implements normalized_ligamma(s, z), a normalized lower incomplete
// gamma function for s < 0.5 only. Both gamma() and normalized_ligamma() can
// be called with an _impl suffix to use an implementation version with a few
// extra precomputed parameters (which may be useful for the caller to reuse).
// See below for details.
//
// Design Rationale:
// Pretty much every line of code in this file is duplicated four times for
// different input types (vec4/vec3/vec2/float). This is unfortunate,
// but Cg doesn't allow function templates. Macros would be far less verbose,
// but they would make the code harder to document and read. I don't expect
// these functions will require a whole lot of maintenance changes unless
// someone ever has need for more robust incomplete gamma functions, so code
// duplication seems to be the lesser evil in this case.
/////////////////////////// GAUSSIAN ERROR FUNCTION //////////////////////////
vec4 erf6(vec4 x)
{
// Requires: x is the standard parameter to erf().
// Returns: Return an Abramowitz/Stegun approximation of erf(), where:
// erf(x) = 2/sqrt(pi) * integral(e**(-x**2))
// This approximation has a max absolute error of 2.5*10**-5
// with solid numerical robustness and efficiency. See:
// https://en.wikipedia.org/wiki/Error_function#Approximation_with_elementary_functions
const vec4 one = vec4(1.0);
const vec4 sign_x = sign(x);
const vec4 t = one/(one + 0.47047*abs(x));
const vec4 result = one - t*(0.3480242 + t*(-0.0958798 + t*0.7478556))*
exp(-(x*x));
return result * sign_x;
}
vec3 erf6(const vec3 x)
{
// vec3 version:
const vec3 one = vec3(1.0);
const vec3 sign_x = sign(x);
const vec3 t = one/(one + 0.47047*abs(x));
const vec3 result = one - t*(0.3480242 + t*(-0.0958798 + t*0.7478556))*
exp(-(x*x));
return result * sign_x;
}
vec2 erf6(const vec2 x)
{
// vec2 version:
const vec2 one = vec2(1.0);
const vec2 sign_x = sign(x);
const vec2 t = one/(one + 0.47047*abs(x));
const vec2 result = one - t*(0.3480242 + t*(-0.0958798 + t*0.7478556))*
exp(-(x*x));
return result * sign_x;
}
float erf6(const float x)
{
// Float version:
const float sign_x = sign(x);
const float t = 1.0/(1.0 + 0.47047*abs(x));
const float result = 1.0 - t*(0.3480242 + t*(-0.0958798 + t*0.7478556))*
exp(-(x*x));
return result * sign_x;
}
vec4 erft(const vec4 x)
{
// Requires: x is the standard parameter to erf().
// Returns: Approximate erf() with the hyperbolic tangent. The error is
// visually noticeable, but it's blazing fast and perceptually
// close...at least on ATI hardware. See:
// http://www.maplesoft.com/applications/view.aspx?SID=5525&view=html
// Warning: Only use this if your hardware drivers correctly implement
// tanh(): My nVidia 8800GTS returns garbage output.
return tanh(1.202760580 * x);
}
vec3 erft(const vec3 x)
{
// vec3 version:
return tanh(1.202760580 * x);
}
vec2 erft(const vec2 x)
{
// vec2 version:
return tanh(1.202760580 * x);
}
float erft(const float x)
{
// Float version:
return tanh(1.202760580 * x);
}
vec4 erf(const vec4 x)
{
// Requires: x is the standard parameter to erf().
// Returns: Some approximation of erf(x), depending on user settings.
#ifdef ERF_FAST_APPROXIMATION
return erft(x);
#else
return erf6(x);
#endif
}
vec3 erf(const vec3 x)
{
// vec3 version:
#ifdef ERF_FAST_APPROXIMATION
return erft(x);
#else
return erf6(x);
#endif
}
vec2 erf(const vec2 x)
{
// vec2 version:
#ifdef ERF_FAST_APPROXIMATION
return erft(x);
#else
return erf6(x);
#endif
}
float erf(const float x)
{
// Float version:
#ifdef ERF_FAST_APPROXIMATION
return erft(x);
#else
return erf6(x);
#endif
}
/////////////////////////// COMPLETE GAMMA FUNCTION //////////////////////////
vec4 gamma_impl(const vec4 s, const vec4 s_inv)
{
// Requires: 1.) s is the standard parameter to the gamma function, and
// it should lie in the [0, 36] range.
// 2.) s_inv = 1.0/s. This implementation function requires
// the caller to precompute this value, giving users the
// opportunity to reuse it.
// Returns: Return approximate gamma function (real-numbered factorial)
// output using the Lanczos approximation with two coefficients
// calculated using Paul Godfrey's method here:
// http://my.fit.edu/~gabdo/gamma.txt
// An optimal g value for s in [0, 36] is ~1.12906830989, with
// a maximum relative error of 0.000463 for 2**16 equally
// evals. We could use three coeffs (0.0000346 error) without
// hurting latency, but this allows more parallelism with
// outside instructions.
const vec4 g = vec4(1.12906830989);
const vec4 c0 = vec4(0.8109119309638332633713423362694399653724431);
const vec4 c1 = vec4(0.4808354605142681877121661197951496120000040);
const vec4 e = vec4(2.71828182845904523536028747135266249775724709);
const vec4 sph = s + vec4(0.5);
const vec4 lanczos_sum = c0 + c1/(s + vec4(1.0));
const vec4 base = (sph + g)/e; // or (s + g + vec4(0.5))/e
// gamma(s + 1) = base**sph * lanczos_sum; divide by s for gamma(s).
// This has less error for small s's than (s -= 1.0) at the beginning.
return (pow(base, sph) * lanczos_sum) * s_inv;
}
vec3 gamma_impl(const vec3 s, const vec3 s_inv)
{
// vec3 version:
const vec3 g = vec3(1.12906830989);
const vec3 c0 = vec3(0.8109119309638332633713423362694399653724431);
const vec3 c1 = vec3(0.4808354605142681877121661197951496120000040);
const vec3 e = vec3(2.71828182845904523536028747135266249775724709);
const vec3 sph = s + vec3(0.5);
const vec3 lanczos_sum = c0 + c1/(s + vec3(1.0));
const vec3 base = (sph + g)/e;
return (pow(base, sph) * lanczos_sum) * s_inv;
}
vec2 gamma_impl(const vec2 s, const vec2 s_inv)
{
// vec2 version:
const vec2 g = vec2(1.12906830989);
const vec2 c0 = vec2(0.8109119309638332633713423362694399653724431);
const vec2 c1 = vec2(0.4808354605142681877121661197951496120000040);
const vec2 e = vec2(2.71828182845904523536028747135266249775724709);
const vec2 sph = s + vec2(0.5);
const vec2 lanczos_sum = c0 + c1/(s + vec2(1.0));
const vec2 base = (sph + g)/e;
return (pow(base, sph) * lanczos_sum) * s_inv;
}
float gamma_impl(const float s, const float s_inv)
{
// Float version:
const float g = 1.12906830989;
const float c0 = 0.8109119309638332633713423362694399653724431;
const float c1 = 0.4808354605142681877121661197951496120000040;
const float e = 2.71828182845904523536028747135266249775724709;
const float sph = s + 0.5;
const float lanczos_sum = c0 + c1/(s + 1.0);
const float base = (sph + g)/e;
return (pow(base, sph) * lanczos_sum) * s_inv;
}
vec4 gamma(const vec4 s)
{
// Requires: s is the standard parameter to the gamma function, and it
// should lie in the [0, 36] range.
// Returns: Return approximate gamma function output with a maximum
// relative error of 0.000463. See gamma_impl for details.
return gamma_impl(s, vec4(1.0)/s);
}
vec3 gamma(const vec3 s)
{
// vec3 version:
return gamma_impl(s, vec3(1.0)/s);
}
vec2 gamma(const vec2 s)
{
// vec2 version:
return gamma_impl(s, vec2(1.0)/s);
}
float gamma(const float s)
{
// Float version:
return gamma_impl(s, 1.0/s);
}
//////////////// INCOMPLETE GAMMA FUNCTIONS (RESTRICTED INPUT) ///////////////
// Lower incomplete gamma function for small s and z (implementation):
vec4 ligamma_small_z_impl(const vec4 s, const vec4 z, const vec4 s_inv)
{
// Requires: 1.) s < ~0.5
// 2.) z <= ~0.775075
// 3.) s_inv = 1.0/s (precomputed for outside reuse)
// Returns: A series representation for the lower incomplete gamma
// function for small s and small z (4 terms).
// The actual "rolled up" summation looks like:
// last_sign = 1.0; last_pow = 1.0; last_factorial = 1.0;
// sum = last_sign * last_pow / ((s + k) * last_factorial)
// for(int i = 0; i < 4; ++i)
// {
// last_sign *= -1.0; last_pow *= z; last_factorial *= i;
// sum += last_sign * last_pow / ((s + k) * last_factorial);
// }
// Unrolled, constant-unfolded and arranged for madds and parallelism:
const vec4 scale = pow(z, s);
vec4 sum = s_inv; // Summation iteration 0 result
// Summation iterations 1, 2, and 3:
const vec4 z_sq = z*z;
const vec4 denom1 = s + vec4(1.0);
const vec4 denom2 = 2.0*s + vec4(4.0);
const vec4 denom3 = 6.0*s + vec4(18.0);
//vec4 denom4 = 24.0*s + vec4(96.0);
sum -= z/denom1;
sum += z_sq/denom2;
sum -= z * z_sq/denom3;
//sum += z_sq * z_sq / denom4;
// Scale and return:
return scale * sum;
}
vec3 ligamma_small_z_impl(const vec3 s, const vec3 z, const vec3 s_inv)
{
// vec3 version:
const vec3 scale = pow(z, s);
vec3 sum = s_inv;
const vec3 z_sq = z*z;
const vec3 denom1 = s + vec3(1.0);
const vec3 denom2 = 2.0*s + vec3(4.0);
const vec3 denom3 = 6.0*s + vec3(18.0);
sum -= z/denom1;
sum += z_sq/denom2;
sum -= z * z_sq/denom3;
return scale * sum;
}
vec2 ligamma_small_z_impl(const vec2 s, const vec2 z, const vec2 s_inv)
{
// vec2 version:
const vec2 scale = pow(z, s);
vec2 sum = s_inv;
const vec2 z_sq = z*z;
const vec2 denom1 = s + vec2(1.0);
const vec2 denom2 = 2.0*s + vec2(4.0);
const vec2 denom3 = 6.0*s + vec2(18.0);
sum -= z/denom1;
sum += z_sq/denom2;
sum -= z * z_sq/denom3;
return scale * sum;
}
float ligamma_small_z_impl(const float s, const float z, const float s_inv)
{
// Float version:
const float scale = pow(z, s);
float sum = s_inv;
const float z_sq = z*z;
const float denom1 = s + 1.0;
const float denom2 = 2.0*s + 4.0;
const float denom3 = 6.0*s + 18.0;
sum -= z/denom1;
sum += z_sq/denom2;
sum -= z * z_sq/denom3;
return scale * sum;
}
// Upper incomplete gamma function for small s and large z (implementation):
vec4 uigamma_large_z_impl(const vec4 s, const vec4 z)
{
// Requires: 1.) s < ~0.5
// 2.) z > ~0.775075
// Returns: Gauss's continued fraction representation for the upper
// incomplete gamma function (4 terms).
// The "rolled up" continued fraction looks like this. The denominator
// is truncated, and it's calculated "from the bottom up:"
// denom = vec4('inf');
// vec4 one = vec4(1.0);
// for(int i = 4; i > 0; --i)
// {
// denom = ((i * 2.0) - one) + z - s + (i * (s - i))/denom;
// }
// Unrolled and constant-unfolded for madds and parallelism:
const vec4 numerator = pow(z, s) * exp(-z);
vec4 denom = vec4(7.0) + z - s;
denom = vec4(5.0) + z - s + (3.0*s - vec4(9.0))/denom;
denom = vec4(3.0) + z - s + (2.0*s - vec4(4.0))/denom;
denom = vec4(1.0) + z - s + (s - vec4(1.0))/denom;
return numerator / denom;
}
vec3 uigamma_large_z_impl(const vec3 s, const vec3 z)
{
// vec3 version:
const vec3 numerator = pow(z, s) * exp(-z);
vec3 denom = vec3(7.0) + z - s;
denom = vec3(5.0) + z - s + (3.0*s - vec3(9.0))/denom;
denom = vec3(3.0) + z - s + (2.0*s - vec3(4.0))/denom;
denom = vec3(1.0) + z - s + (s - vec3(1.0))/denom;
return numerator / denom;
}
vec2 uigamma_large_z_impl(const vec2 s, const vec2 z)
{
// vec2 version:
const vec2 numerator = pow(z, s) * exp(-z);
vec2 denom = vec2(7.0) + z - s;
denom = vec2(5.0) + z - s + (3.0*s - vec2(9.0))/denom;
denom = vec2(3.0) + z - s + (2.0*s - vec2(4.0))/denom;
denom = vec2(1.0) + z - s + (s - vec2(1.0))/denom;
return numerator / denom;
}
float uigamma_large_z_impl(const float s, const float z)
{
// Float version:
const float numerator = pow(z, s) * exp(-z);
float denom = 7.0 + z - s;
denom = 5.0 + z - s + (3.0*s - 9.0)/denom;
denom = 3.0 + z - s + (2.0*s - 4.0)/denom;
denom = 1.0 + z - s + (s - 1.0)/denom;
return numerator / denom;
}
// Normalized lower incomplete gamma function for small s (implementation):
vec4 normalized_ligamma_impl(const vec4 s, const vec4 z,
const vec4 s_inv, const vec4 gamma_s_inv)
{
// Requires: 1.) s < ~0.5
// 2.) s_inv = 1/s (precomputed for outside reuse)
// 3.) gamma_s_inv = 1/gamma(s) (precomputed for outside reuse)
// Returns: Approximate the normalized lower incomplete gamma function
// for s < 0.5. Since we only care about s < 0.5, we only need
// to evaluate two branches (not four) based on z. Each branch
// uses four terms, with a max relative error of ~0.00182. The
// branch threshold and specifics were adapted for fewer terms
// from Gil/Segura/Temme's paper here:
// http://oai.cwi.nl/oai/asset/20433/20433B.pdf
// Evaluate both branches: Real branches test slower even when available.
const vec4 thresh = vec4(0.775075);
bvec4 z_is_large = greaterThan(z , thresh);
vec4 z_size_check = vec4(z_is_large.x ? 1.0 : 0.0, z_is_large.y ? 1.0 : 0.0, z_is_large.z ? 1.0 : 0.0, z_is_large.w ? 1.0 : 0.0);
const vec4 large_z = vec4(1.0) - uigamma_large_z_impl(s, z) * gamma_s_inv;
const vec4 small_z = ligamma_small_z_impl(s, z, s_inv) * gamma_s_inv;
// Combine the results from both branches:
return large_z * vec4(z_size_check) + small_z * vec4(z_size_check);
}
vec3 normalized_ligamma_impl(const vec3 s, const vec3 z,
const vec3 s_inv, const vec3 gamma_s_inv)
{
// vec3 version:
const vec3 thresh = vec3(0.775075);
bvec3 z_is_large = greaterThan(z , thresh);
vec3 z_size_check = vec3(z_is_large.x ? 1.0 : 0.0, z_is_large.y ? 1.0 : 0.0, z_is_large.z ? 1.0 : 0.0);
const vec3 large_z = vec3(1.0) - uigamma_large_z_impl(s, z) * gamma_s_inv;
const vec3 small_z = ligamma_small_z_impl(s, z, s_inv) * gamma_s_inv;
return large_z * vec3(z_size_check) + small_z * vec3(z_size_check);
}
vec2 normalized_ligamma_impl(const vec2 s, const vec2 z,
const vec2 s_inv, const vec2 gamma_s_inv)
{
// vec2 version:
const vec2 thresh = vec2(0.775075);
bvec2 z_is_large = greaterThan(z , thresh);
vec2 z_size_check = vec2(z_is_large.x ? 1.0 : 0.0, z_is_large.y ? 1.0 : 0.0);
const vec2 large_z = vec2(1.0) - uigamma_large_z_impl(s, z) * gamma_s_inv;
const vec2 small_z = ligamma_small_z_impl(s, z, s_inv) * gamma_s_inv;
return large_z * vec2(z_size_check) + small_z * vec2(z_size_check);
}
float normalized_ligamma_impl(const float s, const float z,
const float s_inv, const float gamma_s_inv)
{
// Float version:
const float thresh = 0.775075;
float z_size_check = 0.0;
if (z > thresh) z_size_check = 1.0;
const float large_z = 1.0 - uigamma_large_z_impl(s, z) * gamma_s_inv;
const float small_z = ligamma_small_z_impl(s, z, s_inv) * gamma_s_inv;
return large_z * float(z_size_check) + small_z * float(z_size_check);
}
// Normalized lower incomplete gamma function for small s:
vec4 normalized_ligamma(const vec4 s, const vec4 z)
{
// Requires: s < ~0.5
// Returns: Approximate the normalized lower incomplete gamma function
// for s < 0.5. See normalized_ligamma_impl() for details.
const vec4 s_inv = vec4(1.0)/s;
const vec4 gamma_s_inv = vec4(1.0)/gamma_impl(s, s_inv);
return normalized_ligamma_impl(s, z, s_inv, gamma_s_inv);
}
vec3 normalized_ligamma(const vec3 s, const vec3 z)
{
// vec3 version:
const vec3 s_inv = vec3(1.0)/s;
const vec3 gamma_s_inv = vec3(1.0)/gamma_impl(s, s_inv);
return normalized_ligamma_impl(s, z, s_inv, gamma_s_inv);
}
vec2 normalized_ligamma(const vec2 s, const vec2 z)
{
// vec2 version:
const vec2 s_inv = vec2(1.0)/s;
const vec2 gamma_s_inv = vec2(1.0)/gamma_impl(s, s_inv);
return normalized_ligamma_impl(s, z, s_inv, gamma_s_inv);
}
float normalized_ligamma(const float s, const float z)
{
// Float version:
const float s_inv = 1.0/s;
const float gamma_s_inv = 1.0/gamma_impl(s, s_inv);
return normalized_ligamma_impl(s, z, s_inv, gamma_s_inv);
}
#endif // SPECIAL_FUNCTIONS_H

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crt/shaders/crt-royale/src/tex2Dantialias-old.h
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2
crt/shaders/crt-royale/user-settings.h
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@ -74,7 +74,7 @@
// Enable runtime shader parameters in the Retroarch (etc.) GUI? They override // Enable runtime shader parameters in the Retroarch (etc.) GUI? They override
// many of the options in this file and allow real-time tuning, but many of // many of the options in this file and allow real-time tuning, but many of
// them are slower. Disabling them and using this text file will boost FPS. // them are slower. Disabling them and using this text file will boost FPS.
#define RUNTIME_SHADER_PARAMS_ENABLE //#define RUNTIME_SHADER_PARAMS_ENABLE
// Specify the phosphor bloom sigma at runtime? This option is 10% slower, but // Specify the phosphor bloom sigma at runtime? This option is 10% slower, but
// it's the only way to do a wide-enough full bloom with a runtime dot pitch. // it's the only way to do a wide-enough full bloom with a runtime dot pitch.
#define RUNTIME_PHOSPHOR_BLOOM_SIGMA #define RUNTIME_PHOSPHOR_BLOOM_SIGMA

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include/blur-functions-old.h
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include/blur-functions.h
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@ -1,4 +1,5 @@
#define BLUR_FUNCTIONS #ifndef BLUR_FUNCTIONS_H
#define BLUR_FUNCTIONS_H
///////////////////////////////// MIT LICENSE //////////////////////////////// ///////////////////////////////// MIT LICENSE ////////////////////////////////
@ -200,6 +201,14 @@
// Make a length squared helper macro (for usage with static constants): // Make a length squared helper macro (for usage with static constants):
#define LENGTH_SQ(vec) (dot(vec, vec)) #define LENGTH_SQ(vec) (dot(vec, vec))
////////////////////////////////// INCLUDES //////////////////////////////////
// gamma-management.h relies on pass-specific settings to guide its behavior:
// FIRST_PASS, LAST_PASS, GAMMA_ENCODE_EVERY_FBO, etc. See it for details.
#include "gamma-management.h"
//#include "quad-pixel-communication.h"
#include "special-functions.h"
/////////////////////////////////// HELPERS ////////////////////////////////// /////////////////////////////////// HELPERS //////////////////////////////////
vec4 uv2_to_uv4(vec2 tex_uv) vec4 uv2_to_uv4(vec2 tex_uv)
@ -232,6 +241,258 @@ float get_fast_gaussian_weight_sum_inv(const float sigma)
(sigma - 0.0860587260734721))), 0.399334576340352/sigma); (sigma - 0.0860587260734721))), 0.399334576340352/sigma);
} }
vec3 tex2Dblur17fast(const sampler2D tex, const vec2 tex_uv,
const vec2 dxdy, const float sigma)
{
// Requires: Same as tex2Dblur11()
// Returns: A 1D 17x Gaussian blurred texture lookup using 1 nearest
// neighbor and 8 linear taps. It may be mipmapped depending
// on settings and dxdy.
// First get the texel weights and normalization factor as above.
const float denom_inv = 0.5/(sigma*sigma);
const float w0 = 1.0;
const float w1 = exp(-1.0 * denom_inv);
const float w2 = exp(-4.0 * denom_inv);
const float w3 = exp(-9.0 * denom_inv);
const float w4 = exp(-16.0 * denom_inv);
const float w5 = exp(-25.0 * denom_inv);
const float w6 = exp(-36.0 * denom_inv);
const float w7 = exp(-49.0 * denom_inv);
const float w8 = exp(-64.0 * denom_inv);
//const float weight_sum_inv = 1.0 / (w0 + 2.0 * (
// w1 + w2 + w3 + w4 + w5 + w6 + w7 + w8));
const float weight_sum_inv = get_fast_gaussian_weight_sum_inv(sigma);
// Calculate combined weights and linear sample ratios between texel pairs.
const float w1_2 = w1 + w2;
const float w3_4 = w3 + w4;
const float w5_6 = w5 + w6;
const float w7_8 = w7 + w8;
const float w1_2_ratio = w2/w1_2;
const float w3_4_ratio = w4/w3_4;
const float w5_6_ratio = w6/w5_6;
const float w7_8_ratio = w8/w7_8;
// Statically normalize weights, sum weighted samples, and return:
vec3 sum = vec3(0.0);
sum += w7_8 * tex2D_linearize(tex, tex_uv - (7.0 + w7_8_ratio) * dxdy).rgb;
sum += w5_6 * tex2D_linearize(tex, tex_uv - (5.0 + w5_6_ratio) * dxdy).rgb;
sum += w3_4 * tex2D_linearize(tex, tex_uv - (3.0 + w3_4_ratio) * dxdy).rgb;
sum += w1_2 * tex2D_linearize(tex, tex_uv - (1.0 + w1_2_ratio) * dxdy).rgb;
sum += w0 * tex2D_linearize(tex, tex_uv).rgb;
sum += w1_2 * tex2D_linearize(tex, tex_uv + (1.0 + w1_2_ratio) * dxdy).rgb;
sum += w3_4 * tex2D_linearize(tex, tex_uv + (3.0 + w3_4_ratio) * dxdy).rgb;
sum += w5_6 * tex2D_linearize(tex, tex_uv + (5.0 + w5_6_ratio) * dxdy).rgb;
sum += w7_8 * tex2D_linearize(tex, tex_uv + (7.0 + w7_8_ratio) * dxdy).rgb;
return sum * weight_sum_inv;
}
vec3 tex2Dblur25fast(const sampler2D tex, const vec2 tex_uv,
const vec2 dxdy, const float sigma)
{
// Requires: Same as tex2Dblur11()
// Returns: A 1D 25x Gaussian blurred texture lookup using 1 nearest
// neighbor and 12 linear taps. It may be mipmapped depending
// on settings and dxdy.
// First get the texel weights and normalization factor as above.
const float denom_inv = 0.5/(sigma*sigma);
const float w0 = 1.0;
const float w1 = exp(-1.0 * denom_inv);
const float w2 = exp(-4.0 * denom_inv);
const float w3 = exp(-9.0 * denom_inv);
const float w4 = exp(-16.0 * denom_inv);
const float w5 = exp(-25.0 * denom_inv);
const float w6 = exp(-36.0 * denom_inv);
const float w7 = exp(-49.0 * denom_inv);
const float w8 = exp(-64.0 * denom_inv);
const float w9 = exp(-81.0 * denom_inv);
const float w10 = exp(-100.0 * denom_inv);
const float w11 = exp(-121.0 * denom_inv);
const float w12 = exp(-144.0 * denom_inv);
//const float weight_sum_inv = 1.0 / (w0 + 2.0 * (
// w1 + w2 + w3 + w4 + w5 + w6 + w7 + w8 + w9 + w10 + w11 + w12));
const float weight_sum_inv = get_fast_gaussian_weight_sum_inv(sigma);
// Calculate combined weights and linear sample ratios between texel pairs.
const float w1_2 = w1 + w2;
const float w3_4 = w3 + w4;
const float w5_6 = w5 + w6;
const float w7_8 = w7 + w8;
const float w9_10 = w9 + w10;
const float w11_12 = w11 + w12;
const float w1_2_ratio = w2/w1_2;
const float w3_4_ratio = w4/w3_4;
const float w5_6_ratio = w6/w5_6;
const float w7_8_ratio = w8/w7_8;
const float w9_10_ratio = w10/w9_10;
const float w11_12_ratio = w12/w11_12;
// Statically normalize weights, sum weighted samples, and return:
vec3 sum = vec3(0.0);
sum += w11_12 * tex2D_linearize(tex, tex_uv - (11.0 + w11_12_ratio) * dxdy).rgb;
sum += w9_10 * tex2D_linearize(tex, tex_uv - (9.0 + w9_10_ratio) * dxdy).rgb;
sum += w7_8 * tex2D_linearize(tex, tex_uv - (7.0 + w7_8_ratio) * dxdy).rgb;
sum += w5_6 * tex2D_linearize(tex, tex_uv - (5.0 + w5_6_ratio) * dxdy).rgb;
sum += w3_4 * tex2D_linearize(tex, tex_uv - (3.0 + w3_4_ratio) * dxdy).rgb;
sum += w1_2 * tex2D_linearize(tex, tex_uv - (1.0 + w1_2_ratio) * dxdy).rgb;
sum += w0 * tex2D_linearize(tex, tex_uv).rgb;
sum += w1_2 * tex2D_linearize(tex, tex_uv + (1.0 + w1_2_ratio) * dxdy).rgb;
sum += w3_4 * tex2D_linearize(tex, tex_uv + (3.0 + w3_4_ratio) * dxdy).rgb;
sum += w5_6 * tex2D_linearize(tex, tex_uv + (5.0 + w5_6_ratio) * dxdy).rgb;
sum += w7_8 * tex2D_linearize(tex, tex_uv + (7.0 + w7_8_ratio) * dxdy).rgb;
sum += w9_10 * tex2D_linearize(tex, tex_uv + (9.0 + w9_10_ratio) * dxdy).rgb;
sum += w11_12 * tex2D_linearize(tex, tex_uv + (11.0 + w11_12_ratio) * dxdy).rgb;
return sum * weight_sum_inv;
}
vec3 tex2Dblur31fast(const sampler2D tex, const vec2 tex_uv,
const vec2 dxdy, const float sigma)
{
// Requires: Same as tex2Dblur11()
// Returns: A 1D 31x Gaussian blurred texture lookup using 16 linear
// taps. It may be mipmapped depending on settings and dxdy.
// First get the texel weights and normalization factor as above.
const float denom_inv = 0.5/(sigma*sigma);
const float w0 = 1.0;
const float w1 = exp(-1.0 * denom_inv);
const float w2 = exp(-4.0 * denom_inv);
const float w3 = exp(-9.0 * denom_inv);
const float w4 = exp(-16.0 * denom_inv);
const float w5 = exp(-25.0 * denom_inv);
const float w6 = exp(-36.0 * denom_inv);
const float w7 = exp(-49.0 * denom_inv);
const float w8 = exp(-64.0 * denom_inv);
const float w9 = exp(-81.0 * denom_inv);
const float w10 = exp(-100.0 * denom_inv);
const float w11 = exp(-121.0 * denom_inv);
const float w12 = exp(-144.0 * denom_inv);
const float w13 = exp(-169.0 * denom_inv);
const float w14 = exp(-196.0 * denom_inv);
const float w15 = exp(-225.0 * denom_inv);
//const float weight_sum_inv = 1.0 /
// (w0 + 2.0 * (w1 + w2 + w3 + w4 + w5 + w6 + w7 + w8 +
// w9 + w10 + w11 + w12 + w13 + w14 + w15));
const float weight_sum_inv = get_fast_gaussian_weight_sum_inv(sigma);
// Calculate combined weights and linear sample ratios between texel pairs.
// The center texel (with weight w0) is used twice, so halve its weight.
const float w0_1 = w0 * 0.5 + w1;
const float w2_3 = w2 + w3;
const float w4_5 = w4 + w5;
const float w6_7 = w6 + w7;
const float w8_9 = w8 + w9;
const float w10_11 = w10 + w11;
const float w12_13 = w12 + w13;
const float w14_15 = w14 + w15;
const float w0_1_ratio = w1/w0_1;
const float w2_3_ratio = w3/w2_3;
const float w4_5_ratio = w5/w4_5;
const float w6_7_ratio = w7/w6_7;
const float w8_9_ratio = w9/w8_9;
const float w10_11_ratio = w11/w10_11;
const float w12_13_ratio = w13/w12_13;
const float w14_15_ratio = w15/w14_15;
// Statically normalize weights, sum weighted samples, and return:
vec3 sum = vec3(0.0);
sum += w14_15 * tex2D_linearize(tex, tex_uv - (14.0 + w14_15_ratio) * dxdy).rgb;
sum += w12_13 * tex2D_linearize(tex, tex_uv - (12.0 + w12_13_ratio) * dxdy).rgb;
sum += w10_11 * tex2D_linearize(tex, tex_uv - (10.0 + w10_11_ratio) * dxdy).rgb;
sum += w8_9 * tex2D_linearize(tex, tex_uv - (8.0 + w8_9_ratio) * dxdy).rgb;
sum += w6_7 * tex2D_linearize(tex, tex_uv - (6.0 + w6_7_ratio) * dxdy).rgb;
sum += w4_5 * tex2D_linearize(tex, tex_uv - (4.0 + w4_5_ratio) * dxdy).rgb;
sum += w2_3 * tex2D_linearize(tex, tex_uv - (2.0 + w2_3_ratio) * dxdy).rgb;
sum += w0_1 * tex2D_linearize(tex, tex_uv - w0_1_ratio * dxdy).rgb;
sum += w0_1 * tex2D_linearize(tex, tex_uv + w0_1_ratio * dxdy).rgb;
sum += w2_3 * tex2D_linearize(tex, tex_uv + (2.0 + w2_3_ratio) * dxdy).rgb;
sum += w4_5 * tex2D_linearize(tex, tex_uv + (4.0 + w4_5_ratio) * dxdy).rgb;
sum += w6_7 * tex2D_linearize(tex, tex_uv + (6.0 + w6_7_ratio) * dxdy).rgb;
sum += w8_9 * tex2D_linearize(tex, tex_uv + (8.0 + w8_9_ratio) * dxdy).rgb;
sum += w10_11 * tex2D_linearize(tex, tex_uv + (10.0 + w10_11_ratio) * dxdy).rgb;
sum += w12_13 * tex2D_linearize(tex, tex_uv + (12.0 + w12_13_ratio) * dxdy).rgb;
sum += w14_15 * tex2D_linearize(tex, tex_uv + (14.0 + w14_15_ratio) * dxdy).rgb;
return sum * weight_sum_inv;
}
vec3 tex2Dblur43fast(const sampler2D tex, const vec2 tex_uv,
const vec2 dxdy, const float sigma)
{
// Requires: Same as tex2Dblur11()
// Returns: A 1D 43x Gaussian blurred texture lookup using 22 linear
// taps. It may be mipmapped depending on settings and dxdy.
// First get the texel weights and normalization factor as above.
const float denom_inv = 0.5/(sigma*sigma);
const float w0 = 1.0;
const float w1 = exp(-1.0 * denom_inv);
const float w2 = exp(-4.0 * denom_inv);
const float w3 = exp(-9.0 * denom_inv);
const float w4 = exp(-16.0 * denom_inv);
const float w5 = exp(-25.0 * denom_inv);
const float w6 = exp(-36.0 * denom_inv);
const float w7 = exp(-49.0 * denom_inv);
const float w8 = exp(-64.0 * denom_inv);
const float w9 = exp(-81.0 * denom_inv);
const float w10 = exp(-100.0 * denom_inv);
const float w11 = exp(-121.0 * denom_inv);
const float w12 = exp(-144.0 * denom_inv);
const float w13 = exp(-169.0 * denom_inv);
const float w14 = exp(-196.0 * denom_inv);
const float w15 = exp(-225.0 * denom_inv);
const float w16 = exp(-256.0 * denom_inv);
const float w17 = exp(-289.0 * denom_inv);
const float w18 = exp(-324.0 * denom_inv);
const float w19 = exp(-361.0 * denom_inv);
const float w20 = exp(-400.0 * denom_inv);
const float w21 = exp(-441.0 * denom_inv);
//const float weight_sum_inv = 1.0 /
// (w0 + 2.0 * (w1 + w2 + w3 + w4 + w5 + w6 + w7 + w8 + w9 + w10 + w11 +
// w12 + w13 + w14 + w15 + w16 + w17 + w18 + w19 + w20 + w21));
const float weight_sum_inv = get_fast_gaussian_weight_sum_inv(sigma);
// Calculate combined weights and linear sample ratios between texel pairs.
// The center texel (with weight w0) is used twice, so halve its weight.
const float w0_1 = w0 * 0.5 + w1;
const float w2_3 = w2 + w3;
const float w4_5 = w4 + w5;
const float w6_7 = w6 + w7;
const float w8_9 = w8 + w9;
const float w10_11 = w10 + w11;
const float w12_13 = w12 + w13;
const float w14_15 = w14 + w15;
const float w16_17 = w16 + w17;
const float w18_19 = w18 + w19;
const float w20_21 = w20 + w21;
const float w0_1_ratio = w1/w0_1;
const float w2_3_ratio = w3/w2_3;
const float w4_5_ratio = w5/w4_5;
const float w6_7_ratio = w7/w6_7;
const float w8_9_ratio = w9/w8_9;
const float w10_11_ratio = w11/w10_11;
const float w12_13_ratio = w13/w12_13;
const float w14_15_ratio = w15/w14_15;
const float w16_17_ratio = w17/w16_17;
const float w18_19_ratio = w19/w18_19;
const float w20_21_ratio = w21/w20_21;
// Statically normalize weights, sum weighted samples, and return:
vec3 sum = vec3(0.0);
sum += w20_21 * tex2D_linearize(tex, tex_uv - (20.0 + w20_21_ratio) * dxdy).rgb;
sum += w18_19 * tex2D_linearize(tex, tex_uv - (18.0 + w18_19_ratio) * dxdy).rgb;
sum += w16_17 * tex2D_linearize(tex, tex_uv - (16.0 + w16_17_ratio) * dxdy).rgb;
sum += w14_15 * tex2D_linearize(tex, tex_uv - (14.0 + w14_15_ratio) * dxdy).rgb;
sum += w12_13 * tex2D_linearize(tex, tex_uv - (12.0 + w12_13_ratio) * dxdy).rgb;
sum += w10_11 * tex2D_linearize(tex, tex_uv - (10.0 + w10_11_ratio) * dxdy).rgb;
sum += w8_9 * tex2D_linearize(tex, tex_uv - (8.0 + w8_9_ratio) * dxdy).rgb;
sum += w6_7 * tex2D_linearize(tex, tex_uv - (6.0 + w6_7_ratio) * dxdy).rgb;
sum += w4_5 * tex2D_linearize(tex, tex_uv - (4.0 + w4_5_ratio) * dxdy).rgb;
sum += w2_3 * tex2D_linearize(tex, tex_uv - (2.0 + w2_3_ratio) * dxdy).rgb;
sum += w0_1 * tex2D_linearize(tex, tex_uv - w0_1_ratio * dxdy).rgb;
sum += w0_1 * tex2D_linearize(tex, tex_uv + w0_1_ratio * dxdy).rgb;
sum += w2_3 * tex2D_linearize(tex, tex_uv + (2.0 + w2_3_ratio) * dxdy).rgb;
sum += w4_5 * tex2D_linearize(tex, tex_uv + (4.0 + w4_5_ratio) * dxdy).rgb;
sum += w6_7 * tex2D_linearize(tex, tex_uv + (6.0 + w6_7_ratio) * dxdy).rgb;
sum += w8_9 * tex2D_linearize(tex, tex_uv + (8.0 + w8_9_ratio) * dxdy).rgb;
sum += w10_11 * tex2D_linearize(tex, tex_uv + (10.0 + w10_11_ratio) * dxdy).rgb;
sum += w12_13 * tex2D_linearize(tex, tex_uv + (12.0 + w12_13_ratio) * dxdy).rgb;
sum += w14_15 * tex2D_linearize(tex, tex_uv + (14.0 + w14_15_ratio) * dxdy).rgb;
sum += w16_17 * tex2D_linearize(tex, tex_uv + (16.0 + w16_17_ratio) * dxdy).rgb;
sum += w18_19 * tex2D_linearize(tex, tex_uv + (18.0 + w18_19_ratio) * dxdy).rgb;
sum += w20_21 * tex2D_linearize(tex, tex_uv + (20.0 + w20_21_ratio) * dxdy).rgb;
return sum * weight_sum_inv;
}
//////////////////// ARBITRARILY RESIZABLE ONE-PASS BLURS //////////////////// //////////////////// ARBITRARILY RESIZABLE ONE-PASS BLURS ////////////////////
vec3 tex2Dblur3x3resize(const sampler2D tex, const vec2 tex_uv, vec3 tex2Dblur3x3resize(const sampler2D tex, const vec2 tex_uv,
@ -279,3 +540,64 @@ vec3 tex2Dblur3x3resize(const sampler2D texture, const vec2 tex_uv,
{ {
return tex2Dblur3x3resize(texture, tex_uv, dxdy, blur3_std_dev); return tex2Dblur3x3resize(texture, tex_uv, dxdy, blur3_std_dev);
} }
vec3 tex2Dblur9fast(const sampler2D tex, const vec2 tex_uv,
const vec2 dxdy, const float sigma)
{
// Requires: Same as tex2Dblur11()
// Returns: A 1D 9x Gaussian blurred texture lookup using 1 nearest
// neighbor and 4 linear taps. It may be mipmapped depending
// on settings and dxdy.
// First get the texel weights and normalization factor as above.
const float denom_inv = 0.5/(sigma*sigma);
const float w0 = 1.0;
const float w1 = exp(-1.0 * denom_inv);
const float w2 = exp(-4.0 * denom_inv);
const float w3 = exp(-9.0 * denom_inv);
const float w4 = exp(-16.0 * denom_inv);
const float weight_sum_inv = 1.0 / (w0 + 2.0 * (w1 + w2 + w3 + w4));
// Calculate combined weights and linear sample ratios between texel pairs.
const float w12 = w1 + w2;
const float w34 = w3 + w4;
const float w12_ratio = w2/w12;
const float w34_ratio = w4/w34;
// Statically normalize weights, sum weighted samples, and return:
vec3 sum = vec3(0.0);
sum += w34 * tex2D_linearize(tex, tex_uv - (3.0 + w34_ratio) * dxdy).rgb;
sum += w12 * tex2D_linearize(tex, tex_uv - (1.0 + w12_ratio) * dxdy).rgb;
sum += w0 * tex2D_linearize(tex, tex_uv).rgb;
sum += w12 * tex2D_linearize(tex, tex_uv + (1.0 + w12_ratio) * dxdy).rgb;
sum += w34 * tex2D_linearize(tex, tex_uv + (3.0 + w34_ratio) * dxdy).rgb;
return sum * weight_sum_inv;
}
vec3 tex2Dblur9fast(const sampler2D tex, const vec2 tex_uv,
const vec2 dxdy)
{
return tex2Dblur9fast(tex, tex_uv, dxdy, blur9_std_dev);
}
vec3 tex2Dblur17fast(const sampler2D texture, const vec2 tex_uv,
const vec2 dxdy)
{
return tex2Dblur17fast(texture, tex_uv, dxdy, blur17_std_dev);
}
vec3 tex2Dblur25fast(const sampler2D texture, const vec2 tex_uv,
const vec2 dxdy)
{
return tex2Dblur25fast(texture, tex_uv, dxdy, blur25_std_dev);
}
vec3 tex2Dblur43fast(const sampler2D texture, const vec2 tex_uv,
const vec2 dxdy)
{
return tex2Dblur43fast(texture, tex_uv, dxdy, blur43_std_dev);
}
vec3 tex2Dblur31fast(const sampler2D texture, const vec2 tex_uv,
const vec2 dxdy)
{
return tex2Dblur31fast(texture, tex_uv, dxdy, blur31_std_dev);
}
#endif // BLUR_FUNCTIONS_H

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#ifndef GAMMA_MANAGEMENT_H
#define GAMMA_MANAGEMENT_H
///////////////////////////////// MIT LICENSE ////////////////////////////////
// Copyright (C) 2014 TroggleMonkey
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to
// deal in the Software without restriction, including without limitation the
// rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
// sell copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
// IN THE SOFTWARE.
///////////////////////////////// DESCRIPTION ////////////////////////////////
// This file provides gamma-aware tex*D*() and encode_output() functions.
// Requires: Before #include-ing this file, the including file must #define
// the following macros when applicable and follow their rules:
// 1.) #define FIRST_PASS if this is the first pass.
// 2.) #define LAST_PASS if this is the last pass.
// 3.) If sRGB is available, set srgb_framebufferN = "true" for
// every pass except the last in your .cgp preset.
// 4.) If sRGB isn't available but you want gamma-correctness with
// no banding, #define GAMMA_ENCODE_EVERY_FBO each pass.
// 5.) #define SIMULATE_CRT_ON_LCD if desired (precedence over 5-7)
// 6.) #define SIMULATE_GBA_ON_LCD if desired (precedence over 6-7)
// 7.) #define SIMULATE_LCD_ON_CRT if desired (precedence over 7)
// 8.) #define SIMULATE_GBA_ON_CRT if desired (precedence over -)
// If an option in [5, 8] is #defined in the first or last pass, it
// should be #defined for both. It shouldn't make a difference
// whether it's #defined for intermediate passes or not.
// Optional: The including file (or an earlier included file) may optionally
// #define a number of macros indicating it will override certain
// macros and associated constants are as follows:
// static constants with either static or uniform constants. The
// 1.) OVERRIDE_STANDARD_GAMMA: The user must first define:
// static const float ntsc_gamma
// static const float pal_gamma
// static const float crt_reference_gamma_high
// static const float crt_reference_gamma_low
// static const float lcd_reference_gamma
// static const float crt_office_gamma
// static const float lcd_office_gamma
// 2.) OVERRIDE_DEVICE_GAMMA: The user must first define:
// static const float crt_gamma
// static const float gba_gamma
// static const float lcd_gamma
// 3.) OVERRIDE_FINAL_GAMMA: The user must first define:
// static const float input_gamma
// static const float intermediate_gamma
// static const float output_gamma
// (intermediate_gamma is for GAMMA_ENCODE_EVERY_FBO.)
// 4.) OVERRIDE_ALPHA_ASSUMPTIONS: The user must first define:
// static const bool assume_opaque_alpha
// The gamma constant overrides must be used in every pass or none,
// and OVERRIDE_FINAL_GAMMA bypasses all of the SIMULATE* macros.
// OVERRIDE_ALPHA_ASSUMPTIONS may be set on a per-pass basis.
// Usage: After setting macros appropriately, ignore gamma correction and
// replace all tex*D*() calls with equivalent gamma-aware
// tex*D*_linearize calls, except:
// 1.) When you read an LUT, use regular tex*D or a gamma-specified
// function, depending on its gamma encoding:
// tex*D*_linearize_gamma (takes a runtime gamma parameter)
// 2.) If you must read pass0's original input in a later pass, use
// tex2D_linearize_ntsc_gamma. If you want to read pass0's
// input with gamma-corrected bilinear filtering, consider
// creating a first linearizing pass and reading from the input
// of pass1 later.
// Then, return encode_output(color) from every fragment shader.
// Finally, use the global gamma_aware_bilinear boolean if you want
// to statically branch based on whether bilinear filtering is
// gamma-correct or not (e.g. for placing Gaussian blur samples).
//
// Detailed Policy:
// tex*D*_linearize() functions enforce a consistent gamma-management policy
// based on the FIRST_PASS and GAMMA_ENCODE_EVERY_FBO settings. They assume
// their input texture has the same encoding characteristics as the input for
// the current pass (which doesn't apply to the exceptions listed above).
// Similarly, encode_output() enforces a policy based on the LAST_PASS and
// GAMMA_ENCODE_EVERY_FBO settings. Together, they result in one of the
// following two pipelines.
// Typical pipeline with intermediate sRGB framebuffers:
// linear_color = pow(pass0_encoded_color, input_gamma);
// intermediate_output = linear_color; // Automatic sRGB encoding
// linear_color = intermediate_output; // Automatic sRGB decoding
// final_output = pow(intermediate_output, 1.0/output_gamma);
// Typical pipeline without intermediate sRGB framebuffers:
// linear_color = pow(pass0_encoded_color, input_gamma);
// intermediate_output = pow(linear_color, 1.0/intermediate_gamma);
// linear_color = pow(intermediate_output, intermediate_gamma);
// final_output = pow(intermediate_output, 1.0/output_gamma);
// Using GAMMA_ENCODE_EVERY_FBO is much slower, but it's provided as a way to
// easily get gamma-correctness without banding on devices where sRGB isn't
// supported.
//
// Use This Header to Maximize Code Reuse:
// The purpose of this header is to provide a consistent interface for texture
// reads and output gamma-encoding that localizes and abstracts away all the
// annoying details. This greatly reduces the amount of code in each shader
// pass that depends on the pass number in the .cgp preset or whether sRGB
// FBO's are being used: You can trivially change the gamma behavior of your
// whole pass by commenting or uncommenting 1-3 #defines. To reuse the same
// code in your first, Nth, and last passes, you can even put it all in another
// header file and #include it from skeleton .cg files that #define the
// appropriate pass-specific settings.
//
// Rationale for Using Three Macros:
// This file uses GAMMA_ENCODE_EVERY_FBO instead of an opposite macro like
// SRGB_PIPELINE to ensure sRGB is assumed by default, which hopefully imposes
// a lower maintenance burden on each pass. At first glance it seems we could
// accomplish everything with two macros: GAMMA_CORRECT_IN / GAMMA_CORRECT_OUT.
// This works for simple use cases where input_gamma == output_gamma, but it
// breaks down for more complex scenarios like CRT simulation, where the pass
// number determines the gamma encoding of the input and output.
/////////////////////////////// BASE CONSTANTS ///////////////////////////////
// Set standard gamma constants, but allow users to override them:
#ifndef OVERRIDE_STANDARD_GAMMA
// Standard encoding gammas:
const float ntsc_gamma = 2.2; // Best to use NTSC for PAL too?
const float pal_gamma = 2.8; // Never actually 2.8 in practice
// Typical device decoding gammas (only use for emulating devices):
// CRT/LCD reference gammas are higher than NTSC and Rec.709 video standard
// gammas: The standards purposely undercorrected for an analog CRT's
// assumed 2.5 reference display gamma to maintain contrast in assumed
// [dark] viewing conditions: http://www.poynton.com/PDFs/GammaFAQ.pdf
// These unstated assumptions about display gamma and perceptual rendering
// intent caused a lot of confusion, and more modern CRT's seemed to target
// NTSC 2.2 gamma with circuitry. LCD displays seem to have followed suit
// (they struggle near black with 2.5 gamma anyway), especially PC/laptop
// displays designed to view sRGB in bright environments. (Standards are
// also in flux again with BT.1886, but it's underspecified for displays.)
const float crt_reference_gamma_high = 2.5; // In (2.35, 2.55)
const float crt_reference_gamma_low = 2.35; // In (2.35, 2.55)
const float lcd_reference_gamma = 2.5; // To match CRT
const float crt_office_gamma = 2.2; // Circuitry-adjusted for NTSC
const float lcd_office_gamma = 2.2; // Approximates sRGB
#endif // OVERRIDE_STANDARD_GAMMA
// Assuming alpha == 1.0 might make it easier for users to avoid some bugs,
// but only if they're aware of it.
#ifndef OVERRIDE_ALPHA_ASSUMPTIONS
const bool assume_opaque_alpha = false;
#endif
/////////////////////// DERIVED CONSTANTS AS FUNCTIONS ///////////////////////
// gamma-management.h should be compatible with overriding gamma values with
// runtime user parameters, but we can only define other global constants in
// terms of static constants, not uniform user parameters. To get around this
// limitation, we need to define derived constants using functions.
// Set device gamma constants, but allow users to override them:
#ifdef OVERRIDE_DEVICE_GAMMA
// The user promises to globally define the appropriate constants:
float get_crt_gamma() { return crt_gamma; }
float get_gba_gamma() { return gba_gamma; }
float get_lcd_gamma() { return lcd_gamma; }
#else
float get_crt_gamma() { return crt_reference_gamma_high; }
float get_gba_gamma() { return 3.5; } // Game Boy Advance; in (3.0, 4.0)
float get_lcd_gamma() { return lcd_office_gamma; }
#endif // OVERRIDE_DEVICE_GAMMA
// Set decoding/encoding gammas for the first/lass passes, but allow overrides:
#ifdef OVERRIDE_FINAL_GAMMA
// The user promises to globally define the appropriate constants:
float get_intermediate_gamma() { return intermediate_gamma; }
float get_input_gamma() { return input_gamma; }
float get_output_gamma() { return output_gamma; }
#else
// If we gamma-correct every pass, always use ntsc_gamma between passes to
// ensure middle passes don't need to care if anything is being simulated:
float get_intermediate_gamma() { return ntsc_gamma; }
#ifdef SIMULATE_CRT_ON_LCD
float get_input_gamma() { return get_crt_gamma(); }
float get_output_gamma() { return get_lcd_gamma(); }
#else
#ifdef SIMULATE_GBA_ON_LCD
float get_input_gamma() { return get_gba_gamma(); }
float get_output_gamma() { return get_lcd_gamma(); }
#else
#ifdef SIMULATE_LCD_ON_CRT
float get_input_gamma() { return get_lcd_gamma(); }
float get_output_gamma() { return get_crt_gamma(); }
#else
#ifdef SIMULATE_GBA_ON_CRT
float get_input_gamma() { return get_gba_gamma(); }
float get_output_gamma() { return get_crt_gamma(); }
#else // Don't simulate anything:
float get_input_gamma() { return ntsc_gamma; }
float get_output_gamma() { return ntsc_gamma; }
#endif // SIMULATE_GBA_ON_CRT
#endif // SIMULATE_LCD_ON_CRT
#endif // SIMULATE_GBA_ON_LCD
#endif // SIMULATE_CRT_ON_LCD
#endif // OVERRIDE_FINAL_GAMMA
// Set decoding/encoding gammas for the current pass. Use static constants for
// linearize_input and gamma_encode_output, because they aren't derived, and
// they let the compiler do dead-code elimination.
#ifndef GAMMA_ENCODE_EVERY_FBO
#ifdef FIRST_PASS
const bool linearize_input = true;
float get_pass_input_gamma() { return get_input_gamma(); }
#else
const bool linearize_input = false;
float get_pass_input_gamma() { return 1.0; }
#endif
#ifdef LAST_PASS
const bool gamma_encode_output = true;
float get_pass_output_gamma() { return get_output_gamma(); }
#else
const bool gamma_encode_output = false;
float get_pass_output_gamma() { return 1.0; }
#endif
#else
const bool linearize_input = true;
const bool gamma_encode_output = true;
#ifdef FIRST_PASS
float get_pass_input_gamma() { return get_input_gamma(); }
#else
float get_pass_input_gamma() { return get_intermediate_gamma(); }
#endif
#ifdef LAST_PASS
float get_pass_output_gamma() { return get_output_gamma(); }
#else
float get_pass_output_gamma() { return get_intermediate_gamma(); }
#endif
#endif
// Users might want to know if bilinear filtering will be gamma-correct:
const bool gamma_aware_bilinear = !linearize_input;
////////////////////// COLOR ENCODING/DECODING FUNCTIONS /////////////////////
vec4 encode_output(const vec4 color)
{
if(gamma_encode_output)
{
if(assume_opaque_alpha)
{
return vec4(pow(color.rgb, vec3(1.0/get_pass_output_gamma())), 1.0);
}
else
{
return vec4(pow(color.rgb, vec3(1.0/get_pass_output_gamma())), color.a);
}
}
else
{
return color;
}
}
vec4 decode_input(const vec4 color)
{
if(linearize_input)
{
if(assume_opaque_alpha)
{
return vec4(pow(color.rgb, vec3(get_pass_input_gamma())), 1.0);
}
else
{
return vec4(pow(color.rgb, vec3(get_pass_input_gamma())), color.a);
}
}
else
{
return color;
}
}
vec4 decode_gamma_input(const vec4 color, const vec3 gamma)
{
if(assume_opaque_alpha)
{
return vec4(pow(color.rgb, vec3(gamma)), 1.0);
}
else
{
return vec4(pow(color.rgb, vec3(gamma)), color.a);
}
}
/////////////////////////// TEXTURE LOOKUP WRAPPERS //////////////////////////
// "SMART" LINEARIZING TEXTURE LOOKUP FUNCTIONS:
// Provide a wide array of linearizing texture lookup wrapper functions. The
// Cg shader spec Retroarch uses only allows for 2D textures, but 1D and 3D
// lookups are provided for completeness in case that changes someday. Nobody
// is likely to use the *fetch and *proj functions, but they're included just
// in case. The only tex*D texture sampling functions omitted are:
// - tex*Dcmpbias
// - tex*Dcmplod
// - tex*DARRAY*
// - tex*DMS*
// - Variants returning integers
// Standard line length restrictions are ignored below for vertical brevity.
/*
// tex1D:
vec4 tex1D_linearize(const sampler1D texture, const float tex_coords)
{ return decode_input(tex1D(texture, tex_coords)); }
vec4 tex1D_linearize(const sampler1D texture, const vec2 tex_coords)
{ return decode_input(tex1D(texture, tex_coords)); }
vec4 tex1D_linearize(const sampler1D texture, const float tex_coords, const int texel_off)
{ return decode_input(tex1D(texture, tex_coords, texel_off)); }
vec4 tex1D_linearize(const sampler1D texture, const vec2 tex_coords, const int texel_off)
{ return decode_input(tex1D(texture, tex_coords, texel_off)); }
vec4 tex1D_linearize(const sampler1D texture, const float tex_coords, const float dx, const float dy)
{ return decode_input(tex1D(texture, tex_coords, dx, dy)); }
vec4 tex1D_linearize(const sampler1D texture, const vec2 tex_coords, const float dx, const float dy)
{ return decode_input(tex1D(texture, tex_coords, dx, dy)); }
vec4 tex1D_linearize(const sampler1D texture, const float tex_coords, const float dx, const float dy, const int texel_off)
{ return decode_input(tex1D(texture, tex_coords, dx, dy, texel_off)); }
vec4 tex1D_linearize(const sampler1D texture, const vec2 tex_coords, const float dx, const float dy, const int texel_off)
{ return decode_input(tex1D(texture, tex_coords, dx, dy, texel_off)); }
// tex1Dbias:
vec4 tex1Dbias_linearize(const sampler1D texture, const vec4 tex_coords)
{ return decode_input(tex1Dbias(texture, tex_coords)); }
vec4 tex1Dbias_linearize(const sampler1D texture, const vec4 tex_coords, const int texel_off)
{ return decode_input(tex1Dbias(texture, tex_coords, texel_off)); }
// tex1Dfetch:
vec4 tex1Dfetch_linearize(const sampler1D texture, const int4 tex_coords)
{ return decode_input(tex1Dfetch(texture, tex_coords)); }
vec4 tex1Dfetch_linearize(const sampler1D texture, const int4 tex_coords, const int texel_off)
{ return decode_input(tex1Dfetch(texture, tex_coords, texel_off)); }
// tex1Dlod:
vec4 tex1Dlod_linearize(const sampler1D texture, const vec4 tex_coords)
{ return decode_input(tex1Dlod(texture, tex_coords)); }
vec4 tex1Dlod_linearize(const sampler1D texture, const vec4 tex_coords, const int texel_off)
{ return decode_input(tex1Dlod(texture, tex_coords, texel_off)); }
// tex1Dproj:
vec4 tex1Dproj_linearize(const sampler1D texture, const vec2 tex_coords)
{ return decode_input(tex1Dproj(texture, tex_coords)); }
vec4 tex1Dproj_linearize(const sampler1D texture, const vec3 tex_coords)
{ return decode_input(tex1Dproj(texture, tex_coords)); }
vec4 tex1Dproj_linearize(const sampler1D texture, const vec2 tex_coords, const int texel_off)
{ return decode_input(tex1Dproj(texture, tex_coords, texel_off)); }
vec4 tex1Dproj_linearize(const sampler1D texture, const vec3 tex_coords, const int texel_off)
{ return decode_input(tex1Dproj(texture, tex_coords, texel_off)); }
*/
// tex2D:
vec4 tex2D_linearize(const sampler2D tex, const vec2 tex_coords)
{ return decode_input(vec4(texture(tex, tex_coords))); }
vec4 tex2D_linearize(const sampler2D tex, const vec3 tex_coords)
{ return decode_input(vec4(texture(tex, tex_coords))); }
vec4 tex2D_linearize(const sampler2D tex, const vec2 tex_coords, const int texel_off)
{ return decode_input(vec4(texture(tex, tex_coords, texel_off))); }
vec4 tex2D_linearize(const sampler2D tex, const vec3 tex_coords, const int texel_off)
{ return decode_input(vec4(texture(tex, tex_coords, texel_off))); }
vec4 tex2D_linearize(const sampler2D tex, const vec2 tex_coords, const vec2 dx, const vec2 dy)
{ return decode_input(vec4(texture(tex, tex_coords, dx, dy))); }
vec4 tex2D_linearize(const sampler2D tex, const vec3 tex_coords, const vec2 dx, const vec2 dy)
{ return decode_input(vec4(texture(tex, tex_coords, dx, dy))); }
vec4 tex2D_linearize(const sampler2D tex, const vec2 tex_coords, const vec2 dx, const vec2 dy, const int texel_off)
{ return decode_input(vec4(texture(tex, tex_coords, dx, dy, texel_off))); }
vec4 tex2D_linearize(const sampler2D tex, const vec3 tex_coords, const vec2 dx, const vec2 dy, const int texel_off)
{ return decode_input(vec4(texture(tex, tex_coords, dx, dy, texel_off))); }
// tex2Dbias:
vec4 tex2Dbias_linearize(const sampler2D tex, const vec4 tex_coords)
{ return decode_input(vec4(tex2Dbias(tex, tex_coords))); }
vec4 tex2Dbias_linearize(const sampler2D tex, const vec4 tex_coords, const int texel_off)
{ return decode_input(vec4(tex2Dbias(tex, tex_coords, texel_off))); }
// tex2Dfetch:
vec4 tex2Dfetch_linearize(const sampler2D tex, const ivec4 tex_coords)
{ return decode_input(vec4(texture2Dfetch(tex, tex_coords))); }
vec4 tex2Dfetch_linearize(const sampler2D tex, const ivec4 tex_coords, const int texel_off)
{ return decode_input(vec4(texture2Dfetch(tex, tex_coords, texel_off))); }
// tex2Dlod:
vec4 tex2Dlod_linearize(const sampler2D tex, const vec4 tex_coords)
{ return decode_input(vec4(texture2Dlod(tex, tex_coords))); }
vec4 tex2Dlod_linearize(const sampler2D tex, const vec4 tex_coords, const int texel_off)
{ return decode_input(vec4(texture2Dlod(tex, tex_coords, texel_off))); }
// tex2Dproj:
vec4 tex2Dproj_linearize(const sampler2D tex, const vec3 tex_coords)
{ return decode_input(vec4(tex2Dproj(tex, tex_coords))); }
vec4 tex2Dproj_linearize(const sampler2D tex, const vec4 tex_coords)
{ return decode_input(vec4(tex2Dproj(tex, tex_coords))); }
vec4 tex2Dproj_linearize(const sampler2D tex, const vec3 tex_coords, const int texel_off)
{ return decode_input(vec4(tex2Dproj(tex, tex_coords, texel_off))); }
vec4 tex2Dproj_linearize(const sampler2D tex, const vec4 tex_coords, const int texel_off)
{ return decode_input(vec4(tex2Dproj(tex, tex_coords, texel_off))); }
/*
// tex3D:
vec4 tex3D_linearize(const sampler3D texture, const vec3 tex_coords)
{ return decode_input(tex3D(texture, tex_coords)); }
vec4 tex3D_linearize(const sampler3D texture, const vec3 tex_coords, const int texel_off)
{ return decode_input(tex3D(texture, tex_coords, texel_off)); }
vec4 tex3D_linearize(const sampler3D texture, const vec3 tex_coords, const vec3 dx, const vec3 dy)
{ return decode_input(tex3D(texture, tex_coords, dx, dy)); }
vec4 tex3D_linearize(const sampler3D texture, const vec3 tex_coords, const vec3 dx, const vec3 dy, const int texel_off)
{ return decode_input(tex3D(texture, tex_coords, dx, dy, texel_off)); }
// tex3Dbias:
vec4 tex3Dbias_linearize(const sampler3D texture, const vec4 tex_coords)
{ return decode_input(tex3Dbias(texture, tex_coords)); }
vec4 tex3Dbias_linearize(const sampler3D texture, const vec4 tex_coords, const int texel_off)
{ return decode_input(tex3Dbias(texture, tex_coords, texel_off)); }
// tex3Dfetch:
vec4 tex3Dfetch_linearize(const sampler3D texture, const int4 tex_coords)
{ return decode_input(tex3Dfetch(texture, tex_coords)); }
vec4 tex3Dfetch_linearize(const sampler3D texture, const int4 tex_coords, const int texel_off)
{ return decode_input(tex3Dfetch(texture, tex_coords, texel_off)); }
// tex3Dlod:
vec4 tex3Dlod_linearize(const sampler3D texture, const vec4 tex_coords)
{ return decode_input(tex3Dlod(texture, tex_coords)); }
vec4 tex3Dlod_linearize(const sampler3D texture, const vec4 tex_coords, const int texel_off)
{ return decode_input(tex3Dlod(texture, tex_coords, texel_off)); }
// tex3Dproj:
vec4 tex3Dproj_linearize(const sampler3D texture, const vec4 tex_coords)
{ return decode_input(tex3Dproj(texture, tex_coords)); }
vec4 tex3Dproj_linearize(const sampler3D texture, const vec4 tex_coords, const int texel_off)
{ return decode_input(tex3Dproj(texture, tex_coords, texel_off)); }
*/
// NONSTANDARD "SMART" LINEARIZING TEXTURE LOOKUP FUNCTIONS:
// This narrow selection of nonstandard tex2D* functions can be useful:
// tex2Dlod0: Automatically fill in the tex2D LOD parameter for mip level 0.
vec4 tex2Dlod0_linearize(const sampler2D texture, const vec2 tex_coords)
{ return decode_input(vec4(texture2Dlod(texture, vec4(tex_coords, 0.0, 0.0)))); }
vec4 tex2Dlod0_linearize(const sampler2D texture, const vec2 tex_coords, const int texel_off)
{ return decode_input(vec4(texture2Dlod(texture, vec4(tex_coords, 0.0, 0.0), texel_off))); }
// MANUALLY LINEARIZING TEXTURE LOOKUP FUNCTIONS:
// Provide a narrower selection of tex2D* wrapper functions that decode an
// input sample with a specified gamma value. These are useful for reading
// LUT's and for reading the input of pass0 in a later pass.
// tex2D:
vec4 tex2D_linearize_gamma(const sampler2D tex, const vec2 tex_coords, const vec3 gamma)
{ return decode_gamma_input(vec4(texture(tex, tex_coords), vec3(gamma))); }
vec4 tex2D_linearize_gamma(const sampler2D tex, const vec3 tex_coords, const vec3 gamma)
{ return decode_gamma_input(vec4(texture(tex, tex_coords), vec3(gamma))); }
vec4 tex2D_linearize_gamma(const sampler2D tex, const vec2 tex_coords, const int texel_off, const vec3 gamma)
{ return decode_gamma_input(vec4(texture(tex, tex_coords, texel_off), vec3(gamma))); }
vec4 tex2D_linearize_gamma(const sampler2D tex, const vec3 tex_coords, const int texel_off, const vec3 gamma)
{ return decode_gamma_input(vec4(texture(tex, tex_coords, texel_off), vec3(gamma))); }
vec4 tex2D_linearize_gamma(const sampler2D tex, const vec2 tex_coords, const vec2 dx, const vec2 dy, const vec3 gamma)
{ return decode_gamma_input(vec4(texture(tex, tex_coords, dx, dy), vec3(gamma))); }
vec4 tex2D_linearize_gamma(const sampler2D tex, const vec3 tex_coords, const vec2 dx, const vec2 dy, const vec3 gamma)
{ return decode_gamma_input(vec4(texture(tex, tex_coords, dx, dy), vec3(gamma))); }
vec4 tex2D_linearize_gamma(const sampler2D tex, const vec2 tex_coords, const vec2 dx, const vec2 dy, const int texel_off, const vec3 gamma)
{ return decode_gamma_input(vec4(texture(tex, tex_coords, dx, dy, texel_off), vec3(gamma))); }
vec4 tex2D_linearize_gamma(const sampler2D tex, const vec3 tex_coords, const vec2 dx, const vec2 dy, const int texel_off, const vec3 gamma)
{ return decode_gamma_input(vec4(texture(tex, tex_coords, dx, dy, texel_off), vec3(gamma))); }
// tex2Dbias:
vec4 tex2Dbias_linearize_gamma(const sampler2D tex, const vec4 tex_coords, const vec3 gamma)
{ return decode_gamma_input(vec4(tex2Dbias(tex, tex_coords), vec3(gamma))); }
vec4 tex2Dbias_linearize_gamma(const sampler2D tex, const vec4 tex_coords, const int texel_off, const vec3 gamma)
{ return decode_gamma_input(vec4(tex2Dbias(tex, tex_coords, texel_off), vec3(gamma))); }
// tex2Dfetch:
vec4 tex2Dfetch_linearize_gamma(const sampler2D tex, const int4 tex_coords, const vec3 gamma)
{ return decode_gamma_input(vec4(tex2Dfetch(tex, tex_coords), vec3(gamma))); }
vec4 tex2Dfetch_linearize_gamma(const sampler2D tex, const int4 tex_coords, const int texel_off, const vec3 gamma)
{ return decode_gamma_input(vec4(tex2Dfetch(tex, tex_coords, texel_off), vec3(gamma))); }
// tex2Dlod:
vec4 tex2Dlod_linearize_gamma(const sampler2D tex, const vec4 tex_coords, const vec3 gamma)
{ return decode_gamma_input(vec4(tex2Dlod(tex, tex_coords), vec3(gamma))); }
vec4 tex2Dlod_linearize_gamma(const sampler2D tex, const vec4 tex_coords, const int texel_off, const vec3 gamma)
{ return decode_gamma_input(vec4(tex2Dlod(tex, tex_coords, texel_off), vec3(gamma))); }
#endif // GAMMA_MANAGEMENT_H

5
include/gamma-management.h
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@ -1,3 +1,6 @@
#ifndef GAMMA_MANAGEMENT_H
#define GAMMA_MANAGEMENT_H
/////////////////////////////// BASE CONSTANTS /////////////////////////////// /////////////////////////////// BASE CONSTANTS ///////////////////////////////
// Set standard gamma constants, but allow users to override them: // Set standard gamma constants, but allow users to override them:
@ -158,3 +161,5 @@ vec4 encode_output(const vec4 color)
//#define tex2D_linearize(C, D, E) decode_input(vec4(texture(C, D, E))) //#define tex2D_linearize(C, D, E) decode_input(vec4(texture(C, D, E)))
//vec4 tex2D_linearize(const sampler2D tex, const vec2 tex_coords, const int texel_off) //vec4 tex2D_linearize(const sampler2D tex, const vec2 tex_coords, const int texel_off)
//{ return decode_input(vec4(texture(tex, tex_coords, texel_off))); } //{ return decode_input(vec4(texture(tex, tex_coords, texel_off))); }
#endif // GAMMA_MANAGEMENT_H

498
include/special-functions-old.h
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@ -1,498 +0,0 @@
#ifndef SPECIAL_FUNCTIONS_H
#define SPECIAL_FUNCTIONS_H
///////////////////////////////// MIT LICENSE ////////////////////////////////
// Copyright (C) 2014 TroggleMonkey
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to
// deal in the Software without restriction, including without limitation the
// rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
// sell copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
// IN THE SOFTWARE.
///////////////////////////////// DESCRIPTION ////////////////////////////////
// This file implements the following mathematical special functions:
// 1.) erf() = 2/sqrt(pi) * indefinite_integral(e**(-x**2))
// 2.) gamma(s), a real-numbered extension of the integer factorial function
// It also implements normalized_ligamma(s, z), a normalized lower incomplete
// gamma function for s < 0.5 only. Both gamma() and normalized_ligamma() can
// be called with an _impl suffix to use an implementation version with a few
// extra precomputed parameters (which may be useful for the caller to reuse).
// See below for details.
//
// Design Rationale:
// Pretty much every line of code in this file is duplicated four times for
// different input types (vec4/vec3/vec2/float). This is unfortunate,
// but Cg doesn't allow function templates. Macros would be far less verbose,
// but they would make the code harder to document and read. I don't expect
// these functions will require a whole lot of maintenance changes unless
// someone ever has need for more robust incomplete gamma functions, so code
// duplication seems to be the lesser evil in this case.
/////////////////////////// GAUSSIAN ERROR FUNCTION //////////////////////////
vec4 erf6(vec4 x)
{
// Requires: x is the standard parameter to erf().
// Returns: Return an Abramowitz/Stegun approximation of erf(), where:
// erf(x) = 2/sqrt(pi) * integral(e**(-x**2))
// This approximation has a max absolute error of 2.5*10**-5
// with solid numerical robustness and efficiency. See:
// https://en.wikipedia.org/wiki/Error_function#Approximation_with_elementary_functions
const vec4 one = vec4(1.0);
const vec4 sign_x = sign(x);
const vec4 t = one/(one + 0.47047*abs(x));
const vec4 result = one - t*(0.3480242 + t*(-0.0958798 + t*0.7478556))*
exp(-(x*x));
return result * sign_x;
}
vec3 erf6(const vec3 x)
{
// vec3 version:
const vec3 one = vec3(1.0);
const vec3 sign_x = sign(x);
const vec3 t = one/(one + 0.47047*abs(x));
const vec3 result = one - t*(0.3480242 + t*(-0.0958798 + t*0.7478556))*
exp(-(x*x));
return result * sign_x;
}
vec2 erf6(const vec2 x)
{
// vec2 version:
const vec2 one = vec2(1.0);
const vec2 sign_x = sign(x);
const vec2 t = one/(one + 0.47047*abs(x));
const vec2 result = one - t*(0.3480242 + t*(-0.0958798 + t*0.7478556))*
exp(-(x*x));
return result * sign_x;
}
float erf6(const float x)
{
// Float version:
const float sign_x = sign(x);
const float t = 1.0/(1.0 + 0.47047*abs(x));
const float result = 1.0 - t*(0.3480242 + t*(-0.0958798 + t*0.7478556))*
exp(-(x*x));
return result * sign_x;
}
vec4 erft(const vec4 x)
{
// Requires: x is the standard parameter to erf().
// Returns: Approximate erf() with the hyperbolic tangent. The error is
// visually noticeable, but it's blazing fast and perceptually
// close...at least on ATI hardware. See:
// http://www.maplesoft.com/applications/view.aspx?SID=5525&view=html
// Warning: Only use this if your hardware drivers correctly implement
// tanh(): My nVidia 8800GTS returns garbage output.
return tanh(1.202760580 * x);
}
vec3 erft(const vec3 x)
{
// vec3 version:
return tanh(1.202760580 * x);
}
vec2 erft(const vec2 x)
{
// vec2 version:
return tanh(1.202760580 * x);
}
float erft(const float x)
{
// Float version:
return tanh(1.202760580 * x);
}
vec4 erf(const vec4 x)
{
// Requires: x is the standard parameter to erf().
// Returns: Some approximation of erf(x), depending on user settings.
#ifdef ERF_FAST_APPROXIMATION
return erft(x);
#else
return erf6(x);
#endif
}
vec3 erf(const vec3 x)
{
// vec3 version:
#ifdef ERF_FAST_APPROXIMATION
return erft(x);
#else
return erf6(x);
#endif
}
vec2 erf(const vec2 x)
{
// vec2 version:
#ifdef ERF_FAST_APPROXIMATION
return erft(x);
#else
return erf6(x);
#endif
}
float erf(const float x)
{
// Float version:
#ifdef ERF_FAST_APPROXIMATION
return erft(x);
#else
return erf6(x);
#endif
}
/////////////////////////// COMPLETE GAMMA FUNCTION //////////////////////////
vec4 gamma_impl(const vec4 s, const vec4 s_inv)
{
// Requires: 1.) s is the standard parameter to the gamma function, and
// it should lie in the [0, 36] range.
// 2.) s_inv = 1.0/s. This implementation function requires
// the caller to precompute this value, giving users the
// opportunity to reuse it.
// Returns: Return approximate gamma function (real-numbered factorial)
// output using the Lanczos approximation with two coefficients
// calculated using Paul Godfrey's method here:
// http://my.fit.edu/~gabdo/gamma.txt
// An optimal g value for s in [0, 36] is ~1.12906830989, with
// a maximum relative error of 0.000463 for 2**16 equally
// evals. We could use three coeffs (0.0000346 error) without
// hurting latency, but this allows more parallelism with
// outside instructions.
const vec4 g = vec4(1.12906830989);
const vec4 c0 = vec4(0.8109119309638332633713423362694399653724431);
const vec4 c1 = vec4(0.4808354605142681877121661197951496120000040);
const vec4 e = vec4(2.71828182845904523536028747135266249775724709);
const vec4 sph = s + vec4(0.5);
const vec4 lanczos_sum = c0 + c1/(s + vec4(1.0));
const vec4 base = (sph + g)/e; // or (s + g + vec4(0.5))/e
// gamma(s + 1) = base**sph * lanczos_sum; divide by s for gamma(s).
// This has less error for small s's than (s -= 1.0) at the beginning.
return (pow(base, sph) * lanczos_sum) * s_inv;
}
vec3 gamma_impl(const vec3 s, const vec3 s_inv)
{
// vec3 version:
const vec3 g = vec3(1.12906830989);
const vec3 c0 = vec3(0.8109119309638332633713423362694399653724431);
const vec3 c1 = vec3(0.4808354605142681877121661197951496120000040);
const vec3 e = vec3(2.71828182845904523536028747135266249775724709);
const vec3 sph = s + vec3(0.5);
const vec3 lanczos_sum = c0 + c1/(s + vec3(1.0));
const vec3 base = (sph + g)/e;
return (pow(base, sph) * lanczos_sum) * s_inv;
}
vec2 gamma_impl(const vec2 s, const vec2 s_inv)
{
// vec2 version:
const vec2 g = vec2(1.12906830989);
const vec2 c0 = vec2(0.8109119309638332633713423362694399653724431);
const vec2 c1 = vec2(0.4808354605142681877121661197951496120000040);
const vec2 e = vec2(2.71828182845904523536028747135266249775724709);
const vec2 sph = s + vec2(0.5);
const vec2 lanczos_sum = c0 + c1/(s + vec2(1.0));
const vec2 base = (sph + g)/e;
return (pow(base, sph) * lanczos_sum) * s_inv;
}
float gamma_impl(const float s, const float s_inv)
{
// Float version:
const float g = 1.12906830989;
const float c0 = 0.8109119309638332633713423362694399653724431;
const float c1 = 0.4808354605142681877121661197951496120000040;
const float e = 2.71828182845904523536028747135266249775724709;
const float sph = s + 0.5;
const float lanczos_sum = c0 + c1/(s + 1.0);
const float base = (sph + g)/e;
return (pow(base, sph) * lanczos_sum) * s_inv;
}
vec4 gamma(const vec4 s)
{
// Requires: s is the standard parameter to the gamma function, and it
// should lie in the [0, 36] range.
// Returns: Return approximate gamma function output with a maximum
// relative error of 0.000463. See gamma_impl for details.
return gamma_impl(s, vec4(1.0)/s);
}
vec3 gamma(const vec3 s)
{
// vec3 version:
return gamma_impl(s, vec3(1.0)/s);
}
vec2 gamma(const vec2 s)
{
// vec2 version:
return gamma_impl(s, vec2(1.0)/s);
}
float gamma(const float s)
{
// Float version:
return gamma_impl(s, 1.0/s);
}
//////////////// INCOMPLETE GAMMA FUNCTIONS (RESTRICTED INPUT) ///////////////
// Lower incomplete gamma function for small s and z (implementation):
vec4 ligamma_small_z_impl(const vec4 s, const vec4 z, const vec4 s_inv)
{
// Requires: 1.) s < ~0.5
// 2.) z <= ~0.775075
// 3.) s_inv = 1.0/s (precomputed for outside reuse)
// Returns: A series representation for the lower incomplete gamma
// function for small s and small z (4 terms).
// The actual "rolled up" summation looks like:
// last_sign = 1.0; last_pow = 1.0; last_factorial = 1.0;
// sum = last_sign * last_pow / ((s + k) * last_factorial)
// for(int i = 0; i < 4; ++i)
// {
// last_sign *= -1.0; last_pow *= z; last_factorial *= i;
// sum += last_sign * last_pow / ((s + k) * last_factorial);
// }
// Unrolled, constant-unfolded and arranged for madds and parallelism:
const vec4 scale = pow(z, s);
vec4 sum = s_inv; // Summation iteration 0 result
// Summation iterations 1, 2, and 3:
const vec4 z_sq = z*z;
const vec4 denom1 = s + vec4(1.0);
const vec4 denom2 = 2.0*s + vec4(4.0);
const vec4 denom3 = 6.0*s + vec4(18.0);
//vec4 denom4 = 24.0*s + vec4(96.0);
sum -= z/denom1;
sum += z_sq/denom2;
sum -= z * z_sq/denom3;
//sum += z_sq * z_sq / denom4;
// Scale and return:
return scale * sum;
}
vec3 ligamma_small_z_impl(const vec3 s, const vec3 z, const vec3 s_inv)
{
// vec3 version:
const vec3 scale = pow(z, s);
vec3 sum = s_inv;
const vec3 z_sq = z*z;
const vec3 denom1 = s + vec3(1.0);
const vec3 denom2 = 2.0*s + vec3(4.0);
const vec3 denom3 = 6.0*s + vec3(18.0);
sum -= z/denom1;
sum += z_sq/denom2;
sum -= z * z_sq/denom3;
return scale * sum;
}
vec2 ligamma_small_z_impl(const vec2 s, const vec2 z, const vec2 s_inv)
{
// vec2 version:
const vec2 scale = pow(z, s);
vec2 sum = s_inv;
const vec2 z_sq = z*z;
const vec2 denom1 = s + vec2(1.0);
const vec2 denom2 = 2.0*s + vec2(4.0);
const vec2 denom3 = 6.0*s + vec2(18.0);
sum -= z/denom1;
sum += z_sq/denom2;
sum -= z * z_sq/denom3;
return scale * sum;
}
float ligamma_small_z_impl(const float s, const float z, const float s_inv)
{
// Float version:
const float scale = pow(z, s);
float sum = s_inv;
const float z_sq = z*z;
const float denom1 = s + 1.0;
const float denom2 = 2.0*s + 4.0;
const float denom3 = 6.0*s + 18.0;
sum -= z/denom1;
sum += z_sq/denom2;
sum -= z * z_sq/denom3;
return scale * sum;
}
// Upper incomplete gamma function for small s and large z (implementation):
vec4 uigamma_large_z_impl(const vec4 s, const vec4 z)
{
// Requires: 1.) s < ~0.5
// 2.) z > ~0.775075
// Returns: Gauss's continued fraction representation for the upper
// incomplete gamma function (4 terms).
// The "rolled up" continued fraction looks like this. The denominator
// is truncated, and it's calculated "from the bottom up:"
// denom = vec4('inf');
// vec4 one = vec4(1.0);
// for(int i = 4; i > 0; --i)
// {
// denom = ((i * 2.0) - one) + z - s + (i * (s - i))/denom;
// }
// Unrolled and constant-unfolded for madds and parallelism:
const vec4 numerator = pow(z, s) * exp(-z);
vec4 denom = vec4(7.0) + z - s;
denom = vec4(5.0) + z - s + (3.0*s - vec4(9.0))/denom;
denom = vec4(3.0) + z - s + (2.0*s - vec4(4.0))/denom;
denom = vec4(1.0) + z - s + (s - vec4(1.0))/denom;
return numerator / denom;
}
vec3 uigamma_large_z_impl(const vec3 s, const vec3 z)
{
// vec3 version:
const vec3 numerator = pow(z, s) * exp(-z);
vec3 denom = vec3(7.0) + z - s;
denom = vec3(5.0) + z - s + (3.0*s - vec3(9.0))/denom;
denom = vec3(3.0) + z - s + (2.0*s - vec3(4.0))/denom;
denom = vec3(1.0) + z - s + (s - vec3(1.0))/denom;
return numerator / denom;
}
vec2 uigamma_large_z_impl(const vec2 s, const vec2 z)
{
// vec2 version:
const vec2 numerator = pow(z, s) * exp(-z);
vec2 denom = vec2(7.0) + z - s;
denom = vec2(5.0) + z - s + (3.0*s - vec2(9.0))/denom;
denom = vec2(3.0) + z - s + (2.0*s - vec2(4.0))/denom;
denom = vec2(1.0) + z - s + (s - vec2(1.0))/denom;
return numerator / denom;
}
float uigamma_large_z_impl(const float s, const float z)
{
// Float version:
const float numerator = pow(z, s) * exp(-z);
float denom = 7.0 + z - s;
denom = 5.0 + z - s + (3.0*s - 9.0)/denom;
denom = 3.0 + z - s + (2.0*s - 4.0)/denom;
denom = 1.0 + z - s + (s - 1.0)/denom;
return numerator / denom;
}
// Normalized lower incomplete gamma function for small s (implementation):
vec4 normalized_ligamma_impl(const vec4 s, const vec4 z,
const vec4 s_inv, const vec4 gamma_s_inv)
{
// Requires: 1.) s < ~0.5
// 2.) s_inv = 1/s (precomputed for outside reuse)
// 3.) gamma_s_inv = 1/gamma(s) (precomputed for outside reuse)
// Returns: Approximate the normalized lower incomplete gamma function
// for s < 0.5. Since we only care about s < 0.5, we only need
// to evaluate two branches (not four) based on z. Each branch
// uses four terms, with a max relative error of ~0.00182. The
// branch threshold and specifics were adapted for fewer terms
// from Gil/Segura/Temme's paper here:
// http://oai.cwi.nl/oai/asset/20433/20433B.pdf
// Evaluate both branches: Real branches test slower even when available.
const vec4 thresh = vec4(0.775075);
const bool4 z_is_large = z > thresh;
const vec4 large_z = vec4(1.0) - uigamma_large_z_impl(s, z) * gamma_s_inv;
const vec4 small_z = ligamma_small_z_impl(s, z, s_inv) * gamma_s_inv;
// Combine the results from both branches:
return large_z * vec4(z_is_large) + small_z * vec4(!z_is_large);
}
vec3 normalized_ligamma_impl(const vec3 s, const vec3 z,
const vec3 s_inv, const vec3 gamma_s_inv)
{
// vec3 version:
const vec3 thresh = vec3(0.775075);
const bool3 z_is_large = z > thresh;
const vec3 large_z = vec3(1.0) - uigamma_large_z_impl(s, z) * gamma_s_inv;
const vec3 small_z = ligamma_small_z_impl(s, z, s_inv) * gamma_s_inv;
return large_z * vec3(z_is_large) + small_z * vec3(!z_is_large);
}
vec2 normalized_ligamma_impl(const vec2 s, const vec2 z,
const vec2 s_inv, const vec2 gamma_s_inv)
{
// vec2 version:
const vec2 thresh = vec2(0.775075);
const bool2 z_is_large = z > thresh;
const vec2 large_z = vec2(1.0) - uigamma_large_z_impl(s, z) * gamma_s_inv;
const vec2 small_z = ligamma_small_z_impl(s, z, s_inv) * gamma_s_inv;
return large_z * vec2(z_is_large) + small_z * vec2(!z_is_large);
}
float normalized_ligamma_impl(const float s, const float z,
const float s_inv, const float gamma_s_inv)
{
// Float version:
const float thresh = 0.775075;
const bool z_is_large = z > thresh;
const float large_z = 1.0 - uigamma_large_z_impl(s, z) * gamma_s_inv;
const float small_z = ligamma_small_z_impl(s, z, s_inv) * gamma_s_inv;
return large_z * float(z_is_large) + small_z * float(!z_is_large);
}
// Normalized lower incomplete gamma function for small s:
vec4 normalized_ligamma(const vec4 s, const vec4 z)
{
// Requires: s < ~0.5
// Returns: Approximate the normalized lower incomplete gamma function
// for s < 0.5. See normalized_ligamma_impl() for details.
const vec4 s_inv = vec4(1.0)/s;
const vec4 gamma_s_inv = vec4(1.0)/gamma_impl(s, s_inv);
return normalized_ligamma_impl(s, z, s_inv, gamma_s_inv);
}
vec3 normalized_ligamma(const vec3 s, const vec3 z)
{
// vec3 version:
const vec3 s_inv = vec3(1.0)/s;
const vec3 gamma_s_inv = vec3(1.0)/gamma_impl(s, s_inv);
return normalized_ligamma_impl(s, z, s_inv, gamma_s_inv);
}
vec2 normalized_ligamma(const vec2 s, const vec2 z)
{
// vec2 version:
const vec2 s_inv = vec2(1.0)/s;
const vec2 gamma_s_inv = vec2(1.0)/gamma_impl(s, s_inv);
return normalized_ligamma_impl(s, z, s_inv, gamma_s_inv);
}
float normalized_ligamma(const float s, const float z)
{
// Float version:
const float s_inv = 1.0/s;
const float gamma_s_inv = 1.0/gamma_impl(s, s_inv);
return normalized_ligamma_impl(s, z, s_inv, gamma_s_inv);
}
#endif // SPECIAL_FUNCTIONS_H

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include/special-functions.h
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@ -1,3 +1,7 @@
#ifndef SPECIAL_FUNCTIONS_H
#define SPECIAL_FUNCTIONS_H
///////////////////////////////// MIT LICENSE //////////////////////////////// ///////////////////////////////// MIT LICENSE ////////////////////////////////
// Copyright (C) 2014 TroggleMonkey // Copyright (C) 2014 TroggleMonkey
@ -490,3 +494,5 @@ float normalized_ligamma(const float s, const float z)
const float gamma_s_inv = 1.0/gamma_impl(s, s_inv); const float gamma_s_inv = 1.0/gamma_impl(s, s_inv);
return normalized_ligamma_impl(s, z, s_inv, gamma_s_inv); return normalized_ligamma_impl(s, z, s_inv, gamma_s_inv);
} }
#endif // SPECIAL_FUNCTIONS_H