more work on royale, long way to go

crt/shaders/crt-royale/src/bloom-functions.h

@@ -0,0 +1,214 @@
+#define BLOOM_FUNCTIONS
+
+///////////////////////////////  BLOOM CONSTANTS  //////////////////////////////
+
+//  Compute constants with manual inlines of the functions below:
+const float bloom_diff_thresh = 1.0/256.0;
+
+//  Assume an extremely large viewport size for asymptotic results:
+const float max_viewport_size_x = 1080.0*1024.0*(4.0/3.0);
+
+///////////////////////////////////  HELPERS  //////////////////////////////////
+
+float get_min_sigma_to_blur_triad(const float triad_size,
+    const float thresh)
+{
+    //  Requires:   1.) triad_size is the final phosphor triad size in pixels
+    //              2.) thresh is the max desired pixel difference in the
+    //                  blurred triad (e.g. 1.0/256.0).
+    //  Returns:    Return the minimum sigma that will fully blur a phosphor
+    //              triad on the screen to an even color, within thresh.
+    //              This closed-form function was found by curve-fitting data.
+    //  Estimate: max error = ~0.086036, mean sq. error = ~0.0013387:
+    return -0.05168 + 0.6113*triad_size -
+        1.122*triad_size*sqrt(0.000416 + thresh);
+    //  Estimate: max error = ~0.16486, mean sq. error = ~0.0041041:
+    //return 0.5985*triad_size - triad_size*sqrt(thresh)
+}
+
+float get_absolute_scale_blur_sigma(const float thresh)
+{
+    //  Requires:   1.) min_expected_triads must be a global float.  The number
+    //                  of horizontal phosphor triads in the final image must be
+    //                  >= min_allowed_viewport_triads.x for realistic results.
+    //              2.) bloom_approx_scale_x must be a global float equal to the
+    //                  absolute horizontal scale of BLOOM_APPROX.
+    //              3.) bloom_approx_scale_x/min_allowed_viewport_triads.x
+    //                  should be <= 1.1658025090 to keep the final result <
+    //                  0.62666015625 (the largest sigma ensuring the largest
+    //                  unused texel weight stays < 1.0/256.0 for a 3x3 blur).
+    //              4.) thresh is the max desired pixel difference in the
+    //                  blurred triad (e.g. 1.0/256.0).
+    //  Returns:    Return the minimum Gaussian sigma that will blur the pass
+    //              output as much as it would have taken to blur away
+    //              bloom_approx_scale_x horizontal phosphor triads.
+    //  Description:
+    //  BLOOM_APPROX should look like a downscaled phosphor blur.  Ideally, we'd
+    //  use the same blur sigma as the actual phosphor bloom and scale it down
+    //  to the current resolution with (bloom_approx_scale_x/viewport_size_x), but
+    //  we don't know the viewport size in this pass.  Instead, we'll blur as
+    //  much as it would take to blur away min_allowed_viewport_triads.x.  This
+    //  will blur "more than necessary" if the user actually uses more triads,
+    //  but that's not terrible either, because blurring a constant fraction of
+    //  the viewport may better resemble a true optical bloom anyway (since the
+    //  viewport will generally be about the same fraction of each player's
+    //  field of view, regardless of screen size and resolution).
+    //  Assume an extremely large viewport size for asymptotic results.
+    return bloom_approx_scale_x/max_viewport_size_x *
+        get_min_sigma_to_blur_triad(
+            max_viewport_size_x/min_allowed_viewport_triads.x, thresh);
+}
+
+float get_center_weight(const float sigma)
+{
+    //  Given a Gaussian blur sigma, get the blur weight for the center texel.
+    #ifdef RUNTIME_PHOSPHOR_BLOOM_SIGMA
+        return get_fast_gaussian_weight_sum_inv(sigma);
+    #else
+        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);
+        //  Note: If the implementation uses a smaller blur than the max allowed,
+        //  the worst case scenario is that the center weight will be overestimated,
+        //  so we'll put a bit more energy into the brightpass...no huge deal.
+        //  Then again, if the implementation uses a larger blur than the max
+        //  "allowed" because of dynamic branching, the center weight could be
+        //  underestimated, which is more of a problem...consider always using
+        #ifdef PHOSPHOR_BLOOM_TRIADS_LARGER_THAN_12_PIXELS
+            //  43x blur:
+            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));
+        #else
+        #ifdef PHOSPHOR_BLOOM_TRIADS_LARGER_THAN_9_PIXELS
+            //  31x blur:
+            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));
+        #else
+        #ifdef PHOSPHOR_BLOOM_TRIADS_LARGER_THAN_6_PIXELS
+            //  25x blur:
+            const float weight_sum_inv = 1.0 / (w0 + 2.0 * (
+                w1 + w2 + w3 + w4 + w5 + w6 + w7 + w8 + w9 + w10 + w11 + w12));
+        #else
+        #ifdef PHOSPHOR_BLOOM_TRIADS_LARGER_THAN_3_PIXELS
+            //  17x blur:
+            const float weight_sum_inv = 1.0 / (w0 + 2.0 * (
+                w1 + w2 + w3 + w4 + w5 + w6 + w7 + w8));
+        #else
+            //  9x blur:
+            const float weight_sum_inv = 1.0 / (w0 + 2.0 * (w1 + w2 + w3 + w4));
+        #endif  //  PHOSPHOR_BLOOM_TRIADS_LARGER_THAN_3_PIXELS
+        #endif  //  PHOSPHOR_BLOOM_TRIADS_LARGER_THAN_6_PIXELS
+        #endif  //  PHOSPHOR_BLOOM_TRIADS_LARGER_THAN_9_PIXELS
+        #endif  //  PHOSPHOR_BLOOM_TRIADS_LARGER_THAN_12_PIXELS
+        const float center_weight = weight_sum_inv * weight_sum_inv;
+        return center_weight;
+    #endif
+}
+
+float get_bloom_approx_sigma(const float output_size_x_runtime,
+    const float estimated_viewport_size_x)
+{
+    //  Requires:   1.) output_size_x_runtime == BLOOM_APPROX.output_size.x.
+    //                  This is included for dynamic codepaths just in case the
+    //                  following two globals are incorrect:
+    //              2.) bloom_approx_size_x_for_skip should == the same
+    //                  if PHOSPHOR_BLOOM_FAKE is #defined
+    //              3.) bloom_approx_size_x should == the same otherwise
+    //  Returns:    For gaussian4x4, return a dynamic small bloom sigma that's
+    //              as close to optimal as possible given available information.
+    //              For blur3x3, return the a static small bloom sigma that
+    //              works well for typical cases.  Otherwise, we're using simple
+    //              bilinear filtering, so use static calculations.
+    //  Assume the default static value.  This is a compromise that ensures
+    //  typical triads are blurred, even if unusually large ones aren't.
+    const float mask_num_triads_static =
+        max(min_allowed_viewport_triads.x, mask_num_triads_desired_static);
+    const float mask_num_triads_from_size =
+        estimated_viewport_size_x/mask_triad_size_desired;
+    const float mask_num_triads_runtime = max(min_allowed_viewport_triads.x,
+        mix(mask_num_triads_from_size, mask_num_triads_desired,
+            mask_specify_num_triads));
+    //  Assume an extremely large viewport size for asymptotic results:
+     const float max_viewport_size_x = 1080.0*1024.0*(4.0/3.0);
+    if(bloom_approx_filter > 1.5)   //  4x4 true Gaussian resize
+    {
+        //  Use the runtime num triads and output size:
+        const float asymptotic_triad_size =
+            max_viewport_size_x/mask_num_triads_runtime;
+        const float asymptotic_sigma = get_min_sigma_to_blur_triad(
+            asymptotic_triad_size, bloom_diff_thresh);
+        const float bloom_approx_sigma =
+            asymptotic_sigma * output_size_x_runtime/max_viewport_size_x;
+        //  The BLOOM_APPROX input has to be ORIG_LINEARIZED to avoid moire, but
+        //  account for the Gaussian scanline sigma from the last pass too.
+        //  The bloom will be too wide horizontally but tall enough vertically.
+        return length(vec2(bloom_approx_sigma, beam_max_sigma));
+    }
+    else    //  3x3 blur resize (the bilinear resize doesn't need a sigma)
+    {
+        //  We're either using blur3x3 or bilinear filtering.  The biggest
+        //  reason to choose blur3x3 is to avoid dynamic weights, so use a
+        //  static calculation.
+        #ifdef PHOSPHOR_BLOOM_FAKE
+            const float output_size_x_static =
+                bloom_approx_size_x_for_fake;
+        #else
+            const float output_size_x_static = bloom_approx_size_x;
+        #endif
+        const float asymptotic_triad_size =
+            max_viewport_size_x/mask_num_triads_static;
+        const float asymptotic_sigma = get_min_sigma_to_blur_triad(
+            asymptotic_triad_size, bloom_diff_thresh);
+        const float bloom_approx_sigma =
+            asymptotic_sigma * output_size_x_static/max_viewport_size_x;
+        //  The BLOOM_APPROX input has to be ORIG_LINEARIZED to avoid moire, but
+        //  try accounting for the Gaussian scanline sigma from the last pass
+        //  too; use the static default value:
+        return length(vec2(bloom_approx_sigma, beam_max_sigma_static));
+    }
+}
+
+float get_final_bloom_sigma(const float bloom_sigma_runtime)
+{
+    //  Requires:   1.) bloom_sigma_runtime is a precalculated sigma that's
+    //                  optimal for the [known] triad size.
+    //              2.) Call this from a fragment shader (not a vertex shader),
+    //                  or blurring with static sigmas won't be constant-folded.
+    //  Returns:    Return the optimistic static sigma if the triad size is
+    //              known at compile time.  Otherwise return the optimal runtime
+    //              sigma (10% slower) or an implementation-specific compromise
+    //              between an optimistic or pessimistic static sigma.
+    //  Notes:      Call this from the fragment shader, NOT the vertex shader,
+    //              so static sigmas can be constant-folded!
+    const float bloom_sigma_optimistic = get_min_sigma_to_blur_triad(
+        mask_triad_size_desired_static, bloom_diff_thresh);
+    #ifdef RUNTIME_PHOSPHOR_BLOOM_SIGMA
+        return bloom_sigma_runtime;
+    #else
+        //  Overblurring looks as bad as underblurring, so assume average-size
+        //  triads, not worst-case huge triads:
+        return bloom_sigma_optimistic;
+    #endif
+}

crt/shaders/crt-royale/src/blur-functions.h

@@ -0,0 +1,281 @@
+#define BLUR_FUNCTIONS
+
+/////////////////////////////////  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);
+}
+
+////////////////////  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);
+}

crt/shaders/crt-royale/src/crt-royale-bloom-approx.slang

@@ -0,0 +1,349 @@
+#version 450
+
+layout(push_constant) uniform Push
+{
+	vec4 SourceSize;
+	vec4 OriginalSize;
+	vec4 OutputSize;
+	uint FrameCount;
+	vec4 ORIG_LINEARIZEDSize;
+} registers;
+
+#include "params.inc"
+
+/////////////////////////////  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 "includes.h"
+
+///////////////////////////////////  HELPERS  //////////////////////////////////
+
+///////////////////////////////////  HELPERS  //////////////////////////////////
+
+vec3 tex2Dresize_gaussian4x4(const sampler2D tex, const vec2 tex_uv,
+    const vec2 dxdy, const vec2 texture_size, const vec2 texture_size_inv,
+    const vec2 tex_uv_to_pixel_scale, const float sigma)
+{
+    //  Requires:   1.) All requirements of gamma-management.h must be satisfied!
+    //              2.) filter_linearN must == "true" in your .cgp preset.
+    //              3.) mipmap_inputN must == "true" in your .cgp preset if
+    //                  IN.output_size << SRC.video_size.
+    //              4.) dxdy should contain the uv pixel spacing:
+    //                      dxdy = max(vec2(1.0),
+    //                          SRC.video_size/IN.output_size)/SRC.texture_size;
+    //              5.) texture_size == SRC.texture_size
+    //              6.) texture_size_inv == vec2(1.0)/SRC.texture_size
+    //              7.) tex_uv_to_pixel_scale == IN.output_size *
+    //                      SRC.texture_size / SRC.video_size;
+    //              8.) sigma is the desired Gaussian standard deviation, in
+    //                  terms of output pixels.  It should be < ~0.66171875 to
+    //                  ensure the first unused sample (outside the 4x4 box) has
+    //                  a weight < 1.0/256.0.
+    //  Returns:    A true 4x4 Gaussian resize of the input.
+    //  Description:
+    //  Given correct inputs, this Gaussian resizer samples 4 pixel locations
+    //  along each downsized dimension and/or 4 texel locations along each
+    //  upsized dimension.  It computes dynamic weights based on the pixel-space
+    //  distance of each sample from the destination pixel.  It is arbitrarily
+    //  resizable and higher quality than tex2Dblur3x3_resize, but it's slower.
+    //  TODO: Move this to a more suitable file once there are others like it.
+    const float denom_inv = 0.5/(sigma*sigma);
+    //  We're taking 4x4 samples, and we're snapping to texels for upsizing.
+    //  Find texture coords for sample 5 (second row, second column):
+    const vec2 curr_texel = tex_uv * texture_size;
+    const vec2 prev_texel =
+        floor(curr_texel - vec2(under_half)) + vec2(0.5);
+    const vec2 prev_texel_uv = prev_texel * texture_size_inv;
+    const bvec2 snap = lessThanEqual(dxdy , texture_size_inv);
+    const vec2 sample5_downsize_uv = tex_uv - 0.5 * dxdy;
+    const vec2 sample5_uv = mix(sample5_downsize_uv, prev_texel_uv, snap);
+    //  Compute texture coords for other samples:
+    const vec2 dx = vec2(dxdy.x, 0.0);
+    const vec2 sample0_uv = sample5_uv - dxdy;
+    const vec2 sample10_uv = sample5_uv + dxdy;
+    const vec2 sample15_uv = sample5_uv + 2.0 * dxdy;
+    const vec2 sample1_uv = sample0_uv + dx;
+    const vec2 sample2_uv = sample0_uv + 2.0 * dx;
+    const vec2 sample3_uv = sample0_uv + 3.0 * dx;
+    const vec2 sample4_uv = sample5_uv - dx;
+    const vec2 sample6_uv = sample5_uv + dx;
+    const vec2 sample7_uv = sample5_uv + 2.0 * dx;
+    const vec2 sample8_uv = sample10_uv - 2.0 * dx;
+    const vec2 sample9_uv = sample10_uv - dx;
+    const vec2 sample11_uv = sample10_uv + dx;
+    const vec2 sample12_uv = sample15_uv - 3.0 * dx;
+    const vec2 sample13_uv = sample15_uv - 2.0 * dx;
+    const vec2 sample14_uv = sample15_uv - dx;
+    //  Load each sample:
+    const vec3 sample0 = tex2D_linearize(tex, sample0_uv).rgb;
+    const vec3 sample1 = tex2D_linearize(tex, sample1_uv).rgb;
+    const vec3 sample2 = tex2D_linearize(tex, sample2_uv).rgb;
+    const vec3 sample3 = tex2D_linearize(tex, sample3_uv).rgb;
+    const vec3 sample4 = tex2D_linearize(tex, sample4_uv).rgb;
+    const vec3 sample5 = tex2D_linearize(tex, sample5_uv).rgb;
+    const vec3 sample6 = tex2D_linearize(tex, sample6_uv).rgb;
+    const vec3 sample7 = tex2D_linearize(tex, sample7_uv).rgb;
+    const vec3 sample8 = tex2D_linearize(tex, sample8_uv).rgb;
+    const vec3 sample9 = tex2D_linearize(tex, sample9_uv).rgb;
+    const vec3 sample10 = tex2D_linearize(tex, sample10_uv).rgb;
+    const vec3 sample11 = tex2D_linearize(tex, sample11_uv).rgb;
+    const vec3 sample12 = tex2D_linearize(tex, sample12_uv).rgb;
+    const vec3 sample13 = tex2D_linearize(tex, sample13_uv).rgb;
+    const vec3 sample14 = tex2D_linearize(tex, sample14_uv).rgb;
+    const vec3 sample15 = tex2D_linearize(tex, sample15_uv).rgb;
+    //  Compute destination pixel offsets for each sample:
+    const vec2 dest_pixel = tex_uv * tex_uv_to_pixel_scale;
+    const vec2 sample0_offset = sample0_uv * tex_uv_to_pixel_scale - dest_pixel;
+    const vec2 sample1_offset = sample1_uv * tex_uv_to_pixel_scale - dest_pixel;
+    const vec2 sample2_offset = sample2_uv * tex_uv_to_pixel_scale - dest_pixel;
+    const vec2 sample3_offset = sample3_uv * tex_uv_to_pixel_scale - dest_pixel;
+    const vec2 sample4_offset = sample4_uv * tex_uv_to_pixel_scale - dest_pixel;
+    const vec2 sample5_offset = sample5_uv * tex_uv_to_pixel_scale - dest_pixel;
+    const vec2 sample6_offset = sample6_uv * tex_uv_to_pixel_scale - dest_pixel;
+    const vec2 sample7_offset = sample7_uv * tex_uv_to_pixel_scale - dest_pixel;
+    const vec2 sample8_offset = sample8_uv * tex_uv_to_pixel_scale - dest_pixel;
+    const vec2 sample9_offset = sample9_uv * tex_uv_to_pixel_scale - dest_pixel;
+    const vec2 sample10_offset = sample10_uv * tex_uv_to_pixel_scale - dest_pixel;
+    const vec2 sample11_offset = sample11_uv * tex_uv_to_pixel_scale - dest_pixel;
+    const vec2 sample12_offset = sample12_uv * tex_uv_to_pixel_scale - dest_pixel;
+    const vec2 sample13_offset = sample13_uv * tex_uv_to_pixel_scale - dest_pixel;
+    const vec2 sample14_offset = sample14_uv * tex_uv_to_pixel_scale - dest_pixel;
+    const vec2 sample15_offset = sample15_uv * tex_uv_to_pixel_scale - dest_pixel;
+    //  Compute Gaussian sample weights:
+    const float w0 = exp(-LENGTH_SQ(sample0_offset) * denom_inv);
+    const float w1 = exp(-LENGTH_SQ(sample1_offset) * denom_inv);
+    const float w2 = exp(-LENGTH_SQ(sample2_offset) * denom_inv);
+    const float w3 = exp(-LENGTH_SQ(sample3_offset) * denom_inv);
+    const float w4 = exp(-LENGTH_SQ(sample4_offset) * denom_inv);
+    const float w5 = exp(-LENGTH_SQ(sample5_offset) * denom_inv);
+    const float w6 = exp(-LENGTH_SQ(sample6_offset) * denom_inv);
+    const float w7 = exp(-LENGTH_SQ(sample7_offset) * denom_inv);
+    const float w8 = exp(-LENGTH_SQ(sample8_offset) * denom_inv);
+    const float w9 = exp(-LENGTH_SQ(sample9_offset) * denom_inv);
+    const float w10 = exp(-LENGTH_SQ(sample10_offset) * denom_inv);
+    const float w11 = exp(-LENGTH_SQ(sample11_offset) * denom_inv);
+    const float w12 = exp(-LENGTH_SQ(sample12_offset) * denom_inv);
+    const float w13 = exp(-LENGTH_SQ(sample13_offset) * denom_inv);
+    const float w14 = exp(-LENGTH_SQ(sample14_offset) * denom_inv);
+    const float w15 = exp(-LENGTH_SQ(sample15_offset) * denom_inv);
+    const float weight_sum_inv = 1.0/(
+        w0 + w1 + w2 + w3 + w4 + w5 + w6 + w7 +
+        w8 +w9 + w10 + w11 + w12 + w13 + w14 + w15);
+    //  Weight and sum the samples:
+    const vec3 sum = w0 * sample0 + w1 * sample1 + w2 * sample2 + w3 * sample3 +
+        w4 * sample4 + w5 * sample5 + w6 * sample6 + w7 * sample7 +
+        w8 * sample8 + w9 * sample9 + w10 * sample10 + w11 * sample11 +
+        w12 * sample12 + w13 * sample13 + w14 * sample14 + w15 * sample15;
+    return sum * weight_sum_inv;
+}
+
+#pragma stage vertex
+layout(location = 0) in vec4 Position;
+layout(location = 1) in vec2 TexCoord;
+layout(location = 0) out vec2 tex_uv;
+layout(location = 1) out float estimated_viewport_size_x;
+layout(location = 2) out vec2 blur_dxdy;
+layout(location = 3) out vec2 uv_scanline_step;
+layout(location = 4) out vec2 texture_size_inv;
+layout(location = 5) out vec2 tex_uv_to_pixel_scale;
+
+void main()
+{
+    //  This vertex shader copies blurs/vertex-shader-blur-one-pass-resize.h,
+    //  except we're using a different source image.
+   gl_Position = params.MVP * Position;
+   const vec2 video_uv = TexCoord;
+   tex_uv = video_uv;
+    //  The last pass (vertical scanlines) had a viewport y scale, so we can
+    //  use it to calculate a better runtime sigma:
+	estimated_viewport_size_x = registers.SourceSize.y * params.geom_aspect_ratio_x / params.geom_aspect_ratio_y;
+   
+    //  Get the uv sample distance between output pixels.  We're using a resize
+    //  blur, so arbitrary upsizing will be acceptable if filter_linearN =
+    //  "true," and arbitrary downsizing will be acceptable if mipmap_inputN =
+    //  "true" too.  The blur will be much more accurate if a true 4x4 Gaussian
+    //  resize is used instead of tex2Dblur3x3_resize (which samples between
+    //  texels even for upsizing).
+	const vec2 dxdy_min_scale = registers.ORIG_LINEARIZEDSize.xy / registers.OutputSize.xy;
+    texture_size_inv = vec2(1.0) * registers.ORIG_LINEARIZEDSize.zw;
+    if(bloom_approx_filter > 1.5)   //  4x4 true Gaussian resize
+    {
+        //  For upsizing, we'll snap to texels and sample the nearest 4.
+        const vec2 dxdy_scale = max(dxdy_min_scale, vec2(1.0));
+        blur_dxdy = dxdy_scale * texture_size_inv;
+    }
+    else
+    {
+        const vec2 dxdy_scale = dxdy_min_scale;
+        blur_dxdy = dxdy_scale * texture_size_inv;
+	}
+	
+	tex_uv_to_pixel_scale = registers.OutputSize.xy;
+//  texture_size_inv = texture_size_inv; <- commented out because it's pointless in slang
+
+    //  Detecting interlacing again here lets us apply convergence offsets in
+    //  this pass.  il_step_multiple contains the (texel, scanline) step
+    //  multiple: 1 for progressive, 2 for interlaced.
+    const vec2 orig_video_size = registers.ORIG_LINEARIZEDSize.xy;
+	float interlace_check = 0.0;
+	if (is_interlaced(orig_video_size.y) == true) interlace_check = 1.0;
+    const float y_step = 1.0 + interlace_check;
+    const vec2 il_step_multiple = vec2(1.0, y_step);
+    //  Get the uv distance between (texels, same-field scanlines):
+    uv_scanline_step = il_step_multiple * registers.ORIG_LINEARIZEDSize.zw;
+}
+
+#pragma stage fragment
+layout(location = 0) in vec2 tex_uv;
+layout(location = 1) in float estimated_viewport_size_x;
+layout(location = 2) in vec2 blur_dxdy;
+layout(location = 3) in vec2 uv_scanline_step;
+layout(location = 4) in vec2 texture_size_inv;
+layout(location = 5) in vec2 tex_uv_to_pixel_scale;
+layout(location = 0) out vec4 FragColor;
+layout(set = 0, binding = 2) uniform sampler2D Source;
+layout(set = 0, binding = 3) uniform sampler2D ORIG_LINEARIZED;
+
+void main()
+{
+    //  Would a viewport-relative size work better for this pass?  (No.)
+    //  PROS:
+    //  1.) Instead of writing an absolute size to user-cgp-constants.h, we'd
+    //      write a viewport scale.  That number could be used to directly scale
+    //      the viewport-resolution bloom sigma and/or triad size to a smaller
+    //      scale.  This way, we could calculate an optimal dynamic sigma no
+    //      matter how the dot pitch is specified.
+    //  CONS:
+    //  1.) Texel smearing would be much worse at small viewport sizes, but
+    //      performance would be much worse at large viewport sizes, so there
+    //      would be no easy way to calculate a decent scale.
+    //  2.) Worse, we could no longer get away with using a constant-size blur!
+    //      Instead, we'd have to face all the same difficulties as the real
+    //      phosphor bloom, which requires static #ifdefs to decide the blur
+    //      size based on the expected triad size...a dynamic value.
+    //  3.) Like the phosphor bloom, we'd have less control over making the blur
+    //      size correct for an optical blur.  That said, we likely overblur (to
+    //      maintain brightness) more than the eye would do by itself: 20/20
+    //      human vision distinguishes ~1 arc minute, or 1/60 of a degree.  The
+    //      highest viewing angle recommendation I know of is THX's 40.04 degree
+    //      recommendation, at which 20/20 vision can distinguish about 2402.4
+    //      lines.  Assuming the "TV lines" definition, that means 1201.2
+    //      distinct light lines and 1201.2 distinct dark lines can be told
+    //      apart, i.e. 1201.2 pairs of lines.  This would correspond to 1201.2
+    //      pairs of alternating lit/unlit phosphors, so 2402.4 phosphors total
+    //      (if they're alternately lit).  That's a max of 800.8 triads.  Using
+    //      a more popular 30 degree viewing angle recommendation, 20/20 vision
+    //      can distinguish 1800 lines, or 600 triads of alternately lit
+    //      phosphors.  In contrast, we currently blur phosphors all the way
+    //      down to 341.3 triads to ensure full brightness.
+    //  4.) Realistically speaking, we're usually just going to use bilinear
+    //      filtering in this pass anyway, but it only works well to limit
+    //      bandwidth if it's done at a small constant scale.
+    
+    //  Get the constants we need to sample:
+	const vec2 texture_size = registers.ORIG_LINEARIZEDSize.xy;
+	vec2 tex_uv_r, tex_uv_g, tex_uv_b;
+	
+	if(beam_misconvergence)
+    {
+        const vec2 convergence_offsets_r = get_convergence_offsets_r_vector();
+        const vec2 convergence_offsets_g = get_convergence_offsets_g_vector();
+        const vec2 convergence_offsets_b = get_convergence_offsets_b_vector();
+        tex_uv_r = tex_uv - vec2(params.convergence_offset_x_r, params.convergence_offset_y_r) * uv_scanline_step;
+        tex_uv_g = tex_uv - vec2(params.convergence_offset_x_g, params.convergence_offset_y_g) * uv_scanline_step;
+        tex_uv_b = tex_uv - vec2(params.convergence_offset_x_b, params.convergence_offset_y_b) * uv_scanline_step;
+    }
+	//  Get the blur sigma:
+    const float bloom_approx_sigma = get_bloom_approx_sigma(registers.OutputSize.x, estimated_viewport_size_x);
+	
+	//  Sample the resized and blurred texture, and apply convergence offsets if
+    //  necessary.  Applying convergence offsets here triples our samples from
+    //  16/9/1 to 48/27/3, but faster and easier than sampling BLOOM_APPROX and
+    //  HALATION_BLUR 3 times at full resolution every time they're used.
+    vec3 color_r, color_g, color_b, color;
+	if(bloom_approx_filter > 1.5)
+    {
+        //  Use a 4x4 Gaussian resize.  This is slower but technically correct.
+        if(beam_misconvergence)
+        {
+            color_r = tex2Dresize_gaussian4x4(ORIG_LINEARIZED, tex_uv_r,
+                blur_dxdy, texture_size, texture_size_inv,
+                tex_uv_to_pixel_scale, bloom_approx_sigma);
+            color_g = tex2Dresize_gaussian4x4(ORIG_LINEARIZED, tex_uv_g,
+                blur_dxdy, texture_size, texture_size_inv,
+                tex_uv_to_pixel_scale, bloom_approx_sigma);
+            color_b = tex2Dresize_gaussian4x4(ORIG_LINEARIZED, tex_uv_b,
+                blur_dxdy, texture_size, texture_size_inv,
+                tex_uv_to_pixel_scale, bloom_approx_sigma);
+        }
+        else
+        {
+            color = tex2Dresize_gaussian4x4(ORIG_LINEARIZED, tex_uv,
+                blur_dxdy, texture_size, texture_size_inv,
+                tex_uv_to_pixel_scale, bloom_approx_sigma);
+        }
+    }
+    else if(bloom_approx_filter > 0.5)
+    {
+        //  Use a 3x3 resize blur.  This is the softest option, because we're
+        //  blurring already blurry bilinear samples.  It doesn't play quite as
+        //  nicely with convergence offsets, but it has its charms.
+        if(beam_misconvergence)
+        {
+            color_r = tex2Dblur3x3resize(ORIG_LINEARIZED, tex_uv_r,
+                blur_dxdy, bloom_approx_sigma);
+            color_g = tex2Dblur3x3resize(ORIG_LINEARIZED, tex_uv_g,
+                blur_dxdy, bloom_approx_sigma);
+            color_b = tex2Dblur3x3resize(ORIG_LINEARIZED, tex_uv_b,
+                blur_dxdy, bloom_approx_sigma);
+        }
+        else
+        {
+            color = tex2Dblur3x3resize(ORIG_LINEARIZED, tex_uv, blur_dxdy);
+        }
+    }
+    else
+    {
+        //  Use bilinear sampling.  This approximates a 4x4 Gaussian resize MUCH
+        //  better than tex2Dblur3x3_resize for the very small sigmas we're
+        //  likely to use at small output resolutions.  (This estimate becomes
+        //  too sharp above ~400x300, but the blurs break down above that
+        //  resolution too, unless min_allowed_viewport_triads is high enough to
+        //  keep bloom_approx_scale_x/min_allowed_viewport_triads < ~1.1658025.)
+        if(beam_misconvergence)
+        {
+            color_r = tex2D_linearize(ORIG_LINEARIZED, tex_uv_r).rgb;
+            color_g = tex2D_linearize(ORIG_LINEARIZED, tex_uv_g).rgb;
+            color_b = tex2D_linearize(ORIG_LINEARIZED, tex_uv_b).rgb;
+        }
+        else
+        {
+            color = tex2D_linearize(ORIG_LINEARIZED, tex_uv).rgb;
+        }
+    }
+	//  Pack the colors from the red/green/blue beams into a single vector:
+    if(beam_misconvergence)
+    {
+        color = vec3(color_r.r, color_g.g, color_b.b);
+    }
+    //  Encode and output the blurred image:
+   FragColor = vec4(color, 1.0);
+}

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

@@ -6,56 +6,6 @@ layout(push_constant) uniform Push
 	uint FrameCount;
 } registers;
 
-layout(std140, set = 0, binding = 0) uniform UBO
-{
-	mat4 MVP;
-	float crt_gamma;
-    float lcd_gamma;
-    float levels_contrast;
-    float halation_weight;
-    float diffusion_weight;
-    float bloom_underestimate_levels;
-    float bloom_excess;
-    float beam_min_sigma;
-    float beam_max_sigma;
-    float beam_spot_power;
-    float beam_min_shape;
-    float beam_max_shape;
-    float beam_shape_power;
-    float beam_horiz_filter;
-    float beam_horiz_sigma;
-    float beam_horiz_linear_rgb_weight;
-    float convergence_offset_x_r;
-    float convergence_offset_x_g;
-    float convergence_offset_x_b;
-    float convergence_offset_y_r;
-    float convergence_offset_y_g;
-    float convergence_offset_y_b;
-    float mask_type;
-    float mask_sample_mode_desired;
-    float mask_specify_num_triads;
-    float mask_triad_size_desired;
-    float mask_num_triads_desired;
-    float aa_subpixel_r_offset_x_runtime;
-    float aa_subpixel_r_offset_y_runtime;
-    float aa_cubic_c;
-    float aa_gauss_sigma;
-    float geom_mode_runtime;
-    float geom_radius;
-    float geom_view_dist;
-    float geom_tilt_angle_x;
-    float geom_tilt_angle_y;
-    float geom_aspect_ratio_x;
-    float geom_aspect_ratio_y;
-    float geom_overscan_x;
-    float geom_overscan_y;
-    float border_size;
-    float border_darkness;
-    float border_compress;
-    float interlace_bff;
-    float interlace_1080i;
-} params;
-
 /////////////////////////////  GPL LICENSE NOTICE  /////////////////////////////
 
 //  crt-royale: A full-featured CRT shader, with cheese.
@@ -88,211 +38,7 @@ layout(std140, set = 0, binding = 0) uniform UBO
 
 //////////////////////////////////  INCLUDES  //////////////////////////////////
 
-#include "../user-settings.h"
+#include "includes.h"
-#include "bind-shader-params.h"
-//#include "../../../../include/gamma-management.h"
-//#include "scanline-functions.h"
-
-// from scanline-functions.h //
-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 = true;}
-		else
-			{hd_interlace = false;}
-		return (sd_interlace || hd_interlace);
-    }
-    else
-    {
-        return false;
-    }
-}
-// end scanline-functions.h //
-
-// from gamma-management.h //
-///////////////////////////////  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
-
-#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
-
-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 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;
-    }
-}
-
-#define tex2D_linearize(C, D) decode_input(vec4(texture(C, D)))
-//vec4 tex2D_linearize(const sampler2D tex, const vec2 tex_coords)
-//{   return decode_input(vec4(texture(tex, tex_coords)));   }
-
-//#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)
-//{   return decode_input(vec4(texture(tex, tex_coords, texel_off)));    }
-
-// end gamma-management.h //
 
 #pragma stage vertex
 layout(location = 0) in vec4 Position;

crt/shaders/crt-royale/src/crt-royale-scanlines-vertical-interlacing.slang

@@ -0,0 +1,237 @@
+#version 450
+
+layout(push_constant) uniform Push
+{
+	vec4 SourceSize;
+	vec4 OriginalSize;
+	vec4 OutputSize;
+	uint FrameCount;
+} registers;
+
+#include "params.inc"
+
+/////////////////////////////  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 "includes.h"
+
+#pragma stage vertex
+layout(location = 0) in vec4 Position;
+layout(location = 1) in vec2 TexCoord;
+layout(location = 0) out vec2 tex_uv;
+layout(location = 1) out vec2 uv_step;
+layout(location = 2) out vec2 il_step_multiple;
+layout(location = 3) out float pixel_height_in_scanlines;
+
+void main()
+{
+   gl_Position = params.MVP * Position;
+   tex_uv = TexCoord;
+   
+    //  Detect interlacing: il_step_multiple indicates the step multiple between
+    //  lines: 1 is for progressive sources, and 2 is for interlaced sources.
+    const vec2 video_size = registers.SourceSize.xy;
+	float interlace_check = is_interlaced(video_size.y) ? 1.0 : 0.0;
+    const float y_step = 1.0 + interlace_check;
+    il_step_multiple = vec2(1.0, y_step);
+    //  Get the uv tex coords step between one texel (x) and scanline (y):
+    uv_step = il_step_multiple * registers.SourceSize.zw;
+	
+	//  If shader parameters are used, {min, max}_{sigma, shape} are runtime
+    //  values.  Compute {sigma, shape}_range outside of scanline_contrib() so
+    //  they aren't computed once per scanline (6 times per fragment and up to
+    //  18 times per vertex):
+	const float sigma_range = max(params.beam_max_sigma, params.beam_min_sigma) -
+        params.beam_min_sigma;
+    const float shape_range = max(params.beam_max_shape, params.beam_min_shape) -
+        params.beam_min_shape;
+		
+	//  We need the pixel height in scanlines for antialiased/integral sampling:
+    pixel_height_in_scanlines = (video_size.y * registers.OutputSize.w) / 
+        il_step_multiple.y;
+}
+
+#pragma stage fragment
+layout(location = 0) in vec2 tex_uv;
+layout(location = 1) in vec2 uv_step;
+layout(location = 2) in vec2 il_step_multiple;
+layout(location = 3) in float pixel_height_in_scanlines;
+layout(location = 0) out vec4 FragColor;
+layout(set = 0, binding = 2) uniform sampler2D Source;
+
+void main()
+{
+    //  This pass: Sample multiple (misconverged?) scanlines to the final
+    //  vertical resolution.  Temporarily auto-dim the output to avoid clipping.
+
+    //  Read some attributes into local variables:
+    const vec2 texture_size = registers.SourceSize.xy;
+    const vec2 texture_size_inv = registers.SourceSize.zw;
+    const float frame_count = vec2(registers.FrameCount, registers.FrameCount).x;
+    const float ph = pixel_height_in_scanlines;
+	
+	//  Get the uv coords of the previous scanline (in this field), and the
+    //  scanline's distance from this sample, in scanlines.
+    float dist;
+    const vec2 scanline_uv = get_last_scanline_uv(tex_uv, texture_size,
+        texture_size_inv, il_step_multiple, frame_count, dist);
+    //  Consider 2, 3, 4, or 6 scanlines numbered 0-5: The previous and next
+    //  scanlines are numbered 2 and 3.  Get scanline colors colors (ignore
+    //  horizontal sampling, since since registers.OutputSize.x = video_size.x).
+    //  NOTE: Anisotropic filtering creates interlacing artifacts, which is why
+    //  ORIG_LINEARIZED bobbed any interlaced input before this pass.
+    const vec2 v_step = vec2(0.0, uv_step.y);
+    const vec3 scanline2_color = tex2D_linearize(Source, scanline_uv).rgb;
+    const vec3 scanline3_color =
+        tex2D_linearize(Source, scanline_uv + v_step).rgb;
+    vec3 scanline0_color, scanline1_color, scanline4_color, scanline5_color,
+        scanline_outside_color;
+    float dist_round;
+    //  Use scanlines 0, 1, 4, and 5 for a total of 6 scanlines:
+	if(beam_num_scanlines > 5.5)
+    {
+        scanline1_color =
+            tex2D_linearize(Source, scanline_uv - v_step).rgb;
+        scanline4_color =
+            tex2D_linearize(Source, scanline_uv + 2.0 * v_step).rgb;
+        scanline0_color =
+            tex2D_linearize(Source, scanline_uv - 2.0 * v_step).rgb;
+        scanline5_color =
+            tex2D_linearize(Source, scanline_uv + 3.0 * v_step).rgb;
+    }
+	//  Use scanlines 1, 4, and either 0 or 5 for a total of 5 scanlines:
+    else if(beam_num_scanlines > 4.5)
+    {
+        scanline1_color =
+            tex2D_linearize(Source, scanline_uv - v_step).rgb;
+        scanline4_color =
+            tex2D_linearize(Source, scanline_uv + 2.0 * v_step).rgb;
+        //  dist is in [0, 1]
+        dist_round = round(dist);
+        const vec2 sample_0_or_5_uv_off =
+            mix(-2.0 * v_step, 3.0 * v_step, dist_round);
+        //  Call this "scanline_outside_color" to cope with the conditional
+        //  scanline number:
+        scanline_outside_color = tex2D_linearize(
+            Source, scanline_uv + sample_0_or_5_uv_off).rgb;
+    }
+	//  Use scanlines 1 and 4 for a total of 4 scanlines:
+    else if(beam_num_scanlines > 3.5)
+    {
+        scanline1_color =
+            tex2D_linearize(Source, scanline_uv - v_step).rgb;
+        scanline4_color =
+            tex2D_linearize(Source, scanline_uv + 2.0 * v_step).rgb;
+    }
+    //  Use scanline 1 or 4 for a total of 3 scanlines:
+    else if(beam_num_scanlines > 2.5)
+    {
+        //  dist is in [0, 1]
+        dist_round = round(dist);
+        const vec2 sample_1or4_uv_off =
+            mix(-v_step, 2.0 * v_step, dist_round);
+        scanline_outside_color = tex2D_linearize(
+            Source, scanline_uv + sample_1or4_uv_off).rgb;
+    }
+	
+	//  Compute scanline contributions, accounting for vertical convergence.
+    //  Vertical convergence offsets are in units of current-field scanlines.
+    //  dist2 means "positive sample distance from scanline 2, in scanlines:"
+    vec3 dist2 = vec3(dist);
+    if(beam_misconvergence)
+    {
+        const vec3 convergence_offsets_vert_rgb =
+            get_convergence_offsets_y_vector();
+        dist2 = vec3(dist) - convergence_offsets_vert_rgb;
+    }
+	//  Calculate {sigma, shape}_range outside of scanline_contrib so it's only
+    //  done once per pixel (not 6 times) with runtime params.  Don't reuse the
+    //  vertex shader calculations, so static versions can be constant-folded.
+    const float sigma_range = max(params.beam_max_sigma, params.beam_min_sigma) -
+        params.beam_min_sigma;
+    const float shape_range = max(params.beam_max_shape, params.beam_min_shape) -
+        params.beam_min_shape;
+	//  Calculate and sum final scanline contributions, starting with lines 2/3.
+    //  There is no normalization step, because we're not interpolating a
+    //  continuous signal.  Instead, each scanline is an additive light source.
+    const vec3 scanline2_contrib = scanline_contrib(dist2,
+        scanline2_color, ph, sigma_range, shape_range);
+    const vec3 scanline3_contrib = scanline_contrib(abs(vec3(1.0) - dist2),
+        scanline3_color, ph, sigma_range, shape_range);
+    vec3 scanline_intensity = scanline2_contrib + scanline3_contrib;
+	
+	if(beam_num_scanlines > 5.5)
+    {
+        vec3 scanline0_contrib =
+            scanline_contrib(dist2 + vec3(2.0), scanline0_color,
+                ph, sigma_range, shape_range);
+        vec3 scanline1_contrib =
+            scanline_contrib(dist2 + vec3(1.0), scanline1_color,
+                ph, sigma_range, shape_range);
+        vec3 scanline4_contrib =
+            scanline_contrib(abs(vec3(2.0) - dist2), scanline4_color,
+                ph, sigma_range, shape_range);
+        vec3 scanline5_contrib =
+            scanline_contrib(abs(vec3(3.0) - dist2), scanline5_color,
+                ph, sigma_range, shape_range);
+        scanline_intensity += scanline0_contrib + scanline1_contrib +
+            scanline4_contrib + scanline5_contrib;
+    }
+    else if(beam_num_scanlines > 4.5)
+    {
+        vec3 scanline1_contrib =
+            scanline_contrib(dist2 + vec3(1.0), scanline1_color,
+                ph, sigma_range, shape_range);
+        vec3 scanline4_contrib =
+            scanline_contrib(abs(vec3(2.0) - dist2), scanline4_color,
+                ph, sigma_range, shape_range);
+        vec3 dist0or5 = mix(
+            dist2 + vec3(2.0), vec3(3.0) - dist2, dist_round);
+        vec3 scanline0or5_contrib = scanline_contrib(
+            dist0or5, scanline_outside_color, ph, sigma_range, shape_range);
+        scanline_intensity += scanline1_contrib + scanline4_contrib +
+            scanline0or5_contrib;
+    }
+    else if(beam_num_scanlines > 3.5)
+    {
+        vec3 scanline1_contrib =
+            scanline_contrib(dist2 + vec3(1.0), scanline1_color,
+                ph, sigma_range, shape_range);
+        vec3 scanline4_contrib =
+            scanline_contrib(abs(vec3(2.0) - dist2), scanline4_color,
+                ph, sigma_range, shape_range);
+        scanline_intensity += scanline1_contrib + scanline4_contrib;
+    }
+    else if(beam_num_scanlines > 2.5)
+    {
+        vec3 dist1or4 = mix(
+            dist2 + vec3(1.0), vec3(2.0) - dist2, dist_round);
+        vec3 scanline1or4_contrib = scanline_contrib(
+            dist1or4, scanline_outside_color, ph, sigma_range, shape_range);
+        scanline_intensity += scanline1or4_contrib;
+    }
+	
+	//  Auto-dim the image to avoid clipping, encode if necessary, and output.
+    //  My original idea was to compute a minimal auto-dim factor and put it in
+    //  the alpha channel, but it wasn't working, at least not reliably.  This
+    //  is faster anyway, levels_autodim_temp = 0.5 isn't causing banding.
+   FragColor = vec4(encode_output(vec4(scanline_intensity * levels_autodim_temp, 1.0)));
+}

crt/shaders/crt-royale/src/gamma-management-old.h

@@ -0,0 +1,547 @@
+#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
+

crt/shaders/crt-royale/src/gamma-management.h

@@ -0,0 +1,160 @@
+///////////////////////////////  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
+
+#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
+
+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 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;
+    }
+}
+
+#define tex2D_linearize(C, D) decode_input(vec4(texture(C, D)))
+//vec4 tex2D_linearize(const sampler2D tex, const vec2 tex_coords)
+//{   return decode_input(vec4(texture(tex, tex_coords)));   }
+
+//#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)
+//{   return decode_input(vec4(texture(tex, tex_coords, texel_off)));    }

crt/shaders/crt-royale/src/includes.h

@@ -0,0 +1,10 @@
+#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"

crt/shaders/crt-royale/src/quad-pixel-communication.h

@@ -0,0 +1,243 @@
+#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
+

crt/shaders/crt-royale/src/scanline-functions-old.h

@@ -0,0 +1,572 @@
+#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
+

crt/shaders/crt-royale/src/scanline-functions.h

@@ -1,6 +1,3 @@
-#ifndef SCANLINE_FUNCTIONS_H
-#define SCANLINE_FUNCTIONS_H
-
 /////////////////////////////  GPL LICENSE NOTICE  /////////////////////////////
 
 //  crt-royale: A full-featured CRT shader, with cheese.
@@ -22,15 +19,77 @@
 
 //////////////////////////////////  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  /////////////////////////////
-/*
+
-inline float3 get_gaussian_sigma(const float3 color, const float sigma_range)
+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 = true;}
+		else
+			{hd_interlace = false;}
+		return (sd_interlace || hd_interlace);
+    }
+    else
+    {
+        return false;
+    }
+}
+
+vec2 get_last_scanline_uv(const vec2 tex_uv, const vec2 texture_size,
+    const vec2 texture_size_inv, const vec2 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) *
+        mod(frame_count + float(interlace_bff), 2.0);
+    const vec2 curr_texel = tex_uv * texture_size;
+    //  Use under_half to fix a rounding bug right around exact texel locations.
+    const vec2 prev_texel_num = floor(curr_texel - vec2(under_half));
+    const float wrong_field = mod(
+        prev_texel_num.y + field_offset, il_step_multiple.y);
+    const vec2 scanline_texel_num = prev_texel_num - vec2(0.0, wrong_field);
+    //  Snap to the center of the previous scanline in the current field:
+    const vec2 scanline_texel = scanline_texel_num + vec2(0.5);
+    const vec2 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;
+}
+
+vec3 get_gaussian_sigma(const vec3 color, const float sigma_range)
 {
     //  Requires:   Globals:
     //              1.) beam_min_sigma and beam_max_sigma are global floats
@@ -82,19 +141,19 @@ inline float3 get_gaussian_sigma(const float3 color, const float sigma_range)
     if(beam_spot_shape_function < 0.5)
     {
         //  Use a power function:
-        return float3(beam_min_sigma) + sigma_range *
+        return vec3(beam_min_sigma) + sigma_range *
-            pow(color, beam_spot_power);
+            pow(color, vec3(beam_spot_power));
     }
     else
     {
         //  Use a spherical function:
-        const float3 color_minus_1 = color - float3(1.0);
+        const vec3 color_minus_1 = color - vec3(1.0);
-        return float3(beam_min_sigma) + sigma_range *
+        return vec3(beam_min_sigma) + sigma_range *
-            sqrt(float3(1.0) - color_minus_1*color_minus_1);
+            sqrt(vec3(1.0) - color_minus_1*color_minus_1);
     }
 }
 
-inline float3 get_generalized_gaussian_beta(const float3 color,
+vec3 get_generalized_gaussian_beta(const vec3 color,
     const float shape_range)
 {
     //  Requires:   Globals:
@@ -120,11 +179,11 @@ inline float3 get_generalized_gaussian_beta(const float3 color,
     //      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);
+    return beam_min_shape + shape_range * pow(color, vec3(beam_shape_power));
 }
 
-float3 scanline_gaussian_integral_contrib(const float3 dist,
+vec3 scanline_gaussian_integral_contrib(const vec3 dist,
-    const float3 color, const float pixel_height, const float sigma_range)
+    const vec3 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
@@ -145,16 +204,16 @@ float3 scanline_gaussian_integral_contrib(const float3 dist,
     //  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 vec3 sigma = get_gaussian_sigma(color, sigma_range);
-    const float3 ph_offset = float3(pixel_height * 0.5);
+    const vec3 ph_offset = vec3(pixel_height * 0.5);
-    const float3 denom_inv = 1.0/(sigma*sqrt(2.0));
+    const vec3 denom_inv = 1.0/(sigma*sqrt(2.0));
-    const float3 integral_high = erf((dist + ph_offset)*denom_inv);
+    const vec3 integral_high = erf((dist + ph_offset)*denom_inv);
-    const float3 integral_low = erf((dist - ph_offset)*denom_inv);
+    const vec3 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,
+vec3 scanline_generalized_gaussian_integral_contrib(const vec3 dist,
-    const float3 color, const float pixel_height, const float sigma_range,
+    const vec3 color, const float pixel_height, const float sigma_range,
     const float shape_range)
 {
     //  Requires:   1.) Requirements of scanline_gaussian_integral_contrib()
@@ -176,44 +235,44 @@ float3 scanline_generalized_gaussian_integral_contrib(const float3 dist,
     //  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 vec3 alpha = sqrt(2.0) * get_gaussian_sigma(color, sigma_range);
-    const float3 beta = get_generalized_gaussian_beta(color, shape_range);
+    const vec3 beta = get_generalized_gaussian_beta(color, shape_range);
-    const float3 alpha_inv = float3(1.0)/alpha;
+    const vec3 alpha_inv = vec3(1.0)/alpha;
-    const float3 s = float3(1.0)/beta;
+    const vec3 s = vec3(1.0)/beta;
-    const float3 ph_offset = float3(pixel_height * 0.5);
+    const vec3 ph_offset = vec3(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 vec3 gamma_s_inv = vec3(1.0)/gamma_impl(s, beta);
-    const float3 dist1 = dist + ph_offset;
+    const vec3 dist1 = dist + ph_offset;
-    const float3 dist0 = dist - ph_offset;
+    const vec3 dist0 = dist - ph_offset;
-    const float3 integral_high = sign(dist1) * normalized_ligamma_impl(
+    const vec3 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(
+    const vec3 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,
+vec3 scanline_gaussian_sampled_contrib(const vec3 dist, const vec3 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);
+    const vec3 sigma = get_gaussian_sigma(color, sigma_range);
     //  Avoid repeated divides:
-    const float3 sigma_inv = float3(1.0)/sigma;
+    const vec3 sigma_inv = vec3(1.0)/sigma;
-    const float3 inner_denom_inv = 0.5 * sigma_inv * sigma_inv;
+    const vec3 inner_denom_inv = 0.5 * sigma_inv * sigma_inv;
-    const float3 outer_denom_inv = sigma_inv/sqrt(2.0*pi);
+    const vec3 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 vec3 sample_offset = vec3(pixel_height/3.0);
-        const float3 dist2 = dist + sample_offset;
+        const vec3 dist2 = dist + sample_offset;
-        const float3 dist3 = abs(dist - sample_offset);
+        const vec3 dist3 = abs(dist - sample_offset);
         //  Average three pure Gaussian samples:
-        const float3 scale = color/3.0 * outer_denom_inv;
+        const vec3 scale = color/3.0 * outer_denom_inv;
-        const float3 weight1 = exp(-(dist*dist)*inner_denom_inv);
+        const vec3 weight1 = exp(-(dist*dist)*inner_denom_inv);
-        const float3 weight2 = exp(-(dist2*dist2)*inner_denom_inv);
+        const vec3 weight2 = exp(-(dist2*dist2)*inner_denom_inv);
-        const float3 weight3 = exp(-(dist3*dist3)*inner_denom_inv);
+        const vec3 weight3 = exp(-(dist3*dist3)*inner_denom_inv);
         return scale * (weight1 + weight2 + weight3);
     }
     else
@@ -222,30 +281,30 @@ float3 scanline_gaussian_sampled_contrib(const float3 dist, const float3 color,
     }
 }
 
-float3 scanline_generalized_gaussian_sampled_contrib(const float3 dist,
+vec3 scanline_generalized_gaussian_sampled_contrib(const vec3 dist,
-    const float3 color, const float pixel_height, const float sigma_range,
+    const vec3 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 vec3 alpha = sqrt(2.0) * get_gaussian_sigma(color, sigma_range);
-    const float3 beta = get_generalized_gaussian_beta(color, shape_range);
+    const vec3 beta = get_generalized_gaussian_beta(color, shape_range);
     //  Avoid repeated divides:
-    const float3 alpha_inv = float3(1.0)/alpha;
+    const vec3 alpha_inv = vec3(1.0)/alpha;
-    const float3 beta_inv = float3(1.0)/beta;
+    const vec3 beta_inv = vec3(1.0)/beta;
-    const float3 scale = color * beta * 0.5 * alpha_inv /
+    const vec3 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 vec3 sample_offset = vec3(pixel_height/3.0);
-        const float3 dist2 = dist + sample_offset;
+        const vec3 dist2 = dist + sample_offset;
-        const float3 dist3 = abs(dist - sample_offset);
+        const vec3 dist3 = abs(dist - sample_offset);
         //  Average three generalized Gaussian samples:
-        const float3 weight1 = exp(-pow(abs(dist*alpha_inv), beta));
+        const vec3 weight1 = exp(-pow(abs(dist*alpha_inv), beta));
-        const float3 weight2 = exp(-pow(abs(dist2*alpha_inv), beta));
+        const vec3 weight2 = exp(-pow(abs(dist2*alpha_inv), beta));
-        const float3 weight3 = exp(-pow(abs(dist3*alpha_inv), beta));
+        const vec3 weight3 = exp(-pow(abs(dist3*alpha_inv), beta));
         return scale/3.0 * (weight1 + weight2 + weight3);
     }
     else
@@ -254,7 +313,7 @@ float3 scanline_generalized_gaussian_sampled_contrib(const float3 dist,
     }
 }
 
-inline float3 scanline_contrib(float3 dist, float3 color,
+vec3 scanline_contrib(vec3 dist, vec3 color,
     float pixel_height, const float sigma_range, const float shape_range)
 {
     //  Requires:   1.) Requirements of scanline_gaussian_integral_contrib()
@@ -292,281 +351,3 @@ inline float3 scanline_contrib(float3 dist, float3 color,
         }
     }
 }
-
-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
-

crt/shaders/crt-royale/src/special-functions-old.h

@@ -0,0 +1,498 @@
+#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
+
+

crt/shaders/crt-royale/src/special-functions.h

@@ -0,0 +1,492 @@
+/////////////////////////////////  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);
+}

crt/shaders/crt-royale/src/user-preset-constants.h

@@ -12,6 +12,7 @@
 //  this shader: One does a viewport-scale bloom, and the other skips it.  The
 //  latter benefits from a higher bloom_approx_scale_x, so save both separately:
 const float bloom_approx_size_x = 320.0;
+const float bloom_approx_scale_x = 320.0; //dunno why this is necessary
 const float bloom_approx_size_x_for_fake = 400.0;
 //  Copy the viewport-relative scales of the phosphor mask resize passes
 //  (MASK_RESIZE and the pass immediately preceding it):