+#include <math.h>
#include <assert.h>
+#include "effect_util.h"
#include "gamma_expansion_effect.h"
#include "util.h"
register_int("source_curve", (int *)&source_curve);
}
-std::string GammaExpansionEffect::output_glsl()
+std::string GammaExpansionEffect::output_fragment_shader()
{
- switch (source_curve) {
- case GAMMA_sRGB:
- return read_file("gamma_expansion_effect_srgb.glsl");
- case GAMMA_REC_709: // and GAMMA_REC_601
- // Not implemented yet.
- assert(false);
- default:
- assert(false);
+ if (source_curve == GAMMA_LINEAR) {
+ return read_file("identity.frag");
+ }
+ if (source_curve == GAMMA_sRGB ||
+ source_curve == GAMMA_REC_709 || // Also includes Rec. 601, and 10-bit Rec. 2020.
+ source_curve == GAMMA_REC_2020_12_BIT) {
+ return read_file("gamma_expansion_effect.frag");
+ }
+ assert(false);
+}
+
+void GammaExpansionEffect::set_gl_state(GLuint glsl_program_num, const std::string &prefix, unsigned *sampler_num)
+{
+ Effect::set_gl_state(glsl_program_num, prefix, sampler_num);
+
+ // All of these curves follow a continuous curve that's piecewise defined;
+ // very low values (up to some β) are linear. Above β, we have a power curve
+ // that looks like this:
+ //
+ // y = ((x + ɑ - 1) / ɑ)^ɣ
+ //
+ // However, pow() is relatively slow in GLSL, so we approximate this
+ // part by a minimax polynomial, whose coefficients are precalculated
+ // in Maple. (It is very hard to accurately model the curve as a whole
+ // using minimax polynomials; both Maple and Mathematically generally
+ // just error out if you ask them to optimize over 0..1 with a higher-degree
+ // polynomial.)
+ //
+ // We put some extra weight on areas near β to keep a continuous curve,
+ // and near 1.0, since we'd really like f(1.0) = 1.0, or approximately so.
+ // The following Maple commands, using sRGB below as an example, will
+ // compute the coefficients:
+ //
+ // > alpha := 1.055;
+ // > beta := 0.04045;
+ // > gamma_ := 2.4;
+ // > w := x -> piecewise(x < beta + 0.001, 10, x > 0.999, 10, 1);
+ // > numapprox[minimax](((x + alpha - 1) / alpha)^gamma_, x=beta..1, [4,0], w(x), 'maxerror');
+ //
+ // The variable 'maxerror' will then contain the maximum absolute error
+ // at any point of the curve, and we report this along with the absolute
+ // error at beta and at 1.0. Keep in mind that along this curve,
+ // the smallest minimum difference between any two 8-bit sRGB pixel levels
+ // (in the exponential part of the curve) in linear light is that
+ // between 11/255 and 12/255, which is about 0.00033 (or three to four
+ // times of the sRGB maxerror below). The choice of a fourth-degree
+ // polynomial was made with this in mind; we have not cared equally
+ // much about 10- and 12-bit Rec. 2020.
+ //
+ // NOTE: The error at beta is compared to the _linear_ part of the curve.
+ // Since the standards give these with only a few decimals, it means that
+ // the linear and exponential parts will not match up exactly, and even
+ // a perfect approximation will have error > 0 here; sometimes, even larger
+ // than maxerror for the curve itself.
+
+ if (source_curve == GAMMA_sRGB) {
+ // From the Wikipedia article on sRGB; ɑ (called a+1 there) = 1.055,
+ // β = 0.04045, ɣ = 2.4.
+ // maxerror = 0.000094
+ // error at beta = 0.000012
+ // error at 1.0 = 0.000012
+ //
+ // Note that the worst _relative_ error by far is just at the beginning
+ // of the exponential curve, ie., just around β.
+ set_uniform_float(glsl_program_num, prefix, "linear_scale", 1.0 / 12.92);
+ set_uniform_float(glsl_program_num, prefix, "c0", 0.001324469581);
+ set_uniform_float(glsl_program_num, prefix, "c1", 0.02227416690);
+ set_uniform_float(glsl_program_num, prefix, "c2", 0.5917615253);
+ set_uniform_float(glsl_program_num, prefix, "c3", 0.4733532353);
+ set_uniform_float(glsl_program_num, prefix, "c4", -0.08880738120);
+ set_uniform_float(glsl_program_num, prefix, "beta", 0.04045);
+ }
+ if (source_curve == GAMMA_REC_709) { // Also includes Rec. 601, and 10-bit Rec. 2020.
+ // Rec. 2020, page 3; ɑ = 1.099, β = 0.018 * 4.5, ɣ = 1/0.45.
+ // maxerror = 0.000043
+ // error at beta = 0.000051 (see note above!)
+ // error at 1.0 = 0.000004
+ //
+ // Note that Rec. 2020 only gives the other direction, which is why
+ // our beta and gamma are different from the numbers mentioned
+ // (we've inverted the formula).
+ set_uniform_float(glsl_program_num, prefix, "linear_scale", 1.0 / 4.5);
+ set_uniform_float(glsl_program_num, prefix, "c0", 0.005137028744);
+ set_uniform_float(glsl_program_num, prefix, "c1", 0.09802596889);
+ set_uniform_float(glsl_program_num, prefix, "c2", 0.7255768864);
+ set_uniform_float(glsl_program_num, prefix, "c3", 0.2135067966);
+ set_uniform_float(glsl_program_num, prefix, "c4", -0.04225094667);
+ set_uniform_float(glsl_program_num, prefix, "beta", 0.018 * 4.5);
+ }
+ if (source_curve == GAMMA_REC_2020_12_BIT) {
+ // Rec. 2020, page 3; ɑ = 1.0993, β = 0.0181 * 4.5, ɣ = 1/0.45.
+ // maxerror = 0.000042
+ // error at beta = 0.000005
+ // error at 1.0 = 0.000004
+ //
+ // Note that Rec. 2020 only gives the other direction, which is why
+ // our beta and gamma are different from the numbers mentioned
+ // (we've inverted the formula).
+ set_uniform_float(glsl_program_num, prefix, "linear_scale", 1.0 / 4.5);
+ set_uniform_float(glsl_program_num, prefix, "c0", 0.005167545928);
+ set_uniform_float(glsl_program_num, prefix, "c1", 0.09835585809);
+ set_uniform_float(glsl_program_num, prefix, "c2", 0.7254820139);
+ set_uniform_float(glsl_program_num, prefix, "c3", 0.2131291155);
+ set_uniform_float(glsl_program_num, prefix, "c4", -0.04213877222);
+ set_uniform_float(glsl_program_num, prefix, "beta", 0.0181 * 4.5);
}
}
projects / movit / blobdiff