+ Effect::set_gl_state(glsl_program_num, prefix, sampler_num);
+
+ // See GammaExpansionEffect for more details about the approximations in use;
+ // we will primarily deal with the differences here.
+ //
+ // Like in expansion, we have a piecewise curve that for very low values
+ // (up to some β) are linear. Above β, we have a power curve that looks
+ // like this:
+ //
+ // y = ɑ x^ɣ - (ɑ - 1)
+ //
+ // Like in expansion, we want to approximate this by some minimax polynomial
+ // in the range β..1. However, in this case, ɣ is typically around 0.4, and
+ // x^0.4 is actually very hard to approximate accurately in this range.
+ // We do a little trick by instead asking for a polynomial of s=sqrt(x),
+ // which means we instead need something like s^0.8, which is much easier.
+ // This warps the input space a bit as seen by the minimax algorithm,
+ // but since we are optimizing for _maximum_ error and not _average_,
+ // we should not add any extra weighting factors.
+ //
+ // However, since we have problems reaching the desired accuracy (~25%
+ // of a pixel level), especially for sRGB, we modify w(x) from
+ // GammaExpansionEffect to remove the special handling of the area
+ // around β; it is not really as useful when the next step is just a
+ // dither and round anyway. We keep it around 1, though, since that
+ // seems to hurt less.
+ //
+ // The Maple commands this time around become (again using sRGB as an example):
+ //
+ // > alpha := 1.055;
+ // > beta := 0.0031308;
+ // > gamma_ := 1.0/2.4;
+ // > w := x -> piecewise(x > 0.999, 10, 1);
+ // > numapprox[minimax](alpha * (x^2)^gamma_ - (alpha - 1), x=sqrt(beta)..1, [4,0], w(x^2), 'maxerror');
+ //
+ // Since the error here is possible to interpret on a uniform scale,
+ // we also show it as a value relative to a 8-, 10- or 12-bit pixel level,
+ // as appropriate.
+
+ if (destination_curve == GAMMA_sRGB) {
+ // From the Wikipedia article on sRGB; ɑ (called a+1 there) = 1.055,
+ // β = 0.0031308, ɣ = 1/2.4.
+ // maxerror = 0.000785 = 0.200 * 255
+ // error at 1.0 = 0.000078 = 0.020 * 255
+ set_uniform_float(glsl_program_num, prefix, "linear_scale", 12.92);
+ set_uniform_float(glsl_program_num, prefix, "c0", -0.03679675939);
+ set_uniform_float(glsl_program_num, prefix, "c1", 1.443803073);
+ set_uniform_float(glsl_program_num, prefix, "c2", -0.9239780987);
+ set_uniform_float(glsl_program_num, prefix, "c3", 0.8060491596);
+ set_uniform_float(glsl_program_num, prefix, "c4", -0.2891558568);
+ set_uniform_float(glsl_program_num, prefix, "beta", 0.0031308);
+ }
+ if (destination_curve == GAMMA_REC_709) { // Also includes Rec. 601, and 10-bit Rec. 2020.
+ // Rec. 2020, page 3; ɑ = 1.099, β = 0.018, ɣ = 0.45.
+ // maxerror = 0.000131 = 0.033 * 255 = 0.134 * 1023
+ // error at 1.0 = 0.000013 = 0.003 * 255 = 0.013 * 1023
+ set_uniform_float(glsl_program_num, prefix, "linear_scale", 4.5);
+ set_uniform_float(glsl_program_num, prefix, "c0", -0.08541688528);
+ set_uniform_float(glsl_program_num, prefix, "c1", 1.292793370);
+ set_uniform_float(glsl_program_num, prefix, "c2", -0.4070417645);
+ set_uniform_float(glsl_program_num, prefix, "c3", 0.2923891828);
+ set_uniform_float(glsl_program_num, prefix, "c4", -0.09273699351);
+ set_uniform_float(glsl_program_num, prefix, "beta", 0.018);
+ }
+ if (destination_curve == GAMMA_REC_2020_12_BIT) {
+ // Rec. 2020, page 3; ɑ = 1.0993, β = 0.0181, ɣ = 0.45.
+ // maxerror = 0.000130 = 0.533 * 4095
+ // error at 1.0 = 0.000013 = 0.053 * 4095
+ //
+ // Note that this error is above one half of a pixel level,
+ // which means that a few values will actually be off in the lowest
+ // bit. (Removing the constraint for x=1 will only take this down
+ // from 0.553 to 0.501; adding a fifth order can get it down to
+ // 0.167, although this assumes working in fp64 and not fp32.)
+ set_uniform_float(glsl_program_num, prefix, "linear_scale", 4.5);
+ set_uniform_float(glsl_program_num, prefix, "c0", -0.08569685663);
+ set_uniform_float(glsl_program_num, prefix, "c1", 1.293000900);
+ set_uniform_float(glsl_program_num, prefix, "c2", -0.4067291321);
+ set_uniform_float(glsl_program_num, prefix, "c3", 0.2919741179);
+ set_uniform_float(glsl_program_num, prefix, "c4", -0.09256205770);
+ set_uniform_float(glsl_program_num, prefix, "beta", 0.0181);