emitterColumnQ16()

bool fl::anonymous_namespace{device_solve.cpp.hpp}::emitterColumnQ16	(	const i32(&)	xy[2],
		i32	luminance,
		i64(&)	column[3] )

One emitter's XYZ column at its own luminance, all in s16.16.

xyY_to_XYZ is x * Y * inv_y, which C++ groups left to right and so scales before it divides. This divides first, deliberately: in fixed point x * Y discards low bits the divide would have used. Measured against the float derivation over the study's corpus and four luminance sets, the worst coefficient error is 2899 ULP dividing first against 7363 scaling first, and the colour figure is the same either way. See ci/color_fixed_profile_study.py.

Definition at line 158 of file device_solve.cpp.hpp.

                                                     {
    const i32 x = xy[0];
    const i32 y = xy[1];
    // The float guard rejects a `y` at or below 1e-6; in Q16 anything under
    // half a step quantises to zero, and dividing by it is the failure the
    // float path cannot have.
    if (y <= 0 || luminance <= 0 || x <= 0) {
        return false;
    }
    if (static_cast<i64>(x) + static_cast<i64>(y) > kQ16One) {
        // Outside the CIE simplex, so z would be negative for a physical
        // emitter.
        return false;
    }
    const i64 z = kQ16One - static_cast<i64>(x) - static_cast<i64>(y);
    const i64 x_over_y = roundedDivideQ16(static_cast<i64>(x) * kQ16One, y);
    const i64 z_over_y = roundedDivideQ16(z * kQ16One, y);
    column[0] = roundedDivideQ16(x_over_y * luminance, kQ16One);
    column[1] = luminance;
    column[2] = roundedDivideQ16(z_over_y * luminance, kQ16One);
    for (int i = 0; i < 3; ++i) {
        // The inverse works in i32, so a column that does not fit is refused
        // here rather than wrapped on the way in.
        if (column[i] > 2147483647LL || column[i] < -2147483648LL) {
            return false;
        }
    }
    return true;
}

References emitterColumnQ16(), fl::FL_NO_EXCEPT, kQ16One, roundedDivideQ16(), fl::x, xy(), fl::y, and z.

Referenced by emitterColumnQ16().

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