impeller_hal/

blend.rs

//! How a draw combines with what a target already holds.
//!
//! Two families live here, and they differ in kind rather than degree.
//!
//! The Porter-Duff modes decide *where* each side survives, and are expressible
//! with fixed-function blend factors: they work on every device with no
//! extension and no capability gate, which is why they came first. A renderer
//! unable to composite without an extension would be unusable on the hardware
//! least likely to have one.
//!
//! The separable modes — multiply, screen, overlay and the rest — mix the two
//! sides *arithmetically*, channel by channel. No combination of blend factors
//! expresses that, so they need an advanced-blend extension and are
//! capability-gated. Their formulas are fixed by the specification, which is
//! what makes them testable against a computed expectation rather than against
//! a recorded picture.
//!
//! The non-separable modes — hue, saturation, color and luminosity — need the
//! same extension and differ again in kind: each output channel depends on all
//! three input channels, because they are stated in terms of a color's hue,
//! saturation and luminosity rather than of its components. They are checked
//! against what they are named for rather than against values: whether hue kept
//! the backdrop's luminosity, whether saturation took the source's.
//!
//! Every mode assumes **premultiplied** color, which is what the render target
//! holds. The factors differ from the straight-alpha forms: source-over is
//! `ONE` rather than `SRC_ALPHA`, because the source has already been scaled.

/// A factor a blend equation multiplies one side by.
///
/// Portable rather than each backend naming its own, so the Porter-Duff table
/// below exists once instead of once per backend, where the two copies would
/// drift.
#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
pub enum BlendFactor {
    Zero,
    One,
    SrcAlpha,
    OneMinusSrcAlpha,
    DstAlpha,
    OneMinusDstAlpha,
    DstColor,
}

/// The factors for one blend mode.
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub struct BlendFactors {
    pub src: BlendFactor,
    pub dst: BlendFactor,
}

impl BlendFactors {
    const fn new(src: BlendFactor, dst: BlendFactor) -> Self {
        Self { src, dst }
    }
}

/// How a draw combines with what a target already holds.
///
/// Three families: the Porter-Duff set, which decides which of the source and
/// destination survive and where; the separable modes, which mix the two
/// arithmetically channel by channel; and the non-separable modes, which
/// exchange whole attributes of a color. Only the first works everywhere.
#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash, Default)]
pub enum BlendMode {
    /// Leave nothing behind. Neither source nor destination survives.
    Clear,
    /// Replace the destination outright, alpha included.
    ///
    /// Not the same as [`Self::SrcOver`] with an opaque source: this overwrites
    /// destination alpha too, which decides whether a layer composites
    /// correctly when it is itself drawn onto something else.
    Src,
    /// Keep the destination and discard the source.
    Dst,
    /// Source over destination: the default for drawing one thing on another.
    #[default]
    SrcOver,
    /// Destination over source, as though the source were drawn underneath.
    DstOver,
    /// Source, clipped to where the destination is.
    SrcIn,
    /// Destination, clipped to where the source is.
    DstIn,
    /// Source, clipped to where the destination is not.
    SrcOut,
    /// Destination, clipped to where the source is not.
    DstOut,
    /// Source drawn on top, but only within the destination's shape.
    SrcATop,
    /// Destination drawn on top, but only within the source's shape.
    DstATop,
    /// Whichever of the two is not overlapped by the other.
    Xor,
    /// The two added together, saturating.
    ///
    /// Used for light accumulation, where overlapping contributions should
    /// brighten rather than replace.
    Plus,
    /// The two multiplied together.
    Modulate,

    // Everything below mixes the two sides arithmetically and requires
    // advanced blending. The formulas are the separable ones from the
    // compositing specification, applied per channel to unpremultiplied color.
    /// Multiply the two, which always darkens.
    Multiply,
    /// The inverse of multiplying the inverses, which always lightens.
    Screen,
    /// Multiply or screen depending on the destination, so the destination
    /// decides the contrast.
    Overlay,
    /// The darker of the two, per channel.
    Darken,
    /// The lighter of the two, per channel.
    Lighten,
    /// Brighten the destination in proportion to the source.
    ColorDodge,
    /// Darken the destination in proportion to the inverse of the source.
    ColorBurn,
    /// Overlay with the roles reversed, so the source decides the contrast.
    HardLight,
    /// A gentler hard-light, without the hard transition at the midpoint.
    SoftLight,
    /// The absolute difference, which inverts where the two agree.
    Difference,
    /// Like difference, but with a softer response near the midpoint.
    Exclusion,

    // Everything below is non-separable: each output channel depends on all
    // three input channels, because these are stated in terms of a color's
    // hue, saturation and luminosity rather than of its components.
    /// The source's hue, with the backdrop's saturation and luminosity.
    Hue,
    /// The source's saturation, with the backdrop's hue and luminosity.
    Saturation,
    /// The source's hue and saturation, with the backdrop's luminosity.
    Color,
    /// The source's luminosity, with the backdrop's hue and saturation.
    Luminosity,
}

impl BlendMode {
    /// Whether this mode changes the destination where the source is absent.
    ///
    /// The modes for which "the source drew nothing here" is not the same as
    /// "leave this pixel alone": `DstIn` zeroes what the source did not cover,
    /// `Clear` zeroes everything, `Src` replaces it. A layer composited with
    /// one of these has to cover everything it might affect rather than only
    /// what it drew, so it is the test for whether a layer's target may be
    /// narrowed to its content.
    ///
    /// The same nine upstream lists in `Entity::IsBlendModeDestructive`, and
    /// the reason to match it exactly is that this decides a target's size:
    /// a mode missing here is a layer that silently stops masking what it
    /// used to.
    pub fn is_destructive(self) -> bool {
        matches!(
            self,
            Self::Clear
                | Self::Src
                | Self::SrcIn
                | Self::DstIn
                | Self::SrcOut
                | Self::DstOut
                | Self::DstATop
                | Self::Xor
                | Self::Modulate
        )
    }

    /// The modes every device can do, with no extension.
    pub const PORTER_DUFF: &'static [Self] = &[
        Self::Clear,
        Self::Src,
        Self::Dst,
        Self::SrcOver,
        Self::DstOver,
        Self::SrcIn,
        Self::DstIn,
        Self::SrcOut,
        Self::DstOut,
        Self::SrcATop,
        Self::DstATop,
        Self::Xor,
        Self::Plus,
        Self::Modulate,
    ];

    /// The modes that need advanced blending.
    pub const ADVANCED: &'static [Self] = &[
        Self::Multiply,
        Self::Screen,
        Self::Overlay,
        Self::Darken,
        Self::Lighten,
        Self::ColorDodge,
        Self::ColorBurn,
        Self::HardLight,
        Self::SoftLight,
        Self::Difference,
        Self::Exclusion,
        Self::Hue,
        Self::Saturation,
        Self::Color,
        Self::Luminosity,
    ];

    /// Every mode, for exhaustive tests and reporting.
    ///
    /// Deliberately *not* what a backend iterates to decide what it supports —
    /// that is what [`Self::is_advanced`] and the capability flag are for.
    pub const ALL: &'static [Self] = &[
        Self::Clear,
        Self::Src,
        Self::Dst,
        Self::SrcOver,
        Self::DstOver,
        Self::SrcIn,
        Self::DstIn,
        Self::SrcOut,
        Self::DstOut,
        Self::SrcATop,
        Self::DstATop,
        Self::Xor,
        Self::Plus,
        Self::Modulate,
        Self::Multiply,
        Self::Screen,
        Self::Overlay,
        Self::Darken,
        Self::Lighten,
        Self::ColorDodge,
        Self::ColorBurn,
        Self::HardLight,
        Self::SoftLight,
        Self::Difference,
        Self::Exclusion,
        Self::Hue,
        Self::Saturation,
        Self::Color,
        Self::Luminosity,
    ];

    /// Whether this mode needs advanced blending.
    ///
    /// Callers check [`crate::Capabilities::advanced_blend`] before using one, and a
    /// backend without it refuses rather than substituting something that looks
    /// close: a silently wrong blend mode is a picture nobody can debug from.
    /// The number a shader reads to identify this mode.
    ///
    /// Spelled out rather than cast from the discriminant, because the
    /// discriminant is an implementation detail a reordering would change and
    /// this number is written into a uniform buffer that a shader decodes. The
    /// two must agree, and only one of them is visible from the shader.
    pub const fn code(self) -> f32 {
        match self {
            Self::Clear => 0.0,
            Self::Src => 1.0,
            Self::Dst => 2.0,
            Self::SrcOver => 3.0,
            Self::DstOver => 4.0,
            Self::SrcIn => 5.0,
            Self::DstIn => 6.0,
            Self::SrcOut => 7.0,
            Self::DstOut => 8.0,
            Self::SrcATop => 9.0,
            Self::DstATop => 10.0,
            Self::Xor => 11.0,
            Self::Plus => 12.0,
            Self::Modulate => 13.0,
            Self::Multiply => 14.0,
            Self::Screen => 15.0,
            Self::Overlay => 16.0,
            Self::Darken => 17.0,
            Self::Lighten => 18.0,
            Self::ColorDodge => 19.0,
            Self::ColorBurn => 20.0,
            Self::HardLight => 21.0,
            Self::SoftLight => 22.0,
            Self::Difference => 23.0,
            Self::Exclusion => 24.0,
            Self::Hue => 25.0,
            Self::Saturation => 26.0,
            Self::Color => 27.0,
            Self::Luminosity => 28.0,
        }
    }

    pub const fn is_advanced(self) -> bool {
        !matches!(
            self,
            Self::Clear
                | Self::Src
                | Self::Dst
                | Self::SrcOver
                | Self::DstOver
                | Self::SrcIn
                | Self::DstIn
                | Self::SrcOut
                | Self::DstOut
                | Self::SrcATop
                | Self::DstATop
                | Self::Xor
                | Self::Plus
                | Self::Modulate
        )
    }

    /// The factors this mode blends with, assuming premultiplied color.
    ///
    /// `None` for an advanced mode: those are not expressible as factors at
    /// all, which is exactly why they need an extension. Returning an
    /// option rather than a plausible pair keeps a backend from silently
    /// rendering the wrong thing.
    pub const fn factors(self) -> Option<BlendFactors> {
        use BlendFactor::*;
        Some(match self {
            Self::Clear => BlendFactors::new(Zero, Zero),
            Self::Src => BlendFactors::new(One, Zero),
            Self::Dst => BlendFactors::new(Zero, One),
            Self::SrcOver => BlendFactors::new(One, OneMinusSrcAlpha),
            Self::DstOver => BlendFactors::new(OneMinusDstAlpha, One),
            Self::SrcIn => BlendFactors::new(DstAlpha, Zero),
            Self::DstIn => BlendFactors::new(Zero, SrcAlpha),
            Self::SrcOut => BlendFactors::new(OneMinusDstAlpha, Zero),
            Self::DstOut => BlendFactors::new(Zero, OneMinusSrcAlpha),
            Self::SrcATop => BlendFactors::new(DstAlpha, OneMinusSrcAlpha),
            Self::DstATop => BlendFactors::new(OneMinusDstAlpha, SrcAlpha),
            Self::Xor => BlendFactors::new(OneMinusDstAlpha, OneMinusSrcAlpha),
            Self::Plus => BlendFactors::new(One, One),
            Self::Modulate => BlendFactors::new(DstColor, Zero),
            _ => return None,
        })
    }

    /// Whether the destination contributes to the result.
    ///
    /// A mode that ignores it can skip loading the target on a tiler, which is
    /// a bandwidth saving rather than a correctness one.
    pub const fn reads_destination(self) -> bool {
        match self.factors() {
            Some(factors) => {
                !matches!(factors.dst, BlendFactor::Zero)
                    || matches!(
                        factors.src,
                        BlendFactor::DstAlpha
                            | BlendFactor::OneMinusDstAlpha
                            | BlendFactor::DstColor
                    )
            }
            // Every advanced mode is a function of both sides by definition.
            None => true,
        }
    }

    /// Whether a source scaled by coverage composites as though the shape were
    /// partly there.
    ///
    /// This is what decides whether a shape may be antialiased by computing
    /// coverage in the fragment stage rather than by multisampling. Such a
    /// shape is drawn on a quad larger than itself and emits a fragment
    /// everywhere on it, including where coverage is nothing — so the mode has
    /// to leave the destination alone for a fully transparent source, or the
    /// quad erases what is behind it in the gap between the two.
    ///
    /// Which is exactly the destination factor being `One` or
    /// `OneMinusSrcAlpha`: the source term vanishes with the alpha whatever its
    /// own factor is, so only the destination's own weight is left. Every
    /// advanced mode qualifies as well — their equations carry a
    /// `(1 - source alpha)` on the destination by construction, and reduce to
    /// it when the source contributes nothing.
    ///
    /// The same condition happens to be what makes the partly covered edge
    /// correct rather than merely harmless. Weighting a premultiplied source by
    /// coverage and compositing gives the same answer as mixing the unweighted
    /// result into the destination by coverage, which is what multisampling
    /// would have produced.
    pub const fn respects_coverage(self) -> bool {
        match self.factors() {
            Some(factors) => matches!(
                factors.dst,
                BlendFactor::One | BlendFactor::OneMinusSrcAlpha
            ),
            None => true,
        }
    }

    /// Whether this simply writes the source, so blending can be switched off.
    pub const fn is_plain_write(self) -> bool {
        matches!(self, Self::Src)
    }

    pub const fn name(self) -> &'static str {
        match self {
            Self::Clear => "clear",
            Self::Src => "src",
            Self::Dst => "dst",
            Self::SrcOver => "src-over",
            Self::DstOver => "dst-over",
            Self::SrcIn => "src-in",
            Self::DstIn => "dst-in",
            Self::SrcOut => "src-out",
            Self::DstOut => "dst-out",
            Self::SrcATop => "src-atop",
            Self::DstATop => "dst-atop",
            Self::Xor => "xor",
            Self::Plus => "plus",
            Self::Modulate => "modulate",
            Self::Multiply => "multiply",
            Self::Screen => "screen",
            Self::Overlay => "overlay",
            Self::Darken => "darken",
            Self::Lighten => "lighten",
            Self::ColorDodge => "color-dodge",
            Self::ColorBurn => "color-burn",
            Self::HardLight => "hard-light",
            Self::SoftLight => "soft-light",
            Self::Difference => "difference",
            Self::Exclusion => "exclusion",
            Self::Hue => "hue",
            Self::Saturation => "saturation",
            Self::Color => "color",
            Self::Luminosity => "luminosity",
        }
    }
}

impl std::fmt::Display for BlendMode {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        f.write_str(self.name())
    }
}

/// The separable blend function `B(Cb, Cs)`, on one unpremultiplied channel.
///
/// This is the compositing specification's definition transcribed directly.
/// It exists so there is exactly one statement of what each mode means: the
/// conformance tests check the hardware against it, and any future software
/// path evaluates it. Nothing here is a second implementation of the backend
/// mapping — that maps an enum to an extension's blend op and shares no code
/// with this, which is what makes checking one against the other meaningful.
///
/// Returns `None` for a mode that is not separable-advanced.
pub fn separable_blend(mode: BlendMode, backdrop: f32, source: f32) -> Option<f32> {
    let (cb, cs) = (backdrop, source);
    let multiply = |a: f32, b: f32| a * b;
    let screen = |a: f32, b: f32| a + b - a * b;
    // Hard-light is its own function *and* the body of overlay with the two
    // sides exchanged, so it is written once and called twice.
    let hard_light = |cb: f32, cs: f32| {
        if cs <= 0.5 {
            multiply(cb, 2.0 * cs)
        } else {
            screen(cb, 2.0 * cs - 1.0)
        }
    };
    Some(match mode {
        BlendMode::Multiply => multiply(cb, cs),
        BlendMode::Screen => screen(cb, cs),
        BlendMode::Overlay => hard_light(cs, cb),
        BlendMode::Darken => cb.min(cs),
        BlendMode::Lighten => cb.max(cs),
        BlendMode::ColorDodge => {
            // The order of these three cases is load-bearing: a black backdrop
            // stays black even under a full-strength source, and only then does
            // a full-strength source saturate. Swapping them makes the corner
            // where both hold produce white instead of black.
            if cb <= 0.0 {
                0.0
            } else if cs >= 1.0 {
                1.0
            } else {
                (cb / (1.0 - cs)).min(1.0)
            }
        }
        BlendMode::ColorBurn => {
            if cb >= 1.0 {
                1.0
            } else if cs <= 0.0 {
                0.0
            } else {
                1.0 - ((1.0 - cb) / cs).min(1.0)
            }
        }
        BlendMode::HardLight => hard_light(cb, cs),
        BlendMode::SoftLight => {
            if cs <= 0.5 {
                cb - (1.0 - 2.0 * cs) * cb * (1.0 - cb)
            } else {
                // The specification's D(Cb): a cubic below a quarter, a square
                // root above it, chosen so the two meet with equal slope.
                let d = if cb <= 0.25 {
                    ((16.0 * cb - 12.0) * cb + 4.0) * cb
                } else {
                    cb.sqrt()
                };
                cb + (2.0 * cs - 1.0) * (d - cb)
            }
        }
        BlendMode::Difference => (cs - cb).abs(),
        BlendMode::Exclusion => cs + cb - 2.0 * cs * cb,
        _ => return None,
    })
}

/// The non-separable blend function, on unpremultiplied color.
///
/// These are stated in terms of a color's luminosity and saturation rather than
/// of its components, so each output channel depends on all three inputs — the
/// reason they cannot go through [`separable_blend`] and the reason they are a
/// separate family rather than four more entries in the same table.
///
/// The helpers below are the specification's, transcribed directly. The one
/// that repays reading is the clip: setting a luminosity can push a channel
/// outside zero to one, and clipping each channel independently would change
/// the hue that the whole operation exists to preserve. Scaling the color
/// toward its own luminosity instead brings it back into range along a line
/// that holds hue fixed.
///
/// Returns `None` for a mode that is not non-separable-advanced.
pub fn nonseparable_blend(
    mode: BlendMode,
    backdrop: [f32; 3],
    source: [f32; 3],
) -> Option<[f32; 3]> {
    // The specification's coefficients, which weight green far above blue
    // because the eye does. Not the same as any of the standard luma matrices,
    // and deliberately so: this is what the compositing specification says.
    fn lum(c: [f32; 3]) -> f32 {
        0.3 * c[0] + 0.59 * c[1] + 0.11 * c[2]
    }

    fn clip_color(mut c: [f32; 3]) -> [f32; 3] {
        let l = lum(c);
        let n = c[0].min(c[1]).min(c[2]);
        let x = c[0].max(c[1]).max(c[2]);
        if n < 0.0 {
            // Guarded because a color whose luminosity equals its darkest
            // channel is already flat, and the scale would divide by zero.
            let span = l - n;
            if span > 0.0 {
                for channel in &mut c {
                    *channel = l + (*channel - l) * l / span;
                }
            }
        }
        if x > 1.0 {
            let span = x - l;
            if span > 0.0 {
                for channel in &mut c {
                    *channel = l + (*channel - l) * (1.0 - l) / span;
                }
            }
        }
        c
    }

    fn set_lum(mut c: [f32; 3], l: f32) -> [f32; 3] {
        let d = l - lum(c);
        for channel in &mut c {
            *channel += d;
        }
        clip_color(c)
    }

    fn sat(c: [f32; 3]) -> f32 {
        c[0].max(c[1]).max(c[2]) - c[0].min(c[1]).min(c[2])
    }

    /// Rescale a color to a given saturation, keeping which channel is which.
    ///
    /// Written by index rather than by sorting the components, because the
    /// result has to go back where it came from: the middle channel of the
    /// input stays the middle channel of the output.
    fn set_sat(c: [f32; 3], s: f32) -> [f32; 3] {
        let mut order = [0usize, 1, 2];
        order.sort_by(|a, b| {
            c[*a]
                .partial_cmp(&c[*b])
                .unwrap_or(std::cmp::Ordering::Equal)
        });
        let (low, mid, high) = (order[0], order[1], order[2]);
        let mut out = [0.0f32; 3];
        if c[high] > c[low] {
            out[mid] = (c[mid] - c[low]) * s / (c[high] - c[low]);
            out[high] = s;
        }
        // A flat color has no saturation to scale, so it stays flat at zero
        // rather than being given one arbitrarily.
        out[low] = 0.0;
        out
    }

    let (cb, cs) = (backdrop, source);
    Some(match mode {
        BlendMode::Hue => set_lum(set_sat(cs, sat(cb)), lum(cb)),
        BlendMode::Saturation => set_lum(set_sat(cb, sat(cs)), lum(cb)),
        BlendMode::Color => set_lum(cs, lum(cb)),
        BlendMode::Luminosity => set_lum(cb, lum(cs)),
        _ => return None,
    })
}

/// An advanced mode applied to premultiplied colors, giving premultiplied color.
///
/// The blend function itself is defined on unpremultiplied channels, so this
/// un-premultiplies, blends, and recombines using the specification's
/// composite: the blended color applies only where the two sides overlap, and
/// each side survives alone where the other is absent.
pub fn blend_advanced(mode: BlendMode, source: [f32; 4], backdrop: [f32; 4]) -> Option<[f32; 4]> {
    let (a_s, a_b) = (source[3], backdrop[3]);
    let mut out = [0.0f32; 4];
    out[3] = a_s + a_b - a_s * a_b;

    // Dividing by a zero alpha would give a NaN that then propagates through a
    // term the same alpha multiplies away, so the color under a fully
    // transparent side is taken as zero rather than computed.
    //
    // Clamped for a second reason, stated separately because it is a different
    // one: the formulas below are defined on channels between zero and one and
    // not outside, so a component describing a color the sRGB primaries cannot
    // hold has to be brought to the triangle's edge before a mode is evaluated.
    // The shader states the same domain at the same place, because these two
    // exist to be checked against each other and a domain named in one and not
    // the other is how they begin to disagree.
    let straight = |c: [f32; 4], a: f32| {
        if a > 0.0 {
            [
                (c[0] / a).clamp(0.0, 1.0),
                (c[1] / a).clamp(0.0, 1.0),
                (c[2] / a).clamp(0.0, 1.0),
            ]
        } else {
            [0.0; 3]
        }
    };
    let cs = straight(source, a_s);
    let cb = straight(backdrop, a_b);

    // The whole-color family first. A non-separable mode has no per-channel
    // form, and trying the separable table first would have it fall through to
    // a `None` that reads as "not an advanced mode at all".
    let blended = match nonseparable_blend(mode, cb, cs) {
        Some(blended) => blended,
        None => {
            let mut per_channel = [0.0f32; 3];
            for (channel, slot) in per_channel.iter_mut().enumerate() {
                *slot = separable_blend(mode, cb[channel], cs[channel])?;
            }
            per_channel
        }
    };

    for channel in 0..3 {
        out[channel] = a_s * (1.0 - a_b) * cs[channel]
            + a_s * a_b * blended[channel]
            + (1.0 - a_s) * a_b * cb[channel];
    }
    Some(out)
}

#[cfg(test)]
mod coverage_tests {
    use super::*;

    #[test]
    fn a_mode_respects_coverage_when_a_transparent_source_changes_nothing() {
        // Worked out from the factors rather than listed, so a mode added later
        // is classified rather than forgotten. These are the answers that
        // classification has to produce.
        for mode in [
            BlendMode::SrcOver,
            BlendMode::DstOver,
            BlendMode::Dst,
            BlendMode::Plus,
            BlendMode::Xor,
            BlendMode::SrcATop,
            BlendMode::DstOut,
        ] {
            assert!(mode.respects_coverage(), "{} should", mode.name());
        }
        // These discard the destination where the source is transparent, so a
        // quad larger than its shape would erase what is behind it.
        for mode in [
            BlendMode::Clear,
            BlendMode::Src,
            BlendMode::SrcIn,
            BlendMode::DstIn,
            BlendMode::SrcOut,
            BlendMode::DstATop,
            BlendMode::Modulate,
        ] {
            assert!(!mode.respects_coverage(), "{} should not", mode.name());
        }
    }

    #[test]
    fn every_advanced_mode_respects_coverage() {
        // Their equations carry a (1 - source alpha) on the destination by
        // construction, so a transparent source leaves it whole.
        for mode in BlendMode::ALL {
            if mode.is_advanced() {
                assert!(mode.respects_coverage(), "{} should", mode.name());
            }
        }
    }
}

#[cfg(test)]
mod tests {
    use super::*;

    /// Evaluate a factor against premultiplied source and destination.
    fn value(factor: BlendFactor, src: [f32; 4], dst: [f32; 4], channel: usize) -> f32 {
        match factor {
            BlendFactor::Zero => 0.0,
            BlendFactor::One => 1.0,
            BlendFactor::SrcAlpha => src[3],
            BlendFactor::OneMinusSrcAlpha => 1.0 - src[3],
            BlendFactor::DstAlpha => dst[3],
            BlendFactor::OneMinusDstAlpha => 1.0 - dst[3],
            BlendFactor::DstColor => dst[channel],
        }
    }

    /// The blend equation, as the hardware applies it.
    fn blend(mode: BlendMode, src: [f32; 4], dst: [f32; 4]) -> [f32; 4] {
        let f = mode.factors().expect("Porter-Duff mode");
        let mut out = [0.0f32; 4];
        for channel in 0..4 {
            out[channel] = (src[channel] * value(f.src, src, dst, channel)
                + dst[channel] * value(f.dst, src, dst, channel))
            .clamp(0.0, 1.0);
        }
        out
    }

    fn close(a: [f32; 4], b: [f32; 4]) -> bool {
        a.iter().zip(&b).all(|(x, y)| (x - y).abs() < 1e-5)
    }

    // Premultiplied half-opaque red and opaque blue.
    const SRC: [f32; 4] = [0.5, 0.0, 0.0, 0.5];
    const DST: [f32; 4] = [0.0, 0.0, 1.0, 1.0];

    #[test]
    fn clear_leaves_nothing() {
        assert!(close(blend(BlendMode::Clear, SRC, DST), [0.0; 4]));
    }

    #[test]
    fn src_and_dst_each_keep_one_side_entirely() {
        assert!(close(blend(BlendMode::Src, SRC, DST), SRC));
        assert!(close(blend(BlendMode::Dst, SRC, DST), DST));
    }

    #[test]
    fn source_over_and_destination_over_are_mirror_images() {
        // Half-opaque red over opaque blue: half the blue survives.
        assert!(close(
            blend(BlendMode::SrcOver, SRC, DST),
            [0.5, 0.0, 0.5, 1.0]
        ));
        // The other way round, the destination is opaque so nothing shows
        // through and the source is entirely hidden.
        assert!(close(blend(BlendMode::DstOver, SRC, DST), DST));
    }

    #[test]
    fn the_in_modes_clip_one_side_to_the_other() {
        // Source clipped to an opaque destination is the source unchanged.
        assert!(close(blend(BlendMode::SrcIn, SRC, DST), SRC));
        // Destination clipped to a half-opaque source keeps half of it.
        assert!(close(
            blend(BlendMode::DstIn, SRC, DST),
            [0.0, 0.0, 0.5, 0.5]
        ));
    }

    #[test]
    fn the_out_modes_are_the_complement_of_the_in_modes() {
        // The destination is opaque, so there is nowhere the source is outside
        // it: source-out leaves nothing.
        assert!(close(blend(BlendMode::SrcOut, SRC, DST), [0.0; 4]));
        // Half the destination lies outside a half-opaque source.
        assert!(close(
            blend(BlendMode::DstOut, SRC, DST),
            [0.0, 0.0, 0.5, 0.5]
        ));
    }

    #[test]
    fn atop_keeps_the_shape_of_the_side_it_is_named_for() {
        // Source atop destination has the destination's shape: alpha stays at
        // the destination's, which is what distinguishes it from source-over.
        let result = blend(BlendMode::SrcATop, SRC, DST);
        assert!((result[3] - DST[3]).abs() < 1e-5, "alpha should follow dst");
        assert!(close(result, [0.5, 0.0, 0.5, 1.0]));
    }

    #[test]
    fn xor_keeps_only_what_the_other_side_does_not_cover() {
        // An opaque destination covers everything, so only the part of the
        // destination outside the half-opaque source survives.
        assert!(close(blend(BlendMode::Xor, SRC, DST), [0.0, 0.0, 0.5, 0.5]));
    }

    #[test]
    fn plus_accumulates_and_saturates() {
        let sum = blend(BlendMode::Plus, SRC, DST);
        assert!(close(sum, [0.5, 0.0, 1.0, 1.0]));
        // Saturating rather than wrapping: two bright sources must not go dark.
        let bright = blend(BlendMode::Plus, [0.8, 0.8, 0.8, 1.0], [0.8, 0.8, 0.8, 1.0]);
        assert!(close(bright, [1.0, 1.0, 1.0, 1.0]));
    }

    #[test]
    fn modulate_multiplies_the_two() {
        let result = blend(
            BlendMode::Modulate,
            [0.5, 1.0, 0.5, 1.0],
            [0.5, 0.5, 1.0, 1.0],
        );
        assert!(close(result, [0.25, 0.5, 0.5, 1.0]));
    }

    #[test]
    fn only_src_can_skip_blending_entirely() {
        // Everything else needs the hardware to combine two sides, so treating
        // another mode as a plain write would silently drop the destination.
        for mode in BlendMode::PORTER_DUFF {
            assert_eq!(
                mode.is_plain_write(),
                *mode == BlendMode::Src,
                "{mode} misreported whether it is a plain write"
            );
        }
    }

    #[test]
    fn modes_that_ignore_the_destination_are_identified() {
        // A mode that never reads the target can skip loading it on a tiler.
        for mode in [BlendMode::Clear, BlendMode::Src] {
            assert!(!mode.reads_destination(), "{mode}");
        }
        for mode in [
            BlendMode::SrcOver,
            BlendMode::DstOver,
            BlendMode::SrcIn,
            BlendMode::Modulate,
            BlendMode::Xor,
        ] {
            assert!(mode.reads_destination(), "{mode}");
        }
    }

    #[test]
    fn the_separable_modes_hit_their_defining_fixed_points() {
        // Each identity below is what the mode is *for*, so getting one wrong
        // means the transcription is wrong regardless of what the hardware does.
        let cases: &[(BlendMode, f32, f32, f32)] = &[
            (BlendMode::Multiply, 0.5, 0.5, 0.25),
            (BlendMode::Screen, 0.5, 0.5, 0.75),
            (BlendMode::Darken, 0.2, 0.8, 0.2),
            (BlendMode::Lighten, 0.2, 0.8, 0.8),
            (BlendMode::Difference, 0.2, 0.8, 0.6),
            (BlendMode::Exclusion, 0.5, 0.5, 0.5),
            // Half-strength hard-light and overlay are both the identity on the
            // side that decides the contrast.
            (BlendMode::HardLight, 0.3, 0.5, 0.3),
            (BlendMode::Overlay, 0.5, 0.3, 0.3),
            // Half-strength soft-light leaves the backdrop untouched.
            (BlendMode::SoftLight, 0.3, 0.5, 0.3),
            // The dodge and burn corners, where the ordering of the guards shows.
            (BlendMode::ColorDodge, 0.0, 1.0, 0.0),
            (BlendMode::ColorDodge, 0.25, 0.5, 0.5),
            (BlendMode::ColorBurn, 1.0, 0.0, 1.0),
            (BlendMode::ColorBurn, 0.5, 0.5, 0.0),
        ];
        for &(mode, cb, cs, want) in cases {
            let got = separable_blend(mode, cb, cs).expect("separable");
            assert!(
                (got - want).abs() < 1e-6,
                "{mode}(backdrop {cb}, source {cs}) gave {got}, want {want}"
            );
        }
    }

    #[test]
    fn soft_light_is_continuous_where_its_two_branches_meet() {
        // The branches join at a source of one half and at a backdrop of one
        // quarter; a transcription error in either shows as a step.
        for &(cb, cs) in &[(0.25, 0.5), (0.2499, 0.75), (0.5, 0.4999)] {
            let here = separable_blend(BlendMode::SoftLight, cb, cs).unwrap();
            let there = separable_blend(BlendMode::SoftLight, cb + 2e-4, cs + 2e-4).unwrap();
            assert!((here - there).abs() < 1e-3, "step at ({cb}, {cs})");
        }
    }

    #[test]
    fn an_advanced_mode_over_nothing_is_just_the_source() {
        // Where the backdrop is absent the blend function has nothing to mix
        // with, so every mode must reduce to the source unchanged.
        let src = [0.3, 0.0, 0.15, 0.6];
        for mode in BlendMode::ADVANCED {
            let out = blend_advanced(*mode, src, [0.0; 4]).expect("advanced");
            assert!(close(out, src), "{mode} over nothing gave {out:?}");
        }
    }

    #[test]
    fn the_non_separable_modes_take_what_they_are_named_for() {
        // Each of these is defined as taking some attributes from one side and
        // the rest from the other, so the check is which side each attribute
        // came from rather than a value someone recorded.
        fn lum(c: [f32; 3]) -> f32 {
            0.3 * c[0] + 0.59 * c[1] + 0.11 * c[2]
        }
        fn sat(c: [f32; 3]) -> f32 {
            c[0].max(c[1]).max(c[2]) - c[0].min(c[1]).min(c[2])
        }

        // Two requirements on these inputs, and both were found by getting them
        // wrong. They must differ in luminosity and in saturation, or two of
        // these four modes look identical — the first pair tried here agreed on
        // luminosity exactly, by coincidence. And the results must stay inside
        // zero to one, because the clip that brings an out-of-range color back
        // reduces its saturation; that is correct behavior and would make the
        // exact assertions below wrong, so the clip has a test of its own.
        let cb = [0.15, 0.55, 0.35];
        let cs = [0.75, 0.5, 0.45];
        assert!((lum(cb) - lum(cs)).abs() > 0.05);
        assert!((sat(cb) - sat(cs)).abs() > 0.05);

        let close = |a: f32, b: f32| (a - b).abs() < 1e-4;

        let hue = nonseparable_blend(BlendMode::Hue, cb, cs).unwrap();
        assert!(close(lum(hue), lum(cb)), "hue kept the wrong luminosity");
        assert!(close(sat(hue), sat(cb)), "hue kept the wrong saturation");

        let saturation = nonseparable_blend(BlendMode::Saturation, cb, cs).unwrap();
        assert!(
            close(lum(saturation), lum(cb)),
            "saturation moved luminosity"
        );
        assert!(
            close(sat(saturation), sat(cs)),
            "saturation did not take the source's"
        );

        let color = nonseparable_blend(BlendMode::Color, cb, cs).unwrap();
        assert!(close(lum(color), lum(cb)), "color moved luminosity");

        let luminosity = nonseparable_blend(BlendMode::Luminosity, cb, cs).unwrap();
        assert!(
            close(lum(luminosity), lum(cs)),
            "luminosity did not take the source's"
        );
        assert!(
            close(sat(luminosity), sat(cb)),
            "luminosity moved saturation"
        );
    }

    #[test]
    fn setting_a_luminosity_keeps_every_channel_in_range() {
        // Shifting a color's luminosity pushes channels outside zero to one,
        // and clipping each independently would change the hue the operation
        // exists to preserve. Scaling toward the luminosity is what brings them
        // back along a line that holds hue fixed -- so this checks the range
        // and, separately, that the result is still a scaling of the original.
        for (cb, cs) in [
            ([0.02, 0.02, 0.9], [0.99, 0.99, 0.99]),
            ([0.99, 0.5, 0.02], [0.01, 0.01, 0.01]),
            ([0.0, 0.0, 0.0], [1.0, 1.0, 1.0]),
            ([1.0, 1.0, 1.0], [0.0, 0.0, 0.0]),
        ] {
            for mode in [BlendMode::Color, BlendMode::Luminosity, BlendMode::Hue] {
                let out = nonseparable_blend(mode, cb, cs).unwrap();
                for channel in out {
                    assert!(
                        (-1e-5..=1.0 + 1e-5).contains(&channel),
                        "{mode} on {cb:?} and {cs:?} gave {out:?}"
                    );
                    assert!(channel.is_finite(), "{mode} produced {out:?}");
                }
            }
        }
    }

    #[test]
    fn a_flat_backdrop_has_no_saturation_to_take() {
        // A gray has no hue and no saturation, so a mode asking for either gets
        // a gray back. The guard that makes this work is also the one that
        // stops a division by zero, which is why it is worth pinning.
        let gray = [0.4, 0.4, 0.4];
        let colorful = [0.9, 0.2, 0.5];
        let hue = nonseparable_blend(BlendMode::Hue, gray, colorful).unwrap();
        assert!(
            hue.iter().all(|c| (c - hue[0]).abs() < 1e-5),
            "hue from a gray backdrop came back colored: {hue:?}"
        );
        let saturation = nonseparable_blend(BlendMode::Saturation, gray, colorful).unwrap();
        assert!(
            saturation.iter().all(|c| (c - saturation[0]).abs() < 1e-5),
            "saturating a gray produced color from nothing: {saturation:?}"
        );
    }

    #[test]
    fn the_two_families_do_not_overlap() {
        // Every mode belongs to exactly one family, and the family it claims
        // agrees with whether it has factors.
        assert_eq!(
            BlendMode::PORTER_DUFF.len() + BlendMode::ADVANCED.len(),
            BlendMode::ALL.len()
        );
        for mode in BlendMode::ALL {
            assert_eq!(
                mode.is_advanced(),
                mode.factors().is_none(),
                "{mode} disagrees with itself about which family it is in"
            );
            let has_formula = separable_blend(*mode, 0.5, 0.5).is_some()
                || nonseparable_blend(*mode, [0.5; 3], [0.5; 3]).is_some();
            assert_eq!(
                mode.is_advanced(),
                has_formula,
                "{mode} has no advanced formula but claims to be advanced"
            );
            // And never both, since the two families are evaluated differently
            // and a mode in both would take whichever path was tried first.
            assert!(
                !(separable_blend(*mode, 0.5, 0.5).is_some()
                    && nonseparable_blend(*mode, [0.5; 3], [0.5; 3]).is_some()),
                "{mode} has a formula in both families"
            );
        }
    }

    #[test]
    fn every_mode_has_a_distinct_name() {
        let mut names: Vec<&str> = BlendMode::ALL.iter().map(|m| m.name()).collect();
        names.sort_unstable();
        let count = names.len();
        names.dedup();
        assert_eq!(names.len(), count, "duplicate blend mode name");
    }
}