retex-engine 1.0.0-rc.2

//! Converting math lists to horizontal lists (*TeX: The Program*
//! §699–§767, with e-TeX's `\middle`) the way LuaTeX does it for
//! traditional (TFM) fonts.
//!
//! LuaTeX keeps TeX82's algorithm but takes the font-dependent values from
//! the `\Umath…` parameters of the current style (see
//! [`crate::mathparams`]). Observed differences from TeX82, all
//! established with black-box tests:
//!
//! * glyphs made from math characters are protected (subtype 256), so
//!   that the node processing of an enclosing box leaves them alone;
//! * italic corrections are kern nodes of subtype "italic", the other
//!   kerns made here are font kerns;
//! * a missing character from an undefined family is reported each time
//!   it is fetched (the field is not reset to empty);
//! * a null delimiter of a `\left`/`\right` fence is not shifted to the
//!   axis.

use crate::Engine;
use crate::build::PackSpec;
use crate::fonts::LigOp;
use crate::math::{Field, cramped_style, denom_style, half, num_style, sub_style, sup_style};
use crate::mathparams::mp;
use crate::nodes::{
    AttrList, DEFAULT_CODE, NodeData, NodeRef, fence_sub, glue_sub, id, kern_sub, list_sub,
    noad_opt, noad_sub, radical_sub,
};
use crate::primitives_gen::{assign_dimen as dp, assign_int as ip};

/// Glyph subtype of characters made by `mlist_to_hlist`.
pub const PROTECTED_GLYPH: u16 = 256;

/// The TeX82 type of a noad, for the two passes.
#[derive(Clone, Copy, Debug, PartialEq, Eq)]
pub enum NoadType {
    /// Ord.
    Ord = 0,
    /// Op.
    Op = 1,
    /// Bin.
    Bin = 2,
    /// Rel.
    Rel = 3,
    /// Open.
    Open = 4,
    /// Close.
    Close = 5,
    /// Punct.
    Punct = 6,
    /// Inner.
    Inner = 7,
    /// Radical.
    Radical,
    /// Fraction.
    Fraction,
    /// Underline.
    Under,
    /// Overline.
    Over,
    /// Math accent.
    Accent,
    /// `\vcenter`.
    Vcenter,
    /// `\left`.
    Left,
    /// `\right` or `\middle`.
    Right,
}

/// TeX's inter-atom spacing table (§764): 0 none, 1 conditional thin,
/// 2 thin, 3 conditional medium, 4 conditional thick.
const MATH_SPACING: &[u8; 64] = b"0234000122*4000133**3**344*0400400*000000234000111*1111112341011";

impl Engine {
    /// Whether font `f` is an OpenType math font (it has `MathConstants`),
    /// which LuaTeX treats differently from TFM fonts.
    pub fn is_opentype_math_font(&self, f: u32) -> bool {
        self.font(f).math_constants.is_some()
    }

    /// The spacing between atoms of classes `l` and `r` in `style`: the
    /// `\Umath…spacing` parameter when set (plain glue), otherwise TeX's
    /// table with the current `\thinmuskip`, `\medmuskip` or
    /// `\thickmuskip` (named glue), or none.
    pub fn math_spacing(&self, l: u32, r: u32, style: u32) -> Option<(crate::glue::Glue, u16)> {
        let p = 49 + l * 8 + r;
        let v = self.math_param_value(p, style);
        if v != crate::codes::UNDEFINED_MATH_PARAM {
            return Some((self.math_param_glue(v), 0));
        }
        let c = MATH_SPACING[(l * 8 + r) as usize];
        let x = match c {
            b'1' if style < 4 => glue_sub::THIN_MU_SKIP,
            b'2' => glue_sub::THIN_MU_SKIP,
            b'3' if style < 4 => glue_sub::MED_MU_SKIP,
            b'4' if style < 4 => glue_sub::THICK_MU_SKIP,
            _ => return None,
        };
        let par = match x {
            glue_sub::THIN_MU_SKIP => crate::primitives_gen::assign_mu_glue::THINMUSKIP,
            glue_sub::MED_MU_SKIP => crate::primitives_gen::assign_mu_glue::MEDMUSKIP,
            _ => crate::primitives_gen::assign_mu_glue::THICKMUSKIP,
        };
        Some((self.eqtb.glue(par + crate::eqtb::MU_GLUE_OFFSET), x))
    }
}

/// The state of the conversion (`cur_style`, `cur_size`, `cur_mu`).
#[derive(Clone, Copy, Debug, Default)]
pub struct MathState {
    /// The current style.
    pub style: i32,
    /// The current size: 0 text, 1 script, 2 scriptscript.
    pub size: u32,
    /// The math unit.
    pub mu: i32,
    /// A kern to put after the operator box being converted (an OpenType
    /// operator's italic correction, negated, before its subscript).
    pub op_kern: i32,
}

/// The size belonging to a style.
pub fn style_size(s: i32) -> u32 {
    if s < 4 { 0 } else { ((s - 2) / 2) as u32 }
}

impl Engine {
    /// The TeX82 type of noad `q` (`None` for nodes).
    pub fn noad_type(&self, q: NodeRef) -> Option<NoadType> {
        Some(match self.nodes.id(q) {
            id::NOAD => match self.nodes.subtype(q) {
                noad_sub::ORD => NoadType::Ord,
                noad_sub::OP_DISPLAY_LIMITS | noad_sub::OP_LIMITS | noad_sub::OP_NO_LIMITS => {
                    NoadType::Op
                }
                noad_sub::BIN => NoadType::Bin,
                noad_sub::REL => NoadType::Rel,
                noad_sub::OPEN => NoadType::Open,
                noad_sub::CLOSE => NoadType::Close,
                noad_sub::PUNCT => NoadType::Punct,
                noad_sub::INNER => NoadType::Inner,
                noad_sub::UNDER => NoadType::Under,
                noad_sub::OVER => NoadType::Over,
                _ => NoadType::Vcenter,
            },
            id::RADICAL => NoadType::Radical,
            id::ACCENT => NoadType::Accent,
            id::FRACTION => NoadType::Fraction,
            id::FENCE => {
                if self.nodes.subtype(q) == fence_sub::LEFT {
                    NoadType::Left
                } else {
                    NoadType::Right
                }
            }
            _ => return None,
        })
    }

    /// Sets up `cur_size` and `cur_mu` for `cur_style`.
    fn set_cur_style(&mut self, s: i32) {
        self.ts.math.style = s;
        self.ts.math.size = style_size(s);
        let q = self.math_par(mp::QUAD);
        self.ts.math.mu = retex_arith::x_over_n(q, 18).map_or(0, |r| r.quotient);
    }

    /// Math parameter `p` in the current style (0 when undefined).
    pub fn math_par(&self, p: u32) -> i32 {
        let v = self.math_param_value(p, self.ts.math.style as u32);
        if v == crate::codes::UNDEFINED_MATH_PARAM {
            0
        } else {
            v
        }
    }

    /// Math parameter `p` in the current style, `None` when undefined.
    fn math_par_opt(&self, p: u32) -> Option<i32> {
        let v = self.math_param_value(p, self.ts.math.style as u32);
        (v != crate::codes::UNDEFINED_MATH_PARAM).then_some(v)
    }

    /// Converts mlist `mlist` in style `style` into an hlist, which is
    /// returned (`mlist_to_hlist`). `penalties` asks for line-break
    /// penalties after binary operators and relations.
    pub fn mlist_to_hlist(&mut self, mlist: NodeRef, style: i32, penalties: bool) -> NodeRef {
        self.fonts.sync_dense();
        self.init_math_params_once();
        let saved = self.ts.math;
        let saved_attr = self.ts.attr_override.clone();
        let r = self.mlist_to_hlist_rec(mlist, style, penalties);
        self.ts.math = saved;
        self.ts.attr_override = saved_attr;
        r
    }

    /// The attributes of node `p` (none for a null pointer).
    fn attr_of(&self, p: NodeRef) -> Option<AttrList> {
        if p.is_null() {
            None
        } else {
            self.nodes.attr(p).cloned()
        }
    }

    /// Makes new nodes take attributes `a`; returns the previous setting.
    fn attr_set(&mut self, a: Option<AttrList>) -> Option<Option<AttrList>> {
        self.ts.attr_override.replace(a)
    }

    /// Makes new nodes take the attributes of `p`; returns the previous
    /// setting. Observed: LuaTeX gives the nodes it builds for a noad the
    /// attributes of the noad, or of the kernel or delimiter they come
    /// from, not the current ones.
    fn attr_from(&mut self, p: NodeRef) -> Option<Option<AttrList>> {
        let a = self.attr_of(p);
        self.attr_set(a)
    }

    fn attr_restore(&mut self, saved: Option<Option<AttrList>>) {
        self.ts.attr_override = saved;
    }

    fn get_new_hlist(&self, q: NodeRef) -> NodeRef {
        match self.nodes.data(q) {
            NodeData::Noad(n) => n.new_hlist,
            NodeData::Fraction(f) => f.new_hlist,
            NodeData::Fence(f) => f.new_hlist,
            _ => NodeRef::NULL,
        }
    }

    fn set_new_hlist(&mut self, q: NodeRef, p: NodeRef) {
        match self.nodes.data_mut(q) {
            NodeData::Noad(n) => n.new_hlist = p,
            NodeData::Fraction(f) => f.new_hlist = p,
            NodeData::Fence(f) => f.new_hlist = p,
            _ => {}
        }
    }

    fn mlist_to_hlist_rec(&mut self, mlist: NodeRef, style: i32, penalties: bool) -> NodeRef {
        let mut q = mlist;
        let mut r = NodeRef::NULL;
        let mut r_type = NoadType::Op;
        let mut max_h = 0i32;
        let mut max_d = 0i32;
        self.set_cur_style(style);
        while !q.is_null() {
            // reswitch:
            let mut delta = 0;
            let Some(mut t) = self.noad_type(q) else {
                // Nodes that can appear in an mlist.
                let next = self.first_pass_node(q, &mut max_h, &mut max_d);
                q = next;
                continue;
            };
            let saved_attr = self.attr_from(q);
            let mut action = Action::Convert;
            loop {
                match t {
                    NoadType::Bin => {
                        if matches!(
                            r_type,
                            NoadType::Bin
                                | NoadType::Op
                                | NoadType::Rel
                                | NoadType::Open
                                | NoadType::Punct
                                | NoadType::Left
                        ) {
                            self.nodes.set_subtype(q, noad_sub::ORD);
                            t = NoadType::Ord;
                            continue;
                        }
                    }
                    NoadType::Rel | NoadType::Close | NoadType::Punct | NoadType::Right => {
                        if r_type == NoadType::Bin {
                            self.nodes.set_subtype(r, noad_sub::ORD);
                        }
                        if t == NoadType::Right {
                            action = Action::DoneWithNoad;
                        }
                    }
                    NoadType::Left => action = Action::DoneWithNoad,
                    NoadType::Fraction => {
                        self.make_fraction(q);
                        action = Action::CheckDimensions;
                    }
                    NoadType::Op => {
                        delta = self.make_op(q);
                        if self.nodes.subtype(q) == noad_sub::OP_LIMITS {
                            action = Action::CheckDimensions;
                        }
                    }
                    NoadType::Ord => self.make_ord(q),
                    NoadType::Open | NoadType::Inner => {}
                    NoadType::Radical => self.make_radical(q),
                    NoadType::Over => self.make_over(q),
                    NoadType::Under => self.make_under(q),
                    NoadType::Accent => self.make_math_accent(q),
                    NoadType::Vcenter => self.make_vcenter(q),
                }
                break;
            }
            if action == Action::Convert {
                self.convert_nucleus(q, delta);
            }
            if action != Action::DoneWithNoad {
                // check_dimensions:
                let nh = self.get_new_hlist(q);
                let (h, d) = self.list_height_depth(nh);
                if h > max_h {
                    max_h = h;
                }
                if d > max_d {
                    max_d = d;
                }
            }
            // done_with_noad:
            r = q;
            r_type = self.noad_type(r).unwrap_or(NoadType::Ord);
            if r_type == NoadType::Right {
                r_type = NoadType::Left;
                self.set_cur_style(style);
            }
            self.attr_restore(saved_attr);
            q = self.nodes.next(q);
        }
        if r_type == NoadType::Bin {
            self.nodes.set_subtype(r, noad_sub::ORD);
        }
        self.second_pass(mlist, style, penalties, max_h, max_d)
    }

    /// The height and depth an `hpack` of list `p` would have.
    fn list_height_depth(&mut self, p: NodeRef) -> (i32, i32) {
        let saved = self.ts.adjust_tail.take();
        let pre = self.ts.pre_adjust_tail.take();
        let z = self.hpack_quiet(p);
        self.ts.adjust_tail = saved;
        self.ts.pre_adjust_tail = pre;
        let (h, d) = self
            .nodes
            .box_data(z)
            .map_or((0, 0), |b| (b.height, b.depth));
        self.nodes.set_list_ptr(z, NodeRef::NULL);
        self.nodes.free(z);
        (h, d)
    }

    /// `hpack(p, natural)` without over/underfull reports (natural size
    /// never reports anyway).
    fn hpack_quiet(&mut self, p: NodeRef) -> NodeRef {
        self.hpack(p, PackSpec::NATURAL)
    }

    /// First-pass processing of a node in an mlist; returns the next item.
    fn first_pass_node(&mut self, q: NodeRef, max_h: &mut i32, max_d: &mut i32) -> NodeRef {
        match self.nodes.data(q) {
            NodeData::Style { style } => {
                let s = i32::from(*style);
                self.set_cur_style(s);
            }
            NodeData::Choice(c) => {
                let c = **c;
                let k = (self.ts.math.style / 2) as usize;
                let p = c[k.min(3)];
                for (i, l) in c.iter().enumerate() {
                    if i != k.min(3) {
                        self.nodes.flush_list(*l);
                    }
                }
                let st = self.ts.math.style as u8;
                *self.nodes.get_mut(q) = crate::nodes::Node {
                    data: NodeData::Style { style: st },
                    id: id::STYLE,
                    subtype: u16::from(st),
                    ..self.nodes.get(q).clone()
                };
                if !p.is_null() {
                    let z = self.nodes.next(q);
                    self.nodes.link(q, p);
                    let t = self.nodes.tail_of(p);
                    self.nodes.link(t, z);
                }
            }
            NodeData::Rule { height, depth, .. } => {
                if *height > *max_h {
                    *max_h = *height;
                }
                if *depth > *max_d {
                    *max_d = *depth;
                }
            }
            NodeData::Glue { spec, .. } => {
                let spec = *spec;
                let sub = self.nodes.subtype(q);
                if sub == glue_sub::MU_GLUE {
                    let g = self.math_glue(spec, self.ts.math.mu);
                    if let NodeData::Glue { spec, .. } = self.nodes.data_mut(q) {
                        *spec = g;
                    }
                    self.nodes.set_subtype(q, glue_sub::USER);
                } else if self.ts.math.size != 0 && sub == glue_sub::COND_MATH_GLUE {
                    let p = self.nodes.next(q);
                    if !p.is_null() && matches!(self.nodes.id(p), id::GLUE | id::KERN) {
                        let n = self.nodes.next(p);
                        self.nodes.link(q, n);
                        if n.is_null() {
                            self.nodes.set_next(q, NodeRef::NULL);
                        }
                        self.nodes.set_next(p, NodeRef::NULL);
                        self.nodes.flush_list(p);
                    }
                }
            }
            NodeData::Kern { kern, .. } => {
                if self.nodes.subtype(q) == glue_sub::MU_GLUE {
                    let w = self.mu_mult(*kern, self.ts.math.mu);
                    if let NodeData::Kern { kern, .. } = self.nodes.data_mut(q) {
                        *kern = w;
                    }
                    // LuaTeX marks converted \mkern kerns as italic kerns.
                    self.nodes.set_subtype(q, kern_sub::ITALIC);
                }
            }
            _ => {}
        }
        self.nodes.next(q)
    }

    /// Converts a mu dimension (`mu_mult` of `math_kern`).
    fn mu_mult(&self, x: i32, m: i32) -> i32 {
        let r = retex_arith::x_over_n_unchecked(m, 0o200000);
        let (mut n, mut f) = (r.quotient, r.remainder);
        if f < 0 {
            n -= 1;
            f += 0o200000;
        }
        let frac = retex_arith::xn_over_d(x, f, 0o200000).map_or(0, |r| r.quotient);
        retex_arith::nx_plus_y(n, x, frac).unwrap_or(0)
    }

    /// Converts mu glue to ordinary glue (`math_glue`).
    pub fn math_glue(&self, g: crate::glue::Glue, m: i32) -> crate::glue::Glue {
        let mut r = g;
        r.width = self.mu_mult(g.width, m);
        if g.stretch_order == 0 {
            r.stretch = self.mu_mult(g.stretch, m);
        }
        if g.shrink_order == 0 {
            r.shrink = self.mu_mult(g.shrink, m);
        }
        r
    }

    // ----- fetching characters ------------------------------------------

    /// The font, character and metrics of a `math_char` kernel (`fetch`).
    /// Reports an undefined family or a missing character.
    fn fetch(&mut self, k: NodeRef) -> Option<(u32, u32, crate::fonts::CharMetrics)> {
        let (fam, chr) = match self.nodes.data(k) {
            NodeData::MathChar { fam, chr } => (*fam, *chr),
            _ => return None,
        };
        let size = self.ts.math.size;
        let f = self.fam_fnt(fam, size);
        if f == 0 {
            self.print_err("");
            self.print_size(size);
            self.printer.print_int(i64::from(fam));
            self.printer.print_str(" is undefined (character ");
            self.printer.print_int(i64::from(chr));
            self.printer.print_char(')' as u32);
            self.help(&[
                "Somewhere in the math formula just ended, you used the",
                "stated character from an undefined font family. For example,",
                "plain TeX doesn't allow \\it or \\sl in subscripts. Proceed,",
                "and I'll try to forget that I needed that character.",
            ]);
            self.error();
            return None;
        }
        match self.fonts.char_metrics(f, chr) {
            Some(m) => Some((f, chr, *m)),
            None => {
                self.char_warning(f, chr);
                None
            }
        }
    }

    /// Prints `\textfont`, `\scriptfont` or `\scriptscriptfont`
    /// (`print_size`).
    pub fn print_size(&mut self, s: u32) {
        self.print_esc_str(match s {
            0 => "textfont",
            1 => "scriptfont",
            _ => "scriptscriptfont",
        });
    }

    /// Reports a missing character (`char_warning`) when
    /// `\tracinglostchars` is positive.
    pub fn char_warning(&mut self, f: u32, c: u32) {
        if self.eqtb.int(ip::TRACINGLOSTCHARS) > 0 {
            let old = self.eqtb.int(ip::TRACINGONLINE);
            self.begin_diagnostic();
            self.printer.print_nl("Missing character: There is no ");
            self.printer.print_char(c);
            // Observed: with the code point, as for text characters.
            self.printer.print_str(&format!(" (U+{c:04X}) in font "));
            let name = self.font(f).name.clone();
            self.printer.print_bytes(&name);
            self.printer.print_char('!' as u32);
            self.end_diagnostic(false);
            let _ = old;
        }
    }

    /// A protected glyph node for a math character.
    fn new_math_glyph(&mut self, f: u32, c: u32) -> NodeRef {
        let g = self.new_char_node(f, c);
        self.nodes.set_subtype(g, PROTECTED_GLYPH);
        g
    }

    /// A box holding one character, whose width includes the italic
    /// correction (`char_box`).
    fn char_box(&mut self, f: u32, c: u32) -> NodeRef {
        let m = self.fonts.char_metrics(f, c).copied().unwrap_or_default();
        // OpenType math boxes leave out the italic correction (observed).
        let italic = if self.is_opentype_math_font(f) {
            0
        } else {
            m.italic
        };
        let b = self.new_null_box_node(true);
        let g = self.new_math_glyph(f, c);
        if let Some(bd) = self.nodes.box_data_mut(b) {
            bd.width = m.width + italic;
            bd.height = m.height;
            bd.depth = m.depth;
            bd.head = g;
        }
        self.nodes.set_subtype(b, list_sub::MATH_CHAR);
        b
    }

    /// The TFM tag and remainder of character `c` in font `f`
    /// (0 none, 1 lig/kern, 2 list, 3 extensible).
    fn char_tag(&self, f: u32, c: u32) -> (u8, u32) {
        if let Some(t) = self.tfm_of(f)
            && let Some(ci) = t.char_info(c)
        {
            return (ci.tag, u32::from(ci.remainder));
        }
        if let Some(m) = self.math_char(f, c) {
            if let Some(n) = m.next {
                return (2, n);
            }
            if m.vert.is_some() {
                return (3, c);
            }
        }
        (0, 0)
    }

    // ----- boxes ----------------------------------------------------------

    /// Puts a noad field into a box of subtype `sub` in style `s`
    /// (`clean_box`).
    fn clean_box(&mut self, k: NodeRef, s: i32, sub: u16) -> NodeRef {
        let mut q;
        let kid = if k.is_null() { 0 } else { self.nodes.id(k) };
        match kid {
            id::MATH_CHAR | id::MATH_TEXT_CHAR => {
                let n = self.new_noad(noad_sub::ORD);
                let kc = self.nodes.copy_node(k);
                self.set_noad_field(n, Field::Nucleus, kc);
                q = self.clean_box_mlist(n, s);
            }
            id::SUB_BOX => {
                q = self.nodes.list_ptr_kernel(k);
                self.nodes.set_kernel_list(k, NodeRef::NULL);
            }
            id::SUB_MLIST => {
                let l = self.nodes.list_ptr_kernel(k);
                self.nodes.set_kernel_list(k, NodeRef::NULL);
                q = self.clean_box_mlist(l, s);
            }
            _ => {
                q = self.new_null_box_node(true);
            }
        }
        // found: a new box takes the attributes of its first node
        // (observed).
        let x = if q.is_null() {
            self.hpack_quiet(q)
        } else if !self.nodes.is_glyph(q)
            && self.nodes.next(q).is_null()
            && matches!(self.nodes.id(q), id::HLIST | id::VLIST)
            && self.nodes.box_data(q).is_some_and(|b| b.shift == 0)
        {
            q
        } else {
            let saved = self.attr_from(q);
            let x = self.hpack_quiet(q);
            self.attr_restore(saved);
            x
        };
        self.nodes.set_subtype(x, sub);
        // Simplify a trivial box.
        q = self.nodes.list_ptr(x);
        if !q.is_null() && self.nodes.is_glyph(q) {
            let r = self.nodes.next(q);
            if !r.is_null() && self.nodes.next(r).is_null() && self.nodes.id(r) == id::KERN {
                self.nodes.free(r);
                self.nodes.set_next(q, NodeRef::NULL);
            }
        }
        x
    }

    fn clean_box_mlist(&mut self, l: NodeRef, s: i32) -> NodeRef {
        let saved = self.ts.math;
        let r = self.mlist_to_hlist_rec(l, s, false);
        self.ts.math = saved;
        r
    }

    /// Centers box `b` in a box of width `w` (`rebox`).
    fn rebox(&mut self, b: NodeRef, w: i32) -> NodeRef {
        let bw = self.nodes.box_data(b).map_or(0, |x| x.width);
        let lp = self.nodes.list_ptr(b);
        if bw != w && !lp.is_null() {
            // The new nodes take the attributes of the box (observed).
            let saved = self.attr_from(b);
            let mut b = b;
            if self.nodes.id(b) == id::VLIST {
                b = self.hpack_quiet(b);
            }
            let mut p = self.nodes.list_ptr(b);
            let bw = self.nodes.box_data(b).map_or(0, |x| x.width);
            if self.nodes.is_glyph(p) && self.nodes.next(p).is_null() {
                let (f, c) = {
                    let g = self.nodes.glyph(p).expect("glyph");
                    (g.font, g.chr)
                };
                let v = self.fonts.char_metrics(f, c).map_or(0, |m| m.width);
                if v != bw {
                    let k = self.new_kern_node(bw - v, kern_sub::FONT);
                    self.nodes.link(p, k);
                }
            }
            self.nodes.set_list_ptr(b, NodeRef::NULL);
            self.nodes.free(b);
            let ss = crate::glue::Glue {
                stretch: retex_arith::UNITY,
                stretch_order: crate::glue::FIL,
                shrink: retex_arith::UNITY,
                shrink_order: crate::glue::FIL,
                ..crate::glue::Glue::ZERO
            };
            let g1 = self.new_glue_node(ss, glue_sub::USER);
            self.nodes.link(g1, p);
            while !self.nodes.next(p).is_null() {
                p = self.nodes.next(p);
            }
            let g2 = self.new_glue_node(ss, glue_sub::USER);
            self.nodes.link(p, g2);
            let r = self.hpack(g1, PackSpec::Exactly(w));
            self.attr_restore(saved);
            r
        } else {
            if let Some(x) = self.nodes.box_data_mut(b) {
                x.width = w;
            }
            b
        }
    }

    /// A rule of thickness `t` (`fraction_rule`).
    fn fraction_rule(&mut self, t: i32) -> NodeRef {
        self.new_node(
            id::RULE,
            0,
            NodeData::Rule {
                width: crate::typeset::NULL_FLAG,
                depth: 0,
                height: t,
                dir: 0,
                index: 0,
                left: 0,
                right: 0,
            },
        )
    }

    /// Box `b` under a kern `k`, a rule `t` and a kern `top` (`overbar`).
    fn overbar(&mut self, b: NodeRef, k: i32, t: i32, top: i32) -> NodeRef {
        let p = self.new_kern_node(k, kern_sub::FONT);
        self.nodes.link(p, b);
        let q = self.fraction_rule(t);
        self.nodes.link(q, p);
        let p = self.new_kern_node(top, kern_sub::FONT);
        self.nodes.link(p, q);
        self.vpack(p, PackSpec::NATURAL)
    }

    // ----- delimiters -----------------------------------------------------

    /// A box with the smallest variant of delimiter `d` whose height plus
    /// depth is at least `v`, built from extensible pieces if needed,
    /// centered on the axis of size `s` (`var_delimiter`).
    /// Its nodes take the attributes of the delimiter (none for a null
    /// one; observed).
    pub fn var_delimiter(&mut self, d: NodeRef, s: u32, v: i32, shift: bool) -> NodeRef {
        let saved = self.attr_from(d);
        let b = self.var_delimiter_box(d, s, v, shift);
        self.attr_restore(saved);
        b
    }

    fn var_delimiter_box(&mut self, d: NodeRef, s: u32, v: i32, shift: bool) -> NodeRef {
        let (sf, sc, lf, lc) = self.delim_fields(d);
        let mut best: Option<(u32, u32, bool)> = None;
        let mut w = 0i32;
        'search: for (z0, x0) in [(sf, sc), (lf, lc)] {
            if z0 == 0 && x0 == 0 {
                continue;
            }
            let mut z = s as i32;
            while z >= 0 {
                let g = self.fam_fnt(z0, z as u32);
                if g != 0 {
                    let mut y = x0;
                    let mut guard = 0;
                    loop {
                        guard += 1;
                        if guard > 256 {
                            break;
                        }
                        let Some(m) = self.fonts.char_metrics(g, y).copied() else {
                            break;
                        };
                        let (tag, rem) = self.char_tag(g, y);
                        // An OpenType variant is used when it is large
                        // enough; the assembly only after the last one.
                        let opentype = self.is_opentype_math_font(g);
                        if tag == 3 && !opentype {
                            best = Some((g, y, true));
                            break 'search;
                        }
                        let u = m.height + m.depth;
                        if u > w {
                            best = Some((g, y, false));
                            w = u;
                            if u >= v {
                                break 'search;
                            }
                        }
                        if opentype && self.vert_parts(g, y).is_some() {
                            best = Some((g, y, true));
                            break 'search;
                        }
                        if tag == 2 {
                            y = rem;
                        } else {
                            break;
                        }
                    }
                }
                z -= 1;
            }
        }
        let b = match best {
            Some((f, c, true)) if self.is_opentype_math_font(f) => {
                let saved = self.ts.math;
                self.set_cur_style(if s == 0 { 2 } else { 2 * s as i32 + 2 });
                let overlap = self.math_par(mp::CONNECTOR_OVERLAP_MIN);
                self.ts.math = saved;
                self.ot_extensible_box(f, c, v, overlap)
            }
            Some((f, c, true)) => self.extensible_box(f, c, v),
            Some((f, c, false)) => self.char_box(f, c),
            None => {
                let b = self.new_null_box_node(true);
                let nds = self.eqtb.dimen(dp::NULLDELIMITERSPACE);
                if let Some(bd) = self.nodes.box_data_mut(b) {
                    bd.width = nds;
                }
                self.nodes.set_subtype(b, list_sub::V_DELIMITER);
                if !shift {
                    return b;
                }
                b
            }
        };
        let saved = self.ts.math;
        self.set_cur_style(if s == 0 { 2 } else { 2 * s as i32 + 2 });
        let axis = self.math_par(mp::AXIS);
        self.ts.math = saved;
        if let Some(bd) = self.nodes.box_data_mut(b) {
            bd.shift = half(bd.height - bd.depth) - axis;
        }
        b
    }

    /// For a nucleus that is a list of one accent noad on a character
    /// (possibly accented itself), that character's font and code.
    fn nested_accent_char(&mut self, k: NodeRef) -> Option<(u32, u32)> {
        if k.is_null() || self.nodes.id(k) != id::SUB_MLIST {
            return None;
        }
        let l = self.nodes.list_ptr_kernel(k);
        if l.is_null()
            || !self.nodes.next(l).is_null()
            || self.noad_type(l) != Some(NoadType::Accent)
        {
            return None;
        }
        let n = self.noad_field(l, Field::Nucleus);
        if n.is_null() {
            return None;
        }
        if self.nodes.id(n) == id::MATH_CHAR {
            return self.fetch(n).map(|(f, c, _)| (f, c));
        }
        self.nested_accent_char(n)
    }

    /// The vertical extensible parts of OpenType math character `c`.
    fn vert_parts(&self, f: u32, c: u32) -> Option<std::rc::Rc<[crate::fonts::ExtPart]>> {
        self.math_char(f, c)?.vert.clone()
    }

    /// Builds the vertical assembly of OpenType math character `c` with
    /// height plus depth at least `v`, as LuaTeX does (observed with Latin
    /// Modern Math): each extender is repeated the smallest number of
    /// times that lets the parts, overlapping by at least `overlap`, reach
    /// `v`; the parts are boxes as high as their glyphs, separated by
    /// glue that removes the largest overlap the connectors allow and
    /// stretches back to the smallest; the vbox is set to `v`.
    fn ot_extensible_box(&mut self, f: u32, c: u32, v: i32, overlap: i32) -> NodeRef {
        let parts = self
            .vert_parts(f, c)
            .unwrap_or_else(|| std::rc::Rc::from(Vec::new()));
        let expand = |n: usize| -> Vec<crate::fonts::ExtPart> {
            let mut out = Vec::new();
            for p in parts.iter() {
                let k = if p.extender { n } else { 1 };
                for _ in 0..k {
                    out.push(*p);
                }
            }
            out
        };
        let joint = |a: &crate::fonts::ExtPart, b: &crate::fonts::ExtPart| {
            let max = a.end.min(b.start).max(0);
            (max, overlap.min(max))
        };
        let largest = |seq: &[crate::fonts::ExtPart]| -> i64 {
            let mut t: i64 = seq.iter().map(|p| i64::from(p.advance)).sum();
            for w in seq.windows(2) {
                t -= i64::from(joint(&w[0], &w[1]).1);
            }
            t
        };
        let has_extender = parts.iter().any(|p| p.extender);
        let mut n = 0;
        let mut seq = expand(n);
        while has_extender && largest(&seq) < i64::from(v) && n < 1000 {
            n += 1;
            seq = expand(n);
        }
        // Build the vbox from the top down.
        let mut head = NodeRef::NULL;
        let mut tail = NodeRef::NULL;
        let mut width = 0;
        for (i, p) in seq.iter().enumerate().rev() {
            if i + 1 < seq.len() {
                let (max, min) = joint(p, &seq[i + 1]);
                let g = crate::glue::Glue {
                    width: -max,
                    stretch: max - min,
                    ..crate::glue::Glue::ZERO
                };
                let gn = self.new_glue_node(g, 0);
                self.nodes.link(tail, gn);
                tail = gn;
            }
            let m = self
                .fonts
                .char_metrics(f, p.code)
                .copied()
                .unwrap_or_default();
            let b = self.new_null_box_node(true);
            self.nodes.set_subtype(b, list_sub::MATH_CHAR);
            let gl = self.new_math_glyph(f, p.code);
            // Observed: the box is as high as the glyph (height plus
            // depth), not as its advance in the assembly, where they differ
            // (Libertinus Math).
            if let Some(bd) = self.nodes.box_data_mut(b) {
                bd.width = m.width;
                bd.height = m.height + m.depth;
                bd.depth = 0;
                bd.head = gl;
            }
            width = width.max(m.width);
            if head.is_null() {
                head = b;
            } else {
                self.nodes.link(tail, b);
            }
            tail = b;
        }
        let natural = largest(&seq) as i32;
        let target = v.max(natural.min(v));
        let b = self.vpack(head, crate::build::PackSpec::Exactly(target));
        self.nodes.set_subtype(b, list_sub::V_EXTENSIBLE);
        if let Some(bd) = self.nodes.box_data_mut(b) {
            bd.width = width;
        }
        b
    }

    /// Builds an extensible character from the recipe of `c` in font `f`
    /// (§713–§714).
    fn extensible_box(&mut self, f: u32, c: u32, v: i32) -> NodeRef {
        let recipe = self
            .tfm_of(f)
            .and_then(|t| {
                let (_, rem) = self.char_tag(f, c);
                t.exten.get(rem as usize).copied()
            })
            .unwrap_or([0, 0, 0, 0]);
        let [top, mid, bot, rep] = recipe.map(u32::from);
        let hd = |e: &Engine, ch: u32| {
            e.fonts
                .char_metrics(f, ch)
                .map_or(0, |m| m.height + m.depth)
        };
        let b = self.new_null_box_node(false);
        let u = hd(self, rep);
        let mut w = 0;
        let rm = self.fonts.char_metrics(f, rep).copied().unwrap_or_default();
        let width = rm.width + rm.italic;
        if bot != 0 {
            w += hd(self, bot);
        }
        if mid != 0 {
            w += hd(self, mid);
        }
        if top != 0 {
            w += hd(self, top);
        }
        let mut n = 0;
        if u > 0 {
            while w < v {
                w += u;
                n += 1;
                if mid != 0 {
                    w += u;
                }
            }
        }
        if let Some(bd) = self.nodes.box_data_mut(b) {
            bd.width = width;
        }
        if bot != 0 {
            self.stack_into_box(b, f, bot);
        }
        for _ in 0..n {
            self.stack_into_box(b, f, rep);
        }
        if mid != 0 {
            self.stack_into_box(b, f, mid);
            for _ in 0..n {
                self.stack_into_box(b, f, rep);
            }
        }
        if top != 0 {
            self.stack_into_box(b, f, top);
        }
        // LuaTeX gives the whole height to the box (TeX82 keeps the
        // height of the topmost piece and puts the rest in the depth).
        if let Some(bd) = self.nodes.box_data_mut(b) {
            bd.height = w;
            bd.depth = 0;
        }
        self.nodes.set_subtype(b, list_sub::V_EXTENSIBLE);
        b
    }

    fn stack_into_box(&mut self, b: NodeRef, f: u32, c: u32) {
        let p = self.char_box(f, c);
        let head = self.nodes.list_ptr(b);
        self.nodes.link(p, head);
        self.nodes.set_list_ptr(b, p);
        let h = self.nodes.box_data(p).map_or(0, |x| x.height);
        if let Some(bd) = self.nodes.box_data_mut(b) {
            bd.height = h;
        }
    }

    // ----- the make_… procedures -----------------------------------------

    fn take_field(&mut self, q: NodeRef, f: Field) -> NodeRef {
        let k = self.noad_field(q, f);
        self.set_noad_field(q, f, NodeRef::NULL);
        k
    }

    /// Replaces the nucleus of `q` by a `sub_box` holding `b`.
    fn set_nucleus_box(&mut self, q: NodeRef, b: NodeRef) {
        let old = self.take_field(q, Field::Nucleus);
        self.nodes.flush_list(old);
        let k = self.new_sub_list(false, b);
        self.set_noad_field(q, Field::Nucleus, k);
    }

    fn make_over(&mut self, q: NodeRef) {
        let k = self.noad_field(q, Field::Nucleus);
        let st = cramped_style(self.ts.math.style);
        let x = self.clean_box(k, st, list_sub::NUCLEUS);
        // The bar takes the attributes of the nucleus (observed).
        let saved = self.attr_from(k);
        let b = self.overbar(
            x,
            self.math_par(mp::OVERBAR_VGAP),
            self.math_par(mp::OVERBAR_RULE),
            self.math_par(mp::OVERBAR_KERN),
        );
        self.attr_restore(saved);
        self.nodes.set_subtype(b, list_sub::OVER);
        self.set_nucleus_box(q, b);
    }

    fn make_under(&mut self, q: NodeRef) {
        let k = self.noad_field(q, Field::Nucleus);
        let x = self.clean_box(k, self.ts.math.style, list_sub::NUCLEUS);
        let p = self.new_kern_node(self.math_par(mp::UNDERBAR_VGAP), kern_sub::FONT);
        self.nodes.link(x, p);
        let r = self.fraction_rule(self.math_par(mp::UNDERBAR_RULE));
        self.nodes.link(p, r);
        let y = self.vpack(x, PackSpec::NATURAL);
        self.nodes.set_subtype(y, list_sub::UNDER);
        let (yh, yd) = self
            .nodes
            .box_data(y)
            .map_or((0, 0), |b| (b.height, b.depth));
        let xh = self.nodes.box_data(x).map_or(0, |b| b.height);
        let delta = yh + yd + self.math_par(mp::UNDERBAR_KERN);
        if let Some(b) = self.nodes.box_data_mut(y) {
            b.height = xh;
            b.depth = delta - xh;
        }
        self.set_nucleus_box(q, y);
    }

    fn make_vcenter(&mut self, q: NodeRef) {
        let k = self.noad_field(q, Field::Nucleus);
        let v = self.nodes.list_ptr_kernel(k);
        if v.is_null() || self.nodes.id(v) != id::VLIST {
            self.confusion("vcenter");
        }
        let axis = self.math_par(mp::AXIS);
        if let Some(b) = self.nodes.box_data_mut(v) {
            let delta = b.height + b.depth;
            b.height = axis + half(delta);
            b.depth = delta - b.height;
        }
    }

    fn make_radical(&mut self, q: NodeRef) {
        let sub = self.nodes.subtype(q);
        match sub {
            radical_sub::UUNDERDELIMITER
            | radical_sub::UOVERDELIMITER
            | radical_sub::UDELIMITERUNDER
            | radical_sub::UDELIMITEROVER
            | radical_sub::UHEXTENSIBLE => {
                self.make_delimiter_radical(q, sub);
                return;
            }
            _ => {}
        }
        let k = self.noad_field(q, Field::Nucleus);
        let x = self.clean_box(k, cramped_style(self.ts.math.style), list_sub::NUCLEUS);
        let (xh, xd) = self
            .nodes
            .box_data(x)
            .map_or((0, 0), |b| (b.height, b.depth));
        let mut clr = self.math_par(mp::RADICAL_VGAP);
        let theta = self.math_par_opt(mp::RADICAL_RULE);
        let kern = self.math_par(mp::RADICAL_KERN);
        let t = theta.unwrap_or(self.math_par(mp::FRACTION_RULE));
        let left = self.nodes.noad(q).map_or(NodeRef::NULL, |n| n.left);
        let size = self.ts.math.size;
        let y = self.var_delimiter(left, size, xh + xd + clr + t, true);
        let (yh, yd) = self
            .nodes
            .box_data(y)
            .map_or((0, 0), |b| (b.height, b.depth));
        let theta = if let Some(th) = theta {
            // With \Umathradicalrule set (OpenType fonts): the sign's whole
            // size counts, and its top is put at the top of the rule.
            let delta = yh + yd - th - (xh + xd + clr);
            if delta > 0 {
                clr += half(delta);
            }
            if let Some(b) = self.nodes.box_data_mut(y) {
                b.shift = yh - (xh + clr + th);
            }
            th
        } else {
            // TeX82 assumes the sign's height is the rule thickness. LuaTeX
            // gives an extensible sign its whole size as height, so measure
            // it from its topmost piece and convert.
            let top_h = if self.nodes.id(y) == id::VLIST {
                let h = self.nodes.list_ptr(y);
                self.nodes.box_data(h).map_or(yh, |b| b.height)
            } else {
                yh
            };
            let eq_depth = yh + yd - top_h;
            let delta = eq_depth - (xh + xd + clr);
            if delta > 0 {
                clr += half(delta);
            }
            if let Some(b) = self.nodes.box_data_mut(y) {
                b.shift = -(xh + clr) + (yh - top_h);
            }
            top_h
        };
        // The kern above the rule is \Umathradicalkern, the default rule
        // thickness for traditional fonts, even where the sign's height
        // (the rule) differs from it (observed with newtxmath).
        // The bar takes the attributes of the delimiter (observed).
        let saved = self.attr_from(left);
        let ob = self.overbar(x, clr, theta, kern);
        self.attr_restore(saved);
        self.nodes.set_subtype(ob, list_sub::RADICAL);
        self.nodes.link(y, ob);
        let deg = self.noad_field(q, Field::Degree);
        let list = if deg.is_null() {
            y
        } else {
            // \Uroot: the degree in scriptscript style.
            let r = self.clean_box(deg, 6, list_sub::DEGREE);
            let (rw, rh, rd) = self
                .nodes
                .box_data(r)
                .map_or((0, 0, 0), |b| (b.width, b.height, b.depth));
            let _ = rd;
            let before = self.math_par(mp::RADICAL_DEGREE_BEFORE);
            let after = self.math_par(mp::RADICAL_DEGREE_AFTER);
            let raise = self.math_par(mp::RADICAL_DEGREE_RAISE);
            let (yh2, yd2, ys) = self
                .nodes
                .box_data(y)
                .map_or((0, 0, 0), |b| (b.height, b.depth, b.shift));
            let ytot = yh2 + yd2;
            let shift = retex_arith::xn_over_d(ytot, raise, 100).map_or(0, |r| r.quotient);
            // The degree's baseline is `raise` percent of the sign's size
            // above the sign's bottom.
            if self.math_par_opt(mp::RADICAL_RULE).is_some() {
                if let Some(b) = self.nodes.box_data_mut(r) {
                    b.shift = -(shift - (yd2 + ys));
                }
            } else if let Some(b) = self.nodes.box_data_mut(r) {
                b.shift = -(shift - yd2 + b.shift.min(0));
            }
            let _ = rh;
            // The kerns take the attributes of the degree (observed).
            let saved = self.attr_from(r);
            let k1 = self.new_kern_node(before, kern_sub::FONT);
            let k2 = self.new_kern_node(after, kern_sub::FONT);
            self.attr_restore(saved);
            let _ = rw;
            self.nodes.link(k1, r);
            self.nodes.link(r, k2);
            self.nodes.link(k2, y);
            k1
        };
        let b = self.hpack_quiet(list);
        self.set_nucleus_box(q, b);
    }

    /// `\Uoverdelimiter` and friends: a delimiter above or below the
    /// nucleus, as observed in LuaTeX. `\Uoverdelimiter` puts the nucleus,
    /// in superscript style, over the delimiter and `\Uunderdelimiter`
    /// puts it, in subscript style, under it; `\Udelimiterover` and
    /// `\Udelimiterunder` put the delimiter over or under a nucleus in the
    /// current style, measuring the gap from the delimiter's baseline.
    /// Both boxes take the larger width; the baseline is the delimiter's
    /// for the first two, the nucleus's for the others.
    fn make_delimiter_radical(&mut self, q: NodeRef, sub: u16) {
        let k = self.noad_field(q, Field::Nucleus);
        let cs = self.ts.math.style;
        let left = self.nodes.noad(q).map_or(NodeRef::NULL, |n| n.left);
        let size = self.ts.math.size;
        if sub == radical_sub::UHEXTENSIBLE {
            let width = self.nodes.noad(q).map_or(0, |n| n.width);
            let y = self.h_delimiter(left, size, width);
            let b = self.hpack_quiet(y);
            self.set_nucleus_box(q, b);
            return;
        }
        let st = match sub {
            radical_sub::UOVERDELIMITER => sup_style(cs),
            radical_sub::UUNDERDELIMITER => sub_style(cs),
            _ => cs,
        };
        let x = if k.is_null() {
            self.new_null_box_node(true)
        } else {
            self.clean_box(k, st, list_sub::NUCLEUS)
        };
        // Observed: \Udelimiterover and \Udelimiterunder take the
        // delimiter in the script size (like limits), the others in the
        // current size; it is made as wide as the nucleus.
        let dsize = match sub {
            radical_sub::UDELIMITEROVER | radical_sub::UDELIMITERUNDER => (size + 1).min(2),
            _ => size,
        };
        let xw0 = self.nodes.box_data(x).map_or(0, |b| b.width);
        let y = self.h_delimiter(left, dsize, xw0);
        let dim = |e: &Self, b: NodeRef| {
            e.nodes
                .box_data(b)
                .map_or((0, 0, 0), |b| (b.width, b.height, b.depth))
        };
        let (xw, xh, xd) = dim(self, x);
        let (yw, yh, yd) = dim(self, y);
        let w = xw.max(yw);
        for b in [x, y] {
            if let Some(bd) = self.nodes.box_data_mut(b) {
                bd.width = w;
            }
        }
        let over = matches!(
            sub,
            radical_sub::UOVERDELIMITER | radical_sub::UDELIMITEROVER
        );
        let (vgap, bgap) = if over {
            (
                self.math_par(mp::OVER_DELIMITER_VGAP),
                self.math_par(mp::OVER_DELIMITER_BGAP),
            )
        } else {
            (
                self.math_par(mp::UNDER_DELIMITER_VGAP),
                self.math_par(mp::UNDER_DELIMITER_BGAP),
            )
        };
        let (top, bottom, kern) = match sub {
            radical_sub::UOVERDELIMITER => (x, y, vgap.max(bgap - yh - xd)),
            radical_sub::UUNDERDELIMITER => (y, x, vgap.max(bgap - xh - yd)),
            radical_sub::UDELIMITEROVER => (y, x, vgap.max(bgap - xh - (yh + yd)) - yd),
            _ => (x, y, vgap.max(bgap - xd - (yh + yd)) - yh),
        };
        let kk = self.new_kern_node(kern, kern_sub::FONT);
        self.nodes.link(top, kk);
        self.nodes.link(kk, bottom);
        let v = self.vpack(top, PackSpec::NATURAL);
        self.nodes.set_subtype(
            v,
            if over {
                list_sub::OVER_DELIMITER
            } else {
                list_sub::UNDER_DELIMITER
            },
        );
        // Under the nucleus or the delimiter on top, the baseline is that
        // of the top box.
        if matches!(
            sub,
            radical_sub::UUNDERDELIMITER | radical_sub::UDELIMITERUNDER
        ) {
            let th = self.nodes.box_data(top).map_or(0, |b| b.height);
            if let Some(b) = self.nodes.box_data_mut(v) {
                let tot = b.height + b.depth;
                b.height = th;
                b.depth = tot - th;
            }
        }
        self.set_nucleus_box(q, v);
    }

    /// A horizontal delimiter of size `s` at least `w` wide: for an
    /// OpenType font the first variant that wide, else the assembly of
    /// the last one stretched to `w` (observed: as the vertical one, with
    /// the parts in boxes as wide as their glyphs and the connector
    /// overlap of the current style); for other fonts the character.
    /// Its nodes take the delimiter's attributes.
    fn h_delimiter(&mut self, d: NodeRef, s: u32, w: i32) -> NodeRef {
        let saved = self.attr_from(d);
        let (sf, sc, _, _) = self.delim_fields(d);
        let f = self.fam_fnt(sf, s);
        let b = if f == 0 || self.fonts.char_metrics(f, sc).is_none() {
            self.new_null_box_node(true)
        } else if !self.is_opentype_math_font(f) {
            self.char_box(f, sc)
        } else {
            let mut c = sc;
            let mut guard = 0;
            let mut assembly = None;
            loop {
                guard += 1;
                let m = self.fonts.char_metrics(f, c).copied().unwrap_or_default();
                if m.width >= w || guard > 256 {
                    break;
                }
                if let Some(parts) = self.math_char(f, c).and_then(|mc| mc.horiz.clone()) {
                    assembly = Some(parts);
                    break;
                }
                match self.math_char(f, c).and_then(|mc| mc.next) {
                    Some(n) if self.fonts.char_metrics(f, n).is_some() => c = n,
                    _ => break,
                }
            }
            match assembly {
                Some(parts) => {
                    let overlap = self.math_par(mp::CONNECTOR_OVERLAP_MIN);
                    self.ot_h_extensible_box(f, &parts, w, overlap)
                }
                None => self.char_box(f, c),
            }
        };
        self.attr_restore(saved);
        b
    }

    /// The horizontal assembly of `parts` (left first) in font `f`, `w`
    /// wide (see [`Engine::ot_extensible_box`]).
    fn ot_h_extensible_box(
        &mut self,
        f: u32,
        parts: &[crate::fonts::ExtPart],
        w: i32,
        overlap: i32,
    ) -> NodeRef {
        let expand = |n: usize| -> Vec<crate::fonts::ExtPart> {
            let mut out = Vec::new();
            for p in parts.iter() {
                let k = if p.extender { n } else { 1 };
                for _ in 0..k {
                    out.push(*p);
                }
            }
            out
        };
        let joint = |a: &crate::fonts::ExtPart, b: &crate::fonts::ExtPart| {
            let max = a.end.min(b.start).max(0);
            (max, overlap.min(max))
        };
        let largest = |seq: &[crate::fonts::ExtPart]| -> i64 {
            let mut t: i64 = seq.iter().map(|p| i64::from(p.advance)).sum();
            for win in seq.windows(2) {
                t -= i64::from(joint(&win[0], &win[1]).1);
            }
            t
        };
        let has_extender = parts.iter().any(|p| p.extender);
        let mut n = 0;
        let mut seq = expand(n);
        while has_extender && largest(&seq) < i64::from(w) && n < 1000 {
            n += 1;
            seq = expand(n);
        }
        let mut head = NodeRef::NULL;
        let mut tail = NodeRef::NULL;
        for (i, p) in seq.iter().enumerate() {
            if i > 0 {
                let (max, min) = joint(&seq[i - 1], p);
                let g = crate::glue::Glue {
                    width: -max,
                    stretch: max - min,
                    ..crate::glue::Glue::ZERO
                };
                let gn = self.new_glue_node(g, 0);
                self.nodes.link(tail, gn);
                tail = gn;
            }
            let b = self.char_box(f, p.code);
            if head.is_null() {
                head = b;
            } else {
                self.nodes.link(tail, b);
            }
            tail = b;
        }
        let natural = largest(&seq) as i32;
        let target = w.max(natural.min(w));
        let b = self.hpack(head, PackSpec::Exactly(target));
        self.nodes.set_subtype(b, list_sub::H_EXTENSIBLE);
        b
    }

    /// Places a math accent (`make_math_accent`).
    fn make_math_accent(&mut self, q: NodeRef) {
        let acc = self.nodes.noad(q).map_or(NodeRef::NULL, |n| n.accent);
        if acc.is_null() {
            // A bottom accent only: place it below the nucleus.
            self.make_bottom_accent(q);
            return;
        }
        let Some((f, mut c, mut i)) = self.fetch(acc) else {
            return;
        };
        // Compute the amount of skew.
        let mut s = 0;
        let nuc = self.noad_field(q, Field::Nucleus);
        let mut nuc_char = None;
        if !nuc.is_null()
            && self.nodes.id(nuc) == id::MATH_CHAR
            && let Some((nf, nc, _)) = self.fetch(nuc)
        {
            nuc_char = Some((nf, nc));
            let sk = self.font(nf).skew_char;
            if sk >= 0
                && let Some(LigOp::Kern(k)) = self.lig_kern_step(nf, nc, sk as u32)
            {
                s = k;
            }
        }
        let st = cramped_style(self.ts.math.style);
        let mut char_nucleus = !nuc.is_null() && self.nodes.id(nuc) == id::MATH_CHAR;
        if nuc_char.is_none()
            && self.is_opentype_math_font(f)
            && let Some(fc) = self.nested_accent_char(nuc)
        {
            // An accent on an accented character attaches like one on the
            // character (observed with \hat{\hat{x}}).
            nuc_char = Some(fc);
            char_nucleus = true;
        }
        let mut x = self.clean_box(nuc, st, list_sub::NUCLEUS);
        let (w, mut h) = self
            .nodes
            .box_data(x)
            .map_or((0, 0), |b| (b.width, b.height));
        // Switch to a larger accent if available and appropriate.
        let fixed = matches!(
            self.nodes.subtype(q),
            crate::nodes::accent_sub::FIXED_TOP | crate::nodes::accent_sub::FIXED_BOTH
        );
        if !fixed {
            loop {
                let (tag, rem) = self.char_tag(f, c);
                if tag != 2 {
                    break;
                }
                let Some(m) = self.fonts.char_metrics(f, rem).copied() else {
                    break;
                };
                if m.width > w {
                    break;
                }
                c = rem;
                i = m;
            }
        }
        let _ = i;
        let opentype = self.is_opentype_math_font(f);
        // OpenType fonts lower the accent by at most AccentBaseHeight.
        let xh = if opentype {
            self.font(f)
                .math_constants
                .as_ref()
                .and_then(|m| m.get("AccentBaseHeight").copied())
                .unwrap_or_else(|| self.x_height(f))
        } else {
            self.x_height(f)
        };
        let mut delta = if h < xh { h } else { xh };
        let sup = self.noad_field(q, Field::Sup);
        let sub = self.noad_field(q, Field::Sub);
        if (!sup.is_null() || !sub.is_null())
            && !nuc.is_null()
            && self.nodes.id(nuc) == id::MATH_CHAR
        {
            // Swap the subscript and superscript into box x.
            self.nodes.flush_list(x);
            let n = self.new_noad(noad_sub::ORD);
            let nk = self.take_field(q, Field::Nucleus);
            let a = self.take_field(q, Field::Sup);
            let b = self.take_field(q, Field::Sub);
            self.set_noad_field(n, Field::Nucleus, nk);
            self.set_noad_field(n, Field::Sup, a);
            self.set_noad_field(n, Field::Sub, b);
            let k = self.new_sub_list(true, n);
            self.set_noad_field(q, Field::Nucleus, k);
            x = self.clean_box(k, self.ts.math.style, list_sub::NUCLEUS);
            let nh = self.nodes.box_data(x).map_or(0, |b| b.height);
            delta = delta + nh - h;
            h = nh;
        }
        // The accent's box takes the accent's attributes (observed).
        let saved = self.attr_from(acc);
        let y = self.char_box(f, c);
        self.attr_restore(saved);
        let yw = self.nodes.box_data(y).map_or(0, |b| b.width);
        let shift = if opentype {
            // Top accent attachments: that of a character nucleus (else
            // half its width) minus that of the accent (else half its
            // width).
            let a = if char_nucleus {
                nuc_char
                    .and_then(|(nf, nc)| self.math_char(nf, nc).and_then(|m| m.top_accent))
                    .unwrap_or(half(w))
            } else {
                half(w)
            };
            let b = self
                .math_char(f, c)
                .and_then(|m| m.top_accent)
                .unwrap_or(half(yw));
            a - b
        } else if char_nucleus {
            // For a character nucleus LuaTeX follows TeX82; otherwise it
            // centers one unit to the right (observed: half(w - wa) + 1).
            s + half(w - yw)
        } else {
            s + half(w - yw) + 1
        };
        if let Some(b) = self.nodes.box_data_mut(y) {
            b.shift = shift;
            b.width = 0;
        }
        let p = self.new_kern_node(-delta, kern_sub::FONT);
        self.nodes.link(p, x);
        self.nodes.link(y, p);
        let y = self.vpack(y, PackSpec::NATURAL);
        self.nodes.set_subtype(y, list_sub::ACCENT);
        let mut xw = self.nodes.box_data(x).map_or(0, |b| b.width);
        // Observed: an OpenType accent on a character includes the
        // character's italic correction unless it ends the list.
        if opentype
            && !self.nodes.next(q).is_null()
            && let Some((nf, nc)) = nuc_char
            && self.nodes.id(nuc) == id::MATH_CHAR
        {
            xw += self.fonts.char_metrics(nf, nc).map_or(0, |m| m.italic);
        }
        let yh = self.nodes.box_data(y).map_or(0, |b| b.height);
        if let Some(b) = self.nodes.box_data_mut(y) {
            b.width = xw;
        }
        if yh < h {
            let p = self.new_kern_node(h - yh, kern_sub::FONT);
            let l = self.nodes.list_ptr(y);
            self.nodes.link(p, l);
            self.nodes.set_list_ptr(y, p);
            if let Some(b) = self.nodes.box_data_mut(y) {
                b.height = h;
            }
        }
        self.set_nucleus_box(q, y);
        let bot = self.nodes.noad(q).map_or(NodeRef::NULL, |n| n.bot_accent);
        if !bot.is_null() {
            self.make_bottom_accent(q);
        }
    }

    /// A bottom accent (`\Umathaccent bottom`): centered below the
    /// nucleus.
    fn make_bottom_accent(&mut self, q: NodeRef) {
        let bot = match self.nodes.noad_mut(q) {
            Some(n) => std::mem::replace(&mut n.bot_accent, NodeRef::NULL),
            None => return,
        };
        let Some((f, mut c, _)) = self.fetch(bot) else {
            self.nodes.flush_list(bot);
            return;
        };
        let bot_attr = self.attr_of(bot);
        self.nodes.flush_list(bot);
        let fixed = matches!(
            self.nodes.subtype(q),
            crate::nodes::accent_sub::FIXED_BOTTOM | crate::nodes::accent_sub::FIXED_BOTH
        );
        let nuc = self.noad_field(q, Field::Nucleus);
        let char_nucleus = !nuc.is_null() && self.nodes.id(nuc) == id::MATH_CHAR;
        let nuc_char = if char_nucleus {
            self.fetch(nuc).map(|(nf, nc, _)| (nf, nc))
        } else {
            None
        };
        // As for top accents, the scripts of a character go inside.
        let sup = self.noad_field(q, Field::Sup);
        let sub = self.noad_field(q, Field::Sub);
        let x = if char_nucleus && (!sup.is_null() || !sub.is_null()) {
            let n = self.new_noad(noad_sub::ORD);
            let nk = self.take_field(q, Field::Nucleus);
            let a = self.take_field(q, Field::Sup);
            let b = self.take_field(q, Field::Sub);
            self.set_noad_field(n, Field::Nucleus, nk);
            self.set_noad_field(n, Field::Sup, a);
            self.set_noad_field(n, Field::Sub, b);
            let k = self.new_sub_list(true, n);
            self.set_noad_field(q, Field::Nucleus, k);
            self.clean_box(k, self.ts.math.style, list_sub::NUCLEUS)
        } else {
            self.clean_box(nuc, self.ts.math.style, list_sub::NUCLEUS)
        };
        let (bw, xh) = self
            .nodes
            .box_data(x)
            .map_or((0, 0), |b| (b.width, b.height));
        // The accent is centred on the character itself, not on the box
        // with its scripts (observed).
        let w = match nuc_char {
            Some((nf, nc)) => self.fonts.char_metrics(nf, nc).map_or(bw, |m| {
                if self.is_opentype_math_font(nf) {
                    m.width
                } else {
                    m.width + m.italic
                }
            }),
            None => bw,
        };
        // Switch to a wider accent if available, as for top accents.
        if !fixed {
            loop {
                let (tag, rem) = self.char_tag(f, c);
                if tag != 2 {
                    break;
                }
                match self.fonts.char_metrics(f, rem) {
                    Some(m) if m.width <= w => c = rem,
                    _ => break,
                }
            }
        }
        let saved = self.attr_set(bot_attr);
        let y = self.char_box(f, c);
        self.attr_restore(saved);
        let yw = self.nodes.box_data(y).map_or(0, |b| b.width);
        let shift = if self.is_opentype_math_font(f) {
            let a = nuc_char
                .filter(|_| self.noad_field(q, Field::Sup).is_null())
                .and_then(|(nf, nc)| self.math_char(nf, nc).and_then(|m| m.top_accent))
                .unwrap_or(half(w));
            let b = self
                .math_char(f, c)
                .and_then(|m| m.top_accent)
                .unwrap_or(half(yw));
            a - b
        } else if nuc_char.is_some() {
            half(w - yw)
        } else {
            w / 2 - yw / 2 + 1
        };
        if let Some(b) = self.nodes.box_data_mut(y) {
            b.shift = shift;
            b.width = 0;
        }
        self.nodes.link(x, y);
        // Observed: the nucleus and the accent are packed naturally and
        // the box is lowered so that the nucleus keeps its baseline.
        let v = self.vpack(x, PackSpec::NATURAL);
        self.nodes.set_subtype(v, list_sub::ACCENT);
        if let Some(b) = self.nodes.box_data_mut(v) {
            b.shift = b.height - xh;
            b.width = bw;
        }
        self.set_nucleus_box(q, v);
    }

    /// Builds a generalized fraction (`make_fraction`).
    fn make_fraction(&mut self, q: NodeRef) {
        let (mut thickness, num, denom, left, right, options) = match self.nodes.data(q) {
            NodeData::Fraction(f) => (f.thickness, f.num, f.denom, f.left, f.right, f.options),
            _ => return,
        };
        if thickness == DEFAULT_CODE {
            thickness = self.math_par(mp::FRACTION_RULE);
        }
        let cs = self.ts.math.style;
        let mut x = self.clean_box(num, num_style(cs), list_sub::NUMERATOR);
        let mut z = self.clean_box(denom, denom_style(cs), list_sub::DENOMINATOR);
        let (xw, zw) = (
            self.nodes.box_data(x).map_or(0, |b| b.width),
            self.nodes.box_data(z).map_or(0, |b| b.width),
        );
        if xw < zw {
            x = self.rebox(x, zw);
        } else {
            z = self.rebox(z, xw);
        }
        let (mut shift_up, mut shift_down) = if thickness == 0 {
            (
                self.math_par(mp::STACK_NUM_UP),
                self.math_par(mp::STACK_DENOM_DOWN),
            )
        } else {
            (
                self.math_par(mp::FRACTION_NUM_UP),
                self.math_par(mp::FRACTION_DENOM_DOWN),
            )
        };
        let (xh, xd) = self
            .nodes
            .box_data(x)
            .map_or((0, 0), |b| (b.height, b.depth));
        let (zh, zd) = self
            .nodes
            .box_data(z)
            .map_or((0, 0), |b| (b.height, b.depth));
        let axis = self.math_par(mp::AXIS);
        let delta;
        if thickness == 0 {
            let clr = self.math_par(mp::STACK_VGAP);
            delta = half(clr - ((shift_up - xd) - (zh - shift_down)));
            if delta > 0 {
                shift_up += delta;
                shift_down += delta;
            }
        } else {
            let exact = options & noad_opt::EXACT == noad_opt::EXACT;
            let (clr_n, clr_d) = if exact {
                (0, 0)
            } else if thickness == self.math_par(mp::FRACTION_RULE) {
                (
                    self.math_par(mp::FRACTION_NUM_VGAP),
                    self.math_par(mp::FRACTION_DENOM_VGAP),
                )
            } else if cs < 2 {
                (3 * thickness, 3 * thickness)
            } else {
                (thickness, thickness)
            };
            delta = half(thickness);
            let delta1 = clr_n - ((shift_up - xd) - (axis + delta));
            let delta2 = clr_d - ((axis - delta) - (zh - shift_down));
            if delta1 > 0 {
                shift_up += delta1;
            }
            if delta2 > 0 {
                shift_down += delta2;
            }
        }
        // Construct a vlist box for the fraction.
        let v = self.new_null_box_node(false);
        self.nodes.set_subtype(v, list_sub::FRACTION);
        let width = self.nodes.box_data(x).map_or(0, |b| b.width);
        if let Some(b) = self.nodes.box_data_mut(v) {
            b.height = shift_up + xh;
            b.depth = zd + shift_down;
            b.width = width;
        }
        let p;
        if thickness == 0 {
            p = self.new_kern_node((shift_up - xd) - (zh - shift_down), kern_sub::FONT);
            self.nodes.link(p, z);
        } else {
            let y = self.fraction_rule(thickness);
            let p2 = self.new_kern_node((axis - delta) - (zh - shift_down), kern_sub::FONT);
            self.nodes.link(y, p2);
            self.nodes.link(p2, z);
            p = self.new_kern_node((shift_up - xd) - (axis + delta), kern_sub::FONT);
            self.nodes.link(p, y);
        }
        self.nodes.link(x, p);
        self.nodes.set_list_ptr(v, x);
        // Put the fraction into a box with its delimiters.
        let dsize = self.math_par(mp::FRACTION_DEL_SIZE);
        let size = self.ts.math.size;
        // A null delimiter given explicitly (`\atopwithdelims..`) stays
        // on the baseline; a missing one (`\atop`) is centered on the axis
        // (observed).
        let lx = self.var_delimiter(left, size, dsize, left.is_null());
        self.nodes.link(lx, v);
        let rz = self.var_delimiter(right, size, dsize, right.is_null());
        self.nodes.link(v, rz);
        let h = self.hpack_quiet(lx);
        self.nodes.set_subtype(h, list_sub::FRACTION);
        self.set_new_hlist(q, h);
    }

    /// Builds an operator (`make_op`); returns the italic correction.
    fn make_op(&mut self, q: NodeRef) -> i32 {
        let cs = self.ts.math.style;
        if self.nodes.subtype(q) == noad_sub::OP_DISPLAY_LIMITS && cs < 2 {
            self.nodes.set_subtype(q, noad_sub::OP_LIMITS);
        }
        let limits = self.nodes.subtype(q) == noad_sub::OP_LIMITS;
        let nuc = self.noad_field(q, Field::Nucleus);
        let mut delta = 0;
        let mut opentype = false;
        if !nuc.is_null() && self.nodes.id(nuc) == id::MATH_CHAR {
            if let Some((f, c, m)) = self.fetch(nuc) {
                let mut m = m;
                if cs < 2 && self.is_opentype_math_font(f) {
                    // Observed (TeX Gyre Termes Math): the first variant
                    // at least DisplayOperatorMinHeight high (height plus
                    // depth), else the largest.
                    let target = self.math_par(mp::OPERATOR_SIZE);
                    let mut c = c;
                    let mut guard = 0;
                    while m.height + m.depth < target && guard < 64 {
                        guard += 1;
                        let (tag, rem) = self.char_tag(f, c);
                        let Some(m2) = self
                            .fonts
                            .char_metrics(f, rem)
                            .copied()
                            .filter(|_| tag == 2)
                        else {
                            break;
                        };
                        m = m2;
                        c = rem;
                    }
                    if let NodeData::MathChar { chr, .. } = self.nodes.data_mut(nuc) {
                        *chr = c;
                    }
                } else if cs < 2 {
                    let (tag, rem) = self.char_tag(f, c);
                    if tag == 2
                        && let Some(m2) = self.fonts.char_metrics(f, rem).copied()
                    {
                        m = m2;
                        if let NodeData::MathChar { chr, .. } = self.nodes.data_mut(nuc) {
                            *chr = rem;
                        }
                    }
                }
                delta = m.italic;
                opentype = self.is_opentype_math_font(f);
            }
            let x = self.clean_box(nuc, cs, list_sub::NUCLEUS);
            let has_sub = !self.noad_field(q, Field::Sub).is_null();
            let axis = self.math_par(mp::AXIS);
            if let Some(b) = self.nodes.box_data_mut(x) {
                if has_sub && !limits && !opentype {
                    b.width -= delta;
                }
                b.shift = half(b.height - b.depth) - axis;
            }
            self.set_nucleus_box(q, x);
            // An OpenType operator's box has no italic correction; with
            // \nolimits the subscript moves left by it (a font kern) and
            // a lone superscript is not moved.
            if opentype && !limits {
                if has_sub {
                    self.ts.math.op_kern = -delta;
                } else {
                    delta = 0;
                }
            }
        }
        if limits {
            // Construct a box with limits above and below it.
            let supk = self.noad_field(q, Field::Sup);
            let subk = self.noad_field(q, Field::Sub);
            let x = self.clean_box(supk, sup_style(cs), list_sub::SUP);
            let nk = self.noad_field(q, Field::Nucleus);
            let y = self.clean_box(nk, cs, list_sub::NUCLEUS);
            let z = self.clean_box(subk, sub_style(cs), list_sub::SUB);
            let v = self.new_null_box_node(false);
            self.nodes.set_subtype(v, list_sub::LIMITS);
            let wy = self.nodes.box_data(y).map_or(0, |b| b.width);
            let wx = self.nodes.box_data(x).map_or(0, |b| b.width);
            let wz = self.nodes.box_data(z).map_or(0, |b| b.width);
            let wv = wy.max(wx).max(wz);
            let x = self.rebox(x, wv);
            let y = self.rebox(y, wv);
            let z = self.rebox(z, wv);
            if let Some(b) = self.nodes.box_data_mut(x) {
                b.shift = half(delta);
            }
            if let Some(b) = self.nodes.box_data_mut(z) {
                b.shift = -half(delta);
            }
            let (yh, yd) = self
                .nodes
                .box_data(y)
                .map_or((0, 0), |b| (b.height, b.depth));
            let (mut vh, mut vd) = (yh, yd);
            let kern = self.math_par(mp::LIMIT_ABOVE_KERN);
            let kern_below = self.math_par(mp::LIMIT_BELOW_KERN);
            let head;
            if supk.is_null() {
                self.nodes.free(x);
                head = y;
            } else {
                let (xh, xd) = self
                    .nodes
                    .box_data(x)
                    .map_or((0, 0), |b| (b.height, b.depth));
                let mut shift_up = self.math_par(mp::LIMIT_ABOVE_BGAP) - xd;
                let g1 = self.math_par(mp::LIMIT_ABOVE_VGAP);
                if shift_up < g1 {
                    shift_up = g1;
                }
                let p = self.new_kern_node(shift_up, kern_sub::FONT);
                self.nodes.link(p, y);
                self.nodes.link(x, p);
                let p = self.new_kern_node(kern, kern_sub::FONT);
                self.nodes.link(p, x);
                head = p;
                vh += kern + xh + xd + shift_up;
            }
            if subk.is_null() {
                self.nodes.free(z);
            } else {
                let (zh, zd) = self
                    .nodes
                    .box_data(z)
                    .map_or((0, 0), |b| (b.height, b.depth));
                let mut shift_down = self.math_par(mp::LIMIT_BELOW_BGAP) - zh;
                let g2 = self.math_par(mp::LIMIT_BELOW_VGAP);
                if shift_down < g2 {
                    shift_down = g2;
                }
                let p = self.new_kern_node(shift_down, kern_sub::FONT);
                self.nodes.link(y, p);
                self.nodes.link(p, z);
                let p = self.new_kern_node(kern_below, kern_sub::FONT);
                self.nodes.link(z, p);
                vd += kern_below + zh + zd + shift_down;
            }
            if let Some(b) = self.nodes.box_data_mut(v) {
                b.width = wv;
                b.height = vh;
                b.depth = vd;
                b.head = head;
            }
            // The scripts are now part of the box.
            let a = self.take_field(q, Field::Sup);
            let b = self.take_field(q, Field::Sub);
            self.nodes.flush_list(a);
            self.nodes.flush_list(b);
            self.set_new_hlist(q, v);
        }
        delta
    }

    /// Ligatures and kerns between ordinary characters (`make_ord`).
    fn make_ord(&mut self, q: NodeRef) {
        'restart: loop {
            if !self.noad_field(q, Field::Sub).is_null()
                || !self.noad_field(q, Field::Sup).is_null()
            {
                return;
            }
            let nuc = self.noad_field(q, Field::Nucleus);
            if nuc.is_null() || self.nodes.id(nuc) != id::MATH_CHAR {
                return;
            }
            let p = self.nodes.next(q);
            if p.is_null()
                || self.nodes.id(p) != id::NOAD
                || !matches!(
                    self.nodes.subtype(p),
                    noad_sub::ORD
                        | noad_sub::OP_DISPLAY_LIMITS
                        | noad_sub::OP_LIMITS
                        | noad_sub::OP_NO_LIMITS
                        | noad_sub::BIN
                        | noad_sub::REL
                        | noad_sub::OPEN
                        | noad_sub::CLOSE
                        | noad_sub::PUNCT
                )
            {
                return;
            }
            let pn = self.noad_field(p, Field::Nucleus);
            if pn.is_null() || self.nodes.id(pn) != id::MATH_CHAR {
                return;
            }
            let (qfam, pfam, pchr) = match (self.nodes.data(nuc), self.nodes.data(pn)) {
                (NodeData::MathChar { fam: a, .. }, NodeData::MathChar { fam: b, chr }) => {
                    (*a, *b, *chr)
                }
                _ => return,
            };
            if qfam != pfam {
                return;
            }
            self.nodes.get_mut(nuc).id = id::MATH_TEXT_CHAR;
            let Some((f, c, _)) = self.fetch(nuc) else {
                return;
            };
            let Some(op) = self
                .lig_kern_step(f, c, pchr)
                .or_else(|| self.base_mode_kern(f, c, pchr))
            else {
                return;
            };
            match op {
                LigOp::Kern(k) => {
                    let kn = self.new_kern_node(k, kern_sub::FONT);
                    let n = self.nodes.next(q);
                    self.nodes.link(kn, n);
                    self.nodes.link(q, kn);
                    return;
                }
                LigOp::Lig { op, chr } => {
                    match op {
                        1 | 5 => self.set_char(nuc, chr),
                        2 | 6 => self.set_char(pn, chr),
                        3 | 7 | 11 => {
                            let r = self.new_noad(noad_sub::ORD);
                            let k = self.new_math_char(qfam, chr);
                            if op >= 11 {
                                self.nodes.get_mut(k).id = id::MATH_TEXT_CHAR;
                            }
                            self.set_noad_field(r, Field::Nucleus, k);
                            self.nodes.link(q, r);
                            self.nodes.link(r, p);
                        }
                        _ => {
                            let n = self.nodes.next(p);
                            self.nodes.link(q, n);
                            if n.is_null() {
                                self.nodes.set_next(q, NodeRef::NULL);
                            }
                            self.set_char(nuc, chr);
                            let a = self.take_field(p, Field::Sub);
                            let b = self.take_field(p, Field::Sup);
                            self.set_noad_field(q, Field::Sub, a);
                            self.set_noad_field(q, Field::Sup, b);
                            self.nodes.set_next(p, NodeRef::NULL);
                            self.nodes.flush_list(p);
                        }
                    }
                    if op > 3 {
                        return;
                    }
                    self.nodes.get_mut(nuc).id = id::MATH_CHAR;
                    continue 'restart;
                }
            }
        }
    }

    fn set_char(&mut self, k: NodeRef, c: u32) {
        if let NodeData::MathChar { chr, .. } = self.nodes.data_mut(k) {
            *chr = c;
        }
    }

    /// Converts the nucleus of `q` to an hlist and attaches the scripts
    /// (§754–§755).
    fn convert_nucleus(&mut self, q: NodeRef, delta: i32) {
        let mut delta = delta;
        let nuc = self.noad_field(q, Field::Nucleus);
        let kid = if nuc.is_null() { 0 } else { self.nodes.id(nuc) };
        let has_sub = !self.noad_field(q, Field::Sub).is_null();
        let p = match kid {
            id::MATH_CHAR | id::MATH_TEXT_CHAR => match self.fetch(nuc) {
                Some((f, c, m)) => {
                    delta = m.italic;
                    // The glyph and its italic correction take the
                    // character's attributes (observed).
                    let saved = self.attr_from(nuc);
                    let p = self.new_math_glyph(f, c);
                    let has_sup = !self.noad_field(q, Field::Sup).is_null();
                    if self.is_opentype_math_font(f) {
                        // Observed: an OpenType math character gets its
                        // italic correction before a character of the same
                        // family (a "text char"), before a superscript and
                        // in its scripts, but not otherwise.
                        if kid == id::MATH_CHAR && !has_sup && !has_sub {
                            delta = 0;
                        }
                    } else if kid == id::MATH_TEXT_CHAR
                        && self.font(f).params.get(2).copied().unwrap_or(0) != 0
                    {
                        delta = 0;
                    }
                    // Observed: an OpenType character's italic correction
                    // before another character takes the noad's attributes.
                    if kid == id::MATH_TEXT_CHAR && self.is_opentype_math_font(f) {
                        self.attr_restore(saved.clone());
                    }
                    if !has_sub && delta != 0 {
                        let k = self.new_kern_node(delta, kern_sub::ITALIC);
                        self.nodes.link(p, k);
                        delta = 0;
                    }
                    self.attr_restore(saved);
                    p
                }
                None => NodeRef::NULL,
            },
            id::SUB_BOX => {
                let b = self.nodes.list_ptr_kernel(nuc);
                self.nodes.set_kernel_list(nuc, NodeRef::NULL);
                let k = std::mem::take(&mut self.ts.math.op_kern);
                if k != 0 && !b.is_null() {
                    let kn = self.new_kern_node(k, kern_sub::FONT);
                    self.nodes.link(b, kn);
                }
                b
            }
            id::SUB_MLIST => {
                let l = self.nodes.list_ptr_kernel(nuc);
                self.nodes.set_kernel_list(nuc, NodeRef::NULL);
                let hl = self.clean_box_mlist(l, self.ts.math.style);
                // The box takes the sub-list's attributes (observed).
                let saved = self.attr_from(nuc);
                let b = self.hpack_quiet(hl);
                self.attr_restore(saved);
                b
            }
            _ => {
                // LuaTeX gives an empty nucleus with scripts an empty box.
                if has_sub || !self.noad_field(q, Field::Sup).is_null() {
                    self.new_null_box_node(true)
                } else {
                    NodeRef::NULL
                }
            }
        };
        self.set_new_hlist(q, p);
        let has_sup = !self.noad_field(q, Field::Sup).is_null();
        if !has_sub && !has_sup {
            return;
        }
        self.make_scripts(q, delta);
    }

    /// Attaches subscript and superscript (`make_scripts`).
    fn make_scripts(&mut self, q: NodeRef, delta: i32) {
        let p = self.get_new_hlist(q);
        let cs = self.ts.math.style;
        let (mut shift_up, mut shift_down);
        if !p.is_null() && self.nodes.is_glyph(p) {
            shift_up = 0;
            shift_down = 0;
        } else {
            let (h, d) = self.list_height_depth(p);
            shift_up = h - self.math_par(mp::SUP_SHIFT_DROP);
            shift_down = d + self.math_par(mp::SUB_SHIFT_DROP);
        }
        let opts = self.nodes.noad(q).map_or(0, |n| n.options);
        let supk = self.take_field(q, Field::Sup);
        let subk = self.take_field(q, Field::Sub);
        if !p.is_null() && self.nodes.is_glyph(p) {
            // LuaTeX looks at character scripts in the current size (for
            // OpenType math kerns), which reports undefined families.
            for k in [supk, subk] {
                if !k.is_null() && self.nodes.id(k) == id::MATH_CHAR {
                    let _ = self.fetch(k);
                }
            }
        }
        let script_space = self.math_par(mp::SPACE_AFTER_SCRIPT);
        let x;
        if supk.is_null() {
            // A subscript without superscript.
            let st = if opts & noad_opt::NO_SUB_SCRIPT == noad_opt::NO_SUB_SCRIPT {
                cs
            } else {
                sub_style(cs)
            };
            x = self.clean_box(subk, st, list_sub::SUB);
            self.nodes.flush_list(subk);
            let xh = self.nodes.box_data(x).map_or(0, |b| b.height);
            if let Some(b) = self.nodes.box_data_mut(x) {
                b.width += script_space;
            }
            let s1 = self.math_par(mp::SUB_SHIFT_DOWN);
            if shift_down < s1 {
                shift_down = s1;
            }
            let clr = xh - self.math_par(mp::SUB_TOP_MAX);
            if shift_down < clr {
                shift_down = clr;
            }
            if let Some(b) = self.nodes.box_data_mut(x) {
                b.shift = shift_down;
            }
        } else {
            let st = if opts & noad_opt::NO_SUPER_SCRIPT == noad_opt::NO_SUPER_SCRIPT {
                cs
            } else {
                sup_style(cs)
            };
            let sx = self.clean_box(supk, st, list_sub::SUP);
            self.nodes.flush_list(supk);
            let xd = self.nodes.box_data(sx).map_or(0, |b| b.depth);
            if let Some(b) = self.nodes.box_data_mut(sx) {
                b.width += script_space;
            }
            let clr = self.math_par(mp::SUP_SHIFT_UP);
            if shift_up < clr {
                shift_up = clr;
            }
            let clr = xd + self.math_par(mp::SUP_BOTTOM_MIN);
            if shift_up < clr {
                shift_up = clr;
            }
            if subk.is_null() {
                if let Some(b) = self.nodes.box_data_mut(sx) {
                    b.shift = -shift_up;
                }
                x = sx;
            } else {
                let st = if opts & noad_opt::NO_SUB_SCRIPT == noad_opt::NO_SUB_SCRIPT {
                    cs
                } else {
                    sub_style(cs)
                };
                let y = self.clean_box(subk, st, list_sub::SUB);
                self.nodes.flush_list(subk);
                let yh = self.nodes.box_data(y).map_or(0, |b| b.height);
                if let Some(b) = self.nodes.box_data_mut(y) {
                    b.width += script_space;
                }
                let s2 = self.math_par(mp::SUB_SUP_SHIFT_DOWN);
                if shift_down < s2 {
                    shift_down = s2;
                }
                let mut clr =
                    self.math_par(mp::SUB_SUP_VGAP) - ((shift_up - xd) - (yh - shift_down));
                if clr > 0 {
                    shift_down += clr;
                    clr = self.math_par(mp::SUP_SUB_BOTTOM_MAX) - (shift_up - xd);
                    if clr > 0 {
                        shift_up += clr;
                        shift_down -= clr;
                    }
                }
                if let Some(b) = self.nodes.box_data_mut(sx) {
                    b.shift = delta;
                }
                let p = self.new_kern_node((shift_up - xd) - (yh - shift_down), kern_sub::FONT);
                self.nodes.link(sx, p);
                self.nodes.link(p, y);
                x = self.vpack(sx, PackSpec::NATURAL);
                self.nodes.set_subtype(x, list_sub::SCRIPTS);
                if let Some(b) = self.nodes.box_data_mut(x) {
                    b.shift = shift_down;
                }
            }
        }
        let nh = self.get_new_hlist(q);
        if nh.is_null() {
            self.set_new_hlist(q, x);
        } else {
            let t = self.nodes.tail_of(nh);
            self.nodes.link(t, x);
        }
    }

    /// The box of `\Uvextensible`, as observed in LuaTeX: without a
    /// height and depth the delimiter's smallest variant, unshifted;
    /// otherwise the variant for their sum, centered on the baseline (on
    /// the axis with `axis`), in a box as high and deep as asked (raised
    /// by the axis with `axis`), or as the delimiter with `exact`.
    fn extensible_fence(
        &mut self,
        delim: NodeRef,
        height: i32,
        depth: i32,
        options: u32,
        axis: i32,
    ) -> NodeRef {
        let size = self.ts.math.size;
        if height == 0 && depth == 0 {
            let b = self.var_delimiter(delim, size, 0, false);
            if let Some(bd) = self.nodes.box_data_mut(b) {
                bd.shift = 0;
            }
            return b;
        }
        let up = if options & noad_opt::AXIS == noad_opt::AXIS {
            axis
        } else {
            0
        };
        let b = self.var_delimiter(delim, size, height + depth, false);
        if let Some(bd) = self.nodes.box_data_mut(b) {
            bd.shift = half(bd.height - bd.depth) - up;
        }
        let w = self.hpack_quiet(b);
        if options & noad_opt::EXACT != noad_opt::EXACT
            && let Some(bd) = self.nodes.box_data_mut(w)
        {
            bd.height = height + up;
            bd.depth = depth - up;
        }
        w
    }

    /// Builds the delimiter of a fence (`make_left_right`).
    fn make_left_right(&mut self, q: NodeRef, style: i32, max_d: i32, max_h: i32) -> NoadType {
        self.set_cur_style(style);
        let (delim, height, depth, options) = match self.nodes.data(q) {
            NodeData::Fence(f) => (f.delim, f.height, f.depth, f.options),
            _ => (NodeRef::NULL, 0, 0, 0),
        };
        let axis = self.math_par(mp::AXIS);
        if self.nodes.subtype(q) == fence_sub::NO {
            let b = self.extensible_fence(delim, height, depth, options, axis);
            self.set_new_hlist(q, b);
            return NoadType::Close;
        }
        let b = if height != 0 || depth != 0 {
            let total = height + depth;
            let b = self.var_delimiter(delim, self.ts.math.size, total, true);
            if options & noad_opt::NO_AXIS == noad_opt::NO_AXIS
                && let Some(bd) = self.nodes.box_data_mut(b)
            {
                bd.shift = 0;
            }
            b
        } else {
            let mut delta2 = max_d + axis;
            let mut delta1 = max_h + max_d - delta2;
            if delta2 > delta1 {
                delta1 = delta2;
            }
            let mut delta = (delta1 / 500) * self.eqtb.int(ip::DELIMITERFACTOR);
            delta2 = delta1 + delta1 - self.eqtb.dimen(dp::DELIMITERSHORTFALL);
            if delta < delta2 {
                delta = delta2;
            }
            self.var_delimiter(delim, self.ts.math.size, delta, false)
        };
        self.set_new_hlist(q, b);
        if self.nodes.subtype(q) == fence_sub::LEFT {
            NoadType::Open
        } else {
            NoadType::Close
        }
    }

    // ----- the second pass ---------------------------------------------

    fn second_pass(
        &mut self,
        mlist: NodeRef,
        style: i32,
        penalties: bool,
        max_h: i32,
        max_d: i32,
    ) -> NodeRef {
        let head = self.nodes.new_temp();
        let mut p = head;
        let mut q = mlist;
        let mut r_type: Option<NoadType> = None;
        self.set_cur_style(style);
        let binpen = self.eqtb.int(ip::BINOPPENALTY);
        let relpen = self.eqtb.int(ip::RELPENALTY);
        while !q.is_null() {
            let next = self.nodes.next(q);
            let Some(nt) = self.noad_type(q) else {
                if let NodeData::Style { style } = self.nodes.data(q) {
                    let s = i32::from(*style);
                    self.set_cur_style(s);
                    self.nodes.free(q);
                } else {
                    self.nodes.link(p, q);
                    self.nodes.set_next(q, NodeRef::NULL);
                    p = q;
                }
                q = next;
                continue;
            };
            let mut t = NoadType::Ord;
            let mut pen = 10000;
            match nt {
                NoadType::Op
                | NoadType::Open
                | NoadType::Close
                | NoadType::Punct
                | NoadType::Inner => t = nt,
                NoadType::Bin => {
                    t = NoadType::Bin;
                    pen = binpen;
                }
                NoadType::Rel => {
                    t = NoadType::Rel;
                    pen = relpen;
                }
                NoadType::Fraction => t = NoadType::Inner,
                NoadType::Left | NoadType::Right => {
                    let saved = self.attr_from(q);
                    t = self.make_left_right(q, style, max_d, max_h);
                    self.attr_restore(saved);
                }
                _ => {}
            }
            // Inter-element spacing.
            if let Some(rt) = r_type {
                let style = self.ts.math.style as u32;
                if let Some((g, sub)) = self.math_spacing(rt as u32, t as u32, style) {
                    let y = self.math_glue(g, self.ts.math.mu);
                    // Observed: the glue takes the attributes of the node
                    // before it.
                    let saved = self.attr_from(p);
                    let z = self.new_glue_node(y, sub);
                    self.attr_restore(saved);
                    self.nodes.link(p, z);
                    p = z;
                }
            }
            // Append the new_hlist entries and penalties.
            let nh = self.get_new_hlist(q);
            self.set_new_hlist(q, NodeRef::NULL);
            if !nh.is_null() {
                self.nodes.link(p, nh);
                p = self.nodes.tail_of(nh);
            }
            if penalties && !next.is_null() && pen < 10000 {
                let nid = self.nodes.id(next);
                let next_is_rel = self.noad_type(next) == Some(NoadType::Rel);
                if nid != id::PENALTY && !next_is_rel {
                    // Observed: the penalty takes the noad's attributes.
                    let saved = self.attr_from(q);
                    let z = self.new_penalty_node(pen);
                    self.attr_restore(saved);
                    self.nodes.set_subtype(z, 5);
                    self.nodes.link(p, z);
                    p = z;
                }
            }
            if nt == NoadType::Right {
                t = NoadType::Open;
            }
            r_type = Some(t);
            // delete_q:
            self.nodes.set_next(q, NodeRef::NULL);
            self.nodes.flush_list(q);
            q = next;
        }
        let first = self.nodes.next(head);
        self.nodes.free(head);
        if !first.is_null() {
            self.nodes.set_prev(first, NodeRef::NULL);
        }
        first
    }
}

#[derive(Clone, Copy, PartialEq, Eq)]
enum Action {
    Convert,
    CheckDimensions,
    DoneWithNoad,
}