retex_engine/

math.rs

//! Building math lists (*TeX: The Program* §1136–§1206, with e-TeX's
//! `\middle` and LuaTeX's extensions).
//!
//! A formula is read into an mlist of noads (see [`crate::nodes`]), which
//! [`crate::mlist`] converts into an hlist when the formula ends. LuaTeX
//! differences implemented here (established with black-box tests):
//!
//! * there is no "insufficient symbol fonts" check;
//! * `\mathchar`, `\Umathchar` and math characters given by `\mathchardef`
//!   are accepted in horizontal mode, where they typeset the character
//!   from the text font of the family (vertical mode starts a paragraph);
//! * the `Missing delimiter` help text has no full stop after "proceed";
//! * the `\Umath…` variants (`\Uradical`, `\Uroot`, `\Umathaccent`,
//!   `\Uleft`, `\Uskewed`, `\Ustack`, `\Usuperscript`, …) are supported with
//!   their keywords.

use std::rc::Rc;

use crate::Engine;
use crate::build::PackSpec;
use crate::cmd::Cmd;
use crate::eqtb::{Loc, Val};
use crate::input::TokKind;
use crate::maincontrol::{IGNORE_DEPTH, Mode};
use crate::nodes::{
    DEFAULT_CODE, FenceData, FractionData, NodeData, NodeRef, accent_sub, fence_sub, id, noad_opt,
    noad_sub, radical_sub,
};
use crate::primitives_gen::{assign_dimen as dp, assign_int as ip, assign_toks as tp};
use crate::save::GroupCode;
use crate::token::Token;

/// A noad field that `scan_math` fills.
#[derive(Clone, Copy, Debug, PartialEq, Eq)]
pub enum Field {
    /// The nucleus.
    Nucleus = 0,
    /// The superscript.
    Sup = 1,
    /// The subscript.
    Sub = 2,
    /// The degree of a `\Uroot`.
    Degree = 3,
}

impl Field {
    fn from_i64(v: i64) -> Field {
        match v & 3 {
            0 => Field::Nucleus,
            1 => Field::Sup,
            2 => Field::Sub,
            _ => Field::Degree,
        }
    }
}

fn field_ref(noad: NodeRef, f: Field) -> i64 {
    (i64::from(noad.0) << 2) | f as i64
}

fn field_from_ref(v: i64) -> (NodeRef, Field) {
    (NodeRef((v >> 2) as u32), Field::from_i64(v))
}

/// A math character: class (0–7, 8 for "math active"), family, character.
#[derive(Clone, Copy, Debug, PartialEq, Eq)]
pub struct MathChar {
    /// The class.
    pub class: u32,
    /// The family.
    pub fam: u32,
    /// The character.
    pub chr: u32,
}

impl MathChar {
    /// A `math_given` value (see [`Engine::scan_math_given`]).
    pub fn from_given(g: u32) -> MathChar {
        if g & crate::codes::MATH_GIVEN_PACKED != 0 {
            MathChar::from_packed(i64::from(g & !crate::codes::MATH_GIVEN_PACKED))
        } else {
            MathChar::from_classic(g as i32)
        }
    }

    /// Decodes TeX's 15-bit form (`"8000` is math active).
    pub fn from_classic(c: i32) -> MathChar {
        if c >= 0x8000 {
            return MathChar {
                class: 8,
                fam: 0,
                chr: 0,
            };
        }
        let c = c.max(0) as u32;
        MathChar {
            class: c >> 12,
            fam: (c >> 8) & 0xF,
            chr: c & 0xFF,
        }
    }

    /// Decodes LuaTeX's packed form (`\Umathcharnum`, `\mathcode`).
    pub fn from_packed(v: i64) -> MathChar {
        if v == crate::codes::MATH_ACTIVE {
            return MathChar {
                class: 8,
                fam: 0,
                chr: 0,
            };
        }
        MathChar {
            class: crate::codes::math_class(v),
            fam: crate::codes::math_fam(v),
            chr: crate::codes::math_char(v),
        }
    }
}

/// The parts (small family, small character, large family, large
/// character) of an internal delimiter code, or `None` for −1.
pub fn delcode_parts(v: i64) -> Option<(u32, u32, u32, u32)> {
    if v < 0 {
        return None;
    }
    if v & (1 << 62) != 0 {
        Some((
            ((v >> 53) & 0xF) as u32,
            ((v >> 32) & 0xFF) as u32,
            ((v >> 21) & 0xF) as u32,
            (v & 0xFF) as u32,
        ))
    } else {
        Some((((v >> 21) & 0xFF) as u32, (v & 0x1F_FFFF) as u32, 0, 0))
    }
}

/// The noad subtype for a math class.
fn class_subtype(class: u32) -> u16 {
    match class {
        1 => noad_sub::OP_DISPLAY_LIMITS,
        2 => noad_sub::BIN,
        3 => noad_sub::REL,
        4 => noad_sub::OPEN,
        5 => noad_sub::CLOSE,
        6 => noad_sub::PUNCT,
        _ => noad_sub::ORD,
    }
}

/// `cramped_style`.
pub const fn cramped_style(s: i32) -> i32 {
    2 * (s / 2) + 1
}

/// `sub_style`.
pub const fn sub_style(s: i32) -> i32 {
    2 * (s / 4) + 4 + 1
}

/// `sup_style`.
pub const fn sup_style(s: i32) -> i32 {
    2 * (s / 4) + 4 + (s % 2)
}

/// `num_style`.
pub const fn num_style(s: i32) -> i32 {
    s + 2 - 2 * (s / 6)
}

/// `denom_style`.
pub const fn denom_style(s: i32) -> i32 {
    2 * (s / 2) + 1 + 2 - 2 * (s / 6)
}

impl Engine {
    // ----- node constructors ------------------------------------------

    /// A new noad of the given subtype with empty fields (`new_noad`).
    pub fn new_noad(&mut self, sub: u16) -> NodeRef {
        self.new_node(id::NOAD, sub, NodeData::Noad(Box::default()))
    }

    /// A new `math_char` kernel.
    pub fn new_math_char(&mut self, fam: u32, chr: u32) -> NodeRef {
        self.new_node(id::MATH_CHAR, 0, NodeData::MathChar { fam, chr })
    }

    /// A new `sub_box` or `sub_mlist` kernel.
    pub fn new_sub_list(&mut self, mlist: bool, head: NodeRef) -> NodeRef {
        self.new_node(
            if mlist { id::SUB_MLIST } else { id::SUB_BOX },
            0,
            NodeData::SubList { head },
        )
    }

    /// A new delimiter node.
    pub fn new_delim(&mut self, parts: (u32, u32, u32, u32)) -> NodeRef {
        self.new_node(
            id::DELIM,
            0,
            NodeData::Delim {
                small_fam: parts.0,
                small_char: parts.1,
                large_fam: parts.2,
                large_char: parts.3,
            },
        )
    }

    /// A new style node.
    pub fn new_style(&mut self, s: u8) -> NodeRef {
        self.new_node(id::STYLE, u16::from(s), NodeData::Style { style: s })
    }

    /// The kernel in field `f` of noad `p`.
    pub fn noad_field(&self, p: NodeRef, f: Field) -> NodeRef {
        match self.nodes.noad(p) {
            Some(n) => match f {
                Field::Nucleus => n.nucleus,
                Field::Sup => n.sup,
                Field::Sub => n.sub,
                Field::Degree => n.degree,
            },
            None => NodeRef::NULL,
        }
    }

    /// Replaces the kernel in field `f` of noad `p` (the old one is not
    /// freed).
    pub fn set_noad_field(&mut self, p: NodeRef, f: Field, k: NodeRef) {
        if let Some(n) = self.nodes.noad_mut(p) {
            match f {
                Field::Nucleus => n.nucleus = k,
                Field::Sup => n.sup = k,
                Field::Sub => n.sub = k,
                Field::Degree => n.degree = k,
            }
        }
    }

    // ----- entering math mode -----------------------------------------

    /// Enters a math level (`push_math`).
    fn push_math(&mut self, c: GroupCode, style: i32) {
        self.push_nest(Mode::Math);
        self.cur_list_mut().incompleat_noad = NodeRef::NULL;
        self.cur_list_mut().math_style = style;
        self.new_save_level(c);
        if c == GroupCode::MathShift {
            self.begin_math_dirs();
        }
    }

    /// `$` in horizontal mode (`init_math`).
    pub fn init_math(&mut self) {
        let shift_cs = self.cur_cmd == Cmd::MathShiftCs;
        let display = if shift_cs {
            // \Ustartmath (2) or \Ustartdisplaymath (0).
            self.cur_chr == 0 && self.mode == Mode::Horizontal
        } else {
            self.get_token();
            if self.cur_cmd == Cmd::MathShift && self.mode == Mode::Horizontal {
                true
            } else {
                self.back_input();
                false
            }
        };
        if display {
            self.go_into_display_math();
        } else {
            self.go_into_ordinary_math();
        }
    }

    fn go_into_ordinary_math(&mut self) {
        self.push_math(GroupCode::MathShift, 2);
        self.eq_define(Loc::IntPar(ip::FAM), Val::Int(-1));
        let t = self.eqtb.toks_param(tp::EVERYMATH).clone();
        if !t.is_empty() {
            self.begin_token_list(t, TokKind::EveryMathText);
        }
    }

    /// Starts a display: breaks the paragraph so far into lines and
    /// computes `\predisplaysize`, `\displaywidth` and `\displayindent`.
    fn go_into_display_math(&mut self) {
        let max_dimen = 0o7777777777;
        let mut w = -max_dimen;
        let (head, tail) = (self.cur_list().head, self.cur_list().tail);
        let only_local_par = self.nodes.next(head) == tail
            && matches!(self.nodes.data(tail), NodeData::LocalPar { .. });
        if head == tail || only_local_par {
            // `\noindent$$` or `$${ }$$`.
            if only_local_par {
                self.nodes.flush_list(tail);
                self.nodes.set_next(head, NodeRef::NULL);
            }
            self.pop_nest();
        } else {
            let wp = self.eqtb.int(ip::DISPLAYWIDOWPENALTY);
            self.line_break(wp);
            w = self.pre_display_width();
        }
        // Now in vertical mode: the length and shift of the display lines.
        let prev_graf = self.cur_list().prev_graf;
        let (l, s) = self.display_line_size(prev_graf);
        self.push_math(GroupCode::MathShift, 0);
        self.mode = Mode::DisplayMath;
        self.cur_list_mut().mode = Mode::DisplayMath;
        self.eq_define(Loc::IntPar(ip::FAM), Val::Int(-1));
        self.eq_define(Loc::DimenPar(dp::PREDISPLAYSIZE), Val::Int(i64::from(w)));
        self.eq_define(Loc::DimenPar(dp::DISPLAYWIDTH), Val::Int(i64::from(l)));
        self.eq_define(Loc::DimenPar(dp::DISPLAYINDENT), Val::Int(i64::from(s)));
        let t = self.eqtb.toks_param(tp::EVERYDISPLAY).clone();
        if !t.is_empty() {
            self.begin_token_list(t, TokKind::EveryDisplayText);
        }
        if self.nest.len() == 2 {
            self.build_page();
        }
    }

    /// The natural width by which the last line of the paragraph before a
    /// display extends to the right, plus two quads (`\predisplaygapfactor`
    /// thousandths of a quad); `max_dimen` if it depends on glue setting.
    fn pre_display_width(&mut self) -> i32 {
        let max_dimen = 0o7777777777;
        let jb = self.ts.just_box;
        if jb.is_null() {
            return -max_dimen;
        }
        let Some(b) = self.nodes.box_data(jb).cloned() else {
            return -max_dimen;
        };
        let f = self.eqtb.cur_font.val;
        let gap = self.eqtb.int(ip::PREDISPLAYGAPFACTOR);
        let q = self.quad(f);
        // Observed: (quad div 1000) * \predisplaygapfactor.
        let extra = (q / 1000).wrapping_mul(gap);
        let mut v = b.shift + extra;
        let mut w = -max_dimen;
        let mut p = b.head;
        while !p.is_null() {
            let (d, visible) = match self.nodes.data(p) {
                NodeData::Glyph(_) => (self.glyph_dimensions(p).0, true),
                NodeData::Box(bx) => (bx.width, true),
                NodeData::Rule { width, .. } => (*width, true),
                NodeData::Kern { kern, .. } => (*kern, false),
                NodeData::MarginKern { width, .. } => (*width, false),
                NodeData::Math { .. } => (self.nodes.width(p), false),
                NodeData::Glue { spec, .. } => {
                    let spec = *spec;
                    if b.glue_sign == 1 {
                        if b.glue_order == spec.stretch_order && spec.stretch != 0 {
                            v = max_dimen;
                        }
                    } else if b.glue_sign == 2
                        && b.glue_order == spec.shrink_order
                        && spec.shrink != 0
                    {
                        v = max_dimen;
                    }
                    (
                        spec.width,
                        self.nodes.subtype(p) >= crate::nodes::glue_sub::A_LEADERS,
                    )
                }
                _ => (0, false),
            };
            if visible {
                if v < max_dimen {
                    v += d;
                    w = v;
                } else {
                    w = max_dimen;
                    break;
                }
            } else if v < max_dimen {
                v += d;
            }
            p = self.nodes.next(p);
        }
        w
    }

    /// The length and shift of line `prev_graf + 2` (§1149).
    fn display_line_size(&self, prev_graf: i32) -> (i32, i32) {
        let hsize = self.eqtb.dimen(dp::HSIZE);
        match &self.eqtb.par_shape.val {
            None => {
                let hi = self.eqtb.dimen(dp::HANGINDENT);
                let ha = self.eqtb.int(ip::HANGAFTER);
                if hi != 0 && ((ha >= 0 && prev_graf + 2 > ha) || (prev_graf + 1 < -ha)) {
                    (hsize - hi.abs(), if hi > 0 { hi } else { 0 })
                } else {
                    (hsize, 0)
                }
            }
            Some(shape) => {
                let n = (shape.len() / 2) as i32;
                let i = if prev_graf + 2 >= n { n } else { prev_graf + 2 };
                let k = 2 * (i.max(1) as usize - 1);
                let indent = shape.get(k).copied().unwrap_or(0);
                let len = shape.get(k + 1).copied().unwrap_or(hsize);
                (len, indent)
            }
        }
    }

    // ----- the main switch --------------------------------------------

    /// Commands in math mode (the `mmode+…` cases of `main_control`).
    pub fn math_command(&mut self) {
        let cmd = self.cur_cmd;
        match cmd {
            Cmd::Letter | Cmd::OtherChar | Cmd::CharGiven => {
                let code = self.eqtb.math.get(self.cur_chr);
                self.set_math_char(MathChar::from_packed(code));
            }
            Cmd::CharNum => {
                self.scan_char_num();
                self.cur_chr = self.cur_val as u32;
                let code = self.eqtb.math.get(self.cur_chr);
                self.set_math_char(MathChar::from_packed(code));
            }
            Cmd::MathCharNum => {
                let mc = self.scan_math_char_num();
                self.set_math_char(mc);
            }
            Cmd::MathGiven => {
                let mc = MathChar::from_given(self.cur_chr);
                self.set_math_char(mc);
            }
            Cmd::XmathGiven => {
                let mc = MathChar::from_packed(i64::from(self.cur_chr));
                self.set_math_char(mc);
            }
            Cmd::DelimNum => {
                let mc = self.scan_delim_num_char();
                self.set_math_char(mc);
            }
            Cmd::LeftBrace => {
                let n = self.new_noad(noad_sub::ORD);
                self.tail_append(n);
                self.back_input();
                let st = self.cur_list().math_style;
                self.scan_math(n, Field::Nucleus, st);
            }
            Cmd::MathComp => {
                let sub = self.cur_chr as u16;
                let n = self.new_noad(sub);
                self.tail_append(n);
                let st = self.cur_list().math_style;
                let st = if sub == noad_sub::OVER || sub == noad_sub::UNDER {
                    if sub == noad_sub::OVER {
                        cramped_style(st)
                    } else {
                        st
                    }
                } else {
                    st
                };
                self.scan_math(n, Field::Nucleus, st);
            }
            Cmd::LimitSwitch => self.math_limit_switch(),
            Cmd::SupMark | Cmd::SubMark => {
                let sup = cmd == Cmd::SupMark;
                self.sub_sup(sup, false);
            }
            Cmd::SuperSubScript => {
                let sup = self.cur_chr == Cmd::SupMark as u32;
                self.sub_sup(sup, false);
            }
            Cmd::NoSuperSubScript => {
                let sup = self.cur_chr == Cmd::SupMark as u32;
                self.sub_sup(sup, true);
            }
            Cmd::Radical => self.math_radical(),
            Cmd::Accent | Cmd::MathAccent => self.math_ac(),
            Cmd::Vcenter => {
                self.scan_spec(GroupCode::Vcenter, None);
                self.normal_paragraph();
                self.push_nest(Mode::InternalVertical);
                self.cur_list_mut().prev_depth = IGNORE_DEPTH;
                let t = self.eqtb.toks_param(tp::EVERYVBOX).clone();
                if !t.is_empty() {
                    self.begin_token_list(t, TokKind::EveryVboxText);
                }
            }
            Cmd::MathStyle => {
                let s = self.cur_chr.min(7) as u8;
                let n = self.new_style(s);
                self.tail_append(n);
                self.cur_list_mut().math_style = i32::from(s);
            }
            Cmd::NonScript => {
                let g = self.new_glue_node(
                    crate::glue::Glue::ZERO,
                    crate::nodes::glue_sub::COND_MATH_GLUE,
                );
                self.tail_append(g);
            }
            Cmd::MathChoice => {
                if self.cur_chr == 0 {
                    self.append_choices();
                } else {
                    // \Ustack: a subformula in numerator style.
                    let n = self.new_noad(noad_sub::ORD);
                    self.tail_append(n);
                    let st = num_style(self.cur_list().math_style);
                    self.scan_left_brace();
                    let sub = self.new_sub_list(true, NodeRef::NULL);
                    self.set_noad_field(n, Field::Nucleus, sub);
                    self.push_saved(field_ref(n, Field::Nucleus));
                    self.push_math(GroupCode::Math, st);
                }
            }
            Cmd::Above => self.math_fraction(),
            Cmd::MathShift => {
                if self.save.cur_group == GroupCode::MathShift {
                    self.after_math();
                } else {
                    self.off_save();
                }
            }
            Cmd::MathShiftCs => {
                // \Ustopmath (3) and \Ustopdisplaymath (1) end the
                // formula; the start commands are not allowed here.
                let c = self.cur_chr;
                let ok = (c == 3 && self.mode == Mode::Math)
                    || (c == 1 && self.mode == Mode::DisplayMath);
                if (c == 1 || c == 3) && self.save.cur_group == GroupCode::MathShift && ok {
                    self.after_math();
                } else if c == 1 || c == 3 {
                    if self.save.cur_group == GroupCode::MathShift {
                        self.print_err("Invalid math code");
                        self.help(&["I'm going to ignore this math shift command."]);
                        self.error();
                    } else {
                        self.off_save();
                    }
                } else {
                    self.report_illegal_case();
                }
            }
            Cmd::EqNo => {
                if self.privileged() {
                    if self.save.cur_group == GroupCode::MathShift {
                        self.start_eq_no();
                    } else {
                        self.off_save();
                    }
                }
            }
            Cmd::LeftRight => self.math_left_right(),
            Cmd::Endv
            | Cmd::ParEnd
            | Cmd::Stop
            | Cmd::Vskip
            | Cmd::UnVbox
            | Cmd::Valign
            | Cmd::Hrule => self.insert_dollar_sign(),
            Cmd::Halign => {
                if self.privileged() {
                    if self.save.cur_group == GroupCode::MathShift {
                        self.init_align();
                    } else {
                        self.off_save();
                    }
                }
            }
            _ => {
                let (c, r) = (self.cur_cmd, self.cur_chr);
                let s = self.print_to_string(|e| e.print_cmd_chr(c, r));
                self.not_implemented(&String::from_utf8_lossy(&s));
            }
        }
    }

    /// `\mathchar`, `\Umathchar` and `\Umathcharnum`.
    fn scan_math_char_num(&mut self) -> MathChar {
        match self.cur_chr {
            0 => {
                let g = self.scan_math_given();
                MathChar::from_given(g)
            }
            1 => {
                let v = self.scan_umath_triple();
                MathChar::from_packed(v)
            }
            _ => {
                self.scan_int();
                MathChar::from_packed(i64::from(self.cur_val))
            }
        }
    }

    /// `\delimiter` (its 15-bit part) and `\Udelimiter` as a math character.
    fn scan_delim_num_char(&mut self) -> MathChar {
        if self.cur_chr == 0 {
            self.scan_twenty_seven_bit_int();
            MathChar::from_classic(self.cur_val / 0o10000)
        } else {
            let v = self.scan_umath_triple();
            MathChar::from_packed(v)
        }
    }

    /// Whether `\fam` is a valid family (`fam_in_range`).
    fn fam_in_range(&self) -> Option<u32> {
        let f = self.eqtb.int(ip::FAM);
        if (0..crate::eqtb::NUM_FAMILIES as i32).contains(&f) {
            Some(f as u32)
        } else {
            None
        }
    }

    /// The family of a math character, taking class 7 and `\fam` into
    /// account.
    fn effective_fam(&self, mc: MathChar) -> u32 {
        if mc.class == 7
            && let Some(f) = self.fam_in_range()
        {
            return f;
        }
        let vf = self.eqtb.int(ip::VARIABLEFAM);
        if vf >= 0
            && mc.fam == vf as u32
            && let Some(f) = self.fam_in_range()
        {
            return f;
        }
        mc.fam
    }

    /// Treats `cur_chr` as an active character (§1152).
    fn treat_as_active(&mut self) {
        let cs = self.hash.active(self.cur_chr);
        self.cur_cs = cs;
        let m = self.eqtb.meaning(cs).clone();
        self.cur_cmd = m.cmd;
        self.cur_chr = m.chr;
        self.x_token();
        self.back_input();
    }

    /// Appends a noad for a math character (`set_math_char`).
    fn set_math_char(&mut self, mc: MathChar) {
        if mc.class >= 8 {
            self.treat_as_active();
            return;
        }
        let fam = self.effective_fam(mc);
        let k = self.new_math_char(fam, mc.chr);
        let sub = class_subtype(mc.class);
        let p = self.new_noad(sub);
        self.set_noad_field(p, Field::Nucleus, k);
        self.tail_append(p);
    }

    /// Fills field `f` of noad `p` with the next math character or
    /// subformula (`scan_math`); `style` is the style of a subformula.
    /// Returns true if a subformula group was opened.
    fn scan_math(&mut self, p: NodeRef, f: Field, style: i32) -> bool {
        self.scan_math_flag(p, f, style, 0)
    }

    /// [`scan_math`](Self::scan_math) with extra bits in the saved field
    /// reference (bit 62: scan the nucleus when the group ends).
    fn scan_math_flag(&mut self, p: NodeRef, f: Field, style: i32, flag: i64) -> bool {
        self.get_nonblank_nonrelax_noncall();
        let mc = loop {
            match self.cur_cmd {
                Cmd::Letter | Cmd::OtherChar | Cmd::CharGiven => {
                    let code = self.eqtb.math.get(self.cur_chr);
                    let mc = MathChar::from_packed(code);
                    if mc.class == 8 {
                        self.treat_as_active();
                        self.get_nonblank_nonrelax_noncall();
                        continue;
                    }
                    break mc;
                }
                Cmd::CharNum => {
                    self.scan_char_num();
                    self.cur_chr = self.cur_val as u32;
                    self.cur_cmd = Cmd::CharGiven;
                }
                Cmd::MathCharNum => break self.scan_math_char_num(),
                Cmd::MathGiven => break MathChar::from_given(self.cur_chr),
                Cmd::XmathGiven => break MathChar::from_packed(i64::from(self.cur_chr)),
                Cmd::DelimNum => break self.scan_delim_num_char(),
                _ => {
                    // A subformula enclosed in braces.
                    self.back_input();
                    self.scan_left_brace();
                    let sub = self.new_sub_list(true, NodeRef::NULL);
                    let old = self.noad_field(p, f);
                    self.nodes.flush_list(old);
                    self.set_noad_field(p, f, sub);
                    self.push_saved(field_ref(p, f) | flag);
                    self.push_math(GroupCode::Math, style);
                    return true;
                }
            }
        };
        self.finish_scan_math(p, f, mc);
        false
    }

    fn finish_scan_math(&mut self, p: NodeRef, f: Field, mc: MathChar) {
        let fam = if mc.class == 8 {
            0
        } else {
            self.effective_fam(mc)
        };
        let k = self.new_math_char(fam, mc.chr);
        let old = self.noad_field(p, f);
        self.nodes.flush_list(old);
        self.set_noad_field(p, f, k);
    }

    /// `\limits`, `\nolimits`, `\displaylimits` (`math_limit_switch`).
    fn math_limit_switch(&mut self) {
        let (head, tail) = (self.cur_list().head, self.cur_list().tail);
        if head != tail
            && self.nodes.id(tail) == id::NOAD
            && matches!(
                self.nodes.subtype(tail),
                noad_sub::OP_DISPLAY_LIMITS | noad_sub::OP_LIMITS | noad_sub::OP_NO_LIMITS
            )
        {
            self.nodes.set_subtype(tail, self.cur_chr as u16);
            return;
        }
        self.print_err("Limit controls must follow a math operator");
        self.help(&["I'm ignoring this misplaced \\limits or \\nolimits command."]);
        self.error();
    }

    /// Scans a delimiter (`scan_delimiter`); `radical` selects TeX's
    /// 27-bit form, `fam_char` LuaTeX's `<fam> <char>` form. Returns a new
    /// delimiter node.
    fn scan_delimiter(&mut self, radical: bool, fam_char: bool) -> NodeRef {
        let parts: Option<(u32, u32, u32, u32)> = if fam_char {
            self.scan_math_family();
            let fam = self.cur_val as u32;
            self.scan_char_num();
            Some((fam, self.cur_val as u32, 0, 0))
        } else if radical {
            self.scan_twenty_seven_bit_int();
            classic_delimiter(self.cur_val)
        } else {
            self.get_nonblank_nonrelax_noncall();
            match self.cur_cmd {
                Cmd::Letter | Cmd::OtherChar => delcode_parts(self.eqtb.del.get(self.cur_chr)),
                Cmd::DelimNum => {
                    if self.cur_chr == 0 {
                        self.scan_twenty_seven_bit_int();
                        classic_delimiter(self.cur_val)
                    } else {
                        let v = self.scan_umath_triple();
                        let mc = MathChar::from_packed(v);
                        Some((mc.fam, mc.chr, 0, 0))
                    }
                }
                _ => None,
            }
        };
        let parts = match parts {
            Some(p) => p,
            None => {
                self.print_err("Missing delimiter (. inserted)");
                self.help(&[
                    "I was expecting to see something like `(' or `\\{' or",
                    "`\\}' here. If you typed, e.g., `{' instead of `\\{', you",
                    "should probably delete the `{' by typing `1' now, so that",
                    "braces don't get unbalanced. Otherwise just proceed",
                    "Acceptable delimiters are characters whose \\delcode is",
                    "nonnegative, or you can use `\\delimiter <delimiter code>'.",
                ]);
                self.back_error();
                (0, 0, 0, 0)
            }
        };
        self.new_delim(parts)
    }

    /// `\radical` and LuaTeX's radical-like commands (`math_radical`).
    fn math_radical(&mut self) {
        let c = self.cur_chr as u16;
        let p = self.new_node(id::RADICAL, c, NodeData::Noad(Box::default()));
        self.tail_append(p);
        let mut opts = 0u32;
        let mut width = 0i32;
        if c == radical_sub::UHEXTENSIBLE || c >= radical_sub::UUNDERDELIMITER {
            loop {
                if self.scan_keyword("width") {
                    self.scan_normal_dimen();
                    width = self.cur_val;
                } else if self.scan_keyword("left") {
                    opts |= noad_opt::LEFT;
                } else if self.scan_keyword("middle") {
                    opts |= noad_opt::MIDDLE;
                } else if self.scan_keyword("right") {
                    opts |= noad_opt::RIGHT;
                } else {
                    break;
                }
            }
        }
        let d = self.scan_delimiter(c == radical_sub::RADICAL, c != radical_sub::RADICAL);
        if let Some(n) = self.nodes.noad_mut(p) {
            n.left = d;
            n.options = opts;
            n.width = width;
        }
        let st = self.cur_list().math_style;
        match c {
            radical_sub::UHEXTENSIBLE => {}
            radical_sub::UROOT => {
                // The degree first, then the radicand. The degree is a
                // subformula in scriptscript style.
                // The radicand follows when the degree group ends.
                if !self.scan_math_flag(p, Field::Degree, 6, 1 << 62) {
                    self.scan_math(p, Field::Nucleus, cramped_style(st));
                }
            }
            radical_sub::UUNDERDELIMITER => {
                self.scan_math(p, Field::Nucleus, sub_style(st));
            }
            radical_sub::UOVERDELIMITER => {
                self.scan_math(p, Field::Nucleus, sup_style(st));
            }
            radical_sub::UDELIMITERUNDER => {
                self.scan_math(p, Field::Nucleus, st);
            }
            _ => {
                self.scan_math(p, Field::Nucleus, cramped_style(st));
            }
        }
    }

    /// Scans `[fixed] <class> <fam> <char>` for `\Umathaccent`.
    fn scan_accent_char(&mut self, umath: bool) -> (NodeRef, bool) {
        let fixed = umath && self.scan_keyword("fixed");
        let mc = if umath {
            let v = self.scan_umath_triple();
            MathChar::from_packed(v)
        } else {
            let g = self.scan_math_given();
            MathChar::from_given(g)
        };
        let fam = if mc.class == 8 {
            0
        } else {
            self.effective_fam(mc)
        };
        (self.new_math_char(fam, mc.chr), fixed)
    }

    /// `\mathaccent` and `\Umathaccent` (`math_ac`).
    fn math_ac(&mut self) {
        if self.cur_cmd == Cmd::Accent {
            self.back_input();
            self.get_token();
            self.print_err("Please use ");
            self.print_esc_str("mathaccent");
            self.printer.print_str(" for accents in math mode");
            self.help(&[
                "I'm changing \\accent to \\mathaccent here; wish me luck.",
                "(Accents are not the same in formulas as they are in text.)",
            ]);
            self.error();
        }
        let umath = self.cur_cmd == Cmd::MathAccent && self.cur_chr == 1;
        let p = self.new_node(
            id::ACCENT,
            accent_sub::BOTH_FLEXIBLE,
            NodeData::Noad(Box::default()),
        );
        self.tail_append(p);
        let mut sub = accent_sub::BOTH_FLEXIBLE;
        let (mut top, mut bot) = (NodeRef::NULL, NodeRef::NULL);
        let fraction = 0;
        let mut overlay = false;
        if umath {
            let (want_top, want_bot) = if self.scan_keyword("bottom") {
                (false, true)
            } else if self.scan_keyword("both") {
                (true, true)
            } else if self.scan_keyword("overlay") {
                overlay = true;
                (true, false)
            } else {
                let _ = self.scan_keyword("top");
                (true, false)
            };
            if want_top {
                let (k, fixed) = self.scan_accent_char(true);
                top = k;
                if fixed {
                    sub |= accent_sub::FIXED_TOP;
                }
            }
            if want_bot {
                let (k, fixed) = self.scan_accent_char(true);
                bot = k;
                if fixed {
                    sub |= accent_sub::FIXED_BOTTOM;
                }
            }
        } else {
            top = self.scan_accent_char(false).0;
        }
        self.nodes.set_subtype(p, sub);
        if let Some(n) = self.nodes.noad_mut(p) {
            n.accent = top;
            n.bot_accent = bot;
            n.fraction = fraction;
            if overlay {
                n.options |= noad_opt::OVERLAY;
            }
        }
        let st = cramped_style(self.cur_list().math_style);
        self.scan_math(p, Field::Nucleus, st);
    }

    /// `^` and `_` (`sub_sup`); `no_style` is set for `\Unosuperscript`
    /// and `\Unosubscript`.
    fn sub_sup(&mut self, sup: bool, no_style: bool) {
        let field = if sup { Field::Sup } else { Field::Sub };
        let (head, tail) = (self.cur_list().head, self.cur_list().tail);
        let mut target = NodeRef::NULL;
        let mut t_nonempty = false;
        if tail != head && self.nodes.scripts_allowed(tail) {
            target = tail;
            t_nonempty = !self.noad_field(tail, field).is_null();
        }
        if target.is_null() || t_nonempty {
            // Observed: the new noad's nucleus is an empty sub-list.
            let n = self.new_noad(noad_sub::ORD);
            let k = self.new_sub_list(true, NodeRef::NULL);
            self.set_noad_field(n, Field::Nucleus, k);
            self.tail_append(n);
            target = n;
            if t_nonempty {
                if sup {
                    self.print_err("Double superscript");
                    self.help(&["I treat `x^1^2' essentially like `x^1{}^2'."]);
                } else {
                    self.print_err("Double subscript");
                    self.help(&["I treat `x_1_2' essentially like `x_1{}_2'."]);
                }
                self.error();
            }
        }
        let st = self.cur_list().math_style;
        let style = if no_style {
            if let Some(n) = self.nodes.noad_mut(target) {
                n.options |= if sup {
                    noad_opt::NO_SUPER_SCRIPT
                } else {
                    noad_opt::NO_SUB_SCRIPT
                };
            }
            st
        } else if sup {
            sup_style(st)
        } else {
            sub_style(st)
        };
        self.scan_math(target, field, style);
    }

    /// `\over`, `\atop`, `\above` and their variants (`math_fraction`).
    fn math_fraction(&mut self) {
        let c = self.cur_chr;
        // LuaTeX codes: above 0, over 1, atop 2, skewed 3; +4 with delims.
        let delimited = c >= 4;
        let kind = c % 4;
        if !self.cur_list().incompleat_noad.is_null() {
            if delimited {
                let a = self.scan_delimiter(false, false);
                let b = self.scan_delimiter(false, false);
                self.nodes.flush_list(a);
                self.nodes.flush_list(b);
            }
            if kind == 3 {
                let m = self.scan_delimiter(false, false);
                self.nodes.flush_list(m);
                self.scan_fraction_options();
            } else if kind == 0 {
                let _ = self.scan_keyword("exact");
                self.scan_normal_dimen();
            }
            self.print_err("Ambiguous; you need another { and }");
            self.help(&[
                "I'm ignoring this fraction specification, since I don't",
                "know whether a construction like `x \\over y \\over z'",
                "means `{x \\over y} \\over z' or `x \\over {y \\over z}'.",
            ]);
            self.error();
            return;
        }
        let head = self.cur_list().head;
        let first = self.nodes.next(head);
        let num = self.new_sub_list(true, first);
        let mut fr = FractionData {
            thickness: DEFAULT_CODE,
            num,
            denom: NodeRef::NULL,
            left: NodeRef::NULL,
            right: NodeRef::NULL,
            middle: NodeRef::NULL,
            options: 0,
            new_hlist: NodeRef::NULL,
        };
        self.nodes.set_next(head, NodeRef::NULL);
        self.cur_list_mut().tail = head;
        if delimited {
            fr.left = self.scan_delimiter(false, false);
            fr.right = self.scan_delimiter(false, false);
        }
        match kind {
            0 => {
                if self.scan_keyword("exact") {
                    fr.options |= noad_opt::EXACT;
                }
                self.scan_normal_dimen();
                fr.thickness = self.cur_val;
            }
            1 => fr.thickness = DEFAULT_CODE,
            2 => fr.thickness = 0,
            _ => {
                fr.middle = self.scan_delimiter(false, false);
                fr.options |= self.scan_fraction_options();
                fr.thickness = 0;
            }
        }
        let n = self.new_node(id::FRACTION, 0, NodeData::Fraction(Box::new(fr)));
        self.cur_list_mut().incompleat_noad = n;
        // The denominator is read in the cramped style (observed with
        // \mathstyle; in \Ustack this gives the denominator style).
        let st = cramped_style(self.cur_list().math_style);
        self.cur_list_mut().math_style = st;
    }

    /// The `noaxis`/`exact` options of `\Uskewed`.
    fn scan_fraction_options(&mut self) -> u32 {
        let mut o = 0;
        loop {
            if self.scan_keyword("noaxis") {
                o |= noad_opt::NO_AXIS;
            } else if self.scan_keyword("exact") {
                o |= noad_opt::EXACT;
            } else {
                return o;
            }
        }
    }

    /// Finishes the current mlist and pops the nest (`fin_mlist`); `p`, if
    /// not null, is a right (or middle) fence ending the list.
    fn fin_mlist(&mut self, p: NodeRef) -> NodeRef {
        let inc = self.cur_list().incompleat_noad;
        let head = self.cur_list().head;
        let q;
        if !inc.is_null() {
            let first = self.nodes.next(head);
            let denom = self.new_sub_list(true, first);
            if let NodeData::Fraction(f) = self.nodes.data_mut(inc) {
                f.denom = denom;
            }
            if p.is_null() {
                q = inc;
            } else {
                // A \left…\over…\right: the left fence (and any middle
                // fences up to delim_ptr) stays outside the fraction.
                let num = match self.nodes.data(inc) {
                    NodeData::Fraction(f) => f.num,
                    _ => NodeRef::NULL,
                };
                let num_list = self.nodes.list_ptr_kernel(num);
                q = num_list;
                let dp = self.cur_list().delim_ptr;
                if num_list.is_null() || self.nodes.id(num_list) != id::FENCE || dp.is_null() {
                    self.confusion("right");
                }
                let after = self.nodes.next(dp);
                self.nodes.set_kernel_list(num, after);
                if !after.is_null() {
                    self.nodes.set_prev(after, NodeRef::NULL);
                }
                self.nodes.link(dp, inc);
                self.nodes.link(inc, p);
            }
        } else {
            let tail = self.cur_list().tail;
            self.nodes.link(tail, p);
            q = self.nodes.next(head);
        }
        self.nodes.set_next(head, NodeRef::NULL);
        if !q.is_null() {
            self.nodes.set_prev(q, NodeRef::NULL);
        }
        self.pop_nest();
        q
    }

    /// Right braces ending math groups, `\mathchoice` groups and
    /// `\vcenter` (cases of `handle_right_brace`).
    pub fn math_right_brace(&mut self) {
        match self.save.cur_group {
            GroupCode::Math => {
                self.unsave();
                let r = self.pop_saved();
                let root_follows = r & (1 << 62) != 0;
                let (noad, f) = field_from_ref(r & !(1 << 62));
                let p = self.fin_mlist(NodeRef::NULL);
                let k = self.noad_field(noad, f);
                self.nodes.set_kernel_list(k, p);
                if !p.is_null() && self.nodes.next(p).is_null() {
                    let pid = self.nodes.id(p);
                    // Observed: \mathflattenmode says which single noads
                    // are flattened (1 ord, 2 bin, 4 rel, 8 punct,
                    // 16 inner).
                    let flatten = self.eqtb.int(ip::MATHFLATTENMODE);
                    let bit = match self.nodes.subtype(p) {
                        noad_sub::ORD => 1,
                        noad_sub::BIN => 2,
                        noad_sub::REL => 4,
                        noad_sub::PUNCT => 8,
                        noad_sub::INNER => 16,
                        _ => 0,
                    };
                    if pid == id::NOAD && flatten & bit != 0 {
                        let (sub, sup) = (
                            self.noad_field(p, Field::Sub),
                            self.noad_field(p, Field::Sup),
                        );
                        if sub.is_null() && sup.is_null() {
                            // {x}: the field becomes x's nucleus.
                            let nuc = self.noad_field(p, Field::Nucleus);
                            self.set_noad_field(p, Field::Nucleus, NodeRef::NULL);
                            self.nodes.flush_list(p);
                            self.nodes.set_kernel_list(k, NodeRef::NULL);
                            self.nodes.flush_list(k);
                            self.set_noad_field(noad, f, nuc);
                        }
                    } else if pid == id::ACCENT
                        && f == Field::Nucleus
                        && noad == self.cur_list().tail
                        && self.nodes.id(noad) == id::NOAD
                        && self.nodes.subtype(noad) == noad_sub::ORD
                    {
                        // Replace the tail of the list by the accent noad.
                        let head = self.cur_list().head;
                        let mut q = head;
                        while self.nodes.next(q) != noad {
                            q = self.nodes.next(q);
                        }
                        self.nodes.set_kernel_list(k, NodeRef::NULL);
                        self.nodes.link(q, p);
                        self.nodes.set_next(noad, NodeRef::NULL);
                        self.nodes.flush_list(noad);
                        self.cur_list_mut().tail = p;
                    }
                }
                if root_follows {
                    let st = cramped_style(self.cur_list().math_style);
                    self.scan_math(noad, Field::Nucleus, st);
                }
            }
            GroupCode::MathChoice => self.build_choices(),
            GroupCode::Vcenter => {
                if self.par_token_before_group_end(1) {
                    return;
                }
                self.end_graf();
                self.unsave();
                let (spec, _dir) = self.pop_spec_pub();
                let head = self.cur_list().head;
                let first = self.nodes.next(head);
                self.nodes.set_next(head, NodeRef::NULL);
                let first = self.filter_list("vpack_filter", first, "vcenter");
                let d = self.eqtb.dimen(dp::BOXMAXDEPTH);
                let b = self.vpackage(first, spec, d);
                self.pop_nest();
                let n = self.new_noad(noad_sub::VCENTER);
                let k = self.new_sub_list(false, b);
                self.set_noad_field(n, Field::Nucleus, k);
                self.tail_append(n);
            }
            _ => self.confusion("rightbrace"),
        }
    }

    /// `\mathchoice` (`append_choices`).
    fn append_choices(&mut self) {
        let c = self.new_node(
            id::CHOICE,
            0,
            NodeData::Choice(Box::new([NodeRef::NULL; 4])),
        );
        self.tail_append(c);
        self.push_saved(0);
        self.push_math(GroupCode::MathChoice, 0);
        self.scan_left_brace();
    }

    /// The end of one of the four `\mathchoice` lists (`build_choices`).
    fn build_choices(&mut self) {
        self.unsave();
        let p = self.fin_mlist(NodeRef::NULL);
        let k = self.pop_saved();
        let tail = self.cur_list().tail;
        if let NodeData::Choice(c) = self.nodes.data_mut(tail) {
            c[(k as usize).min(3)] = p;
        }
        if k >= 3 {
            return;
        }
        self.push_saved(k + 1);
        self.push_math(GroupCode::MathChoice, 2 * (k as i32 + 1));
        self.scan_left_brace();
    }

    /// `\left`, `\middle`, `\right` and their `\U…` forms
    /// (`math_left_right`).
    fn math_left_right(&mut self) {
        let c = self.cur_chr;
        // LuaTeX codes: left 1, middle 2, right 3; \Uleft 11, \Umiddle 12,
        // \Uright 13, \Uvextensible 14.
        if c == 14 {
            self.math_vextensible();
            return;
        }
        let t = match c % 10 {
            1 => fence_sub::LEFT,
            2 => fence_sub::MIDDLE,
            _ => fence_sub::RIGHT,
        };
        if t != fence_sub::LEFT && self.save.cur_group != GroupCode::MathLeft {
            if self.save.cur_group == GroupCode::MathShift {
                // LuaTeX reads the delimiter without checking it.
                self.get_nonblank_nonrelax_noncall();
                if self.cur_cmd == Cmd::DelimNum {
                    if self.cur_chr == 0 {
                        self.scan_twenty_seven_bit_int();
                    } else {
                        self.scan_umath_triple();
                    }
                }
                self.print_err("Extra ");
                if t == fence_sub::MIDDLE {
                    self.print_esc_str("middle");
                    self.help(&["I'm ignoring a \\middle that had no matching \\left."]);
                } else {
                    self.print_esc_str("right");
                    self.help(&["I'm ignoring a \\right that had no matching \\left."]);
                }
                self.error();
            } else {
                self.off_save();
            }
            return;
        }
        let mut fe = FenceData {
            class: -1,
            ..FenceData::default()
        };
        if c >= 10 {
            loop {
                if self.scan_keyword("height") {
                    self.scan_normal_dimen();
                    fe.height = self.cur_val;
                } else if self.scan_keyword("depth") {
                    self.scan_normal_dimen();
                    fe.depth = self.cur_val;
                } else if self.scan_keyword("axis") {
                    fe.options |= noad_opt::AXIS;
                } else if self.scan_keyword("noaxis") {
                    fe.options |= noad_opt::NO_AXIS;
                } else if self.scan_keyword("exact") {
                    fe.options |= noad_opt::EXACT;
                } else if self.scan_keyword("class") {
                    self.scan_int();
                    fe.class = self.cur_val;
                } else {
                    break;
                }
            }
        }
        fe.delim = self.scan_delimiter(false, false);
        let p = self.new_node(id::FENCE, t, NodeData::Fence(Box::new(fe)));
        let q = if t == fence_sub::LEFT {
            p
        } else {
            let q = self.fin_mlist(p);
            self.unsave();
            q
        };
        if t != fence_sub::RIGHT {
            let st = self.cur_list().math_style;
            self.push_math(GroupCode::MathLeft, st);
            let head = self.cur_list().head;
            self.nodes.link(head, q);
            self.cur_list_mut().tail = p;
            self.cur_list_mut().delim_ptr = p;
        } else {
            let n = self.new_noad(noad_sub::INNER);
            let k = self.new_sub_list(true, q);
            self.set_noad_field(n, Field::Nucleus, k);
            self.tail_append(n);
        }
    }

    /// `\Uvextensible`: a stand-alone extensible delimiter.
    fn math_vextensible(&mut self) {
        let mut fe = FenceData {
            class: -1,
            ..FenceData::default()
        };
        loop {
            if self.scan_keyword("height") {
                self.scan_normal_dimen();
                fe.height = self.cur_val;
            } else if self.scan_keyword("depth") {
                self.scan_normal_dimen();
                fe.depth = self.cur_val;
            } else if self.scan_keyword("axis") {
                fe.options |= noad_opt::AXIS;
            } else if self.scan_keyword("noaxis") {
                fe.options |= noad_opt::NO_AXIS;
            } else if self.scan_keyword("exact") {
                fe.options |= noad_opt::EXACT;
            } else {
                break;
            }
        }
        fe.delim = self.scan_delimiter(false, false);
        // Observed: a fence of subtype "no".
        let p = self.new_node(id::FENCE, fence_sub::NO, NodeData::Fence(Box::new(fe)));
        let n = self.new_noad(noad_sub::INNER);
        let k = self.new_sub_list(true, p);
        self.set_noad_field(n, Field::Nucleus, k);
        self.tail_append(n);
    }

    /// `\eqno` and `\leqno` in display math (`start_eq_no`).
    fn start_eq_no(&mut self) {
        self.push_saved(i64::from(self.cur_chr));
        self.go_into_ordinary_math();
    }

    /// Appends a box in math mode as an ord noad with a `sub_box`
    /// nucleus (§1076).
    pub fn math_box_end(&mut self, b: NodeRef) {
        let n = self.new_noad(noad_sub::ORD);
        let k = self.new_sub_list(false, b);
        self.set_noad_field(n, Field::Nucleus, k);
        self.tail_append(n);
    }

    /// Mathchars in horizontal mode: LuaTeX typesets the character in the
    /// text font of its family.
    pub fn math_char_in_text(&mut self) {
        let mc = match self.cur_cmd {
            Cmd::MathCharNum => self.scan_math_char_num(),
            Cmd::MathGiven => MathChar::from_given(self.cur_chr),
            _ => MathChar::from_packed(i64::from(self.cur_chr)),
        };
        if mc.class >= 8 {
            self.treat_as_active();
            return;
        }
        let f = self.fam_fnt(mc.fam, 0);
        let g = self.new_char_node(f, mc.chr);
        self.tail_append(g);
        self.cur_list_mut().space_factor = 1000;
    }

    /// The font of family `fam` in size `size` (0 text, 1 script,
    /// 2 scriptscript): `fam_fnt`.
    pub fn fam_fnt(&self, fam: u32, size: u32) -> u32 {
        self.eqtb
            .math_font
            .get((size * crate::eqtb::NUM_FAMILIES as u32 + fam) as usize)
            .map_or(0, |s| s.val)
    }

    // ----- leaving math mode ------------------------------------------

    /// The end of a formula (`after_math`).
    fn after_math(&mut self) {
        let mut m = self.mode;
        let mut l = false;
        let mut p = self.fin_mlist(NodeRef::NULL);
        let a;
        if self.mode == Mode::DisplayMath && m == Mode::Math {
            // The end of an equation number.
            self.check_dollar_follows();
            let hl = self.formula_to_hlist(p, 2, false);
            a = self.hpack(hl, PackSpec::NATURAL);
            self.take_outer_math_dirs();
            self.unsave();
            if self.pop_saved() == 1 {
                l = true;
            }
            m = self.mode;
            p = self.fin_mlist(NodeRef::NULL);
        } else {
            a = NodeRef::NULL;
        }
        if m == Mode::Math {
            self.finish_math_in_text(p);
        } else {
            if a.is_null() {
                self.check_dollar_follows();
            }
            self.finish_displayed_math(p, a, l);
        }
    }

    /// The math and text directions outside the formula whose group is
    /// the current one.
    fn take_outer_math_dirs(&mut self) -> Option<(i32, i32)> {
        let level = self.save.cur_level;
        while let Some(&(l, m, t)) = self.outer_math_dirs.last() {
            if l < level {
                break;
            }
            self.outer_math_dirs.pop();
            if l == level {
                return Some((m, t));
            }
        }
        None
    }

    /// Checks that a second `$` ends a display.
    fn check_dollar_follows(&mut self) {
        self.get_x_token();
        if self.cur_cmd != Cmd::MathShift
            && !(self.cur_cmd == Cmd::MathShiftCs && self.cur_chr == 1)
        {
            self.print_err("Display math should end with $$");
            self.help(&[
                "The `$' that I just saw supposedly matches a previous `$$'.",
                "So I shall assume that you typed `$$' both times.",
            ]);
            self.back_error();
        }
    }

    fn finish_math_in_text(&mut self, p: NodeRef) {
        let ms = self.eqtb.dimen(dp::MATHSURROUND);
        let mg = self
            .eqtb
            .glue(crate::primitives_gen::assign_glue::MATHSURROUNDSKIP);
        let pen = self.mode == Mode::Horizontal;
        // As in TeX, the formula's group ends last: the opening math node
        // is the tail while the mlist_to_hlist callback runs (luamml reads
        // it), and the nodes take the attributes inside the formula.
        // A formula whose direction differs from the text's is wrapped in
        // direction nodes (see `dirs`).
        // The directions are those outside the formula.
        let (math_dir, text_dir) = self.take_outer_math_dirs().unwrap_or((
            self.dir_param(crate::primitives_gen::assign_dir::MATHDIR),
            self.dir_param(crate::primitives_gen::assign_dir::TEXTDIR),
        ));
        let wrap = (math_dir != text_dir).then(|| math_dir.rem_euclid(4) as i8);
        let b = self.new_math_node(ms, mg, 0);
        self.tail_append(b);
        if let Some(d) = wrap {
            let p = self.new_dir_node(d, false);
            self.tail_append(p);
        }
        let hl = self.formula_to_hlist(p, 2, pen);
        let tail = self.cur_list().tail;
        self.nodes.link(tail, hl);
        let mut t = tail;
        while !self.nodes.next(t).is_null() {
            t = self.nodes.next(t);
        }
        self.cur_list_mut().tail = t;
        if let Some(d) = wrap {
            let p = self.new_dir_node(d, true);
            self.tail_append(p);
        }
        let e = self.new_math_node(ms, mg, 1);
        self.tail_append(e);
        self.cur_list_mut().space_factor = 1000;
        self.unsave();
    }

    /// A math node with `\mathsurround` and `\mathsurroundskip`.
    fn new_math_node(&mut self, surround: i32, skip: crate::glue::Glue, sub: u16) -> NodeRef {
        let p = self.new_node(
            id::MATH,
            sub,
            NodeData::Math {
                surround,
                glue: crate::glue::Glue::ZERO,
            },
        );
        if (skip.width != 0 || skip.stretch != 0 || skip.shrink != 0)
            && let NodeData::Math { glue, .. } = self.nodes.data_mut(p)
        {
            *glue = skip;
        }
        p
    }

    /// Places a finished display (§1199–§1205).
    fn finish_displayed_math(&mut self, p: NodeRef, a: NodeRef, l: bool) {
        use crate::nodes::glue_sub as gs;
        self.take_outer_math_dirs();
        let hl = self.formula_to_hlist(p, 0, false);
        let adj_head = self.nodes.new_temp();
        self.ts.adjust_tail = Some(adj_head);
        let mut b = self.hpack(hl, PackSpec::NATURAL);
        let p = self.nodes.list_ptr(b);
        let t = self.ts.adjust_tail.unwrap_or(adj_head);
        self.ts.adjust_tail = None;
        let mut w = self.nodes.box_data(b).map_or(0, |x| x.width);
        let z = self.eqtb.dimen(dp::DISPLAYWIDTH);
        let s = self.eqtb.dimen(dp::DISPLAYINDENT);
        let (mut e, q) = if a.is_null() {
            (0, 0)
        } else {
            let e = self.nodes.box_data(a).map_or(0, |x| x.width);
            let f2 = self.fam_fnt(2, 0);
            let mq = self.math_quad_text(f2);
            let step = self.eqtb.int(ip::MATHEQNOGAPSTEP);
            let gap = if step == 1000 {
                mq
            } else {
                retex_arith::xn_over_d(mq, step, 1000).map_or(0, |r| r.quotient)
            };
            (e, e + gap)
        };
        if w + q > z {
            // Squeeze the equation as much as possible.
            let tot = self.ts.last_totals;
            if e != 0
                && (w - tot.1[0] + q <= z
                    || tot.1[1] != 0
                    || tot.1[2] != 0
                    || tot.1[3] != 0
                    || tot.1[4] != 0)
            {
                self.nodes.set_list_ptr(b, NodeRef::NULL);
                self.nodes.free(b);
                b = self.hpack(p, PackSpec::Exactly(z - q));
            } else {
                e = 0;
                if w > z {
                    self.nodes.set_list_ptr(b, NodeRef::NULL);
                    self.nodes.free(b);
                    b = self.hpack(p, PackSpec::Exactly(z));
                }
            }
            w = self.nodes.box_data(b).map_or(0, |x| x.width);
        }
        self.nodes.set_subtype(b, 6); // equation
        // The displacement of the left edge of the equation.
        let mut d = half(z - w);
        if e > 0 && d < 2 * e {
            d = half(z - w - e);
            let p = self.nodes.list_ptr(b);
            if !p.is_null() && self.nodes.id(p) == id::GLUE {
                d = 0;
            }
        }
        // The glue or equation number preceding the display.
        let pen = self.new_penalty_node(self.eqtb.int(ip::PREDISPLAYPENALTY));
        self.tail_append(pen);
        let pds = self.eqtb.dimen(dp::PREDISPLAYSIZE);
        let (g1, mut g2) = if d + s <= pds || l {
            (gs::ABOVE_DISPLAY, gs::BELOW_DISPLAY)
        } else {
            (gs::ABOVE_DISPLAY_SHORT, gs::BELOW_DISPLAY_SHORT)
        };
        let mode = self.eqtb.int(ip::MATHDISPLAYSKIPMODE);
        if l && e == 0 {
            if let Some(bd) = self.nodes.box_data_mut(a) {
                bd.shift = s;
            }
            self.nodes.set_subtype(a, 7);
            self.append_to_vlist(a);
            let pen = self.new_penalty_node(10000);
            self.tail_append(pen);
        } else {
            self.append_display_skip(g1, mode, true);
        }
        // The display and perhaps the equation number. LuaTeX packs an
        // equation with its number into a box of the display width:
        // kern d, equation, kern, number (or number, kern, equation,
        // kern d for \leqno), not shifted by d.
        if e != 0 {
            let r = self.new_kern_node(z - w - e - d, 0);
            self.nodes.set_subtype(a, 7);
            // Observed: the kern after a \leqno equation is z - w - d
            // (which makes the line wider than z when d was reduced).
            let k = self.new_kern_node(if l { z - w - d } else { d }, 0);
            if l {
                self.nodes.link(a, r);
                self.nodes.link(r, b);
                self.nodes.link(b, k);
                b = a;
            } else {
                self.nodes.link(k, b);
                self.nodes.link(b, r);
                self.nodes.link(r, a);
                b = k;
            }
            b = self.hpack(b, PackSpec::NATURAL);
            d = 0;
        }
        if let Some(bd) = self.nodes.box_data_mut(b) {
            bd.shift = s + d;
        }
        self.append_to_vlist(b);
        // The glue or equation number following the display.
        if !a.is_null() && e == 0 && !l {
            let pen = self.new_penalty_node(10000);
            self.tail_append(pen);
            let aw = self.nodes.box_data(a).map_or(0, |x| x.width);
            if let Some(bd) = self.nodes.box_data_mut(a) {
                bd.shift = s + z - aw;
            }
            self.nodes.set_subtype(a, 7);
            self.append_to_vlist(a);
            g2 = 0;
        }
        if t != adj_head {
            let first = self.nodes.next(adj_head);
            let tail = self.cur_list().tail;
            self.nodes.link(tail, first);
            self.cur_list_mut().tail = t;
        }
        self.nodes.free(adj_head);
        let pen = self.new_penalty_node(self.eqtb.int(ip::POSTDISPLAYPENALTY));
        self.tail_append(pen);
        if g2 > 0 {
            self.append_display_skip(g2, mode, false);
        }
        self.resume_after_display();
    }

    /// Appends `\abovedisplayskip` and friends, honouring
    /// `\mathdisplayskipmode` (0 and 1: TeX's rule, an above skip always
    /// and a below skip always; 2: only when not zero; 3: never).
    fn append_display_skip(&mut self, sub: u16, mode: i32, _above: bool) {
        let g = self.eqtb.glue(crate::build::glue_param_of_subtype(sub));
        let zero = g.width == 0 && g.stretch == 0 && g.shrink == 0;
        let skip = match mode {
            2 => zero,
            3 => true,
            _ => false,
        };
        if !skip {
            let n = self.new_param_glue(sub);
            self.tail_append(n);
        }
    }

    /// `math_quad(text_size)` from the font in family 2.
    fn math_quad_text(&self, f2: u32) -> i32 {
        let v = self.math_param_value(0, 2);
        if v != crate::codes::UNDEFINED_MATH_PARAM {
            v
        } else {
            self.quad(f2)
        }
    }

    /// The value of math parameter `p` in style `s`.
    pub fn math_param_value(&self, p: u32, s: u32) -> i32 {
        self.eqtb
            .math_param
            .get(&(p * 8 + s))
            .map_or(crate::codes::UNDEFINED_MATH_PARAM, |x| x.val)
    }

    /// Resumes the paragraph after a display (`resume_after_display`).
    fn resume_after_display(&mut self) {
        if self.save.cur_group != GroupCode::MathShift {
            self.confusion("display");
        }
        self.unsave();
        let pg = self.cur_list().prev_graf + 3;
        self.cur_list_mut().prev_graf = pg;
        self.push_nest(Mode::Horizontal);
        self.cur_list_mut().space_factor = 1000;
        let l = self.cur_lang() as i32;
        self.cur_list_mut().clang = l;
        let lp = self.new_local_par();
        self.tail_append(lp);
        // Scan an optional space.
        self.get_x_token();
        if self.cur_cmd != Cmd::Spacer {
            self.back_input();
        }
        if self.nest.len() == 2 {
            self.build_page();
        }
    }

    /// Finishes an alignment in a display (§1206).
    pub fn finish_display_alignment(&mut self, p: NodeRef, q: NodeRef, aux_save: i32) {
        self.do_assignments();
        if self.cur_cmd != Cmd::MathShift {
            self.print_err("Missing $$ inserted");
            self.help(&[
                "Displays can use special alignments (like \\eqalignno)",
                "only if nothing but the alignment itself is between $$'s.",
            ]);
            self.back_error();
        } else {
            self.check_dollar_follows();
        }
        self.pop_nest();
        let pen = self.new_penalty_node(self.eqtb.int(ip::PREDISPLAYPENALTY));
        self.tail_append(pen);
        let g = self.new_param_glue(crate::nodes::glue_sub::ABOVE_DISPLAY);
        self.tail_append(g);
        let tail = self.cur_list().tail;
        self.nodes.link(tail, p);
        if !p.is_null() {
            self.cur_list_mut().tail = q;
        }
        let pen = self.new_penalty_node(self.eqtb.int(ip::POSTDISPLAYPENALTY));
        self.tail_append(pen);
        let g = self.new_param_glue(crate::nodes::glue_sub::BELOW_DISPLAY);
        self.tail_append(g);
        self.cur_list_mut().prev_depth = aux_save;
        self.resume_after_display();
    }

    /// Empties the current math list (`flush_math`).
    pub fn flush_math(&mut self) {
        let head = self.cur_list().head;
        let first = self.nodes.next(head);
        self.nodes.flush_list(first);
        let inc = self.cur_list().incompleat_noad;
        self.nodes.flush_list(inc);
        self.nodes.set_next(head, NodeRef::NULL);
        self.cur_list_mut().tail = head;
        self.cur_list_mut().incompleat_noad = NodeRef::NULL;
    }

    /// Inserts the tokens of a list as if typed (used by error recovery).
    pub fn ins_tokens(&mut self, toks: Vec<Token>) {
        self.ins_list(Rc::from(toks));
    }
}

pub use retex_arith::half;

/// The parts of a TeX 27-bit delimiter code.
fn classic_delimiter(v: i32) -> Option<(u32, u32, u32, u32)> {
    if v < 0 {
        return None;
    }
    let v = v as u32;
    Some((
        (v / 0o4000000) % 16,
        (v / 0o10000) % 256,
        (v / 256) % 16,
        v % 256,
    ))
}