sva-samples 0.6.0

// Concern: truncates every series to the terms the profile leaves, once per collapse | Non-concern: evaluating what is left (point.rs) | IO: (&SpectralSum or &Body) -> the same, series-free

use std::f64::consts::TAU;

use sva_formula::affine::{Axis, axis, exact_constant};
use sva_formula::closed_form::{Bound, Series, children, map_children};
use sva_formula::series::{mentions_line, ratio, substitute};
use sva_formula::spectral_sum::atom::{Exp, Factors, Singular, SpectralAtom};
use sva_formula::table::series::{Shape, read};
use sva_formula::{
    Body, C64, Codomain, Env, Lane, NodeId, ParamId, Part, Run, SpectralSum, Ty, Unary, Var, lines,
};

use crate::error::CollapseError;
use crate::profile::Profile;

/// What a series is truncated against: the observation's own ceiling, the amplitude a
/// dropped tail provably stays within, and the floor a tail no bound sums falls under.
#[derive(Clone, Copy, Debug, PartialEq)]
pub struct Audible {
    ceiling: f64,
    precision: f64,
    floor_db: f64,
}

impl Audible {
    pub fn of(profile: &Profile, rate: u32) -> Audible {
        let ceiling = profile.ceiling(rate);
        Audible {
            ceiling,
            precision: profile.half_lsb(),
            floor_db: profile.floor(ceiling),
        }
    }
}

/// A line series is placed analytically under `sva_formula`'s own bound; an expanded one
/// becomes a formula the sample loop walks, which is what this caps.
const MAX_EXPANDED_TERMS: usize = 1 << 13;

/// FORMAT 6.2 truncates a series once, at collapse: every term the ceiling and the precision
/// leave becomes an ordinary atom before the first sample is read.
pub fn spectral_sum(n: &SpectralSum, band: Audible) -> Result<SpectralSum, CollapseError> {
    if n.lanes.iter().all(|l| l.series.is_empty()) {
        return Ok(n.clone());
    }
    let mut lanes = Vec::with_capacity(n.lanes.len());
    for lane in &n.lanes {
        let mut held = Lane {
            series: Vec::new(),
            ..lane.clone()
        };
        for s in &lane.series {
            held.atoms.extend(atoms(s, band)?);
        }
        lanes.push(held);
    }
    Ok(SpectralSum::of(n.var, lanes))
}

/// The same truncation over a written closed form, whose series a spectral sum never reached.
pub fn written(f: &Body, band: Audible) -> Result<Body, CollapseError> {
    if let Body::Series(s) = f {
        return expanded(s, band);
    }
    let mut found = None;
    let out = map_children(f, |p| match written(&p.body, band) {
        Ok(body) => Part::new(p.origin, body),
        Err(e) => {
            found = Some(e);
            p.clone()
        }
    });
    match found {
        Some(e) => Err(e),
        None => Ok(out),
    }
}

fn atoms(s: &Series, band: Audible) -> Result<Vec<SpectralAtom>, CollapseError> {
    let (body, window) = sva_formula::crop_peeled(&s.term.body);
    let bare = Series {
        term: Part::new(s.term.origin, body),
        ..s.clone()
    };
    let taken = enumerated(&bare, band);
    if !taken.is_empty() {
        return Ok(taken
            .into_iter()
            .map(|l| {
                SpectralAtom::new(
                    l.amp,
                    Factors {
                        exp: Some(Exp::at(0.0, TAU * l.hz)),
                        ind: window,
                        ..Factors::NONE
                    },
                    Singular::Regular,
                    s.term.origin,
                )
            })
            .collect());
    }
    let body = expanded(s, band)?;
    let held = sva_formula::normalize(&body, Var::T)
        .map_err(|_| CollapseError::NotEvaluable("a series term"))?;
    Ok(held.lanes.into_iter().flat_map(|l| l.atoms).collect())
}

/// A line series keeps its terms as runs; anything else is summed term by term.
fn expanded(s: &Series, band: Audible) -> Result<Body, CollapseError> {
    let taken = enumerated(s, band);
    if !taken.is_empty() {
        let runs = Run::of(&taken).into_iter();
        return Ok(sum(runs.map(|r| Body::Run(Box::new(r))).collect()));
    }
    let count = terms(s, band)?;
    let mut parts = Vec::with_capacity(count);
    for i in 0..count {
        let form = substitute(&s.term.body, s.index, (s.lo + i as i64) as f64);
        parts.push(written(&form, band)?);
    }
    Ok(sum(parts))
}

fn enumerated(s: &Series, band: Audible) -> Vec<sva_formula::Line> {
    match read(&s.term.body) {
        Some(Shape::Lines(_)) => lines(s, band.ceiling, band.floor_db, band.precision).taken,
        _ => Vec::new(),
    }
}

fn sum(parts: Vec<Body>) -> Body {
    match parts.len() {
        0 => Body::Const(C64::ZERO),
        1 => parts.into_iter().next().expect("one part"),
        _ => Body::Add(parts.into_iter().map(Part::bare).collect()),
    }
}

/// A nesting is priced whole before it expands: a written bound counts like the floor's.
fn terms(s: &Series, band: Audible) -> Result<usize, CollapseError> {
    let cost = cost(s, band).ok_or(CollapseError::NotEvaluable(
        "a series whose term count no coefficient bounds",
    ))?;
    if cost.depth == 1 && cost.own > MAX_EXPANDED_TERMS {
        return Err(CollapseError::NotEvaluable(
            "a series of more terms than one instant expands",
        ));
    }
    match cost.terms > MAX_EXPANDED_TERMS {
        true => Err(CollapseError::NestedSeries {
            depth: cost.depth,
            terms: cost.terms,
            bound: MAX_EXPANDED_TERMS,
        }),
        false => Ok(cost.own),
    }
}

/// Series deep, terms the whole nesting takes, terms this level alone takes.
struct Cost {
    depth: usize,
    terms: usize,
    own: usize,
}

fn cost(s: &Series, band: Audible) -> Option<Cost> {
    let own = counted(s, band)?;
    let inside = substitute(&s.term.body, s.index, s.lo as f64);
    let (depth, inner) = price(&inside, band)?;
    Some(Cost {
        depth: depth + 1,
        terms: own.saturating_mul(inner),
        own,
    })
}

/// A sum of series costs their counts added; every other spelling multiplies.
fn price(f: &Body, band: Audible) -> Option<(usize, usize)> {
    if let Body::Series(s) = f {
        let cost = cost(s, band)?;
        return Some((cost.depth, cost.terms));
    }
    let summed = matches!(f, Body::Add(_));
    let mut depth = 0;
    let mut terms: usize = if summed { 0 } else { 1 };
    for p in children(f) {
        let (d, n) = price(&p.body, band)?;
        depth = depth.max(d);
        terms = match summed {
            true => terms.saturating_add(n),
            false => terms.saturating_mul(n),
        };
    }
    Some((depth, terms.max(1)))
}

/// A geometric magnitude bound stops where its whole tail rounds away; any other stand-in at
/// the profile's floor.
fn counted(s: &Series, band: Audible) -> Option<usize> {
    let hi = match s.hi {
        Bound::Finite(n) => return usize::try_from((n - s.lo + 1).max(0)).ok(),
        Bound::Infinite => MAX_EXPANDED_TERMS,
    };
    let bound = bound(&s.term.body, band)?;
    let ratio = match bound.exact {
        true => ratio(&bound.body, s.index).filter(|r| *r < 1.0),
        false => None,
    };
    let floor = 10f64.powf(band.floor_db / 20.0);
    let mut peak = 0.0f64;
    for i in 0..hi {
        let at = substitute(&bound.body, s.index, (s.lo + i as i64) as f64);
        let held = exact_constant(&at)?.abs();
        peak = peak.max(held);
        let gone = match ratio {
            Some(r) => held / (1.0 - r) <= band.precision,
            None => peak > 0.0 && held < peak * floor,
        };
        if gone {
            return Some(i.max(1));
        }
    }
    None
}

/// A term's coefficient in the index. `exact` where it bounds the term's magnitude; elsewhere
/// it only stands in, a turning factor or a name read as one.
struct Bounded {
    body: Body,
    exact: bool,
}

fn bound(f: &Body, band: Audible) -> Option<Bounded> {
    let held = |body: Body, exact: bool| Some(Bounded { body, exact });
    let under = |p: &Part| bound(&p.body, band).map(|b| (Part::new(p.origin, b.body), b.exact));
    let all = |parts: &[Part], wrap: &dyn Fn(Part) -> Part| {
        let mut exact = true;
        let mut kept = Vec::with_capacity(parts.len());
        for p in parts {
            let (part, known) = under(p)?;
            exact &= known;
            kept.push(wrap(part));
        }
        Some((kept, exact))
    };
    match f {
        Body::Series(s) => match total(s, band) {
            Some(sum) => held(Body::Const(C64::real(sum)), true),
            None => held(Body::Const(C64::ONE), false),
        },
        Body::Line | Body::Node(_) => held(Body::Const(C64::ONE), false),
        Body::Mul(parts) => {
            let (kept, exact) = all(parts, &|p| p)?;
            held(Body::Mul(kept), exact)
        }
        Body::Add(parts) => {
            let (kept, exact) = all(parts, &|p| Part::bare(Body::Apply(Unary::Abs, p)))?;
            held(Body::Add(kept), exact)
        }
        Body::Div(a, b) if !mentions_line(&b.body) => {
            let (num, exact) = under(a)?;
            held(Body::Div(num, b.clone()), exact)
        }
        Body::Div(a, b) => {
            let ((num, _), (den, _)) = (under(a)?, under(b)?);
            held(Body::Div(num, den), false)
        }
        Body::Apply(Unary::Sin | Unary::Cos | Unary::Tanh | Unary::Sat, arg) => {
            held(Body::Const(C64::ONE), real(&arg.body))
        }
        Body::Crop { of, .. } | Body::Shift { of, .. } | Body::Warp { of, .. } => {
            bound(&of.body, band)
        }
        Body::Pow(base, n) => {
            let (part, exact) = under(base)?;
            held(Body::Pow(part, *n), exact && *n >= 0)
        }
        other if !mentions_line(other) => held(other.clone(), true),
        _ => None,
    }
}

/// A geometric series sums to its first bound over `1 - ratio`; any other to what it keeps.
fn total(s: &Series, band: Audible) -> Option<f64> {
    let bound = bound(&s.term.body, band).filter(|b| b.exact)?.body;
    let at = |i: i64| Some(exact_constant(&substitute(&bound, s.index, i as f64))?.abs());
    if let (Bound::Infinite, Some(r)) = (s.hi, ratio(&bound, s.index).filter(|r| *r < 1.0)) {
        return Some(at(s.lo)? / (1.0 - r));
    }
    let kept = i64::try_from(counted(s, band).filter(|n| *n <= MAX_EXPANDED_TERMS)?).ok()?;
    (s.lo..s.lo + kept).try_fold(0.0, |held, i| Some(held + at(i)?))
}

fn real(f: &Body) -> bool {
    axis(f, &Unread) == Axis::Real
}

struct Unread;

impl Env for Unread {
    fn node(&self, _: NodeId) -> Ty {
        Ty::form(Var::T, false, Codomain::Complex)
    }

    fn param(&self, _: ParamId) -> Ty {
        Ty::form(Var::T, false, Codomain::Complex)
    }
}