Grcov report - integer

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use conjure_cp::ast::{Expression as Expr, GroundDomain};

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use conjure_cp::ast::{SATIntEncoding, SymbolTable};

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use conjure_cp::rule_engine::{

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    ApplicationError, ApplicationError::RuleNotApplicable, ApplicationResult, Reduction,

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    register_rule,

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};

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use conjure_cp::ast::Metadata;

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use conjure_cp::ast::{Atom, Literal, Moo, Range};

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use conjure_cp::into_matrix_expr;

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use conjure_cp::{bug, essence_expr};

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/// This function takes a target expression and a vector of ranges and creates an expression representing the ranges with the target expression as the subject

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///

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/// E.g. x : int(4), int(10..20), int(30..) ~~> Or(x=4, 10<=x<=20, x>=30)

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fn int_domain_to_expr(subject: Expr, ranges: &Vec<Range<i32>>) -> Expr {

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    let mut output = vec![];

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    let value = Moo::new(subject);

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    for range in ranges {

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        match range {

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            Range::Single(x) => output.push(essence_expr!(&value = &x)),

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            Range::Bounded(x, y) => output.push(essence_expr!("&value >= &x /\\ &value <= &y")),

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            _ => bug!("Unbounded domains not supported for SAT"),

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    Expr::Or(Metadata::new(), Moo::new(into_matrix_expr!(output)))

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/// This function confirms that all of the input expressions are log SATInts, and returns vectors for each input of their bits

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/// This function also extends all vectors such that they have the same lengths

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/// The vector lengths is either `n` for bit_count = Some(n), otherwise the length of the longest operand

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pub fn validate_log_int_operands(

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    exprs: Vec<Expr>,

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    bit_count: Option<u32>,

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) -> Result<Vec<Vec<Expr>>, ApplicationError> {

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    // TODO: In the future it may be possible to optimize operations between integers with different bit sizes

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    // Collect inner bit vectors from each SATInt

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    // TODO: this file should be encoding agnostic so this needs to moved to the log_int_ops.rs file, do this once the direct ints have been merged to main though

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    let mut out: Vec<Vec<Expr>> = exprs

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        .into_iter()

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        .map(|expr| {

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            let Expr::SATInt(_, SATIntEncoding::Log, inner, _) = expr else {

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                return Err(RuleNotApplicable);

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};

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            let Some(bits) = inner.as_ref().clone().unwrap_list() else {

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                return Err(RuleNotApplicable);

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};

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            Ok(bits)

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})

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        .collect::<Result<_, _>>()?;

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    // Determine target length

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    let max_len = bit_count

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        .map(|b| b as usize)

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        .unwrap_or_else(|| out.iter().map(|v| v.len()).max().unwrap_or(0));

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    // Extend or crop each vector

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    for v in &mut out {

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        if v.len() < max_len {

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            // pad with the last element

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            if let Some(last) = v.last().cloned() {

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                v.resize(max_len, last);

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        } else if v.len() > max_len {

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            // crop extra elements

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            v.truncate(max_len);

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    Ok(out)

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/// Converts an integer decision variable to SATInt form, creating a new representation of boolean variables if

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/// one does not yet exist

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///

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/// ```text

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///  x

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///  ~~>

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///  SATInt([x#00, x#01, ...])

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///

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///  new variables:

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///  find x#00: bool

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///  find x#01: bool

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///  ...

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///

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/// ```

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#[register_rule(("SAT_Direct", 9500))]

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fn integer_decision_representation_direct(expr: &Expr, symbols: &SymbolTable) -> ApplicationResult {

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    // thing we are representing must be a reference

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    let Expr::Atomic(_, Atom::Reference(name)) = expr else {

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        return Err(RuleNotApplicable);

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};

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    // thing we are representing must be a variable

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    // symbols

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    //     .lookup(name)

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    //     .ok_or(RuleNotApplicable)?

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    //     .as_var()

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    //     .ok_or(RuleNotApplicable)?;

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    // thing we are representing must be an integer

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    let dom = name.resolved_domain().ok_or(RuleNotApplicable)?;

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    let GroundDomain::Int(ranges) = dom.as_ref() else {

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        return Err(RuleNotApplicable);

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};

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    let (min, max) = ranges

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        .iter()

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        .fold((i32::MAX, i32::MIN), |(min_a, max_b), range| {

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                min_a.min(*range.low().unwrap()),

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                max_b.max(*range.high().unwrap()),

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});

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    let mut symbols = symbols.clone();

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    let new_name = &name.name().to_owned();

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    let repr_exists = symbols

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        .get_representation(new_name, &["sat_direct_int"])

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        .is_some();

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    let representation = symbols

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        .get_or_add_representation(new_name, &["sat_direct_int"])

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        .ok_or(RuleNotApplicable)?;

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    let bits: Vec<Expr> = representation[0]

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        .clone()

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        .expression_down(&symbols)?

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        .into_values()

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        .collect();

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    let cnf_int = Expr::SATInt(

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        Metadata::new(),

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        SATIntEncoding::Direct,

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        Moo::new(into_matrix_expr!(bits.clone())),

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        (min, max),

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);

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    if !repr_exists {

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        // Domain constraint: the integer must take one of its valid values

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        let constraints = vec![int_domain_to_expr(cnf_int.clone(), ranges)];

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        // At-Most-One constraints: only one bit can be true.

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        let mut clauses = vec![];

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        for i in 0..bits.len() {

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            for j in i + 1..bits.len() {

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                clauses.push(conjure_cp::ast::CnfClause::new(vec![

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                    Expr::Not(Metadata::new(), Moo::new(bits[i].clone())),

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                    Expr::Not(Metadata::new(), Moo::new(bits[j].clone())),

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                ]));

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        let mut reduction = Reduction::cnf(cnf_int, clauses, symbols);

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        reduction.new_top = constraints;

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        Ok(reduction)

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    } else {

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        Ok(Reduction::pure(cnf_int))

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#[register_rule(("SAT_Order", 9500))]

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fn integer_decision_representation_order(expr: &Expr, symbols: &SymbolTable) -> ApplicationResult {

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    // thing we are representing must be a reference

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    let Expr::Atomic(_, Atom::Reference(name)) = expr else {

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        return Err(RuleNotApplicable);

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};

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    // thing we are representing must be an integer

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    let dom = name.resolved_domain().ok_or(RuleNotApplicable)?;

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    let GroundDomain::Int(ranges) = dom.as_ref() else {

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        return Err(RuleNotApplicable);

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};

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    let (min, max) = ranges

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        .iter()

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        .fold((i32::MAX, i32::MIN), |(min_a, max_b), range| {

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                min_a.min(*range.low().unwrap()),

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                max_b.max(*range.high().unwrap()),

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});

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    let mut symbols = symbols.clone();

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    let new_name = &name.name().to_owned();

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    let repr_exists = symbols

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        .get_representation(new_name, &["sat_order_int"])

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        .is_some();

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    let representation = symbols

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        .get_or_add_representation(new_name, &["sat_order_int"])

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        .ok_or(RuleNotApplicable)?;

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    let bits: Vec<Expr> = representation[0]

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        .clone()

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        .expression_down(&symbols)?

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        .into_values()

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        .collect();

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    let cnf_int = Expr::SATInt(

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        Metadata::new(),

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        SATIntEncoding::Order,

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        Moo::new(into_matrix_expr!(bits.clone())),

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        (min, max),

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);

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    if !repr_exists {

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        // Domain constraint: the integer must take one of its valid values

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        let constraints = vec![int_domain_to_expr(cnf_int.clone(), ranges)];

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        // Ordering constraints: b_i -> b_{i-1} which is !b_i or b_{i-1}

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        let mut clauses = vec![];

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        for i in 1..bits.len() {

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            clauses.push(conjure_cp::ast::CnfClause::new(vec![

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                Expr::Not(Metadata::new(), Moo::new(bits[i].clone())),

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                bits[i - 1].clone(),

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            ]));

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        if !bits.is_empty() {

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            // Domain constraint: a >= min, which is b_min.

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            clauses.push(conjure_cp::ast::CnfClause::new(vec![bits[0].clone()]));

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        let mut reduction = Reduction::cnf(cnf_int, clauses, symbols);

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        reduction.new_top = constraints;

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        Ok(reduction)

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    } else {

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        Ok(Reduction::pure(cnf_int))

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/// Converts an integer decision variable to SATInt form (Log encoding)

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#[register_rule(("SAT_Log", 9500))]

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fn integer_decision_representation_log(expr: &Expr, symbols: &SymbolTable) -> ApplicationResult {

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    // thing we are representing must be a reference

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    let Expr::Atomic(_, Atom::Reference(name)) = expr else {

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        return Err(RuleNotApplicable);

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};

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    // thing we are representing must be a variable

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    // symbols

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    //     .lookup(name)

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    //     .ok_or(RuleNotApplicable)?

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    //     .as_var()

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    //     .ok_or(RuleNotApplicable)?;

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    // thing we are representing must be an integer

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    let dom = name.resolved_domain().ok_or(RuleNotApplicable)?;

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    let GroundDomain::Int(ranges) = dom.as_ref() else {

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        return Err(RuleNotApplicable);

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};

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    let (min, max) = ranges

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        .iter()

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        .fold((i32::MAX, i32::MIN), |(min_a, max_b), range| {

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                min_a.min(*range.low().unwrap()),

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                max_b.max(*range.high().unwrap()),

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});

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    let mut symbols = symbols.clone();

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    let new_name = &name.name().to_owned();

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    let repr_exists = symbols

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        .get_representation(new_name, &["sat_log_int"])

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        .is_some();

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    let representation = symbols

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        .get_or_add_representation(new_name, &["sat_log_int"])

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        .ok_or(RuleNotApplicable)?;

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    let bits = representation[0]

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        .clone()

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        .expression_down(&symbols)?

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        .into_values()

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        .collect();

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    let cnf_int = Expr::SATInt(

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        Metadata::new(),

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        SATIntEncoding::Log,

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        Moo::new(into_matrix_expr!(bits)),

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        (min, max),

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);

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    if !repr_exists {

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        // add domain ranges as constraints if this is the first time the representation is added

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        Ok(Reduction::new(

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            cnf_int.clone(),

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            vec![int_domain_to_expr(cnf_int, ranges)], // contains domain rules

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            symbols,

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))

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    } else {

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        Ok(Reduction::pure(cnf_int))

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/// Converts an integer literal to SATInt form

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///

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/// ```text

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///  3

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///  ~~>

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///  SATInt([true,true,false,false,false,false,false,false;int(1..)])

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///

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/// ```

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#[register_rule(("SAT_Log", 9500))]

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9

fn literal_cnf_int(expr: &Expr, _: &SymbolTable) -> ApplicationResult {

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    let value = {

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        if let Expr::Atomic(_, Atom::Literal(Literal::Int(v))) = expr {

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*v

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        } else {

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9

            return Err(RuleNotApplicable);

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};

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    //TODO: add support for negatives

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    //TODO: Adding constant optimization to all int operations should hopefully make this rule redundant

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    let mut binary_encoding = vec![];

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    let bit_count = bit_magnitude(value);

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    let mut value_mut = value as u32;

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    for _ in 0..bit_count {

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        binary_encoding.push(Expr::Atomic(

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            Metadata::new(),

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            Atom::Literal(Literal::Bool((value_mut & 1) != 0)),

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));

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        value_mut >>= 1;

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    Ok(Reduction::pure(Expr::SATInt(

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        Metadata::new(),

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        SATIntEncoding::Log,

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        Moo::new(into_matrix_expr!(binary_encoding)),

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        (value, value),

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)))

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9

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/// Determine the number of bits required to encode an i32 in 2s complement

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pub fn bit_magnitude(x: i32) -> usize {

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    if x >= 0 {

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        // positive: bits = highest set bit + 1 sign bit

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        (1 + (32 - x.leading_zeros())).try_into().unwrap()

357

    } else {

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        // negative: bits = highest set bit in magnitude

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        (33 - (!x).leading_zeros()).try_into().unwrap()

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/// Given two vectors of expressions, extend the shorter one by repeating its last element until both are the same length

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pub fn match_bits_length(a: Vec<Expr>, b: Vec<Expr>) -> (Vec<Expr>, Vec<Expr>) {

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    let len_a = a.len();

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    let len_b = b.len();

367

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    if len_a < len_b {

369

        let last_a = a.last().cloned().unwrap();

370

        let mut a_extended = a;

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        a_extended.resize(len_b, last_a);

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        (a_extended, b)

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    } else if len_b < len_a {

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        let last_b = b.last().cloned().unwrap();

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        let mut b_extended = b;

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        b_extended.resize(len_a, last_b);

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        (a, b_extended)

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    } else {

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        (a, b)

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