inline comparison instructions.

This commit is contained in:
Mark Thom
2017-12-04 21:01:23 -07:00
parent 8e5aaf02a4
commit cf6a47272a
8 changed files with 110 additions and 123 deletions

View File

@@ -8,6 +8,8 @@ pub struct ArithExprIterator<'a> {
state_stack: Vec<IteratorState<'a>> state_stack: Vec<IteratorState<'a>>
} }
pub type ArithCont = (Code, Option<ArithmeticTerm>);
impl<'a> ArithExprIterator<'a> { impl<'a> ArithExprIterator<'a> {
fn push_subterm(&mut self, lvl: Level, term: &'a Term) { fn push_subterm(&mut self, lvl: Level, term: &'a Term) {
self.state_stack.push(IteratorState::to_state(lvl, term)); self.state_stack.push(IteratorState::to_state(lvl, term));
@@ -73,14 +75,13 @@ impl<'a> Iterator for ArithExprIterator<'a> {
pub struct ArithmeticEvaluator<'a> { pub struct ArithmeticEvaluator<'a> {
bindings: &'a AllocVarDict<'a>, bindings: &'a AllocVarDict<'a>,
target_int: usize,
interm: Vec<ArithmeticTerm>, interm: Vec<ArithmeticTerm>,
interm_c: usize interm_c: usize
} }
impl<'a> ArithmeticEvaluator<'a> { impl<'a> ArithmeticEvaluator<'a> {
pub fn new(bindings: &'a AllocVarDict<'a>, target_int: usize) -> Self { pub fn new(bindings: &'a AllocVarDict<'a>, target_int: usize) -> Self {
ArithmeticEvaluator { bindings, target_int, interm: Vec::new(), interm_c: target_int } ArithmeticEvaluator { bindings, interm: Vec::new(), interm_c: target_int }
} }
fn get_unary_instr(name: &Atom, a1: ArithmeticTerm, t: usize) fn get_unary_instr(name: &Atom, a1: ArithmeticTerm, t: usize)
@@ -180,7 +181,7 @@ impl<'a> ArithmeticEvaluator<'a> {
Ok(()) Ok(())
} }
pub fn eval(&mut self, term: &Term) -> Result<Code, ArithmeticError> { pub fn eval(&mut self, term: &Term) -> Result<ArithCont, ArithmeticError> {
let mut code = Vec::new(); let mut code = Vec::new();
for term_ref in term.arith_expr_iter()? { for term_ref in term.arith_expr_iter()? {
@@ -212,18 +213,6 @@ impl<'a> ArithmeticEvaluator<'a> {
} }
} }
Ok((code, self.interm.pop()))
if let Some(arith_term) = self.interm.pop() {
let t = self.target_int;
match arith_term {
n @ ArithmeticTerm::Integer(_) => code.push(move_at!(n, t)),
n @ ArithmeticTerm::Float(_) => code.push(move_at!(n, t)),
r @ ArithmeticTerm::Reg(_) => code.push(move_at!(r, t)),
_ => {}
};
}
Ok(code)
} }
} }

View File

@@ -315,6 +315,7 @@ pub enum Term {
} }
pub enum InlinedQueryTerm { pub enum InlinedQueryTerm {
CompareNumber(CompareNumberQT, Vec<Box<Term>>),
IsAtomic(Vec<Box<Term>>), IsAtomic(Vec<Box<Term>>),
IsVar(Vec<Box<Term>>) IsVar(Vec<Box<Term>>)
} }
@@ -322,8 +323,9 @@ pub enum InlinedQueryTerm {
impl InlinedQueryTerm { impl InlinedQueryTerm {
pub fn arity(&self) -> usize { pub fn arity(&self) -> usize {
match self { match self {
&InlinedQueryTerm::CompareNumber(_, _) => 2,
&InlinedQueryTerm::IsAtomic(_) => 1, &InlinedQueryTerm::IsAtomic(_) => 1,
&InlinedQueryTerm::IsVar(_) => 1 &InlinedQueryTerm::IsVar(_) => 1
} }
} }
} }
@@ -341,7 +343,6 @@ pub enum CompareNumberQT {
pub enum QueryTerm { pub enum QueryTerm {
CallN(Vec<Box<Term>>), CallN(Vec<Box<Term>>),
Catch(Vec<Box<Term>>), Catch(Vec<Box<Term>>),
CompareNumber(CompareNumberQT, Vec<Box<Term>>),
Cut, Cut,
Is(Vec<Box<Term>>), Is(Vec<Box<Term>>),
Inlined(InlinedQueryTerm), Inlined(InlinedQueryTerm),
@@ -353,7 +354,6 @@ impl QueryTerm {
pub fn arity(&self) -> usize { pub fn arity(&self) -> usize {
match self { match self {
&QueryTerm::Catch(_) => 3, &QueryTerm::Catch(_) => 3,
&QueryTerm::CompareNumber(_, _) => 2,
&QueryTerm::Throw(_) => 1, &QueryTerm::Throw(_) => 1,
&QueryTerm::Inlined(ref term) => term.arity(), &QueryTerm::Inlined(ref term) => term.arity(),
&QueryTerm::Is(_) => 2, &QueryTerm::Is(_) => 2,
@@ -709,6 +709,7 @@ pub enum ArithmeticInstruction {
pub enum BuiltInInstruction { pub enum BuiltInInstruction {
CleanUpBlock, CleanUpBlock,
CompareNumber(CompareNumberQT, ArithmeticTerm, ArithmeticTerm),
DuplicateTerm, DuplicateTerm,
EraseBall, EraseBall,
Fail, Fail,
@@ -735,10 +736,8 @@ pub enum ControlInstruction {
Execute(Atom, usize), Execute(Atom, usize),
ExecuteN(usize), ExecuteN(usize),
Goto(usize, usize), // p, arity. Goto(usize, usize), // p, arity.
CompareNumberCall(CompareNumberQT), IsCall(RegType, ArithmeticTerm),
CompareNumberExecute(CompareNumberQT), IsExecute(RegType, ArithmeticTerm),
IsCall(RegType),
IsExecute(RegType),
Proceed, Proceed,
ThrowCall, ThrowCall,
ThrowExecute, ThrowExecute,
@@ -757,8 +756,8 @@ impl ControlInstruction {
&ControlInstruction::ThrowExecute => true, &ControlInstruction::ThrowExecute => true,
&ControlInstruction::Goto(_, _) => true, &ControlInstruction::Goto(_, _) => true,
&ControlInstruction::Proceed => true, &ControlInstruction::Proceed => true,
&ControlInstruction::IsCall(_) => true, &ControlInstruction::IsCall(_, _) => true,
&ControlInstruction::IsExecute(_) => true, &ControlInstruction::IsExecute(_, _) => true,
_ => false _ => false
} }
} }
@@ -790,7 +789,6 @@ pub enum FactInstruction {
} }
pub enum QueryInstruction { pub enum QueryInstruction {
MoveArithmeticTerm(ArithmeticTerm, usize),
GetVariable(RegType, usize), GetVariable(RegType, usize),
PutConstant(Level, Constant, RegType), PutConstant(Level, Constant, RegType),
PutList(Level, RegType), PutList(Level, RegType),

View File

@@ -230,12 +230,16 @@ impl<'a, TermMarker: Allocator<'a>> CodeGenerator<'a, TermMarker>
ConjunctInfo::new(vs, num_of_chunks, has_deep_cut) ConjunctInfo::new(vs, num_of_chunks, has_deep_cut)
} }
fn add_conditional_call_inlined(term: &InlinedQueryTerm, code: &mut Code) fn add_conditional_call_inlined(_: &InlinedQueryTerm, code: &mut Code)
{ {
code.push(proceed!());
/*
match term { match term {
&InlinedQueryTerm::IsAtomic(_) | &InlinedQueryTerm::IsVar(_) => &InlinedQueryTerm::IsAtomic(_) | &InlinedQueryTerm::IsVar(_) =>
code.push(proceed!()) code.push(proceed!())
}; };
*/
} }
fn add_conditional_call(code: &mut Code, qt: &QueryTerm, pvs: usize) fn add_conditional_call(code: &mut Code, qt: &QueryTerm, pvs: usize)
@@ -276,10 +280,8 @@ impl<'a, TermMarker: Allocator<'a>> CodeGenerator<'a, TermMarker>
*ctrl = ControlInstruction::Execute(name, arity), *ctrl = ControlInstruction::Execute(name, arity),
ControlInstruction::CallN(arity) => ControlInstruction::CallN(arity) =>
*ctrl = ControlInstruction::ExecuteN(arity), *ctrl = ControlInstruction::ExecuteN(arity),
ControlInstruction::CompareNumberCall(cmp) => ControlInstruction::IsCall(r, at) =>
*ctrl = ControlInstruction::CompareNumberExecute(cmp), *ctrl = ControlInstruction::IsExecute(r, at),
ControlInstruction::IsCall(r) =>
*ctrl = ControlInstruction::IsExecute(r),
ControlInstruction::CatchCall => ControlInstruction::CatchCall =>
*ctrl = ControlInstruction::CatchExecute, *ctrl = ControlInstruction::CatchExecute,
ControlInstruction::ThrowCall => ControlInstruction::ThrowCall =>
@@ -293,21 +295,33 @@ impl<'a, TermMarker: Allocator<'a>> CodeGenerator<'a, TermMarker>
} }
fn compile_inlined(&mut self, term: &'a InlinedQueryTerm, term_loc: GenContext, code: &mut Code) fn compile_inlined(&mut self, term: &'a InlinedQueryTerm, term_loc: GenContext, code: &mut Code)
-> Result<(), ParserError>
{ {
match term { match term {
&InlinedQueryTerm::CompareNumber(cmp, ref terms) => {
let (mut lcode, at_1) = self.call_arith_eval(terms[0].as_ref(), 1)?;
let (mut rcode, at_2) = self.call_arith_eval(terms[1].as_ref(), 2)?;
code.append(&mut lcode);
code.append(&mut rcode);
code.push(compare_number_instr!(cmp,
at_1.unwrap_or(interm!(1)),
at_2.unwrap_or(interm!(2))));
},
&InlinedQueryTerm::IsAtomic(ref inner_term) => &InlinedQueryTerm::IsAtomic(ref inner_term) =>
match inner_term[0].as_ref() { match inner_term[0].as_ref() {
&Term::AnonVar | &Term::Clause(_, _, _) | &Term::Cons(_, _, _) => { &Term::AnonVar | &Term::Clause(_, _, _) | &Term::Cons(_, _, _) => {
code.push(fail!()); code.push(fail!());
}, },
&Term::Constant(_, _) => { &Term::Constant(_, _) => {
code.push(succeed!()); code.push(succeed!());
}, },
&Term::Var(ref vr, ref name) => { &Term::Var(ref vr, ref name) => {
let r = self.mark_non_callable(name, 1, term_loc, vr, code); let r = self.mark_non_callable(name, 1, term_loc, vr, code);
code.push(is_atomic!(r)); code.push(is_atomic!(r));
} }
}, },
&InlinedQueryTerm::IsVar(ref inner_term) => &InlinedQueryTerm::IsVar(ref inner_term) =>
match inner_term[0].as_ref() { match inner_term[0].as_ref() {
&Term::Constant(_, _) | &Term::Clause(_, _, _) | &Term::Cons(_, _, _) => { &Term::Constant(_, _) | &Term::Clause(_, _, _) | &Term::Cons(_, _, _) => {
@@ -322,9 +336,12 @@ impl<'a, TermMarker: Allocator<'a>> CodeGenerator<'a, TermMarker>
} }
} }
} }
Ok(())
} }
fn call_arith_eval(&self, term: &'a Term, target_int: usize) -> Result<Code, ArithmeticError> { fn call_arith_eval(&self, term: &'a Term, target_int: usize) -> Result<ArithCont, ArithmeticError>
{
let mut evaluator = ArithmeticEvaluator::new(self.marker.bindings(), target_int); let mut evaluator = ArithmeticEvaluator::new(self.marker.bindings(), target_int);
evaluator.eval(term) evaluator.eval(term)
} }
@@ -360,10 +377,10 @@ impl<'a, TermMarker: Allocator<'a>> CodeGenerator<'a, TermMarker>
}); });
}, },
&QueryTerm::Inlined(ref term) => &QueryTerm::Inlined(ref term) =>
self.compile_inlined(term, term_loc, code), self.compile_inlined(term, term_loc, code)?,
&QueryTerm::Is(ref terms) => { &QueryTerm::Is(ref terms) => {
let mut arith_code = self.call_arith_eval(terms[1].as_ref(), 1)?; let (mut acode, at) = try!(self.call_arith_eval(terms[1].as_ref(), 1));
code.append(&mut arith_code); code.append(&mut acode);
match terms[0].as_ref() { match terms[0].as_ref() {
&Term::Var(ref vr, ref name) => { &Term::Var(ref vr, ref name) => {
@@ -373,35 +390,26 @@ impl<'a, TermMarker: Allocator<'a>> CodeGenerator<'a, TermMarker>
vr, vr,
code); code);
code.push(is_call!(r)); code.push(is_call!(r, at.unwrap_or(interm!(1))));
}, },
&Term::Constant(_, Constant::Float(fl)) => { &Term::Constant(_, Constant::Float(fl)) => {
code.push(query![put_constant!(Level::Shallow, code.push(query![put_constant!(Level::Shallow,
Constant::Float(fl), Constant::Float(fl),
temp_v!(1))]); temp_v!(1))]);
code.push(is_call!(temp_v!(1))); code.push(is_call!(temp_v!(1), at.unwrap_or(interm!(1))));
}, },
&Term::Constant(_, Constant::Integer(ref bi)) => { &Term::Constant(_, Constant::Integer(ref bi)) => {
let bi = bi.clone(); let bi = bi.clone();
code.push(query![put_constant!(Level::Shallow, code.push(query![put_constant!(Level::Shallow,
Constant::Integer(bi), Constant::Integer(bi),
temp_v!(1))]); temp_v!(1))]);
code.push(is_call!(temp_v!(1))); code.push(is_call!(temp_v!(1), at.unwrap_or(interm!(1))));
}, },
_ => { _ => {
code.push(fail!()); code.push(fail!());
} }
} }
}, },
&QueryTerm::CompareNumber(cmp, ref terms) => {
let mut larith_code = self.call_arith_eval(terms[0].as_ref(), 1)?;
let mut rarith_code = self.call_arith_eval(terms[1].as_ref(), 2)?;
code.append(&mut larith_code);
code.append(&mut rarith_code);
code.push(compare_number_call!(cmp));
},
_ if chunk_num == 0 => { _ if chunk_num == 0 => {
self.marker.reset_arg(term.arity()); self.marker.reset_arg(term.arity());

View File

@@ -46,8 +46,6 @@ impl fmt::Display for FactInstruction {
impl fmt::Display for QueryInstruction { impl fmt::Display for QueryInstruction {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
match self { match self {
&QueryInstruction::MoveArithmeticTerm(ref at, ref r) =>
write!(f, "move_arithmetic_term {}, {}", at, r),
&QueryInstruction::GetVariable(ref x, ref a) => &QueryInstruction::GetVariable(ref x, ref a) =>
write!(f, "query:get_variable {}, A{}", x, a), write!(f, "query:get_variable {}, A{}", x, a),
&QueryInstruction::PutConstant(Level::Shallow, ref constant, ref r) => &QueryInstruction::PutConstant(Level::Shallow, ref constant, ref r) =>
@@ -107,11 +105,7 @@ impl fmt::Display for ControlInstruction {
&ControlInstruction::CatchCall => &ControlInstruction::CatchCall =>
write!(f, "call_catch"), write!(f, "call_catch"),
&ControlInstruction::CatchExecute => &ControlInstruction::CatchExecute =>
write!(f, "execute_catch"), write!(f, "execute_catch"),
&ControlInstruction::CompareNumberCall(cmp) =>
write!(f, "n_compare_call {}", cmp),
&ControlInstruction::CompareNumberExecute(cmp) =>
write!(f, "n_compare_execute {}", cmp),
&ControlInstruction::ExecuteN(arity) => &ControlInstruction::ExecuteN(arity) =>
write!(f, "execute_N {}", arity), write!(f, "execute_N {}", arity),
&ControlInstruction::Deallocate => &ControlInstruction::Deallocate =>
@@ -126,10 +120,10 @@ impl fmt::Display for ControlInstruction {
write!(f, "call_throw"), write!(f, "call_throw"),
&ControlInstruction::ThrowExecute => &ControlInstruction::ThrowExecute =>
write!(f, "execute_throw"), write!(f, "execute_throw"),
&ControlInstruction::IsCall(r) => &ControlInstruction::IsCall(r, ref at) =>
write!(f, "is_call {}", r), write!(f, "is_call {}, {}", r, at),
&ControlInstruction::IsExecute(r) => &ControlInstruction::IsExecute(r, ref at) =>
write!(f, "is_execute {}", r), write!(f, "is_execute {}, {}", r, at),
} }
} }
} }
@@ -153,6 +147,8 @@ impl fmt::Display for BuiltInInstruction {
match self { match self {
&BuiltInInstruction::CleanUpBlock => &BuiltInInstruction::CleanUpBlock =>
write!(f, "clean_up_block"), write!(f, "clean_up_block"),
&BuiltInInstruction::CompareNumber(cmp, ref at_1, ref at_2) =>
write!(f, "number_test {}, {}, {} ", cmp, at_1, at_2),
&BuiltInInstruction::DuplicateTerm => &BuiltInInstruction::DuplicateTerm =>
write!(f, "duplicate_term X1"), write!(f, "duplicate_term X1"),
&BuiltInInstruction::EraseBall => &BuiltInInstruction::EraseBall =>

View File

@@ -40,9 +40,10 @@ impl<'a> QueryIterator<'a> {
let state = IteratorState::Clause(0, ClauseType::Catch, terms); let state = IteratorState::Clause(0, ClauseType::Catch, terms);
QueryIterator { state_stack: vec![state] } QueryIterator { state_stack: vec![state] }
}, },
&QueryTerm::CompareNumber(_, ref terms) | &QueryTerm::Is(ref terms) => { &QueryTerm::Inlined(InlinedQueryTerm::CompareNumber(_, ref terms))
let state = IteratorState::Clause(0, ClauseType::Is, terms); | &QueryTerm::Is(ref terms) => {
QueryIterator { state_stack: vec![state] } let state = IteratorState::Clause(0, ClauseType::Is, terms);
QueryIterator { state_stack: vec![state] }
}, },
&QueryTerm::Inlined(InlinedQueryTerm::IsAtomic(ref terms)) &QueryTerm::Inlined(InlinedQueryTerm::IsAtomic(ref terms))
| &QueryTerm::Inlined(InlinedQueryTerm::IsVar(ref terms)) => | &QueryTerm::Inlined(InlinedQueryTerm::IsVar(ref terms)) =>
@@ -270,7 +271,7 @@ impl<'a> ChunkedIterator<'a>
arity = child_terms.len(); arity = child_terms.len();
break; break;
}, },
&QueryTerm::Is(_) | &QueryTerm::CompareNumber(_, _) => { &QueryTerm::Is(_) => {
result.push(term); result.push(term);
arity = 2; arity = 2;
break; break;

View File

@@ -1379,10 +1379,6 @@ impl MachineState {
fn execute_query_instr(&mut self, instr: &QueryInstruction) { fn execute_query_instr(&mut self, instr: &QueryInstruction) {
match instr { match instr {
&QueryInstruction::MoveArithmeticTerm(ref at, t) => {
let n = try_or_fail!(self, self.get_number(at));
self.interms[t - 1] = n;
},
&QueryInstruction::GetVariable(norm, arg) => &QueryInstruction::GetVariable(norm, arg) =>
self[norm] = self.registers[arg].clone(), self[norm] = self.registers[arg].clone(),
&QueryInstruction::PutConstant(_, ref constant, reg) => &QueryInstruction::PutConstant(_, ref constant, reg) =>
@@ -1609,6 +1605,22 @@ impl MachineState {
fn execute_built_in_instr(&mut self, code_dir: &CodeDir, instr: &BuiltInInstruction) fn execute_built_in_instr(&mut self, code_dir: &CodeDir, instr: &BuiltInInstruction)
{ {
match instr { match instr {
&BuiltInInstruction::CompareNumber(cmp, ref at_1, ref at_2) => {
let n1 = try_or_fail!(self, self.get_number(at_1));
let n2 = try_or_fail!(self, self.get_number(at_2));
self.fail = match cmp {
CompareNumberQT::GreaterThan if !(n1.gt(n2)) => true,
CompareNumberQT::GreaterThanOrEqual if !(n1.gte(n2)) => true,
CompareNumberQT::LessThan if !(n1.lt(n2)) => true,
CompareNumberQT::LessThanOrEqual if !(n1.lte(n2)) => true,
CompareNumberQT::NotEqual if !(n1.ne(n2)) => true,
CompareNumberQT::Equal if !(n1.eq(n2)) => true,
_ => false
};
self.p += 1;
},
&BuiltInInstruction::DuplicateTerm => { &BuiltInInstruction::DuplicateTerm => {
let old_h = self.h; let old_h = self.h;
@@ -1743,21 +1755,6 @@ impl MachineState {
} }
}; };
} }
fn handle_n_compare(&mut self, cmp: CompareNumberQT) {
let n1 = self.interms[0].clone();
let n2 = self.interms[1].clone();
self.fail = match cmp {
CompareNumberQT::GreaterThan if !(n1.gt(n2)) => true,
CompareNumberQT::GreaterThanOrEqual if !(n1.gte(n2)) => true,
CompareNumberQT::LessThan if !(n1.lt(n2)) => true,
CompareNumberQT::LessThanOrEqual if !(n1.lte(n2)) => true,
CompareNumberQT::NotEqual if !(n1.ne(n2)) => true,
CompareNumberQT::Equal if !(n1.eq(n2)) => true,
_ => false
};
}
fn execute_ctrl_instr(&mut self, code_dir: &CodeDir, instr: &ControlInstruction) fn execute_ctrl_instr(&mut self, code_dir: &CodeDir, instr: &ControlInstruction)
{ {
@@ -1837,27 +1834,19 @@ impl MachineState {
}, },
&ControlInstruction::ThrowExecute => { &ControlInstruction::ThrowExecute => {
self.goto_throw(); self.goto_throw();
}, },
&ControlInstruction::CompareNumberCall(cmp) => { &ControlInstruction::IsCall(r, ref at) => {
self.handle_n_compare(cmp); let a1 = self[r].clone();
let a2 = try_or_fail!(self, self.get_number(at));
self.unify(a1, Addr::Con(Constant::from(a2)));
self.p += 1; self.p += 1;
}, },
&ControlInstruction::CompareNumberExecute(cmp) => { &ControlInstruction::IsExecute(r, ref at) => {
self.handle_n_compare(cmp);
self.p = self.cp;
},
&ControlInstruction::IsCall(r) => {
let a1 = self[r].clone(); let a1 = self[r].clone();
let a2 = Addr::Con(Constant::from(self.interms[0].clone())); let a2 = try_or_fail!(self, self.get_number(at));
self.unify(a1, a2); self.unify(a1, Addr::Con(Constant::from(a2)));
self.p += 1;
},
&ControlInstruction::IsExecute(r) => {
let a1 = self[r].clone();
let a2 = Addr::Con(Constant::from(self.interms[0].clone()));
self.unify(a1, a2);
self.p = self.cp; self.p = self.cp;
} }
}; };

View File

@@ -16,9 +16,21 @@ macro_rules! deallocate {
) )
} }
macro_rules! move_at { macro_rules! compare_number {
($at:expr, $r:expr) => ( ($cmp: expr, $terms: expr) => (
Line::Query(vec![QueryInstruction::MoveArithmeticTerm($at, $r)]) QueryTerm::Inlined(InlinedQueryTerm::CompareNumber($cmp, $terms))
)
}
macro_rules! compare_number_instr {
($cmp: expr, $at_1: expr, $at_2: expr) => (
Line::BuiltIn(BuiltInInstruction::CompareNumber($cmp, $at_1, $at_2))
)
}
macro_rules! interm {
($n: expr) => (
ArithmeticTerm::Interm($n)
) )
} }
@@ -50,12 +62,6 @@ macro_rules! fact {
) )
} }
macro_rules! compare_number_call {
($cmp: expr) => (
Line::Control(ControlInstruction::CompareNumberCall($cmp))
)
}
macro_rules! temp_v { macro_rules! temp_v {
($x:expr) => ( ($x:expr) => (
RegType::Temp($x) RegType::Temp($x)
@@ -216,8 +222,8 @@ macro_rules! unify {
} }
macro_rules! is_call { macro_rules! is_call {
($r:expr) => ( ($r:expr, $at:expr) => (
Line::Control(ControlInstruction::IsCall($r)) Line::Control(ControlInstruction::IsCall($r, $at))
) )
} }