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commit-id:f3de9727
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orizi committed May 29, 2024
1 parent c8ef96a commit 0062671
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36 changes: 30 additions & 6 deletions corelib/src/test/integer_test.cairo
Original file line number Diff line number Diff line change
Expand Up @@ -2006,13 +2006,20 @@ mod bounded_int {
a: T1, b: T2
) -> (DRR::DivT, DRR::RemT) implicits(RangeCheck) nopanic;

/// Same as `bounded_int_div_rem`, but unwraps the result into felt252s.
fn bounded_int_div_rem_unwrapped<T1, T2, impl DRR: DivRemRes<T1, T2>>(
a: T1, b: T2
) -> (felt252, felt252) {
let (q, r) = bounded_int_div_rem(a, b);
(upcast(q), upcast(r))
}

impl SmallNumDivRemRes of DivRemRes<BoundedInt<128, 255>, BoundedInt<3, 8>> {
type DivT = BoundedInt<16, 85>;
type RemT = BoundedInt<0, 7>;
}
fn div_rem_helper(a: u128, b: u128) -> (felt252, felt252) {
let (q, r) = bounded_int_div_rem(bi_value::<128, 255>(a), bi_value::<3, 8>(b));
(upcast(q), upcast(r))
bounded_int_div_rem_unwrapped(bi_value::<128, 255>(a), bi_value::<3, 8>(b))
}

#[test]
Expand All @@ -2028,8 +2035,7 @@ mod bounded_int {
type RemT = BoundedInt<0, 0xfffffffffffffffffffffffffffffffe>;
}
fn div_rem_wide_helper(a: u128, b: u128) -> (felt252, felt252) {
let (q, r) = bounded_int_div_rem(a, bi_value::<1, 0xffffffffffffffffffffffffffffffff>(b));
(upcast(q), upcast(r))
bounded_int_div_rem_unwrapped(a, bi_value::<1, 0xffffffffffffffffffffffffffffffff>(b))
}

#[test]
Expand Down Expand Up @@ -2057,8 +2063,7 @@ mod bounded_int {
>(
a: BoundedInt<A, A>
) -> (felt252, felt252) {
let (q, r) = bounded_int_div_rem::<BoundedInt<0, A_MAX>>(upcast(a), bi_const::<B>());
(upcast(q), upcast(r))
bounded_int_div_rem_unwrapped::<BoundedInt<0, A_MAX>>(upcast(a), bi_const::<B>())
}

const POW_2_124: felt252 = 0x10000000000000000000000000000000;
Expand All @@ -2071,6 +2076,17 @@ mod bounded_int {
impl U251Pow128DivRemRes =
helpers::DivRemResImpl<POW_2_251, U128_MAX, POW_2_123, { U128_MAX - 1 }>;

// Test an extreme case where BoundedIntDivRemAlgorithm::KnownSmallLhs is used,
// and `min{b, q} = lhs_upper_sqrt - 1`.
type MaxRootLhs =
BoundedInt<1, 0x1000000000000000000000000000001000000000000000000000000000001>;
type MaxRootRhs =
BoundedInt<0x20000000000000000000000000000, { 0x100000000000000000000000000000000 - 1 }>;
impl MaxRootDivRemRes of DivRemRes<MaxRootLhs, MaxRootRhs,> {
type DivT = BoundedInt<0, 0x80000000000000000000000000000080>;
type RemT = BoundedInt<0, { 0x100000000000000000000000000000000 - 2 }>;
}

#[test]
fn test_div_rem_small_quotient() {
assert!(div_rem_small_quotient_helper::<U128_MAX, POW_2_124>(bi_const::<0>()) == (0, 0));
Expand All @@ -2084,6 +2100,14 @@ mod bounded_int {
assert!(
div_rem_small_quotient_helper::<POW_2_251, U128_MAX>(dividend) == (POW_2_123, POW_2_123)
);
assert!(
bounded_int_div_rem_unwrapped::<
MaxRootLhs, MaxRootRhs
>(
0x1000000000000000000000000000001000000000000000000000000000000,
0x1000000000000000000000000000000
) == (0x1000000000000000000000000000001, 0)
);
}

trait BIConstrain<T, const BOUNDARY: felt252> {
Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -372,10 +372,10 @@ pub fn core_libfunc_ap_change<InfoProvider: InvocationApChangeInfoProvider>(
| BoundedIntConcreteLibfunc::Mul(_) => vec![ApChange::Known(0)],
BoundedIntConcreteLibfunc::DivRem(libfunc) => {
vec![ApChange::Known(
match BoundedIntDivRemAlgorithm::new(&libfunc.lhs, &libfunc.rhs).unwrap() {
match BoundedIntDivRemAlgorithm::try_new(&libfunc.lhs, &libfunc.rhs).unwrap() {
BoundedIntDivRemAlgorithm::KnownSmallRhs => 5,
BoundedIntDivRemAlgorithm::KnownSmallQuotient(_) => 6,
BoundedIntDivRemAlgorithm::KnownSmallLhs(_) => 7,
BoundedIntDivRemAlgorithm::KnownSmallQuotient { .. } => 6,
BoundedIntDivRemAlgorithm::KnownSmallLhs { .. } => 7,
},
)]
}
Expand Down
6 changes: 3 additions & 3 deletions crates/cairo-lang-sierra-gas/src/core_libfunc_cost_base.rs
Original file line number Diff line number Diff line change
Expand Up @@ -458,14 +458,14 @@ pub fn core_libfunc_cost(
| BoundedIntConcreteLibfunc::Mul(_) => vec![ConstCost::steps(0).into()],
BoundedIntConcreteLibfunc::DivRem(libfunc) => {
vec![
match BoundedIntDivRemAlgorithm::new(&libfunc.lhs, &libfunc.rhs).unwrap() {
match BoundedIntDivRemAlgorithm::try_new(&libfunc.lhs, &libfunc.rhs).unwrap() {
BoundedIntDivRemAlgorithm::KnownSmallRhs => {
ConstCost { steps: 7, holes: 0, range_checks: 3 }
}
BoundedIntDivRemAlgorithm::KnownSmallQuotient(_) => {
BoundedIntDivRemAlgorithm::KnownSmallQuotient { .. } => {
ConstCost { steps: 9, holes: 0, range_checks: 4 }
}
BoundedIntDivRemAlgorithm::KnownSmallLhs(_) => {
BoundedIntDivRemAlgorithm::KnownSmallLhs { .. } => {
ConstCost { steps: 11, holes: 0, range_checks: 4 }
}
}
Expand Down
34 changes: 14 additions & 20 deletions crates/cairo-lang-sierra-to-casm/src/invocations/int/bounded.rs
Original file line number Diff line number Diff line change
Expand Up @@ -51,13 +51,13 @@ pub fn build_div_rem(
) -> Result<CompiledInvocation, InvocationError> {
let [range_check, a, b] = builder.try_get_single_cells()?;

let alg = BoundedIntDivRemAlgorithm::new(lhs, rhs).unwrap();
let alg = BoundedIntDivRemAlgorithm::try_new(lhs, rhs).unwrap();

let mut casm_builder = CasmBuilder::default();
let rc_slack = match &alg {
BoundedIntDivRemAlgorithm::KnownSmallRhs => 2,
BoundedIntDivRemAlgorithm::KnownSmallQuotient(_) => 3,
BoundedIntDivRemAlgorithm::KnownSmallLhs(_) => 4,
BoundedIntDivRemAlgorithm::KnownSmallQuotient { .. }
| BoundedIntDivRemAlgorithm::KnownSmallLhs { .. } => 3,
};
add_input_variables! {casm_builder,
buffer(rc_slack) range_check;
Expand All @@ -72,10 +72,10 @@ pub fn build_div_rem(

let (q_is_small, b_or_q_bound_rc_value) = match alg {
BoundedIntDivRemAlgorithm::KnownSmallRhs => (None, None),
BoundedIntDivRemAlgorithm::KnownSmallQuotient(_) => {
BoundedIntDivRemAlgorithm::KnownSmallQuotient { .. } => {
(None, Some(casm_builder.alloc_var(false)))
}
BoundedIntDivRemAlgorithm::KnownSmallLhs(_) => {
BoundedIntDivRemAlgorithm::KnownSmallLhs { .. } => {
(Some(casm_builder.alloc_var(false)), Some(casm_builder.alloc_var(false)))
}
};
Expand Down Expand Up @@ -113,32 +113,26 @@ pub fn build_div_rem(
// For this case `q + 1 <= q_max + 1 <= 2**128` and `b < rhs.upper` therefore
// `(q + 1) * b < 2**128 * rhs.upper <= prime`.
}
BoundedIntDivRemAlgorithm::KnownSmallQuotient(q_bound) => {
BoundedIntDivRemAlgorithm::KnownSmallQuotient { q_upper_bound } => {
let b_or_q_bound_rc_value = b_or_q_bound_rc_value.unwrap();
// For this case `(q + 1) <= q_bound`, and `b < rhs.upper <= 2**128` therefore
// `(q + 1) * b < q_bound * 2**128 < prime`.
casm_build_extend! {casm_builder,
const u128_bound_minus_q_upper = (BigInt::one().shl(128) - q_bound) as BigInt;
const u128_bound_minus_q_upper = (BigInt::one().shl(128) - q_upper_bound) as BigInt;
assert b_or_q_bound_rc_value = q + u128_bound_minus_q_upper;
assert b_or_q_bound_rc_value = *(range_check++);
}
}
BoundedIntDivRemAlgorithm::KnownSmallLhs(lhs_upper_sqrt) => {
BoundedIntDivRemAlgorithm::KnownSmallLhs { lhs_upper_sqrt } => {
let q_is_small = q_is_small.unwrap();
let b_or_q_bound_rc_value = b_or_q_bound_rc_value.unwrap();
casm_build_extend! {casm_builder,
// For this case we know that `(lhs_upper_sqrt + 1) * 2**128 < prime`.
// First note that `(q + 1) * b <= (min(q, b) + 1) * max(q, b)`, since:
// ```
// max((min(q, b) + 1) * max(q, b), (max(q, b) + 1) * min(q, b)) ==
// max(min(q, b) * max(q, b) + max(q, b), max(q, b) * min(q, b) + min(q, b)) ==
// min(q, b) * max(q, b) + max(max(q, b), min(q, b)) ==
// min(q, b) * max(q, b) + max(q, b) == (min(q, b) + 1) * max(q, b)
// ```
// Since `b * q < lhs.upper`, `min(b, q) <= sqrt(lhs.upper)`.
// Since `b` and `q` are less than 2**128, `max(b, q) < 2**128`.
// Therefore `(min(q, b) + 1) * max(q, b) <= (lhs_upper_sqrt + 1) * 2**128 < prime`.
// We can now guess which whether `b` or `q` is small enough and verify.
// Note that for a honest prover, `min{q, b} < root`, as otherwise
// `lhs_upper > a >= q * b >= root ** 2` (and on the other hand,
// by the definition of `root`: `root ** 2 >= lhs_upper`).
// Therefore we require `min{q, b} < root`, which guarantees that:
// q * b + r < min{q, b} * max{q, b} + 2**128 <=
// (root - 1) * 2**128 + 2**128 <= root * 2**128 < prime.
const limiter_bound = lhs_upper_sqrt.clone();
hint TestLessThan {lhs: q, rhs: limiter_bound} into {dst: q_is_small};
const u128_bound_minus_limiter_bound = (BigInt::one().shl(128) - lhs_upper_sqrt) as BigInt;
Expand Down
50 changes: 28 additions & 22 deletions crates/cairo-lang-sierra/src/extensions/modules/bounded_int.rs
Original file line number Diff line number Diff line change
Expand Up @@ -168,7 +168,7 @@ impl NamedLibfunc for BoundedIntDivRemLibfunc {
return Err(SpecializationError::UnsupportedGenericArg);
}
// Making sure the algorithm is runnable.
if BoundedIntDivRemAlgorithm::new(&lhs_range, &rhs_range).is_none() {
if BoundedIntDivRemAlgorithm::try_new(&lhs_range, &rhs_range).is_none() {
return Err(SpecializationError::UnsupportedGenericArg);
}
let quotient_min = lhs_range.lower / (&rhs_range.upper - 1);
Expand Down Expand Up @@ -226,34 +226,43 @@ pub enum BoundedIntDivRemAlgorithm {
/// The rhs is small enough to be multiplied by `2**128` without wraparound.
KnownSmallRhs,
/// The quotient is small enough to be multiplied by `2**128` without wraparound.
KnownSmallQuotient(BigInt),
KnownSmallQuotient { q_upper_bound: BigInt },
/// The lhs is small enough so that its square root plus 1 can be multiplied by `2**128`
/// without wraparound.
KnownSmallLhs(BigInt),
/// `lhs_upper_sqrt` is the square root of the upper bound of the lhs, rounded up.
KnownSmallLhs { lhs_upper_sqrt: BigInt },
}
impl BoundedIntDivRemAlgorithm {
/// Returns the algorithm to use for division and remainder of bounded integers.
/// Fails if the div_rem of the ranges is not supported yet.
///
/// Assumption: `lhs` is non-negative and `rhs` is positive.
pub fn new(lhs: &Range, rhs: &Range) -> Option<Self> {
pub fn try_new(lhs: &Range, rhs: &Range) -> Option<Self> {
let prime = Felt252::prime().to_bigint().unwrap();
let q_max = (&lhs.upper - 1) / &rhs.lower;
let u128_limit = BigInt::one().shl(128);
// `q` is range checked in all algorithm variants, so `q_max` must be smaller than `2**128`.
require(q_max < u128_limit)?;
// `r` is range checked in all algorithm variants, so `lhs.upper` must be at most `2**128`.
require(rhs.upper <= u128_limit)?;
// `r` is range checked in all algorithm variants, so `rhs.upper` must be at most
// `2**128 + 1`.
require(rhs.upper <= &u128_limit + 1)?;
if &rhs.upper * &u128_limit < prime {
return Some(Self::KnownSmallRhs);
}
let q_upper_bound = q_max + 1;
if &q_upper_bound * &u128_limit < prime {
return Some(Self::KnownSmallQuotient(q_upper_bound));
return Some(Self::KnownSmallQuotient { q_upper_bound });
}
let root = lhs.upper.sqrt();
if (&root + 1) * &u128_limit < prime {
return Some(Self::KnownSmallLhs(root));
let mut lhs_upper_sqrt = lhs.upper.sqrt();
// Round lhs_upper_sqrt up.
if lhs_upper_sqrt.pow(2) != lhs.upper {
lhs_upper_sqrt += 1;
}
if &lhs_upper_sqrt * &u128_limit < prime {
// Make sure `lhs_upper_sqrt < 2**128`, since the value bounded by root is range
// checked.
require(lhs_upper_sqrt < u128_limit)?;
return Some(Self::KnownSmallLhs { lhs_upper_sqrt });
}
// No algorithm found.
None
Expand All @@ -280,15 +289,12 @@ impl NamedLibfunc for BoundedIntConstrainLibfunc {
_ => Err(SpecializationError::WrongNumberOfGenericArgs),
}?;
let range = Range::from_type(context, ty.clone())?;
let under_range = Range::half_open(range.lower, boundary.clone());
let over_range = Range::half_open(boundary.clone(), range.upper);
require(
under_range.size() >= BigInt::one()
&& over_range.size() >= BigInt::one()
&& under_range.is_small_range()
&& over_range.is_small_range(),
)
.ok_or(SpecializationError::UnsupportedGenericArg)?;
require(&range.lower < boundary && boundary < &range.upper)
.ok_or(SpecializationError::UnsupportedGenericArg)?;
let low_range = Range::half_open(range.lower, boundary.clone());
let high_range = Range::half_open(boundary.clone(), range.upper);
require(low_range.is_small_range() && high_range.is_small_range())
.ok_or(SpecializationError::UnsupportedGenericArg)?;
let range_check_type = context.get_concrete_type(RangeCheckType::id(), &[])?;
let branch_signature = |rng: Range| {
Ok(BranchSignature {
Expand All @@ -307,7 +313,7 @@ impl NamedLibfunc for BoundedIntConstrainLibfunc {
ParamSignature::new(range_check_type.clone()).with_allow_add_const(),
ParamSignature::new(ty.clone()),
],
branch_signatures: vec![branch_signature(under_range)?, branch_signature(over_range)?],
branch_signatures: vec![branch_signature(low_range)?, branch_signature(high_range)?],
fallthrough: Some(0),
})
}
Expand Down Expand Up @@ -349,8 +355,8 @@ fn specialize_helper(
Range::from_type(context, lhs.clone())?,
Range::from_type(context, rhs.clone())?,
);
Ok(LibfuncSignature::new_non_branch(
vec![lhs, rhs],
Ok(LibfuncSignature::new_non_branch_ex(
vec![ParamSignature::new(lhs), ParamSignature::new(rhs).with_allow_const()],
vec![OutputVarInfo {
ty: bounded_int_ty(context, min_result, max_result)?,
ref_info: OutputVarReferenceInfo::Deferred(DeferredOutputKind::Generic),
Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -12,7 +12,7 @@ use crate::extensions::lib_func::{
SierraApChange, SignatureSpecializationContext,
};
use crate::extensions::modules::get_u256_type;
use crate::extensions::utils::{fixed_size_array_ty, reinterpret_cast_signature};
use crate::extensions::utils::fixed_size_array_ty;
use crate::extensions::{
NamedType, NoGenericArgsGenericLibfunc, NoGenericArgsGenericType, OutputVarReferenceInfo,
SpecializationError,
Expand Down Expand Up @@ -207,9 +207,15 @@ impl NoGenericArgsGenericLibfunc for Sha256StateHandleInitLibfunc {
&self,
context: &dyn SignatureSpecializationContext,
) -> Result<LibfuncSignature, SpecializationError> {
Ok(reinterpret_cast_signature(
sha256_state_handle_unwrapped_type(context)?,
context.get_concrete_type(Sha256StateHandleType::id(), &[])?,
Ok(LibfuncSignature::new_non_branch_ex(
vec![
ParamSignature::new(sha256_state_handle_unwrapped_type(context)?).with_allow_all(),
],
vec![OutputVarInfo {
ty: context.get_concrete_type(Sha256StateHandleType::id(), &[])?,
ref_info: OutputVarReferenceInfo::Deferred(DeferredOutputKind::Generic),
}],
SierraApChange::Known { new_vars_only: false },
))
}
}
Expand All @@ -224,9 +230,16 @@ impl NoGenericArgsGenericLibfunc for Sha256StateHandleDigestLibfunc {
&self,
context: &dyn SignatureSpecializationContext,
) -> Result<LibfuncSignature, SpecializationError> {
Ok(reinterpret_cast_signature(
context.get_concrete_type(Sha256StateHandleType::id(), &[])?,
sha256_state_handle_unwrapped_type(context)?,
Ok(LibfuncSignature::new_non_branch_ex(
vec![
ParamSignature::new(context.get_concrete_type(Sha256StateHandleType::id(), &[])?)
.with_allow_all(),
],
vec![OutputVarInfo {
ty: sha256_state_handle_unwrapped_type(context)?,
ref_info: OutputVarReferenceInfo::Deferred(DeferredOutputKind::Generic),
}],
SierraApChange::Known { new_vars_only: false },
))
}
}
Expand Down
42 changes: 42 additions & 0 deletions tests/e2e_test_data/libfuncs/bounded_int
Original file line number Diff line number Diff line change
Expand Up @@ -115,6 +115,48 @@ test::foo@0([0]: i8, [1]: i8) -> (BoundedInt<-16256, 16384>);

//! > ==========================================================================

//! > bounded_int_add with const libfunc

//! > test_runner_name
SmallE2ETestRunner

//! > cairo
extern type BoundedInt<const MIN: felt252, const MAX: felt252>;
const MIN_I8: felt252 = -128;
const MAX_I8: felt252 = 127;
type AddType = BoundedInt<{MIN_I8 + MIN_I8}, {MAX_I8 + MAX_I8}>;

extern fn bounded_int_add<T1, T2>(a: T1, b: T2) -> AddType nopanic;

fn foo(a: i8) -> AddType {
bounded_int_add(a, 50_i8)
}

//! > casm
[ap + 0] = [fp + -3] + 50, ap++;
ret;

//! > function_costs
test::foo: OrderedHashMap({Const: 100})

//! > sierra_code
type i8 = i8 [storable: true, drop: true, dup: true, zero_sized: false];
type BoundedInt<-256, 254> = BoundedInt<-256, 254> [storable: true, drop: true, dup: true, zero_sized: false];
type Const<i8, 50> = Const<i8, 50> [storable: false, drop: false, dup: false, zero_sized: false];

libfunc const_as_immediate<Const<i8, 50>> = const_as_immediate<Const<i8, 50>>;
libfunc bounded_int_add<i8, i8> = bounded_int_add<i8, i8>;
libfunc store_temp<BoundedInt<-256, 254>> = store_temp<BoundedInt<-256, 254>>;

const_as_immediate<Const<i8, 50>>() -> ([1]); // 0
bounded_int_add<i8, i8>([0], [1]) -> ([2]); // 1
store_temp<BoundedInt<-256, 254>>([2]) -> ([2]); // 2
return([2]); // 3

test::foo@0([0]: i8) -> (BoundedInt<-256, 254>);

//! > ==========================================================================

//! > bounded_int_div_rem libfunc

//! > test_runner_name
Expand Down

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