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use super::*;
impl<F: PrimeField> Boolean<F> {
/// Conditionally selects one of `first` and `second` based on the value of
/// `self`:
///
/// If `self.is_eq(&Boolean::TRUE)`, this outputs `first`; else, it outputs
/// `second`.
/// ```
/// # fn main() -> Result<(), ark_relations::gr1cs::SynthesisError> {
/// // We'll use the BLS12-381 scalar field for our constraints.
/// use ark_test_curves::bls12_381::Fr;
/// use ark_relations::gr1cs::*;
/// use ark_r1cs_std::prelude::*;
///
/// let cs = ConstraintSystem::<Fr>::new_ref();
///
/// let a = Boolean::new_witness(cs.clone(), || Ok(true))?;
/// let b = Boolean::new_witness(cs.clone(), || Ok(false))?;
///
/// let cond = Boolean::new_witness(cs.clone(), || Ok(true))?;
///
/// cond.select(&a, &b)?.enforce_equal(&Boolean::TRUE)?;
/// cond.select(&b, &a)?.enforce_equal(&Boolean::FALSE)?;
///
/// assert!(cs.is_satisfied().unwrap());
/// # Ok(())
/// # }
/// ```
#[tracing::instrument(target = "gr1cs", skip(first, second))]
pub fn select<T: CondSelectGadget<F>>(
&self,
first: &T,
second: &T,
) -> Result<T, SynthesisError> {
T::conditionally_select(&self, first, second)
}
}
impl<F: PrimeField> CondSelectGadget<F> for Boolean<F> {
#[tracing::instrument(target = "gr1cs")]
fn conditionally_select(
cond: &Boolean<F>,
true_val: &Self,
false_val: &Self,
) -> Result<Self, SynthesisError> {
use Boolean::*;
match cond {
Constant(true) => Ok(true_val.clone()),
Constant(false) => Ok(false_val.clone()),
cond @ Var(_) => match (true_val, false_val) {
(x, &Constant(false)) => Ok(cond & x),
(&Constant(false), x) => Ok((!cond) & x),
(&Constant(true), x) => Ok(cond | x),
(x, &Constant(true)) => Ok((!cond) | x),
(a, b) => {
let cs = cond.cs();
let result: Boolean<F> =
AllocatedBool::new_witness_without_booleanity_check(cs.clone(), || {
let cond = cond.value()?;
Ok(if cond { a.value()? } else { b.value()? })
})?
.into();
// a = self; b = other; c = cond;
//
// r = c * a + (1 - c) * b
// r = b + c * (a - b)
// c * (a - b) = r - b
//
// If a, b, cond are all boolean, so is r.
//
// self | other | cond | result
// -----|-------|----------------
// 0 | 0 | 1 | 0
// 0 | 1 | 1 | 0
// 1 | 0 | 1 | 1
// 1 | 1 | 1 | 1
// 0 | 0 | 0 | 0
// 0 | 1 | 0 | 1
// 1 | 0 | 0 | 0
// 1 | 1 | 0 | 1
cs.enforce_r1cs_constraint(
|| cond.lc(),
|| lc_diff![a.variable(), b.variable()],
|| lc_diff![result.variable(), b.variable()],
)?;
Ok(result)
},
},
}
}
}
#[cfg(test)]
mod tests {
use super::*;
use crate::{
alloc::{AllocVar, AllocationMode},
boolean::test_utils::run_binary_exhaustive,
prelude::EqGadget,
GR1CSVar,
};
use ark_test_curves::bls12_381::Fr;
#[test]
fn or() {
run_binary_exhaustive::<Fr>(|a, b| {
let cs = a.cs().or(b.cs());
let both_constant = a.is_constant() && b.is_constant();
let expected_mode = if both_constant {
AllocationMode::Constant
} else {
AllocationMode::Witness
};
for cond in [true, false] {
let expected = Boolean::new_variable(
cs.clone(),
|| Ok(if cond { a.value()? } else { b.value()? }),
expected_mode,
)?;
let cond = Boolean::new_variable(cs.clone(), || Ok(cond), expected_mode)?;
let computed = cond.select(&a, &b)?;
assert_eq!(expected.value(), computed.value());
expected.enforce_equal(&computed)?;
if !both_constant {
assert!(cs.is_satisfied().unwrap());
}
}
Ok(())
})
.unwrap()
}
}