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use itertools::izip;
use p3_air::AirBuilder;
use p3_field::AbstractField;
use p3_field::PrimeField32;
use sp1_derive::AlignedBorrow;
use crate::air::BaseAirBuilder;
use crate::{
bytes::{event::ByteRecord, ByteLookupEvent, ByteOpcode},
stark::SP1AirBuilder,
};
/// Operation columns for verifying that an element is within the range `[0, modulus)`.
#[derive(Debug, Clone, Copy, AlignedBorrow)]
#[repr(C)]
pub struct AssertLtColsBytes<T, const N: usize> {
/// Boolean flags to indicate the first byte in which the element is smaller than the modulus.
pub(crate) byte_flags: [T; N],
pub(crate) a_comparison_byte: T,
pub(crate) b_comparison_byte: T,
}
impl<F: PrimeField32, const N: usize> AssertLtColsBytes<F, N> {
pub fn populate(
&mut self,
record: &mut impl ByteRecord,
shard: u32,
channel: u8,
a: &[u8],
b: &[u8],
) {
let mut byte_flags = vec![0u8; N];
for (a_byte, b_byte, flag) in
izip!(a.iter().rev(), b.iter().rev(), byte_flags.iter_mut().rev())
{
assert!(a_byte <= b_byte);
if a_byte < b_byte {
*flag = 1;
self.a_comparison_byte = F::from_canonical_u8(*a_byte);
self.b_comparison_byte = F::from_canonical_u8(*b_byte);
record.add_byte_lookup_event(ByteLookupEvent {
opcode: ByteOpcode::LTU,
shard,
channel,
a1: 1,
a2: 0,
b: *a_byte,
c: *b_byte,
});
break;
}
}
for (byte, flag) in izip!(byte_flags.iter(), self.byte_flags.iter_mut()) {
*flag = F::from_canonical_u8(*byte);
}
}
}
impl<V: Copy, const N: usize> AssertLtColsBytes<V, N> {
pub fn eval<
AB: SP1AirBuilder<Var = V>,
Ea: Into<AB::Expr> + Clone,
Eb: Into<AB::Expr> + Clone,
>(
&self,
builder: &mut AB,
a: &[Ea],
b: &[Eb],
shard: impl Into<AB::Expr> + Clone,
channel: impl Into<AB::Expr> + Clone,
is_real: impl Into<AB::Expr> + Clone,
) where
V: Into<AB::Expr>,
{
// The byte flags give a specification of which byte is `first_eq`, i,e, the first most
// significant byte for which the element `a` is smaller than `b`. To verify the
// less-than claim we need to check that:
// * For all bytes until `first_eq` the element `a` byte is equal to the `b` byte.
// * For the `first_eq` byte the `a`` byte is smaller than the `b`byte.
// * all byte flags are boolean.
// * only one byte flag is set to one, and the rest are set to zero.
// Check the flags are of valid form.
// Verrify that only one flag is set to one.
let mut sum_flags: AB::Expr = AB::Expr::zero();
for &flag in self.byte_flags.iter() {
// Assert that the flag is boolean.
builder.assert_bool(flag);
// Add the flag to the sum.
sum_flags += flag.into();
}
// Assert that the sum is equal to one.
builder.when(is_real.clone()).assert_one(sum_flags);
// Check the less-than condition.
// A flag to indicate whether an equality check is necessary (this is for all bytes from
// most significant until the first inequality.
let mut is_inequality_visited = AB::Expr::zero();
// The bytes of the modulus.
let a: [AB::Expr; N] = core::array::from_fn(|i| a[i].clone().into());
let b: [AB::Expr; N] = core::array::from_fn(|i| b[i].clone().into());
let mut first_lt_byte = AB::Expr::zero();
let mut b_comparison_byte = AB::Expr::zero();
for (a_byte, b_byte, &flag) in
izip!(a.iter().rev(), b.iter().rev(), self.byte_flags.iter().rev())
{
// Once the byte flag was set to one, we turn off the quality check flag.
// We can do this by calculating the sum of the flags since only `1` is set to `1`.
is_inequality_visited += flag.into();
first_lt_byte += a_byte.clone() * flag;
b_comparison_byte += b_byte.clone() * flag;
builder
.when_not(is_inequality_visited.clone())
.when(is_real.clone())
.assert_eq(a_byte.clone(), b_byte.clone());
}
builder
.when(is_real.clone())
.assert_eq(self.a_comparison_byte, first_lt_byte);
builder
.when(is_real.clone())
.assert_eq(self.b_comparison_byte, b_comparison_byte);
// Send the comparison interaction.
builder.send_byte(
ByteOpcode::LTU.as_field::<AB::F>(),
AB::F::one(),
self.a_comparison_byte,
self.b_comparison_byte,
shard,
channel,
is_real,
)
}
}
/// Operation columns for verifying that an element is within the range `[0, modulus)`.
#[derive(Debug, Clone, Copy, AlignedBorrow)]
#[repr(C)]
pub struct AssertLtColsBits<T, const N: usize> {
/// Boolean flags to indicate the first byte in which the element is smaller than the modulus.
pub(crate) bit_flags: [T; N],
}
impl<F: PrimeField32, const N: usize> AssertLtColsBits<F, N> {
pub fn populate(&mut self, a: &[u32], b: &[u32]) {
let mut bit_flags = vec![0u8; N];
for (a_bit, b_bit, flag) in
izip!(a.iter().rev(), b.iter().rev(), bit_flags.iter_mut().rev())
{
assert!(a_bit <= b_bit);
debug_assert!(*a_bit == 0 || *a_bit == 1);
debug_assert!(*b_bit == 0 || *b_bit == 1);
if a_bit < b_bit {
*flag = 1;
break;
}
}
for (bit, flag) in izip!(bit_flags.iter(), self.bit_flags.iter_mut()) {
*flag = F::from_canonical_u8(*bit);
}
}
}
impl<V: Copy, const N: usize> AssertLtColsBits<V, N> {
pub fn eval<
AB: SP1AirBuilder<Var = V>,
Ea: Into<AB::Expr> + Clone,
Eb: Into<AB::Expr> + Clone,
>(
&self,
builder: &mut AB,
a: &[Ea],
b: &[Eb],
is_real: impl Into<AB::Expr> + Clone,
) where
V: Into<AB::Expr>,
{
// The bit flags give a specification of which bit is `first_lt`, i,e, the first most
// significant bit for which the element `a` is smaller than `b`. To verify the
// less-than claim we need to check that:
// * For all bytes until `first_lt` the element `a` byte is equal to the `b` byte.
// * For the `first_lt` bit the `a`` bit is smaller than the `b` bit.
// * all bit flags are boolean.
// * only one bit flag is set to one, and the rest are set to zero.
// Check the flags are of valid form.
// Verrify that only one flag is set to one.
let mut sum_flags: AB::Expr = AB::Expr::zero();
for &flag in self.bit_flags.iter() {
// Assert that the flag is boolean.
builder.assert_bool(flag);
// Add the flag to the sum.
sum_flags += flag.into();
}
// Assert that the sum is equal to one.
builder.when(is_real.clone()).assert_one(sum_flags);
// Check the less-than condition.
// A flag to indicate whether an equality check is necessary (this is for all bits from
// most significant until the first inequality.
let mut is_inequality_visited = AB::Expr::zero();
// The bits of the elements.
let a: [AB::Expr; N] = core::array::from_fn(|i| a[i].clone().into());
let b: [AB::Expr; N] = core::array::from_fn(|i| b[i].clone().into());
// Calculate the bit which is the first inequality.
let mut a_comparison_bit = AB::Expr::zero();
let mut b_comparison_bit = AB::Expr::zero();
for (a_bit, b_bit, &flag) in
izip!(a.iter().rev(), b.iter().rev(), self.bit_flags.iter().rev())
{
// Once the bit flag was set to one, we turn off the quality check flag.
// We can do this by calculating the sum of the flags since only `1` is set to `1`.
is_inequality_visited += flag.into();
a_comparison_bit += a_bit.clone() * flag;
b_comparison_bit += b_bit.clone() * flag;
builder
.when(is_real.clone())
.when_not(is_inequality_visited.clone())
.assert_eq(a_bit.clone(), b_bit.clone());
}
builder
.when(is_real.clone())
.assert_eq(a_comparison_bit, AB::F::zero());
builder
.when(is_real.clone())
.assert_eq(b_comparison_bit, AB::F::one());
}
}