phantom_zone/

decomposer.rs

use itertools::{izip, Itertools};
use num_traits::{FromPrimitive, PrimInt, ToPrimitive, WrappingAdd, WrappingSub};
use std::fmt::{Debug, Display};

use crate::{
    backend::ArithmeticOps,
    parameters::{
        DecompositionCount, DecompostionLogBase, DoubleDecomposerParams, SingleDecomposerParams,
    },
    utils::log2,
};

fn gadget_vector<T: PrimInt>(logq: usize, logb: usize, d: usize) -> Vec<T> {
    assert!(logq >= (logb * d));
    let ignored_bits = logq - (logb * d);

    (0..d)
        .into_iter()
        .map(|i| T::one() << (logb * i + ignored_bits))
        .collect_vec()
}

pub trait RlweDecomposer {
    type Element;
    type D: Decomposer<Element = Self::Element>;

    /// Decomposer for RLWE Part A
    fn a(&self) -> &Self::D;
    /// Decomposer for RLWE Part B
    fn b(&self) -> &Self::D;
}

impl<D> RlweDecomposer for (D, D)
where
    D: Decomposer,
{
    type D = D;
    type Element = D::Element;
    fn a(&self) -> &Self::D {
        &self.0
    }
    fn b(&self) -> &Self::D {
        &self.1
    }
}

impl<D> DoubleDecomposerParams for D
where
    D: RlweDecomposer,
{
    type Base = DecompostionLogBase;
    type Count = DecompositionCount;

    fn decomposition_base(&self) -> Self::Base {
        assert!(
            Decomposer::decomposition_base(self.a()) == Decomposer::decomposition_base(self.b())
        );
        Decomposer::decomposition_base(self.a())
    }
    fn decomposition_count_a(&self) -> Self::Count {
        Decomposer::decomposition_count(self.a())
    }
    fn decomposition_count_b(&self) -> Self::Count {
        Decomposer::decomposition_count(self.b())
    }
}

impl<D> SingleDecomposerParams for D
where
    D: Decomposer,
{
    type Base = DecompostionLogBase;
    type Count = DecompositionCount;
    fn decomposition_base(&self) -> Self::Base {
        Decomposer::decomposition_base(self)
    }
    fn decomposition_count(&self) -> Self::Count {
        Decomposer::decomposition_count(self)
    }
}

pub trait Decomposer {
    type Element;
    type Iter: Iterator<Item = Self::Element>;
    fn new(q: Self::Element, logb: usize, d: usize) -> Self;

    fn decompose_to_vec(&self, v: &Self::Element) -> Vec<Self::Element>;
    fn decompose_iter(&self, v: &Self::Element) -> Self::Iter;
    fn decomposition_count(&self) -> DecompositionCount;
    fn decomposition_base(&self) -> DecompostionLogBase;
    fn gadget_vector(&self) -> Vec<Self::Element>;
}

pub struct DefaultDecomposer<T> {
    /// Ciphertext modulus
    q: T,
    /// Log of ciphertext modulus
    logq: usize,
    /// Log of base B
    logb: usize,
    /// base B
    b: T,
    /// (B - 1). To simulate (% B) as &(B-1), that is extract least significant
    /// logb bits
    b_mask: T,
    /// B/2
    bby2: T,
    /// Decomposition count
    d: usize,
    /// No. of bits to ignore in rounding
    ignore_bits: usize,
}

pub trait NumInfo {
    const BITS: u32;
}

impl NumInfo for u64 {
    const BITS: u32 = u64::BITS;
}
impl NumInfo for u32 {
    const BITS: u32 = u32::BITS;
}
impl NumInfo for u128 {
    const BITS: u32 = u128::BITS;
}

impl<T: PrimInt + NumInfo + Debug> DefaultDecomposer<T> {
    fn recompose<Op>(&self, limbs: &[T], modq_op: &Op) -> T
    where
        Op: ArithmeticOps<Element = T>,
    {
        let mut value = T::zero();
        let gadget_vector = gadget_vector(self.logq, self.logb, self.d);
        assert!(limbs.len() == gadget_vector.len());
        izip!(limbs.iter(), gadget_vector.iter())
            .for_each(|(d_el, beta)| value = modq_op.add(&value, &modq_op.mul(d_el, beta)));

        value
    }
}

impl<
        T: PrimInt
            + ToPrimitive
            + FromPrimitive
            + WrappingSub
            + WrappingAdd
            + NumInfo
            + From<bool>
            + Display
            + Debug,
    > Decomposer for DefaultDecomposer<T>
{
    type Element = T;
    type Iter = DecomposerIter<T>;

    fn new(q: T, logb: usize, d: usize) -> DefaultDecomposer<T> {
        // if q is power of 2, then `BITS - leading_zeros` outputs logq + 1.
        let logq = log2(&q);
        assert!(
            logq >= (logb * d),
            "Decomposer wants logq >= logb*d but got logq={logq}, logb={logb}, d={d}"
        );

        let ignore_bits = logq - (logb * d);

        DefaultDecomposer {
            q,
            logq,
            logb,
            b: T::one() << logb,
            b_mask: (T::one() << logb) - T::one(),
            bby2: T::one() << (logb - 1),
            d,
            ignore_bits,
        }
    }

    fn decompose_to_vec(&self, value: &T) -> Vec<T> {
        let q = self.q;
        let logb = self.logb;
        let b = T::one() << logb;
        let full_mask = b - T::one();
        let bby2 = b >> 1;

        let mut value = *value;
        if value >= (q >> 1) {
            value = !(q - value) + T::one()
        }
        value = round_value(value, self.ignore_bits);
        let mut out = Vec::with_capacity(self.d);
        for _ in 0..(self.d) {
            let k_i = value & full_mask;

            value = (value - k_i) >> logb;

            if k_i > bby2 || (k_i == bby2 && ((value & T::one()) == T::one())) {
                out.push(q - (b - k_i));
                value = value + T::one();
            } else {
                out.push(k_i);
            }
        }

        return out;
    }

    fn decomposition_count(&self) -> DecompositionCount {
        DecompositionCount(self.d)
    }

    fn decomposition_base(&self) -> DecompostionLogBase {
        DecompostionLogBase(self.logb)
    }

    fn decompose_iter(&self, value: &T) -> DecomposerIter<T> {
        let mut value = *value;
        if value >= (self.q >> 1) {
            value = !(self.q - value) + T::one()
        }
        value = round_value(value, self.ignore_bits);

        DecomposerIter {
            value,
            q: self.q,
            logq: self.logq,
            logb: self.logb,
            b: self.b,
            bby2: self.bby2,
            b_mask: self.b_mask,
            steps_left: self.d,
        }
    }

    fn gadget_vector(&self) -> Vec<T> {
        return gadget_vector(self.logq, self.logb, self.d);
    }
}

impl<T: PrimInt> DefaultDecomposer<T> {}

pub struct DecomposerIter<T> {
    /// Value to decompose
    value: T,
    steps_left: usize,
    /// (1 << logb) - 1 (for % (1<<logb); i.e. to extract least signiciant logb
    /// bits)
    b_mask: T,
    logb: usize,
    // b/2 = 1 << (logb-1)
    bby2: T,
    /// Ciphertext modulus
    q: T,
    /// Log of ciphertext modulus
    logq: usize,
    /// b = 1 << logb
    b: T,
}

impl<T: PrimInt + From<bool> + WrappingSub + Display> Iterator for DecomposerIter<T> {
    type Item = T;

    fn next(&mut self) -> Option<Self::Item> {
        if self.steps_left != 0 {
            self.steps_left -= 1;
            let k_i = self.value & self.b_mask;

            self.value = (self.value - k_i) >> self.logb;

            // if k_i > self.bby2 || (k_i == self.bby2 && ((self.value &
            // T::one()) == T::one())) {     self.value = self.value
            // + T::one();     Some(self.q + k_i - self.b)
            // } else {
            //     Some(k_i)
            // }

            // Following is without branching impl of the commented version above. It
            // happens to speed up bootstrapping for `SMALL_MP_BOOL_PARAMS` (& other
            // parameters as well but I haven't tested) by roughly 15ms.
            // Suprisingly the improvement does not show up when I benchmark
            // `decomposer_iter` in isolation. Putting this remark here as a
            // future task to investiage (TODO).
            let carry_bool =
                k_i > self.bby2 || (k_i == self.bby2 && ((self.value & T::one()) == T::one()));
            let carry = <T as From<bool>>::from(carry_bool);
            let neg_carry = (T::zero().wrapping_sub(&carry));
            self.value = self.value + carry;
            Some((neg_carry & self.q) + k_i - (carry << self.logb))

            // Some(
            //     (self.q & ((carry << self.logq) - (T::one() & carry))) + k_i
            // - (carry << self.logb), )

            // Some(k_i)
        } else {
            None
        }
    }
}

fn round_value<T: PrimInt + WrappingAdd>(value: T, ignore_bits: usize) -> T {
    if ignore_bits == 0 {
        return value;
    }

    let ignored_msb = (value & ((T::one() << ignore_bits) - T::one())) >> (ignore_bits - 1);
    (value >> ignore_bits).wrapping_add(&ignored_msb)
}

#[cfg(test)]
mod tests {

    use itertools::Itertools;
    use rand::{thread_rng, Rng};

    use crate::{
        backend::{ModInit, ModularOpsU64},
        decomposer::round_value,
        utils::generate_prime,
    };

    use super::{Decomposer, DefaultDecomposer};

    #[test]
    fn decomposition_works() {
        let ring_size = 1 << 11;

        let mut rng = thread_rng();

        for logq in [37, 55] {
            let logb = 11;
            let d = 3;
            // let mut stats = vec![Stats::new(); d];

            for i in [true, false] {
                let q = if i {
                    generate_prime(logq, 2 * ring_size, 1u64 << logq).unwrap()
                } else {
                    1u64 << logq
                };
                let decomposer = DefaultDecomposer::new(q, logb, d);
                let modq_op = ModularOpsU64::new(q);
                for _ in 0..1000000 {
                    let value = rng.gen_range(0..q);
                    let limbs = decomposer.decompose_to_vec(&value);
                    let limbs_from_iter = decomposer.decompose_iter(&value).collect_vec();
                    assert_eq!(limbs, limbs_from_iter);
                    let value_back = round_value(
                        decomposer.recompose(&limbs, &modq_op),
                        decomposer.ignore_bits,
                    );
                    let rounded_value = round_value(value, decomposer.ignore_bits);
                    assert!((rounded_value as i64 - value_back as i64).abs() <= 1,);

                    // izip!(stats.iter_mut(), limbs.iter()).for_each(|(s, l)| {
                    //     s.add_more(&vec![q.map_element_to_i64(l)]);
                    // });
                }
            }

            // stats.iter().enumerate().for_each(|(index, s)| {
            //     println!(
            //         "Limb {index} - Mean: {}, Std: {}",
            //         s.mean(),
            //         s.std_dev().abs().log2()
            //     );
            // });
        }
    }
}