1use itertools::Itertools;
  2use num_traits::{AsPrimitive, FromPrimitive, Num, One, PrimInt, ToPrimitive, WrappingSub, Zero};
  3use std::{fmt::Debug, marker::PhantomData, ops::Rem};
  4
  5use crate::backend::{ArithmeticOps, ModularOpsU64};
  6
  7fn gadget_vector<T: PrimInt>(logq: usize, logb: usize, d: usize) -> Vec<T> {
  8    let d_ideal = (logq as f64 / logb as f64).ceil().to_usize().unwrap();
  9    let ignored_limbs = d_ideal - d;
 10    (ignored_limbs..ignored_limbs + d)
 11        .into_iter()
 12        .map(|i| T::one() << (logb * i))
 13        .collect_vec()
 14}
 15
 16pub trait RlweDecomposer {
 17    type Element;
 18    type D: Decomposer<Element = Self::Element>;
 19
 20    /// Decomposer for RLWE Part A
 21    fn a(&self) -> &Self::D;
 22    /// Decomposer for RLWE Part B
 23    fn b(&self) -> &Self::D;
 24}
 25
 26impl<D> RlweDecomposer for (D, D)
 27where
 28    D: Decomposer,
 29{
 30    type D = D;
 31    type Element = D::Element;
 32    fn a(&self) -> &Self::D {
 33        &self.0
 34    }
 35    fn b(&self) -> &Self::D {
 36        &self.1
 37    }
 38}
 39
 40pub trait Decomposer {
 41    type Element;
 42    fn new(q: Self::Element, logb: usize, d: usize) -> Self;
 43    //FIXME(Jay): there's no reason why it returns a vec instead of an iterator
 44    fn decompose(&self, v: &Self::Element) -> Vec<Self::Element>;
 45    fn decomposition_count(&self) -> usize;
 46}
 47
 48// TODO(Jay): Shouldn't Decompose also return corresponding gadget vector ?
 49pub struct DefaultDecomposer<T> {
 50    q: T,
 51    logq: usize,
 52    logb: usize,
 53    d: usize,
 54    ignore_bits: usize,
 55    ignore_limbs: usize,
 56}
 57
 58pub trait NumInfo {
 59    const BITS: u32;
 60}
 61
 62impl NumInfo for u64 {
 63    const BITS: u32 = u64::BITS;
 64}
 65impl NumInfo for u32 {
 66    const BITS: u32 = u32::BITS;
 67}
 68impl NumInfo for u128 {
 69    const BITS: u32 = u128::BITS;
 70}
 71
 72impl<T: PrimInt + NumInfo + Debug> DefaultDecomposer<T> {
 73    fn recompose<Op>(&self, limbs: &[T], modq_op: &Op) -> T
 74    where
 75        Op: ArithmeticOps<Element = T>,
 76    {
 77        let mut value = T::zero();
 78        for i in 0..self.d {
 79            value = modq_op.add(
 80                &value,
 81                &(modq_op.mul(
 82                    &limbs[i],
 83                    &(T::one() << (self.logb * (i + self.ignore_limbs))),
 84                )),
 85            )
 86        }
 87        value
 88    }
 89
 90    pub(crate) fn gadget_vector(&self) -> Vec<T> {
 91        return gadget_vector(self.logq, self.logb, self.d);
 92    }
 93}
 94
 95impl<T: PrimInt + ToPrimitive + FromPrimitive + WrappingSub + NumInfo> Decomposer
 96    for DefaultDecomposer<T>
 97{
 98    type Element = T;
 99
100    fn new(q: T, logb: usize, d: usize) -> DefaultDecomposer<T> {
101        // if q is power of 2, then `BITS - leading_zeros` outputs logq + 1.
102        let logq = if q & (q - T::one()) == T::zero() {
103            (T::BITS - q.leading_zeros() - 1) as usize
104        } else {
105            (T::BITS - q.leading_zeros()) as usize
106        };
107
108        let d_ideal = (logq as f64 / logb as f64).ceil().to_usize().unwrap();
109        let ignore_limbs = (d_ideal - d);
110        let ignore_bits = (d_ideal - d) * logb;
111
112        DefaultDecomposer {
113            q,
114            logq,
115            logb,
116            d,
117            ignore_bits,
118            ignore_limbs,
119        }
120    }
121
122    // TODO(Jay): Outline the caveat
123    fn decompose(&self, value: &T) -> Vec<T> {
124        let mut value = round_value(*value, self.ignore_bits);
125
126        let q = self.q;
127        let logb = self.logb;
128        let b = T::one() << logb;
129        let full_mask = b - T::one();
130        let bby2 = b >> 1;
131
132        if value >= (q >> 1) {
133            value = !(q - value) + T::one()
134        }
135
136        let mut out = Vec::with_capacity(self.d);
137        for _ in 0..self.d {
138            let k_i = value & full_mask;
139
140            value = (value - k_i) >> logb;
141
142            if k_i > bby2 || (k_i == bby2 && ((value & T::one()) == T::one())) {
143                out.push(q - (b - k_i));
144                value = value + T::one();
145            } else {
146                out.push(k_i);
147            }
148        }
149
150        return out;
151    }
152
153    fn decomposition_count(&self) -> usize {
154        self.d
155    }
156}
157
158fn round_value<T: PrimInt>(value: T, ignore_bits: usize) -> T {
159    if ignore_bits == 0 {
160        return value;
161    }
162
163    let ignored_msb = (value & ((T::one() << ignore_bits) - T::one())) >> (ignore_bits - 1);
164    (value >> ignore_bits) + ignored_msb
165}
166
167#[cfg(test)]
168mod tests {
169
170    use rand::{thread_rng, Rng};
171
172    use crate::{
173        backend::{ModInit, ModularOpsU64},
174        decomposer::round_value,
175        utils::{generate_prime, Stats, TryConvertFrom1},
176    };
177
178    use super::{Decomposer, DefaultDecomposer};
179
180    #[test]
181    fn decomposition_works() {
182        let logq = 55;
183        let logb = 11;
184        let d = 5;
185        let ring_size = 1 << 11;
186
187        let mut rng = thread_rng();
188        let mut stats = Stats { samples: vec![] };
189
190        for i in [true] {
191            let q = if i {
192                generate_prime(logq, 2 * ring_size, 1u64 << logq).unwrap()
193            } else {
194                1u64 << logq
195            };
196            let decomposer = DefaultDecomposer::new(q, logb, d);
197            let modq_op = ModularOpsU64::new(q);
198            for _ in 0..100000 {
199                let value = rng.gen_range(0..q);
200                let limbs = decomposer.decompose(&value);
201                let value_back = decomposer.recompose(&limbs, &modq_op);
202                let rounded_value =
203                    round_value(value, decomposer.ignore_bits) << decomposer.ignore_bits;
204                stats.add_more(&Vec::<i64>::try_convert_from(&limbs, &q));
205                assert_eq!(
206                    rounded_value, value_back,
207                    "Expected {rounded_value} got {value_back} for q={q}"
208                );
209            }
210        }
211        println!("Mean: {}", stats.mean());
212        println!("Std: {}", stats.std_dev().abs().log2());
213    }
214}