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 + Debug + 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    /// Signed BNAF decomposition. Only returns most significant `d`
123    /// decomposition limbs
124    ///
125    /// Implements algorithm 3 of https://eprint.iacr.org/2021/1161.pdf
126    fn decompose(&self, value: &T) -> Vec<T> {
127        let mut value = round_value(*value, self.ignore_bits);
128
129        let q = self.q;
130        let logb = self.logb;
131        let b = T::one() << logb;
132        let full_mask = b - T::one();
133        let bby2 = b >> 1;
134
135        if value > (q >> 1) {
136            value = !(q - value) + T::one()
137        }
138
139        let mut out = Vec::with_capacity(self.d);
140        for _ in 0..self.d {
141            let k_i = value & full_mask;
142            value = (value - k_i) >> logb;
143
144            if k_i > bby2 || (k_i == bby2 && ((value & full_mask) >= bby2)) {
145                out.push(q - (b - k_i));
146                value = value + T::one();
147            } else {
148                out.push(k_i)
149            }
150        }
151
152        return out;
153    }
154
155    fn decomposition_count(&self) -> usize {
156        self.d
157    }
158}
159
160// impl<T> Decomposer for dyn AsRef<DefaultDecomposer<T>>
161// where
162//     DefaultDecomposer<T>: Decomposer<Element = T>,
163// {
164//     type Element = T;
165
166//     fn new(q: Self::Element, logb: usize, d: usize) -> Self {
167//         DefaultDecomposer::<T>::new(q, logb, d)
168//     }
169
170//     fn decompose(&self, v: &Self::Element) -> Vec<Self::Element> {
171//         todo!()
172//     }
173
174//     fn decomposition_count(&self) -> usize {
175//         todo!()
176//     }
177// }
178
179// impl<U: AsRef<DefaultDecomposer<T>>> Decomposer for U
180// where
181//     DefaultDecomposer<T>: Decomposer,
182// {
183//     type Element = T;
184
185//     fn new(q: Self::Element, logb: usize, d: usize) -> Self {
186//         todo!()
187//     }
188
189//     fn decompose(&self, v: &Self::Element) -> Vec<Self::Element> {
190//         todo!()
191//     }
192
193//     fn decomposition_count(&self) -> usize {
194//         todo!()
195//     }
196// }
197
198fn round_value<T: PrimInt>(value: T, ignore_bits: usize) -> T {
199    if ignore_bits == 0 {
200        return value;
201    }
202
203    let ignored_msb = (value & ((T::one() << ignore_bits) - T::one())) >> (ignore_bits - 1);
204    (value >> ignore_bits) + ignored_msb
205}
206
207#[cfg(test)]
208mod tests {
209    use num_traits::Float;
210    use rand::{thread_rng, Rng};
211
212    use crate::{
213        backend::{ModInit, ModularOpsU64},
214        decomposer::round_value,
215        utils::{generate_prime, Stats, TryConvertFrom1},
216    };
217
218    use super::{Decomposer, DefaultDecomposer};
219
220    #[test]
221    fn decomposition_works() {
222        let logq = 50;
223        let logb = 5;
224        let d = 10;
225
226        let mut rng = thread_rng();
227        let mut stats = Stats { samples: vec![] };
228
229        // q is prime of bits logq and i is true, other q = 1<<logq
230        // FIXME: Test fails when q is prime, albeit the difference is minute
231        for i in [false] {
232            let q = if i {
233                generate_prime(logq, 1 << 4, 1u64 << logq).unwrap()
234            } else {
235                1u64 << logq
236            };
237            let decomposer = DefaultDecomposer::new(q, logb, d);
238            let modq_op = ModularOpsU64::new(q);
239            for _ in 0..1000 {
240                let value = rng.gen_range(0..q);
241                let limbs = decomposer.decompose(&value);
242                let value_back = decomposer.recompose(&limbs, &modq_op);
243                let rounded_value =
244                    round_value(value, decomposer.ignore_bits) << decomposer.ignore_bits;
245                stats.add_more(&Vec::<i64>::try_convert_from(&limbs, &q));
246                assert_eq!(
247                    rounded_value, value_back,
248                    "Expected {rounded_value} got {value_back} for q={q}"
249                );
250            }
251        }
252        println!("Mean: {}", stats.mean());
253        println!("Std: {}", stats.std_dev());
254    }
255}