tfhe 1.6.1

use super::ServerKey;
use crate::core_crypto::prelude::UnsignedInteger;
use crate::integer::ciphertext::boolean_value::BooleanBlock;
use crate::integer::ciphertext::IntegerRadixCiphertext;
use crate::integer::prelude::ServerKeyDefaultCMux;
use crate::shortint::{Ciphertext, MessageModulus};
use rayon::prelude::*;

#[derive(Debug, Copy, Clone)]
pub(crate) enum ComparisonKind {
    Less,
    LessOrEqual,
    Greater,
    GreaterOrEqual,
}

/// This blocks contains part of the information necessary to conclude, for signed ciphertext
/// it just needs some input borrow
///
/// There are 2 possibilities:
///
/// * If a block can encrypt at least 4 bits (carry + msg) then the block contains information that
///   will allow determining the result of x < y in one PBS
/// * Otherwise the information is split in 2 blocks and a cmux will be required later
pub(crate) enum PreparedSignedCheck {
    // The information could be coded on 1 block
    // because a block store at least 4 bits of information
    Unified(Ciphertext),
    // The information had to be split
    Split((Ciphertext, Ciphertext)),
}

/// Given the last block of 2 _signed_ numbers x and y, and a borrow (0 or 1)
///
/// returns whether x < y
pub(crate) fn is_x_less_than_y_given_input_borrow(
    last_x_block: u64,
    last_y_block: u64,
    borrow: u64,
    message_modulus: MessageModulus,
) -> u64 {
    let last_bit_pos = message_modulus.0.ilog2() - 1;

    let mask = (1 << last_bit_pos) - 1;
    let x_without_last_bit = last_x_block & mask;
    let y_without_last_bit = last_y_block & mask;

    let input_borrow_to_last_bit = x_without_last_bit < (y_without_last_bit + borrow);

    let result = last_x_block.wrapping_sub(last_y_block + borrow);

    let output_sign_bit = (result >> last_bit_pos) & 1;
    let output_borrow = last_x_block < (last_y_block + borrow);

    let overflow_flag = input_borrow_to_last_bit ^ output_borrow;

    output_sign_bit ^ u64::from(overflow_flag)
}

impl ServerKey {
    pub fn unchecked_eq_parallelized<T>(&self, lhs: &T, rhs: &T) -> BooleanBlock
    where
        T: IntegerRadixCiphertext,
    {
        // Even though the corresponding function
        // may already exist in self.key
        // we generate our own lut to do fewer allocations
        // one for all the threads as opposed to one per thread
        let lut = self
            .key
            .generate_lookup_table_bivariate(|x, y| u64::from(x == y));
        let mut block_comparisons = lhs.blocks().to_vec();
        block_comparisons
            .par_iter_mut()
            .zip(rhs.blocks().par_iter())
            .for_each(|(lhs_block, rhs_block)| {
                self.key
                    .unchecked_apply_lookup_table_bivariate_assign(lhs_block, rhs_block, &lut);
            });

        let is_equal_result = self.are_all_comparisons_block_true(block_comparisons);

        BooleanBlock::new_unchecked(is_equal_result)
    }

    pub fn unchecked_ne_parallelized<T>(&self, lhs: &T, rhs: &T) -> BooleanBlock
    where
        T: IntegerRadixCiphertext,
    {
        // Even though the corresponding function
        // may already exist in self.key
        // we generate our own lut to do fewer allocations
        // one for all the threads as opposed to one per thread
        let lut = self
            .key
            .generate_lookup_table_bivariate(|x, y| u64::from(x != y));
        let mut block_comparisons = lhs.blocks().to_vec();
        block_comparisons
            .par_iter_mut()
            .zip(rhs.blocks().par_iter())
            .for_each(|(lhs_block, rhs_block)| {
                self.key
                    .unchecked_apply_lookup_table_bivariate_assign(lhs_block, rhs_block, &lut);
            });

        let result = self.is_at_least_one_comparisons_block_true(block_comparisons);
        BooleanBlock::new_unchecked(result)
    }

    /// This implements all comparisons (<, <=, >, >=) for both signed and unsigned
    ///
    /// * inputs must have the same number of blocks
    /// * block carries of both inputs must be empty
    /// * carry modulus == message modulus
    fn compare<T>(&self, a: &T, b: &T, compare: ComparisonKind) -> BooleanBlock
    where
        T: IntegerRadixCiphertext,
    {
        assert_eq!(
            a.blocks().len(),
            b.blocks().len(),
            "lhs and rhs must have the same number of blocks"
        );

        assert!(a.block_carries_are_empty(), "Block carries must be empty");
        assert!(b.block_carries_are_empty(), "Block carries must be empty");
        assert_eq!(
            self.carry_modulus().0,
            self.message_modulus().0,
            "The carry modulus must be == to the message modulus"
        );

        if a.blocks().is_empty() {
            // We interpret empty as 0
            return match compare {
                ComparisonKind::Less | ComparisonKind::Greater => {
                    self.create_trivial_boolean_block(false)
                }
                ComparisonKind::LessOrEqual | ComparisonKind::GreaterOrEqual => {
                    self.create_trivial_boolean_block(true)
                }
            };
        }

        // We have that `a < b` <=> `does_sub_overflows(a, b)` and we know how to do this.
        // Now, to have other comparisons, we will re-express them as less than (`<`)
        // with some potential boolean negation
        //
        // Note that for signed ciphertext it's not the overflowing sub that is used,
        // but it's still something that is based on the subtraction
        //
        // For both signed and unsigned, a subtraction with borrow is used
        // (as opposed to adding the negation)
        let (lhs, rhs, invert_subtraction_result) = match compare {
            // The easiest case, nothing changes
            ComparisonKind::Less => (a, b, false),
            //     `a <= b`
            // <=> `not(b < a)`
            // <=> `not(does_sub_overflows(b, a))`
            ComparisonKind::LessOrEqual => (b, a, true),
            //     `a > b`
            // <=> `b < a`
            // <=> `does_sub_overflows(b, a)`
            ComparisonKind::Greater => (b, a, false),
            //     `a >= b`
            // <=> `b <= a`
            // <=> `not(a < b)`
            // <=> `not(does_sub_overflows(a, b))`
            ComparisonKind::GreaterOrEqual => (a, b, true),
        };

        // When there is only one block in both operands,
        // we can take a shortcut by using bivariate PBS.
        if a.blocks().len() == 1 {
            let lut = if T::IS_SIGNED {
                self.key.generate_lookup_table_bivariate(|x, y| {
                    u64::from(invert_subtraction_result)
                        ^ is_x_less_than_y_given_input_borrow(x, y, 0, self.message_modulus())
                })
            } else {
                self.key.generate_lookup_table_bivariate(|x, y| {
                    let overflowed = x < y;
                    u64::from(invert_subtraction_result ^ overflowed)
                })
            };
            let result = self.key.unchecked_apply_lookup_table_bivariate(
                &lhs.blocks()[0],
                &rhs.blocks()[0],
                &lut,
            );
            return BooleanBlock::new_unchecked(result);
        }

        let sub_blocks = lhs
            .blocks()
            .iter()
            .zip(rhs.blocks().iter())
            .map(|(lhs_b, rhs_b)| self.key.unchecked_sub(lhs_b, rhs_b))
            .collect::<Vec<_>>();

        let block_modulus = self.message_modulus().0 * self.carry_modulus().0;
        let num_bits_in_block = block_modulus.ilog2();
        let grouping_size = num_bits_in_block as usize;

        // We are going to group blocks and compute how each group propagates/generates a borrow
        //
        // Again, in unsigned representation the output borrow of the whole operation (i.e. the
        // borrow generated by the last group) tells us the result of the comparison. For signed
        // representation we need to XOR the overflow flag and the sign bit of the result.
        let block_states = {
            let message_modulus = self.message_modulus().0;

            let mut first_grouping_luts = vec![{
                let first_block_state_fn = |block| {
                    if block < message_modulus {
                        1 // Borrows
                    } else {
                        0 // Nothing
                    }
                };
                self.key.generate_lookup_table(first_block_state_fn)
            }];
            for i in 1..grouping_size {
                let state_fn = |block| {
                    #[allow(clippy::comparison_chain)]
                    let r = if block < message_modulus {
                        2 // Borrows
                    } else if block == message_modulus {
                        1 // Propagates a borrow
                    } else {
                        0 // Does not borrow
                    };

                    r << (i - 1)
                };
                first_grouping_luts.push(self.key.generate_lookup_table(state_fn));
            }

            let other_block_state_luts = (0..grouping_size)
                .map(|i| {
                    let state_fn = |block| {
                        #[allow(clippy::comparison_chain)]
                        let r = if block < message_modulus {
                            2 // Generates borrow
                        } else if block == message_modulus {
                            1 // Propagates a borrow
                        } else {
                            0 // Does not borrow
                        };

                        r << i
                    };
                    self.key.generate_lookup_table(state_fn)
                })
                .collect::<Vec<_>>();

            let block_states =
                // With unsigned ciphertexts as, overflow (i.e. does the last block needs to borrow)
                // directly translates to lhs < rhs we compute the blocks states for all the blocks
                //
                // For signed numbers, we need to do something more specific with the last block
                // thus, we don't compute the last block state
                sub_blocks[..sub_blocks.len() - usize::from(T::IS_SIGNED)]
                    .par_iter()
                    .enumerate()
                    .map(|(index, block)| {
                        let grouping_index = index / grouping_size;
                        let is_in_first_grouping = grouping_index == 0;
                        let index_in_grouping = index % (grouping_size);

                        let luts = if is_in_first_grouping {
                            &first_grouping_luts[index_in_grouping]
                        } else {
                            &other_block_state_luts[index_in_grouping]
                        };

                        self.key.apply_lookup_table(block, luts)
                    })
                    .collect::<Vec<_>>();

            block_states
        };

        // group borrows and simulator of last block
        let (
            (group_borrows, use_sequential_algorithm_to_resolve_grouping_carries),
            maybe_prepared_signed_check,
        ) = rayon::join(
            || {
                self.compute_group_borrow_state(
                    // May only invert if T is not signed
                    // As when there is only one group, in the unsigned case since overflow
                    // directly translate to lhs < rhs, we can ask the LUT used to do the
                    // inversion for us.
                    //
                    // In signed case as it's a bit more complex, we never want to
                    !T::IS_SIGNED && invert_subtraction_result,
                    grouping_size,
                    block_states,
                )
            },
            || {
                // When the ciphertexts are signed, finding whether lhs < rhs by doing a sub
                // is less direct than in unsigned where we can check for overflow.
                if T::IS_SIGNED && self.message_modulus().0 > 2 {
                    // Luckily, when the blocks have 4 bits, we can precompute and store in a block
                    // the 2 possible values for `lhs < rhs` depending on whether the last block
                    // will be borrowed from.
                    let lut = self.key.generate_lookup_table_bivariate(|x, y| {
                        let b0 =
                            is_x_less_than_y_given_input_borrow(x, y, 0, self.message_modulus());
                        let b1 =
                            is_x_less_than_y_given_input_borrow(x, y, 1, self.message_modulus());
                        ((b1 << 1) | b0) << 2
                    });

                    Some(PreparedSignedCheck::Unified(
                        self.key.apply_lookup_table_bivariate(
                            lhs.blocks().last().unwrap(),
                            rhs.blocks().last().unwrap(),
                            &lut,
                        ),
                    ))
                } else if T::IS_SIGNED {
                    Some(PreparedSignedCheck::Split(rayon::join(
                        || {
                            let lut = self.key.generate_lookup_table_bivariate(|x, y| {
                                is_x_less_than_y_given_input_borrow(x, y, 1, self.message_modulus())
                            });
                            self.key.apply_lookup_table_bivariate(
                                lhs.blocks().last().unwrap(),
                                rhs.blocks().last().unwrap(),
                                &lut,
                            )
                        },
                        || {
                            let lut = self.key.generate_lookup_table_bivariate(|x, y| {
                                is_x_less_than_y_given_input_borrow(x, y, 0, self.message_modulus())
                            });
                            self.key.apply_lookup_table_bivariate(
                                lhs.blocks().last().unwrap(),
                                rhs.blocks().last().unwrap(),
                                &lut,
                            )
                        },
                    )))
                } else {
                    None
                }
            },
        );

        self.finish_comparison(
            group_borrows,
            grouping_size,
            use_sequential_algorithm_to_resolve_grouping_carries,
            maybe_prepared_signed_check,
            invert_subtraction_result,
        )
    }

    pub(crate) fn finish_comparison(
        &self,
        mut group_borrows: Vec<Ciphertext>,
        grouping_size: usize,
        use_sequential_algorithm_to_resolve_grouping_carries: bool,
        maybe_prepared_signed_check: Option<PreparedSignedCheck>,
        invert_result: bool,
    ) -> BooleanBlock {
        let mut last_group_borrow_state = group_borrows.pop().unwrap();

        // Third step: resolving borrow propagation between the groups
        let resolved_borrows = if group_borrows.is_empty() {
            // There was only one group, and the borrow generated by this group
            // has already been added to the `overflow_block`, just earlier
            if maybe_prepared_signed_check.is_some() {
                // There is still one step to determine the result of the comparison
                // being done further down.
                // It will require an input borrow for the last group
                // which is 0 here because there was only one group thus,
                // the last group is the same as the first group,
                // and the input borrow of the first group is 0
                vec![]
            } else {
                // When unsigned, the result is already known at this point
                return BooleanBlock::new_unchecked(last_group_borrow_state);
            }
        } else if use_sequential_algorithm_to_resolve_grouping_carries {
            self.resolve_carries_of_groups_sequentially(group_borrows, grouping_size)
        } else {
            self.resolve_carries_of_groups_using_hillis_steele(group_borrows)
        };

        match maybe_prepared_signed_check {
            None => {
                // For unsigned numbers, if the last block borrows, then the subtraction
                // overflowed, which directly means lhs < rhs
                self.key.unchecked_add_assign(
                    &mut last_group_borrow_state,
                    // For unsigned, we know that if we are here,
                    // resolved_borrows is not empty
                    resolved_borrows.last().unwrap(),
                );
                let lut = self.key.generate_lookup_table(|block| {
                    let overflowed = (block >> 1) & 1;
                    u64::from(invert_result) ^ overflowed
                });

                self.key
                    .apply_lookup_table_assign(&mut last_group_borrow_state, &lut);

                BooleanBlock::new_unchecked(last_group_borrow_state)
            }
            Some(PreparedSignedCheck::Unified(ct)) => {
                // For signed numbers its less direct to do lhs < rhs using subtraction
                // fortunately when we have at least 4 bits we can encode all the needed information
                // in one block and conclude in 1 PBS
                if let Some(input_borrow) = resolved_borrows.last() {
                    self.key
                        .unchecked_add_assign(&mut last_group_borrow_state, input_borrow);
                }

                self.key
                    .unchecked_add_assign(&mut last_group_borrow_state, &ct);
                let lut = self.key.generate_lookup_table(|block| {
                    // The overflow block already contains the borrow,
                    // but the position of the borrow is one less bit further
                    let index = if resolved_borrows.is_empty() { 0 } else { 1 };
                    let input_borrow = (block >> index) & 1;

                    // Here, depending on the input borrow, we retrieve
                    // the bit that tells us if lhs < rhs
                    let r = if input_borrow == 1 {
                        (block >> 3) & 1
                    } else {
                        (block >> 2) & 1
                    };
                    u64::from(invert_result) ^ r
                });

                self.key
                    .apply_lookup_table_assign(&mut last_group_borrow_state, &lut);

                BooleanBlock::new_unchecked(last_group_borrow_state)
            }
            Some(PreparedSignedCheck::Split((if_input_borrow_is_1, if_input_borrow_is_0))) => {
                if let Some(input_borrow) = resolved_borrows.last() {
                    self.key
                        .unchecked_add_assign(&mut last_group_borrow_state, input_borrow);
                    let lut = self.key.generate_lookup_table(|x| (x >> 1) & 1);
                    self.key
                        .apply_lookup_table_assign(&mut last_group_borrow_state, &lut);
                }

                let if_input_borrow_is_1 = BooleanBlock::new_unchecked(if_input_borrow_is_1);
                let if_input_borrow_is_0 = BooleanBlock::new_unchecked(if_input_borrow_is_0);
                let condition = BooleanBlock::new_unchecked(last_group_borrow_state);
                let result = self.if_then_else_parallelized(
                    &condition,
                    &if_input_borrow_is_1,
                    &if_input_borrow_is_0,
                );
                if invert_result {
                    self.boolean_bitnot(&result)
                } else {
                    result
                }
            }
        }
    }

    /// The invert_result boolean is only used when there is one and only one group
    pub(crate) fn compute_group_borrow_state(
        &self,
        invert_result: bool,
        grouping_size: usize,
        block_states: Vec<Ciphertext>,
    ) -> (Vec<Ciphertext>, bool) {
        if block_states.len() == 1 {
            return (block_states, true);
        }

        let message_modulus = self.key.message_modulus.0;
        let block_modulus = message_modulus * self.carry_modulus().0;
        let num_bits_in_block = block_modulus.ilog2();
        let num_blocks = block_states.len();
        let num_groups = num_blocks.div_ceil(grouping_size);

        let num_groupings = num_blocks.div_ceil(grouping_size);
        let num_carry_to_resolve = num_groupings - 1;

        let sequential_depth = (num_carry_to_resolve as u32) / (grouping_size as u32 - 1);

        let hillis_steel_depth = if num_carry_to_resolve == 0 {
            0
        } else {
            num_carry_to_resolve.ceil_ilog2()
        };

        let use_sequential_algorithm_to_resolved_grouping_carries = if num_bits_in_block >= 4 {
            sequential_depth <= hillis_steel_depth
        } else {
            true // Hillis-Steele base propagation requires 4 bits
        };

        // This will be used only if there are at least 2 groups
        let first_group_propagation_lut = self
            .key
            .generate_lookup_table(|block| (block >> (num_bits_in_block as u64 - 1)) & 1);

        // This stores the LUTs that output the propagation result of the other groupings
        let grouping_chunk_pgn_luts = if use_sequential_algorithm_to_resolved_grouping_carries {
            // When using the sequential algorithm for the propagation of one grouping to the
            // other we need to shift the PGN state to the correct position, so we later, when
            // using them only lwe_add is needed and so noise management is easy
            //
            // Also, these LUTs are 'negacylic', they are made to exploit the padding bit
            // resulting blocks from these LUTs must be added the constant `1 << index`.
            (0..grouping_size - 1)
                .map(|i| {
                    self.key.generate_lookup_table(|block| {
                        // All bits set to 1 (e.g. 0b1111), means propagate
                        if block == (block_modulus - 1) {
                            0
                        } else {
                            // u64::MAX is -1 in two's complement
                            // We apply the modulus including the padding bit
                            (u64::MAX << i) % (1 << (num_bits_in_block + 1))
                        }
                    })
                })
                .collect::<Vec<_>>()
        } else {
            // This LUT is for when we are using Hillis-Steele prefix-scan to propagate carries
            // between groupings. When using this propagation, the encoding of the states
            // are a bit different.
            //
            // Also, these LUTs are 'negacylic', they are made to exploit the padding bit
            // resulting blocks from these LUTs must be added the constant `1`.
            vec![self.key.generate_lookup_table(|block| {
                if block == (block_modulus - 1) {
                    // All bits set to 1 (e.g. 0b1111), means propagate
                    2
                } else {
                    // u64::MAX is -1 in tow's complement
                    // We apply the modulus including the padding bit
                    u64::MAX % (block_modulus * 2)
                }
            })]
        };

        // The last group may not be full
        let mut num_blocks_in_last_group = block_states.len() % grouping_size;
        if num_blocks_in_last_group == 0 {
            num_blocks_in_last_group = grouping_size;
        }
        let (last_group_lut, last_group_lut_corrector) = if num_groups == 1 {
            // The last group is the only one
            let lut = self.key.generate_lookup_table(|cum_sum_block| {
                let index_of_last_block = num_blocks_in_last_group - 1;
                let overflowed = (cum_sum_block >> index_of_last_block) & 1;
                u64::from(invert_result) ^ overflowed
            });
            (lut, 0)
        } else {
            let may_have_its_padding_bit_set = num_blocks_in_last_group == grouping_size;
            if may_have_its_padding_bit_set {
                let lut = self.key.generate_lookup_table(|cum_sum_block| {
                    if cum_sum_block == (block_modulus - 1) {
                        0
                    } else {
                        // u64::MAX is -1 in tow's complement
                        // We apply the modulus including the padding bit
                        u64::MAX % (1 << (num_bits_in_block + 1))
                    }
                });
                (lut, 1)
            } else {
                let lut = self.key.generate_lookup_table(|cum_sum_block| {
                    let propagate_state = (1 << num_blocks_in_last_group) - 1;
                    #[allow(clippy::comparison_chain)]
                    if cum_sum_block > propagate_state {
                        2 // Generates
                    } else if cum_sum_block == propagate_state {
                        1 // Propagate
                    } else {
                        0
                    }
                });
                (lut, 0)
            }
        };

        // Stores for each group, the cum sum the block state of each of its member
        let group_propagation_state = block_states
            .par_chunks(grouping_size)
            .enumerate()
            .map(|(i, grouping)| {
                let mut result = grouping[0].clone();
                for other in &grouping[1..] {
                    self.key.unchecked_add_assign(&mut result, other);
                }

                // i == (num_groups - 1) takes precedence over
                // i == 0 as when num_groups -1 == 0, the correct lut to use is
                // the last group lut
                if i == num_groups - 1 {
                    self.key
                        .apply_lookup_table_assign(&mut result, &last_group_lut);
                    self.key
                        .unchecked_scalar_add_assign(&mut result, last_group_lut_corrector)
                } else if i == 0 {
                    self.key
                        .apply_lookup_table_assign(&mut result, &first_group_propagation_lut)
                } else {
                    let index = if use_sequential_algorithm_to_resolved_grouping_carries {
                        // Select the correct LUT so that the result
                        // is aligned to the correct position for sequential algorithm
                        // to work
                        (i - 1) % (grouping_size - 1)
                    } else {
                        0
                    };
                    self.key
                        .apply_lookup_table_assign(&mut result, &grouping_chunk_pgn_luts[index]);

                    let corrector = if use_sequential_algorithm_to_resolved_grouping_carries {
                        1 << ((i - 1) % (grouping_size - 1))
                    } else {
                        1
                    };
                    self.key.unchecked_scalar_add_assign(&mut result, corrector);
                    result.degree = crate::shortint::ciphertext::Degree::new(3);
                }

                result
            })
            .collect::<Vec<_>>();

        (
            group_propagation_state,
            use_sequential_algorithm_to_resolved_grouping_carries,
        )
    }

    pub fn unchecked_gt_parallelized<T>(&self, lhs: &T, rhs: &T) -> BooleanBlock
    where
        T: IntegerRadixCiphertext,
    {
        self.compare(lhs, rhs, ComparisonKind::Greater)
    }

    pub fn unchecked_ge_parallelized<T>(&self, lhs: &T, rhs: &T) -> BooleanBlock
    where
        T: IntegerRadixCiphertext,
    {
        self.compare(lhs, rhs, ComparisonKind::GreaterOrEqual)
    }

    pub fn unchecked_lt_parallelized<T>(&self, lhs: &T, rhs: &T) -> BooleanBlock
    where
        T: IntegerRadixCiphertext,
    {
        self.compare(lhs, rhs, ComparisonKind::Less)
    }

    pub fn unchecked_le_parallelized<T>(&self, lhs: &T, rhs: &T) -> BooleanBlock
    where
        T: IntegerRadixCiphertext,
    {
        self.compare(lhs, rhs, ComparisonKind::LessOrEqual)
    }

    pub fn unchecked_max_parallelized<T>(&self, lhs: &T, rhs: &T) -> T
    where
        T: IntegerRadixCiphertext,
    {
        let is_superior = self.unchecked_gt_parallelized(lhs, rhs);
        self.unchecked_if_then_else_parallelized(&is_superior, lhs, rhs)
    }

    pub fn unchecked_min_parallelized<T>(&self, lhs: &T, rhs: &T) -> T
    where
        T: IntegerRadixCiphertext,
    {
        let is_inferior = self.unchecked_lt_parallelized(lhs, rhs);
        self.unchecked_if_then_else_parallelized(&is_inferior, lhs, rhs)
    }

    pub fn smart_eq_parallelized<T>(&self, lhs: &mut T, rhs: &mut T) -> BooleanBlock
    where
        T: IntegerRadixCiphertext,
    {
        rayon::join(
            || {
                if !lhs.block_carries_are_empty() {
                    self.full_propagate_parallelized(lhs);
                }
            },
            || {
                if !rhs.block_carries_are_empty() {
                    self.full_propagate_parallelized(rhs);
                }
            },
        );
        self.unchecked_eq_parallelized(lhs, rhs)
    }

    pub fn smart_ne_parallelized<T>(&self, lhs: &mut T, rhs: &mut T) -> BooleanBlock
    where
        T: IntegerRadixCiphertext,
    {
        rayon::join(
            || {
                if !lhs.block_carries_are_empty() {
                    self.full_propagate_parallelized(lhs);
                }
            },
            || {
                if !rhs.block_carries_are_empty() {
                    self.full_propagate_parallelized(rhs);
                }
            },
        );
        self.unchecked_ne_parallelized(lhs, rhs)
    }

    pub fn smart_gt_parallelized<T>(&self, lhs: &mut T, rhs: &mut T) -> BooleanBlock
    where
        T: IntegerRadixCiphertext,
    {
        if !lhs.block_carries_are_empty() {
            self.full_propagate_parallelized(lhs);
        }
        if !rhs.block_carries_are_empty() {
            self.full_propagate_parallelized(rhs);
        }
        self.unchecked_gt_parallelized(lhs, rhs)
    }

    pub fn smart_ge_parallelized<T>(&self, lhs: &mut T, rhs: &mut T) -> BooleanBlock
    where
        T: IntegerRadixCiphertext,
    {
        if !lhs.block_carries_are_empty() {
            self.full_propagate_parallelized(lhs);
        }
        if !rhs.block_carries_are_empty() {
            self.full_propagate_parallelized(rhs);
        }
        self.unchecked_ge_parallelized(lhs, rhs)
    }

    pub fn smart_lt_parallelized<T>(&self, lhs: &mut T, rhs: &mut T) -> BooleanBlock
    where
        T: IntegerRadixCiphertext,
    {
        if !lhs.block_carries_are_empty() {
            self.full_propagate_parallelized(lhs);
        }
        if !rhs.block_carries_are_empty() {
            self.full_propagate_parallelized(rhs);
        }
        self.unchecked_lt_parallelized(lhs, rhs)
    }

    pub fn smart_le_parallelized<T>(&self, lhs: &mut T, rhs: &mut T) -> BooleanBlock
    where
        T: IntegerRadixCiphertext,
    {
        if !lhs.block_carries_are_empty() {
            self.full_propagate_parallelized(lhs);
        }
        if !rhs.block_carries_are_empty() {
            self.full_propagate_parallelized(rhs);
        }
        self.unchecked_le_parallelized(lhs, rhs)
    }

    pub fn smart_max_parallelized<T>(&self, lhs: &mut T, rhs: &mut T) -> T
    where
        T: IntegerRadixCiphertext,
    {
        if !lhs.block_carries_are_empty() {
            self.full_propagate_parallelized(lhs);
        }
        if !rhs.block_carries_are_empty() {
            self.full_propagate_parallelized(rhs);
        }
        self.unchecked_max_parallelized(lhs, rhs)
    }

    pub fn smart_min_parallelized<T>(&self, lhs: &mut T, rhs: &mut T) -> T
    where
        T: IntegerRadixCiphertext,
    {
        if !lhs.block_carries_are_empty() {
            self.full_propagate_parallelized(lhs);
        }
        if !rhs.block_carries_are_empty() {
            self.full_propagate_parallelized(rhs);
        }
        self.unchecked_min_parallelized(lhs, rhs)
    }

    pub fn eq_parallelized<T>(&self, lhs: &T, rhs: &T) -> BooleanBlock
    where
        T: IntegerRadixCiphertext,
    {
        let mut tmp_lhs;
        let mut tmp_rhs;
        let (lhs, rhs) = match (lhs.block_carries_are_empty(), rhs.block_carries_are_empty()) {
            (true, true) => (lhs, rhs),
            (true, false) => {
                tmp_rhs = rhs.clone();
                self.full_propagate_parallelized(&mut tmp_rhs);
                (lhs, &tmp_rhs)
            }
            (false, true) => {
                tmp_lhs = lhs.clone();
                self.full_propagate_parallelized(&mut tmp_lhs);
                (&tmp_lhs, rhs)
            }
            (false, false) => {
                tmp_lhs = lhs.clone();
                tmp_rhs = rhs.clone();
                rayon::join(
                    || self.full_propagate_parallelized(&mut tmp_lhs),
                    || self.full_propagate_parallelized(&mut tmp_rhs),
                );
                (&tmp_lhs, &tmp_rhs)
            }
        };

        self.unchecked_eq_parallelized(lhs, rhs)
    }

    pub fn ne_parallelized<T>(&self, lhs: &T, rhs: &T) -> BooleanBlock
    where
        T: IntegerRadixCiphertext,
    {
        let mut tmp_lhs;
        let mut tmp_rhs;
        let (lhs, rhs) = match (lhs.block_carries_are_empty(), rhs.block_carries_are_empty()) {
            (true, true) => (lhs, rhs),
            (true, false) => {
                tmp_rhs = rhs.clone();
                self.full_propagate_parallelized(&mut tmp_rhs);
                (lhs, &tmp_rhs)
            }
            (false, true) => {
                tmp_lhs = lhs.clone();
                self.full_propagate_parallelized(&mut tmp_lhs);
                (&tmp_lhs, rhs)
            }
            (false, false) => {
                tmp_lhs = lhs.clone();
                tmp_rhs = rhs.clone();
                rayon::join(
                    || self.full_propagate_parallelized(&mut tmp_lhs),
                    || self.full_propagate_parallelized(&mut tmp_rhs),
                );
                (&tmp_lhs, &tmp_rhs)
            }
        };

        self.unchecked_ne_parallelized(lhs, rhs)
    }

    pub fn gt_parallelized<T>(&self, lhs: &T, rhs: &T) -> BooleanBlock
    where
        T: IntegerRadixCiphertext,
    {
        let mut tmp_lhs;
        let mut tmp_rhs;
        let (lhs, rhs) = match (lhs.block_carries_are_empty(), rhs.block_carries_are_empty()) {
            (true, true) => (lhs, rhs),
            (true, false) => {
                tmp_rhs = rhs.clone();
                self.full_propagate_parallelized(&mut tmp_rhs);
                (lhs, &tmp_rhs)
            }
            (false, true) => {
                tmp_lhs = lhs.clone();
                self.full_propagate_parallelized(&mut tmp_lhs);
                (&tmp_lhs, rhs)
            }
            (false, false) => {
                tmp_lhs = lhs.clone();
                tmp_rhs = rhs.clone();
                rayon::join(
                    || self.full_propagate_parallelized(&mut tmp_lhs),
                    || self.full_propagate_parallelized(&mut tmp_rhs),
                );
                (&tmp_lhs, &tmp_rhs)
            }
        };

        self.unchecked_gt_parallelized(lhs, rhs)
    }

    pub fn ge_parallelized<T>(&self, lhs: &T, rhs: &T) -> BooleanBlock
    where
        T: IntegerRadixCiphertext,
    {
        let mut tmp_lhs;
        let mut tmp_rhs;
        let (lhs, rhs) = match (lhs.block_carries_are_empty(), rhs.block_carries_are_empty()) {
            (true, true) => (lhs, rhs),
            (true, false) => {
                tmp_rhs = rhs.clone();
                self.full_propagate_parallelized(&mut tmp_rhs);
                (lhs, &tmp_rhs)
            }
            (false, true) => {
                tmp_lhs = lhs.clone();
                self.full_propagate_parallelized(&mut tmp_lhs);
                (&tmp_lhs, rhs)
            }
            (false, false) => {
                tmp_lhs = lhs.clone();
                tmp_rhs = rhs.clone();
                rayon::join(
                    || self.full_propagate_parallelized(&mut tmp_lhs),
                    || self.full_propagate_parallelized(&mut tmp_rhs),
                );
                (&tmp_lhs, &tmp_rhs)
            }
        };

        self.unchecked_ge_parallelized(lhs, rhs)
    }

    pub fn lt_parallelized<T>(&self, lhs: &T, rhs: &T) -> BooleanBlock
    where
        T: IntegerRadixCiphertext,
    {
        let mut tmp_lhs;
        let mut tmp_rhs;
        let (lhs, rhs) = match (lhs.block_carries_are_empty(), rhs.block_carries_are_empty()) {
            (true, true) => (lhs, rhs),
            (true, false) => {
                tmp_rhs = rhs.clone();
                self.full_propagate_parallelized(&mut tmp_rhs);
                (lhs, &tmp_rhs)
            }
            (false, true) => {
                tmp_lhs = lhs.clone();
                self.full_propagate_parallelized(&mut tmp_lhs);
                (&tmp_lhs, rhs)
            }
            (false, false) => {
                tmp_lhs = lhs.clone();
                tmp_rhs = rhs.clone();
                rayon::join(
                    || self.full_propagate_parallelized(&mut tmp_lhs),
                    || self.full_propagate_parallelized(&mut tmp_rhs),
                );
                (&tmp_lhs, &tmp_rhs)
            }
        };

        self.unchecked_lt_parallelized(lhs, rhs)
    }

    pub fn le_parallelized<T>(&self, lhs: &T, rhs: &T) -> BooleanBlock
    where
        T: IntegerRadixCiphertext,
    {
        let mut tmp_lhs;
        let mut tmp_rhs;
        let (lhs, rhs) = match (lhs.block_carries_are_empty(), rhs.block_carries_are_empty()) {
            (true, true) => (lhs, rhs),
            (true, false) => {
                tmp_rhs = rhs.clone();
                self.full_propagate_parallelized(&mut tmp_rhs);
                (lhs, &tmp_rhs)
            }
            (false, true) => {
                tmp_lhs = lhs.clone();
                self.full_propagate_parallelized(&mut tmp_lhs);
                (&tmp_lhs, rhs)
            }
            (false, false) => {
                tmp_lhs = lhs.clone();
                tmp_rhs = rhs.clone();
                rayon::join(
                    || self.full_propagate_parallelized(&mut tmp_lhs),
                    || self.full_propagate_parallelized(&mut tmp_rhs),
                );
                (&tmp_lhs, &tmp_rhs)
            }
        };

        self.unchecked_le_parallelized(lhs, rhs)
    }

    pub fn max_parallelized<T>(&self, lhs: &T, rhs: &T) -> T
    where
        T: IntegerRadixCiphertext,
    {
        let mut tmp_lhs;
        let mut tmp_rhs;

        let (lhs, rhs) = match (lhs.block_carries_are_empty(), rhs.block_carries_are_empty()) {
            (true, true) => (lhs, rhs),
            (true, false) => {
                tmp_rhs = rhs.clone();
                self.full_propagate_parallelized(&mut tmp_rhs);
                (lhs, &tmp_rhs)
            }
            (false, true) => {
                tmp_lhs = lhs.clone();
                self.full_propagate_parallelized(&mut tmp_lhs);
                (&tmp_lhs, rhs)
            }
            (false, false) => {
                tmp_lhs = lhs.clone();
                tmp_rhs = rhs.clone();
                rayon::join(
                    || self.full_propagate_parallelized(&mut tmp_lhs),
                    || self.full_propagate_parallelized(&mut tmp_rhs),
                );
                (&tmp_lhs, &tmp_rhs)
            }
        };

        self.unchecked_max_parallelized(lhs, rhs)
    }

    pub fn min_parallelized<T>(&self, lhs: &T, rhs: &T) -> T
    where
        T: IntegerRadixCiphertext,
    {
        let mut tmp_lhs;
        let mut tmp_rhs;

        let (lhs, rhs) = match (lhs.block_carries_are_empty(), rhs.block_carries_are_empty()) {
            (true, true) => (lhs, rhs),
            (true, false) => {
                tmp_rhs = rhs.clone();
                self.full_propagate_parallelized(&mut tmp_rhs);
                (lhs, &tmp_rhs)
            }
            (false, true) => {
                tmp_lhs = lhs.clone();
                self.full_propagate_parallelized(&mut tmp_lhs);
                (&tmp_lhs, rhs)
            }
            (false, false) => {
                tmp_lhs = lhs.clone();
                tmp_rhs = rhs.clone();
                rayon::join(
                    || self.full_propagate_parallelized(&mut tmp_lhs),
                    || self.full_propagate_parallelized(&mut tmp_rhs),
                );
                (&tmp_lhs, &tmp_rhs)
            }
        };

        self.unchecked_min_parallelized(lhs, rhs)
    }
}