1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169

use util::binary_search_function;
use rank::{BitRankSupport, RankSupport};
use space_usage::SpaceUsage;
use bit_vector::Bits;
pub use super::{SelectSupport, SelectSupport1, SelectSupport0};

/// Performs a select query by binary searching rank queries.
pub struct BinSearchSelect<'a, Rank: 'a> {
    rank_support: &'a Rank,
}

/// Creates a new binary search select support based on a rank support.
impl<'a, Rank: RankSupport + 'a>
BinSearchSelect<'a, Rank> {
    /// Creates a new binary search selection support given a rank
    /// support.
    pub fn new(rank_support: &'a Rank) -> Self {
        BinSearchSelect {
            rank_support: rank_support,
        }
    }

    /// Borrows a reference to the underlying rank support.
    pub fn inner(&self) -> &'a Rank {
        &self.rank_support
    }
}

impl<'a, Rank: Bits + 'a>
Bits for BinSearchSelect<'a, Rank> {
    type Block = Rank::Block;

    fn block_len(&self) -> usize {
        self.rank_support.block_len()
    }

    fn bit_len(&self) -> u64 {
        self.rank_support.bit_len()
    }

    fn get_block(&self, index: usize) -> Self::Block {
        self.rank_support.get_block(index)
    }

    fn get_bit(&self, index: u64) -> bool {
        self.rank_support.get_bit(index)
    }
}

impl<'a, Rank: RankSupport + 'a>
RankSupport for BinSearchSelect<'a, Rank> {
    type Over = Rank::Over;

    fn rank(&self, index: u64, value: Self::Over) -> u64 {
        self.rank_support.rank(index, value)
    }

    fn limit(&self) -> u64 {
        self.rank_support.limit()
    }
}

impl<'a, Rank: BitRankSupport + 'a>
BitRankSupport for BinSearchSelect<'a, Rank> {
    fn rank1(&self, index: u64) -> u64 {
        self.rank_support.rank1(index)
    }
}

// If we had access to the representation of the rank structure, we
// could search level by level rather than at arbitrary bit addresses.
// But then this algorithm would be tied to that representation.

macro_rules! impl_select_support_b {
    ($select_support:ident, $select:ident, $rank: ident)
        =>
    {
        impl<'a, Rank: BitRankSupport + 'a>
        $select_support for BinSearchSelect<'a, Rank> {
            fn $select(&self, index: u64) -> Option<u64> {
                binary_search_function(0, self.limit(), index + 1,
                                       |i| self.$rank(i))
            }
        }
    }
}

impl_select_support_b!(SelectSupport1, select1, rank1);
impl_select_support_b!(SelectSupport0, select0, rank0);

impl<'a, Rank: RankSupport + 'a>
SelectSupport for BinSearchSelect<'a, Rank> {
    type Over = Rank::Over;

    fn select(&self, index: u64, value: Rank::Over) -> Option<u64> {
        binary_search_function(0, self.limit(), index + 1,
                               |i| self.rank(i, value))
    }
}

impl<'a, Rank: BitRankSupport + 'a>
SpaceUsage for BinSearchSelect<'a, Rank> {
    #[inline]
    fn is_stack_only() -> bool { true }
}

#[cfg(test)]
mod test {
    use super::*;
    use rank::*;

    #[test]
    fn select1() {
        let vec = vec![ 0b00000000000001110000000000000001u32; 1024 ];
        let rank = JacobsonRank::new(&*vec);
        let select = BinSearchSelect::new(&rank);

        assert_eq!(1, select.rank1(0));
        assert_eq!(1, select.rank1(1));
        assert_eq!(1, select.rank1(2));
        assert_eq!(1, select.rank1(15));
        assert_eq!(2, select.rank1(16));
        assert_eq!(3, select.rank1(17));
        assert_eq!(4, select.rank1(18));
        assert_eq!(4, select.rank1(19));
        assert_eq!(4, select.rank1(20));
        assert_eq!(5, select.rank1(32));

        assert_eq!(Some(0), select.select1(0));
        assert_eq!(Some(16), select.select1(1));
        assert_eq!(Some(17), select.select1(2));
        assert_eq!(Some(18), select.select1(3));
        assert_eq!(Some(32), select.select1(4));
        assert_eq!(Some(3200), select.select1(400));
        assert_eq!(Some(3216), select.select1(401));

        assert_eq!(Some(8 * 4092), select.select1(4092));
        assert_eq!(Some(8 * 4092 + 16), select.select1(4093));
        assert_eq!(Some(8 * 4092 + 17), select.select1(4094));
        assert_eq!(Some(8 * 4092 + 18), select.select1(4095));
        assert_eq!(None, select.select1(4096))
    }

    #[test]
    fn select2() {
        let vec = vec![ 0b10101010101010101010101010101010u32; 1024 ];
        let rank = JacobsonRank::new(&*vec);
        let select = BinSearchSelect::new(&rank);

        assert_eq!(Some(1), select.select1(0));
        assert_eq!(Some(3), select.select1(1));
        assert_eq!(Some(5), select.select1(2));
        assert_eq!(Some(7), select.select1(3));
        assert_eq!(Some(919), select.select1(459));
    }

    #[test]
    fn select3() {
        let vec = vec![ 0b11111111111111111111111111111111u32; 1024 ];
        let rank = JacobsonRank::new(&*vec);
        let select = BinSearchSelect::new(&rank);

        assert_eq!(Some(0), select.select1(0));
        assert_eq!(Some(1), select.select1(1));
        assert_eq!(Some(2), select.select1(2));
        assert_eq!(Some(32767), select.select1(32767));
        assert_eq!(None, select.select1(32768));
    }
}