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
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
use std::fmt::Debug;

#[cfg(feature = "serde")]
use serde::{Deserialize, Serialize};

use crate::prelude::*;

#[derive(Copy, Clone, Debug, Hash, Eq, PartialEq, Default)]
#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
pub enum SearchSortedSide {
    #[default]
    Any,
    Left,
    Right,
}

/// Computes the first point on [lo, hi) where f is true, assuming it is first
/// always false and then always true. It is assumed f(hi) is true.
/// midpoint is a function that returns some lo < i < hi if one exists, else lo.
fn lower_bound<I, F, M>(mut lo: I, mut hi: I, midpoint: M, f: F) -> I
where
    I: PartialEq + Eq,
    M: Fn(&I, &I) -> I,
    F: Fn(&I) -> bool,
{
    loop {
        let m = midpoint(&lo, &hi);
        if m == lo {
            return if f(&lo) { lo } else { hi };
        }

        if f(&m) {
            hi = m;
        } else {
            lo = m;
        }
    }
}

/// Search through a series of chunks for the first position where f(x) is true,
/// assuming it is first always false and then always true. It repeats this for
/// each value in search_values. If the search value is null null_idx is returned.
///
/// Assumes the chunks are non-empty.
pub fn lower_bound_chunks<'a, T, F>(
    chunks: &[&'a T::Array],
    search_values: impl Iterator<Item = Option<T::Physical<'a>>>,
    null_idx: IdxSize,
    f: F,
) -> Vec<IdxSize>
where
    T: PolarsDataType,
    F: Fn(&'a T::Array, usize, &T::Physical<'a>) -> bool,
{
    if chunks.is_empty() {
        return search_values.map(|_| 0).collect();
    }

    // Fast-path: only a single chunk.
    if chunks.len() == 1 {
        let chunk = &chunks[0];
        return search_values
            .map(|ov| {
                if let Some(v) = ov {
                    lower_bound(0, chunk.len(), |l, r| (l + r) / 2, |m| f(chunk, *m, &v)) as IdxSize
                } else {
                    null_idx
                }
            })
            .collect();
    }

    // Multiple chunks, precompute prefix sum of lengths so we can look up
    // in O(1) the global position of chunk i.
    let mut sz = 0;
    let mut chunk_len_prefix_sum = Vec::with_capacity(chunks.len() + 1);
    for c in chunks {
        chunk_len_prefix_sum.push(sz);
        sz += c.len();
    }
    chunk_len_prefix_sum.push(sz);

    // For each search value do a binary search on (chunk_idx, idx_in_chunk) pairs.
    search_values
        .map(|ov| {
            let Some(v) = ov else {
                return null_idx;
            };
            let left = (0, 0);
            let right = (chunks.len(), 0);
            let midpoint = |l: &(usize, usize), r: &(usize, usize)| {
                if l.0 == r.0 {
                    // Within same chunk.
                    (l.0, (l.1 + r.1) / 2)
                } else if l.0 + 1 == r.0 {
                    // Two adjacent chunks, might have to be l or r.
                    let left_len = chunks[l.0].len() - l.1;

                    let logical_mid = (left_len + r.1) / 2;
                    if logical_mid < left_len {
                        (l.0, l.1 + logical_mid)
                    } else {
                        (r.0, logical_mid - left_len)
                    }
                } else {
                    // Has a chunk in between.
                    ((l.0 + r.0) / 2, 0)
                }
            };

            let bound = lower_bound(left, right, midpoint, |m| {
                f(unsafe { chunks.get_unchecked(m.0) }, m.1, &v)
            });

            (chunk_len_prefix_sum[bound.0] + bound.1) as IdxSize
        })
        .collect()
}

#[allow(clippy::collapsible_else_if)]
pub fn binary_search_ca<'a, T>(
    ca: &'a ChunkedArray<T>,
    search_values: impl Iterator<Item = Option<T::Physical<'a>>>,
    side: SearchSortedSide,
    descending: bool,
) -> Vec<IdxSize>
where
    T: PolarsDataType,
    T::Physical<'a>: TotalOrd + Debug + Copy,
{
    let chunks: Vec<_> = ca.downcast_iter().filter(|c| c.len() > 0).collect();
    let has_nulls = ca.null_count() > 0;
    let nulls_last = has_nulls && chunks[0].get(0).is_some();
    let null_idx = if nulls_last {
        if side == SearchSortedSide::Right {
            ca.len()
        } else {
            ca.len() - ca.null_count()
        }
    } else {
        if side == SearchSortedSide::Right {
            ca.null_count()
        } else {
            0
        }
    } as IdxSize;

    if !descending {
        if !has_nulls {
            if side == SearchSortedSide::Right {
                lower_bound_chunks::<T, _>(
                    &chunks,
                    search_values,
                    null_idx,
                    |chunk, i, sv| unsafe { chunk.value_unchecked(i).tot_gt(sv) },
                )
            } else {
                lower_bound_chunks::<T, _>(
                    &chunks,
                    search_values,
                    null_idx,
                    |chunk, i, sv| unsafe { chunk.value_unchecked(i).tot_ge(sv) },
                )
            }
        } else {
            if side == SearchSortedSide::Right {
                lower_bound_chunks::<T, _>(&chunks, search_values, null_idx, |chunk, i, sv| {
                    if let Some(v) = unsafe { chunk.get_unchecked(i) } {
                        v.tot_gt(sv)
                    } else {
                        nulls_last
                    }
                })
            } else {
                lower_bound_chunks::<T, _>(&chunks, search_values, null_idx, |chunk, i, sv| {
                    if let Some(v) = unsafe { chunk.get_unchecked(i) } {
                        v.tot_ge(sv)
                    } else {
                        nulls_last
                    }
                })
            }
        }
    } else {
        if !has_nulls {
            if side == SearchSortedSide::Right {
                lower_bound_chunks::<T, _>(
                    &chunks,
                    search_values,
                    null_idx,
                    |chunk, i, sv| unsafe { chunk.value_unchecked(i).tot_lt(sv) },
                )
            } else {
                lower_bound_chunks::<T, _>(
                    &chunks,
                    search_values,
                    null_idx,
                    |chunk, i, sv| unsafe { chunk.value_unchecked(i).tot_le(sv) },
                )
            }
        } else {
            if side == SearchSortedSide::Right {
                lower_bound_chunks::<T, _>(&chunks, search_values, null_idx, |chunk, i, sv| {
                    if let Some(v) = unsafe { chunk.get_unchecked(i) } {
                        v.tot_lt(sv)
                    } else {
                        nulls_last
                    }
                })
            } else {
                lower_bound_chunks::<T, _>(&chunks, search_values, null_idx, |chunk, i, sv| {
                    if let Some(v) = unsafe { chunk.get_unchecked(i) } {
                        v.tot_le(sv)
                    } else {
                        nulls_last
                    }
                })
            }
        }
    }
}