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

use crate::{
    add_ops::repr::{sub_large, sub_large_dword, sub_large_ref_val},
    buffer::Buffer,
    cmp,
    div_const::{ConstDivisor, ConstDivisorRepr},
    helper_macros::debug_assert_zero,
    math,
    primitive::shrink_dword,
    repr::{Repr, TypedRepr, TypedReprRef},
    shift,
    ubig::UBig,
};
use num_modular::Reducer;

use super::{
    repr::{ReducedDword, ReducedLarge, ReducedRepr, ReducedWord},
    Reduced,
};

impl ConstDivisor {
    /// If target is larger than the normalized divisor, then subtract it once.
    fn reduce_once(&self, target: UBig) -> UBig {
        if !self.check(&target) {
            match &self.0 {
                ConstDivisorRepr::Single(d) => target - d.normalized_divisor(),
                ConstDivisorRepr::Double(d) => target - d.normalized_divisor(),
                ConstDivisorRepr::Large(d) => {
                    match target.into_repr() {
                        TypedRepr::Small(s) => UBig::from_dword(s), // no need to reduce
                        TypedRepr::Large(s) => UBig(sub_large(s, &d.normalized_divisor)),
                    }
                }
            }
        } else {
            target
        }
    }

    /// Reduce -target
    fn reduce_negate(&self, target: UBig) -> UBig {
        match &self.0 {
            ConstDivisorRepr::Single(d) => d.normalized_divisor() - target,
            ConstDivisorRepr::Double(d) => d.normalized_divisor() - target,
            ConstDivisorRepr::Large(d) => match target.into_repr() {
                TypedRepr::Small(s) => {
                    UBig(sub_large_dword(d.normalized_divisor.as_ref().into(), s))
                }
                TypedRepr::Large(s) => UBig(sub_large_ref_val(&d.normalized_divisor, s)),
            },
        }
    }

    fn convert_from_normalized(&self, target: &UBig) -> Reduced {
        match &self.0 {
            ConstDivisorRepr::Single(d) => {
                Reduced::from_single(ReducedWord(target.try_into().unwrap()), d)
            }
            ConstDivisorRepr::Double(d) => {
                Reduced::from_double(ReducedDword(target.try_into().unwrap()), d)
            }
            ConstDivisorRepr::Large(d) => {
                let mut buf = Buffer::allocate_exact(d.normalized_divisor.len());
                let words = target.as_words();
                buf.push_slice(words);
                buf.push_zeros(d.normalized_divisor.len() - words.len());
                Reduced::from_large(ReducedLarge(buf.into_boxed_slice()), d)
            }
        }
    }

    fn convert_to_normalized(&self, target: Reduced) -> UBig {
        // this function is for internal use only!
        // it's not checked whether `target` is using `self` as the ring!
        match target.repr() {
            ReducedRepr::Single(raw, _) => UBig(Repr::from_word(raw.0)),
            ReducedRepr::Double(raw, _) => UBig(Repr::from_dword(raw.0)),
            ReducedRepr::Large(raw, _) => {
                let mut buf = Buffer::from(raw.0.as_ref());
                buf.pop_zeros();
                UBig(Repr::from_buffer(buf))
            }
        }
    }
}

impl Reducer<UBig> for ConstDivisor {
    #[inline]
    fn new(m: &UBig) -> Self {
        ConstDivisor::new(m.clone())
    }

    fn transform(&self, target: UBig) -> UBig {
        UBig(match &self.0 {
            ConstDivisorRepr::Single(d) => Repr::from_word(ReducedWord::from_ubig(&target, d).0),
            ConstDivisorRepr::Double(d) => Repr::from_dword(ReducedDword::from_ubig(&target, d).0),
            ConstDivisorRepr::Large(d) => Repr::from_buffer(d.rem_repr(target.into_repr())),
        })
    }
    fn check(&self, target: &UBig) -> bool {
        // check whether target < self.divisor()
        match (&self.0, target.repr()) {
            (ConstDivisorRepr::Single(d), TypedReprRef::RefSmall(dw)) => match shrink_dword(dw) {
                Some(w) => d.0.check(&w),
                None => false,
            },
            (ConstDivisorRepr::Single(_), TypedReprRef::RefLarge(_)) => false,
            (ConstDivisorRepr::Double(d), TypedReprRef::RefSmall(dw)) => d.0.check(&dw),
            (ConstDivisorRepr::Double(_), TypedReprRef::RefLarge(_)) => false,
            (ConstDivisorRepr::Large(_), TypedReprRef::RefSmall(_)) => true,
            (ConstDivisorRepr::Large(d), TypedReprRef::RefLarge(words)) => {
                cmp::cmp_in_place(words, &d.normalized_divisor).is_le()
                    && words[0] & math::ones_word(d.shift) == 0 // must be shifted
            }
        }
    }

    #[inline]
    fn modulus(&self) -> UBig {
        self.value()
    }

    fn residue(&self, target: UBig) -> UBig {
        UBig(match target.into_repr() {
            TypedRepr::Small(dw) => match &self.0 {
                ConstDivisorRepr::Single(d) => {
                    Repr::from_word(shrink_dword(dw).unwrap() >> d.0.shift())
                }
                ConstDivisorRepr::Double(d) => Repr::from_dword(dw >> d.0.shift()),
                ConstDivisorRepr::Large(d) => Repr::from_dword(dw >> d.shift),
            },
            TypedRepr::Large(mut buffer) => {
                if let ConstDivisorRepr::Large(d) = &self.0 {
                    debug_assert_zero!(shift::shr_in_place(&mut buffer, d.shift));
                    Repr::from_buffer(buffer)
                } else {
                    unreachable!()
                }
            }
        })
    }

    #[inline(always)]
    fn is_zero(&self, target: &UBig) -> bool {
        target.is_zero()
    }

    #[inline]
    fn add(&self, lhs: &UBig, rhs: &UBig) -> UBig {
        self.reduce_once(lhs + rhs)
    }
    #[inline]
    fn dbl(&self, target: UBig) -> UBig {
        self.reduce_once(target << 1)
    }
    #[inline]
    fn sub(&self, lhs: &UBig, rhs: &UBig) -> UBig {
        if lhs >= rhs {
            lhs - rhs
        } else {
            self.reduce_negate(rhs - lhs)
        }
    }
    #[inline]
    fn neg(&self, target: UBig) -> UBig {
        if target.is_zero() {
            target
        } else {
            self.reduce_negate(target)
        }
    }

    // for the following operations, copying is relatively cheap and the implementations of
    // the `Reduced` type are relied on.

    #[inline]
    fn mul(&self, lhs: &UBig, rhs: &UBig) -> UBig {
        let lhs = self.convert_from_normalized(lhs);
        let rhs = self.convert_from_normalized(rhs);
        self.convert_to_normalized(lhs * rhs)
    }
    #[inline]
    fn sqr(&self, target: UBig) -> UBig {
        self.convert_to_normalized(self.convert_from_normalized(&target).sqr())
    }
    #[inline]
    fn inv(&self, target: UBig) -> Option<UBig> {
        self.convert_from_normalized(&target)
            .inv()
            .map(|v| self.convert_to_normalized(v))
    }
    #[inline]
    fn pow(&self, base: UBig, exp: &UBig) -> UBig {
        self.convert_to_normalized(self.convert_from_normalized(&base).pow(exp))
    }
}