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
use crate::natural::Natural;
use malachite_base::num::arithmetic::traits::{
    ModPowerOf2Shl, ModPowerOf2ShlAssign, ModPowerOf2Shr, ModPowerOf2ShrAssign, UnsignedAbs,
};
use malachite_base::num::basic::signeds::PrimitiveSigned;
use malachite_base::num::logic::traits::SignificantBits;
use std::ops::{Shr, ShrAssign};

fn mod_power_of_2_shr_ref<'a, U, S: PrimitiveSigned + UnsignedAbs<Output = U>>(
    x: &'a Natural,
    bits: S,
    pow: u64,
) -> Natural
where
    &'a Natural: ModPowerOf2Shl<U, Output = Natural> + Shr<U, Output = Natural>,
{
    assert!(
        x.significant_bits() <= pow,
        "x must be reduced mod 2^pow, but {x} >= 2^{pow}"
    );
    if bits >= S::ZERO {
        x >> bits.unsigned_abs()
    } else {
        x.mod_power_of_2_shl(bits.unsigned_abs(), pow)
    }
}

fn mod_power_of_2_shr_assign<U, S: PrimitiveSigned + UnsignedAbs<Output = U>>(
    x: &mut Natural,
    bits: S,
    pow: u64,
) where
    Natural: ModPowerOf2ShlAssign<U> + ShrAssign<U>,
{
    assert!(
        x.significant_bits() <= pow,
        "x must be reduced mod 2^pow, but {x} >= 2^{pow}"
    );
    if bits >= S::ZERO {
        *x >>= bits.unsigned_abs();
    } else {
        x.mod_power_of_2_shl_assign(bits.unsigned_abs(), pow);
    }
}

macro_rules! impl_mod_power_of_2_shr_signed {
    ($t:ident) => {
        impl ModPowerOf2Shr<$t> for Natural {
            type Output = Natural;

            /// Right-shifts a [`Natural`] (divides it by a power of 2) modulo $2^k$. The
            /// [`Natural`] must be already reduced modulo $2^k$. The [`Natural`] is taken by
            /// value.
            ///
            /// $f(x, n, k) = y$, where $x, y < 2^k$ and
            /// $\lfloor 2^{-n}x \rfloor \equiv y \mod 2^k$.
            ///
            /// # Worst-case complexity
            /// $T(n) = O(n)$
            ///
            /// $M(n) = O(n)$
            ///
            /// where $T$ is time, $M$ is additional memory, and $n$ is `pow`.
            ///
            /// # Panics
            /// Panics if `self` is greater than or equal to $2^k$.
            ///
            /// # Examples
            /// See [here](super::mod_power_of_2_shr#mod_power_of_2_shr).
            #[inline]
            fn mod_power_of_2_shr(mut self, bits: $t, pow: u64) -> Natural {
                self.mod_power_of_2_shr_assign(bits, pow);
                self
            }
        }

        impl<'a> ModPowerOf2Shr<$t> for &'a Natural {
            type Output = Natural;

            /// Right-shifts a [`Natural`] (divides it by a power of 2) modulo $2^k$. The
            /// [`Natural`] must be already reduced modulo $2^k$. The [`Natural`] is taken by
            /// reference.
            ///
            /// $f(x, n, k) = y$, where $x, y < 2^k$ and
            /// $\lfloor 2^{-n}x \rfloor \equiv y \mod 2^k$.
            ///
            /// # Worst-case complexity
            /// $T(n) = O(n)$
            ///
            /// $M(n) = O(n)$
            ///
            /// where $T$ is time, $M$ is additional memory, and $n$ is `pow`.
            ///
            /// # Panics
            /// Panics if `self` is greater than or equal to $2^k$.
            ///
            /// # Examples
            /// See [here](super::mod_power_of_2_shr#mod_power_of_2_shr).
            #[inline]
            fn mod_power_of_2_shr(self, bits: $t, pow: u64) -> Natural {
                mod_power_of_2_shr_ref(self, bits, pow)
            }
        }

        impl ModPowerOf2ShrAssign<$t> for Natural {
            /// Right-shifts a [`Natural`] (divides it by a power of 2) modulo $2^k$, in place. The
            /// [`Natural`] must be already reduced modulo $2^k$.
            ///
            /// $x \gets y$, where $x, y < 2^k$ and $\lfloor 2^{-n}x \rfloor \equiv y \mod 2^k$.
            ///
            /// # Worst-case complexity
            /// $T(n) = O(n)$
            ///
            /// $M(n) = O(n)$
            ///
            /// where $T$ is time, $M$ is additional memory, and $n$ is `pow`.
            ///
            /// # Panics
            /// Panics if `self` is greater than or equal to $2^k$.
            ///
            /// # Examples
            /// See [here](super::mod_power_of_2_shr#mod_power_of_2_shr_assign).
            #[inline]
            fn mod_power_of_2_shr_assign(&mut self, bits: $t, pow: u64) {
                mod_power_of_2_shr_assign(self, bits, pow);
            }
        }
    };
}
apply_to_signeds!(impl_mod_power_of_2_shr_signed);