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
//! [`UInt`] addition operations.

use super::UInt;
use crate::{Checked, CheckedSub, Limb, Wrapping, Zero};
use core::ops::{Sub, SubAssign};
use subtle::CtOption;

impl<const LIMBS: usize> UInt<LIMBS> {
    /// Computes `a - (b + borrow)`, returning the result along with the new borrow.
    #[inline(always)]
    pub const fn sbb(&self, rhs: &Self, mut borrow: Limb) -> (Self, Limb) {
        let mut limbs = [Limb::ZERO; LIMBS];
        let mut i = 0;

        while i < LIMBS {
            let (w, b) = self.limbs[i].sbb(rhs.limbs[i], borrow);
            limbs[i] = w;
            borrow = b;
            i += 1;
        }

        (Self { limbs }, borrow)
    }

    /// Perform saturating subtraction, returning `ZERO` on underflow.
    pub const fn saturating_sub(&self, rhs: &Self) -> Self {
        let (res, underflow) = self.sbb(rhs, Limb::ZERO);

        if underflow.0 == 0 {
            res
        } else {
            Self::ZERO
        }
    }

    /// Perform wrapping subtraction, discarding underflow and wrapping around
    /// the boundary of the type.
    pub const fn wrapping_sub(&self, rhs: &Self) -> Self {
        self.sbb(rhs, Limb::ZERO).0
    }
}

impl<const LIMBS: usize> CheckedSub<&UInt<LIMBS>> for UInt<LIMBS> {
    type Output = Self;

    fn checked_sub(&self, rhs: &Self) -> CtOption<Self> {
        let (result, underflow) = self.sbb(rhs, Limb::ZERO);
        CtOption::new(result, underflow.is_zero())
    }
}

impl<const LIMBS: usize> Sub for Wrapping<UInt<LIMBS>> {
    type Output = Self;

    fn sub(self, rhs: Self) -> Wrapping<UInt<LIMBS>> {
        Wrapping(self.0.wrapping_sub(&rhs.0))
    }
}

impl<const LIMBS: usize> Sub<&Wrapping<UInt<LIMBS>>> for Wrapping<UInt<LIMBS>> {
    type Output = Wrapping<UInt<LIMBS>>;

    fn sub(self, rhs: &Wrapping<UInt<LIMBS>>) -> Wrapping<UInt<LIMBS>> {
        Wrapping(self.0.wrapping_sub(&rhs.0))
    }
}

impl<const LIMBS: usize> Sub<Wrapping<UInt<LIMBS>>> for &Wrapping<UInt<LIMBS>> {
    type Output = Wrapping<UInt<LIMBS>>;

    fn sub(self, rhs: Wrapping<UInt<LIMBS>>) -> Wrapping<UInt<LIMBS>> {
        Wrapping(self.0.wrapping_sub(&rhs.0))
    }
}

impl<const LIMBS: usize> Sub<&Wrapping<UInt<LIMBS>>> for &Wrapping<UInt<LIMBS>> {
    type Output = Wrapping<UInt<LIMBS>>;

    fn sub(self, rhs: &Wrapping<UInt<LIMBS>>) -> Wrapping<UInt<LIMBS>> {
        Wrapping(self.0.wrapping_sub(&rhs.0))
    }
}

impl<const LIMBS: usize> SubAssign for Wrapping<UInt<LIMBS>> {
    fn sub_assign(&mut self, other: Self) {
        *self = *self - other;
    }
}

impl<const LIMBS: usize> SubAssign<&Wrapping<UInt<LIMBS>>> for Wrapping<UInt<LIMBS>> {
    fn sub_assign(&mut self, other: &Self) {
        *self = *self - other;
    }
}

impl<const LIMBS: usize> Sub for Checked<UInt<LIMBS>> {
    type Output = Self;

    fn sub(self, rhs: Self) -> Checked<UInt<LIMBS>> {
        Checked(
            self.0
                .and_then(|lhs| rhs.0.and_then(|rhs| lhs.checked_sub(&rhs))),
        )
    }
}

impl<const LIMBS: usize> Sub<&Checked<UInt<LIMBS>>> for Checked<UInt<LIMBS>> {
    type Output = Checked<UInt<LIMBS>>;

    fn sub(self, rhs: &Checked<UInt<LIMBS>>) -> Checked<UInt<LIMBS>> {
        Checked(
            self.0
                .and_then(|lhs| rhs.0.and_then(|rhs| lhs.checked_sub(&rhs))),
        )
    }
}

impl<const LIMBS: usize> Sub<Checked<UInt<LIMBS>>> for &Checked<UInt<LIMBS>> {
    type Output = Checked<UInt<LIMBS>>;

    fn sub(self, rhs: Checked<UInt<LIMBS>>) -> Checked<UInt<LIMBS>> {
        Checked(
            self.0
                .and_then(|lhs| rhs.0.and_then(|rhs| lhs.checked_sub(&rhs))),
        )
    }
}

impl<const LIMBS: usize> Sub<&Checked<UInt<LIMBS>>> for &Checked<UInt<LIMBS>> {
    type Output = Checked<UInt<LIMBS>>;

    fn sub(self, rhs: &Checked<UInt<LIMBS>>) -> Checked<UInt<LIMBS>> {
        Checked(
            self.0
                .and_then(|lhs| rhs.0.and_then(|rhs| lhs.checked_sub(&rhs))),
        )
    }
}

impl<const LIMBS: usize> SubAssign for Checked<UInt<LIMBS>> {
    fn sub_assign(&mut self, other: Self) {
        *self = *self - other;
    }
}

impl<const LIMBS: usize> SubAssign<&Checked<UInt<LIMBS>>> for Checked<UInt<LIMBS>> {
    fn sub_assign(&mut self, other: &Self) {
        *self = *self - other;
    }
}

#[cfg(test)]
mod tests {
    use crate::{CheckedSub, Limb, U128};

    #[test]
    fn sbb_no_borrow() {
        let (res, borrow) = U128::ONE.sbb(&U128::ONE, Limb::ZERO);
        assert_eq!(res, U128::ZERO);
        assert_eq!(borrow, Limb::ZERO);
    }

    #[test]
    fn sbb_with_borrow() {
        let (res, borrow) = U128::ZERO.sbb(&U128::ONE, Limb::ZERO);

        assert_eq!(res, U128::MAX);
        assert_eq!(borrow, Limb::MAX);
    }

    #[test]
    fn wrapping_sub_no_borrow() {
        assert_eq!(U128::ONE.wrapping_sub(&U128::ONE), U128::ZERO);
    }

    #[test]
    fn wrapping_sub_with_borrow() {
        assert_eq!(U128::ZERO.wrapping_sub(&U128::ONE), U128::MAX);
    }

    #[test]
    fn checked_sub_ok() {
        let result = U128::ONE.checked_sub(&U128::ONE);
        assert_eq!(result.unwrap(), U128::ZERO);
    }

    #[test]
    fn checked_sub_overflow() {
        let result = U128::ZERO.checked_sub(&U128::ONE);
        assert!(!bool::from(result.is_some()));
    }
}