num_bigint/biguint/
addition.rs

#[cfg(not(u64_digit))]
use super::u32_from_u128;
use super::{BigUint, IntDigits};

use crate::big_digit::{self, BigDigit};
use crate::UsizePromotion;

use core::iter::Sum;
use core::ops::{Add, AddAssign};
use num_traits::{CheckedAdd, Zero};

#[cfg(all(use_addcarry, target_arch = "x86_64"))]
use core::arch::x86_64 as arch;

#[cfg(all(use_addcarry, target_arch = "x86"))]
use core::arch::x86 as arch;

// Add with carry:
#[cfg(all(use_addcarry, u64_digit))]
#[inline]
fn adc(carry: u8, a: u64, b: u64, out: &mut u64) -> u8 {
    // Safety: There are absolutely no safety concerns with calling `_addcarry_u64`.
    // It's just unsafe for API consistency with other intrinsics.
    unsafe { arch::_addcarry_u64(carry, a, b, out) }
}

#[cfg(all(use_addcarry, not(u64_digit)))]
#[inline]
fn adc(carry: u8, a: u32, b: u32, out: &mut u32) -> u8 {
    // Safety: There are absolutely no safety concerns with calling `_addcarry_u32`.
    // It's just unsafe for API consistency with other intrinsics.
    unsafe { arch::_addcarry_u32(carry, a, b, out) }
}

// fallback for environments where we don't have an addcarry intrinsic
#[cfg(not(use_addcarry))]
#[inline]
fn adc(carry: u8, a: BigDigit, b: BigDigit, out: &mut BigDigit) -> u8 {
    use crate::big_digit::DoubleBigDigit;

    let sum = DoubleBigDigit::from(a) + DoubleBigDigit::from(b) + DoubleBigDigit::from(carry);
    *out = sum as BigDigit;
    (sum >> big_digit::BITS) as u8
}

/// Two argument addition of raw slices, `a += b`, returning the carry.
///
/// This is used when the data `Vec` might need to resize to push a non-zero carry, so we perform
/// the addition first hoping that it will fit.
///
/// The caller _must_ ensure that `a` is at least as long as `b`.
#[inline]
pub(super) fn __add2(a: &mut [BigDigit], b: &[BigDigit]) -> BigDigit {
    debug_assert!(a.len() >= b.len());

    let mut carry = 0;
    let (a_lo, a_hi) = a.split_at_mut(b.len());

    for (a, b) in a_lo.iter_mut().zip(b) {
        carry = adc(carry, *a, *b, a);
    }

    if carry != 0 {
        for a in a_hi {
            carry = adc(carry, *a, 0, a);
            if carry == 0 {
                break;
            }
        }
    }

    carry as BigDigit
}

/// Two argument addition of raw slices:
/// a += b
///
/// The caller _must_ ensure that a is big enough to store the result - typically this means
/// resizing a to max(a.len(), b.len()) + 1, to fit a possible carry.
pub(super) fn add2(a: &mut [BigDigit], b: &[BigDigit]) {
    let carry = __add2(a, b);

    debug_assert!(carry == 0);
}

forward_all_binop_to_val_ref_commutative!(impl Add for BigUint, add);
forward_val_assign!(impl AddAssign for BigUint, add_assign);

impl<'a> Add<&'a BigUint> for BigUint {
    type Output = BigUint;

    fn add(mut self, other: &BigUint) -> BigUint {
        self += other;
        self
    }
}
impl<'a> AddAssign<&'a BigUint> for BigUint {
    #[inline]
    fn add_assign(&mut self, other: &BigUint) {
        let self_len = self.data.len();
        let carry = if self_len < other.data.len() {
            let lo_carry = __add2(&mut self.data[..], &other.data[..self_len]);
            self.data.extend_from_slice(&other.data[self_len..]);
            __add2(&mut self.data[self_len..], &[lo_carry])
        } else {
            __add2(&mut self.data[..], &other.data[..])
        };
        if carry != 0 {
            self.data.push(carry);
        }
    }
}

promote_unsigned_scalars!(impl Add for BigUint, add);
promote_unsigned_scalars_assign!(impl AddAssign for BigUint, add_assign);
forward_all_scalar_binop_to_val_val_commutative!(impl Add<u32> for BigUint, add);
forward_all_scalar_binop_to_val_val_commutative!(impl Add<u64> for BigUint, add);
forward_all_scalar_binop_to_val_val_commutative!(impl Add<u128> for BigUint, add);

impl Add<u32> for BigUint {
    type Output = BigUint;

    #[inline]
    fn add(mut self, other: u32) -> BigUint {
        self += other;
        self
    }
}

impl AddAssign<u32> for BigUint {
    #[inline]
    fn add_assign(&mut self, other: u32) {
        if other != 0 {
            if self.data.is_empty() {
                self.data.push(0);
            }

            let carry = __add2(&mut self.data, &[other as BigDigit]);
            if carry != 0 {
                self.data.push(carry);
            }
        }
    }
}

impl Add<u64> for BigUint {
    type Output = BigUint;

    #[inline]
    fn add(mut self, other: u64) -> BigUint {
        self += other;
        self
    }
}

impl AddAssign<u64> for BigUint {
    #[cfg(not(u64_digit))]
    #[inline]
    fn add_assign(&mut self, other: u64) {
        let (hi, lo) = big_digit::from_doublebigdigit(other);
        if hi == 0 {
            *self += lo;
        } else {
            while self.data.len() < 2 {
                self.data.push(0);
            }

            let carry = __add2(&mut self.data, &[lo, hi]);
            if carry != 0 {
                self.data.push(carry);
            }
        }
    }

    #[cfg(u64_digit)]
    #[inline]
    fn add_assign(&mut self, other: u64) {
        if other != 0 {
            if self.data.is_empty() {
                self.data.push(0);
            }

            let carry = __add2(&mut self.data, &[other as BigDigit]);
            if carry != 0 {
                self.data.push(carry);
            }
        }
    }
}

impl Add<u128> for BigUint {
    type Output = BigUint;

    #[inline]
    fn add(mut self, other: u128) -> BigUint {
        self += other;
        self
    }
}

impl AddAssign<u128> for BigUint {
    #[cfg(not(u64_digit))]
    #[inline]
    fn add_assign(&mut self, other: u128) {
        if other <= u128::from(u64::max_value()) {
            *self += other as u64
        } else {
            let (a, b, c, d) = u32_from_u128(other);
            let carry = if a > 0 {
                while self.data.len() < 4 {
                    self.data.push(0);
                }
                __add2(&mut self.data, &[d, c, b, a])
            } else {
                debug_assert!(b > 0);
                while self.data.len() < 3 {
                    self.data.push(0);
                }
                __add2(&mut self.data, &[d, c, b])
            };

            if carry != 0 {
                self.data.push(carry);
            }
        }
    }

    #[cfg(u64_digit)]
    #[inline]
    fn add_assign(&mut self, other: u128) {
        let (hi, lo) = big_digit::from_doublebigdigit(other);
        if hi == 0 {
            *self += lo;
        } else {
            while self.data.len() < 2 {
                self.data.push(0);
            }

            let carry = __add2(&mut self.data, &[lo, hi]);
            if carry != 0 {
                self.data.push(carry);
            }
        }
    }
}

impl CheckedAdd for BigUint {
    #[inline]
    fn checked_add(&self, v: &BigUint) -> Option<BigUint> {
        Some(self.add(v))
    }
}

impl_sum_iter_type!(BigUint);
num_bigint/biguint/addition.rs

num_bigint/biguint/
addition.rs
