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use awint_internals::*;
use const_fn::const_fn;
use crate::Bits;
// TODO optimize for high leading zero and trailing zero cases
/// # Multiplication
impl Bits {
/// Assigns `cin + (self * rhs)` to `self` and returns the overflow
#[const_fn(cfg(feature = "const_support"))]
pub const fn digit_cin_mul_(&mut self, cin: Digit, rhs: Digit) -> Digit {
let mut carry = cin;
unsafe_for_each_mut!(
self,
x,
{
let tmp = widen_mul_add(*x, rhs, carry);
*x = tmp.0;
carry = tmp.1;
},
false
);
let oflow = if self.extra() == 0 {
carry
} else {
(self.last() >> self.extra()) | (carry << (BITS - self.extra()))
};
self.clear_unused_bits();
oflow
}
/// Add-assigns `lhs * rhs` to `self` and returns if overflow happened
#[const_fn(cfg(feature = "const_support"))]
#[must_use]
pub const fn digit_mul_add_(&mut self, lhs: &Self, rhs: Digit) -> Option<bool> {
let mut mul_carry = 0;
let mut add_carry = 0;
unsafe_binop_for_each_mut!(
self,
lhs,
self_x,
lhs_x,
{
let tmp0 = widen_mul_add(lhs_x, rhs, mul_carry);
mul_carry = tmp0.1;
let tmp1 = widen_add(*self_x, tmp0.0, add_carry);
add_carry = tmp1.1;
*self_x = tmp1.0;
},
true
);
Some((mul_carry != 0) || (add_carry != 0))
}
/// Multiplies `lhs` by `rhs` and add-assigns the product to `self`. Three
/// operands eliminates the need for an allocating temporary.
#[const_fn(cfg(feature = "const_support"))]
#[must_use]
pub const fn mul_add_(&mut self, lhs: &Self, rhs: &Self) -> Option<()> {
if self.bw() != lhs.bw() || self.bw() != rhs.bw() {
return None
}
unsafe {
const_for!(lhs_i in {0..self.total_digits()} {
// carry from the short multiplication
let mut carry0 = 0;
let mut carry1 = 0;
const_for!(rhs_i in {0..(self.total_digits() - lhs_i)} {
let tmp0 =
widen_mul_add(lhs.get_unchecked(lhs_i), rhs.get_unchecked(rhs_i), carry0);
carry0 = tmp0.1;
let tmp1 = widen_add(self.get_unchecked(lhs_i + rhs_i), tmp0.0, carry1);
carry1 = tmp1.1;
*self.get_unchecked_mut(lhs_i + rhs_i) = tmp1.0;
});
});
}
self.clear_unused_bits();
Some(())
}
/// Multiply-assigns `self` by `rhs`. `pad` is a scratchpad that will be
/// mutated arbitrarily.
#[const_fn(cfg(feature = "const_support"))]
#[must_use]
pub const fn mul_(&mut self, rhs: &Self, pad: &mut Self) -> Option<()> {
if self.bw() != rhs.bw() || self.bw() != pad.bw() {
return None
}
pad.zero_();
unsafe {
const_for!(self_i in {0..self.total_digits()} {
// carry from the short multiplication
let mut carry0 = 0;
let mut carry1 = 0;
const_for!(rhs_i in {0..(self.total_digits() - self_i)} {
let tmp0 =
widen_mul_add(self.get_unchecked(self_i), rhs.get_unchecked(rhs_i), carry0);
carry0 = tmp0.1;
let tmp1 = widen_add(pad.get_unchecked(self_i + rhs_i), tmp0.0, carry1);
carry1 = tmp1.1;
*pad.get_unchecked_mut(self_i + rhs_i) = tmp1.0;
});
});
}
pad.clear_unused_bits();
self.copy_(pad).unwrap();
Some(())
}
/// Arbitrarily-unsigned-multiplies `lhs` by `rhs` and add-assigns the
/// product to `self`. This function is equivalent to:
/// ```
/// use awint::awi::*;
///
/// fn arb_umul_(add: &mut Bits, lhs: &Bits, rhs: &Bits) {
/// let mut resized_lhs = Awi::zero(add.nzbw());
/// // Note that this function is specified as unsigned,
/// // because we use `zero_resize_`
/// resized_lhs.zero_resize_(lhs);
/// let mut resized_rhs = Awi::zero(add.nzbw());
/// resized_rhs.zero_resize_(rhs);
/// add.mul_add_(&resized_lhs, &resized_rhs).unwrap();
/// }
/// ```
/// except that it avoids allocation and is more efficient overall
#[const_fn(cfg(feature = "const_support"))]
pub const fn arb_umul_add_(&mut self, lhs: &Self, rhs: &Self) {
// first, we swap references so that `x0.bw() <= x1.bw()`
let (x0, x1) = if lhs.bw() <= rhs.bw() {
(lhs, rhs)
} else {
(rhs, lhs)
};
let x0_upper_bound = if self.total_digits() < x0.total_digits() {
self.total_digits()
} else {
x0.total_digits()
};
// Safety: all the `get_unchecked_` are in bounds, since `x0_i < x0_upper_bound
// < x0.total_digits()` and there are independent checks every loop for the
// `x1_i` and `self_i` cases.
unsafe {
const_for!(x0_i in {0..x0_upper_bound} {
// carry from the short multiplication
let mut carry0 = 0;
let mut carry1 = 0;
let mut x1_i = 0;
let mut self_i = x0_i;
loop {
if x1_i >= x1.total_digits() || self_i >= self.total_digits() {
break
}
let tmp0 =
widen_mul_add(x0.get_unchecked(x0_i), x1.get_unchecked(x1_i), carry0);
carry0 = tmp0.1;
let tmp1 = widen_add(self.get_unchecked(self_i), tmp0.0, carry1);
carry1 = tmp1.1;
*self.get_unchecked_mut(self_i) = tmp1.0;
x1_i += 1;
self_i += 1;
}
// handle the last short multiplication carry if `self` continues
if self_i < self.total_digits() {
let tmp = widen_add(self.get_unchecked(self_i), carry0, carry1);
*self.get_unchecked_mut(self_i) = tmp.0;
carry1 = tmp.1;
self_i += 1;
// handle arbitrarily many addition carries
while self_i < self.total_digits() && carry1 != 0 {
let tmp = widen_add(self.get_unchecked(self_i), carry1, 0);
*self.get_unchecked_mut(self_i) = tmp.0;
carry1 = tmp.1;
self_i += 1;
}
}
});
}
self.clear_unused_bits();
}
/// Arbitrarily-signed-multiplies `lhs` by `rhs` and add-assigns the product
/// to `self`. Has the same behavior as [Bits::arb_umul_add_] except that is
/// interprets the arguments as signed. `lhs` and `rhs` are marked
/// mutable but their values are not changed by this function.
#[const_fn(cfg(feature = "const_support"))]
pub const fn arb_imul_add_(&mut self, lhs: &mut Self, rhs: &mut Self) {
let lhs_msb = lhs.msb();
let rhs_msb = rhs.msb();
lhs.neg_(lhs_msb);
rhs.neg_(rhs_msb);
self.neg_(lhs_msb != rhs_msb);
self.arb_umul_add_(lhs, rhs);
lhs.neg_(lhs_msb);
rhs.neg_(rhs_msb);
self.neg_(lhs_msb != rhs_msb);
}
}