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macro_rules! impl_div_rem {
(
$unsigned_name:ident,
$signed_name:ident,
$test_name:ident,
$n_h:expr,
$uH:ident,
$uX:ident,
$uD:ident,
$iD:ident,
$($unsigned_attr:meta),*;
$($signed_attr:meta),*
) => {
$(
#[$unsigned_attr]
)*
pub fn $unsigned_name(duo: $uD, div: $uD) -> ($uD,$uD) {
#[inline(always)]
pub fn carrying_mul(lhs: $uX, rhs: $uX) -> ($uX, $uX) {
let temp = (lhs as $uD).wrapping_mul(rhs as $uD);
(temp as $uX, (temp >> ($n_h * 2)) as $uX)
}
#[inline(always)]
pub fn carrying_mul_add(lhs: $uX, mul: $uX, add: $uX) -> ($uX, $uX) {
let temp = (lhs as $uD).wrapping_mul(mul as $uD).wrapping_add(add as $uD);
(temp as $uX, (temp >> ($n_h * 2)) as $uX)
}
let n = $n_h * 2;
let d_n = n * 2;
let div_leading_zeros = div.leading_zeros();
if div_leading_zeros >= (n + $n_h) {
if div_leading_zeros == d_n {
panic!("division by zero")
}
let div_lo = (div as $uH) as $uX;
let duo_hi = (duo >> n) as $uX;
let quo_hi = duo_hi.wrapping_div(div_lo);
let rem_2 = duo_hi.wrapping_rem(div_lo) as $uH;
let duo_mid =
((rem_2 as $uX) << $n_h) |
(((duo >> $n_h) as $uH) as $uX);
let quo_1 = duo_mid.wrapping_div(div_lo) as $uH;
let rem_1 = duo_mid.wrapping_rem(div_lo) as $uH;
let duo_lo =
((rem_1 as $uX) << $n_h) |
((duo as $uH) as $uX);
let quo_0 = duo_lo.wrapping_div(div_lo) as $uH;
(
((quo_hi as $uD) << n) | ((quo_1 as $uD) << $n_h) | (quo_0 as $uD),
(duo_lo.wrapping_rem(div_lo) as $uH) as $uD
)
} else if div_leading_zeros < $n_h {
let duo_leading_zeros = duo.leading_zeros();
if duo_leading_zeros >= div_leading_zeros {
if duo >= div {
return (1,duo.wrapping_sub(div))
} else {
return (0,duo)
}
}
let duo_hi = (duo >> n) as $uX;
let div_hi = (div >> n) as $uX;
let mult = duo_hi.wrapping_div(div_hi);
let div_lo = div as $uX;
let (temp_lo,carry) = carrying_mul(mult,div_lo);
let (temp_hi,overflow) = carrying_mul_add(mult,div_hi,carry);
if (overflow != 0) || (((temp_lo as $uD) | ((temp_hi as $uD) << n)) > duo) {
let (temp_lo,carry) = carrying_mul(mult.wrapping_sub(1),div_lo);
let temp_hi = mult.wrapping_sub(1).wrapping_mul(div_hi).wrapping_add(carry);
return (
mult.wrapping_sub(1) as $uD,
duo.wrapping_sub((temp_lo as $uD) | ((temp_hi as $uD) << n))
)
} else {
return (
mult as $uD,
duo.wrapping_sub((temp_lo as $uD) | ((temp_hi as $uD) << n))
)
}
} else {
let mut duo_leading_zeros = duo.leading_zeros();
if duo_leading_zeros >= div_leading_zeros {
if duo >= div {
return (1,duo.wrapping_sub(div))
} else {
return (0,duo)
}
}
if duo_leading_zeros >= n {
return (
(duo as $uX).wrapping_div(div as $uX) as $uD,
(duo as $uX).wrapping_rem(div as $uX) as $uD
)
}
let mut duo = duo;
let div_lesser_places = (n + $n_h).wrapping_sub(div_leading_zeros);
let div_sig_n_h = (div >> div_lesser_places) as $uH;
let div_sig_n_h_add1 = (div_sig_n_h as $uX).wrapping_add(1);
let mut quo: $uD = 0;
loop {
let duo_lesser_places = n.wrapping_sub(duo_leading_zeros);
let duo_sig_n = (duo >> duo_lesser_places) as $uX;
let mult = duo_sig_n.wrapping_div(div_sig_n_h_add1) as $uD;
if duo_lesser_places > div_lesser_places {
let place = duo_lesser_places.wrapping_sub(div_lesser_places);
quo = quo.wrapping_add(mult << place);
let temp = div.wrapping_mul(mult);
duo = duo.wrapping_sub(temp << place);
} else {
let place = div_lesser_places.wrapping_sub(duo_lesser_places);
let temp = (mult >> place) as $uX;
quo = quo.wrapping_add(temp as $uD);
let div_lo = div as $uX;
let div_hi = (div >> n) as $uX;
let (temp_lo,carry) = carrying_mul(temp,div_lo);
let temp_hi = temp.wrapping_mul(div_hi).wrapping_add(carry);
duo = duo.wrapping_sub((temp_lo as $uD) | ((temp_hi as $uD) << n));
}
duo_leading_zeros = duo.leading_zeros();
if duo_leading_zeros >= div_leading_zeros {
if duo >= div {
return (
quo.wrapping_add(1),
duo.wrapping_sub(div)
)
} else {
return (
quo,
duo
)
}
}
if duo_leading_zeros >= n {
return (
quo.wrapping_add((duo as $uX).wrapping_div(div as $uX) as $uD),
(duo as $uX).wrapping_rem(div as $uX) as $uD
)
}
}
}
}
$(
#[$signed_attr]
)*
pub fn $signed_name(duo: $iD, div: $iD) -> ($iD,$iD) {
match (duo < 0, div < 0) {
(false,false) => {
let t = $unsigned_name(duo as $uD,div as $uD);
(t.0 as $iD,t.1 as $iD)
},
(true,false) => {
let t = $unsigned_name(duo.wrapping_neg() as $uD,div as $uD);
((t.0 as $iD).wrapping_neg(),(t.1 as $iD).wrapping_neg())
},
(false,true) => {
let t = $unsigned_name(duo as $uD,div.wrapping_neg() as $uD);
((t.0 as $iD).wrapping_neg(),t.1 as $iD)
},
(true,true) => {
let t = $unsigned_name(duo.wrapping_neg() as $uD,div.wrapping_neg() as $uD);
(t.0 as $iD,(t.1 as $iD).wrapping_neg())
},
}
}
#[test]
fn $test_name() {
type T = $uD;
let n = $n_h * 4;
let mut lhs0: T = 0;
for i0 in 0..n {
lhs0 <<= 1;
lhs0 |= 1;
let mut lhs1 = lhs0;
for i1 in 0..i0 {
lhs1 ^= 1 << i1;
let mut rhs0: T = 0;
for i2 in 0..n {
rhs0 <<= 1;
rhs0 |= 1;
let mut rhs1 = rhs0;
for i3 in 0..i2 {
rhs1 ^= 1 << i3;
if rhs1 == 0 {
continue
}
assert_eq!((lhs1 / rhs1, lhs1 % rhs1),$unsigned_name(lhs1,rhs1));
assert_eq!(((lhs1 as $iD) / (rhs1 as $iD), (lhs1 as $iD) % (rhs1 as $iD)),$signed_name(lhs1 as $iD,rhs1 as $iD));
}
}
}
}
}
}
}
impl_div_rem!(u32_div_rem, i32_div_rem, u32_i32_div_rem_test, 8u32, u8, u16, u32, i32, inline, doc = "Computes the quotient and remainder of `duo` divided by `rem` and returns them as a tuple."; inline, doc = "Computes the quotient and remainder of `duo` divided by `rem` and returns them as a tuple.");
impl_div_rem!(u64_div_rem, i64_div_rem, u64_i64_div_rem_test, 16u32, u16, u32, u64, i64, inline, doc = "Computes the quotient and remainder of `duo` divided by `rem` and returns them as a tuple."; inline, doc = "Computes the quotient and remainder of `duo` divided by `rem` and returns them as a tuple.");
impl_div_rem!(u128_div_rem, i128_div_rem, u128_i128_div_rem_test, 32u32, u32, u64, u128, i128, inline, doc = "Computes the quotient and remainder of `duo` divided by `rem` and returns them as a tuple."; inline, doc = "Computes the quotient and remainder of `duo` divided by `rem` and returns them as a tuple.");