Simplify udivmodti4 for our special case
This isn't faster, just easier to understand.
This commit is contained in:
David Tolnay
parent
f05d2d62c3
commit
23d280dc7a
20
src/lib.rs
20
src/lib.rs
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@ -43,16 +43,10 @@ macro_rules! impl_Integer {
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($($t:ident),* as $conv_fn:ident) =>
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(impl_Integer!(
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$($t),* as $conv_fn,
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(|n:$conv_fn, d:$conv_fn, rem:Option<&mut $conv_fn>| {
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match rem {
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Some(rem) => *rem = n % d,
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_ => {},
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}
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n / d
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})
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|n:$conv_fn| (n / 10000, (n % 10000) as isize)
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););
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($($t:ident),* as $conv_fn:ident, $divmod:expr) => ($(
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($($t:ident),* as $conv_fn:ident, $divmod_10000:expr) => ($(
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impl Integer for $t {
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fn write<W: io::Write>(self, mut wr: W) -> io::Result<usize> {
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let mut buf = unsafe { mem::uninitialized() };
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@ -80,13 +74,13 @@ macro_rules! impl_Integer {
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// eagerly decode 4 characters at a time
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if <$t>::max_value() as u64 >= 10000 {
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while n >= 10000 {
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let mut rem = 0;
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// division with remainder on u128 is badly optimized by LLVM.
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// see “udiv128.rs” for more info.
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n = $divmod(n, 10000, Some(&mut rem));
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let (q, r) = $divmod_10000(n);
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n = q;
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let d1 = (rem as isize / 100) << 1;
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let d2 = (rem as isize % 100) << 1;
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let d1 = (r / 100) << 1;
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let d2 = (r % 100) << 1;
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curr -= 4;
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ptr::copy_nonoverlapping(lut_ptr.offset(d1), buf_ptr.offset(curr), 2);
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ptr::copy_nonoverlapping(lut_ptr.offset(d2), buf_ptr.offset(curr + 2), 2);
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@ -135,4 +129,4 @@ impl_Integer!(isize, usize as u32);
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#[cfg(target_pointer_width = "64")]
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impl_Integer!(isize, usize as u64);
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#[cfg(all(feature = "i128"))]
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impl_Integer!(i128, u128 as u128, udiv128::udivmodti4);
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impl_Integer!(i128, u128 as u128, udiv128::udivmod_10000);
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203
src/udiv128.rs
203
src/udiv128.rs
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@ -21,205 +21,42 @@
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// (https://github.com/rust-lang/rust/issues/44545) and to allow function
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// inlining which doesn’t happen with the intrinsic.
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const BITS: u32 = 128;
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const BITS_HALF: u32 = 64;
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trait LargeInt {
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fn low(self) -> u64;
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fn high(self) -> u64;
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fn from_parts(low: u64, high: u64) -> Self;
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pub fn udivmod_10000(n: u128) -> (u128, isize) {
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let high = (n >> 64) as u64;
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if high == 0 {
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let low = n as u64;
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return ((low / 10000) as u128, (low % 10000) as isize);
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}
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trait Int {
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fn aborting_div(self, other: Self) -> Self;
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fn aborting_rem(self, other: Self) -> Self;
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}
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let leading_zeros_10000 = 114;
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debug_assert_eq!(leading_zeros_10000, 10000u128.leading_zeros());
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let sr = 1 + leading_zeros_10000 - high.leading_zeros();
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impl LargeInt for u128 {
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fn low(self) -> u64 {
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self as u64
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}
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fn high(self) -> u64 {
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(self >> 64) as u64
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}
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fn from_parts(low: u64, high: u64) -> u128 {
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low as u128 | ((high as u128) << 64)
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}
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}
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impl Int for u64 {
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fn aborting_div(self, other: u64) -> u64 {
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<u64>::checked_div(self, other).unwrap()
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}
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fn aborting_rem(self, other: u64) -> u64 {
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<u64>::checked_rem(self, other).unwrap()
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}
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}
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pub fn udivmodti4(n: u128, d: u128, rem: Option<&mut u128>) -> u128 {
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// NOTE X is unknown, K != 0
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if n.high() == 0 {
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if d.high() == 0 {
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// 0 X
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// ---
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// 0 X
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if let Some(rem) = rem {
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*rem = <u128>::from(n.low().aborting_rem(d.low()));
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}
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return <u128>::from(n.low().aborting_div(d.low()))
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} else {
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// 0 X
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// ---
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// K X
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if let Some(rem) = rem {
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*rem = n;
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}
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return 0;
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};
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}
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let mut sr;
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let mut q;
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let mut r;
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if d.low() == 0 {
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if d.high() == 0 {
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// K X
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// ---
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// 0 0
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// NOTE This should be unreachable in safe Rust because the program will panic before
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// this intrinsic is called
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unreachable!();
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}
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if n.low() == 0 {
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// K 0
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// ---
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// K 0
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if let Some(rem) = rem {
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*rem = <u128>::from_parts(0, n.high().aborting_rem(d.high()));
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}
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return <u128>::from(n.high().aborting_div(d.high()))
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}
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// K K
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// ---
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// K 0
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if d.high().is_power_of_two() {
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if let Some(rem) = rem {
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*rem = <u128>::from_parts(n.low(), n.high() & (d.high() - 1));
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}
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return <u128>::from(n.high() >> d.high().trailing_zeros());
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}
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sr = d.high().leading_zeros().wrapping_sub(n.high().leading_zeros());
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// D > N
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if sr > BITS_HALF - 2 {
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if let Some(rem) = rem {
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*rem = n;
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}
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return 0;
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}
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sr += 1;
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// 1 <= sr <= BITS_HALF - 1
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q = n << (BITS - sr);
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r = n >> sr;
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} else if d.high() == 0 {
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// K X
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// ---
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// 0 K
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if d.low().is_power_of_two() {
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if let Some(rem) = rem {
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*rem = <u128>::from(n.low() & (d.low() - 1));
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}
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if d.low() == 1 {
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return n;
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} else {
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let sr = d.low().trailing_zeros();
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return n >> sr;
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};
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}
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sr = 1 + BITS_HALF + d.low().leading_zeros() - n.high().leading_zeros();
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// 2 <= sr <= u64::BITS - 1
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q = n << (BITS - sr);
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r = n >> sr;
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} else {
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// K X
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// ---
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// K K
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sr = d.high().leading_zeros().wrapping_sub(n.high().leading_zeros());
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// D > N
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if sr > BITS_HALF - 1 {
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if let Some(rem) = rem {
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*rem = n;
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}
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return 0;
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}
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sr += 1;
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// 1 <= sr <= BITS_HALF
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q = n << (BITS - sr);
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r = n >> sr;
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}
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// Not a special case
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// q and r are initialized with
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// q = n << (u64::BITS - sr)
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// r = n >> sr
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// 1 <= sr <= u64::BITS - 1
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let mut carry = 0;
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// 52 <= sr <= 115
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let mut q: u128 = n << (128 - sr);
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let mut r: u128 = n >> sr;
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let mut carry: u64 = 0;
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// Don't use a range because they may generate references to memcpy in unoptimized code
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//
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// Loop invariants: r < 10000; carry is 0 or 1
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let mut i = 0;
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while i < sr {
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i += 1;
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// r:q = ((r:q) << 1) | carry
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r = (r << 1) | (q >> (BITS - 1));
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r = (r << 1) | (q >> 127);
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q = (q << 1) | carry as u128;
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// carry = 0
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// if r >= d {
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// r -= d;
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// if r >= 10000 {
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// r -= 10000;
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// carry = 1;
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// }
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let s = (d.wrapping_sub(r).wrapping_sub(1)) as i128 >> (BITS - 1);
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let s = 10000u128.wrapping_sub(r).wrapping_sub(1) as i128 >> 127;
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carry = (s & 1) as u64;
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r -= d & s as u128;
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r -= 10000u128 & s as u128;
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}
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if let Some(rem) = rem {
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*rem = r;
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}
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(q << 1) | carry as u128
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}
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#[cfg(test)]
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#[test]
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fn test_udivmodti4() {
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let primes = [
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3, 7, 31, 73, 127, 179, 233, 283, 353,
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419, 467, 547, 607, 661, 739, 811, 877, 947,
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];
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for (i, d) in (0..128).cycle().zip(primes.iter().cycle()).take(1_000) {
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let n = 1u128 << i;
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let mut rem = 0;
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let q = udivmodti4(n, *d, Some(&mut rem));
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assert_eq!(q, n / d);
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assert_eq!(rem, n % d);
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}
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((q << 1) | carry as u128, r as isize)
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}
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