put div intrinsics in their own module + some docs

This commit is contained in:
Jorge Aparicio 2016-08-11 01:26:27 -05:00
parent a84579d3c1
commit 3ff25d956a
3 changed files with 314 additions and 309 deletions

278
src/div.rs Normal file
View File

@ -0,0 +1,278 @@
use {Int, LargeInt, U64};
/// Returns `n / d`
#[no_mangle]
pub extern "C" fn __udivsi3(n: u32, d: u32) -> u32 {
let u32_bits = u32::bits() as u32;
// Special cases
if d == 0 {
return 0; // ?!
}
if n == 0 {
return 0;
}
let mut sr = d.leading_zeros().wrapping_sub(n.leading_zeros());
// d > n
if sr > u32_bits - 1 {
return 0;
}
// d == 1
if sr == u32_bits - 1 {
return n;
}
sr = sr + 1;
// 1 <= sr <= u32_bits - 1
let mut q = n << (u32_bits - sr);
let mut r = n >> sr;
let mut carry = 0;
for _ in 0..sr {
// r:q = ((r:q) << 1) | carry
r = (r << 1) | (q >> (u32_bits - 1));
q = (q << 1) | carry;
// carry = 0;
// if r > d {
// r -= d;
// carry = 1;
// }
let s = (d.wrapping_sub(r).wrapping_sub(1)) as i32 >> (u32_bits - 1);
carry = (s & 1) as u32;
r -= d & s as u32;
}
q = (q << 1) | carry;
q
}
/// Returns `n / d` and sets `*rem = n % d`
#[no_mangle]
pub extern "C" fn __udivmodsi4(a: u32, b: u32, rem: Option<&mut u32>) -> u32 {
let d = __udivsi3(a, b);
if let Some(rem) = rem {
*rem = a - (d * b);
}
return d;
}
/// Returns `n / d` and sets `*rem = n % d`
#[no_mangle]
pub extern "C" fn __udivmoddi4(n: u64, d: u64, rem: Option<&mut u64>) -> u64 {
let u32_bits = u32::bits() as u32;
let u64_bits = u64::bits() as u32;
// NOTE X is unknown, K != 0
if n.high() == 0 {
if d.high() == 0 {
// 0 X
// ---
// 0 X
if let Some(rem) = rem {
*rem = u64::from(n.low() % d.low());
}
return u64::from(n.low() / d.low());
} else
// d.high() != 0
{
// 0 X
// ---
// K X
if let Some(rem) = rem {
*rem = u64::from(n.low());
}
return 0;
};
}
let mut sr;
let mut q = U64 { low: 0, high: 0 };
let mut r = U64 { low: 0, high: 0 };
// n.high() != 0
if d.low() == 0 {
if d.high() == 0 {
// K X
// ---
// 0 0
// NOTE copied verbatim from compiler-rt. This probably lets the intrinsic decide how to
// handle the division by zero (SIGFPE, 0, etc.). But this part shouldn't be reachable
// from safe code.
if let Some(rem) = rem {
*rem = u64::from(n.high() % d.low());
}
return u64::from(n.high() / d.low());
}
// d.high() != 0
if n.low() == 0 {
// K 0
// ---
// K 0
if let Some(rem) = rem {
*rem = U64 {
low: 0,
high: n.high() % d.high(),
}[..];
}
return u64::from(n.high() / d.high());
}
// n.low() != 0
// K K
// ---
// K 0
if d.high().is_power_of_two() {
if let Some(rem) = rem {
*rem = U64 {
low: n.low(),
high: n.high() & (d.high() - 1),
}[..];
}
return u64::from(n.high() >> d.high().trailing_zeros());
}
sr = d.high().leading_zeros().wrapping_sub(n.high().leading_zeros());
// D > N
if sr > u32_bits - 2 {
if let Some(rem) = rem {
*rem = n;
}
return 0;
}
sr = sr + 1;
// 1 <= sr <= u32_bits - 1
// q = n << (u64_bits - sr);
q.low = 0;
q.high = n.low() << (u32_bits - sr);
// r = n >> sr
r.high = n.high() >> sr;
r.low = (n.high() << (u32_bits - sr)) | (n.low() >> sr);
} else
// d.low() != 0
{
if d.high() == 0 {
// K X
// ---
// 0 K
if d.low().is_power_of_two() {
if let Some(rem) = rem {
*rem = u64::from(n.low() & (d.low() - 1));
}
if d.low() == 1 {
return n;
} else {
let sr = d.low().trailing_zeros();
return U64 {
low: (n.high() << (u32_bits - sr)) | (n.low() >> sr),
high: n.high() >> sr,
}[..];
};
}
sr = 1 + u32_bits + d.low().leading_zeros() - n.high().leading_zeros();
// 2 <= sr <= u64_bits - 1
// q = n << (u64_bits - sr)
// r = n >> sr;
if sr == u32_bits {
q.low = 0;
q.high = n.low();
r.high = 0;
r.low = n.high();
} else if sr < u32_bits
// 2 <= sr <= u32_bits - 1
{
q.low = 0;
q.high = n.low() << (u32_bits - sr);
r.high = n.high() >> sr;
r.low = (n.high() << (u32_bits - sr)) | (n.low() >> sr);
} else
// u32_bits + 1 <= sr <= u64_bits - 1
{
q.low = n.low() << (u64_bits - sr);
q.high = (n.high() << (u64_bits - sr)) | (n.low() >> (sr - u32_bits));
r.high = 0;
r.low = n.high() >> (sr - u32_bits);
}
} else
// d.high() != 0
{
// K X
// ---
// K K
sr = d.high().leading_zeros().wrapping_sub(n.high().leading_zeros());
// D > N
if sr > u32_bits - 1 {
if let Some(rem) = rem {
*rem = n;
return 0;
}
}
sr += 1;
// 1 <= sr <= u32_bits
// q = n << (u64_bits - sr)
q.low = 0;
if sr == u32_bits {
q.high = n.low();
r.high = 0;
r.low = n.high();
} else {
q.high = n.low() << (u32_bits - sr);
r.high = n.high() >> sr;
r.low = (n.high() << (u32_bits - sr)) | (n.low() >> sr);
}
}
}
// Not a special case
// q and r are initialized with
// q = n << (u64_bits - sr)
// r = n >> sr
// 1 <= sr <= u64_bits - 1
let mut carry = 0;
for _ in 0..sr {
// r:q = ((r:q) << 1) | carry
r[..] = (r[..] << 1) | (q[..] >> 63);
q[..] = (q[..] << 1) | carry as u64;
// carry = 0
// if r >= d {
// r -= d;
// carry = 1;
// }
let s = (d.wrapping_sub(r[..]).wrapping_sub(1)) as i64 >> (u64_bits - 1);
carry = (s & 1) as u32;
r[..] -= d & s as u64;
}
q[..] = (q[..] << 1) | carry as u64;
if let Some(rem) = rem {
*rem = r[..];
}
q[..]
}

View File

@ -15,9 +15,13 @@ extern crate quickcheck;
#[cfg(target_arch = "arm")]
pub mod arm;
pub mod div;
#[cfg(test)]
mod test;
use core::ops::{Index, IndexMut, RangeFull};
/// Trait for some basic operations on integers
trait Int {
fn bits() -> usize;
@ -85,6 +89,36 @@ impl LargeInt for i64 {
}
}
/// Union-like access to the 32-bit words that make an `u64`: `x.low` and `x.high`. The whole `u64`
/// can be accessed via the expression `x[..]`, which can be used in lvalue or rvalue position.
#[cfg(target_endian = "little")]
#[repr(C)]
struct U64 {
low: u32,
high: u32,
}
#[cfg(target_endian = "big")]
#[repr(C)]
struct U64 {
high: u32,
low: u32,
}
impl Index<RangeFull> for U64 {
type Output = u64;
fn index(&self, _: RangeFull) -> &u64 {
unsafe { &*(self as *const _ as *const u64) }
}
}
impl IndexMut<RangeFull> for U64 {
fn index_mut(&mut self, _: RangeFull) -> &mut u64 {
unsafe { &mut *(self as *const _ as *mut u64) }
}
}
macro_rules! absv_i2 {
($intrinsic:ident : $ty:ty) => {
#[no_mangle]
@ -104,310 +138,3 @@ absv_i2!(__absvsi2: i32);
absv_i2!(__absvdi2: i64);
// TODO(rust-lang/35118)?
// absv_i2!(__absvti2, i128);
/// Return `n / d` and `*rem = n % d`
#[no_mangle]
pub extern "C" fn __udivmoddi4(n: u64, d: u64, rem: Option<&mut u64>) -> u64 {
use core::ops::{Index, IndexMut, RangeFull};
#[cfg(target_endian = "little")]
#[repr(C)]
struct U64 {
low: u32,
high: u32,
}
#[cfg(target_endian = "big")]
#[repr(C)]
struct U64 {
high: u32,
low: u32,
}
impl Index<RangeFull> for U64 {
type Output = u64;
fn index(&self, _: RangeFull) -> &u64 {
unsafe { &*(self as *const _ as *const u64) }
}
}
impl IndexMut<RangeFull> for U64 {
fn index_mut(&mut self, _: RangeFull) -> &mut u64 {
unsafe { &mut *(self as *const _ as *mut u64) }
}
}
let u32_bits = u32::bits() as u32;
let u64_bits = u64::bits() as u32;
// NOTE X is unknown, K != 0
if n.high() == 0 {
if d.high() == 0 {
// 0 X
// ---
// 0 X
if let Some(rem) = rem {
*rem = u64::from(n.low() % d.low());
}
return u64::from(n.low() / d.low());
} else
// d.high() != 0
{
// 0 X
// ---
// K X
if let Some(rem) = rem {
*rem = u64::from(n.low());
}
return 0;
};
}
let mut sr;
let mut q = U64 { low: 0, high: 0 };
let mut r = U64 { low: 0, high: 0 };
// n.high() != 0
if d.low() == 0 {
if d.high() == 0 {
// K X
// ---
// 0 0
// NOTE copied verbatim from compiler-rt. This probably lets the intrinsic decide how to
// handle the division by zero (SIGFPE, 0, etc.). But this part shouldn't be reachable
// from safe code.
if let Some(rem) = rem {
*rem = u64::from(n.high() % d.low());
}
return u64::from(n.high() / d.low());
}
// d.high() != 0
if n.low() == 0 {
// K 0
// ---
// K 0
if let Some(rem) = rem {
*rem = U64 {
low: 0,
high: n.high() % d.high(),
}[..];
}
return u64::from(n.high() / d.high());
}
// n.low() != 0
// K K
// ---
// K 0
if d.high().is_power_of_two() {
if let Some(rem) = rem {
*rem = U64 {
low: n.low(),
high: n.high() & (d.high() - 1),
}[..];
}
return u64::from(n.high() >> d.high().trailing_zeros());
}
sr = d.high().leading_zeros().wrapping_sub(n.high().leading_zeros());
// D > N
if sr > u32_bits - 2 {
if let Some(rem) = rem {
*rem = n;
}
return 0;
}
sr = sr + 1;
// 1 <= sr <= u32_bits - 1
// q = n << (u64_bits - sr);
q.low = 0;
q.high = n.low() << (u32_bits - sr);
// r = n >> sr
r.high = n.high() >> sr;
r.low = (n.high() << (u32_bits - sr)) | (n.low() >> sr);
} else
// d.low() != 0
{
if d.high() == 0 {
// K X
// ---
// 0 K
if d.low().is_power_of_two() {
if let Some(rem) = rem {
*rem = u64::from(n.low() & (d.low() - 1));
}
if d.low() == 1 {
return n;
} else {
let sr = d.low().trailing_zeros();
return U64 {
low: (n.high() << (u32_bits - sr)) | (n.low() >> sr),
high: n.high() >> sr,
}[..];
};
}
sr = 1 + u32_bits + d.low().leading_zeros() - n.high().leading_zeros();
// 2 <= sr <= u64_bits - 1
// q = n << (u64_bits - sr)
// r = n >> sr;
if sr == u32_bits {
q.low = 0;
q.high = n.low();
r.high = 0;
r.low = n.high();
} else if sr < u32_bits
// 2 <= sr <= u32_bits - 1
{
q.low = 0;
q.high = n.low() << (u32_bits - sr);
r.high = n.high() >> sr;
r.low = (n.high() << (u32_bits - sr)) | (n.low() >> sr);
} else
// u32_bits + 1 <= sr <= u64_bits - 1
{
q.low = n.low() << (u64_bits - sr);
q.high = (n.high() << (u64_bits - sr)) | (n.low() >> (sr - u32_bits));
r.high = 0;
r.low = n.high() >> (sr - u32_bits);
}
} else
// d.high() != 0
{
// K X
// ---
// K K
sr = d.high().leading_zeros().wrapping_sub(n.high().leading_zeros());
// D > N
if sr > u32_bits - 1 {
if let Some(rem) = rem {
*rem = n;
return 0;
}
}
sr += 1;
// 1 <= sr <= u32_bits
// q = n << (u64_bits - sr)
q.low = 0;
if sr == u32_bits {
q.high = n.low();
r.high = 0;
r.low = n.high();
} else {
q.high = n.low() << (u32_bits - sr);
r.high = n.high() >> sr;
r.low = (n.high() << (u32_bits - sr)) | (n.low() >> sr);
}
}
}
// Not a special case
// q and r are initialized with
// q = n << (u64_bits - sr)
// r = n >> sr
// 1 <= sr <= u64_bits - 1
let mut carry = 0;
for _ in 0..sr {
// r:q = ((r:q) << 1) | carry
r[..] = (r[..] << 1) | (q[..] >> 63);
q[..] = (q[..] << 1) | carry as u64;
// carry = 0
// if r >= d {
// r -= d;
// carry = 1;
// }
let s = (d.wrapping_sub(r[..]).wrapping_sub(1)) as i64 >> (u64_bits - 1);
carry = (s & 1) as u32;
r[..] -= d & s as u64;
}
q[..] = (q[..] << 1) | carry as u64;
if let Some(rem) = rem {
*rem = r[..];
}
q[..]
}
/// Return `n / d` and `*rem = n % d`
#[no_mangle]
pub extern "C" fn __udivmodsi4(a: u32, b: u32, rem: Option<&mut u32>) -> u32 {
let d = __udivsi3(a, b);
if let Some(rem) = rem {
*rem = a - (d * b);
}
return d;
}
/// Return `n / d`
#[no_mangle]
pub extern "C" fn __udivsi3(n: u32, d: u32) -> u32 {
let u32_bits = u32::bits() as u32;
// Special cases
if d == 0 {
return 0; // ?!
}
if n == 0 {
return 0;
}
let mut sr = d.leading_zeros().wrapping_sub(n.leading_zeros());
// d > n
if sr > u32_bits - 1 {
return 0;
}
// d == 1
if sr == u32_bits - 1 {
return n;
}
sr = sr + 1;
// 1 <= sr <= u32_bits - 1
let mut q = n << (u32_bits - sr);
let mut r = n >> sr;
let mut carry = 0;
for _ in 0..sr {
// r:q = ((r:q) << 1) | carry
r = (r << 1) | (q >> (u32_bits - 1));
q = (q << 1) | carry;
// carry = 0;
// if r > d {
// r -= d;
// carry = 1;
// }
let s = (d.wrapping_sub(r).wrapping_sub(1)) as i32 >> (u32_bits - 1);
carry = (s & 1) as u32;
r -= d & s as u32;
}
q = (q << 1) | carry;
q
}

View File

@ -36,7 +36,7 @@ quickcheck! {
TestResult::discard()
} else {
let mut r = 0;
let q = ::__udivmoddi4(a, b, Some(&mut r));
let q = ::div::__udivmoddi4(a, b, Some(&mut r));
TestResult::from_bool(q * b + r == a)
}
@ -49,7 +49,7 @@ quickcheck! {
TestResult::discard()
} else {
let mut r = 0;
let q = ::__udivmodsi4(a, b, Some(&mut r));
let q = ::div::__udivmodsi4(a, b, Some(&mut r));
TestResult::from_bool(q * b + r == a)
}