bigint: simplify the add2/sub2 loops
This splits the main arithmetic loops from the final carry/borrow propagation, and also normalizes the slice lengths before iteration. This lets the optimizer generate better code for these functions.
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@ -90,6 +90,16 @@ fn fib_100(b: &mut Bencher) {
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b.iter(|| fib(100));
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}
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#[bench]
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fn fib_1000(b: &mut Bencher) {
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b.iter(|| fib(1000));
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}
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#[bench]
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fn fib_10000(b: &mut Bencher) {
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b.iter(|| fib(10000));
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}
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#[bench]
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fn fac_to_string(b: &mut Bencher) {
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let fac = factorial(100);
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@ -90,6 +90,7 @@ use std::str::{self, FromStr};
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use std::fmt;
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#[cfg(test)]
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use std::hash;
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use std::cmp;
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use std::cmp::Ordering::{self, Less, Greater, Equal};
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use std::{f32, f64};
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use std::{u8, i64, u64};
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@ -173,12 +174,7 @@ fn sbb(a: BigDigit, b: BigDigit, borrow: &mut BigDigit) -> BigDigit {
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(*borrow as DoubleBigDigit));
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// hi * (base) + lo == 1*(base) + ai - bi - borrow
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// => ai - bi - borrow < 0 <=> hi == 0
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//
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*borrow = if hi == 0 {
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1
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} else {
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0
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};
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*borrow = (hi == 0) as BigDigit;
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lo
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}
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@ -755,20 +751,22 @@ forward_all_binop_to_val_ref_commutative!(impl Add for BigUint, add);
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#[must_use]
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#[inline]
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fn __add2(a: &mut [BigDigit], b: &[BigDigit]) -> BigDigit {
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let mut b_iter = b.iter();
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debug_assert!(a.len() >= b.len());
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let mut carry = 0;
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let (a_lo, a_hi) = a.split_at_mut(b.len());
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for ai in a.iter_mut() {
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if let Some(bi) = b_iter.next() {
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*ai = adc(*ai, *bi, &mut carry);
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} else if carry != 0 {
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*ai = adc(*ai, 0, &mut carry);
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} else {
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break;
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for (a, b) in a_lo.iter_mut().zip(b) {
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*a = adc(*a, *b, &mut carry);
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}
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if carry != 0 {
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for a in a_hi {
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*a = adc(*a, 0, &mut carry);
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if carry == 0 { break }
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}
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}
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debug_assert!(b_iter.next() == None);
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carry
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}
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@ -832,21 +830,25 @@ impl<'a> Add<&'a BigUint> for BigUint {
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forward_all_binop_to_val_ref!(impl Sub for BigUint, sub);
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fn sub2(a: &mut [BigDigit], b: &[BigDigit]) {
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let mut b_iter = b.iter();
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let mut borrow = 0;
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for ai in a.iter_mut() {
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if let Some(bi) = b_iter.next() {
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*ai = sbb(*ai, *bi, &mut borrow);
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} else if borrow != 0 {
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*ai = sbb(*ai, 0, &mut borrow);
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} else {
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break;
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let len = cmp::min(a.len(), b.len());
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let (a_lo, a_hi) = a.split_at_mut(len);
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let (b_lo, b_hi) = b.split_at(len);
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for (a, b) in a_lo.iter_mut().zip(b_lo) {
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*a = sbb(*a, *b, &mut borrow);
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}
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if borrow != 0 {
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for a in a_hi {
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*a = sbb(*a, 0, &mut borrow);
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if borrow == 0 { break }
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}
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}
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// note: we're _required_ to fail on underflow
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assert!(borrow == 0 && b_iter.all(|x| *x == 0),
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assert!(borrow == 0 && b_hi.iter().all(|x| *x == 0),
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"Cannot subtract b from a because b is larger than a.");
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}
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@ -866,14 +868,14 @@ fn sub_sign(a: &[BigDigit], b: &[BigDigit]) -> BigInt {
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match cmp_slice(a, b) {
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Greater => {
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let mut ret = BigUint::from_slice(a);
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sub2(&mut ret.data[..], b);
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BigInt::from_biguint(Plus, ret.normalize())
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let mut a = a.to_vec();
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sub2(&mut a, b);
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BigInt::new(Plus, a)
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}
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Less => {
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let mut ret = BigUint::from_slice(b);
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sub2(&mut ret.data[..], a);
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BigInt::from_biguint(Minus, ret.normalize())
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let mut b = b.to_vec();
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sub2(&mut b, a);
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BigInt::new(Minus, b)
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}
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_ => Zero::zero(),
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}
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