bigint: refactor BigUint ops

As much as possible, ops are forwarded to val-ref so the LHS memory can
be reused for the result.  This reduces the number of clones required.

src/bigint.rs

@@ -86,7 +86,6 @@ pub type BigDigit = u32;
 pub type DoubleBigDigit = u64;
 
 pub const ZERO_BIG_DIGIT: BigDigit = 0;
-static ZERO_VEC: [BigDigit; 1] = [ZERO_BIG_DIGIT];
 
 #[allow(non_snake_case)]
 pub mod big_digit {
@@ -237,7 +236,26 @@ macro_rules! forward_val_val_binop {
 
             #[inline]
             fn $method(self, other: $res) -> $res {
-                (&self).$method(&other)
+                // forward to val-ref
+                $imp::$method(self, &other)
+            }
+        }
+    }
+}
+
+macro_rules! forward_val_val_binop_commutative {
+    (impl $imp:ident for $res:ty, $method:ident) => {
+        impl $imp<$res> for $res {
+            type Output = $res;
+
+            #[inline]
+            fn $method(self, other: $res) -> $res {
+                // forward to val-ref, with the larger capacity as val
+                if self.data.capacity() >= other.data.capacity() {
+                    $imp::$method(self, &other)
+                } else {
+                    $imp::$method(other, &self)
+                }
             }
         }
     }
@@ -250,7 +268,22 @@ macro_rules! forward_ref_val_binop {
 
             #[inline]
             fn $method(self, other: $res) -> $res {
-                self.$method(&other)
+                // forward to ref-ref
+                $imp::$method(self, &other)
+            }
+        }
+    }
+}
+
+macro_rules! forward_ref_val_binop_commutative {
+    (impl $imp:ident for $res:ty, $method:ident) => {
+        impl<'a> $imp<$res> for &'a $res {
+            type Output = $res;
+
+            #[inline]
+            fn $method(self, other: $res) -> $res {
+                // reverse, forward to val-ref
+                $imp::$method(other, self)
             }
         }
     }
@@ -263,58 +296,121 @@ macro_rules! forward_val_ref_binop {
 
             #[inline]
             fn $method(self, other: &$res) -> $res {
-                (&self).$method(other)
+                // forward to ref-ref
+                $imp::$method(&self, other)
             }
         }
     }
 }
 
-macro_rules! forward_all_binop {
+macro_rules! forward_ref_ref_binop {
+    (impl $imp:ident for $res:ty, $method:ident) => {
+        impl<'a, 'b> $imp<&'b $res> for &'a $res {
+            type Output = $res;
+
+            #[inline]
+            fn $method(self, other: &$res) -> $res {
+                // forward to val-ref
+                $imp::$method(self.clone(), other)
+            }
+        }
+    }
+}
+
+macro_rules! forward_ref_ref_binop_commutative {
+    (impl $imp:ident for $res:ty, $method:ident) => {
+        impl<'a, 'b> $imp<&'b $res> for &'a $res {
+            type Output = $res;
+
+            #[inline]
+            fn $method(self, other: &$res) -> $res {
+                // forward to val-ref, choosing the larger to clone
+                if self.data.len() >= other.data.len() {
+                    $imp::$method(self.clone(), other)
+                } else {
+                    $imp::$method(other.clone(), self)
+                }
+            }
+        }
+    }
+}
+
+// Forward everything to ref-ref, when reusing storage is not helpful
+macro_rules! forward_all_binop_to_ref_ref {
     (impl $imp:ident for $res:ty, $method:ident) => {
         forward_val_val_binop!(impl $imp for $res, $method);
-        forward_ref_val_binop!(impl $imp for $res, $method);
         forward_val_ref_binop!(impl $imp for $res, $method);
+        forward_ref_val_binop!(impl $imp for $res, $method);
     };
 }
 
-forward_all_binop!(impl BitAnd for BigUint, bitand);
+// Forward everything to val-ref, so LHS storage can be reused
+macro_rules! forward_all_binop_to_val_ref {
+    (impl $imp:ident for $res:ty, $method:ident) => {
+        forward_val_val_binop!(impl $imp for $res, $method);
+        forward_ref_val_binop!(impl $imp for $res, $method);
+        forward_ref_ref_binop!(impl $imp for $res, $method);
+    };
+}
 
-impl<'a, 'b> BitAnd<&'b BigUint> for &'a BigUint {
+// Forward everything to val-ref, commutatively, so either LHS or RHS storage can be reused
+macro_rules! forward_all_binop_to_val_ref_commutative {
+    (impl $imp:ident for $res:ty, $method:ident) => {
+        forward_val_val_binop_commutative!(impl $imp for $res, $method);
+        forward_ref_val_binop_commutative!(impl $imp for $res, $method);
+        forward_ref_ref_binop_commutative!(impl $imp for $res, $method);
+    };
+}
+
+forward_all_binop_to_val_ref_commutative!(impl BitAnd for BigUint, bitand);
+
+impl<'a> BitAnd<&'a BigUint> for BigUint {
     type Output = BigUint;
 
     #[inline]
     fn bitand(self, other: &BigUint) -> BigUint {
-        BigUint::new(self.data.iter().zip(other.data.iter()).map(|(ai, bi)| *ai & *bi).collect())
+        let mut data = self.data;
+        for (ai, &bi) in data.iter_mut().zip(other.data.iter()) {
+            *ai &= bi;
+        }
+        data.truncate(other.data.len());
+        BigUint::new(data)
     }
 }
 
-forward_all_binop!(impl BitOr for BigUint, bitor);
+forward_all_binop_to_val_ref_commutative!(impl BitOr for BigUint, bitor);
 
-impl<'a, 'b> BitOr<&'b BigUint> for &'a BigUint {
+impl<'a> BitOr<&'a BigUint> for BigUint {
     type Output = BigUint;
 
     fn bitor(self, other: &BigUint) -> BigUint {
-        let zeros = ZERO_VEC.iter().cycle();
+        let mut data = self.data;
-        let (a, b) = if self.data.len() > other.data.len() { (self, other) } else { (other, self) };
+        for (ai, &bi) in data.iter_mut().zip(other.data.iter()) {
-        let ored = a.data.iter().zip(b.data.iter().chain(zeros)).map(
+            *ai |= bi;
-            |(ai, bi)| *ai | *bi
+        }
-                ).collect();
+        if other.data.len() > data.len() {
-        return BigUint::new(ored);
+            let extra = &other.data[data.len()..];
+            data.extend(extra.iter().cloned());
+        }
+        BigUint::new(data)
     }
 }
 
-forward_all_binop!(impl BitXor for BigUint, bitxor);
+forward_all_binop_to_val_ref_commutative!(impl BitXor for BigUint, bitxor);
 
-impl<'a, 'b> BitXor<&'b BigUint> for &'a BigUint {
+impl<'a> BitXor<&'a BigUint> for BigUint {
     type Output = BigUint;
 
     fn bitxor(self, other: &BigUint) -> BigUint {
-        let zeros = ZERO_VEC.iter().cycle();
+        let mut data = self.data;
-        let (a, b) = if self.data.len() > other.data.len() { (self, other) } else { (other, self) };
+        for (ai, &bi) in data.iter_mut().zip(other.data.iter()) {
-        let xored = a.data.iter().zip(b.data.iter().chain(zeros)).map(
+            *ai ^= bi;
-            |(ai, bi)| *ai ^ *bi
+        }
-                ).collect();
+        if other.data.len() > data.len() {
-        return BigUint::new(xored);
+            let extra = &other.data[data.len()..];
+            data.extend(extra.iter().cloned());
+        }
+        BigUint::new(data)
     }
 }
 
@@ -332,7 +428,7 @@ impl<'a> Shl<usize> for &'a BigUint {
     fn shl(self, rhs: usize) -> BigUint {
         let n_unit = rhs / big_digit::BITS;
         let n_bits = rhs % big_digit::BITS;
-        return self.shl_unit(n_unit).shl_bits(n_bits);
+        self.shl_unit(n_unit).shl_bits(n_bits)
     }
 }
 
@@ -350,7 +446,7 @@ impl<'a> Shr<usize> for &'a BigUint {
     fn shr(self, rhs: usize) -> BigUint {
         let n_unit = rhs / big_digit::BITS;
         let n_bits = rhs % big_digit::BITS;
-        return self.shr_unit(n_unit).shr_bits(n_bits);
+        self.shr_unit(n_unit).shr_bits(n_bits)
     }
 }
 
@@ -369,70 +465,85 @@ impl One for BigUint {
 
 impl Unsigned for BigUint {}
 
-forward_all_binop!(impl Add for BigUint, add);
+forward_all_binop_to_val_ref_commutative!(impl Add for BigUint, add);
 
-impl<'a, 'b> Add<&'b BigUint> for &'a BigUint {
+impl<'a> Add<&'a BigUint> for BigUint {
     type Output = BigUint;
 
     fn add(self, other: &BigUint) -> BigUint {
-        let zeros = ZERO_VEC.iter().cycle();
+        let mut sum = self.data;
-        let (a, b) = if self.data.len() > other.data.len() { (self, other) } else { (other, self) };
+
+        if other.data.len() > sum.len() {
+            let additional = other.data.len() - sum.len();
+            sum.reserve(additional);
+            sum.extend(repeat(ZERO_BIG_DIGIT).take(additional));
+        }
+        let other_iter = other.data.iter().cloned().chain(repeat(ZERO_BIG_DIGIT));
 
         let mut carry = 0;
-        let mut sum: Vec<BigDigit> =  a.data.iter().zip(b.data.iter().chain(zeros)).map(|(ai, bi)| {
+        for (a, b) in sum.iter_mut().zip(other_iter) {
-            let (hi, lo) = big_digit::from_doublebigdigit(
+            let d = (*a as DoubleBigDigit)
-                (*ai as DoubleBigDigit) + (*bi as DoubleBigDigit) + (carry as DoubleBigDigit));
+                + (b as DoubleBigDigit)
+                + (carry as DoubleBigDigit);
+            let (hi, lo) = big_digit::from_doublebigdigit(d);
             carry = hi;
-            lo
+            *a = lo;
-        }).collect();
+        }
+
         if carry != 0 { sum.push(carry); }
-        return BigUint::new(sum);
+        BigUint::new(sum)
     }
 }
 
-forward_all_binop!(impl Sub for BigUint, sub);
+forward_all_binop_to_val_ref!(impl Sub for BigUint, sub);
 
-impl<'a, 'b> Sub<&'b BigUint> for &'a BigUint {
+impl<'a> Sub<&'a BigUint> for BigUint {
     type Output = BigUint;
 
     fn sub(self, other: &BigUint) -> BigUint {
-        let new_len = cmp::max(self.data.len(), other.data.len());
+        let mut diff = self.data;
-        let zeros = ZERO_VEC.iter().cycle();
+        let other = &other.data;
-        let (a, b) = (self.data.iter().chain(zeros.clone()), other.data.iter().chain(zeros));
+        assert!(diff.len() >= other.len(), "arithmetic operation overflowed");
 
-        let mut borrow = 0isize;
+        let mut borrow: DoubleBigDigit = 0;
-        let diff: Vec<BigDigit> =  a.take(new_len).zip(b).map(|(ai, bi)| {
+        for (a, &b) in diff.iter_mut().zip(other.iter()) {
-            let (hi, lo) = big_digit::from_doublebigdigit(
+            let d = big_digit::BASE - borrow
-                big_digit::BASE
+                + (*a as DoubleBigDigit)
-                    + (*ai as DoubleBigDigit)
+                - (b as DoubleBigDigit);
-                    - (*bi as DoubleBigDigit)
+            let (hi, lo) = big_digit::from_doublebigdigit(d);
-                    - (borrow as DoubleBigDigit)
-                    );
             /*
             hi * (base) + lo == 1*(base) + ai - bi - borrow
             => ai - bi - borrow < 0 <=> hi == 0
              */
             borrow = if hi == 0 { 1 } else { 0 };
-            lo
+            *a = lo;
-        }).collect();
+        }
 
-        assert!(borrow == 0,
+        for a in &mut diff[other.len()..] {
-                "Cannot subtract other from self because other is larger than self.");
+            if borrow == 0 { break }
-        return BigUint::new(diff);
+            let d = big_digit::BASE - borrow
+                + (*a as DoubleBigDigit);
+            let (hi, lo) = big_digit::from_doublebigdigit(d);
+            borrow = if hi == 0 { 1 } else { 0 };
+            *a = lo;
+        }
+
+        assert!(borrow == 0, "arithmetic operation overflowed");
+        BigUint::new(diff)
     }
 }
 
 
-forward_all_binop!(impl Mul for BigUint, mul);
+forward_all_binop_to_val_ref_commutative!(impl Mul for BigUint, mul);
 
-impl<'a, 'b> Mul<&'b BigUint> for &'a BigUint {
+impl<'a> Mul<&'a BigUint> for BigUint {
     type Output = BigUint;
 
     fn mul(self, other: &BigUint) -> BigUint {
         if self.is_zero() || other.is_zero() { return Zero::zero(); }
 
         let (s_len, o_len) = (self.data.len(), other.data.len());
-        if s_len == 1 { return mul_digit(other, self.data[0]);  }
+        if s_len == 1 { return mul_digit(other.clone(), self.data[0]);  }
         if o_len == 1 { return mul_digit(self,  other.data[0]); }
 
         // Using Karatsuba multiplication
@@ -442,7 +553,7 @@ impl<'a, 'b> Mul<&'b BigUint> for &'a BigUint {
         //   a0*b0
         let half_len = cmp::max(s_len, o_len) / 2;
         let (s_hi, s_lo) = cut_at(self,  half_len);
-        let (o_hi, o_lo) = cut_at(other, half_len);
+        let (o_hi, o_lo) = cut_at(other.clone(), half_len);
 
         let ll = &s_lo * &o_lo;
         let hh = &s_hi * &o_hi;
@@ -459,27 +570,30 @@ impl<'a, 'b> Mul<&'b BigUint> for &'a BigUint {
         return ll + mm.shl_unit(half_len) + hh.shl_unit(half_len * 2);
 
 
-        fn mul_digit(a: &BigUint, n: BigDigit) -> BigUint {
+        fn mul_digit(a: BigUint, n: BigDigit) -> BigUint {
             if n == 0 { return Zero::zero(); }
-            if n == 1 { return a.clone(); }
+            if n == 1 { return a; }
 
             let mut carry = 0;
-            let mut prod: Vec<BigDigit> = a.data.iter().map(|ai| {
+            let mut prod = a.data;
-                let (hi, lo) = big_digit::from_doublebigdigit(
+            for a in &mut prod {
-                    (*ai as DoubleBigDigit) * (n as DoubleBigDigit) + (carry as DoubleBigDigit)
+                let d = (*a as DoubleBigDigit)
-                        );
+                    * (n as DoubleBigDigit)
+                    + (carry as DoubleBigDigit);
+                let (hi, lo) = big_digit::from_doublebigdigit(d);
                 carry = hi;
-                lo
+                *a = lo;
-            }).collect();
+            }
             if carry != 0 { prod.push(carry); }
-            return BigUint::new(prod);
+            BigUint::new(prod)
         }
 
         #[inline]
-        fn cut_at(a: &BigUint, n: usize) -> (BigUint, BigUint) {
+        fn cut_at(mut a: BigUint, n: usize) -> (BigUint, BigUint) {
             let mid = cmp::min(a.data.len(), n);
-            (BigUint::from_slice(&a.data[mid ..]),
+            let hi = BigUint::from_slice(&a.data[mid ..]);
-             BigUint::from_slice(&a.data[.. mid]))
+            a.data.truncate(mid);
+            (hi, BigUint::new(a.data))
         }
 
         #[inline]
@@ -494,7 +608,7 @@ impl<'a, 'b> Mul<&'b BigUint> for &'a BigUint {
 }
 
 
-forward_all_binop!(impl Div for BigUint, div);
+forward_all_binop_to_ref_ref!(impl Div for BigUint, div);
 
 impl<'a, 'b> Div<&'b BigUint> for &'a BigUint {
     type Output = BigUint;
@@ -506,7 +620,7 @@ impl<'a, 'b> Div<&'b BigUint> for &'a BigUint {
     }
 }
 
-forward_all_binop!(impl Rem for BigUint, rem);
+forward_all_binop_to_ref_ref!(impl Rem for BigUint, rem);
 
 impl<'a, 'b> Rem<&'b BigUint> for &'a BigUint {
     type Output = BigUint;
@@ -587,10 +701,10 @@ impl Integer for BigUint {
     fn div_mod_floor(&self, other: &BigUint) -> (BigUint, BigUint) {
         if other.is_zero() { panic!() }
         if self.is_zero() { return (Zero::zero(), Zero::zero()); }
-        if *other == One::one() { return ((*self).clone(), Zero::zero()); }
+        if *other == One::one() { return (self.clone(), Zero::zero()); }
 
         match self.cmp(other) {
-            Less    => return (Zero::zero(), (*self).clone()),
+            Less    => return (Zero::zero(), self.clone()),
             Equal   => return (One::one(), Zero::zero()),
             Greater => {} // Do nothing
         }
@@ -1007,48 +1121,53 @@ impl BigUint {
 
     #[inline]
     fn shl_unit(&self, n_unit: usize) -> BigUint {
-        if n_unit == 0 || self.is_zero() { return (*self).clone(); }
+        if n_unit == 0 || self.is_zero() { return self.clone(); }
 
-        let mut v = repeat(ZERO_BIG_DIGIT).take(n_unit).collect::<Vec<_>>();
+        let mut v = vec![0; n_unit];
         v.extend(self.data.iter().cloned());
         BigUint::new(v)
     }
 
     #[inline]
-    fn shl_bits(&self, n_bits: usize) -> BigUint {
+    fn shl_bits(self, n_bits: usize) -> BigUint {
-        if n_bits == 0 || self.is_zero() { return (*self).clone(); }
+        if n_bits == 0 || self.is_zero() { return self; }
+
+        assert!(n_bits < big_digit::BITS);
 
         let mut carry = 0;
-        let mut shifted: Vec<BigDigit> = self.data.iter().map(|elem| {
+        let mut shifted = self.data;
-            let (hi, lo) = big_digit::from_doublebigdigit(
+        for elem in shifted.iter_mut() {
-                (*elem as DoubleBigDigit) << n_bits | (carry as DoubleBigDigit)
+            let new_carry = *elem >> (big_digit::BITS - n_bits);
-            );
+            *elem = (*elem << n_bits) | carry;
-            carry = hi;
+            carry = new_carry;
-            lo
+        }
-        }).collect();
+        if carry != 0 {
-        if carry != 0 { shifted.push(carry); }
+            shifted.push(carry);
-        return BigUint::new(shifted);
+        }
+        BigUint::new(shifted)
     }
 
     #[inline]
     fn shr_unit(&self, n_unit: usize) -> BigUint {
-        if n_unit == 0 { return (*self).clone(); }
+        if n_unit == 0 { return self.clone(); }
         if self.data.len() < n_unit { return Zero::zero(); }
         BigUint::from_slice(&self.data[n_unit ..])
     }
 
     #[inline]
-    fn shr_bits(&self, n_bits: usize) -> BigUint {
+    fn shr_bits(self, n_bits: usize) -> BigUint {
-        if n_bits == 0 || self.data.is_empty() { return (*self).clone(); }
+        if n_bits == 0 || self.data.is_empty() { return self; }
+
+        assert!(n_bits < big_digit::BITS);
 
         let mut borrow = 0;
-        let mut shifted_rev = Vec::with_capacity(self.data.len());
+        let mut shifted = self.data;
-        for elem in self.data.iter().rev() {
+        for elem in shifted.iter_mut().rev() {
-            shifted_rev.push((*elem >> n_bits) | borrow);
+            let new_borrow = *elem << (big_digit::BITS - n_bits);
-            borrow = *elem << (big_digit::BITS - n_bits);
+            *elem = (*elem >> n_bits) | borrow;
+            borrow = new_borrow;
         }
-        let shifted = { shifted_rev.reverse(); shifted_rev };
+        BigUint::new(shifted)
-        return BigUint::new(shifted);
     }
 
     /// Determines the fewest bits necessary to express the `BigUint`.