diff --git a/bigint/src/algorithms.rs b/bigint/src/algorithms.rs
index 0afd6b1..604fee2 100644
--- a/bigint/src/algorithms.rs
+++ b/bigint/src/algorithms.rs
@@ -85,6 +85,15 @@ pub fn mac_with_carry(a: BigDigit, b: BigDigit, c: BigDigit, carry: &mut BigDigi
     lo
 }
 
+#[inline]
+pub fn mul_with_carry(a: BigDigit, b: BigDigit, carry: &mut BigDigit) -> BigDigit {
+    let (hi, lo) = big_digit::from_doublebigdigit((a as DoubleBigDigit) * (b as DoubleBigDigit) +
+                                                  (*carry as DoubleBigDigit));
+
+    *carry = hi;
+    lo
+}
+
 /// Divide a two digit numerator by a one digit divisor, returns quotient and remainder:
 ///
 /// Note: the caller must ensure that both the quotient and remainder will fit into a single digit.
@@ -377,6 +386,14 @@ pub fn mul3(x: &[BigDigit], y: &[BigDigit]) -> BigUint {
     prod.normalize()
 }
 
+pub fn scalar_mul(a: &mut [BigDigit], b: BigDigit) -> BigDigit {
+    let mut carry = 0;
+    for a in a.iter_mut() {
+        *a = mul_with_carry(*a, b, &mut carry);
+    }
+    carry
+}
+
 pub fn div_rem(u: &BigUint, d: &BigUint) -> (BigUint, BigUint) {
     if d.is_zero() {
         panic!()
@@ -416,7 +433,7 @@ pub fn div_rem(u: &BigUint, d: &BigUint) -> (BigUint, BigUint) {
     // q0, our guess, is calculated by dividing the last few digits of a by the last digit of b
     // - this should give us a guess that is "close" to the actual quotient, but is possibly
     // greater than the actual quotient. If q0 * b > a, we simply use iterated subtraction
-    // until we have a guess such that q0 & b <= a.
+    // until we have a guess such that q0 * b <= a.
     //
 
     let bn = *b.data.last().unwrap();
diff --git a/bigint/src/bigint.rs b/bigint/src/bigint.rs
index b86ca52..259f619 100644
--- a/bigint/src/bigint.rs
+++ b/bigint/src/bigint.rs
@@ -23,11 +23,14 @@ use self::Sign::{Minus, NoSign, Plus};
 
 use super::ParseBigIntError;
 use super::big_digit;
-use super::big_digit::BigDigit;
+use super::big_digit::{BigDigit, DoubleBigDigit};
 use biguint;
 use biguint::to_str_radix_reversed;
 use biguint::BigUint;
 
+use UsizePromotion;
+use IsizePromotion;
+
 #[cfg(test)]
 #[path = "tests/bigint.rs"]
 mod bigint_tests;
@@ -299,6 +302,26 @@ impl Signed for BigInt {
     }
 }
 
+// A convenience method for getting the absolute value of an i32 in a u32.
+#[inline]
+fn i32_abs_as_u32(a: i32) -> u32 {
+    if a == i32::min_value() {
+        a as u32
+    } else {
+        a.abs() as u32
+    }
+}
+
+// A convenience method for getting the absolute value of an i64 in a u64.
+#[inline]
+fn i64_abs_as_u64(a: i64) -> u64 {
+    if a == i64::min_value() {
+        a as u64
+    } else {
+        a.abs() as u64
+    }
+}
+
 // We want to forward to BigUint::add, but it's not clear how that will go until
 // we compare both sign and magnitude.  So we duplicate this body for every
 // val/ref combination, deferring that decision to BigUint's own forwarding.
@@ -362,6 +385,75 @@ impl Add<BigInt> for BigInt {
     }
 }
 
+promote_all_scalars!(impl Add for BigInt, add);
+forward_all_scalar_binop_to_val_val_commutative!(impl Add<BigDigit> for BigInt, add);
+forward_all_scalar_binop_to_val_val_commutative!(impl Add<DoubleBigDigit> for BigInt, add);
+
+impl Add<BigDigit> for BigInt {
+    type Output = BigInt;
+
+    #[inline]
+    fn add(self, other: BigDigit) -> BigInt {
+        match self.sign {
+            NoSign => From::from(other),
+            Plus => BigInt::from_biguint(Plus, self.data + other),
+            Minus =>
+                match self.data.cmp(&From::from(other)) {
+                    Equal => Zero::zero(),
+                    Less => BigInt::from_biguint(Plus, other - self.data),
+                    Greater => BigInt::from_biguint(Minus, self.data - other),
+                }
+        }
+    }
+}
+
+impl Add<DoubleBigDigit> for BigInt {
+    type Output = BigInt;
+
+    #[inline]
+    fn add(self, other: DoubleBigDigit) -> BigInt {
+        match self.sign {
+            NoSign => From::from(other),
+            Plus => BigInt::from_biguint(Plus, self.data + other),
+            Minus =>
+                match self.data.cmp(&From::from(other)) {
+                    Equal => Zero::zero(),
+                    Less => BigInt::from_biguint(Plus, other - self.data),
+                    Greater => BigInt::from_biguint(Minus, self.data - other),
+                }
+        }
+    }
+}
+
+forward_all_scalar_binop_to_val_val_commutative!(impl Add<i32> for BigInt, add);
+forward_all_scalar_binop_to_val_val_commutative!(impl Add<i64> for BigInt, add);
+
+impl Add<i32> for BigInt {
+    type Output = BigInt;
+
+    #[inline]
+    fn add(self, other: i32) -> BigInt {
+        if other >= 0 {
+            self + other as u32
+        } else {
+            self - i32_abs_as_u32(other)
+        }
+    }
+}
+
+impl Add<i64> for BigInt {
+    type Output = BigInt;
+
+    #[inline]
+    fn add(self, other: i64) -> BigInt {
+        if other >= 0 {
+            self + other as u64
+        } else {
+            self - i64_abs_as_u64(other)
+        }
+    }
+}
+
 // We want to forward to BigUint::sub, but it's not clear how that will go until
 // we compare both sign and magnitude.  So we duplicate this body for every
 // val/ref combination, deferring that decision to BigUint's own forwarding.
@@ -425,6 +517,119 @@ impl Sub<BigInt> for BigInt {
     }
 }
 
+promote_all_scalars!(impl Sub for BigInt, sub);
+forward_all_scalar_binop_to_val_val!(impl Sub<BigDigit> for BigInt, sub);
+forward_all_scalar_binop_to_val_val!(impl Sub<DoubleBigDigit> for BigInt, sub);
+
+impl Sub<BigDigit> for BigInt {
+    type Output = BigInt;
+
+    #[inline]
+    fn sub(self, other: BigDigit) -> BigInt {
+        match self.sign {
+            NoSign => BigInt::from_biguint(Minus, From::from(other)),
+            Minus => BigInt::from_biguint(Minus, self.data + other),
+            Plus =>
+                match self.data.cmp(&From::from(other)) {
+                    Equal => Zero::zero(),
+                    Greater => BigInt::from_biguint(Plus, self.data - other),
+                    Less => BigInt::from_biguint(Minus, other - self.data),
+                }
+        }
+    }
+}
+
+impl Sub<BigInt> for BigDigit {
+    type Output = BigInt;
+
+    #[inline]
+    fn sub(self, other: BigInt) -> BigInt {
+        -(other - self)
+    }
+}
+
+impl Sub<DoubleBigDigit> for BigInt {
+    type Output = BigInt;
+
+    #[inline]
+    fn sub(self, other: DoubleBigDigit) -> BigInt {
+        match self.sign {
+            NoSign => BigInt::from_biguint(Minus, From::from(other)),
+            Minus => BigInt::from_biguint(Minus, self.data + other),
+            Plus =>
+                match self.data.cmp(&From::from(other)) {
+                    Equal => Zero::zero(),
+                    Greater => BigInt::from_biguint(Plus, self.data - other),
+                    Less => BigInt::from_biguint(Minus, other - self.data),
+                }
+        }
+    }
+}
+
+impl Sub<BigInt> for DoubleBigDigit {
+    type Output = BigInt;
+
+    #[inline]
+    fn sub(self, other: BigInt) -> BigInt {
+        -(other - self)
+    }
+}
+
+forward_all_scalar_binop_to_val_val!(impl Sub<i32> for BigInt, sub);
+forward_all_scalar_binop_to_val_val!(impl Sub<i64> for BigInt, sub);
+
+impl Sub<i32> for BigInt {
+    type Output = BigInt;
+
+    #[inline]
+    fn sub(self, other: i32) -> BigInt {
+        if other >= 0 {
+            self - other as u32
+        } else {
+            self + i32_abs_as_u32(other)
+        }
+    }
+}
+
+impl Sub<BigInt> for i32 {
+    type Output = BigInt;
+
+    #[inline]
+    fn sub(self, other: BigInt) -> BigInt {
+        if self >= 0 {
+            self as u32 - other
+        } else {
+            -other - i32_abs_as_u32(self)
+        }
+    }
+}
+
+impl Sub<i64> for BigInt {
+    type Output = BigInt;
+
+    #[inline]
+    fn sub(self, other: i64) -> BigInt {
+        if other >= 0 {
+            self - other as u64
+        } else {
+            self + i64_abs_as_u64(other)
+        }
+    }
+}
+
+impl Sub<BigInt> for i64 {
+    type Output = BigInt;
+
+    #[inline]
+    fn sub(self, other: BigInt) -> BigInt {
+        if self >= 0 {
+            self as u64 - other
+        } else {
+            -other - i64_abs_as_u64(self)
+        }
+    }
+}
+
 forward_all_binop_to_ref_ref!(impl Mul for BigInt, mul);
 
 impl<'a, 'b> Mul<&'b BigInt> for &'a BigInt {
@@ -436,6 +641,57 @@ impl<'a, 'b> Mul<&'b BigInt> for &'a BigInt {
     }
 }
 
+promote_all_scalars!(impl Mul for BigInt, mul);
+forward_all_scalar_binop_to_val_val_commutative!(impl Mul<BigDigit> for BigInt, mul);
+forward_all_scalar_binop_to_val_val_commutative!(impl Mul<DoubleBigDigit> for BigInt, mul);
+
+impl Mul<BigDigit> for BigInt {
+    type Output = BigInt;
+
+    #[inline]
+    fn mul(self, other: BigDigit) -> BigInt {
+        BigInt::from_biguint(self.sign, self.data * other)
+    }
+}
+
+impl Mul<DoubleBigDigit> for BigInt {
+    type Output = BigInt;
+
+    #[inline]
+    fn mul(self, other: DoubleBigDigit) -> BigInt {
+        BigInt::from_biguint(self.sign, self.data * other)
+    }
+}
+
+forward_all_scalar_binop_to_val_val_commutative!(impl Mul<i32> for BigInt, mul);
+forward_all_scalar_binop_to_val_val_commutative!(impl Mul<i64> for BigInt, mul);
+
+impl Mul<i32> for BigInt {
+    type Output = BigInt;
+
+    #[inline]
+    fn mul(self, other: i32) -> BigInt {
+        if other >= 0 {
+            self * other as u32
+        } else {
+            -(self * i32_abs_as_u32(other))
+        }
+    }
+}
+
+impl Mul<i64> for BigInt {
+    type Output = BigInt;
+
+    #[inline]
+    fn mul(self, other: i64) -> BigInt {
+        if other >= 0 {
+            self * other as u64
+        } else {
+            -(self * i64_abs_as_u64(other))
+        }
+    }
+}
+
 forward_all_binop_to_ref_ref!(impl Div for BigInt, div);
 
 impl<'a, 'b> Div<&'b BigInt> for &'a BigInt {
@@ -448,6 +704,101 @@ impl<'a, 'b> Div<&'b BigInt> for &'a BigInt {
     }
 }
 
+promote_all_scalars!(impl Div for BigInt, div);
+forward_all_scalar_binop_to_val_val!(impl Div<BigDigit> for BigInt, div);
+forward_all_scalar_binop_to_val_val!(impl Div<DoubleBigDigit> for BigInt, div);
+
+impl Div<BigDigit> for BigInt {
+    type Output = BigInt;
+
+    #[inline]
+    fn div(self, other: BigDigit) -> BigInt {
+        BigInt::from_biguint(self.sign, self.data / other)
+    }
+}
+
+impl Div<BigInt> for BigDigit {
+    type Output = BigInt;
+
+    #[inline]
+    fn div(self, other: BigInt) -> BigInt {
+        BigInt::from_biguint(other.sign, self / other.data)
+    }
+}
+
+impl Div<DoubleBigDigit> for BigInt {
+    type Output = BigInt;
+
+    #[inline]
+    fn div(self, other: DoubleBigDigit) -> BigInt {
+        BigInt::from_biguint(self.sign, self.data / other)
+    }
+}
+
+impl Div<BigInt> for DoubleBigDigit {
+    type Output = BigInt;
+
+    #[inline]
+    fn div(self, other: BigInt) -> BigInt {
+        BigInt::from_biguint(other.sign, self / other.data)
+    }
+}
+
+forward_all_scalar_binop_to_val_val!(impl Div<i32> for BigInt, div);
+forward_all_scalar_binop_to_val_val!(impl Div<i64> for BigInt, div);
+
+impl Div<i32> for BigInt {
+    type Output = BigInt;
+
+    #[inline]
+    fn div(self, other: i32) -> BigInt {
+        if other >= 0 {
+            self / other as u32
+        } else {
+            -(self / i32_abs_as_u32(other))
+        }
+    }
+}
+
+impl Div<BigInt> for i32 {
+    type Output = BigInt;
+
+    #[inline]
+    fn div(self, other: BigInt) -> BigInt {
+        if self >= 0 {
+            self as u32 / other
+        } else {
+            -(i32_abs_as_u32(self) / other)
+        }
+    }
+}
+
+impl Div<i64> for BigInt {
+    type Output = BigInt;
+
+    #[inline]
+    fn div(self, other: i64) -> BigInt {
+        if other >= 0 {
+            self / other as u64
+        } else {
+            -(self / i64_abs_as_u64(other))
+        }
+    }
+}
+
+impl Div<BigInt> for i64 {
+    type Output = BigInt;
+
+    #[inline]
+    fn div(self, other: BigInt) -> BigInt {
+        if self >= 0 {
+            self as u64 / other
+        } else {
+            -(i64_abs_as_u64(self) / other)
+        }
+    }
+}
+
 forward_all_binop_to_ref_ref!(impl Rem for BigInt, rem);
 
 impl<'a, 'b> Rem<&'b BigInt> for &'a BigInt {
@@ -460,6 +811,101 @@ impl<'a, 'b> Rem<&'b BigInt> for &'a BigInt {
     }
 }
 
+promote_all_scalars!(impl Rem for BigInt, rem);
+forward_all_scalar_binop_to_val_val!(impl Rem<BigDigit> for BigInt, rem);
+forward_all_scalar_binop_to_val_val!(impl Rem<DoubleBigDigit> for BigInt, rem);
+
+impl Rem<BigDigit> for BigInt {
+    type Output = BigInt;
+
+    #[inline]
+    fn rem(self, other: BigDigit) -> BigInt {
+        BigInt::from_biguint(self.sign, self.data % other)
+    }
+}
+
+impl Rem<BigInt> for BigDigit {
+    type Output = BigInt;
+
+    #[inline]
+    fn rem(self, other: BigInt) -> BigInt {
+        BigInt::from_biguint(Plus, self % other.data)
+    }
+}
+
+impl Rem<DoubleBigDigit> for BigInt {
+    type Output = BigInt;
+
+    #[inline]
+    fn rem(self, other: DoubleBigDigit) -> BigInt {
+        BigInt::from_biguint(self.sign, self.data % other)
+    }
+}
+
+impl Rem<BigInt> for DoubleBigDigit {
+    type Output = BigInt;
+
+    #[inline]
+    fn rem(self, other: BigInt) -> BigInt {
+        BigInt::from_biguint(Plus, self % other.data)
+    }
+}
+
+forward_all_scalar_binop_to_val_val!(impl Rem<i32> for BigInt, rem);
+forward_all_scalar_binop_to_val_val!(impl Rem<i64> for BigInt, rem);
+
+impl Rem<i32> for BigInt {
+    type Output = BigInt;
+
+    #[inline]
+    fn rem(self, other: i32) -> BigInt {
+        if other >= 0 {
+            self % other as u32
+        } else {
+            self % i32_abs_as_u32(other)
+        }
+    }
+}
+
+impl Rem<BigInt> for i32 {
+    type Output = BigInt;
+
+    #[inline]
+    fn rem(self, other: BigInt) -> BigInt {
+        if self >= 0 {
+            self as u32 % other
+        } else {
+            -(i32_abs_as_u32(self) % other)
+        }
+    }
+}
+
+impl Rem<i64> for BigInt {
+    type Output = BigInt;
+
+    #[inline]
+    fn rem(self, other: i64) -> BigInt {
+        if other >= 0 {
+            self % other as u64
+        } else {
+            self % i64_abs_as_u64(other)
+        }
+    }
+}
+
+impl Rem<BigInt> for i64 {
+    type Output = BigInt;
+
+    #[inline]
+    fn rem(self, other: BigInt) -> BigInt {
+        if self >= 0 {
+            self as u64 % other
+        } else {
+            -(i64_abs_as_u64(self) % other)
+        }
+    }
+}
+
 impl Neg for BigInt {
     type Output = BigInt;
 
diff --git a/bigint/src/biguint.rs b/bigint/src/biguint.rs
index 340aaae..2c2d046 100644
--- a/bigint/src/biguint.rs
+++ b/bigint/src/biguint.rs
@@ -22,11 +22,13 @@ mod algorithms;
 pub use self::algorithms::big_digit;
 pub use self::big_digit::{BigDigit, DoubleBigDigit, ZERO_BIG_DIGIT};
 
-use self::algorithms::{mac_with_carry, mul3, div_rem, div_rem_digit};
+use self::algorithms::{mac_with_carry, mul3, scalar_mul, div_rem, div_rem_digit};
 use self::algorithms::{__add2, add2, sub2, sub2rev};
 use self::algorithms::{biguint_shl, biguint_shr};
 use self::algorithms::{cmp_slice, fls, ilog2};
 
+use UsizePromotion;
+
 use ParseBigIntError;
 
 #[cfg(test)]
@@ -394,6 +396,51 @@ impl<'a> Add<&'a BigUint> for BigUint {
     }
 }
 
+promote_unsigned_scalars!(impl Add for BigUint, add);
+forward_all_scalar_binop_to_val_val_commutative!(impl Add<BigDigit> for BigUint, add);
+forward_all_scalar_binop_to_val_val_commutative!(impl Add<DoubleBigDigit> for BigUint, add);
+
+impl Add<BigDigit> for BigUint {
+    type Output = BigUint;
+
+    #[inline]
+    fn add(mut self, other: BigDigit) -> BigUint {
+        if other != 0 {
+            if self.data.len() == 0 {
+                self.data.push(0);
+            }
+
+            let carry = __add2(&mut self.data, &[other]);
+            if carry != 0 {
+                self.data.push(carry);
+            }
+        }
+        self
+    }
+}
+
+impl Add<DoubleBigDigit> for BigUint {
+    type Output = BigUint;
+
+    #[inline]
+    fn add(mut self, other: DoubleBigDigit) -> BigUint {
+        let (hi, lo) = big_digit::from_doublebigdigit(other);
+        if hi == 0 {
+            self + lo
+        } else {
+            while self.data.len() < 2 {
+                self.data.push(0);
+            }
+
+            let carry = __add2(&mut self.data, &[lo, hi]);
+            if carry != 0 {
+                self.data.push(carry);
+            }
+            self
+        }
+    }
+}
+
 forward_val_val_binop!(impl Sub for BigUint, sub);
 forward_ref_ref_binop!(impl Sub for BigUint, sub);
 
@@ -420,6 +467,60 @@ impl<'a> Sub<BigUint> for &'a BigUint {
     }
 }
 
+promote_unsigned_scalars!(impl Sub for BigUint, sub);
+forward_all_scalar_binop_to_val_val!(impl Sub<BigDigit> for BigUint, sub);
+forward_all_scalar_binop_to_val_val!(impl Sub<DoubleBigDigit> for BigUint, sub);
+
+impl Sub<BigDigit> for BigUint {
+    type Output = BigUint;
+
+    #[inline]
+    fn sub(mut self, other: BigDigit) -> BigUint {
+        sub2(&mut self.data[..], &[other]);
+        self.normalize()
+    }
+}
+
+impl Sub<BigUint> for BigDigit {
+    type Output = BigUint;
+
+    #[inline]
+    fn sub(self, mut other: BigUint) -> BigUint {
+        if other.data.len() == 0 {
+            other.data.push(0);
+        }
+
+        sub2rev(&[self], &mut other.data[..]);
+        other.normalize()
+    }
+}
+
+impl Sub<DoubleBigDigit> for BigUint {
+    type Output = BigUint;
+
+    #[inline]
+    fn sub(mut self, other: DoubleBigDigit) -> BigUint {
+        let (hi, lo) = big_digit::from_doublebigdigit(other);
+        sub2(&mut self.data[..], &[lo, hi]);
+        self.normalize()
+    }
+}
+
+impl Sub<BigUint> for DoubleBigDigit {
+    type Output = BigUint;
+
+    #[inline]
+    fn sub(self, mut other: BigUint) -> BigUint {
+        while other.data.len() < 2 {
+            other.data.push(0);
+        }
+
+        let (hi, lo) = big_digit::from_doublebigdigit(self);
+        sub2rev(&[lo, hi], &mut other.data[..]);
+        other.normalize()
+    }
+}
+
 forward_all_binop_to_ref_ref!(impl Mul for BigUint, mul);
 
 impl<'a, 'b> Mul<&'b BigUint> for &'a BigUint {
@@ -431,6 +532,44 @@ impl<'a, 'b> Mul<&'b BigUint> for &'a BigUint {
     }
 }
 
+promote_unsigned_scalars!(impl Mul for BigUint, mul);
+forward_all_scalar_binop_to_val_val_commutative!(impl Mul<BigDigit> for BigUint, mul);
+forward_all_scalar_binop_to_val_val_commutative!(impl Mul<DoubleBigDigit> for BigUint, mul);
+
+impl Mul<BigDigit> for BigUint {
+    type Output = BigUint;
+
+    #[inline]
+    fn mul(mut self, other: BigDigit) -> BigUint {
+        if other == 0 {
+            self.data.clear();
+        } else {
+            let carry = scalar_mul(&mut self.data[..], other);
+            if carry != 0 {
+                self.data.push(carry);
+            }
+        }
+        self
+    }
+}
+
+impl Mul<DoubleBigDigit> for BigUint {
+    type Output = BigUint;
+
+    #[inline]
+    fn mul(mut self, other: DoubleBigDigit) -> BigUint {
+        if other == 0 {
+            self.data.clear();
+            self
+        } else if other <= BigDigit::max_value() as DoubleBigDigit {
+            self * other as BigDigit
+        } else {
+            let (hi, lo) = big_digit::from_doublebigdigit(other);
+            mul3(&self.data[..], &[lo, hi])
+        }
+    }
+}
+
 forward_all_binop_to_ref_ref!(impl Div for BigUint, div);
 
 impl<'a, 'b> Div<&'b BigUint> for &'a BigUint {
@@ -439,7 +578,58 @@ impl<'a, 'b> Div<&'b BigUint> for &'a BigUint {
     #[inline]
     fn div(self, other: &BigUint) -> BigUint {
         let (q, _) = self.div_rem(other);
-        return q;
+        q
+    }
+}
+
+promote_unsigned_scalars!(impl Div for BigUint, div);
+forward_all_scalar_binop_to_val_val!(impl Div<BigDigit> for BigUint, div);
+forward_all_scalar_binop_to_val_val!(impl Div<DoubleBigDigit> for BigUint, div);
+
+impl Div<BigDigit> for BigUint {
+    type Output = BigUint;
+
+    #[inline]
+    fn div(self, other: BigDigit) -> BigUint {
+        let (q, _) = div_rem_digit(self, other);
+        q
+    }
+}
+
+impl Div<BigUint> for BigDigit {
+    type Output = BigUint;
+
+    #[inline]
+    fn div(self, other: BigUint) -> BigUint {
+        match other.data.len() {
+            0 => panic!(),
+            1 => From::from(self / other.data[0]),
+            _ => Zero::zero(),
+        }
+    }
+}
+
+impl Div<DoubleBigDigit> for BigUint {
+    type Output = BigUint;
+
+    #[inline]
+    fn div(self, other: DoubleBigDigit) -> BigUint {
+        let (q, _) = self.div_rem(&From::from(other));
+        q
+    }
+}
+
+impl Div<BigUint> for DoubleBigDigit {
+    type Output = BigUint;
+
+    #[inline]
+    fn div(self, other: BigUint) -> BigUint {
+        match other.data.len() {
+            0 => panic!(),
+            1 => From::from(self / other.data[0] as u64),
+            2 => From::from(self / big_digit::to_doublebigdigit(other.data[1], other.data[0])),
+            _ => Zero::zero(),
+        }
     }
 }
 
@@ -451,7 +641,58 @@ impl<'a, 'b> Rem<&'b BigUint> for &'a BigUint {
     #[inline]
     fn rem(self, other: &BigUint) -> BigUint {
         let (_, r) = self.div_rem(other);
-        return r;
+        r
+    }
+}
+
+promote_unsigned_scalars!(impl Rem for BigUint, rem);
+forward_all_scalar_binop_to_val_val!(impl Rem<BigDigit> for BigUint, rem);
+forward_all_scalar_binop_to_val_val!(impl Rem<DoubleBigDigit> for BigUint, rem);
+
+impl Rem<BigDigit> for BigUint {
+    type Output = BigUint;
+
+    #[inline]
+    fn rem(self, other: BigDigit) -> BigUint {
+        let (_, r) = div_rem_digit(self, other);
+        From::from(r)
+    }
+}
+
+impl Rem<BigUint> for BigDigit {
+    type Output = BigUint;
+
+    #[inline]
+    fn rem(self, other: BigUint) -> BigUint {
+        match other.data.len() {
+            0 => panic!(),
+            1 => From::from(self % other.data[0]),
+            _ => From::from(self)
+        }
+    }
+}
+
+impl Rem<DoubleBigDigit> for BigUint {
+    type Output = BigUint;
+
+    #[inline]
+    fn rem(self, other: DoubleBigDigit) -> BigUint {
+        let (_, r) = self.div_rem(&From::from(other));
+        r
+    }
+}
+
+impl Rem<BigUint> for DoubleBigDigit {
+    type Output = BigUint;
+
+    #[inline]
+    fn rem(self, other: BigUint) -> BigUint {
+        match other.data.len() {
+            0 => panic!(),
+            1 => From::from(self % other.data[0] as u64),
+            2 => From::from(self % big_digit::to_doublebigdigit(other.data[0], other.data[1])),
+            _ => From::from(self),
+        }
     }
 }
 
diff --git a/bigint/src/lib.rs b/bigint/src/lib.rs
index 586eeec..02b9992 100644
--- a/bigint/src/lib.rs
+++ b/bigint/src/lib.rs
@@ -88,6 +88,16 @@ use std::error::Error;
 use std::num::ParseIntError;
 use std::fmt;
 
+#[cfg(target_pointer_width = "32")]
+type UsizePromotion = u32;
+#[cfg(target_pointer_width = "64")]
+type UsizePromotion = u64;
+
+#[cfg(target_pointer_width = "32")]
+type IsizePromotion = i32;
+#[cfg(target_pointer_width = "64")]
+type IsizePromotion = i64;
+
 #[derive(Debug, PartialEq)]
 pub enum ParseBigIntError {
     ParseInt(ParseIntError),
diff --git a/bigint/src/macros.rs b/bigint/src/macros.rs
index 39f45a4..7705f55 100644
--- a/bigint/src/macros.rs
+++ b/bigint/src/macros.rs
@@ -105,6 +105,125 @@ macro_rules! forward_ref_ref_binop_commutative {
     }
 }
 
+macro_rules! forward_scalar_val_val_binop_commutative {
+    (impl $imp:ident<$scalar:ty> for $res:ty, $method: ident) => {
+        impl $imp<$res> for $scalar {
+            type Output = $res;
+
+            #[inline]
+            fn $method(self, other: $res) -> $res {
+                $imp::$method(other, self)
+            }
+        }
+    }
+}
+
+macro_rules! forward_scalar_val_ref_binop {
+    (impl $imp:ident<$scalar:ty> for $res:ty, $method:ident) => {
+        impl<'a> $imp<&'a $scalar> for $res {
+            type Output = $res;
+
+            #[inline]
+            fn $method(self, other: &$scalar) -> $res {
+                $imp::$method(self, *other)
+            }
+        }
+
+        impl<'a> $imp<$res> for &'a $scalar {
+            type Output = $res;
+
+            #[inline]
+            fn $method(self, other: $res) -> $res {
+                $imp::$method(*self, other)
+            }
+        }
+    }
+}
+
+macro_rules! forward_scalar_ref_val_binop {
+    (impl $imp:ident<$scalar:ty> for $res:ty, $method:ident) => {
+        impl<'a> $imp<$scalar> for &'a $res {
+            type Output = $res;
+
+            #[inline]
+            fn $method(self, other: $scalar) -> $res {
+                $imp::$method(self.clone(), other)
+            }
+        }
+
+        impl<'a> $imp<&'a $res> for $scalar {
+            type Output = $res;
+
+            #[inline]
+            fn $method(self, other: &$res) -> $res {
+                $imp::$method(self, other.clone())
+            }
+        }
+    }
+}
+
+macro_rules! forward_scalar_ref_ref_binop {
+    (impl $imp:ident<$scalar:ty> for $res:ty, $method:ident) => {
+        impl<'a, 'b> $imp<&'b $scalar> for &'a $res {
+            type Output = $res;
+
+            #[inline]
+            fn $method(self, other: &$scalar) -> $res {
+                $imp::$method(self.clone(), *other)
+            }
+        }
+
+        impl<'a, 'b> $imp<&'a $res> for &'b $scalar {
+            type Output = $res;
+
+            #[inline]
+            fn $method(self, other: &$res) -> $res {
+                $imp::$method(*self, other.clone())
+            }
+        }
+    }
+}
+
+macro_rules! promote_scalars {
+    (impl $imp:ident<$promo:ty> for $res:ty, $method:ident, $( $scalar:ty ),*) => {
+        $(
+            forward_all_scalar_binop_to_val_val!(impl $imp<$scalar> for $res, $method);
+
+            impl $imp<$scalar> for $res {
+                type Output = $res;
+
+                #[inline]
+                fn $method(self, other: $scalar) -> $res {
+                    $imp::$method(self, other as $promo)
+                }
+            }
+
+            impl $imp<$res> for $scalar {
+                type Output = $res;
+
+                #[inline]
+                fn $method(self, other: $res) -> $res {
+                    $imp::$method(self as $promo, other)
+                }
+            }
+        )*
+    }
+}
+
+macro_rules! promote_unsigned_scalars {
+    (impl $imp:ident for $res:ty, $method:ident) => {
+        promote_scalars!(impl $imp<u32> for $res, $method, u8, u16);
+        promote_scalars!(impl $imp<UsizePromotion> for $res, $method, usize);
+    }
+}
+
+macro_rules! promote_signed_scalars {
+    (impl $imp:ident for $res:ty, $method:ident) => {
+        promote_scalars!(impl $imp<i32> for $res, $method, i8, i16);
+        promote_scalars!(impl $imp<IsizePromotion> for $res, $method, isize);
+    }
+}
+
 // 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) => {
@@ -131,3 +250,25 @@ macro_rules! forward_all_binop_to_val_ref_commutative {
         forward_ref_ref_binop_commutative!(impl $imp for $res, $method);
     };
 }
+
+macro_rules! forward_all_scalar_binop_to_val_val {
+    (impl $imp:ident<$scalar:ty> for $res:ty, $method:ident) => {
+        forward_scalar_val_ref_binop!(impl $imp<$scalar> for $res, $method);
+        forward_scalar_ref_val_binop!(impl $imp<$scalar> for $res, $method);
+        forward_scalar_ref_ref_binop!(impl $imp<$scalar> for $res, $method);
+    }
+}
+
+macro_rules! forward_all_scalar_binop_to_val_val_commutative {
+    (impl $imp:ident<$scalar:ty> for $res:ty, $method:ident) => {
+        forward_scalar_val_val_binop_commutative!(impl $imp<$scalar> for $res, $method);
+        forward_all_scalar_binop_to_val_val!(impl $imp<$scalar> for $res, $method);
+    }
+}
+
+macro_rules! promote_all_scalars {
+    (impl $imp:ident for $res:ty, $method:ident) => {
+        promote_unsigned_scalars!(impl $imp for $res, $method);
+        promote_signed_scalars!(impl $imp for $res, $method);
+    }
+}
\ No newline at end of file
diff --git a/bigint/src/tests/bigint.rs b/bigint/src/tests/bigint.rs
index aa4319d..9fbebb0 100644
--- a/bigint/src/tests/bigint.rs
+++ b/bigint/src/tests/bigint.rs
@@ -24,6 +24,25 @@ macro_rules! assert_op {
     };
 }
 
+/// Assert that an op works for scalar left or right
+macro_rules! assert_scalar_op {
+    (($($to:ident),*) $left:ident $op:tt $right:ident == $expected:expr) => {
+        $(
+            if let Some(left) = $left.$to() {
+                assert_op!(left $op $right == $expected);
+            }
+            if let Some(right) = $right.$to() {
+                assert_op!($left $op right == $expected);
+            }
+        )*
+    };
+    ($left:ident $op:tt $right:ident == $expected:expr) => {
+        assert_scalar_op!((to_u8, to_u16, to_u32, to_u64, to_usize,
+                           to_i8, to_i16, to_i32, to_i64, to_isize)
+                          $left $op $right == $expected);
+    };
+}
+
 #[test]
 fn test_from_biguint() {
     fn check(inp_s: Sign, inp_n: usize, ans_s: Sign, ans_n: usize) {
@@ -552,6 +571,26 @@ fn test_add() {
     }
 }
 
+#[test]
+fn test_scalar_add() {
+    for elm in SUM_TRIPLES.iter() {
+        let (a_vec, b_vec, c_vec) = *elm;
+        let a = BigInt::from_slice(Plus, a_vec);
+        let b = BigInt::from_slice(Plus, b_vec);
+        let c = BigInt::from_slice(Plus, c_vec);
+        let (na, nb, nc) = (-&a, -&b, -&c);
+
+        assert_scalar_op!(a + b == c);
+        assert_scalar_op!(b + a == c);
+        assert_scalar_op!(c + na == b);
+        assert_scalar_op!(c + nb == a);
+        assert_scalar_op!(a + nc == nb);
+        assert_scalar_op!(b + nc == na);
+        assert_scalar_op!(na + nb == nc);
+        assert_scalar_op!(a + na == Zero::zero());
+    }
+}
+
 #[test]
 fn test_sub() {
     for elm in SUM_TRIPLES.iter() {
@@ -572,6 +611,26 @@ fn test_sub() {
     }
 }
 
+#[test]
+fn test_scalar_sub() {
+    for elm in SUM_TRIPLES.iter() {
+        let (a_vec, b_vec, c_vec) = *elm;
+        let a = BigInt::from_slice(Plus, a_vec);
+        let b = BigInt::from_slice(Plus, b_vec);
+        let c = BigInt::from_slice(Plus, c_vec);
+        let (na, nb, nc) = (-&a, -&b, -&c);
+
+        assert_scalar_op!(c - a == b);
+        assert_scalar_op!(c - b == a);
+        assert_scalar_op!(nb - a == nc);
+        assert_scalar_op!(na - b == nc);
+        assert_scalar_op!(b - na == c);
+        assert_scalar_op!(a - nb == c);
+        assert_scalar_op!(nc - na == nb);
+        assert_scalar_op!(a - a == Zero::zero());
+    }
+}
+
 const M: u32 = ::std::u32::MAX;
 static MUL_TRIPLES: &'static [(&'static [BigDigit],
            &'static [BigDigit],
@@ -603,6 +662,7 @@ static DIV_REM_QUADRUPLES: &'static [(&'static [BigDigit],
            &'static [BigDigit],
            &'static [BigDigit],
            &'static [BigDigit])] = &[(&[1], &[2], &[], &[1]),
+                                     (&[3], &[2], &[1], &[1]),
                                      (&[1, 1], &[2], &[M / 2 + 1], &[1]),
                                      (&[1, 1, 1], &[2], &[M / 2 + 1, M / 2 + 1], &[1]),
                                      (&[0, 1], &[N1], &[1], &[1]),
@@ -637,6 +697,24 @@ fn test_mul() {
     }
 }
 
+#[test]
+fn test_scalar_mul() {
+    for elm in MUL_TRIPLES.iter() {
+        let (a_vec, b_vec, c_vec) = *elm;
+        let a = BigInt::from_slice(Plus, a_vec);
+        let b = BigInt::from_slice(Plus, b_vec);
+        let c = BigInt::from_slice(Plus, c_vec);
+        let (na, nb, nc) = (-&a, -&b, -&c);
+
+        assert_scalar_op!(a * b == c);
+        assert_scalar_op!(b * a == c);
+        assert_scalar_op!(na * nb == c);
+
+        assert_scalar_op!(na * b == nc);
+        assert_scalar_op!(nb * a == nc);
+    }
+}
+
 #[test]
 fn test_div_mod_floor() {
     fn check_sub(a: &BigInt, b: &BigInt, ans_d: &BigInt, ans_m: &BigInt) {
@@ -743,6 +821,65 @@ fn test_div_rem() {
     }
 }
 
+#[test]
+fn test_scalar_div_rem() {
+    fn check_sub(a: &BigInt, b: BigDigit, ans_q: &BigInt, ans_r: &BigInt) {
+        let (q, r) = (a / b, a % b);
+        if !r.is_zero() {
+            assert_eq!(r.sign, a.sign);
+        }
+        assert!(r.abs() <= From::from(b));
+        assert!(*a == b * &q + &r);
+        assert!(q == *ans_q);
+        assert!(r == *ans_r);
+
+        let (a, b, ans_q, ans_r) = (a.clone(), b.clone(), ans_q.clone(), ans_r.clone());
+        assert_op!(a / b == ans_q);
+        assert_op!(a % b == ans_r);
+
+        if b <= i32::max_value() as u32 {
+            let nb = -(b as i32);
+            assert_op!(a / nb == -ans_q.clone());
+            assert_op!(a % nb == ans_r);
+        }
+    }
+
+    fn check(a: &BigInt, b: BigDigit, q: &BigInt, r: &BigInt) {
+        check_sub(a, b, q, r);
+        check_sub(&a.neg(), b, &q.neg(), &r.neg());
+    }
+
+    for elm in MUL_TRIPLES.iter() {
+        let (a_vec, b_vec, c_vec) = *elm;
+        let a = BigInt::from_slice(Plus, a_vec);
+        let b = BigInt::from_slice(Plus, b_vec);
+        let c = BigInt::from_slice(Plus, c_vec);
+
+        if a_vec.len() == 1 && a_vec[0] != 0 {
+            let a = a_vec[0];
+            check(&c, a, &b, &Zero::zero());
+        }
+
+        if b_vec.len() == 1 && b_vec[0] != 0 {
+            let b = b_vec[0];
+            check(&c, b, &a, &Zero::zero());
+        }
+    }
+
+    for elm in DIV_REM_QUADRUPLES.iter() {
+        let (a_vec, b_vec, c_vec, d_vec) = *elm;
+        let a = BigInt::from_slice(Plus, a_vec);
+        let c = BigInt::from_slice(Plus, c_vec);
+        let d = BigInt::from_slice(Plus, d_vec);
+
+        if b_vec.len() == 1 && b_vec[0] != 0 {
+            let b = b_vec[0];
+            check(&a, b, &c, &d);
+        }
+    }
+
+}
+
 #[test]
 fn test_checked_add() {
     for elm in SUM_TRIPLES.iter() {
diff --git a/bigint/src/tests/biguint.rs b/bigint/src/tests/biguint.rs
index 7c5a423..0f3b743 100644
--- a/bigint/src/tests/biguint.rs
+++ b/bigint/src/tests/biguint.rs
@@ -25,6 +25,24 @@ macro_rules! assert_op {
     };
 }
 
+/// Assert that an op works for scalar left or right
+macro_rules! assert_scalar_op {
+    (($($to:ident),*) $left:ident $op:tt $right:ident == $expected:expr) => {
+        $(
+            if let Some(left) = $left.$to() {
+                assert_op!(left $op $right == $expected);
+            }
+            if let Some(right) = $right.$to() {
+                assert_op!($left $op right == $expected);
+            }
+        )*
+    };
+    ($left:ident $op:tt $right:ident == $expected:expr) => {
+        assert_scalar_op!((to_u8, to_u16, to_u32, to_u64, to_usize)
+                          $left $op $right == $expected);
+    };
+}
+
 #[test]
 fn test_from_slice() {
     fn check(slice: &[BigDigit], data: &[BigDigit]) {
@@ -690,6 +708,19 @@ fn test_add() {
     }
 }
 
+#[test]
+fn test_scalar_add() {
+    for elm in SUM_TRIPLES.iter() {
+        let (a_vec, b_vec, c_vec) = *elm;
+        let a = BigUint::from_slice(a_vec);
+        let b = BigUint::from_slice(b_vec);
+        let c = BigUint::from_slice(c_vec);
+
+        assert_scalar_op!(a + b == c);
+        assert_scalar_op!(b + a == c);
+    }
+}
+
 #[test]
 fn test_sub() {
     for elm in SUM_TRIPLES.iter() {
@@ -703,6 +734,19 @@ fn test_sub() {
     }
 }
 
+#[test]
+fn test_scalar_sub() {
+    for elm in SUM_TRIPLES.iter() {
+        let (a_vec, b_vec, c_vec) = *elm;
+        let a = BigUint::from_slice(a_vec);
+        let b = BigUint::from_slice(b_vec);
+        let c = BigUint::from_slice(c_vec);
+
+        assert_scalar_op!(c - a == b);
+        assert_scalar_op!(c - b == a);
+    }
+}
+
 #[test]
 #[should_panic]
 fn test_sub_fail_on_underflow() {
@@ -741,6 +785,7 @@ const DIV_REM_QUADRUPLES: &'static [(&'static [BigDigit],
            &'static [BigDigit],
            &'static [BigDigit],
            &'static [BigDigit])] = &[(&[1], &[2], &[], &[1]),
+                                     (&[3], &[2], &[1], &[1]),
                                      (&[1, 1], &[2], &[M / 2 + 1], &[1]),
                                      (&[1, 1, 1], &[2], &[M / 2 + 1, M / 2 + 1], &[1]),
                                      (&[0, 1], &[N1], &[1], &[1]),
@@ -770,6 +815,19 @@ fn test_mul() {
     }
 }
 
+#[test]
+fn test_scalar_mul() {
+    for elm in MUL_TRIPLES.iter() {
+        let (a_vec, b_vec, c_vec) = *elm;
+        let a = BigUint::from_slice(a_vec);
+        let b = BigUint::from_slice(b_vec);
+        let c = BigUint::from_slice(c_vec);
+
+        assert_scalar_op!(a * b == c);
+        assert_scalar_op!(b * a == c);
+    }
+}
+
 #[test]
 fn test_div_rem() {
     for elm in MUL_TRIPLES.iter() {
@@ -805,6 +863,39 @@ fn test_div_rem() {
     }
 }
 
+#[test]
+fn test_scalar_div_rem() {
+    for elm in MUL_TRIPLES.iter() {
+        let (a_vec, b_vec, c_vec) = *elm;
+        let a = BigUint::from_slice(a_vec);
+        let b = BigUint::from_slice(b_vec);
+        let c = BigUint::from_slice(c_vec);
+
+        if !a.is_zero() {
+            assert_scalar_op!(c / a == b);
+            assert_scalar_op!(c % a == Zero::zero());
+        }
+
+        if !b.is_zero() {
+            assert_scalar_op!(c / b == a);
+            assert_scalar_op!(c % b == Zero::zero());
+        }
+    }
+
+    for elm in DIV_REM_QUADRUPLES.iter() {
+        let (a_vec, b_vec, c_vec, d_vec) = *elm;
+        let a = BigUint::from_slice(a_vec);
+        let b = BigUint::from_slice(b_vec);
+        let c = BigUint::from_slice(c_vec);
+        let d = BigUint::from_slice(d_vec);
+
+        if !b.is_zero() {
+            assert_scalar_op!(a / b == c);
+            assert_scalar_op!(a % b == d);
+        }
+    }
+}
+
 #[test]
 fn test_checked_add() {
     for elm in SUM_TRIPLES.iter() {