diff --git a/src/private/conversion.nim b/src/private/conversion.nim
index 3430853..53ffc57 100644
--- a/src/private/conversion.nim
+++ b/src/private/conversion.nim
@@ -10,22 +10,27 @@
 import  ./uint_type,
         macros
 
+# converter mpUint64*(x: MpUintImpl[uint32]): uint64 =
+#   cast[ptr uint64](unsafeAddr x)[]
 
-proc toSubtype*[T: SomeInteger](b: bool, typ: typedesc[T]): T {.noSideEffect, inline.}=
+proc initMpUintImpl*[T: BaseUint](x: T): MpUintImpl[T] {.inline,noSideEffect.} =
+  result.lo = x
+
+proc toSubtype*[T: SomeInteger](b: bool, _: typedesc[T]): T {.noSideEffect, inline.}=
   b.T
 
-proc toSubtype*[T: MpUintImpl](b: bool, typ: typedesc[T]): T {.noSideEffect, inline.}=
+proc toSubtype*[T: MpUintImpl](b: bool, _: typedesc[T]): T {.noSideEffect, inline.}=
   type SubTy = type result.lo
   result.lo = toSubtype(b, SubTy)
 
-proc zero*(typ: typedesc[BaseUint]): typ {.compileTime.} =
-  typ()
+proc zero*[T: BaseUint](_: typedesc[T]): T {.noSideEffect, inline.}=
+  result = T(0)
 
-proc one*[T: BaseUint](typ: typedesc[T]): T {.noSideEffect, inline.}=
+proc one*[T: BaseUint](_: typedesc[T]): T {.noSideEffect, inline.}=
   when T is SomeUnsignedInt:
-    T(1)
+    result = T(1)
   else:
-    result.lo = 1
+    result.lo = one(type result.lo)
 
 proc toUint*(n: MpUIntImpl): auto {.noSideEffect, inline.}=
   ## Casts a multiprecision integer to an uint of the same size
diff --git a/src/private/stdlib_bitops.nim b/src/private/stdlib_bitops.nim
index 6bd60d6..c56df67 100644
--- a/src/private/stdlib_bitops.nim
+++ b/src/private/stdlib_bitops.nim
@@ -25,7 +25,7 @@
 ## may return undefined and/or platform dependant value if given invalid input.
 
 const useBuiltins* = not defined(noIntrinsicsBitOpts)
-const noUndefined* = defined(noUndefinedBitOpts)
+# const noUndefined* = defined(noUndefinedBitOpts)
 const useGCC_builtins* = (defined(gcc) or defined(llvm_gcc) or defined(clang)) and useBuiltins
 const useICC_builtins* = defined(icc) and useBuiltins
 const useVCC_builtins* = defined(vcc) and useBuiltins
@@ -88,3 +88,24 @@ elif useICC_builtins:
     var index: uint32
     discard fnc(index.addr, v)
     index.int
+
+
+proc countLeadingZeroBits*(x: SomeInteger): int {.inline, nosideeffect.} =
+  ## Returns the number of leading zero bits in integer.
+  ## If `x` is zero, when ``noUndefinedBitOpts`` is set, result is 0,
+  ## otherwise result is undefined.
+
+  # when noUndefined:
+  if x == 0:
+    return 0
+
+  when nimvm:
+      when sizeof(x) <= 4: result = sizeof(x)*8 - 1 - fastlog2_nim(x.uint32)
+      else:                result = sizeof(x)*8 - 1 - fastlog2_nim(x.uint64)
+  else:
+    when useGCC_builtins:
+      when sizeof(x) <= 4: result = builtin_clz(x.uint32).int - (32 - sizeof(x)*8)
+      else:                result = builtin_clzll(x.uint64).int
+    else:
+      when sizeof(x) <= 4: result = sizeof(x)*8 - 1 - fastlog2_nim(x.uint32)
+      else: result = sizeof(x)*8 - 1 - fastlog2_nim(x.uint64)
diff --git a/src/private/uint_binary_ops.nim b/src/private/uint_binary_ops.nim
index d1e4152..8c5b5f2 100644
--- a/src/private/uint_binary_ops.nim
+++ b/src/private/uint_binary_ops.nim
@@ -7,10 +7,13 @@
 #
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
-import  ./bithacks, ./conversion,
+import  ./bithacks, ./conversion, ./stdlib_bitops,
         ./uint_type,
         ./uint_comparison,
-        ./uint_bitwise_ops
+        ./uint_bitwise_ops,
+        ./size_mpuintimpl
+
+# ############ Addition & Substraction ############ #
 
 proc `+=`*(x: var MpUintImpl, y: MpUintImpl) {.noSideEffect, inline.}=
   ## In-place addition for multi-precision unsigned int
@@ -45,6 +48,8 @@ proc `-`*(x, y: MpUintImpl): MpUintImpl {.noSideEffect, noInit, inline.}=
   result -= y
 
 
+# ################### Multiplication ################### #
+
 proc naiveMulImpl[T: MpUintImpl](x, y: T): MpUintImpl[T] {.noSideEffect, noInit, inline.}
   # Forward declaration
 
@@ -57,10 +62,10 @@ proc naiveMul[T: BaseUint](x, y: T): MpUintImpl[T] {.noSideEffect, noInit, inlin
 
   elif T.sizeof == 8: # uint64 or MpUint[uint32]
     # We cannot double uint64 to uint128
-    naiveMulImpl(x.toMpUintImpl, y.toMpUintImpl)
+    cast[type result](naiveMulImpl(x.toMpUintImpl, y.toMpUintImpl))
   else:
     # Case: at least uint128 * uint128 --> uint256
-    naiveMulImpl(x, y)
+    cast[type result](naiveMulImpl(x, y))
 
 
 proc naiveMulImpl[T: MpUintImpl](x, y: T): MpUintImpl[T] {.noSideEffect, noInit, inline.}=
@@ -78,7 +83,7 @@ proc naiveMulImpl[T: MpUintImpl](x, y: T): MpUintImpl[T] {.noSideEffect, noInit,
   #     and introduce branching
   #   - More total operations means more register moves
 
-  const halfSize = x.size_mpuintimpl div 2
+  const halfSize = size_mpuintimpl(x) div 2
   let
     z0 = naiveMul(x.lo, y.lo)
     tmp = naiveMul(x.hi, y.lo)
@@ -87,10 +92,10 @@ proc naiveMulImpl[T: MpUintImpl](x, y: T): MpUintImpl[T] {.noSideEffect, noInit,
   z1 += naiveMul(x.hi, y.lo)
   let z2 = (z1 < tmp).toSubtype(T) + naiveMul(x.hi, y.hi)
 
-  let tmp2  = z1.lo shl halfSize
+  let tmp2  = initMpUintImpl(z1.lo shl halfSize)
   result.lo = tmp2
   result.lo += z0
-  result.hi = (result.lo < tmp2).toSubtype(T) + z2 + z1.hi
+  result.hi = (result.lo < tmp2).toSubtype(T) + z2 + initMpUintImpl(z1.hi)
 
 proc `*`*(x, y: MpUintImpl): MpUintImpl {.noSideEffect, noInit.}=
   ## Multiplication for multi-precision unsigned uint
@@ -111,44 +116,115 @@ proc `*`*(x, y: MpUintImpl): MpUintImpl {.noSideEffect, noInit.}=
   # If T is a type
   # For T * T --> T we don't need to compute z2 as it always overflow
   # For T * T --> 2T (uint64 * uint64 --> uint128) we use extra precision multiplication
-
   result = naiveMul(x.lo, y.lo)
   result.hi += (naiveMul(x.hi, y.lo) + naiveMul(x.lo, y.hi)).lo
 
-proc divmod*(x, y: MpUintImpl): tuple[quot, rem: MpUintImpl] {.noSideEffect.}=
-  ## Division for multi-precision unsigned uint
-  ## Returns quotient + reminder in a (quot, rem) tuple
-  #
-  # Implementation through binary shift division
-  if unlikely(y.isZero):
-    raise newException(DivByZeroError, "You attempted to divide by zero")
 
-  type SubTy = type x.lo
+# ################### Division ################### #
+from ./primitive_divmod import divmod
+
+proc divmod*(x, y: MpUintImpl): tuple[quot, rem: MpUintImpl] {.noSideEffect.}
+
+proc div2n1n[T: BaseUint](x_hi, x_lo, y: T): tuple[quot, rem: T] {.noSideEffect, noInit.} =
+  const
+    size = size_mpuintimpl(x_hi)
+    halfSize = size div 2
+    halfMask = (one(T) shl halfSize) - one(T)
+    base = one(T) shl halfSize
+
+  if unlikely(x_hi >= y):
+    raise newException(ValueError, "Division overflow")
+
+  let clz = countLeadingZeroBits(y) # We assume that for 0 clz returns 0
+
+  # normalization, shift so that the MSB is at 2^n
+  let xn = MpUintImpl[T](hi: x_hi, lo: x_lo) shl clz
+  let yn = y shl clz
+
+  # Break divisor in 2 and dividend in 4
+  let yn_hi = yn shr halfSize
+  let yn_lo = yn and halfMask
+
+  let xnlohi = xn.lo shr halfSize
+  let xnlolo = xn.lo and halfMask
+
+  # First half of the quotient
+  var (q1, r) = divmod(xn.hi, yn_hi)
+
+  while (q1 >= base) or ((q1 * yn_lo) > (base * r + xnlohi)):
+    q1 -= one(T)
+    r += yn_hi
+    if r >= base:
+      break
+
+  # Remove it
+  let xn_rest = xn.hi shl halfSize + xnlohi - (q1 * yn)
+
+  # Second half
+  var (q2, s) = divmod(xn_rest, yn_hi)
 
   var
-    shift = x.bit_length - y.bit_length
-    d = y shl shift
+    q2_ynlo = q2 * yn_lo
+    sbase_xnlolo = (s shl halfSize) or xnlolo
 
-  result.rem  = x
+  while (q2 >= base) or (q2_ynlo > sbase_xnlolo):
+    q2 -= one(T)
+    s += yn_hi
+    if s >= base:
+      break
+    else:
+      q2_ynlo -= yn_lo
+      sbase_xnlolo = (s shl halfSize) or xnlolo
 
-  while shift >= 0:
-    result.quot += result.quot
-    if result.rem >= d:
-      result.rem -= d
-      result.quot.lo = result.quot.lo or one(SubTy)
 
-    d = d shr 1
-    dec(shift)
+  result.quot = (q1 shl halfSize) or q2
+  result.rem = ((xn_rest shl halfSize) + xnlolo - q2 * yn) shr clz
 
-  # Performance note:
-  # The performance of this implementation is extremely dependant on shl and shr.
-  #
-  # Probably the most efficient algorithm that can benefit from MpUInt data structure is
-  # the recursive fast division by Burnikel and Ziegler (http://www.mpi-sb.mpg.de/~ziegler/TechRep.ps.gz):
-  #  - Python implementation: https://bugs.python.org/file11060/fast_div.py and discussion https://bugs.python.org/issue3451
-  #  - C++ implementation: https://github.com/linbox-team/givaro/blob/master/src/kernel/recint/rudiv.h
-  #  - The Handbook of Elliptic and Hyperelliptic Cryptography Algorithm 10.35 on page 188 has a more explicit version of the div2NxN algorithm. This algorithm is directly recursive and avoids the mutual recursion of the original paper's calls between div2NxN and div3Nx2N.
-  #  - Comparison of fast division algorithms fro large integers: http://bioinfo.ict.ac.cn/~dbu/AlgorithmCourses/Lectures/Hasselstrom2003.pdf
+proc divmod*(x, y: MpUintImpl): tuple[quot, rem: MpUintImpl] {.noSideEffect.}=
+
+  # Using divide and conquer algorithm.
+  if y.hi.isZero:
+    if x.hi < y.lo: # Bit length of quotient x/y < bit_length(MpUintImpl) / 2
+      (result.quot.lo, result.rem.lo) = div2n1n(x.hi, x.lo, y.lo)
+    else:           # Quotient can overflow the subtype so we split work
+      (result.quot.hi, result.rem.hi) = divmod(x.hi, y.hi)
+      (result.quot.lo, result.rem.lo) = div2n1n(result.rem.hi, x.lo, y.lo)
+      result.rem.hi = zero(type result.rem.hi)
+    return
+
+  const
+    size = size_mpuintimpl(x)
+    halfSize = size div 2
+
+  block:
+    # Normalization of divisor
+    let clz = countLeadingZeroBits(x.hi)
+    let yn = (y shl clz)
+
+    # Prevent overflows
+    let xn = x shr 1
+
+    # Get the quotient
+    block:
+      let (qlo, _) = div2n1n(x.hi, x.lo, yn.hi)
+      result.quot.lo = qlo
+
+    # Undo normalization
+    result.quot = result.quot shr (halfSize - 1 - clz) # -1 to correct for xn shift
+
+  if not result.quot.isZero:
+    result.quot -= one(type result.quot)
+  # Quotient is correct or too small by one
+  # We will fix that once we know the remainder
+
+  # Remainder
+  result.rem = x - (y * result.quot)
+
+  # Fix quotient and reminder if we're off by one
+  if result.rem >= y:
+    # one more division round
+    result.quot += one(type result.quot)
+    result.rem -= y
 
 proc `div`*(x, y: MpUintImpl): MpUintImpl {.inline, noSideEffect.} =
   ## Division operation for multi-precision unsigned uint
@@ -157,3 +233,72 @@ proc `div`*(x, y: MpUintImpl): MpUintImpl {.inline, noSideEffect.} =
 proc `mod`*(x, y: MpUintImpl): MpUintImpl {.inline, noSideEffect.} =
   ## Division operation for multi-precision unsigned uint
   divmod(x,y).rem
+
+
+# ######################################################################
+# Division implementations
+#
+# Division is the most costly operation
+# And also of critical importance for cryptography application
+
+# ##### Research #####
+
+# Overview of division algorithms:
+# - https://gmplib.org/manual/Division-Algorithms.html#Division-Algorithms
+# - https://gmplib.org/~tege/division-paper.pdf
+# - Comparison of fast division algorithms for large integers: http://bioinfo.ict.ac.cn/~dbu/AlgorithmCourses/Lectures/Hasselstrom2003.pdf
+
+# Libdivide has an implementations faster than hardware if dividing by the same number is needed
+# - http://libdivide.com/documentation.html
+# - https://github.com/ridiculousfish/libdivide/blob/master/libdivide.h
+# Furthermore libdivide also has branchless implementations
+
+# Current implementation
+# Currently we use the divide and conquer algorithm. Implementations can be found in
+# - Hacker's delight: http://www.hackersdelight.org/hdcodetxt/divDouble.c.txt
+# - Libdivide
+# - Code project: https://www.codeproject.com/Tips/785014/UInt-Division-Modulus
+# - Cuda-uint128 (unfinished): https://github.com/curtisseizert/CUDA-uint128/blob/master/cuda_uint128.h
+# - Mpdecimal: https://github.com/status-im/nim-decimal/blob/9b65e95299cb582b14e0ae9a656984a2ce0bab03/decimal/mpdecimal_wrapper/generated/basearith.c#L305-L412
+
+# Probably the most efficient algorithm that can benefit from MpUInt recursive data structure is
+# the recursive fast division by Burnikel and Ziegler (http://www.mpi-sb.mpg.de/~ziegler/TechRep.ps.gz):
+#  - Python implementation: https://bugs.python.org/file11060/fast_div.py and discussion https://bugs.python.org/issue3451
+#  - C++ implementation: https://github.com/linbox-team/givaro/blob/master/src/kernel/recint/rudiv.h
+#  - The Handbook of Elliptic and Hyperelliptic Cryptography Algorithm 10.35 on page 188 has a more explicit version of the div2NxN algorithm. This algorithm is directly recursive and avoids the mutual recursion of the original paper's calls between div2NxN and div3Nx2N.
+
+# Other libraries that can be used as reference for alternative (?) implementations:
+# - TTMath: https://github.com/status-im/nim-ttmath/blob/8f6ff2e57b65a350479c4012a53699e262b19975/src/headers/ttmathuint.h#L1530-L2383
+# - LibTomMath: https://github.com/libtom/libtommath
+# - Google Abseil: https://github.com/abseil/abseil-cpp/tree/master/absl/numeric
+# - Crypto libraries like libsecp256k1, OpenSSL, ... though they are not generics. (uint256 only for example)
+# Note: GMP/MPFR are GPL. The papers can be used but not their code.
+
+# ######################################################################
+# School division
+
+# proc divmod*(x, y: MpUintImpl): tuple[quot, rem: MpUintImpl] {.noSideEffect.}=
+#   ## Division for multi-precision unsigned uint
+#   ## Returns quotient + reminder in a (quot, rem) tuple
+#   #
+#   # Implementation through binary shift division
+#   if unlikely(y.isZero):
+#     raise newException(DivByZeroError, "You attempted to divide by zero")
+
+#   type SubTy = type x.lo
+
+#   var
+#     shift = x.bit_length - y.bit_length
+#     d = y shl shift
+
+#   result.rem  = x
+
+#   while shift >= 0:
+#     result.quot += result.quot
+#     if result.rem >= d:
+#       result.rem -= d
+#       result.quot.lo = result.quot.lo or one(SubTy)
+
+#     d = d shr 1
+#     dec(shift)
+
diff --git a/src/private/uint_bitwise_ops.nim b/src/private/uint_bitwise_ops.nim
index 61b5c24..d1302d1 100644
--- a/src/private/uint_bitwise_ops.nim
+++ b/src/private/uint_bitwise_ops.nim
@@ -30,7 +30,7 @@ proc `xor`*(x, y: MpUintImpl): MpUintImpl {.noInit, noSideEffect, inline.}=
   result.lo = x.lo xor y.lo
   result.hi = x.hi xor y.hi
 
-proc `shl`*[T: MpUintImpl](x: T, y: SomeInteger): T {.noInit, inline, noSideEffect.}=
+proc `shl`*(x: MpUintImpl, y: SomeInteger): MpUintImpl {.noInit, inline, noSideEffect.}=
   ## Compute the `shift left` operation of x and y
   # Note: inlining this poses codegen/aliasing issue when doing `x = x shl 1`
   const halfSize = size_mpuintimpl(x) div 2
@@ -42,7 +42,7 @@ proc `shl`*[T: MpUintImpl](x: T, y: SomeInteger): T {.noInit, inline, noSideEffe
               else: 0.SubTy
 
 
-proc `shr`*[T: MpUintImpl](x: T, y: SomeInteger): T {.noInit, inline, noSideEffect.}=
+proc `shr`*(x: MpUintImpl, y: SomeInteger): MpUintImpl {.noInit, inline, noSideEffect.}=
   ## Compute the `shift right` operation of x and y
   # Note: inlining this poses codegen/aliasing issue when doing `x = x shl 1`
   const halfSize = size_mpuintimpl(x) div 2
@@ -52,4 +52,3 @@ proc `shr`*[T: MpUintImpl](x: T, y: SomeInteger): T {.noInit, inline, noSideEffe
   result.lo = (x.lo shr y) or (x.hi shl (y - halfSize)) # the shl is not a mistake
   result.hi = if y < halfSize: x.hi shr y
               else: 0.SubTy
-
diff --git a/tests/test_muldiv.nim b/tests/test_muldiv.nim
index 65555f8..10a0a21 100644
--- a/tests/test_muldiv.nim
+++ b/tests/test_muldiv.nim
@@ -34,7 +34,7 @@ suite "Testing multiplication implementation":
 
 
 suite "Testing division and modulo implementation":
-  test "Divmod returns the correct result":
+  test "Divmod(100, 13) returns the correct result":
 
     let a = 100.initMpUint(64)
     let b = 13.initMpUint(64)
@@ -42,3 +42,17 @@ suite "Testing division and modulo implementation":
 
     check: cast[uint64](qr.quot) == 7'u64
     check: cast[uint64](qr.rem)  == 9'u64
+
+  test "Divmod(2^64, 3) returns the correct result":
+    let a = 1.initMpUint(128) shl 64
+    let b = 3.initMpUint(128)
+
+    let qr = divmod(a, b)
+
+    let q = cast[MpUintImpl[uint64]](qr.quot)
+    let r = cast[MpUintImpl[uint64]](qr.rem)
+
+    check: q.lo == 6148914691236517205'u64
+    check: q.hi == 0'u64
+    check: r.lo == 1'u64
+    check: r.hi == 0'u64