diff --git a/effekt/shared/src/main/scala/effekt/core/vm/Builtin.scala b/effekt/shared/src/main/scala/effekt/core/vm/Builtin.scala
index 70ccfcf5e..4356dc342 100644
--- a/effekt/shared/src/main/scala/effekt/core/vm/Builtin.scala
+++ b/effekt/shared/src/main/scala/effekt/core/vm/Builtin.scala
@@ -129,8 +129,30 @@ lazy val integers: Builtins = Map(
   builtin("effekt::infixMul(Int, Int)") {
     case As.Int(x) :: As.Int(y) :: Nil => Value.Int(x * y)
   },
+  builtin("effekt::rem(Int, Int)") {
+    case As.Int(x) :: As.Int(y) :: Nil => Value.Int(x - y * (x / y))
+  },
+  builtin("effekt::quot(Int, Int)") {
+    case As.Int(x) :: As.Int(y) :: Nil => Value.Int(x / y)
+  },
+  builtin("effekt::div(Int, Int)") {
+    case As.Int(x) :: As.Int(y) :: Nil =>
+      val q = x / y
+      val r = x - y * (x / y)
+      if (r < 0) {
+        Value.Int(q - y.sign)
+      } else {
+        Value.Int(q)
+      }
+  },
   builtin("effekt::mod(Int, Int)") {
-    case As.Int(x) :: As.Int(y) :: Nil => Value.Int(x % y)
+    case As.Int(x) :: As.Int(y) :: Nil =>
+      val r = x - y * (x / y)
+      if (r < 0) {
+        Value.Int(r + y.abs)
+      } else {
+        Value.Int(r)
+      }
   },
   builtin("effekt::infixDiv(Int, Int)") {
     case As.Int(x) :: As.Int(y) :: Nil => Value.Int(x / y)
@@ -150,6 +172,9 @@ lazy val integers: Builtins = Map(
   builtin("effekt::bitwiseXor(Int, Int)") {
     case As.Int(x) :: As.Int(y) :: Nil => Value.Int(x ^ y)
   },
+  builtin("effekt::bitwiseMsb(Int)") {
+    case As.Int(x) :: Nil => Value.Int(x >> 63)
+  },
 
   // Comparison
   // ----------
diff --git a/examples/stdlib/mod.check b/examples/stdlib/mod.check
new file mode 100644
index 000000000..16c3c158f
--- /dev/null
+++ b/examples/stdlib/mod.check
@@ -0,0 +1,10 @@
+8 `divmod` 3 = 2, 2
+8 `divmod` -3 = -2, 2
+-8 `divmod` 3 = -3, 1
+-8 `divmod` -3 = 3, 1
+
+8 `quotrem` 3 = 2, 2
+8 `quotrem` -3 = -2, 2
+-8 `quotrem` 3 = -2, -2
+-8 `quotrem` -3 = 2, -2
+
diff --git a/examples/stdlib/mod.effekt b/examples/stdlib/mod.effekt
new file mode 100644
index 000000000..268659f39
--- /dev/null
+++ b/examples/stdlib/mod.effekt
@@ -0,0 +1,15 @@
+def main() = {
+  val ops = [
+    (box { (x: Int, y: Int) => (x.div(y), x.mod(y), x == y * x.div(y) + x.mod(y)) }, "divmod"),
+    (box { (x: Int, y: Int) => (x.quot(y), x.rem(y), x == y * x.quot(y) + x.rem(y)) }, "quotrem"),
+  ]
+  ops.foreach { case (op, name) =>
+    [8, 8.neg].foreach { dividend =>
+      [3, 3.neg].foreach { divisor =>
+        val (q, r, assertion) = op(dividend, divisor)
+        println(s"${dividend.show} `${name}` ${divisor.show} = ${q.show}, ${r.show}")
+      }
+    }
+    println("")
+  }
+}
diff --git a/libraries/common/effekt.effekt b/libraries/common/effekt.effekt
index 05a2883d7..a47fe2f9b 100644
--- a/libraries/common/effekt.effekt
+++ b/libraries/common/effekt.effekt
@@ -319,6 +319,12 @@ extern def infixNeq(x: Bool, y: Bool) at {}: Bool =
 
 // Math ops
 // ========
+
+// Numeric representations in the backends:
+// LLVM: int64_t (64-bit integer)
+// JS: 64-bit floating-point (64-bit IEEE 754)
+// Chez: 64-bit integer
+
 extern def infixAdd(x: Int, y: Int) at {}: Int =
   js "(${x} + ${y})"
   chez "(+ ${x} ${y})"
@@ -332,8 +338,8 @@ extern def infixMul(x: Int, y: Int) at {}: Int =
   vm "effekt::infixMul(Int, Int)"
 
 extern def infixDiv(x: Int, y: Int) at {}: Int =
-  js "Math.floor(${x} / ${y})"
-  chez "(floor (/ ${x} ${y}))"
+  js "Math.trunc(${x} / ${y})"
+  chez "(truncate (/ ${x} ${y}))"
   llvm "%z = sdiv %Int ${x}, ${y} ret %Int %z"
   vm "effekt::infixDiv(Int, Int)"
 
@@ -343,11 +349,31 @@ extern def infixSub(x: Int, y: Int) at {}: Int =
   llvm "%z = sub  %Int ${x}, ${y} ret %Int %z"
   vm "effekt::infixSub(Int, Int)"
 
-extern def mod(x: Int, y: Int) at {}: Int =
-  js "(${x} % ${y})"
-  chez "(modulo ${x} ${y})"
-  llvm "%z = srem %Int ${x}, ${y} ret %Int %z"
-  vm "effekt::mod(Int, Int)"
+/// Computes the quotient based on truncated-division
+def quot(x: Int, y: Int): Int =
+  infixDiv(x, y)
+
+/// Computes the remainder based on truncated-division
+ extern def rem(x: Int, y: Int) at {}: Int =
+   llvm "%z = srem %Int ${x}, ${y} ret %Int %z"
+   default { x - y * (x / y) }
+
+/// Computes the result of Euclidean division
+def div(x: Int, y: Int): Int = {
+  val q = x / y
+  val r = x.rem(y)
+  val rNeg = r.bitwiseMsb
+  val ySign = y.bitwiseMsb.bitwiseOr(1)
+  q - rNeg.bitwiseAnd(ySign)
+}
+
+/// Computes the result of Euclidean modulo
+def mod(x: Int, y: Int): Int = {
+  val r = x.rem(y)
+  val rNeg = r.bitwiseMsb
+  val absY = y.bitwiseXor(y.bitwiseMsb) - y.bitwiseMsb
+  r + rNeg.bitwiseAnd(absY)
+}
 
 extern def infixAdd(x: Double, y: Double) at {}: Double =
   js "(${x} + ${y})"
@@ -677,6 +703,11 @@ extern def bitwiseXor(x: Int, y: Int) at {}: Int =
   llvm "%z = xor %Int ${x}, ${y} ret %Int %z"
   vm "effekt::bitwiseXor(Int, Int)"
 
+extern def bitwiseMsb(x: Int) at {}: Int =
+   js "${x} >> 31"
+   chez "(bitwise-arithmetic-shift-right ${x} 63)"
+   llvm "%z = ashr %Int ${x}, 63 ret %Int %z"
+   vm "effekt::bitwiseMsb(Int)"
 
 // Byte operations
 // ===============