Add Euclidean-based div and mod

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
+

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("")
+  }
+}

libraries/common/effekt.effekt

@@ -332,8 +332,8 @@ 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 +343,27 @@ 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)
+  q - (r.bitwiseShr(31).bitwiseAnd(y.bitwiseShr(31).bitwiseOr(1)))
+}
+
+/// Computes the result of Euclidean modulo
+def mod(x: Int, y: Int): Int = {
+  val r = x.rem(y)
+  r + y.abs.bitwiseAnd(r.bitwiseShr(31))
+}
 
 extern def infixAdd(x: Double, y: Double) at {}: Double =
   js "(${x} + ${y})"