Add BinInt, implement divmod and just for fun, add Nat.scala (#1194)

* Add BinInt, implement divmod and just for fun, add Nat.scala

* improve Nat.scala test coverage

* improve cmp_BinInt

core/src/main/scala/org/bykn/bosatsu/Nat.scala

@@ -0,0 +1,219 @@
+package org.bykn.bosatsu
+import org.bykn.bosatsu.Nat.Shift
+import org.bykn.bosatsu.Nat.Small
+
+import Nat._
+
+sealed abstract class Nat { lhs =>
+  def toBigInt: BigInt =
+    lhs match {
+      case Small(asInt) =>
+        BigInt(toLong(asInt))
+      case Shift(x, b) =>
+        // m(x + 1) + b
+        two_32_BigInt * (x.inc.toBigInt) + toLong(b)
+    }
+
+  override def toString = toBigInt.toString
+
+  def maybeLong: Option[Long] =
+    lhs match {
+      case Small(asInt) => Some(toLong(asInt))
+      case Shift(x, b) =>
+        // 2^32 * (x + 1) + b
+        x.maybeLong match {
+          case Some(v0) =>
+            if (v0 < Int.MaxValue) {
+              val value = v0 + 1
+              Some((value << 32) + toLong(b))
+            }
+            else None
+          case None => None
+        }
+    }
+
+
+  def inc: Nat =
+    lhs match {
+      case Small(asInt) =>
+        val next = asInt + 1
+        if (next != 0) wrapInt(next)
+        else two_32
+      case Shift(x, b) =>
+        // m(x + 1) + b
+        val b1 = b + 1
+        if (b1 != 0) Shift(x, b1)
+        else {
+          // m(x + 1) + m
+          // m(x + 1 + 1) 
+          Shift(x.inc, 0)
+        }
+    }
+
+  def dec: Nat =
+    lhs match {
+      case Small(asInt) =>
+        if (asInt != 0) wrapInt(asInt - 1) 
+        else zero
+      case Shift(x, b) =>
+        if (b != 0) Shift(x, b - 1)
+        else {
+          if (x.isZero) wrapInt(-1)
+          else Shift(x.dec, -1)
+        }
+    }
+
+  def isZero: Boolean =
+    lhs match {
+      case Small(0) => true
+      case _ => false
+    }
+
+  // this * 2^32
+  def shift_32: Nat =
+    lhs match {
+      case Small(asInt) =>
+        if (asInt == 0) zero
+        else {
+          // m*(b - 1 + 1)
+          Shift(wrapInt(asInt - 1), 0)
+        }
+      case Shift(x, b) =>
+        // m*(m*(x + 1) + b)
+        // m*((m(x + 1) + (b - 1)) + 1) + 0
+        if (b != 0) {
+          val b1 = b - 1
+          Shift(Shift(x, b1), 0)
+        }
+        else if (x.isZero) {
+          // m * (m(0 + 1) + 0)
+          // m * ((m - 1) + 1) + 0
+          val inner = wrapLong(0xFFFFFFFFL)
+          Shift(inner, 0)
+        }
+        else {
+          // x > 0
+          //m(m(x + 1)) =
+          //m(m(x + 1) - 1 + 1) + 0
+          //m((m(x + 1) - 1) + 1) + 0
+          val inner = x.inc.shift_32.dec
+          Shift(inner, 0)
+        }
+    }
+
+  def +(rhs: Nat): Nat = {
+    lhs match {
+      case Small(l) =>
+        rhs match {
+          case Small(r) =>
+            wrapLong(toLong(l) + toLong(r))
+          case Shift(x, b) => 
+            val res = toLong(l) + toLong(b)
+            val low = lowBits(res)
+            val high = highBits(res)
+            if (high == 0) Shift(x, low)
+            else {
+              Shift(x + wrapInt(high), low)
+            }
+        }
+
+      case Shift(x, b) =>
+        rhs match {
+          case Small(l) => 
+            val res = toLong(l) + toLong(b)
+            val low = lowBits(res)
+            val high = highBits(res)
+            if (high == 0) Shift(x, low)
+            else {
+              Shift(x + wrapInt(high), low)
+            }
+          case Shift(x1, b1) =>
+            // (m(x + 1) + b) + (m (x1 + 1) + b1) = m(x + x1 + 1 + 1) + (b + b1)
+            val res = toLong(b) + toLong(b1)
+            val low = lowBits(res)
+            val high = highBits(res)
+            val xs = (x + x1).inc
+            if (high == 0) Shift(xs, low)
+            else {
+              Shift(xs + wrapInt(high), low)
+            }
+        }
+    }
+  }
+  def *(rhs: Nat): Nat = {
+    lhs match {
+      case Small(l) =>
+        if (l == 0) zero
+        else (rhs match {
+          case Small(r) =>
+            // can't overflow Long
+            wrapLong(toLong(l) * toLong(r))
+          case Shift(x, b) => 
+            // (m(x + 1) + b) * l
+            (x.inc * lhs).shift_32 + wrapInt(b) * lhs
+        })
+
+      case Shift(x, b) =>
+        // (m(x + 1) + b) * rhs
+        // (x + 1)*rhs*m + b * rhs
+        (rhs * x.inc).shift_32 + rhs * wrapInt(b)
+    }
+  }
+}
+
+object Nat {
+  private val two_32_BigInt = BigInt(1L << 32)
+
+  private val intMaskLow: Long = 0xFFFFFFFFL
+  def toLong(i: Int): Long = i.toLong & intMaskLow
+  def lowBits(l: Long): Int = l.toInt
+  private def highBits(l: Long): Int = lowBits(l >> 32)
+
+  // all numbers from [0, 2^{32} - 1]
+  private case class Small(asInt: Int) extends Nat
+  // base * (x + 1) + b
+  private case class Shift(x: Nat, b: Int) extends Nat
+
+  private val cache: Array[Small] =
+    Array.tabulate(1024)(Small(_))
+
+  val zero: Nat = cache(0)
+  val one: Nat = cache(1)
+  val two_32: Nat = Shift(zero, 0)
+
+  // if the number is <= 0, return 0
+  def fromInt(i: Int): Nat =
+    if (i < 0) zero
+    else if (i < cache.length) cache(i)
+    else Small(i)
+
+  // if the number is <= 0, return 0
+  def fromLong(l: Long): Nat =
+    if (l < 0) zero
+    else wrapLong(l)
+
+  def wrapInt(i: Int): Nat =
+    if (0 <= i && i < cache.length) cache(i)
+    else Small(i)
+
+  def wrapLong(l: Long): Nat = {
+    val low = lowBits(l)
+    val high = highBits(l)
+    if (high == 0) wrapInt(low)
+    else {
+      Shift(wrapInt(high - 1), low)
+    }
+  }
+
+  // if b < 0 return 0
+  def fromBigInt(b: BigInt): Nat =
+    if (b <= 0) zero
+    else if (b < two_32_BigInt) {
+      fromLong(b.toLong)
+    }
+    else {
+      val low = b % two_32_BigInt
+      val high = b >> 32
+      Shift(fromBigInt(high - 1), lowBits(low.toLong))
+    }
+}

core/src/test/scala/org/bykn/bosatsu/NatTest.scala

@@ -0,0 +1,154 @@
+package org.bykn.bosatsu
+
+import org.scalacheck.{Gen, Prop}
+
+import Prop.forAll
+
+class NatTest extends munit.ScalaCheckSuite {
+
+  override def scalaCheckTestParameters =
+    super.scalaCheckTestParameters
+      .withMinSuccessfulTests(if (Platform.isScalaJvm) 100000 else 100)
+      .withMaxDiscardRatio(10)
+
+  //override def scalaCheckInitialSeed = "YOFqcGzXOFtFVgRFxOmODi5100tVovDS3EPOv0Ihk4C="
+
+  lazy val genNat: Gen[Nat] = {
+    val recur = Gen.lzy(genNat)
+    Gen.frequency(
+      // make sure to exercise the cached table
+      (1, Gen.chooseNum(0, 1024, 1).map(Nat.fromInt(_))),
+      (5, Gen.chooseNum(0, Long.MaxValue, Int.MaxValue.toLong, Int.MaxValue.toLong + 1).map(Nat.fromLong(_))),
+      (1, Gen.zip(recur, recur).map { case (a, b) => a + b }),
+      (1, Gen.zip(recur, recur).map { case (a, b) => a * b })
+    )
+  }
+
+  test("constants are right") {
+    assertEquals(Nat.zero.maybeLong, Some(0L))
+    assertEquals(Nat.one.maybeLong, Some(1L))
+    assertEquals(Nat.two_32.maybeLong, Some(1L << 32))
+  }
+  property("fromInt/maybeLong identity") {
+    forAll { (i: Int) =>
+      val n = Nat.fromInt(i)  
+      n.maybeLong match {
+        case None => fail(s"couldn't maybeLong $i")
+        case Some(l) => assert(i < 0 || (l.toInt == i))
+      }
+    }
+  }
+  property("fromLong/maybeLong identity") {
+    forAll { (i: Long) =>
+      val n = Nat.fromLong(i)  
+      n.maybeLong match {
+        case Some(l) => assert(i < 0 || (l == i))
+        case None => fail(s"couldn't maybeLong $i")
+      }
+    }
+  }
+
+  def trunc(i: Int): Long = if (i < 0) 0L else i.toLong
+
+  property("toLong => lowBits is identity") {
+    val big = 0x80000000L
+
+    assertEquals(Nat.lowBits(big), Int.MinValue, s"${Nat.lowBits(big)}")  
+    forAll(Gen.chooseNum(Int.MinValue, Int.MaxValue)) { (i: Int) =>
+      val l = Nat.toLong(i)
+      assertEquals(Nat.lowBits(Nat.toLong(i)), i, s"long = $l")  
+    }
+  }
+
+  property("x + y homomorphism") {
+    forAll(genNat, genNat) { (ni, nj) =>
+      val nk = ni + nj
+      assertEquals(nk.toBigInt, ni.toBigInt + nj.toBigInt)
+    }
+  }
+
+  property("x * y = y * x") {
+    forAll(genNat, genNat) { (n1, n2) =>
+      assertEquals(n1 * n2, n2 * n1)
+    }
+  }
+
+  property("x + y = y + x") {
+    forAll(genNat, genNat) { (n1, n2) =>
+      assertEquals(n1 + n2, n2 + n1)
+    }
+  }
+
+  property("x * y homomorphism") {
+    forAll(genNat, genNat) { (ni, nj) =>
+      val nk = ni * nj
+      assertEquals(nk.toBigInt, ni.toBigInt * nj.toBigInt)
+    }
+  }
+
+  property("x.inc == x + 1") {
+    forAll(genNat) { n =>
+      val i = n.inc  
+      val a = n + Nat.one
+      assertEquals(i.toBigInt, a.toBigInt)
+    }
+  }
+
+  property("x.dec == x - 1 when x > 0") {
+    forAll(genNat) { n =>
+      val i = n.dec.toBigInt  
+      if (n == Nat.zero) assertEquals(i, BigInt(0))
+      else assertEquals(i, n.toBigInt - 1)
+    }
+  }
+
+  property("x.shift_32 == x.toBigInt * 2^32") {
+    val n1 = BigInt("8588888260151524380556863712485265508")
+    val shift = n1 << 32
+    assertEquals(Nat.fromBigInt(n1).shift_32.toBigInt, shift)
+
+    forAll(genNat) { n =>
+      val s = n.shift_32
+      val viaBigInt = n.toBigInt << 32
+      val viaTimes = n * Nat.two_32
+      assertEquals(s.toBigInt, viaBigInt, s"viaTimes = $viaTimes")
+      assertEquals(s, viaTimes)
+    }
+  }
+
+  property("Nat.fromBigInt/toBigInt") {
+    assertEquals(Nat.fromLong(Long.MaxValue).toBigInt, BigInt(Long.MaxValue))
+
+    forAll { (bi0: BigInt) =>
+      val bi = bi0.abs
+      val n = Nat.fromBigInt(bi)  
+      val b2 = n.toBigInt
+      assertEquals(b2, bi)
+    }
+  }
+
+  property("x.inc.dec == x") {
+    forAll(genNat) { n =>
+      assertEquals(n.inc.dec, n)  
+    }
+  }
+
+  property("x.dec.inc == x || x.isZero") {
+    forAll(genNat) { n =>
+      assert((n.dec.inc == n) || n.isZero)
+    }
+  }
+
+  property("if the value is > Long.MaxValue maybeLong = None") {
+    forAll(genNat) { n =>
+      val bi = n.toBigInt  
+      val ml = n.maybeLong
+      assertEquals(ml.isEmpty, bi > Long.MaxValue)
+    }
+  }
+  property("the string repr matches toBigInt") {
+    forAll(genNat) { n =>
+      assertEquals(n.toString, n.toBigInt.toString)  
+    }
+  }
+}