[stdlib] Int128: Add direct division by some constant powers of ten

Author: lorentey

stdlib/public/core/Int128.swift.gyb

@@ -282,9 +282,7 @@ extension _${U}Int128: FixedWidthInteger {
       self.magnitude.components, by: other.magnitude.components)
     let quotient = Self.Magnitude(q)
     let remainder = Self.Magnitude(r)
-    guard Self.isSigned else {
-      return (Self(quotient), Self(remainder))
-    }
+    % if signed:
     let isNegative = (self.high._isNegative != other.high._isNegative)
     let quotient_ = (isNegative
       ? quotient == Self.min.magnitude ? Self.min : 0 - Self(quotient)
@@ -293,6 +291,9 @@ extension _${U}Int128: FixedWidthInteger {
       ? 0 - Self(remainder)
       : Self(remainder))
     return (quotient_, remainder_)
+    % else:
+    return (quotient, remainder)
+    % end
   }
 
   internal func dividedReportingOverflow(
@@ -799,3 +800,44 @@ private func _wideDivide42<F: FixedWidthInteger & UnsignedInteger>(
 
 extension _UInt128: UnsignedInteger {}
 extension _Int128: SignedNumeric, SignedInteger {}
+
+%{
+# This finds the magic numbers for signed division by a constant, following
+# the algorithm described in [Warren 2013, page 212].
+def magic(w, d):
+  nc = (2 ** (w - 1)) // d * d - 1
+  for p in range(2, 2 * w):
+    pp = 2 ** p
+    delta = d - pp % d
+    if pp > nc * delta:
+      m = (pp + delta) // d
+      overflow = m > 2 ** (w - 1) - 1
+      if overflow:
+        m = m - 2 ** w
+      w2 = w // 2
+      ml = m & (2 ** w2 - 1)
+      mh = m >> w2
+      return (mh, ml, p - w, overflow)
+  raise RuntimeError("No magic found")
+}%
+
+% for exp in [18, 15, 12, 9, 6, 3]:
+%   d = 10 ** exp
+%   (mh, ml, s, overflow) = magic(128, d)
+extension _Int128 {
+  internal func dividedBy1e${exp}() -> (quotient: Self, remainder: Self) {
+    let m = _Int128(high: ${mh}, low: ${ml})
+    var q = self.multipliedFullWidth(by: m).high
+    % if overflow:
+    q &+= self
+    % end
+    % if s > 0:
+    q &>>= ${s}
+    % end
+    // Add 1 to q if self is negative
+    q &+= _Int128(bitPattern: _UInt128(bitPattern: self) &>> 127)
+    let r = self &- q &* (${d} as _Int128)
+    return (q, r)
+  }
+}
+% end