DivisionByConstantInfo.cpp

//===----- DivisonByConstantInfo.cpp - division by constant -*- C++ -*-----===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
///
/// This file implements support for optimizing divisions by a constant
///
//===----------------------------------------------------------------------===//

#include "llvm/Support/DivisionByConstantInfo.h"

using namespace llvm;

/// Calculate the magic numbers required to implement a signed integer division
/// by a constant as a sequence of multiplies, adds and shifts.  Requires that
/// the divisor not be 0, 1, or -1.  Taken from "Hacker's Delight", Henry S.
/// Warren, Jr., Chapter 10.
SignedDivisionByConstantInfo SignedDivisionByConstantInfo::get(const APInt &D) {
  unsigned P;
  APInt AD, ANC, Delta, Q1, R1, Q2, R2, T;
  APInt SignedMin = APInt::getSignedMinValue(D.getBitWidth());
  struct SignedDivisionByConstantInfo Retval;

  AD = D.abs();
  T = SignedMin + (D.lshr(D.getBitWidth() - 1));
  ANC = T - 1 - T.urem(AD);  // absolute value of NC
  P = D.getBitWidth() - 1;   // initialize P
  Q1 = SignedMin.udiv(ANC);  // initialize Q1 = 2P/abs(NC)
  R1 = SignedMin - Q1 * ANC; // initialize R1 = rem(2P,abs(NC))
  Q2 = SignedMin.udiv(AD);   // initialize Q2 = 2P/abs(D)
  R2 = SignedMin - Q2 * AD;  // initialize R2 = rem(2P,abs(D))
  do {
    P = P + 1;
    Q1 = Q1 << 1;      // update Q1 = 2P/abs(NC)
    R1 = R1 << 1;      // update R1 = rem(2P/abs(NC))
    if (R1.uge(ANC)) { // must be unsigned comparison
      Q1 = Q1 + 1;
      R1 = R1 - ANC;
    }
    Q2 = Q2 << 1;     // update Q2 = 2P/abs(D)
    R2 = R2 << 1;     // update R2 = rem(2P/abs(D))
    if (R2.uge(AD)) { // must be unsigned comparison
      Q2 = Q2 + 1;
      R2 = R2 - AD;
    }
    Delta = AD - R2;
  } while (Q1.ult(Delta) || (Q1 == Delta && R1 == 0));

  Retval.Magic = Q2 + 1;
  if (D.isNegative())
    Retval.Magic = -Retval.Magic;           // resulting magic number
  Retval.ShiftAmount = P - D.getBitWidth(); // resulting shift
  return Retval;
}

/// Calculate the magic numbers required to implement an unsigned integer
/// division by a constant as a sequence of multiplies, adds and shifts.
/// Requires that the divisor not be 0.  Taken from "Hacker's Delight", Henry
/// S. Warren, Jr., chapter 10.
/// LeadingZeros can be used to simplify the calculation if the upper bits
/// of the divided value are known zero.
UnsignedDivisonByConstantInfo
UnsignedDivisonByConstantInfo::get(const APInt &D, unsigned LeadingZeros) {
  unsigned P;
  APInt NC, Delta, Q1, R1, Q2, R2;
  struct UnsignedDivisonByConstantInfo Retval;
  Retval.IsAdd = false; // initialize "add" indicator
  APInt AllOnes = APInt::getAllOnes(D.getBitWidth()).lshr(LeadingZeros);
  APInt SignedMin = APInt::getSignedMinValue(D.getBitWidth());
  APInt SignedMax = APInt::getSignedMaxValue(D.getBitWidth());

  NC = AllOnes - (AllOnes - D).urem(D);
  P = D.getBitWidth() - 1;  // initialize P
  Q1 = SignedMin.udiv(NC);  // initialize Q1 = 2P/NC
  R1 = SignedMin - Q1 * NC; // initialize R1 = rem(2P,NC)
  Q2 = SignedMax.udiv(D);   // initialize Q2 = (2P-1)/D
  R2 = SignedMax - Q2 * D;  // initialize R2 = rem((2P-1),D)
  do {
    P = P + 1;
    if (R1.uge(NC - R1)) {
      Q1 = Q1 + Q1 + 1;  // update Q1
      R1 = R1 + R1 - NC; // update R1
    } else {
      Q1 = Q1 + Q1; // update Q1
      R1 = R1 + R1; // update R1
    }
    if ((R2 + 1).uge(D - R2)) {
      if (Q2.uge(SignedMax))
        Retval.IsAdd = true;
      Q2 = Q2 + Q2 + 1;     // update Q2
      R2 = R2 + R2 + 1 - D; // update R2
    } else {
      if (Q2.uge(SignedMin))
        Retval.IsAdd = true;
      Q2 = Q2 + Q2;     // update Q2
      R2 = R2 + R2 + 1; // update R2
    }
    Delta = D - 1 - R2;
  } while (P < D.getBitWidth() * 2 &&
           (Q1.ult(Delta) || (Q1 == Delta && R1 == 0)));
  Retval.Magic = Q2 + 1;                    // resulting magic number
  Retval.ShiftAmount = P - D.getBitWidth(); // resulting shift
  return Retval;
}