Fraction.h

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//===- Fraction.h - MLIR Fraction Class -------------------------*- 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 is a simple class to represent fractions. It supports arithmetic,
// comparison, floor, and ceiling operations.
//
//===----------------------------------------------------------------------===//
 
#ifndef MLIR_ANALYSIS_PRESBURGER_FRACTION_H
#define MLIR_ANALYSIS_PRESBURGER_FRACTION_H
 
#include "mlir/Analysis/Presburger/MPInt.h"
#include "mlir/Support/MathExtras.h"
 
namespace mlir {
namespace presburger {
 
/// A class to represent fractions. The sign of the fraction is represented
/// in the sign of the numerator; the denominator is always positive.
///
/// Note that overflows may occur if the numerator or denominator are not
/// representable by 64-bit integers.
struct Fraction {
  /// Default constructor initializes the represented rational number to zero.
  Fraction() = default;
 
  /// Construct a Fraction from a numerator and denominator.
  Fraction(const MPInt &oNum, const MPInt &oDen = MPInt(1))
      : num(oNum), den(oDen) {
    if (den < 0) {
      num = -num;
      den = -den;
    }
  }
  /// Overloads for passing literals.
  Fraction(const MPInt &num, int64_t den) : Fraction(num, MPInt(den)) {}
  Fraction(int64_t num, const MPInt &den = MPInt(1))
      : Fraction(MPInt(num), den) {}
  Fraction(int64_t num, int64_t den) : Fraction(MPInt(num), MPInt(den)) {}
 
  // Return the value of the fraction as an integer. This should only be called
  // when the fraction's value is really an integer.
  MPInt getAsInteger() const {
    assert(num % den == 0 && "Get as integer called on non-integral fraction!");
    return num / den;
  }
 
  llvm::raw_ostream &print(llvm::raw_ostream &os) const {
    return os << "(" << num << "/" << den << ")";
  }
 
  /// The numerator and denominator, respectively. The denominator is always
  /// positive.
  MPInt num{0}, den{1};
};
 
/// Three-way comparison between two fractions.
/// Returns +1, 0, and -1 if the first fraction is greater than, equal to, or
/// less than the second fraction, respectively.
inline int compare(const Fraction &x, const Fraction &y) {
  MPInt diff = x.num * y.den - y.num * x.den;
  if (diff > 0)
    return +1;
  if (diff < 0)
    return -1;
  return 0;
}
 
inline MPInt floor(const Fraction &f) { return floorDiv(f.num, f.den); }
 
inline MPInt ceil(const Fraction &f) { return ceilDiv(f.num, f.den); }
 
inline Fraction operator-(const Fraction &x) { return Fraction(-x.num, x.den); }
 
inline bool operator<(const Fraction &x, const Fraction &y) {
  return compare(x, y) < 0;
}
 
inline bool operator<=(const Fraction &x, const Fraction &y) {
  return compare(x, y) <= 0;
}
 
inline bool operator==(const Fraction &x, const Fraction &y) {
  return compare(x, y) == 0;
}
 
inline bool operator!=(const Fraction &x, const Fraction &y) {
  return compare(x, y) != 0;
}
 
inline bool operator>(const Fraction &x, const Fraction &y) {
  return compare(x, y) > 0;
}
 
inline bool operator>=(const Fraction &x, const Fraction &y) {
  return compare(x, y) >= 0;
}
 
inline Fraction abs(const Fraction &f) {
  assert(f.den > 0 && "denominator of fraction must be positive!");
  return Fraction(abs(f.num), f.den);
}
 
inline Fraction reduce(const Fraction &f) {
  if (f == Fraction(0))
    return Fraction(0, 1);
  MPInt g = gcd(abs(f.num), abs(f.den));
  return Fraction(f.num / g, f.den / g);
}
 
inline Fraction operator*(const Fraction &x, const Fraction &y) {
  return reduce(Fraction(x.num * y.num, x.den * y.den));
}
 
inline Fraction operator/(const Fraction &x, const Fraction &y) {
  return reduce(Fraction(x.num * y.den, x.den * y.num));
}
 
inline Fraction operator+(const Fraction &x, const Fraction &y) {
  return reduce(Fraction(x.num * y.den + x.den * y.num, x.den * y.den));
}
 
inline Fraction operator-(const Fraction &x, const Fraction &y) {
  return reduce(Fraction(x.num * y.den - x.den * y.num, x.den * y.den));
}
 
// Find the integer nearest to a given fraction.
inline MPInt round(const Fraction &f) {
  MPInt rem = f.num % f.den;
  return (f.num / f.den) + (rem > f.den / 2);
}
 
inline Fraction &operator+=(Fraction &x, const Fraction &y) {
  x = x + y;
  return x;
}
 
inline Fraction &operator-=(Fraction &x, const Fraction &y) {
  x = x - y;
  return x;
}
 
inline Fraction &operator/=(Fraction &x, const Fraction &y) {
  x = x / y;
  return x;
}
 
inline Fraction &operator*=(Fraction &x, const Fraction &y) {
  x = x * y;
  return x;
}
 
inline llvm::raw_ostream &operator<<(llvm::raw_ostream &os, const Fraction &x) {
  x.print(os);
  return os;
}
 
} // namespace presburger
} // namespace mlir
 
#endif // MLIR_ANALYSIS_PRESBURGER_FRACTION_H