// Copyright 2014 The Chromium Authors. All rights reserved.
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file.

#ifndef BASE_NUMERICS_SAFE_CONVERSIONS_IMPL_H_
#define BASE_NUMERICS_SAFE_CONVERSIONS_IMPL_H_

#include <limits.h>
#include <stdint.h>

#include <limits>

#include "base/template_util.h"

namespace base {
namespace internal {

// The std library doesn't provide a binary max_exponent for integers, however
// we can compute one by adding one to the number of non-sign bits. This allows
// for accurate range comparisons between floating point and integer types.
template <typename NumericType>
struct MaxExponent {
  static const int value = std::numeric_limits<NumericType>::is_iec559
                               ? std::numeric_limits<NumericType>::max_exponent
                               : (sizeof(NumericType) * 8 + 1 -
                                  std::numeric_limits<NumericType>::is_signed);
};

enum IntegerRepresentation {
  INTEGER_REPRESENTATION_UNSIGNED,
  INTEGER_REPRESENTATION_SIGNED
};

// A range for a given nunmeric Src type is contained for a given numeric Dst
// type if both numeric_limits<Src>::max() <= numeric_limits<Dst>::max() and
// numeric_limits<Src>::min() >= numeric_limits<Dst>::min() are true.
// We implement this as template specializations rather than simple static
// comparisons to ensure type correctness in our comparisons.
enum NumericRangeRepresentation {
  NUMERIC_RANGE_NOT_CONTAINED,
  NUMERIC_RANGE_CONTAINED
};

// Helper templates to statically determine if our destination type can contain
// maximum and minimum values represented by the source type.

template <
    typename Dst,
    typename Src,
    IntegerRepresentation DstSign = std::numeric_limits<Dst>::is_signed
                                            ? INTEGER_REPRESENTATION_SIGNED
                                            : INTEGER_REPRESENTATION_UNSIGNED,
    IntegerRepresentation SrcSign =
        std::numeric_limits<Src>::is_signed
            ? INTEGER_REPRESENTATION_SIGNED
            : INTEGER_REPRESENTATION_UNSIGNED >
struct StaticDstRangeRelationToSrcRange;

// Same sign: Dst is guaranteed to contain Src only if its range is equal or
// larger.
template <typename Dst, typename Src, IntegerRepresentation Sign>
struct StaticDstRangeRelationToSrcRange<Dst, Src, Sign, Sign> {
  static const NumericRangeRepresentation value =
      MaxExponent<Dst>::value >= MaxExponent<Src>::value
          ? NUMERIC_RANGE_CONTAINED
          : NUMERIC_RANGE_NOT_CONTAINED;
};

// Unsigned to signed: Dst is guaranteed to contain source only if its range is
// larger.
template <typename Dst, typename Src>
struct StaticDstRangeRelationToSrcRange<Dst,
                                        Src,
                                        INTEGER_REPRESENTATION_SIGNED,
                                        INTEGER_REPRESENTATION_UNSIGNED> {
  static const NumericRangeRepresentation value =
      MaxExponent<Dst>::value > MaxExponent<Src>::value
          ? NUMERIC_RANGE_CONTAINED
          : NUMERIC_RANGE_NOT_CONTAINED;
};

// Signed to unsigned: Dst cannot be statically determined to contain Src.
template <typename Dst, typename Src>
struct StaticDstRangeRelationToSrcRange<Dst,
                                        Src,
                                        INTEGER_REPRESENTATION_UNSIGNED,
                                        INTEGER_REPRESENTATION_SIGNED> {
  static const NumericRangeRepresentation value = NUMERIC_RANGE_NOT_CONTAINED;
};

enum RangeConstraint {
  RANGE_VALID = 0x0,  // Value can be represented by the destination type.
  RANGE_UNDERFLOW = 0x1,  // Value would overflow.
  RANGE_OVERFLOW = 0x2,  // Value would underflow.
  RANGE_INVALID = RANGE_UNDERFLOW | RANGE_OVERFLOW  // Invalid (i.e. NaN).
};

// Helper function for coercing an int back to a RangeContraint.
inline RangeConstraint GetRangeConstraint(int integer_range_constraint) {
  DCHECK(integer_range_constraint >= RANGE_VALID &&
         integer_range_constraint <= RANGE_INVALID);
  return static_cast<RangeConstraint>(integer_range_constraint);
}

// This function creates a RangeConstraint from an upper and lower bound
// check by taking advantage of the fact that only NaN can be out of range in
// both directions at once.
inline RangeConstraint GetRangeConstraint(bool is_in_upper_bound,
                                   bool is_in_lower_bound) {
  return GetRangeConstraint((is_in_upper_bound ? 0 : RANGE_OVERFLOW) |
                            (is_in_lower_bound ? 0 : RANGE_UNDERFLOW));
}

// The following helper template addresses a corner case in range checks for
// conversion from a floating-point type to an integral type of smaller range
// but larger precision (e.g. float -> unsigned). The problem is as follows:
//   1. Integral maximum is always one less than a power of two, so it must be
//      truncated to fit the mantissa of the floating point. The direction of
//      rounding is implementation defined, but by default it's always IEEE
//      floats, which round to nearest and thus result in a value of larger
//      magnitude than the integral value.
//      Example: float f = UINT_MAX; // f is 4294967296f but UINT_MAX
//                                   // is 4294967295u.
//   2. If the floating point value is equal to the promoted integral maximum
//      value, a range check will erroneously pass.
//      Example: (4294967296f <= 4294967295u) // This is true due to a precision
//                                            // loss in rounding up to float.
//   3. When the floating point value is then converted to an integral, the
//      resulting value is out of range for the target integral type and
//      thus is implementation defined.
//      Example: unsigned u = (float)INT_MAX; // u will typically overflow to 0.
// To fix this bug we manually truncate the maximum value when the destination
// type is an integral of larger precision than the source floating-point type,
// such that the resulting maximum is represented exactly as a floating point.
template <typename Dst, typename Src>
struct NarrowingRange {
  typedef typename std::numeric_limits<Src> SrcLimits;
  typedef typename std::numeric_limits<Dst> DstLimits;

  static Dst max() {
    // The following logic avoids warnings where the max function is
    // instantiated with invalid values for a bit shift (even though
    // such a function can never be called).
    static const int shift =
        (MaxExponent<Src>::value > MaxExponent<Dst>::value &&
         SrcLimits::digits < DstLimits::digits && SrcLimits::is_iec559 &&
         DstLimits::is_integer)
            ? (DstLimits::digits - SrcLimits::digits)
            : 0;

    // We use UINTMAX_C below to avoid compiler warnings about shifting floating
    // points. Since it's a compile time calculation, it shouldn't have any
    // performance impact.
    return DstLimits::max() - static_cast<Dst>((UINTMAX_C(1) << shift) - 1);
  }

  static Dst min() {
    return std::numeric_limits<Dst>::is_iec559 ? -DstLimits::max()
                                               : DstLimits::min();
  }
};

template <
    typename Dst,
    typename Src,
    IntegerRepresentation DstSign = std::numeric_limits<Dst>::is_signed
                                            ? INTEGER_REPRESENTATION_SIGNED
                                            : INTEGER_REPRESENTATION_UNSIGNED,
    IntegerRepresentation SrcSign = std::numeric_limits<Src>::is_signed
                                            ? INTEGER_REPRESENTATION_SIGNED
                                            : INTEGER_REPRESENTATION_UNSIGNED,
    NumericRangeRepresentation DstRange =
        StaticDstRangeRelationToSrcRange<Dst, Src>::value >
struct DstRangeRelationToSrcRangeImpl;

// The following templates are for ranges that must be verified at runtime. We
// split it into checks based on signedness to avoid confusing casts and
// compiler warnings on signed an unsigned comparisons.

// Dst range is statically determined to contain Src: Nothing to check.
template <typename Dst,
          typename Src,
          IntegerRepresentation DstSign,
          IntegerRepresentation SrcSign>
struct DstRangeRelationToSrcRangeImpl<Dst,
                                      Src,
                                      DstSign,
                                      SrcSign,
                                      NUMERIC_RANGE_CONTAINED> {
  static RangeConstraint Check(Src value) { return RANGE_VALID; }
};

// Signed to signed narrowing: Both the upper and lower boundaries may be
// exceeded.
template <typename Dst, typename Src>
struct DstRangeRelationToSrcRangeImpl<Dst,
                                      Src,
                                      INTEGER_REPRESENTATION_SIGNED,
                                      INTEGER_REPRESENTATION_SIGNED,
                                      NUMERIC_RANGE_NOT_CONTAINED> {
  static RangeConstraint Check(Src value) {
    return GetRangeConstraint((value <= NarrowingRange<Dst, Src>::max()),
                              (value >= NarrowingRange<Dst, Src>::min()));
  }
};

// Unsigned to unsigned narrowing: Only the upper boundary can be exceeded.
template <typename Dst, typename Src>
struct DstRangeRelationToSrcRangeImpl<Dst,
                                      Src,
                                      INTEGER_REPRESENTATION_UNSIGNED,
                                      INTEGER_REPRESENTATION_UNSIGNED,
                                      NUMERIC_RANGE_NOT_CONTAINED> {
  static RangeConstraint Check(Src value) {
    return GetRangeConstraint(value <= NarrowingRange<Dst, Src>::max(), true);
  }
};

// Unsigned to signed: The upper boundary may be exceeded.
template <typename Dst, typename Src>
struct DstRangeRelationToSrcRangeImpl<Dst,
                                      Src,
                                      INTEGER_REPRESENTATION_SIGNED,
                                      INTEGER_REPRESENTATION_UNSIGNED,
                                      NUMERIC_RANGE_NOT_CONTAINED> {
  static RangeConstraint Check(Src value) {
    return sizeof(Dst) > sizeof(Src)
               ? RANGE_VALID
               : GetRangeConstraint(
                     value <= static_cast<Src>(NarrowingRange<Dst, Src>::max()),
                     true);
  }
};

// Signed to unsigned: The upper boundary may be exceeded for a narrower Dst,
// and any negative value exceeds the lower boundary.
template <typename Dst, typename Src>
struct DstRangeRelationToSrcRangeImpl<Dst,
                                      Src,
                                      INTEGER_REPRESENTATION_UNSIGNED,
                                      INTEGER_REPRESENTATION_SIGNED,
                                      NUMERIC_RANGE_NOT_CONTAINED> {
  static RangeConstraint Check(Src value) {
    return (MaxExponent<Dst>::value >= MaxExponent<Src>::value)
               ? GetRangeConstraint(true, value >= static_cast<Src>(0))
               : GetRangeConstraint(
                     value <= static_cast<Src>(NarrowingRange<Dst, Src>::max()),
                     value >= static_cast<Src>(0));
  }
};

template <typename Dst, typename Src>
inline RangeConstraint DstRangeRelationToSrcRange(Src value) {
  static_assert(std::numeric_limits<Src>::is_specialized,
                "Argument must be numeric.");
  static_assert(std::numeric_limits<Dst>::is_specialized,
                "Result must be numeric.");
  return DstRangeRelationToSrcRangeImpl<Dst, Src>::Check(value);
}

}  // namespace internal
}  // namespace base

#endif  // BASE_NUMERICS_SAFE_CONVERSIONS_IMPL_H_