File: TypeSafeSignMath.h

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#pragma once

#include <c10/macros/Macros.h>
#include <limits>
#include <type_traits>

C10_CLANG_DIAGNOSTIC_PUSH()
#if C10_CLANG_HAS_WARNING("-Wstring-conversion")
C10_CLANG_DIAGNOSTIC_IGNORE("-Wstring-conversion")
#endif
#if C10_CLANG_HAS_WARNING("-Wimplicit-int-float-conversion")
C10_CLANG_DIAGNOSTIC_IGNORE("-Wimplicit-int-float-conversion")
#endif

namespace c10 {

/// Returns false since we cannot have x < 0 if x is unsigned.
template <typename T>
static inline constexpr bool is_negative(
    const T& /*x*/,
    std::true_type /*is_unsigned*/) {
  return false;
}

/// Returns true if a signed variable x < 0
template <typename T>
static inline constexpr bool is_negative(
    const T& x,
    std::false_type /*is_unsigned*/) {
  return x < T(0);
}

/// Returns true if x < 0
/// NOTE: Will fail on an unsigned custom type
///       For the most part it's possible to fix this if
///       the custom type has a constexpr constructor.
///       However, notably, c10::Half does not :-(
template <typename T>
inline constexpr bool is_negative(const T& x) {
  return is_negative(x, std::is_unsigned<T>());
}

/// Returns the sign of an unsigned variable x as 0, 1
template <typename T>
static inline constexpr int signum(const T& x, std::true_type /*is_unsigned*/) {
  return T(0) < x;
}

/// Returns the sign of a signed variable x as -1, 0, 1
template <typename T>
static inline constexpr int signum(
    const T& x,
    std::false_type /*is_unsigned*/) {
  return (T(0) < x) - (x < T(0));
}

/// Returns the sign of x as -1, 0, 1
/// NOTE: Will fail on an unsigned custom type
///       For the most part it's possible to fix this if
///       the custom type has a constexpr constructor.
///       However, notably, c10::Half does not :-(
template <typename T>
inline constexpr int signum(const T& x) {
  return signum(x, std::is_unsigned<T>());
}

/// Returns true if a and b are not both negative
template <typename T, typename U>
inline constexpr bool signs_differ(const T& a, const U& b) {
  return is_negative(a) != is_negative(b);
}

// Suppress sign compare warning when compiling with GCC
// as later does not account for short-circuit rule before
// raising the warning, see https://godbolt.org/z/Tr3Msnz99
#ifdef __GNUC__
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wsign-compare"
#endif

/// Returns true if x is greater than the greatest value of the type Limit
template <typename Limit, typename T>
inline constexpr bool greater_than_max(const T& x) {
  constexpr bool can_overflow =
      std::numeric_limits<T>::digits > std::numeric_limits<Limit>::digits;
  return can_overflow && x > std::numeric_limits<Limit>::max();
}

#ifdef __GNUC__
#pragma GCC diagnostic pop
#endif

/// Returns true if x < lowest(Limit). Standard comparison
template <typename Limit, typename T>
static inline constexpr bool less_than_lowest(
    const T& x,
    std::false_type /*limit_is_unsigned*/,
    std::false_type /*x_is_unsigned*/) {
  return x < std::numeric_limits<Limit>::lowest();
}

/// Returns false since all the limit is signed and therefore includes
/// negative values but x cannot be negative because it is unsigned
template <typename Limit, typename T>
static inline constexpr bool less_than_lowest(
    const T& /*x*/,
    std::false_type /*limit_is_unsigned*/,
    std::true_type /*x_is_unsigned*/) {
  return false;
}

/// Returns true if x < 0, where 0 is constructed from T.
/// Limit is not signed, so its lower value is zero
template <typename Limit, typename T>
static inline constexpr bool less_than_lowest(
    const T& x,
    std::true_type /*limit_is_unsigned*/,
    std::false_type /*x_is_unsigned*/) {
  return x < T(0);
}

/// Returns false sign both types are unsigned
template <typename Limit, typename T>
static inline constexpr bool less_than_lowest(
    const T& /*x*/,
    std::true_type /*limit_is_unsigned*/,
    std::true_type /*x_is_unsigned*/) {
  return false;
}

/// Returns true if x is less than the lowest value of type T
/// NOTE: Will fail on an unsigned custom type
///       For the most part it's possible to fix this if
///       the custom type has a constexpr constructor.
///       However, notably, c10::Half does not :
template <typename Limit, typename T>
inline constexpr bool less_than_lowest(const T& x) {
  return less_than_lowest<Limit>(
      x, std::is_unsigned<Limit>(), std::is_unsigned<T>());
}

} // namespace c10

C10_CLANG_DIAGNOSTIC_POP()