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#ifndef SRC_TINT_LANG_CORE_NUMBER_H_
#define SRC_TINT_LANG_CORE_NUMBER_H_
#include <stdint.h>
#include <cmath>
#include <functional>
#include <limits>
#include <optional>
#include "src/tint/utils/macros/compiler.h"
#include "src/tint/utils/result/result.h"
#include "src/tint/utils/text/string_stream.h"
#include "src/tint/utils/traits/traits.h"
// Forward declaration
namespace tint::core {
/// Number wraps a integer or floating point number, enforcing explicit casting.
template <typename T>
struct Number;
} // namespace tint::core
namespace tint::core::detail {
/// Base template for IsNumber
template <typename T>
struct IsNumber : std::false_type {};
/// Specialization for IsNumber
template <typename T>
struct IsNumber<Number<T>> : std::true_type {};
/// An empty structure used as a unique template type for Number when
/// specializing for the f16 type.
struct NumberKindF16 {};
/// Helper for obtaining the underlying type for a Number.
template <typename T>
struct NumberUnwrapper {
/// When T is not a Number, then type defined to be T.
using type = T;
};
/// NumberUnwrapper specialization for Number<T>.
template <typename T>
struct NumberUnwrapper<Number<T>> {
/// The Number's underlying type.
using type = typename Number<T>::type;
};
} // namespace tint::core::detail
namespace tint::core {
/// Evaluates to true iff T is a Number
template <typename T>
constexpr bool IsNumber = tint::core::detail::IsNumber<T>::value;
/// Resolves to the underlying type for a Number.
template <typename T>
using UnwrapNumber = typename tint::core::detail::NumberUnwrapper<T>::type;
/// Evaluates to true iff T or Number<T> is a floating-point type or is NumberKindF16.
template <typename T>
constexpr bool IsFloatingPoint = std::is_floating_point_v<UnwrapNumber<T>> ||
std::is_same_v<UnwrapNumber<T>, tint::core::detail::NumberKindF16>;
/// Evaluates to true iff T or Number<T> is an integral type.
template <typename T>
constexpr bool IsIntegral = std::is_integral_v<UnwrapNumber<T>>;
/// Evaluates to true iff T or Number<T> is a signed integer type.
template <typename T>
constexpr bool IsSignedIntegral =
std::is_integral_v<UnwrapNumber<T>> && std::is_signed_v<UnwrapNumber<T>>;
/// Evaluates to true iff T or Number<T> is an unsigned integer type.
template <typename T>
constexpr bool IsUnsignedIntegral =
std::is_integral_v<UnwrapNumber<T>> && std::is_unsigned_v<UnwrapNumber<T>>;
/// Evaluates to true iff T is an integer type, floating-point type or is NumberKindF16.
template <typename T>
constexpr bool IsNumeric = IsIntegral<T> || IsFloatingPoint<T>;
/// Returns the bit width of T
template <typename T>
constexpr size_t BitWidth = sizeof(UnwrapNumber<T>) * 8;
/// NumberBase is a CRTP base class for Number<T>
template <typename NumberT>
struct NumberBase {
/// @returns value of type `Number<T>` with the highest value for that type.
static NumberT Highest() { return NumberT(NumberT::kHighestValue); }
/// @returns value of type `Number<T>` with the lowest value for that type.
static NumberT Lowest() { return NumberT(NumberT::kLowestValue); }
/// @returns value of type `Number<T>` with the smallest value for that type.
static NumberT Smallest() { return NumberT(NumberT::kSmallestValue); }
/// @returns value of type `Number<T>` that represents NaN for that type.
static NumberT NaN() {
return NumberT(std::numeric_limits<UnwrapNumber<NumberT>>::quiet_NaN());
}
/// @returns value of type `Number<T>` that represents infinity for that type.
static NumberT Inf() { return NumberT(std::numeric_limits<UnwrapNumber<NumberT>>::infinity()); }
};
/// Number wraps a integer or floating point number, enforcing explicit casting.
template <typename T>
struct Number : NumberBase<Number<T>> {
static_assert(IsNumeric<T>, "Number<T> constructed with non-numeric type");
/// type is the underlying type of the Number
using type = T;
/// Number of bits in the number.
static constexpr size_t kNumBits = sizeof(T) * 8;
/// Highest finite representable value of this type.
static constexpr type kHighestValue = std::numeric_limits<type>::max();
/// Lowest finite representable value of this type.
static constexpr type kLowestValue = std::numeric_limits<type>::lowest();
/// Smallest positive normal value of this type.
static constexpr type kSmallestValue =
std::is_integral_v<type> ? 0 : std::numeric_limits<type>::min();
/// Smallest positive subnormal value of this type, 0 for integral type.
static constexpr type kSmallestSubnormalValue =
std::is_integral_v<type> ? 0 : std::numeric_limits<type>::denorm_min();
/// Constructor. The value is zero-initialized.
Number() = default;
/// Constructor.
/// @param v the value to initialize this Number to
template <typename U>
explicit Number(U v) : value(static_cast<T>(v)) {}
/// Constructor.
/// @param v the value to initialize this Number to
template <typename U>
explicit Number(Number<U> v) : value(static_cast<T>(v.value)) {}
/// Conversion operator
/// @returns the value as T
operator T() const { return value; }
/// Negation operator
/// @returns the negative value of the number
Number operator-() const { return Number(-value); }
/// Assignment operator
/// @param v the new value
/// @returns this Number so calls can be chained
Number& operator=(T v) {
value = v;
return *this;
}
/// The number value
type value = {};
};
/// Writes the number to the ostream.
/// @param out the stream to write to
/// @param num the Number
/// @return the stream so calls can be chained
template <typename STREAM, typename T, typename = traits::EnableIfIsOStream<STREAM>>
auto& operator<<(STREAM& out, Number<T> num) {
return out << num.value;
}
/// The partial specification of Number for f16 type, storing the f16 value as float,
/// and enforcing proper explicit casting.
template <>
struct Number<tint::core::detail::NumberKindF16>
: NumberBase<Number<tint::core::detail::NumberKindF16>> {
/// C++ does not have a native float16 type, so we use a 32-bit float instead.
using type = float;
/// Number of bits in the number.
static constexpr size_t kNumBits = 16;
/// Highest finite representable value of this type.
static constexpr type kHighestValue = 65504.0f; // 2¹⁵ × (1 + 1023/1024)
/// Lowest finite representable value of this type.
static constexpr type kLowestValue = -65504.0f;
/// Smallest positive normal value of this type.
/// binary16 0_00001_0000000000, value is 2⁻¹⁴.
static constexpr type kSmallestValue = 0x1p-14f;
/// Smallest positive subnormal value of this type.
/// binary16 0_00000_0000000001, value is 2⁻¹⁴ * 2⁻¹⁰ = 2⁻²⁴.
static constexpr type kSmallestSubnormalValue = 0x1p-24f;
/// Constructor. The value is zero-initialized.
Number() = default;
/// Constructor.
/// @param v the value to initialize this Number to
template <typename U>
explicit Number(U v) : value(Quantize(static_cast<type>(v))) {}
/// Constructor.
/// @param v the value to initialize this Number to
template <typename U>
explicit Number(Number<U> v) : value(Quantize(static_cast<type>(v.value))) {}
/// Conversion operator
/// @returns the value as the internal representation type of F16
operator float() const { return value; }
/// Negation operator
/// @returns the negative value of the number
Number operator-() const { return Number<tint::core::detail::NumberKindF16>(-value); }
/// Assignment operator with parameter as native floating point type
/// @param v the new value
/// @returns this Number so calls can be chained
Number& operator=(type v) {
value = Quantize(v);
return *this;
}
/// Get the binary16 bit pattern in type uint16_t of this value.
/// @returns the binary16 bit pattern, in type uint16_t, of the stored quantized f16 value. If
/// the value is NaN, the returned value will be 0x7e00u. If the value is positive infinity, the
/// returned value will be 0x7c00u. If the input value is negative infinity, the returned value
/// will be 0xfc00u.
uint16_t BitsRepresentation() const;
/// Creates an f16 value from the uint16_t bit representation.
/// @param bits the bits to convert from
/// @returns the binary16 value based off the provided bit pattern.
static Number<tint::core::detail::NumberKindF16> FromBits(uint16_t bits);
/// @param value the input float32 value
/// @returns the float32 value quantized to the smaller float16 value, through truncation of the
/// mantissa bits (no rounding). If the float32 value is too large (positive or negative) to be
/// represented by a float16 value, then the returned value will be positive or negative
/// infinity.
static type Quantize(type value);
/// The number value, stored as float
type value = {};
};
/// `AInt` is a type alias to `Number<int64_t>`.
using AInt = Number<int64_t>;
/// `AFloat` is a type alias to `Number<double>`.
using AFloat = Number<double>;
/// `i32` is a type alias to `Number<int32_t>`.
using i32 = Number<int32_t>;
/// `u32` is a type alias to `Number<uint32_t>`.
using u32 = Number<uint32_t>;
/// `f32` is a type alias to `Number<float>`
using f32 = Number<float>;
/// `f16` is a type alias to `Number<detail::NumberKindF16>`, which should be IEEE 754 binary16.
/// However since C++ don't have native binary16 type, the value is stored as float.
using f16 = Number<tint::core::detail::NumberKindF16>;
/// The algorithms in this module require support for infinity and quiet NaNs on
/// floating point types.
static_assert(std::numeric_limits<float>::has_infinity);
static_assert(std::numeric_limits<float>::has_quiet_NaN);
static_assert(std::numeric_limits<double>::has_infinity);
static_assert(std::numeric_limits<double>::has_quiet_NaN);
template <typename T, tint::traits::EnableIf<IsFloatingPoint<T>>* = nullptr>
inline const auto kPi = T(UnwrapNumber<T>(3.14159265358979323846));
/// True iff T is an abstract number type
template <typename T>
constexpr bool IsAbstract = std::is_same_v<T, AInt> || std::is_same_v<T, AFloat>;
/// @returns the friendly name of Number type T
template <typename T, tint::traits::EnableIf<IsNumber<T>>* = nullptr>
const char* FriendlyName() {
if constexpr (std::is_same_v<T, AInt>) {
return "abstract-int";
} else if constexpr (std::is_same_v<T, AFloat>) {
return "abstract-float";
} else if constexpr (std::is_same_v<T, i32>) {
return "i32";
} else if constexpr (std::is_same_v<T, u32>) {
return "u32";
} else if constexpr (std::is_same_v<T, f32>) {
return "f32";
} else if constexpr (std::is_same_v<T, f16>) {
return "f16";
} else {
static_assert(!sizeof(T), "Unhandled type");
}
}
/// @returns the friendly name of T when T is bool
template <typename T, tint::traits::EnableIf<std::is_same_v<T, bool>>* = nullptr>
const char* FriendlyName() {
return "bool";
}
/// Enumerator of failure reasons when converting from one number to another.
enum class ConversionFailure {
kExceedsPositiveLimit, // The value was too big (+'ve) to fit in the target type
kExceedsNegativeLimit, // The value was too big (-'ve) to fit in the target type
};
/// Writes the conversion failure message to the ostream.
/// @param out the stream to write to
/// @param failure the ConversionFailure
/// @return the stream so calls can be chained
template <typename STREAM, typename = traits::EnableIfIsOStream<STREAM>>
auto& operator<<(STREAM& out, ConversionFailure failure) {
switch (failure) {
case ConversionFailure::kExceedsPositiveLimit:
return out << "value exceeds positive limit for type";
case ConversionFailure::kExceedsNegativeLimit:
return out << "value exceeds negative limit for type";
}
return out << "<unknown>";
}
/// Converts a number from one type to another, checking that the value fits in the target type.
/// @param num the value to convert
/// @returns the resulting value of the conversion, or a failure reason.
template <typename TO, typename FROM>
tint::Result<TO, ConversionFailure> CheckedConvert(Number<FROM> num) {
// Use the highest-precision integer or floating-point type to perform the comparisons.
using T = std::conditional_t<IsFloatingPoint<UnwrapNumber<TO>> || IsFloatingPoint<FROM>,
AFloat::type, AInt::type>;
const auto value = static_cast<T>(num.value);
if (value > static_cast<T>(TO::kHighestValue)) {
return ConversionFailure::kExceedsPositiveLimit;
}
if (value < static_cast<T>(TO::kLowestValue)) {
return ConversionFailure::kExceedsNegativeLimit;
}
return TO(value); // Success
}
/// Equality operator.
/// @param a the LHS number
/// @param b the RHS number
/// @returns true if the numbers `a` and `b` are exactly equal.
/// For floating point types, negative zero equals zero.
/// IEEE 754 says "Comparison shall ignore the sign of zero (so +0 = -0)."
template <typename A, typename B>
bool operator==(Number<A> a, Number<B> b) {
// Use the highest-precision integer or floating-point type to perform the comparisons.
using T =
std::conditional_t<IsFloatingPoint<A> || IsFloatingPoint<B>, AFloat::type, AInt::type>;
auto va = static_cast<T>(a.value);
auto vb = static_cast<T>(b.value);
return std::equal_to<T>()(va, vb);
}
/// Inequality operator.
/// @param a the LHS number
/// @param b the RHS number
/// @returns true if the numbers `a` and `b` are exactly unequal. Also considers sign bit.
template <typename A, typename B>
bool operator!=(Number<A> a, Number<B> b) {
return !(a == b);
}
/// Equality operator.
/// @param a the LHS number
/// @param b the RHS number
/// @returns true if the numbers `a` and `b` are exactly equal.
template <typename A, typename B>
std::enable_if_t<IsNumeric<B>, bool> operator==(Number<A> a, B b) {
return a == Number<B>(b);
}
/// Inequality operator.
/// @param a the LHS number
/// @param b the RHS number
/// @returns true if the numbers `a` and `b` are exactly unequal.
template <typename A, typename B>
std::enable_if_t<IsNumeric<B>, bool> operator!=(Number<A> a, B b) {
return !(a == b);
}
/// Equality operator.
/// @param a the LHS number
/// @param b the RHS number
/// @returns true if the numbers `a` and `b` are exactly equal.
template <typename A, typename B>
std::enable_if_t<IsNumeric<A>, bool> operator==(A a, Number<B> b) {
return Number<A>(a) == b;
}
/// Inequality operator.
/// @param a the LHS number
/// @param b the RHS number
/// @returns true if the numbers `a` and `b` are exactly unequal.
template <typename A, typename B>
std::enable_if_t<IsNumeric<A>, bool> operator!=(A a, Number<B> b) {
return !(a == b);
}
/// Define 'TINT_HAS_OVERFLOW_BUILTINS' if the compiler provide overflow checking builtins.
/// If the compiler does not support these builtins, then these are emulated with algorithms
/// described in:
/// https://wiki.sei.cmu.edu/confluence/display/c/INT32-C.+Ensure+that+operations+on+signed+integers+do+not+result+in+overflow
#if defined(__GNUC__) && __GNUC__ >= 5
#define TINT_HAS_OVERFLOW_BUILTINS
#elif defined(__clang__)
#if __has_builtin(__builtin_add_overflow) && __has_builtin(__builtin_mul_overflow)
#define TINT_HAS_OVERFLOW_BUILTINS
#endif
#endif
/// @param a the LHS number
/// @param b the RHS number
/// @returns a + b, or an empty optional if the resulting value overflowed the AInt
inline std::optional<AInt> CheckedAdd(AInt a, AInt b) {
int64_t result;
#ifdef TINT_HAS_OVERFLOW_BUILTINS
if (__builtin_add_overflow(a.value, b.value, &result)) {
return {};
}
#else // TINT_HAS_OVERFLOW_BUILTINS
if (a.value >= 0) {
if (b.value > AInt::kHighestValue - a.value) {
return {};
}
} else {
if (b.value < AInt::kLowestValue - a.value) {
return {};
}
}
result = a.value + b.value;
#endif // TINT_HAS_OVERFLOW_BUILTINS
return AInt(result);
}
/// @param a the LHS number
/// @param b the RHS number
/// @returns a + b, or an empty optional if the resulting value overflowed the float value
template <typename FloatingPointT,
typename = tint::traits::EnableIf<IsFloatingPoint<FloatingPointT>>>
inline std::optional<FloatingPointT> CheckedAdd(FloatingPointT a, FloatingPointT b) {
auto result = FloatingPointT{a.value + b.value};
if (!std::isfinite(result.value)) {
return {};
}
return result;
}
/// @param a the LHS number
/// @param b the RHS number
/// @returns a - b, or an empty optional if the resulting value overflowed the AInt
inline std::optional<AInt> CheckedSub(AInt a, AInt b) {
int64_t result;
#ifdef TINT_HAS_OVERFLOW_BUILTINS
if (__builtin_sub_overflow(a.value, b.value, &result)) {
return {};
}
#else // TINT_HAS_OVERFLOW_BUILTINS
if (b.value >= 0) {
if (a.value < AInt::kLowestValue + b.value) {
return {};
}
} else {
if (a.value > AInt::kHighestValue + b.value) {
return {};
}
}
result = a.value - b.value;
#endif // TINT_HAS_OVERFLOW_BUILTINS
return AInt(result);
}
/// @param a the LHS number
/// @param b the RHS number
/// @returns a + b, or an empty optional if the resulting value overflowed the float value
template <typename FloatingPointT,
typename = tint::traits::EnableIf<IsFloatingPoint<FloatingPointT>>>
inline std::optional<FloatingPointT> CheckedSub(FloatingPointT a, FloatingPointT b) {
auto result = FloatingPointT{a.value - b.value};
if (!std::isfinite(result.value)) {
return {};
}
return result;
}
/// @param a the LHS number
/// @param b the RHS number
/// @returns a * b, or an empty optional if the resulting value overflowed the AInt
inline std::optional<AInt> CheckedMul(AInt a, AInt b) {
int64_t result;
#ifdef TINT_HAS_OVERFLOW_BUILTINS
if (__builtin_mul_overflow(a.value, b.value, &result)) {
return {};
}
#else // TINT_HAS_OVERFLOW_BUILTINS
if (a > 0) {
if (b > 0) {
if (a > (AInt::kHighestValue / b)) {
return {};
}
} else {
if (b < (AInt::kLowestValue / a)) {
return {};
}
}
} else {
if (b > 0) {
if (a < (AInt::kLowestValue / b)) {
return {};
}
} else {
if ((a != 0) && (b < (AInt::kHighestValue / a))) {
return {};
}
}
}
result = a.value * b.value;
#endif // TINT_HAS_OVERFLOW_BUILTINS
return AInt(result);
}
/// @param a the LHS number
/// @param b the RHS number
/// @returns a * b, or an empty optional if the resulting value overflowed the float value
template <typename FloatingPointT,
typename = tint::traits::EnableIf<IsFloatingPoint<FloatingPointT>>>
inline std::optional<FloatingPointT> CheckedMul(FloatingPointT a, FloatingPointT b) {
auto result = FloatingPointT{a.value * b.value};
if (!std::isfinite(result.value)) {
return {};
}
return result;
}
/// @param a the LHS number
/// @param b the RHS number
/// @returns a / b, or an empty optional if the resulting value overflowed the AInt
inline std::optional<AInt> CheckedDiv(AInt a, AInt b) {
if (b == 0) {
return {};
}
if (b == -1 && a == AInt::Lowest()) {
return {};
}
return AInt{a.value / b.value};
}
/// @param a the LHS number
/// @param b the RHS number
/// @returns a / b, or an empty optional if the resulting value overflowed the float value
template <typename FloatingPointT,
typename = tint::traits::EnableIf<IsFloatingPoint<FloatingPointT>>>
inline std::optional<FloatingPointT> CheckedDiv(FloatingPointT a, FloatingPointT b) {
if (b == FloatingPointT{0.0}) {
return {};
}
auto result = FloatingPointT{a.value / b.value};
if (!std::isfinite(result.value)) {
return {};
}
return result;
}
namespace detail {
/// @param e1 the LHS number
/// @param e2 the RHS number
/// @returns the remainder of e1 / e2
template <typename T>
inline T Mod(T e1, T e2) {
if constexpr (IsIntegral<T>) {
return e1 % e2;
} else {
return e1 - e2 * std::trunc(e1 / e2);
}
}
} // namespace detail
/// @param a the LHS number
/// @param b the RHS number
/// @returns the remainder of a / b, or an empty optional if the resulting value overflowed the AInt
inline std::optional<AInt> CheckedMod(AInt a, AInt b) {
if (b == 0) {
return {};
}
if (b == -1 && a == AInt::Lowest()) {
return {};
}
return AInt{tint::core::detail::Mod(a.value, b.value)};
}
/// @param a the LHS number
/// @param b the RHS number
/// @returns the remainder of a / b, or an empty optional if the resulting value overflowed the
/// float value
template <typename FloatingPointT,
typename = tint::traits::EnableIf<IsFloatingPoint<FloatingPointT>>>
inline std::optional<FloatingPointT> CheckedMod(FloatingPointT a, FloatingPointT b) {
if (b == FloatingPointT{0.0}) {
return {};
}
auto result = FloatingPointT{tint::core::detail::Mod(a.value, b.value)};
if (!std::isfinite(result.value)) {
return {};
}
return result;
}
/// @param a the LHS number of the multiply
/// @param b the RHS number of the multiply
/// @param c the RHS number of the addition
/// @returns a * b + c, or an empty optional if the value overflowed the AInt
inline std::optional<AInt> CheckedMadd(AInt a, AInt b, AInt c) {
if (auto mul = CheckedMul(a, b)) {
return CheckedAdd(mul.value(), c);
}
return {};
}
/// @param base the base number of the exponent operation
/// @param exp the exponent
/// @returns the value of `base` raised to the power `exp`, or an empty optional if the operation
/// cannot be performed.
template <typename FloatingPointT,
typename = tint::traits::EnableIf<IsFloatingPoint<FloatingPointT>>>
inline std::optional<FloatingPointT> CheckedPow(FloatingPointT base, FloatingPointT exp) {
static_assert(IsNumber<FloatingPointT>);
if ((base < 0) || (base == 0 && exp <= 0)) {
return {};
}
auto result = FloatingPointT{std::pow(base.value, exp.value)};
if (!std::isfinite(result.value)) {
return {};
}
return result;
}
} // namespace tint::core
namespace tint::core::number_suffixes {
/// Literal suffix for abstract integer literals
inline AInt operator""_a(unsigned long long int value) { // NOLINT
return AInt(static_cast<int64_t>(value));
}
/// Literal suffix for abstract float literals
inline AFloat operator""_a(long double value) { // NOLINT
return AFloat(static_cast<double>(value));
}
/// Literal suffix for i32 literals
inline i32 operator""_i(unsigned long long int value) { // NOLINT
return i32(static_cast<int32_t>(value));
}
/// Literal suffix for u32 literals
inline u32 operator""_u(unsigned long long int value) { // NOLINT
return u32(static_cast<uint32_t>(value));
}
/// Literal suffix for f32 literals
inline f32 operator""_f(long double value) { // NOLINT
return f32(static_cast<double>(value));
}
/// Literal suffix for f32 literals
inline f32 operator""_f(unsigned long long int value) { // NOLINT
return f32(static_cast<double>(value));
}
/// Literal suffix for f16 literals
inline f16 operator""_h(long double value) { // NOLINT
return f16(static_cast<double>(value));
}
/// Literal suffix for f16 literals
inline f16 operator""_h(unsigned long long int value) { // NOLINT
return f16(static_cast<double>(value));
}
} // namespace tint::core::number_suffixes
namespace std {
/// Custom std::hash specialization for tint::Number<T>
template <typename T>
class hash<tint::core::Number<T>> {
public:
/// @param n the Number
/// @return the hash value
inline std::size_t operator()(const tint::core::Number<T>& n) const {
return std::hash<decltype(n.value)>()(n.value);
}
};
} // namespace std
#endif // SRC_TINT_LANG_CORE_NUMBER_H_