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568 lines
22 KiB
C++
568 lines
22 KiB
C++
// Copyright 2017 The Chromium Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style license that can be
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// found in the LICENSE file.
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#ifndef BASE_NUMERICS_CHECKED_MATH_IMPL_H_
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#define BASE_NUMERICS_CHECKED_MATH_IMPL_H_
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#include <stddef.h>
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#include <stdint.h>
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#include <climits>
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#include <cmath>
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#include <cstdlib>
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#include <limits>
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#include <type_traits>
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#include "base/numerics/safe_conversions.h"
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#include "base/numerics/safe_math_shared_impl.h"
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namespace base {
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namespace internal {
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template <typename T>
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constexpr bool CheckedAddImpl(T x, T y, T* result) {
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static_assert(std::is_integral<T>::value, "Type must be integral");
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// Since the value of x+y is undefined if we have a signed type, we compute
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// it using the unsigned type of the same size.
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using UnsignedDst = typename std::make_unsigned<T>::type;
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using SignedDst = typename std::make_signed<T>::type;
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UnsignedDst ux = static_cast<UnsignedDst>(x);
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UnsignedDst uy = static_cast<UnsignedDst>(y);
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UnsignedDst uresult = static_cast<UnsignedDst>(ux + uy);
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*result = static_cast<T>(uresult);
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// Addition is valid if the sign of (x + y) is equal to either that of x or
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// that of y.
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return (std::is_signed<T>::value)
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? static_cast<SignedDst>((uresult ^ ux) & (uresult ^ uy)) >= 0
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: uresult >= uy; // Unsigned is either valid or underflow.
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}
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template <typename T, typename U, class Enable = void>
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struct CheckedAddOp {};
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template <typename T, typename U>
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struct CheckedAddOp<T,
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U,
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typename std::enable_if<std::is_integral<T>::value &&
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std::is_integral<U>::value>::type> {
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using result_type = typename MaxExponentPromotion<T, U>::type;
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template <typename V>
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static constexpr bool Do(T x, U y, V* result) {
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// TODO(jschuh) Make this "constexpr if" once we're C++17.
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if (CheckedAddFastOp<T, U>::is_supported)
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return CheckedAddFastOp<T, U>::Do(x, y, result);
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// Double the underlying type up to a full machine word.
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using FastPromotion = typename FastIntegerArithmeticPromotion<T, U>::type;
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using Promotion =
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typename std::conditional<(IntegerBitsPlusSign<FastPromotion>::value >
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IntegerBitsPlusSign<intptr_t>::value),
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typename BigEnoughPromotion<T, U>::type,
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FastPromotion>::type;
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// Fail if either operand is out of range for the promoted type.
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// TODO(jschuh): This could be made to work for a broader range of values.
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if (BASE_NUMERICS_UNLIKELY(!IsValueInRangeForNumericType<Promotion>(x) ||
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!IsValueInRangeForNumericType<Promotion>(y))) {
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return false;
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}
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Promotion presult = {};
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bool is_valid = true;
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if (IsIntegerArithmeticSafe<Promotion, T, U>::value) {
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presult = static_cast<Promotion>(x) + static_cast<Promotion>(y);
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} else {
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is_valid = CheckedAddImpl(static_cast<Promotion>(x),
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static_cast<Promotion>(y), &presult);
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}
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*result = static_cast<V>(presult);
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return is_valid && IsValueInRangeForNumericType<V>(presult);
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}
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};
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template <typename T>
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constexpr bool CheckedSubImpl(T x, T y, T* result) {
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static_assert(std::is_integral<T>::value, "Type must be integral");
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// Since the value of x+y is undefined if we have a signed type, we compute
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// it using the unsigned type of the same size.
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using UnsignedDst = typename std::make_unsigned<T>::type;
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using SignedDst = typename std::make_signed<T>::type;
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UnsignedDst ux = static_cast<UnsignedDst>(x);
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UnsignedDst uy = static_cast<UnsignedDst>(y);
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UnsignedDst uresult = static_cast<UnsignedDst>(ux - uy);
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*result = static_cast<T>(uresult);
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// Subtraction is valid if either x and y have same sign, or (x-y) and x have
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// the same sign.
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return (std::is_signed<T>::value)
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? static_cast<SignedDst>((uresult ^ ux) & (ux ^ uy)) >= 0
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: x >= y;
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}
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template <typename T, typename U, class Enable = void>
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struct CheckedSubOp {};
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template <typename T, typename U>
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struct CheckedSubOp<T,
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U,
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typename std::enable_if<std::is_integral<T>::value &&
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std::is_integral<U>::value>::type> {
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using result_type = typename MaxExponentPromotion<T, U>::type;
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template <typename V>
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static constexpr bool Do(T x, U y, V* result) {
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// TODO(jschuh) Make this "constexpr if" once we're C++17.
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if (CheckedSubFastOp<T, U>::is_supported)
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return CheckedSubFastOp<T, U>::Do(x, y, result);
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// Double the underlying type up to a full machine word.
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using FastPromotion = typename FastIntegerArithmeticPromotion<T, U>::type;
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using Promotion =
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typename std::conditional<(IntegerBitsPlusSign<FastPromotion>::value >
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IntegerBitsPlusSign<intptr_t>::value),
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typename BigEnoughPromotion<T, U>::type,
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FastPromotion>::type;
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// Fail if either operand is out of range for the promoted type.
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// TODO(jschuh): This could be made to work for a broader range of values.
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if (BASE_NUMERICS_UNLIKELY(!IsValueInRangeForNumericType<Promotion>(x) ||
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!IsValueInRangeForNumericType<Promotion>(y))) {
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return false;
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}
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Promotion presult = {};
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bool is_valid = true;
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if (IsIntegerArithmeticSafe<Promotion, T, U>::value) {
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presult = static_cast<Promotion>(x) - static_cast<Promotion>(y);
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} else {
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is_valid = CheckedSubImpl(static_cast<Promotion>(x),
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static_cast<Promotion>(y), &presult);
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}
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*result = static_cast<V>(presult);
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return is_valid && IsValueInRangeForNumericType<V>(presult);
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}
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};
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template <typename T>
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constexpr bool CheckedMulImpl(T x, T y, T* result) {
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static_assert(std::is_integral<T>::value, "Type must be integral");
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// Since the value of x*y is potentially undefined if we have a signed type,
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// we compute it using the unsigned type of the same size.
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using UnsignedDst = typename std::make_unsigned<T>::type;
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using SignedDst = typename std::make_signed<T>::type;
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const UnsignedDst ux = SafeUnsignedAbs(x);
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const UnsignedDst uy = SafeUnsignedAbs(y);
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UnsignedDst uresult = static_cast<UnsignedDst>(ux * uy);
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const bool is_negative =
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std::is_signed<T>::value && static_cast<SignedDst>(x ^ y) < 0;
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*result = is_negative ? 0 - uresult : uresult;
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// We have a fast out for unsigned identity or zero on the second operand.
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// After that it's an unsigned overflow check on the absolute value, with
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// a +1 bound for a negative result.
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return uy <= UnsignedDst(!std::is_signed<T>::value || is_negative) ||
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ux <= (std::numeric_limits<T>::max() + UnsignedDst(is_negative)) / uy;
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}
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template <typename T, typename U, class Enable = void>
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struct CheckedMulOp {};
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template <typename T, typename U>
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struct CheckedMulOp<T,
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U,
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typename std::enable_if<std::is_integral<T>::value &&
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std::is_integral<U>::value>::type> {
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using result_type = typename MaxExponentPromotion<T, U>::type;
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template <typename V>
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static constexpr bool Do(T x, U y, V* result) {
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// TODO(jschuh) Make this "constexpr if" once we're C++17.
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if (CheckedMulFastOp<T, U>::is_supported)
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return CheckedMulFastOp<T, U>::Do(x, y, result);
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using Promotion = typename FastIntegerArithmeticPromotion<T, U>::type;
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// Verify the destination type can hold the result (always true for 0).
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if (BASE_NUMERICS_UNLIKELY((!IsValueInRangeForNumericType<Promotion>(x) ||
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!IsValueInRangeForNumericType<Promotion>(y)) &&
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x && y)) {
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return false;
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}
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Promotion presult = {};
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bool is_valid = true;
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if (CheckedMulFastOp<Promotion, Promotion>::is_supported) {
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// The fast op may be available with the promoted type.
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is_valid = CheckedMulFastOp<Promotion, Promotion>::Do(x, y, &presult);
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} else if (IsIntegerArithmeticSafe<Promotion, T, U>::value) {
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presult = static_cast<Promotion>(x) * static_cast<Promotion>(y);
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} else {
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is_valid = CheckedMulImpl(static_cast<Promotion>(x),
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static_cast<Promotion>(y), &presult);
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}
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*result = static_cast<V>(presult);
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return is_valid && IsValueInRangeForNumericType<V>(presult);
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}
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};
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// Division just requires a check for a zero denominator or an invalid negation
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// on signed min/-1.
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template <typename T, typename U, class Enable = void>
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struct CheckedDivOp {};
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template <typename T, typename U>
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struct CheckedDivOp<T,
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U,
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typename std::enable_if<std::is_integral<T>::value &&
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std::is_integral<U>::value>::type> {
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using result_type = typename MaxExponentPromotion<T, U>::type;
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template <typename V>
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static constexpr bool Do(T x, U y, V* result) {
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if (BASE_NUMERICS_UNLIKELY(!y))
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return false;
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// The overflow check can be compiled away if we don't have the exact
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// combination of types needed to trigger this case.
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using Promotion = typename BigEnoughPromotion<T, U>::type;
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if (BASE_NUMERICS_UNLIKELY(
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(std::is_signed<T>::value && std::is_signed<U>::value &&
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IsTypeInRangeForNumericType<T, Promotion>::value &&
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static_cast<Promotion>(x) ==
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std::numeric_limits<Promotion>::lowest() &&
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y == static_cast<U>(-1)))) {
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return false;
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}
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// This branch always compiles away if the above branch wasn't removed.
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if (BASE_NUMERICS_UNLIKELY((!IsValueInRangeForNumericType<Promotion>(x) ||
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!IsValueInRangeForNumericType<Promotion>(y)) &&
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x)) {
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return false;
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}
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Promotion presult = Promotion(x) / Promotion(y);
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*result = static_cast<V>(presult);
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return IsValueInRangeForNumericType<V>(presult);
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}
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};
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template <typename T, typename U, class Enable = void>
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struct CheckedModOp {};
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template <typename T, typename U>
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struct CheckedModOp<T,
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U,
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typename std::enable_if<std::is_integral<T>::value &&
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std::is_integral<U>::value>::type> {
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using result_type = typename MaxExponentPromotion<T, U>::type;
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template <typename V>
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static constexpr bool Do(T x, U y, V* result) {
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using Promotion = typename BigEnoughPromotion<T, U>::type;
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if (BASE_NUMERICS_LIKELY(y)) {
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Promotion presult = static_cast<Promotion>(x) % static_cast<Promotion>(y);
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*result = static_cast<Promotion>(presult);
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return IsValueInRangeForNumericType<V>(presult);
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}
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return false;
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}
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};
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template <typename T, typename U, class Enable = void>
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struct CheckedLshOp {};
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// Left shift. Shifts less than 0 or greater than or equal to the number
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// of bits in the promoted type are undefined. Shifts of negative values
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// are undefined. Otherwise it is defined when the result fits.
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template <typename T, typename U>
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struct CheckedLshOp<T,
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U,
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typename std::enable_if<std::is_integral<T>::value &&
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std::is_integral<U>::value>::type> {
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using result_type = T;
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template <typename V>
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static constexpr bool Do(T x, U shift, V* result) {
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// Disallow negative numbers and verify the shift is in bounds.
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if (BASE_NUMERICS_LIKELY(!IsValueNegative(x) &&
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as_unsigned(shift) <
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as_unsigned(std::numeric_limits<T>::digits))) {
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// Shift as unsigned to avoid undefined behavior.
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*result = static_cast<V>(as_unsigned(x) << shift);
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// If the shift can be reversed, we know it was valid.
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return *result >> shift == x;
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}
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// Handle the legal corner-case of a full-width signed shift of zero.
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return std::is_signed<T>::value && !x &&
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as_unsigned(shift) == as_unsigned(std::numeric_limits<T>::digits);
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}
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};
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template <typename T, typename U, class Enable = void>
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struct CheckedRshOp {};
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// Right shift. Shifts less than 0 or greater than or equal to the number
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// of bits in the promoted type are undefined. Otherwise, it is always defined,
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// but a right shift of a negative value is implementation-dependent.
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template <typename T, typename U>
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struct CheckedRshOp<T,
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U,
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typename std::enable_if<std::is_integral<T>::value &&
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std::is_integral<U>::value>::type> {
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using result_type = T;
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template <typename V>
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static bool Do(T x, U shift, V* result) {
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// Use the type conversion push negative values out of range.
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if (BASE_NUMERICS_LIKELY(as_unsigned(shift) <
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IntegerBitsPlusSign<T>::value)) {
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T tmp = x >> shift;
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*result = static_cast<V>(tmp);
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return IsValueInRangeForNumericType<V>(tmp);
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}
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return false;
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}
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};
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template <typename T, typename U, class Enable = void>
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struct CheckedAndOp {};
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// For simplicity we support only unsigned integer results.
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template <typename T, typename U>
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struct CheckedAndOp<T,
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U,
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typename std::enable_if<std::is_integral<T>::value &&
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std::is_integral<U>::value>::type> {
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using result_type = typename std::make_unsigned<
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typename MaxExponentPromotion<T, U>::type>::type;
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template <typename V>
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static constexpr bool Do(T x, U y, V* result) {
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result_type tmp = static_cast<result_type>(x) & static_cast<result_type>(y);
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*result = static_cast<V>(tmp);
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return IsValueInRangeForNumericType<V>(tmp);
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}
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};
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template <typename T, typename U, class Enable = void>
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struct CheckedOrOp {};
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// For simplicity we support only unsigned integers.
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template <typename T, typename U>
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struct CheckedOrOp<T,
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U,
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typename std::enable_if<std::is_integral<T>::value &&
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std::is_integral<U>::value>::type> {
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using result_type = typename std::make_unsigned<
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typename MaxExponentPromotion<T, U>::type>::type;
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template <typename V>
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static constexpr bool Do(T x, U y, V* result) {
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result_type tmp = static_cast<result_type>(x) | static_cast<result_type>(y);
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*result = static_cast<V>(tmp);
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return IsValueInRangeForNumericType<V>(tmp);
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}
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};
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template <typename T, typename U, class Enable = void>
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struct CheckedXorOp {};
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// For simplicity we support only unsigned integers.
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template <typename T, typename U>
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struct CheckedXorOp<T,
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U,
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typename std::enable_if<std::is_integral<T>::value &&
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std::is_integral<U>::value>::type> {
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using result_type = typename std::make_unsigned<
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typename MaxExponentPromotion<T, U>::type>::type;
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template <typename V>
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static constexpr bool Do(T x, U y, V* result) {
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result_type tmp = static_cast<result_type>(x) ^ static_cast<result_type>(y);
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*result = static_cast<V>(tmp);
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return IsValueInRangeForNumericType<V>(tmp);
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}
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};
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// Max doesn't really need to be implemented this way because it can't fail,
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// but it makes the code much cleaner to use the MathOp wrappers.
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template <typename T, typename U, class Enable = void>
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struct CheckedMaxOp {};
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template <typename T, typename U>
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struct CheckedMaxOp<
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T,
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U,
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typename std::enable_if<std::is_arithmetic<T>::value &&
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std::is_arithmetic<U>::value>::type> {
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using result_type = typename MaxExponentPromotion<T, U>::type;
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template <typename V>
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static constexpr bool Do(T x, U y, V* result) {
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result_type tmp = IsGreater<T, U>::Test(x, y) ? static_cast<result_type>(x)
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: static_cast<result_type>(y);
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*result = static_cast<V>(tmp);
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return IsValueInRangeForNumericType<V>(tmp);
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}
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};
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// Min doesn't really need to be implemented this way because it can't fail,
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// but it makes the code much cleaner to use the MathOp wrappers.
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template <typename T, typename U, class Enable = void>
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struct CheckedMinOp {};
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template <typename T, typename U>
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struct CheckedMinOp<
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T,
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U,
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typename std::enable_if<std::is_arithmetic<T>::value &&
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std::is_arithmetic<U>::value>::type> {
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using result_type = typename LowestValuePromotion<T, U>::type;
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template <typename V>
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static constexpr bool Do(T x, U y, V* result) {
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result_type tmp = IsLess<T, U>::Test(x, y) ? static_cast<result_type>(x)
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: static_cast<result_type>(y);
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*result = static_cast<V>(tmp);
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return IsValueInRangeForNumericType<V>(tmp);
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}
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};
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// This is just boilerplate that wraps the standard floating point arithmetic.
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// A macro isn't the nicest solution, but it beats rewriting these repeatedly.
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#define BASE_FLOAT_ARITHMETIC_OPS(NAME, OP) \
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template <typename T, typename U> \
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struct Checked##NAME##Op< \
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T, U, \
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typename std::enable_if<std::is_floating_point<T>::value || \
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std::is_floating_point<U>::value>::type> { \
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using result_type = typename MaxExponentPromotion<T, U>::type; \
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template <typename V> \
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static constexpr bool Do(T x, U y, V* result) { \
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using Promotion = typename MaxExponentPromotion<T, U>::type; \
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Promotion presult = x OP y; \
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*result = static_cast<V>(presult); \
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return IsValueInRangeForNumericType<V>(presult); \
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} \
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};
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BASE_FLOAT_ARITHMETIC_OPS(Add, +)
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BASE_FLOAT_ARITHMETIC_OPS(Sub, -)
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BASE_FLOAT_ARITHMETIC_OPS(Mul, *)
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BASE_FLOAT_ARITHMETIC_OPS(Div, /)
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#undef BASE_FLOAT_ARITHMETIC_OPS
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// Floats carry around their validity state with them, but integers do not. So,
|
|
// we wrap the underlying value in a specialization in order to hide that detail
|
|
// and expose an interface via accessors.
|
|
enum NumericRepresentation {
|
|
NUMERIC_INTEGER,
|
|
NUMERIC_FLOATING,
|
|
NUMERIC_UNKNOWN
|
|
};
|
|
|
|
template <typename NumericType>
|
|
struct GetNumericRepresentation {
|
|
static const NumericRepresentation value =
|
|
std::is_integral<NumericType>::value
|
|
? NUMERIC_INTEGER
|
|
: (std::is_floating_point<NumericType>::value ? NUMERIC_FLOATING
|
|
: NUMERIC_UNKNOWN);
|
|
};
|
|
|
|
template <typename T,
|
|
NumericRepresentation type = GetNumericRepresentation<T>::value>
|
|
class CheckedNumericState {};
|
|
|
|
// Integrals require quite a bit of additional housekeeping to manage state.
|
|
template <typename T>
|
|
class CheckedNumericState<T, NUMERIC_INTEGER> {
|
|
private:
|
|
// is_valid_ precedes value_ because member intializers in the constructors
|
|
// are evaluated in field order, and is_valid_ must be read when initializing
|
|
// value_.
|
|
bool is_valid_;
|
|
T value_;
|
|
|
|
// Ensures that a type conversion does not trigger undefined behavior.
|
|
template <typename Src>
|
|
static constexpr T WellDefinedConversionOrZero(const Src value,
|
|
const bool is_valid) {
|
|
using SrcType = typename internal::UnderlyingType<Src>::type;
|
|
return (std::is_integral<SrcType>::value || is_valid)
|
|
? static_cast<T>(value)
|
|
: static_cast<T>(0);
|
|
}
|
|
|
|
public:
|
|
template <typename Src, NumericRepresentation type>
|
|
friend class CheckedNumericState;
|
|
|
|
constexpr CheckedNumericState() : is_valid_(true), value_(0) {}
|
|
|
|
template <typename Src>
|
|
constexpr CheckedNumericState(Src value, bool is_valid)
|
|
: is_valid_(is_valid && IsValueInRangeForNumericType<T>(value)),
|
|
value_(WellDefinedConversionOrZero(value, is_valid_)) {
|
|
static_assert(std::is_arithmetic<Src>::value, "Argument must be numeric.");
|
|
}
|
|
|
|
// Copy constructor.
|
|
template <typename Src>
|
|
constexpr CheckedNumericState(const CheckedNumericState<Src>& rhs)
|
|
: is_valid_(rhs.IsValid()),
|
|
value_(WellDefinedConversionOrZero(rhs.value(), is_valid_)) {}
|
|
|
|
template <typename Src>
|
|
constexpr explicit CheckedNumericState(Src value)
|
|
: is_valid_(IsValueInRangeForNumericType<T>(value)),
|
|
value_(WellDefinedConversionOrZero(value, is_valid_)) {}
|
|
|
|
constexpr bool is_valid() const { return is_valid_; }
|
|
constexpr T value() const { return value_; }
|
|
};
|
|
|
|
// Floating points maintain their own validity, but need translation wrappers.
|
|
template <typename T>
|
|
class CheckedNumericState<T, NUMERIC_FLOATING> {
|
|
private:
|
|
T value_;
|
|
|
|
// Ensures that a type conversion does not trigger undefined behavior.
|
|
template <typename Src>
|
|
static constexpr T WellDefinedConversionOrNaN(const Src value,
|
|
const bool is_valid) {
|
|
using SrcType = typename internal::UnderlyingType<Src>::type;
|
|
return (StaticDstRangeRelationToSrcRange<T, SrcType>::value ==
|
|
NUMERIC_RANGE_CONTAINED ||
|
|
is_valid)
|
|
? static_cast<T>(value)
|
|
: std::numeric_limits<T>::quiet_NaN();
|
|
}
|
|
|
|
public:
|
|
template <typename Src, NumericRepresentation type>
|
|
friend class CheckedNumericState;
|
|
|
|
constexpr CheckedNumericState() : value_(0.0) {}
|
|
|
|
template <typename Src>
|
|
constexpr CheckedNumericState(Src value, bool is_valid)
|
|
: value_(WellDefinedConversionOrNaN(value, is_valid)) {}
|
|
|
|
template <typename Src>
|
|
constexpr explicit CheckedNumericState(Src value)
|
|
: value_(WellDefinedConversionOrNaN(
|
|
value,
|
|
IsValueInRangeForNumericType<T>(value))) {}
|
|
|
|
// Copy constructor.
|
|
template <typename Src>
|
|
constexpr CheckedNumericState(const CheckedNumericState<Src>& rhs)
|
|
: value_(WellDefinedConversionOrNaN(
|
|
rhs.value(),
|
|
rhs.is_valid() && IsValueInRangeForNumericType<T>(rhs.value()))) {}
|
|
|
|
constexpr bool is_valid() const {
|
|
// Written this way because std::isfinite is not reliably constexpr.
|
|
return MustTreatAsConstexpr(value_)
|
|
? value_ <= std::numeric_limits<T>::max() &&
|
|
value_ >= std::numeric_limits<T>::lowest()
|
|
: std::isfinite(value_);
|
|
}
|
|
constexpr T value() const { return value_; }
|
|
};
|
|
|
|
} // namespace internal
|
|
} // namespace base
|
|
|
|
#endif // BASE_NUMERICS_CHECKED_MATH_IMPL_H_
|