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Add 128-bit operations to bigint
This commit is contained in:
Victor Zverovich
parent
ef54f9aa38
commit
b4dc7a1d34
@ -368,23 +368,36 @@ class bigint {
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if (carry != 0) bigits_.push_back(carry);
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}
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FMT_CONSTEXPR20 void multiply(uint64_t value) {
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const bigit mask = ~bigit(0);
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const double_bigit lower = value & mask;
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const double_bigit upper = value >> bigit_bits;
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double_bigit carry = 0;
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template <typename UInt, FMT_ENABLE_IF(std::is_same<UInt, uint64_t>::value ||
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std::is_same<UInt, uint128_t>::value)>
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FMT_CONSTEXPR20 void multiply(UInt value) {
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const UInt lower = static_cast<bigit>(value);
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const UInt upper = value >> bigit_bits;
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UInt carry = 0;
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for (size_t i = 0, n = bigits_.size(); i < n; ++i) {
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double_bigit result = bigits_[i] * lower + (carry & mask);
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UInt result = lower * bigits_[i] + static_cast<bigit>(carry);
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carry =
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bigits_[i] * upper + (result >> bigit_bits) + (carry >> bigit_bits);
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upper * bigits_[i] + (result >> bigit_bits) + (carry >> bigit_bits);
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bigits_[i] = static_cast<bigit>(result);
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}
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while (carry != 0) {
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bigits_.push_back(carry & mask);
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bigits_.push_back(static_cast<bigit>(carry));
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carry >>= bigit_bits;
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}
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}
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template <typename UInt, FMT_ENABLE_IF(std::is_same<UInt, uint64_t>::value ||
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std::is_same<UInt, uint128_t>::value)>
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FMT_CONSTEXPR20 void assign(UInt n) {
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size_t num_bigits = 0;
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do {
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bigits_[num_bigits++] = static_cast<bigit>(n);
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n >>= bigit_bits;
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} while (n != 0);
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bigits_.resize(num_bigits);
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exp_ = 0;
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}
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public:
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FMT_CONSTEXPR20 bigint() : exp_(0) {}
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explicit bigint(uint64_t n) { assign(n); }
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@ -400,14 +413,9 @@ class bigint {
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exp_ = other.exp_;
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}
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FMT_CONSTEXPR20 void assign(uint64_t n) {
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size_t num_bigits = 0;
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do {
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bigits_[num_bigits++] = n & ~bigit(0);
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n >>= bigit_bits;
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} while (n != 0);
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bigits_.resize(num_bigits);
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exp_ = 0;
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template <typename Int> FMT_CONSTEXPR20 void operator=(Int n) {
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FMT_ASSERT(n > 0, "");
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assign(uint64_or_128_t<Int>(n));
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}
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FMT_CONSTEXPR20 int num_bigits() const {
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@ -478,14 +486,14 @@ class bigint {
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// Assigns pow(10, exp) to this bigint.
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FMT_CONSTEXPR20 void assign_pow10(int exp) {
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FMT_ASSERT(exp >= 0, "");
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if (exp == 0) return assign(1);
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if (exp == 0) return *this = 1;
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// Find the top bit.
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int bitmask = 1;
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while (exp >= bitmask) bitmask <<= 1;
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bitmask >>= 1;
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// pow(10, exp) = pow(5, exp) * pow(2, exp). First compute pow(5, exp) by
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// repeated squaring and multiplication.
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assign(5);
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*this = 5;
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bitmask >>= 1;
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while (bitmask != 0) {
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square();
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@ -2061,12 +2069,12 @@ FMT_CONSTEXPR20 inline void format_dragon(fp value, unsigned flags,
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bool is_predecessor_closer = (flags & dragon::predecessor_closer) != 0;
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int shift = is_predecessor_closer ? 2 : 1;
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if (value.e >= 0) {
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numerator.assign(value.f);
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numerator = value.f;
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numerator <<= value.e + shift;
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lower.assign(1);
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lower = 1;
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lower <<= value.e;
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if (is_predecessor_closer) {
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upper_store.assign(1);
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upper_store = 1;
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upper_store <<= value.e + 1;
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upper = &upper_store;
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}
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@ -2082,16 +2090,16 @@ FMT_CONSTEXPR20 inline void format_dragon(fp value, unsigned flags,
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}
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numerator *= value.f;
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numerator <<= shift;
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denominator.assign(1);
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denominator = 1;
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denominator <<= shift - value.e;
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} else {
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numerator.assign(value.f);
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numerator = value.f;
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numerator <<= shift;
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denominator.assign_pow10(exp10);
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denominator <<= shift - value.e;
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lower.assign(1);
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lower = 1;
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if (is_predecessor_closer) {
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upper_store.assign(1ULL << 1);
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upper_store = 1ULL << 1;
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upper = &upper_store;
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}
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}
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@ -2278,13 +2286,14 @@ FMT_HEADER_ONLY_CONSTEXPR20 int format_float(Float value, int precision,
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} // namespace detail
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template <> struct formatter<detail::bigint> {
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FMT_CONSTEXPR format_parse_context::iterator parse(
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format_parse_context& ctx) {
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FMT_CONSTEXPR auto parse(format_parse_context& ctx)
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-> format_parse_context::iterator {
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return ctx.begin();
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}
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format_context::iterator format(const detail::bigint& n,
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format_context& ctx) {
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template <typename FormatContext>
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auto format(const detail::bigint& n, FormatContext& ctx) const ->
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typename FormatContext::iterator {
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auto out = ctx.out();
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bool first = true;
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for (auto i = n.bigits_.size(); i > 0; --i) {
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@ -339,6 +339,10 @@ class uint128_fallback {
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const uint128_fallback& rhs) -> bool {
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return !(lhs == rhs);
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}
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friend auto operator>(const uint128_fallback& lhs,
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const uint128_fallback& rhs) -> bool {
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return lhs.hi_ != rhs.hi_ ? lhs.hi_ > rhs.hi_ : lhs.lo_ > rhs.lo_;
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}
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friend auto operator|(const uint128_fallback& lhs,
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const uint128_fallback& rhs) -> uint128_fallback {
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return {lhs.hi_ | rhs.hi_, lhs.lo_ | rhs.lo_};
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@ -347,6 +351,16 @@ class uint128_fallback {
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const uint128_fallback& rhs) -> uint128_fallback {
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return {lhs.hi_ & rhs.hi_, lhs.lo_ & rhs.lo_};
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}
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friend auto operator+(const uint128_fallback& lhs,
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const uint128_fallback& rhs) -> uint128_fallback {
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auto result = uint128_fallback(lhs);
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result += rhs;
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return result;
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}
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friend auto operator*(const uint128_fallback&, uint32_t) -> uint128_fallback {
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FMT_ASSERT(false, "");
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return {};
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}
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friend auto operator-(const uint128_fallback& lhs, uint64_t rhs)
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-> uint128_fallback {
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FMT_ASSERT(lhs.lo_ >= rhs, "");
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@ -973,10 +987,9 @@ template <typename T>
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using uint32_or_64_or_128_t =
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conditional_t<num_bits<T>() <= 32 && !FMT_REDUCE_INT_INSTANTIATIONS,
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uint32_t,
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conditional_t<num_bits<T>() <= 64, uint64_t, uint128_opt>>;
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conditional_t<num_bits<T>() <= 64, uint64_t, uint128_t>>;
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template <typename T>
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using uint64_or_128_t =
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conditional_t<num_bits<T>() <= 64, uint64_t, uint128_opt>;
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using uint64_or_128_t = conditional_t<num_bits<T>() <= 64, uint64_t, uint128_t>;
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#define FMT_POWERS_OF_10(factor) \
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factor * 10, (factor)*100, (factor)*1000, (factor)*10000, (factor)*100000, \
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@ -24,9 +24,9 @@ static_assert(!std::is_copy_constructible<bigint>::value, "");
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static_assert(!std::is_copy_assignable<bigint>::value, "");
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TEST(bigint_test, construct) {
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EXPECT_EQ("", fmt::format("{}", bigint()));
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EXPECT_EQ("42", fmt::format("{}", bigint(0x42)));
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EXPECT_EQ("123456789abcedf0", fmt::format("{}", bigint(0x123456789abcedf0)));
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EXPECT_EQ(fmt::to_string(bigint()), "");
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EXPECT_EQ(fmt::to_string(bigint(0x42)), "42");
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EXPECT_EQ(fmt::to_string(bigint(0x123456789abcedf0)), "123456789abcedf0");
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}
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TEST(bigint_test, compare) {
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@ -72,46 +72,56 @@ TEST(bigint_test, add_compare) {
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TEST(bigint_test, shift_left) {
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bigint n(0x42);
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n <<= 0;
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EXPECT_EQ("42", fmt::format("{}", n));
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EXPECT_EQ(fmt::to_string(n), "42");
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n <<= 1;
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EXPECT_EQ("84", fmt::format("{}", n));
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EXPECT_EQ(fmt::to_string(n), "84");
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n <<= 25;
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EXPECT_EQ("108000000", fmt::format("{}", n));
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EXPECT_EQ(fmt::to_string(n), "108000000");
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}
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TEST(bigint_test, multiply) {
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bigint n(0x42);
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EXPECT_THROW(n *= 0, assertion_failure);
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n *= 1;
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EXPECT_EQ("42", fmt::format("{}", n));
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EXPECT_EQ(fmt::to_string(n), "42");
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n *= 2;
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EXPECT_EQ("84", fmt::format("{}", n));
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EXPECT_EQ(fmt::to_string(n), "84");
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n *= 0x12345678;
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EXPECT_EQ("962fc95e0", fmt::format("{}", n));
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EXPECT_EQ(fmt::to_string(n), "962fc95e0");
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bigint bigmax(max_value<uint32_t>());
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bigmax *= max_value<uint32_t>();
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EXPECT_EQ("fffffffe00000001", fmt::format("{}", bigmax));
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bigmax.assign(max_value<uint64_t>());
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bigmax *= max_value<uint64_t>();
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EXPECT_EQ("fffffffffffffffe0000000000000001", fmt::format("{}", bigmax));
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EXPECT_EQ(fmt::to_string(bigmax), "fffffffe00000001");
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const auto max64 = max_value<uint64_t>();
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bigmax = max64;
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bigmax *= max64;
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EXPECT_EQ(fmt::to_string(bigmax), "fffffffffffffffe0000000000000001");
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const auto max128 = (fmt::detail::uint128_t(max64) << 64) | max64;
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bigmax = max128;
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// bigmax *= max128;
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// EXPECT_EQ(fmt::to_string(bigmax),
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// "fffffffffffffffffffffffffffffffe00000000000000000000000000000001");
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}
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TEST(bigint_test, square) {
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bigint n0(0);
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n0.square();
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EXPECT_EQ("0", fmt::format("{}", n0));
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EXPECT_EQ(fmt::to_string(n0), "0");
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bigint n1(0x100);
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n1.square();
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EXPECT_EQ("10000", fmt::format("{}", n1));
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EXPECT_EQ(fmt::to_string(n1), "10000");
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bigint n2(0xfffffffff);
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n2.square();
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EXPECT_EQ("ffffffffe000000001", fmt::format("{}", n2));
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EXPECT_EQ(fmt::to_string(n2), "ffffffffe000000001");
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bigint n3(max_value<uint64_t>());
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n3.square();
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EXPECT_EQ("fffffffffffffffe0000000000000001", fmt::format("{}", n3));
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EXPECT_EQ(fmt::to_string(n3), "fffffffffffffffe0000000000000001");
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bigint n4;
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n4.assign_pow10(10);
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EXPECT_EQ("2540be400", fmt::format("{}", n4));
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EXPECT_EQ(fmt::to_string(n4), "2540be400");
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}
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TEST(bigint_test, divmod_assign_zero_divisor) {
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@ -133,8 +143,8 @@ TEST(bigint_test, divmod_assign_unaligned) {
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n2.assign_pow10(100);
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int result = n1.divmod_assign(n2);
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EXPECT_EQ(result, 9406);
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EXPECT_EQ("10f8353019583bfc29ffc8f564e1b9f9d819dbb4cf783e4507eca1539220p96",
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fmt::format("{}", n1));
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EXPECT_EQ(fmt::to_string(n1),
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"10f8353019583bfc29ffc8f564e1b9f9d819dbb4cf783e4507eca1539220p96");
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}
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TEST(bigint_test, divmod_assign) {
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@ -142,19 +152,19 @@ TEST(bigint_test, divmod_assign) {
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bigint n1(100);
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int result = n1.divmod_assign(bigint(10));
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EXPECT_EQ(result, 10);
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EXPECT_EQ("0", fmt::format("{}", n1));
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EXPECT_EQ(fmt::to_string(n1), "0");
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// pow(10, 100) / (42 << 320):
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n1.assign_pow10(100);
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result = n1.divmod_assign(bigint(42) <<= 320);
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EXPECT_EQ(result, 111);
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EXPECT_EQ("13ad2594c37ceb0b2784c4ce0bf38ace408e211a7caab24308a82e8f10p96",
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fmt::format("{}", n1));
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EXPECT_EQ(fmt::to_string(n1),
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"13ad2594c37ceb0b2784c4ce0bf38ace408e211a7caab24308a82e8f10p96");
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// 42 / 100:
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bigint n2(42);
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n1.assign_pow10(2);
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result = n2.divmod_assign(n1);
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EXPECT_EQ(result, 0);
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EXPECT_EQ("2a", fmt::format("{}", n2));
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EXPECT_EQ(fmt::to_string(n2), "2a");
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}
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template <bool is_iec559> void run_double_tests() {
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@ -173,8 +183,8 @@ TEST(fp_test, double_tests) {
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TEST(fp_test, normalize) {
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const auto v = fp(0xbeef, 42);
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auto normalized = normalize(v);
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EXPECT_EQ(0xbeef000000000000, normalized.f);
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EXPECT_EQ(-6, normalized.e);
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EXPECT_EQ(normalized.f, 0xbeef000000000000);
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EXPECT_EQ(normalized.e, -6);
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}
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TEST(fp_test, multiply) {
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@ -200,8 +210,8 @@ TEST(fp_test, get_cached_power) {
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cache <<= power.e;
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exact.align(cache);
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cache.align(exact);
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auto exact_str = fmt::format("{}", exact);
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auto cache_str = fmt::format("{}", cache);
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auto exact_str = fmt::to_string(exact);
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auto cache_str = fmt::to_string(cache);
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EXPECT_EQ(exact_str.size(), cache_str.size());
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EXPECT_EQ(exact_str.substr(0, 15), cache_str.substr(0, 15));
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int diff = cache_str[15] - exact_str[15];
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@ -212,11 +222,11 @@ TEST(fp_test, get_cached_power) {
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} else {
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cache.assign_pow10(-dec_exp);
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cache *= power.f + 1; // Inexact check.
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exact.assign(1);
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exact = 1;
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exact <<= -power.e;
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exact.align(cache);
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auto exact_str = fmt::format("{}", exact);
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auto cache_str = fmt::format("{}", cache);
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auto exact_str = fmt::to_string(exact);
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auto cache_str = fmt::to_string(cache);
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EXPECT_EQ(exact_str.size(), cache_str.size());
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EXPECT_EQ(exact_str.substr(0, 16), cache_str.substr(0, 16));
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}
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@ -242,25 +252,25 @@ TEST(fp_test, dragonbox_max_k) {
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TEST(fp_test, get_round_direction) {
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using fmt::detail::get_round_direction;
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using fmt::detail::round_direction;
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EXPECT_EQ(round_direction::down, get_round_direction(100, 50, 0));
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EXPECT_EQ(round_direction::up, get_round_direction(100, 51, 0));
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EXPECT_EQ(round_direction::down, get_round_direction(100, 40, 10));
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EXPECT_EQ(round_direction::up, get_round_direction(100, 60, 10));
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EXPECT_EQ(get_round_direction(100, 50, 0), round_direction::down);
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EXPECT_EQ(get_round_direction(100, 51, 0), round_direction::up);
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EXPECT_EQ(get_round_direction(100, 40, 10), round_direction::down);
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EXPECT_EQ(get_round_direction(100, 60, 10), round_direction::up);
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for (size_t i = 41; i < 60; ++i)
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EXPECT_EQ(round_direction::unknown, get_round_direction(100, i, 10));
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EXPECT_EQ(get_round_direction(100, i, 10), round_direction::unknown);
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uint64_t max = max_value<uint64_t>();
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EXPECT_THROW(get_round_direction(100, 100, 0), assertion_failure);
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EXPECT_THROW(get_round_direction(100, 0, 100), assertion_failure);
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EXPECT_THROW(get_round_direction(100, 0, 50), assertion_failure);
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// Check that remainder + error doesn't overflow.
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EXPECT_EQ(round_direction::up, get_round_direction(max, max - 1, 2));
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EXPECT_EQ(get_round_direction(max, max - 1, 2), round_direction::up);
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// Check that 2 * (remainder + error) doesn't overflow.
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EXPECT_EQ(round_direction::unknown,
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get_round_direction(max, max / 2 + 1, max / 2));
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EXPECT_EQ(get_round_direction(max, max / 2 + 1, max / 2),
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round_direction::unknown);
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// Check that remainder - error doesn't overflow.
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EXPECT_EQ(round_direction::unknown, get_round_direction(100, 40, 41));
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EXPECT_EQ(get_round_direction(100, 40, 41), round_direction::unknown);
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// Check that 2 * (remainder - error) doesn't overflow.
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EXPECT_EQ(round_direction::up, get_round_direction(max, max - 1, 1));
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EXPECT_EQ(get_round_direction(max, max - 1, 1), round_direction::up);
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}
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TEST(fp_test, fixed_handler) {
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@ -283,20 +293,20 @@ TEST(fp_test, fixed_handler) {
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}
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TEST(fp_test, grisu_format_compiles_with_on_ieee_double) {
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fmt::memory_buffer buf;
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auto buf = fmt::memory_buffer();
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format_float(0.42, -1, fmt::detail::float_specs(), buf);
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}
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TEST(format_impl_test, format_error_code) {
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std::string msg = "error 42", sep = ": ";
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{
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fmt::memory_buffer buffer;
|
||||
auto buffer = fmt::memory_buffer();
|
||||
format_to(fmt::appender(buffer), "garbage");
|
||||
fmt::detail::format_error_code(buffer, 42, "test");
|
||||
EXPECT_EQ("test: " + msg, to_string(buffer));
|
||||
EXPECT_EQ(to_string(buffer), "test: " + msg);
|
||||
}
|
||||
{
|
||||
fmt::memory_buffer buffer;
|
||||
auto buffer = fmt::memory_buffer();
|
||||
auto prefix =
|
||||
std::string(fmt::inline_buffer_size - msg.size() - sep.size() + 1, 'x');
|
||||
fmt::detail::format_error_code(buffer, 42, prefix);
|
||||
@ -317,7 +327,7 @@ TEST(format_impl_test, format_error_code) {
|
||||
// Test with a message that doesn't fit into the buffer.
|
||||
prefix += 'x';
|
||||
fmt::detail::format_error_code(buffer, codes[i], prefix);
|
||||
EXPECT_EQ(msg, to_string(buffer));
|
||||
EXPECT_EQ(to_string(buffer), msg);
|
||||
}
|
||||
}
|
||||
|
||||
@ -333,8 +343,8 @@ template <typename Int> void test_count_digits() {
|
||||
for (Int i = 0; i < 10; ++i) EXPECT_EQ(1u, fmt::detail::count_digits(i));
|
||||
for (Int i = 1, n = 1, end = max_value<Int>() / 10; n <= end; ++i) {
|
||||
n *= 10;
|
||||
EXPECT_EQ(i, fmt::detail::count_digits(n - 1));
|
||||
EXPECT_EQ(i + 1, fmt::detail::count_digits(n));
|
||||
EXPECT_EQ(fmt::detail::count_digits(n - 1), i);
|
||||
EXPECT_EQ(fmt::detail::count_digits(n), i + 1);
|
||||
}
|
||||
}
|
||||
|
||||
@ -345,11 +355,9 @@ TEST(format_impl_test, count_digits) {
|
||||
|
||||
#ifdef _WIN32
|
||||
# include <windows.h>
|
||||
#endif
|
||||
|
||||
#ifdef _WIN32
|
||||
TEST(format_impl_test, write_console_signature) {
|
||||
decltype(WriteConsoleW)* p = fmt::detail::WriteConsoleW;
|
||||
decltype(::WriteConsoleW)* p = fmt::detail::WriteConsoleW;
|
||||
(void)p;
|
||||
}
|
||||
#endif
|
||||
|
||||
Loading…
Reference in New Issue
Block a user