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https://github.com/fmtlib/fmt.git
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Implement more bigint operations
This commit is contained in:
Victor Zverovich
parent
c41cea8b18
commit
b60114533f
@ -496,23 +496,81 @@ class bigint {
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using bigit = uint32_t;
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using double_bigit = uint64_t;
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basic_memory_buffer<bigit> bigits_;
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int exp_;
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static FMT_CONSTEXPR_DECL const int bigit_bits = bits<bigit>::value;
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friend struct formatter<bigint>;
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void assign(uint64_t n) {
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int num_bigits = bits<uint64_t>::value / bigit_bits;
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bigits_.resize(num_bigits);
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for (int i = 0; i < num_bigits; ++i) {
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bigits_[i] = n & ~bigit(0);
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int 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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}
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} while (n != 0);
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bigits_.resize(num_bigits);
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}
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public:
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bigint() {}
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explicit bigint(uint64_t n) { assign(n); }
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bigint() : exp_(0) {}
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template <typename Int> explicit bigint(Int n) : exp_(0) {
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assign(uint32_or_64_or_128_t<Int>(to_unsigned(n)));
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}
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bigint(const bigint&) = delete;
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void operator=(const bigint&) = delete;
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int num_bigits() const { return static_cast<int>(bigits_.size()) + exp_; }
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bigint& operator<<=(int shift) {
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assert(shift >= 0);
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exp_ += shift / bigit_bits;
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shift %= bigit_bits;
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if (shift == 0) return *this;
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bigit carry = 0;
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for (size_t i = 0, n = bigits_.size(); i < n; ++i) {
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bigit c = bigits_[i] >> (bigit_bits - shift);
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bigits_[i] = (bigits_[i] << shift) + carry;
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carry = c;
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}
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if (carry != 0) bigits_.push_back(carry);
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return *this;
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}
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bigint& operator*=(uint32_t value) {
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assert(value > 0);
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// Verify that the computation cannot overflow.
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constexpr double_bigit max_bigit = max_value<bigit>();
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constexpr double_bigit max_double_bigit = max_value<double_bigit>();
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static_assert(max_bigit * max_bigit <= max_double_bigit - max_bigit, "");
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bigit carry = 0;
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const double_bigit wide_value = value;
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for (size_t i = 0, n = bigits_.size(); i < n; ++i) {
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double_bigit result = bigits_[i] * wide_value + carry;
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bigits_[i] = static_cast<bigit>(result);
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carry = static_cast<bigit>(result >> bigit_bits);
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}
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if (carry != 0) bigits_.push_back(carry);
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return *this;
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}
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friend bool operator<=(const bigint& lhs, const bigint& rhs) {
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int num_lhs_bigits = lhs.num_bigits(), num_rhs_bigits = rhs.num_bigits();
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if (num_lhs_bigits != num_rhs_bigits)
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return num_lhs_bigits < num_rhs_bigits;
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int lhs_bigit_index = static_cast<int>(lhs.bigits_.size()) - 1;
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int rhs_bigit_index = static_cast<int>(rhs.bigits_.size()) - 1;
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int end = lhs_bigit_index > rhs_bigit_index
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? lhs_bigit_index - rhs_bigit_index
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: 0;
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for (; lhs_bigit_index >= end; --lhs_bigit_index, --rhs_bigit_index) {
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bigit lhs_bigit = lhs.bigits_[lhs_bigit_index];
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bigit rhs_bigit = rhs.bigits_[rhs_bigit_index];
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if (lhs_bigit != rhs_bigit) return lhs_bigit < rhs_bigit;
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}
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return lhs_bigit_index <= rhs_bigit_index;
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}
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// Assigns pow(10, exp) to this bigint.
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void assign_pow10(int exp) {
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@ -534,14 +592,11 @@ class bigint {
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*this <<= exp; // Multiply by pow(2, exp) by shifting.
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}
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bigint(const bigint&) = delete;
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void operator=(const bigint&) = delete;
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void square() {
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basic_memory_buffer<bigit> n(std::move(bigits_));
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int num_bigits = static_cast<int>(bigits_.size());
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int num_result_bigints = 2 * num_bigits;
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bigits_.resize(num_result_bigints);
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int num_result_bigits = 2 * num_bigits;
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bigits_.resize(num_result_bigits);
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using accumulator_t = conditional_t<FMT_USE_INT128, uint128_t, accumulator>;
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auto sum = accumulator_t();
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for (int bigit_index = 0; bigit_index < num_bigits; ++bigit_index) {
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@ -555,7 +610,7 @@ class bigint {
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sum >>= bits<bigit>::value; // Compute the carry.
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}
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// Do the same for the top half.
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for (int bigit_index = num_bigits; bigit_index < num_result_bigints;
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for (int bigit_index = num_bigits; bigit_index < num_result_bigits;
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++bigit_index) {
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for (int j = num_bigits - 1, i = bigit_index - j; i < num_bigits;
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++i, --j) {
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@ -564,35 +619,26 @@ class bigint {
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bigits_[bigit_index] = static_cast<bigit>(sum);
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sum >>= bits<bigit>::value;
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}
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// Remove leading zeros.
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--num_result_bigits;
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while (num_result_bigits > 0 && bigits_[num_result_bigits] == 0)
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--num_result_bigits;
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bigits_.resize(num_result_bigits + 1);
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exp_ *= 2;
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}
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bigint& operator<<=(int shift) {
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assert(shift >= 0 && shift < bigit_bits);
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bigit carry = 0;
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for (size_t i = 0, n = bigits_.size(); i < n; ++i) {
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bigit c = shift != 0 ? bigits_[i] >> (bigit_bits - shift) : 0;
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bigits_[i] = (bigits_[i] << shift) + carry;
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carry = c;
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// Divides this bignum by divisor, assigning the remainder to this and
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// returning the quotient.
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int divmod_assign(const bigint& divisor) {
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bigit lhs_bigit = bigits_[bigits_.size() - 1];
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bigit rhs_bigit = divisor.bigits_[divisor.bigits_.size() - 1];
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// TODO: test the case of rhs == max
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bigit quotient =
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(rhs_bigit + 1 != 0) ? lhs_bigit / (rhs_bigit + 1) : lhs_bigit;
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while (divisor <= *this) {
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// TODO: subtract
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}
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if (carry != 0) bigits_.push_back(carry);
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return *this;
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}
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bigint& operator*=(uint32_t value) {
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assert(value > 0);
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// Verify that the computation doesn't overflow.
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constexpr double_bigit max32 = max_value<bigit>();
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constexpr double_bigit max64 = max_value<double_bigit>();
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static_assert(max32 * max32 <= max64 - max32, "");
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bigit carry = 0;
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const double_bigit wide_value = value;
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for (size_t i = 0, n = bigits_.size(); i < n; ++i) {
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double_bigit result = bigits_[i] * wide_value + carry;
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bigits_[i] = static_cast<bigit>(result);
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carry = static_cast<bigit>(result >> bigit_bits);
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}
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if (carry != 0) bigits_.push_back(carry);
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return *this;
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return quotient;
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}
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};
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@ -816,12 +862,25 @@ template <int GRISU_VERSION> struct grisu_shortest_handler {
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}
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};
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// Format value using a variation of the Fixed-Precision Positive Floating-Point
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// Printout ((FPP)^2) algorithm by Steele & White.
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FMT_FUNC void fallback_format(const fp& value, int exp10) {
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bigint big_value(value.f), pow10;
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bigint big_value(value.f); // R in (FPP)^2.
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bigint pow10; // S in (FPP)^2.
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bigint lower(uint32_t(1)); // M^- in (FPP)^2.
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bigint upper(uint32_t(1)); // M^+ in (FPP)^2.
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if (value.e >= 0) {
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big_value <<= value.e;
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big_value <<= value.e + 1;
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pow10.assign_pow10(exp10);
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pow10 <<= 1;
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lower <<= value.e;
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upper <<= value.e;
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} else {
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// TODO: handle negative exponent
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}
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// v = (big_value / pow10) * pow(10, exp10).
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int digit = big_value.divmod_assign(pow10);
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(void)digit;
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// TODO
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}
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@ -982,13 +1041,14 @@ template <> struct formatter<internal::bigint> {
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for (auto i = n.bigits_.size(); i > 0; --i) {
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auto value = n.bigits_[i - 1];
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if (first) {
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if (value == 0 && i > 1) continue;
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out = format_to(out, "{:x}", value);
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first = false;
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continue;
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}
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out = format_to(out, "{:08x}", value);
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}
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if (n.exp_ > 0)
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out = format_to(out, "p{}", n.exp_ * internal::bigint::bigit_bits);
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return out;
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}
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};
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@ -35,6 +35,21 @@ TEST(BigIntTest, Construct) {
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EXPECT_EQ("123456789abcedf0", fmt::format("{}", bigint(0x123456789abcedf0)));
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}
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TEST(BigIntTest, LessEqual) {
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bigint n1(42);
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bigint n2(42);
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EXPECT_TRUE(n1 <= n2);
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n2 <<= 32;
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EXPECT_TRUE(n1 <= n2);
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EXPECT_FALSE(n2 <= n1);
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bigint n3(43);
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EXPECT_TRUE(n1 <= n3);
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EXPECT_FALSE(n3 <= n1);
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bigint n4(42 * 0x100000001);
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EXPECT_TRUE(n2 <= n4);
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EXPECT_FALSE(n4 <= n2);
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}
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TEST(BigIntTest, ShiftLeft) {
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bigint n(0x42);
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n <<= 0;
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@ -89,6 +104,9 @@ TEST(BigIntTest, Square) {
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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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bigint n4;
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n4.assign_pow10(10);
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EXPECT_EQ("2540be400", fmt::format("{}", n4));
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}
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template <bool is_iec559> void test_construct_from_double() {
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@ -321,8 +339,7 @@ TEST(FormatTest, CountCodePoints) {
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// Tests fmt::internal::count_digits for integer type Int.
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template <typename Int> void test_count_digits() {
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for (Int i = 0; i < 10; ++i) EXPECT_EQ(1u, fmt::internal::count_digits(i));
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for (Int i = 1, n = 1, end = max_value<Int>() / 10; n <= end;
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++i) {
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for (Int i = 1, n = 1, end = max_value<Int>() / 10; n <= end; ++i) {
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n *= 10;
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EXPECT_EQ(i, fmt::internal::count_digits(n - 1));
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EXPECT_EQ(i + 1, fmt::internal::count_digits(n));
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