ceph/src/rapidjson/include/rapidjson/internal/biginteger.h

   1 // Tencent is pleased to support the open source community by making RapidJSON available.
   2 //
   3 // Copyright (C) 2015 THL A29 Limited, a Tencent company, and Milo Yip. All rights reserved.
   4 //
   5 // Licensed under the MIT License (the "License"); you may not use this file except
   6 // in compliance with the License. You may obtain a copy of the License at
   7 //
   8 // http://opensource.org/licenses/MIT
   9 //
  10 // Unless required by applicable law or agreed to in writing, software distributed
  11 // under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR
  12 // CONDITIONS OF ANY KIND, either express or implied. See the License for the
  13 // specific language governing permissions and limitations under the License.
  14
  15 #ifndef RAPIDJSON_BIGINTEGER_H_
  16 #define RAPIDJSON_BIGINTEGER_H_
  17
  18 #include "../rapidjson.h"
  19
  20 #if defined(_MSC_VER) && defined(_M_AMD64)
  21 #include <intrin.h> // for _umul128
  22 #pragma intrinsic(_umul128)
  23 #endif
  24
  25 RAPIDJSON_NAMESPACE_BEGIN
  26 namespace internal {
  27
  28 class BigInteger {
  29 public:
  30     typedef uint64_t Type;
  31
  32     BigInteger(const BigInteger& rhs) : count_(rhs.count_) {
  33         std::memcpy(digits_, rhs.digits_, count_ * sizeof(Type));
  34     }
  35
  36     explicit BigInteger(uint64_t u) : count_(1) {
  37         digits_[0] = u;
  38     }
  39
  40     BigInteger(const char* decimals, size_t length) : count_(1) {
  41         RAPIDJSON_ASSERT(length > 0);
  42         digits_[0] = 0;
  43         size_t i = 0;
  44         const size_t kMaxDigitPerIteration = 19;  // 2^64 = 18446744073709551616 > 10^19
  45         while (length >= kMaxDigitPerIteration) {
  46             AppendDecimal64(decimals + i, decimals + i + kMaxDigitPerIteration);
  47             length -= kMaxDigitPerIteration;
  48             i += kMaxDigitPerIteration;
  49         }
  50
  51         if (length > 0)
  52             AppendDecimal64(decimals + i, decimals + i + length);
  53     }
  54
  55     BigInteger& operator=(const BigInteger &rhs)
  56     {
  57         if (this != &rhs) {
  58             count_ = rhs.count_;
  59             std::memcpy(digits_, rhs.digits_, count_ * sizeof(Type));
  60         }
  61         return *this;
  62     }
  63
  64     BigInteger& operator=(uint64_t u) {
  65         digits_[0] = u;
  66         count_ = 1;
  67         return *this;
  68     }
  69
  70     BigInteger& operator+=(uint64_t u) {
  71         Type backup = digits_[0];
  72         digits_[0] += u;
  73         for (size_t i = 0; i < count_ - 1; i++) {
  74             if (digits_[i] >= backup)
  75                 return *this; // no carry
  76             backup = digits_[i + 1];
  77             digits_[i + 1] += 1;
  78         }
  79
  80         // Last carry
  81         if (digits_[count_ - 1] < backup)
  82             PushBack(1);
  83
  84         return *this;
  85     }
  86
  87     BigInteger& operator*=(uint64_t u) {
  88         if (u == 0) return *this = 0;
  89         if (u == 1) return *this;
  90         if (*this == 1) return *this = u;
  91
  92         uint64_t k = 0;
  93         for (size_t i = 0; i < count_; i++) {
  94             uint64_t hi;
  95             digits_[i] = MulAdd64(digits_[i], u, k, &hi);
  96             k = hi;
  97         }
  98
  99         if (k > 0)
 100             PushBack(k);
 101
 102         return *this;
 103     }
 104
 105     BigInteger& operator*=(uint32_t u) {
 106         if (u == 0) return *this = 0;
 107         if (u == 1) return *this;
 108         if (*this == 1) return *this = u;
 109
 110         uint64_t k = 0;
 111         for (size_t i = 0; i < count_; i++) {
 112             const uint64_t c = digits_[i] >> 32;
 113             const uint64_t d = digits_[i] & 0xFFFFFFFF;
 114             const uint64_t uc = u * c;
 115             const uint64_t ud = u * d;
 116             const uint64_t p0 = ud + k;
 117             const uint64_t p1 = uc + (p0 >> 32);
 118             digits_[i] = (p0 & 0xFFFFFFFF) | (p1 << 32);
 119             k = p1 >> 32;
 120         }
 121
 122         if (k > 0)
 123             PushBack(k);
 124
 125         return *this;
 126     }
 127
 128     BigInteger& operator<<=(size_t shift) {
 129         if (IsZero() || shift == 0) return *this;
 130
 131         size_t offset = shift / kTypeBit;
 132         size_t interShift = shift % kTypeBit;
 133         RAPIDJSON_ASSERT(count_ + offset <= kCapacity);
 134
 135         if (interShift == 0) {
 136             std::memmove(&digits_[count_ - 1 + offset], &digits_[count_ - 1], count_ * sizeof(Type));
 137             count_ += offset;
 138         }
 139         else {
 140             digits_[count_] = 0;
 141             for (size_t i = count_; i > 0; i--)
 142                 digits_[i + offset] = (digits_[i] << interShift) | (digits_[i - 1] >> (kTypeBit - interShift));
 143             digits_[offset] = digits_[0] << interShift;
 144             count_ += offset;
 145             if (digits_[count_])
 146                 count_++;
 147         }
 148
 149         std::memset(digits_, 0, offset * sizeof(Type));
 150
 151         return *this;
 152     }
 153
 154     bool operator==(const BigInteger& rhs) const {
 155         return count_ == rhs.count_ && std::memcmp(digits_, rhs.digits_, count_ * sizeof(Type)) == 0;
 156     }
 157
 158     bool operator==(const Type rhs) const {
 159         return count_ == 1 && digits_[0] == rhs;
 160     }
 161
 162     BigInteger& MultiplyPow5(unsigned exp) {
 163         static const uint32_t kPow5[12] = {
 164             5,
 165             5 * 5,
 166             5 * 5 * 5,
 167             5 * 5 * 5 * 5,
 168             5 * 5 * 5 * 5 * 5,
 169             5 * 5 * 5 * 5 * 5 * 5,
 170             5 * 5 * 5 * 5 * 5 * 5 * 5,
 171             5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
 172             5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
 173             5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
 174             5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
 175             5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5
 176         };
 177         if (exp == 0) return *this;
 178         for (; exp >= 27; exp -= 27) *this *= RAPIDJSON_UINT64_C2(0X6765C793, 0XFA10079D); // 5^27
 179         for (; exp >= 13; exp -= 13) *this *= static_cast<uint32_t>(1220703125u); // 5^13
 180         if (exp > 0)                 *this *= kPow5[exp - 1];
 181         return *this;
 182     }
 183
 184     // Compute absolute difference of this and rhs.
 185     // Assume this != rhs
 186     bool Difference(const BigInteger& rhs, BigInteger* out) const {
 187         int cmp = Compare(rhs);
 188         RAPIDJSON_ASSERT(cmp != 0);
 189         const BigInteger *a, *b;  // Makes a > b
 190         bool ret;
 191         if (cmp < 0) { a = &rhs; b = this; ret = true; }
 192         else         { a = this; b = &rhs; ret = false; }
 193
 194         Type borrow = 0;
 195         for (size_t i = 0; i < a->count_; i++) {
 196             Type d = a->digits_[i] - borrow;
 197             if (i < b->count_)
 198                 d -= b->digits_[i];
 199             borrow = (d > a->digits_[i]) ? 1 : 0;
 200             out->digits_[i] = d;
 201             if (d != 0)
 202                 out->count_ = i + 1;
 203         }
 204
 205         return ret;
 206     }
 207
 208     int Compare(const BigInteger& rhs) const {
 209         if (count_ != rhs.count_)
 210             return count_ < rhs.count_ ? -1 : 1;
 211
 212         for (size_t i = count_; i-- > 0;)
 213             if (digits_[i] != rhs.digits_[i])
 214                 return digits_[i] < rhs.digits_[i] ? -1 : 1;
 215
 216         return 0;
 217     }
 218
 219     size_t GetCount() const { return count_; }
 220     Type GetDigit(size_t index) const { RAPIDJSON_ASSERT(index < count_); return digits_[index]; }
 221     bool IsZero() const { return count_ == 1 && digits_[0] == 0; }
 222
 223 private:
 224     void AppendDecimal64(const char* begin, const char* end) {
 225         uint64_t u = ParseUint64(begin, end);
 226         if (IsZero())
 227             *this = u;
 228         else {
 229             unsigned exp = static_cast<unsigned>(end - begin);
 230             (MultiplyPow5(exp) <<= exp) += u;   // *this = *this * 10^exp + u
 231         }
 232     }
 233
 234     void PushBack(Type digit) {
 235         RAPIDJSON_ASSERT(count_ < kCapacity);
 236         digits_[count_++] = digit;
 237     }
 238
 239     static uint64_t ParseUint64(const char* begin, const char* end) {
 240         uint64_t r = 0;
 241         for (const char* p = begin; p != end; ++p) {
 242             RAPIDJSON_ASSERT(*p >= '0' && *p <= '9');
 243             r = r * 10u + static_cast<unsigned>(*p - '0');
 244         }
 245         return r;
 246     }
 247
 248     // Assume a * b + k < 2^128
 249     static uint64_t MulAdd64(uint64_t a, uint64_t b, uint64_t k, uint64_t* outHigh) {
 250 #if defined(_MSC_VER) && defined(_M_AMD64)
 251         uint64_t low = _umul128(a, b, outHigh) + k;
 252         if (low < k)
 253             (*outHigh)++;
 254         return low;
 255 #elif (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6)) && defined(__x86_64__)
 256         __extension__ typedef unsigned __int128 uint128;
 257         uint128 p = static_cast<uint128>(a) * static_cast<uint128>(b);
 258         p += k;
 259         *outHigh = static_cast<uint64_t>(p >> 64);
 260         return static_cast<uint64_t>(p);
 261 #else
 262         const uint64_t a0 = a & 0xFFFFFFFF, a1 = a >> 32, b0 = b & 0xFFFFFFFF, b1 = b >> 32;
 263         uint64_t x0 = a0 * b0, x1 = a0 * b1, x2 = a1 * b0, x3 = a1 * b1;
 264         x1 += (x0 >> 32); // can't give carry
 265         x1 += x2;
 266         if (x1 < x2)
 267             x3 += (static_cast<uint64_t>(1) << 32);
 268         uint64_t lo = (x1 << 32) + (x0 & 0xFFFFFFFF);
 269         uint64_t hi = x3 + (x1 >> 32);
 270
 271         lo += k;
 272         if (lo < k)
 273             hi++;
 274         *outHigh = hi;
 275         return lo;
 276 #endif
 277     }
 278
 279     static const size_t kBitCount = 3328;  // 64bit * 54 > 10^1000
 280     static const size_t kCapacity = kBitCount / sizeof(Type);
 281     static const size_t kTypeBit = sizeof(Type) * 8;
 282
 283     Type digits_[kCapacity];
 284     size_t count_;
 285 };
 286
 287 } // namespace internal
 288 RAPIDJSON_NAMESPACE_END
 289
 290 #endif // RAPIDJSON_BIGINTEGER_H_