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1 // Protocol Buffers - Google's data interchange format
2 // Copyright 2008 Google Inc.  All rights reserved.
3 // https://developers.google.com/protocol-buffers/
4 //
5 // Redistribution and use in source and binary forms, with or without
6 // modification, are permitted provided that the following conditions are
7 // met:
8 //
9 //     * Redistributions of source code must retain the above copyright
10 // notice, this list of conditions and the following disclaimer.
11 //     * Redistributions in binary form must reproduce the above
12 // copyright notice, this list of conditions and the following disclaimer
13 // in the documentation and/or other materials provided with the
14 // distribution.
15 //     * Neither the name of Google Inc. nor the names of its
16 // contributors may be used to endorse or promote products derived from
17 // this software without specific prior written permission.
18 //
19 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
20 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
21 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
22 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
23 // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
24 // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
25 // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
26 // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
27 // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
28 // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
29 // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
30 
31 #include <google/protobuf/stubs/int128.h>
32 
33 #include <iomanip>
34 #include <ostream>  // NOLINT(readability/streams)
35 #include <sstream>
36 
37 namespace google {
38 namespace protobuf {
39 
40 const uint128_pod kuint128max = {
41     static_cast<uint64>(GOOGLE_LONGLONG(0xFFFFFFFFFFFFFFFF)),
42     static_cast<uint64>(GOOGLE_LONGLONG(0xFFFFFFFFFFFFFFFF))
43 };
44 
45 // Returns the 0-based position of the last set bit (i.e., most significant bit)
46 // in the given uint64. The argument may not be 0.
47 //
48 // For example:
49 //   Given: 5 (decimal) == 101 (binary)
50 //   Returns: 2
51 #define STEP(T, n, pos, sh)                   \
52   do {                                        \
53     if ((n) >= (static_cast<T>(1) << (sh))) { \
54       (n) = (n) >> (sh);                      \
55       (pos) |= (sh);                          \
56     }                                         \
57   } while (0)
Fls64(uint64 n)58 static inline int Fls64(uint64 n) {
59   GOOGLE_DCHECK_NE(0, n);
60   int pos = 0;
61   STEP(uint64, n, pos, 0x20);
62   uint32 n32 = n;
63   STEP(uint32, n32, pos, 0x10);
64   STEP(uint32, n32, pos, 0x08);
65   STEP(uint32, n32, pos, 0x04);
66   return pos + ((GOOGLE_ULONGLONG(0x3333333322221100) >> (n32 << 2)) & 0x3);
67 }
68 #undef STEP
69 
70 // Like Fls64() above, but returns the 0-based position of the last set bit
71 // (i.e., most significant bit) in the given uint128. The argument may not be 0.
Fls128(uint128 n)72 static inline int Fls128(uint128 n) {
73   if (uint64 hi = Uint128High64(n)) {
74     return Fls64(hi) + 64;
75   }
76   return Fls64(Uint128Low64(n));
77 }
78 
79 // Long division/modulo for uint128 implemented using the shift-subtract
80 // division algorithm adapted from:
81 // http://stackoverflow.com/questions/5386377/division-without-using
DivModImpl(uint128 dividend,uint128 divisor,uint128 * quotient_ret,uint128 * remainder_ret)82 void uint128::DivModImpl(uint128 dividend, uint128 divisor,
83                          uint128* quotient_ret, uint128* remainder_ret) {
84   if (divisor == 0) {
85     GOOGLE_LOG(FATAL) << "Division or mod by zero: dividend.hi=" << dividend.hi_
86                       << ", lo=" << dividend.lo_;
87   }
88 
89   if (divisor > dividend) {
90     *quotient_ret = 0;
91     *remainder_ret = dividend;
92     return;
93   }
94 
95   if (divisor == dividend) {
96     *quotient_ret = 1;
97     *remainder_ret = 0;
98     return;
99   }
100 
101   uint128 denominator = divisor;
102   uint128 position = 1;
103   uint128 quotient = 0;
104 
105   // Left aligns the MSB of the denominator and the dividend.
106   int shift = Fls128(dividend) - Fls128(denominator);
107   denominator <<= shift;
108   position <<= shift;
109 
110   // Uses shift-subtract algorithm to divide dividend by denominator. The
111   // remainder will be left in dividend.
112   while (position > 0) {
113     if (dividend >= denominator) {
114       dividend -= denominator;
115       quotient |= position;
116     }
117     position >>= 1;
118     denominator >>= 1;
119   }
120 
121   *quotient_ret = quotient;
122   *remainder_ret = dividend;
123 }
124 
operator /=(const uint128 & divisor)125 uint128& uint128::operator/=(const uint128& divisor) {
126   uint128 quotient = 0;
127   uint128 remainder = 0;
128   DivModImpl(*this, divisor, &quotient, &remainder);
129   *this = quotient;
130   return *this;
131 }
operator %=(const uint128 & divisor)132 uint128& uint128::operator%=(const uint128& divisor) {
133   uint128 quotient = 0;
134   uint128 remainder = 0;
135   DivModImpl(*this, divisor, &quotient, &remainder);
136   *this = remainder;
137   return *this;
138 }
139 
operator <<(std::ostream & o,const uint128 & b)140 std::ostream& operator<<(std::ostream& o, const uint128& b) {
141   std::ios_base::fmtflags flags = o.flags();
142 
143   // Select a divisor which is the largest power of the base < 2^64.
144   uint128 div;
145   std::streamsize div_base_log;
146   switch (flags & std::ios::basefield) {
147     case std::ios::hex:
148       div = static_cast<uint64>(GOOGLE_ULONGLONG(0x1000000000000000));  // 16^15
149       div_base_log = 15;
150       break;
151     case std::ios::oct:
152       div = static_cast<uint64>(GOOGLE_ULONGLONG(01000000000000000000000));  // 8^21
153       div_base_log = 21;
154       break;
155     default:  // std::ios::dec
156       div = static_cast<uint64>(GOOGLE_ULONGLONG(10000000000000000000));  // 10^19
157       div_base_log = 19;
158       break;
159   }
160 
161   // Now piece together the uint128 representation from three chunks of
162   // the original value, each less than "div" and therefore representable
163   // as a uint64.
164   std::ostringstream os;
165   std::ios_base::fmtflags copy_mask =
166       std::ios::basefield | std::ios::showbase | std::ios::uppercase;
167   os.setf(flags & copy_mask, copy_mask);
168   uint128 high = b;
169   uint128 low;
170   uint128::DivModImpl(high, div, &high, &low);
171   uint128 mid;
172   uint128::DivModImpl(high, div, &high, &mid);
173   if (high.lo_ != 0) {
174     os << high.lo_;
175     os << std::noshowbase << std::setfill('0') << std::setw(div_base_log);
176     os << mid.lo_;
177     os << std::setw(div_base_log);
178   } else if (mid.lo_ != 0) {
179     os << mid.lo_;
180     os << std::noshowbase << std::setfill('0') << std::setw(div_base_log);
181   }
182   os << low.lo_;
183   std::string rep = os.str();
184 
185   // Add the requisite padding.
186   std::streamsize width = o.width(0);
187   if (width > rep.size()) {
188     if ((flags & std::ios::adjustfield) == std::ios::left) {
189       rep.append(width - rep.size(), o.fill());
190     } else {
191       rep.insert(static_cast<std::string::size_type>(0),
192                  width - rep.size(), o.fill());
193     }
194   }
195 
196   // Stream the final representation in a single "<<" call.
197   return o << rep;
198 }
199 
200 }  // namespace protobuf
201 }  // namespace google
202