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<div class="title">saturated_arithmetic.h</div> </div>
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<a href="saturated__arithmetic_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// Copyright 2010-2018 Google LLC</span></div>
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<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
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<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">// you may not use this file except in compliance with the License.</span></div>
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<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// You may obtain a copy of the License at</span></div>
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<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
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<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
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<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
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<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
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<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment">// See the License for the specific language governing permissions and</span></div>
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<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment">// limitations under the License.</span></div>
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<div class="line"><a name="l00013"></a><span class="lineno"> 13</span>  </div>
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<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="preprocessor">#ifndef OR_TOOLS_UTIL_SATURATED_ARITHMETIC_H_</span></div>
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<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="preprocessor">#define OR_TOOLS_UTIL_SATURATED_ARITHMETIC_H_</span></div>
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<div class="line"><a name="l00016"></a><span class="lineno"> 16</span>  </div>
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<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="preprocessor">#include "absl/base/casts.h"</span></div>
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<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="preprocessor">#include "<a class="code" href="integral__types_8h.html">ortools/base/integral_types.h</a>"</span></div>
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<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="preprocessor">#include "<a class="code" href="bitset_8h.html">ortools/util/bitset.h</a>"</span></div>
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<div class="line"><a name="l00020"></a><span class="lineno"> 20</span>  </div>
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<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="keyword">namespace </span><a class="code" href="namespaceoperations__research.html">operations_research</a> {</div>
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<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="comment">// ---------- Overflow utility functions ----------</span></div>
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<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>  </div>
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<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment">// Implement two's complement addition and subtraction on int64s.</span></div>
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<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment">// The C and C++ standards specify that the overflow of signed integers is</span></div>
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<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment">// undefined. This is because of the different possible representations that may</span></div>
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<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment">// be used for signed integers (one's complement, two's complement, sign and</span></div>
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<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="comment">// magnitude). Such overflows are detected by Address Sanitizer with</span></div>
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<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="comment">// -fsanitize=signed-integer-overflow.</span></div>
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<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment">// Simple, portable overflow detection on current machines relies on</span></div>
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<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment">// these two functions. For example, if the sign of the sum of two positive</span></div>
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<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment">// integers is negative, there has been an overflow.</span></div>
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<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment">// Note that the static assert will break if the code is compiled on machines</span></div>
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<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment">// which do not use two's complement.</span></div>
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<div class="line"><a name="l00038"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#a7765571e7ec374ba667a3ccd16dcd124"> 38</a></span> <span class="keyword">inline</span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> <a class="code" href="namespaceoperations__research.html#a7765571e7ec374ba667a3ccd16dcd124">TwosComplementAddition</a>(<a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> x, <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> y) {</div>
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<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  static_assert(<span class="keyword">static_cast<</span><a class="code" href="integral__types_8h.html#abc0f5bc07737e498f287334775dff2b6">uint64</a><span class="keyword">></span>(-1LL) == ~0ULL,</div>
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<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  <span class="stringliteral">"The target architecture does not use two's complement."</span>);</div>
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<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <span class="keywordflow">return</span> absl::bit_cast<int64>(<span class="keyword">static_cast<</span><a class="code" href="integral__types_8h.html#abc0f5bc07737e498f287334775dff2b6">uint64</a><span class="keyword">></span>(x) + <span class="keyword">static_cast<</span><a class="code" href="integral__types_8h.html#abc0f5bc07737e498f287334775dff2b6">uint64</a><span class="keyword">></span>(y));</div>
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<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> }</div>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  </div>
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<div class="line"><a name="l00044"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#a2510acb08f15d9d639b286e91dfae6f2"> 44</a></span> <span class="keyword">inline</span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> <a class="code" href="namespaceoperations__research.html#a2510acb08f15d9d639b286e91dfae6f2">TwosComplementSubtraction</a>(<a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> x, <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> y) {</div>
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<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  static_assert(<span class="keyword">static_cast<</span><a class="code" href="integral__types_8h.html#abc0f5bc07737e498f287334775dff2b6">uint64</a><span class="keyword">></span>(-1LL) == ~0ULL,</div>
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<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  <span class="stringliteral">"The target architecture does not use two's complement."</span>);</div>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  <span class="keywordflow">return</span> absl::bit_cast<int64>(<span class="keyword">static_cast<</span><a class="code" href="integral__types_8h.html#abc0f5bc07737e498f287334775dff2b6">uint64</a><span class="keyword">></span>(x) - <span class="keyword">static_cast<</span><a class="code" href="integral__types_8h.html#abc0f5bc07737e498f287334775dff2b6">uint64</a><span class="keyword">></span>(y));</div>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> }</div>
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<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  </div>
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<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="comment">// Helper function that returns true if an overflow has occured in computing</span></div>
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<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment">// sum = x + y. sum is expected to be computed elsewhere.</span></div>
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<div class="line"><a name="l00052"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#aa1a2e7e0cdde05b5ef898461b90eede0"> 52</a></span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceoperations__research.html#aa1a2e7e0cdde05b5ef898461b90eede0">AddHadOverflow</a>(<a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> x, <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> y, <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> sum) {</div>
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<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="comment">// Overflow cannot occur if operands have different signs.</span></div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="comment">// It can only occur if sign(x) == sign(y) and sign(sum) != sign(x),</span></div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <span class="comment">// which is equivalent to: sign(x) != sign(sum) && sign(y) != sign(sum).</span></div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="comment">// This is captured when the expression below is negative.</span></div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  DCHECK_EQ(sum, <a class="code" href="namespaceoperations__research.html#a7765571e7ec374ba667a3ccd16dcd124">TwosComplementAddition</a>(x, y));</div>
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<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="keywordflow">return</span> ((x ^ sum) & (y ^ sum)) < 0;</div>
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<div class="line"><a name="l00059"></a><span class="lineno"> 59</span> }</div>
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<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  </div>
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<div class="line"><a name="l00061"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#a5fd04dbb1346d8877b5ed54aa291ffbc"> 61</a></span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceoperations__research.html#a5fd04dbb1346d8877b5ed54aa291ffbc">SubHadOverflow</a>(<a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> x, <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> y, <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> diff) {</div>
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<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="comment">// This is the same reasoning as for AddHadOverflow. We have x = diff + y.</span></div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="comment">// The formula is the same, with 'x' and diff exchanged.</span></div>
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<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  DCHECK_EQ(diff, <a class="code" href="namespaceoperations__research.html#a2510acb08f15d9d639b286e91dfae6f2">TwosComplementSubtraction</a>(x, y));</div>
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<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceoperations__research.html#aa1a2e7e0cdde05b5ef898461b90eede0">AddHadOverflow</a>(diff, y, x);</div>
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<div class="line"><a name="l00066"></a><span class="lineno"> 66</span> }</div>
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<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  </div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span> <span class="comment">// A note on overflow treatment.</span></div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</span> <span class="comment">// kint64min and kint64max are treated as infinity.</span></div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span> <span class="comment">// Thus if the computation overflows, the result is always kint64m(ax/in).</span></div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span> <span class="comment">// Note(user): this is actually wrong: when computing A-B, if A is kint64max</span></div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="comment">// and B is finite, then A-B won't be kint64max: overflows aren't sticky.</span></div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="comment">// TODO(user): consider making some operations overflow-sticky, some others</span></div>
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<div class="line"><a name="l00075"></a><span class="lineno"> 75</span> <span class="comment">// not, but make an explicit choice throughout.</span></div>
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<div class="line"><a name="l00076"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#af85f78b7f431f22bf062f8df29e9b41f"> 76</a></span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceoperations__research.html#af85f78b7f431f22bf062f8df29e9b41f">AddOverflows</a>(<a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> x, <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> y) {</div>
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<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceoperations__research.html#aa1a2e7e0cdde05b5ef898461b90eede0">AddHadOverflow</a>(x, y, <a class="code" href="namespaceoperations__research.html#a7765571e7ec374ba667a3ccd16dcd124">TwosComplementAddition</a>(x, y));</div>
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<div class="line"><a name="l00078"></a><span class="lineno"> 78</span> }</div>
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<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  </div>
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<div class="line"><a name="l00080"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#a5a78d7de748c8b1aa1bc9f00c5e59f17"> 80</a></span> <span class="keyword">inline</span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> <a class="code" href="namespaceoperations__research.html#a5a78d7de748c8b1aa1bc9f00c5e59f17">SubOverflows</a>(<a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> x, <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> y) {</div>
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<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceoperations__research.html#a5fd04dbb1346d8877b5ed54aa291ffbc">SubHadOverflow</a>(x, y, <a class="code" href="namespaceoperations__research.html#a2510acb08f15d9d639b286e91dfae6f2">TwosComplementSubtraction</a>(x, y));</div>
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<div class="line"><a name="l00082"></a><span class="lineno"> 82</span> }</div>
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<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  </div>
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<div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <span class="comment">// Performs *b += a and returns false iff the addition overflow or underflow.</span></div>
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<div class="line"><a name="l00085"></a><span class="lineno"> 85</span> <span class="comment">// This function only works for typed integer type (IntType<>).</span></div>
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<div class="line"><a name="l00086"></a><span class="lineno"> 86</span> <span class="keyword">template</span> <<span class="keyword">typename</span> IntegerType></div>
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<div class="line"><a name="l00087"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#ae1bd0133149b70b678b123524541aaad"> 87</a></span> <span class="keywordtype">bool</span> <a class="code" href="namespaceoperations__research.html#ae1bd0133149b70b678b123524541aaad">SafeAddInto</a>(IntegerType <a class="code" href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a>, IntegerType* <a class="code" href="constraint__solver_2table_8cc.html#a344010e26426d6a13411648d988bc9b6">b</a>) {</div>
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<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  <span class="keyword">const</span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> x = <a class="code" href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a>.value();</div>
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<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  <span class="keyword">const</span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> y = <a class="code" href="constraint__solver_2table_8cc.html#a344010e26426d6a13411648d988bc9b6">b</a>->value();</div>
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<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <span class="keyword">const</span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> sum = <a class="code" href="namespaceoperations__research.html#a7765571e7ec374ba667a3ccd16dcd124">TwosComplementAddition</a>(x, y);</div>
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<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <span class="keywordflow">if</span> (<a class="code" href="namespaceoperations__research.html#aa1a2e7e0cdde05b5ef898461b90eede0">AddHadOverflow</a>(x, y, sum)) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  *<a class="code" href="constraint__solver_2table_8cc.html#a344010e26426d6a13411648d988bc9b6">b</a> = sum;</div>
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<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><a name="l00094"></a><span class="lineno"> 94</span> }</div>
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<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  </div>
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<div class="line"><a name="l00096"></a><span class="lineno"> 96</span> <span class="comment">// Returns kint64max if x >= 0 and kint64min if x < 0.</span></div>
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<div class="line"><a name="l00097"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#a29f503f49388eeb29b06c6423d0aaeb6"> 97</a></span> <span class="keyword">inline</span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> <a class="code" href="namespaceoperations__research.html#a29f503f49388eeb29b06c6423d0aaeb6">CapWithSignOf</a>(<a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> x) {</div>
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<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="comment">// return kint64max if x >= 0 or kint64max + 1 (== kint64min) if x < 0.</span></div>
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<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceoperations__research.html#a7765571e7ec374ba667a3ccd16dcd124">TwosComplementAddition</a>(<a class="code" href="integral__types_8h.html#a74ea76ea27f48fb1b6e148e1577b3719">kint64max</a>, <span class="keyword">static_cast<</span><a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a><span class="keyword">></span>(x < 0));</div>
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<div class="line"><a name="l00100"></a><span class="lineno"> 100</span> }</div>
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<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  </div>
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<div class="line"><a name="l00102"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#a974e8ea7651bd25ff7edf9b1c33393a4"> 102</a></span> <span class="keyword">inline</span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> <a class="code" href="namespaceoperations__research.html#a974e8ea7651bd25ff7edf9b1c33393a4">CapAddGeneric</a>(<a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> x, <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> y) {</div>
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<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="keyword">const</span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> result = <a class="code" href="namespaceoperations__research.html#a7765571e7ec374ba667a3ccd16dcd124">TwosComplementAddition</a>(x, y);</div>
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<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceoperations__research.html#aa1a2e7e0cdde05b5ef898461b90eede0">AddHadOverflow</a>(x, y, result) ? <a class="code" href="namespaceoperations__research.html#a29f503f49388eeb29b06c6423d0aaeb6">CapWithSignOf</a>(x) : result;</div>
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<div class="line"><a name="l00105"></a><span class="lineno"> 105</span> }</div>
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<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  </div>
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<div class="line"><a name="l00107"></a><span class="lineno"> 107</span> <span class="preprocessor">#if defined(__GNUC__) && defined(__x86_64__)</span></div>
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<div class="line"><a name="l00108"></a><span class="lineno"> 108</span> <span class="comment">// TODO(user): port this to other architectures.</span></div>
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<div class="line"><a name="l00109"></a><span class="lineno"> 109</span> <span class="keyword">inline</span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> CapAddFast(<a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> x, <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> y) {</div>
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<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <span class="keyword">const</span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> cap = <a class="code" href="namespaceoperations__research.html#a29f503f49388eeb29b06c6423d0aaeb6">CapWithSignOf</a>(x);</div>
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<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> result = x;</div>
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<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="comment">// clang-format off</span></div>
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<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="keyword">asm</span> <span class="keyword">volatile</span>( <span class="comment">// 'volatile': ask compiler optimizer "keep as is".</span></div>
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<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  <span class="stringliteral">"\t"</span> <span class="stringliteral">"addq %[y],%[result]"</span></div>
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<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <span class="stringliteral">"\n\t"</span> <span class="stringliteral">"cmovoq %[cap],%[result]"</span> <span class="comment">// Conditional move if overflow.</span></div>
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<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  : [result] <span class="stringliteral">"=r"</span>(result) <span class="comment">// Output</span></div>
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<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  : <span class="stringliteral">"[result]"</span> (result), [y] <span class="stringliteral">"r"</span>(y), [cap] <span class="stringliteral">"r"</span>(cap) <span class="comment">// Input.</span></div>
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<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  : <span class="stringliteral">"cc"</span> <span class="comment">/* Clobbered registers */</span> );</div>
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<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <span class="comment">// clang-format on</span></div>
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<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="keywordflow">return</span> result;</div>
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<div class="line"><a name="l00121"></a><span class="lineno"> 121</span> }</div>
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<div class="line"><a name="l00122"></a><span class="lineno"> 122</span> <span class="preprocessor">#endif</span></div>
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<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  </div>
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<div class="line"><a name="l00124"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#a99264812cf177270e521f226a5c012c3"> 124</a></span> <span class="keyword">inline</span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> <a class="code" href="namespaceoperations__research.html#a99264812cf177270e521f226a5c012c3">CapAdd</a>(<a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> x, <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> y) {</div>
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<div class="line"><a name="l00125"></a><span class="lineno"> 125</span> <span class="preprocessor">#if defined(__GNUC__) && defined(__x86_64__)</span></div>
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<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  <span class="keywordflow">return</span> CapAddFast(x, y);</div>
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<div class="line"><a name="l00127"></a><span class="lineno"> 127</span> <span class="preprocessor">#else</span></div>
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<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceoperations__research.html#a974e8ea7651bd25ff7edf9b1c33393a4">CapAddGeneric</a>(x, y);</div>
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<div class="line"><a name="l00129"></a><span class="lineno"> 129</span> <span class="preprocessor">#endif</span></div>
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<div class="line"><a name="l00130"></a><span class="lineno"> 130</span> }</div>
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<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  </div>
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<div class="line"><a name="l00132"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#a43c47f9b8343b3ebf98671abffdd0f9a"> 132</a></span> <span class="keyword">inline</span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> <a class="code" href="namespaceoperations__research.html#a43c47f9b8343b3ebf98671abffdd0f9a">CapSubGeneric</a>(<a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> x, <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> y) {</div>
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<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <span class="keyword">const</span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> result = <a class="code" href="namespaceoperations__research.html#a2510acb08f15d9d639b286e91dfae6f2">TwosComplementSubtraction</a>(x, y);</div>
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<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceoperations__research.html#a5fd04dbb1346d8877b5ed54aa291ffbc">SubHadOverflow</a>(x, y, result) ? <a class="code" href="namespaceoperations__research.html#a29f503f49388eeb29b06c6423d0aaeb6">CapWithSignOf</a>(x) : result;</div>
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<div class="line"><a name="l00135"></a><span class="lineno"> 135</span> }</div>
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<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  </div>
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<div class="line"><a name="l00137"></a><span class="lineno"> 137</span> <span class="preprocessor">#if defined(__GNUC__) && defined(__x86_64__)</span></div>
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<div class="line"><a name="l00138"></a><span class="lineno"> 138</span> <span class="comment">// TODO(user): port this to other architectures.</span></div>
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<div class="line"><a name="l00139"></a><span class="lineno"> 139</span> <span class="keyword">inline</span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> CapSubFast(<a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> x, <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> y) {</div>
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<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  <span class="keyword">const</span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> cap = <a class="code" href="namespaceoperations__research.html#a29f503f49388eeb29b06c6423d0aaeb6">CapWithSignOf</a>(x);</div>
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<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> result = x;</div>
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<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  <span class="comment">// clang-format off</span></div>
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<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  <span class="keyword">asm</span> <span class="keyword">volatile</span>( <span class="comment">// 'volatile': ask compiler optimizer "keep as is".</span></div>
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<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  <span class="stringliteral">"\t"</span> <span class="stringliteral">"subq %[y],%[result]"</span></div>
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<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  <span class="stringliteral">"\n\t"</span> <span class="stringliteral">"cmovoq %[cap],%[result]"</span> <span class="comment">// Conditional move if overflow.</span></div>
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<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  : [result] <span class="stringliteral">"=r"</span>(result) <span class="comment">// Output</span></div>
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<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  : <span class="stringliteral">"[result]"</span> (result), [y] <span class="stringliteral">"r"</span>(y), [cap] <span class="stringliteral">"r"</span>(cap) <span class="comment">// Input.</span></div>
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<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  : <span class="stringliteral">"cc"</span> <span class="comment">/* Clobbered registers */</span> );</div>
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<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  <span class="comment">// clang-format on</span></div>
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<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <span class="keywordflow">return</span> result;</div>
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<div class="line"><a name="l00151"></a><span class="lineno"> 151</span> }</div>
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<div class="line"><a name="l00152"></a><span class="lineno"> 152</span> <span class="preprocessor">#endif</span></div>
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<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  </div>
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<div class="line"><a name="l00154"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#a228fe84d99348c2b62bb4f70a6371d9b"> 154</a></span> <span class="keyword">inline</span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> <a class="code" href="namespaceoperations__research.html#a228fe84d99348c2b62bb4f70a6371d9b">CapSub</a>(<a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> x, <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> y) {</div>
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<div class="line"><a name="l00155"></a><span class="lineno"> 155</span> <span class="preprocessor">#if defined(__GNUC__) && defined(__x86_64__)</span></div>
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<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  <span class="keywordflow">return</span> CapSubFast(x, y);</div>
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<div class="line"><a name="l00157"></a><span class="lineno"> 157</span> <span class="preprocessor">#else</span></div>
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<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceoperations__research.html#a43c47f9b8343b3ebf98671abffdd0f9a">CapSubGeneric</a>(x, y);</div>
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<div class="line"><a name="l00159"></a><span class="lineno"> 159</span> <span class="preprocessor">#endif</span></div>
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<div class="line"><a name="l00160"></a><span class="lineno"> 160</span> }</div>
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<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  </div>
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<div class="line"><a name="l00162"></a><span class="lineno"> 162</span> <span class="comment">// Note(user): -kint64min != kint64max, but kint64max == ~kint64min.</span></div>
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<div class="line"><a name="l00163"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#a8641e02da1d67eaa03fb37b66834a775"> 163</a></span> <span class="keyword">inline</span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> <a class="code" href="namespaceoperations__research.html#a8641e02da1d67eaa03fb37b66834a775">CapOpp</a>(<a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> v) { <span class="keywordflow">return</span> v == <a class="code" href="integral__types_8h.html#af458164b470cbba416d5ed579e00ff60">kint64min</a> ? ~v : -v; }</div>
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<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  </div>
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<div class="line"><a name="l00165"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1cap__prod__util.html"> 165</a></span> <span class="keyword">namespace </span>cap_prod_util {</div>
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<div class="line"><a name="l00166"></a><span class="lineno"> 166</span> <span class="comment">// Returns an unsigned int equal to the absolute value of n, in a way that</span></div>
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<div class="line"><a name="l00167"></a><span class="lineno"> 167</span> <span class="comment">// will not produce overflows.</span></div>
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<div class="line"><a name="l00168"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1cap__prod__util.html#ad44bdae4de79b78925cbf0fafaff273c"> 168</a></span> <span class="keyword">inline</span> <a class="code" href="integral__types_8h.html#abc0f5bc07737e498f287334775dff2b6">uint64</a> <a class="code" href="namespaceoperations__research_1_1cap__prod__util.html#ad44bdae4de79b78925cbf0fafaff273c">uint_abs</a>(<a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> n) {</div>
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<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  <span class="keywordflow">return</span> n < 0 ? ~static_cast<uint64>(n) + 1 : <span class="keyword">static_cast<</span><a class="code" href="integral__types_8h.html#abc0f5bc07737e498f287334775dff2b6">uint64</a><span class="keyword">></span>(n);</div>
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<div class="line"><a name="l00170"></a><span class="lineno"> 170</span> }</div>
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<div class="line"><a name="l00171"></a><span class="lineno"> 171</span> } <span class="comment">// namespace cap_prod_util</span></div>
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<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  </div>
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<div class="line"><a name="l00173"></a><span class="lineno"> 173</span> <span class="comment">// The generic algorithm computes a bound on the number of bits necessary to</span></div>
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<div class="line"><a name="l00174"></a><span class="lineno"> 174</span> <span class="comment">// store the result. For this it uses the position of the most significant bits</span></div>
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<div class="line"><a name="l00175"></a><span class="lineno"> 175</span> <span class="comment">// of each of the arguments.</span></div>
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<div class="line"><a name="l00176"></a><span class="lineno"> 176</span> <span class="comment">// If the result needs at least 64 bits, then return a capped value.</span></div>
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<div class="line"><a name="l00177"></a><span class="lineno"> 177</span> <span class="comment">// If the result needs at most 63 bits, then return the product.</span></div>
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<div class="line"><a name="l00178"></a><span class="lineno"> 178</span> <span class="comment">// Otherwise, the result may use 63 or 64 bits: compute the product</span></div>
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<div class="line"><a name="l00179"></a><span class="lineno"> 179</span> <span class="comment">// as a uint64, and cap it if necessary.</span></div>
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<div class="line"><a name="l00180"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#a20add29e703b41d64b8a01127aab2497"> 180</a></span> <span class="keyword">inline</span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> <a class="code" href="namespaceoperations__research.html#a20add29e703b41d64b8a01127aab2497">CapProdGeneric</a>(<a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> x, <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> y) {</div>
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<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  <span class="keyword">const</span> <a class="code" href="integral__types_8h.html#abc0f5bc07737e498f287334775dff2b6">uint64</a> <a class="code" href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a> = <a class="code" href="namespaceoperations__research_1_1cap__prod__util.html#ad44bdae4de79b78925cbf0fafaff273c">cap_prod_util::uint_abs</a>(x);</div>
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<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  <span class="keyword">const</span> <a class="code" href="integral__types_8h.html#abc0f5bc07737e498f287334775dff2b6">uint64</a> <a class="code" href="constraint__solver_2table_8cc.html#a344010e26426d6a13411648d988bc9b6">b</a> = <a class="code" href="namespaceoperations__research_1_1cap__prod__util.html#ad44bdae4de79b78925cbf0fafaff273c">cap_prod_util::uint_abs</a>(y);</div>
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<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  <span class="comment">// Let MSB(x) denote the most significant bit of x. We have:</span></div>
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<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  <span class="comment">// MSB(x) + MSB(y) <= MSB(x * y) <= MSB(x) + MSB(y) + 1</span></div>
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<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> msb_sum =</div>
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<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  <a class="code" href="namespaceoperations__research.html#a2f9ef253c023106392eb1495a277616b">MostSignificantBitPosition64</a>(<a class="code" href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a>) + <a class="code" href="namespaceoperations__research.html#a2f9ef253c023106392eb1495a277616b">MostSignificantBitPosition64</a>(<a class="code" href="constraint__solver_2table_8cc.html#a344010e26426d6a13411648d988bc9b6">b</a>);</div>
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<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> kMaxBitIndexInInt64 = 63;</div>
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<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  <span class="keywordflow">if</span> (msb_sum <= kMaxBitIndexInInt64 - 2) <span class="keywordflow">return</span> x * y;</div>
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<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  <span class="comment">// Catch a == 0 or b == 0 now, as MostSignificantBitPosition64(0) == 0.</span></div>
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<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  <span class="comment">// TODO(user): avoid this by writing function Log2(a) with Log2(0) == -1.</span></div>
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<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  <span class="keywordflow">if</span> (<a class="code" href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a> == 0 || <a class="code" href="constraint__solver_2table_8cc.html#a344010e26426d6a13411648d988bc9b6">b</a> == 0) <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  <span class="keyword">const</span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> cap = <a class="code" href="namespaceoperations__research.html#a29f503f49388eeb29b06c6423d0aaeb6">CapWithSignOf</a>(x ^ y);</div>
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<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  <span class="keywordflow">if</span> (msb_sum >= kMaxBitIndexInInt64) <span class="keywordflow">return</span> cap;</div>
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<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  <span class="comment">// The corner case is when msb_sum == 62, i.e. at least 63 bits will be</span></div>
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<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  <span class="comment">// needed to store the product. The following product will never overflow</span></div>
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<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  <span class="comment">// on uint64, since msb_sum == 62.</span></div>
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<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  <span class="keyword">const</span> <a class="code" href="integral__types_8h.html#abc0f5bc07737e498f287334775dff2b6">uint64</a> u_prod = <a class="code" href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a> * <a class="code" href="constraint__solver_2table_8cc.html#a344010e26426d6a13411648d988bc9b6">b</a>;</div>
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<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <span class="comment">// The overflow cases are captured by one of the following conditions:</span></div>
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<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <span class="comment">// (cap >= 0 && u_prod >= static_cast<uint64>(kint64max) or</span></div>
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<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  <span class="comment">// (cap < 0 && u_prod >= static_cast<uint64>(kint64min)).</span></div>
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<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  <span class="comment">// These can be optimized as follows (and if the condition is false, it is</span></div>
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<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  <span class="comment">// safe to compute x * y.</span></div>
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<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  <span class="keywordflow">if</span> (u_prod >= <span class="keyword">static_cast<</span><a class="code" href="integral__types_8h.html#abc0f5bc07737e498f287334775dff2b6">uint64</a><span class="keyword">></span>(cap)) <span class="keywordflow">return</span> cap;</div>
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<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  <span class="keyword">const</span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> abs_result = absl::bit_cast<int64>(u_prod);</div>
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<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  <span class="keywordflow">return</span> cap < 0 ? -abs_result : abs_result;</div>
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<div class="line"><a name="l00206"></a><span class="lineno"> 206</span> }</div>
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<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  </div>
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<div class="line"><a name="l00208"></a><span class="lineno"> 208</span> <span class="preprocessor">#if defined(__GNUC__) && defined(__x86_64__)</span></div>
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<div class="line"><a name="l00209"></a><span class="lineno"> 209</span> <span class="comment">// TODO(user): port this to other architectures.</span></div>
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<div class="line"><a name="l00210"></a><span class="lineno"> 210</span> <span class="keyword">inline</span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> CapProdFast(<a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> x, <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> y) {</div>
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<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  <span class="comment">// cap = kint64max if x and y have the same sign, cap = kint64min</span></div>
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<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <span class="comment">// otherwise.</span></div>
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<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  <span class="keyword">const</span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> cap = <a class="code" href="namespaceoperations__research.html#a29f503f49388eeb29b06c6423d0aaeb6">CapWithSignOf</a>(x ^ y);</div>
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<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> result = x;</div>
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<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  <span class="comment">// Here, we use the fact that imul of two signed 64-integers returns a 128-bit</span></div>
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<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  <span class="comment">// result -- we care about the lower 64 bits. More importantly, imul also sets</span></div>
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<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  <span class="comment">// the carry flag if 64 bits were not enough.</span></div>
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<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  <span class="comment">// We therefore use cmovc to return cap if the carry was set.</span></div>
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<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <span class="comment">// clang-format off</span></div>
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<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  <span class="keyword">asm</span> <span class="keyword">volatile</span>( <span class="comment">// 'volatile': ask compiler optimizer "keep as is".</span></div>
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<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  <span class="stringliteral">"\n\t"</span> <span class="stringliteral">"imulq %[y],%[result]"</span></div>
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<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  <span class="stringliteral">"\n\t"</span> <span class="stringliteral">"cmovcq %[cap],%[result]"</span> <span class="comment">// Conditional move if carry.</span></div>
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<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  : [result] <span class="stringliteral">"=r"</span>(result) <span class="comment">// Output</span></div>
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<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  : <span class="stringliteral">"[result]"</span> (result), [y] <span class="stringliteral">"r"</span>(y), [cap] <span class="stringliteral">"r"</span>(cap) <span class="comment">// Input.</span></div>
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<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  : <span class="stringliteral">"cc"</span> <span class="comment">/* Clobbered registers */</span>);</div>
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<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  <span class="comment">// clang-format on</span></div>
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<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  <span class="keywordflow">return</span> result;</div>
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<div class="line"><a name="l00228"></a><span class="lineno"> 228</span> }</div>
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<div class="line"><a name="l00229"></a><span class="lineno"> 229</span> <span class="preprocessor">#endif</span></div>
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<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  </div>
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<div class="line"><a name="l00231"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#ab216763dccd16f5060d2fbcfb08173fb"> 231</a></span> <span class="keyword">inline</span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> <a class="code" href="namespaceoperations__research.html#ab216763dccd16f5060d2fbcfb08173fb">CapProd</a>(<a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> x, <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> y) {</div>
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<div class="line"><a name="l00232"></a><span class="lineno"> 232</span> <span class="preprocessor">#if defined(__GNUC__) && defined(__x86_64__)</span></div>
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<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  <span class="keywordflow">return</span> CapProdFast(x, y);</div>
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<div class="line"><a name="l00234"></a><span class="lineno"> 234</span> <span class="preprocessor">#else</span></div>
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<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceoperations__research.html#a20add29e703b41d64b8a01127aab2497">CapProdGeneric</a>(x, y);</div>
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<div class="line"><a name="l00236"></a><span class="lineno"> 236</span> <span class="preprocessor">#endif</span></div>
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<div class="line"><a name="l00237"></a><span class="lineno"> 237</span> }</div>
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<div class="line"><a name="l00238"></a><span class="lineno"> 238</span> } <span class="comment">// namespace operations_research</span></div>
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<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  </div>
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<div class="line"><a name="l00240"></a><span class="lineno"> 240</span> <span class="preprocessor">#endif // OR_TOOLS_UTIL_SATURATED_ARITHMETIC_H_</span></div>
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</div><!-- fragment --></div><!-- contents -->
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</div><!-- doc-content -->
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<div class="ttc" id="aintegral__types_8h_html"><div class="ttname"><a href="integral__types_8h.html">integral_types.h</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_a228fe84d99348c2b62bb4f70a6371d9b"><div class="ttname"><a href="namespaceoperations__research.html#a228fe84d99348c2b62bb4f70a6371d9b">operations_research::CapSub</a></div><div class="ttdeci">int64 CapSub(int64 x, int64 y)</div><div class="ttdef"><b>Definition:</b> <a href="saturated__arithmetic_8h_source.html#l00154">saturated_arithmetic.h:154</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_aa1a2e7e0cdde05b5ef898461b90eede0"><div class="ttname"><a href="namespaceoperations__research.html#aa1a2e7e0cdde05b5ef898461b90eede0">operations_research::AddHadOverflow</a></div><div class="ttdeci">bool AddHadOverflow(int64 x, int64 y, int64 sum)</div><div class="ttdef"><b>Definition:</b> <a href="saturated__arithmetic_8h_source.html#l00052">saturated_arithmetic.h:52</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_ab216763dccd16f5060d2fbcfb08173fb"><div class="ttname"><a href="namespaceoperations__research.html#ab216763dccd16f5060d2fbcfb08173fb">operations_research::CapProd</a></div><div class="ttdeci">int64 CapProd(int64 x, int64 y)</div><div class="ttdef"><b>Definition:</b> <a href="saturated__arithmetic_8h_source.html#l00231">saturated_arithmetic.h:231</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_a8641e02da1d67eaa03fb37b66834a775"><div class="ttname"><a href="namespaceoperations__research.html#a8641e02da1d67eaa03fb37b66834a775">operations_research::CapOpp</a></div><div class="ttdeci">int64 CapOpp(int64 v)</div><div class="ttdef"><b>Definition:</b> <a href="saturated__arithmetic_8h_source.html#l00163">saturated_arithmetic.h:163</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_ae1bd0133149b70b678b123524541aaad"><div class="ttname"><a href="namespaceoperations__research.html#ae1bd0133149b70b678b123524541aaad">operations_research::SafeAddInto</a></div><div class="ttdeci">bool SafeAddInto(IntegerType a, IntegerType *b)</div><div class="ttdef"><b>Definition:</b> <a href="saturated__arithmetic_8h_source.html#l00087">saturated_arithmetic.h:87</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html"><div class="ttname"><a href="namespaceoperations__research.html">operations_research</a></div><div class="ttdoc">The vehicle routing library lets one model and solve generic vehicle routing problems ranging from th...</div><div class="ttdef"><b>Definition:</b> <a href="dense__doubly__linked__list_8h_source.html#l00021">dense_doubly_linked_list.h:21</a></div></div>
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<div class="ttc" id="aintegral__types_8h_html_af458164b470cbba416d5ed579e00ff60"><div class="ttname"><a href="integral__types_8h.html#af458164b470cbba416d5ed579e00ff60">kint64min</a></div><div class="ttdeci">static const int64 kint64min</div><div class="ttdef"><b>Definition:</b> <a href="integral__types_8h_source.html#l00060">integral_types.h:60</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_a5a78d7de748c8b1aa1bc9f00c5e59f17"><div class="ttname"><a href="namespaceoperations__research.html#a5a78d7de748c8b1aa1bc9f00c5e59f17">operations_research::SubOverflows</a></div><div class="ttdeci">int64 SubOverflows(int64 x, int64 y)</div><div class="ttdef"><b>Definition:</b> <a href="saturated__arithmetic_8h_source.html#l00080">saturated_arithmetic.h:80</a></div></div>
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<div class="ttc" id="aintegral__types_8h_html_a7cde0074dfd288f2d70c0e035dacb28a"><div class="ttname"><a href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a></div><div class="ttdeci">int64_t int64</div><div class="ttdef"><b>Definition:</b> <a href="integral__types_8h_source.html#l00034">integral_types.h:34</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_a7765571e7ec374ba667a3ccd16dcd124"><div class="ttname"><a href="namespaceoperations__research.html#a7765571e7ec374ba667a3ccd16dcd124">operations_research::TwosComplementAddition</a></div><div class="ttdeci">int64 TwosComplementAddition(int64 x, int64 y)</div><div class="ttdef"><b>Definition:</b> <a href="saturated__arithmetic_8h_source.html#l00038">saturated_arithmetic.h:38</a></div></div>
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<div class="ttc" id="aconstraint__solver_2table_8cc_html_af730895c6c6ef6e03caaf6251192dfd2"><div class="ttname"><a href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a></div><div class="ttdeci">int64 a</div><div class="ttdef"><b>Definition:</b> <a href="constraint__solver_2table_8cc_source.html#l00042">constraint_solver/table.cc:42</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_a99264812cf177270e521f226a5c012c3"><div class="ttname"><a href="namespaceoperations__research.html#a99264812cf177270e521f226a5c012c3">operations_research::CapAdd</a></div><div class="ttdeci">int64 CapAdd(int64 x, int64 y)</div><div class="ttdef"><b>Definition:</b> <a href="saturated__arithmetic_8h_source.html#l00124">saturated_arithmetic.h:124</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_a20add29e703b41d64b8a01127aab2497"><div class="ttname"><a href="namespaceoperations__research.html#a20add29e703b41d64b8a01127aab2497">operations_research::CapProdGeneric</a></div><div class="ttdeci">int64 CapProdGeneric(int64 x, int64 y)</div><div class="ttdef"><b>Definition:</b> <a href="saturated__arithmetic_8h_source.html#l00180">saturated_arithmetic.h:180</a></div></div>
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<div class="ttc" id="aintegral__types_8h_html_abc0f5bc07737e498f287334775dff2b6"><div class="ttname"><a href="integral__types_8h.html#abc0f5bc07737e498f287334775dff2b6">uint64</a></div><div class="ttdeci">uint64_t uint64</div><div class="ttdef"><b>Definition:</b> <a href="integral__types_8h_source.html#l00039">integral_types.h:39</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_a2f9ef253c023106392eb1495a277616b"><div class="ttname"><a href="namespaceoperations__research.html#a2f9ef253c023106392eb1495a277616b">operations_research::MostSignificantBitPosition64</a></div><div class="ttdeci">int MostSignificantBitPosition64(uint64 n)</div><div class="ttdef"><b>Definition:</b> <a href="bitset_8h_source.html#l00231">bitset.h:231</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_a974e8ea7651bd25ff7edf9b1c33393a4"><div class="ttname"><a href="namespaceoperations__research.html#a974e8ea7651bd25ff7edf9b1c33393a4">operations_research::CapAddGeneric</a></div><div class="ttdeci">int64 CapAddGeneric(int64 x, int64 y)</div><div class="ttdef"><b>Definition:</b> <a href="saturated__arithmetic_8h_source.html#l00102">saturated_arithmetic.h:102</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_a29f503f49388eeb29b06c6423d0aaeb6"><div class="ttname"><a href="namespaceoperations__research.html#a29f503f49388eeb29b06c6423d0aaeb6">operations_research::CapWithSignOf</a></div><div class="ttdeci">int64 CapWithSignOf(int64 x)</div><div class="ttdef"><b>Definition:</b> <a href="saturated__arithmetic_8h_source.html#l00097">saturated_arithmetic.h:97</a></div></div>
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<div class="ttc" id="aconstraint__solver_2table_8cc_html_a344010e26426d6a13411648d988bc9b6"><div class="ttname"><a href="constraint__solver_2table_8cc.html#a344010e26426d6a13411648d988bc9b6">b</a></div><div class="ttdeci">int64 b</div><div class="ttdef"><b>Definition:</b> <a href="constraint__solver_2table_8cc_source.html#l00043">constraint_solver/table.cc:43</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_a43c47f9b8343b3ebf98671abffdd0f9a"><div class="ttname"><a href="namespaceoperations__research.html#a43c47f9b8343b3ebf98671abffdd0f9a">operations_research::CapSubGeneric</a></div><div class="ttdeci">int64 CapSubGeneric(int64 x, int64 y)</div><div class="ttdef"><b>Definition:</b> <a href="saturated__arithmetic_8h_source.html#l00132">saturated_arithmetic.h:132</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_a2510acb08f15d9d639b286e91dfae6f2"><div class="ttname"><a href="namespaceoperations__research.html#a2510acb08f15d9d639b286e91dfae6f2">operations_research::TwosComplementSubtraction</a></div><div class="ttdeci">int64 TwosComplementSubtraction(int64 x, int64 y)</div><div class="ttdef"><b>Definition:</b> <a href="saturated__arithmetic_8h_source.html#l00044">saturated_arithmetic.h:44</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_af85f78b7f431f22bf062f8df29e9b41f"><div class="ttname"><a href="namespaceoperations__research.html#af85f78b7f431f22bf062f8df29e9b41f">operations_research::AddOverflows</a></div><div class="ttdeci">bool AddOverflows(int64 x, int64 y)</div><div class="ttdef"><b>Definition:</b> <a href="saturated__arithmetic_8h_source.html#l00076">saturated_arithmetic.h:76</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1cap__prod__util_html_ad44bdae4de79b78925cbf0fafaff273c"><div class="ttname"><a href="namespaceoperations__research_1_1cap__prod__util.html#ad44bdae4de79b78925cbf0fafaff273c">operations_research::cap_prod_util::uint_abs</a></div><div class="ttdeci">uint64 uint_abs(int64 n)</div><div class="ttdef"><b>Definition:</b> <a href="saturated__arithmetic_8h_source.html#l00168">saturated_arithmetic.h:168</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_a5fd04dbb1346d8877b5ed54aa291ffbc"><div class="ttname"><a href="namespaceoperations__research.html#a5fd04dbb1346d8877b5ed54aa291ffbc">operations_research::SubHadOverflow</a></div><div class="ttdeci">bool SubHadOverflow(int64 x, int64 y, int64 diff)</div><div class="ttdef"><b>Definition:</b> <a href="saturated__arithmetic_8h_source.html#l00061">saturated_arithmetic.h:61</a></div></div>
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<div class="ttc" id="abitset_8h_html"><div class="ttname"><a href="bitset_8h.html">bitset.h</a></div></div>
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<div class="ttc" id="aintegral__types_8h_html_a74ea76ea27f48fb1b6e148e1577b3719"><div class="ttname"><a href="integral__types_8h.html#a74ea76ea27f48fb1b6e148e1577b3719">kint64max</a></div><div class="ttdeci">static const int64 kint64max</div><div class="ttdef"><b>Definition:</b> <a href="integral__types_8h_source.html#l00062">integral_types.h:62</a></div></div>
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